LMFDB - Embedded newform 2960.1.fm.a.2357.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2960,1,Mod(1157,2960)]

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, 3, 3, 8]))

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

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

chi := DirichletCharacter("2960.1157");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2960 = 2^{4} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2960.fm (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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.0.350464000.5

Embedding invariants

Embedding label			2357.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2960.2357
Dual form			2960.1.fm.a.1453.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$3$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$3$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i
$6$	1.00000			1.00000
$7$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$7$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$8$			1.00000i			1.00000i
$9$		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	$0.5\pi$
$12$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$13$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$13$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$14$	−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		−0.965926	−	0.258819i	$-0.916667\pi$
$17$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$18$		0			0
$19$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$19$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$20$	0.866025	−	0.500000i	0.866025	−	0.500000i
$21$	0.366025	−	1.36603i	0.366025	−	1.36603i
$22$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$23$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$23$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$24$	0.500000	−	0.866025i	0.500000	−	0.866025i
$25$	0.500000	+	0.866025i	0.500000	+	0.866025i
$26$	−1.00000			−1.00000
$27$			1.00000i			1.00000i
$28$	1.36603	+	0.366025i	1.36603	+	0.366025i
$29$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$29$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$30$	0.866025	+	0.500000i	0.866025	+	0.500000i
$31$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$31$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.866025	+	0.500000i	0.866025	+	0.500000i
$33$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$34$		0			0
$35$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$36$		0			0
$37$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$37$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$38$		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	$0.833333\pi$
$42$	0.366025	+	1.36603i	0.366025	+	1.36603i
$43$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$43$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$44$	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	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$			1.00000i			1.00000i
$49$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$50$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$51$		0			0
$52$	0.866025	−	0.500000i	0.866025	−	0.500000i
$53$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$53$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$54$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$55$	0.366025	+	1.36603i	0.366025	+	1.36603i
$56$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$57$		0			0
$58$		0			0
$59$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$59$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$60$	−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	$-0.333333\pi$
$62$	0.866025	−	0.500000i	0.866025	−	0.500000i
$63$		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		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$		0			0
$69$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$70$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$71$	−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	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$	1.00000			1.00000
$75$		−	1.00000i		−	1.00000i
$76$		0			0
$77$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$78$	0.866025	+	0.500000i	0.866025	+	0.500000i
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		−	1.00000i		−	1.00000i
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	1.00000			1.00000
$83$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$83$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$84$	−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
$92$	1.36603	−	0.366025i	1.36603	−	0.366025i
$93$	0.866025	+	0.500000i	0.866025	+	0.500000i
$94$		0			0
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	0.500000	−	0.866025i	0.500000	−	0.866025i
$99$		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			$\pi$
$104$	−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
$107$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$107$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$108$	0.866025	+	0.500000i	0.866025	+	0.500000i
$109$		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		0.258819	−	0.965926i	$-0.416667\pi$
$113$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$114$		0			0
$115$	0.366025	+	1.36603i	0.366025	+	1.36603i
$116$		0			0
$117$		0			0
$118$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$119$		0			0
$120$	0.866025	−	0.500000i	0.866025	−	0.500000i
$121$			1.00000i			1.00000i
$122$	1.00000	+	1.00000i	1.00000	+	1.00000i
$123$	0.500000	+	0.866025i	0.500000	+	0.866025i
$124$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$125$			1.00000i			1.00000i
$126$		0			0
$127$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$127$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$128$	0.866025	−	0.500000i	0.866025	−	0.500000i
$129$	0.866025	+	0.500000i	0.866025	+	0.500000i
$130$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$131$	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	$0.333333\pi$
$132$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	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
$142$	2.00000			2.00000
$143$	0.366025	+	1.36603i	0.366025	+	1.36603i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.00000			1.00000
$148$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$149$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$149$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$150$	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
$155$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$156$	−1.00000			−1.00000
$157$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$157$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$158$		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
$162$			1.00000i			1.00000i
$163$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$163$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$164$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$165$	0.366025	−	1.36603i	0.366025	−	1.36603i
$166$		0			0
$167$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$168$	1.36603	+	0.366025i	1.36603	+	0.366025i
