LMFDB - Embedded newform 2013.1.bm.d.731.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,1,Mod(548,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6, 5]))

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

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

chi := DirichletCharacter("2013.548");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2013.bm (of order $10$, degree $4$, 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:	$1.00461787043$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{20}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{20} - \cdots)$

Embedding invariants

Embedding label			731.1
Root			$0.987688 - 0.156434i$ of defining polynomial
Character	$\chi$	$=$	2013.731
Dual form			2013.1.bm.d.548.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550672 - 1.69480i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.76007 + 1.27877i) q^{4} +(0.550672 - 1.69480i) q^{6} +(1.69480 + 1.23134i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.550672 - 1.69480i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.76007 + 1.27877i) q^{4} +(0.550672 - 1.69480i) q^{6} +(1.69480 + 1.23134i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.987688 - 0.156434i) q^{11} -2.17557 q^{12} +(0.587785 + 1.80902i) q^{13} +(0.481305 - 1.48131i) q^{16} +(-0.610425 + 1.87869i) q^{17} +(1.44168 - 1.04744i) q^{18} +(-0.951057 - 0.690983i) q^{19} +(0.278768 + 1.76007i) q^{22} +0.907981 q^{23} +(0.647354 + 1.99235i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(2.74224 - 1.99235i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.734572 + 0.533698i) q^{29} -0.680668 q^{32} +(-0.707107 - 0.707107i) q^{33} +3.52015 q^{34} +(-1.76007 - 1.27877i) q^{36} +(-0.647354 + 1.99235i) q^{38} +(-0.587785 + 1.80902i) q^{39} +(1.93845 - 0.987688i) q^{44} +(-0.500000 - 1.53884i) q^{46} +(1.26007 - 0.915497i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.550672 + 1.69480i) q^{50} +(-1.59811 + 1.16110i) q^{51} +(-3.34786 - 2.43236i) q^{52} +(0.550672 + 1.69480i) q^{53} +1.78201 q^{54} +(-0.363271 - 1.11803i) q^{57} +(1.30902 + 0.951057i) q^{58} +(-0.253116 + 0.183900i) q^{59} +(-0.309017 + 0.951057i) q^{61} +(-0.106480 - 0.327712i) q^{64} +(-0.809017 + 1.58779i) q^{66} +(-1.32802 - 4.08723i) q^{68} +(0.734572 + 0.533698i) q^{69} +(0.437016 - 1.34500i) q^{71} +(-0.647354 + 1.99235i) q^{72} +(0.500000 - 0.363271i) q^{73} +(-0.309017 - 0.951057i) q^{75} +2.55754 q^{76} +3.38959 q^{78} +(-0.809017 + 0.587785i) q^{81} -0.907981 q^{87} +(-1.48131 - 1.48131i) q^{88} +1.97538 q^{89} +(-1.59811 + 1.16110i) q^{92} +(-0.550672 - 0.400087i) q^{96} -1.78201 q^{98} +(-0.156434 - 0.987688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 4 * q^4 - 4 * q^9	$ 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9} - 16 q^{12} - 16 q^{16} + 4 q^{22} - 4 q^{25} + 4 q^{27} + 8 q^{34} - 4 q^{36} - 8 q^{46} - 4 q^{48} - 4 q^{49} - 20 q^{52} + 12 q^{58} + 4 q^{61} - 16 q^{64} - 4 q^{66} + 8 q^{73} + 4 q^{75} + 40 q^{76} - 4 q^{81}+O(q^{100}) $ 16 * q + 4 * q^3 - 4 * q^4 - 4 * q^9 - 16 * q^12 - 16 * q^16 + 4 * q^22 - 4 * q^25 + 4 * q^27 + 8 * q^34 - 4 * q^36 - 8 * q^46 - 4 * q^48 - 4 * q^49 - 20 * q^52 + 12 * q^58 + 4 * q^61 - 16 * q^64 - 4 * q^66 + 8 * q^73 + 4 * q^75 + 40 * q^76 - 4 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2013\mathbb{Z}\right)^\times$.

