LMFDB - Embedded newform 1776.1.z.b.221.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1776,1,Mod(221,1776)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1776, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 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("1776.221");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1776 = 2^{4} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1776.z (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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.227328.2

Embedding invariants

Embedding label			221.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1776.221
Dual form			1776.1.z.b.1109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-0.707107 - 0.707107i) q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-0.707107 - 0.707107i) q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.707107 + 0.707107i) q^{13} -1.00000 q^{14} -1.41421i q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +(0.707107 - 0.707107i) q^{19} +(-1.00000 + 1.00000i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(0.707107 - 0.707107i) q^{22} +1.00000i q^{23} +(0.707107 + 0.707107i) q^{24} -1.00000i q^{25} +(0.707107 + 0.707107i) q^{26} +(-0.707107 - 0.707107i) q^{27} +1.00000i q^{28} -1.41421 q^{30} +1.41421i q^{31} -1.00000i q^{32} +1.00000 q^{33} +1.00000i q^{34} +(-1.00000 - 1.00000i) q^{35} +1.00000i q^{36} +(-0.707107 - 0.707107i) q^{37} +(-0.707107 - 0.707107i) q^{38} +1.00000i q^{39} +(1.00000 + 1.00000i) q^{40} +1.41421 q^{41} +(-0.707107 + 0.707107i) q^{42} +(-0.707107 - 0.707107i) q^{44} +(-1.00000 - 1.00000i) q^{45} +1.00000 q^{46} +1.41421i q^{47} +(0.707107 - 0.707107i) q^{48} -1.00000 q^{50} +(-0.707107 + 0.707107i) q^{51} +(0.707107 - 0.707107i) q^{52} +(0.707107 + 0.707107i) q^{53} +(-0.707107 + 0.707107i) q^{54} +1.41421 q^{55} +1.00000 q^{56} -1.00000i q^{57} +(-1.00000 + 1.00000i) q^{59} +1.41421i q^{60} +1.41421 q^{62} -1.00000 q^{63} -1.00000 q^{64} +1.41421i q^{65} -1.00000i q^{66} +1.00000 q^{68} +(0.707107 + 0.707107i) q^{69} +(-1.00000 + 1.00000i) q^{70} -1.41421 q^{71} +1.00000 q^{72} -1.00000i q^{73} +(-0.707107 + 0.707107i) q^{74} +(-0.707107 - 0.707107i) q^{75} +(-0.707107 + 0.707107i) q^{76} +(0.707107 - 0.707107i) q^{77} +1.00000 q^{78} +(1.00000 - 1.00000i) q^{80} -1.00000 q^{81} -1.41421i q^{82} +(-0.707107 + 0.707107i) q^{83} +(0.707107 + 0.707107i) q^{84} +(-1.00000 + 1.00000i) q^{85} +(-0.707107 + 0.707107i) q^{88} -1.00000i q^{89} +(-1.00000 + 1.00000i) q^{90} +(0.707107 + 0.707107i) q^{91} -1.00000i q^{92} +(1.00000 + 1.00000i) q^{93} +1.41421 q^{94} -1.41421i q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^5	$ 4 q - 4 q^{4} + 4 q^{5} - 4 q^{10} - 4 q^{14} + 4 q^{16} - 4 q^{17} - 4 q^{18} - 4 q^{20} + 4 q^{33} - 4 q^{35} + 4 q^{40} - 4 q^{45} + 4 q^{46} - 4 q^{50} + 4 q^{56} - 4 q^{59} - 4 q^{63} - 4 q^{64} + 4 q^{68} - 4 q^{70} + 4 q^{72} + 4 q^{78} + 4 q^{80} - 4 q^{81} - 4 q^{85} - 4 q^{90} + 4 q^{93}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 - 4 * q^10 - 4 * q^14 + 4 * q^16 - 4 * q^17 - 4 * q^18 - 4 * q^20 + 4 * q^33 - 4 * q^35 + 4 * q^40 - 4 * q^45 + 4 * q^46 - 4 * q^50 + 4 * q^56 - 4 * q^59 - 4 * q^63 - 4 * q^64 + 4 * q^68 - 4 * q^70 + 4 * q^72 + 4 * q^78 + 4 * q^80 - 4 * q^81 - 4 * q^85 - 4 * q^90 + 4 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1776\mathbb{Z}\right)^\times$.

