LMFDB - Embedded newform 3997.1.cz.a.580.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3997,1,Mod(13,3997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3997, base_ring=CyclotomicField(570))

chi = DirichletCharacter(H, H._module([285, 352]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3997.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3997 = 7 \cdot 571 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3997.cz (of order $570$, degree $144$, 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:	$1.99476285549$
Analytic rank:	$0$
Dimension:	$144$
Coefficient field:	$\Q(\zeta_{570})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} + \cdots + 1 $ x^144 - x^143 + x^142 + x^139 - x^138 + x^137 - x^129 + x^128 - x^127 + x^125 - 2x^124 + 2x^123 - x^122 + x^120 - x^119 + x^118 + x^114 - x^113 + x^112 - x^110 + 2x^109 - 2x^108 + x^107 - x^105 + x^104 - x^103 - x^99 + x^98 - x^97 + x^95 - 2x^94 + 2x^93 - x^92 + x^90 - x^89 + x^88 - x^87 + x^86 - x^85 + x^84 - x^83 + x^81 - 2x^80 + 2x^79 - 2x^78 + x^77 - x^75 + x^74 - x^73 + x^72 - x^71 + x^70 - x^69 + x^67 - 2x^66 + 2x^65 - 2x^64 + x^63 - x^61 + x^60 - x^59 + x^58 - x^57 + x^56 - x^55 + x^54 - x^52 + 2x^51 - 2x^50 + x^49 - x^47 + x^46 - x^45 - x^41 + x^40 - x^39 + x^37 - 2x^36 + 2x^35 - x^34 + x^32 - x^31 + x^30 + x^26 - x^25 + x^24 - x^22 + 2x^21 - 2x^20 + x^19 - x^17 + x^16 - x^15 + x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{285}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{285} - \cdots)$

Embedding invariants

Embedding label			580.1
Root			$-0.731980 + 0.681326i$ of defining polynomial
Character	$\chi$	$=$	3997.580
Dual form			3997.1.cz.a.1840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76667 - 0.499567i) q^{2} +(2.01965 - 1.24147i) q^{4} +(0.828009 - 0.560715i) q^{7} +(1.70440 - 1.85147i) q^{8} +(0.999757 + 0.0220445i) q^{9} +O(q^{10})$	\(q+(1.76667 - 0.499567i) q^{2} +(2.01965 - 1.24147i) q^{4} +(0.828009 - 0.560715i) q^{7} +(1.70440 - 1.85147i) q^{8} +(0.999757 + 0.0220445i) q^{9} +(-0.925691 + 0.175528i) q^{11} +(1.18271 - 1.40425i) q^{14} +(1.01573 - 2.00714i) q^{16} +(1.77726 - 0.460501i) q^{18} +(-1.54771 + 0.772545i) q^{22} +(-1.60834 + 0.737426i) q^{23} +(-0.992658 + 0.120958i) q^{25} +(0.976173 - 2.16040i) q^{28} +(-0.849008 + 1.15512i) q^{29} +(0.309319 - 1.58354i) q^{32} +(2.04652 - 1.19665i) q^{36} +(0.257613 + 0.146846i) q^{37} +(-0.0222153 + 0.0738748i) q^{43} +(-1.65166 + 1.50372i) q^{44} +(-2.47301 + 2.10626i) q^{46} +(0.371197 - 0.928554i) q^{49} +(-1.69327 + 0.709592i) q^{50} +(-0.902370 + 0.332196i) q^{53} +(0.373110 - 2.48872i) q^{56} +(-0.922860 + 2.46485i) q^{58} +(0.840168 - 0.542326i) q^{63} +(-0.0588558 - 0.710284i) q^{64} +(0.327226 - 1.89651i) q^{67} +(1.23426 + 1.37079i) q^{71} +(1.74480 - 1.81345i) q^{72} +(0.528478 + 0.130734i) q^{74} +(-0.668059 + 0.664387i) q^{77} +(-0.960112 - 0.341483i) q^{79} +(0.999028 + 0.0440782i) q^{81} +(-0.00234170 + 0.141611i) q^{86} +(-1.25276 + 2.01306i) q^{88} +(-2.33277 + 3.48604i) q^{92} +(0.191909 - 1.82589i) q^{98} +(-0.929336 + 0.155079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) $ 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9	$ 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9 + 6 * q^11 + q^14 + 6 * q^16 - 9 * q^18 + 21 * q^22 + 3 * q^23 - q^25 - 10 * q^28 - 4 * q^29 - 5 * q^32 - 2 * q^37 - 9 * q^43 - 20 * q^44 - 34 * q^46 + 2 * q^49 - 2 * q^50 + 6 * q^53 - 8 * q^56 - q^58 - q^63 + 11 * q^64 + 20 * q^67 + 3 * q^71 + 23 * q^72 - 31 * q^74 + q^77 + 6 * q^79 - q^81 + 7 * q^86 - 9 * q^88 + 9 * q^92 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{1}{285}\right)$	$-1$

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 $

$2$	1.76667	−	0.499567i	1.76667	−	0.499567i	0.775409	−	0.631460i	$-0.217544\pi$
$2$	1.76667	−	0.499567i	1.76667	−	0.499567i	0.991264	+	0.131892i	$0.0421053\pi$
$3$		0			0		−0.999939	−	0.0110229i	$-0.996491\pi$
$3$		0			0		0.999939	+	0.0110229i	$0.00350877\pi$
$4$	2.01965	−	1.24147i	2.01965	−	1.24147i
$5$		0			0		−0.0605901	−	0.998163i	$-0.519298\pi$
$5$		0			0		0.0605901	+	0.998163i	$0.480702\pi$
$6$		0			0
$7$	0.828009	−	0.560715i	0.828009	−	0.560715i
$7$	0.828009	−	0.560715i	0.828009	−	0.560715i
$8$	1.70440	−	1.85147i	1.70440	−	1.85147i
$9$	0.999757	+	0.0220445i	0.999757	+	0.0220445i
$10$		0			0
$11$	−0.925691	+	0.175528i	−0.925691	+	0.175528i	−0.627176	−	0.778877i	$-0.715789\pi$
$11$	−0.925691	+	0.175528i	−0.925691	+	0.175528i	−0.298515	+	0.954405i	$0.596491\pi$
$12$		0			0
$13$		0			0		−0.739446	−	0.673216i	$-0.764912\pi$
$13$		0			0		0.739446	+	0.673216i	$0.235088\pi$
$14$	1.18271	−	1.40425i	1.18271	−	1.40425i
$15$		0			0
$16$	1.01573	−	2.00714i	1.01573	−	2.00714i
$17$		0			0		−0.159156	−	0.987253i	$-0.550877\pi$
$17$		0			0		0.159156	+	0.987253i	$0.449123\pi$
$18$	1.77726	−	0.460501i	1.77726	−	0.460501i
$19$		0			0		0.319482	−	0.947592i	$-0.396491\pi$
$19$		0			0		−0.319482	+	0.947592i	$0.603509\pi$
$20$		0			0
$21$		0			0
$22$	−1.54771	+	0.772545i	−1.54771	+	0.772545i
$23$	−1.60834	+	0.737426i	−1.60834	+	0.737426i	−0.998482	−	0.0550878i	$-0.982456\pi$
$23$	−1.60834	+	0.737426i	−1.60834	+	0.737426i	−0.609854	+	0.792514i	$0.708772\pi$
$24$		0			0
$25$	−0.992658	+	0.120958i	−0.992658	+	0.120958i
$26$		0			0
$27$		0			0
$28$	0.976173	−	2.16040i	0.976173	−	2.16040i
$29$	−0.849008	+	1.15512i	−0.849008	+	1.15512i	0.137354	+	0.990522i	$0.456140\pi$
$29$	−0.849008	+	1.15512i	−0.849008	+	1.15512i	−0.986361	+	0.164595i	$0.947368\pi$
$30$		0			0
$31$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$31$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$32$	0.309319	−	1.58354i	0.309319	−	1.58354i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.04652	−	1.19665i	2.04652	−	1.19665i
