LMFDB - Embedded newform 2960.1.dn.a.1173.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2960,1,Mod(877,2960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2960, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 3, 4]))

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

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

chi := DirichletCharacter("2960.877");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2960 = 2^{4} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2960.dn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.0.350464000.5

Embedding invariants

Embedding label			1173.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2960.1173
Dual form			2960.1.dn.a.2637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.36603 - 0.366025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.36603 - 0.366025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(1.00000 + 1.00000i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.00000 + 1.00000i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{20} +(0.366025 - 1.36603i) q^{21} +(-0.366025 + 1.36603i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} +1.00000 q^{27} +(-0.366025 + 1.36603i) q^{28} +(0.500000 - 0.866025i) q^{30} -1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.36603 - 0.366025i) q^{33} +(0.366025 - 1.36603i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(1.36603 - 0.366025i) q^{42} -1.00000i q^{43} +(-1.36603 + 0.366025i) q^{44} +(-1.36603 - 0.366025i) q^{46} -1.00000 q^{48} +(0.866025 - 0.500000i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} +(0.866025 - 0.500000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.36603 - 0.366025i) q^{55} +(-1.36603 + 0.366025i) q^{56} +(-1.36603 - 0.366025i) q^{59} +1.00000 q^{60} +(-0.366025 - 1.36603i) q^{61} +(-0.500000 - 0.866025i) q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(1.00000 + 1.00000i) q^{66} +(0.366025 + 1.36603i) q^{69} +(1.36603 - 0.366025i) q^{70} +(-1.73205 - 1.00000i) q^{71} -1.00000 q^{74} -1.00000 q^{75} +(1.73205 + 1.00000i) q^{77} +(-0.500000 + 0.866025i) q^{78} -1.00000 q^{80} +(0.500000 - 0.866025i) q^{81} -1.00000i q^{82} +(1.00000 + 1.00000i) q^{84} +(0.866025 - 0.500000i) q^{86} +(-1.00000 - 1.00000i) q^{88} +(-0.366025 + 1.36603i) q^{91} +(-0.366025 - 1.36603i) q^{92} +(-0.500000 + 0.866025i) q^{93} +(-0.500000 - 0.866025i) q^{96} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 4 q^{23} - 2 q^{24} - 2 q^{25} - 4 q^{26} + 4 q^{27} + 2 q^{28} + 2 q^{30} - 4 q^{31} + 2 q^{32} + 2 q^{33} - 2 q^{35} - 2 q^{37} + 2 q^{39} - 2 q^{40} + 2 q^{42} - 2 q^{44} - 2 q^{46} - 4 q^{48} + 2 q^{50} - 2 q^{52} + 2 q^{54} + 2 q^{55} - 2 q^{56} - 2 q^{59} + 4 q^{60} + 2 q^{61} - 2 q^{62} + 4 q^{64} + 2 q^{65} + 4 q^{66} - 2 q^{69} + 2 q^{70} - 4 q^{74} - 4 q^{75} - 2 q^{78} - 4 q^{80} + 2 q^{81} + 4 q^{84} - 4 q^{88} + 2 q^{91} + 2 q^{92} - 2 q^{93} - 2 q^{96}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 - 4 * q^8 + 4 * q^10 + 4 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 - 2 * q^16 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 4 * q^23 - 2 * q^24 - 2 * q^25 - 4 * q^26 + 4 * q^27 + 2 * q^28 + 2 * q^30 - 4 * q^31 + 2 * q^32 + 2 * q^33 - 2 * q^35 - 2 * q^37 + 2 * q^39 - 2 * q^40 + 2 * q^42 - 2 * q^44 - 2 * q^46 - 4 * q^48 + 2 * q^50 - 2 * q^52 + 2 * q^54 + 2 * q^55 - 2 * q^56 - 2 * q^59 + 4 * q^60 + 2 * q^61 - 2 * q^62 + 4 * q^64 + 2 * q^65 + 4 * q^66 - 2 * q^69 + 2 * q^70 - 4 * q^74 - 4 * q^75 - 2 * q^78 - 4 * q^80 + 2 * q^81 + 4 * q^84 - 4 * q^88 + 2 * q^91 + 2 * q^92 - 2 * q^93 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2960\mathbb{Z}\right)^\times$.

