LMFDB - Embedded newform 3332.1.be.c.407.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3332,1,Mod(407,3332)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3332.407"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3332, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 10, 7])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3332 = 2^{2} \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3332.be (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.66288462209$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
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			407.2
Root			$-0.974928 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	3332.407
Dual form			3332.1.be.c.1359.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.222521 - 0.974928i) q^{2} +(0.974928 - 1.22252i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.974928 - 1.22252i) q^{6} +(-0.781831 - 0.623490i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-0.321552 - 1.40881i) q^{9} +(0.433884 - 1.90097i) q^{11} +(-1.40881 + 0.678448i) q^{12} +(-0.0990311 + 0.433884i) q^{13} +(-0.781831 + 0.623490i) q^{14} +(0.623490 + 0.781831i) q^{16} +(-0.900969 + 0.433884i) q^{17} -1.44504 q^{18} +(-1.52446 + 0.347948i) q^{21} +(-1.75676 - 0.846011i) q^{22} +(1.75676 + 0.846011i) q^{23} +(0.347948 + 1.52446i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.400969 + 0.193096i) q^{26} +(-0.626980 - 0.301938i) q^{27} +(0.433884 + 0.900969i) q^{28} -1.56366 q^{31} +(0.900969 - 0.433884i) q^{32} +(-1.90097 - 2.38374i) q^{33} +(0.222521 + 0.974928i) q^{34} +(-0.321552 + 1.40881i) q^{36} +(0.433884 + 0.544073i) q^{39} +1.56366i q^{42} +(-1.21572 + 1.52446i) q^{44} +(1.21572 - 1.52446i) q^{46} +1.56366 q^{48} +(0.222521 + 0.974928i) q^{49} -1.00000 q^{50} +(-0.347948 + 1.52446i) q^{51} +(0.277479 - 0.347948i) q^{52} +(-1.12349 - 0.541044i) q^{53} +(-0.433884 + 0.544073i) q^{54} +(0.974928 - 0.222521i) q^{56} +(-0.347948 + 1.52446i) q^{62} +(-0.626980 + 1.30194i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-2.74698 + 1.32288i) q^{66} +1.00000 q^{68} +(2.74698 - 1.32288i) q^{69} +(1.40881 + 0.678448i) q^{71} +(1.30194 + 0.626980i) q^{72} +(-1.40881 - 0.678448i) q^{75} +(-1.52446 + 1.21572i) q^{77} +(0.626980 - 0.301938i) q^{78} +1.94986 q^{79} +(0.321552 - 0.154851i) q^{81} +(1.52446 + 0.347948i) q^{84} +(1.21572 + 1.52446i) q^{88} +(0.277479 + 1.21572i) q^{89} +(0.347948 - 0.277479i) q^{91} +(-1.21572 - 1.52446i) q^{92} +(-1.52446 + 1.91161i) q^{93} +(0.347948 - 1.52446i) q^{96} +1.00000 q^{98} -2.81762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 12 q^{9} - 10 q^{13} - 2 q^{16} - 2 q^{17} - 16 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 14 q^{33} + 2 q^{34} - 12 q^{36} + 2 q^{49} - 12 q^{50} + 4 q^{52} - 4 q^{53}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 - 12 * q^9 - 10 * q^13 - 2 * q^16 - 2 * q^17 - 16 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 14 * q^33 + 2 * q^34 - 12 * q^36 + 2 * q^49 - 12 * q^50 + 4 * q^52 - 4 * q^53 - 2 * q^64 - 14 * q^66 + 12 * q^68 + 14 * q^69 - 2 * q^72 + 12 * q^81 + 4 * q^89 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$.