$n$	$1222$	$1343$	$1465$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.550672	−	1.69480i	−0.550672	−	1.69480i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−0.550672	−	1.69480i	−0.550672	−	1.69480i	0.156434	−	0.987688i	$-0.450000\pi$
$3$	0.809017	+	0.587785i	0.809017	+	0.587785i
$3$	0.809017	+	0.587785i	0.809017	+	0.587785i
$4$	−1.76007	+	1.27877i	−1.76007	+	1.27877i
$5$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$5$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$6$	0.550672	−	1.69480i	0.550672	−	1.69480i
$7$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$7$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$8$	1.69480	+	1.23134i	1.69480	+	1.23134i
$9$	0.309017	+	0.951057i	0.309017	+	0.951057i
$10$		0			0
$11$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$11$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$12$	−2.17557			−2.17557
$13$	0.587785	+	1.80902i	0.587785	+	1.80902i	0.587785	+	0.809017i	$0.300000\pi$
$13$	0.587785	+	1.80902i	0.587785	+	1.80902i			1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$	0.481305	−	1.48131i	0.481305	−	1.48131i
$17$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.156434	+	0.987688i	$0.550000\pi$
$17$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.453990	+	0.891007i	$0.650000\pi$
$18$	1.44168	−	1.04744i	1.44168	−	1.04744i
$19$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$19$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$20$		0			0
$21$		0			0
$22$	0.278768	+	1.76007i	0.278768	+	1.76007i
$23$	0.907981			0.907981			0.453990	−	0.891007i	$-0.350000\pi$
$23$	0.907981			0.907981			0.453990	+	0.891007i	$0.350000\pi$
$24$	0.647354	+	1.99235i	0.647354	+	1.99235i
$25$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$26$	2.74224	−	1.99235i	2.74224	−	1.99235i
$27$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$28$		0			0
$29$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	−0.891007	−	0.453990i	$-0.850000\pi$
$29$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	0.156434	+	0.987688i	$0.450000\pi$
$30$		0			0
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$	−0.680668			−0.680668
$33$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$34$	3.52015			3.52015
$35$		0			0
$36$	−1.76007	−	1.27877i	−1.76007	−	1.27877i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$	−0.647354	+	1.99235i	−0.647354	+	1.99235i
$39$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$40$		0			0
$41$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$41$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	1.93845	−	0.987688i	1.93845	−	0.987688i
$45$		0			0
$46$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$	1.26007	−	0.915497i	1.26007	−	0.915497i
$49$	0.309017	−	0.951057i	0.309017	−	0.951057i
$50$	−0.550672	+	1.69480i	−0.550672	+	1.69480i
$51$	−1.59811	+	1.16110i	−1.59811	+	1.16110i
$52$	−3.34786	−	2.43236i	−3.34786	−	2.43236i
$53$	0.550672	+	1.69480i	0.550672	+	1.69480i	0.707107	+	0.707107i	$0.250000\pi$
$53$	0.550672	+	1.69480i	0.550672	+	1.69480i	−0.156434	+	0.987688i	$0.550000\pi$
$54$	1.78201			1.78201
$55$		0			0
$56$		0			0
$57$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$58$	1.30902	+	0.951057i	1.30902	+	0.951057i
$59$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$59$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$60$		0			0
$61$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$61$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$62$		0			0
$63$		0			0
$64$	−0.106480	−	0.327712i	−0.106480	−	0.327712i
$65$		0			0
$66$	−0.809017	+	1.58779i	−0.809017	+	1.58779i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	−1.32802	−	4.08723i	−1.32802	−	4.08723i
$69$	0.734572	+	0.533698i	0.734572	+	0.533698i
$70$		0			0
$71$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$71$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$72$	−0.647354	+	1.99235i	−0.647354	+	1.99235i
$73$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$73$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$74$		0			0
$75$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$76$	2.55754			2.55754
$77$		0			0
$78$	3.38959			3.38959
$79$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$79$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$		0			0
$83$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$83$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.907981			−0.907981
$88$	−1.48131	−	1.48131i	−1.48131	−	1.48131i
$89$	1.97538			1.97538			0.987688	−	0.156434i	$-0.0500000\pi$
$89$	1.97538			1.97538			0.987688	+	0.156434i	$0.0500000\pi$
$90$		0			0
$91$		0			0
$92$	−1.59811	+	1.16110i	−1.59811	+	1.16110i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.550672	−	0.400087i	−0.550672	−	0.400087i
$97$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$97$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$98$	−1.78201			−1.78201
$99$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$100$	2.17557			2.17557
$101$	−0.437016	−	1.34500i	−0.437016	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$101$	−0.437016	−	1.34500i	−0.437016	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$102$	2.84786	+	2.06909i	2.84786	+	2.06909i
$103$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$103$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$104$	−1.23134	+	3.78968i	−1.23134	+	3.78968i
$105$		0			0
$106$	2.56909	−	1.86655i	2.56909	−	1.86655i
$107$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$107$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$108$	−0.672288	−	2.06909i	−0.672288	−	2.06909i
