LMFDB - Embedded newform 3330.2.e.d.739.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(739,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3330.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.1
Root			$1.78647i$ of defining polynomial
Character	$\chi$	$=$	3330.739
Dual form			3330.2.e.d.739.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-2.21736 - 0.288618i) q^{5} -3.14934i q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.21736 - 0.288618i) q^{5} -3.14934i q^{7} +1.00000 q^{8} +(-2.21736 - 0.288618i) q^{10} +0.908956 q^{11} +2.22269 q^{13} -3.14934i q^{14} +1.00000 q^{16} -2.10043 q^{17} +4.16694i q^{19} +(-2.21736 - 0.288618i) q^{20} +0.908956 q^{22} +7.66680 q^{23} +(4.83340 + 1.27994i) q^{25} +2.22269 q^{26} -3.14934i q^{28} +2.69676i q^{29} -5.96563i q^{31} +1.00000 q^{32} -2.10043 q^{34} +(-0.908956 + 6.98323i) q^{35} +(-1.10043 - 5.98240i) q^{37} +4.16694i q^{38} +(-2.21736 - 0.288618i) q^{40} -2.32312 q^{41} -5.72663 q^{43} +0.908956 q^{44} +7.66680 q^{46} -8.89435i q^{47} -2.91834 q^{49} +(4.83340 + 1.27994i) q^{50} +2.22269 q^{52} -9.37592i q^{53} +(-2.01549 - 0.262341i) q^{55} -3.14934i q^{56} +2.69676i q^{58} -5.55880i q^{59} -3.16611i q^{61} -5.96563i q^{62} +1.00000 q^{64} +(-4.92850 - 0.641508i) q^{65} -7.64933i q^{67} -2.10043 q^{68} +(-0.908956 + 6.98323i) q^{70} -13.5157 q^{71} +2.14851i q^{73} +(-1.10043 - 5.98240i) q^{74} +4.16694i q^{76} -2.86261i q^{77} +3.35774i q^{79} +(-2.21736 - 0.288618i) q^{80} -2.32312 q^{82} -16.2776i q^{83} +(4.65741 + 0.606222i) q^{85} -5.72663 q^{86} +0.908956 q^{88} -8.35832i q^{89} -7.00000i q^{91} +7.66680 q^{92} -8.89435i q^{94} +(1.20265 - 9.23962i) q^{95} -5.14283 q^{97} -2.91834 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8	$ 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8} + 3 q^{10} - 2 q^{13} + 10 q^{16} - 18 q^{17} + 3 q^{20} - 10 q^{23} + 5 q^{25} - 2 q^{26} + 10 q^{32} - 18 q^{34} - 8 q^{37} + 3 q^{40} + 4 q^{41} - 10 q^{43} - 10 q^{46} - 8 q^{49} + 5 q^{50} - 2 q^{52} + 5 q^{55} + 10 q^{64} - 2 q^{65} - 18 q^{68} + 20 q^{71} - 8 q^{74} + 3 q^{80} + 4 q^{82} - 28 q^{85} - 10 q^{86} - 10 q^{92} - 2 q^{95} + 2 q^{97} - 8 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8 + 3 * q^10 - 2 * q^13 + 10 * q^16 - 18 * q^17 + 3 * q^20 - 10 * q^23 + 5 * q^25 - 2 * q^26 + 10 * q^32 - 18 * q^34 - 8 * q^37 + 3 * q^40 + 4 * q^41 - 10 * q^43 - 10 * q^46 - 8 * q^49 + 5 * q^50 - 2 * q^52 + 5 * q^55 + 10 * q^64 - 2 * q^65 - 18 * q^68 + 20 * q^71 - 8 * q^74 + 3 * q^80 + 4 * q^82 - 28 * q^85 - 10 * q^86 - 10 * q^92 - 2 * q^95 + 2 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.21736	−	0.288618i	−0.991635	−	0.129074i
$5$	−2.21736	−	0.288618i	−0.991635	−	0.129074i
$6$		0			0
$7$		−	3.14934i		−	1.19034i	−0.803600	−	0.595169i	$-0.797085\pi$
$7$		−	3.14934i		−	1.19034i	0.803600	−	0.595169i	$-0.202915\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.21736	−	0.288618i	−0.701192	−	0.0912690i
$11$	0.908956			0.274061			0.137030	−	0.990567i	$-0.456244\pi$
$11$	0.908956			0.274061			0.137030	+	0.990567i	$0.456244\pi$
$12$		0			0
$13$	2.22269			0.616462			0.308231	−	0.951311i	$-0.400263\pi$
$13$	2.22269			0.616462			0.308231	+	0.951311i	$0.400263\pi$
$14$		−	3.14934i		−	0.841696i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.10043			−0.509429			−0.254714	−	0.967016i	$-0.581981\pi$
$17$	−2.10043			−0.509429			−0.254714	+	0.967016i	$0.581981\pi$
$18$		0			0
$19$			4.16694i			0.955962i	0.878370	+	0.477981i	$0.158631\pi$
$19$			4.16694i			0.955962i	−0.878370	+	0.477981i	$0.841369\pi$
$20$	−2.21736	−	0.288618i	−0.495817	−	0.0645370i
$21$		0			0
$22$	0.908956			0.193790
$23$	7.66680			1.59864			0.799319	−	0.600907i	$-0.205194\pi$
$23$	7.66680			1.59864			0.799319	+	0.600907i	$0.205194\pi$
$24$		0			0
$25$	4.83340	+	1.27994i	0.966680	+	0.255988i
$26$	2.22269			0.435905
$27$		0			0
$28$		−	3.14934i		−	0.595169i
$29$			2.69676i			0.500775i	0.968146	+	0.250387i	$0.0805580\pi$
$29$			2.69676i			0.500775i	−0.968146	+	0.250387i	$0.919442\pi$
$30$		0			0
$31$		−	5.96563i		−	1.07146i	−0.844390	−	0.535729i	$-0.820037\pi$
$31$		−	5.96563i		−	1.07146i	0.844390	−	0.535729i	$-0.179963\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.10043			−0.360221
$35$	−0.908956	+	6.98323i	−0.153642	+	1.18038i
$36$		0			0
$37$	−1.10043	−	5.98240i	−0.180909	−	0.983500i
$37$	−1.10043	−	5.98240i	−0.180909	−	0.983500i
$38$			4.16694i			0.675967i
$39$		0			0
$40$	−2.21736	−	0.288618i	−0.350596	−	0.0456345i
$41$	−2.32312			−0.362810			−0.181405	−	0.983409i	$-0.558064\pi$
$41$	−2.32312			−0.362810			−0.181405	+	0.983409i	$0.558064\pi$
$42$		0			0
$43$	−5.72663			−0.873302			−0.436651	−	0.899631i	$-0.643836\pi$
$43$	−5.72663			−0.873302			−0.436651	+	0.899631i	$0.643836\pi$
$44$	0.908956			0.137030
$45$		0			0
$46$	7.66680			1.13041
$47$		−	8.89435i		−	1.29737i	−0.761055	−	0.648687i	$-0.775318\pi$
$47$		−	8.89435i		−	1.29737i	0.761055	−	0.648687i	$-0.224682\pi$
$48$		0			0
$49$	−2.91834			−0.416906
$50$	4.83340	+	1.27994i	0.683546	+	0.181011i
$51$		0			0
$52$	2.22269			0.308231
$53$		−	9.37592i		−	1.28788i	−0.765075	−	0.643941i	$-0.777298\pi$
$53$		−	9.37592i		−	1.28788i	0.765075	−	0.643941i	$-0.222702\pi$
$54$		0			0
$55$	−2.01549	−	0.262341i	−0.271768	−	0.0353741i
$56$		−	3.14934i		−	0.420848i
$57$		0			0
$58$			2.69676i			0.354101i
$59$		−	5.55880i		−	0.723694i	−0.932238	−	0.361847i	$-0.882146\pi$
$59$		−	5.55880i		−	0.723694i	0.932238	−	0.361847i	$-0.117854\pi$
$60$		0			0
$61$		−	3.16611i		−	0.405378i	−0.979243	−	0.202689i	$-0.935032\pi$
$61$		−	3.16611i		−	0.405378i	0.979243	−	0.202689i	$-0.0649681\pi$
$62$		−	5.96563i		−	0.757636i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.92850	−	0.641508i	−0.611306	−	0.0795692i
$66$		0			0
$67$		−	7.64933i		−	0.934515i	−0.884121	−	0.467257i	$-0.845242\pi$
$67$		−	7.64933i		−	0.934515i	0.884121	−	0.467257i	$-0.154758\pi$
$68$	−2.10043			−0.254714
$69$		0			0
$70$	−0.908956	+	6.98323i	−0.108641	+	0.834656i
$71$	−13.5157			−1.60402			−0.802008	−	0.597313i	$-0.796235\pi$
$71$	−13.5157			−1.60402			−0.802008	+	0.597313i	$0.796235\pi$