$n$	$223$	$593$	$1297$	$1333$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	1.00000i
$2$		−	1.00000i		−	1.00000i
$3$	0.707107	−	0.707107i	0.707107	−	0.707107i
$3$	0.707107	−	0.707107i	0.707107	−	0.707107i
$4$	−1.00000			−1.00000
$5$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$5$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$6$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$7$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$8$			1.00000i			1.00000i
$9$		−	1.00000i		−	1.00000i
$10$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$11$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$11$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$12$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$13$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$13$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$14$	−1.00000			−1.00000
$15$		−	1.41421i		−	1.41421i
$16$	1.00000			1.00000
$17$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$18$	−1.00000			−1.00000
$19$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$19$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$20$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$21$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$22$	0.707107	−	0.707107i	0.707107	−	0.707107i
$23$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$23$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.707107	+	0.707107i	0.707107	+	0.707107i
$25$		−	1.00000i		−	1.00000i
$26$	0.707107	+	0.707107i	0.707107	+	0.707107i
$27$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$28$			1.00000i			1.00000i
$29$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$29$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$30$	−1.41421			−1.41421
$31$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$31$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$32$		−	1.00000i		−	1.00000i
$33$	1.00000			1.00000
$34$			1.00000i			1.00000i
$35$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$36$			1.00000i			1.00000i
$37$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$37$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$38$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$39$			1.00000i			1.00000i
$40$	1.00000	+	1.00000i	1.00000	+	1.00000i
$41$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$41$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$42$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$45$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$46$	1.00000			1.00000
$47$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$47$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$48$	0.707107	−	0.707107i	0.707107	−	0.707107i
$49$		0			0
$50$	−1.00000			−1.00000
$51$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$52$	0.707107	−	0.707107i	0.707107	−	0.707107i
$53$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$53$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$54$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$55$	1.41421			1.41421
$56$	1.00000			1.00000
$57$		−	1.00000i		−	1.00000i
$58$		0			0
$59$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$59$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$60$			1.41421i			1.41421i
$61$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$61$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$62$	1.41421			1.41421
$63$	−1.00000			−1.00000
$64$	−1.00000			−1.00000
$65$			1.41421i			1.41421i
$66$		−	1.00000i		−	1.00000i
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$	1.00000			1.00000
$69$	0.707107	+	0.707107i	0.707107	+	0.707107i
$70$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$71$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$71$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$72$	1.00000			1.00000
$73$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$73$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$74$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$75$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$76$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$77$	0.707107	−	0.707107i	0.707107	−	0.707107i
$78$	1.00000			1.00000
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	1.00000	−	1.00000i	1.00000	−	1.00000i
$81$	−1.00000			−1.00000
$82$		−	1.41421i		−	1.41421i
$83$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$83$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$84$	0.707107	+	0.707107i	0.707107	+	0.707107i
$85$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$86$		0			0
$87$		0			0
$88$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$89$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$89$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$90$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$91$	0.707107	+	0.707107i	0.707107	+	0.707107i
$92$		−	1.00000i		−	1.00000i
$93$	1.00000	+	1.00000i	1.00000	+	1.00000i
$94$	1.41421			1.41421
$95$		−	1.41421i		−	1.41421i
$96$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		0			0
$99$	0.707107	−	0.707107i	0.707107	−	0.707107i
$100$			1.00000i			1.00000i
$101$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$101$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$102$	0.707107	+	0.707107i	0.707107	+	0.707107i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$105$	−1.41421			−1.41421
$106$	0.707107	−	0.707107i	0.707107	−	0.707107i
$107$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$107$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$108$	0.707107	+	0.707107i	0.707107	+	0.707107i
$109$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$109$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$110$		−	1.41421i		−	1.41421i
$111$	−1.00000			−1.00000
$112$		−	1.00000i		−	1.00000i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	−1.00000			−1.00000
$115$	1.00000	+	1.00000i	1.00000	+	1.00000i
$116$		0			0
$117$	0.707107	+	0.707107i	0.707107	+	0.707107i
$118$	1.00000	+	1.00000i	1.00000	+	1.00000i
$119$			1.00000i			1.00000i
$120$	1.41421			1.41421
$121$		0			0
$122$		0			0
$123$	1.00000	−	1.00000i	1.00000	−	1.00000i
$124$		−	1.41421i		−	1.41421i
$125$		0			0
$126$			1.00000i			1.00000i
$127$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$127$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$128$			1.00000i			1.00000i
$129$		0			0
$130$	1.41421			1.41421
$131$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$131$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$132$	−1.00000			−1.00000
$133$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$134$		0			0