$109$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$109$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$	−1.69480	+	1.23134i	−1.69480	+	1.23134i
$115$		0			0
$116$	0.610425	−	1.87869i	0.610425	−	1.87869i
$117$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$118$	0.451057	+	0.327712i	0.451057	+	0.327712i
$119$		0			0
$120$		0			0
$121$	0.951057	+	0.309017i	0.951057	+	0.309017i
$122$	1.78201			1.78201
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$127$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$128$	−1.04744	+	0.761010i	−1.04744	+	0.761010i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	2.14879	+	0.340334i	2.14879	+	0.340334i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−3.34786	+	2.43236i	−3.34786	+	2.43236i
$137$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$137$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$138$	0.500000	−	1.53884i	0.500000	−	1.53884i
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$		0			0
$142$	−2.52015			−2.52015
$143$	−0.297556	−	1.87869i	−0.297556	−	1.87869i
$144$	1.55754			1.55754
$145$		0			0
$146$	−0.891007	−	0.647354i	−0.891007	−	0.647354i
$147$	0.809017	−	0.587785i	0.809017	−	0.587785i
$148$		0			0
$149$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$149$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$150$	−1.44168	+	1.04744i	−1.44168	+	1.04744i
$151$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$151$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$152$	−0.761010	−	2.34215i	−0.761010	−	2.34215i
$153$	−1.97538			−1.97538
$154$		0			0
$155$		0			0
$156$	−1.27877	−	3.93564i	−1.27877	−	3.93564i
$157$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$157$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$158$		0			0
$159$	−0.550672	+	1.69480i	−0.550672	+	1.69480i
$160$		0			0
$161$		0			0
$162$	1.44168	+	1.04744i	1.44168	+	1.04744i
$163$	0.587785	+	1.80902i	0.587785	+	1.80902i	0.587785	+	0.809017i	$0.300000\pi$
$163$	0.587785	+	1.80902i	0.587785	+	1.80902i			1.00000i	$0.5\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$167$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$168$		0			0
$169$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$170$		0			0
$171$	0.363271	−	1.11803i	0.363271	−	1.11803i
$172$		0			0
$173$	−1.14412	−	0.831254i	−1.14412	−	0.831254i	−0.156434	−	0.987688i	$-0.550000\pi$
$173$	−1.14412	−	0.831254i	−1.14412	−	0.831254i	−0.987688	+	0.156434i	$0.950000\pi$
$174$	0.500000	+	1.53884i	0.500000	+	1.53884i
$175$		0			0
$176$	−0.707107	+	1.38778i	−0.707107	+	1.38778i
$177$	−0.312869			−0.312869
$178$	−1.08779	−	3.34786i	−1.08779	−	3.34786i
$179$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$179$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$180$		0			0
$181$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$181$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$182$		0			0
$183$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$184$	1.53884	+	1.11803i	1.53884	+	1.11803i
$185$		0			0
$186$		0			0
$187$	0.896802	−	1.76007i	0.896802	−	1.76007i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.253116	−	0.183900i	0.253116	−	0.183900i	−0.453990	−	0.891007i	$-0.650000\pi$
$191$	0.253116	−	0.183900i	0.253116	−	0.183900i	0.707107	+	0.707107i	$0.250000\pi$
$192$	0.106480	−	0.327712i	0.106480	−	0.327712i
$193$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$193$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$194$		0			0
$195$		0			0
$196$	0.672288	+	2.06909i	0.672288	+	2.06909i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−1.58779	+	0.809017i	−1.58779	+	0.809017i
$199$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$199$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$200$	−0.647354	−	1.99235i	−0.647354	−	1.99235i
$201$		0			0
$202$	−2.03884	+	1.48131i	−2.03884	+	1.48131i
$203$		0			0
$204$	1.32802	−	4.08723i	1.32802	−	4.08723i
$205$		0			0
$206$	−2.74224	−	1.99235i	−2.74224	−	1.99235i
$207$	0.280582	+	0.863541i	0.280582	+	0.863541i
$208$	2.96261			2.96261
$209$	0.831254	+	0.831254i	0.831254	+	0.831254i
$210$		0			0
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$	−3.13647	−	2.27878i	−3.13647	−	2.27878i
$213$	1.14412	−	0.831254i	1.14412	−	0.831254i
$214$		0			0
$215$		0			0
$216$	−1.69480	+	1.23134i	−1.69480	+	1.23134i
$217$		0			0
$218$	−0.891007	−	2.74224i	−0.891007	−	2.74224i
$219$	0.618034			0.618034
$220$		0			0
$221$	−3.75739			−3.75739
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$		0			0
$225$	0.309017	−	0.951057i	0.309017	−	0.951057i
$226$		0			0
$227$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$227$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.987688	+	0.156434i	$0.0500000\pi$
$228$	2.06909	+	1.50328i	2.06909	+	1.50328i
$229$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$229$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$230$		0			0
$231$		0			0
$232$	−1.90211			−1.90211
$233$	0.0966818	+	0.297556i	0.0966818	+	0.297556i	0.987688	−	0.156434i	$-0.0500000\pi$
$233$	0.0966818	+	0.297556i	0.0966818	+	0.297556i	−0.891007	+	0.453990i	$0.850000\pi$
$234$	2.74224	+	1.99235i	2.74224	+	1.99235i
$235$		0			0
$236$	0.210338	−	0.647354i	0.210338	−	0.647354i
$237$		0			0
$238$		0			0
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		−	1.78201i		−	1.78201i
$243$	−1.00000			−1.00000
$244$	−0.672288	−	2.06909i	−0.672288	−	2.06909i
$245$		0			0
$246$		0			0
$247$	0.690983	−	2.12663i	0.690983	−	2.12663i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.453990	+	0.891007i	$0.350000\pi$
$251$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.156434	+	0.987688i	$0.450000\pi$
$252$		0			0
$253$	−0.896802	−	0.142040i	−0.896802	−	0.142040i