$72$		0			0
$73$			2.14851i			0.251464i	0.992064	+	0.125732i	$0.0401279\pi$
$73$			2.14851i			0.251464i	−0.992064	+	0.125732i	$0.959872\pi$
$74$	−1.10043	−	5.98240i	−0.127922	−	0.695439i
$75$		0			0
$76$			4.16694i			0.477981i
$77$		−	2.86261i		−	0.326225i
$78$		0			0
$79$			3.35774i			0.377775i	0.981999	+	0.188888i	$0.0604882\pi$
$79$			3.35774i			0.377775i	−0.981999	+	0.188888i	$0.939512\pi$
$80$	−2.21736	−	0.288618i	−0.247909	−	0.0322685i
$81$		0			0
$82$	−2.32312			−0.256545
$83$		−	16.2776i		−	1.78670i	−0.449361	−	0.893350i	$-0.648348\pi$
$83$		−	16.2776i		−	1.78670i	0.449361	−	0.893350i	$-0.351652\pi$
$84$		0			0
$85$	4.65741	+	0.606222i	0.505167	+	0.0657540i
$86$	−5.72663			−0.617518
$87$		0			0
$88$	0.908956			0.0968951
$89$		−	8.35832i		−	0.885980i	−0.896527	−	0.442990i	$-0.853918\pi$
$89$		−	8.35832i		−	0.885980i	0.896527	−	0.442990i	$-0.146082\pi$
$90$		0			0
$91$		−	7.00000i		−	0.733799i
$92$	7.66680			0.799319
$93$		0			0
$94$		−	8.89435i		−	0.917382i
$95$	1.20265	−	9.23962i	0.123390	−	0.947965i
$96$		0			0
$97$	−5.14283			−0.522175			−0.261087	−	0.965315i	$-0.584081\pi$
$97$	−5.14283			−0.522175			−0.261087	+	0.965315i	$0.584081\pi$
$98$	−2.91834			−0.294797
$99$		0			0
$100$	4.83340	+	1.27994i	0.483340	+	0.127994i
$101$	3.20212			0.318623			0.159311	−	0.987228i	$-0.449073\pi$
$101$	3.20212			0.318623			0.159311	+	0.987228i	$0.449073\pi$
$102$		0			0
$103$	17.6871			1.74276			0.871382	−	0.490605i	$-0.163224\pi$
$103$	17.6871			1.74276			0.871382	+	0.490605i	$0.163224\pi$
$104$	2.22269			0.217952
$105$		0			0
$106$		−	9.37592i		−	0.910670i
$107$		−	6.75126i		−	0.652669i	−0.945254	−	0.326335i	$-0.894186\pi$
$107$		−	6.75126i		−	0.652669i	0.945254	−	0.326335i	$-0.105814\pi$
$108$		0			0
$109$			10.5304i			1.00863i	0.863520	+	0.504314i	$0.168255\pi$
$109$			10.5304i			1.00863i	−0.863520	+	0.504314i	$0.831745\pi$
$110$	−2.01549	−	0.262341i	−0.192169	−	0.0250133i
$111$		0			0
$112$		−	3.14934i		−	0.297585i
$113$	−6.32365			−0.594879			−0.297439	−	0.954741i	$-0.596133\pi$
$113$	−6.32365			−0.594879			−0.297439	+	0.954741i	$0.596133\pi$
$114$		0			0
$115$	−17.0001	−	2.21278i	−1.58527	−	0.206342i
$116$			2.69676i			0.250387i
$117$		0			0
$118$		−	5.55880i		−	0.511729i
$119$			6.61496i			0.606393i
$120$		0			0
$121$	−10.1738			−0.924891
$122$		−	3.16611i		−	0.286646i
$123$		0			0
$124$		−	5.96563i		−	0.535729i
$125$	−10.3480	−	4.23310i	−0.925552	−	0.378620i
$126$		0			0
$127$			15.0472i			1.33522i	0.744512	+	0.667609i	$0.232682\pi$
$127$			15.0472i			1.33522i	−0.744512	+	0.667609i	$0.767318\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−4.92850	−	0.641508i	−0.432258	−	0.0562639i
$131$			3.31974i			0.290047i	0.989428	+	0.145024i	$0.0463258\pi$
$131$			3.31974i			0.290047i	−0.989428	+	0.145024i	$0.953674\pi$
$132$		0			0
$133$	13.1231			1.13792
$134$		−	7.64933i		−	0.660802i
$135$		0			0
$136$	−2.10043			−0.180110
$137$			17.9355i			1.53234i	0.642640	+	0.766168i	$0.277839\pi$
$137$			17.9355i			1.53234i	−0.642640	+	0.766168i	$0.722161\pi$
$138$		0			0
$139$	12.7472			1.08120			0.540601	−	0.841279i	$-0.318197\pi$
$139$	12.7472			1.08120			0.540601	+	0.841279i	$0.318197\pi$
$140$	−0.908956	+	6.98323i	−0.0768208	+	0.590191i
$141$		0			0
$142$	−13.5157			−1.13421
$143$	2.02033			0.168948
$144$		0			0
$145$	0.778332	−	5.97969i	0.0646370	−	0.496586i
$146$			2.14851i			0.177812i
$147$		0			0
$148$	−1.10043	−	5.98240i	−0.0904547	−	0.491750i
$149$	6.83795			0.560186			0.280093	−	0.959973i	$-0.409635\pi$
$149$	6.83795			0.560186			0.280093	+	0.959973i	$0.409635\pi$
$150$		0			0
$151$	−2.80702			−0.228432			−0.114216	−	0.993456i	$-0.536436\pi$
$151$	−2.80702			−0.228432			−0.114216	+	0.993456i	$0.536436\pi$
$152$			4.16694i			0.337984i
$153$		0			0
$154$		−	2.86261i		−	0.230676i
$155$	−1.72179	+	13.2280i	−0.138297	+	1.06250i
$156$		0			0
$157$		−	7.28275i		−	0.581227i	−0.956841	−	0.290613i	$-0.906141\pi$
$157$		−	7.28275i		−	0.581227i	0.956841	−	0.290613i	$-0.0938593\pi$
$158$			3.35774i			0.267127i
$159$		0			0
$160$	−2.21736	−	0.288618i	−0.175298	−	0.0228173i
$161$		−	24.1454i		−	1.90292i
$162$		0			0
$163$	22.2319			1.74134			0.870669	−	0.491870i	$-0.163686\pi$
$163$	22.2319			1.74134			0.870669	+	0.491870i	$0.163686\pi$
$164$	−2.32312			−0.181405
$165$		0			0
$166$		−	16.2776i		−	1.26339i
$167$	11.5050			0.890286			0.445143	−	0.895459i	$-0.353153\pi$
$167$	11.5050			0.890286			0.445143	+	0.895459i	$0.353153\pi$
$168$		0			0
$169$	−8.05966			−0.619974
$170$	4.65741	+	0.606222i	0.357207	+	0.0464951i
$171$		0			0
$172$	−5.72663			−0.436651
$173$		−	15.7081i		−	1.19427i	−0.802142	−	0.597134i	$-0.796306\pi$
$173$		−	15.7081i		−	1.19427i	0.802142	−	0.597134i	$-0.203694\pi$
$174$		0			0
$175$	4.03097	−	15.2220i	0.304713	−	1.15068i
$176$	0.908956			0.0685152
$177$		0			0
$178$		−	8.35832i		−	0.626483i
$179$		−	11.3128i		−	0.845560i	−0.906232	−	0.422780i	$-0.861054\pi$
$179$		−	11.3128i		−	0.845560i	0.906232	−	0.422780i	$-0.138946\pi$
$180$		0			0
$181$	18.3136			1.36124			0.680618	−	0.732638i	$-0.261711\pi$
$181$	18.3136			1.36124			0.680618	+	0.732638i	$0.261711\pi$
$182$		−	7.00000i		−	0.518874i
$183$		0			0
$184$	7.66680			0.565204
$185$	0.713423	+	13.5827i	0.0524519	+	0.998623i
$186$		0			0
$187$	−1.90920			−0.139614
$188$		−	8.89435i		−	0.648687i
$189$		0			0
$190$	1.20265	−	9.23962i	0.0872497	−	0.670313i
$191$			7.66002i			0.554260i	0.960832	+	0.277130i	$0.0893832\pi$
$191$			7.66002i			0.554260i	−0.960832	+	0.277130i	$0.910617\pi$
$192$		0			0
$193$	−19.3148			−1.39031			−0.695156	−	0.718859i	$-0.744665\pi$
$193$	−19.3148			−1.39031			−0.695156	+	0.718859i	$0.744665\pi$
$194$	−5.14283			−0.369233
$195$		0			0
$196$	−2.91834			−0.208453
$197$			13.1193i			0.934709i	0.884070	+	0.467354i	$0.154793\pi$
$197$			13.1193i			0.934709i	−0.884070	+	0.467354i	$0.845207\pi$
$198$		0			0
$199$		−	6.04548i		−	0.428553i	−0.976773	−	0.214277i	$-0.931261\pi$
$199$		−	6.04548i		−	0.428553i	0.976773	−	0.214277i	$-0.0687394\pi$
$200$	4.83340	+	1.27994i	0.341773	+	0.0905056i
$201$		0			0
$202$	3.20212			0.225300
