LMFDB - Embedded newform 3800.1.eb.c.3707.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3800,1,Mod(243,3800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3800, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 18, 27, 22]))

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

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

chi := DirichletCharacter("3800.243");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3800 = 2^{3} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3800.eb (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:	$1.89644704801$
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			3707.2
Root			$-0.906308 - 0.422618i$ of defining polynomial
Character	$\chi$	$=$	3800.3707
Dual form			3800.1.eb.c.2043.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 + 0.819152i) q^{2} +(-0.163799 - 1.87223i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.43969 - 1.20805i) q^{6} +(-0.965926 + 0.258819i) q^{8} +(-2.49362 + 0.439693i) q^{9} +O(q^{10})$	\(q+(0.573576 + 0.819152i) q^{2} +(-0.163799 - 1.87223i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.43969 - 1.20805i) q^{6} +(-0.965926 + 0.258819i) q^{8} +(-2.49362 + 0.439693i) q^{9} +(-0.939693 + 1.62760i) q^{11} +(1.81535 + 0.486421i) q^{12} +(-0.766044 - 0.642788i) q^{16} +(-1.79046 - 1.79046i) q^{18} +(0.642788 + 0.766044i) q^{19} +(-1.87223 + 0.163799i) q^{22} +(0.642788 + 1.76604i) q^{24} +(0.745240 + 2.78127i) q^{27} +(0.0871557 - 0.996195i) q^{32} +(3.20116 + 1.49273i) q^{33} +(0.439693 - 2.49362i) q^{36} +(-0.258819 + 0.965926i) q^{38} +(-1.26604 + 1.50881i) q^{41} +(-0.731996 + 1.56977i) q^{43} +(-1.20805 - 1.43969i) q^{44} +(-1.07797 + 1.53950i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-1.85083 + 2.20574i) q^{54} +(1.32893 - 1.32893i) q^{57} +(-0.223238 + 1.26604i) q^{59} +(0.866025 - 0.500000i) q^{64} +(0.613341 + 3.47843i) q^{66} +(0.284489 + 0.199201i) q^{67} +(2.29485 - 1.07011i) q^{72} +(1.96212 - 0.171663i) q^{73} +(-0.939693 + 0.342020i) q^{76} +(2.70574 - 0.984808i) q^{81} +(-1.96212 - 0.171663i) q^{82} +(-1.24177 - 0.332731i) q^{83} +(-1.70574 + 0.300767i) q^{86} +(0.486421 - 1.81535i) q^{88} +(1.32683 - 1.11334i) q^{89} -1.87939 q^{96} +(1.07797 + 1.53950i) q^{97} +(-0.0871557 - 0.996195i) q^{98} +(1.62760 - 4.47178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{6}+O(q^{10}) $ 24 * q + 12 * q^6	$ 24 q + 12 q^{6} - 12 q^{36} - 12 q^{41} - 12 q^{66} + 24 q^{81}+O(q^{100}) $ 24 * q + 12 * q^6 - 12 * q^36 - 12 * q^41 - 12 * q^66 + 24 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times$.

$n$	$401$	$951$	$1901$	$1977$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.573576	+	0.819152i	0.573576	+	0.819152i
$2$	0.573576	+	0.819152i	0.573576	+	0.819152i
$3$	−0.163799	−	1.87223i	−0.163799	−	1.87223i	−0.422618	−	0.906308i	$-0.638889\pi$
$3$	−0.163799	−	1.87223i	−0.163799	−	1.87223i	0.258819	−	0.965926i	$-0.416667\pi$
$4$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$5$		0			0
$5$		0			0
$6$	1.43969	−	1.20805i	1.43969	−	1.20805i
$7$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$7$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$8$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$9$	−2.49362	+	0.439693i	−2.49362	+	0.439693i
$10$		0			0
$11$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$11$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$12$	1.81535	+	0.486421i	1.81535	+	0.486421i
$13$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$13$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$14$		0			0
$15$		0			0
$16$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$17$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$17$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$18$	−1.79046	−	1.79046i	−1.79046	−	1.79046i
$19$	0.642788	+	0.766044i	0.642788	+	0.766044i
$19$	0.642788	+	0.766044i	0.642788	+	0.766044i
$20$		0			0
$21$		0			0
$22$	−1.87223	+	0.163799i	−1.87223	+	0.163799i
$23$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$23$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$24$	0.642788	+	1.76604i	0.642788	+	1.76604i
$25$		0			0
$26$		0			0
$27$	0.745240	+	2.78127i	0.745240	+	2.78127i
$28$		0			0
$29$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$29$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$33$	3.20116	+	1.49273i	3.20116	+	1.49273i
$34$		0			0
$35$		0			0
$36$	0.439693	−	2.49362i	0.439693	−	2.49362i
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$39$		0			0
$40$		0			0
$41$	−1.26604	+	1.50881i	−1.26604	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$41$	−1.26604	+	1.50881i	−1.26604	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$42$		0			0
$43$	−0.731996	+	1.56977i	−0.731996	+	1.56977i	0.0871557	+	0.996195i	$0.472222\pi$
$43$	−0.731996	+	1.56977i	−0.731996	+	1.56977i	−0.819152	+	0.573576i	$0.805556\pi$
$44$	−1.20805	−	1.43969i	−1.20805	−	1.43969i
$45$		0			0
$46$		0			0
$47$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$47$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$48$	−1.07797	+	1.53950i	−1.07797	+	1.53950i
$49$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$53$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$54$	−1.85083	+	2.20574i	−1.85083	+	2.20574i
$55$		0			0
$56$		0			0
$57$	1.32893	−	1.32893i	1.32893	−	1.32893i