$254$		0			0
$255$		0			0
$256$	1.58779	+	1.15359i	1.58779	+	1.15359i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	−0.327712	−	2.06909i	−0.327712	−	2.06909i
$265$		0			0
$266$		0			0
$267$	1.59811	+	1.16110i	1.59811	+	1.16110i
$268$		0			0
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$		0			0
$271$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$271$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$272$	2.48912	+	1.80845i	2.48912	+	1.80845i
$273$		0			0
$274$		0			0
$275$	0.707107	+	0.707107i	0.707107	+	0.707107i
$276$	−1.97538			−1.97538
$277$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$277$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.280582	+	0.863541i	−0.280582	+	0.863541i	0.707107	+	0.707107i	$0.250000\pi$
$281$	−0.280582	+	0.863541i	−0.280582	+	0.863541i	−0.987688	+	0.156434i	$0.950000\pi$
$282$		0			0
$283$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$283$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$284$	0.950759	+	2.92614i	0.950759	+	2.92614i
$285$		0			0
$286$	−3.02015	+	1.53884i	−3.02015	+	1.53884i
$287$		0			0
$288$	−0.210338	−	0.647354i	−0.210338	−	0.647354i
$289$	−2.34786	−	1.70582i	−2.34786	−	1.70582i
$290$		0			0
$291$		0			0
$292$	−0.415497	+	1.27877i	−0.415497	+	1.27877i
$293$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$293$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$294$	−1.44168	−	1.04744i	−1.44168	−	1.04744i
$295$		0			0
$296$		0			0
$297$	0.453990	−	0.891007i	0.453990	−	0.891007i
$298$		0			0
$299$	0.533698	+	1.64255i	0.533698	+	1.64255i
$300$	1.76007	+	1.27877i	1.76007	+	1.27877i
$301$		0			0
$302$		0			0
$303$	0.437016	−	1.34500i	0.437016	−	1.34500i
$304$	−1.48131	+	1.07623i	−1.48131	+	1.07623i
$305$		0			0
$306$	1.08779	+	3.34786i	1.08779	+	3.34786i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	1.90211			1.90211
$310$		0			0
$311$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$311$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$312$	−3.22369	+	2.34215i	−3.22369	+	2.34215i
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$317$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$318$	3.17557			3.17557
$319$	0.809017	−	0.412215i	0.809017	−	0.412215i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.87869	−	1.36495i	1.87869	−	1.36495i
$324$	0.672288	−	2.06909i	0.672288	−	2.06909i
$325$	0.587785	−	1.80902i	0.587785	−	1.80902i
$326$	2.74224	−	1.99235i	2.74224	−	1.99235i
$327$	1.30902	+	0.951057i	1.30902	+	0.951057i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$337$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$338$	3.77436	+	2.74224i	3.77436	+	2.74224i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−2.09488			−2.09488
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.778768	+	2.39680i	−0.778768	+	2.39680i
$347$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$347$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$348$	1.59811	−	1.16110i	1.59811	−	1.16110i
$349$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$349$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$350$		0			0
$351$	−1.90211			−1.90211
$352$	0.672288	+	0.106480i	0.672288	+	0.106480i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	0.172288	+	0.530249i	0.172288	+	0.530249i
$355$		0			0
$356$	−3.47681	+	2.52605i	−3.47681	+	2.52605i
$357$		0			0
$358$		0			0
$359$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$359$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$360$		0			0
$361$	0.118034	+	0.363271i	0.118034	+	0.363271i
$362$		0			0
$363$	0.587785	+	0.809017i	0.587785	+	0.809017i
$364$		0			0
$365$		0			0
$366$	1.44168	+	1.04744i	1.44168	+	1.04744i
$367$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$367$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$368$	0.437016	−	1.34500i	0.437016	−	1.34500i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	−3.47681	−	0.550672i	−3.47681	−	0.550672i
$375$		0			0
$376$		0			0
$377$	−1.39724	−	1.01515i	−1.39724	−	1.01515i
$378$		0			0
$379$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$379$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$380$		0			0
$381$		0			0
$382$	−0.451057	−	0.327712i	−0.451057	−	0.327712i
$383$	−0.610425	−	1.87869i	−0.610425	−	1.87869i	−0.453990	−	0.891007i	$-0.650000\pi$
$383$	−0.610425	−	1.87869i	−0.610425	−	1.87869i	−0.156434	−	0.987688i	$-0.550000\pi$
$384$	−1.29471			−1.29471
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$389$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$390$		0			0
$391$	−0.554254	+	1.70582i	−0.554254	+	1.70582i
$392$	1.69480	−	1.23134i	1.69480	−	1.23134i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	1.53836	+	1.53836i	1.53836	+	1.53836i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	0.891007	+	2.74224i	0.891007	+	2.74224i
$399$		0			0
$400$	−1.26007	+	0.915497i	−1.26007	+	0.915497i
$401$	−0.550672	+	1.69480i	−0.550672	+	1.69480i	0.156434	+	0.987688i	$0.450000\pi$
$401$	−0.550672	+	1.69480i	−0.550672	+	1.69480i	−0.707107	+	0.707107i	$0.750000\pi$
$402$		0			0
$403$		0			0
$404$	2.48912	+	1.80845i	2.48912	+	1.80845i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−4.13818			−4.13818
$409$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$409$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$410$		0			0
$411$		0			0
$412$	−1.27877	+	3.93564i	−1.27877	+	3.93564i
$413$		0			0
$414$	1.30902	−	0.951057i	1.30902	−	0.951057i
$415$		0			0
$416$	−0.400087	−	1.23134i	−0.400087	−	1.23134i
$417$		0			0
$418$	0.951057	−	1.86655i	0.951057	−	1.86655i
$419$	1.78201			1.78201			0.891007	−	0.453990i	$-0.150000\pi$