$203$	8.49300			0.596092
$204$		0			0
$205$	5.15119	+	0.670493i	0.359775	+	0.0468293i
$206$	17.6871			1.23232
$207$		0			0
$208$	2.22269			0.154116
$209$			3.78757i			0.261992i
$210$		0			0
$211$	3.06975			0.211330			0.105665	−	0.994402i	$-0.466303\pi$
$211$	3.06975			0.211330			0.105665	+	0.994402i	$0.466303\pi$
$212$		−	9.37592i		−	0.643941i
$213$		0			0
$214$		−	6.75126i		−	0.461507i
$215$	12.6980	+	1.65281i	0.865997	+	0.112721i
$216$		0			0
$217$	−18.7878			−1.27540
$218$			10.5304i			0.713208i
$219$		0			0
$220$	−2.01549	−	0.262341i	−0.135884	−	0.0176870i
$221$	−4.66860			−0.314044
$222$		0			0
$223$		−	13.9960i		−	0.937243i	−0.883399	−	0.468621i	$-0.844751\pi$
$223$		−	13.9960i		−	0.937243i	0.883399	−	0.468621i	$-0.155249\pi$
$224$		−	3.14934i		−	0.210424i
$225$		0			0
$226$	−6.32365			−0.420643
$227$	−11.9087			−0.790409			−0.395205	−	0.918593i	$-0.629326\pi$
$227$	−11.9087			−0.790409			−0.395205	+	0.918593i	$0.629326\pi$
$228$		0			0
$229$	−7.43448			−0.491285			−0.245642	−	0.969361i	$-0.578999\pi$
$229$	−7.43448			−0.491285			−0.245642	+	0.969361i	$0.578999\pi$
$230$	−17.0001	−	2.21278i	−1.12095	−	0.145906i
$231$		0			0
$232$			2.69676i			0.177051i
$233$		−	15.2152i		−	0.996782i	−0.866952	−	0.498391i	$-0.833924\pi$
$233$		−	15.2152i		−	0.996782i	0.866952	−	0.498391i	$-0.166076\pi$
$234$		0			0
$235$	−2.56707	+	19.7220i	−0.167457	+	1.28652i
$236$		−	5.55880i		−	0.361847i
$237$		0			0
$238$			6.61496i			0.428784i
$239$			29.1359i			1.88465i	0.334705	+	0.942323i	$0.391363\pi$
$239$			29.1359i			1.88465i	−0.334705	+	0.942323i	$0.608637\pi$
$240$		0			0
$241$			7.08791i			0.456572i	0.973594	+	0.228286i	$0.0733121\pi$
$241$			7.08791i			0.456572i	−0.973594	+	0.228286i	$0.926688\pi$
$242$	−10.1738			−0.653997
$243$		0			0
$244$		−	3.16611i		−	0.202689i
$245$	6.47102	+	0.842286i	0.413418	+	0.0538117i
$246$		0			0
$247$			9.26180i			0.589315i
$248$		−	5.96563i		−	0.378818i
$249$		0			0
$250$	−10.3480	−	4.23310i	−0.654464	−	0.267725i
$251$		−	17.3622i		−	1.09589i	−0.836514	−	0.547946i	$-0.815410\pi$
$251$		−	17.3622i		−	1.09589i	0.836514	−	0.547946i	$-0.184590\pi$
$252$		0			0
$253$	6.96879			0.438124
$254$			15.0472i			0.944142i
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.9118			0.867797			0.433899	−	0.900962i	$-0.357138\pi$
$257$	13.9118			0.867797			0.433899	+	0.900962i	$0.357138\pi$
$258$		0			0
$259$	−18.8406	+	3.46562i	−1.17070	+	0.215343i
$260$	−4.92850	−	0.641508i	−0.305653	−	0.0397846i
$261$		0			0
$262$			3.31974i			0.205094i
$263$			0.302157i			0.0186318i	0.999957	+	0.00931590i	$0.00296538\pi$
$263$			0.302157i			0.0186318i	−0.999957	+	0.00931590i	$0.997035\pi$
$264$		0			0
$265$	−2.70606	+	20.7898i	−0.166232	+	1.27711i
$266$	13.1231			0.804630
$267$		0			0
$268$		−	7.64933i		−	0.467257i
$269$	28.8001			1.75597			0.877986	−	0.478687i	$-0.158887\pi$
$269$	28.8001			1.75597			0.877986	+	0.478687i	$0.158887\pi$
$270$		0			0
$271$	1.57340			0.0955770			0.0477885	−	0.998857i	$-0.484783\pi$
$271$	1.57340			0.0955770			0.0477885	+	0.998857i	$0.484783\pi$
$272$	−2.10043			−0.127357
$273$		0			0
$274$			17.9355i			1.08353i
$275$	4.39335	+	1.16341i	0.264929	+	0.0701564i
$276$		0			0
$277$	26.3430			1.58280			0.791398	−	0.611301i	$-0.209354\pi$
$277$	26.3430			1.58280			0.791398	+	0.611301i	$0.209354\pi$
$278$	12.7472			0.764526
$279$		0			0
$280$	−0.908956	+	6.98323i	−0.0543205	+	0.417328i
$281$			9.45482i			0.564027i	0.959410	+	0.282014i	$0.0910024\pi$
$281$			9.45482i			0.564027i	−0.959410	+	0.282014i	$0.908998\pi$
$282$		0			0
$283$	−21.7389			−1.29224			−0.646122	−	0.763234i	$-0.723610\pi$
$283$	−21.7389			−1.29224			−0.646122	+	0.763234i	$0.723610\pi$
$284$	−13.5157			−0.802008
$285$		0			0
$286$	2.02033			0.119464
$287$			7.31628i			0.431866i
$288$		0			0
$289$	−12.5882			−0.740482
$290$	0.778332	−	5.97969i	0.0457053	−	0.351139i
$291$		0			0
$292$			2.14851i			0.125732i
$293$		−	11.1283i		−	0.650121i	−0.945693	−	0.325061i	$-0.894615\pi$
$293$		−	11.1283i		−	0.650121i	0.945693	−	0.325061i	$-0.105385\pi$
$294$		0			0
$295$	−1.60437	+	12.3259i	−0.0934100	+	0.717640i
$296$	−1.10043	−	5.98240i	−0.0639611	−	0.347720i
$297$		0			0
$298$	6.83795			0.396112
$299$	17.0409			0.985500
$300$		0			0
$301$			18.0351i			1.03953i
$302$	−2.80702			−0.161526
$303$		0			0
$304$			4.16694i			0.238990i
$305$	−0.913795	+	7.02041i	−0.0523238	+	0.401987i
$306$		0			0
$307$			15.9903i			0.912615i	0.889822	+	0.456308i	$0.150828\pi$
$307$			15.9903i			0.912615i	−0.889822	+	0.456308i	$0.849172\pi$
$308$		−	2.86261i		−	0.163112i
$309$		0			0
$310$	−1.72179	+	13.2280i	−0.0977910	+	0.751298i
$311$			29.6416i			1.68082i	0.541949	+	0.840411i	$0.317687\pi$
$311$			29.6416i			1.68082i	−0.541949	+	0.840411i	$0.682313\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		−	7.28275i		−	0.410989i
$315$		0			0
$316$			3.35774i			0.188888i
$317$		−	21.1397i		−	1.18732i	−0.804715	−	0.593662i	$-0.797682\pi$
$317$		−	21.1397i		−	1.18732i	0.804715	−	0.593662i	$-0.202318\pi$
$318$		0			0
$319$			2.45123i			0.137243i
$320$	−2.21736	−	0.288618i	−0.123954	−	0.0161342i
$321$		0			0
$322$		−	24.1454i		−	1.34557i
$323$		−	8.75236i		−	0.486994i
$324$		0			0
$325$	10.7431	+	2.84491i	0.595922	+	0.157807i
$326$	22.2319			1.23131
$327$		0			0
$328$	−2.32312			−0.128273
$329$	−28.0113			−1.54431
$330$		0			0
$331$			18.7324i			1.02963i	0.857302	+	0.514814i	$0.172139\pi$
$331$			18.7324i			1.02963i	−0.857302	+	0.514814i	$0.827861\pi$
$332$		−	16.2776i		−	0.893350i
$333$		0			0
$334$	11.5050			0.629528
$335$	−2.20774	+	16.9613i	−0.120621	+	0.926697i
$336$		0			0
$337$			13.9123i			0.757850i	0.925427	+	0.378925i	$0.123706\pi$
$337$			13.9123i			0.757850i	−0.925427	+	0.378925i	$0.876294\pi$
$338$	−8.05966			−0.438388
$339$		0			0
$340$	4.65741	+	0.606222i	0.252584	+	0.0328770i
$341$		−	5.42250i		−	0.293645i
$342$		0			0
$343$		−	12.8545i		−	0.694079i
$344$	−5.72663			−0.308759
$345$		0			0
$346$		−	15.7081i		−	0.844474i
$347$	24.5885			1.31998			0.659990	−	0.751274i	$-0.270560\pi$
$347$	24.5885			1.31998			0.659990	+	0.751274i	$0.270560\pi$
$348$		0			0
