LMFDB - Embedded newform 2013.1.bm.c.1829.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{10}$
Projective field:	Galois closure of 10.0.721218892933132803.1

Embedding invariants

Embedding label			1829.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	2013.1829
Dual form			2013.1.bm.c.1280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.690983i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.118034 - 0.363271i) q^{4} +(-0.951057 - 0.690983i) q^{6} +(-0.224514 - 0.690983i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.690983i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.118034 - 0.363271i) q^{4} +(-0.951057 - 0.690983i) q^{6} +(-0.224514 - 0.690983i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.951057 + 0.309017i) q^{11} +0.381966 q^{12} +(-1.30902 + 0.951057i) q^{13} +(1.00000 + 0.726543i) q^{16} +(-1.53884 - 1.11803i) q^{17} +(0.363271 - 1.11803i) q^{18} +(-0.190983 - 0.587785i) q^{19} +(-1.11803 + 0.363271i) q^{22} -1.17557 q^{23} +(0.587785 - 0.427051i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.587785 - 1.80902i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.363271 + 1.11803i) q^{29} -0.726543 q^{32} +1.00000i q^{33} +2.23607 q^{34} +(0.118034 + 0.363271i) q^{36} +(0.587785 + 0.427051i) q^{38} +(-1.30902 - 0.951057i) q^{39} +(0.224514 - 0.309017i) q^{44} +(1.11803 - 0.812299i) q^{46} +(-0.381966 + 1.17557i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.951057 - 0.690983i) q^{50} +(0.587785 - 1.80902i) q^{51} +(0.190983 + 0.587785i) q^{52} +(-0.951057 + 0.690983i) q^{53} +1.17557 q^{54} +(0.500000 - 0.363271i) q^{57} +(-0.427051 - 1.31433i) q^{58} +(-0.587785 + 1.80902i) q^{59} +(-0.809017 - 0.587785i) q^{61} +(-0.309017 + 0.224514i) q^{64} +(-0.690983 - 0.951057i) q^{66} +(-0.587785 + 0.427051i) q^{68} +(-0.363271 - 1.11803i) q^{69} +(0.587785 + 0.427051i) q^{72} +(-0.500000 + 1.53884i) q^{73} +(-0.809017 + 0.587785i) q^{75} -0.236068 q^{76} +1.90211 q^{78} +(0.309017 - 0.951057i) q^{81} -1.17557 q^{87} -0.726543i q^{88} +1.90211 q^{89} +(-0.138757 + 0.427051i) q^{92} +(-0.224514 - 0.690983i) q^{96} +(1.61803 - 1.17557i) q^{97} +1.17557 q^{98} +(-0.951057 + 0.309017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 8 * q^4 - 2 * q^9	$ 8 q - 2 q^{3} - 8 q^{4} - 2 q^{9} + 12 q^{12} - 6 q^{13} + 8 q^{16} - 6 q^{19} - 2 q^{25} - 2 q^{27} - 8 q^{36} - 6 q^{39} - 12 q^{48} - 2 q^{49} + 6 q^{52} + 4 q^{57} + 10 q^{58} - 2 q^{61} + 2 q^{64} - 10 q^{66} - 4 q^{73} - 2 q^{75} + 16 q^{76} - 2 q^{81} + 4 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 - 8 * q^4 - 2 * q^9 + 12 * q^12 - 6 * q^13 + 8 * q^16 - 6 * q^19 - 2 * q^25 - 2 * q^27 - 8 * q^36 - 6 * q^39 - 12 * q^48 - 2 * q^49 + 6 * q^52 + 4 * q^57 + 10 * q^58 - 2 * q^61 + 2 * q^64 - 10 * q^66 - 4 * q^73 - 2 * q^75 + 16 * q^76 - 2 * q^81 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1222$	$1343$	$1465$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$2$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$4$	0.118034	−	0.363271i	0.118034	−	0.363271i
$5$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$5$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$6$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$7$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$7$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$8$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$		0			0
$11$	0.951057	+	0.309017i	0.951057	+	0.309017i
$11$	0.951057	+	0.309017i	0.951057	+	0.309017i
$12$	0.381966			0.381966
$13$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$13$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$14$		0			0
$15$		0			0
$16$	1.00000	+	0.726543i	1.00000	+	0.726543i
$17$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$17$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$18$	0.363271	−	1.11803i	0.363271	−	1.11803i
$19$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$19$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$23$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$23$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$24$	0.587785	−	0.427051i	0.587785	−	0.427051i
$25$	0.309017	+	0.951057i	0.309017	+	0.951057i
$26$	0.587785	−	1.80902i	0.587785	−	1.80902i
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$		0			0
$29$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$29$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$30$		0			0
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	−0.726543			−0.726543
$33$			1.00000i			1.00000i
$34$	2.23607			2.23607
$35$		0			0
$36$	0.118034	+	0.363271i	0.118034	+	0.363271i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	0.587785	+	0.427051i	0.587785	+	0.427051i
$39$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$40$		0			0