$419$	1.78201			1.78201			0.891007	+	0.453990i	$0.150000\pi$
$420$		0			0
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$		0			0
$423$		0			0
$424$	−1.15359	+	3.55040i	−1.15359	+	3.55040i
$425$	1.59811	−	1.16110i	1.59811	−	1.16110i
$426$	−2.03884	−	1.48131i	−2.03884	−	1.48131i
$427$		0			0
$428$		0			0
$429$	0.863541	−	1.69480i	0.863541	−	1.69480i
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$	1.26007	+	0.915497i	1.26007	+	0.915497i
$433$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$433$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$434$		0			0
$435$		0			0
$436$	−2.84786	+	2.06909i	−2.84786	+	2.06909i
$437$	−0.863541	−	0.627399i	−0.863541	−	0.627399i
$438$	−0.340334	−	1.04744i	−0.340334	−	1.04744i
$439$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$439$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$440$		0			0
$441$	1.00000			1.00000
$442$	2.06909	+	6.36801i	2.06909	+	6.36801i
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$449$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$450$	−1.78201			−1.78201
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−2.03884	−	1.48131i	−2.03884	−	1.48131i
$455$		0			0
$456$	0.761010	−	2.34215i	0.761010	−	2.34215i
$457$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$457$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$458$	−2.74224	+	1.99235i	−2.74224	+	1.99235i
$459$	−1.59811	−	1.16110i	−1.59811	−	1.16110i
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$463$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$464$	0.437016	+	1.34500i	0.437016	+	1.34500i
$465$		0			0
$466$	0.451057	−	0.327712i	0.451057	−	0.327712i
$467$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i	−0.987688	−	0.156434i	$-0.950000\pi$
$467$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i	0.891007	+	0.453990i	$0.150000\pi$
$468$	1.27877	−	3.93564i	1.27877	−	3.93564i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.655423			−0.655423
$473$		0			0
$474$		0			0
$475$	0.363271	+	1.11803i	0.363271	+	1.11803i
$476$		0			0
$477$	−1.44168	+	1.04744i	−1.44168	+	1.04744i
$478$		0			0
$479$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$479$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.06909	+	0.672288i	−2.06909	+	0.672288i
$485$		0			0
$486$	0.550672	+	1.69480i	0.550672	+	1.69480i
$487$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$487$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$488$	−1.69480	+	1.23134i	−1.69480	+	1.23134i
$489$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$490$		0			0
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$	−0.554254	−	1.70582i	−0.554254	−	1.70582i
$494$	−3.98470			−3.98470
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$499$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$500$		0			0
$501$		0			0
$502$	2.84786	−	2.06909i	2.84786	−	2.06909i
$503$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$503$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$504$		0			0
$505$		0			0
$506$	0.253116	+	1.59811i	0.253116	+	1.59811i
$507$	−2.61803			−2.61803
$508$		0			0
$509$	0.253116	+	0.183900i	0.253116	+	0.183900i	0.707107	−	0.707107i	$-0.250000\pi$
$509$	0.253116	+	0.183900i	0.253116	+	0.183900i	−0.453990	+	0.891007i	$0.650000\pi$
$510$		0			0
$511$		0			0
$512$	0.680668	−	2.09488i	0.680668	−	2.09488i
$513$	0.951057	−	0.690983i	0.951057	−	0.690983i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.437016	−	1.34500i	−0.437016	−	1.34500i
$520$		0			0
$521$	1.59811	−	1.16110i	1.59811	−	1.16110i	0.707107	−	0.707107i	$-0.250000\pi$
$521$	1.59811	−	1.16110i	1.59811	−	1.16110i	0.891007	−	0.453990i	$-0.150000\pi$
$522$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.38778	+	0.707107i	−1.38778	+	0.707107i
$529$	−0.175571			−0.175571
$530$		0			0
$531$	−0.253116	−	0.183900i	−0.253116	−	0.183900i
$532$		0			0
$533$		0			0
$534$	1.08779	−	3.34786i	1.08779	−	3.34786i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$540$		0			0
$541$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$541$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$542$	2.33269	+	1.69480i	2.33269	+	1.69480i
$543$		0			0
$544$	0.415497	−	1.27877i	0.415497	−	1.27877i
$545$		0			0
$546$		0			0
$547$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$547$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$548$		0			0
$549$	−1.00000			−1.00000
$550$	0.809017	−	1.58779i	0.809017	−	1.58779i
$551$	1.06740			1.06740
$552$	0.587785	+	1.80902i	0.587785	+	1.80902i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$557$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.76007	−	0.896802i	1.76007	−	0.896802i
$562$	1.61803			1.61803
$563$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$563$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$		0			0
$566$	0.891007	−	2.74224i	0.891007	−	2.74224i
$567$		0			0
$568$	2.39680	−	1.74138i	2.39680	−	1.74138i
$569$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$569$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$570$		0			0
$571$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$571$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$572$	2.92614	+	2.92614i	2.92614	+	2.92614i
$573$	0.312869			0.312869
$574$		0			0
$575$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$576$	0.278768	−	0.202537i	0.278768	−	0.202537i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	−1.59811	+	4.91849i	−1.59811	+	4.91849i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.278768	−	1.76007i	−0.278768	−	1.76007i
$584$	1.29471			1.29471
$585$		0			0
$586$		0			0
$587$	1.44168	−	1.04744i	1.44168	−	1.04744i	0.453990	−	0.891007i	$-0.350000\pi$