$58$		0			0
$59$	−0.223238	+	1.26604i	−0.223238	+	1.26604i	0.642788	+	0.766044i	$0.277778\pi$
$59$	−0.223238	+	1.26604i	−0.223238	+	1.26604i	−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$61$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$62$		0			0
$63$		0			0
$64$	0.866025	−	0.500000i	0.866025	−	0.500000i
$65$		0			0
$66$	0.613341	+	3.47843i	0.613341	+	3.47843i
$67$	0.284489	+	0.199201i	0.284489	+	0.199201i	0.707107	−	0.707107i	$-0.250000\pi$
$67$	0.284489	+	0.199201i	0.284489	+	0.199201i	−0.422618	+	0.906308i	$0.638889\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$71$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$72$	2.29485	−	1.07011i	2.29485	−	1.07011i
$73$	1.96212	−	0.171663i	1.96212	−	0.171663i	0.965926	−	0.258819i	$-0.0833333\pi$
$73$	1.96212	−	0.171663i	1.96212	−	0.171663i	0.996195	+	0.0871557i	$0.0277778\pi$
$74$		0			0
$75$		0			0
$76$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$77$		0			0
$78$		0			0
$79$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$79$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$80$		0			0
$81$	2.70574	−	0.984808i	2.70574	−	0.984808i
$82$	−1.96212	−	0.171663i	−1.96212	−	0.171663i
$83$	−1.24177	−	0.332731i	−1.24177	−	0.332731i	−0.422618	−	0.906308i	$-0.638889\pi$
$83$	−1.24177	−	0.332731i	−1.24177	−	0.332731i	−0.819152	+	0.573576i	$0.805556\pi$
$84$		0			0
$85$		0			0
$86$	−1.70574	+	0.300767i	−1.70574	+	0.300767i
$87$		0			0
$88$	0.486421	−	1.81535i	0.486421	−	1.81535i
$89$	1.32683	−	1.11334i	1.32683	−	1.11334i	0.342020	−	0.939693i	$-0.388889\pi$
$89$	1.32683	−	1.11334i	1.32683	−	1.11334i	0.984808	−	0.173648i	$-0.0555556\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.87939			−1.87939
$97$	1.07797	+	1.53950i	1.07797	+	1.53950i	0.819152	+	0.573576i	$0.194444\pi$
$97$	1.07797	+	1.53950i	1.07797	+	1.53950i	0.258819	+	0.965926i	$0.416667\pi$
$98$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$99$	1.62760	−	4.47178i	1.62760	−	4.47178i
$100$		0			0
$101$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$101$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$102$		0			0
$103$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$103$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$107$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$108$	−2.86843	−	0.250955i	−2.86843	−	0.250955i
$109$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$109$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.245576	+	0.245576i	0.245576	+	0.245576i	0.819152	−	0.573576i	$-0.194444\pi$
$113$	0.245576	+	0.245576i	0.245576	+	0.245576i	−0.573576	+	0.819152i	$0.694444\pi$
$114$	1.85083	+	0.326352i	1.85083	+	0.326352i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.16513	+	0.543308i	−1.16513	+	0.543308i
$119$		0			0
$120$		0			0
$121$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$122$		0			0
$123$	3.03223	+	2.12319i	3.03223	+	2.12319i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$127$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$128$	0.906308	+	0.422618i	0.906308	+	0.422618i
$129$	3.05888	+	1.11334i	3.05888	+	1.11334i
$130$		0			0
$131$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$131$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$132$	−2.49756	+	2.49756i	−2.49756	+	2.49756i
$133$		0			0
$134$			0.347296i			0.347296i
$135$		0			0
$136$		0			0
$137$	−0.289088	−	0.619951i	−0.289088	−	0.619951i	0.707107	−	0.707107i	$-0.250000\pi$
$137$	−0.289088	−	0.619951i	−0.289088	−	0.619951i	−0.996195	+	0.0871557i	$0.972222\pi$
$138$		0			0
$139$	0.223238	+	0.266044i	0.223238	+	0.266044i	0.866025	−	0.500000i	$-0.166667\pi$
$139$	0.223238	+	0.266044i	0.223238	+	0.266044i	−0.642788	+	0.766044i	$0.722222\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.19285	+	1.26604i	2.19285	+	1.26604i
$145$		0			0
$146$	1.26604	+	1.50881i	1.26604	+	1.50881i
$147$	−0.794263	+	1.70330i	−0.794263	+	1.70330i
$148$		0			0
$149$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$149$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−0.819152	−	0.573576i	−0.819152	−	0.573576i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$157$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	2.35865	+	1.65155i	2.35865	+	1.65155i
$163$	−0.332731	−	1.24177i	−0.332731	−	1.24177i	−0.906308	−	0.422618i	$-0.861111\pi$
$163$	−0.332731	−	1.24177i	−0.332731	−	1.24177i	0.573576	−	0.819152i	$-0.305556\pi$
$164$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$165$		0			0
$166$	−0.439693	−	1.20805i	−0.439693	−	1.20805i
$167$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$167$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$168$		0			0
$169$	0.984808	+	0.173648i	0.984808	+	0.173648i
$170$		0			0
$171$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$172$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$173$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$173$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$174$		0			0
$175$		0			0
$176$	1.76604	−	0.642788i	1.76604	−	0.642788i
$177$	2.40690	+	0.210576i	2.40690	+	0.210576i
$178$	1.67303	+	0.448288i	1.67303	+	0.448288i
$179$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$179$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	−0.984808	+	0.173648i	$0.944444\pi$
$180$		0			0
