LMFDB - Embedded newform 860.1.bb.b.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [860,1,Mod(59,860)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(860, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 8]))

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

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

chi := DirichletCharacter("860.59");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 860 = 2^{2} \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	860.bb (of order $14$, degree $6$, 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:	$0.429195910864$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.50570904392000.1

Embedding invariants

Embedding label			379.1
Root			$0.900969 - 0.433884i$ of defining polynomial
Character	$\chi$	$=$	860.379
Dual form			860.1.bb.b.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -0.445042 q^{6} +0.445042 q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.722521 - 0.347948i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -0.445042 q^{6} +0.445042 q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.722521 - 0.347948i) q^{9} +(-0.623490 - 0.781831i) q^{10} +(-0.0990311 + 0.433884i) q^{12} +(0.0990311 - 0.433884i) q^{14} +(-0.400969 - 0.193096i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-0.178448 - 0.781831i) q^{18} +(-0.900969 + 0.433884i) q^{20} +(-0.0440730 - 0.193096i) q^{21} +(-1.62349 + 0.781831i) q^{23} +(0.400969 + 0.193096i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.500000 - 0.626980i) q^{27} +(-0.400969 - 0.193096i) q^{28} +(-0.277479 + 1.21572i) q^{29} +(-0.277479 + 0.347948i) q^{30} +(0.900969 - 0.433884i) q^{32} +(0.277479 - 0.347948i) q^{35} -0.801938 q^{36} +(0.222521 + 0.974928i) q^{40} +(-0.277479 + 1.21572i) q^{41} -0.198062 q^{42} +(-0.623490 - 0.781831i) q^{43} +(0.178448 - 0.781831i) q^{45} +(0.400969 + 1.75676i) q^{46} +(1.80194 + 0.867767i) q^{47} +(0.277479 - 0.347948i) q^{48} -0.801938 q^{49} -1.00000 q^{50} +(-0.722521 + 0.347948i) q^{54} +(-0.277479 + 0.347948i) q^{56} +(1.12349 + 0.541044i) q^{58} +(0.277479 + 0.347948i) q^{60} +(-0.277479 - 1.21572i) q^{61} +(0.321552 - 0.154851i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(1.12349 + 0.541044i) q^{67} +(0.500000 + 0.626980i) q^{69} +(-0.277479 - 0.347948i) q^{70} +(-0.178448 + 0.781831i) q^{72} +(-0.400969 + 0.193096i) q^{75} +1.00000 q^{80} +(0.277479 - 0.347948i) q^{81} +(1.12349 + 0.541044i) q^{82} +(-0.0990311 - 0.433884i) q^{83} +(-0.0440730 + 0.193096i) q^{84} +(-0.900969 + 0.433884i) q^{86} +0.554958 q^{87} +(0.400969 + 1.75676i) q^{89} +(-0.722521 - 0.347948i) q^{90} +1.80194 q^{92} +(1.24698 - 1.56366i) q^{94} +(-0.277479 - 0.347948i) q^{96} +(-0.178448 + 0.781831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 5 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q + q^2 - 5 * q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^7 + q^8 + 4 * q^9	$ 6 q + q^{2} - 5 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} + 4 q^{9} + q^{10} - 5 q^{12} + 5 q^{14} + 2 q^{15} - q^{16} + 3 q^{18} - q^{20} - 4 q^{21} - 5 q^{23} - 2 q^{24} - q^{25} - 3 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} + q^{32} + 2 q^{35} + 4 q^{36} + q^{40} - 2 q^{41} - 10 q^{42} + q^{43} - 3 q^{45} - 2 q^{46} + 2 q^{47} + 2 q^{48} + 4 q^{49} - 6 q^{50} - 4 q^{54} - 2 q^{56} + 2 q^{58} + 2 q^{60} - 2 q^{61} + 6 q^{63} - q^{64} + 2 q^{67} + 3 q^{69} - 2 q^{70} + 3 q^{72} + 2 q^{75} + 6 q^{80} + 2 q^{81} + 2 q^{82} - 5 q^{83} - 4 q^{84} - q^{86} + 4 q^{87} - 2 q^{89} - 4 q^{90} + 2 q^{92} - 2 q^{94} - 2 q^{96} + 3 q^{98}+O(q^{100}) $ 6 * q + q^2 - 5 * q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^7 + q^8 + 4 * q^9 + q^10 - 5 * q^12 + 5 * q^14 + 2 * q^15 - q^16 + 3 * q^18 - q^20 - 4 * q^21 - 5 * q^23 - 2 * q^24 - q^25 - 3 * q^27 + 2 * q^28 - 2 * q^29 - 2 * q^30 + q^32 + 2 * q^35 + 4 * q^36 + q^40 - 2 * q^41 - 10 * q^42 + q^43 - 3 * q^45 - 2 * q^46 + 2 * q^47 + 2 * q^48 + 4 * q^49 - 6 * q^50 - 4 * q^54 - 2 * q^56 + 2 * q^58 + 2 * q^60 - 2 * q^61 + 6 * q^63 - q^64 + 2 * q^67 + 3 * q^69 - 2 * q^70 + 3 * q^72 + 2 * q^75 + 6 * q^80 + 2 * q^81 + 2 * q^82 - 5 * q^83 - 4 * q^84 - q^86 + 4 * q^87 - 2 * q^89 - 4 * q^90 + 2 * q^92 - 2 * q^94 - 2 * q^96 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/860\mathbb{Z}\right)^\times$.

