LMFDB - Embedded newform 2700.1.ca.a.1307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2700,1,Mod(407,2700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2700, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 2, 9]))

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

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

chi := DirichletCharacter("2700.407");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2700.ca (of order $36$, degree $12$, 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:	$1.34747553411$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{36})$
Coefficient field:	$\Q(\zeta_{72})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{12} + 1 $ x^24 - x^12 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{18}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{18} + \cdots)$

Embedding invariants

Embedding label			1307.2
Root			$-0.422618 - 0.906308i$ of defining polynomial
Character	$\chi$	$=$	2700.1307
Dual form			2700.1.ca.a.2543.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0871557 + 0.996195i) q^{2} +(0.906308 - 0.422618i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.500000 + 0.866025i) q^{6} +(0.392349 + 0.560333i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-0.819152 + 0.573576i) q^{12} +(-0.524005 + 0.439693i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.819152 + 0.573576i) q^{18} +(0.592396 + 0.342020i) q^{21} +(0.284489 + 0.199201i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(0.258819 - 0.965926i) q^{27} +(-0.483690 - 0.483690i) q^{28} +(1.50881 + 1.26604i) q^{29} +(0.422618 + 0.906308i) q^{32} +(-0.500000 + 0.866025i) q^{36} +(-0.826352 - 0.984808i) q^{41} +(-0.289088 + 0.619951i) q^{42} +(1.56977 + 0.731996i) q^{43} +(-0.173648 + 0.300767i) q^{46} +(-1.25501 + 0.878770i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.181985 - 0.500000i) q^{49} +(0.984808 + 0.173648i) q^{54} +(0.439693 - 0.524005i) q^{56} +(-1.12973 + 1.61341i) q^{58} +(0.326352 - 1.85083i) q^{61} +(0.681437 + 0.0596180i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.112045 + 1.28068i) q^{67} +(0.342020 + 0.0603074i) q^{69} +(-0.906308 - 0.422618i) q^{72} +(-0.173648 - 0.984808i) q^{81} +(0.909039 - 0.909039i) q^{82} +(-1.52626 + 0.133530i) q^{83} +(-0.642788 - 0.233956i) q^{84} +(-0.592396 + 1.62760i) q^{86} +(1.90250 + 0.509774i) q^{87} +(0.642788 - 1.11334i) q^{89} +(-0.314757 - 0.146774i) q^{92} +(-0.984808 - 1.17365i) q^{94} +(0.766044 + 0.642788i) q^{96} +(0.513958 + 0.137715i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{6} - 12 q^{36} - 24 q^{41} - 12 q^{56} + 12 q^{61}+O(q^{100}) $ 24 * q + 12 * q^6 - 12 * q^36 - 24 * q^41 - 12 * q^56 + 12 * q^61

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times$.

$n$	$1001$	$1351$	$2377$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0871557	+	0.996195i	0.0871557	+	0.996195i
$2$	0.0871557	+	0.996195i	0.0871557	+	0.996195i
$3$	0.906308	−	0.422618i	0.906308	−	0.422618i
$3$	0.906308	−	0.422618i	0.906308	−	0.422618i
$4$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$5$		0			0
$5$		0			0
$6$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$	0.392349	+	0.560333i	0.392349	+	0.560333i	0.965926	−	0.258819i	$-0.0833333\pi$
$7$	0.392349	+	0.560333i	0.392349	+	0.560333i	−0.573576	+	0.819152i	$0.694444\pi$
$8$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$9$	0.642788	−	0.766044i	0.642788	−	0.766044i
$10$		0			0
$11$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$11$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$12$	−0.819152	+	0.573576i	−0.819152	+	0.573576i
$13$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$13$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$14$	−0.524005	+	0.439693i	−0.524005	+	0.439693i
$15$		0			0
$16$	0.939693	−	0.342020i	0.939693	−	0.342020i
$17$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$17$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$18$	0.819152	+	0.573576i	0.819152	+	0.573576i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	0.592396	+	0.342020i	0.592396	+	0.342020i
$22$		0			0
$23$	0.284489	+	0.199201i	0.284489	+	0.199201i	0.707107	−	0.707107i	$-0.250000\pi$
$23$	0.284489	+	0.199201i	0.284489	+	0.199201i	−0.422618	+	0.906308i	$0.638889\pi$
$24$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$25$		0			0
$26$		0			0
$27$	0.258819	−	0.965926i	0.258819	−	0.965926i
$28$	−0.483690	−	0.483690i	−0.483690	−	0.483690i
$29$	1.50881	+	1.26604i	1.50881	+	1.26604i	0.866025	+	0.500000i	$0.166667\pi$
$29$	1.50881	+	1.26604i	1.50881	+	1.26604i	0.642788	+	0.766044i	$0.277778\pi$
$30$		0			0
$31$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$31$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$32$	0.422618	+	0.906308i	0.422618	+	0.906308i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$37$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$41$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	−1.00000			$\pi$
$42$	−0.289088	+	0.619951i	−0.289088	+	0.619951i
$43$	1.56977	+	0.731996i	1.56977	+	0.731996i	0.996195	−	0.0871557i	$-0.0277778\pi$
$43$	1.56977	+	0.731996i	1.56977	+	0.731996i	0.573576	+	0.819152i	$0.305556\pi$
$44$		0			0
$45$		0			0
$46$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$47$	−1.25501	+	0.878770i	−1.25501	+	0.878770i	−0.996195	−	0.0871557i	$-0.972222\pi$
$47$	−1.25501	+	0.878770i	−1.25501	+	0.878770i	−0.258819	+	0.965926i	$0.583333\pi$
$48$	0.707107	−	0.707107i	0.707107	−	0.707107i