$n$	$741$	$1777$	$2481$	$2591$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.500000	+	0.866025i
$2$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$4$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$6$	1.00000			1.00000
$7$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$7$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$8$	−1.00000			−1.00000
$9$		0			0
$10$	1.00000			1.00000
$11$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$11$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$12$	0.500000	+	0.866025i	0.500000	+	0.866025i
$13$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$13$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$14$	1.00000	+	1.00000i	1.00000	+	1.00000i
$15$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$17$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$18$		0			0
$19$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$19$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$20$	0.500000	+	0.866025i	0.500000	+	0.866025i
$21$	0.366025	−	1.36603i	0.366025	−	1.36603i
$22$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$23$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$23$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$24$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$	−1.00000			−1.00000
$27$	1.00000			1.00000
$28$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$29$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$29$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$30$	0.500000	−	0.866025i	0.500000	−	0.866025i
$31$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$31$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.500000	−	0.866025i	0.500000	−	0.866025i
$33$	1.36603	−	0.366025i	1.36603	−	0.366025i
$34$		0			0
$35$	0.366025	−	1.36603i	0.366025	−	1.36603i
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$38$		0			0
$39$	0.500000	+	0.866025i	0.500000	+	0.866025i
$40$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$42$	1.36603	−	0.366025i	1.36603	−	0.366025i
$43$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$43$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$44$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$45$		0			0
$46$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−1.00000			−1.00000
$49$	0.866025	−	0.500000i	0.866025	−	0.500000i
$50$	0.500000	−	0.866025i	0.500000	−	0.866025i
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$53$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$53$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$54$	0.500000	+	0.866025i	0.500000	+	0.866025i
$55$	1.36603	−	0.366025i	1.36603	−	0.366025i
$56$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$57$		0			0
$58$		0			0
$59$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$59$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$60$	1.00000			1.00000
$61$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$61$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$62$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$63$		0			0
$64$	1.00000			1.00000
$65$	0.500000	+	0.866025i	0.500000	+	0.866025i
$66$	1.00000	+	1.00000i	1.00000	+	1.00000i
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	0.366025	+	1.36603i	0.366025	+	1.36603i
$70$	1.36603	−	0.366025i	1.36603	−	0.366025i
$71$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$71$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$72$		0			0
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$	−1.00000			−1.00000
$75$	−1.00000			−1.00000
$76$		0			0
$77$	1.73205	+	1.00000i	1.73205	+	1.00000i
$78$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−1.00000			−1.00000
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$		−	1.00000i		−	1.00000i
$83$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$83$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$84$	1.00000	+	1.00000i	1.00000	+	1.00000i
$85$		0			0
$86$	0.866025	−	0.500000i	0.866025	−	0.500000i
$87$		0			0
$88$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$92$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$93$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$94$		0			0
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$97$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$97$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$98$	0.866025	+	0.500000i	0.866025	+	0.500000i
$99$		0			0
$100$	1.00000			1.00000
$101$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$101$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$102$		0			0
$103$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$103$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$104$	0.500000	−	0.866025i	0.500000	−	0.866025i
$105$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$106$	0.866025	+	0.500000i	0.866025	+	0.500000i
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$108$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$109$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$109$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$110$	1.00000	+	1.00000i	1.00000	+	1.00000i
$111$	0.500000	+	0.866025i	0.500000	+	0.866025i
$112$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$113$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$113$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$114$		0			0
$115$	0.366025	+	1.36603i	0.366025	+	1.36603i
$116$		0			0
$117$		0			0
$118$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$119$		0			0
$120$	0.500000	+	0.866025i	0.500000	+	0.866025i
$121$			1.00000i			1.00000i
$122$	1.00000	−	1.00000i	1.00000	−	1.00000i
$123$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$124$	0.500000	−	0.866025i	0.500000	−	0.866025i
$125$	−1.00000			−1.00000
$126$		0			0
$127$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$127$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$130$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$131$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$131$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$132$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$133$		0			0
$134$		0			0
$135$	0.500000	−	0.866025i	0.500000	−	0.866025i
$136$		0			0
$137$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$137$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$138$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$139$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$139$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$140$	1.00000	+	1.00000i	1.00000	+	1.00000i