$349$	−10.2324			−0.547726			−0.273863	−	0.961769i	$-0.588301\pi$
$349$	−10.2324			−0.547726			−0.273863	+	0.961769i	$0.588301\pi$
$350$	4.03097	−	15.2220i	0.215465	−	0.813651i
$351$		0			0
$352$	0.908956			0.0484475
$353$	1.74540			0.0928981			0.0464491	−	0.998921i	$-0.485209\pi$
$353$	1.74540			0.0928981			0.0464491	+	0.998921i	$0.485209\pi$
$354$		0			0
$355$	29.9692	+	3.90087i	1.59060	+	0.207037i
$356$		−	8.35832i		−	0.442990i
$357$		0			0
$358$		−	11.3128i		−	0.597901i
$359$	−21.1922			−1.11848			−0.559240	−	0.829006i	$-0.688907\pi$
$359$	−21.1922			−1.11848			−0.559240	+	0.829006i	$0.688907\pi$
$360$		0			0
$361$	1.63660			0.0861371
$362$	18.3136			0.962540
$363$		0			0
$364$		−	7.00000i		−	0.366900i
$365$	0.620097	−	4.76402i	0.0324574	−	0.249360i
$366$		0			0
$367$		−	9.69901i		−	0.506284i	−0.967429	−	0.253142i	$-0.918536\pi$
$367$		−	9.69901i		−	0.506284i	0.967429	−	0.253142i	$-0.0814640\pi$
$368$	7.66680			0.399659
$369$		0			0
$370$	0.713423	+	13.5827i	0.0370891	+	0.706133i
$371$	−29.5280			−1.53302
$372$		0			0
$373$			36.8658i			1.90884i	0.298466	+	0.954420i	$0.403525\pi$
$373$			36.8658i			1.90884i	−0.298466	+	0.954420i	$0.596475\pi$
$374$	−1.90920			−0.0987223
$375$		0			0
$376$		−	8.89435i		−	0.458691i
$377$			5.99404i			0.308709i
$378$		0			0
$379$	31.7074			1.62870			0.814351	−	0.580372i	$-0.197093\pi$
$379$	31.7074			1.62870			0.814351	+	0.580372i	$0.197093\pi$
$380$	1.20265	−	9.23962i	0.0616949	−	0.473983i
$381$		0			0
$382$			7.66002i			0.391921i
$383$	3.45325			0.176453			0.0882265	−	0.996100i	$-0.471880\pi$
$383$	3.45325			0.176453			0.0882265	+	0.996100i	$0.471880\pi$
$384$		0			0
$385$	−0.826202	+	6.34745i	−0.0421071	+	0.323496i
$386$	−19.3148			−0.983099
$387$		0			0
$388$	−5.14283			−0.261087
$389$			39.2237i			1.98872i	0.106056	+	0.994360i	$0.466178\pi$
$389$			39.2237i			1.98872i	−0.106056	+	0.994360i	$0.533822\pi$
$390$		0			0
$391$	−16.1036			−0.814392
$392$	−2.91834			−0.147399
$393$		0			0
$394$			13.1193i			0.660939i
$395$	0.969104	−	7.44533i	0.0487609	−	0.374615i
$396$		0			0
$397$		−	5.75234i		−	0.288702i	−0.989527	−	0.144351i	$-0.953891\pi$
$397$		−	5.75234i		−	0.288702i	0.989527	−	0.144351i	$-0.0461094\pi$
$398$		−	6.04548i		−	0.303033i
$399$		0			0
$400$	4.83340	+	1.27994i	0.241670	+	0.0639971i
$401$			24.6273i			1.22983i	0.788594	+	0.614914i	$0.210809\pi$
$401$			24.6273i			1.22983i	−0.788594	+	0.614914i	$0.789191\pi$
$402$		0			0
$403$		−	13.2597i		−	0.660514i
$404$	3.20212			0.159311
$405$		0			0
$406$	8.49300			0.421501
$407$	−1.00024	−	5.43774i	−0.0495801	−	0.269539i
$408$		0			0
$409$		−	25.1947i		−	1.24580i	−0.782302	−	0.622899i	$-0.785955\pi$
$409$		−	25.1947i		−	1.24580i	0.782302	−	0.622899i	$-0.214045\pi$
$410$	5.15119	+	0.670493i	0.254399	+	0.0331133i
$411$		0			0
$412$	17.6871			0.871382
$413$	−17.5065			−0.861441
$414$		0			0
$415$	−4.69801	+	36.0934i	−0.230616	+	1.77175i
$416$	2.22269			0.108976
$417$		0			0
$418$			3.78757i			0.185256i
$419$	−7.19906			−0.351697			−0.175849	−	0.984417i	$-0.556267\pi$
$419$	−7.19906			−0.351697			−0.175849	+	0.984417i	$0.556267\pi$
$420$		0			0
$421$		−	34.0902i		−	1.66145i	−0.556680	−	0.830727i	$-0.687925\pi$
$421$		−	34.0902i		−	1.66145i	0.556680	−	0.830727i	$-0.312075\pi$
$422$	3.06975			0.149433
$423$		0			0
$424$		−	9.37592i		−	0.455335i
$425$	−10.1522	−	2.68843i	−0.492455	−	0.130408i
$426$		0			0
$427$	−9.97114			−0.482537
$428$		−	6.75126i		−	0.326335i
$429$		0			0
$430$	12.6980	+	1.65281i	0.612353	+	0.0797055i
$431$		−	25.2123i		−	1.21443i	−0.794536	−	0.607217i	$-0.792286\pi$
$431$		−	25.2123i		−	1.21443i	0.794536	−	0.607217i	$-0.207714\pi$
$432$		0			0
$433$		−	21.8683i		−	1.05092i	−0.850817	−	0.525462i	$-0.823893\pi$
$433$		−	21.8683i		−	1.05092i	0.850817	−	0.525462i	$-0.176107\pi$
$434$	−18.7878			−0.901843
$435$		0			0
$436$			10.5304i			0.504314i
$437$			31.9471i			1.52824i
$438$		0			0
$439$			9.00956i			0.430003i	0.976614	+	0.215001i	$0.0689756\pi$
$439$			9.00956i			0.430003i	−0.976614	+	0.215001i	$0.931024\pi$
$440$	−2.01549	−	0.262341i	−0.0960845	−	0.0125066i
$441$		0			0
$442$	−4.66860			−0.222062
$443$			2.89007i			0.137311i	0.997640	+	0.0686557i	$0.0218710\pi$
$443$			2.89007i			0.137311i	−0.997640	+	0.0686557i	$0.978129\pi$
$444$		0			0
$445$	−2.41236	+	18.5334i	−0.114357	+	0.878569i
$446$		−	13.9960i		−	0.662731i
$447$		0			0
$448$		−	3.14934i		−	0.148792i
$449$		−	18.1539i		−	0.856738i	−0.903604	−	0.428369i	$-0.859088\pi$
$449$		−	18.1539i		−	0.856738i	0.903604	−	0.428369i	$-0.140912\pi$
$450$		0			0
$451$	−2.11161			−0.0994319
$452$	−6.32365			−0.297439
$453$		0			0
$454$	−11.9087			−0.558904
$455$	−2.02033	+	15.5215i	−0.0947143	+	0.727661i
$456$		0			0
$457$	−10.4140			−0.487146			−0.243573	−	0.969883i	$-0.578320\pi$
$457$	−10.4140			−0.487146			−0.243573	+	0.969883i	$0.578320\pi$
$458$	−7.43448			−0.347391
$459$		0			0
$460$	−17.0001	−	2.21278i	−0.792633	−	0.103171i
$461$		−	17.7433i		−	0.826390i	−0.910643	−	0.413195i	$-0.864413\pi$
$461$		−	17.7433i		−	0.826390i	0.910643	−	0.413195i	$-0.135587\pi$
$462$		0			0
$463$	−11.6293			−0.540457			−0.270229	−	0.962796i	$-0.587099\pi$
$463$	−11.6293			−0.540457			−0.270229	+	0.962796i	$0.587099\pi$
$464$			2.69676i			0.125194i
$465$		0			0
$466$		−	15.2152i		−	0.704831i
$467$	6.25208			0.289312			0.144656	−	0.989482i	$-0.453793\pi$
$467$	6.25208			0.289312			0.144656	+	0.989482i	$0.453793\pi$
$468$		0			0
$469$	−24.0903			−1.11239
$470$	−2.56707	+	19.7220i	−0.118410	+	0.909708i
$471$		0			0
$472$		−	5.55880i		−	0.255864i
$473$	−5.20525			−0.239338
$474$		0			0
$475$	−5.33344	+	20.1405i	−0.244715	+	0.924109i
$476$			6.61496i			0.303196i
$477$		0			0
$478$			29.1359i			1.33265i
$479$			16.4452i			0.751398i	0.926742	+	0.375699i	$0.122597\pi$
$479$			16.4452i			0.751398i	−0.926742	+	0.375699i	$0.877403\pi$
$480$		0			0
$481$	−2.44591	−	13.2970i	−0.111524	−	0.606291i
$482$			7.08791i			0.322845i
$483$		0			0
$484$	−10.1738			−0.462445
$485$	11.4035	+	1.48431i	0.517807	+	0.0673992i
$486$		0			0
$487$	−13.7966			−0.625184			−0.312592	−	0.949887i	$-0.601197\pi$