$n$	$261$	$431$	$517$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.222521	−	0.974928i	0.222521	−	0.974928i
$2$	0.222521	−	0.974928i	0.222521	−	0.974928i
$3$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$3$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$4$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$5$	0.623490	−	0.781831i	0.623490	−	0.781831i
$5$	0.623490	−	0.781831i	0.623490	−	0.781831i
$6$	−0.445042			−0.445042
$7$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$7$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$8$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$9$	0.722521	−	0.347948i	0.722521	−	0.347948i
$10$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$11$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$11$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$12$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$13$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$13$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$14$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$15$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$16$	0.623490	+	0.781831i	0.623490	+	0.781831i
$17$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$17$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$18$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$19$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$19$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$20$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$21$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$22$		0			0
$23$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$23$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$24$	0.400969	+	0.193096i	0.400969	+	0.193096i
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$		0			0
$27$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$28$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$29$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$29$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$30$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$31$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$31$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$32$	0.900969	−	0.433884i	0.900969	−	0.433884i
$33$		0			0
$34$		0			0
$35$	0.277479	−	0.347948i	0.277479	−	0.347948i
$36$	−0.801938			−0.801938
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$	0.222521	+	0.974928i	0.222521	+	0.974928i
$41$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$41$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$42$	−0.198062			−0.198062
$43$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$43$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$44$		0			0
$45$	0.178448	−	0.781831i	0.178448	−	0.781831i
$46$	0.400969	+	1.75676i	0.400969	+	1.75676i
$47$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$47$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$48$	0.277479	−	0.347948i	0.277479	−	0.347948i
$49$	−0.801938			−0.801938
$50$	−1.00000			−1.00000
$51$		0			0
$52$		0			0
$53$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$53$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$54$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$55$		0			0
$56$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$57$		0			0
$58$	1.12349	+	0.541044i	1.12349	+	0.541044i
$59$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$59$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$60$	0.277479	+	0.347948i	0.277479	+	0.347948i
$61$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$61$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$62$		0			0
$63$	0.321552	−	0.154851i	0.321552	−	0.154851i
$64$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$65$		0			0
$66$		0			0
$67$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$67$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$68$		0			0
$69$	0.500000	+	0.626980i	0.500000	+	0.626980i
$70$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$71$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$71$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$72$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$73$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$73$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$74$		0			0
$75$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	1.00000			1.00000
$81$	0.277479	−	0.347948i	0.277479	−	0.347948i
$82$	1.12349	+	0.541044i	1.12349	+	0.541044i
$83$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$83$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$84$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$85$		0			0
$86$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$87$	0.554958			0.554958
$88$		0			0
$89$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$89$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$90$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$91$		0			0
$92$	1.80194			1.80194
$93$		0			0
$94$	1.24698	−	1.56366i	1.24698	−	1.56366i
$95$		0			0
$96$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$97$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$97$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$98$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$99$		0			0
$100$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$101$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$101$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$102$		0			0
$103$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$103$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$104$		0			0
$105$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$106$		0			0
$107$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$107$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$108$	0.178448	+	0.781831i	0.178448	+	0.781831i
$109$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$109$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$110$		0			0
$111$		0			0
$112$	0.277479	+	0.347948i	0.277479	+	0.347948i
$113$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$113$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$116$	0.777479	−	0.974928i	0.777479	−	0.974928i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.400969	−	0.193096i	0.400969	−	0.193096i