$49$	0.181985	−	0.500000i	0.181985	−	0.500000i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$	0.984808	+	0.173648i	0.984808	+	0.173648i
$55$		0			0
$56$	0.439693	−	0.524005i	0.439693	−	0.524005i
$57$		0			0
$58$	−1.12973	+	1.61341i	−1.12973	+	1.61341i
$59$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$59$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$60$		0			0
$61$	0.326352	−	1.85083i	0.326352	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$61$	0.326352	−	1.85083i	0.326352	−	1.85083i	0.500000	−	0.866025i	$-0.333333\pi$
$62$		0			0
$63$	0.681437	+	0.0596180i	0.681437	+	0.0596180i
$64$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$65$		0			0
$66$		0			0
$67$	−0.112045	+	1.28068i	−0.112045	+	1.28068i	0.707107	+	0.707107i	$0.250000\pi$
$67$	−0.112045	+	1.28068i	−0.112045	+	1.28068i	−0.819152	+	0.573576i	$0.805556\pi$
$68$		0			0
$69$	0.342020	+	0.0603074i	0.342020	+	0.0603074i
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−0.906308	−	0.422618i	−0.906308	−	0.422618i
$73$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$73$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$79$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$80$		0			0
$81$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$82$	0.909039	−	0.909039i	0.909039	−	0.909039i
$83$	−1.52626	+	0.133530i	−1.52626	+	0.133530i	−0.819152	−	0.573576i	$-0.805556\pi$
$83$	−1.52626	+	0.133530i	−1.52626	+	0.133530i	−0.707107	+	0.707107i	$0.750000\pi$
$84$	−0.642788	−	0.233956i	−0.642788	−	0.233956i
$85$		0			0
$86$	−0.592396	+	1.62760i	−0.592396	+	1.62760i
$87$	1.90250	+	0.509774i	1.90250	+	0.509774i
$88$		0			0
$89$	0.642788	−	1.11334i	0.642788	−	1.11334i	−0.342020	−	0.939693i	$-0.611111\pi$
$89$	0.642788	−	1.11334i	0.642788	−	1.11334i	0.984808	−	0.173648i	$-0.0555556\pi$
$90$		0			0
$91$		0			0
$92$	−0.314757	−	0.146774i	−0.314757	−	0.146774i
$93$		0			0
$94$	−0.984808	−	1.17365i	−0.984808	−	1.17365i
$95$		0			0
$96$	0.766044	+	0.642788i	0.766044	+	0.642788i
$97$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$97$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$98$	0.513958	+	0.137715i	0.513958	+	0.137715i
$99$		0			0
$100$		0			0
$101$	−1.70574	−	0.300767i	−1.70574	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$101$	−1.70574	−	0.300767i	−1.70574	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$102$		0			0
$103$	0.731996	+	1.56977i	0.731996	+	1.56977i	0.819152	+	0.573576i	$0.194444\pi$
$103$	0.731996	+	1.56977i	0.731996	+	1.56977i	−0.0871557	+	0.996195i	$0.527778\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.32893	−	1.32893i	−1.32893	−	1.32893i	−0.906308	−	0.422618i	$-0.861111\pi$
$107$	−1.32893	−	1.32893i	−1.32893	−	1.32893i	−0.422618	−	0.906308i	$-0.638889\pi$
$108$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$109$		−	0.347296i		−	0.347296i	−0.984808	−	0.173648i	$-0.944444\pi$
$109$		−	0.347296i		−	0.347296i	0.984808	−	0.173648i	$-0.0555556\pi$
$110$		0			0
$111$		0			0
$112$	0.560333	+	0.392349i	0.560333	+	0.392349i
$113$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$113$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$114$		0			0
$115$		0			0
$116$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$122$	1.87223	+	0.163799i	1.87223	+	0.163799i
$123$	−1.16513	−	0.543308i	−1.16513	−	0.543308i
$124$		0			0
$125$		0			0
$126$			0.684040i			0.684040i
$127$	0.509774	+	1.90250i	0.509774	+	1.90250i	0.422618	+	0.906308i	$0.361111\pi$
$127$	0.509774	+	1.90250i	0.509774	+	1.90250i	0.0871557	+	0.996195i	$0.472222\pi$
$128$	−0.573576	−	0.819152i	−0.573576	−	0.819152i
$129$	1.73205			1.73205
$130$		0			0
$131$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$131$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$132$		0			0
$133$		0			0
$134$	−1.28558			−1.28558
$135$		0			0
$136$		0			0
$137$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$137$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$138$	−0.0302689	+	0.345975i	−0.0302689	+	0.345975i
$139$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$139$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$140$		0			0
$141$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$142$		0			0
$143$		0			0
$144$	0.342020	−	0.939693i	0.342020	−	0.939693i
$145$		0			0
$146$		0			0
$147$	−0.0463746	−	0.530064i	−0.0463746	−	0.530064i
$148$		0			0
$149$	−1.50881	+	1.26604i	−1.50881	+	1.26604i	−0.642788	+	0.766044i	$0.722222\pi$
$149$	−1.50881	+	1.26604i	−1.50881	+	1.26604i	−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$151$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$157$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			0.237565i			0.237565i
$162$	0.965926	−	0.258819i	0.965926	−	0.258819i
$163$	−1.22474	−	1.22474i	−1.22474	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$163$	−1.22474	−	1.22474i	−1.22474	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$164$	0.984808	+	0.826352i	0.984808	+	0.826352i
$165$		0			0
$166$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$167$	−0.146774	−	0.314757i	−0.146774	−	0.314757i	0.819152	−	0.573576i	$-0.194444\pi$
$167$	−0.146774	−	0.314757i	−0.146774	−	0.314757i	−0.965926	+	0.258819i	$0.916667\pi$
$168$	0.177043	−	0.660732i	0.177043	−	0.660732i
$169$	0.984808	+	0.173648i	0.984808	+	0.173648i
$170$		0			0
$171$		0			0
$172$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$173$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$173$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$174$	−0.342020	+	1.93969i	−0.342020	+	1.93969i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	1.16513	+	0.543308i	1.16513	+	0.543308i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$		0			0
