LMFDB - Embedded newform 3696.1.bm.c.461.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3696,1,Mod(461,3696)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3696, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("3696.461");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3696.bm (of order $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{12}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{12} + \cdots)$

Embedding invariants

Embedding label			461.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3696.461
Dual form			3696.1.bm.c.2309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.22474 - 1.22474i) q^{5} +(-0.866025 - 0.500000i) q^{6} -1.00000i q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.22474 - 1.22474i) q^{5} +(-0.866025 - 0.500000i) q^{6} -1.00000i q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.866025 + 1.50000i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.366025 + 0.366025i) q^{13} +(0.258819 + 0.965926i) q^{14} +1.73205 q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.258819 - 0.965926i) q^{18} +(1.36603 + 1.36603i) q^{19} +(0.448288 - 1.67303i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-0.500000 + 0.866025i) q^{22} -1.00000 q^{24} -2.00000i q^{25} +(-0.448288 - 0.258819i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.500000 - 0.866025i) q^{28} +(-0.707107 - 0.707107i) q^{29} +(-1.67303 + 0.448288i) q^{30} +(-0.258819 + 0.965926i) q^{32} +1.00000 q^{33} +(-1.22474 - 1.22474i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.366025 + 0.366025i) q^{37} +(-1.67303 - 0.965926i) q^{38} +0.517638i q^{39} +1.73205i q^{40} +(-0.500000 + 0.866025i) q^{42} +(0.258819 - 0.965926i) q^{44} +(1.22474 + 1.22474i) q^{45} -1.93185 q^{47} +(0.965926 - 0.258819i) q^{48} -1.00000 q^{49} +(0.517638 + 1.93185i) q^{50} +(0.500000 + 0.133975i) q^{52} +(0.500000 - 0.866025i) q^{54} -1.73205i q^{55} +(0.707107 + 0.707107i) q^{56} +1.93185i q^{57} +(0.866025 + 0.500000i) q^{58} +(-1.22474 + 1.22474i) q^{59} +(1.50000 - 0.866025i) q^{60} +(-1.00000 - 1.00000i) q^{61} +1.00000 q^{63} -1.00000i q^{64} +0.896575 q^{65} +(-0.965926 + 0.258819i) q^{66} +(1.36603 + 1.36603i) q^{67} +(1.50000 + 0.866025i) q^{70} +(-0.707107 - 0.707107i) q^{72} +1.00000i q^{73} +(0.258819 - 0.448288i) q^{74} +(1.41421 - 1.41421i) q^{75} +(1.86603 + 0.500000i) q^{76} +(-0.707107 - 0.707107i) q^{77} +(-0.133975 - 0.500000i) q^{78} +(-0.448288 - 1.67303i) q^{80} -1.00000 q^{81} +(0.258819 - 0.965926i) q^{84} -1.00000i q^{87} +1.00000i q^{88} -1.41421i q^{89} +(-1.50000 - 0.866025i) q^{90} +(0.366025 - 0.366025i) q^{91} +(1.86603 - 0.500000i) q^{94} +3.34607 q^{95} +(-0.866025 + 0.500000i) q^{96} +(0.965926 - 0.258819i) q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{13} + 4 q^{16} + 4 q^{19} - 4 q^{22} - 8 q^{24} - 4 q^{28} + 8 q^{33} + 4 q^{36} + 4 q^{37} - 4 q^{42} - 8 q^{49} + 4 q^{52} + 4 q^{54} + 12 q^{60} - 8 q^{61} + 8 q^{63} + 4 q^{67} + 12 q^{70} + 8 q^{76} - 8 q^{78} - 8 q^{81} - 12 q^{90} - 4 q^{91} + 8 q^{94}+O(q^{100}) $ 8 * q - 4 * q^13 + 4 * q^16 + 4 * q^19 - 4 * q^22 - 8 * q^24 - 4 * q^28 + 8 * q^33 + 4 * q^36 + 4 * q^37 - 4 * q^42 - 8 * q^49 + 4 * q^52 + 4 * q^54 + 12 * q^60 - 8 * q^61 + 8 * q^63 + 4 * q^67 + 12 * q^70 + 8 * q^76 - 8 * q^78 - 8 * q^81 - 12 * q^90 - 4 * q^91 + 8 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3696\mathbb{Z}\right)^\times$.

