LMFDB - Embedded newform 1176.1.bj.b.1037.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,1,Mod(29,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 7, 7, 6]))

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

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

chi := DirichletCharacter("1176.29");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1176.bj (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:	$0.586900454856$
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 7.1.191341954266624.2

Embedding invariants

Embedding label			1037.1
Root			$0.222521 + 0.974928i$ of defining polynomial
Character	$\chi$	$=$	1176.1037
Dual form			1176.1.bj.b.533.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 - 0.781831i) q^{2} +(0.900969 - 0.433884i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(1.12349 - 0.541044i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(-0.900969 - 0.433884i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.623490 - 0.781831i) q^{2} +(0.900969 - 0.433884i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(1.12349 - 0.541044i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(-0.900969 - 0.433884i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-1.12349 - 0.541044i) q^{10} +(0.277479 + 0.347948i) q^{11} +(0.222521 + 0.974928i) q^{12} +(0.222521 + 0.974928i) q^{14} +(0.777479 - 0.974928i) q^{15} +(-0.900969 - 0.433884i) q^{16} -1.00000 q^{18} +(0.277479 + 1.21572i) q^{20} -1.00000 q^{21} +(0.0990311 - 0.433884i) q^{22} +(0.623490 - 0.781831i) q^{24} +(0.346011 - 0.433884i) q^{25} +(0.222521 - 0.974928i) q^{27} +(0.623490 - 0.781831i) q^{28} +(0.277479 + 1.21572i) q^{29} -1.24698 q^{30} -1.80194 q^{31} +(0.222521 + 0.974928i) q^{32} +(0.400969 + 0.193096i) q^{33} -1.24698 q^{35} +(0.623490 + 0.781831i) q^{36} +(0.777479 - 0.974928i) q^{40} +(0.623490 + 0.781831i) q^{42} +(-0.400969 + 0.193096i) q^{44} +(0.277479 - 1.21572i) q^{45} -1.00000 q^{48} +(0.623490 + 0.781831i) q^{49} -0.554958 q^{50} +(0.445042 - 1.94986i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(0.500000 + 0.240787i) q^{55} -1.00000 q^{56} +(0.777479 - 0.974928i) q^{58} +(1.80194 + 0.867767i) q^{59} +(0.777479 + 0.974928i) q^{60} +(1.12349 + 1.40881i) q^{62} +(-0.900969 + 0.433884i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.0990311 - 0.433884i) q^{66} +(0.777479 + 0.974928i) q^{70} +(0.222521 - 0.974928i) q^{72} +(-1.12349 + 1.40881i) q^{73} +(0.123490 - 0.541044i) q^{75} +(-0.0990311 - 0.433884i) q^{77} -1.80194 q^{79} -1.24698 q^{80} +(-0.222521 - 0.974928i) q^{81} +(-0.777479 + 0.974928i) q^{83} +(0.222521 - 0.974928i) q^{84} +(0.777479 + 0.974928i) q^{87} +(0.400969 + 0.193096i) q^{88} +(-1.12349 + 0.541044i) q^{90} +(-1.62349 + 0.781831i) q^{93} +(0.623490 + 0.781831i) q^{96} -0.445042 q^{97} +(0.222521 - 0.974928i) q^{98} +0.445042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 6 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 - q^7 + q^8 - q^9	$ 6 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - q^{7} + q^{8} - q^{9} - 2 q^{10} + 2 q^{11} + q^{12} + q^{14} + 5 q^{15} - q^{16} - 6 q^{18} + 2 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} - 3 q^{25} + q^{27} - q^{28} + 2 q^{29} + 2 q^{30} - 2 q^{31} + q^{32} - 2 q^{33} + 2 q^{35} - q^{36} + 5 q^{40} - q^{42} + 2 q^{44} + 2 q^{45} - 6 q^{48} - q^{49} - 4 q^{50} + 2 q^{53} - q^{54} + 3 q^{55} - 6 q^{56} + 5 q^{58} + 2 q^{59} + 5 q^{60} + 2 q^{62} - q^{63} - q^{64} - 5 q^{66} + 5 q^{70} + q^{72} - 2 q^{73} - 4 q^{75} - 5 q^{77} - 2 q^{79} + 2 q^{80} - q^{81} - 5 q^{83} + q^{84} + 5 q^{87} - 2 q^{88} - 2 q^{90} - 5 q^{93} - q^{96} - 2 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 - q^7 + q^8 - q^9 - 2 * q^10 + 2 * q^11 + q^12 + q^14 + 5 * q^15 - q^16 - 6 * q^18 + 2 * q^20 - 6 * q^21 + 5 * q^22 - q^24 - 3 * q^25 + q^27 - q^28 + 2 * q^29 + 2 * q^30 - 2 * q^31 + q^32 - 2 * q^33 + 2 * q^35 - q^36 + 5 * q^40 - q^42 + 2 * q^44 + 2 * q^45 - 6 * q^48 - q^49 - 4 * q^50 + 2 * q^53 - q^54 + 3 * q^55 - 6 * q^56 + 5 * q^58 + 2 * q^59 + 5 * q^60 + 2 * q^62 - q^63 - q^64 - 5 * q^66 + 5 * q^70 + q^72 - 2 * q^73 - 4 * q^75 - 5 * q^77 - 2 * q^79 + 2 * q^80 - q^81 - 5 * q^83 + q^84 + 5 * q^87 - 2 * q^88 - 2 * q^90 - 5 * q^93 - q^96 - 2 * q^97 + q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$2$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$3$	0.900969	−	0.433884i	0.900969	−	0.433884i
$3$	0.900969	−	0.433884i	0.900969	−	0.433884i
$4$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$5$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$5$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$6$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$7$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$7$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$8$	0.900969	−	0.433884i	0.900969	−	0.433884i
$9$	0.623490	−	0.781831i	0.623490	−	0.781831i
$10$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$11$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$11$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$12$	0.222521	+	0.974928i	0.222521	+	0.974928i
$13$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$13$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$14$	0.222521	+	0.974928i	0.222521	+	0.974928i
$15$	0.777479	−	0.974928i	0.777479	−	0.974928i
$16$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$17$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$17$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$18$	−1.00000			−1.00000
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	0.277479	+	1.21572i	0.277479	+	1.21572i
$21$	−1.00000			−1.00000
$22$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$23$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$23$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$24$	0.623490	−	0.781831i	0.623490	−	0.781831i
$25$	0.346011	−	0.433884i	0.346011	−	0.433884i
$26$		0			0
$27$	0.222521	−	0.974928i	0.222521	−	0.974928i
$28$	0.623490	−	0.781831i	0.623490	−	0.781831i
$29$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$29$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$30$	−1.24698			−1.24698
