LMFDB - Embedded newform 1032.1.bv.a.395.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1032,1,Mod(131,1032)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1032, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 7, 9]))

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

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

chi := DirichletCharacter("1032.131");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1032 = 2^{3} \cdot 3 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1032.bv (of order $14$, degree $6$, 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:	$0.515035093037$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{14}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{14} - \cdots)$

Embedding invariants

Embedding label			395.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	1032.395
Dual form			1032.1.bv.a.371.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.900969 + 0.433884i) q^{6} +(0.623490 - 0.781831i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.900969 + 0.433884i) q^{6} +(0.623490 - 0.781831i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(-0.846011 - 1.75676i) q^{11} +(-0.623490 + 0.781831i) q^{12} +(0.623490 + 0.781831i) q^{16} +(-0.678448 + 0.541044i) q^{17} +(0.623490 - 0.781831i) q^{18} +(0.376510 - 0.781831i) q^{19} +(1.90097 - 0.433884i) q^{22} +(-0.623490 - 0.781831i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.623490 + 0.781831i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(-1.90097 + 0.433884i) q^{33} +(-0.376510 - 0.781831i) q^{34} +(0.623490 + 0.781831i) q^{36} +(0.678448 + 0.541044i) q^{38} +(1.52446 + 0.347948i) q^{41} +(0.222521 - 0.974928i) q^{43} +1.94986i q^{44} +(0.900969 - 0.433884i) q^{48} -1.00000 q^{49} +1.00000 q^{50} +(0.376510 + 0.781831i) q^{51} +(-0.623490 - 0.781831i) q^{54} +(-0.678448 - 0.541044i) q^{57} +(1.52446 - 1.21572i) q^{59} +(-0.222521 - 0.974928i) q^{64} -1.94986i q^{66} +(1.80194 + 0.867767i) q^{67} +(0.846011 - 0.193096i) q^{68} +(-0.900969 + 0.433884i) q^{72} -1.00000 q^{75} +(-0.678448 + 0.541044i) q^{76} +(0.623490 + 0.781831i) q^{81} +(-0.678448 + 1.40881i) q^{82} +(-1.90097 + 0.433884i) q^{83} +(0.900969 + 0.433884i) q^{86} +(-1.90097 - 0.433884i) q^{88} +(0.277479 + 1.21572i) q^{89} +(0.222521 + 0.974928i) q^{96} +(-0.400969 + 0.193096i) q^{97} +(0.222521 - 0.974928i) q^{98} +1.94986i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 6 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9	$ 6 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9} + q^{12} - q^{16} - q^{18} + 7 q^{19} + 7 q^{22} + q^{24} - q^{25} + q^{27} - q^{32} - 7 q^{33} - 7 q^{34} - q^{36} + q^{43} + q^{48} - 6 q^{49} + 6 q^{50} + 7 q^{51} + q^{54} - q^{64} + 2 q^{67} - q^{72} - 6 q^{75} - q^{81} - 7 q^{83} + q^{86} - 7 q^{88} + 2 q^{89} + q^{96} + 2 q^{97} + q^{98}+O(q^{100}) $ 6 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9 + q^12 - q^16 - q^18 + 7 * q^19 + 7 * q^22 + q^24 - q^25 + q^27 - q^32 - 7 * q^33 - 7 * q^34 - q^36 + q^43 + q^48 - 6 * q^49 + 6 * q^50 + 7 * q^51 + q^54 - q^64 + 2 * q^67 - q^72 - 6 * q^75 - q^81 - 7 * q^83 + q^86 - 7 * q^88 + 2 * q^89 + q^96 + 2 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1032\mathbb{Z}\right)^\times$.