$169$		0			0
$170$		0			0
$171$		0			0
$172$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$173$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$173$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$174$		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	1.00000			$0$
$179$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$180$		0			0
$181$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$181$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$182$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$183$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$184$	−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	$0.666667\pi$
$192$	0.866025	+	0.500000i	0.866025	+	0.500000i
$193$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$193$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$194$		0			0
$195$		−	1.00000i		−	1.00000i
$196$			1.00000i			1.00000i
$197$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$197$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$198$		0			0
$199$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$199$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$200$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$201$		0			0
$202$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$203$		0			0
$204$		0			0
$205$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$206$	1.36603	+	0.366025i	1.36603	+	0.366025i
$207$		0			0
$208$		−	1.00000i		−	1.00000i
$209$		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	$0.250000\pi$
$212$	−1.00000			−1.00000
$213$	1.00000	+	1.73205i	1.00000	+	1.73205i
$214$	−1.00000			−1.00000
$215$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$216$	−1.00000			−1.00000
$217$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$218$		0			0
$219$		0			0
$220$	1.36603	+	0.366025i	1.36603	+	0.366025i
$221$		0			0
$222$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$225$		0			0
$226$		0			0
$227$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$227$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$228$		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	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		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	$-0.166667\pi$
$239$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$240$	−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	$0.166667\pi$
$242$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$243$		0			0
$244$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$245$	−1.00000			−1.00000
$246$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$247$		0			0
$248$		−	1.00000i		−	1.00000i
$249$		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
$253$			2.00000i			2.00000i
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$257$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$258$	−1.00000			−1.00000
$259$	0.366025	−	1.36603i	0.366025	−	1.36603i
$260$	1.00000			1.00000
$261$		0			0
$262$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$263$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$264$	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	1.00000			$0$
$269$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$270$		−	1.00000i		−	1.00000i
$271$	−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
$277$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$277$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$278$		0			0
$279$		0			0
$280$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$281$	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
$283$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$284$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$285$		0			0
$286$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$287$	0.366025	−	1.36603i	0.366025	−	1.36603i
$288$		0			0
$289$	0.866025	+	0.500000i	0.866025	+	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$293$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$294$	−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
$298$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$299$	0.366025	+	1.36603i	0.366025	+	1.36603i
$300$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$301$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$302$	1.00000			1.00000
$303$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$304$		0			0
$305$	0.366025	−	1.36603i	0.366025	−	1.36603i
$306$		0			0
$307$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$307$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$308$	1.00000	+	1.73205i	1.00000	+	1.73205i
$309$	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	$0.166667\pi$
$312$	0.866025	−	0.500000i	0.866025	−	0.500000i
$313$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$313$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$314$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$315$		0			0
$316$		0			0
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$318$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$319$		0			0
$320$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$321$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$322$		−	2.00000i		−	2.00000i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$325$			1.00000i			1.00000i
$326$	0.500000	−	0.866025i	0.500000	−	0.866025i
$327$		0			0
$328$	0.500000	−	0.866025i	0.500000	−	0.866025i
$329$		0			0
$330$	0.366025	+	1.36603i	0.366025	+	1.36603i
$331$		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		−0.258819	−	0.965926i	$-0.583333\pi$
$337$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$338$		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
$345$	0.366025	−	1.36603i	0.366025	−	1.36603i
$346$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$347$		0			0		1.00000			$0$
$347$		0			0		−1.00000			$\pi$
$348$		0			0
$349$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$349$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$350$	0.366025	−	1.36603i	0.366025	−	1.36603i
$351$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$352$	0.366025	+	1.36603i	0.366025	+	1.36603i
$353$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$353$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$354$	1.36603	+	0.366025i	1.36603	+	0.366025i
$355$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$356$		0			0
$357$		0			0
$358$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$359$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$359$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$360$		0			0
$361$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$362$		0			0
$363$	0.500000	−	0.866025i	0.500000	−	0.866025i
$364$	1.00000	+	1.00000i	1.00000	+	1.00000i
$365$		0			0
$366$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$367$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$368$	0.366025	−	1.36603i	0.366025	−	1.36603i
$369$		0			0
$370$	0.866025	+	0.500000i	0.866025	+	0.500000i
$371$	1.00000	−	1.00000i	1.00000	−	1.00000i
$372$	0.866025	−	0.500000i	0.866025	−	0.500000i