$41$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$41$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	0.224514	−	0.309017i	0.224514	−	0.309017i
$45$		0			0
$46$	1.11803	−	0.812299i	1.11803	−	0.812299i
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$	−0.381966	+	1.17557i	−0.381966	+	1.17557i
$49$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$50$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$51$	0.587785	−	1.80902i	0.587785	−	1.80902i
$52$	0.190983	+	0.587785i	0.190983	+	0.587785i
$53$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$53$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$54$	1.17557			1.17557
$55$		0			0
$56$		0			0
$57$	0.500000	−	0.363271i	0.500000	−	0.363271i
$58$	−0.427051	−	1.31433i	−0.427051	−	1.31433i
$59$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$59$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$60$		0			0
$61$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$61$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$62$		0			0
$63$		0			0
$64$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$65$		0			0
$66$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$69$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$70$		0			0
$71$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$71$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$72$	0.587785	+	0.427051i	0.587785	+	0.427051i
$73$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$73$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$74$		0			0
$75$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$76$	−0.236068			−0.236068
$77$		0			0
$78$	1.90211			1.90211
$79$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$79$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$		0			0
$83$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$83$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.17557			−1.17557
$88$		−	0.726543i		−	0.726543i
$89$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$89$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$90$		0			0
$91$		0			0
$92$	−0.138757	+	0.427051i	−0.138757	+	0.427051i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$97$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$97$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$98$	1.17557			1.17557
$99$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$100$	0.381966			0.381966
$101$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$101$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$102$	0.690983	+	2.12663i	0.690983	+	2.12663i
$103$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$103$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$104$	0.951057	+	0.690983i	0.951057	+	0.690983i
$105$		0			0
$106$	0.427051	−	1.31433i	0.427051	−	1.31433i
$107$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$107$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$108$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$109$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$109$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$113$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$114$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$115$		0			0
$116$	0.363271	+	0.263932i	0.363271	+	0.263932i
$117$	0.500000	−	1.53884i	0.500000	−	1.53884i
$118$	−0.690983	−	2.12663i	−0.690983	−	2.12663i
$119$		0			0
$120$		0			0
$121$	0.809017	+	0.587785i	0.809017	+	0.587785i
$122$	1.17557			1.17557
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$127$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$128$	0.363271	−	1.11803i	0.363271	−	1.11803i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	0.363271	+	0.118034i	0.363271	+	0.118034i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.427051	+	1.31433i	−0.427051	+	1.31433i
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$	1.11803	+	0.812299i	1.11803	+	0.812299i
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$144$	−1.23607			−1.23607
$145$		0			0
$146$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$147$	0.309017	−	0.951057i	0.309017	−	0.951057i
$148$		0			0
$149$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$149$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$150$	0.363271	−	1.11803i	0.363271	−	1.11803i
$151$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$151$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$152$	−0.363271	+	0.263932i	−0.363271	+	0.263932i
$153$	1.90211			1.90211
$154$		0			0
$155$		0			0
$156$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$		0			0
$159$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$160$		0			0
$161$		0			0
$162$	0.363271	+	1.11803i	0.363271	+	1.11803i
$163$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$163$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$167$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$168$		0			0