$141$		0			0
$142$		−	2.00000i		−	2.00000i
$143$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	1.00000i		−	1.00000i
$148$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$149$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$149$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$150$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$151$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$151$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$152$		0			0
$153$		0			0
$154$			2.00000i			2.00000i
$155$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$156$	−1.00000			−1.00000
$157$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$157$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$158$		0			0
$159$		−	1.00000i		−	1.00000i
$160$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$161$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$162$	1.00000			1.00000
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$164$	0.866025	−	0.500000i	0.866025	−	0.500000i
$165$	0.366025	−	1.36603i	0.366025	−	1.36603i
$166$		0			0
$167$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$168$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$169$		0			0
$170$		0			0
$171$		0			0
$172$	0.866025	+	0.500000i	0.866025	+	0.500000i
$173$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$173$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$174$		0			0
$175$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$176$	0.366025	−	1.36603i	0.366025	−	1.36603i
$177$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$178$		0			0
$179$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$179$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$180$		0			0
$181$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$181$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$182$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$183$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$184$	1.00000	−	1.00000i	1.00000	−	1.00000i
$185$	0.500000	+	0.866025i	0.500000	+	0.866025i
$186$	−1.00000			−1.00000
$187$		0			0
$188$		0			0
$189$	1.36603	−	0.366025i	1.36603	−	0.366025i
$190$		0			0
$191$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$191$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$193$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$194$		0			0
$195$	1.00000			1.00000
$196$			1.00000i			1.00000i
$197$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$197$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$199$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$200$	0.500000	+	0.866025i	0.500000	+	0.866025i
$201$		0			0
$202$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$203$		0			0
$204$		0			0
$205$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$206$	1.36603	+	0.366025i	1.36603	+	0.366025i
$207$		0			0
$208$	1.00000			1.00000
$209$		0			0
$210$	0.366025	−	1.36603i	0.366025	−	1.36603i
$211$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$211$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$212$			1.00000i			1.00000i
$213$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$214$	1.00000			1.00000
$215$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$216$	−1.00000			−1.00000
$217$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$218$		0			0
$219$		0			0
$220$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$221$		0			0
$222$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$	0.366025	−	1.36603i	0.366025	−	1.36603i
$225$		0			0
$226$		0			0
$227$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$227$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$228$		0			0
$229$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$229$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$230$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$231$	1.73205	−	1.00000i	1.73205	−	1.00000i
$232$		0			0
$233$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$233$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$234$		0			0
$235$		0			0
$236$	1.00000	−	1.00000i	1.00000	−	1.00000i
$237$		0			0
$238$		0			0
$239$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$239$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$240$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$243$		0			0
$244$	1.36603	+	0.366025i	1.36603	+	0.366025i
$245$		−	1.00000i		−	1.00000i
$246$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$247$		0			0
$248$	1.00000			1.00000
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$251$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$251$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$252$		0			0
$253$	−2.00000			−2.00000
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$257$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$258$		−	1.00000i		−	1.00000i
$259$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$260$	−1.00000			−1.00000
$261$		0			0
$262$	0.366025	+	1.36603i	0.366025	+	1.36603i
$263$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$264$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$265$		−	1.00000i		−	1.00000i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$269$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$270$	1.00000			1.00000
$271$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$271$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$272$		0			0
$273$	1.00000	+	1.00000i	1.00000	+	1.00000i
$274$		0			0
$275$	0.366025	−	1.36603i	0.366025	−	1.36603i
$276$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$277$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$277$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$278$		0			0
$279$		0			0
$280$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$281$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$281$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$282$		0			0
$283$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$283$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$284$	1.73205	−	1.00000i	1.73205	−	1.00000i
$285$		0			0
$286$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$287$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$288$		0			0
$289$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$293$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$294$	0.866025	−	0.500000i	0.866025	−	0.500000i
$295$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$296$	0.500000	−	0.866025i	0.500000	−	0.866025i
$297$	1.00000	+	1.00000i	1.00000	+	1.00000i