$373$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$373$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$374$		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	−0.500000	−	0.866025i	$-0.666667\pi$
$379$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$380$		0			0
$381$		0			0
$382$	0.866025	−	0.500000i	0.866025	−	0.500000i
$383$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$383$	0.366025	+	1.36603i	0.366025	+	1.36603i	−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	$-0.833333\pi$
$389$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$390$	0.500000	+	0.866025i	0.500000	+	0.866025i
$391$		0			0
$392$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$393$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$394$	0.500000	−	0.866025i	0.500000	−	0.866025i
$395$		0			0
$396$		0			0
$397$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$397$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$398$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$399$		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
$403$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$404$	1.36603	−	0.366025i	1.36603	−	0.366025i
$405$	0.866025	−	0.500000i	0.866025	−	0.500000i
$406$		0			0
$407$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$408$		0			0
$409$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$409$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$410$	0.866025	+	0.500000i	0.866025	+	0.500000i
$411$		0			0
$412$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$413$			2.00000i			2.00000i
$414$		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	$-0.666667\pi$
$419$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$420$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$421$	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
$427$	1.73205	−	1.00000i	1.73205	−	1.00000i
$428$	0.866025	−	0.500000i	0.866025	−	0.500000i
$429$	0.366025	−	1.36603i	0.366025	−	1.36603i
$430$	1.00000			1.00000
$431$	−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			$\pi$
$432$	0.866025	−	0.500000i	0.866025	−	0.500000i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$	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	$0.333333\pi$
$439$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$440$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$441$		0			0
$442$		0			0
$443$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$443$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$444$	1.00000			1.00000
$445$		0			0
$446$		0			0
$447$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$448$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$449$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$449$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$450$		0			0
$451$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$452$		0			0
$453$	0.500000	+	0.866025i	0.500000	+	0.866025i
$454$		−	1.00000i		−	1.00000i
$455$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$456$		0			0
$457$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$457$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$458$		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	$0.333333\pi$
$462$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$463$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$463$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$464$		0			0
$465$	0.500000	+	0.866025i	0.500000	+	0.866025i
$466$		0			0
$467$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$467$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		−	1.00000i		−	1.00000i
$472$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$473$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$479$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$479$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$480$		−	1.00000i		−	1.00000i
$481$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$482$		0			0
$483$	1.73205	−	1.00000i	1.73205	−	1.00000i
$484$	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			$0$
$488$	1.36603	−	0.366025i	1.36603	−	0.366025i
$489$	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			$\pi$
$492$	1.00000			1.00000
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.500000	+	0.866025i	0.500000	+	0.866025i
$497$	0.732051	−	2.73205i	0.732051	−	2.73205i
$498$		0			0
$499$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$499$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$500$	0.866025	+	0.500000i	0.866025	+	0.500000i
$501$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$502$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$503$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$503$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$504$		0			0
$505$	0.366025	+	1.36603i	0.366025	+	1.36603i
$506$	−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	$0.333333\pi$
$509$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$		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
$518$	0.366025	+	1.36603i	0.366025	+	1.36603i
$519$	−2.00000			−2.00000
$520$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$521$	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
$523$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$523$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$524$	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
$530$	0.500000	+	0.866025i	0.500000	+	0.866025i
$531$		0			0
$532$		0			0
$533$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$534$		0			0
$535$	0.500000	+	0.866025i	0.500000	+	0.866025i
$536$		0			0
$537$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$538$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$539$	−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	$0.250000\pi$
$542$	0.866025	+	0.500000i	0.866025	+	0.500000i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$547$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$547$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$		0			0
$550$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$551$		0			0
$552$	1.36603	−	0.366025i	1.36603	−	0.366025i
$553$		0			0
$554$	−1.00000			−1.00000
$555$			1.00000i			1.00000i
$556$		0			0
$557$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$557$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$558$		0			0
$559$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$560$	1.36603	−	0.366025i	1.36603	−	0.366025i
$561$		0			0
$562$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$563$		0			0		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$			1.00000i			1.00000i
$567$	1.36603	+	0.366025i	1.36603	+	0.366025i
$568$	1.00000	−	1.73205i	1.00000	−	1.73205i
$569$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$569$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$570$		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	$-0.166667\pi$
$572$	1.36603	+	0.366025i	1.36603	+	0.366025i
$573$	0.866025	+	0.500000i	0.866025	+	0.500000i
$574$	0.366025	+	1.36603i	0.366025	+	1.36603i
$575$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$576$		0			0