$181$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$181$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$182$		0			0
$183$	−0.486421	−	1.81535i	−0.486421	−	1.81535i
$184$	0.118782	−	0.326352i	0.118782	−	0.326352i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.08335	−	1.08335i	1.08335	−	1.08335i
$189$	0.642788	−	0.233956i	0.642788	−	0.233956i
$190$		0			0
$191$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$191$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$192$	−0.573576	+	0.819152i	−0.573576	+	0.819152i
$193$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$193$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$194$		0			0
$195$		0			0
$196$	−0.0923963	+	0.524005i	−0.0923963	+	0.524005i
$197$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$197$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$	0.439693	+	1.20805i	0.439693	+	1.20805i
$202$	0.150958	−	1.72546i	0.150958	−	1.72546i
$203$	−0.117425	+	1.34217i	−0.117425	+	1.34217i
$204$		0			0
$205$		0			0
$206$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$207$	0.335463	−	0.0898869i	0.335463	−	0.0898869i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$211$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$212$		0			0
$213$		0			0
$214$	1.20805	−	1.43969i	1.20805	−	1.43969i
$215$		0			0
$216$	−1.00000			−1.00000
$217$		0			0
$218$	0.345975	−	0.0302689i	0.345975	−	0.0302689i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.05308	−	0.737376i	1.05308	−	0.737376i	0.0871557	−	0.996195i	$-0.472222\pi$
$223$	1.05308	−	0.737376i	1.05308	−	0.737376i	0.965926	+	0.258819i	$0.0833333\pi$
$224$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$225$		0			0
$226$		0			0
$227$	−0.906308	−	0.422618i	−0.906308	−	0.422618i	−0.0871557	−	0.996195i	$-0.527778\pi$
$227$	−0.906308	−	0.422618i	−0.906308	−	0.422618i	−0.819152	+	0.573576i	$0.805556\pi$
$228$		0			0
$229$	−0.223238	−	0.266044i	−0.223238	−	0.266044i	0.642788	−	0.766044i	$-0.277778\pi$
$229$	−0.223238	−	0.266044i	−0.223238	−	0.266044i	−0.866025	+	0.500000i	$0.833333\pi$
$230$		0			0
$231$		0			0
$232$	0.832395	−	1.78508i	0.832395	−	1.78508i
$233$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$233$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$239$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$240$		0			0
$241$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$241$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$242$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$243$	−0.573576	−	0.819152i	−0.573576	−	0.819152i
$244$			1.87939i			1.87939i
$245$		0			0
$246$	0.439693	−	1.20805i	0.439693	−	1.20805i
$247$		0			0
$248$		0			0
$249$	−1.32683	+	0.766044i	−1.32683	+	0.766044i
$250$		0			0
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	−0.681437	+	0.0596180i	−0.681437	+	0.0596180i
$253$		0			0
$254$	−1.85083	+	0.673648i	−1.85083	+	0.673648i
$255$		0			0
$256$	0.766044	−	0.642788i	0.766044	−	0.642788i
$257$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$257$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$258$	0.150958	+	1.72546i	0.150958	+	1.72546i
$259$		0			0
$260$		0			0
$261$	1.93969	−	0.342020i	1.93969	−	0.342020i
$262$		0			0
$263$	−0.573576	−	0.819152i	−0.573576	−	0.819152i	0.422618	−	0.906308i	$-0.361111\pi$
$263$	−0.573576	−	0.819152i	−0.573576	−	0.819152i	−0.996195	+	0.0871557i	$0.972222\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.112045	−	1.28068i	0.112045	−	1.28068i
$268$	−0.112045	−	1.28068i	−0.112045	−	1.28068i
$269$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$269$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.347296			−0.347296
$277$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$277$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.233956	+	0.642788i	0.233956	+	0.642788i	1.00000			$0$
$281$	0.233956	+	0.642788i	0.233956	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$282$	−1.38854	−	0.647489i	−1.38854	−	0.647489i
$283$	−1.96212	−	0.171663i	−1.96212	−	0.171663i	−0.965926	−	0.258819i	$-0.916667\pi$
$283$	−1.96212	−	0.171663i	−1.96212	−	0.171663i	−0.996195	+	0.0871557i	$0.972222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.227602	−	0.849421i	0.227602	−	0.849421i
$288$	0.965926	+	0.258819i	0.965926	+	0.258819i
$289$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$293$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$294$	0.524005	−	0.0923963i	0.524005	−	0.0923963i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.39273	−	1.39273i	−1.39273	−	1.39273i
$299$		0			0
$300$		0			0
$301$	0.205737	+	1.16679i	0.205737	+	1.16679i
$302$		0			0
$303$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.90250	−	0.509774i	−1.90250	−	0.509774i	−0.996195	−	0.0871557i	$-0.972222\pi$
$307$	−1.90250	−	0.509774i	−1.90250	−	0.509774i	−0.906308	−	0.422618i	$-0.861111\pi$
$308$		0			0
$309$	1.32683	+	1.11334i	1.32683	+	1.11334i
$310$		0			0
$311$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$311$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$312$		0			0
$313$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$313$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$317$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$322$	−0.236661	+	0.0207051i	−0.236661	+	0.0207051i
$323$		0			0
$324$	0.342020	+	0.939693i	0.342020	+	0.939693i