$135$	−1.41421			−1.41421
$136$		−	1.00000i		−	1.00000i
$137$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$137$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$138$	0.707107	−	0.707107i	0.707107	−	0.707107i
$139$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$139$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$140$	1.00000	+	1.00000i	1.00000	+	1.00000i
$141$	1.00000	+	1.00000i	1.00000	+	1.00000i
$142$			1.41421i			1.41421i
$143$	−1.00000			−1.00000
$144$		−	1.00000i		−	1.00000i
$145$		0			0
$146$	−1.00000			−1.00000
$147$		0			0
$148$	0.707107	+	0.707107i	0.707107	+	0.707107i
$149$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$149$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$150$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$151$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$151$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$152$	0.707107	+	0.707107i	0.707107	+	0.707107i
$153$			1.00000i			1.00000i
$154$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$155$	1.41421	+	1.41421i	1.41421	+	1.41421i
$156$		−	1.00000i		−	1.00000i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$	1.00000			1.00000
$160$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$161$	1.00000			1.00000
$162$			1.00000i			1.00000i
$163$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$163$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$164$	−1.41421			−1.41421
$165$	1.00000	−	1.00000i	1.00000	−	1.00000i
$166$	0.707107	+	0.707107i	0.707107	+	0.707107i
$167$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$168$	0.707107	−	0.707107i	0.707107	−	0.707107i
$169$		0			0
$170$	1.00000	+	1.00000i	1.00000	+	1.00000i
$171$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$172$		0			0
$173$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$173$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$174$		0			0
$175$	−1.00000			−1.00000
$176$	0.707107	+	0.707107i	0.707107	+	0.707107i
$177$			1.41421i			1.41421i
$178$	−1.00000			−1.00000
$179$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$179$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$180$	1.00000	+	1.00000i	1.00000	+	1.00000i
$181$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$181$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$182$	0.707107	−	0.707107i	0.707107	−	0.707107i
$183$		0			0
$184$	−1.00000			−1.00000
$185$	−1.41421			−1.41421
$186$	1.00000	−	1.00000i	1.00000	−	1.00000i
$187$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$188$		−	1.41421i		−	1.41421i
$189$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$190$	−1.41421			−1.41421
$191$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$191$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$192$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$	1.00000	+	1.00000i	1.00000	+	1.00000i
$196$		0			0
$197$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$197$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$198$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$199$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$199$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$200$	1.00000			1.00000
$201$		0			0
$202$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$203$		0			0
$204$	0.707107	−	0.707107i	0.707107	−	0.707107i
$205$	1.41421	−	1.41421i	1.41421	−	1.41421i
$206$		0			0
$207$	1.00000			1.00000
$208$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$209$	1.00000			1.00000
$210$			1.41421i			1.41421i
$211$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$211$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$212$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$213$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$214$	0.707107	−	0.707107i	0.707107	−	0.707107i
$215$		0			0
$216$	0.707107	−	0.707107i	0.707107	−	0.707107i
$217$	1.41421			1.41421
$218$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$219$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$220$	−1.41421			−1.41421
$221$	0.707107	−	0.707107i	0.707107	−	0.707107i
$222$			1.00000i			1.00000i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$	−1.00000			−1.00000
$225$	−1.00000			−1.00000
$226$		0			0
$227$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$227$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$228$			1.00000i			1.00000i
$229$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$229$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$230$	1.00000	−	1.00000i	1.00000	−	1.00000i
$231$		−	1.00000i		−	1.00000i
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	0.707107	−	0.707107i	0.707107	−	0.707107i
$235$	1.41421	+	1.41421i	1.41421	+	1.41421i
$236$	1.00000	−	1.00000i	1.00000	−	1.00000i
$237$		0			0
$238$	1.00000			1.00000
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		−	1.41421i		−	1.41421i
$241$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$241$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$244$		0			0
$245$		0			0
$246$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$247$			1.00000i			1.00000i
$248$	−1.41421			−1.41421
$249$			1.00000i			1.00000i
$250$		0			0
$251$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$251$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$252$	1.00000			1.00000
$253$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$254$			1.00000i			1.00000i
$255$			1.41421i			1.41421i
$256$	1.00000			1.00000
$257$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$260$		−	1.41421i		−	1.41421i
$261$		0			0
$262$	1.00000	−	1.00000i	1.00000	−	1.00000i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$			1.00000i			1.00000i
$265$	1.41421			1.41421
$266$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$267$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$268$		0			0
$269$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$269$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$270$			1.41421i			1.41421i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−1.00000			−1.00000
$273$	1.00000			1.00000
$274$			1.41421i			1.41421i
$275$	0.707107	−	0.707107i	0.707107	−	0.707107i
$276$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$277$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$277$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$278$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$279$	1.41421			1.41421
$280$	1.00000	−	1.00000i	1.00000	−	1.00000i
$281$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$281$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$282$	1.00000	−	1.00000i	1.00000	−	1.00000i