$181$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$181$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−1.07797	−	1.53950i	−1.07797	−	1.53950i
$193$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i	−0.906308	−	0.422618i	$-0.861111\pi$
$193$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i	0.819152	−	0.573576i	$-0.194444\pi$
$194$	−0.642788	+	1.76604i	−0.642788	+	1.76604i
$195$		0			0
$196$	0.766044	−	0.642788i	0.766044	−	0.642788i
$197$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$197$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$198$	4.59662	−	1.23166i	4.59662	−	1.23166i
$199$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$199$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$200$		0			0
$201$	0.326352	−	0.565258i	0.326352	−	0.565258i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.85083	+	0.326352i	−1.85083	+	0.326352i
$210$		0			0
$211$	−1.70574	−	0.300767i	−1.70574	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$211$	−1.70574	−	0.300767i	−1.70574	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$		0			0
$214$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$215$		0			0
$216$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$217$		0			0
$218$		0			0
$219$	−0.642788	−	3.64543i	−0.642788	−	3.64543i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$223$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$224$		0			0
$225$		0			0
$226$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$227$	−1.32893	+	1.32893i	−1.32893	+	1.32893i	−0.422618	+	0.906308i	$0.638889\pi$
$227$	−1.32893	+	1.32893i	−1.32893	+	1.32893i	−0.906308	+	0.422618i	$0.861111\pi$
$228$	0.794263	+	1.70330i	0.794263	+	1.70330i
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.832395	−	1.78508i	0.832395	−	1.78508i	0.258819	−	0.965926i	$-0.416667\pi$
$233$	0.832395	−	1.78508i	0.832395	−	1.78508i	0.573576	−	0.819152i	$-0.305556\pi$
$234$		0			0
$235$		0			0
$236$	−1.11334	−	0.642788i	−1.11334	−	0.642788i
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$241$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	−1.00000			$\pi$
$242$	1.07011	−	2.29485i	1.07011	−	2.29485i
$243$	−1.07011	−	2.29485i	−1.07011	−	2.29485i
$244$		0			0
$245$		0			0
$246$			3.70167i			3.70167i
$247$		0			0
$248$		0			0
$249$	−0.419550	+	2.37939i	−0.419550	+	2.37939i
$250$		0			0
$251$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.173648	+	0.984808i	0.173648	+	0.984808i
$257$	0.284489	+	0.199201i	0.284489	+	0.199201i	0.707107	−	0.707107i	$-0.250000\pi$
$257$	0.284489	+	0.199201i	0.284489	+	0.199201i	−0.422618	+	0.906308i	$0.638889\pi$
$258$	0.842505	+	3.14427i	0.842505	+	3.14427i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.314757	+	0.146774i	−0.314757	+	0.146774i
$263$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$263$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$264$	−3.47843	−	0.613341i	−3.47843	−	0.613341i
$265$		0			0
$266$		0			0
$267$	−2.30177	−	2.30177i	−2.30177	−	2.30177i
$268$	−0.284489	+	0.199201i	−0.284489	+	0.199201i
$269$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$269$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$270$		0			0
$271$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$271$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$272$		0			0
$273$		0			0
$274$	0.342020	−	0.592396i	0.342020	−	0.592396i
$275$		0			0
$276$		0			0
$277$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$277$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$278$	−0.0898869	+	0.335463i	−0.0898869	+	0.335463i
$279$		0			0
$280$		0			0
$281$	−0.673648	+	1.85083i	−0.673648	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$281$	−0.673648	+	1.85083i	−0.673648	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	−0.392349	−	0.560333i	−0.392349	−	0.560333i	0.573576	−	0.819152i	$-0.305556\pi$
$283$	−0.392349	−	0.560333i	−0.392349	−	0.560333i	−0.965926	+	0.258819i	$0.916667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.220686	+	2.52245i	0.220686	+	2.52245i
$289$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$290$		0			0
$291$	2.70574	−	2.27038i	2.70574	−	2.27038i
$292$	−0.509774	+	1.90250i	−0.509774	+	1.90250i
$293$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$293$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$294$	−1.85083	+	0.326352i	−1.85083	+	0.326352i
$295$		0			0
$296$		0			0
$297$	−5.22708	−	1.40059i	−5.22708	−	1.40059i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		−	1.00000i		−	1.00000i
$305$		0			0
$306$		0			0
$307$	0.345975	−	0.0302689i	0.345975	−	0.0302689i	0.0871557	−	0.996195i	$-0.472222\pi$
$307$	0.345975	−	0.0302689i	0.345975	−	0.0302689i	0.258819	+	0.965926i	$0.416667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$		0			0
$313$	−1.61341	−	1.12973i	−1.61341	−	1.12973i	−0.906308	−	0.422618i	$-0.861111\pi$
$313$	−1.61341	−	1.12973i	−1.61341	−	1.12973i	−0.707107	−	0.707107i	$-0.750000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$317$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$322$		0			0
$323$		0			0
$324$			2.87939i			2.87939i
$325$		0			0
$326$	0.826352	−	0.984808i	0.826352	−	0.984808i
$327$		0			0
$328$	0.832395	−	1.78508i	0.832395	−	1.78508i
$329$		0			0
$330$		0			0