$37$	0.257613	+	0.146846i	0.257613	+	0.146846i	0.618553	−	0.785743i	$-0.287719\pi$
$37$	0.257613	+	0.146846i	0.257613	+	0.146846i	−0.360939	+	0.932589i	$0.617544\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$41$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$42$		0			0
$43$	−0.0222153	+	0.0738748i	−0.0222153	+	0.0738748i	−0.968033	−	0.250825i	$-0.919298\pi$
$43$	−0.0222153	+	0.0738748i	−0.0222153	+	0.0738748i	0.945817	+	0.324699i	$0.105263\pi$
$44$	−1.65166	+	1.50372i	−1.65166	+	1.50372i
$45$		0			0
$46$	−2.47301	+	2.10626i	−2.47301	+	2.10626i
$47$		0			0		0.998482	−	0.0550878i	$-0.0175439\pi$
$47$		0			0		−0.998482	+	0.0550878i	$0.982456\pi$
$48$		0			0
$49$	0.371197	−	0.928554i	0.371197	−	0.928554i
$50$	−1.69327	+	0.709592i	−1.69327	+	0.709592i
$51$		0			0
$52$		0			0
$53$	−0.902370	+	0.332196i	−0.902370	+	0.332196i	−0.754107	−	0.656752i	$-0.771930\pi$
$53$	−0.902370	+	0.332196i	−0.902370	+	0.332196i	−0.148264	+	0.988948i	$0.547368\pi$
$54$		0			0
$55$		0			0
$56$	0.373110	−	2.48872i	0.373110	−	2.48872i
$57$		0			0
$58$	−0.922860	+	2.46485i	−0.922860	+	2.46485i
$59$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$59$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$60$		0			0
$61$		0			0		0.884667	−	0.466224i	$-0.154386\pi$
$61$		0			0		−0.884667	+	0.466224i	$0.845614\pi$
$62$		0			0
$63$	0.840168	−	0.542326i	0.840168	−	0.542326i
$64$	−0.0588558	−	0.710284i	−0.0588558	−	0.710284i
$65$		0			0
$66$		0			0
$67$	0.327226	−	1.89651i	0.327226	−	1.89651i	−0.104528	−	0.994522i	$-0.533333\pi$
$67$	0.327226	−	1.89651i	0.327226	−	1.89651i	0.431754	−	0.901991i	$-0.357895\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.23426	+	1.37079i	1.23426	+	1.37079i	0.904357	+	0.426776i	$0.140351\pi$
$71$	1.23426	+	1.37079i	1.23426	+	1.37079i	0.329907	+	0.944013i	$0.392982\pi$
$72$	1.74480	−	1.81345i	1.74480	−	1.81345i
$73$		0			0		−0.00551154	−	0.999985i	$-0.501754\pi$
$73$		0			0		0.00551154	+	0.999985i	$0.498246\pi$
$74$	0.528478	+	0.130734i	0.528478	+	0.130734i
$75$		0			0
$76$		0			0
$77$	−0.668059	+	0.664387i	−0.668059	+	0.664387i
$78$		0			0
$79$	−0.960112	−	0.341483i	−0.960112	−	0.341483i	−0.191711	−	0.981451i	$-0.561404\pi$
$79$	−0.960112	−	0.341483i	−0.960112	−	0.341483i	−0.768401	+	0.639969i	$0.778947\pi$
$80$		0			0
$81$	0.999028	+	0.0440782i	0.999028	+	0.0440782i
$82$		0			0
$83$		0			0		0.256156	−	0.966635i	$-0.417544\pi$
$83$		0			0		−0.256156	+	0.966635i	$0.582456\pi$
$84$		0			0
$85$		0			0
$86$	−0.00234170	+	0.141611i	−0.00234170	+	0.141611i
$87$		0			0
$88$	−1.25276	+	2.01306i	−1.25276	+	2.01306i
$89$		0			0		−0.709053	−	0.705155i	$-0.750877\pi$
$89$		0			0		0.709053	+	0.705155i	$0.249123\pi$
$90$		0			0
$91$		0			0
$92$	−2.33277	+	3.48604i	−2.33277	+	3.48604i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.997024	−	0.0770854i	$-0.975439\pi$
$97$		0			0		0.997024	+	0.0770854i	$0.0245614\pi$
$98$	0.191909	−	1.82589i	0.191909	−	1.82589i
$99$	−0.929336	+	0.155079i	−0.929336	+	0.155079i
$100$	−1.85465	+	1.47665i	−1.85465	+	1.47665i
$101$		0			0		−0.381410	−	0.924406i	$-0.624561\pi$
$101$		0			0		0.381410	+	0.924406i	$0.375439\pi$
$102$		0			0
$103$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$103$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$104$		0			0
$105$		0			0
$106$	−1.42824	+	1.03768i	−1.42824	+	1.03768i
$107$	−0.902573	−	1.78353i	−0.902573	−	1.78353i	−0.480787	−	0.876837i	$-0.659649\pi$
$107$	−0.902573	−	1.78353i	−0.902573	−	1.78353i	−0.421786	−	0.906696i	$-0.638596\pi$
$108$		0			0
$109$	0.846095	−	1.46548i	0.846095	−	1.46548i	−0.0385714	−	0.999256i	$-0.512281\pi$
$109$	0.846095	−	1.46548i	0.846095	−	1.46548i	0.884667	−	0.466224i	$-0.154386\pi$
$110$		0			0
$111$		0			0
$112$	−0.284400	−	2.23147i	−0.284400	−	2.23147i
$113$	0.0644636	+	0.311716i	0.0644636	+	0.311716i	0.999028	−	0.0440782i	$-0.0140351\pi$
$113$	0.0644636	+	0.311716i	0.0644636	+	0.311716i	−0.934564	+	0.355794i	$0.884211\pi$
$114$		0			0
$115$		0			0
$116$	−0.280650	+	3.38695i	−0.280650	+	3.38695i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.104492	+	0.0411049i	−0.104492	+	0.0411049i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.21337	−	1.37783i	1.21337	−	1.37783i
$127$	1.20187	−	0.0265010i	1.20187	−	0.0265010i	0.583317	−	0.812244i	$-0.301754\pi$
$127$	1.20187	−	0.0265010i	1.20187	−	0.0265010i	0.618553	+	0.785743i	$0.287719\pi$
$128$	0.106928	+	0.285593i	0.106928	+	0.285593i
$129$		0			0
$130$		0			0
$131$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$131$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$132$		0			0
$133$		0			0
$134$	−0.369335	−	3.51399i	−0.369335	−	3.51399i
$135$		0			0
$136$		0			0
$137$	1.27893	+	0.155840i	1.27893	+	0.155840i	0.731980	−	0.681326i	$-0.238596\pi$
$137$	1.27893	+	0.155840i	1.27893	+	0.155840i	0.546948	+	0.837166i	$0.315789\pi$
$138$		0			0
$139$		0			0		0.480787	−	0.876837i	$-0.340351\pi$
$139$		0			0		−0.480787	+	0.876837i	$0.659649\pi$
$140$		0			0
$141$		0			0
$142$	2.86534	+	1.80514i	2.86534	+	1.80514i
$143$		0			0
$144$	1.05973	−	1.98426i	1.05973	−	1.98426i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.702593	−	0.0232428i	0.702593	−	0.0232428i
$149$	1.81525	+	0.832298i	1.81525	+	0.832298i	0.930586	+	0.366074i	$0.119298\pi$
$149$	1.81525	+	0.832298i	1.81525	+	0.832298i	0.884667	+	0.466224i	$0.154386\pi$
$150$		0			0
$151$	−0.194545	−	0.0765303i	−0.194545	−	0.0765303i	0.266796	−	0.963753i	$-0.414035\pi$
$151$	−0.194545	−	0.0765303i	−0.194545	−	0.0765303i	−0.461341	+	0.887223i	$0.652632\pi$
$152$		0			0
$153$		0			0
$154$	−0.848336	+	1.50750i	−0.848336	+	1.50750i
$155$		0			0
$156$		0			0
$157$		0			0		0.775409	−	0.631460i	$-0.217544\pi$
$157$		0			0		−0.775409	+	0.631460i	$0.782456\pi$
$158$	−1.86680	−	0.123648i	−1.86680	−	0.123648i
$159$		0			0
$160$		0			0
