LMFDB - Embedded newform 1520.1.bh.c.189.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,1,Mod(189,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 2]))

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

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

chi := DirichletCharacter("1520.189");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1520.bh (of order $4$, degree $2$, 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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{32})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1 $ x^16 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{16}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{16} - \cdots)$

Embedding invariants

Embedding label			189.7
Root			$-0.980785 + 0.195090i$ of defining polynomial
Character	$\chi$	$=$	1520.189
Dual form			1520.1.bh.c.949.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831470 - 0.555570i) q^{2} +(-0.785695 - 0.785695i) q^{3} +(0.382683 - 0.923880i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.08979 - 0.216773i) q^{6} +(-0.195090 - 0.980785i) q^{8} +0.234633i q^{9} +O(q^{10})$	\(q+(0.831470 - 0.555570i) q^{2} +(-0.785695 - 0.785695i) q^{3} +(0.382683 - 0.923880i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.08979 - 0.216773i) q^{6} +(-0.195090 - 0.980785i) q^{8} +0.234633i q^{9} +(-0.195090 + 0.980785i) q^{10} +(-1.30656 + 1.30656i) q^{11} +(-1.02656 + 0.425215i) q^{12} +(-1.38704 - 1.38704i) q^{13} +1.11114 q^{15} +(-0.707107 - 0.707107i) q^{16} +(0.130355 + 0.195090i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(0.382683 + 0.923880i) q^{20} +(-0.360480 + 1.81225i) q^{22} +(-0.617317 + 0.923880i) q^{24} -1.00000i q^{25} +(-1.92388 - 0.382683i) q^{26} +(-0.601345 + 0.601345i) q^{27} +(0.923880 - 0.617317i) q^{30} +(-0.980785 - 0.195090i) q^{32} +2.05312 q^{33} +(0.216773 + 0.0897902i) q^{36} +(1.17588 - 1.17588i) q^{37} +(-0.980785 - 0.195090i) q^{38} +2.17958i q^{39} +(0.831470 + 0.555570i) q^{40} +(0.707107 + 1.70711i) q^{44} +(-0.165911 - 0.165911i) q^{45} +1.11114i q^{48} -1.00000 q^{49} +(-0.555570 - 0.831470i) q^{50} +(-1.81225 + 0.750661i) q^{52} +(0.785695 - 0.785695i) q^{53} +(-0.165911 + 0.834089i) q^{54} -1.84776i q^{55} +1.11114i q^{57} +(0.425215 - 1.02656i) q^{60} +(1.30656 + 1.30656i) q^{61} +(-0.923880 + 0.382683i) q^{64} +1.96157 q^{65} +(1.70711 - 1.14065i) q^{66} +(0.275899 + 0.275899i) q^{67} +(0.230125 - 0.0457747i) q^{72} +(0.324423 - 1.63099i) q^{74} +(-0.785695 + 0.785695i) q^{75} +(-0.923880 + 0.382683i) q^{76} +(1.21091 + 1.81225i) q^{78} +1.00000 q^{80} +1.17958 q^{81} +(1.53636 + 1.02656i) q^{88} +(-0.230125 - 0.0457747i) q^{90} +1.00000 q^{95} +(0.617317 + 0.923880i) q^{96} -1.96157 q^{97} +(-0.831470 + 0.555570i) q^{98} +(-0.306563 - 0.306563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 16 q^{24} - 16 q^{26} - 16 q^{49} + 16 q^{66} + 16 q^{80} - 16 q^{81} + 16 q^{95} + 16 q^{96} + 16 q^{99}+O(q^{100}) $ 16 * q - 16 * q^24 - 16 * q^26 - 16 * q^49 + 16 * q^66 + 16 * q^80 - 16 * q^81 + 16 * q^95 + 16 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.831470	−	0.555570i	0.831470	−	0.555570i
$2$	0.831470	−	0.555570i	0.831470	−	0.555570i
$3$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$3$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	−0.980785	+	0.195090i	$0.937500\pi$
$4$	0.382683	−	0.923880i	0.382683	−	0.923880i
$5$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$5$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$6$	−1.08979	−	0.216773i	−1.08979	−	0.216773i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$9$			0.234633i			0.234633i
$10$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$11$	−1.30656	+	1.30656i	−1.30656	+	1.30656i	−0.382683	+	0.923880i	$0.625000\pi$
$11$	−1.30656	+	1.30656i	−1.30656	+	1.30656i	−0.923880	+	0.382683i	$0.875000\pi$
$12$	−1.02656	+	0.425215i	−1.02656	+	0.425215i
$13$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$13$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$14$		0			0
$15$	1.11114			1.11114
$16$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	0.130355	+	0.195090i	0.130355	+	0.195090i
$19$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$19$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$20$	0.382683	+	0.923880i	0.382683	+	0.923880i
$21$		0			0
$22$	−0.360480	+	1.81225i	−0.360480	+	1.81225i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−0.617317	+	0.923880i	−0.617317	+	0.923880i
$25$		−	1.00000i		−	1.00000i
$26$	−1.92388	−	0.382683i	−1.92388	−	0.382683i
$27$	−0.601345	+	0.601345i	−0.601345	+	0.601345i
$28$		0			0
$29$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$29$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$30$	0.923880	−	0.617317i	0.923880	−	0.617317i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$33$	2.05312			2.05312
$34$		0			0
$35$		0			0
$36$	0.216773	+	0.0897902i	0.216773	+	0.0897902i
$37$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.195090	−	0.980785i	$-0.437500\pi$
$37$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.980785	−	0.195090i	$-0.0625000\pi$
$38$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$39$			2.17958i			2.17958i
$40$	0.831470	+	0.555570i	0.831470	+	0.555570i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	0.707107	+	1.70711i	0.707107	+	1.70711i
$45$	−0.165911	−	0.165911i	−0.165911	−	0.165911i
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$			1.11114i			1.11114i