$n$	$433$	$517$	$689$	$775$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$2$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$3$	0.222521	−	0.974928i	0.222521	−	0.974928i
$3$	0.222521	−	0.974928i	0.222521	−	0.974928i
$4$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$5$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$5$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$6$	0.900969	+	0.433884i	0.900969	+	0.433884i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	0.623490	−	0.781831i	0.623490	−	0.781831i
$9$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$10$		0			0
$11$	−0.846011	−	1.75676i	−0.846011	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$11$	−0.846011	−	1.75676i	−0.846011	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$12$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$13$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$13$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$14$		0			0
$15$		0			0
$16$	0.623490	+	0.781831i	0.623490	+	0.781831i
$17$	−0.678448	+	0.541044i	−0.678448	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$17$	−0.678448	+	0.541044i	−0.678448	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$18$	0.623490	−	0.781831i	0.623490	−	0.781831i
$19$	0.376510	−	0.781831i	0.376510	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$19$	0.376510	−	0.781831i	0.376510	−	0.781831i	1.00000			$0$
$20$		0			0
$21$		0			0
$22$	1.90097	−	0.433884i	1.90097	−	0.433884i
$23$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$23$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$24$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$		0			0
$27$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$28$		0			0
$29$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$29$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$30$		0			0
$31$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$31$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$32$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$33$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$34$	−0.376510	−	0.781831i	−0.376510	−	0.781831i
$35$		0			0
$36$	0.623490	+	0.781831i	0.623490	+	0.781831i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.678448	+	0.541044i	0.678448	+	0.541044i
$39$		0			0
$40$		0			0
$41$	1.52446	+	0.347948i	1.52446	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$41$	1.52446	+	0.347948i	1.52446	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$42$		0			0
$43$	0.222521	−	0.974928i	0.222521	−	0.974928i
$43$	0.222521	−	0.974928i	0.222521	−	0.974928i
$44$			1.94986i			1.94986i
$45$		0			0
$46$		0			0
$47$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$47$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$48$	0.900969	−	0.433884i	0.900969	−	0.433884i
$49$	−1.00000			−1.00000
$50$	1.00000			1.00000
$51$	0.376510	+	0.781831i	0.376510	+	0.781831i
$52$		0			0
$53$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$53$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$54$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$55$		0			0
$56$		0			0
$57$	−0.678448	−	0.541044i	−0.678448	−	0.541044i
$58$		0			0
$59$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$59$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$60$		0			0
$61$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$61$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$62$		0			0
$63$		0			0
$64$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$65$		0			0
$66$		−	1.94986i		−	1.94986i
$67$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$67$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$68$	0.846011	−	0.193096i	0.846011	−	0.193096i
$69$		0			0
$70$		0			0
$71$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$71$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$72$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$73$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$73$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$74$		0			0
$75$	−1.00000			−1.00000
$76$	−0.678448	+	0.541044i	−0.678448	+	0.541044i
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	0.623490	+	0.781831i	0.623490	+	0.781831i
$82$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$83$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$83$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$	0.900969	+	0.433884i	0.900969	+	0.433884i
$87$		0			0
$88$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$89$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$89$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.222521	+	0.974928i	0.222521	+	0.974928i
$97$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$97$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$98$	0.222521	−	0.974928i	0.222521	−	0.974928i
$99$			1.94986i			1.94986i
$100$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$101$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$101$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$102$	−0.846011	+	0.193096i	−0.846011	+	0.193096i
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$107$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$108$	0.900969	−	0.433884i	0.900969	−	0.433884i
$109$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$109$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$113$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$114$	0.678448	−	0.541044i	0.678448	−	0.541044i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.846011	+	1.75676i	0.846011	+	1.75676i