$161$	−0.918230	+	1.51241i	−0.918230	+	1.51241i
$162$	1.78698	−	0.421210i	1.78698	−	0.421210i
$163$	−1.61185	−	1.09152i	−1.61185	−	1.09152i	−0.934564	−	0.355794i	$-0.884211\pi$
$163$	−1.61185	−	1.09152i	−1.61185	−	1.09152i	−0.677282	−	0.735724i	$-0.736842\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$167$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	0.0935596	+	0.995614i	0.0935596	+	0.995614i
$170$		0			0
$171$		0			0
$172$	0.0468465	+	0.176781i	0.0468465	+	0.176781i
$173$		0			0		−0.984487	−	0.175457i	$-0.943860\pi$
$173$		0			0		0.984487	+	0.175457i	$0.0561404\pi$
$174$		0			0
$175$	−0.754107	+	0.656752i	−0.754107	+	0.656752i
$176$	−0.587946	+	2.03628i	−0.587946	+	2.03628i
$177$		0			0
$178$		0			0
$179$	−0.819762	−	1.71259i	−0.819762	−	1.71259i	−0.693336	−	0.720615i	$-0.743860\pi$
$179$	−0.819762	−	1.71259i	−0.819762	−	1.71259i	−0.126427	−	0.991976i	$-0.540351\pi$
$180$		0			0
$181$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$181$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$182$		0			0
$183$		0			0
$184$	−1.37592	+	4.23466i	−1.37592	+	4.23466i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.751208	−	0.221393i	0.751208	−	0.221393i	0.115485	−	0.993309i	$-0.463158\pi$
$191$	0.751208	−	0.221393i	0.751208	−	0.221393i	0.635724	+	0.771917i	$0.280702\pi$
$192$		0			0
$193$	−0.948898	+	1.05386i	−0.948898	+	1.05386i	0.0495838	+	0.998770i	$0.484211\pi$
$193$	−0.948898	+	1.05386i	−0.948898	+	1.05386i	−0.998482	+	0.0550878i	$0.982456\pi$
$194$		0			0
$195$		0			0
$196$	−0.403087	−	2.33618i	−0.403087	−	2.33618i
$197$	−0.198361	−	0.276209i	−0.198361	−	0.276209i	0.701237	−	0.712928i	$-0.252632\pi$
$197$	−0.198361	−	0.276209i	−0.198361	−	0.276209i	−0.899598	+	0.436719i	$0.856140\pi$
$198$	−1.56436	+	0.738239i	−1.56436	+	0.738239i
$199$		0			0		−0.899598	−	0.436719i	$-0.856140\pi$
$199$		0			0		0.899598	+	0.436719i	$0.143860\pi$
$200$	−1.46794	+	2.04404i	−1.46794	+	2.04404i
$201$		0			0
$202$		0			0
$203$	−0.0552946	+	1.43250i	−0.0552946	+	1.43250i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.62420	+	0.701792i	−1.62420	+	0.701792i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.928564	−	0.790858i	−0.928564	−	0.790858i	0.0495838	−	0.998770i	$-0.484211\pi$
$211$	−0.928564	−	0.790858i	−0.928564	−	0.790858i	−0.978148	+	0.207912i	$0.933333\pi$
$212$	−1.41006	+	1.79119i	−1.41006	+	1.79119i
$213$		0			0
$214$	−2.48555	−	2.70002i	−2.48555	−	2.70002i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.762667	−	3.01171i	0.762667	−	3.01171i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.0935596	−	0.995614i	$-0.470175\pi$
$223$		0			0		−0.0935596	+	0.995614i	$0.529825\pi$
$224$	−0.631796	−	1.48462i	−0.631796	−	1.48462i
$225$	−0.995083	+	0.0990455i	−0.995083	+	0.0990455i
$226$	0.269609	+	0.518496i	0.269609	+	0.518496i
$227$		0			0		−0.509516	−	0.860461i	$-0.670175\pi$
$227$		0			0		0.509516	+	0.860461i	$0.329825\pi$
$228$		0			0
$229$		0			0		0.0715891	−	0.997434i	$-0.477193\pi$
$229$		0			0		−0.0715891	+	0.997434i	$0.522807\pi$
$230$		0			0
$231$		0			0
$232$	0.691618	+	3.54070i	0.691618	+	3.54070i
$233$	0.414596	+	1.07123i	0.414596	+	1.07123i	0.970739	+	0.240139i	$0.0771930\pi$
$233$	0.414596	+	1.07123i	0.414596	+	1.07123i	−0.556143	+	0.831087i	$0.687719\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.572457	+	1.90365i	0.572457	+	1.90365i	0.391577	+	0.920146i	$0.371930\pi$
$239$	0.572457	+	1.90365i	0.572457	+	1.90365i	0.180881	+	0.983505i	$0.442105\pi$
$240$		0			0
$241$		0			0		−0.490424	−	0.871484i	$-0.663158\pi$
$241$		0			0		0.490424	+	0.871484i	$0.336842\pi$
$242$	−0.164068	+	0.124820i	−0.164068	+	0.124820i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.989750	−	0.142811i	$-0.0456140\pi$
$251$		0			0		−0.989750	+	0.142811i	$0.954386\pi$
$252$	1.02356	−	2.13835i	1.02356	−	2.13835i
$253$	1.35938	−	0.964936i	1.35938	−	0.964936i
$254$	2.11007	−	0.647234i	2.11007	−	0.647234i
$255$		0			0
$256$	0.753677	+	1.02541i	0.753677	+	1.02541i
$257$		0			0		0.574329	−	0.818625i	$-0.305263\pi$
$257$		0			0		−0.574329	+	0.818625i	$0.694737\pi$
$258$		0			0
$259$	0.295645	−	0.0228579i	0.295645	−	0.0228579i
$260$		0			0
$261$	−0.874265	+	1.13612i	−0.874265	+	1.13612i
$262$		0			0
$263$	−0.350685	+	1.45189i	−0.350685	+	1.45189i	0.471093	+	0.882084i	$0.343860\pi$
$263$	−0.350685	+	1.45189i	−0.350685	+	1.45189i	−0.821778	+	0.569808i	$0.807018\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.69359	−	4.23653i	−1.69359	−	4.23653i
$269$		0			0		−0.995083	−	0.0990455i	$-0.968421\pi$
$269$		0			0		0.995083	+	0.0990455i	$0.0315789\pi$
$270$		0			0
$271$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$271$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$272$		0			0
$273$		0			0
$274$	2.33730	−	0.363592i	2.33730	−	0.363592i
$275$	0.897663	−	0.286208i	0.897663	−	0.286208i
$276$		0			0
$277$	0.113273	−	0.974284i	0.113273	−	0.974284i	−0.809017	−	0.587785i	$-0.800000\pi$
$277$	0.113273	−	0.974284i	0.113273	−	0.974284i	0.922290	−	0.386499i	$-0.126316\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.45566	−	0.446503i	−1.45566	−	0.446503i	−0.537687	−	0.843145i	$-0.680702\pi$
$281$	−1.45566	−	0.446503i	−1.45566	−	0.446503i	−0.917973	+	0.396642i	$0.870175\pi$
$282$		0			0
$283$		0			0		0.213300	−	0.976987i	$-0.431579\pi$
$283$		0			0		−0.213300	+	0.976987i	$0.568421\pi$
$284$	4.19457	+	1.23621i	4.19457	+	1.23621i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.344152	−	1.57634i	0.344152	−	1.57634i
$289$	−0.949339	+	0.314254i	−0.949339	+	0.314254i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.224056	−	0.974576i	$-0.428070\pi$
$293$		0			0		−0.224056	+	0.974576i	$0.571930\pi$
$294$		0			0
$295$		0			0
$296$	0.710958	−	0.226680i	0.710958	−	0.226680i
$297$		0			0