$331$	1.70574	+	0.984808i	1.70574	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$331$	1.70574	+	0.984808i	1.70574	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$332$	0.737376	−	1.05308i	0.737376	−	1.05308i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.647489	+	1.38854i	−0.647489	+	1.38854i	0.258819	+	0.965926i	$0.416667\pi$
$337$	−0.647489	+	1.38854i	−0.647489	+	1.38854i	−0.906308	+	0.422618i	$0.861111\pi$
$338$	0.422618	+	0.906308i	0.422618	+	0.906308i
$339$	0.419550	−	0.500000i	0.419550	−	0.500000i
$340$		0			0
$341$		0			0
$342$	0.220686	−	2.52245i	0.220686	−	2.52245i
$343$		0			0
$344$	0.300767	−	1.70574i	0.300767	−	1.70574i
$345$		0			0
$346$		0			0
$347$	1.78508	+	0.832395i	1.78508	+	0.832395i	0.965926	+	0.258819i	$0.0833333\pi$
$347$	1.78508	+	0.832395i	1.78508	+	0.832395i	0.819152	+	0.573576i	$0.194444\pi$
$348$		0			0
$349$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$349$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$350$		0			0
$351$		0			0
$352$	1.53950	+	1.07797i	1.53950	+	1.07797i
$353$	−0.177043	−	0.660732i	−0.177043	−	0.660732i	−0.996195	−	0.0871557i	$-0.972222\pi$
$353$	−0.177043	−	0.660732i	−0.177043	−	0.660732i	0.819152	−	0.573576i	$-0.194444\pi$
$354$	1.20805	+	2.09240i	1.20805	+	2.09240i
$355$		0			0
$356$	0.592396	+	1.62760i	0.592396	+	1.62760i
$357$		0			0
$358$	−1.28068	+	0.112045i	−1.28068	+	0.112045i
$359$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$359$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$360$		0			0
$361$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$362$		0			0
$363$	−3.89816	+	2.72952i	−3.89816	+	2.72952i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$367$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$368$		0			0
$369$	2.49362	−	4.31908i	2.49362	−	4.31908i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$373$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.73205			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$379$	1.73205			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$383$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$384$	0.642788	−	1.76604i	0.642788	−	1.76604i
$385$		0			0
$386$	0.766044	−	0.642788i	0.766044	−	0.642788i
$387$	1.13510	−	4.23627i	1.13510	−	4.23627i
$388$	−1.81535	+	0.486421i	−1.81535	+	0.486421i
$389$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$389$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$390$		0			0
$391$		0			0
$392$	0.965926	+	0.258819i	0.965926	+	0.258819i
$393$	0.650220	+	0.0568869i	0.650220	+	0.0568869i
$394$		0			0
$395$		0			0
$396$	3.64543	+	3.05888i	3.64543	+	3.05888i
$397$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$397$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.673648	+	0.118782i	0.673648	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$401$	0.673648	+	0.118782i	0.673648	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$402$	0.650220	−	0.0568869i	0.650220	−	0.0568869i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.118782	+	0.673648i	0.118782	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$409$	0.118782	+	0.673648i	0.118782	+	0.673648i	−0.866025	+	0.500000i	$0.833333\pi$
$410$		0			0
$411$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.461531	−	0.461531i	0.461531	−	0.461531i
$418$	−1.32893	−	1.32893i	−1.32893	−	1.32893i
$419$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$419$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$421$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$422$	−0.731996	−	1.56977i	−0.731996	−	1.56977i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.573576	−	0.819152i	0.573576	−	0.819152i
$429$		0			0
$430$		0			0
$431$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$431$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$432$	1.21688	−	2.60961i	1.21688	−	2.60961i
$433$	0.422618	+	0.906308i	0.422618	+	0.906308i	0.996195	+	0.0871557i	$0.0277778\pi$
$433$	0.422618	+	0.906308i	0.422618	+	0.906308i	−0.573576	+	0.819152i	$0.694444\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	2.61747	−	2.61747i	2.61747	−	2.61747i
$439$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$439$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$440$		0			0
$441$	2.37939	+	0.866025i	2.37939	+	0.866025i
$442$		0			0
$443$	0.112045	−	1.28068i	0.112045	−	1.28068i	−0.707107	−	0.707107i	$-0.750000\pi$
$443$	0.112045	−	1.28068i	0.112045	−	1.28068i	0.819152	−	0.573576i	$-0.194444\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.342020	−	0.592396i	−0.342020	−	0.592396i	0.642788	−	0.766044i	$-0.277778\pi$
$449$	−0.342020	−	0.592396i	−0.342020	−	0.592396i	−0.984808	+	0.173648i	$0.944444\pi$
$450$		0			0
$451$	−1.26604	−	3.47843i	−1.26604	−	3.47843i
$452$	−0.314757	+	0.146774i	−0.314757	+	0.146774i
$453$		0			0
$454$	−1.85083	−	0.326352i	−1.85083	−	0.326352i
$455$		0			0
$456$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$457$	−0.909039	−	0.909039i	−0.909039	−	0.909039i	0.0871557	−	0.996195i	$-0.472222\pi$
$457$	−0.909039	−	0.909039i	−0.909039	−	0.909039i	−0.996195	+	0.0871557i	$0.972222\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$461$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$463$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$464$		0			0
$465$		0			0
$466$	1.93969	−	0.342020i	1.93969	−	0.342020i
$467$	−0.660732	+	0.177043i	−0.660732	+	0.177043i	−0.573576	−	0.819152i	$-0.694444\pi$