$n$	$463$	$673$	$1585$	$2465$	$2773$
$\chi(n)$	$1$	$-1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$2$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$3$	0.707107	+	0.707107i	0.707107	+	0.707107i
$3$	0.707107	+	0.707107i	0.707107	+	0.707107i
$4$	0.866025	−	0.500000i	0.866025	−	0.500000i
$5$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$5$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$6$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$7$		−	1.00000i		−	1.00000i
$7$		−	1.00000i		−	1.00000i
$8$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$9$			1.00000i			1.00000i
$10$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$11$	0.707107	−	0.707107i	0.707107	−	0.707107i
$11$	0.707107	−	0.707107i	0.707107	−	0.707107i
$12$	0.965926	+	0.258819i	0.965926	+	0.258819i
$13$	0.366025	+	0.366025i	0.366025	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$13$	0.366025	+	0.366025i	0.366025	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$14$	0.258819	+	0.965926i	0.258819	+	0.965926i
$15$	1.73205			1.73205
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$19$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$19$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$20$	0.448288	−	1.67303i	0.448288	−	1.67303i
$21$	0.707107	−	0.707107i	0.707107	−	0.707107i
$22$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−1.00000			−1.00000
$25$		−	2.00000i		−	2.00000i
$26$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$27$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$28$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$29$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$29$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$30$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$33$	1.00000			1.00000
$34$		0			0
$35$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$36$	0.500000	+	0.866025i	0.500000	+	0.866025i
$37$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$37$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$38$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$39$			0.517638i			0.517638i
$40$			1.73205i			1.73205i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	0.258819	−	0.965926i	0.258819	−	0.965926i
$45$	1.22474	+	1.22474i	1.22474	+	1.22474i
$46$		0			0
$47$	−1.93185			−1.93185			−0.965926	−	0.258819i	$-0.916667\pi$
$47$	−1.93185			−1.93185			−0.965926	+	0.258819i	$0.916667\pi$
$48$	0.965926	−	0.258819i	0.965926	−	0.258819i
$49$	−1.00000			−1.00000
$50$	0.517638	+	1.93185i	0.517638	+	1.93185i
$51$		0			0
$52$	0.500000	+	0.133975i	0.500000	+	0.133975i
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$	0.500000	−	0.866025i	0.500000	−	0.866025i
$55$		−	1.73205i		−	1.73205i
$56$	0.707107	+	0.707107i	0.707107	+	0.707107i
$57$			1.93185i			1.93185i
$58$	0.866025	+	0.500000i	0.866025	+	0.500000i
$59$	−1.22474	+	1.22474i	−1.22474	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$59$	−1.22474	+	1.22474i	−1.22474	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$60$	1.50000	−	0.866025i	1.50000	−	0.866025i
$61$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$61$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$62$		0			0
$63$	1.00000			1.00000
$64$		−	1.00000i		−	1.00000i
$65$	0.896575			0.896575
$66$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$67$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$67$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$		0			0
$70$	1.50000	+	0.866025i	1.50000	+	0.866025i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$73$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$73$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$74$	0.258819	−	0.448288i	0.258819	−	0.448288i
$75$	1.41421	−	1.41421i	1.41421	−	1.41421i
$76$	1.86603	+	0.500000i	1.86603	+	0.500000i
$77$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$78$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$81$	−1.00000			−1.00000
$82$		0			0
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$	0.258819	−	0.965926i	0.258819	−	0.965926i
$85$		0			0
$86$		0			0
$87$		−	1.00000i		−	1.00000i
$88$			1.00000i			1.00000i
$89$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$89$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$90$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$91$	0.366025	−	0.366025i	0.366025	−	0.366025i
$92$		0			0
$93$		0			0
$94$	1.86603	−	0.500000i	1.86603	−	0.500000i
$95$	3.34607			3.34607
$96$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	0.965926	−	0.258819i	0.965926	−	0.258819i
$99$	0.707107	+	0.707107i	0.707107	+	0.707107i
$100$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$101$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$101$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−0.517638			−0.517638
$105$		−	1.73205i		−	1.73205i
$106$		0			0
$107$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$107$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$108$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$	0.448288	+	1.67303i	0.448288	+	1.67303i
$111$	−0.517638			−0.517638
$112$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$115$		0			0
$116$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$117$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$118$	0.866025	−	1.50000i	0.866025	−	1.50000i
$119$		0			0
$120$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$121$		−	1.00000i		−	1.00000i
$122$	1.22474	+	0.707107i	1.22474	+	0.707107i
$123$		0			0
$124$		0			0
$125$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$126$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.258819	+	0.965926i	0.258819	+	0.965926i
$129$		0			0
$130$	−0.866025	+	0.232051i	−0.866025	+	0.232051i
$131$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$131$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$132$	0.866025	−	0.500000i	0.866025	−	0.500000i
$133$	1.36603	−	1.36603i	1.36603	−	1.36603i
$134$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$135$			1.73205i			1.73205i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$139$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$140$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$141$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$142$		0			0