$49$	−1.00000			−1.00000
$50$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$51$		0			0
$52$	−1.81225	+	0.750661i	−1.81225	+	0.750661i
$53$	0.785695	−	0.785695i	0.785695	−	0.785695i	−0.195090	−	0.980785i	$-0.562500\pi$
$53$	0.785695	−	0.785695i	0.785695	−	0.785695i	0.980785	+	0.195090i	$0.0625000\pi$
$54$	−0.165911	+	0.834089i	−0.165911	+	0.834089i
$55$		−	1.84776i		−	1.84776i
$56$		0			0
$57$			1.11114i			1.11114i
$58$		0			0
$59$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$59$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$60$	0.425215	−	1.02656i	0.425215	−	1.02656i
$61$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$61$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$62$		0			0
$63$		0			0
$64$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$65$	1.96157			1.96157
$66$	1.70711	−	1.14065i	1.70711	−	1.14065i
$67$	0.275899	+	0.275899i	0.275899	+	0.275899i	0.831470	−	0.555570i	$-0.187500\pi$
$67$	0.275899	+	0.275899i	0.275899	+	0.275899i	−0.555570	+	0.831470i	$0.687500\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	0.230125	−	0.0457747i	0.230125	−	0.0457747i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	0.324423	−	1.63099i	0.324423	−	1.63099i
$75$	−0.785695	+	0.785695i	−0.785695	+	0.785695i
$76$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$77$		0			0
$78$	1.21091	+	1.81225i	1.21091	+	1.81225i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	1.00000			1.00000
$81$	1.17958			1.17958
$82$		0			0
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.53636	+	1.02656i	1.53636	+	1.02656i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	−0.230125	−	0.0457747i	−0.230125	−	0.0457747i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.00000			1.00000
$96$	0.617317	+	0.923880i	0.617317	+	0.923880i
$97$	−1.96157			−1.96157			−0.980785	−	0.195090i	$-0.937500\pi$
$97$	−1.96157			−1.96157			−0.980785	+	0.195090i	$0.937500\pi$
$98$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$99$	−0.306563	−	0.306563i	−0.306563	−	0.306563i
$100$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$101$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$101$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.923880	−	0.382683i	$-0.125000\pi$
$102$		0			0
$103$		−	1.66294i		−	1.66294i	−0.555570	−	0.831470i	$-0.687500\pi$
$103$		−	1.66294i		−	1.66294i	0.555570	−	0.831470i	$-0.312500\pi$
$104$	−1.08979	+	1.63099i	−1.08979	+	1.63099i
$105$		0			0
$106$	0.216773	−	1.08979i	0.216773	−	1.08979i
$107$	−0.275899	+	0.275899i	−0.275899	+	0.275899i	−0.831470	−	0.555570i	$-0.812500\pi$
$107$	−0.275899	+	0.275899i	−0.275899	+	0.275899i	0.555570	+	0.831470i	$0.312500\pi$
$108$	0.325446	+	0.785695i	0.325446	+	0.785695i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$	−1.02656	−	1.53636i	−1.02656	−	1.53636i
$111$	−1.84776			−1.84776
$112$		0			0
$113$	−1.11114			−1.11114			−0.555570	−	0.831470i	$-0.687500\pi$
$113$	−1.11114			−1.11114			−0.555570	+	0.831470i	$0.687500\pi$
$114$	0.617317	+	0.923880i	0.617317	+	0.923880i
$115$		0			0
$116$		0			0
$117$	0.325446	−	0.325446i	0.325446	−	0.325446i
$118$		0			0
$119$		0			0
$120$	−0.216773	−	1.08979i	−0.216773	−	1.08979i
$121$		−	2.41421i		−	2.41421i
$122$	1.81225	+	0.360480i	1.81225	+	0.360480i
$123$		0			0
$124$		0			0
$125$	0.707107	+	0.707107i	0.707107	+	0.707107i
$126$		0			0
$127$	0.390181			0.390181			0.195090	−	0.980785i	$-0.437500\pi$
$127$	0.390181			0.390181			0.195090	+	0.980785i	$0.437500\pi$
$128$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$129$		0			0
$130$	1.63099	−	1.08979i	1.63099	−	1.08979i
$131$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$131$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$132$	0.785695	−	1.89684i	0.785695	−	1.89684i
$133$		0			0
$134$	0.382683	+	0.0761205i	0.382683	+	0.0761205i
$135$		−	0.850430i		−	0.850430i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	0.541196	−	0.541196i	0.541196	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$139$	0.541196	−	0.541196i	0.541196	−	0.541196i	0.923880	+	0.382683i	$0.125000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.62451			3.62451
$144$	0.165911	−	0.165911i	0.165911	−	0.165911i
$145$		0			0
$146$		0			0
$147$	0.785695	+	0.785695i	0.785695	+	0.785695i
$148$	−0.636379	−	1.53636i	−0.636379	−	1.53636i
$149$	0.541196	−	0.541196i	0.541196	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$149$	0.541196	−	0.541196i	0.541196	−	0.541196i	0.923880	+	0.382683i	$0.125000\pi$
$150$	−0.216773	+	1.08979i	−0.216773	+	1.08979i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	2.01367	+	0.834089i	2.01367	+	0.834089i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$	−1.23463			−1.23463
$160$	0.831470	−	0.555570i	0.831470	−	0.555570i
$161$		0			0
$162$	0.980785	−	0.655340i	0.980785	−	0.655340i
$163$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$163$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$164$		0			0
$165$	−1.45177	+	1.45177i	−1.45177	+	1.45177i
$166$		0			0
$167$			0.390181i			0.390181i	0.980785	+	0.195090i	$0.0625000\pi$
$167$			0.390181i			0.390181i	−0.980785	+	0.195090i	$0.937500\pi$
$168$		0			0
$169$			2.84776i			2.84776i
$170$		0			0
$171$	0.165911	−	0.165911i	0.165911	−	0.165911i
$172$		0			0
$173$	−0.275899	−	0.275899i	−0.275899	−	0.275899i	0.555570	−	0.831470i	$-0.312500\pi$
$173$	−0.275899	−	0.275899i	−0.275899	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$174$		0			0