$325$		0			0
$326$	1.11334	−	1.32683i	1.11334	−	1.32683i
$327$	−0.146774	−	0.314757i	−0.146774	−	0.314757i
$328$	−0.737376	+	1.05308i	−0.737376	+	1.05308i
$329$	−0.984808	−	0.358441i	−0.984808	−	0.358441i
$330$		0			0
$331$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$331$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$332$	1.47988	−	0.396534i	1.47988	−	0.396534i
$333$		0			0
$334$	0.300767	−	0.173648i	0.300767	−	0.173648i
$335$		0			0
$336$	0.673648	+	0.118782i	0.673648	+	0.118782i
$337$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$337$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$338$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.01230	−	0.271245i	1.01230	−	0.271245i
$344$	0.300767	−	1.70574i	0.300767	−	1.70574i
$345$		0			0
$346$		0			0
$347$	0.573576	−	0.819152i	0.573576	−	0.819152i	−0.422618	−	0.906308i	$-0.638889\pi$
$347$	0.573576	−	0.819152i	0.573576	−	0.819152i	0.996195	+	0.0871557i	$0.0277778\pi$
$348$	−1.96212	−	0.171663i	−1.96212	−	0.171663i
$349$	−0.984808	+	1.17365i	−0.984808	+	1.17365i			1.00000i	$0.5\pi$
$349$	−0.984808	+	1.17365i	−0.984808	+	1.17365i	−0.984808	+	0.173648i	$0.944444\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$353$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$354$		0			0
$355$		0			0
$356$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$357$		0			0
$358$		0			0
$359$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$359$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$360$		0			0
$361$	0.500000	+	0.866025i	0.500000	+	0.866025i
$362$	1.70330	+	0.794263i	1.70330	+	0.794263i
$363$	−0.422618	+	0.906308i	−0.422618	+	0.906308i
$364$		0			0
$365$		0			0
$366$	1.76604	−	0.642788i	1.76604	−	0.642788i
$367$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$367$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$368$	0.335463	+	0.0898869i	0.335463	+	0.0898869i
$369$	−1.28558			−1.28558
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$373$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$374$		0			0
$375$		0			0
$376$	1.17365	+	0.984808i	1.17365	+	0.984808i
$377$		0			0
$378$	0.289088	+	0.619951i	0.289088	+	0.619951i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	1.26604	+	1.50881i	1.26604	+	1.50881i
$382$		0			0
$383$	−0.906308	+	0.422618i	−0.906308	+	0.422618i	−0.819152	−	0.573576i	$-0.805556\pi$
$383$	−0.906308	+	0.422618i	−0.906308	+	0.422618i	−0.0871557	+	0.996195i	$0.527778\pi$
$384$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$385$		0			0
$386$		0			0
$387$	1.56977	−	0.731996i	1.56977	−	0.731996i
$388$		0			0
$389$	−1.20805	+	0.439693i	−1.20805	+	0.439693i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$	−1.20805	+	0.439693i	−1.20805	+	0.439693i	−0.342020	+	0.939693i	$0.611111\pi$
$390$		0			0
$391$		0			0
$392$	−0.530064	−	0.0463746i	−0.530064	−	0.0463746i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$397$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.70574	−	0.300767i	1.70574	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$401$	1.70574	−	0.300767i	1.70574	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$402$	−1.16513	+	0.543308i	−1.16513	+	0.543308i
$403$		0			0
$404$	1.73205			1.73205
$405$		0			0
$406$	−1.34730			−1.34730
$407$		0			0
$408$		0			0
$409$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$409$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$410$		0			0
$411$		0			0
$412$	−0.993464	−	1.41881i	−0.993464	−	1.41881i
$413$		0			0
$414$	0.118782	+	0.326352i	0.118782	+	0.326352i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$419$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$420$		0			0
$421$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$421$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$422$		0			0
$423$	−0.133530	+	1.52626i	−0.133530	+	1.52626i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.16513	−	0.543308i	1.16513	−	0.543308i
$428$	1.53950	+	1.07797i	1.53950	+	1.07797i
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$		0			0
$436$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$437$		0			0
$438$		0			0
$439$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$439$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$440$		0			0
$441$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$442$		0			0
$443$	−0.647489	+	1.38854i	−0.647489	+	1.38854i	0.258819	+	0.965926i	$0.416667\pi$
$443$	−0.647489	+	1.38854i	−0.647489	+	1.38854i	−0.906308	+	0.422618i	$0.861111\pi$
$444$		0			0
$445$		0			0
$446$	0.826352	+	0.984808i	0.826352	+	0.984808i
$447$	−0.832395	+	1.78508i	−0.832395	+	1.78508i
$448$	−0.619951	−	0.289088i	−0.619951	−	0.289088i
$449$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$449$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.342020	−	0.939693i	0.342020	−	0.939693i
$455$		0			0
$456$		0			0
$457$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$457$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$458$	0.245576	−	0.245576i	0.245576	−	0.245576i
$459$		0			0
$460$		0			0
$461$	−0.439693	+	0.524005i	−0.439693	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$461$	−0.439693	+	0.524005i	−0.439693	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	0.993464	−	1.41881i	0.993464	−	1.41881i	0.0871557	−	0.996195i	$-0.472222\pi$
$463$	0.993464	−	1.41881i	0.993464	−	1.41881i	0.906308	−	0.422618i	$-0.138889\pi$
$464$	1.85083	+	0.673648i	1.85083	+	0.673648i
$465$		0			0
$466$		0			0