$169$	0.500000	−	1.53884i	0.500000	−	1.53884i
$170$		0			0
$171$	0.500000	+	0.363271i	0.500000	+	0.363271i
$172$		0			0
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$	1.11803	−	0.812299i	1.11803	−	0.812299i
$175$		0			0
$176$	0.726543	+	1.00000i	0.726543	+	1.00000i
$177$	−1.90211			−1.90211
$178$	−1.80902	+	1.31433i	−1.80902	+	1.31433i
$179$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$179$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$180$		0			0
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$	0.309017	−	0.951057i	0.309017	−	0.951057i
$184$	0.263932	+	0.812299i	0.263932	+	0.812299i
$185$		0			0
$186$		0			0
$187$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$191$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$192$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$193$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$193$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$194$	−0.726543	+	2.23607i	−0.726543	+	2.23607i
$195$		0			0
$196$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.690983	−	0.951057i	0.690983	−	0.951057i
$199$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$199$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$200$	0.587785	−	0.427051i	0.587785	−	0.427051i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.587785	−	0.427051i	−0.587785	−	0.427051i
$205$		0			0
$206$	0.587785	+	1.80902i	0.587785	+	1.80902i
$207$	0.951057	−	0.690983i	0.951057	−	0.690983i
$208$	−2.00000			−2.00000
$209$		−	0.618034i		−	0.618034i
$210$		0			0
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$	0.138757	+	0.427051i	0.138757	+	0.427051i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$217$		0			0
$218$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$219$	−1.61803			−1.61803
$220$		0			0
$221$	3.07768			3.07768
$222$		0			0
$223$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$223$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$226$		0			0
$227$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$227$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$228$	−0.0729490	−	0.224514i	−0.0729490	−	0.224514i
$229$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$229$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	0.854102			0.854102
$233$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$233$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$234$	0.587785	+	1.80902i	0.587785	+	1.80902i
$235$		0			0
$236$	0.587785	+	0.427051i	0.587785	+	0.427051i
$237$		0			0
$238$		0			0
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$		0			0
$241$	−2.00000			−2.00000			−1.00000			$\pi$
$241$	−2.00000			−2.00000			−1.00000			$\pi$
$242$	−1.17557			−1.17557
$243$	1.00000			1.00000
$244$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$245$		0			0
$246$		0			0
$247$	0.809017	+	0.587785i	0.809017	+	0.587785i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.53884	+	1.11803i	−1.53884	+	1.11803i	−0.587785	+	0.809017i	$0.700000\pi$
$251$	−1.53884	+	1.11803i	−1.53884	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$252$		0			0
$253$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$254$	−2.35114			−2.35114
$255$		0			0
$256$	0.309017	+	0.951057i	0.309017	+	0.951057i
$257$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$257$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	0.690983	−	0.224514i	0.690983	−	0.224514i
$265$		0			0
$266$		0			0
$267$	0.587785	+	1.80902i	0.587785	+	1.80902i
$268$		0			0
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$		0			0
$271$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$271$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$272$	−0.726543	−	2.23607i	−0.726543	−	2.23607i
$273$		0			0
$274$		0			0
$275$			1.00000i			1.00000i
$276$	−0.449028			−0.449028
$277$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$277$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.951057	+	0.690983i	0.951057	+	0.690983i	0.951057	−	0.309017i	$-0.100000\pi$
$281$	0.951057	+	0.690983i	0.951057	+	0.690983i			1.00000i	$0.5\pi$
$282$		0			0
$283$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$283$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$284$		0			0
$285$		0			0
$286$	1.11803	−	1.53884i	1.11803	−	1.53884i
$287$		0			0
$288$	0.587785	−	0.427051i	0.587785	−	0.427051i
$289$	0.809017	+	2.48990i	0.809017	+	2.48990i
$290$		0			0
$291$	1.61803	+	1.17557i	1.61803	+	1.17557i
$292$	0.500000	+	0.363271i	0.500000	+	0.363271i
$293$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$293$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$294$	0.363271	+	1.11803i	0.363271	+	1.11803i
$295$		0			0
$296$		0			0
$297$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$298$		0			0
$299$	1.53884	−	1.11803i	1.53884	−	1.11803i