$283$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$283$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$284$	1.41421			1.41421
$285$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$286$			1.00000i			1.00000i
$287$		−	1.41421i		−	1.41421i
$288$	−1.00000			−1.00000
$289$		0			0
$290$		0			0
$291$		0			0
$292$			1.00000i			1.00000i
$293$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$293$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$294$		0			0
$295$			2.00000i			2.00000i
$296$	0.707107	−	0.707107i	0.707107	−	0.707107i
$297$		−	1.00000i		−	1.00000i
$298$		0			0
$299$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$300$	0.707107	+	0.707107i	0.707107	+	0.707107i
$301$		0			0
$302$	−1.00000			−1.00000
$303$	−2.00000			−2.00000
$304$	0.707107	−	0.707107i	0.707107	−	0.707107i
$305$		0			0
$306$	1.00000			1.00000
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$309$		0			0
$310$	1.41421	−	1.41421i	1.41421	−	1.41421i
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	−1.00000			−1.00000
$313$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$313$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$314$		0			0
$315$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$316$		0			0
$317$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$317$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$318$		−	1.00000i		−	1.00000i
$319$		0			0
$320$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$321$	1.00000			1.00000
$322$		−	1.00000i		−	1.00000i
$323$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$324$	1.00000			1.00000
$325$	0.707107	+	0.707107i	0.707107	+	0.707107i
$326$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$327$		−	1.00000i		−	1.00000i
$328$			1.41421i			1.41421i
$329$	1.41421			1.41421
$330$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$331$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$331$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$332$	0.707107	−	0.707107i	0.707107	−	0.707107i
$333$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$334$	−1.00000			−1.00000
$335$		0			0
$336$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$337$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$337$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$338$		0			0
$339$		0			0
$340$	1.00000	−	1.00000i	1.00000	−	1.00000i
$341$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$342$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$343$		−	1.00000i		−	1.00000i
$344$		0			0
$345$	1.41421			1.41421
$346$	0.707107	+	0.707107i	0.707107	+	0.707107i
$347$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$347$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$348$		0			0
$349$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$349$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$350$			1.00000i			1.00000i
$351$	1.00000			1.00000
$352$	0.707107	−	0.707107i	0.707107	−	0.707107i
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$	1.41421			1.41421
$355$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$356$			1.00000i			1.00000i
$357$	0.707107	+	0.707107i	0.707107	+	0.707107i
$358$	1.00000	−	1.00000i	1.00000	−	1.00000i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	1.00000	−	1.00000i	1.00000	−	1.00000i
$361$		0			0
$362$	1.00000	+	1.00000i	1.00000	+	1.00000i
$363$		0			0
$364$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$365$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$366$		0			0
$367$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$367$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$368$			1.00000i			1.00000i
$369$		−	1.41421i		−	1.41421i
$370$			1.41421i			1.41421i
$371$	0.707107	−	0.707107i	0.707107	−	0.707107i
$372$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$373$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$373$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$374$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$375$		0			0
$376$	−1.41421			−1.41421
$377$		0			0
$378$	0.707107	+	0.707107i	0.707107	+	0.707107i
$379$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$379$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$380$			1.41421i			1.41421i
$381$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$382$		−	1.00000i		−	1.00000i
$383$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$383$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$384$	0.707107	+	0.707107i	0.707107	+	0.707107i
$385$		−	1.41421i		−	1.41421i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$389$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$390$	1.00000	−	1.00000i	1.00000	−	1.00000i
$391$		−	1.00000i		−	1.00000i
$392$		0			0
$393$	1.41421			1.41421
$394$	0.707107	−	0.707107i	0.707107	−	0.707107i
$395$		0			0
$396$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$397$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$397$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$398$			1.41421i			1.41421i
$399$	−1.00000			−1.00000
$400$		−	1.00000i		−	1.00000i
$401$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$404$	1.41421	+	1.41421i	1.41421	+	1.41421i
$405$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$406$		0			0
$407$		−	1.00000i		−	1.00000i
$408$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$409$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$409$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$410$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$411$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$412$		0			0
$413$	1.00000	+	1.00000i	1.00000	+	1.00000i
$414$		−	1.00000i		−	1.00000i
$415$			1.41421i			1.41421i
$416$	0.707107	+	0.707107i	0.707107	+	0.707107i
$417$		−	1.41421i		−	1.41421i
$418$		−	1.00000i		−	1.00000i
$419$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$419$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$420$	1.41421			1.41421
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	1.00000	−	1.00000i	1.00000	−	1.00000i
$423$	1.41421			1.41421
$424$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$425$			1.00000i			1.00000i
$426$	1.00000	+	1.00000i	1.00000	+	1.00000i
$427$		0			0
$428$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$429$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$430$		0			0
$431$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$431$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$432$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$433$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$433$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$434$		−	1.41421i		−	1.41421i