$467$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$467$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$468$		0			0
$469$	−0.761570	+	0.439693i	−0.761570	+	0.439693i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$479$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$480$		0			0
$481$		0			0
$482$	1.07797	−	1.53950i	1.07797	−	1.53950i
$483$	0.100399	+	0.215307i	0.100399	+	0.215307i
$484$	0.642788	−	0.766044i	0.642788	−	0.766044i
$485$		0			0
$486$	0.766044	−	0.642788i	0.766044	−	0.642788i
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	−1.87223	+	0.163799i	−1.87223	+	0.163799i
$489$	−1.62760	−	0.592396i	−1.62760	−	0.592396i
$490$		0			0
$491$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$491$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$492$	1.24177	+	0.332731i	1.24177	+	0.332731i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.878770	−	1.25501i	−0.878770	−	1.25501i
$499$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$499$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$500$		0			0
$501$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$502$		0			0
$503$	1.81535	+	0.486421i	1.81535	+	0.486421i	0.996195	−	0.0871557i	$-0.0277778\pi$
$503$	1.81535	+	0.486421i	1.81535	+	0.486421i	0.819152	+	0.573576i	$0.194444\pi$
$504$	−0.118782	−	0.673648i	−0.118782	−	0.673648i
$505$		0			0
$506$		0			0
$507$	0.965926	−	0.258819i	0.965926	−	0.258819i
$508$	−0.832395	−	1.78508i	−0.832395	−	1.78508i
$509$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	−0.984808	−	0.173648i	$-0.944444\pi$
$509$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	0.866025	−	0.500000i	$-0.166667\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	+	0.707107i	0.707107	+	0.707107i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−1.70574	+	0.300767i	−1.70574	+	0.300767i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.70574	+	0.984808i	1.70574	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$521$	1.70574	+	0.984808i	1.70574	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$522$	0.509774	+	1.90250i	0.509774	+	1.90250i
$523$	0.177043	−	0.660732i	0.177043	−	0.660732i	−0.819152	−	0.573576i	$-0.805556\pi$
$523$	0.177043	−	0.660732i	0.177043	−	0.660732i	0.996195	−	0.0871557i	$-0.0277778\pi$
$524$		0			0
$525$		0			0
$526$	0.766044	−	0.642788i	0.766044	−	0.642788i
$527$		0			0
$528$		0			0
$529$	−0.300767	−	0.826352i	−0.300767	−	0.826352i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.28558			1.28558
$535$		0			0
$536$	1.26604	−	0.223238i	1.26604	−	0.223238i
$537$		0			0
$538$	0.0596180	+	0.681437i	0.0596180	+	0.681437i
$539$		0			0
$540$		0			0
$541$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$541$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$542$		0			0
$543$	0.163799	−	1.87223i	0.163799	−	1.87223i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.737376	−	1.05308i	−0.737376	−	1.05308i	−0.996195	−	0.0871557i	$-0.972222\pi$
$547$	−0.737376	−	1.05308i	−0.737376	−	1.05308i	0.258819	−	0.965926i	$-0.416667\pi$
$548$		0			0
$549$	−1.20805	−	1.43969i	−1.20805	−	1.43969i
$550$		0			0
$551$		0			0
$552$	−0.0302689	−	0.345975i	−0.0302689	−	0.345975i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$557$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.619951	+	0.289088i	−0.619951	+	0.289088i
$563$	1.25501	+	0.878770i	1.25501	+	0.878770i	0.996195	−	0.0871557i	$-0.0277778\pi$
$563$	1.25501	+	0.878770i	1.25501	+	0.878770i	0.258819	+	0.965926i	$0.416667\pi$
$564$	0.524005	−	1.43969i	0.524005	−	1.43969i
$565$		0			0
$566$		−	1.96962i		−	1.96962i
$567$	0.483690	−	0.483690i	0.483690	−	0.483690i
$568$		0			0
$569$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$569$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$570$		0			0
$571$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$571$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$572$		0			0
$573$		0			0
$574$	0.866025	+	0.152704i	0.866025	+	0.152704i
$575$		0			0
$576$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$577$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$577$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$578$	0.422618	−	0.906308i	0.422618	−	0.906308i
$579$		0			0
$580$		0			0
$581$	−0.673648	−	0.802823i	−0.673648	−	0.802823i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.53950	−	1.07797i	1.53950	−	1.07797i	0.573576	−	0.819152i	$-0.305556\pi$
$587$	1.53950	−	1.07797i	1.53950	−	1.07797i	0.965926	−	0.258819i	$-0.0833333\pi$
$588$	0.137715	+	0.513958i	0.137715	+	0.513958i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$	1.26604	−	1.50881i	1.26604	−	1.50881i
$597$		0			0
$598$		0			0
$599$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$599$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$600$		0			0
$601$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$601$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$602$	−1.14442	+	0.306647i	−1.14442	+	0.306647i
$603$	0.909039	+	0.909039i	0.909039	+	0.909039i
$604$		0			0
$605$		0			0
$606$	−0.592396	−	1.62760i	−0.592396	−	1.62760i
$607$	−0.171663	+	1.96212i	−0.171663	+	1.96212i	0.0871557	+	0.996195i	$0.472222\pi$
$607$	−0.171663	+	1.96212i	−0.171663	+	1.96212i	−0.258819	+	0.965926i	$0.583333\pi$
$608$		0			0
$609$	0.460802	+	1.26604i	0.460802	+	1.26604i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$613$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$614$	0.342020	−	1.93969i	0.342020	−	1.93969i
$615$		0			0
$616$		0			0