$298$	3.62275	+	0.563557i	3.62275	+	0.563557i
$299$		0			0
$300$		0			0
$301$	0.0230283	+	0.0736255i	0.0230283	+	0.0736255i
$302$	−0.381930	−	0.0380154i	−0.381930	−	0.0380154i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.537687	−	0.843145i	$-0.319298\pi$
$307$		0			0		−0.537687	+	0.843145i	$0.680702\pi$
$308$	−0.524425	+	2.17120i	−0.524425	+	2.17120i
$309$		0			0
$310$		0			0
$311$		0			0		0.126427	−	0.991976i	$-0.459649\pi$
$311$		0			0		−0.126427	+	0.991976i	$0.540351\pi$
$312$		0			0
$313$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$313$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$314$		0			0
$315$		0			0
$316$	−2.36303	+	0.502277i	−2.36303	+	0.502277i
$317$	0.844506	−	0.259040i	0.844506	−	0.259040i	0.159156	−	0.987253i	$-0.449123\pi$
$317$	0.844506	−	0.259040i	0.844506	−	0.259040i	0.685350	+	0.728214i	$0.259649\pi$
$318$		0			0
$319$	0.583164	−	1.21831i	0.583164	−	1.21831i
$320$		0			0
$321$		0			0
$322$	−0.866660	+	3.13066i	−0.866660	+	3.13066i
$323$		0			0
$324$	2.07240	−	1.15124i	2.07240	−	1.15124i
$325$		0			0
$326$	−3.39289	−	1.12313i	−3.39289	−	1.12313i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.79124	+	0.797513i	1.79124	+	0.797513i	0.975796	+	0.218681i	$0.0701754\pi$
$331$	1.79124	+	0.797513i	1.79124	+	0.797513i	0.815447	+	0.578832i	$0.196491\pi$
$332$		0			0
$333$	0.254314	+	0.152489i	0.254314	+	0.152489i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.48654	+	0.783413i	1.48654	+	0.783413i	0.996114	−	0.0880708i	$-0.0280702\pi$
$337$	1.48654	+	0.783413i	1.48654	+	0.783413i	0.490424	+	0.871484i	$0.336842\pi$
$338$	0.662665	+	1.71218i	0.662665	+	1.71218i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.213300	−	0.976987i	−0.213300	−	0.976987i
$344$	0.0989135	+	0.167043i	0.0989135	+	0.167043i
$345$		0			0
$346$		0			0
$347$	−0.530415	−	1.24640i	−0.530415	−	1.24640i	−0.942181	−	0.335105i	$-0.891228\pi$
$347$	−0.530415	−	1.24640i	−0.530415	−	1.24640i	0.411766	−	0.911290i	$-0.364912\pi$
$348$		0			0
$349$		0			0		−0.968033	−	0.250825i	$-0.919298\pi$
$349$		0			0		0.968033	+	0.250825i	$0.0807018\pi$
$350$	−1.00417	+	1.53699i	−1.00417	+	1.53699i
$351$		0			0
$352$	−0.00837856	+	1.52016i	−0.00837856	+	1.52016i
$353$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$353$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−2.30381	−	2.61606i	−2.30381	−	2.61606i
$359$	1.23440	−	1.56805i	1.23440	−	1.56805i	0.565270	−	0.824906i	$-0.308772\pi$
$359$	1.23440	−	1.56805i	1.23440	−	1.56805i	0.669131	−	0.743145i	$-0.266667\pi$
$360$		0			0
$361$	−0.795863	−	0.605477i	−0.795863	−	0.605477i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.644194	−	0.764862i	$-0.722807\pi$
$367$		0			0		0.644194	+	0.764862i	$0.277193\pi$
$368$	−0.153520	+	3.97719i	−0.153520	+	3.97719i
$369$		0			0
$370$		0			0
$371$	−0.560903	+	0.781034i	−0.560903	+	0.781034i
$372$		0			0
$373$	0.208879	−	0.0985722i	0.208879	−	0.0985722i	−0.319482	−	0.947592i	$-0.603509\pi$
$373$	0.208879	−	0.0985722i	0.208879	−	0.0985722i	0.528360	+	0.849020i	$0.322807\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.140957	+	1.96392i	0.140957	+	1.96392i	0.245485	+	0.969400i	$0.421053\pi$
$379$	0.140957	+	1.96392i	0.140957	+	1.96392i	−0.104528	+	0.994522i	$0.533333\pi$
$380$		0			0
$381$		0			0
$382$	1.21654	−	0.766408i	1.21654	−	0.766408i
$383$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$383$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$384$		0			0
$385$		0			0
$386$	−1.14992	+	2.33586i	−1.14992	+	2.33586i
$387$	−0.0238384	+	0.0733671i	−0.0238384	+	0.0733671i
$388$		0			0
$389$	0.444197	−	0.0591024i	0.444197	−	0.0591024i	0.0935596	−	0.995614i	$-0.470175\pi$
$389$	0.444197	−	0.0591024i	0.444197	−	0.0591024i	0.350638	+	0.936511i	$0.385965\pi$
$390$		0			0
$391$		0			0
$392$	−1.08652	−	2.26989i	−1.08652	−	2.26989i
$393$		0			0
$394$	−0.488424	−	0.388877i	−0.488424	−	0.388877i
$395$		0			0
$396$	−1.68440	+	1.46695i	−1.68440	+	1.46695i
$397$		0			0		0.360939	−	0.932589i	$-0.382456\pi$
$397$		0			0		−0.360939	+	0.932589i	$0.617544\pi$
$398$		0			0
$399$		0			0
$400$	−0.765496	+	2.11527i	−0.765496	+	2.11527i
$401$	−0.0484666	+	0.0262288i	−0.0484666	+	0.0262288i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.0484666	+	0.0262288i	−0.0484666	+	0.0262288i	0.451533	+	0.892254i	$0.350877\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.617942	+	2.55838i	0.617942	+	2.55838i
$407$	−0.264246	−	0.0907158i	−0.264246	−	0.0907158i
$408$		0			0
$409$		0			0		0.973327	−	0.229424i	$-0.0736842\pi$
$409$		0			0		−0.973327	+	0.229424i	$0.926316\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−2.51884	+	2.05123i	−2.51884	+	2.05123i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.480787	−	0.876837i	$-0.659649\pi$
$419$		0			0		0.480787	+	0.876837i	$0.340351\pi$
$420$		0			0
$421$	−1.08088	+	0.439016i	−1.08088	+	0.439016i	−0.846095	−	0.533032i	$-0.821053\pi$
$421$	−1.08088	+	0.439016i	−1.08088	+	0.439016i	−0.234785	+	0.972047i	$0.575439\pi$
$422$	−2.03556	−	0.933308i	−2.03556	−	0.933308i
$423$		0			0
$424$	−0.922949	+	2.23691i	−0.922949	+	2.23691i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−4.03708	−	2.48159i	−4.03708	−	2.48159i
$429$		0			0
$430$		0			0
$431$	−1.52418	−	0.580262i	−1.52418	−	0.580262i	−0.556143	−	0.831087i	$-0.687719\pi$
$431$	−1.52418	−	0.580262i	−1.52418	−	0.580262i	−0.968033	+	0.250825i	$0.919298\pi$
$432$		0			0
$433$		0			0		0.768401	−	0.639969i	$-0.221053\pi$
$433$		0			0		−0.768401	+	0.639969i	$0.778947\pi$
$434$		0			0
$435$		0			0
$436$	−0.110539	−	4.01015i	−0.110539	−	4.01015i
$437$		0			0
$438$		0			0
$439$		0			0		0.746821	−	0.665025i	$-0.231579\pi$
$439$		0			0		−0.746821	+	0.665025i	$0.768421\pi$
$440$		0			0
$441$	0.391577	−	0.920146i	0.391577	−	0.920146i
$442$		0			0