$31$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$31$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$32$	0.222521	+	0.974928i	0.222521	+	0.974928i
$33$	0.400969	+	0.193096i	0.400969	+	0.193096i
$34$		0			0
$35$	−1.24698			−1.24698
$36$	0.623490	+	0.781831i	0.623490	+	0.781831i
$37$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$37$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$38$		0			0
$39$		0			0
$40$	0.777479	−	0.974928i	0.777479	−	0.974928i
$41$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$41$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$42$	0.623490	+	0.781831i	0.623490	+	0.781831i
$43$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$43$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$44$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$45$	0.277479	−	1.21572i	0.277479	−	1.21572i
$46$		0			0
$47$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$47$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$48$	−1.00000			−1.00000
$49$	0.623490	+	0.781831i	0.623490	+	0.781831i
$50$	−0.554958			−0.554958
$51$		0			0
$52$		0			0
$53$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$53$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$54$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$55$	0.500000	+	0.240787i	0.500000	+	0.240787i
$56$	−1.00000			−1.00000
$57$		0			0
$58$	0.777479	−	0.974928i	0.777479	−	0.974928i
$59$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$59$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$60$	0.777479	+	0.974928i	0.777479	+	0.974928i
$61$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$61$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$62$	1.12349	+	1.40881i	1.12349	+	1.40881i
$63$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$64$	0.623490	−	0.781831i	0.623490	−	0.781831i
$65$		0			0
$66$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$	0.777479	+	0.974928i	0.777479	+	0.974928i
$71$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$71$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$72$	0.222521	−	0.974928i	0.222521	−	0.974928i
$73$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$73$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$74$		0			0
$75$	0.123490	−	0.541044i	0.123490	−	0.541044i
$76$		0			0
$77$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$78$		0			0
$79$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$79$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$80$	−1.24698			−1.24698
$81$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$82$		0			0
$83$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$83$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$84$	0.222521	−	0.974928i	0.222521	−	0.974928i
$85$		0			0
$86$		0			0
$87$	0.777479	+	0.974928i	0.777479	+	0.974928i
$88$	0.400969	+	0.193096i	0.400969	+	0.193096i
$89$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$89$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$90$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$91$		0			0
$92$		0			0
$93$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$94$		0			0
$95$		0			0
$96$	0.623490	+	0.781831i	0.623490	+	0.781831i
$97$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$97$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$98$	0.222521	−	0.974928i	0.222521	−	0.974928i
$99$	0.445042			0.445042
$100$	0.346011	+	0.433884i	0.346011	+	0.433884i
$101$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$101$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$102$		0			0
$103$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$103$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$104$		0			0
$105$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$106$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$107$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$107$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$108$	0.900969	+	0.433884i	0.900969	+	0.433884i
$109$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$109$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$110$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$111$		0			0
$112$	0.623490	+	0.781831i	0.623490	+	0.781831i
$113$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$113$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$114$		0			0
$115$		0			0
$116$	−1.24698			−1.24698
$117$		0			0
$118$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$119$		0			0
$120$	0.277479	−	1.21572i	0.277479	−	1.21572i
$121$	0.178448	−	0.781831i	0.178448	−	0.781831i
$122$		0			0
$123$		0			0
$124$	0.400969	−	1.75676i	0.400969	−	1.75676i
$125$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$126$	0.900969	+	0.433884i	0.900969	+	0.433884i
$127$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$127$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$128$	−1.00000			−1.00000
$129$		0			0
$130$		0			0
$131$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$131$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$132$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$133$		0			0
$134$		0			0
$135$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$136$		0			0
$137$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$137$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$138$		0			0
$139$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$139$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$140$	0.277479	−	1.21572i	0.277479	−	1.21572i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$145$	0.969501	+	1.21572i	0.969501	+	1.21572i
$146$	1.80194			1.80194
$147$	0.900969	+	0.433884i	0.900969	+	0.433884i
$148$		0			0
$149$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$149$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$150$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$151$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$151$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$152$		0			0
$153$		0			0
$154$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$155$	−2.02446	+	0.974928i	−2.02446	+	0.974928i
$156$		0			0
$157$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$157$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$158$	1.12349	+	1.40881i	1.12349	+	1.40881i
$159$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$160$	0.777479	+	0.974928i	0.777479	+	0.974928i