$298$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$299$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$300$	0.500000	−	0.866025i	0.500000	−	0.866025i
$301$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$302$		−	1.00000i		−	1.00000i
$303$	1.36603	−	0.366025i	1.36603	−	0.366025i
$304$		0			0
$305$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$306$		0			0
$307$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$307$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$308$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$309$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$310$	−1.00000			−1.00000
$311$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$311$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$312$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$313$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$313$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$314$	0.866025	+	0.500000i	0.866025	+	0.500000i
$315$		0			0
$316$		0			0
$317$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$317$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$318$	0.866025	−	0.500000i	0.866025	−	0.500000i
$319$		0			0
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$322$	−2.00000			−2.00000
$323$		0			0
$324$	0.500000	+	0.866025i	0.500000	+	0.866025i
$325$	1.00000			1.00000
$326$	0.500000	−	0.866025i	0.500000	−	0.866025i
$327$		0			0
$328$	0.866025	+	0.500000i	0.866025	+	0.500000i
$329$		0			0
$330$	1.36603	−	0.366025i	1.36603	−	0.366025i
$331$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$331$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$332$		0			0
$333$		0			0
$334$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$335$		0			0
$336$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$337$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$337$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$342$		0			0
$343$		0			0
$344$			1.00000i			1.00000i
$345$	1.36603	+	0.366025i	1.36603	+	0.366025i
$346$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$350$	0.366025	−	1.36603i	0.366025	−	1.36603i
$351$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$352$	1.36603	−	0.366025i	1.36603	−	0.366025i
$353$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$353$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$354$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$355$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$356$		0			0
$357$		0			0
$358$	0.366025	−	1.36603i	0.366025	−	1.36603i
$359$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$359$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$360$		0			0
$361$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$362$		0			0
$363$	0.866025	+	0.500000i	0.866025	+	0.500000i
$364$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$365$		0			0
$366$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$367$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$367$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$368$	1.36603	+	0.366025i	1.36603	+	0.366025i
$369$		0			0
$370$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$371$	1.00000	−	1.00000i	1.00000	−	1.00000i
$372$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$373$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$373$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$376$		0			0
$377$		0			0
$378$	1.00000	+	1.00000i	1.00000	+	1.00000i
$379$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$379$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$380$		0			0
$381$		0			0
$382$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$383$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$383$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$384$	1.00000			1.00000
$385$	1.73205	−	1.00000i	1.73205	−	1.00000i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$389$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$390$	0.500000	+	0.866025i	0.500000	+	0.866025i
$391$		0			0
$392$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$393$	1.00000	−	1.00000i	1.00000	−	1.00000i
$394$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$395$		0			0
$396$		0			0
$397$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$397$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$398$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	0.500000	−	0.866025i	0.500000	−	0.866025i
$404$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$405$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$406$		0			0
$407$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$408$		0			0
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$410$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$411$		0			0
$412$	0.366025	+	1.36603i	0.366025	+	1.36603i
$413$	−2.00000			−2.00000
$414$		0			0
$415$		0			0
$416$	0.500000	+	0.866025i	0.500000	+	0.866025i
$417$		0			0
$418$		0			0
$419$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$419$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$420$	1.36603	−	0.366025i	1.36603	−	0.366025i
$421$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$421$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$422$		0			0
$423$		0			0
$424$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$425$		0			0
$426$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$427$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$428$	0.500000	+	0.866025i	0.500000	+	0.866025i
$429$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$430$		−	1.00000i		−	1.00000i
$431$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$431$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$432$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$433$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$433$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$434$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$440$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$441$		0			0
$442$		0			0
$443$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$443$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$444$	−1.00000			−1.00000
$445$		0			0
$446$		0			0
$447$	0.366025	+	1.36603i	0.366025	+	1.36603i
$448$	1.36603	−	0.366025i	1.36603	−	0.366025i
$449$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$449$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$450$		0			0
$451$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$452$		0			0
$453$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$454$			1.00000i			1.00000i