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{5}{7}\right)$	$-1$

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 $

$2$	0.222521	−	0.974928i	0.222521	−	0.974928i
$2$	0.222521	−	0.974928i	0.222521	−	0.974928i
$3$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$3$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$4$	−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	$0.714286\pi$
$6$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$7$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$7$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$8$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$9$	−0.321552	−	1.40881i	−0.321552	−	1.40881i
$10$		0			0
$11$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$11$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$12$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$13$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$13$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$14$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$15$		0			0
$16$	0.623490	+	0.781831i	0.623490	+	0.781831i
$17$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$17$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$18$	−1.44504			−1.44504
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−1.52446	+	0.347948i	−1.52446	+	0.347948i
$22$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$23$	1.75676	+	0.846011i	1.75676	+	0.846011i	0.974928	+	0.222521i	$0.0714286\pi$
$23$	1.75676	+	0.846011i	1.75676	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$24$	0.347948	+	1.52446i	0.347948	+	1.52446i
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$	0.400969	+	0.193096i	0.400969	+	0.193096i
$27$	−0.626980	−	0.301938i	−0.626980	−	0.301938i
$28$	0.433884	+	0.900969i	0.433884	+	0.900969i
$29$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$29$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$30$		0			0
$31$	−1.56366			−1.56366			−0.781831	−	0.623490i	$-0.785714\pi$
$31$	−1.56366			−1.56366			−0.781831	+	0.623490i	$0.785714\pi$
$32$	0.900969	−	0.433884i	0.900969	−	0.433884i
$33$	−1.90097	−	2.38374i	−1.90097	−	2.38374i
$34$	0.222521	+	0.974928i	0.222521	+	0.974928i
$35$		0			0
$36$	−0.321552	+	1.40881i	−0.321552	+	1.40881i
$37$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$37$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$38$		0			0
$39$	0.433884	+	0.544073i	0.433884	+	0.544073i
$40$		0			0
$41$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$41$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$42$			1.56366i			1.56366i
$43$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$43$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$44$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$45$		0			0
$46$	1.21572	−	1.52446i	1.21572	−	1.52446i
$47$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$47$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$48$	1.56366			1.56366
$49$	0.222521	+	0.974928i	0.222521	+	0.974928i
$50$	−1.00000			−1.00000
$51$	−0.347948	+	1.52446i	−0.347948	+	1.52446i
$52$	0.277479	−	0.347948i	0.277479	−	0.347948i
$53$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$53$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$54$	−0.433884	+	0.544073i	−0.433884	+	0.544073i
$55$		0			0
$56$	0.974928	−	0.222521i	0.974928	−	0.222521i
$57$		0			0
$58$		0			0
$59$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$59$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$60$		0			0
$61$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$61$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$62$	−0.347948	+	1.52446i	−0.347948	+	1.52446i
$63$	−0.626980	+	1.30194i	−0.626980	+	1.30194i
$64$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$65$		0			0
$66$	−2.74698	+	1.32288i	−2.74698	+	1.32288i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	1.00000			1.00000
$69$	2.74698	−	1.32288i	2.74698	−	1.32288i
$70$		0			0
$71$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$71$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$72$	1.30194	+	0.626980i	1.30194	+	0.626980i
$73$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$73$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$74$		0			0
$75$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$76$		0			0
$77$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$78$	0.626980	−	0.301938i	0.626980	−	0.301938i
$79$	1.94986			1.94986			0.974928	−	0.222521i	$-0.0714286\pi$
$79$	1.94986			1.94986			0.974928	+	0.222521i	$0.0714286\pi$
$80$		0			0
$81$	0.321552	−	0.154851i	0.321552	−	0.154851i
$82$		0			0
$83$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$83$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$84$	1.52446	+	0.347948i	1.52446	+	0.347948i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.21572	+	1.52446i	1.21572	+	1.52446i
$89$	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
$91$	0.347948	−	0.277479i	0.347948	−	0.277479i
$92$	−1.21572	−	1.52446i	−1.21572	−	1.52446i
$93$	−1.52446	+	1.91161i	−1.52446	+	1.91161i
$94$		0			0
$95$		0			0
$96$	0.347948	−	1.52446i	0.347948	−	1.52446i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	1.00000			1.00000
$99$	−2.81762			−2.81762
$100$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$101$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$101$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$102$	1.40881	+	0.678448i	1.40881	+	0.678448i
$103$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$103$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$104$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$105$		0			0
$106$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$107$	−0.193096	−	0.846011i	−0.193096	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$107$	−0.193096	−	0.846011i	−0.193096	−	0.846011i	0.781831	−	0.623490i	$-0.214286\pi$
$108$	0.433884	+	0.544073i	0.433884	+	0.544073i
$109$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$109$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$110$		0			0
$111$		0			0
$112$		−	1.00000i		−	1.00000i