$161$		0			0
$162$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$163$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$163$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$164$		0			0
$165$	0.554958			0.554958
$166$	1.24698			1.24698
$167$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$167$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$168$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$169$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$173$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$174$	0.277479	−	1.21572i	0.277479	−	1.21572i
$175$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$176$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$177$	2.00000			2.00000
$178$		0			0
$179$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$179$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$180$	1.12349	+	0.541044i	1.12349	+	0.541044i
$181$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$181$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	1.62349	+	0.781831i	1.62349	+	0.781831i
$187$		0			0
$188$		0			0
$189$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$190$		0			0
$191$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$191$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$192$	0.222521	−	0.974928i	0.222521	−	0.974928i
$193$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$193$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$194$	0.277479	+	0.347948i	0.277479	+	0.347948i
$195$		0			0
$196$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$197$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$197$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$198$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$199$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$199$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$200$	0.123490	−	0.541044i	0.123490	−	0.541044i
$201$		0			0
$202$	0.400969	+	0.193096i	0.400969	+	0.193096i
$203$	0.277479	−	1.21572i	0.277479	−	1.21572i
$204$		0			0
$205$		0			0
$206$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	1.12349	+	0.541044i	1.12349	+	0.541044i
$211$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$211$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$212$	1.80194	+	0.867767i	1.80194	+	0.867767i
$213$		0			0
$214$	−1.80194			−1.80194
$215$		0			0
$216$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$217$	1.62349	+	0.781831i	1.62349	+	0.781831i
$218$		0			0
$219$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$220$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$221$		0			0
$222$		0			0
$223$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$223$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$224$	0.222521	−	0.974928i	0.222521	−	0.974928i
$225$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$226$		0			0
$227$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$227$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$228$		0			0
$229$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$229$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$230$		0			0
$231$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$232$	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
$235$		0			0
$236$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$237$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$238$		0			0
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$241$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$241$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$242$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$243$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$244$		0			0
$245$	1.12349	+	0.541044i	1.12349	+	0.541044i
$246$		0			0
$247$		0			0
$248$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$249$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$250$	0.500000	−	0.240787i	0.500000	−	0.240787i
$251$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$251$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$252$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$253$		0			0
$254$	1.12349	−	1.40881i	1.12349	−	1.40881i
$255$		0			0
$256$	0.623490	+	0.781831i	0.623490	+	0.781831i
$257$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$257$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.12349	+	0.541044i	1.12349	+	0.541044i
$262$	0.400969	+	1.75676i	0.400969	+	1.75676i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	0.445042			0.445042
$265$	−0.554958	−	2.43143i	−0.554958	−	2.43143i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$269$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$270$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$271$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$271$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.246980			0.246980
$276$		0			0
$277$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$277$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$278$		0			0
$279$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$280$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$281$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$281$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$282$		0			0
$283$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$283$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.900969	+	0.433884i	0.900969	+	0.433884i
$289$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$290$	0.346011	−	1.51597i	0.346011	−	1.51597i
$291$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$292$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$293$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$293$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$294$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$295$	2.49396			2.49396
$296$		0			0
$297$	0.400969	−	0.193096i	0.400969	−	0.193096i
$298$	0.400969	−	1.75676i	0.400969	−	1.75676i
$299$		0			0
$300$	0.500000	+	0.240787i	0.500000	+	0.240787i
$301$		0			0
$302$	1.80194	−	0.867767i	1.80194	−	0.867767i
$303$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$307$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$308$	0.445042			0.445042
$309$	0.277479	−	0.347948i	0.277479	−	0.347948i