$467$	−0.660732	+	0.177043i	−0.660732	+	0.177043i	−0.0871557	+	0.996195i	$0.527778\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.112045	−	1.28068i	−0.112045	−	1.28068i
$473$	−1.86710	−	2.66650i	−1.86710	−	2.66650i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$479$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$480$		0			0
$481$		0			0
$482$	0.332731	−	1.24177i	0.332731	−	1.24177i
$483$		0			0
$484$	2.49362	−	0.439693i	2.49362	−	0.439693i
$485$		0			0
$486$	1.26604	−	2.19285i	1.26604	−	2.19285i
$487$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$487$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$488$		0			0
$489$	−2.27038	+	0.826352i	−2.27038	+	0.826352i
$490$		0			0
$491$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$491$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$492$	−3.03223	+	2.12319i	−3.03223	+	2.12319i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−2.18972	+	1.02108i	−2.18972	+	1.02108i
$499$	0.524005	+	1.43969i	0.524005	+	1.43969i	0.866025	+	0.500000i	$0.166667\pi$
$499$	0.524005	+	1.43969i	0.524005	+	1.43969i	−0.342020	+	0.939693i	$0.611111\pi$
$500$		0			0
$501$		0			0
$502$	−0.396534	−	1.47988i	−0.396534	−	1.47988i
$503$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$503$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.163799	−	1.87223i	0.163799	−	1.87223i
$508$		0			0
$509$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$509$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$513$	−1.65155	+	2.35865i	−1.65155	+	2.35865i
$514$			0.347296i			0.347296i
$515$		0			0
$516$	−2.09240	+	2.49362i	−2.09240	+	2.49362i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.11334	+	0.642788i	1.11334	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$521$	1.11334	+	0.642788i	1.11334	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$522$		0			0
$523$	−0.573576	+	0.819152i	−0.573576	+	0.819152i	−0.996195	−	0.0871557i	$-0.972222\pi$
$523$	−0.573576	+	0.819152i	−0.573576	+	0.819152i	0.422618	+	0.906308i	$0.361111\pi$
$524$	−0.300767	−	0.173648i	−0.300767	−	0.173648i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.49273	−	3.20116i	−1.49273	−	3.20116i
$529$	0.642788	−	0.766044i	0.642788	−	0.766044i
$530$		0			0
$531$		−	3.25519i		−	3.25519i
$532$		0			0
$533$		0			0
$534$	0.565258	−	3.20574i	0.565258	−	3.20574i
$535$		0			0
$536$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$537$	2.18972	+	1.02108i	2.18972	+	1.02108i
$538$		0			0
$539$	1.62760	−	0.939693i	1.62760	−	0.939693i
$540$		0			0
$541$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$541$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.81262	−	0.845237i	1.81262	−	0.845237i	0.906308	−	0.422618i	$-0.138889\pi$
$547$	1.81262	−	0.845237i	1.81262	−	0.845237i	0.906308	−	0.422618i	$-0.138889\pi$
$548$	0.681437	−	0.0596180i	0.681437	−	0.0596180i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$557$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$557$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.90250	+	0.509774i	−1.90250	+	0.509774i
$563$	0.396534	−	1.47988i	0.396534	−	1.47988i	−0.422618	−	0.906308i	$-0.638889\pi$
$563$	0.396534	−	1.47988i	0.396534	−	1.47988i	0.819152	−	0.573576i	$-0.194444\pi$
$564$		0			0
$565$		0			0
$566$	0.233956	−	0.642788i	0.233956	−	0.642788i
$567$		0			0
$568$		0			0
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$		0			0
$571$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$571$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.93969	+	1.62760i	−1.93969	+	1.62760i
$577$	0.177043	−	0.660732i	0.177043	−	0.660732i	−0.819152	−	0.573576i	$-0.805556\pi$
$577$	0.177043	−	0.660732i	0.177043	−	0.660732i	0.996195	−	0.0871557i	$-0.0277778\pi$
$578$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$579$	−1.85083	+	0.326352i	−1.85083	+	0.326352i
$580$		0			0
$581$		0			0
$582$	3.41174	+	0.914172i	3.41174	+	0.914172i
$583$		0			0
$584$	−1.85083	+	0.673648i	−1.85083	+	0.673648i
$585$		0			0
$586$		0			0
$587$	1.41881	−	0.993464i	1.41881	−	0.993464i	0.422618	−	0.906308i	$-0.361111\pi$
$587$	1.41881	−	0.993464i	1.41881	−	0.993464i	0.996195	−	0.0871557i	$-0.0277778\pi$
$588$	−1.32893	−	1.32893i	−1.32893	−	1.32893i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.619951	−	0.289088i	0.619951	−	0.289088i	−0.0871557	−	0.996195i	$-0.527778\pi$
$593$	0.619951	−	0.289088i	0.619951	−	0.289088i	0.707107	+	0.707107i	$0.250000\pi$
$594$	−1.85083	−	5.08512i	−1.85083	−	5.08512i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$599$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$600$		0			0
$601$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$601$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$602$		0			0
$603$	−0.796994	−	0.371644i	−0.796994	−	0.371644i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$607$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$608$	0.819152	−	0.573576i	0.819152	−	0.573576i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$613$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$614$	0.223238	+	0.266044i	0.223238	+	0.266044i
$615$		0			0
$616$		0			0
$617$	0.737376	−	1.05308i	0.737376	−	1.05308i	−0.258819	−	0.965926i	$-0.583333\pi$
$617$	0.737376	−	1.05308i	0.737376	−	1.05308i	0.996195	−	0.0871557i	$-0.0277778\pi$
$618$		0			0