$175$		0			0
$176$	1.84776			1.84776
$177$		0			0
$178$		0			0
$179$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$179$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$180$	−0.216773	+	0.0897902i	−0.216773	+	0.0897902i
$181$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$181$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$182$		0			0
$183$		−	2.05312i		−	2.05312i
$184$		0			0
$185$			1.66294i			1.66294i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.831470	−	0.555570i	0.831470	−	0.555570i
$191$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$191$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$192$	1.02656	+	0.425215i	1.02656	+	0.425215i
$193$	−0.390181			−0.390181			−0.195090	−	0.980785i	$-0.562500\pi$
$193$	−0.390181			−0.390181			−0.195090	+	0.980785i	$0.562500\pi$
$194$	−1.63099	+	1.08979i	−1.63099	+	1.08979i
$195$	−1.54120	−	1.54120i	−1.54120	−	1.54120i
$196$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$	−0.425215	−	0.0845805i	−0.425215	−	0.0845805i
$199$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$199$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$200$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$201$		−	0.433546i		−	0.433546i
$202$	0.360480	−	1.81225i	0.360480	−	1.81225i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.923880	−	1.38268i	−0.923880	−	1.38268i
$207$		0			0
$208$			1.96157i			1.96157i
$209$	1.84776			1.84776
$210$		0			0
$211$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$211$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$212$	−0.425215	−	1.02656i	−0.425215	−	1.02656i
$213$		0			0
$214$	−0.0761205	+	0.382683i	−0.0761205	+	0.382683i
$215$		0			0
$216$	0.707107	+	0.472474i	0.707107	+	0.472474i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.70711	−	0.707107i	−1.70711	−	0.707107i
$221$		0			0
$222$	−1.53636	+	1.02656i	−1.53636	+	1.02656i
$223$	−1.96157			−1.96157			−0.980785	−	0.195090i	$-0.937500\pi$
$223$	−1.96157			−1.96157			−0.980785	+	0.195090i	$0.937500\pi$
$224$		0			0
$225$	0.234633			0.234633
$226$	−0.923880	+	0.617317i	−0.923880	+	0.617317i
$227$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$227$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$228$	1.02656	+	0.425215i	1.02656	+	0.425215i
$229$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	−0.923880	−	0.382683i	$-0.875000\pi$
$229$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	0.382683	+	0.923880i	$0.375000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	0.0897902	−	0.451406i	0.0897902	−	0.451406i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−0.785695	−	0.785695i	−0.785695	−	0.785695i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−1.34127	−	2.00735i	−1.34127	−	2.00735i
$243$	−0.325446	−	0.325446i	−0.325446	−	0.325446i
$244$	1.70711	−	0.707107i	1.70711	−	0.707107i
$245$	0.707107	−	0.707107i	0.707107	−	0.707107i
$246$		0			0
$247$			1.96157i			1.96157i
$248$		0			0
$249$		0			0
$250$	0.980785	+	0.195090i	0.980785	+	0.195090i
$251$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$251$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$252$		0			0
$253$		0			0
$254$	0.324423	−	0.216773i	0.324423	−	0.216773i
$255$		0			0
$256$			1.00000i			1.00000i
$257$	−0.390181			−0.390181			−0.195090	−	0.980785i	$-0.562500\pi$
$257$	−0.390181			−0.390181			−0.195090	+	0.980785i	$0.562500\pi$
$258$		0			0
$259$		0			0
$260$	0.750661	−	1.81225i	0.750661	−	1.81225i
$261$		0			0
$262$	−1.38704	−	0.275899i	−1.38704	−	0.275899i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−0.400544	−	2.01367i	−0.400544	−	2.01367i
$265$			1.11114i			1.11114i
$266$		0			0
$267$		0			0
$268$	0.360480	−	0.149316i	0.360480	−	0.149316i
$269$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$269$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$270$	−0.472474	−	0.707107i	−0.472474	−	0.707107i
$271$	−0.765367			−0.765367			−0.382683	−	0.923880i	$-0.625000\pi$
$271$	−0.765367			−0.765367			−0.382683	+	0.923880i	$0.625000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.30656	+	1.30656i	1.30656	+	1.30656i
$276$		0			0
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	0.149316	−	0.750661i	0.149316	−	0.750661i
$279$		0			0
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		0			0
$285$	−0.785695	−	0.785695i	−0.785695	−	0.785695i
$286$	3.01367	−	2.01367i	3.01367	−	2.01367i
$287$		0			0
$288$	0.0457747	−	0.230125i	0.0457747	−	0.230125i
$289$	1.00000			1.00000
$290$		0			0
$291$	1.54120	+	1.54120i	1.54120	+	1.54120i
$292$		0			0
$293$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$293$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$294$	1.08979	+	0.216773i	1.08979	+	0.216773i
$295$		0			0
$296$	−1.38268	−	0.923880i	−1.38268	−	0.923880i
$297$		−	1.57139i		−	1.57139i
$298$	0.149316	−	0.750661i	0.149316	−	0.750661i
$299$		0			0
$300$	0.425215	+	1.02656i	0.425215	+	1.02656i
$301$		0			0
$302$		0			0
$303$	−2.05312			−2.05312
$304$			1.00000i			1.00000i
$305$	−1.84776			−1.84776
$306$		0			0
$307$	1.38704	+	1.38704i	1.38704	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$307$	1.38704	+	1.38704i	1.38704	+	1.38704i	0.555570	+	0.831470i	$0.312500\pi$
$308$		0			0
$309$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$310$		0			0
$311$			1.84776i			1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$311$			1.84776i			1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$312$	2.13770	−	0.425215i	2.13770	−	0.425215i