$587$	1.44168	−	1.04744i	1.44168	−	1.04744i	0.987688	−	0.156434i	$-0.0500000\pi$
$588$	−0.672288	+	2.06909i	−0.672288	+	2.06909i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.97538			1.97538			0.987688	−	0.156434i	$-0.0500000\pi$
$593$	1.97538			1.97538			0.987688	+	0.156434i	$0.0500000\pi$
$594$	−1.76007	−	0.278768i	−1.76007	−	0.278768i
$595$		0			0
$596$		0			0
$597$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$598$	2.48990	−	1.80902i	2.48990	−	1.80902i
$599$	0.550672	−	1.69480i	0.550672	−	1.69480i	−0.156434	−	0.987688i	$-0.550000\pi$
$599$	0.550672	−	1.69480i	0.550672	−	1.69480i	0.707107	−	0.707107i	$-0.250000\pi$
$600$	0.647354	−	1.99235i	0.647354	−	1.99235i
$601$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$601$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−2.52015			−2.52015
$607$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$607$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$608$	0.647354	+	0.470330i	0.647354	+	0.470330i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	3.47681	−	2.52605i	3.47681	−	2.52605i
$613$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$613$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$617$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$618$	−1.04744	−	3.22369i	−1.04744	−	3.22369i
$619$	0.951057	+	0.690983i	0.951057	+	0.690983i	0.951057	−	0.309017i	$-0.100000\pi$
$619$	0.951057	+	0.690983i	0.951057	+	0.690983i			1.00000i	$0.5\pi$
$620$		0			0
$621$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$622$	0.778768	−	2.39680i	0.778768	−	2.39680i
$623$		0			0
$624$	2.39680	+	1.74138i	2.39680	+	1.74138i
$625$	0.309017	+	0.951057i	0.309017	+	0.951057i
$626$		0			0
$627$	0.183900	+	1.16110i	0.183900	+	1.16110i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−1.19803	−	3.68715i	−1.19803	−	3.68715i
$637$	1.90211			1.90211
$638$	−1.14412	−	1.14412i	−1.14412	−	1.14412i
$639$	1.41421			1.41421
$640$		0			0
$641$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$641$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$642$		0			0
$643$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$643$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$		0			0
$646$	−3.34786	−	2.43236i	−3.34786	−	2.43236i
$647$	−0.280582	−	0.863541i	−0.280582	−	0.863541i	−0.987688	−	0.156434i	$-0.950000\pi$
$647$	−0.280582	−	0.863541i	−0.280582	−	0.863541i	0.707107	−	0.707107i	$-0.250000\pi$
$648$	−2.09488			−2.09488
$649$	0.278768	−	0.142040i	0.278768	−	0.142040i
$650$	−3.38959			−3.38959
$651$		0			0
$652$	−3.34786	−	2.43236i	−3.34786	−	2.43236i
$653$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$653$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$654$	0.891007	−	2.74224i	0.891007	−	2.74224i
$655$		0			0
$656$		0			0
$657$	0.500000	+	0.363271i	0.500000	+	0.363271i
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$	−3.03979	−	2.20854i	−3.03979	−	2.20854i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.666977	+	0.484587i	−0.666977	+	0.484587i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.453990	−	0.891007i	0.453990	−	0.891007i
$672$		0			0
$673$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$673$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$674$		0			0
$675$	0.809017	−	0.587785i	0.809017	−	0.587785i
$676$	1.76007	−	5.41695i	1.76007	−	5.41695i
$677$	0.0966818	−	0.297556i	0.0966818	−	0.297556i	−0.891007	−	0.453990i	$-0.850000\pi$
$677$	0.0966818	−	0.297556i	0.0966818	−	0.297556i	0.987688	+	0.156434i	$0.0500000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.41421			1.41421
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.790322	+	2.43236i	0.790322	+	2.43236i
$685$		0			0
$686$		0			0
$687$	0.587785	−	1.80902i	0.587785	−	1.80902i
$688$		0			0
$689$	−2.74224	+	1.99235i	−2.74224	+	1.99235i
$690$		0			0
$691$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$691$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$692$	3.07672			3.07672
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$697$		0			0
$698$		0			0
$699$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i
$700$		0			0
$701$	0.253116	+	0.183900i	0.253116	+	0.183900i	0.707107	−	0.707107i	$-0.250000\pi$
$701$	0.253116	+	0.183900i	0.253116	+	0.183900i	−0.453990	+	0.891007i	$0.650000\pi$
$702$	1.04744	+	3.22369i	1.04744	+	3.22369i
$703$		0			0
$704$	0.0539036	+	0.340334i	0.0539036	+	0.340334i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	0.550672	−	0.400087i	0.550672	−	0.400087i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$		0			0
$711$		0			0
$712$	3.34786	+	2.43236i	3.34786	+	2.43236i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	0.451057	+	0.327712i	0.451057	+	0.327712i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$		0			0
$721$		0			0
$722$	0.550672	−	0.400087i	0.550672	−	0.400087i
$723$		0			0
$724$		0			0
$725$	0.907981			0.907981
$726$	1.04744	−	1.44168i	1.04744	−	1.44168i
$727$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$727$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$	0.672288	−	2.06909i	0.672288	−	2.06909i
$733$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$733$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$734$		0			0
$735$		0			0
$736$	−0.618034			−0.618034
$737$		0			0
$738$		0			0
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$	1.80902	−	1.31433i	1.80902	−	1.31433i
$742$		0			0
$743$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$743$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$	0.672288	+	4.24466i	0.672288	+	4.24466i
$749$		0			0
$750$		0			0
$751$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$751$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$752$		0			0