$435$		0			0
$436$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$437$	0.707107	+	0.707107i	0.707107	+	0.707107i
$438$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$439$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$439$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$440$			1.41421i			1.41421i
$441$		0			0
$442$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$	1.00000			1.00000
$445$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$446$		0			0
$447$		0			0
$448$			1.00000i			1.00000i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$			1.00000i			1.00000i
$451$	1.00000	+	1.00000i	1.00000	+	1.00000i
$452$		0			0
$453$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$454$		0			0
$455$	1.41421			1.41421
$456$	1.00000			1.00000
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$459$	0.707107	+	0.707107i	0.707107	+	0.707107i
$460$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$461$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$461$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$462$	−1.00000			−1.00000
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$	2.00000			2.00000
$466$		0			0
$467$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$467$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$468$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$469$		0			0
$470$	1.41421	−	1.41421i	1.41421	−	1.41421i
$471$		0			0
$472$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$473$		0			0
$474$		0			0
$475$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$476$		−	1.00000i		−	1.00000i
$477$	0.707107	−	0.707107i	0.707107	−	0.707107i
$478$		0			0
$479$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$479$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$480$	−1.41421			−1.41421
$481$	1.00000			1.00000
$482$	−1.41421			−1.41421
$483$	0.707107	−	0.707107i	0.707107	−	0.707107i
$484$		0			0
$485$		0			0
$486$	0.707107	+	0.707107i	0.707107	+	0.707107i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		−	1.00000i		−	1.00000i
$490$		0			0
$491$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$491$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$492$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$493$		0			0
$494$	1.00000			1.00000
$495$		−	1.41421i		−	1.41421i
$496$			1.41421i			1.41421i
$497$			1.41421i			1.41421i
$498$	1.00000			1.00000
$499$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$499$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$500$		0			0
$501$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		−	1.00000i		−	1.00000i
$505$	−2.82843			−2.82843
$506$	0.707107	+	0.707107i	0.707107	+	0.707107i
$507$		0			0
$508$	1.00000			1.00000
$509$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$509$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$510$	1.41421			1.41421
$511$	−1.00000			−1.00000
$512$		−	1.00000i		−	1.00000i
$513$	−1.00000			−1.00000
$514$		−	1.00000i		−	1.00000i
$515$		0			0
$516$		0			0
$517$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$518$	0.707107	+	0.707107i	0.707107	+	0.707107i
$519$			1.00000i			1.00000i
$520$	−1.41421			−1.41421
$521$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$521$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$522$		0			0
$523$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$523$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$524$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$525$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$526$		0			0
$527$		−	1.41421i		−	1.41421i
$528$	1.00000			1.00000
$529$		0			0
$530$		−	1.41421i		−	1.41421i
$531$	1.00000	+	1.00000i	1.00000	+	1.00000i
$532$	0.707107	+	0.707107i	0.707107	+	0.707107i
$533$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$534$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$535$	1.41421			1.41421
$536$		0			0
$537$	1.41421			1.41421
$538$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$539$		0			0
$540$	1.41421			1.41421
$541$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$541$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$542$		0			0
$543$			1.41421i			1.41421i
$544$			1.00000i			1.00000i
$545$		−	1.41421i		−	1.41421i
$546$		−	1.00000i		−	1.00000i
$547$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$547$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$548$	1.41421			1.41421
$549$		0			0
$550$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$551$		0			0
$552$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$553$		0			0
$554$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$555$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$556$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$557$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$557$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$558$		−	1.41421i		−	1.41421i
$559$		0			0
$560$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$561$	−1.00000			−1.00000
$562$	−1.00000			−1.00000
$563$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$563$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$564$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$565$		0			0
$566$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$567$			1.00000i			1.00000i
$568$		−	1.41421i		−	1.41421i
$569$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$569$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$570$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$571$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$571$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$572$	1.00000			1.00000
$573$	0.707107	−	0.707107i	0.707107	−	0.707107i
$574$	−1.41421			−1.41421
$575$	1.00000			1.00000
$576$			1.00000i			1.00000i
$577$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$577$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.707107	+	0.707107i	0.707107	+	0.707107i
$582$		0			0
$583$			1.00000i			1.00000i
$584$	1.00000			1.00000
$585$	1.41421			1.41421
$586$	0.707107	−	0.707107i	0.707107	−	0.707107i
$587$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$587$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$588$		0			0
$589$	1.00000	+	1.00000i	1.00000	+	1.00000i
$590$	2.00000			2.00000
$591$	1.00000			1.00000
$592$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−1.00000			−1.00000
$595$	1.00000	+	1.00000i	1.00000	+	1.00000i
$596$		0			0