$300$	0.118034	+	0.363271i	0.118034	+	0.363271i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.236068	−	0.726543i	0.236068	−	0.726543i
$305$		0			0
$306$	−1.80902	+	1.31433i	−1.80902	+	1.31433i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	1.61803			1.61803
$310$		0			0
$311$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$311$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$312$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$313$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$313$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$317$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$318$	1.38197			1.38197
$319$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$324$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$325$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$326$	0.587785	−	1.80902i	0.587785	−	1.80902i
$327$	0.190983	+	0.587785i	0.190983	+	0.587785i
$328$		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		0.309017	−	0.951057i	$-0.400000\pi$
$337$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$338$	0.587785	+	1.80902i	0.587785	+	1.80902i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−0.726543			−0.726543
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$347$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$348$	−0.138757	+	0.427051i	−0.138757	+	0.427051i
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$		0			0
$351$	1.61803			1.61803
$352$	−0.690983	−	0.224514i	−0.690983	−	0.224514i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	1.80902	−	1.31433i	1.80902	−	1.31433i
$355$		0			0
$356$	0.224514	−	0.690983i	0.224514	−	0.690983i
$357$		0			0
$358$		0			0
$359$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$359$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$360$		0			0
$361$	0.500000	−	0.363271i	0.500000	−	0.363271i
$362$		0			0
$363$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$364$		0			0
$365$		0			0
$366$	0.363271	+	1.11803i	0.363271	+	1.11803i
$367$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$367$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$368$	−1.17557	−	0.854102i	−1.17557	−	0.854102i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	2.12663	+	0.690983i	2.12663	+	0.690983i
$375$		0			0
$376$		0			0
$377$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$378$		0			0
$379$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$379$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$380$		0			0
$381$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$382$	−0.690983	−	2.12663i	−0.690983	−	2.12663i
$383$	−1.53884	+	1.11803i	−1.53884	+	1.11803i	−0.587785	+	0.809017i	$0.700000\pi$
$383$	−1.53884	+	1.11803i	−1.53884	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$384$	1.17557			1.17557
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.236068	−	0.726543i	−0.236068	−	0.726543i
$389$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$389$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$390$		0			0
$391$	1.80902	+	1.31433i	1.80902	+	1.31433i
$392$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$393$		0			0
$394$		0			0
$395$		0			0
$396$			0.381966i			0.381966i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$399$		0			0
$400$	−0.381966	+	1.17557i	−0.381966	+	1.17557i
$401$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$401$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.38197			−1.38197
$409$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$409$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$		0			0
$412$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$413$		0			0
$414$	−0.427051	+	1.31433i	−0.427051	+	1.31433i
$415$		0			0
$416$	0.951057	−	0.690983i	0.951057	−	0.690983i
$417$		0			0
$418$	0.427051	+	0.587785i	0.427051	+	0.587785i
$419$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$419$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$420$		0			0
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$		0			0
$424$	0.690983	+	0.502029i	0.690983	+	0.502029i
$425$	0.587785	−	1.80902i	0.587785	−	1.80902i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$		0			0
$435$		0			0
$436$	0.0729490	−	0.224514i	0.0729490	−	0.224514i
$437$	0.224514	+	0.690983i	0.224514	+	0.690983i
$438$	1.53884	−	1.11803i	1.53884	−	1.11803i
$439$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$439$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$440$		0			0
$441$	1.00000			1.00000
$442$	−2.92705	+	2.12663i	−2.92705	+	2.12663i
$443$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$443$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$449$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$450$	1.17557			1.17557
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.363271	−	0.263932i	−0.363271	−	0.263932i