$443$	0.0963226	+	0.257266i	0.0963226	+	0.257266i	0.975796	−	0.218681i	$-0.0701754\pi$
$443$	0.0963226	+	0.257266i	0.0963226	+	0.257266i	−0.879474	+	0.475947i	$0.842105\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.447000	−	0.555120i	−0.447000	−	0.555120i
$449$	1.28912	−	1.22671i	1.28912	−	1.22671i	0.329907	−	0.944013i	$-0.392982\pi$
$449$	1.28912	−	1.22671i	1.28912	−	1.22671i	0.959210	−	0.282694i	$-0.0912281\pi$
$450$	−1.70851	+	0.672092i	−1.70851	+	0.672092i
$451$		0			0
$452$	0.517180	+	0.549525i	0.517180	+	0.549525i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0559054	−	0.920987i	0.0559054	−	0.920987i	−0.857640	−	0.514250i	$-0.828070\pi$
$457$	0.0559054	−	0.920987i	0.0559054	−	0.920987i	0.913545	−	0.406737i	$-0.133333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	−0.609245	+	0.347285i	−0.609245	+	0.347285i	−0.768401	−	0.639969i	$-0.778947\pi$
$463$	−0.609245	+	0.347285i	−0.609245	+	0.347285i	0.159156	+	0.987253i	$0.449123\pi$
$464$	1.45612	+	2.87737i	1.45612	+	2.87737i
$465$		0			0
$466$	1.26760	+	1.68539i	1.26760	+	1.68539i
$467$		0			0		0.996114	−	0.0880708i	$-0.0280702\pi$
$467$		0			0		−0.996114	+	0.0880708i	$0.971930\pi$
$468$		0			0
$469$	−0.792458	−	1.75381i	−0.792458	−	1.75381i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.00759743	−	0.0722847i	0.00759743	−	0.0722847i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.909474	+	0.312223i	−0.909474	+	0.312223i
$478$	1.96235	+	3.07715i	1.96235	+	3.07715i
$479$		0			0		0.556143	−	0.831087i	$-0.312281\pi$
$479$		0			0		−0.556143	+	0.831087i	$0.687719\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.160006	+	0.212741i	−0.160006	+	0.212741i
$485$		0			0
$486$		0			0
$487$	0.766812	−	1.64838i	0.766812	−	1.64838i	0.00551154	−	0.999985i	$-0.498246\pi$
$487$	0.766812	−	1.64838i	0.766812	−	1.64838i	0.761300	−	0.648400i	$-0.224561\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.28743	−	0.556280i	−1.28743	−	0.556280i	−0.360939	−	0.932589i	$-0.617544\pi$
$491$	−1.28743	−	0.556280i	−1.28743	−	0.556280i	−0.926494	+	0.376309i	$0.877193\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.79060	+	0.442955i	1.79060	+	0.442955i
$498$		0			0
$499$	−1.34610	+	1.39906i	−1.34610	+	1.39906i	−0.500000	+	0.866025i	$0.666667\pi$
$499$	−1.34610	+	1.39906i	−1.34610	+	1.39906i	−0.846095	+	0.533032i	$0.821053\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.652586	−	0.757715i	$-0.726316\pi$
$503$		0			0		0.652586	+	0.757715i	$0.273684\pi$
$504$	0.427882	−	2.47989i	0.427882	−	2.47989i
$505$		0			0
$506$	1.91953	−	2.38383i	1.91953	−	2.38383i
$507$		0			0
$508$	2.39445	−	1.54561i	2.39445	−	1.54561i
$509$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$509$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$510$		0			0
$511$		0			0
$512$	1.60311	+	1.24775i	1.60311	+	1.24775i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.510889	−	0.188077i	0.510889	−	0.188077i
$519$		0			0
$520$		0			0
$521$		0			0		0.922290	−	0.386499i	$-0.126316\pi$
$521$		0			0		−0.922290	+	0.386499i	$0.873684\pi$
$522$	−0.976972	+	2.44391i	−0.976972	+	2.44391i
$523$		0			0		0.461341	−	0.887223i	$-0.347368\pi$
$523$		0			0		−0.461341	+	0.887223i	$0.652632\pi$
$524$		0			0
$525$		0			0
$526$	0.105772	+	2.74021i	0.105772	+	2.74021i
$527$		0			0
$528$		0			0
$529$	1.39036	−	1.61434i	1.39036	−	1.61434i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.95362	−	3.83827i	−2.95362	−	3.83827i
$537$		0			0
$538$		0			0
$539$	−0.180627	+	0.924710i	−0.180627	+	0.924710i
$540$		0			0
$541$	0.122496	+	0.363327i	0.122496	+	0.363327i	0.991264	−	0.131892i	$-0.0421053\pi$
$541$	0.122496	+	0.363327i	0.122496	+	0.363327i	−0.868768	+	0.495219i	$0.835088\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.10892	+	1.17827i	−1.10892	+	1.17827i	−0.126427	+	0.991976i	$0.540351\pi$
$547$	−1.10892	+	1.17827i	−1.10892	+	1.17827i	−0.982493	+	0.186298i	$0.940351\pi$
$548$	2.77645	−	1.27301i	2.77645	−	1.27301i
$549$		0			0
$550$	1.44290	−	0.954080i	1.44290	−	0.954080i
$551$		0			0
$552$		0			0
$553$	−0.986456	+	0.255598i	−0.986456	+	0.255598i
$554$	−0.286605	−	1.77783i	−0.286605	−	1.77783i
$555$		0			0
$556$		0			0
$557$	−0.796936	+	0.946215i	−0.796936	+	0.946215i	−0.999453	−	0.0330634i	$-0.989474\pi$
$557$	−0.796936	+	0.946215i	−0.796936	+	0.946215i	0.202517	+	0.979279i	$0.435088\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−2.79473	−	0.0616234i	−2.79473	−	0.0616234i
$563$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$563$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.851919	−	0.523673i	0.851919	−	0.523673i
$568$	4.64166	+	0.0511677i	4.64166	+	0.0511677i
$569$	−1.40872	+	0.398349i	−1.40872	+	0.398349i	−0.889752	−	0.456444i	$-0.849123\pi$
$569$	−1.40872	+	0.398349i	−1.40872	+	0.398349i	−0.518970	+	0.854793i	$0.673684\pi$
$570$		0			0
$571$	0.451533	−	0.892254i	0.451533	−	0.892254i
$571$	0.451533	−	0.892254i	0.451533	−	0.892254i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.50733	−	0.926552i	1.50733	−	0.926552i
$576$	−0.0431837	−	0.711409i	−0.0431837	−	0.711409i
$577$		0			0		0.965209	−	0.261480i	$-0.0842105\pi$
$577$		0			0		−0.965209	+	0.261480i	$0.915789\pi$
$578$	−1.52018	+	1.02944i	−1.52018	+	1.02944i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.777007	−	0.465902i	0.777007	−	0.465902i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$587$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.556408	−	0.367911i	0.556408	−	0.367911i
$593$		0			0		0.894729	−	0.446609i	$-0.147368\pi$
$593$		0			0		−0.894729	+	0.446609i	$0.852632\pi$
$594$		0			0
$595$		0			0
$596$	4.69944	−	0.572637i	4.69944	−	0.572637i
$597$		0			0
$598$		0			0
$599$	0.271689	−	0.601283i	0.271689	−	0.601283i	−0.724425	−	0.689353i	$-0.757895\pi$
$599$	0.271689	−	0.601283i	0.271689	−	0.601283i	0.996114	+	0.0880708i	$0.0280702\pi$