$143$	0.517638			0.517638
$144$	0.866025	+	0.500000i	0.866025	+	0.500000i
$145$	−1.73205			−1.73205
$146$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$147$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$148$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$149$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$149$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$150$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−1.93185			−1.93185
$153$		0			0
$154$	0.866025	+	0.500000i	0.866025	+	0.500000i
$155$		0			0
$156$	0.258819	+	0.448288i	0.258819	+	0.448288i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$	0.866025	+	1.50000i	0.866025	+	1.50000i
$161$		0			0
$162$	0.965926	−	0.258819i	0.965926	−	0.258819i
$163$	0.366025	+	0.366025i	0.366025	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$163$	0.366025	+	0.366025i	0.366025	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$	1.22474	−	1.22474i	1.22474	−	1.22474i
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$			1.00000i			1.00000i
$169$		−	0.732051i		−	0.732051i
$170$		0			0
$171$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$172$		0			0
$173$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$173$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$174$	0.258819	+	0.965926i	0.258819	+	0.965926i
$175$	−2.00000			−2.00000
$176$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$177$	−1.73205			−1.73205
$178$	0.366025	+	1.36603i	0.366025	+	1.36603i
$179$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$179$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$180$	1.67303	+	0.448288i	1.67303	+	0.448288i
$181$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$181$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$182$	−0.258819	+	0.448288i	−0.258819	+	0.448288i
$183$		−	1.41421i		−	1.41421i
$184$		0			0
$185$			0.896575i			0.896575i
$186$		0			0
$187$		0			0
$188$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$189$	0.707107	+	0.707107i	0.707107	+	0.707107i
$190$	−3.23205	+	0.866025i	−3.23205	+	0.866025i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	0.707107	−	0.707107i	0.707107	−	0.707107i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$	0.633975	+	0.633975i	0.633975	+	0.633975i
$196$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	1.41421	+	1.41421i	1.41421	+	1.41421i
$201$			1.93185i			1.93185i
$202$		0			0
$203$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.500000	−	0.133975i	0.500000	−	0.133975i
$209$	1.93185			1.93185
$210$	0.448288	+	1.67303i	0.448288	+	1.67303i
$211$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$211$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$212$		0			0
$213$		0			0
$214$	0.500000	−	0.866025i	0.500000	−	0.866025i
$215$		0			0
$216$		−	1.00000i		−	1.00000i
$217$		0			0
$218$		0			0
$219$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$220$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$221$		0			0
$222$	0.500000	−	0.133975i	0.500000	−	0.133975i
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	0.965926	+	0.258819i	0.965926	+	0.258819i
$225$	2.00000			2.00000
$226$		0			0
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$	0.965926	+	1.67303i	0.965926	+	1.67303i
$229$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$229$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$230$		0			0
$231$		−	1.00000i		−	1.00000i
$232$	1.00000			1.00000
$233$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$233$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$234$	0.258819	−	0.448288i	0.258819	−	0.448288i
$235$	−2.36603	+	2.36603i	−2.36603	+	2.36603i
$236$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$237$		0			0
$238$		0			0
$239$	1.93185			1.93185			0.965926	−	0.258819i	$-0.0833333\pi$
$239$	1.93185			1.93185			0.965926	+	0.258819i	$0.0833333\pi$
$240$	0.866025	−	1.50000i	0.866025	−	1.50000i
$241$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$241$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$242$	0.258819	+	0.965926i	0.258819	+	0.965926i
$243$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$244$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$245$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$246$		0			0
$247$			1.00000i			1.00000i
$248$		0			0
$249$		0			0
$250$	1.50000	+	0.866025i	1.50000	+	0.866025i
$251$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$251$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$252$	0.866025	−	0.500000i	0.866025	−	0.500000i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	−0.517638			−0.517638			−0.258819	−	0.965926i	$-0.583333\pi$
$257$	−0.517638			−0.517638			−0.258819	+	0.965926i	$0.583333\pi$
$258$		0			0
$259$	0.366025	+	0.366025i	0.366025	+	0.366025i
$260$	0.776457	−	0.448288i	0.776457	−	0.448288i
$261$	0.707107	−	0.707107i	0.707107	−	0.707107i
$262$		0			0
$263$			1.93185i			1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$263$			1.93185i			1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$264$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$265$		0			0
$266$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$267$	1.00000	−	1.00000i	1.00000	−	1.00000i
$268$	1.86603	+	0.500000i	1.86603	+	0.500000i
$269$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$269$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$270$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$271$	−1.73205			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$271$	−1.73205			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$	0.517638			0.517638
$274$		0			0
$275$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$276$		0			0
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	0.707107	−	1.22474i	0.707107	−	1.22474i
$279$		0			0
$280$	1.73205			1.73205
$281$		−	0.517638i		−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$281$		−	0.517638i		−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$282$	1.67303	+	0.965926i	1.67303	+	0.965926i