$310$	2.02446	+	0.974928i	2.02446	+	0.974928i
$311$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$311$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$312$		0			0
$313$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$313$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$314$		0			0
$315$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$316$	0.400969	−	1.75676i	0.400969	−	1.75676i
$317$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$317$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$318$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$319$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$320$	0.277479	−	1.21572i	0.277479	−	1.21572i
$321$	0.400969	−	1.75676i	0.400969	−	1.75676i
$322$		0			0
$323$		0			0
$324$	1.00000			1.00000
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$331$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$331$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$332$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.900969	+	0.433884i	0.900969	+	0.433884i
$337$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$337$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$338$	0.900969	−	0.433884i	0.900969	−	0.433884i
$339$		0			0
$340$		0			0
$341$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$342$		0			0
$343$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$344$		0			0
$345$		0			0
$346$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$347$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$347$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$348$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$349$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$349$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$350$	0.500000	+	0.240787i	0.500000	+	0.240787i
$351$		0			0
$352$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$353$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$353$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$354$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.777479	−	0.974928i	0.777479	−	0.974928i
$359$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$359$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$360$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$361$	1.00000			1.00000
$362$		0			0
$363$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$364$		0			0
$365$	−0.500000	+	2.19064i	−0.500000	+	2.19064i
$366$		0			0
$367$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$367$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$372$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	0.123490	+	0.541044i	0.123490	+	0.541044i
$376$		0			0
$377$		0			0
$378$	1.00000			1.00000
$379$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$379$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$380$		0			0
$381$	1.12349	+	1.40881i	1.12349	+	1.40881i
$382$		0			0
$383$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$383$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$384$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$385$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$386$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$387$		0			0
$388$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$389$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$389$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$390$		0			0
$391$		0			0
$392$	0.900969	+	0.433884i	0.900969	+	0.433884i
$393$	−1.80194			−1.80194
$394$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$395$	−2.02446	+	0.974928i	−2.02446	+	0.974928i
$396$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$397$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$397$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$398$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$399$		0			0
$400$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$401$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$401$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$402$		0			0
$403$		0			0
$404$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$405$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$406$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$407$		0			0
$408$		0			0
$409$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$409$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$410$		0			0
$411$		0			0
$412$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$413$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$414$		0			0
$415$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$419$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$420$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$421$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$421$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$422$		0			0
$423$		0			0
$424$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.12349	+	1.40881i	1.12349	+	1.40881i
$429$		0			0
$430$		0			0
$431$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$431$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$432$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$433$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$433$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$434$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$435$	1.40097	+	0.674671i	1.40097	+	0.674671i
$436$		0			0
$437$		0			0
$438$	1.62349	−	0.781831i	1.62349	−	0.781831i
$439$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$439$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$440$	0.554958			0.554958
$441$	1.00000			1.00000
$442$		0			0
$443$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$443$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$444$		0			0
$445$		0			0
$446$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$447$	1.62349	+	0.781831i	1.62349	+	0.781831i
$448$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$449$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$449$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$450$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$451$		0			0
$452$		0			0
$453$	0.445042	+	1.94986i	0.445042	+	1.94986i
$454$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$455$		0			0
$456$		0			0