$597$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$598$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$599$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$599$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$600$	0.707107	−	0.707107i	0.707107	−	0.707107i
$601$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$601$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$602$		0			0
$603$		0			0
$604$			1.00000i			1.00000i
$605$		0			0
$606$			2.00000i			2.00000i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$609$		0			0
$610$		0			0
$611$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$612$		−	1.00000i		−	1.00000i
$613$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$613$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$614$		0			0
$615$		−	2.00000i		−	2.00000i
$616$	0.707107	+	0.707107i	0.707107	+	0.707107i
$617$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$617$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$618$		0			0
$619$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$619$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$620$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$621$	0.707107	−	0.707107i	0.707107	−	0.707107i
$622$		0			0
$623$	−1.00000			−1.00000
$624$			1.00000i			1.00000i
$625$	1.00000			1.00000
$626$			1.41421i			1.41421i
$627$	0.707107	−	0.707107i	0.707107	−	0.707107i
$628$		0			0
$629$	0.707107	+	0.707107i	0.707107	+	0.707107i
$630$	1.00000	+	1.00000i	1.00000	+	1.00000i
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	1.41421			1.41421
$634$		0			0
$635$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$636$	−1.00000			−1.00000
$637$		0			0
$638$		0			0
$639$			1.41421i			1.41421i
$640$	1.00000	+	1.00000i	1.00000	+	1.00000i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		−	1.00000i		−	1.00000i
$643$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$643$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$644$	−1.00000			−1.00000
$645$		0			0
$646$	0.707107	+	0.707107i	0.707107	+	0.707107i
$647$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$647$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$648$		−	1.00000i		−	1.00000i
$649$	−1.41421			−1.41421
$650$	0.707107	−	0.707107i	0.707107	−	0.707107i
$651$	1.00000	−	1.00000i	1.00000	−	1.00000i
$652$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$653$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$653$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$654$	−1.00000			−1.00000
$655$	2.00000			2.00000
$656$	1.41421			1.41421
$657$	−1.00000			−1.00000
$658$		−	1.41421i		−	1.41421i
$659$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$659$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$660$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$661$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$661$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$662$		0			0
$663$		−	1.00000i		−	1.00000i
$664$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$665$	−1.41421			−1.41421
$666$	0.707107	+	0.707107i	0.707107	+	0.707107i
$667$		0			0
$668$			1.00000i			1.00000i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$673$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$673$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$674$			1.00000i			1.00000i
$675$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$676$		0			0
$677$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$677$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$678$		0			0
$679$		0			0
$680$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$681$		0			0
$682$	1.00000	+	1.00000i	1.00000	+	1.00000i
$683$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$683$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$684$	0.707107	+	0.707107i	0.707107	+	0.707107i
$685$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$686$	−1.00000			−1.00000
$687$		−	1.41421i		−	1.41421i
$688$		0			0
$689$	−1.00000			−1.00000
$690$		−	1.41421i		−	1.41421i
$691$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$691$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$692$	0.707107	−	0.707107i	0.707107	−	0.707107i
$693$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$694$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$695$		−	2.00000i		−	2.00000i
$696$		0			0
$697$	−1.41421			−1.41421
$698$	1.00000	−	1.00000i	1.00000	−	1.00000i
$699$		0			0
$700$	1.00000			1.00000
$701$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$701$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$702$		−	1.00000i		−	1.00000i
$703$	−1.00000			−1.00000
$704$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$705$	2.00000			2.00000
$706$		0			0
$707$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$708$		−	1.41421i		−	1.41421i
$709$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$709$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$710$	1.41421	+	1.41421i	1.41421	+	1.41421i
$711$		0			0
$712$	1.00000			1.00000
$713$	−1.41421			−1.41421
$714$	0.707107	−	0.707107i	0.707107	−	0.707107i
$715$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$716$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$717$		0			0
$718$		0			0
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$721$		0			0
$722$		0			0
$723$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$724$	1.00000	−	1.00000i	1.00000	−	1.00000i
$725$		0			0
$726$		0			0
$727$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$727$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$728$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$729$			1.00000i			1.00000i
$730$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$731$		0			0
$732$		0			0
$733$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$733$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$734$			1.00000i			1.00000i
$735$		0			0
$736$	1.00000			1.00000
$737$		0			0
$738$	−1.41421			−1.41421
$739$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$739$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$740$	1.41421			1.41421
$741$	0.707107	+	0.707107i	0.707107	+	0.707107i
$742$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$745$		0			0
$746$		0			0
$747$	0.707107	+	0.707107i	0.707107	+	0.707107i
$748$	0.707107	+	0.707107i	0.707107	+	0.707107i
$749$	0.707107	−	0.707107i	0.707107	−	0.707107i
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$			1.41421i			1.41421i
$753$		0			0
$754$		0			0
$755$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$756$	0.707107	−	0.707107i	0.707107	−	0.707107i