$121$	0.623490	−	0.781831i	0.623490	−	0.781831i
$122$	−1.24698			−1.24698
$123$	0.554958			0.554958
$124$		0			0
$125$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$126$	−0.0794168	−	0.347948i	−0.0794168	−	0.347948i
$127$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$127$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$128$	−1.00000			−1.00000
$129$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$130$		0			0
$131$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$131$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$132$		0			0
$133$		0			0
$134$	0.777479	−	0.974928i	0.777479	−	0.974928i
$135$	−0.801938			−0.801938
$136$		0			0
$137$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$137$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$138$	0.722521	−	0.347948i	0.722521	−	0.347948i
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$141$	0.198062	−	0.867767i	0.198062	−	0.867767i
$142$		0			0
$143$		0			0
$144$	0.722521	+	0.347948i	0.722521	+	0.347948i
$145$	0.777479	+	0.974928i	0.777479	+	0.974928i
$146$		0			0
$147$	0.0794168	+	0.347948i	0.0794168	+	0.347948i
$148$		0			0
$149$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$149$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$150$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$151$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$151$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$157$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$158$		0			0
$159$		0			0
$160$	0.222521	−	0.974928i	0.222521	−	0.974928i
$161$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$162$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$163$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$163$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$164$	0.777479	−	0.974928i	0.777479	−	0.974928i
$165$		0			0
$166$	−0.445042			−0.445042
$167$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$167$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$168$	0.178448	+	0.0859360i	0.178448	+	0.0859360i
$169$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$170$		0			0
$171$		0			0
$172$	0.222521	+	0.974928i	0.222521	+	0.974928i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	0.123490	−	0.541044i	0.123490	−	0.541044i
$175$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$176$		0			0
$177$		0			0
$178$	1.80194			1.80194
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$181$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$181$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$184$	0.400969	−	1.75676i	0.400969	−	1.75676i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$189$	−0.222521	−	0.279032i	−0.222521	−	0.279032i
$190$		0			0
$191$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$191$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$192$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$193$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$193$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$194$		0			0
$195$		0			0
$196$	0.722521	+	0.347948i	0.722521	+	0.347948i
$197$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$197$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$198$		0			0
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	0.900969	+	0.433884i	0.900969	+	0.433884i
$201$	0.123490	−	0.541044i	0.123490	−	0.541044i
$202$	0.277479	−	0.347948i	0.277479	−	0.347948i
$203$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$204$		0			0
$205$	0.777479	+	0.974928i	0.777479	+	0.974928i
$206$	1.62349	−	0.781831i	1.62349	−	0.781831i
$207$	−0.900969	+	1.12978i	−0.900969	+	1.12978i
$208$		0			0
$209$		0			0
$210$	−0.123490	+	0.154851i	−0.123490	+	0.154851i
$211$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$211$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$212$		0			0
$213$		0			0
$214$	−1.80194			−1.80194
$215$	−1.00000			−1.00000
$216$	0.801938			0.801938
$217$		0			0
$218$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$223$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$224$	0.400969	−	0.193096i	0.400969	−	0.193096i
$225$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$226$		0			0
$227$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$227$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$228$		0			0
$229$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$229$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$230$	1.62349	+	0.781831i	1.62349	+	0.781831i
$231$		0			0
$232$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$233$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$233$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$234$		0			0
$235$	1.80194	−	0.867767i	1.80194	−	0.867767i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$241$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$241$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$242$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$243$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$244$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$245$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$246$	0.123490	−	0.541044i	0.123490	−	0.541044i
$247$		0			0
$248$		0			0
$249$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$250$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	−0.356896			−0.356896
$253$		0			0
$254$	0.400969	+	0.193096i	0.400969	+	0.193096i
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	0.277479	+	0.347948i	0.277479	+	0.347948i
$259$		0			0
$260$		0			0
$261$	0.222521	+	0.974928i	0.222521	+	0.974928i
$262$		0			0
$263$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$263$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.722521	−	0.347948i	0.722521	−	0.347948i
$268$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$269$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$269$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$270$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$271$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$271$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$277$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$277$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$278$		0			0