$753$	−0.610425	+	1.87869i	−0.610425	+	1.87869i
$754$	−0.951057	+	2.92705i	−0.951057	+	2.92705i
$755$		0			0
$756$		0			0
$757$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$757$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$758$	−1.10134			−1.10134
$759$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$760$		0			0
$761$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i	0.891007	−	0.453990i	$-0.150000\pi$
$761$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i	−0.987688	+	0.156434i	$0.950000\pi$
$762$		0			0
$763$		0			0
$764$	−0.210338	+	0.647354i	−0.210338	+	0.647354i
$765$		0			0
$766$	−2.84786	+	2.06909i	−2.84786	+	2.06909i
$767$	−0.481456	−	0.349798i	−0.481456	−	0.349798i
$768$	0.606480	+	1.86655i	0.606480	+	1.86655i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	2.03884	+	1.48131i	2.03884	+	1.48131i
$779$		0			0
$780$		0			0
$781$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$782$	3.19623			3.19623
$783$	−0.280582	−	0.863541i	−0.280582	−	0.863541i
$784$	−1.26007	−	0.915497i	−1.26007	−	0.915497i
$785$		0			0
$786$		0			0
$787$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$787$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.951057	−	1.86655i	0.951057	−	1.86655i
$793$	−1.90211			−1.90211
$794$		0			0
$795$		0			0
$796$	2.84786	−	2.06909i	2.84786	−	2.06909i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	0.550672	+	0.400087i	0.550672	+	0.400087i
$801$	0.610425	+	1.87869i	0.610425	+	1.87869i
$802$	3.17557			3.17557
$803$	−0.550672	+	0.280582i	−0.550672	+	0.280582i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.915497	−	2.81761i	0.915497	−	2.81761i
$809$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$809$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$810$		0			0
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$		0			0
$813$	−1.61803			−1.61803
$814$		0			0
$815$		0			0
$816$	0.950759	+	2.92614i	0.950759	+	2.92614i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.734572	−	0.533698i	0.734572	−	0.533698i	−0.156434	−	0.987688i	$-0.550000\pi$
$821$	0.734572	−	0.533698i	0.734572	−	0.533698i	0.891007	+	0.453990i	$0.150000\pi$
$822$		0			0
$823$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$823$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$824$	3.98470			3.98470
$825$	0.156434	+	0.987688i	0.156434	+	0.987688i
$826$		0			0
$827$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$827$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$828$	−1.59811	−	1.16110i	−1.59811	−	1.16110i
$829$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$829$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	0.530249	−	0.385248i	0.530249	−	0.385248i
$833$	1.59811	+	1.16110i	1.59811	+	1.16110i
$834$		0			0
$835$		0			0
$836$	−2.52605	−	0.400087i	−2.52605	−	0.400087i
$837$		0			0
$838$	−0.981305	−	3.02015i	−0.981305	−	3.02015i
$839$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$839$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$840$		0			0
$841$	−0.0542543	+	0.166977i	−0.0542543	+	0.166977i
$842$		0			0
$843$	−0.734572	+	0.533698i	−0.734572	+	0.533698i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$	2.77555			2.77555
$849$	0.500000	+	1.53884i	0.500000	+	1.53884i
$850$	−2.84786	−	2.06909i	−2.84786	−	2.06909i
$851$		0			0
$852$	−0.950759	+	2.92614i	−0.950759	+	2.92614i
$853$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$853$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$	−3.34786	−	0.530249i	−3.34786	−	0.530249i
$859$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$859$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$863$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$864$	0.210338	−	0.647354i	0.210338	−	0.647354i
$865$		0			0
$866$		0			0
$867$	−0.896802	−	2.76007i	−0.896802	−	2.76007i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	2.74224	+	1.99235i	2.74224	+	1.99235i
$873$		0			0
$874$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$875$		0			0
$876$	−1.08779	+	0.790322i	−1.08779	+	0.790322i
$877$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$877$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$878$	−0.340334	−	1.04744i	−0.340334	−	1.04744i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.550672	−	1.69480i	−0.550672	−	1.69480i
$883$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$883$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$884$	6.61328	−	4.80483i	6.61328	−	4.80483i
$885$		0			0
$886$		0			0
$887$	0.253116	−	0.183900i	0.253116	−	0.183900i	−0.453990	−	0.891007i	$-0.650000\pi$
$887$	0.253116	−	0.183900i	0.253116	−	0.183900i	0.707107	+	0.707107i	$0.250000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.891007	−	0.453990i	0.891007	−	0.453990i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.533698	+	1.64255i	−0.533698	+	1.64255i
$898$		0			0
$899$		0			0
$900$	0.672288	+	2.06909i	0.672288	+	2.06909i
$901$	−3.52015			−3.52015
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$907$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$908$	−0.950759	+	2.92614i	−0.950759	+	2.92614i
$909$	1.14412	−	0.831254i	1.14412	−	0.831254i
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$	−1.83099			−1.83099
$913$		0			0
$914$		0			0
$915$		0			0
$916$	3.34786	+	2.43236i	3.34786	+	2.43236i
$917$		0			0
$918$	−1.08779	+	3.34786i	−1.08779	+	3.34786i
$919$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$919$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.68999			2.68999
$924$		0			0
$925$		0			0
$926$	0.647354	+	1.99235i	0.647354	+	1.99235i