$757$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$757$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$758$		0			0
$759$			1.00000i			1.00000i
$760$	1.41421			1.41421
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$	0.707107	+	0.707107i	0.707107	+	0.707107i
$763$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$764$	−1.00000			−1.00000
$765$	1.00000	+	1.00000i	1.00000	+	1.00000i
$766$			1.00000i			1.00000i
$767$		−	1.41421i		−	1.41421i
$768$	0.707107	−	0.707107i	0.707107	−	0.707107i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$	−1.41421			−1.41421
$771$	0.707107	−	0.707107i	0.707107	−	0.707107i
$772$		0			0
$773$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$773$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$774$		0			0
$775$	1.41421			1.41421
$776$		0			0
$777$			1.00000i			1.00000i
$778$		0			0
$779$	1.00000	−	1.00000i	1.00000	−	1.00000i
$780$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$781$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$782$	−1.00000			−1.00000
$783$		0			0
$784$		0			0
$785$		0			0
$786$		−	1.41421i		−	1.41421i
$787$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$787$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$788$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.707107	+	0.707107i	0.707107	+	0.707107i
$793$		0			0
$794$	1.00000	−	1.00000i	1.00000	−	1.00000i
$795$	1.00000	−	1.00000i	1.00000	−	1.00000i
$796$	1.41421			1.41421
$797$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$797$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$798$			1.00000i			1.00000i
$799$		−	1.41421i		−	1.41421i
$800$	−1.00000			−1.00000
$801$	−1.00000			−1.00000
$802$			1.00000i			1.00000i
$803$	0.707107	−	0.707107i	0.707107	−	0.707107i
$804$		0			0
$805$	1.00000	−	1.00000i	1.00000	−	1.00000i
$806$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$807$		−	1.00000i		−	1.00000i
$808$	1.41421	−	1.41421i	1.41421	−	1.41421i
$809$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$809$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$810$	1.00000	+	1.00000i	1.00000	+	1.00000i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$		0			0
$813$		0			0
$814$	−1.00000			−1.00000
$815$		−	1.41421i		−	1.41421i
$816$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$817$		0			0
$818$		−	1.41421i		−	1.41421i
$819$	0.707107	−	0.707107i	0.707107	−	0.707107i
$820$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$821$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$821$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$822$	1.00000	+	1.00000i	1.00000	+	1.00000i
$823$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$823$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$		−	1.00000i		−	1.00000i
$826$	1.00000	−	1.00000i	1.00000	−	1.00000i
$827$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$827$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$828$	−1.00000			−1.00000
$829$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$829$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$830$	1.41421			1.41421
$831$	−1.00000			−1.00000
$832$	0.707107	−	0.707107i	0.707107	−	0.707107i
$833$		0			0
$834$	−1.41421			−1.41421
$835$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$836$	−1.00000			−1.00000
$837$	1.00000	−	1.00000i	1.00000	−	1.00000i
$838$	0.707107	+	0.707107i	0.707107	+	0.707107i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		−	1.41421i		−	1.41421i
$841$		−	1.00000i		−	1.00000i
$842$		0			0
$843$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$844$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$845$		0			0
$846$		−	1.41421i		−	1.41421i
$847$		0			0
$848$	0.707107	+	0.707107i	0.707107	+	0.707107i
$849$	−1.00000			−1.00000
$850$	1.00000			1.00000
$851$	0.707107	−	0.707107i	0.707107	−	0.707107i
$852$	1.00000	−	1.00000i	1.00000	−	1.00000i
$853$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$853$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$854$		0			0
$855$	−1.41421			−1.41421
$856$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$857$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$857$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$858$	0.707107	+	0.707107i	0.707107	+	0.707107i
$859$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$859$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$860$		0			0
$861$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$862$		−	1.00000i		−	1.00000i
$863$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$863$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$864$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$865$			1.41421i			1.41421i
$866$			1.00000i			1.00000i
$867$		0			0
$868$	−1.41421			−1.41421
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.707107	+	0.707107i	0.707107	+	0.707107i
$873$		0			0
$874$	0.707107	−	0.707107i	0.707107	−	0.707107i
$875$		0			0
$876$	0.707107	+	0.707107i	0.707107	+	0.707107i
$877$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$877$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$878$			1.41421i			1.41421i
$879$	1.00000			1.00000
$880$	1.41421			1.41421
$881$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$881$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$882$		0			0
$883$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$883$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$884$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$885$	1.41421	+	1.41421i	1.41421	+	1.41421i
$886$		0			0
$887$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$887$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$888$		−	1.00000i		−	1.00000i
$889$			1.00000i			1.00000i
$890$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$891$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$892$		0			0
$893$	1.00000	+	1.00000i	1.00000	+	1.00000i
$894$		0			0
$895$	2.00000			2.00000
$896$	1.00000			1.00000
$897$	−1.00000			−1.00000
$898$		0			0
$899$		0			0
$900$	1.00000			1.00000
$901$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$902$	1.00000	−	1.00000i	1.00000	−	1.00000i
$903$		0			0
$904$		0			0
$905$			2.00000i			2.00000i
$906$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$907$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$907$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$908$		0			0
$909$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$910$		−	1.41421i		−	1.41421i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		−	1.00000i		−	1.00000i
$913$	−1.00000			−1.00000
$914$		0			0
$915$		0			0
$916$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$917$	1.00000	−	1.00000i	1.00000	−	1.00000i