$577$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$577$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$578$	−1.00000			−1.00000
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.366025	−	1.36603i	0.366025	−	1.36603i
$584$		0			0
$585$		0			0
$586$			1.00000i			1.00000i
$587$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$587$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$588$	0.500000	−	0.866025i	0.500000	−	0.866025i
$589$		0			0
$590$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$591$	1.00000			1.00000
$592$			1.00000i			1.00000i
$593$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$593$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$594$	0.366025	−	1.36603i	0.366025	−	1.36603i
$595$		0			0
$596$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$597$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$598$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$599$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$599$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$600$	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
$605$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$606$	1.00000	+	1.00000i	1.00000	+	1.00000i
$607$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$607$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$608$		0			0
$609$		0			0
$610$	0.366025	+	1.36603i	0.366025	+	1.36603i
$611$		0			0
$612$		0			0
$613$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$613$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$614$	−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		0.258819	−	0.965926i	$-0.416667\pi$
$617$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$618$	−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	$0.250000\pi$
$620$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$621$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$622$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$623$		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
$628$	1.00000			1.00000
$629$		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
$637$	−1.00000			−1.00000
$638$		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	$0.666667\pi$
$642$	0.866025	+	0.500000i	0.866025	+	0.500000i
$643$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$643$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$644$	1.00000	+	1.73205i	1.00000	+	1.73205i
$645$	0.500000	+	0.866025i	0.500000	+	0.866025i
$646$		0			0
$647$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$647$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$648$	0.866025	+	0.500000i	0.866025	+	0.500000i
$649$	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
$652$			1.00000i			1.00000i
$653$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$653$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$654$		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
$668$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$669$		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		0.965926	−	0.258819i	$-0.0833333\pi$
$673$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$674$		0			0
$675$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.866025	−	0.500000i	0.866025	−	0.500000i
$682$	1.36603	+	0.366025i	1.36603	+	0.366025i
$683$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$683$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.500000	+	0.866025i	0.500000	+	0.866025i
$689$		−	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	$0.583333\pi$
$692$		−	2.00000i		−	2.00000i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$699$		0			0
$700$	0.366025	+	1.36603i	0.366025	+	1.36603i
$701$	−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	$0.833333\pi$
$702$		−	1.00000i		−	1.00000i
$703$		0			0
$704$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$705$		0			0
$706$		0			0
$707$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$708$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$709$		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
$717$	−2.00000			−2.00000
$718$	0.866025	−	0.500000i	0.866025	−	0.500000i
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$720$		0			0
$721$	1.00000	−	1.73205i	1.00000	−	1.73205i
$722$	0.500000	−	0.866025i	0.500000	−	0.866025i
$723$		0			0
$724$		0			0
$725$		0			0
$726$			1.00000i			1.00000i
$727$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$727$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$728$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$729$	−1.00000			−1.00000
$730$		0			0
$731$		0			0
$732$	1.00000	+	1.00000i	1.00000	+	1.00000i
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$	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
$742$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$743$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$743$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$744$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$745$	1.36603	−	0.366025i	1.36603	−	0.366025i
$746$			1.00000i			1.00000i
$747$		0			0
$748$		0			0
$749$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$750$			1.00000i			1.00000i
$751$	−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
$753$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$754$		0			0
$755$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$756$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$757$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$757$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$758$	1.36603	−	0.366025i	1.36603	−	0.366025i
$759$	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
$768$	0.866025	−	0.500000i	0.866025	−	0.500000i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$	1.00000	−	1.73205i	1.00000	−	1.73205i
$771$	1.00000	−	1.00000i	1.00000	−	1.00000i
$772$		0			0
$773$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$773$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$774$		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
$780$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$781$	−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
$787$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$787$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$788$			1.00000i			1.00000i
$789$	1.36603	+	0.366025i	1.36603	+	0.366025i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.366025	−	1.36603i	0.366025	−	1.36603i
$794$	0.866025	−	0.500000i	0.866025	−	0.500000i
$795$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$796$	0.500000	−	0.866025i	0.500000	−	0.866025i
$797$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$797$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$			1.00000i			1.00000i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$806$	1.00000			1.00000
$807$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$808$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$810$	−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
$813$			1.00000i			1.00000i
$814$	1.00000	+	1.00000i	1.00000	+	1.00000i
$815$	−1.00000			−1.00000
$816$		0			0
$817$		0			0