$457$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$457$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$461$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$462$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$463$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$463$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$464$	0.277479	−	1.21572i	0.277479	−	1.21572i
$465$	−1.40097	+	1.75676i	−1.40097	+	1.75676i
$466$		0			0
$467$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$467$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	2.00000			2.00000
$473$		0			0
$474$	1.62349	+	0.781831i	1.62349	+	0.781831i
$475$		0			0
$476$		0			0
$477$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$478$		0			0
$479$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$479$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$480$	1.12349	+	0.541044i	1.12349	+	0.541044i
$481$		0			0
$482$	1.12349	−	0.541044i	1.12349	−	0.541044i
$483$		0			0
$484$	0.722521	+	0.347948i	0.722521	+	0.347948i
$485$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$486$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$487$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$487$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$488$		0			0
$489$		0			0
$490$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$491$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$491$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.500000	−	0.240787i	0.500000	−	0.240787i
$496$	1.62349	+	0.781831i	1.62349	+	0.781831i
$497$		0			0
$498$	1.12349	−	0.541044i	1.12349	−	0.541044i
$499$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$499$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$500$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$501$		0			0
$502$	0.400969	+	1.75676i	0.400969	+	1.75676i
$503$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$503$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$504$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$505$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$506$		0			0
$507$	0.222521	+	0.974928i	0.222521	+	0.974928i
$508$	−1.80194			−1.80194
$509$	−2.00000			−2.00000			−1.00000			$\pi$
$509$	−2.00000			−2.00000			−1.00000			$\pi$
$510$		0			0
$511$	1.62349	−	0.781831i	1.62349	−	0.781831i
$512$	0.222521	−	0.974928i	0.222521	−	0.974928i
$513$		0			0
$514$		0			0
$515$	0.346011	−	0.433884i	0.346011	−	0.433884i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$523$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$523$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$524$	1.12349	−	1.40881i	1.12349	−	1.40881i
$525$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$526$		0			0
$527$		0			0
$528$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$529$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$530$	−1.55496	+	1.94986i	−1.55496	+	1.94986i
$531$	1.80194	−	0.867767i	1.80194	−	0.867767i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.500000	−	2.19064i	0.500000	−	2.19064i
$536$		0			0
$537$	0.777479	+	0.974928i	0.777479	+	0.974928i
$538$	1.24698			1.24698
$539$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$540$	1.24698			1.24698
$541$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$541$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$542$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$547$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$548$		0			0
$549$		0			0
$550$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$551$		0			0
$552$		0			0
$553$	1.62349	+	0.781831i	1.62349	+	0.781831i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$557$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$558$	1.80194			1.80194
$559$		0			0
$560$	1.12349	+	0.541044i	1.12349	+	0.541044i
$561$		0			0
$562$		0			0
$563$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$563$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$571$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$577$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$577$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$578$	0.900969	+	0.433884i	0.900969	+	0.433884i
$579$	1.12349	−	1.40881i	1.12349	−	1.40881i
$580$	−1.40097	+	0.674671i	−1.40097	+	0.674671i
$581$	1.12349	−	0.541044i	1.12349	−	0.541044i
$582$	0.400969	+	0.193096i	0.400969	+	0.193096i
$583$	0.801938	−	0.386193i	0.801938	−	0.386193i
$584$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$585$		0			0
$586$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$587$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$587$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$588$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$589$		0			0
$590$	−1.55496	−	1.94986i	−1.55496	−	1.94986i
$591$	0.400969	−	0.193096i	0.400969	−	0.193096i
$592$		0			0
$593$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$593$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$594$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$595$		0			0
$596$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$597$	1.12349	−	1.40881i	1.12349	−	1.40881i
$598$		0			0
$599$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$599$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$600$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$601$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$601$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$602$		0			0
$603$		0			0
$604$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$605$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$606$	0.445042			0.445042
$607$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$607$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$608$		0			0
$609$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$613$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$614$		0			0
$615$		0			0
$616$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$617$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$617$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$618$	−0.445042			−0.445042
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$	−0.500000	−	2.19064i	−0.500000	−	2.19064i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.277479	+	1.21572i	0.277479	+	1.21572i