$283$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$283$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$284$		0			0
$285$	2.36603	+	2.36603i	2.36603	+	2.36603i
$286$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$287$		0			0
$288$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$289$	1.00000			1.00000
$290$	1.67303	−	0.448288i	1.67303	−	0.448288i
$291$		0			0
$292$	0.500000	+	0.866025i	0.500000	+	0.866025i
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	0.866025	+	0.500000i	0.866025	+	0.500000i
$295$			3.00000i			3.00000i
$296$		−	0.517638i		−	0.517638i
$297$			1.00000i			1.00000i
$298$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$299$		0			0
$300$	0.517638	−	1.93185i	0.517638	−	1.93185i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.86603	−	0.500000i	1.86603	−	0.500000i
$305$	−2.44949			−2.44949
$306$		0			0
$307$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$307$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$308$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$309$		0			0
$310$		0			0
$311$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$311$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$312$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$	1.22474	−	1.22474i	1.22474	−	1.22474i
$316$		0			0
$317$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$317$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$318$		0			0
$319$	−1.00000			−1.00000
$320$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$321$	−1.00000			−1.00000
$322$		0			0
$323$		0			0
$324$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$325$	0.732051	−	0.732051i	0.732051	−	0.732051i
$326$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$327$		0			0
$328$		0			0
$329$			1.93185i			1.93185i
$330$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$331$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$331$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$332$		0			0
$333$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$334$		0			0
$335$	3.34607			3.34607
$336$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	0.189469	+	0.707107i	0.189469	+	0.707107i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	0.965926	−	1.67303i	0.965926	−	1.67303i
$343$			1.00000i			1.00000i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$349$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$349$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$350$	1.93185	−	0.517638i	1.93185	−	0.517638i
$351$	−0.517638			−0.517638
$352$	0.500000	+	0.866025i	0.500000	+	0.866025i
$353$	−1.93185			−1.93185			−0.965926	−	0.258819i	$-0.916667\pi$
$353$	−1.93185			−1.93185			−0.965926	+	0.258819i	$0.916667\pi$
$354$	1.67303	−	0.448288i	1.67303	−	0.448288i
$355$		0			0
$356$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$357$		0			0
$358$		0			0
$359$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$359$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$360$	−1.73205			−1.73205
$361$			2.73205i			2.73205i
$362$		0			0
$363$	0.707107	−	0.707107i	0.707107	−	0.707107i
$364$	0.133975	−	0.500000i	0.133975	−	0.500000i
$365$	1.22474	+	1.22474i	1.22474	+	1.22474i
$366$	0.366025	+	1.36603i	0.366025	+	1.36603i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$		0			0
$370$	−0.232051	−	0.866025i	−0.232051	−	0.866025i
$371$		0			0
$372$		0			0
$373$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$373$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$374$		0			0
$375$		−	1.73205i		−	1.73205i
$376$	1.36603	−	1.36603i	1.36603	−	1.36603i
$377$		−	0.517638i		−	0.517638i
$378$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$379$	1.36603	−	1.36603i	1.36603	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$379$	1.36603	−	1.36603i	1.36603	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$380$	2.89778	−	1.67303i	2.89778	−	1.67303i
$381$		0			0
$382$		0			0
$383$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$383$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$384$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$385$	−1.73205			−1.73205
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$389$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$390$	−0.776457	−	0.448288i	−0.776457	−	0.448288i
$391$		0			0
$392$	0.707107	−	0.707107i	0.707107	−	0.707107i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	0.965926	+	0.258819i	0.965926	+	0.258819i
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$		0			0
$399$	1.93185			1.93185
$400$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$403$		0			0
$404$		0			0
$405$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$406$	0.500000	−	0.866025i	0.500000	−	0.866025i
$407$			0.517638i			0.517638i
$408$		0			0
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.22474	+	1.22474i	1.22474	+	1.22474i
$414$		0			0
$415$		0			0
$416$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$417$	−1.41421			−1.41421
$418$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$419$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$419$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$420$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$421$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$421$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$422$		0			0
$423$		−	1.93185i		−	1.93185i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$428$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$429$	0.366025	+	0.366025i	0.366025	+	0.366025i
$430$		0			0
$431$	−0.517638			−0.517638			−0.258819	−	0.965926i	$-0.583333\pi$
$431$	−0.517638			−0.517638			−0.258819	+	0.965926i	$0.583333\pi$
$432$	0.258819	+	0.965926i	0.258819	+	0.965926i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$436$		0			0
$437$		0			0
$438$	0.500000	−	0.866025i	0.500000	−	0.866025i
$439$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$439$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$440$	1.22474	+	1.22474i	1.22474	+	1.22474i
$441$		−	1.00000i		−	1.00000i
$442$		0			0
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$445$	−1.73205	−	1.73205i	−1.73205	−	1.73205i
$446$		0			0
$447$	1.73205			1.73205