$455$	1.00000	+	1.00000i	1.00000	+	1.00000i
$456$		0			0
$457$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$457$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$458$		0			0
$459$		0			0
$460$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$461$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$461$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$462$	1.73205	+	1.00000i	1.73205	+	1.00000i
$463$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$463$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$464$		0			0
$465$	0.500000	+	0.866025i	0.500000	+	0.866025i
$466$		0			0
$467$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$467$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		−	1.00000i		−	1.00000i
$472$	1.36603	+	0.366025i	1.36603	+	0.366025i
$473$	1.00000	−	1.00000i	1.00000	−	1.00000i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$479$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$479$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$480$	−1.00000			−1.00000
$481$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$482$		0			0
$483$	1.00000	+	1.73205i	1.00000	+	1.73205i
$484$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$485$		0			0
$486$		0			0
$487$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$487$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$488$	0.366025	+	1.36603i	0.366025	+	1.36603i
$489$	−1.00000			−1.00000
$490$	0.866025	−	0.500000i	0.866025	−	0.500000i
$491$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$491$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$492$		−	1.00000i		−	1.00000i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.500000	+	0.866025i	0.500000	+	0.866025i
$497$	−2.73205	−	0.732051i	−2.73205	−	0.732051i
$498$		0			0
$499$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$499$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$500$	0.500000	−	0.866025i	0.500000	−	0.866025i
$501$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$502$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$503$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$503$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$504$		0			0
$505$	1.36603	−	0.366025i	1.36603	−	0.366025i
$506$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$507$		0			0
$508$		0			0
$509$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$509$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$		0			0
$514$	0.366025	+	1.36603i	0.366025	+	1.36603i
$515$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$516$	0.866025	−	0.500000i	0.866025	−	0.500000i
$517$		0			0
$518$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$519$	2.00000			2.00000
$520$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$521$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$521$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$522$		0			0
$523$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$523$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$524$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$525$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$526$	1.00000	−	1.00000i	1.00000	−	1.00000i
$527$		0			0
$528$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$529$		−	1.00000i		−	1.00000i
$530$	0.866025	−	0.500000i	0.866025	−	0.500000i
$531$		0			0
$532$		0			0
$533$	0.866025	−	0.500000i	0.866025	−	0.500000i
$534$		0			0
$535$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$536$		0			0
$537$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$538$	0.366025	−	1.36603i	0.366025	−	1.36603i
$539$	1.36603	+	0.366025i	1.36603	+	0.366025i
$540$	0.500000	+	0.866025i	0.500000	+	0.866025i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$	0.500000	−	0.866025i	0.500000	−	0.866025i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$547$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$547$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$548$		0			0
$549$		0			0
$550$	1.36603	−	0.366025i	1.36603	−	0.366025i
$551$		0			0
$552$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$553$		0			0
$554$	1.00000			1.00000
$555$	1.00000			1.00000
$556$		0			0
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$558$		0			0
$559$	0.866025	+	0.500000i	0.866025	+	0.500000i
$560$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$561$		0			0
$562$	0.866025	+	0.500000i	0.866025	+	0.500000i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$		0			0
$566$			1.00000i			1.00000i
$567$	0.366025	−	1.36603i	0.366025	−	1.36603i
$568$	1.73205	+	1.00000i	1.73205	+	1.00000i
$569$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$572$	0.366025	−	1.36603i	0.366025	−	1.36603i
$573$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$574$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$575$	1.36603	+	0.366025i	1.36603	+	0.366025i
$576$		0			0
$577$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$577$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$578$		−	1.00000i		−	1.00000i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.36603	+	0.366025i	1.36603	+	0.366025i
$584$		0			0
$585$		0			0
$586$			1.00000i			1.00000i
$587$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$587$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$588$	0.866025	+	0.500000i	0.866025	+	0.500000i
$589$		0			0
$590$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$591$	1.00000			1.00000
$592$	1.00000			1.00000
$593$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$593$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$594$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$595$		0			0
$596$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$597$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$598$	1.00000	−	1.00000i	1.00000	−	1.00000i
$599$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$599$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$600$	1.00000			1.00000
$601$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$601$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$602$	1.00000	−	1.00000i	1.00000	−	1.00000i
$603$		0			0
$604$	0.866025	−	0.500000i	0.866025	−	0.500000i
$605$	0.866025	+	0.500000i	0.866025	+	0.500000i
$606$	1.00000	+	1.00000i	1.00000	+	1.00000i
$607$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$607$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$608$		0			0
$609$		0			0
$610$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$611$		0			0
$612$		0			0