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.275899	−	0.275899i	−0.275899	−	0.275899i	0.555570	−	0.831470i	$-0.312500\pi$
$317$	−0.275899	−	0.275899i	−0.275899	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$318$	−1.02656	+	0.685925i	−1.02656	+	0.685925i
$319$		0			0
$320$	0.382683	−	0.923880i	0.382683	−	0.923880i
$321$	0.433546			0.433546
$322$		0			0
$323$		0			0
$324$	0.451406	−	1.08979i	0.451406	−	1.08979i
$325$	−1.38704	+	1.38704i	−1.38704	+	1.38704i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.400544	+	2.01367i	−0.400544	+	2.01367i
$331$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$331$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$332$		0			0
$333$	0.275899	+	0.275899i	0.275899	+	0.275899i
$334$	0.216773	+	0.324423i	0.216773	+	0.324423i
$335$	−0.390181			−0.390181
$336$		0			0
$337$	1.66294			1.66294			0.831470	−	0.555570i	$-0.187500\pi$
$337$	1.66294			1.66294			0.831470	+	0.555570i	$0.187500\pi$
$338$	1.58213	+	2.36783i	1.58213	+	2.36783i
$339$	0.873017	+	0.873017i	0.873017	+	0.873017i
$340$		0			0
$341$		0			0
$342$	0.0457747	−	0.230125i	0.0457747	−	0.230125i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.382683	−	0.0761205i	−0.382683	−	0.0761205i
$347$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$347$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$348$		0			0
$349$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$349$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$350$		0			0
$351$	1.66818			1.66818
$352$	1.53636	−	1.02656i	1.53636	−	1.02656i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	0.765367i		−	0.765367i	−0.923880	−	0.382683i	$-0.875000\pi$
$359$		−	0.765367i		−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$360$	−0.130355	+	0.195090i	−0.130355	+	0.195090i
$361$			1.00000i			1.00000i
$362$		0			0
$363$	−1.89684	+	1.89684i	−1.89684	+	1.89684i
$364$		0			0
$365$		0			0
$366$	−1.14065	−	1.70711i	−1.14065	−	1.70711i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$		0			0
$370$	0.923880	+	1.38268i	0.923880	+	1.38268i
$371$		0			0
$372$		0			0
$373$	−0.785695	+	0.785695i	−0.785695	+	0.785695i	−0.980785	−	0.195090i	$-0.937500\pi$
$373$	−0.785695	+	0.785695i	−0.785695	+	0.785695i	0.195090	+	0.980785i	$0.437500\pi$
$374$		0			0
$375$		−	1.11114i		−	1.11114i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$379$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$380$	0.382683	−	0.923880i	0.382683	−	0.923880i
$381$	−0.306563	−	0.306563i	−0.306563	−	0.306563i
$382$	1.17588	−	0.785695i	1.17588	−	0.785695i
$383$	1.66294			1.66294			0.831470	−	0.555570i	$-0.187500\pi$
$383$	1.66294			1.66294			0.831470	+	0.555570i	$0.187500\pi$
$384$	1.08979	−	0.216773i	1.08979	−	0.216773i
$385$		0			0
$386$	−0.324423	+	0.216773i	−0.324423	+	0.216773i
$387$		0			0
$388$	−0.750661	+	1.81225i	−0.750661	+	1.81225i
$389$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$389$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$390$	−2.13770	−	0.425215i	−2.13770	−	0.425215i
$391$		0			0
$392$	0.195090	+	0.980785i	0.195090	+	0.980785i
$393$			1.57139i			1.57139i
$394$		0			0
$395$		0			0
$396$	−0.400544	+	0.165911i	−0.400544	+	0.165911i
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$399$		0			0
$400$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$	−0.240865	−	0.360480i	−0.240865	−	0.360480i
$403$		0			0
$404$	−0.707107	−	1.70711i	−0.707107	−	1.70711i
$405$	−0.834089	+	0.834089i	−0.834089	+	0.834089i
$406$		0			0
$407$			3.07271i			3.07271i
$408$		0			0
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$		0			0
$411$		0			0
$412$	−1.53636	−	0.636379i	−1.53636	−	0.636379i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	1.08979	+	1.63099i	1.08979	+	1.63099i
$417$	−0.850430			−0.850430
$418$	1.53636	−	1.02656i	1.53636	−	1.02656i
$419$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$419$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$		0			0
$423$		0			0
$424$	−0.923880	−	0.617317i	−0.923880	−	0.617317i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.149316	+	0.360480i	0.149316	+	0.360480i
$429$	−2.84776	−	2.84776i	−2.84776	−	2.84776i
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	0.850430			0.850430
$433$	1.11114			1.11114			0.555570	−	0.831470i	$-0.312500\pi$
$433$	1.11114			1.11114			0.555570	+	0.831470i	$0.312500\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	−1.81225	+	0.360480i	−1.81225	+	0.360480i
$441$		−	0.234633i		−	0.234633i
$442$		0			0
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$	−0.707107	+	1.70711i	−0.707107	+	1.70711i
$445$		0			0
$446$	−1.63099	+	1.08979i	−1.63099	+	1.08979i
$447$	−0.850430			−0.850430
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	0.195090	−	0.130355i	0.195090	−	0.130355i
$451$		0			0
$452$	−0.425215	+	1.02656i	−0.425215	+	1.02656i
$453$		0			0
$454$	−1.92388	−	0.382683i	−1.92388	−	0.382683i
$455$		0			0
$456$	1.08979	−	0.216773i	1.08979	−	0.216773i
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$	−0.149316	+	0.750661i	−0.149316	+	0.750661i
$459$		0			0
$460$		0			0
$461$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$461$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$	−0.176130	−	0.425215i	−0.176130	−	0.425215i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$476$		0			0
$477$	0.184350	+	0.184350i	0.184350	+	0.184350i
$478$		0			0