$448$	−1.00000			−1.00000
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	0.896575i		−	0.896575i
$456$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$461$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$462$	0.258819	+	0.965926i	0.258819	+	0.965926i
$463$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$463$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$464$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$465$		0			0
$466$	0.366025	+	1.36603i	0.366025	+	1.36603i
$467$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$467$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$468$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$469$	1.36603	−	1.36603i	1.36603	−	1.36603i
$470$	1.67303	−	2.89778i	1.67303	−	2.89778i
$471$		0			0
$472$		−	1.73205i		−	1.73205i
$473$		0			0
$474$		0			0
$475$	2.73205	−	2.73205i	2.73205	−	2.73205i
$476$		0			0
$477$		0			0
$478$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$481$	−0.267949			−0.267949
$482$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$		0			0
$486$	0.866025	+	0.500000i	0.866025	+	0.500000i
$487$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$487$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$488$	1.41421			1.41421
$489$			0.517638i			0.517638i
$490$	0.866025	−	1.50000i	0.866025	−	1.50000i
$491$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$491$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$492$		0			0
$493$		0			0
$494$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$495$	1.73205			1.73205
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$499$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$500$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$501$		0			0
$502$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$505$		0			0
$506$		0			0
$507$	0.517638	−	0.517638i	0.517638	−	0.517638i
$508$		0			0
$509$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$509$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$510$		0			0
$511$	1.00000			1.00000
$512$	0.707107	+	0.707107i	0.707107	+	0.707107i
$513$	−1.93185			−1.93185
$514$	0.500000	−	0.133975i	0.500000	−	0.133975i
$515$		0			0
$516$		0			0
$517$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$518$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$519$		0			0
$520$	−0.633975	+	0.633975i	−0.633975	+	0.633975i
$521$			0.517638i			0.517638i	0.965926	+	0.258819i	$0.0833333\pi$
$521$			0.517638i			0.517638i	−0.965926	+	0.258819i	$0.916667\pi$
$522$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$523$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$523$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$524$		0			0
$525$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$526$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$527$		0			0
$528$	0.500000	−	0.866025i	0.500000	−	0.866025i
$529$	−1.00000			−1.00000
$530$		0			0
$531$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$532$	0.500000	−	1.86603i	0.500000	−	1.86603i
$533$		0			0
$534$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$535$			1.73205i			1.73205i
$536$	−1.93185			−1.93185
$537$		0			0
$538$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$539$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$540$	0.866025	+	1.50000i	0.866025	+	1.50000i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$	1.67303	−	0.448288i	1.67303	−	0.448288i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$		0			0
$549$	1.00000	−	1.00000i	1.00000	−	1.00000i
$550$	1.73205	+	1.00000i	1.73205	+	1.00000i
$551$		−	1.93185i		−	1.93185i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.633975	+	0.633975i	−0.633975	+	0.633975i
$556$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$557$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$557$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$558$		0			0
$559$		0			0
$560$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$561$		0			0
$562$	0.133975	+	0.500000i	0.133975	+	0.500000i
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$	−1.86603	−	0.500000i	−1.86603	−	0.500000i
$565$		0			0
$566$	0.258819	−	0.448288i	0.258819	−	0.448288i
$567$			1.00000i			1.00000i
$568$		0			0
$569$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$569$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$570$	−2.89778	−	1.67303i	−2.89778	−	1.67303i
$571$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$571$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$572$	0.448288	−	0.258819i	0.448288	−	0.258819i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.00000			1.00000
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$579$		0			0
$580$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$585$			0.896575i			0.896575i
$586$		0			0
$587$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$587$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$588$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$589$		0			0
$590$	−0.776457	−	2.89778i	−0.776457	−	2.89778i
$591$		0			0
$592$	0.133975	+	0.500000i	0.133975	+	0.500000i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$595$		0			0
$596$	0.448288	−	1.67303i	0.448288	−	1.67303i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$			2.00000i			2.00000i
$601$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$601$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$604$		0			0
$605$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$606$		0			0
$607$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$608$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$609$	−1.00000			−1.00000
$610$	2.36603	−	0.633975i	2.36603	−	0.633975i
$611$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$612$		0			0
$613$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$613$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$614$	1.22474	+	0.707107i	1.22474	+	0.707107i
$615$		0			0
$616$	1.00000			1.00000
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$619$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$620$		0			0
$621$		0			0
$622$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$623$	−1.41421			−1.41421