$119$		0			0
$120$		0			0
$121$	−1.74698	+	2.19064i	−1.74698	+	2.19064i
$122$		0			0
$123$	0.678448	−	1.40881i	0.678448	−	1.40881i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$127$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$128$	1.00000			1.00000
$129$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$130$		0			0
$131$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$131$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$132$	1.90097	+	0.433884i	1.90097	+	0.433884i
$133$		0			0
$134$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$135$		0			0
$136$			0.867767i			0.867767i
$137$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$137$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$138$		0			0
$139$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$139$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	−1.00000			$\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$145$		0			0
$146$		0			0
$147$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$148$		0			0
$149$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$149$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$150$	0.222521	−	0.974928i	0.222521	−	0.974928i
$151$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$151$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$152$	−0.376510	−	0.781831i	−0.376510	−	0.781831i
$153$	0.846011	−	0.193096i	0.846011	−	0.193096i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$157$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$163$	0.678448	+	1.40881i	0.678448	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$163$	0.678448	+	1.40881i	0.678448	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$164$	−1.22252	−	0.974928i	−1.22252	−	0.974928i
$165$		0			0
$166$		−	1.94986i		−	1.94986i
$167$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$167$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$168$		0			0
$169$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$170$		0			0
$171$	−0.678448	+	0.541044i	−0.678448	+	0.541044i
$172$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$		0			0
$175$		0			0
$176$	0.846011	−	1.75676i	0.846011	−	1.75676i
$177$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$178$	−1.24698			−1.24698
$179$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$179$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.52446	+	0.734141i	1.52446	+	0.734141i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$191$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$192$	−1.00000			−1.00000
$193$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$193$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$194$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$195$		0			0
$196$	0.900969	+	0.433884i	0.900969	+	0.433884i
$197$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$197$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$198$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$199$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$199$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$200$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$201$	1.24698	−	1.56366i	1.24698	−	1.56366i
$202$		0			0
$203$		0			0
$204$		−	0.867767i		−	0.867767i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.69202			−1.69202
$210$		0			0
$211$	0.678448	−	1.40881i	0.678448	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	0.678448	−	1.40881i	0.678448	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$212$		0			0
$213$		0			0
$214$			1.56366i			1.56366i
$215$		0			0
$216$	0.222521	+	0.974928i	0.222521	+	0.974928i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$223$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$224$		0			0
$225$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$226$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$227$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$227$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$228$	0.376510	+	0.781831i	0.376510	+	0.781831i
$229$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$229$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$233$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$234$		0			0
$235$		0			0
$236$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$237$		0			0
$238$		0			0
$239$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$239$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$240$		0			0
$241$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$241$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$242$	−1.74698	−	2.19064i	−1.74698	−	2.19064i
$243$	0.900969	−	0.433884i	0.900969	−	0.433884i
$244$		0			0
$245$		0			0
$246$	1.22252	+	0.974928i	1.22252	+	0.974928i
$247$		0			0
$248$		0			0
$249$			1.94986i			1.94986i
$250$		0			0
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$257$	2.00000			2.00000			1.00000			$0$
$257$	2.00000			2.00000			1.00000			$0$
$258$	0.623490	−	0.781831i	0.623490	−	0.781831i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$263$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$263$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$264$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$265$		0			0
$266$		0			0
$267$	1.24698			1.24698