$600$		0			0
$601$		0			0		−0.319482	−	0.947592i	$-0.603509\pi$
$601$		0			0		0.319482	+	0.947592i	$0.396491\pi$
$602$	0.0774643	+	0.118568i	0.0774643	+	0.118568i
$603$	0.368954	−	1.88884i	0.368954	−	1.88884i
$604$	−0.487923	+	0.0869586i	−0.487923	+	0.0869586i
$605$		0			0
$606$		0			0
$607$		0			0		0.863256	−	0.504766i	$-0.168421\pi$
$607$		0			0		−0.863256	+	0.504766i	$0.831579\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.29377	−	1.50219i	1.29377	−	1.50219i	0.546948	−	0.837166i	$-0.315789\pi$
$613$	1.29377	−	1.50219i	1.29377	−	1.50219i	0.746821	−	0.665025i	$-0.231579\pi$
$614$		0			0
$615$		0			0
$616$	0.0914544	+	2.36928i	0.0914544	+	2.36928i
$617$	−1.51142	+	1.28728i	−1.51142	+	1.28728i	−0.677282	+	0.735724i	$0.736842\pi$
$617$	−1.51142	+	1.28728i	−1.51142	+	1.28728i	−0.834139	+	0.551554i	$0.814035\pi$
$618$		0			0
$619$		0			0		0.461341	−	0.887223i	$-0.347368\pi$
$619$		0			0		−0.461341	+	0.887223i	$0.652632\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.970739	−	0.240139i	0.970739	−	0.240139i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.0809343	+	0.118108i	0.0809343	+	0.118108i	0.863256	−	0.504766i	$-0.168421\pi$
$631$	0.0809343	+	0.118108i	0.0809343	+	0.118108i	−0.782322	+	0.622874i	$0.785965\pi$
$632$	−2.26866	+	1.19560i	−2.26866	+	1.19560i
$633$		0			0
$634$	1.36256	−	0.879526i	1.36256	−	0.879526i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.421634	−	2.44368i	0.421634	−	2.44368i
$639$	1.20375	+	1.39767i	1.20375	+	1.39767i
$640$		0			0
$641$	1.56613	+	1.16445i	1.56613	+	1.16445i	0.913545	+	0.406737i	$0.133333\pi$
$641$	1.56613	+	1.16445i	1.56613	+	1.16445i	0.652586	+	0.757715i	$0.273684\pi$
$642$		0			0
$643$		0			0		0.693336	−	0.720615i	$-0.256140\pi$
$643$		0			0		−0.693336	+	0.720615i	$0.743860\pi$
$644$	0.0231185	+	4.19450i	0.0231185	+	4.19450i
$645$		0			0
$646$		0			0
$647$		0			0		−0.224056	−	0.974576i	$-0.571930\pi$
$647$		0			0		0.224056	+	0.974576i	$0.428070\pi$
$648$	1.78435	−	1.77455i	1.78435	−	1.77455i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−4.61045	−	0.203418i	−4.61045	−	0.203418i
$653$	−1.43675	−	0.996223i	−1.43675	−	0.996223i	−0.995083	−	0.0990455i	$-0.968421\pi$
$653$	−1.43675	−	0.996223i	−1.43675	−	0.996223i	−0.441671	−	0.897177i	$-0.645614\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.02580	−	1.64835i	1.02580	−	1.64835i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	1.02580	−	1.64835i	1.02580	−	1.64835i	0.716783	−	0.697297i	$-0.245614\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$	3.56295	+	0.514097i	3.56295	+	0.514097i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.525468	+	0.142352i	0.525468	+	0.142352i
$667$	0.513676	−	2.48390i	0.513676	−	2.48390i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.744766	+	1.64826i	0.744766	+	1.64826i	0.761300	+	0.648400i	$0.224561\pi$
$673$	0.744766	+	1.64826i	0.744766	+	1.64826i	−0.0165339	+	0.999863i	$0.505263\pi$
$674$	3.01759	+	0.641409i	3.01759	+	0.641409i
$675$		0			0
$676$	1.42498	+	1.89464i	1.42498	+	1.89464i
$677$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$677$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.0754805	+	0.592239i	0.0754805	+	0.592239i	0.984487	+	0.175457i	$0.0561404\pi$
$683$	0.0754805	+	0.592239i	0.0754805	+	0.592239i	−0.909007	+	0.416782i	$0.863158\pi$
$684$		0			0
$685$		0			0
$686$	−0.864902	−	1.61946i	−0.864902	−	1.61946i
$687$		0			0
$688$	0.125713	+	0.119626i	0.125713	+	0.119626i
$689$		0			0
$690$		0			0
$691$		0			0		−0.768401	−	0.639969i	$-0.778947\pi$
$691$		0			0		0.768401	+	0.639969i	$0.221053\pi$
$692$		0			0
$693$	−0.682543	+	0.649499i	−0.682543	+	0.649499i
$694$	−1.55973	−	1.93699i	−1.55973	−	1.93699i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.707689	+	2.26261i	−0.707689	+	2.26261i
$701$	0.573252	−	1.34706i	0.573252	−	1.34706i	−0.340293	−	0.940319i	$-0.610526\pi$
$701$	0.573252	−	1.34706i	0.573252	−	1.34706i	0.913545	−	0.406737i	$-0.133333\pi$
$702$		0			0
$703$		0			0
$704$	0.179157	+	0.647173i	0.179157	+	0.647173i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.31802	−	1.09773i	1.31802	−	1.09773i	0.329907	−	0.944013i	$-0.392982\pi$
$709$	1.31802	−	1.09773i	1.31802	−	1.09773i	0.988116	−	0.153712i	$-0.0491228\pi$
$710$		0			0
$711$	−0.952351	−	0.362565i	−0.952351	−	0.362565i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−3.78176	−	2.44111i	−3.78176	−	2.44111i
$717$		0			0
$718$	1.39744	−	3.38690i	1.39744	−	3.38690i
$719$		0			0		0.999453	−	0.0330634i	$-0.0105263\pi$
$719$		0			0		−0.999453	+	0.0330634i	$0.989474\pi$
$720$		0			0
$721$		0			0
$722$	−1.70851	−	0.672092i	−1.70851	−	0.672092i
$723$		0			0
$724$		0			0
$725$	0.703054	−	1.24933i	0.703054	−	1.24933i
$726$		0			0
$727$		0			0		−0.980380	−	0.197117i	$-0.936842\pi$
$727$		0			0		0.980380	+	0.197117i	$0.0631579\pi$
$728$		0			0
$729$	0.997814	+	0.0660906i	0.997814	+	0.0660906i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.973327	−	0.229424i	$-0.0736842\pi$
$733$		0			0		−0.973327	+	0.229424i	$0.926316\pi$
$734$		0			0
$735$		0			0
$736$	0.670255	+	2.77496i	0.670255	+	2.77496i
$737$	0.0299805	+	1.81302i	0.0299805	+	1.81302i
$738$		0			0
$739$	−0.188515	+	1.16937i	−0.188515	+	1.16937i	0.701237	+	0.712928i	$0.252632\pi$
$739$	−0.188515	+	1.16937i	−0.188515	+	1.16937i	−0.889752	+	0.456444i	$0.849123\pi$
$740$		0			0
$741$		0			0
$742$	−0.600754	+	1.66004i	−0.600754	+	1.66004i
$743$	−0.0926673	−	0.349691i	−0.0926673	−	0.349691i	0.904357	−	0.426776i	$-0.140351\pi$
$743$	−0.0926673	−	0.349691i	−0.0926673	−	0.349691i	−0.997024	+	0.0770854i	$0.975439\pi$
$744$		0			0
$745$		0			0
$746$	0.319777	−	0.278494i	0.319777	−	0.278494i
$747$		0			0
$748$		0			0
$749$	−1.74739	−	0.970695i	−1.74739	−	0.970695i
$750$		0			0