$279$		0			0
$280$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$281$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$281$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$282$	−0.801938	−	0.386193i	−0.801938	−	0.386193i
$283$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$283$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$288$	0.500000	−	0.626980i	0.500000	−	0.626980i
$289$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$290$	1.12349	−	0.541044i	1.12349	−	0.541044i
$291$		0			0
$292$		0			0
$293$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$293$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$294$	0.356896			0.356896
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.445042	+	1.94986i	0.445042	+	1.94986i
$299$		0			0
$300$	0.445042			0.445042
$301$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$302$		0			0
$303$	0.0440730	−	0.193096i	0.0440730	−	0.193096i
$304$		0			0
$305$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$306$		0			0
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$308$		0			0
$309$	0.500000	−	0.626980i	0.500000	−	0.626980i
$310$		0			0
$311$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$311$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$312$		0			0
$313$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$313$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$314$		0			0
$315$	0.0794168	−	0.347948i	0.0794168	−	0.347948i
$316$		0			0
$317$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$317$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$318$		0			0
$319$		0			0
$320$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$321$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$322$	0.178448	+	0.781831i	0.178448	+	0.781831i
$323$		0			0
$324$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$325$		0			0
$326$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$327$	−0.123490	−	0.154851i	−0.123490	−	0.154851i
$328$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$329$	0.801938	+	0.386193i	0.801938	+	0.386193i
$330$		0			0
$331$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$331$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$332$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$333$		0			0
$334$	0.777479	+	0.974928i	0.777479	+	0.974928i
$335$	1.12349	−	0.541044i	1.12349	−	0.541044i
$336$	0.123490	−	0.154851i	0.123490	−	0.154851i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−1.00000			−1.00000
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.801938			−0.801938
$344$	1.00000			1.00000
$345$	0.801938			0.801938
$346$		0			0
$347$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$347$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$348$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$349$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$349$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$350$	−0.445042			−0.445042
$351$		0			0
$352$		0			0
$353$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$353$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$354$		0			0
$355$		0			0
$356$	0.400969	−	1.75676i	0.400969	−	1.75676i
$357$		0			0
$358$		0			0
$359$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$359$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$360$	0.500000	+	0.626980i	0.500000	+	0.626980i
$361$	0.623490	+	0.781831i	0.623490	+	0.781831i
$362$	0.277479	+	1.21572i	0.277479	+	1.21572i
$363$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$364$		0			0
$365$		0			0
$366$	0.123490	+	0.541044i	0.123490	+	0.541044i
$367$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$367$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$368$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$369$	0.222521	+	0.974928i	0.222521	+	0.974928i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$373$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$374$		0			0
$375$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$376$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$377$		0			0
$378$	−0.321552	+	0.154851i	−0.321552	+	0.154851i
$379$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$379$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$380$		0			0
$381$	0.198062			0.198062
$382$		0			0
$383$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$383$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$384$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$385$		0			0
$386$		0			0
$387$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$388$		0			0
$389$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$389$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$390$		0			0
$391$		0			0
$392$	0.500000	−	0.626980i	0.500000	−	0.626980i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$397$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$398$		0			0
$399$		0			0
$400$	0.623490	−	0.781831i	0.623490	−	0.781831i
$401$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$401$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$402$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$403$		0			0
$404$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$405$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$406$	0.500000	+	0.240787i	0.500000	+	0.240787i
$407$		0			0
$408$		0			0
$409$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$409$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$410$	1.12349	−	0.541044i	1.12349	−	0.541044i
$411$		0			0
$412$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$413$		0			0
$414$	0.900969	+	1.12978i	0.900969	+	1.12978i
$415$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$	0.123490	+	0.154851i	0.123490	+	0.154851i
$421$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$421$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$422$		0			0
$423$	1.60388			1.60388
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$428$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$429$		0			0