$457$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$457$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$458$	0.587785	−	1.80902i	0.587785	−	1.80902i
$459$	0.587785	+	1.80902i	0.587785	+	1.80902i
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$463$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$464$	−1.17557	+	0.854102i	−1.17557	+	0.854102i
$465$		0			0
$466$	−0.690983	+	2.12663i	−0.690983	+	2.12663i
$467$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$467$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$468$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.38197			1.38197
$473$		0			0
$474$		0			0
$475$	0.500000	−	0.363271i	0.500000	−	0.363271i
$476$		0			0
$477$	0.363271	−	1.11803i	0.363271	−	1.11803i
$478$		0			0
$479$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$479$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$480$		0			0
$481$		0			0
$482$	1.90211	−	1.38197i	1.90211	−	1.38197i
$483$		0			0
$484$	0.309017	−	0.224514i	0.309017	−	0.224514i
$485$		0			0
$486$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$487$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$487$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$488$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$489$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$490$		0			0
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$	1.80902	−	1.31433i	1.80902	−	1.31433i
$494$	−1.17557			−1.17557
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$499$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$500$		0			0
$501$		0			0
$502$	0.690983	−	2.12663i	0.690983	−	2.12663i
$503$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$503$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$504$		0			0
$505$		0			0
$506$	1.31433	−	0.427051i	1.31433	−	0.427051i
$507$	1.61803			1.61803
$508$	0.618034	−	0.449028i	0.618034	−	0.449028i
$509$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$509$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$521$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$522$	1.11803	+	0.812299i	1.11803	+	0.812299i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.726543	+	1.00000i	−0.726543	+	1.00000i
$529$	0.381966			0.381966
$530$		0			0
$531$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$532$		0			0
$533$		0			0
$534$	−1.80902	−	1.31433i	−1.80902	−	1.31433i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$540$		0			0
$541$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$541$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$542$	0.224514	+	0.690983i	0.224514	+	0.690983i
$543$		0			0
$544$	1.11803	+	0.812299i	1.11803	+	0.812299i
$545$		0			0
$546$		0			0
$547$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$547$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$548$		0			0
$549$	1.00000			1.00000
$550$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$551$	0.726543			0.726543
$552$	−0.690983	+	0.502029i	−0.690983	+	0.502029i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$557$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.11803	−	1.53884i	1.11803	−	1.53884i
$562$	−1.38197			−1.38197
$563$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$563$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$		0			0
$566$	−0.587785	−	0.427051i	−0.587785	−	0.427051i
$567$		0			0
$568$		0			0
$569$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$569$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$570$		0			0
$571$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$571$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$572$			0.618034i			0.618034i
$573$	−1.90211			−1.90211
$574$		0			0
$575$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$576$	0.118034	−	0.363271i	0.118034	−	0.363271i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	−2.48990	−	1.80902i	−2.48990	−	1.80902i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	−2.35114			−2.35114
$583$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$584$	1.17557			1.17557
$585$		0			0
$586$		0			0
$587$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$587$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$588$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$593$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$594$	1.11803	+	0.363271i	1.11803	+	0.363271i
$595$		0			0
$596$		0			0
$597$	0.190983	+	0.587785i	0.190983	+	0.587785i
$598$	−0.690983	+	2.12663i	−0.690983	+	2.12663i
$599$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$599$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$600$	0.587785	+	0.427051i	0.587785	+	0.427051i
$601$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$601$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$607$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$608$	0.138757	+	0.427051i	0.138757	+	0.427051i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.224514	−	0.690983i	0.224514	−	0.690983i