$626$	1.12349	+	1.40881i	1.12349	+	1.40881i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.24698			1.24698
$631$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$631$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$632$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$633$		0			0
$634$	0.400969	−	0.193096i	0.400969	−	0.193096i
$635$	1.40097	+	1.75676i	1.40097	+	1.75676i
$636$	2.00000			2.00000
$637$		0			0
$638$	0.554958			0.554958
$639$		0			0
$640$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$641$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$641$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$642$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$643$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$643$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$647$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$648$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$649$	0.198062	+	0.867767i	0.198062	+	0.867767i
$650$		0			0
$651$	1.80194			1.80194
$652$		0			0
$653$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$653$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$654$		0			0
$655$	−2.24698			−2.24698
$656$		0			0
$657$	0.400969	+	1.75676i	0.400969	+	1.75676i
$658$		0			0
$659$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$659$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$660$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$661$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$661$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$662$		0			0
$663$		0			0
$664$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$670$		0			0
$671$		0			0
$672$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$673$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$673$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$674$	0.445042	+	1.94986i	0.445042	+	1.94986i
$675$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$676$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$677$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$677$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$678$		0			0
$679$	0.400969	+	0.193096i	0.400969	+	0.193096i
$680$		0			0
$681$	0.400969	−	0.193096i	0.400969	−	0.193096i
$682$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$683$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$683$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$684$		0			0
$685$		0			0
$686$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$691$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$692$	1.12349	+	0.541044i	1.12349	+	0.541044i
$693$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$694$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$695$		0			0
$696$	1.12349	+	0.541044i	1.12349	+	0.541044i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$701$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$701$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$702$		0			0
$703$		0			0
$704$	0.445042			0.445042
$705$		0			0
$706$		0			0
$707$	0.445042			0.445042
$708$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$709$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$709$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$710$		0			0
$711$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.24698			−1.24698
$717$		0			0
$718$		0			0
$719$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$719$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$720$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$721$	−0.445042			−0.445042
$722$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$723$	0.277479	+	1.21572i	0.277479	+	1.21572i
$724$		0			0
$725$	0.623490	+	0.300257i	0.623490	+	0.300257i
$726$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$727$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$727$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$728$		0			0
$729$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$730$	2.02446	−	0.974928i	2.02446	−	0.974928i
$731$		0			0
$732$		0			0
$733$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$733$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$734$	−2.00000			−2.00000
$735$	1.24698			1.24698
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$739$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$740$		0			0
$741$		0			0
$742$	2.00000			2.00000
$743$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$743$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$744$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$745$	2.02446	+	0.974928i	2.02446	+	0.974928i
$746$		0			0
$747$	0.277479	+	1.21572i	0.277479	+	1.21572i
$748$		0			0
$749$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$750$	0.346011	−	0.433884i	0.346011	−	0.433884i
$751$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$751$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$752$		0			0
$753$	−1.80194			−1.80194
$754$		0			0
$755$	0.554958	+	2.43143i	0.554958	+	2.43143i
$756$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$757$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$757$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$761$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$762$	0.400969	−	1.75676i	0.400969	−	1.75676i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.900969	+	0.433884i	0.900969	+	0.433884i
$769$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$769$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$770$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$771$		0			0
$772$	0.400969	+	1.75676i	0.400969	+	1.75676i
$773$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$773$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$774$		0			0
$775$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$776$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$777$		0			0
$778$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.24698			1.24698
$784$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$785$		0			0
$786$	1.12349	+	1.40881i	1.12349	+	1.40881i
$787$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$787$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$788$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$789$		0			0