$624$	0.448288	+	0.258819i	0.448288	+	0.258819i
$625$	−1.00000			−1.00000
$626$		0			0
$627$	1.36603	+	1.36603i	1.36603	+	1.36603i
$628$		0			0
$629$		0			0
$630$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$638$	0.965926	−	0.258819i	0.965926	−	0.258819i
$639$		0			0
$640$	1.50000	+	0.866025i	1.50000	+	0.866025i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	0.965926	−	0.258819i	0.965926	−	0.258819i
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1.93185i			1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$647$			1.93185i			1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$648$	0.707107	−	0.707107i	0.707107	−	0.707107i
$649$			1.73205i			1.73205i
$650$	−0.517638	+	0.896575i	−0.517638	+	0.896575i
$651$		0			0
$652$	0.500000	+	0.133975i	0.500000	+	0.133975i
$653$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$653$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.00000			−1.00000
$658$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$659$	−1.22474	−	1.22474i	−1.22474	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$659$	−1.22474	−	1.22474i	−1.22474	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$660$	0.448288	−	1.67303i	0.448288	−	1.67303i
$661$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$661$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$662$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$663$		0			0
$664$		0			0
$665$		−	3.34607i		−	3.34607i
$666$	0.448288	+	0.258819i	0.448288	+	0.258819i
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−3.23205	+	0.866025i	−3.23205	+	0.866025i
$671$	−1.41421			−1.41421
$672$	0.500000	+	0.866025i	0.500000	+	0.866025i
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$	1.41421	+	1.41421i	1.41421	+	1.41421i
$676$	−0.366025	−	0.633975i	−0.366025	−	0.633975i
$677$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$677$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$683$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$684$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$685$		0			0
$686$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$691$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$692$		0			0
$693$	0.707107	−	0.707107i	0.707107	−	0.707107i
$694$		0			0
$695$			2.44949i			2.44949i
$696$	0.707107	+	0.707107i	0.707107	+	0.707107i
$697$		0			0
$698$	1.67303	+	0.965926i	1.67303	+	0.965926i
$699$	1.00000	−	1.00000i	1.00000	−	1.00000i
$700$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$701$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$701$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$702$	0.500000	−	0.133975i	0.500000	−	0.133975i
$703$	−1.00000			−1.00000
$704$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$705$	−3.34607			−3.34607
$706$	1.86603	−	0.500000i	1.86603	−	0.500000i
$707$		0			0
$708$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$709$	0.366025	−	0.366025i	0.366025	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$709$	0.366025	−	0.366025i	0.366025	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$710$		0			0
$711$		0			0
$712$	1.00000	+	1.00000i	1.00000	+	1.00000i
$713$		0			0
$714$		0			0
$715$	0.633975	−	0.633975i	0.633975	−	0.633975i
$716$		0			0
$717$	1.36603	+	1.36603i	1.36603	+	1.36603i
$718$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$719$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$719$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$720$	1.67303	−	0.448288i	1.67303	−	0.448288i
$721$		0			0
$722$	−0.707107	−	2.63896i	−0.707107	−	2.63896i
$723$	0.707107	+	0.707107i	0.707107	+	0.707107i
$724$		0			0
$725$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$726$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$			0.517638i			0.517638i
$729$		−	1.00000i		−	1.00000i
$730$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$731$		0			0
$732$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$733$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$733$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$734$		0			0
$735$	−1.73205			−1.73205
$736$		0			0
$737$	1.93185			1.93185
$738$		0			0
$739$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$739$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$740$	0.448288	+	0.776457i	0.448288	+	0.776457i
$741$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$742$		0			0
$743$		−	1.93185i		−	1.93185i	−0.258819	−	0.965926i	$-0.583333\pi$
$743$		−	1.93185i		−	1.93185i	0.258819	−	0.965926i	$-0.416667\pi$
$744$		0			0
$745$		−	3.00000i		−	3.00000i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.707107	+	0.707107i	0.707107	+	0.707107i
$750$	0.448288	+	1.67303i	0.448288	+	1.67303i
$751$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$751$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$752$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$753$	1.73205			1.73205
$754$	0.133975	+	0.500000i	0.133975	+	0.500000i
$755$		0			0
$756$	0.965926	+	0.258819i	0.965926	+	0.258819i
$757$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$757$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$758$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$759$		0			0
$760$	−2.36603	+	2.36603i	−2.36603	+	2.36603i
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.36603	−	0.366025i	1.36603	−	0.366025i
$767$	−0.896575			−0.896575
$768$	0.258819	−	0.965926i	0.258819	−	0.965926i
$769$	−1.73205			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$769$	−1.73205			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$770$	1.67303	−	0.448288i	1.67303	−	0.448288i
$771$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$772$		0			0
$773$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$773$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			0.517638i			0.517638i
$778$		0			0
$779$		0			0
$780$	0.866025	+	0.232051i	0.866025	+	0.232051i
$781$		0			0
$782$		0			0
$783$	1.00000			1.00000
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$		0			0
$786$		0			0
$787$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$787$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$788$		0			0