$927$	1.53884	+	1.11803i	1.53884	+	1.11803i
$928$	0.500000	−	0.363271i	0.500000	−	0.363271i
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$932$	−0.550672	−	0.400087i	−0.550672	−	0.400087i
$933$	0.437016	+	1.34500i	0.437016	+	1.34500i
$934$	0.557537			0.557537
$935$		0			0
$936$	−3.98470			−3.98470
$937$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$937$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.550672	−	1.69480i	0.550672	−	1.69480i	−0.156434	−	0.987688i	$-0.550000\pi$
$941$	0.550672	−	1.69480i	0.550672	−	1.69480i	0.707107	−	0.707107i	$-0.250000\pi$
$942$		0			0
$943$		0			0
$944$	0.150585	+	0.463454i	0.150585	+	0.463454i
$945$		0			0
$946$		0			0
$947$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$947$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$948$		0			0
$949$	0.951057	+	0.690983i	0.951057	+	0.690983i
$950$	1.69480	−	1.23134i	1.69480	−	1.23134i
$951$		0			0
$952$		0			0
$953$	−1.44168	+	1.04744i	−1.44168	+	1.04744i	−0.453990	+	0.891007i	$0.650000\pi$
$953$	−1.44168	+	1.04744i	−1.44168	+	1.04744i	−0.987688	+	0.156434i	$0.950000\pi$
$954$	2.56909	+	1.86655i	2.56909	+	1.86655i
$955$		0			0
$956$		0			0
$957$	0.896802	+	0.142040i	0.896802	+	0.142040i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$967$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$968$	1.23134	+	1.69480i	1.23134	+	1.69480i
$969$	2.32219			2.32219
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$	1.76007	−	1.27877i	1.76007	−	1.27877i
$973$		0			0
$974$	0.340334	−	1.04744i	0.340334	−	1.04744i
$975$	1.53884	−	1.11803i	1.53884	−	1.11803i
$976$	1.26007	+	0.915497i	1.26007	+	0.915497i
$977$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$977$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$978$	3.38959			3.38959
$979$	−1.95106	−	0.309017i	−1.95106	−	0.309017i
$980$		0			0
$981$	0.500000	+	1.53884i	0.500000	+	1.53884i
$982$		0			0
$983$	1.59811	−	1.16110i	1.59811	−	1.16110i	0.707107	−	0.707107i	$-0.250000\pi$
$983$	1.59811	−	1.16110i	1.59811	−	1.16110i	0.891007	−	0.453990i	$-0.150000\pi$
$984$		0			0
$985$		0			0
$986$	−2.58580	+	1.87869i	−2.58580	+	1.87869i
$987$		0			0
$988$	1.50328	+	4.62663i	1.50328	+	4.62663i
$989$		0			0
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$997$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.1.bm.d.731.1	yes	16
3.2	odd	2	inner	2013.1.bm.d.731.4	yes	16
11.9	even	5	inner	2013.1.bm.d.548.1	✓	16
33.20	odd	10	inner	2013.1.bm.d.548.4	yes	16
61.60	even	2	inner	2013.1.bm.d.731.4	yes	16
183.182	odd	2	CM	2013.1.bm.d.731.1	yes	16
671.548	even	10	inner	2013.1.bm.d.548.4	yes	16
2013.548	odd	10	inner	2013.1.bm.d.548.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.1.bm.d.548.1	✓	16	11.9	even	5	inner
2013.1.bm.d.548.1	✓	16	2013.548	odd	10	inner
2013.1.bm.d.548.4	yes	16	33.20	odd	10	inner
2013.1.bm.d.548.4	yes	16	671.548	even	10	inner
2013.1.bm.d.731.1	yes	16	1.1	even	1	trivial
2013.1.bm.d.731.1	yes	16	183.182	odd	2	CM
2013.1.bm.d.731.4	yes	16	3.2	odd	2	inner
2013.1.bm.d.731.4	yes	16	61.60	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2013.bm (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.550672 - 1.69480i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.76007 + 1.27877i) q^{4} +(0.550672 - 1.69480i) q^{6} +(1.69480 + 1.23134i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.550672 - 1.69480i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.76007 + 1.27877i) q^{4} +(0.550672 - 1.69480i) q^{6} +(1.69480 + 1.23134i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.987688 - 0.156434i) q^{11} -2.17557 q^{12} +(0.587785 + 1.80902i) q^{13} +(0.481305 - 1.48131i) q^{16} +(-0.610425 + 1.87869i) q^{17} +(1.44168 - 1.04744i) q^{18} +(-0.951057 - 0.690983i) q^{19} +(0.278768 + 1.76007i) q^{22} +0.907981 q^{23} +(0.647354 + 1.99235i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(2.74224 - 1.99235i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.734572 + 0.533698i) q^{29} -0.680668 q^{32} +(-0.707107 - 0.707107i) q^{33} +3.52015 q^{34} +(-1.76007 - 1.27877i) q^{36} +(-0.647354 + 1.99235i) q^{38} +(-0.587785 + 1.80902i) q^{39} +(1.93845 - 0.987688i) q^{44} +(-0.500000 - 1.53884i) q^{46} +(1.26007 - 0.915497i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.550672 + 1.69480i) q^{50} +(-1.59811 + 1.16110i) q^{51} +(-3.34786 - 2.43236i) q^{52} +(0.550672 + 1.69480i) q^{53} +1.78201 q^{54} +(-0.363271 - 1.11803i) q^{57} +(1.30902 + 0.951057i) q^{58} +(-0.253116 + 0.183900i) q^{59} +(-0.309017 + 0.951057i) q^{61} +(-0.106480 - 0.327712i) q^{64} +(-0.809017 + 1.58779i) q^{66} +(-1.32802 - 4.08723i) q^{68} +(0.734572 + 0.533698i) q^{69} +(0.437016 - 1.34500i) q^{71} +(-0.647354 + 1.99235i) q^{72} +(0.500000 - 0.363271i) q^{73} +(-0.309017 - 0.951057i) q^{75} +2.55754 q^{76} +3.38959 q^{78} +(-0.809017 + 0.587785i) q^{81} -0.907981 q^{87} +(-1.48131 - 1.48131i) q^{88} +1.97538 q^{89} +(-1.59811 + 1.16110i) q^{92} +(-0.550672 - 0.400087i) q^{96} -1.78201 q^{98} +(-0.156434 - 0.987688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 4 * q^4 - 4 * q^9	\( 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9} - 16 q^{12} - 16 q^{16} + 4 q^{22} - 4 q^{25} + 4 q^{27} + 8 q^{34} - 4 q^{36} - 8 q^{46} - 4 q^{48} - 4 q^{49} - 20 q^{52} + 12 q^{58} + 4 q^{61} - 16 q^{64} - 4 q^{66} + 8 q^{73} + 4 q^{75} + 40 q^{76} - 4 q^{81}+O(q^{100}) \) 16 * q + 4 * q^3 - 4 * q^4 - 4 * q^9 - 16 * q^12 - 16 * q^16 + 4 * q^22 - 4 * q^25 + 4 * q^27 + 8 * q^34 - 4 * q^36 - 8 * q^46 - 4 * q^48 - 4 * q^49 - 20 * q^52 + 12 * q^58 + 4 * q^61 - 16 * q^64 - 4 * q^66 + 8 * q^73 + 4 * q^75 + 40 * q^76 - 4 * q^81

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