$479$	−1.84776			−1.84776			−0.923880	−	0.382683i	$-0.875000\pi$
$479$	−1.84776			−1.84776			−0.923880	+	0.382683i	$0.875000\pi$
$480$	−1.08979	−	0.216773i	−1.08979	−	0.216773i
$481$	−3.26197			−3.26197
$482$		0			0
$483$		0			0
$484$	−2.23044	−	0.923880i	−2.23044	−	0.923880i
$485$	1.38704	−	1.38704i	1.38704	−	1.38704i
$486$	−0.451406	−	0.0897902i	−0.451406	−	0.0897902i
$487$		−	1.11114i		−	1.11114i	−0.831470	−	0.555570i	$-0.812500\pi$
$487$		−	1.11114i		−	1.11114i	0.831470	−	0.555570i	$-0.187500\pi$
$488$	1.02656	−	1.53636i	1.02656	−	1.53636i
$489$		0			0
$490$	0.195090	−	0.980785i	0.195090	−	0.980785i
$491$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$491$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$492$		0			0
$493$		0			0
$494$	1.08979	+	1.63099i	1.08979	+	1.63099i
$495$	0.433546			0.433546
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.541196	+	0.541196i	0.541196	+	0.541196i	0.923880	−	0.382683i	$-0.125000\pi$
$499$	0.541196	+	0.541196i	0.541196	+	0.541196i	−0.382683	+	0.923880i	$0.625000\pi$
$500$	0.923880	−	0.382683i	0.923880	−	0.382683i
$501$	0.306563	−	0.306563i	0.306563	−	0.306563i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$			1.84776i			1.84776i
$506$		0			0
$507$	2.23747	−	2.23747i	2.23747	−	2.23747i
$508$	0.149316	−	0.360480i	0.149316	−	0.360480i
$509$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$509$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$510$		0			0
$511$		0			0
$512$	0.555570	+	0.831470i	0.555570	+	0.831470i
$513$	0.850430			0.850430
$514$	−0.324423	+	0.216773i	−0.324423	+	0.216773i
$515$	1.17588	+	1.17588i	1.17588	+	1.17588i
$516$		0			0
$517$		0			0
$518$		0			0
$519$			0.433546i			0.433546i
$520$	−0.382683	−	1.92388i	−0.382683	−	1.92388i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.195090	−	0.980785i	$-0.437500\pi$
$523$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.980785	−	0.195090i	$-0.0625000\pi$
$524$	−1.30656	+	0.541196i	−1.30656	+	0.541196i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.45177	−	1.45177i	−1.45177	−	1.45177i
$529$	−1.00000			−1.00000
$530$	0.617317	+	0.923880i	0.617317	+	0.923880i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		−	0.390181i		−	0.390181i
$536$	0.216773	−	0.324423i	0.216773	−	0.324423i
$537$		0			0
$538$		0			0
$539$	1.30656	−	1.30656i	1.30656	−	1.30656i
$540$	−0.785695	−	0.325446i	−0.785695	−	0.325446i
$541$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$541$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$542$	−0.636379	+	0.425215i	−0.636379	+	0.425215i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.17588	−	1.17588i	−1.17588	−	1.17588i	−0.980785	−	0.195090i	$-0.937500\pi$
$547$	−1.17588	−	1.17588i	−1.17588	−	1.17588i	−0.195090	−	0.980785i	$-0.562500\pi$
$548$		0			0
$549$	−0.306563	+	0.306563i	−0.306563	+	0.306563i
$550$	1.81225	+	0.360480i	1.81225	+	0.360480i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.30656	−	1.30656i	1.30656	−	1.30656i
$556$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.17588	+	1.17588i	1.17588	+	1.17588i	0.980785	+	0.195090i	$0.0625000\pi$
$563$	1.17588	+	1.17588i	1.17588	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$564$		0			0
$565$	0.785695	−	0.785695i	0.785695	−	0.785695i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$	−1.08979	−	0.216773i	−1.08979	−	0.216773i
$571$	0.541196	−	0.541196i	0.541196	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$571$	0.541196	−	0.541196i	0.541196	−	0.541196i	0.923880	+	0.382683i	$0.125000\pi$
$572$	1.38704	−	3.34861i	1.38704	−	3.34861i
$573$	−1.11114	−	1.11114i	−1.11114	−	1.11114i
$574$		0			0
$575$		0			0
$576$	−0.0897902	−	0.216773i	−0.0897902	−	0.216773i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.831470	−	0.555570i	0.831470	−	0.555570i
$579$	0.306563	+	0.306563i	0.306563	+	0.306563i
$580$		0			0
$581$		0			0
$582$	2.13770	+	0.425215i	2.13770	+	0.425215i
$583$			2.05312i			2.05312i
$584$		0			0
$585$			0.460249i			0.460249i
$586$	−0.324423	+	1.63099i	−0.324423	+	1.63099i
$587$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$587$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$588$	1.02656	−	0.425215i	1.02656	−	0.425215i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.66294			−1.66294
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−0.873017	−	1.30656i	−0.873017	−	1.30656i
$595$		0			0
$596$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$597$	−1.11114	+	1.11114i	−1.11114	+	1.11114i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	0.923880	+	0.617317i	0.923880	+	0.617317i
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$	−0.0647351	+	0.0647351i	−0.0647351	+	0.0647351i
$604$		0			0
$605$	1.70711	+	1.70711i	1.70711	+	1.70711i
$606$	−1.70711	+	1.14065i	−1.70711	+	1.14065i
$607$	1.11114			1.11114			0.555570	−	0.831470i	$-0.312500\pi$
$607$	1.11114			1.11114			0.555570	+	0.831470i	$0.312500\pi$
$608$	0.555570	+	0.831470i	0.555570	+	0.831470i
$609$		0			0
$610$	−1.53636	+	1.02656i	−1.53636	+	1.02656i
$611$		0			0
$612$		0			0
$613$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$613$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$614$	1.92388	+	0.382683i	1.92388	+	0.382683i
$615$		0			0
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$	−0.360480	+	1.81225i	−0.360480	+	1.81225i
$619$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$619$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.923880	−	0.382683i	$-0.125000\pi$