$113$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$113$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.643104			0.643104
$118$		0			0
$119$	0.974928	+	0.222521i	0.974928	+	0.222521i
$120$		0			0
$121$	−2.52446	−	1.21572i	−2.52446	−	1.21572i
$122$		0			0
$123$		0			0
$124$	1.40881	+	0.678448i	1.40881	+	0.678448i
$125$		0			0
$126$	1.12978	+	0.900969i	1.12978	+	0.900969i
$127$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$127$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$128$	−1.00000			−1.00000
$129$		0			0
$130$		0			0
$131$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$131$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$132$	0.678448	+	2.97247i	0.678448	+	2.97247i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.222521	−	0.974928i	0.222521	−	0.974928i
$137$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$137$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	−1.00000			$\pi$
$138$	−0.678448	−	2.97247i	−0.678448	−	2.97247i
$139$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$139$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$140$		0			0
$141$		0			0
$142$	0.974928	−	1.22252i	0.974928	−	1.22252i
$143$	0.781831	+	0.376510i	0.781831	+	0.376510i
$144$	0.900969	−	1.12978i	0.900969	−	1.12978i
$145$		0			0
$146$		0			0
$147$	1.40881	+	0.678448i	1.40881	+	0.678448i
$148$		0			0
$149$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$149$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$150$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$151$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$151$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$152$		0			0
$153$	0.900969	+	1.12978i	0.900969	+	1.12978i
$154$	0.846011	+	1.75676i	0.846011	+	1.75676i
$155$		0			0
$156$	−0.154851	−	0.678448i	−0.154851	−	0.678448i
$157$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$157$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$158$	0.433884	−	1.90097i	0.433884	−	1.90097i
$159$	−1.75676	+	0.846011i	−1.75676	+	0.846011i
$160$		0			0
$161$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$162$	−0.0794168	−	0.347948i	−0.0794168	−	0.347948i
$163$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$163$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.781831	+	0.376510i	−0.781831	+	0.376510i	−0.781831	−	0.623490i	$-0.785714\pi$
$167$	−0.781831	+	0.376510i	−0.781831	+	0.376510i			1.00000i	$0.5\pi$
$168$	0.678448	−	1.40881i	0.678448	−	1.40881i
$169$	0.722521	+	0.347948i	0.722521	+	0.347948i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$173$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$174$		0			0
$175$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$176$	1.75676	−	0.846011i	1.75676	−	0.846011i
$177$		0			0
$178$	1.24698			1.24698
$179$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$179$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$180$		0			0
$181$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$181$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$182$	−0.193096	−	0.400969i	−0.193096	−	0.400969i
$183$		0			0
$184$	−1.75676	+	0.846011i	−1.75676	+	0.846011i
$185$		0			0
$186$	1.52446	+	1.91161i	1.52446	+	1.91161i
$187$	0.433884	+	1.90097i	0.433884	+	1.90097i
$188$		0			0
$189$	0.301938	+	0.626980i	0.301938	+	0.626980i
$190$		0			0
$191$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$191$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$192$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$193$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$193$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$194$		0			0
$195$		0			0
$196$	0.222521	−	0.974928i	0.222521	−	0.974928i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.626980	+	2.74698i	−0.626980	+	2.74698i
$199$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$199$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$200$	0.900969	+	0.433884i	0.900969	+	0.433884i
$201$		0			0
$202$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$203$		0			0
$204$	0.974928	−	1.22252i	0.974928	−	1.22252i
$205$		0			0
$206$		0			0
$207$	0.626980	−	2.74698i	0.626980	−	2.74698i
$208$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$209$		0			0
$210$		0			0
$211$	−0.193096	−	0.846011i	−0.193096	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$211$	−0.193096	−	0.846011i	−0.193096	−	0.846011i	0.781831	−	0.623490i	$-0.214286\pi$
$212$	0.777479	+	0.974928i	0.777479	+	0.974928i
$213$	2.20291	−	1.06086i	2.20291	−	1.06086i
$214$	−0.867767			−0.867767
$215$		0			0
$216$	0.626980	−	0.301938i	0.626980	−	0.301938i
$217$	1.22252	+	0.974928i	1.22252	+	0.974928i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$222$		0			0
$223$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$223$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$224$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$225$	−1.30194	+	0.626980i	−1.30194	+	0.626980i
$226$		0			0
$227$	1.56366			1.56366			0.781831	−	0.623490i	$-0.214286\pi$
$227$	1.56366			1.56366			0.781831	+	0.623490i	$0.214286\pi$
$228$		0			0
$229$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$229$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$230$		0			0
$231$			3.04892i			3.04892i
$232$		0			0
$233$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$233$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$234$	0.143104	−	0.626980i	0.143104	−	0.626980i
$235$		0			0
$236$		0			0
$237$	1.90097	−	2.38374i	1.90097	−	2.38374i
$238$	0.433884	−	0.900969i	0.433884	−	0.900969i
$239$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$239$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$240$		0			0
$241$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$241$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$242$	−1.74698	+	2.19064i	−1.74698	+	2.19064i
$243$	0.279032	−	1.22252i	0.279032	−	1.22252i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.974928	−	1.22252i	0.974928	−	1.22252i
$249$		0			0
$250$		0			0
