LMFDB - Embedded newform 3332.1.cc.c.1971.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(135,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 32, 21]))

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

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

chi := DirichletCharacter("3332.135");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$3332 = 2^{2} \cdot 7^{2} \cdot 17$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3332.cc (of order $42$ , degree $12$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66288462209$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{84})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1$ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{42}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{42} - \cdots)$

Embedding invariants

Embedding label			1971.1
Root			$0.930874 + 0.365341i$ of defining polynomial
Character	$\chi$	$=$	3332.1971
Dual form			3332.1.cc.c.1087.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.733052 - 0.680173i) q^{2} +(-0.294755 + 0.0444272i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(-0.185853 + 0.233052i) q^{6} +(-0.781831 + 0.623490i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.870666 + 0.268565i) q^{9} +(1.29991 + 0.400969i) q^{11} +(0.0222759 + 0.297251i) q^{12} +(-0.326239 - 1.42935i) q^{13} +(-0.149042 + 0.988831i) q^{14} +(-0.988831 - 0.149042i) q^{16} +(0.826239 - 0.563320i) q^{17} +(-0.455573 + 0.789075i) q^{18} +(0.202749 - 0.218511i) q^{21} +(1.22563 - 0.590232i) q^{22} +(-1.61105 - 1.09839i) q^{23} +(0.218511 + 0.202749i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(-1.21135 - 0.825886i) q^{26} +(0.513267 - 0.247176i) q^{27} +(0.563320 + 0.826239i) q^{28} +(0.781831 - 1.35417i) q^{31} +(-0.826239 + 0.563320i) q^{32} +(-0.400969 - 0.0604363i) q^{33} +(0.222521 - 0.974928i) q^{34} +(0.202749 + 0.888301i) q^{36} +(0.159662 + 0.406813i) q^{39} -0.298085i q^{42} +(0.496990 - 1.26631i) q^{44} +(-1.92808 + 0.290611i) q^{46} +0.298085 q^{48} +(0.222521 - 0.974928i) q^{49} -1.00000 q^{50} +(-0.218511 + 0.202749i) q^{51} +(-1.44973 + 0.218511i) q^{52} +(0.0546039 - 0.728639i) q^{53} +(0.208129 - 0.530303i) q^{54} +(0.974928 + 0.222521i) q^{56} +(-0.347948 - 1.52446i) q^{62} +(0.513267 - 0.752824i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-0.335038 + 0.228425i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(0.523663 + 0.252183i) q^{69} +(-1.67738 + 0.807782i) q^{71} +(0.752824 + 0.513267i) q^{72} +(0.246289 + 0.167917i) q^{75} +(-1.26631 + 0.496990i) q^{77} +(0.393744 + 0.189617i) q^{78} +(0.294755 + 0.510531i) q^{79} +(0.612517 - 0.417607i) q^{81} +(-0.202749 - 0.218511i) q^{84} +(-0.496990 - 1.26631i) q^{88} +(1.88980 - 0.582926i) q^{89} +(1.14625 + 0.914101i) q^{91} +(-1.21572 + 1.52446i) q^{92} +(-0.170287 + 0.433884i) q^{93} +(0.218511 - 0.202749i) q^{96} +(-0.500000 - 0.866025i) q^{98} -1.23947 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52}+ \cdots - 12 q^{98}+O(q^{100})$ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 + 10 * q^13 + 2 * q^16 + 2 * q^17 + 10 * q^18 + 6 * q^21 + 2 * q^25 - 2 * q^26 - 2 * q^32 + 8 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^49 - 24 * q^50 + 2 * q^52 - 2 * q^53 - 4 * q^64 - 22 * q^66 - 12 * q^68 - 14 * q^69 - 4 * q^72 - 6 * q^77 + 30 * q^81 - 6 * q^84 + 2 * q^89 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$ .