$751$	0.446800	+	0.667687i	0.446800	+	0.667687i	0.984487	−	0.175457i	$-0.0561404\pi$
$751$	0.446800	+	0.667687i	0.446800	+	0.667687i	−0.537687	+	0.843145i	$0.680702\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.318593	−	0.283699i	−0.318593	−	0.283699i	0.490424	−	0.871484i	$-0.336842\pi$
$757$	−0.318593	−	0.283699i	−0.318593	−	0.283699i	−0.809017	+	0.587785i	$0.800000\pi$
$758$	1.23014	+	3.39919i	1.23014	+	3.39919i
$759$		0			0
$760$		0			0
$761$		0			0		0.999939	−	0.0110229i	$-0.00350877\pi$
$761$		0			0		−0.999939	+	0.0110229i	$0.996491\pi$
$762$		0			0
$763$	−0.121142	−	1.68785i	−0.121142	−	1.68785i
$764$	1.24232	−	1.37974i	1.24232	−	1.37974i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$769$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$770$		0			0
$771$		0			0
$772$	−0.608103	+	3.30645i	−0.608103	+	3.30645i
$773$		0			0		−0.618553	−	0.785743i	$-0.712281\pi$
$773$		0			0		0.618553	+	0.785743i	$0.287719\pi$
$774$	−0.00546287	+	0.141525i	−0.00546287	+	0.141525i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.755225	−	0.326321i	0.755225	−	0.326321i
$779$		0			0
$780$		0			0
$781$	−1.38316	−	1.05228i	−1.38316	−	1.05228i
$782$		0			0
$783$		0			0
$784$	−1.48670	−	1.68821i	−1.48670	−	1.68821i
$785$		0			0
$786$		0			0
$787$		0			0		0.701237	−	0.712928i	$-0.252632\pi$
$787$		0			0		−0.701237	+	0.712928i	$0.747368\pi$
$788$	−0.743525	−	0.311585i	−0.743525	−	0.311585i
$789$		0			0
$790$		0			0
$791$	0.228160	+	0.221958i	0.228160	+	0.221958i
$792$	−1.29684	+	1.98496i	−1.29684	+	1.98496i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.461341	−	0.887223i	$-0.652632\pi$
$797$		0			0		0.461341	+	0.887223i	$0.347368\pi$
$798$		0			0
$799$		0			0
$800$	−0.115507	+	1.60933i	−0.115507	+	1.60933i
$801$		0			0
$802$	−0.0725216	+	0.0705501i	−0.0725216	+	0.0705501i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.493960	−	0.296184i	−0.493960	−	0.296184i	0.245485	−	0.969400i	$-0.421053\pi$
$809$	−0.493960	−	0.296184i	−0.493960	−	0.296184i	−0.739446	+	0.673216i	$0.764912\pi$
$810$		0			0
$811$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$811$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$812$	1.66673	+	2.96179i	1.66673	+	2.96179i
$813$		0			0
$814$	−0.512155	−	0.0282564i	−0.512155	−	0.0282564i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.785955	+	1.59653i	0.785955	+	1.59653i	0.802489	+	0.596667i	$0.203509\pi$
$821$	0.785955	+	1.59653i	0.785955	+	1.59653i	−0.0165339	+	0.999863i	$0.505263\pi$
$822$		0			0
$823$	0.704146	−	1.47105i	0.704146	−	1.47105i	−0.170028	−	0.985439i	$-0.554386\pi$
$823$	0.704146	−	1.47105i	0.704146	−	1.47105i	0.874174	−	0.485613i	$-0.161404\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.11154	−	1.51231i	−1.11154	−	1.51231i	−0.834139	−	0.551554i	$-0.814035\pi$
$827$	−1.11154	−	1.51231i	−1.11154	−	1.51231i	−0.277403	−	0.960754i	$-0.589474\pi$
$828$	−2.40906	+	3.43377i	−2.40906	+	3.43377i
$829$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$829$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.371197	−	0.928554i	$-0.621053\pi$
$839$		0			0		0.371197	+	0.928554i	$0.378947\pi$
$840$		0			0
$841$	−0.314966	−	1.00700i	−0.314966	−	1.00700i
$842$	−1.69024	+	1.31557i	−1.69024	+	1.31557i
$843$		0			0
$844$	−2.85720	−	0.444468i	−2.85720	−	0.444468i
$845$		0			0
$846$		0			0
$847$	−0.0634719	+	0.0926253i	−0.0634719	+	0.0926253i
$848$	−0.249803	+	2.14861i	−0.249803	+	2.14861i
$849$		0			0
$850$		0			0
$851$	−0.522617	−	0.0462068i	−0.522617	−	0.0462068i
$852$		0			0
$853$		0			0		0.949339	−	0.314254i	$-0.101754\pi$
$853$		0			0		−0.949339	+	0.314254i	$0.898246\pi$
$854$		0			0
$855$		0			0
$856$	−4.84051	−	1.36877i	−4.84051	−	1.36877i
$857$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$857$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$858$		0			0
$859$		0			0		0.213300	−	0.976987i	$-0.431579\pi$
$859$		0			0		−0.213300	+	0.976987i	$0.568421\pi$
$860$		0			0
$861$		0			0
$862$	−2.98260	−	0.263705i	−2.98260	−	0.263705i
$863$	−0.995622	−	1.59986i	−0.995622	−	1.59986i	−0.782322	−	0.622874i	$-0.785965\pi$
$863$	−0.995622	−	1.59986i	−0.995622	−	1.59986i	−0.213300	−	0.976987i	$-0.568421\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.948707	+	0.147582i	0.948707	+	0.147582i
$870$		0			0
$871$		0			0
$872$	−1.27121	−	4.06429i	−1.27121	−	4.06429i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.706561	+	1.61080i	0.706561	+	1.61080i	0.789141	+	0.614213i	$0.210526\pi$
$877$	0.706561	+	1.61080i	0.706561	+	1.61080i	−0.0825793	+	0.996584i	$0.526316\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.609854	−	0.792514i	$-0.291228\pi$
$881$		0			0		−0.609854	+	0.792514i	$0.708772\pi$
$882$	0.232113	−	1.82122i	0.232113	−	1.82122i
$883$	−1.82165	+	0.140842i	−1.82165	+	0.140842i	−0.942181	−	0.335105i	$-0.891228\pi$
$883$	−1.82165	+	0.140842i	−1.82165	+	0.140842i	−0.879474	+	0.475947i	$0.842105\pi$
$884$		0			0
$885$		0			0
$886$	0.298692	+	0.406386i	0.298692	+	0.406386i
$887$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$887$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$888$		0			0
$889$	0.980300	−	0.695850i	0.980300	−	0.695850i
$890$		0			0
$891$	−0.932528	+	0.134554i	−0.932528	+	0.134554i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.248674	+	0.176517i	0.248674	+	0.176517i
$897$		0			0
$898$	1.66463	−	2.81119i	1.66463	−	2.81119i
$899$		0			0
$900$	−1.88675	+	1.43540i	−1.88675	+	1.43540i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.687005	+	0.411936i	0.687005	+	0.411936i
$905$		0			0
$906$		0			0
$907$	0.146833	+	1.26294i	0.146833	+	1.26294i	0.840168	+	0.542326i	$0.182456\pi$
$907$	0.146833	+	1.26294i	0.146833	+	1.26294i	−0.693336	+	0.720615i	$0.743860\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.43043	−	1.39154i	1.43043	−	1.39154i	0.669131	−	0.743145i	$-0.266667\pi$