$620$		0			0
$621$		0			0
$622$	1.02656	+	1.53636i	1.02656	+	1.53636i
$623$		0			0
$624$	1.54120	−	1.54120i	1.54120	−	1.54120i
$625$	−1.00000			−1.00000
$626$		0			0
$627$	−1.45177	−	1.45177i	−1.45177	−	1.45177i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		−	0.765367i		−	0.765367i	−0.923880	−	0.382683i	$-0.875000\pi$
$631$		−	0.765367i		−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$632$		0			0
$633$		0			0
$634$	−0.382683	−	0.0761205i	−0.382683	−	0.0761205i
$635$	−0.275899	+	0.275899i	−0.275899	+	0.275899i
$636$	−0.472474	+	1.14065i	−0.472474	+	1.14065i
$637$	1.38704	+	1.38704i	1.38704	+	1.38704i
$638$		0			0
$639$		0			0
$640$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	0.360480	−	0.240865i	0.360480	−	0.240865i
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−0.230125	−	1.15692i	−0.230125	−	1.15692i
$649$		0			0
$650$	−0.382683	+	1.92388i	−0.382683	+	1.92388i
$651$		0			0
$652$		0			0
$653$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$653$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$654$		0			0
$655$	1.41421			1.41421
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$659$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$660$	0.785695	+	1.89684i	0.785695	+	1.89684i
$661$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$661$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.382683	+	0.0761205i	0.382683	+	0.0761205i
$667$		0			0
$668$	0.360480	+	0.149316i	0.360480	+	0.149316i
$669$	1.54120	+	1.54120i	1.54120	+	1.54120i
$670$	−0.324423	+	0.216773i	−0.324423	+	0.216773i
$671$	−3.41421			−3.41421
$672$		0			0
$673$	−1.66294			−1.66294			−0.831470	−	0.555570i	$-0.812500\pi$
$673$	−1.66294			−1.66294			−0.831470	+	0.555570i	$0.812500\pi$
$674$	1.38268	−	0.923880i	1.38268	−	0.923880i
$675$	0.601345	+	0.601345i	0.601345	+	0.601345i
$676$	2.63099	+	1.08979i	2.63099	+	1.08979i
$677$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.195090	−	0.980785i	$-0.437500\pi$
$677$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.980785	−	0.195090i	$-0.0625000\pi$
$678$	1.21091	+	0.240865i	1.21091	+	0.240865i
$679$		0			0
$680$		0			0
$681$			2.17958i			2.17958i
$682$		0			0
$683$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$683$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$684$	−0.0897902	−	0.216773i	−0.0897902	−	0.216773i
$685$		0			0
$686$		0			0
$687$	0.850430			0.850430
$688$		0			0
$689$	−2.17958			−2.17958
$690$		0			0
$691$	−1.30656	−	1.30656i	−1.30656	−	1.30656i	−0.923880	−	0.382683i	$-0.875000\pi$
$691$	−1.30656	−	1.30656i	−1.30656	−	1.30656i	−0.382683	−	0.923880i	$-0.625000\pi$
$692$	−0.360480	+	0.149316i	−0.360480	+	0.149316i
$693$		0			0
$694$		0			0
$695$			0.765367i			0.765367i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$701$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$702$	1.38704	−	0.926790i	1.38704	−	0.926790i
$703$	−1.66294			−1.66294
$704$	0.707107	−	1.70711i	0.707107	−	1.70711i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$709$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−2.56292	+	2.56292i	−2.56292	+	2.56292i
$716$		0			0
$717$		0			0
$718$	−0.425215	−	0.636379i	−0.425215	−	0.636379i
$719$	0.765367			0.765367			0.382683	−	0.923880i	$-0.375000\pi$
$719$	0.765367			0.765367			0.382683	+	0.923880i	$0.375000\pi$
$720$			0.234633i			0.234633i
$721$		0			0
$722$	0.555570	+	0.831470i	0.555570	+	0.831470i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.523336	+	2.63099i	−0.523336	+	2.63099i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$		−	0.668179i		−	0.668179i
$730$		0			0
$731$		0			0
$732$	−1.89684	−	0.785695i	−1.89684	−	0.785695i
$733$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$733$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$734$		0			0
$735$	−1.11114			−1.11114
$736$		0			0
$737$	−0.720960			−0.720960
$738$		0			0
$739$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$739$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$740$	1.53636	+	0.636379i	1.53636	+	0.636379i
$741$	1.54120	−	1.54120i	1.54120	−	1.54120i
$742$		0			0
$743$		−	1.96157i		−	1.96157i	−0.195090	−	0.980785i	$-0.562500\pi$
$743$		−	1.96157i		−	1.96157i	0.195090	−	0.980785i	$-0.437500\pi$
$744$		0			0
$745$			0.765367i			0.765367i
$746$	−0.216773	+	1.08979i	−0.216773	+	1.08979i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.617317	−	0.923880i	−0.617317	−	0.923880i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		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
$760$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$761$		−	1.84776i		−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$761$		−	1.84776i		−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$762$	−0.425215	−	0.0845805i	−0.425215	−	0.0845805i
$763$		0			0
$764$	0.541196	−	1.30656i	0.541196	−	1.30656i
$765$		0			0
$766$	1.38268	−	0.923880i	1.38268	−	0.923880i
$767$		0			0
$768$	0.785695	−	0.785695i	0.785695	−	0.785695i
$769$	0.765367			0.765367			0.382683	−	0.923880i	$-0.375000\pi$
$769$	0.765367			0.765367			0.382683	+	0.923880i	$0.375000\pi$
$770$		0			0
$771$	0.306563	+	0.306563i	0.306563	+	0.306563i
$772$	−0.149316	+	0.360480i	−0.149316	+	0.360480i
$773$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$773$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$774$		0			0
$775$		0			0
$776$	0.382683	+	1.92388i	0.382683	+	1.92388i
$777$		0			0