$487$	−13.7966			−0.625184			−0.312592	+	0.949887i	$0.601197\pi$
$488$		−	3.16611i		−	0.143323i
$489$		0			0
$490$	6.47102	+	0.842286i	0.292331	+	0.0380506i
$491$	39.0410			1.76190			0.880949	−	0.473211i	$-0.156905\pi$
$491$	39.0410			1.76190			0.880949	+	0.473211i	$0.156905\pi$
$492$		0			0
$493$		−	5.66434i		−	0.255109i
$494$			9.26180i			0.416708i
$495$		0			0
$496$		−	5.96563i		−	0.267865i
$497$			42.5655i			1.90932i
$498$		0			0
$499$			40.0886i			1.79461i	0.441410	+	0.897306i	$0.354479\pi$
$499$			40.0886i			1.79461i	−0.441410	+	0.897306i	$0.645521\pi$
$500$	−10.3480	−	4.23310i	−0.462776	−	0.189310i
$501$		0			0
$502$		−	17.3622i		−	0.774913i
$503$	12.0731			0.538312			0.269156	−	0.963097i	$-0.413255\pi$
$503$	12.0731			0.538312			0.269156	+	0.963097i	$0.413255\pi$
$504$		0			0
$505$	−7.10026	−	0.924190i	−0.315958	−	0.0411259i
$506$	6.96879			0.309800
$507$		0			0
$508$			15.0472i			0.667609i
$509$	−4.36466			−0.193460			−0.0967300	−	0.995311i	$-0.530838\pi$
$509$	−4.36466			−0.193460			−0.0967300	+	0.995311i	$0.530838\pi$
$510$		0			0
$511$	6.76637			0.299327
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.9118			0.613625
$515$	−39.2188	−	5.10482i	−1.72819	−	0.224945i
$516$		0			0
$517$		−	8.08458i		−	0.355559i
$518$	−18.8406	+	3.46562i	−0.827808	+	0.152271i
$519$		0			0
$520$	−4.92850	−	0.641508i	−0.216129	−	0.0281320i
$521$	16.7088			0.732025			0.366013	−	0.930610i	$-0.380723\pi$
$521$	16.7088			0.732025			0.366013	+	0.930610i	$0.380723\pi$
$522$		0			0
$523$	−32.5266			−1.42229			−0.711144	−	0.703047i	$-0.751823\pi$
$523$	−32.5266			−1.42229			−0.711144	+	0.703047i	$0.751823\pi$
$524$			3.31974i			0.145024i
$525$		0			0
$526$			0.302157i			0.0131747i
$527$			12.5304i			0.545832i
$528$		0			0
$529$	35.7798			1.55564
$530$	−2.70606	+	20.7898i	−0.117544	+	0.903052i
$531$		0			0
$532$	13.1231			0.568959
$533$	−5.16356			−0.223659
$534$		0			0
$535$	−1.94854	+	14.9700i	−0.0842426	+	0.647210i
$536$		−	7.64933i		−	0.330401i
$537$		0			0
$538$	28.8001			1.24166
$539$	−2.65265			−0.114258
$540$		0			0
$541$		−	19.2331i		−	0.826894i	−0.910528	−	0.413447i	$-0.864325\pi$
$541$		−	19.2331i		−	0.826894i	0.910528	−	0.413447i	$-0.135675\pi$
$542$	1.57340			0.0675832
$543$		0			0
$544$	−2.10043			−0.0900551
$545$	3.03926	−	23.3497i	0.130188	−	1.00019i
$546$		0			0
$547$	8.88173			0.379755			0.189878	−	0.981808i	$-0.439191\pi$
$547$	8.88173			0.379755			0.189878	+	0.981808i	$0.439191\pi$
$548$			17.9355i			0.766168i
$549$		0			0
$550$	4.39335	+	1.16341i	0.187333	+	0.0496080i
$551$	−11.2372			−0.478722
$552$		0			0
$553$	10.5747			0.449680
$554$	26.3430			1.11921
$555$		0			0
$556$	12.7472			0.540601
$557$	−44.3010			−1.87709			−0.938547	−	0.345150i	$-0.887828\pi$
$557$	−44.3010			−1.87709			−0.938547	+	0.345150i	$0.887828\pi$
$558$		0			0
$559$	−12.7285			−0.538358
$560$	−0.908956	+	6.98323i	−0.0384104	+	0.295095i
$561$		0			0
$562$			9.45482i			0.398828i
$563$	−19.8885			−0.838202			−0.419101	−	0.907940i	$-0.637655\pi$
$563$	−19.8885			−0.838202			−0.419101	+	0.907940i	$0.637655\pi$
$564$		0			0
$565$	14.0218	+	1.82512i	0.589903	+	0.0767834i
$566$	−21.7389			−0.913754
$567$		0			0
$568$	−13.5157			−0.567106
$569$		−	3.13170i		−	0.131288i	−0.997843	−	0.0656439i	$-0.979090\pi$
$569$		−	3.13170i		−	0.131288i	0.997843	−	0.0656439i	$-0.0209101\pi$
$570$		0			0
$571$	−19.2774			−0.806732			−0.403366	−	0.915039i	$-0.632160\pi$
$571$	−19.2774			−0.806732			−0.403366	+	0.915039i	$0.632160\pi$
$572$	2.02033			0.0844741
$573$		0			0
$574$			7.31628i			0.305376i
$575$	37.0567	+	9.81306i	1.54537	+	0.409233i
$576$		0			0
$577$	24.8001			1.03244			0.516220	−	0.856456i	$-0.327339\pi$
$577$	24.8001			1.03244			0.516220	+	0.856456i	$0.327339\pi$
$578$	−12.5882			−0.523600
$579$		0			0
$580$	0.778332	−	5.97969i	0.0323185	−	0.248293i
$581$	−51.2637			−2.12678
$582$		0			0
$583$		−	8.52230i		−	0.352958i
$584$			2.14851i			0.0889058i
$585$		0			0
$586$		−	11.1283i		−	0.459705i
$587$	16.1319			0.665836			0.332918	−	0.942956i	$-0.391967\pi$
$587$	16.1319			0.665836			0.332918	+	0.942956i	$0.391967\pi$
$588$		0			0
$589$	24.8584			1.02427
$590$	−1.60437	+	12.3259i	−0.0660508	+	0.507448i
$591$		0			0
$592$	−1.10043	−	5.98240i	−0.0452273	−	0.245875i
$593$			28.2040i			1.15820i	0.815256	+	0.579100i	$0.196596\pi$
$593$			28.2040i			1.15820i	−0.815256	+	0.579100i	$0.803404\pi$
$594$		0			0
$595$	1.90920	−	14.6678i	0.0782695	−	0.601320i
$596$	6.83795			0.280093
$597$		0			0
$598$	17.0409			0.696854
$599$	24.8280			1.01444			0.507222	−	0.861815i	$-0.330672\pi$
$599$	24.8280			1.01444			0.507222	+	0.861815i	$0.330672\pi$
$600$		0			0
$601$	−2.87745			−0.117374			−0.0586868	−	0.998276i	$-0.518691\pi$
$601$	−2.87745			−0.117374			−0.0586868	+	0.998276i	$0.518691\pi$
$602$			18.0351i			0.735056i
$603$		0			0
$604$	−2.80702			−0.114216
$605$	22.5590	+	2.93634i	0.917154	+	0.119379i
$606$		0			0
$607$	−25.7881			−1.04671			−0.523353	−	0.852116i	$-0.675319\pi$
$607$	−25.7881			−1.04671			−0.523353	+	0.852116i	$0.675319\pi$
$608$			4.16694i			0.168992i
$609$		0			0
$610$	−0.913795	+	7.02041i	−0.0369985	+	0.284248i
$611$		−	19.7694i		−	0.799783i
$612$		0			0
$613$		−	32.4248i		−	1.30962i	−0.755792	−	0.654812i	$-0.772748\pi$
$613$		−	32.4248i		−	1.30962i	0.755792	−	0.654812i	$-0.227252\pi$
$614$			15.9903i			0.645317i
$615$		0			0
$616$		−	2.86261i		−	0.115338i
$617$			5.69333i			0.229205i	0.993411	+	0.114602i	$0.0365594\pi$
$617$			5.69333i			0.229205i	−0.993411	+	0.114602i	$0.963441\pi$
$618$		0			0
$619$	−4.76393			−0.191478			−0.0957392	−	0.995406i	$-0.530521\pi$
$619$	−4.76393			−0.191478			−0.0957392	+	0.995406i	$0.530521\pi$
$620$	−1.72179	+	13.2280i	−0.0691487	+	0.531248i
$621$		0			0
$622$			29.6416i			1.18852i
$623$	−26.3232			−1.05462
$624$		0			0
$625$	21.7235	+	12.3729i	0.868940	+	0.494918i
$626$	−10.0000			−0.399680
$627$		0			0
$628$		−	7.28275i		−	0.290613i
$629$	2.31137	+	12.5656i	0.0921604	+	0.501023i
$630$		0			0
$631$			8.72673i			0.347405i	0.984798	+	0.173703i	$0.0555732\pi$
$631$			8.72673i			0.347405i	−0.984798	+	0.173703i	$0.944427\pi$
$632$			3.35774i			0.133564i