$268$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$269$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$269$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$270$		0			0
$271$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$271$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$272$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$273$		0			0
$274$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$275$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$276$		0			0
$277$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$277$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$278$	1.12349	−	0.541044i	1.12349	−	0.541044i
$279$		0			0
$280$		0			0
$281$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$281$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$282$		0			0
$283$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$283$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.00000			1.00000
$289$	−0.0549581	+	0.240787i	−0.0549581	+	0.240787i
$290$		0			0
$291$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$292$		0			0
$293$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$293$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$294$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$295$		0			0
$296$		0			0
$297$	1.90097	+	0.433884i	1.90097	+	0.433884i
$298$		0			0
$299$		0			0
$300$	0.900969	+	0.433884i	0.900969	+	0.433884i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.846011	−	0.193096i	0.846011	−	0.193096i
$305$		0			0
$306$			0.867767i			0.867767i
$307$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$307$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$311$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$312$		0			0
$313$	1.52446	+	0.347948i	1.52446	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$313$	1.52446	+	0.347948i	1.52446	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$317$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		−	1.56366i		−	1.56366i
$322$		0			0
$323$	0.167563	+	0.734141i	0.167563	+	0.734141i
$324$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$325$		0			0
$326$	−1.52446	+	0.347948i	−1.52446	+	0.347948i
$327$		0			0
$328$	1.22252	−	0.974928i	1.22252	−	0.974928i
$329$		0			0
$330$		0			0
$331$	−1.52446	−	1.21572i	−1.52446	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$331$	−1.52446	−	1.21572i	−1.52446	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$332$	1.90097	+	0.433884i	1.90097	+	0.433884i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$337$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$338$	1.00000			1.00000
$339$	1.62349	−	0.781831i	1.62349	−	0.781831i
$340$		0			0
$341$		0			0
$342$	−0.376510	−	0.781831i	−0.376510	−	0.781831i
$343$		0			0
$344$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$345$		0			0
$346$		0			0
$347$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$347$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$348$		0			0
$349$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$349$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$350$		0			0
$351$		0			0
$352$	1.52446	+	1.21572i	1.52446	+	1.21572i
$353$	0.678448	+	1.40881i	0.678448	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$353$	0.678448	+	1.40881i	0.678448	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$354$	1.90097	−	0.433884i	1.90097	−	0.433884i
$355$		0			0
$356$	0.277479	−	1.21572i	0.277479	−	1.21572i
$357$		0			0
$358$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$359$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$359$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$360$		0			0
$361$	0.153989	+	0.193096i	0.153989	+	0.193096i
$362$		0			0
$363$	1.74698	+	2.19064i	1.74698	+	2.19064i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$367$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$368$		0			0
$369$	−1.22252	−	0.974928i	−1.22252	−	0.974928i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$373$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$374$	−1.05496	+	1.32288i	−1.05496	+	1.32288i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$379$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$383$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$384$	0.222521	−	0.974928i	0.222521	−	0.974928i
$385$		0			0
$386$	0.445042			0.445042
$387$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$388$	0.445042			0.445042
$389$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$389$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$390$		0			0
$391$		0			0
$392$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$393$	1.12349	+	0.541044i	1.12349	+	0.541044i
$394$		0			0
$395$		0			0
$396$	0.846011	−	1.75676i	0.846011	−	1.75676i
$397$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$397$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$398$		0			0
$399$		0			0
$400$	0.623490	−	0.781831i	0.623490	−	0.781831i
$401$	−1.90097	−	0.433884i	−1.90097	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$401$	−1.90097	−	0.433884i	−1.90097	−	0.433884i	−1.00000			$\pi$
$402$	1.24698	+	1.56366i	1.24698	+	1.56366i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.846011	+	0.193096i	0.846011	+	0.193096i
$409$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$409$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$410$		0			0
$411$	0.277479	+	0.347948i	0.277479	+	0.347948i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$418$	0.376510	−	1.64960i	0.376510	−	1.64960i