$617$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$617$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$618$	−0.993464	+	1.41881i	−0.993464	+	1.41881i
$619$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$619$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$620$		0			0
$621$	0.266044	−	0.223238i	0.266044	−	0.223238i
$622$		0			0
$623$	0.876039	−	0.0766435i	0.876039	−	0.0766435i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$631$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.673648	−	0.118782i	−0.673648	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$641$	−0.673648	−	0.118782i	−0.673648	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	0.486421	−	1.81535i	0.486421	−	1.81535i
$643$	0.832395	+	1.78508i	0.832395	+	1.78508i	0.573576	+	0.819152i	$0.305556\pi$
$643$	0.832395	+	1.78508i	0.832395	+	1.78508i	0.258819	+	0.965926i	$0.416667\pi$
$644$	−0.0412527	−	0.233956i	−0.0412527	−	0.233956i
$645$		0			0
$646$		0			0
$647$	0.245576	+	0.245576i	0.245576	+	0.245576i	0.819152	−	0.573576i	$-0.194444\pi$
$647$	0.245576	+	0.245576i	0.245576	+	0.245576i	−0.573576	+	0.819152i	$0.694444\pi$
$648$	−0.906308	+	0.422618i	−0.906308	+	0.422618i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.41881	+	0.993464i	1.41881	+	0.993464i
$653$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$653$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$654$	0.300767	−	0.173648i	0.300767	−	0.173648i
$655$		0			0
$656$	−1.11334	−	0.642788i	−1.11334	−	0.642788i
$657$		0			0
$658$	0.271245	−	1.01230i	0.271245	−	1.01230i
$659$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$659$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$660$		0			0
$661$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$661$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$662$		0			0
$663$		0			0
$664$	0.524005	+	1.43969i	0.524005	+	1.43969i
$665$		0			0
$666$		0			0
$667$	0.177043	+	0.660732i	0.177043	+	0.660732i
$668$	0.199201	+	0.284489i	0.199201	+	0.284489i
$669$	0.642788	−	1.11334i	0.642788	−	1.11334i
$670$		0			0
$671$		0			0
$672$	−0.0596180	+	0.681437i	−0.0596180	+	0.681437i
$673$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$673$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$674$		0			0
$675$		0			0
$676$	−1.00000			−1.00000
$677$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$677$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.00000			−1.00000
$682$		0			0
$683$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$683$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$684$		0			0
$685$		0			0
$686$	0.358441	+	0.984808i	0.358441	+	0.984808i
$687$	−0.314757	−	0.146774i	−0.314757	−	0.146774i
$688$	1.72546	+	0.150958i	1.72546	+	0.150958i
$689$		0			0
$690$		0			0
$691$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$691$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$692$		0			0
$693$		0			0
$694$	0.866025	+	0.500000i	0.866025	+	0.500000i
$695$		0			0
$696$		−	1.96962i		−	1.96962i
$697$		0			0
$698$	−1.25501	−	0.878770i	−1.25501	−	0.878770i
$699$		0			0
$700$		0			0
$701$			1.28558i			1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$701$			1.28558i			1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.500715	−	1.07379i	−0.500715	−	1.07379i
$708$		0			0
$709$	−1.50881	−	0.266044i	−1.50881	−	0.266044i	−0.642788	−	0.766044i	$-0.722222\pi$
$709$	−1.50881	−	0.266044i	−1.50881	−	0.266044i	−0.866025	+	0.500000i	$0.833333\pi$
$710$		0			0
$711$		0			0
$712$	−1.24177	−	0.332731i	−1.24177	−	0.332731i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$		0			0
$721$	−0.592396	+	1.02606i	−0.592396	+	1.02606i
$722$	−0.819152	+	0.573576i	−0.819152	+	0.573576i
$723$	−1.81535	−	0.486421i	−1.81535	−	0.486421i
$724$	−0.642788	+	1.76604i	−0.642788	+	1.76604i
$725$		0			0
$726$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$727$	−0.681437	+	0.0596180i	−0.681437	+	0.0596180i	−0.422618	−	0.906308i	$-0.638889\pi$
$727$	−0.681437	+	0.0596180i	−0.681437	+	0.0596180i	−0.258819	+	0.965926i	$0.583333\pi$
$728$		0			0
$729$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$730$		0			0
$731$		0			0
$732$	0.794263	+	1.70330i	0.794263	+	1.70330i
$733$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$733$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$734$		0			0
$735$		0			0
$736$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$737$		0			0
$738$	−0.112045	−	1.28068i	−0.112045	−	1.28068i
$739$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$739$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.133530	+	1.52626i	−0.133530	+	1.52626i	0.573576	+	0.819152i	$0.305556\pi$
$743$	−0.133530	+	1.52626i	−0.133530	+	1.52626i	−0.707107	+	0.707107i	$0.750000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.878770	+	1.25501i	−0.878770	+	1.25501i
$748$		0			0
$749$	0.223238	−	1.26604i	0.223238	−	1.26604i
$750$		0			0
$751$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$751$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$752$	−0.878770	+	1.25501i	−0.878770	+	1.25501i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.592396	+	0.342020i	−0.592396	+	0.342020i
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.439693	−	1.20805i	0.439693	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	0.439693	−	1.20805i	0.439693	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$762$	−1.39273	+	1.39273i	−1.39273	+	1.39273i
$763$	0.194602	−	0.136262i	0.194602	−	0.136262i
$764$		0			0
$765$		0			0