$430$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	0.178448	−	0.781831i	0.178448	−	0.781831i
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$		0			0
$435$	0.346011	−	0.433884i	0.346011	−	0.433884i
$436$	−0.445042			−0.445042
$437$		0			0
$438$		0			0
$439$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$439$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$440$		0			0
$441$	−0.579417	+	0.279032i	−0.579417	+	0.279032i
$442$		0			0
$443$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$443$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$444$		0			0
$445$	1.62349	+	0.781831i	1.62349	+	0.781831i
$446$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$447$	0.554958	+	0.695895i	0.554958	+	0.695895i
$448$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$449$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$449$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$450$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$455$		0			0
$456$		0			0
$457$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$457$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$458$	1.12349	+	0.541044i	1.12349	+	0.541044i
$459$		0			0
$460$	1.12349	−	1.40881i	1.12349	−	1.40881i
$461$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$461$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$462$		0			0
$463$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$463$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$464$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$465$		0			0
$466$		0			0
$467$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$467$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$468$		0			0
$469$	0.500000	+	0.240787i	0.500000	+	0.240787i
$470$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$	−0.445042			−0.445042
$481$		0			0
$482$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$483$	0.222521	+	0.279032i	0.222521	+	0.279032i
$484$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$485$		0			0
$486$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$487$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$487$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$488$	1.12349	+	0.541044i	1.12349	+	0.541044i
$489$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$490$	0.500000	+	0.626980i	0.500000	+	0.626980i
$491$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$491$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$492$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0440730	+	0.193096i	0.0440730	+	0.193096i
$499$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$499$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$500$	0.623490	+	0.781831i	0.623490	+	0.781831i
$501$	0.500000	+	0.240787i	0.500000	+	0.240787i
$502$		0			0
$503$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$503$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$504$	−0.0794168	+	0.347948i	−0.0794168	+	0.347948i
$505$	0.400969	−	0.193096i	0.400969	−	0.193096i
$506$		0			0
$507$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$508$	0.277479	−	0.347948i	0.277479	−	0.347948i
$509$	2.00000			2.00000			1.00000			$0$
$509$	2.00000			2.00000			1.00000			$0$
$510$		0			0
$511$		0			0
$512$	0.900969	+	0.433884i	0.900969	+	0.433884i
$513$		0			0
$514$		0			0
$515$	1.80194			1.80194
$516$	0.400969	−	0.193096i	0.400969	−	0.193096i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$521$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$522$	1.00000			1.00000
$523$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$523$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$524$		0			0
$525$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$526$	0.777479	+	0.974928i	0.777479	+	0.974928i
$527$		0			0
$528$		0			0
$529$	1.40097	−	1.75676i	1.40097	−	1.75676i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$535$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$536$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$537$		0			0
$538$	0.277479	+	1.21572i	0.277479	+	1.21572i
$539$		0			0
$540$	0.722521	+	0.347948i	0.722521	+	0.347948i
$541$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$541$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$542$		0			0
$543$	0.346011	+	0.433884i	0.346011	+	0.433884i
$544$		0			0
$545$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$546$		0			0
$547$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$547$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$548$		0			0
$549$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$550$		0			0
$551$		0			0
$552$	−0.801938			−0.801938
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$557$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$558$		0			0
$559$		0			0
$560$	0.445042			0.445042
$561$		0			0
$562$	0.277479	+	1.21572i	0.277479	+	1.21572i
$563$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$563$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$564$	−0.554958	+	0.695895i	−0.554958	+	0.695895i
$565$		0			0
$566$	1.24698			1.24698
$567$	0.123490	−	0.154851i	0.123490	−	0.154851i
$568$		0			0
$569$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$569$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$570$		0			0
$571$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$571$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$572$		0			0
$573$		0			0
$574$	0.500000	+	0.240787i	0.500000	+	0.240787i
$575$	1.12349	+	1.40881i	1.12349	+	1.40881i
$576$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$577$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$577$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$578$	0.900969	+	0.433884i	0.900969	+	0.433884i
$579$		0			0
$580$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$581$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$587$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$588$	0.0794168	−	0.347948i	0.0794168	−	0.347948i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$593$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$594$		0			0
$595$		0			0
$596$	2.00000			2.00000
$597$		0			0