$419$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$419$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$420$		0			0
$421$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$421$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$422$	1.22252	+	0.974928i	1.22252	+	0.974928i
$423$		0			0
$424$		0			0
$425$	0.678448	+	0.541044i	0.678448	+	0.541044i
$426$		0			0
$427$		0			0
$428$	−1.52446	−	0.347948i	−1.52446	−	0.347948i
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−1.00000			−1.00000
$433$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$433$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$439$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$440$		0			0
$441$	0.900969	+	0.433884i	0.900969	+	0.433884i
$442$		0			0
$443$	−1.22252	−	0.974928i	−1.22252	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$443$	−1.22252	−	0.974928i	−1.22252	−	0.974928i	−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$449$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$450$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$451$	−0.678448	−	2.97247i	−0.678448	−	2.97247i
$452$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$453$		0			0
$454$	0.400969	+	0.193096i	0.400969	+	0.193096i
$455$		0			0
$456$	−0.846011	+	0.193096i	−0.846011	+	0.193096i
$457$	1.22252	−	0.974928i	1.22252	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$457$	1.22252	−	0.974928i	1.22252	−	0.974928i	1.00000			$0$
$458$		0			0
$459$		−	0.867767i		−	0.867767i
$460$		0			0
$461$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$461$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$462$		0			0
$463$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$463$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$464$		0			0
$465$		0			0
$466$	1.80194			1.80194
$467$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$467$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		−	1.94986i		−	1.94986i
$473$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$474$		0			0
$475$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$	0.846011	+	1.75676i	0.846011	+	1.75676i
$483$		0			0
$484$	2.52446	−	1.21572i	2.52446	−	1.21572i
$485$		0			0
$486$	0.222521	+	0.974928i	0.222521	+	0.974928i
$487$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$487$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$488$		0			0
$489$	1.52446	−	0.347948i	1.52446	−	0.347948i
$490$		0			0
$491$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$491$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$492$	−1.22252	+	0.974928i	−1.22252	+	0.974928i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$499$	−1.52446	+	1.21572i	−1.52446	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$499$	−1.52446	+	1.21572i	−1.52446	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$503$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.00000			−1.00000
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$		0			0
$512$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$513$	0.376510	+	0.781831i	0.376510	+	0.781831i
$514$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$515$		0			0
$516$	0.623490	+	0.781831i	0.623490	+	0.781831i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$521$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$522$		0			0
$523$			1.56366i			1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$523$			1.56366i			1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$524$	0.777479	−	0.974928i	0.777479	−	0.974928i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.52446	−	1.21572i	−1.52446	−	1.21572i
$529$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$530$		0			0
$531$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$532$		0			0
$533$		0			0
$534$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$535$		0			0
$536$	1.80194	−	0.867767i	1.80194	−	0.867767i
$537$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$538$		0			0
$539$	0.846011	+	1.75676i	0.846011	+	1.75676i
$540$		0			0
$541$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$541$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$542$		0			0
$543$		0			0
$544$	0.376510	−	0.781831i	0.376510	−	0.781831i
$545$		0			0
$546$		0			0
$547$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$547$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$548$	0.400969	−	0.193096i	0.400969	−	0.193096i
$549$		0			0
$550$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.277479	+	1.21572i	0.277479	+	1.21572i
$557$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$557$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.05496	−	1.32288i	1.05496	−	1.32288i
$562$		0			0
$563$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$563$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$564$		0			0
$565$		0			0
$566$	−1.80194			−1.80194
$567$		0			0
$568$		0			0
$569$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$569$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$570$		0			0
$571$	−1.90097	−	0.433884i	−1.90097	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$571$	−1.90097	−	0.433884i	−1.90097	−	0.433884i	−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$577$	1.90097	−	0.433884i	1.90097	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$577$	1.90097	−	0.433884i	1.90097	−	0.433884i	1.00000			$0$
$578$	−0.222521	−	0.107160i	−0.222521	−	0.107160i
$579$	−0.445042			−0.445042
$580$		0			0
$581$		0			0