$633$		0			0
$634$		−	21.1397i		−	0.839564i
$635$	4.34288	−	33.3650i	0.172342	−	1.32405i
$636$		0			0
$637$	−6.48656			−0.257007
$638$			2.45123i			0.0970453i
$639$		0			0
$640$	−2.21736	−	0.288618i	−0.0876490	−	0.0114086i
$641$	41.1790			1.62647			0.813237	−	0.581933i	$-0.197703\pi$
$641$	41.1790			1.62647			0.813237	+	0.581933i	$0.197703\pi$
$642$		0			0
$643$	6.12834			0.241678			0.120839	−	0.992672i	$-0.461441\pi$
$643$	6.12834			0.241678			0.120839	+	0.992672i	$0.461441\pi$
$644$		−	24.1454i		−	0.951460i
$645$		0			0
$646$		−	8.75236i		−	0.344357i
$647$	−31.3270			−1.23159			−0.615796	−	0.787905i	$-0.711166\pi$
$647$	−31.3270			−1.23159			−0.615796	+	0.787905i	$0.711166\pi$
$648$		0			0
$649$		−	5.05270i		−	0.198336i
$650$	10.7431	+	2.84491i	0.421380	+	0.111587i
$651$		0			0
$652$	22.2319			0.870669
$653$	0.716146			0.0280250			0.0140125	−	0.999902i	$-0.495540\pi$
$653$	0.716146			0.0280250			0.0140125	+	0.999902i	$0.495540\pi$
$654$		0			0
$655$	0.958138	−	7.36108i	0.0374375	−	0.287621i
$656$	−2.32312			−0.0907024
$657$		0			0
$658$	−28.0113			−1.09200
$659$	10.8796			0.423810			0.211905	−	0.977290i	$-0.432033\pi$
$659$	10.8796			0.423810			0.211905	+	0.977290i	$0.432033\pi$
$660$		0			0
$661$		−	37.4927i		−	1.45830i	−0.684355	−	0.729149i	$-0.739916\pi$
$661$		−	37.4927i		−	1.45830i	0.684355	−	0.729149i	$-0.260084\pi$
$662$			18.7324i			0.728057i
$663$		0			0
$664$		−	16.2776i		−	0.631694i
$665$	−29.0987	−	3.78757i	−1.12840	−	0.146876i
$666$		0			0
$667$			20.6755i			0.800558i
$668$	11.5050			0.445143
$669$		0			0
$670$	−2.20774	+	16.9613i	−0.0852922	+	0.655274i
$671$		−	2.87785i		−	0.111098i
$672$		0			0
$673$			38.2532i			1.47455i	0.675591	+	0.737277i	$0.263889\pi$
$673$			38.2532i			1.47455i	−0.675591	+	0.737277i	$0.736111\pi$
$674$			13.9123i			0.535881i
$675$		0			0
$676$	−8.05966			−0.309987
$677$			45.0250i			1.73045i	0.501381	+	0.865227i	$0.332825\pi$
$677$			45.0250i			1.73045i	−0.501381	+	0.865227i	$0.667175\pi$
$678$		0			0
$679$			16.1965i			0.621565i
$680$	4.65741	+	0.606222i	0.178604	+	0.0232475i
$681$		0			0
$682$		−	5.42250i		−	0.207638i
$683$	34.7787			1.33077			0.665384	−	0.746501i	$-0.268268\pi$
$683$	34.7787			1.33077			0.665384	+	0.746501i	$0.268268\pi$
$684$		0			0
$685$	5.17652	−	39.7696i	0.197785	−	1.51952i
$686$		−	12.8545i		−	0.490788i
$687$		0			0
$688$	−5.72663			−0.218326
$689$		−	20.8397i		−	0.793931i
$690$		0			0
$691$	38.8781			1.47899			0.739497	−	0.673160i	$-0.235063\pi$
$691$	38.8781			1.47899			0.739497	+	0.673160i	$0.235063\pi$
$692$		−	15.7081i		−	0.597134i
$693$		0			0
$694$	24.5885			0.933367
$695$	−28.2652	−	3.67907i	−1.07216	−	0.139555i
$696$		0			0
$697$	4.87954			0.184826
$698$	−10.2324			−0.387301
$699$		0			0
$700$	4.03097	−	15.2220i	0.152356	−	0.575338i
$701$		−	41.6474i		−	1.57300i	−0.617589	−	0.786501i	$-0.711890\pi$
$701$		−	41.6474i		−	1.57300i	0.617589	−	0.786501i	$-0.288110\pi$
$702$		0			0
$703$	24.9283	−	4.58542i	0.940188	−	0.172942i
$704$	0.908956			0.0342576
$705$		0			0
$706$	1.74540			0.0656889
$707$		−	10.0846i		−	0.379269i
$708$		0			0
$709$			3.86911i			0.145307i	0.997357	+	0.0726537i	$0.0231468\pi$
$709$			3.86911i			0.145307i	−0.997357	+	0.0726537i	$0.976853\pi$
$710$	29.9692	+	3.90087i	1.12472	+	0.146397i
$711$		0			0
$712$		−	8.35832i		−	0.313241i
$713$		−	45.7373i		−	1.71287i
$714$		0			0
$715$	−4.47980	−	0.583102i	−0.167535	−	0.0218068i
$716$		−	11.3128i		−	0.422780i
$717$		0			0
$718$	−21.1922			−0.790884
$719$	26.4440			0.986194			0.493097	−	0.869974i	$-0.335865\pi$
$719$	26.4440			0.986194			0.493097	+	0.869974i	$0.335865\pi$
$720$		0			0
$721$		−	55.7028i		−	2.07448i
$722$	1.63660			0.0609081
$723$		0			0
$724$	18.3136			0.680618
$725$	−3.45169	+	13.0345i	−0.128193	+	0.484089i
$726$		0			0
$727$	−28.3958			−1.05314			−0.526571	−	0.850131i	$-0.676522\pi$
$727$	−28.3958			−1.05314			−0.526571	+	0.850131i	$0.676522\pi$
$728$		−	7.00000i		−	0.259437i
$729$		0			0
$730$	0.620097	−	4.76402i	0.0229508	−	0.176324i
$731$	12.0284			0.444885
$732$		0			0
$733$			19.8801i			0.734289i	0.930164	+	0.367144i	$0.119664\pi$
$733$			19.8801i			0.734289i	−0.930164	+	0.367144i	$0.880336\pi$
$734$		−	9.69901i		−	0.357997i
$735$		0			0
$736$	7.66680			0.282602
$737$		−	6.95291i		−	0.256114i
$738$		0			0
$739$	−42.1224			−1.54950			−0.774749	−	0.632269i	$-0.782124\pi$
$739$	−42.1224			−1.54950			−0.774749	+	0.632269i	$0.782124\pi$
$740$	0.713423	+	13.5827i	0.0262259	+	0.499312i
$741$		0			0
$742$	−29.5280			−1.08401
$743$			23.5575i			0.864242i	0.901816	+	0.432121i	$0.142235\pi$
$743$			23.5575i			0.864242i	−0.901816	+	0.432121i	$0.857765\pi$
$744$		0			0
$745$	−15.1622	−	1.97355i	−0.555500	−	0.0723054i
$746$			36.8658i			1.34975i
$747$		0			0
$748$	−1.90920			−0.0698072
$749$	−21.2620			−0.776897
$750$		0			0
$751$	32.6454			1.19125			0.595624	−	0.803263i	$-0.296905\pi$
$751$	32.6454			1.19125			0.595624	+	0.803263i	$0.296905\pi$
$752$		−	8.89435i		−	0.324344i
$753$		0			0
$754$			5.99404i			0.218290i
$755$	6.22419	+	0.810158i	0.226522	+	0.0294847i
$756$		0			0
$757$	30.3562			1.10331			0.551657	−	0.834071i	$-0.313996\pi$
$757$	30.3562			1.10331			0.551657	+	0.834071i	$0.313996\pi$
$758$	31.7074			1.15167
$759$		0			0
$760$	1.20265	−	9.23962i	0.0436249	−	0.335156i
$761$	38.6682			1.40172			0.700860	−	0.713299i	$-0.252800\pi$
$761$	38.6682			1.40172			0.700860	+	0.713299i	$0.252800\pi$
$762$		0			0
$763$	33.1638			1.20061
$764$			7.66002i			0.277130i
$765$		0			0
$766$	3.45325			0.124771
$767$		−	12.3555i		−	0.446130i
$768$		0			0
$769$		−	23.8517i		−	0.860114i	−0.902802	−	0.430057i	$-0.858494\pi$
$769$		−	23.8517i		−	0.860114i	0.902802	−	0.430057i	$-0.141506\pi$
$770$	−0.826202	+	6.34745i	−0.0297742	+	0.228746i
$771$		0			0
$772$	−19.3148			−0.695156
$773$			38.4580i			1.38324i	0.722262	+	0.691620i	$0.243103\pi$
$773$			38.4580i			1.38324i	−0.722262	+	0.691620i	$0.756897\pi$
$774$		0			0
$775$	7.63566	−	28.8343i	0.274281	−	1.03576i
$776$	−5.14283			−0.184617
$777$		0			0
$778$			39.2237i			1.40624i
$779$		−	9.68029i		−	0.346832i
$780$		0			0
