LMFDB - Embedded newform 3100.1.z.a.2051.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3100,1,Mod(1451,3100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3100, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3100.1451");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3100 = 2^{2} \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3100.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.54710153916$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 124)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.15376.1

Embedding invariants

Embedding label			2051.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3100.2051
Dual form			3100.1.z.a.1451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.00000 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +(0.866025 - 0.500000i) q^{26} -1.00000i q^{27} +(0.866025 + 0.500000i) q^{28} +1.00000i q^{31} +1.00000i q^{32} +1.00000 q^{33} +(0.866025 + 0.500000i) q^{34} +(0.500000 - 0.866025i) q^{37} +(0.500000 - 0.866025i) q^{38} -1.00000i q^{39} +(-0.500000 - 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{42} +(0.866025 + 0.500000i) q^{43} +(-0.866025 + 0.500000i) q^{44} +(0.866025 + 0.500000i) q^{48} +(0.866025 - 0.500000i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +1.00000 q^{54} +(-0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(0.866025 + 0.500000i) q^{59} -1.00000 q^{62} -1.00000 q^{64} +1.00000i q^{66} +(-0.866025 + 0.500000i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(-0.866025 + 0.500000i) q^{71} +(0.500000 + 0.866025i) q^{73} +(0.866025 + 0.500000i) q^{74} +(0.866025 + 0.500000i) q^{76} -1.00000 q^{77} +1.00000 q^{78} +(0.866025 + 0.500000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +(0.866025 - 0.500000i) q^{83} +(0.500000 + 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +1.00000i q^{91} +(-0.500000 + 0.866025i) q^{93} +(-0.500000 + 0.866025i) q^{96} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{13} + 2 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{21} + 2 q^{22} + 2 q^{24} + 4 q^{33} + 2 q^{37} + 2 q^{38} - 2 q^{41} + 2 q^{52} - 2 q^{53} + 4 q^{54} - 2 q^{56} - 2 q^{57} - 4 q^{62} - 4 q^{64} - 2 q^{68} + 2 q^{73} - 4 q^{77} + 4 q^{78} + 2 q^{81} + 2 q^{84} - 2 q^{86} - 2 q^{88} - 2 q^{93} - 2 q^{96}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^13 + 2 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^21 + 2 * q^22 + 2 * q^24 + 4 * q^33 + 2 * q^37 + 2 * q^38 - 2 * q^41 + 2 * q^52 - 2 * q^53 + 4 * q^54 - 2 * q^56 - 2 * q^57 - 4 * q^62 - 4 * q^64 - 2 * q^68 + 2 * q^73 - 4 * q^77 + 4 * q^78 + 2 * q^81 + 2 * q^84 - 2 * q^86 - 2 * q^88 - 2 * q^93 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times$.

$n$	$1551$	$1801$	$2977$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3100.1.z.a.2051.2		4
4.3	odd	2	inner	3100.1.z.a.2051.1		4
5.2	odd	4		3100.1.t.a.2299.2		4
5.3	odd	4		3100.1.t.b.2299.2		4
5.4	even	2		124.1.i.a.67.1	✓	4
15.14	odd	2		1116.1.x.a.811.2		4
20.3	even	4		3100.1.t.a.2299.1		4
20.7	even	4		3100.1.t.b.2299.1		4
20.19	odd	2		124.1.i.a.67.2	yes	4
31.25	even	3	inner	3100.1.z.a.1451.2		4
40.19	odd	2		1984.1.s.a.191.1		4
40.29	even	2		1984.1.s.a.191.2		4
60.59	even	2		1116.1.x.a.811.1		4
124.87	odd	6	inner	3100.1.z.a.1451.1		4
155.4	even	10		3844.1.n.e.235.2		16
155.9	even	30		3844.1.l.d.1335.1		8
155.14	even	30		3844.1.n.e.3615.1		16
155.19	even	30		3844.1.n.e.3727.2		16
155.24	odd	30		3844.1.n.f.1299.2		16
155.29	odd	10		3844.1.n.f.547.2		16
155.34	odd	30		3844.1.n.f.3331.1		16
155.39	even	10		3844.1.n.e.3699.1		16
155.44	odd	30		3844.1.l.c.3511.1		8