$582$	−0.445042			−0.445042
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$587$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$588$	0.623490	−	0.781831i	0.623490	−	0.781831i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$593$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$594$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$599$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$600$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$601$			1.94986i			1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$601$			1.94986i			1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$602$		0			0
$603$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$607$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$608$			0.867767i			0.867767i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$613$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$613$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$614$	0.400969	−	1.75676i	0.400969	−	1.75676i
$615$		0			0
$616$		0			0
$617$	0.376510	−	0.781831i	0.376510	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$617$	0.376510	−	0.781831i	0.376510	−	0.781831i	1.00000			$0$
$618$		0			0
$619$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$619$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$627$	−0.376510	+	1.64960i	−0.376510	+	1.64960i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$631$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$632$		0			0
$633$	−1.22252	−	0.974928i	−1.22252	−	0.974928i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$641$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$642$	1.52446	+	0.347948i	1.52446	+	0.347948i
$643$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$643$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$644$		0			0
$645$		0			0
$646$	−0.753020			−0.753020
$647$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$647$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$648$	1.00000			1.00000
$649$	−3.42543	−	1.64960i	−3.42543	−	1.64960i
$650$		0			0
$651$		0			0
$652$		−	1.56366i		−	1.56366i
$653$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$653$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$654$		0			0
$655$		0			0
$656$	0.678448	+	1.40881i	0.678448	+	1.40881i
$657$		0			0
$658$		0			0
$659$	−0.846011	−	0.193096i	−0.846011	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$659$	−0.846011	−	0.193096i	−0.846011	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	1.52446	−	1.21572i	1.52446	−	1.21572i
$663$		0			0
$664$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$673$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$674$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$675$	0.900969	+	0.433884i	0.900969	+	0.433884i
$676$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$677$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$677$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$678$	0.400969	+	1.75676i	0.400969	+	1.75676i
$679$		0			0
$680$		0			0
$681$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$682$		0			0
$683$	0.678448	+	0.541044i	0.678448	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$683$	0.678448	+	0.541044i	0.678448	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$684$	0.846011	−	0.193096i	0.846011	−	0.193096i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.900969	−	0.433884i	0.900969	−	0.433884i
$689$		0			0
$690$		0			0
$691$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$691$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$692$		0			0
$693$		0			0
$694$	1.80194			1.80194
$695$		0			0
$696$		0			0
$697$	−1.22252	+	0.588735i	−1.22252	+	0.588735i
$698$		0			0
$699$	−1.80194			−1.80194
$700$		0			0
$701$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$701$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$702$		0			0
$703$		0			0
$704$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$705$		0			0
$706$	−1.52446	+	0.347948i	−1.52446	+	0.347948i
$707$		0			0
$708$			1.94986i			1.94986i
$709$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$709$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$710$		0			0
$711$		0			0
$712$	1.12349	+	0.541044i	1.12349	+	0.541044i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.400969	+	0.193096i	0.400969	+	0.193096i
$717$		0			0
$718$		0			0
$719$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$719$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$720$		0			0
$721$		0			0
$722$	−0.222521	+	0.107160i	−0.222521	+	0.107160i
$723$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$724$		0			0
$725$		0			0
$726$	−2.52446	+	1.21572i	−2.52446	+	1.21572i
$727$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$727$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$728$		0			0
$729$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$730$		0			0
$731$	0.376510	+	0.781831i	0.376510	+	0.781831i
$732$		0			0
$733$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$733$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	3.89971i		−	3.89971i
$738$	1.22252	−	0.974928i	1.22252	−	0.974928i
$739$	1.22252	+	0.974928i	1.22252	+	0.974928i	1.00000			$0$
$739$	1.22252	+	0.974928i	1.22252	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$743$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.90097	+	0.433884i	1.90097	+	0.433884i
$748$	−1.05496	−	1.32288i	−1.05496	−	1.32288i
$749$		0			0