$766$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$767$		0			0
$768$	0.422618	−	0.906308i	0.422618	−	0.906308i
$769$	1.20805	+	1.43969i	1.20805	+	1.43969i	0.866025	+	0.500000i	$0.166667\pi$
$769$	1.20805	+	1.43969i	1.20805	+	1.43969i	0.342020	+	0.939693i	$0.388889\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$773$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$774$	0.866025	+	1.50000i	0.866025	+	1.50000i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.543308	−	1.16513i	−0.543308	−	1.16513i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.61341	−	1.12973i	1.61341	−	1.12973i
$784$		−	0.532089i		−	0.532089i
$785$		0			0
$786$		0			0
$787$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$787$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$788$		0			0
$789$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$797$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.439693	−	1.20805i	−0.439693	−	1.20805i
$802$	0.448288	+	1.67303i	0.448288	+	1.67303i
$803$		0			0
$804$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$805$		0			0
$806$		0			0
$807$	0.619951	−	0.289088i	0.619951	−	0.289088i
$808$	0.150958	+	1.72546i	0.150958	+	1.72546i
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−0.117425	−	1.34217i	−0.117425	−	1.34217i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.258819	+	0.965926i	0.258819	+	0.965926i
$819$		0			0
$820$		0			0
$821$	0.673648	+	1.85083i	0.673648	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$821$	0.673648	+	1.85083i	0.673648	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$822$		0			0
$823$	−0.681437	−	0.0596180i	−0.681437	−	0.0596180i	−0.258819	−	0.965926i	$-0.583333\pi$
$823$	−0.681437	−	0.0596180i	−0.681437	−	0.0596180i	−0.422618	+	0.906308i	$0.638889\pi$
$824$	1.32683	−	1.11334i	1.32683	−	1.11334i
$825$		0			0
$826$		0			0
$827$	−0.0898869	+	0.335463i	−0.0898869	+	0.335463i	−0.996195	−	0.0871557i	$-0.972222\pi$
$827$	−0.0898869	+	0.335463i	−0.0898869	+	0.335463i	0.906308	+	0.422618i	$0.138889\pi$
$828$	−0.314757	+	0.146774i	−0.314757	+	0.146774i
$829$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$829$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$839$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$840$		0			0
$841$	0.500000	+	2.83564i	0.500000	+	2.83564i
$842$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$843$	0.483690	+	0.483690i	0.483690	+	0.483690i
$844$		0			0
$845$		0			0
$846$	−1.53209			−1.53209
$847$	−0.660732	−	0.177043i	−0.660732	−	0.177043i
$848$		0			0
$849$	−1.85083	+	0.673648i	−1.85083	+	0.673648i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$853$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$854$	0.642788	+	1.11334i	0.642788	+	1.11334i
$855$		0			0
$856$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$857$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$857$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$858$		0			0
$859$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$859$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$860$		0			0
$861$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$862$		0			0
$863$	1.32893	−	1.32893i	1.32893	−	1.32893i	0.422618	−	0.906308i	$-0.361111\pi$
$863$	1.32893	−	1.32893i	1.32893	−	1.32893i	0.906308	−	0.422618i	$-0.138889\pi$
$864$	0.984808	−	0.173648i	0.984808	−	0.173648i
$865$		0			0
$866$		0			0
$867$	−0.996195	−	0.0871557i	−0.996195	−	0.0871557i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.335463	+	0.0898869i	−0.335463	+	0.0898869i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$877$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$881$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$882$	0.435862	−	0.305194i	0.435862	−	0.305194i
$883$	1.24177	−	0.332731i	1.24177	−	0.332731i	0.422618	−	0.906308i	$-0.361111\pi$
$883$	1.24177	−	0.332731i	1.24177	−	0.332731i	0.819152	+	0.573576i	$0.194444\pi$
$884$		0			0
$885$		0			0
$886$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$887$	−0.573576	+	0.819152i	−0.573576	+	0.819152i	−0.996195	−	0.0871557i	$-0.972222\pi$
$887$	−0.573576	+	0.819152i	−0.573576	+	0.819152i	0.422618	+	0.906308i	$0.361111\pi$
$888$		0			0
$889$	−0.866025	+	1.03209i	−0.866025	+	1.03209i
$890$		0			0
$891$		0			0
$892$	−0.909039	+	0.909039i	−0.909039	+	0.909039i
$893$		0			0
$894$	−1.85083	−	0.673648i	−1.85083	−	0.673648i
$895$		0			0
$896$	0.233956	−	0.642788i	0.233956	−	0.642788i
$897$		0			0
$898$	1.41881	−	0.993464i	1.41881	−	0.993464i
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	0.679569	+	0.970525i	0.679569	+	0.970525i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.289088	−	0.619951i	0.289088	−	0.619951i	−0.707107	−	0.707107i	$-0.750000\pi$
$907$	0.289088	−	0.619951i	0.289088	−	0.619951i	0.996195	+	0.0871557i	$0.0277778\pi$
$908$	0.965926	+	0.258819i	0.965926	+	0.258819i
$909$	−1.32683	+	1.11334i	−1.32683	+	1.11334i
$910$		0			0
$911$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$911$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.266044	+	0.223238i	0.266044	+	0.223238i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$922$	−0.560333	−	0.392349i	−0.560333	−	0.392349i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.50000	+	0.866025i	1.50000	+	0.866025i
$927$	1.67303	+	0.448288i	1.67303	+	0.448288i
$928$	−0.509774	+	1.90250i	−0.509774	+	1.90250i
$929$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.984808	−	0.173648i	$-0.944444\pi$