$598$		0			0
$599$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$599$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$600$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$601$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$601$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$602$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$603$	1.00000			1.00000
$604$		0			0
$605$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$606$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$607$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$607$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$608$		0			0
$609$	0.246980			0.246980
$610$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$611$		0			0
$612$		0			0
$613$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$613$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$614$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$615$	0.346011	−	0.433884i	0.346011	−	0.433884i
$616$		0			0
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$619$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$619$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$620$		0			0
$621$	1.30194	+	0.626980i	1.30194	+	0.626980i
$622$		0			0
$623$	0.178448	+	0.781831i	0.178448	+	0.781831i
$624$		0			0
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.321552	−	0.154851i	−0.321552	−	0.154851i
$631$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$631$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.277479	+	0.347948i	0.277479	+	0.347948i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$641$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$641$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$642$	0.178448	+	0.781831i	0.178448	+	0.781831i
$643$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$643$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$644$	0.801938			0.801938
$645$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$646$		0			0
$647$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$647$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$648$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.24698			−1.24698
$653$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$653$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$654$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$655$		0			0
$656$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$657$		0			0
$658$	0.554958	−	0.695895i	0.554958	−	0.695895i
$659$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$659$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$660$		0			0
$661$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$661$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$662$		0			0
$663$		0			0
$664$	0.400969	+	0.193096i	0.400969	+	0.193096i
$665$		0			0
$666$		0			0
$667$	−0.500000	−	2.19064i	−0.500000	−	2.19064i
$668$	1.12349	−	0.541044i	1.12349	−	0.541044i
$669$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$670$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$671$		0			0
$672$	−0.123490	−	0.154851i	−0.123490	−	0.154851i
$673$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$673$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$674$		0			0
$675$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$676$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$677$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$677$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.890084			−0.890084
$682$		0			0
$683$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$683$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$687$	0.554958			0.554958
$688$	0.222521	−	0.974928i	0.222521	−	0.974928i
$689$		0			0
$690$	0.178448	−	0.781831i	0.178448	−	0.781831i
$691$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$691$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$692$		0			0
$693$		0			0
$694$	−1.80194			−1.80194
$695$		0			0
$696$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$697$		0			0
$698$	0.277479	+	0.347948i	0.277479	+	0.347948i
$699$		0			0
$700$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$701$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$701$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.554958	−	0.695895i	−0.554958	−	0.695895i
$706$		0			0
$707$	0.178448	+	0.0859360i	0.178448	+	0.0859360i
$708$		0			0
$709$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$709$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$710$		0			0
$711$		0			0
$712$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$719$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$720$	0.722521	−	0.347948i	0.722521	−	0.347948i
$721$	0.500000	+	0.626980i	0.500000	+	0.626980i
$722$	0.900969	−	0.433884i	0.900969	−	0.433884i
$723$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$724$	1.24698			1.24698
$725$	1.24698			1.24698
$726$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$727$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$727$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$	0.554958			0.554958
$733$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$733$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$734$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$735$	0.321552	+	0.154851i	0.321552	+	0.154851i
$736$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$737$		0			0
$738$	1.00000			1.00000
$739$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$739$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$743$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$744$		0			0
$745$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$746$		0			0
$747$	−0.222521	−	0.279032i	−0.222521	−	0.279032i
$748$		0			0
$749$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$750$	0.400969	+	0.193096i	0.400969	+	0.193096i
$751$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$751$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$752$	0.445042	+	1.94986i	0.445042	+	1.94986i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.0794168	+	0.347948i	0.0794168	+	0.347948i