155.49	even	30		3844.1.l.d.3511.1		8
155.54	odd	10		3844.1.n.f.3699.1		16
155.59	even	30		3844.1.n.e.3331.1		16
155.64	even	10		3844.1.n.e.547.2		16
155.69	even	30		3844.1.n.e.1299.2		16
155.74	odd	30		3844.1.n.f.3727.2		16
155.79	odd	30		3844.1.n.f.3615.1		16
155.84	odd	30		3844.1.l.c.1335.1		8
155.87	odd	12		3100.1.t.a.1699.1		4
155.89	odd	10		3844.1.n.f.235.2		16
155.99	odd	6		3844.1.i.d.2443.1		4
155.104	odd	30		3844.1.l.c.3271.2		8
155.109	even	10		3844.1.n.e.1807.1		16
155.114	odd	30		3844.1.l.c.531.2		8
155.118	odd	12		3100.1.t.b.1699.1		4
155.119	odd	6		3844.1.b.c.1923.1		2
155.129	even	6		3844.1.b.d.1923.1		2
155.134	even	30		3844.1.l.d.531.2		8
155.139	odd	10		3844.1.n.f.1807.1		16
155.144	even	30		3844.1.l.d.3271.2		8
155.149	even	6		124.1.i.a.87.1	yes	4
155.154	odd	2		3844.1.i.d.439.1		4
465.149	odd	6		1116.1.x.a.955.2		4
620.19	odd	30		3844.1.n.e.3727.1		16
620.39	odd	10		3844.1.n.e.3699.2		16
620.59	odd	30		3844.1.n.e.3331.2		16
620.79	even	30		3844.1.n.f.3615.2		16
620.87	even	12		3100.1.t.b.1699.2		4
620.99	even	6		3844.1.i.d.2443.2		4
620.119	even	6		3844.1.b.c.1923.2		2
620.139	even	10		3844.1.n.f.1807.2		16
620.159	odd	10		3844.1.n.e.235.1		16
620.179	even	30		3844.1.n.f.1299.1		16
620.199	even	30		3844.1.l.c.3511.2		8
620.219	odd	10		3844.1.n.e.547.1		16
620.239	even	30		3844.1.l.c.1335.2		8
620.259	even	30		3844.1.l.c.3271.1		8
620.299	odd	30		3844.1.l.d.3271.1		8
620.319	odd	30		3844.1.l.d.1335.2		8
620.339	even	10		3844.1.n.f.547.1		16
620.359	odd	30		3844.1.l.d.3511.2		8
620.379	odd	30		3844.1.n.e.1299.1		16
620.399	even	10		3844.1.n.f.235.1		16
620.419	odd	10		3844.1.n.e.1807.2		16
620.439	odd	6		3844.1.b.d.1923.2		2
620.459	odd	6		124.1.i.a.87.2	yes	4
620.479	odd	30		3844.1.n.e.3615.2		16
620.499	even	30		3844.1.n.f.3331.2		16
620.519	even	10		3844.1.n.f.3699.2		16
620.539	even	30		3844.1.n.f.3727.1		16
620.579	even	30		3844.1.l.c.531.1		8
620.583	even	12		3100.1.t.a.1699.2		4
620.599	odd	30		3844.1.l.d.531.1		8
620.619	even	2		3844.1.i.d.439.2		4
1240.149	even	6		1984.1.s.a.831.1		4
1240.459	odd	6		1984.1.s.a.831.2		4
1860.1079	even	6		1116.1.x.a.955.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.1.i.a.67.1	✓	4	5.4	even	2
124.1.i.a.67.2	yes	4	20.19	odd	2
124.1.i.a.87.1	yes	4	155.149	even	6
124.1.i.a.87.2	yes	4	620.459	odd	6
1116.1.x.a.811.1		4	60.59	even	2
1116.1.x.a.811.2		4	15.14	odd	2
1116.1.x.a.955.1		4	1860.1079	even	6
1116.1.x.a.955.2		4	465.149	odd	6
1984.1.s.a.191.1		4	40.19	odd	2
1984.1.s.a.191.2		4	40.29	even	2
1984.1.s.a.831.1		4	1240.149	even	6
1984.1.s.a.831.2		4	1240.459	odd	6
3100.1.t.a.1699.1		4	155.87	odd	12
3100.1.t.a.1699.2		4	620.583	even	12
3100.1.t.a.2299.1		4	20.3	even	4
3100.1.t.a.2299.2		4	5.2	odd	4
3100.1.t.b.1699.1		4	155.118	odd	12
3100.1.t.b.1699.2		4	620.87	even	12
3100.1.t.b.2299.1		4	20.7	even	4
3100.1.t.b.2299.2		4	5.3	odd	4
3100.1.z.a.1451.1		4	124.87	odd	6	inner
3100.1.z.a.1451.2		4	31.25	even	3	inner
3100.1.z.a.2051.1		4	4.3	odd	2	inner
3100.1.z.a.2051.2		4	1.1	even	1	trivial
3844.1.b.c.1923.1		2	155.119	odd	6
3844.1.b.c.1923.2		2	620.119	even	6
3844.1.b.d.1923.1		2	155.129	even	6
3844.1.b.d.1923.2		2	620.439	odd	6
3844.1.i.d.439.1		4	155.154	odd	2
3844.1.i.d.439.2		4	620.619	even	2
3844.1.i.d.2443.1		4	155.99	odd	6
3844.1.i.d.2443.2		4	620.99	even	6
3844.1.l.c.531.1		8	620.579	even	30
3844.1.l.c.531.2		8	155.114	odd	30
3844.1.l.c.1335.1		8	155.84	odd	30
3844.1.l.c.1335.2		8	620.239	even	30
3844.1.l.c.3271.1		8	620.259	even	30
3844.1.l.c.3271.2		8	155.104	odd	30
3844.1.l.c.3511.1		8	155.44	odd	30
3844.1.l.c.3511.2		8	620.199	even	30
3844.1.l.d.531.1		8	620.599	odd	30