$613$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$613$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$619$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$619$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$620$		0			0
$621$	0.951057	+	0.690983i	0.951057	+	0.690983i
$622$		0			0
$623$		0			0
$624$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$625$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$626$		0			0
$627$	0.587785	−	0.190983i	0.587785	−	0.190983i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.363271	+	0.263932i	−0.363271	+	0.263932i
$637$	1.61803			1.61803
$638$		−	1.38197i		−	1.38197i
$639$		0			0
$640$		0			0
$641$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$641$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$642$		0			0
$643$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$643$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$644$		0			0
$645$		0			0
$646$	−0.427051	−	1.31433i	−0.427051	−	1.31433i
$647$	0.951057	−	0.690983i	0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$647$	0.951057	−	0.690983i	0.951057	−	0.690983i	0.951057	+	0.309017i	$0.100000\pi$
$648$	−0.726543			−0.726543
$649$	−1.11803	+	1.53884i	−1.11803	+	1.53884i
$650$	1.90211			1.90211
$651$		0			0
$652$	0.190983	+	0.587785i	0.190983	+	0.587785i
$653$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$653$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$654$	−0.587785	−	0.427051i	−0.587785	−	0.427051i
$655$		0			0
$656$		0			0
$657$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$658$		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
$663$	0.951057	+	2.92705i	0.951057	+	2.92705i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.427051	−	1.31433i	0.427051	−	1.31433i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$672$		0			0
$673$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$673$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$674$		0			0
$675$	0.309017	−	0.951057i	0.309017	−	0.951057i
$676$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$677$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$677$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.190983	−	0.138757i	0.190983	−	0.138757i
$685$		0			0
$686$		0			0
$687$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$688$		0			0
$689$	0.587785	−	1.80902i	0.587785	−	1.80902i
$690$		0			0
$691$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$691$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.263932	+	0.812299i	0.263932	+	0.812299i
$697$		0			0
$698$		0			0
$699$	1.53884	+	1.11803i	1.53884	+	1.11803i
$700$		0			0
$701$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$701$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$702$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$703$		0			0
$704$	−0.363271	+	0.118034i	−0.363271	+	0.118034i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$		0			0
$712$	−0.427051	−	1.31433i	−0.427051	−	1.31433i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−0.690983	−	2.12663i	−0.690983	−	2.12663i
$719$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$719$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$		0			0
$722$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$723$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$724$		0			0
$725$	−1.17557			−1.17557
$726$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$727$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$727$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$		0			0
$731$		0			0
$732$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$733$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$733$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$734$	−0.726543	−	2.23607i	−0.726543	−	2.23607i
$735$		0			0
$736$	0.854102			0.854102
$737$		0			0
$738$		0			0
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$742$		0			0
$743$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$743$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$	−0.690983	+	0.224514i	−0.690983	+	0.224514i
$749$		0			0
$750$		0			0
$751$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$751$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$752$		0			0
$753$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$754$	1.80902	+	1.31433i	1.80902	+	1.31433i
$755$		0			0
$756$		0			0
$757$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$757$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$758$	−1.90211			−1.90211
$759$		−	1.17557i		−	1.17557i
$760$		0			0
$761$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$761$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$762$	−0.726543	−	2.23607i	−0.726543	−	2.23607i