$757$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$757$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$761$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$762$	0.0440730	−	0.193096i	0.0440730	−	0.193096i
$763$	0.178448	−	0.0859360i	0.178448	−	0.0859360i
$764$		0			0
$765$		0			0
$766$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$767$		0			0
$768$	0.445042			0.445042
$769$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$769$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.900969	−	0.433884i	0.900969	−	0.433884i
$784$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$785$		0			0
$786$		0			0
$787$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$787$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$788$		0			0
$789$	0.500000	+	0.240787i	0.500000	+	0.240787i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$797$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$798$		0			0
$799$		0			0
$800$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$801$	0.900969	+	1.12978i	0.900969	+	1.12978i
$802$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$803$		0			0
$804$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$805$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$806$		0			0
$807$	0.346011	+	0.433884i	0.346011	+	0.433884i
$808$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$809$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$809$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$810$	−0.445042			−0.445042
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.346011	−	0.433884i	0.346011	−	0.433884i
$813$		0			0
$814$		0			0
$815$	0.277479	−	1.21572i	0.277479	−	1.21572i
$816$		0			0
$817$		0			0
$818$	0.445042			0.445042
$819$		0			0
$820$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$821$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$821$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$822$		0			0
$823$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$823$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$824$	−1.80194			−1.80194
$825$		0			0
$826$		0			0
$827$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$827$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	−1.00000			$\pi$
$828$	1.30194	−	0.626980i	1.30194	−	0.626980i
$829$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$829$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$830$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.277479	+	1.21572i	0.277479	+	1.21572i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$839$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$840$	0.178448	−	0.0859360i	0.178448	−	0.0859360i
$841$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$842$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$843$	0.346011	+	0.433884i	0.346011	+	0.433884i
$844$		0			0
$845$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$846$	0.356896	−	1.56366i	0.356896	−	1.56366i
$847$	0.277479	−	0.347948i	0.277479	−	0.347948i
$848$		0			0
$849$	0.500000	−	0.240787i	0.500000	−	0.240787i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	−0.554958			−0.554958
$855$		0			0
$856$	1.62349	+	0.781831i	1.62349	+	0.781831i
$857$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$857$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	0.900969	+	0.433884i	0.900969	+	0.433884i
$861$	0.246980			0.246980
$862$		0			0
$863$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$863$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$864$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$865$		0			0
$866$		0			0
$867$	0.445042			0.445042
$868$		0			0
$869$		0			0
$870$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$871$		0			0
$872$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$873$		0			0
$874$		0			0
$875$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$876$		0			0
$877$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$877$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$881$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$882$	0.143104	+	0.626980i	0.143104	+	0.626980i
$883$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$883$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$884$		0			0
$885$		0			0
$886$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$887$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$887$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$888$		0			0
$889$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$890$	1.12349	−	1.40881i	1.12349	−	1.40881i
$891$		0			0
$892$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$893$		0			0
$894$	0.801938	−	0.386193i	0.801938	−	0.386193i
$895$		0			0
$896$	−0.445042			−0.445042
$897$		0			0
$898$	0.277479	−	0.347948i	0.277479	−	0.347948i
$899$		0			0
$900$	0.178448	+	0.781831i	0.178448	+	0.781831i
$901$		0			0
$902$		0			0
$903$	−0.123490	+	0.154851i	−0.123490	+	0.154851i
$904$		0			0
$905$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$906$		0			0
$907$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$907$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$908$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$909$	0.356896			0.356896
$910$		0			0
$911$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$911$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$916$	0.777479	−	0.974928i	0.777479	−	0.974928i
$917$		0			0
$918$		0			0
$919$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$919$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$920$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$921$	0.198062	+	0.867767i	0.198062	+	0.867767i
$922$	1.12349	+	0.541044i	1.12349	+	0.541044i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$927$	1.30194	+	0.626980i	1.30194	+	0.626980i
$928$	0.277479	+	1.21572i	0.277479	+	1.21572i
$929$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$929$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$935$		0			0
$936$		0			0
$937$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$937$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$938$	0.346011	−	0.433884i	0.346011	−	0.433884i
$939$		0			0
$940$	−2.00000			−2.00000