$619$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$619$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		−	1.96962i		−	1.96962i
$627$	0.914172	+	3.41174i	0.914172	+	3.41174i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$631$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$632$		0			0
$633$	−0.283709	+	3.24280i	−0.283709	+	3.24280i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.233956	−	0.642788i	−0.233956	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$641$	−0.233956	−	0.642788i	−0.233956	−	0.642788i	−1.00000			$\pi$
$642$	−1.70330	+	0.794263i	−1.70330	+	0.794263i
$643$	1.96212	−	0.171663i	1.96212	−	0.171663i	0.965926	−	0.258819i	$-0.0833333\pi$
$643$	1.96212	−	0.171663i	1.96212	−	0.171663i	0.996195	+	0.0871557i	$0.0277778\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$	−2.35865	+	1.65155i	−2.35865	+	1.65155i
$649$	−1.85083	−	1.55303i	−1.85083	−	1.55303i
$650$		0			0
$651$		0			0
$652$	1.28068	+	0.112045i	1.28068	+	0.112045i
$653$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$653$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$654$		0			0
$655$		0			0
$656$	1.93969	−	0.342020i	1.93969	−	0.342020i
$657$	−4.81731	+	1.29079i	−4.81731	+	1.29079i
$658$		0			0
$659$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$659$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$660$		0			0
$661$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$661$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$662$	0.171663	+	1.96212i	0.171663	+	1.96212i
$663$		0			0
$664$	1.28558			1.28558
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$673$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$674$	−1.50881	+	0.266044i	−1.50881	+	0.266044i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$677$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$678$	0.650220	+	0.0568869i	0.650220	+	0.0568869i
$679$		0			0
$680$		0			0
$681$	2.70574	+	2.27038i	2.70574	+	2.27038i
$682$		0			0
$683$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$683$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$684$	2.19285	−	1.26604i	2.19285	−	1.26604i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.56977	−	0.731996i	1.56977	−	0.731996i
$689$		0			0
$690$		0			0
$691$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$691$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$		0			0
$694$	0.342020	+	1.93969i	0.342020	+	1.93969i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−3.47843	−	1.26604i	−3.47843	−	1.26604i
$700$		0			0
$701$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$701$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$702$		0			0
$703$		0			0
$704$			1.87939i			1.87939i
$705$		0			0
$706$	0.439693	−	0.524005i	0.439693	−	0.524005i
$707$		0			0
$708$	−1.02108	+	2.18972i	−1.02108	+	2.18972i
$709$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$709$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$710$		0			0
$711$		0			0
$712$	−0.993464	+	1.41881i	−0.993464	+	1.41881i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.826352	−	0.984808i	−0.826352	−	0.984808i
$717$		0			0
$718$		0			0
$719$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$719$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$720$		0			0
$721$		0			0
$722$	−0.906308	+	0.422618i	−0.906308	+	0.422618i
$723$	−1.70843	+	1.70843i	−1.70843	+	1.70843i
$724$		0			0
$725$		0			0
$726$	−4.47178	−	1.62760i	−4.47178	−	1.62760i
$727$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$727$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$728$		0			0
$729$	−1.62760	+	0.939693i	−1.62760	+	0.939693i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$733$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.591550	+	0.275844i	−0.591550	+	0.275844i
$738$	4.96826	−	0.434667i	4.96826	−	0.434667i
$739$	1.85083	+	0.326352i	1.85083	+	0.326352i	0.984808	−	0.173648i	$-0.0555556\pi$
$739$	1.85083	+	0.326352i	1.85083	+	0.326352i	0.866025	+	0.500000i	$0.166667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$743$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.24280	+	0.283709i	3.24280	+	0.283709i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$751$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$752$		0			0
$753$	−0.745240	+	2.78127i	−0.745240	+	2.78127i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$757$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$758$	0.993464	+	1.41881i	0.993464	+	1.41881i
$759$		0			0
$760$		0			0
$761$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$761$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.81535	−	0.486421i	1.81535	−	0.486421i
$769$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$769$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$770$		0			0
$771$	0.326352	−	0.565258i	0.326352	−	0.565258i
$772$	0.965926	+	0.258819i	0.965926	+	0.258819i
$773$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$773$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$774$	4.12122	−	1.50000i	4.12122	−	1.50000i
$775$		0			0
$776$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$777$		0			0
$778$		0			0
$779$	−1.96962			−1.96962
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.342020	+	0.939693i	0.342020	+	0.939693i
$785$		0			0
$786$	0.326352	+	0.565258i	0.326352	+	0.565258i
$787$	−0.396534	−	1.47988i	−0.396534	−	1.47988i	−0.819152	−	0.573576i	$-0.805556\pi$