$911$	1.43043	−	1.39154i	1.43043	−	1.39154i	0.761300	−	0.648400i	$-0.224561\pi$
$912$		0			0
$913$		0			0
$914$	−0.361329	−	1.65501i	−0.361329	−	1.65501i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.186199	+	1.98144i	−0.186199	+	1.98144i	0.00551154	+	0.999985i	$0.498246\pi$
$919$	−0.186199	+	1.98144i	−0.186199	+	1.98144i	−0.191711	+	0.981451i	$0.561404\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.273484	−	0.114608i	−0.273484	−	0.114608i
$926$	−0.902845	+	0.917898i	−0.902845	+	0.917898i
$927$		0			0
$928$	1.56656	+	1.70174i	1.56656	+	1.70174i
$929$		0			0		−0.660898	−	0.750475i	$-0.729825\pi$
$929$		0			0		0.660898	+	0.750475i	$0.270175\pi$
$930$		0			0
$931$		0			0
$932$	2.16723	+	1.64879i	2.16723	+	1.64879i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.731980	−	0.681326i	$-0.238596\pi$
$937$		0			0		−0.731980	+	0.681326i	$0.761404\pi$
$938$	−2.27616	−	2.70252i	−2.27616	−	2.70252i
$939$		0			0
$940$		0			0
$941$		0			0		0.180881	−	0.983505i	$-0.442105\pi$
$941$		0			0		−0.180881	+	0.983505i	$0.557895\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.0226889	−	0.131499i	−0.0226889	−	0.131499i
$947$	−1.06056	+	1.28777i	−1.06056	+	1.28777i	−0.104528	+	0.994522i	$0.533333\pi$
$947$	−1.06056	+	1.28777i	−1.06056	+	1.28777i	−0.956036	+	0.293250i	$0.905263\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.27609	−	0.803925i	1.27609	−	0.803925i	0.287976	−	0.957638i	$-0.407018\pi$
$953$	1.27609	−	0.803925i	1.27609	−	0.803925i	0.988116	+	0.153712i	$0.0491228\pi$
$954$	−1.45077	+	1.00594i	−1.45077	+	1.00594i
$955$		0			0
$956$	3.51949	+	3.13401i	3.51949	+	3.13401i
$957$		0			0
$958$		0			0
$959$	1.14635	−	0.588077i	1.14635	−	0.588077i
$960$		0			0
$961$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$962$		0			0
$963$	−0.863037	−	1.80300i	−0.863037	−	1.80300i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.47526	−	1.28480i	1.47526	−	1.28480i	0.601081	−	0.799188i	$-0.294737\pi$
$967$	1.47526	−	1.28480i	1.47526	−	1.28480i	0.874174	−	0.485613i	$-0.161404\pi$
$968$	−0.101991	+	0.263523i	−0.101991	+	0.263523i
$969$		0			0
$970$		0			0
$971$		0			0		0.340293	−	0.940319i	$-0.389474\pi$
$971$		0			0		−0.340293	+	0.940319i	$0.610526\pi$
$972$		0			0
$973$		0			0
$974$	0.531226	−	3.29523i	0.531226	−	3.29523i
$975$		0			0
$976$		0			0
$977$	−0.174303	−	0.721643i	−0.174303	−	0.721643i	−0.989750	−	0.142811i	$-0.954386\pi$
$977$	−0.174303	−	0.721643i	−0.174303	−	0.721643i	0.815447	−	0.578832i	$-0.196491\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.878195	−	1.44647i	0.878195	−	1.44647i
$982$	−2.55237	−	0.339605i	−2.55237	−	0.339605i
$983$		0			0		0.942181	−	0.335105i	$-0.108772\pi$
$983$		0			0		−0.942181	+	0.335105i	$0.891228\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.0187476	−	0.135198i	−0.0187476	−	0.135198i
$990$		0			0
$991$	−1.72436	−	0.678331i	−1.72436	−	0.678331i	−0.724425	−	0.689353i	$-0.757895\pi$
$991$	−1.72436	−	0.678331i	−1.72436	−	0.678331i	−0.999939	+	0.0110229i	$0.996491\pi$
$992$		0			0
$993$		0			0
$994$	3.38470	−	0.111971i	3.38470	−	0.111971i
$995$		0			0
$996$		0			0
$997$		0			0		−0.840168	−	0.542326i	$-0.817544\pi$
$997$		0			0		0.840168	+	0.542326i	$0.182456\pi$
$998$	−1.67919	+	3.14414i	−1.67919	+	3.14414i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.580.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.580.1	✓	144
571.127	even	285	inner	3997.1.cz.a.1840.1	yes	144
3997.1840	odd	570	inner	3997.1.cz.a.1840.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.580.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.580.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.1840.1	yes	144	571.127	even	285	inner
3997.1.cz.a.1840.1	yes	144	3997.1840	odd	570	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:	\( N \)	\(=\)	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3997.cz (of order \(570\), degree \(144\), minimal)

\(f(q)\)	\(=\)	\(q+(1.76667 - 0.499567i) q^{2} +(2.01965 - 1.24147i) q^{4} +(0.828009 - 0.560715i) q^{7} +(1.70440 - 1.85147i) q^{8} +(0.999757 + 0.0220445i) q^{9} +O(q^{10})\)	\(q+(1.76667 - 0.499567i) q^{2} +(2.01965 - 1.24147i) q^{4} +(0.828009 - 0.560715i) q^{7} +(1.70440 - 1.85147i) q^{8} +(0.999757 + 0.0220445i) q^{9} +(-0.925691 + 0.175528i) q^{11} +(1.18271 - 1.40425i) q^{14} +(1.01573 - 2.00714i) q^{16} +(1.77726 - 0.460501i) q^{18} +(-1.54771 + 0.772545i) q^{22} +(-1.60834 + 0.737426i) q^{23} +(-0.992658 + 0.120958i) q^{25} +(0.976173 - 2.16040i) q^{28} +(-0.849008 + 1.15512i) q^{29} +(0.309319 - 1.58354i) q^{32} +(2.04652 - 1.19665i) q^{36} +(0.257613 + 0.146846i) q^{37} +(-0.0222153 + 0.0738748i) q^{43} +(-1.65166 + 1.50372i) q^{44} +(-2.47301 + 2.10626i) q^{46} +(0.371197 - 0.928554i) q^{49} +(-1.69327 + 0.709592i) q^{50} +(-0.902370 + 0.332196i) q^{53} +(0.373110 - 2.48872i) q^{56} +(-0.922860 + 2.46485i) q^{58} +(0.840168 - 0.542326i) q^{63} +(-0.0588558 - 0.710284i) q^{64} +(0.327226 - 1.89651i) q^{67} +(1.23426 + 1.37079i) q^{71} +(1.74480 - 1.81345i) q^{72} +(0.528478 + 0.130734i) q^{74} +(-0.668059 + 0.664387i) q^{77} +(-0.960112 - 0.341483i) q^{79} +(0.999028 + 0.0440782i) q^{81} +(-0.00234170 + 0.141611i) q^{86} +(-1.25276 + 2.01306i) q^{88} +(-2.33277 + 3.48604i) q^{92} +(0.191909 - 1.82589i) q^{98} +(-0.929336 + 0.155079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9 + 6 * q^11 + q^14 + 6 * q^16 - 9 * q^18 + 21 * q^22 + 3 * q^23 - q^25 - 10 * q^28 - 4 * q^29 - 5 * q^32 - 2 * q^37 - 9 * q^43 - 20 * q^44 - 34 * q^46 + 2 * q^49 - 2 * q^50 + 6 * q^53 - 8 * q^56 - q^58 - q^63 + 11 * q^64 + 20 * q^67 + 3 * q^71 + 23 * q^72 - 31 * q^74 + q^77 + 6 * q^79 - q^81 + 7 * q^86 - 9 * q^88 + 9 * q^92 + 6 * q^98 - 2 * q^99

Introduction

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