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{20}{21}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.733052	−	0.680173i	0.733052	−	0.680173i
$2$	0.733052	−	0.680173i	0.733052	−	0.680173i
$3$	−0.294755	+	0.0444272i	−0.294755	+	0.0444272i	−0.294755	−	0.955573i	$-0.595238\pi$
$3$	−0.294755	+	0.0444272i	−0.294755	+	0.0444272i			1.00000i	$0.5\pi$
$4$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$5$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$5$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$6$	−0.185853	+	0.233052i	−0.185853	+	0.233052i
$7$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$7$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$8$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$9$	−0.870666	+	0.268565i	−0.870666	+	0.268565i
$10$		0			0
$11$	1.29991	+	0.400969i	1.29991	+	0.400969i	0.866025	−	0.500000i	$-0.166667\pi$
$11$	1.29991	+	0.400969i	1.29991	+	0.400969i	0.433884	+	0.900969i	$0.357143\pi$
$12$	0.0222759	+	0.297251i	0.0222759	+	0.297251i
$13$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	−0.826239	−	0.563320i	$-0.809524\pi$
$13$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	0.500000	−	0.866025i	$-0.333333\pi$
$14$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$15$		0			0
$16$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$17$	0.826239	−	0.563320i	0.826239	−	0.563320i
$17$	0.826239	−	0.563320i	0.826239	−	0.563320i
$18$	−0.455573	+	0.789075i	−0.455573	+	0.789075i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	0.202749	−	0.218511i	0.202749	−	0.218511i
$22$	1.22563	−	0.590232i	1.22563	−	0.590232i
$23$	−1.61105	−	1.09839i	−1.61105	−	1.09839i	−0.930874	−	0.365341i	$-0.880952\pi$
$23$	−1.61105	−	1.09839i	−1.61105	−	1.09839i	−0.680173	−	0.733052i	$-0.738095\pi$
$24$	0.218511	+	0.202749i	0.218511	+	0.202749i
$25$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$26$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$27$	0.513267	−	0.247176i	0.513267	−	0.247176i
$28$	0.563320	+	0.826239i	0.563320	+	0.826239i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$	0.781831	−	1.35417i	0.781831	−	1.35417i	−0.149042	−	0.988831i	$-0.547619\pi$
$31$	0.781831	−	1.35417i	0.781831	−	1.35417i	0.930874	−	0.365341i	$-0.119048\pi$
$32$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$33$	−0.400969	−	0.0604363i	−0.400969	−	0.0604363i
$34$	0.222521	−	0.974928i	0.222521	−	0.974928i
$35$		0			0
$36$	0.202749	+	0.888301i	0.202749	+	0.888301i
$37$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$37$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$38$		0			0
$39$	0.159662	+	0.406813i	0.159662	+	0.406813i
$40$		0			0
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$		−	0.298085i		−	0.298085i
$43$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$43$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$44$	0.496990	−	1.26631i	0.496990	−	1.26631i
$45$		0			0
$46$	−1.92808	+	0.290611i	−1.92808	+	0.290611i
$47$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$47$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$48$	0.298085			0.298085
$49$	0.222521	−	0.974928i	0.222521	−	0.974928i
$50$	−1.00000			−1.00000
$51$	−0.218511	+	0.202749i	−0.218511	+	0.202749i
$52$	−1.44973	+	0.218511i	−1.44973	+	0.218511i
$53$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$53$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$54$	0.208129	−	0.530303i	0.208129	−	0.530303i
$55$		0			0
$56$	0.974928	+	0.222521i	0.974928	+	0.222521i
$57$		0			0
$58$		0			0
$59$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$59$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$60$		0			0
$61$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$61$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$62$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$63$	0.513267	−	0.752824i	0.513267	−	0.752824i
$64$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$65$		0			0
$66$	−0.335038	+	0.228425i	−0.335038	+	0.228425i