3844.1.l.d.531.2		8	155.134	even	30
3844.1.l.d.1335.1		8	155.9	even	30
3844.1.l.d.1335.2		8	620.319	odd	30
3844.1.l.d.3271.1		8	620.299	odd	30
3844.1.l.d.3271.2		8	155.144	even	30
3844.1.l.d.3511.1		8	155.49	even	30
3844.1.l.d.3511.2		8	620.359	odd	30
3844.1.n.e.235.1		16	620.159	odd	10
3844.1.n.e.235.2		16	155.4	even	10
3844.1.n.e.547.1		16	620.219	odd	10
3844.1.n.e.547.2		16	155.64	even	10
3844.1.n.e.1299.1		16	620.379	odd	30
3844.1.n.e.1299.2		16	155.69	even	30
3844.1.n.e.1807.1		16	155.109	even	10
3844.1.n.e.1807.2		16	620.419	odd	10
3844.1.n.e.3331.1		16	155.59	even	30
3844.1.n.e.3331.2		16	620.59	odd	30
3844.1.n.e.3615.1		16	155.14	even	30
3844.1.n.e.3615.2		16	620.479	odd	30
3844.1.n.e.3699.1		16	155.39	even	10
3844.1.n.e.3699.2		16	620.39	odd	10
3844.1.n.e.3727.1		16	620.19	odd	30
3844.1.n.e.3727.2		16	155.19	even	30
3844.1.n.f.235.1		16	620.399	even	10
3844.1.n.f.235.2		16	155.89	odd	10
3844.1.n.f.547.1		16	620.339	even	10
3844.1.n.f.547.2		16	155.29	odd	10
3844.1.n.f.1299.1		16	620.179	even	30
3844.1.n.f.1299.2		16	155.24	odd	30
3844.1.n.f.1807.1		16	155.139	odd	10
3844.1.n.f.1807.2		16	620.139	even	10
3844.1.n.f.3331.1		16	155.34	odd	30
3844.1.n.f.3331.2		16	620.499	even	30
3844.1.n.f.3615.1		16	155.79	odd	30
3844.1.n.f.3615.2		16	620.79	even	30
3844.1.n.f.3699.1		16	155.54	odd	10
3844.1.n.f.3699.2		16	620.519	even	10
3844.1.n.f.3727.1		16	620.539	even	30
3844.1.n.f.3727.2		16	155.74	odd	30

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:	\( N \)	\(=\)	\( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3100.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.00000 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +(0.866025 - 0.500000i) q^{26} -1.00000i q^{27} +(0.866025 + 0.500000i) q^{28} +1.00000i q^{31} +1.00000i q^{32} +1.00000 q^{33} +(0.866025 + 0.500000i) q^{34} +(0.500000 - 0.866025i) q^{37} +(0.500000 - 0.866025i) q^{38} -1.00000i q^{39} +(-0.500000 - 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{42} +(0.866025 + 0.500000i) q^{43} +(-0.866025 + 0.500000i) q^{44} +(0.866025 + 0.500000i) q^{48} +(0.866025 - 0.500000i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +1.00000 q^{54} +(-0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(0.866025 + 0.500000i) q^{59} -1.00000 q^{62} -1.00000 q^{64} +1.00000i q^{66} +(-0.866025 + 0.500000i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(-0.866025 + 0.500000i) q^{71} +(0.500000 + 0.866025i) q^{73} +(0.866025 + 0.500000i) q^{74} +(0.866025 + 0.500000i) q^{76} -1.00000 q^{77} +1.00000 q^{78} +(0.866025 + 0.500000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +(0.866025 - 0.500000i) q^{83} +(0.500000 + 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +1.00000i q^{91} +(-0.500000 + 0.866025i) q^{93} +(-0.500000 + 0.866025i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{13} + 2 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{21} + 2 q^{22} + 2 q^{24} + 4 q^{33} + 2 q^{37} + 2 q^{38} - 2 q^{41} + 2 q^{52} - 2 q^{53} + 4 q^{54} - 2 q^{56} - 2 q^{57} - 4 q^{62} - 4 q^{64} - 2 q^{68} + 2 q^{73} - 4 q^{77} + 4 q^{78} + 2 q^{81} + 2 q^{84} - 2 q^{86} - 2 q^{88} - 2 q^{93} - 2 q^{96}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^13 + 2 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^21 + 2 * q^22 + 2 * q^24 + 4 * q^33 + 2 * q^37 + 2 * q^38 - 2 * q^41 + 2 * q^52 - 2 * q^53 + 4 * q^54 - 2 * q^56 - 2 * q^57 - 4 * q^62 - 4 * q^64 - 2 * q^68 + 2 * q^73 - 4 * q^77 + 4 * q^78 + 2 * q^81 + 2 * q^84 - 2 * q^86 - 2 * q^88 - 2 * q^93 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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