$790$	2.02446	+	0.974928i	2.02446	+	0.974928i
$791$		0			0
$792$	0.400969	−	0.193096i	0.400969	−	0.193096i
$793$		0			0
$794$		0			0
$795$	−1.55496	−	1.94986i	−1.55496	−	1.94986i
$796$	0.400969	+	1.75676i	0.400969	+	1.75676i
$797$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$797$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.240787i	0.500000	+	0.240787i
$801$		0			0
$802$		0			0
$803$	−0.801938			−0.801938
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$808$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$809$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$809$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$810$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$811$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$811$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$812$	1.12349	+	0.541044i	1.12349	+	0.541044i
$813$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$819$		0			0
$820$		0			0
$821$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$821$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$822$		0			0
$823$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$823$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$824$	0.277479	−	0.347948i	0.277479	−	0.347948i
$825$	0.222521	−	0.107160i	0.222521	−	0.107160i
$826$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$827$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$827$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$828$		0			0
$829$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$829$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$830$	1.40097	−	0.674671i	1.40097	−	0.674671i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$838$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$839$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$839$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$840$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$841$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.277479	+	1.21572i	0.277479	+	1.21572i
$846$		0			0
$847$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$848$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$853$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$854$		0			0
$855$		0			0
$856$	0.400969	−	1.75676i	0.400969	−	1.75676i
$857$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$857$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$858$		0			0
$859$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$859$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	1.00000			1.00000
$865$	−0.346011	−	1.51597i	−0.346011	−	1.51597i
$866$	1.12349	+	0.541044i	1.12349	+	0.541044i
$867$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$868$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$869$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$870$	−0.346011	−	1.51597i	−0.346011	−	1.51597i
$871$		0			0
$872$		0			0
$873$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$874$		0			0
$875$	0.346011	−	0.433884i	0.346011	−	0.433884i
$876$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$877$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$877$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$878$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$879$	0.400969	−	0.193096i	0.400969	−	0.193096i
$880$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	2.24698	−	1.08209i	2.24698	−	1.08209i
$886$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$887$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$887$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$888$		0			0
$889$	0.400969	−	1.75676i	0.400969	−	1.75676i
$890$		0			0
$891$	0.277479	−	0.347948i	0.277479	−	0.347948i
$892$	0.400969	+	0.193096i	0.400969	+	0.193096i
$893$		0			0
$894$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$895$	0.969501	+	1.21572i	0.969501	+	1.21572i
$896$	0.900969	+	0.433884i	0.900969	+	0.433884i
$897$		0			0
$898$		0			0
$899$	−0.500000	−	2.19064i	−0.500000	−	2.19064i
$900$	0.554958			0.554958
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.24698	−	1.56366i	1.24698	−	1.56366i
$907$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$907$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$908$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$909$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$910$		0			0
$911$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$911$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$912$		0			0
$913$	−0.554958			−0.554958
$914$	0.277479	+	1.21572i	0.277479	+	1.21572i
$915$		0			0
$916$		0			0
$917$	1.12349	+	1.40881i	1.12349	+	1.40881i
$918$		0			0
$919$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$919$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$920$		0			0
$921$		0			0
$922$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$923$		0			0
$924$	0.400969	−	0.193096i	0.400969	−	0.193096i
$925$		0			0
$926$	1.12349	−	0.541044i	1.12349	−	0.541044i
$927$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$928$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$929$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$929$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$930$	2.24698			2.24698
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.400969	−	0.193096i	0.400969	−	0.193096i
$935$		0			0
$936$		0			0
$937$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$937$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$938$		0			0
$939$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$940$		0			0
$941$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$941$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$942$		0			0
$943$		0			0
$944$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$945$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$946$		0			0
$947$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$947$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$948$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$949$		0			0
$950$		0			0
$951$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$952$		0			0
$953$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$953$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$954$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$955$		0			0