$781$	−12.2852			−0.439598
$782$	−16.1036			−0.575862
$783$		0			0
$784$	−2.91834			−0.104226
$785$	−2.10193	+	16.1485i	−0.0750212	+	0.576365i
$786$		0			0
$787$			39.3808i			1.40378i	0.712288	+	0.701888i	$0.247659\pi$
$787$			39.3808i			1.40378i	−0.712288	+	0.701888i	$0.752341\pi$
$788$			13.1193i			0.467354i
$789$		0			0
$790$	0.969104	−	7.44533i	0.0344792	−	0.264893i
$791$			19.9153i			0.708107i
$792$		0			0
$793$		−	7.03726i		−	0.249901i
$794$		−	5.75234i		−	0.204143i
$795$		0			0
$796$		−	6.04548i		−	0.214277i
$797$	28.0428			0.993327			0.496663	−	0.867943i	$-0.334558\pi$
$797$	28.0428			0.993327			0.496663	+	0.867943i	$0.334558\pi$
$798$		0			0
$799$			18.6820i			0.660920i
$800$	4.83340	+	1.27994i	0.170886	+	0.0452528i
$801$		0			0
$802$			24.6273i			0.869620i
$803$			1.95290i			0.0689163i
$804$		0			0
$805$	−6.96879	+	53.5390i	−0.245617	+	1.88700i
$806$		−	13.2597i		−	0.467054i
$807$		0			0
$808$	3.20212			0.112650
$809$		−	6.86304i		−	0.241292i	−0.992696	−	0.120646i	$-0.961503\pi$
$809$		−	6.86304i		−	0.241292i	0.992696	−	0.120646i	$-0.0384965\pi$
$810$		0			0
$811$	−13.4852			−0.473529			−0.236765	−	0.971567i	$-0.576087\pi$
$811$	−13.4852			−0.473529			−0.236765	+	0.971567i	$0.576087\pi$
$812$	8.49300			0.298046
$813$		0			0
$814$	−1.00024	−	5.43774i	−0.0350585	−	0.190593i
$815$	−49.2962	−	6.41653i	−1.72677	−	0.224761i
$816$		0			0
$817$		−	23.8625i		−	0.834844i
$818$		−	25.1947i		−	0.880913i
$819$		0			0
$820$	5.15119	+	0.670493i	0.179887	+	0.0234146i
$821$	20.0198			0.698697			0.349349	−	0.936993i	$-0.386403\pi$
$821$	20.0198			0.698697			0.349349	+	0.936993i	$0.386403\pi$
$822$		0			0
$823$			6.23551i			0.217356i	0.994077	+	0.108678i	$0.0346618\pi$
$823$			6.23551i			0.217356i	−0.994077	+	0.108678i	$0.965338\pi$
$824$	17.6871			0.616160
$825$		0			0
$826$	−17.5065			−0.609130
$827$	−33.7887			−1.17495			−0.587475	−	0.809243i	$-0.699878\pi$
$827$	−33.7887			−1.17495			−0.587475	+	0.809243i	$0.699878\pi$
$828$		0			0
$829$			31.8041i			1.10460i	0.833645	+	0.552301i	$0.186250\pi$
$829$			31.8041i			1.10460i	−0.833645	+	0.552301i	$0.813750\pi$
$830$	−4.69801	+	36.0934i	−0.163070	+	1.25282i
$831$		0			0
$832$	2.22269			0.0770578
$833$	6.12977			0.212384
$834$		0			0
$835$	−25.5108	−	3.32056i	−0.882839	−	0.114913i
$836$			3.78757i			0.130996i
$837$		0			0
$838$	−7.19906			−0.248687
$839$	−1.55322			−0.0536233			−0.0268116	−	0.999641i	$-0.508535\pi$
$839$	−1.55322			−0.0536233			−0.0268116	+	0.999641i	$0.508535\pi$
$840$		0			0
$841$	21.7275			0.749224
$842$		−	34.0902i		−	1.17483i
$843$		0			0
$844$	3.06975			0.105665
$845$	17.8712	+	2.32616i	0.614788	+	0.0800225i
$846$		0			0
$847$			32.0407i			1.10093i
$848$		−	9.37592i		−	0.321970i
$849$		0			0
$850$	−10.1522	−	2.68843i	−0.348218	−	0.0922123i
$851$	−8.43677	−	45.8658i	−0.289209	−	1.57226i
$852$		0			0
$853$	−37.4272			−1.28148			−0.640741	−	0.767757i	$-0.721373\pi$
$853$	−37.4272			−1.28148			−0.640741	+	0.767757i	$0.721373\pi$
$854$	−9.97114			−0.341206
$855$		0			0
$856$		−	6.75126i		−	0.230753i
$857$	21.2048			0.724341			0.362171	−	0.932112i	$-0.382036\pi$
$857$	21.2048			0.724341			0.362171	+	0.932112i	$0.382036\pi$
$858$		0			0
$859$			41.1942i			1.40553i	0.711424	+	0.702764i	$0.248051\pi$
$859$			41.1942i			1.40553i	−0.711424	+	0.702764i	$0.751949\pi$
$860$	12.6980	+	1.65281i	0.432999	+	0.0563603i
$861$		0			0
$862$		−	25.2123i		−	0.858734i
$863$			42.7716i			1.45596i	0.685597	+	0.727982i	$0.259541\pi$
$863$			42.7716i			1.45596i	−0.685597	+	0.727982i	$0.740459\pi$
$864$		0			0
$865$	−4.53365	+	34.8306i	−0.154149	+	1.18428i
$866$		−	21.8683i		−	0.743115i
$867$		0			0
$868$	−18.7878			−0.637699
$869$			3.05204i			0.103533i
$870$		0			0
$871$		−	17.0021i		−	0.576093i
$872$			10.5304i			0.356604i
$873$		0			0
$874$			31.9471i			1.08063i
$875$	−13.3315	+	32.5893i	−0.450686	+	1.10172i
$876$		0			0
$877$			50.8976i			1.71869i	0.511397	+	0.859345i	$0.329128\pi$
$877$			50.8976i			1.71869i	−0.511397	+	0.859345i	$0.670872\pi$
$878$			9.00956i			0.304058i
$879$		0			0
$880$	−2.01549	−	0.262341i	−0.0679420	−	0.00884352i
$881$	44.1155			1.48629			0.743144	−	0.669132i	$-0.233334\pi$
$881$	44.1155			1.48629			0.743144	+	0.669132i	$0.233334\pi$
$882$		0			0
$883$	−46.0708			−1.55041			−0.775203	−	0.631713i	$-0.782352\pi$
$883$	−46.0708			−1.55041			−0.775203	+	0.631713i	$0.782352\pi$
$884$	−4.66860			−0.157022
$885$		0			0
$886$			2.89007i			0.0970939i
$887$			41.8693i			1.40583i	0.711272	+	0.702916i	$0.248119\pi$
$887$			41.8693i			1.40583i	−0.711272	+	0.702916i	$0.751881\pi$
$888$		0			0
$889$	47.3886			1.58936
$890$	−2.41236	+	18.5334i	−0.0808626	+	0.621242i
$891$		0			0
$892$		−	13.9960i		−	0.468621i
$893$	37.0622			1.24024
$894$		0			0
$895$	−3.26508	+	25.0846i	−0.109140	+	0.838487i
$896$		−	3.14934i		−	0.105212i
$897$		0			0
$898$		−	18.1539i		−	0.605805i
$899$	16.0878			0.536560
$900$		0			0
$901$			19.6935i			0.656084i
$902$	−2.11161			−0.0703089
$903$		0			0
$904$	−6.32365			−0.210321
$905$	−40.6078	−	5.28563i	−1.34985	−	0.175700i
$906$		0			0
$907$	30.2279			1.00370			0.501851	−	0.864954i	$-0.332653\pi$
$907$	30.2279			1.00370			0.501851	+	0.864954i	$0.332653\pi$
$908$	−11.9087			−0.395205
$909$		0			0
$910$	−2.02033	+	15.5215i	−0.0669731	+	0.514534i
$911$		−	8.01080i		−	0.265409i	−0.991156	−	0.132705i	$-0.957634\pi$
$911$		−	8.01080i		−	0.265409i	0.991156	−	0.132705i	$-0.0423662\pi$
$912$		0			0
$913$		−	14.7956i		−	0.489664i
$914$	−10.4140			−0.344464
$915$		0			0
$916$	−7.43448			−0.245642
$917$	10.4550			0.345255
$918$		0			0
$919$			27.1395i			0.895249i	0.894222	+	0.447624i	$0.147730\pi$
$919$			27.1395i			0.895249i	−0.894222	+	0.447624i	$0.852270\pi$
$920$	−17.0001	−	2.21278i	−0.560476	−	0.0729531i
$921$		0			0
$922$		−	17.7433i		−	0.584346i
$923$	−30.0411			−0.988816
$924$		0			0
$925$	2.33831	−	30.3238i	0.0768831	−	0.997040i
$926$	−11.6293			−0.382161
$927$		0			0
$928$			2.69676i			0.0885253i
$929$	−47.1557			−1.54713			−0.773564	−	0.633719i	$-0.781528\pi$
$929$	−47.1557			−1.54713			−0.773564	+	0.633719i	$0.781528\pi$
$930$		0			0
$931$		−	12.1606i		−	0.398546i