$941$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$941$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$	−0.500000	−	2.19064i	−0.500000	−	2.19064i
$944$		0			0
$945$	−0.356896			−0.356896
$946$		0			0
$947$	−2.00000			−2.00000			−1.00000			$\pi$
$947$	−2.00000			−2.00000			−1.00000			$\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$961$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$962$		0			0
$963$	−0.900969	−	1.12978i	−0.900969	−	1.12978i
$964$	0.400969	+	1.75676i	0.400969	+	1.75676i
$965$		0			0
$966$	0.321552	−	0.154851i	0.321552	−	0.154851i
$967$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$967$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$968$	0.222521	+	0.974928i	0.222521	+	0.974928i
$969$		0			0
$970$		0			0
$971$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$971$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$972$	0.623490	+	0.781831i	0.623490	+	0.781831i
$973$		0			0
$974$	1.62349	+	0.781831i	1.62349	+	0.781831i
$975$		0			0
$976$	0.777479	−	0.974928i	0.777479	−	0.974928i
$977$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$977$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$978$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$979$		0			0
$980$	0.722521	−	0.347948i	0.722521	−	0.347948i
$981$	0.222521	−	0.279032i	0.222521	−	0.279032i
$982$		0			0
$983$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$983$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$984$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$985$		0			0
$986$		0			0
$987$	0.0881460	−	0.386193i	0.0881460	−	0.386193i
$988$		0			0
$989$	1.62349	+	0.781831i	1.62349	+	0.781831i
$990$		0			0
$991$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$991$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.198062			0.198062
$997$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$997$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	860.1.bb.b.379.1	yes	6
4.3	odd	2		860.1.bb.a.379.1	yes	6
5.4	even	2		860.1.bb.a.379.1	yes	6
20.19	odd	2	CM	860.1.bb.b.379.1	yes	6
43.16	even	7	inner	860.1.bb.b.59.1	yes	6
172.59	odd	14		860.1.bb.a.59.1	✓	6
215.59	even	14		860.1.bb.a.59.1	✓	6
860.59	odd	14	inner	860.1.bb.b.59.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
860.1.bb.a.59.1	✓	6	172.59	odd	14
860.1.bb.a.59.1	✓	6	215.59	even	14
860.1.bb.a.379.1	yes	6	4.3	odd	2
860.1.bb.a.379.1	yes	6	5.4	even	2
860.1.bb.b.59.1	yes	6	43.16	even	7	inner
860.1.bb.b.59.1	yes	6	860.59	odd	14	inner
860.1.bb.b.379.1	yes	6	1.1	even	1	trivial
860.1.bb.b.379.1	yes	6	20.19	odd	2	CM

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:	\( N \)	\(=\)	\( 860 = 2^{2} \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	860.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -0.445042 q^{6} +0.445042 q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.722521 - 0.347948i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -0.445042 q^{6} +0.445042 q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.722521 - 0.347948i) q^{9} +(-0.623490 - 0.781831i) q^{10} +(-0.0990311 + 0.433884i) q^{12} +(0.0990311 - 0.433884i) q^{14} +(-0.400969 - 0.193096i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-0.178448 - 0.781831i) q^{18} +(-0.900969 + 0.433884i) q^{20} +(-0.0440730 - 0.193096i) q^{21} +(-1.62349 + 0.781831i) q^{23} +(0.400969 + 0.193096i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.500000 - 0.626980i) q^{27} +(-0.400969 - 0.193096i) q^{28} +(-0.277479 + 1.21572i) q^{29} +(-0.277479 + 0.347948i) q^{30} +(0.900969 - 0.433884i) q^{32} +(0.277479 - 0.347948i) q^{35} -0.801938 q^{36} +(0.222521 + 0.974928i) q^{40} +(-0.277479 + 1.21572i) q^{41} -0.198062 q^{42} +(-0.623490 - 0.781831i) q^{43} +(0.178448 - 0.781831i) q^{45} +(0.400969 + 1.75676i) q^{46} +(1.80194 + 0.867767i) q^{47} +(0.277479 - 0.347948i) q^{48} -0.801938 q^{49} -1.00000 q^{50} +(-0.722521 + 0.347948i) q^{54} +(-0.277479 + 0.347948i) q^{56} +(1.12349 + 0.541044i) q^{58} +(0.277479 + 0.347948i) q^{60} +(-0.277479 - 1.21572i) q^{61} +(0.321552 - 0.154851i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(1.12349 + 0.541044i) q^{67} +(0.500000 + 0.626980i) q^{69} +(-0.277479 - 0.347948i) q^{70} +(-0.178448 + 0.781831i) q^{72} +(-0.400969 + 0.193096i) q^{75} +1.00000 q^{80} +(0.277479 - 0.347948i) q^{81} +(1.12349 + 0.541044i) q^{82} +(-0.0990311 - 0.433884i) q^{83} +(-0.0440730 + 0.193096i) q^{84} +(-0.900969 + 0.433884i) q^{86} +0.554958 q^{87} +(0.400969 + 1.75676i) q^{89} +(-0.722521 - 0.347948i) q^{90} +1.80194 q^{92} +(1.24698 - 1.56366i) q^{94} +(-0.277479 - 0.347948i) q^{96} +(-0.178448 + 0.781831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 5 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q + q^2 - 5 * q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^7 + q^8 + 4 * q^9	\( 6 q + q^{2} - 5 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} + 4 q^{9} + q^{10} - 5 q^{12} + 5 q^{14} + 2 q^{15} - q^{16} + 3 q^{18} - q^{20} - 4 q^{21} - 5 q^{23} - 2 q^{24} - q^{25} - 3 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} + q^{32} + 2 q^{35} + 4 q^{36} + q^{40} - 2 q^{41} - 10 q^{42} + q^{43} - 3 q^{45} - 2 q^{46} + 2 q^{47} + 2 q^{48} + 4 q^{49} - 6 q^{50} - 4 q^{54} - 2 q^{56} + 2 q^{58} + 2 q^{60} - 2 q^{61} + 6 q^{63} - q^{64} + 2 q^{67} + 3 q^{69} - 2 q^{70} + 3 q^{72} + 2 q^{75} + 6 q^{80} + 2 q^{81} + 2 q^{82} - 5 q^{83} - 4 q^{84} - q^{86} + 4 q^{87} - 2 q^{89} - 4 q^{90} + 2 q^{92} - 2 q^{94} - 2 q^{96} + 3 q^{98}+O(q^{100}) \) 6 * q + q^2 - 5 * q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^7 + q^8 + 4 * q^9 + q^10 - 5 * q^12 + 5 * q^14 + 2 * q^15 - q^16 + 3 * q^18 - q^20 - 4 * q^21 - 5 * q^23 - 2 * q^24 - q^25 - 3 * q^27 + 2 * q^28 - 2 * q^29 - 2 * q^30 + q^32 + 2 * q^35 + 4 * q^36 + q^40 - 2 * q^41 - 10 * q^42 + q^43 - 3 * q^45 - 2 * q^46 + 2 * q^47 + 2 * q^48 + 4 * q^49 - 6 * q^50 - 4 * q^54 - 2 * q^56 + 2 * q^58 + 2 * q^60 - 2 * q^61 + 6 * q^63 - q^64 + 2 * q^67 + 3 * q^69 - 2 * q^70 + 3 * q^72 + 2 * q^75 + 6 * q^80 + 2 * q^81 + 2 * q^82 - 5 * q^83 - 4 * q^84 - q^86 + 4 * q^87 - 2 * q^89 - 4 * q^90 + 2 * q^92 - 2 * q^94 - 2 * q^96 + 3 * q^98

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