$918$	0.707107	−	0.707107i	0.707107	−	0.707107i
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$921$		0			0
$922$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$923$	1.00000	−	1.00000i	1.00000	−	1.00000i
$924$			1.00000i			1.00000i
$925$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$929$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$930$		−	2.00000i		−	2.00000i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	1.00000	−	1.00000i	1.00000	−	1.00000i
$935$	−1.41421			−1.41421
$936$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$937$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$937$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$938$		0			0
$939$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$940$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$941$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$941$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$942$		0			0
$943$			1.41421i			1.41421i
$944$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$945$			1.41421i			1.41421i
$946$		0			0
$947$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$947$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$948$		0			0
$949$	0.707107	+	0.707107i	0.707107	+	0.707107i
$950$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$951$		0			0
$952$	−1.00000			−1.00000
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$955$	1.00000	−	1.00000i	1.00000	−	1.00000i
$956$		0			0
$957$		0			0
$958$			1.00000i			1.00000i
$959$			1.41421i			1.41421i
$960$			1.41421i			1.41421i
$961$	−1.00000			−1.00000
$962$		−	1.00000i		−	1.00000i
$963$	0.707107	−	0.707107i	0.707107	−	0.707107i
$964$			1.41421i			1.41421i
$965$		0			0
$966$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$967$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$967$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$968$		0			0
$969$			1.00000i			1.00000i
$970$		0			0
$971$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$971$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$972$	0.707107	−	0.707107i	0.707107	−	0.707107i
$973$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$974$		0			0
$975$	1.00000			1.00000
$976$		0			0
$977$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$978$	−1.00000			−1.00000
$979$	0.707107	−	0.707107i	0.707107	−	0.707107i
$980$		0			0
$981$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$982$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	1.00000	+	1.00000i	1.00000	+	1.00000i
$985$	1.41421			1.41421
$986$		0			0
$987$	1.00000	−	1.00000i	1.00000	−	1.00000i
$988$		−	1.00000i		−	1.00000i
$989$		0			0
$990$	−1.41421			−1.41421
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	1.41421			1.41421
$993$		0			0
$994$	1.41421			1.41421
$995$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$996$		−	1.00000i		−	1.00000i
$997$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$997$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$998$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$999$			1.00000i			1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1776.1.z.b.221.2	yes	4
3.2	odd	2		1776.1.z.a.221.1	✓	4
16.5	even	4	inner	1776.1.z.b.1109.1	yes	4
37.36	even	2		1776.1.z.a.221.2	yes	4
48.5	odd	4		1776.1.z.a.1109.2	yes	4
111.110	odd	2	inner	1776.1.z.b.221.1	yes	4
592.517	even	4		1776.1.z.a.1109.1	yes	4
1776.1109	odd	4	inner	1776.1.z.b.1109.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1776.1.z.a.221.1	✓	4	3.2	odd	2
1776.1.z.a.221.2	yes	4	37.36	even	2
1776.1.z.a.1109.1	yes	4	592.517	even	4
1776.1.z.a.1109.2	yes	4	48.5	odd	4
1776.1.z.b.221.1	yes	4	111.110	odd	2	inner
1776.1.z.b.221.2	yes	4	1.1	even	1	trivial
1776.1.z.b.1109.1	yes	4	16.5	even	4	inner
1776.1.z.b.1109.2	yes	4	1776.1109	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1776.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-0.707107 - 0.707107i) q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-0.707107 - 0.707107i) q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.707107 + 0.707107i) q^{13} -1.00000 q^{14} -1.41421i q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +(0.707107 - 0.707107i) q^{19} +(-1.00000 + 1.00000i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(0.707107 - 0.707107i) q^{22} +1.00000i q^{23} +(0.707107 + 0.707107i) q^{24} -1.00000i q^{25} +(0.707107 + 0.707107i) q^{26} +(-0.707107 - 0.707107i) q^{27} +1.00000i q^{28} -1.41421 q^{30} +1.41421i q^{31} -1.00000i q^{32} +1.00000 q^{33} +1.00000i q^{34} +(-1.00000 - 1.00000i) q^{35} +1.00000i q^{36} +(-0.707107 - 0.707107i) q^{37} +(-0.707107 - 0.707107i) q^{38} +1.00000i q^{39} +(1.00000 + 1.00000i) q^{40} +1.41421 q^{41} +(-0.707107 + 0.707107i) q^{42} +(-0.707107 - 0.707107i) q^{44} +(-1.00000 - 1.00000i) q^{45} +1.00000 q^{46} +1.41421i q^{47} +(0.707107 - 0.707107i) q^{48} -1.00000 q^{50} +(-0.707107 + 0.707107i) q^{51} +(0.707107 - 0.707107i) q^{52} +(0.707107 + 0.707107i) q^{53} +(-0.707107 + 0.707107i) q^{54} +1.41421 q^{55} +1.00000 q^{56} -1.00000i q^{57} +(-1.00000 + 1.00000i) q^{59} +1.41421i q^{60} +1.41421 q^{62} -1.00000 q^{63} -1.00000 q^{64} +1.41421i q^{65} -1.00000i q^{66} +1.00000 q^{68} +(0.707107 + 0.707107i) q^{69} +(-1.00000 + 1.00000i) q^{70} -1.41421 q^{71} +1.00000 q^{72} -1.00000i q^{73} +(-0.707107 + 0.707107i) q^{74} +(-0.707107 - 0.707107i) q^{75} +(-0.707107 + 0.707107i) q^{76} +(0.707107 - 0.707107i) q^{77} +1.00000 q^{78} +(1.00000 - 1.00000i) q^{80} -1.00000 q^{81} -1.41421i q^{82} +(-0.707107 + 0.707107i) q^{83} +(0.707107 + 0.707107i) q^{84} +(-1.00000 + 1.00000i) q^{85} +(-0.707107 + 0.707107i) q^{88} -1.00000i q^{89} +(-1.00000 + 1.00000i) q^{90} +(0.707107 + 0.707107i) q^{91} -1.00000i q^{92} +(1.00000 + 1.00000i) q^{93} +1.41421 q^{94} -1.41421i q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^5	\( 4 q - 4 q^{4} + 4 q^{5} - 4 q^{10} - 4 q^{14} + 4 q^{16} - 4 q^{17} - 4 q^{18} - 4 q^{20} + 4 q^{33} - 4 q^{35} + 4 q^{40} - 4 q^{45} + 4 q^{46} - 4 q^{50} + 4 q^{56} - 4 q^{59} - 4 q^{63} - 4 q^{64} + 4 q^{68} - 4 q^{70} + 4 q^{72} + 4 q^{78} + 4 q^{80} - 4 q^{81} - 4 q^{85} - 4 q^{90} + 4 q^{93}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 - 4 * q^10 - 4 * q^14 + 4 * q^16 - 4 * q^17 - 4 * q^18 - 4 * q^20 + 4 * q^33 - 4 * q^35 + 4 * q^40 - 4 * q^45 + 4 * q^46 - 4 * q^50 + 4 * q^56 - 4 * q^59 - 4 * q^63 - 4 * q^64 + 4 * q^68 - 4 * q^70 + 4 * q^72 + 4 * q^78 + 4 * q^80 - 4 * q^81 - 4 * q^85 - 4 * q^90 + 4 * q^93

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