$750$		0			0
$751$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$751$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$757$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$758$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$759$		0			0
$760$		0			0
$761$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$761$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.900969	+	0.433884i	0.900969	+	0.433884i
$769$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$769$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$770$		0			0
$771$	0.445042	−	1.94986i	0.445042	−	1.94986i
$772$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$775$		0			0
$776$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$777$		0			0
$778$		0			0
$779$	0.846011	−	1.06086i	0.846011	−	1.06086i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$785$		0			0
$786$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$787$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$787$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.52446	+	1.21572i	1.52446	+	1.21572i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$797$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$798$		0			0
$799$		0			0
$800$	0.623490	+	0.781831i	0.623490	+	0.781831i
$801$	0.277479	−	1.21572i	0.277479	−	1.21572i
$802$	0.846011	−	1.75676i	0.846011	−	1.75676i
$803$		0			0
$804$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.678448	−	0.541044i	−0.678448	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$809$	−0.678448	−	0.541044i	−0.678448	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.376510	+	0.781831i	−0.376510	+	0.781831i
$817$	−0.678448	−	0.541044i	−0.678448	−	0.541044i
$818$			1.56366i			1.56366i
$819$		0			0
$820$		0			0
$821$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$821$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$822$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	0.846011	+	1.75676i	0.846011	+	1.75676i
$826$		0			0
$827$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$827$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−1.00000			$\pi$
$828$		0			0
$829$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$829$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.678448	−	0.541044i	0.678448	−	0.541044i
$834$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$835$		0			0
$836$	1.52446	+	0.734141i	1.52446	+	0.734141i
$837$		0			0
$838$	0.277479	+	1.21572i	0.277479	+	1.21572i
$839$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$839$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$840$		0			0
$841$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$842$		0			0
$843$		0			0
$844$	−1.22252	+	0.974928i	−1.22252	+	0.974928i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.80194			1.80194
$850$	−0.678448	+	0.541044i	−0.678448	+	0.541044i
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$	0.678448	−	1.40881i	0.678448	−	1.40881i
$857$	−0.846011	+	0.193096i	−0.846011	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$857$	−0.846011	+	0.193096i	−0.846011	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$858$		0			0
$859$		−	1.56366i		−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$859$		−	1.56366i		−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$863$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$864$	0.222521	−	0.974928i	0.222521	−	0.974928i
$865$		0			0
$866$			1.56366i			1.56366i
$867$	0.222521	+	0.107160i	0.222521	+	0.107160i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.445042			0.445042
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$877$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.846011	−	0.193096i	0.846011	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$881$	0.846011	−	0.193096i	0.846011	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$882$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$883$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$883$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$884$		0			0
$885$		0			0
$886$	1.22252	−	0.974928i	1.22252	−	0.974928i
$887$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$887$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.846011	−	1.75676i	0.846011	−	1.75676i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.277479	−	0.347948i	0.277479	−	0.347948i
$899$		0			0
$900$	0.623490	−	0.781831i	0.623490	−	0.781831i
$901$		0			0
$902$	3.04892			3.04892
$903$		0			0
$904$	1.80194			1.80194
$905$		0			0
$906$		0			0
$907$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$907$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$908$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$909$		0			0
$910$		0			0
$911$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$911$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$912$		−	0.867767i		−	0.867767i
$913$	2.37047	+	2.97247i	2.37047	+	2.97247i
$914$	0.678448	+	1.40881i	0.678448	+	1.40881i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.846011	+	0.193096i	0.846011	+	0.193096i
$919$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$919$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$920$		0			0
$921$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$929$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$930$		0			0
$931$	−0.376510	+	0.781831i	−0.376510	+	0.781831i
$932$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$933$		0			0