$251$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$251$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$252$	1.12978	−	0.900969i	1.12978	−	0.900969i
$253$	2.37047	−	2.97247i	2.37047	−	2.97247i
$254$		0			0
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$257$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$257$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.75676	+	0.846011i	−1.75676	+	0.846011i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	3.04892			3.04892
$265$		0			0
$266$		0			0
$267$	1.75676	+	0.846011i	1.75676	+	0.846011i
$268$		0			0
$269$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$269$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$270$		0			0
$271$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$271$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$272$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$273$		−	0.695895i		−	0.695895i
$274$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$275$	−1.94986			−1.94986
$276$	−3.04892			−3.04892
$277$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$277$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$278$	−1.21572	−	1.52446i	−1.21572	−	1.52446i
$279$	0.502799	+	2.20291i	0.502799	+	2.20291i
$280$		0			0
$281$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$281$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$282$		0			0
$283$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$283$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$284$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$285$		0			0
$286$	0.541044	−	0.678448i	0.541044	−	0.678448i
$287$		0			0
$288$	−0.900969	−	1.12978i	−0.900969	−	1.12978i
$289$	0.623490	−	0.781831i	0.623490	−	0.781831i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$293$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$294$	0.974928	−	1.22252i	0.974928	−	1.22252i
$295$		0			0
$296$		0			0
$297$	−0.846011	+	1.06086i	−0.846011	+	1.06086i
$298$	1.12349	+	0.541044i	1.12349	+	0.541044i
$299$	−0.541044	+	0.678448i	−0.541044	+	0.678448i
$300$	0.974928	+	1.22252i	0.974928	+	1.22252i
$301$		0			0
$302$		0			0
$303$	−0.154851	−	0.678448i	−0.154851	−	0.678448i
$304$		0			0
$305$		0			0
$306$	1.30194	−	0.626980i	1.30194	−	0.626980i
$307$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$307$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$308$	1.90097	−	0.433884i	1.90097	−	0.433884i
$309$		0			0
$310$		0			0
$311$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$311$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$312$	−0.695895			−0.695895
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$315$		0			0
$316$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$317$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$317$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$318$	0.433884	+	1.90097i	0.433884	+	1.90097i
$319$		0			0
$320$		0			0
$321$	−1.22252	−	0.588735i	−1.22252	−	0.588735i
$322$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$323$		0			0
$324$	−0.356896			−0.356896
$325$	0.445042			0.445042
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$331$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$332$		0			0
$333$		0			0
$334$	0.193096	+	0.846011i	0.193096	+	0.846011i
$335$		0			0
$336$	−1.22252	−	0.974928i	−1.22252	−	0.974928i
$337$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$337$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$338$	0.500000	−	0.626980i	0.500000	−	0.626980i
$339$		0			0
$340$		0			0
$341$	−0.678448	+	2.97247i	−0.678448	+	2.97247i
$342$		0			0
$343$	0.433884	−	0.900969i	0.433884	−	0.900969i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.781831	−	0.376510i	−0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$347$	−0.781831	−	0.376510i	−0.781831	−	0.376510i	−0.781831	+	0.623490i	$0.785714\pi$
$348$		0			0
$349$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$349$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$350$	0.781831	+	0.623490i	0.781831	+	0.623490i
$351$	0.193096	−	0.242135i	0.193096	−	0.242135i
$352$	−0.433884	−	1.90097i	−0.433884	−	1.90097i
$353$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$353$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$354$		0			0
$355$		0			0
$356$	0.277479	−	1.21572i	0.277479	−	1.21572i
$357$	1.22252	−	0.974928i	1.22252	−	0.974928i
$358$		0			0
$359$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$359$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$360$		0			0
$361$	1.00000			1.00000
$362$		0			0
$363$	−3.94740	+	1.90097i	−3.94740	+	1.90097i
$364$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i
$365$		0			0
$366$		0			0
$367$	0.193096	+	0.846011i	0.193096	+	0.846011i	0.974928	+	0.222521i	$0.0714286\pi$
$367$	0.193096	+	0.846011i	0.193096	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$368$	0.433884	+	1.90097i	0.433884	+	1.90097i
$369$		0			0
$370$		0			0
$371$	0.541044	+	1.12349i	0.541044	+	1.12349i
$372$	2.20291	−	1.06086i	2.20291	−	1.06086i
$373$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$373$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$374$	1.94986			1.94986
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.678448	−	0.154851i	0.678448	−	0.154851i
$379$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$379$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$383$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$384$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$389$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$390$		0			0
$391$	−1.94986			−1.94986
$392$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$393$	−3.04892			−3.04892
$394$		0			0
$395$		0			0
$396$	2.53859	+	1.22252i	2.53859	+	1.22252i
$397$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$397$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$398$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$399$		0			0
$400$	0.623490	−	0.781831i	0.623490	−	0.781831i
$401$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$401$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$402$		0			0
$403$	0.154851	−	0.678448i	0.154851	−	0.678448i