$613$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$613$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$614$	0.866025	−	0.500000i	0.866025	−	0.500000i
$615$			1.00000i			1.00000i
$616$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$617$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$617$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$618$	1.00000	−	1.00000i	1.00000	−	1.00000i
$619$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$619$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$620$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$621$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$622$	0.866025	+	0.500000i	0.866025	+	0.500000i
$623$		0			0
$624$	0.500000	−	0.866025i	0.500000	−	0.866025i
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$	0.366025	+	1.36603i	0.366025	+	1.36603i
$627$		0			0
$628$			1.00000i			1.00000i
$629$		0			0
$630$		0			0
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$632$		0			0
$633$		0			0
$634$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$635$		0			0
$636$	0.866025	+	0.500000i	0.866025	+	0.500000i
$637$			1.00000i			1.00000i
$638$		0			0
$639$		0			0
$640$	1.00000			1.00000
$641$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$641$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	0.500000	−	0.866025i	0.500000	−	0.866025i
$643$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$643$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$644$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$645$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$646$		0			0
$647$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$647$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$648$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$649$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$650$	0.500000	+	0.866025i	0.500000	+	0.866025i
$651$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$652$	1.00000			1.00000
$653$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$654$		0			0
$655$	1.00000	−	1.00000i	1.00000	−	1.00000i
$656$			1.00000i			1.00000i
$657$		0			0
$658$		0			0
$659$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$659$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$660$	1.00000	+	1.00000i	1.00000	+	1.00000i
$661$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$661$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.366025	−	1.36603i	0.366025	−	1.36603i
$669$		0			0
$670$		0			0
$671$	1.00000	−	1.73205i	1.00000	−	1.73205i
$672$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$673$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$673$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$676$		0			0
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.866025	−	0.500000i	0.866025	−	0.500000i
$682$	0.366025	−	1.36603i	0.366025	−	1.36603i
$683$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$683$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$689$			1.00000i			1.00000i
$690$	0.366025	+	1.36603i	0.366025	+	1.36603i
$691$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$691$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$692$	−2.00000			−2.00000
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.36603	−	0.366025i	1.36603	−	0.366025i
$699$		0			0
$700$	1.36603	−	0.366025i	1.36603	−	0.366025i
$701$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$701$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$702$	−1.00000			−1.00000
$703$		0			0
$704$	1.00000	+	1.00000i	1.00000	+	1.00000i
$705$		0			0
$706$		0			0
$707$	1.73205	+	1.00000i	1.73205	+	1.00000i
$708$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$709$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$709$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$710$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$711$		0			0
$712$		0			0
$713$	1.00000	−	1.00000i	1.00000	−	1.00000i
$714$		0			0
$715$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$716$	1.36603	−	0.366025i	1.36603	−	0.366025i
$717$			2.00000i			2.00000i
$718$	0.500000	+	0.866025i	0.500000	+	0.866025i
$719$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$719$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	1.00000	−	1.73205i	1.00000	−	1.73205i
$722$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$723$		0			0
$724$		0			0
$725$		0			0
$726$			1.00000i			1.00000i
$727$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$727$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$728$	0.366025	−	1.36603i	0.366025	−	1.36603i
$729$	1.00000			1.00000
$730$		0			0
$731$		0			0
$732$	1.00000	−	1.00000i	1.00000	−	1.00000i
$733$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$733$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$734$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$735$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$736$	0.366025	+	1.36603i	0.366025	+	1.36603i
$737$		0			0
$738$		0			0
$739$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$739$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$740$	−1.00000			−1.00000
$741$		0			0
$742$	1.36603	+	0.366025i	1.36603	+	0.366025i
$743$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$743$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$744$	0.500000	−	0.866025i	0.500000	−	0.866025i
$745$	0.366025	+	1.36603i	0.366025	+	1.36603i
$746$			1.00000i			1.00000i
$747$		0			0
$748$		0			0
$749$	0.366025	−	1.36603i	0.366025	−	1.36603i
$750$	−1.00000			−1.00000
$751$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$751$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	1.36603	−	0.366025i	1.36603	−	0.366025i
$754$		0			0
$755$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$756$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$757$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$757$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$758$	0.366025	+	1.36603i	0.366025	+	1.36603i
$759$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$760$		0			0
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$		0			0
$763$		0			0
$764$	0.500000	−	0.866025i	0.500000	−	0.866025i
$765$		0			0
$766$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$767$	1.00000	−	1.00000i	1.00000	−	1.00000i
$768$	0.500000	+	0.866025i	0.500000	+	0.866025i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$	1.73205	+	1.00000i	1.73205	+	1.00000i
$771$	1.00000	−	1.00000i	1.00000	−	1.00000i
$772$		0			0