$956$		0			0
$957$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$958$		0			0
$959$		0			0
$960$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$961$	2.24698			2.24698
$962$		0			0
$963$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$964$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$965$	1.40097	−	1.75676i	1.40097	−	1.75676i
$966$		0			0
$967$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$967$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$968$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$969$		0			0
$970$	0.500000	+	0.240787i	0.500000	+	0.240787i
$971$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$971$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$972$	0.900969	−	0.433884i	0.900969	−	0.433884i
$973$		0			0
$974$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$975$		0			0
$976$		0			0
$977$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$977$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$978$		0			0
$979$		0			0
$980$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$981$		0			0
$982$	0.777479	+	0.974928i	0.777479	+	0.974928i
$983$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$983$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$984$		0			0
$985$	0.500000	−	0.240787i	0.500000	−	0.240787i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$991$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$991$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$992$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$993$		0			0
$994$		0			0
$995$	1.40097	−	1.75676i	1.40097	−	1.75676i
$996$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$997$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$997$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.1.bj.b.1037.1	yes	6
3.2	odd	2		1176.1.bj.a.1037.1	yes	6
8.5	even	2		1176.1.bj.a.1037.1	yes	6
24.5	odd	2	CM	1176.1.bj.b.1037.1	yes	6
49.43	even	7	inner	1176.1.bj.b.533.1	yes	6
147.92	odd	14		1176.1.bj.a.533.1	✓	6
392.141	even	14		1176.1.bj.a.533.1	✓	6
1176.533	odd	14	inner	1176.1.bj.b.533.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.1.bj.a.533.1	✓	6	147.92	odd	14
1176.1.bj.a.533.1	✓	6	392.141	even	14
1176.1.bj.a.1037.1	yes	6	3.2	odd	2
1176.1.bj.a.1037.1	yes	6	8.5	even	2
1176.1.bj.b.533.1	yes	6	49.43	even	7	inner
1176.1.bj.b.533.1	yes	6	1176.533	odd	14	inner
1176.1.bj.b.1037.1	yes	6	1.1	even	1	trivial
1176.1.bj.b.1037.1	yes	6	24.5	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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1176.bj (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 - 0.781831i) q^{2} +(0.900969 - 0.433884i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(1.12349 - 0.541044i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(-0.900969 - 0.433884i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.623490 - 0.781831i) q^{2} +(0.900969 - 0.433884i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(1.12349 - 0.541044i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(-0.900969 - 0.433884i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-1.12349 - 0.541044i) q^{10} +(0.277479 + 0.347948i) q^{11} +(0.222521 + 0.974928i) q^{12} +(0.222521 + 0.974928i) q^{14} +(0.777479 - 0.974928i) q^{15} +(-0.900969 - 0.433884i) q^{16} -1.00000 q^{18} +(0.277479 + 1.21572i) q^{20} -1.00000 q^{21} +(0.0990311 - 0.433884i) q^{22} +(0.623490 - 0.781831i) q^{24} +(0.346011 - 0.433884i) q^{25} +(0.222521 - 0.974928i) q^{27} +(0.623490 - 0.781831i) q^{28} +(0.277479 + 1.21572i) q^{29} -1.24698 q^{30} -1.80194 q^{31} +(0.222521 + 0.974928i) q^{32} +(0.400969 + 0.193096i) q^{33} -1.24698 q^{35} +(0.623490 + 0.781831i) q^{36} +(0.777479 - 0.974928i) q^{40} +(0.623490 + 0.781831i) q^{42} +(-0.400969 + 0.193096i) q^{44} +(0.277479 - 1.21572i) q^{45} -1.00000 q^{48} +(0.623490 + 0.781831i) q^{49} -0.554958 q^{50} +(0.445042 - 1.94986i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(0.500000 + 0.240787i) q^{55} -1.00000 q^{56} +(0.777479 - 0.974928i) q^{58} +(1.80194 + 0.867767i) q^{59} +(0.777479 + 0.974928i) q^{60} +(1.12349 + 1.40881i) q^{62} +(-0.900969 + 0.433884i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.0990311 - 0.433884i) q^{66} +(0.777479 + 0.974928i) q^{70} +(0.222521 - 0.974928i) q^{72} +(-1.12349 + 1.40881i) q^{73} +(0.123490 - 0.541044i) q^{75} +(-0.0990311 - 0.433884i) q^{77} -1.80194 q^{79} -1.24698 q^{80} +(-0.222521 - 0.974928i) q^{81} +(-0.777479 + 0.974928i) q^{83} +(0.222521 - 0.974928i) q^{84} +(0.777479 + 0.974928i) q^{87} +(0.400969 + 0.193096i) q^{88} +(-1.12349 + 0.541044i) q^{90} +(-1.62349 + 0.781831i) q^{93} +(0.623490 + 0.781831i) q^{96} -0.445042 q^{97} +(0.222521 - 0.974928i) q^{98} +0.445042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 6 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 - q^7 + q^8 - q^9	\( 6 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - q^{7} + q^{8} - q^{9} - 2 q^{10} + 2 q^{11} + q^{12} + q^{14} + 5 q^{15} - q^{16} - 6 q^{18} + 2 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} - 3 q^{25} + q^{27} - q^{28} + 2 q^{29} + 2 q^{30} - 2 q^{31} + q^{32} - 2 q^{33} + 2 q^{35} - q^{36} + 5 q^{40} - q^{42} + 2 q^{44} + 2 q^{45} - 6 q^{48} - q^{49} - 4 q^{50} + 2 q^{53} - q^{54} + 3 q^{55} - 6 q^{56} + 5 q^{58} + 2 q^{59} + 5 q^{60} + 2 q^{62} - q^{63} - q^{64} - 5 q^{66} + 5 q^{70} + q^{72} - 2 q^{73} - 4 q^{75} - 5 q^{77} - 2 q^{79} + 2 q^{80} - q^{81} - 5 q^{83} + q^{84} + 5 q^{87} - 2 q^{88} - 2 q^{90} - 5 q^{93} - q^{96} - 2 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 - q^7 + q^8 - q^9 - 2 * q^10 + 2 * q^11 + q^12 + q^14 + 5 * q^15 - q^16 - 6 * q^18 + 2 * q^20 - 6 * q^21 + 5 * q^22 - q^24 - 3 * q^25 + q^27 - q^28 + 2 * q^29 + 2 * q^30 - 2 * q^31 + q^32 - 2 * q^33 + 2 * q^35 - q^36 + 5 * q^40 - q^42 + 2 * q^44 + 2 * q^45 - 6 * q^48 - q^49 - 4 * q^50 + 2 * q^53 - q^54 + 3 * q^55 - 6 * q^56 + 5 * q^58 + 2 * q^59 + 5 * q^60 + 2 * q^62 - q^63 - q^64 - 5 * q^66 + 5 * q^70 + q^72 - 2 * q^73 - 4 * q^75 - 5 * q^77 - 2 * q^79 + 2 * q^80 - q^81 - 5 * q^83 + q^84 + 5 * q^87 - 2 * q^88 - 2 * q^90 - 5 * q^93 - q^96 - 2 * q^97 + q^98 + 2 * q^99

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