$787$	−0.396534	−	1.47988i	−0.396534	−	1.47988i	0.422618	−	0.906308i	$-0.361111\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.414754	+	4.74066i	−0.414754	+	4.74066i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$797$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−2.81908	+	3.35965i	−2.81908	+	3.35965i
$802$	0.289088	+	0.619951i	0.289088	+	0.619951i
$803$	−1.56439	+	3.35485i	−1.56439	+	3.35485i
$804$	0.419550	+	0.500000i	0.419550	+	0.500000i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.32683	+	0.766044i	1.32683	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$809$	1.32683	+	0.766044i	1.32683	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$810$		0			0
$811$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$811$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$818$	−0.483690	+	0.483690i	−0.483690	+	0.483690i
$819$		0			0
$820$		0			0
$821$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$821$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$822$	−1.16513	−	0.543308i	−1.16513	−	0.543308i
$823$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$823$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.53950	−	1.07797i	−1.53950	−	1.07797i	−0.965926	−	0.258819i	$-0.916667\pi$
$827$	−1.53950	−	1.07797i	−1.53950	−	1.07797i	−0.573576	−	0.819152i	$-0.694444\pi$
$828$		0			0
$829$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$829$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$	0.642788	+	0.113341i	0.642788	+	0.113341i
$835$		0			0
$836$	0.326352	−	1.85083i	0.326352	−	1.85083i
$837$		0			0
$838$	−1.63830	+	1.14715i	−1.63830	+	1.14715i
$839$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$839$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$840$		0			0
$841$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$842$		0			0
$843$	3.57554	+	0.958062i	3.57554	+	0.958062i
$844$	0.866025	−	1.50000i	0.866025	−	1.50000i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.984808	+	0.826352i	−0.984808	+	0.826352i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$853$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$854$		0			0
$855$		0			0
$856$	1.00000			1.00000
$857$	0.878770	+	1.25501i	0.878770	+	1.25501i	0.965926	+	0.258819i	$0.0833333\pi$
$857$	0.878770	+	1.25501i	0.878770	+	1.25501i	−0.0871557	+	0.996195i	$0.527778\pi$
$858$		0			0
$859$	0.118782	−	0.326352i	0.118782	−	0.326352i	−0.866025	−	0.500000i	$-0.833333\pi$
$859$	0.118782	−	0.326352i	0.118782	−	0.326352i	0.984808	+	0.173648i	$0.0555556\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$863$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$864$	2.83564	−	0.500000i	2.83564	−	0.500000i
$865$		0			0
$866$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$867$	1.81535	+	0.486421i	1.81535	+	0.486421i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−3.36496	−	3.36496i	−3.36496	−	3.36496i
$874$		0			0
$875$		0			0
$876$	3.64543	+	0.642788i	3.64543	+	0.642788i
$877$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$877$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$881$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$882$	0.655353	+	2.44581i	0.655353	+	2.44581i
$883$	−1.05308	−	0.737376i	−1.05308	−	0.737376i	−0.0871557	−	0.996195i	$-0.527778\pi$
$883$	−1.05308	−	0.737376i	−1.05308	−	0.737376i	−0.965926	+	0.258819i	$0.916667\pi$
$884$		0			0
$885$		0			0
$886$	1.11334	−	0.642788i	1.11334	−	0.642788i
$887$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$887$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.939693	+	5.32926i	−0.939693	+	5.32926i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.289088	−	0.619951i	0.289088	−	0.619951i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	2.12319	−	3.03223i	2.12319	−	3.03223i
$903$		0			0
$904$	−0.300767	−	0.173648i	−0.300767	−	0.173648i
$905$		0			0
$906$		0			0
$907$	0.647489	−	1.38854i	0.647489	−	1.38854i	−0.258819	−	0.965926i	$-0.583333\pi$
$907$	0.647489	−	1.38854i	0.647489	−	1.38854i	0.906308	−	0.422618i	$-0.138889\pi$
$908$	−0.794263	−	1.70330i	−0.794263	−	1.70330i
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−1.87223	+	0.163799i	−1.87223	+	0.163799i
$913$	1.70843	−	1.70843i	1.70843	−	1.70843i
$914$	0.223238	−	1.26604i	0.223238	−	1.26604i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$919$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$920$		0			0
$921$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.50881	+	0.266044i	1.50881	+	0.266044i	0.866025	−	0.500000i	$-0.166667\pi$
$929$	1.50881	+	0.266044i	1.50881	+	0.266044i	0.642788	+	0.766044i	$0.277778\pi$
$930$		0			0
$931$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$932$	1.39273	+	1.39273i	1.39273	+	1.39273i
$933$		0			0
$934$	−0.524005	−	0.439693i	−0.524005	−	0.439693i
$935$		0			0
$936$		0			0
$937$	0.681437	+	0.0596180i	0.681437	+	0.0596180i	0.422618	−	0.906308i	$-0.361111\pi$
$937$	0.681437	+	0.0596180i	0.681437	+	0.0596180i	0.258819	+	0.965926i	$0.416667\pi$
$938$		0			0
$939$	−1.85083	+	3.20574i	−1.85083	+	3.20574i
$940$		0			0
$941$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$941$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$942$		0			0
$943$		0			0
$944$	0.984808	−	0.826352i	0.984808	−	0.826352i
$945$		0			0
$946$	1.11334	−	3.05888i	1.11334	−	3.05888i