$763$		0			0
$764$	0.587785	+	0.427051i	0.587785	+	0.427051i
$765$		0			0
$766$	0.690983	−	2.12663i	0.690983	−	2.12663i
$767$	−0.951057	−	2.92705i	−0.951057	−	2.92705i
$768$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$		0			0
$775$		0			0
$776$	−1.17557	−	0.854102i	−1.17557	−	0.854102i
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−2.62866			−2.62866
$783$	0.951057	−	0.690983i	0.951057	−	0.690983i
$784$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$785$		0			0
$786$		0			0
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.427051	+	0.587785i	0.427051	+	0.587785i
$793$	1.61803			1.61803
$794$		0			0
$795$		0			0
$796$	0.0729490	−	0.224514i	0.0729490	−	0.224514i
$797$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$797$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$798$		0			0
$799$		0			0
$800$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$801$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$802$	1.38197			1.38197
$803$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$809$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$		0			0
$813$	0.618034			0.618034
$814$		0			0
$815$		0			0
$816$	1.90211	−	1.38197i	1.90211	−	1.38197i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$821$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$	−1.17557			−1.17557
$825$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$826$		0			0
$827$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$827$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$828$	−0.138757	−	0.427051i	−0.138757	−	0.427051i
$829$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$829$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$830$		0			0
$831$		0			0
$832$	0.190983	−	0.587785i	0.190983	−	0.587785i
$833$	0.587785	+	1.80902i	0.587785	+	1.80902i
$834$		0			0
$835$		0			0
$836$	−0.224514	−	0.0729490i	−0.224514	−	0.0729490i
$837$		0			0
$838$	−1.11803	+	0.812299i	−1.11803	+	0.812299i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$842$		0			0
$843$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$	−1.45309			−1.45309
$849$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$850$	0.690983	+	2.12663i	0.690983	+	2.12663i
$851$		0			0
$852$		0			0
$853$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$853$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$	1.80902	+	0.587785i	1.80902	+	0.587785i
$859$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$859$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$863$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$864$	0.587785	+	0.427051i	0.587785	+	0.427051i
$865$		0			0
$866$		0			0
$867$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.138757	−	0.427051i	−0.138757	−	0.427051i
$873$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$874$	−0.690983	−	0.502029i	−0.690983	−	0.502029i
$875$		0			0
$876$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$	1.53884	−	1.11803i	1.53884	−	1.11803i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$	0.363271	−	1.11803i	0.363271	−	1.11803i
$885$		0			0
$886$		0			0
$887$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$887$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.587785	−	0.809017i	0.587785	−	0.809017i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.53884	+	1.11803i	1.53884	+	1.11803i
$898$		0			0
$899$		0			0
$900$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$901$	2.23607			2.23607
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$907$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$	0.763932			0.763932
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.190983	+	0.587785i	0.190983	+	0.587785i
$917$		0			0
$918$	−1.80902	−	1.31433i	−1.80902	−	1.31433i
$919$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$919$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.587785	−	0.427051i	0.587785	−	0.427051i
$927$	0.500000	+	1.53884i	0.500000	+	1.53884i
$928$	0.263932	−	0.812299i	0.263932	−	0.812299i
$929$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$929$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$930$		0			0
$931$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$932$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$933$		0			0
$934$	−2.23607			−2.23607
$935$		0			0
$936$	−1.17557			−1.17557
$937$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$937$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$941$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$942$		0			0
$943$		0			0
$944$	−1.90211	+	1.38197i	−1.90211	+	1.38197i
$945$		0			0
$946$		0			0
$947$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$947$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$948$		0			0
$949$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$950$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$951$		0			0