$934$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$935$		0			0
$936$		0			0
$937$	−0.846011	−	1.75676i	−0.846011	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$937$	−0.846011	−	1.75676i	−0.846011	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$938$		0			0
$939$	0.678448	−	1.40881i	0.678448	−	1.40881i
$940$		0			0
$941$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$941$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$942$		0			0
$943$		0			0
$944$	1.90097	+	0.433884i	1.90097	+	0.433884i
$945$		0			0
$946$		−	1.94986i		−	1.94986i
$947$		−	0.867767i		−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$947$		−	0.867767i		−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$948$		0			0
$949$		0			0
$950$	0.376510	−	0.781831i	0.376510	−	0.781831i
$951$		0			0
$952$		0			0
$953$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$953$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$962$		0			0
$963$	−1.52446	−	0.347948i	−1.52446	−	0.347948i
$964$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$965$		0			0
$966$		0			0
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	0.623490	+	2.73169i	0.623490	+	2.73169i
$969$	0.753020			0.753020
$970$		0			0
$971$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$971$	1.52446	−	0.347948i	1.52446	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$972$	−1.00000			−1.00000
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.846011	+	0.193096i	0.846011	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$977$	0.846011	+	0.193096i	0.846011	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$978$			1.56366i			1.56366i
$979$	1.90097	−	1.51597i	1.90097	−	1.51597i
$980$		0			0
$981$		0			0
$982$	1.80194			1.80194
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	−0.678448	−	1.40881i	−0.678448	−	1.40881i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$991$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$992$		0			0
$993$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$994$		0			0
$995$		0			0
$996$	0.846011	−	1.75676i	0.846011	−	1.75676i
$997$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$997$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$998$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1032.1.bv.a.395.1	yes	6
3.2	odd	2		1032.1.bv.b.395.1	yes	6
8.3	odd	2	CM	1032.1.bv.a.395.1	yes	6
24.11	even	2		1032.1.bv.b.395.1	yes	6
43.27	odd	14		1032.1.bv.b.371.1	yes	6
129.113	even	14	inner	1032.1.bv.a.371.1	✓	6
344.27	even	14		1032.1.bv.b.371.1	yes	6
1032.371	odd	14	inner	1032.1.bv.a.371.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1032.1.bv.a.371.1	✓	6	129.113	even	14	inner
1032.1.bv.a.371.1	✓	6	1032.371	odd	14	inner
1032.1.bv.a.395.1	yes	6	1.1	even	1	trivial
1032.1.bv.a.395.1	yes	6	8.3	odd	2	CM
1032.1.bv.b.371.1	yes	6	43.27	odd	14
1032.1.bv.b.371.1	yes	6	344.27	even	14
1032.1.bv.b.395.1	yes	6	3.2	odd	2
1032.1.bv.b.395.1	yes	6	24.11	even	2

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:	\( N \)	\(=\)	\( 1032 = 2^{3} \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1032.bv (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.900969 + 0.433884i) q^{6} +(0.623490 - 0.781831i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.900969 + 0.433884i) q^{6} +(0.623490 - 0.781831i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(-0.846011 - 1.75676i) q^{11} +(-0.623490 + 0.781831i) q^{12} +(0.623490 + 0.781831i) q^{16} +(-0.678448 + 0.541044i) q^{17} +(0.623490 - 0.781831i) q^{18} +(0.376510 - 0.781831i) q^{19} +(1.90097 - 0.433884i) q^{22} +(-0.623490 - 0.781831i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.623490 + 0.781831i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(-1.90097 + 0.433884i) q^{33} +(-0.376510 - 0.781831i) q^{34} +(0.623490 + 0.781831i) q^{36} +(0.678448 + 0.541044i) q^{38} +(1.52446 + 0.347948i) q^{41} +(0.222521 - 0.974928i) q^{43} +1.94986i q^{44} +(0.900969 - 0.433884i) q^{48} -1.00000 q^{49} +1.00000 q^{50} +(0.376510 + 0.781831i) q^{51} +(-0.623490 - 0.781831i) q^{54} +(-0.678448 - 0.541044i) q^{57} +(1.52446 - 1.21572i) q^{59} +(-0.222521 - 0.974928i) q^{64} -1.94986i q^{66} +(1.80194 + 0.867767i) q^{67} +(0.846011 - 0.193096i) q^{68} +(-0.900969 + 0.433884i) q^{72} -1.00000 q^{75} +(-0.678448 + 0.541044i) q^{76} +(0.623490 + 0.781831i) q^{81} +(-0.678448 + 1.40881i) q^{82} +(-1.90097 + 0.433884i) q^{83} +(0.900969 + 0.433884i) q^{86} +(-1.90097 - 0.433884i) q^{88} +(0.277479 + 1.21572i) q^{89} +(0.222521 + 0.974928i) q^{96} +(-0.400969 + 0.193096i) q^{97} +(0.222521 - 0.974928i) q^{98} +1.94986i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 6 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9	\( 6 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9} + q^{12} - q^{16} - q^{18} + 7 q^{19} + 7 q^{22} + q^{24} - q^{25} + q^{27} - q^{32} - 7 q^{33} - 7 q^{34} - q^{36} + q^{43} + q^{48} - 6 q^{49} + 6 q^{50} + 7 q^{51} + q^{54} - q^{64} + 2 q^{67} - q^{72} - 6 q^{75} - q^{81} - 7 q^{83} + q^{86} - 7 q^{88} + 2 q^{89} + q^{96} + 2 q^{97} + q^{98}+O(q^{100}) \) 6 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9 + q^12 - q^16 - q^18 + 7 * q^19 + 7 * q^22 + q^24 - q^25 + q^27 - q^32 - 7 * q^33 - 7 * q^34 - q^36 + q^43 + q^48 - 6 * q^49 + 6 * q^50 + 7 * q^51 + q^54 - q^64 + 2 * q^67 - q^72 - 6 * q^75 - q^81 - 7 * q^83 + q^86 - 7 * q^88 + 2 * q^89 + q^96 + 2 * q^97 + q^98

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