$947$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$947$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.163799	+	1.87223i	0.163799	+	1.87223i	0.422618	+	0.906308i	$0.361111\pi$
$953$	0.163799	+	1.87223i	0.163799	+	1.87223i	−0.258819	+	0.965926i	$0.583333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.500000	−	0.866025i	0.500000	−	0.866025i
$962$		0			0
$963$	2.52245	+	0.220686i	2.52245	+	0.220686i
$964$	1.20805	−	0.439693i	1.20805	−	0.439693i
$965$		0			0
$966$		0			0
$967$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$967$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$968$	1.79046	+	1.79046i	1.79046	+	1.79046i
$969$		0			0
$970$		0			0
$971$	0.673648	+	0.118782i	0.673648	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$971$	0.673648	+	0.118782i	0.673648	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$972$	2.52245	−	0.220686i	2.52245	−	0.220686i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.396534	+	1.47988i	0.396534	+	1.47988i	0.819152	+	0.573576i	$0.194444\pi$
$977$	0.396534	+	1.47988i	0.396534	+	1.47988i	−0.422618	+	0.906308i	$0.638889\pi$
$978$	−1.97915	−	1.38581i	−1.97915	−	1.38581i
$979$	0.565258	+	3.20574i	0.565258	+	3.20574i
$980$		0			0
$981$		0			0
$982$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$983$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$983$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$984$	−3.47843	−	1.26604i	−3.47843	−	1.26604i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$991$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$992$		0			0
$993$	1.56439	−	3.35485i	1.56439	−	3.35485i
$994$		0			0
$995$		0			0
$996$	−2.09240	−	1.20805i	−2.09240	−	1.20805i
$997$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$997$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$998$	−0.878770	+	1.25501i	−0.878770	+	1.25501i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3800.1.eb.c.3707.2	yes	24
5.2	odd	4	inner	3800.1.eb.c.2643.1	yes	24
5.3	odd	4	inner	3800.1.eb.c.2643.2	yes	24
5.4	even	2	inner	3800.1.eb.c.3707.1	yes	24
8.3	odd	2	CM	3800.1.eb.c.3707.2	yes	24
19.10	odd	18	inner	3800.1.eb.c.3107.2	yes	24
40.3	even	4	inner	3800.1.eb.c.2643.2	yes	24
40.19	odd	2	inner	3800.1.eb.c.3707.1	yes	24
40.27	even	4	inner	3800.1.eb.c.2643.1	yes	24
95.29	odd	18	inner	3800.1.eb.c.3107.1	yes	24
95.48	even	36	inner	3800.1.eb.c.2043.2	yes	24
95.67	even	36	inner	3800.1.eb.c.2043.1	✓	24
152.67	even	18	inner	3800.1.eb.c.3107.2	yes	24
760.67	odd	36	inner	3800.1.eb.c.2043.1	✓	24
760.219	even	18	inner	3800.1.eb.c.3107.1	yes	24
760.523	odd	36	inner	3800.1.eb.c.2043.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3800.1.eb.c.2043.1	✓	24	95.67	even	36	inner
3800.1.eb.c.2043.1	✓	24	760.67	odd	36	inner
3800.1.eb.c.2043.2	yes	24	95.48	even	36	inner
3800.1.eb.c.2043.2	yes	24	760.523	odd	36	inner
3800.1.eb.c.2643.1	yes	24	5.2	odd	4	inner
3800.1.eb.c.2643.1	yes	24	40.27	even	4	inner
3800.1.eb.c.2643.2	yes	24	5.3	odd	4	inner
3800.1.eb.c.2643.2	yes	24	40.3	even	4	inner
3800.1.eb.c.3107.1	yes	24	95.29	odd	18	inner
3800.1.eb.c.3107.1	yes	24	760.219	even	18	inner
3800.1.eb.c.3107.2	yes	24	19.10	odd	18	inner
3800.1.eb.c.3107.2	yes	24	152.67	even	18	inner
3800.1.eb.c.3707.1	yes	24	5.4	even	2	inner
3800.1.eb.c.3707.1	yes	24	40.19	odd	2	inner
3800.1.eb.c.3707.2	yes	24	1.1	even	1	trivial
3800.1.eb.c.3707.2	yes	24	8.3	odd	2	CM

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:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3800.eb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.163799 - 1.87223i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.43969 - 1.20805i) q^{6} +(-0.965926 + 0.258819i) q^{8} +(-2.49362 + 0.439693i) q^{9} +O(q^{10})\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.163799 - 1.87223i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.43969 - 1.20805i) q^{6} +(-0.965926 + 0.258819i) q^{8} +(-2.49362 + 0.439693i) q^{9} +(-0.939693 + 1.62760i) q^{11} +(1.81535 + 0.486421i) q^{12} +(-0.766044 - 0.642788i) q^{16} +(-1.79046 - 1.79046i) q^{18} +(0.642788 + 0.766044i) q^{19} +(-1.87223 + 0.163799i) q^{22} +(0.642788 + 1.76604i) q^{24} +(0.745240 + 2.78127i) q^{27} +(0.0871557 - 0.996195i) q^{32} +(3.20116 + 1.49273i) q^{33} +(0.439693 - 2.49362i) q^{36} +(-0.258819 + 0.965926i) q^{38} +(-1.26604 + 1.50881i) q^{41} +(-0.731996 + 1.56977i) q^{43} +(-1.20805 - 1.43969i) q^{44} +(-1.07797 + 1.53950i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-1.85083 + 2.20574i) q^{54} +(1.32893 - 1.32893i) q^{57} +(-0.223238 + 1.26604i) q^{59} +(0.866025 - 0.500000i) q^{64} +(0.613341 + 3.47843i) q^{66} +(0.284489 + 0.199201i) q^{67} +(2.29485 - 1.07011i) q^{72} +(1.96212 - 0.171663i) q^{73} +(-0.939693 + 0.342020i) q^{76} +(2.70574 - 0.984808i) q^{81} +(-1.96212 - 0.171663i) q^{82} +(-1.24177 - 0.332731i) q^{83} +(-1.70574 + 0.300767i) q^{86} +(0.486421 - 1.81535i) q^{88} +(1.32683 - 1.11334i) q^{89} -1.87939 q^{96} +(1.07797 + 1.53950i) q^{97} +(-0.0871557 - 0.996195i) q^{98} +(1.62760 - 4.47178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{6}+O(q^{10}) \) 24 * q + 12 * q^6	\( 24 q + 12 q^{6} - 12 q^{36} - 12 q^{41} - 12 q^{66} + 24 q^{81}+O(q^{100}) \) 24 * q + 12 * q^6 - 12 * q^36 - 12 * q^41 - 12 * q^66 + 24 * q^81

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