$404$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$409$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$409$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$410$		0			0
$411$	−1.94986			−1.94986
$412$		0			0
$413$		0			0
$414$	−2.53859	−	1.22252i	−2.53859	−	1.22252i
$415$		0			0
$416$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$417$	−0.678448	−	2.97247i	−0.678448	−	2.97247i
$418$		0			0
$419$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$419$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$420$		0			0
$421$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$421$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$422$	−0.867767			−0.867767
$423$		0			0
$424$	1.12349	−	0.541044i	1.12349	−	0.541044i
$425$	0.623490	+	0.781831i	0.623490	+	0.781831i
$426$	−0.544073	−	2.38374i	−0.544073	−	2.38374i
$427$		0			0
$428$	−0.193096	+	0.846011i	−0.193096	+	0.846011i
$429$	1.22252	−	0.588735i	1.22252	−	0.588735i
$430$		0			0
$431$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$431$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$432$	−0.154851	−	0.678448i	−0.154851	−	0.678448i
$433$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$433$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$434$	1.22252	−	0.974928i	1.22252	−	0.974928i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$439$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$440$		0			0
$441$	1.30194	−	0.626980i	1.30194	−	0.626980i
$442$	−0.445042			−0.445042
$443$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$443$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.21572	+	1.52446i	1.21572	+	1.52446i
$448$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$449$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$449$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$450$	0.321552	+	1.40881i	0.321552	+	1.40881i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.347948	−	1.52446i	0.347948	−	1.52446i
$455$		0			0
$456$		0			0
$457$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$457$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$458$	1.62349	−	0.781831i	1.62349	−	0.781831i
$459$	0.695895			0.695895
$460$		0			0
$461$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$461$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$462$	2.97247	+	0.678448i	2.97247	+	0.678448i
$463$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$463$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$467$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$468$	−0.579417	−	0.279032i	−0.579417	−	0.279032i
$469$		0			0
$470$		0			0
$471$	−0.695895			−0.695895
$472$		0			0
$473$		0			0
$474$	−1.90097	−	2.38374i	−1.90097	−	2.38374i
$475$		0			0
$476$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$477$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$478$		0			0
$479$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$479$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−2.97247	−	0.678448i	−2.97247	−	0.678448i
$484$	1.74698	+	2.19064i	1.74698	+	2.19064i
$485$		0			0
$486$	−1.12978	−	0.544073i	−1.12978	−	0.544073i
$487$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$487$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$497$	−0.678448	−	1.40881i	−0.678448	−	1.40881i
$498$		0			0
$499$	0.433884	+	1.90097i	0.433884	+	1.90097i	0.433884	+	0.900969i	$0.357143\pi$
$499$	0.433884	+	1.90097i	0.433884	+	1.90097i			1.00000i	$0.500000\pi$
$500$		0			0
$501$	−0.301938	+	1.32288i	−0.301938	+	1.32288i
$502$		0			0
$503$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$503$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$504$	−0.626980	−	1.30194i	−0.626980	−	1.30194i
$505$		0			0
$506$	−2.37047	−	2.97247i	−2.37047	−	2.97247i
$507$	1.12978	−	0.544073i	1.12978	−	0.544073i
$508$		0			0
$509$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$509$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$510$		0			0
$511$		0			0
$512$	0.900969	+	0.433884i	0.900969	+	0.433884i
$513$		0			0
$514$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$523$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$524$	0.433884	+	1.90097i	0.433884	+	1.90097i
$525$	0.678448	+	1.40881i	0.678448	+	1.40881i
$526$		0			0
$527$	1.40881	−	0.678448i	1.40881	−	0.678448i
$528$	0.678448	−	2.97247i	0.678448	−	2.97247i
$529$	1.74698	+	2.19064i	1.74698	+	2.19064i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.21572	−	1.52446i	1.21572	−	1.52446i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.94986			1.94986
$540$		0			0
$541$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$541$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$542$		0			0
$543$		0			0
$544$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$545$		0			0
$546$	−0.678448	−	0.154851i	−0.678448	−	0.154851i
$547$	0.541044	−	0.678448i	0.541044	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$547$	0.541044	−	0.678448i	0.541044	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$548$	0.277479	+	1.21572i	0.277479	+	1.21572i
$549$		0			0
$550$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$551$		0			0
$552$	−0.678448	+	2.97247i	−0.678448	+	2.97247i
$553$	−1.52446	−	1.21572i	−1.52446	−	1.21572i
$554$		0			0
$555$		0			0
$556$	−1.75676	+	0.846011i	−1.75676	+	0.846011i
$557$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$557$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$558$	2.25956			2.25956
$559$		0			0
$560$		0			0
$561$	2.74698	+	1.32288i	2.74698	+	1.32288i
$562$	1.80194	+	0.867767i	1.80194	+	0.867767i
$563$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$563$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$564$		0			0
$565$		0			0
$566$	1.75676	+	0.846011i	1.75676	+	0.846011i
$567$	−0.347948	−	0.0794168i	−0.347948	−	0.0794168i
$568$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$569$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$569$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$	1.40881	−	0.678448i	1.40881	−	0.678448i	0.433884	−	0.900969i	$-0.357143\pi$