$773$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$773$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$774$		0			0
$775$	0.500000	+	0.866025i	0.500000	+	0.866025i
$776$		0			0
$777$	1.00000	+	1.00000i	1.00000	+	1.00000i
$778$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$779$		0			0
$780$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$781$	−0.732051	−	2.73205i	−0.732051	−	2.73205i
$782$		0			0
$783$		0			0
$784$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$785$		−	1.00000i		−	1.00000i
$786$	1.36603	+	0.366025i	1.36603	+	0.366025i
$787$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$787$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$788$	−1.00000			−1.00000
$789$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.36603	+	0.366025i	1.36603	+	0.366025i
$794$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$795$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$796$	0.500000	−	0.866025i	0.500000	−	0.866025i
$797$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$797$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$	−1.00000			−1.00000
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	1.00000	+	1.73205i	1.00000	+	1.73205i
$806$	1.00000			1.00000
$807$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$808$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$809$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$809$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$810$	0.500000	−	0.866025i	0.500000	−	0.866025i
$811$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$811$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$812$		0			0
$813$	−1.00000			−1.00000
$814$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$815$	−1.00000			−1.00000
$816$		0			0
$817$		0			0
$818$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$819$		0			0
$820$		−	1.00000i		−	1.00000i
$821$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$821$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$823$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$824$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$825$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$826$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$827$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$827$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$828$		0			0
$829$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$830$		0			0
$831$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$832$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$833$		0			0
$834$		0			0
$835$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$836$		0			0
$837$	−1.00000			−1.00000
$838$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$839$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$839$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$840$	1.00000	+	1.00000i	1.00000	+	1.00000i
$841$		−	1.00000i		−	1.00000i
$842$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$843$		−	1.00000i		−	1.00000i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.366025	+	1.36603i	0.366025	+	1.36603i
$848$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$849$	0.866025	−	0.500000i	0.866025	−	0.500000i
$850$		0			0
$851$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$852$		−	2.00000i		−	2.00000i
$853$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$853$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$854$	1.00000	−	1.73205i	1.00000	−	1.73205i
$855$		0			0
$856$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$857$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$857$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$858$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$859$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$859$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$860$	0.866025	−	0.500000i	0.866025	−	0.500000i
$861$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$862$	−1.00000			−1.00000
$863$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$863$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$864$	0.500000	−	0.866025i	0.500000	−	0.866025i
$865$	2.00000			2.00000
$866$		0			0
$867$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$868$	0.366025	−	1.36603i	0.366025	−	1.36603i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$876$		0			0
$877$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$877$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$878$	1.00000			1.00000
$879$	0.866025	−	0.500000i	0.866025	−	0.500000i
$880$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$881$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$881$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$882$		0			0
$883$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$883$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$884$		0			0
$885$	0.366025	+	1.36603i	0.366025	+	1.36603i
$886$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$887$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$887$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$888$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$889$		0			0
$890$		0			0
$891$	1.36603	−	0.366025i	1.36603	−	0.366025i
$892$		0			0
$893$		0			0
$894$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$895$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$896$	1.00000	+	1.00000i	1.00000	+	1.00000i
$897$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$898$		−	1.00000i		−	1.00000i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	1.00000	−	1.00000i	1.00000	−	1.00000i
$903$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$904$		0			0
$905$		0			0
$906$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$909$		0			0
$910$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$911$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$911$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$916$		0			0
$917$	2.00000			2.00000
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$921$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$922$	0.366025	+	1.36603i	0.366025	+	1.36603i
$923$	1.73205	−	1.00000i	1.73205	−	1.00000i
$924$			2.00000i			2.00000i
$925$	1.00000			1.00000
$926$	1.00000	+	1.00000i	1.00000	+	1.00000i
$927$		0			0
$928$		0			0
$929$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$929$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$930$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$931$		0			0
$932$		0			0
$933$		−	1.00000i		−	1.00000i