$818$	0.866025	+	0.500000i	0.866025	+	0.500000i
$819$		0			0
$820$	−1.00000			−1.00000
$821$	−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
$823$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$823$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−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		0.500000	−	0.866025i	$-0.333333\pi$
$827$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$828$		0			0
$829$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$829$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$830$		0			0
$831$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$832$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$833$		0			0
$834$		0			0
$835$	0.366025	−	1.36603i	0.366025	−	1.36603i
$836$		0			0
$837$		−	1.00000i		−	1.00000i
$838$	0.366025	+	1.36603i	0.366025	+	1.36603i
$839$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$839$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$840$	1.00000	+	1.00000i	1.00000	+	1.00000i
$841$		−	1.00000i		−	1.00000i
$842$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$843$	−1.00000			−1.00000
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$848$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$849$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$850$		0			0
$851$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$852$	2.00000			2.00000
$853$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$853$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$854$	−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			$0$
$858$	0.366025	+	1.36603i	0.366025	+	1.36603i
$859$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$859$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$860$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$861$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$862$		−	1.00000i		−	1.00000i
$863$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$863$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$864$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$865$	2.00000			2.00000
$866$		0			0
$867$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$868$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$869$		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
$877$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$877$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$878$		−	1.00000i		−	1.00000i
$879$	−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
$883$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$883$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$884$		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			1.00000i	$0.5\pi$
$887$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$888$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$889$		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
$895$	0.366025	+	1.36603i	0.366025	+	1.36603i
$896$	1.00000	+	1.00000i	1.00000	+	1.00000i
$897$	0.366025	−	1.36603i	0.366025	−	1.36603i
$898$	−1.00000			−1.00000
$899$		0			0
$900$		0			0
$901$		0			0
$902$	1.00000	+	1.00000i	1.00000	+	1.00000i
$903$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$904$		0			0
$905$		0			0
$906$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$	0.500000	+	0.866025i	0.500000	+	0.866025i
$909$		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
$917$			2.00000i			2.00000i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$921$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$922$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$923$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$924$		−	2.00000i		−	2.00000i
$925$		−	1.00000i		−	1.00000i
$926$	1.00000	+	1.00000i	1.00000	+	1.00000i
$927$		0			0
$928$		0			0
$929$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$929$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$930$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$931$		0			0
$932$		0			0
$933$	−1.00000			−1.00000
$934$	0.866025	−	0.500000i	0.866025	−	0.500000i
$935$		0			0
$936$		0			0
$937$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$937$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$938$		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	$0.333333\pi$
$942$	0.500000	+	0.866025i	0.500000	+	0.866025i
$943$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$944$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$945$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$946$	1.36603	+	0.366025i	1.36603	+	0.366025i
$947$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$947$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$			1.00000i			1.00000i
$952$		0			0
$953$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$953$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$954$		0			0
$955$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$956$		−	2.00000i		−	2.00000i
$957$		0			0
$958$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$959$		0			0
$960$	0.500000	+	0.866025i	0.500000	+	0.866025i
$961$		0			0
$962$	0.866025	+	0.500000i	0.866025	+	0.500000i
$963$		0			0
$964$		0			0
$965$		0			0
$966$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$967$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$967$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$968$	−1.00000			−1.00000
$969$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$977$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$978$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$979$		0			0
$980$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$981$		0			0
$982$	1.36603	+	0.366025i	1.36603	+	0.366025i
$983$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$983$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$984$	−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	$0.333333\pi$
$992$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$993$		0			0
$994$	0.732051	+	2.73205i	0.732051	+	2.73205i
$995$	0.866025	+	0.500000i	0.866025	+	0.500000i
$996$		0			0
$997$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$997$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$998$		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.fm.a.2357.1	yes	4
5.3	odd	4		2960.1.dn.a.1173.1	yes	4
16.13	even	4		2960.1.dn.a.877.1	✓	4
37.10	even	3	inner	2960.1.fm.a.1157.1	yes	4
80.13	odd	4	inner	2960.1.fm.a.2653.1	yes	4
185.158	odd	12		2960.1.dn.a.2933.1	yes	4
592.269	even	12		2960.1.dn.a.2637.1	yes	4
2960.1453	odd	12	inner	2960.1.fm.a.1453.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2960.1.dn.a.877.1	✓	4	16.13	even	4
2960.1.dn.a.1173.1	yes	4	5.3	odd	4
2960.1.dn.a.2637.1	yes	4	592.269	even	12
2960.1.dn.a.2933.1	yes	4	185.158	odd	12
2960.1.fm.a.1157.1	yes	4	37.10	even	3	inner
2960.1.fm.a.1453.1	yes	4	2960.1453	odd	12	inner
2960.1.fm.a.2357.1	yes	4	1.1	even	1	trivial
2960.1.fm.a.2653.1	yes	4	80.13	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

Introduction

L-functions

Modular forms

Varieties

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Database

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