$571$	1.40881	−	0.678448i	1.40881	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$572$	−0.541044	−	0.678448i	−0.541044	−	0.678448i
$573$		0			0
$574$		0			0
$575$	0.433884	−	1.90097i	0.433884	−	1.90097i
$576$	−1.30194	+	0.626980i	−1.30194	+	0.626980i
$577$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$577$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$578$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.51597	+	1.90097i	−1.51597	+	1.90097i
$584$		0			0
$585$		0			0
$586$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$593$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$594$	0.846011	+	1.06086i	0.846011	+	1.06086i
$595$		0			0
$596$	0.777479	−	0.974928i	0.777479	−	0.974928i
$597$	−0.544073	−	2.38374i	−0.544073	−	2.38374i
$598$	0.541044	+	0.678448i	0.541044	+	0.678448i
$599$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$599$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$600$	1.40881	−	0.678448i	1.40881	−	0.678448i
$601$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$601$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.695895			−0.695895
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.321552	−	1.40881i	−0.321552	−	1.40881i
$613$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$613$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$614$		0			0
$615$		0			0
$616$		−	1.94986i		−	1.94986i
$617$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$617$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$	−0.846011	−	1.06086i	−0.846011	−	1.06086i
$622$		0			0
$623$	0.541044	−	1.12349i	0.541044	−	1.12349i
$624$	−0.154851	+	0.678448i	−0.154851	+	0.678448i
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$		0			0
$627$		0			0
$628$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$629$		0			0
$630$		0			0
$631$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$631$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$632$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$633$	−1.22252	−	0.588735i	−1.22252	−	0.588735i
$634$		0			0
$635$		0			0
$636$	1.94986			1.94986
$637$	−0.445042			−0.445042
$638$		0			0
$639$	0.502799	−	2.20291i	0.502799	−	2.20291i
$640$		0			0
$641$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$641$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$642$	−0.846011	+	1.06086i	−0.846011	+	1.06086i
$643$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$643$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$644$			1.94986i			1.94986i
$645$		0			0
$646$		0			0
$647$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$647$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$648$	−0.0794168	+	0.347948i	−0.0794168	+	0.347948i
$649$		0			0
$650$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$651$	2.38374	−	0.544073i	2.38374	−	0.544073i
$652$		0			0
$653$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$653$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$659$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$660$		0			0
$661$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$661$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$662$		0			0
$663$	−0.626980	−	0.301938i	−0.626980	−	0.301938i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.867767			0.867767
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.22252	+	0.974928i	−1.22252	+	0.974928i
$673$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$673$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$674$		0			0
$675$	−0.154851	+	0.678448i	−0.154851	+	0.678448i
$676$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$677$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$677$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.52446	−	1.91161i	1.52446	−	1.91161i
$682$	2.74698	+	1.32288i	2.74698	+	1.32288i
$683$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$683$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$684$		0			0
$685$		0			0
$686$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$687$	2.81762			2.81762
$688$		0			0
$689$	0.346011	−	0.433884i	0.346011	−	0.433884i
$690$		0			0
$691$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$691$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$692$		0			0
$693$	2.20291	+	1.75676i	2.20291	+	1.75676i
$694$	−0.541044	+	0.678448i	−0.541044	+	0.678448i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$699$		0			0
$700$	0.781831	−	0.623490i	0.781831	−	0.623490i
$701$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$701$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$702$	−0.193096	−	0.242135i	−0.193096	−	0.242135i
$703$		0			0
$704$	−1.94986			−1.94986
$705$		0			0
$706$	1.80194	−	0.867767i	1.80194	−	0.867767i
$707$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i
$708$		0			0
$709$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$709$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$710$		0			0
$711$	−0.626980	−	2.74698i	−0.626980	−	2.74698i
$712$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$713$	−2.74698	−	1.32288i	−2.74698	−	1.32288i
$714$	−0.678448	−	1.40881i	−0.678448	−	1.40881i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$719$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$720$		0			0
$721$		0			0
$722$	0.222521	−	0.974928i	0.222521	−	0.974928i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.974928	+	4.27144i	0.974928	+	4.27144i
$727$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$727$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$728$			0.445042i			0.445042i
$729$	−1.00000	−	1.25396i	−1.00000	−	1.25396i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$733$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$734$	0.867767			0.867767
$735$		0			0
$736$	1.94986			1.94986
$737$		0			0
$738$		0			0
$739$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$739$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$740$		0			0
$741$		0			0
$742$	1.21572	−	0.277479i	1.21572	−	0.277479i
$743$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$743$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$744$	−0.544073	−	2.38374i	−0.544073	−	2.38374i