$789$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$790$		0			0
$791$		0			0
$792$	−1.00000			−1.00000
$793$		−	0.732051i		−	0.732051i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$797$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$798$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$799$		0			0
$800$	1.93185	+	0.517638i	1.93185	+	0.517638i
$801$	1.41421			1.41421
$802$		0			0
$803$	0.707107	+	0.707107i	0.707107	+	0.707107i
$804$	0.965926	+	1.67303i	0.965926	+	1.67303i
$805$		0			0
$806$		0			0
$807$			2.00000i			2.00000i
$808$		0			0
$809$			1.93185i			1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$809$			1.93185i			1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$810$	0.866025	−	1.50000i	0.866025	−	1.50000i
$811$	1.36603	−	1.36603i	1.36603	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$811$	1.36603	−	1.36603i	1.36603	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$812$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$813$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$814$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$815$	0.896575			0.896575
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.366025	+	0.366025i	0.366025	+	0.366025i
$820$		0			0
$821$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$821$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$822$		0			0
$823$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$824$		0			0
$825$		−	2.00000i		−	2.00000i
$826$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$827$	−1.22474	+	1.22474i	−1.22474	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$827$	−1.22474	+	1.22474i	−1.22474	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$828$		0			0
$829$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$829$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$830$		0			0
$831$		0			0
$832$	0.366025	−	0.366025i	0.366025	−	0.366025i
$833$		0			0
$834$	1.36603	−	0.366025i	1.36603	−	0.366025i
$835$		0			0
$836$	1.67303	−	0.965926i	1.67303	−	0.965926i
$837$		0			0
$838$	0.866025	+	0.500000i	0.866025	+	0.500000i
$839$			1.93185i			1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$839$			1.93185i			1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$840$	1.22474	+	1.22474i	1.22474	+	1.22474i
$841$		0			0
$842$	0.965926	−	1.67303i	0.965926	−	1.67303i
$843$	0.366025	−	0.366025i	0.366025	−	0.366025i
$844$		0			0
$845$	−0.896575	−	0.896575i	−0.896575	−	0.896575i
$846$	0.500000	+	1.86603i	0.500000	+	1.86603i
$847$	−1.00000			−1.00000
$848$		0			0
$849$	−0.517638			−0.517638
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$853$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$854$	0.707107	−	1.22474i	0.707107	−	1.22474i
$855$			3.34607i			3.34607i
$856$		−	1.00000i		−	1.00000i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$859$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$859$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$860$		0			0
$861$		0			0
$862$	0.500000	−	0.133975i	0.500000	−	0.133975i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$865$		0			0
$866$		0			0
$867$	0.707107	+	0.707107i	0.707107	+	0.707107i
$868$		0			0
$869$		0			0
$870$	1.50000	+	0.866025i	1.50000	+	0.866025i
$871$			1.00000i			1.00000i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$876$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$877$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$877$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$878$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$879$		0			0
$880$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$881$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$881$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$882$	0.258819	+	0.965926i	0.258819	+	0.965926i
$883$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$883$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$884$		0			0
$885$	−2.12132	+	2.12132i	−2.12132	+	2.12132i
$886$		0			0
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	0.366025	−	0.366025i	0.366025	−	0.366025i
$889$		0			0
$890$	2.12132	+	1.22474i	2.12132	+	1.22474i
$891$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$892$		0			0
$893$	−2.63896	−	2.63896i	−2.63896	−	2.63896i
$894$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$895$		0			0
$896$	0.965926	−	0.258819i	0.965926	−	0.258819i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.73205	−	1.00000i	1.73205	−	1.00000i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$907$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$	0.232051	+	0.866025i	0.232051	+	0.866025i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	1.67303	+	0.965926i	1.67303	+	0.965926i
$913$		0			0
$914$		0			0
$915$	−1.73205	−	1.73205i	−1.73205	−	1.73205i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$		−	1.41421i		−	1.41421i
$922$		0			0
$923$		0			0
$924$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$925$	0.732051	+	0.732051i	0.732051	+	0.732051i
$926$	0.965926	−	0.258819i	0.965926	−	0.258819i
$927$		0			0
$928$	0.866025	−	0.500000i	0.866025	−	0.500000i
$929$	−0.517638			−0.517638			−0.258819	−	0.965926i	$-0.583333\pi$
$929$	−0.517638			−0.517638			−0.258819	+	0.965926i	$0.583333\pi$
$930$		0			0
$931$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$932$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$933$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$934$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$935$		0			0
$936$		−	0.517638i		−	0.517638i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$939$		0			0
$940$	−0.866025	+	3.23205i	−0.866025	+	3.23205i
$941$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$941$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$942$		0			0
$943$		0			0
$944$	0.448288	+	1.67303i	0.448288	+	1.67303i
$945$	1.73205			1.73205
$946$		0			0
$947$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$947$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$948$		0			0
$949$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$950$	−1.93185	+	3.34607i	−1.93185	+	3.34607i
$951$		0			0
$952$		0			0