$952$		0			0
$953$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$953$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$954$	0.427051	+	1.31433i	0.427051	+	1.31433i
$955$		0			0
$956$		0			0
$957$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.309017	−	0.951057i	0.309017	−	0.951057i
$962$		0			0
$963$		0			0
$964$	−0.236068	+	0.726543i	−0.236068	+	0.726543i
$965$		0			0
$966$		0			0
$967$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$967$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$968$	0.224514	−	0.690983i	0.224514	−	0.690983i
$969$	−1.17557			−1.17557
$970$		0			0
$971$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$971$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$972$	0.118034	−	0.363271i	0.118034	−	0.363271i
$973$		0			0
$974$	1.53884	+	1.11803i	1.53884	+	1.11803i
$975$	0.500000	−	1.53884i	0.500000	−	1.53884i
$976$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$	1.90211			1.90211
$979$	1.80902	+	0.587785i	1.80902	+	0.587785i
$980$		0			0
$981$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$982$		0			0
$983$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$983$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$984$		0			0
$985$		0			0
$986$	−0.812299	+	2.50000i	−0.812299	+	2.50000i
$987$		0			0
$988$	0.309017	−	0.224514i	0.309017	−	0.224514i
$989$		0			0
$990$		0			0
$991$	−2.00000			−2.00000			−1.00000			$\pi$
$991$	−2.00000			−2.00000			−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.1.bm.c.1829.1	yes	8
3.2	odd	2	inner	2013.1.bm.c.1829.2	yes	8
11.4	even	5	inner	2013.1.bm.c.1280.1	✓	8
33.26	odd	10	inner	2013.1.bm.c.1280.2	yes	8
61.60	even	2	inner	2013.1.bm.c.1829.2	yes	8
183.182	odd	2	CM	2013.1.bm.c.1829.1	yes	8
671.609	even	10	inner	2013.1.bm.c.1280.2	yes	8
2013.1280	odd	10	inner	2013.1.bm.c.1280.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.1.bm.c.1280.1	✓	8	11.4	even	5	inner
2013.1.bm.c.1280.1	✓	8	2013.1280	odd	10	inner
2013.1.bm.c.1280.2	yes	8	33.26	odd	10	inner
2013.1.bm.c.1280.2	yes	8	671.609	even	10	inner
2013.1.bm.c.1829.1	yes	8	1.1	even	1	trivial
2013.1.bm.c.1829.1	yes	8	183.182	odd	2	CM
2013.1.bm.c.1829.2	yes	8	3.2	odd	2	inner
2013.1.bm.c.1829.2	yes	8	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.690983i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.118034 - 0.363271i) q^{4} +(-0.951057 - 0.690983i) q^{6} +(-0.224514 - 0.690983i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.690983i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.118034 - 0.363271i) q^{4} +(-0.951057 - 0.690983i) q^{6} +(-0.224514 - 0.690983i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.951057 + 0.309017i) q^{11} +0.381966 q^{12} +(-1.30902 + 0.951057i) q^{13} +(1.00000 + 0.726543i) q^{16} +(-1.53884 - 1.11803i) q^{17} +(0.363271 - 1.11803i) q^{18} +(-0.190983 - 0.587785i) q^{19} +(-1.11803 + 0.363271i) q^{22} -1.17557 q^{23} +(0.587785 - 0.427051i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.587785 - 1.80902i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.363271 + 1.11803i) q^{29} -0.726543 q^{32} +1.00000i q^{33} +2.23607 q^{34} +(0.118034 + 0.363271i) q^{36} +(0.587785 + 0.427051i) q^{38} +(-1.30902 - 0.951057i) q^{39} +(0.224514 - 0.309017i) q^{44} +(1.11803 - 0.812299i) q^{46} +(-0.381966 + 1.17557i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.951057 - 0.690983i) q^{50} +(0.587785 - 1.80902i) q^{51} +(0.190983 + 0.587785i) q^{52} +(-0.951057 + 0.690983i) q^{53} +1.17557 q^{54} +(0.500000 - 0.363271i) q^{57} +(-0.427051 - 1.31433i) q^{58} +(-0.587785 + 1.80902i) q^{59} +(-0.809017 - 0.587785i) q^{61} +(-0.309017 + 0.224514i) q^{64} +(-0.690983 - 0.951057i) q^{66} +(-0.587785 + 0.427051i) q^{68} +(-0.363271 - 1.11803i) q^{69} +(0.587785 + 0.427051i) q^{72} +(-0.500000 + 1.53884i) q^{73} +(-0.809017 + 0.587785i) q^{75} -0.236068 q^{76} +1.90211 q^{78} +(0.309017 - 0.951057i) q^{81} -1.17557 q^{87} -0.726543i q^{88} +1.90211 q^{89} +(-0.138757 + 0.427051i) q^{92} +(-0.224514 - 0.690983i) q^{96} +(1.61803 - 1.17557i) q^{97} +1.17557 q^{98} +(-0.951057 + 0.309017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 8 * q^4 - 2 * q^9	\( 8 q - 2 q^{3} - 8 q^{4} - 2 q^{9} + 12 q^{12} - 6 q^{13} + 8 q^{16} - 6 q^{19} - 2 q^{25} - 2 q^{27} - 8 q^{36} - 6 q^{39} - 12 q^{48} - 2 q^{49} + 6 q^{52} + 4 q^{57} + 10 q^{58} - 2 q^{61} + 2 q^{64} - 10 q^{66} - 4 q^{73} - 2 q^{75} + 16 q^{76} - 2 q^{81} + 4 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 - 8 * q^4 - 2 * q^9 + 12 * q^12 - 6 * q^13 + 8 * q^16 - 6 * q^19 - 2 * q^25 - 2 * q^27 - 8 * q^36 - 6 * q^39 - 12 * q^48 - 2 * q^49 + 6 * q^52 + 4 * q^57 + 10 * q^58 - 2 * q^61 + 2 * q^64 - 10 * q^66 - 4 * q^73 - 2 * q^75 + 16 * q^76 - 2 * q^81 + 4 * q^97

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