$778$	0.275899	−	1.38704i	0.275899	−	1.38704i
$779$		0			0
$780$	−2.01367	+	0.834089i	−2.01367	+	0.834089i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.707107	+	0.707107i	0.707107	+	0.707107i
$785$		0			0
$786$	0.873017	+	1.30656i	0.873017	+	1.30656i
$787$	−1.17588	−	1.17588i	−1.17588	−	1.17588i	−0.980785	−	0.195090i	$-0.937500\pi$
$787$	−1.17588	−	1.17588i	−1.17588	−	1.17588i	−0.195090	−	0.980785i	$-0.562500\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.240865	+	0.360480i	−0.240865	+	0.360480i
$793$		−	3.62451i		−	3.62451i
$794$		0			0
$795$	0.873017	−	0.873017i	0.873017	−	0.873017i
$796$	−1.30656	−	0.541196i	−1.30656	−	0.541196i
$797$	1.17588	+	1.17588i	1.17588	+	1.17588i	0.980785	+	0.195090i	$0.0625000\pi$
$797$	1.17588	+	1.17588i	1.17588	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$798$		0			0
$799$		0			0
$800$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−0.400544	−	0.165911i	−0.400544	−	0.165911i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.53636	−	1.02656i	−1.53636	−	1.02656i
$809$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$809$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$810$	−0.230125	+	1.15692i	−0.230125	+	1.15692i
$811$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$811$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$	0.601345	+	0.601345i	0.601345	+	0.601345i
$814$	1.70711	+	2.55487i	1.70711	+	2.55487i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$821$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$822$		0			0
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$	−1.63099	+	0.324423i	−1.63099	+	0.324423i
$825$		−	2.05312i		−	2.05312i
$826$		0			0
$827$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$827$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$828$		0			0
$829$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$829$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$830$		0			0
$831$		0			0
$832$	1.81225	+	0.750661i	1.81225	+	0.750661i
$833$		0			0
$834$	−0.707107	+	0.472474i	−0.707107	+	0.472474i
$835$	−0.275899	−	0.275899i	−0.275899	−	0.275899i
$836$	0.707107	−	1.70711i	0.707107	−	1.70711i
$837$		0			0
$838$	1.38704	+	0.275899i	1.38704	+	0.275899i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$			1.00000i			1.00000i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.01367	−	2.01367i	−2.01367	−	2.01367i
$846$		0			0
$847$		0			0
$848$	−1.11114			−1.11114
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$853$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$854$		0			0
$855$			0.234633i			0.234633i
$856$	0.324423	+	0.216773i	0.324423	+	0.216773i
$857$			0.390181i			0.390181i	0.980785	+	0.195090i	$0.0625000\pi$
$857$			0.390181i			0.390181i	−0.980785	+	0.195090i	$0.937500\pi$
$858$	−3.94996	−	0.785695i	−3.94996	−	0.785695i
$859$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$859$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.390181			0.390181			0.195090	−	0.980785i	$-0.437500\pi$
$863$	0.390181			0.390181			0.195090	+	0.980785i	$0.437500\pi$
$864$	0.707107	−	0.472474i	0.707107	−	0.472474i
$865$	0.390181			0.390181
$866$	0.923880	−	0.617317i	0.923880	−	0.617317i
$867$	−0.785695	−	0.785695i	−0.785695	−	0.785695i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	0.765367i		−	0.765367i
$872$		0			0
$873$		−	0.460249i		−	0.460249i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.785695	+	0.785695i	0.785695	+	0.785695i	0.980785	−	0.195090i	$-0.0625000\pi$
$877$	0.785695	+	0.785695i	0.785695	+	0.785695i	−0.195090	+	0.980785i	$0.562500\pi$
$878$		0			0
$879$	1.84776			1.84776
$880$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$881$	−0.765367			−0.765367			−0.382683	−	0.923880i	$-0.625000\pi$
$881$	−0.765367			−0.765367			−0.382683	+	0.923880i	$0.625000\pi$
$882$	−0.130355	−	0.195090i	−0.130355	−	0.195090i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			1.11114i			1.11114i	0.831470	+	0.555570i	$0.187500\pi$
$887$			1.11114i			1.11114i	−0.831470	+	0.555570i	$0.812500\pi$
$888$	0.360480	+	1.81225i	0.360480	+	1.81225i
$889$		0			0
$890$		0			0
$891$	−1.54120	+	1.54120i	−1.54120	+	1.54120i
$892$	−0.750661	+	1.81225i	−0.750661	+	1.81225i
$893$		0			0
$894$	−0.707107	+	0.472474i	−0.707107	+	0.472474i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.0897902	−	0.216773i	0.0897902	−	0.216773i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.216773	+	1.08979i	0.216773	+	1.08979i
$905$		0			0
$906$		0			0
$907$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$907$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$908$	−1.81225	+	0.750661i	−1.81225	+	0.750661i
$909$	0.306563	+	0.306563i	0.306563	+	0.306563i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	0.785695	−	0.785695i	0.785695	−	0.785695i
$913$		0			0
$914$		0			0
$915$	1.45177	+	1.45177i	1.45177	+	1.45177i
$916$	0.292893	+	0.707107i	0.292893	+	0.707107i
$917$		0			0
$918$		0			0
$919$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$919$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$920$		0			0
$921$		−	2.17958i		−	2.17958i
$922$	−1.38704	−	0.275899i	−1.38704	−	0.275899i
$923$		0			0
$924$		0			0
$925$	−1.17588	−	1.17588i	−1.17588	−	1.17588i
$926$		0			0
$927$	0.390181			0.390181
$928$		0			0
$929$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$929$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$930$		0			0
$931$	0.707107	+	0.707107i	0.707107	+	0.707107i
$932$		0			0