$745$		0			0
$746$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$747$		0			0
$748$	0.433884	−	1.90097i	0.433884	−	1.90097i
$749$	−0.376510	+	0.781831i	−0.376510	+	0.781831i
$750$		0			0
$751$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$751$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		−	0.695895i		−	0.695895i
$757$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$757$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$758$		0			0
$759$	−1.32288	−	5.79590i	−1.32288	−	5.79590i
$760$		0			0
$761$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$761$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.974928	+	1.22252i	0.974928	+	1.22252i
$769$	0.445042	+	1.94986i	0.445042	+	1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$769$	0.445042	+	1.94986i	0.445042	+	1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$770$		0			0
$771$	0.695895	−	3.04892i	0.695895	−	3.04892i
$772$		0			0
$773$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$773$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$774$		0			0
$775$	0.347948	+	1.52446i	0.347948	+	1.52446i
$776$		0			0
$777$		0			0
$778$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$779$		0			0
$780$		0			0
$781$	1.90097	−	2.38374i	1.90097	−	2.38374i
$782$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$783$		0			0
$784$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$785$		0			0
$786$	−0.678448	+	2.97247i	−0.678448	+	2.97247i
$787$	0.541044	−	0.678448i	0.541044	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$787$	0.541044	−	0.678448i	0.541044	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.75676	−	2.20291i	1.75676	−	2.20291i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$797$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$797$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$798$		0			0
$799$		0			0
$800$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$801$	1.62349	−	0.781831i	1.62349	−	0.781831i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.626980	−	0.301938i	−0.626980	−	0.301938i
$807$		0			0
$808$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$809$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$809$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$810$		0			0
$811$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$811$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$817$		0			0
$818$	0.277479	+	1.21572i	0.277479	+	1.21572i
$819$	−0.502799	−	0.400969i	−0.502799	−	0.400969i
$820$		0			0
$821$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$821$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$822$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$823$	0.974928	+	1.22252i	0.974928	+	1.22252i	0.974928	+	0.222521i	$0.0714286\pi$
$823$	0.974928	+	1.22252i	0.974928	+	1.22252i			1.00000i	$0.5\pi$
$824$		0			0
$825$	−1.90097	+	2.38374i	−1.90097	+	2.38374i
$826$		0			0
$827$	−0.541044	−	0.678448i	−0.541044	−	0.678448i	0.433884	−	0.900969i	$-0.357143\pi$
$827$	−0.541044	−	0.678448i	−0.541044	−	0.678448i	−0.974928	+	0.222521i	$0.928571\pi$
$828$	−1.75676	+	2.20291i	−1.75676	+	2.20291i
$829$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$829$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$830$		0			0
$831$		0			0
$832$	0.445042			0.445042
$833$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$834$	−3.04892			−3.04892
$835$		0			0
$836$		0			0
$837$	0.980386	+	0.472129i	0.980386	+	0.472129i
$838$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$839$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$839$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$840$		0			0
$841$	0.623490	−	0.781831i	0.623490	−	0.781831i
$842$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$843$	1.94986	+	2.44504i	1.94986	+	2.44504i
$844$	−0.193096	+	0.846011i	−0.193096	+	0.846011i
$845$		0			0
$846$		0			0
$847$	1.21572	+	2.52446i	1.21572	+	2.52446i
$848$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$849$	1.90097	+	2.38374i	1.90097	+	2.38374i
$850$	0.900969	−	0.433884i	0.900969	−	0.433884i
$851$		0			0
$852$	−2.44504			−2.44504
$853$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$853$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$854$		0			0
$855$		0			0
$856$	0.781831	+	0.376510i	0.781831	+	0.376510i
$857$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$857$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$858$	−0.301938	−	1.32288i	−0.301938	−	1.32288i
$859$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$859$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−0.695895			−0.695895
$865$		0			0
$866$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$867$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$868$	−0.678448	−	1.40881i	−0.678448	−	1.40881i
$869$	0.846011	−	3.70662i	0.846011	−	3.70662i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$877$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$878$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$879$	−0.433884	+	0.544073i	−0.433884	+	0.544073i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.321552	−	1.40881i	−0.321552	−	1.40881i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$885$		0			0
$886$		0			0
$887$	−1.21572	+	1.52446i	−1.21572	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$887$	−1.21572	+	1.52446i	−1.21572	+	1.52446i	−0.781831	+	0.623490i	$0.785714\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.154851	−	0.678448i	−0.154851	−	0.678448i
$892$		0			0
$893$		0			0
$894$	1.75676	−	0.846011i	1.75676	−	0.846011i
$895$		0			0
$896$	0.781831	+	0.623490i	0.781831	+	0.623490i
$897$	0.301938	+	1.32288i	0.301938	+	1.32288i
$898$		0			0
$899$		0			0
$900$	1.44504			1.44504
$901$	1.24698			1.24698
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.347948	+	1.52446i	0.347948	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$907$	0.347948	+	1.52446i	0.347948	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$908$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$909$	−0.579417	−	0.279032i	−0.579417	−	0.279032i