$934$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$935$		0			0
$936$		0			0
$937$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$937$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$938$		0			0
$939$	1.00000	−	1.00000i	1.00000	−	1.00000i
$940$		0			0
$941$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$941$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$942$	0.866025	−	0.500000i	0.866025	−	0.500000i
$943$	1.36603	−	0.366025i	1.36603	−	0.366025i
$944$	0.366025	+	1.36603i	0.366025	+	1.36603i
$945$	0.366025	−	1.36603i	0.366025	−	1.36603i
$946$	1.36603	+	0.366025i	1.36603	+	0.366025i
$947$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$947$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$			1.00000i			1.00000i
$952$		0			0
$953$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$953$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$954$		0			0
$955$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$956$		−	2.00000i		−	2.00000i
$957$		0			0
$958$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$959$		0			0
$960$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$961$		0			0
$962$	0.500000	−	0.866025i	0.500000	−	0.866025i
$963$		0			0
$964$		0			0
$965$		0			0
$966$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$967$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$968$		−	1.00000i		−	1.00000i
$969$		0			0
$970$		0			0
$971$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$972$		0			0
$973$		0			0
$974$	0.366025	−	1.36603i	0.366025	−	1.36603i
$975$	0.500000	−	0.866025i	0.500000	−	0.866025i
$976$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$977$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$977$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$978$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$979$		0			0
$980$	0.866025	+	0.500000i	0.866025	+	0.500000i
$981$		0			0
$982$	0.366025	−	1.36603i	0.366025	−	1.36603i
$983$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$983$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$984$	0.866025	−	0.500000i	0.866025	−	0.500000i
$985$	1.00000			1.00000
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.00000	+	1.00000i	1.00000	+	1.00000i
$990$		0			0
$991$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$991$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$992$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$993$		0			0
$994$	−0.732051	−	2.73205i	−0.732051	−	2.73205i
$995$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$996$		0			0
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$998$		0			0
$999$	−0.500000	+	0.866025i	−0.500000	+	0.866025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2960.1.dn.a.1173.1	yes	4
5.2	odd	4		2960.1.fm.a.2357.1	yes	4
16.13	even	4		2960.1.fm.a.2653.1	yes	4
37.10	even	3	inner	2960.1.dn.a.2933.1	yes	4
80.77	odd	4	inner	2960.1.dn.a.877.1	✓	4
185.47	odd	12		2960.1.fm.a.1157.1	yes	4
592.269	even	12		2960.1.fm.a.1453.1	yes	4
2960.2637	odd	12	inner	2960.1.dn.a.2637.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2960.1.dn.a.877.1	✓	4	80.77	odd	4	inner
2960.1.dn.a.1173.1	yes	4	1.1	even	1	trivial
2960.1.dn.a.2637.1	yes	4	2960.2637	odd	12	inner
2960.1.dn.a.2933.1	yes	4	37.10	even	3	inner
2960.1.fm.a.1157.1	yes	4	185.47	odd	12
2960.1.fm.a.1453.1	yes	4	592.269	even	12
2960.1.fm.a.2357.1	yes	4	5.2	odd	4
2960.1.fm.a.2653.1	yes	4	16.13	even	4

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:	\( N \)	\(=\)	\( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2960.dn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.36603 - 0.366025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.36603 - 0.366025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(1.00000 + 1.00000i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.00000 + 1.00000i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{20} +(0.366025 - 1.36603i) q^{21} +(-0.366025 + 1.36603i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} +1.00000 q^{27} +(-0.366025 + 1.36603i) q^{28} +(0.500000 - 0.866025i) q^{30} -1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.36603 - 0.366025i) q^{33} +(0.366025 - 1.36603i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(1.36603 - 0.366025i) q^{42} -1.00000i q^{43} +(-1.36603 + 0.366025i) q^{44} +(-1.36603 - 0.366025i) q^{46} -1.00000 q^{48} +(0.866025 - 0.500000i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} +(0.866025 - 0.500000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.36603 - 0.366025i) q^{55} +(-1.36603 + 0.366025i) q^{56} +(-1.36603 - 0.366025i) q^{59} +1.00000 q^{60} +(-0.366025 - 1.36603i) q^{61} +(-0.500000 - 0.866025i) q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(1.00000 + 1.00000i) q^{66} +(0.366025 + 1.36603i) q^{69} +(1.36603 - 0.366025i) q^{70} +(-1.73205 - 1.00000i) q^{71} -1.00000 q^{74} -1.00000 q^{75} +(1.73205 + 1.00000i) q^{77} +(-0.500000 + 0.866025i) q^{78} -1.00000 q^{80} +(0.500000 - 0.866025i) q^{81} -1.00000i q^{82} +(1.00000 + 1.00000i) q^{84} +(0.866025 - 0.500000i) q^{86} +(-1.00000 - 1.00000i) q^{88} +(-0.366025 + 1.36603i) q^{91} +(-0.366025 - 1.36603i) q^{92} +(-0.500000 + 0.866025i) q^{93} +(-0.500000 - 0.866025i) q^{96} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 4 q^{23} - 2 q^{24} - 2 q^{25} - 4 q^{26} + 4 q^{27} + 2 q^{28} + 2 q^{30} - 4 q^{31} + 2 q^{32} + 2 q^{33} - 2 q^{35} - 2 q^{37} + 2 q^{39} - 2 q^{40} + 2 q^{42} - 2 q^{44} - 2 q^{46} - 4 q^{48} + 2 q^{50} - 2 q^{52} + 2 q^{54} + 2 q^{55} - 2 q^{56} - 2 q^{59} + 4 q^{60} + 2 q^{61} - 2 q^{62} + 4 q^{64} + 2 q^{65} + 4 q^{66} - 2 q^{69} + 2 q^{70} - 4 q^{74} - 4 q^{75} - 2 q^{78} - 4 q^{80} + 2 q^{81} + 4 q^{84} - 4 q^{88} + 2 q^{91} + 2 q^{92} - 2 q^{93} - 2 q^{96}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 - 4 * q^8 + 4 * q^10 + 4 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 - 2 * q^16 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 4 * q^23 - 2 * q^24 - 2 * q^25 - 4 * q^26 + 4 * q^27 + 2 * q^28 + 2 * q^30 - 4 * q^31 + 2 * q^32 + 2 * q^33 - 2 * q^35 - 2 * q^37 + 2 * q^39 - 2 * q^40 + 2 * q^42 - 2 * q^44 - 2 * q^46 - 4 * q^48 + 2 * q^50 - 2 * q^52 + 2 * q^54 + 2 * q^55 - 2 * q^56 - 2 * q^59 + 4 * q^60 + 2 * q^61 - 2 * q^62 + 4 * q^64 + 2 * q^65 + 4 * q^66 - 2 * q^69 + 2 * q^70 - 4 * q^74 - 4 * q^75 - 2 * q^78 - 4 * q^80 + 2 * q^81 + 4 * q^84 - 4 * q^88 + 2 * q^91 + 2 * q^92 - 2 * q^93 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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