$932$		−	15.2152i		−	0.498391i
$933$		0			0
$934$	6.25208			0.204574
$935$	4.23339	+	0.551029i	0.138447	+	0.0180206i
$936$		0			0
$937$		−	22.2885i		−	0.728133i	−0.931373	−	0.364066i	$-0.881388\pi$
$937$		−	22.2885i		−	0.728133i	0.931373	−	0.364066i	$-0.118612\pi$
$938$	−24.0903			−0.786578
$939$		0			0
$940$	−2.56707	+	19.7220i	−0.0837286	+	0.643261i
$941$	−43.0380			−1.40300			−0.701499	−	0.712670i	$-0.747486\pi$
$941$	−43.0380			−1.40300			−0.701499	+	0.712670i	$0.747486\pi$
$942$		0			0
$943$	−17.8109			−0.580001
$944$		−	5.55880i		−	0.180923i
$945$		0			0
$946$	−5.20525			−0.169237
$947$	−16.4353			−0.534075			−0.267038	−	0.963686i	$-0.586045\pi$
$947$	−16.4353			−0.534075			−0.267038	+	0.963686i	$0.586045\pi$
$948$		0			0
$949$			4.77545i			0.155018i
$950$	−5.33344	+	20.1405i	−0.173040	+	0.653444i
$951$		0			0
$952$			6.61496i			0.214392i
$953$		−	48.5182i		−	1.57166i	−0.618443	−	0.785830i	$-0.712236\pi$
$953$		−	48.5182i		−	1.57166i	0.618443	−	0.785830i	$-0.287764\pi$
$954$		0			0
$955$	2.21082	−	16.9851i	0.0715405	−	0.549623i
$956$			29.1359i			0.942323i
$957$		0			0
$958$			16.4452i			0.531319i
$959$	56.4851			1.82400
$960$		0			0
$961$	−4.58873			−0.148024
$962$	−2.44591	−	13.2970i	−0.0788593	−	0.428712i
$963$		0			0
$964$			7.08791i			0.228286i
$965$	42.8280	+	5.57461i	1.37868	+	0.179453i
$966$		0			0
$967$	21.0002			0.675322			0.337661	−	0.941268i	$-0.390364\pi$
$967$	21.0002			0.675322			0.337661	+	0.941268i	$0.390364\pi$
$968$	−10.1738			−0.326998
$969$		0			0
$970$	11.4035	+	1.48431i	0.366145	+	0.0476584i
$971$	−11.8732			−0.381028			−0.190514	−	0.981684i	$-0.561016\pi$
$971$	−11.8732			−0.381028			−0.190514	+	0.981684i	$0.561016\pi$
$972$		0			0
$973$		−	40.1452i		−	1.28700i
$974$	−13.7966			−0.442072
$975$		0			0
$976$		−	3.16611i		−	0.101345i
$977$	−31.2226			−0.998900			−0.499450	−	0.866343i	$-0.666465\pi$
$977$	−31.2226			−0.998900			−0.499450	+	0.866343i	$0.666465\pi$
$978$		0			0
$979$		−	7.59735i		−	0.242812i
$980$	6.47102	+	0.842286i	0.206709	+	0.0269058i
$981$		0			0
$982$	39.0410			1.24585
$983$			57.5637i			1.83600i	0.396583	+	0.917999i	$0.370196\pi$
$983$			57.5637i			1.83600i	−0.396583	+	0.917999i	$0.629804\pi$
$984$		0			0
$985$	3.78646	−	29.0902i	0.120647	−	0.926890i
$986$		−	5.66434i		−	0.180389i
$987$		0			0
$988$			9.26180i			0.294657i
$989$	−43.9049			−1.39609
$990$		0			0
$991$		−	14.9985i		−	0.476442i	−0.971211	−	0.238221i	$-0.923436\pi$
$991$		−	14.9985i		−	0.476442i	0.971211	−	0.238221i	$-0.0765642\pi$
$992$		−	5.96563i		−	0.189409i
$993$		0			0
$994$			42.5655i			1.35010i
$995$	−1.74484	+	13.4050i	−0.0553150	+	0.424968i
$996$		0			0
$997$	1.43497			0.0454459			0.0227229	−	0.999742i	$-0.492766\pi$
$997$	1.43497			0.0454459			0.0227229	+	0.999742i	$0.492766\pi$
$998$			40.0886i			1.26898i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.e.d.739.1		10
3.2	odd	2		370.2.c.a.369.2	✓	10
5.4	even	2		3330.2.e.c.739.9		10
15.2	even	4		1850.2.d.i.1701.2		20
15.8	even	4		1850.2.d.i.1701.19		20
15.14	odd	2		370.2.c.b.369.9	yes	10
37.36	even	2		3330.2.e.c.739.10		10
111.110	odd	2		370.2.c.b.369.2	yes	10
185.184	even	2	inner	3330.2.e.d.739.2		10
555.332	even	4		1850.2.d.i.1701.12		20
555.443	even	4		1850.2.d.i.1701.9		20
555.554	odd	2		370.2.c.a.369.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.2	✓	10	3.2	odd	2
370.2.c.a.369.9	yes	10	555.554	odd	2
370.2.c.b.369.2	yes	10	111.110	odd	2
370.2.c.b.369.9	yes	10	15.14	odd	2
1850.2.d.i.1701.2		20	15.2	even	4
1850.2.d.i.1701.9		20	555.443	even	4
1850.2.d.i.1701.12		20	555.332	even	4
1850.2.d.i.1701.19		20	15.8	even	4
3330.2.e.c.739.9		10	5.4	even	2
3330.2.e.c.739.10		10	37.36	even	2
3330.2.e.d.739.1		10	1.1	even	1	trivial
3330.2.e.d.739.2		10	185.184	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.21736 - 0.288618i) q^{5} -3.14934i q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.21736 - 0.288618i) q^{5} -3.14934i q^{7} +1.00000 q^{8} +(-2.21736 - 0.288618i) q^{10} +0.908956 q^{11} +2.22269 q^{13} -3.14934i q^{14} +1.00000 q^{16} -2.10043 q^{17} +4.16694i q^{19} +(-2.21736 - 0.288618i) q^{20} +0.908956 q^{22} +7.66680 q^{23} +(4.83340 + 1.27994i) q^{25} +2.22269 q^{26} -3.14934i q^{28} +2.69676i q^{29} -5.96563i q^{31} +1.00000 q^{32} -2.10043 q^{34} +(-0.908956 + 6.98323i) q^{35} +(-1.10043 - 5.98240i) q^{37} +4.16694i q^{38} +(-2.21736 - 0.288618i) q^{40} -2.32312 q^{41} -5.72663 q^{43} +0.908956 q^{44} +7.66680 q^{46} -8.89435i q^{47} -2.91834 q^{49} +(4.83340 + 1.27994i) q^{50} +2.22269 q^{52} -9.37592i q^{53} +(-2.01549 - 0.262341i) q^{55} -3.14934i q^{56} +2.69676i q^{58} -5.55880i q^{59} -3.16611i q^{61} -5.96563i q^{62} +1.00000 q^{64} +(-4.92850 - 0.641508i) q^{65} -7.64933i q^{67} -2.10043 q^{68} +(-0.908956 + 6.98323i) q^{70} -13.5157 q^{71} +2.14851i q^{73} +(-1.10043 - 5.98240i) q^{74} +4.16694i q^{76} -2.86261i q^{77} +3.35774i q^{79} +(-2.21736 - 0.288618i) q^{80} -2.32312 q^{82} -16.2776i q^{83} +(4.65741 + 0.606222i) q^{85} -5.72663 q^{86} +0.908956 q^{88} -8.35832i q^{89} -7.00000i q^{91} +7.66680 q^{92} -8.89435i q^{94} +(1.20265 - 9.23962i) q^{95} -5.14283 q^{97} -2.91834 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8	\( 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8} + 3 q^{10} - 2 q^{13} + 10 q^{16} - 18 q^{17} + 3 q^{20} - 10 q^{23} + 5 q^{25} - 2 q^{26} + 10 q^{32} - 18 q^{34} - 8 q^{37} + 3 q^{40} + 4 q^{41} - 10 q^{43} - 10 q^{46} - 8 q^{49} + 5 q^{50} - 2 q^{52} + 5 q^{55} + 10 q^{64} - 2 q^{65} - 18 q^{68} + 20 q^{71} - 8 q^{74} + 3 q^{80} + 4 q^{82} - 28 q^{85} - 10 q^{86} - 10 q^{92} - 2 q^{95} + 2 q^{97} - 8 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8 + 3 * q^10 - 2 * q^13 + 10 * q^16 - 18 * q^17 + 3 * q^20 - 10 * q^23 + 5 * q^25 - 2 * q^26 + 10 * q^32 - 18 * q^34 - 8 * q^37 + 3 * q^40 + 4 * q^41 - 10 * q^43 - 10 * q^46 - 8 * q^49 + 5 * q^50 - 2 * q^52 + 5 * q^55 + 10 * q^64 - 2 * q^65 - 18 * q^68 + 20 * q^71 - 8 * q^74 + 3 * q^80 + 4 * q^82 - 28 * q^85 - 10 * q^86 - 10 * q^92 - 2 * q^95 + 2 * q^97 - 8 * q^98

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