$933$	1.45177	−	1.45177i	1.45177	−	1.45177i
$934$		0			0
$935$		0			0
$936$	−0.382683	−	0.255701i	−0.382683	−	0.255701i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$941$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$947$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$948$		0			0
$949$		0			0
$950$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$951$			0.433546i			0.433546i
$952$		0			0
$953$			1.96157i			1.96157i	0.195090	+	0.980785i	$0.437500\pi$
$953$			1.96157i			1.96157i	−0.195090	+	0.980785i	$0.562500\pi$
$954$	0.255701	+	0.0508621i	0.255701	+	0.0508621i
$955$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$956$		0			0
$957$		0			0
$958$	−1.53636	+	1.02656i	−1.53636	+	1.02656i
$959$		0			0
$960$	−1.02656	+	0.425215i	−1.02656	+	0.425215i
$961$	1.00000			1.00000
$962$	−2.71223	+	1.81225i	−2.71223	+	1.81225i
$963$	−0.0647351	−	0.0647351i	−0.0647351	−	0.0647351i
$964$		0			0
$965$	0.275899	−	0.275899i	0.275899	−	0.275899i
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−2.36783	+	0.470990i	−2.36783	+	0.470990i
$969$		0			0
$970$	0.382683	−	1.92388i	0.382683	−	1.92388i
$971$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$971$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$972$	−0.425215	+	0.176130i	−0.425215	+	0.176130i
$973$		0			0
$974$	−0.617317	−	0.923880i	−0.617317	−	0.923880i
$975$	2.17958			2.17958
$976$		−	1.84776i		−	1.84776i
$977$	−1.66294			−1.66294			−0.831470	−	0.555570i	$-0.812500\pi$
$977$	−1.66294			−1.66294			−0.831470	+	0.555570i	$0.812500\pi$
$978$		0			0
$979$		0			0
$980$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$981$		0			0
$982$	−0.390181	+	1.96157i	−0.390181	+	1.96157i
$983$			1.66294i			1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$983$			1.66294i			1.66294i	−0.555570	+	0.831470i	$0.687500\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.81225	+	0.750661i	1.81225	+	0.750661i
$989$		0			0
$990$	0.360480	−	0.240865i	0.360480	−	0.240865i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.00000	+	1.00000i	1.00000	+	1.00000i
$996$		0			0
$997$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$997$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$998$	0.750661	+	0.149316i	0.750661	+	0.149316i
$999$			1.41421i			1.41421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.1.bh.c.189.7	yes	16
5.4	even	2	inner	1520.1.bh.c.189.2	✓	16
16.5	even	4	inner	1520.1.bh.c.949.7	yes	16
19.18	odd	2	inner	1520.1.bh.c.189.2	✓	16
80.69	even	4	inner	1520.1.bh.c.949.2	yes	16
95.94	odd	2	CM	1520.1.bh.c.189.7	yes	16
304.37	odd	4	inner	1520.1.bh.c.949.2	yes	16
1520.949	odd	4	inner	1520.1.bh.c.949.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1520.1.bh.c.189.2	✓	16	5.4	even	2	inner
1520.1.bh.c.189.2	✓	16	19.18	odd	2	inner
1520.1.bh.c.189.7	yes	16	1.1	even	1	trivial
1520.1.bh.c.189.7	yes	16	95.94	odd	2	CM
1520.1.bh.c.949.2	yes	16	80.69	even	4	inner
1520.1.bh.c.949.2	yes	16	304.37	odd	4	inner
1520.1.bh.c.949.7	yes	16	16.5	even	4	inner
1520.1.bh.c.949.7	yes	16	1520.949	odd	4	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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bh (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831470 - 0.555570i) q^{2} +(-0.785695 - 0.785695i) q^{3} +(0.382683 - 0.923880i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.08979 - 0.216773i) q^{6} +(-0.195090 - 0.980785i) q^{8} +0.234633i q^{9} +O(q^{10})\)	\(q+(0.831470 - 0.555570i) q^{2} +(-0.785695 - 0.785695i) q^{3} +(0.382683 - 0.923880i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.08979 - 0.216773i) q^{6} +(-0.195090 - 0.980785i) q^{8} +0.234633i q^{9} +(-0.195090 + 0.980785i) q^{10} +(-1.30656 + 1.30656i) q^{11} +(-1.02656 + 0.425215i) q^{12} +(-1.38704 - 1.38704i) q^{13} +1.11114 q^{15} +(-0.707107 - 0.707107i) q^{16} +(0.130355 + 0.195090i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(0.382683 + 0.923880i) q^{20} +(-0.360480 + 1.81225i) q^{22} +(-0.617317 + 0.923880i) q^{24} -1.00000i q^{25} +(-1.92388 - 0.382683i) q^{26} +(-0.601345 + 0.601345i) q^{27} +(0.923880 - 0.617317i) q^{30} +(-0.980785 - 0.195090i) q^{32} +2.05312 q^{33} +(0.216773 + 0.0897902i) q^{36} +(1.17588 - 1.17588i) q^{37} +(-0.980785 - 0.195090i) q^{38} +2.17958i q^{39} +(0.831470 + 0.555570i) q^{40} +(0.707107 + 1.70711i) q^{44} +(-0.165911 - 0.165911i) q^{45} +1.11114i q^{48} -1.00000 q^{49} +(-0.555570 - 0.831470i) q^{50} +(-1.81225 + 0.750661i) q^{52} +(0.785695 - 0.785695i) q^{53} +(-0.165911 + 0.834089i) q^{54} -1.84776i q^{55} +1.11114i q^{57} +(0.425215 - 1.02656i) q^{60} +(1.30656 + 1.30656i) q^{61} +(-0.923880 + 0.382683i) q^{64} +1.96157 q^{65} +(1.70711 - 1.14065i) q^{66} +(0.275899 + 0.275899i) q^{67} +(0.230125 - 0.0457747i) q^{72} +(0.324423 - 1.63099i) q^{74} +(-0.785695 + 0.785695i) q^{75} +(-0.923880 + 0.382683i) q^{76} +(1.21091 + 1.81225i) q^{78} +1.00000 q^{80} +1.17958 q^{81} +(1.53636 + 1.02656i) q^{88} +(-0.230125 - 0.0457747i) q^{90} +1.00000 q^{95} +(0.617317 + 0.923880i) q^{96} -1.96157 q^{97} +(-0.831470 + 0.555570i) q^{98} +(-0.306563 - 0.306563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 16 q^{24} - 16 q^{26} - 16 q^{49} + 16 q^{66} + 16 q^{80} - 16 q^{81} + 16 q^{95} + 16 q^{96} + 16 q^{99}+O(q^{100}) \) 16 * q - 16 * q^24 - 16 * q^26 - 16 * q^49 + 16 * q^66 + 16 * q^80 - 16 * q^81 + 16 * q^95 + 16 * q^96 + 16 * q^99

Introduction

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