$929$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.642788	+	0.766044i	$0.722222\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$935$		0			0
$936$		0			0
$937$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$937$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$938$	−0.504395	−	0.720350i	−0.504395	−	0.720350i
$939$		0			0
$940$		0			0
$941$	−1.26604	+	0.223238i	−1.26604	+	0.223238i	−0.766044	−	0.642788i	$-0.777778\pi$
$941$	−1.26604	+	0.223238i	−1.26604	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$942$		0			0
$943$	−0.0389129	−	0.444777i	−0.0389129	−	0.444777i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.133530	+	1.52626i	0.133530	+	1.52626i	0.707107	+	0.707107i	$0.250000\pi$
$947$	0.133530	+	1.52626i	0.133530	+	1.52626i	−0.573576	+	0.819152i	$0.694444\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$953$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$962$		0			0
$963$	−1.87223	+	0.163799i	−1.87223	+	0.163799i
$964$	1.62760	+	0.939693i	1.62760	+	0.939693i
$965$		0			0
$966$	−0.205737	+	0.118782i	−0.205737	+	0.118782i
$967$	1.78508	−	0.832395i	1.78508	−	0.832395i	0.819152	−	0.573576i	$-0.194444\pi$
$967$	1.78508	−	0.832395i	1.78508	−	0.832395i	0.965926	−	0.258819i	$-0.0833333\pi$
$968$	0.819152	+	0.573576i	0.819152	+	0.573576i
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	0.707107	+	0.707107i	0.707107	+	0.707107i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$977$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$977$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$978$	0.448288	−	1.67303i	0.448288	−	1.67303i
$979$		0			0
$980$		0			0
$981$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$982$		0			0
$983$	0.794263	−	1.70330i	0.794263	−	1.70330i	0.0871557	−	0.996195i	$-0.472222\pi$
$983$	0.794263	−	1.70330i	0.794263	−	1.70330i	0.707107	−	0.707107i	$-0.250000\pi$
$984$	−0.223238	+	1.26604i	−0.223238	+	1.26604i
$985$		0			0
$986$		0			0
$987$	−1.04402	+	0.0913401i	−1.04402	+	0.0913401i
$988$		0			0
$989$	0.300767	+	0.520945i	0.300767	+	0.520945i
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.17365	−	0.984808i	1.17365	−	0.984808i
$997$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$997$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2700.1.ca.a.1307.2	yes	24
4.3	odd	2	inner	2700.1.ca.a.1307.1	yes	24
5.2	odd	4	inner	2700.1.ca.a.443.1	✓	24
5.3	odd	4	inner	2700.1.ca.a.443.2	yes	24
5.4	even	2	inner	2700.1.ca.a.1307.1	yes	24
20.3	even	4	inner	2700.1.ca.a.443.1	✓	24
20.7	even	4	inner	2700.1.ca.a.443.2	yes	24
20.19	odd	2	CM	2700.1.ca.a.1307.2	yes	24
27.5	odd	18	inner	2700.1.ca.a.707.1	yes	24
108.59	even	18	inner	2700.1.ca.a.707.2	yes	24
135.32	even	36	inner	2700.1.ca.a.2543.2	yes	24
135.59	odd	18	inner	2700.1.ca.a.707.2	yes	24
135.113	even	36	inner	2700.1.ca.a.2543.1	yes	24
540.59	even	18	inner	2700.1.ca.a.707.1	yes	24
540.167	odd	36	inner	2700.1.ca.a.2543.1	yes	24
540.383	odd	36	inner	2700.1.ca.a.2543.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2700.1.ca.a.443.1	✓	24	5.2	odd	4	inner
2700.1.ca.a.443.1	✓	24	20.3	even	4	inner
2700.1.ca.a.443.2	yes	24	5.3	odd	4	inner
2700.1.ca.a.443.2	yes	24	20.7	even	4	inner
2700.1.ca.a.707.1	yes	24	27.5	odd	18	inner
2700.1.ca.a.707.1	yes	24	540.59	even	18	inner
2700.1.ca.a.707.2	yes	24	108.59	even	18	inner
2700.1.ca.a.707.2	yes	24	135.59	odd	18	inner
2700.1.ca.a.1307.1	yes	24	4.3	odd	2	inner
2700.1.ca.a.1307.1	yes	24	5.4	even	2	inner
2700.1.ca.a.1307.2	yes	24	1.1	even	1	trivial
2700.1.ca.a.1307.2	yes	24	20.19	odd	2	CM
2700.1.ca.a.2543.1	yes	24	135.113	even	36	inner
2700.1.ca.a.2543.1	yes	24	540.167	odd	36	inner
2700.1.ca.a.2543.2	yes	24	135.32	even	36	inner
2700.1.ca.a.2543.2	yes	24	540.383	odd	36	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:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2700.ca (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.906308 - 0.422618i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.500000 + 0.866025i) q^{6} +(0.392349 + 0.560333i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-0.819152 + 0.573576i) q^{12} +(-0.524005 + 0.439693i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.819152 + 0.573576i) q^{18} +(0.592396 + 0.342020i) q^{21} +(0.284489 + 0.199201i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(0.258819 - 0.965926i) q^{27} +(-0.483690 - 0.483690i) q^{28} +(1.50881 + 1.26604i) q^{29} +(0.422618 + 0.906308i) q^{32} +(-0.500000 + 0.866025i) q^{36} +(-0.826352 - 0.984808i) q^{41} +(-0.289088 + 0.619951i) q^{42} +(1.56977 + 0.731996i) q^{43} +(-0.173648 + 0.300767i) q^{46} +(-1.25501 + 0.878770i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.181985 - 0.500000i) q^{49} +(0.984808 + 0.173648i) q^{54} +(0.439693 - 0.524005i) q^{56} +(-1.12973 + 1.61341i) q^{58} +(0.326352 - 1.85083i) q^{61} +(0.681437 + 0.0596180i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.112045 + 1.28068i) q^{67} +(0.342020 + 0.0603074i) q^{69} +(-0.906308 - 0.422618i) q^{72} +(-0.173648 - 0.984808i) q^{81} +(0.909039 - 0.909039i) q^{82} +(-1.52626 + 0.133530i) q^{83} +(-0.642788 - 0.233956i) q^{84} +(-0.592396 + 1.62760i) q^{86} +(1.90250 + 0.509774i) q^{87} +(0.642788 - 1.11334i) q^{89} +(-0.314757 - 0.146774i) q^{92} +(-0.984808 - 1.17365i) q^{94} +(0.766044 + 0.642788i) q^{96} +(0.513958 + 0.137715i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{6} - 12 q^{36} - 24 q^{41} - 12 q^{56} + 12 q^{61}+O(q^{100}) \) 24 * q + 12 * q^6 - 12 * q^36 - 24 * q^41 - 12 * q^56 + 12 * q^61

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