$953$			0.517638i			0.517638i	0.965926	+	0.258819i	$0.0833333\pi$
$953$			0.517638i			0.517638i	−0.965926	+	0.258819i	$0.916667\pi$
$954$		0			0
$955$		0			0
$956$	1.67303	−	0.965926i	1.67303	−	0.965926i
$957$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$958$		0			0
$959$		0			0
$960$		−	1.73205i		−	1.73205i
$961$	1.00000			1.00000
$962$	0.258819	−	0.0693504i	0.258819	−	0.0693504i
$963$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$964$	0.866025	−	0.500000i	0.866025	−	0.500000i
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	0.707107	+	0.707107i	0.707107	+	0.707107i
$969$		0			0
$970$		0			0
$971$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$971$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$972$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$973$	1.00000	+	1.00000i	1.00000	+	1.00000i
$974$	0.517638	+	1.93185i	0.517638	+	1.93185i
$975$	1.03528			1.03528
$976$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$977$		0			0		1.00000			$0$
$977$		0			0		−1.00000			$\pi$
$978$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$979$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$980$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$981$		0			0
$982$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$983$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$983$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$988$	0.500000	+	0.866025i	0.500000	+	0.866025i
$989$		0			0
$990$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$991$	1.73205			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$991$	1.73205			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$	1.41421			1.41421
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$997$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$998$	0.448288	+	0.258819i	0.448288	+	0.258819i
$999$		−	0.517638i		−	0.517638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3696.1.bm.c.461.1	✓	8
3.2	odd	2	inner	3696.1.bm.c.461.4	yes	8
7.6	odd	2		3696.1.bm.d.461.1	yes	8
11.10	odd	2		3696.1.bm.d.461.4	yes	8
16.5	even	4	inner	3696.1.bm.c.2309.1	yes	8
21.20	even	2		3696.1.bm.d.461.4	yes	8
33.32	even	2		3696.1.bm.d.461.1	yes	8
48.5	odd	4	inner	3696.1.bm.c.2309.4	yes	8
77.76	even	2	inner	3696.1.bm.c.461.4	yes	8
112.69	odd	4		3696.1.bm.d.2309.1	yes	8
176.21	odd	4		3696.1.bm.d.2309.4	yes	8
231.230	odd	2	CM	3696.1.bm.c.461.1	✓	8
336.293	even	4		3696.1.bm.d.2309.4	yes	8
528.197	even	4		3696.1.bm.d.2309.1	yes	8
1232.1077	even	4	inner	3696.1.bm.c.2309.4	yes	8
3696.2309	odd	4	inner	3696.1.bm.c.2309.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3696.1.bm.c.461.1	✓	8	1.1	even	1	trivial
3696.1.bm.c.461.1	✓	8	231.230	odd	2	CM
3696.1.bm.c.461.4	yes	8	3.2	odd	2	inner
3696.1.bm.c.461.4	yes	8	77.76	even	2	inner
3696.1.bm.c.2309.1	yes	8	16.5	even	4	inner
3696.1.bm.c.2309.1	yes	8	3696.2309	odd	4	inner
3696.1.bm.c.2309.4	yes	8	48.5	odd	4	inner
3696.1.bm.c.2309.4	yes	8	1232.1077	even	4	inner
3696.1.bm.d.461.1	yes	8	7.6	odd	2
3696.1.bm.d.461.1	yes	8	33.32	even	2
3696.1.bm.d.461.4	yes	8	11.10	odd	2
3696.1.bm.d.461.4	yes	8	21.20	even	2
3696.1.bm.d.2309.1	yes	8	112.69	odd	4
3696.1.bm.d.2309.1	yes	8	528.197	even	4
3696.1.bm.d.2309.4	yes	8	176.21	odd	4
3696.1.bm.d.2309.4	yes	8	336.293	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3696.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.22474 - 1.22474i) q^{5} +(-0.866025 - 0.500000i) q^{6} -1.00000i q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.22474 - 1.22474i) q^{5} +(-0.866025 - 0.500000i) q^{6} -1.00000i q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.866025 + 1.50000i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.366025 + 0.366025i) q^{13} +(0.258819 + 0.965926i) q^{14} +1.73205 q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.258819 - 0.965926i) q^{18} +(1.36603 + 1.36603i) q^{19} +(0.448288 - 1.67303i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-0.500000 + 0.866025i) q^{22} -1.00000 q^{24} -2.00000i q^{25} +(-0.448288 - 0.258819i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.500000 - 0.866025i) q^{28} +(-0.707107 - 0.707107i) q^{29} +(-1.67303 + 0.448288i) q^{30} +(-0.258819 + 0.965926i) q^{32} +1.00000 q^{33} +(-1.22474 - 1.22474i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.366025 + 0.366025i) q^{37} +(-1.67303 - 0.965926i) q^{38} +0.517638i q^{39} +1.73205i q^{40} +(-0.500000 + 0.866025i) q^{42} +(0.258819 - 0.965926i) q^{44} +(1.22474 + 1.22474i) q^{45} -1.93185 q^{47} +(0.965926 - 0.258819i) q^{48} -1.00000 q^{49} +(0.517638 + 1.93185i) q^{50} +(0.500000 + 0.133975i) q^{52} +(0.500000 - 0.866025i) q^{54} -1.73205i q^{55} +(0.707107 + 0.707107i) q^{56} +1.93185i q^{57} +(0.866025 + 0.500000i) q^{58} +(-1.22474 + 1.22474i) q^{59} +(1.50000 - 0.866025i) q^{60} +(-1.00000 - 1.00000i) q^{61} +1.00000 q^{63} -1.00000i q^{64} +0.896575 q^{65} +(-0.965926 + 0.258819i) q^{66} +(1.36603 + 1.36603i) q^{67} +(1.50000 + 0.866025i) q^{70} +(-0.707107 - 0.707107i) q^{72} +1.00000i q^{73} +(0.258819 - 0.448288i) q^{74} +(1.41421 - 1.41421i) q^{75} +(1.86603 + 0.500000i) q^{76} +(-0.707107 - 0.707107i) q^{77} +(-0.133975 - 0.500000i) q^{78} +(-0.448288 - 1.67303i) q^{80} -1.00000 q^{81} +(0.258819 - 0.965926i) q^{84} -1.00000i q^{87} +1.00000i q^{88} -1.41421i q^{89} +(-1.50000 - 0.866025i) q^{90} +(0.366025 - 0.366025i) q^{91} +(1.86603 - 0.500000i) q^{94} +3.34607 q^{95} +(-0.866025 + 0.500000i) q^{96} +(0.965926 - 0.258819i) q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{13} + 4 q^{16} + 4 q^{19} - 4 q^{22} - 8 q^{24} - 4 q^{28} + 8 q^{33} + 4 q^{36} + 4 q^{37} - 4 q^{42} - 8 q^{49} + 4 q^{52} + 4 q^{54} + 12 q^{60} - 8 q^{61} + 8 q^{63} + 4 q^{67} + 12 q^{70} + 8 q^{76} - 8 q^{78} - 8 q^{81} - 12 q^{90} - 4 q^{91} + 8 q^{94}+O(q^{100}) \) 8 * q - 4 * q^13 + 4 * q^16 + 4 * q^19 - 4 * q^22 - 8 * q^24 - 4 * q^28 + 8 * q^33 + 4 * q^36 + 4 * q^37 - 4 * q^42 - 8 * q^49 + 4 * q^52 + 4 * q^54 + 12 * q^60 - 8 * q^61 + 8 * q^63 + 4 * q^67 + 12 * q^70 + 8 * q^76 - 8 * q^78 - 8 * q^81 - 12 * q^90 - 4 * q^91 + 8 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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