$910$		0			0
$911$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$911$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$912$		0			0
$913$		0			0
$914$	0.400969	−	0.193096i	0.400969	−	0.193096i
$915$		0			0
$916$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$917$			1.94986i			1.94986i
$918$	0.154851	−	0.678448i	0.154851	−	0.678448i
$919$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$919$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$920$		0			0
$921$		0			0
$922$	0.277479	+	1.21572i	0.277479	+	1.21572i
$923$	−0.433884	+	0.544073i	−0.433884	+	0.544073i
$924$	1.32288	−	2.74698i	1.32288	−	2.74698i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$929$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.400969	+	0.502799i	−0.400969	+	0.502799i
$937$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$937$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$941$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$942$	−0.154851	+	0.678448i	−0.154851	+	0.678448i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$947$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$948$	−2.74698	+	1.32288i	−2.74698	+	1.32288i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$953$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$953$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$954$	1.62349	+	0.781831i	1.62349	+	0.781831i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	1.75676	+	0.846011i	1.75676	+	0.846011i
$959$			1.24698i			1.24698i
$960$		0			0
$961$	1.44504			1.44504
$962$		0			0
$963$	−1.12978	+	0.544073i	−1.12978	+	0.544073i
$964$		0			0
$965$		0			0
$966$	−1.32288	+	2.74698i	−1.32288	+	2.74698i
$967$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$967$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$968$	2.52446	−	1.21572i	2.52446	−	1.21572i
$969$		0			0
$970$		0			0
$971$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$971$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$972$	−0.781831	+	0.980386i	−0.781831	+	0.980386i
$973$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$974$		0			0
$975$	0.433884	−	0.544073i	0.433884	−	0.544073i
$976$		0			0
$977$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$978$		0			0
$979$	2.43143			2.43143
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$983$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$991$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$992$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$993$		0			0
$994$	−1.52446	+	0.347948i	−1.52446	+	0.347948i
$995$		0			0
$996$		0			0
$997$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$997$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$998$	1.94986			1.94986
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.be.c.407.2	yes	12
4.3	odd	2	inner	3332.1.be.c.407.1	✓	12
17.16	even	2	inner	3332.1.be.c.407.1	✓	12
49.36	even	7	inner	3332.1.be.c.1359.2	yes	12
68.67	odd	2	CM	3332.1.be.c.407.2	yes	12
196.183	odd	14	inner	3332.1.be.c.1359.1	yes	12
833.526	even	14	inner	3332.1.be.c.1359.1	yes	12
3332.1359	odd	14	inner	3332.1.be.c.1359.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.be.c.407.1	✓	12	4.3	odd	2	inner
3332.1.be.c.407.1	✓	12	17.16	even	2	inner
3332.1.be.c.407.2	yes	12	1.1	even	1	trivial
3332.1.be.c.407.2	yes	12	68.67	odd	2	CM
3332.1.be.c.1359.1	yes	12	196.183	odd	14	inner
3332.1.be.c.1359.1	yes	12	833.526	even	14	inner
3332.1.be.c.1359.2	yes	12	49.36	even	7	inner
3332.1.be.c.1359.2	yes	12	3332.1359	odd	14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.be (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(0.974928 - 1.22252i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.974928 - 1.22252i) q^{6} +(-0.781831 - 0.623490i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-0.321552 - 1.40881i) q^{9} +(0.433884 - 1.90097i) q^{11} +(-1.40881 + 0.678448i) q^{12} +(-0.0990311 + 0.433884i) q^{13} +(-0.781831 + 0.623490i) q^{14} +(0.623490 + 0.781831i) q^{16} +(-0.900969 + 0.433884i) q^{17} -1.44504 q^{18} +(-1.52446 + 0.347948i) q^{21} +(-1.75676 - 0.846011i) q^{22} +(1.75676 + 0.846011i) q^{23} +(0.347948 + 1.52446i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.400969 + 0.193096i) q^{26} +(-0.626980 - 0.301938i) q^{27} +(0.433884 + 0.900969i) q^{28} -1.56366 q^{31} +(0.900969 - 0.433884i) q^{32} +(-1.90097 - 2.38374i) q^{33} +(0.222521 + 0.974928i) q^{34} +(-0.321552 + 1.40881i) q^{36} +(0.433884 + 0.544073i) q^{39} +1.56366i q^{42} +(-1.21572 + 1.52446i) q^{44} +(1.21572 - 1.52446i) q^{46} +1.56366 q^{48} +(0.222521 + 0.974928i) q^{49} -1.00000 q^{50} +(-0.347948 + 1.52446i) q^{51} +(0.277479 - 0.347948i) q^{52} +(-1.12349 - 0.541044i) q^{53} +(-0.433884 + 0.544073i) q^{54} +(0.974928 - 0.222521i) q^{56} +(-0.347948 + 1.52446i) q^{62} +(-0.626980 + 1.30194i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-2.74698 + 1.32288i) q^{66} +1.00000 q^{68} +(2.74698 - 1.32288i) q^{69} +(1.40881 + 0.678448i) q^{71} +(1.30194 + 0.626980i) q^{72} +(-1.40881 - 0.678448i) q^{75} +(-1.52446 + 1.21572i) q^{77} +(0.626980 - 0.301938i) q^{78} +1.94986 q^{79} +(0.321552 - 0.154851i) q^{81} +(1.52446 + 0.347948i) q^{84} +(1.21572 + 1.52446i) q^{88} +(0.277479 + 1.21572i) q^{89} +(0.347948 - 0.277479i) q^{91} +(-1.21572 - 1.52446i) q^{92} +(-1.52446 + 1.91161i) q^{93} +(0.347948 - 1.52446i) q^{96} +1.00000 q^{98} -2.81762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 12 q^{9} - 10 q^{13} - 2 q^{16} - 2 q^{17} - 16 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 14 q^{33} + 2 q^{34} - 12 q^{36} + 2 q^{49} - 12 q^{50} + 4 q^{52} - 4 q^{53}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 - 12 * q^9 - 10 * q^13 - 2 * q^16 - 2 * q^17 - 16 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 14 * q^33 + 2 * q^34 - 12 * q^36 + 2 * q^49 - 12 * q^50 + 4 * q^52 - 4 * q^53 - 2 * q^64 - 14 * q^66 + 12 * q^68 + 14 * q^69 - 2 * q^72 + 12 * q^81 + 4 * q^89 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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