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$69$	0.523663	+	0.252183i	0.523663	+	0.252183i
$70$		0			0
$71$	−1.67738	+	0.807782i	−1.67738	+	0.807782i	−0.680173	+	0.733052i	$0.738095\pi$
$71$	−1.67738	+	0.807782i	−1.67738	+	0.807782i	−0.997204	+	0.0747301i	$0.976190\pi$
$72$	0.752824	+	0.513267i	0.752824	+	0.513267i
$73$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$73$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$74$		0			0
$75$	0.246289	+	0.167917i	0.246289	+	0.167917i
$76$		0			0
$77$	−1.26631	+	0.496990i	−1.26631	+	0.496990i
$78$	0.393744	+	0.189617i	0.393744	+	0.189617i
$79$	0.294755	+	0.510531i	0.294755	+	0.510531i	0.974928	−	0.222521i	$-0.0714286\pi$
$79$	0.294755	+	0.510531i	0.294755	+	0.510531i	−0.680173	+	0.733052i	$0.738095\pi$
$80$		0			0
$81$	0.612517	−	0.417607i	0.612517	−	0.417607i
$82$		0			0
$83$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$83$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$84$	−0.202749	−	0.218511i	−0.202749	−	0.218511i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.496990	−	1.26631i	−0.496990	−	1.26631i
$89$	1.88980	−	0.582926i	1.88980	−	0.582926i	0.900969	−	0.433884i	$-0.142857\pi$
$89$	1.88980	−	0.582926i	1.88980	−	0.582926i	0.988831	−	0.149042i	$-0.0476190\pi$
$90$		0			0
$91$	1.14625	+	0.914101i	1.14625	+	0.914101i
$92$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$93$	−0.170287	+	0.433884i	−0.170287	+	0.433884i
$94$		0			0
$95$		0			0
$96$	0.218511	−	0.202749i	0.218511	−	0.202749i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$99$	−1.23947			−1.23947
$100$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$101$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i	−0.365341	−	0.930874i	$-0.619048\pi$
$101$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i	−0.0747301	+	0.997204i	$0.523810\pi$
$102$	−0.0222759	+	0.297251i	−0.0222759	+	0.297251i
$103$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$103$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$104$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$105$		0			0
$106$	−0.455573	−	0.571270i	−0.455573	−	0.571270i
$107$	−1.90580	+	0.587862i	−1.90580	+	0.587862i	−0.930874	+	0.365341i	$0.880952\pi$
$107$	−1.90580	+	0.587862i	−1.90580	+	0.587862i	−0.974928	+	0.222521i	$0.928571\pi$
$108$	−0.208129	−	0.530303i	−0.208129	−	0.530303i
$109$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$109$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$110$		0			0
$111$		0			0
$112$	0.866025	−	0.500000i	0.866025	−	0.500000i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.667917	+	1.15687i	0.667917	+	1.15687i
$118$		0			0
$119$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$120$		0			0
$121$	0.702749	+	0.479126i	0.702749	+	0.479126i
$122$		0			0
$123$		0			0
$124$	−1.29196	−	0.880843i	−1.29196	−	0.880843i
$125$		0			0
$126$	−0.135799	−	0.900969i	−0.135799	−	0.900969i
$127$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$127$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$	1.92808	+	0.290611i	1.92808	+	0.290611i	0.997204	−	0.0747301i	$-0.0238095\pi$
$131$	1.92808	+	0.290611i	1.92808	+	0.290611i	0.930874	+	0.365341i	$0.119048\pi$
$132$	−0.0902318	+	0.395331i	−0.0902318	+	0.395331i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$137$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.500000	+	0.866025i	$0.333333\pi$
$137$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.222521	+	0.974928i	$0.428571\pi$
$138$	0.555400	−	0.171318i	0.555400	−	0.171318i
$139$	−0.367554	−	0.460898i	−0.367554	−	0.460898i	0.563320	−	0.826239i	$-0.309524\pi$
$139$	−0.367554	−	0.460898i	−0.367554	−	0.460898i	−0.930874	+	0.365341i	$0.880952\pi$
$140$		0			0
$141$		0			0
$142$	−0.680173	+	1.73305i	−0.680173	+	1.73305i
$143$	0.149042	−	1.98883i	0.149042	−	1.98883i
$144$	0.900969	−	0.135799i	0.900969	−	0.135799i
$145$		0			0
$146$		0			0
$147$	−0.0222759	+	0.297251i	−0.0222759	+	0.297251i
$148$		0			0
$149$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$149$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$150$	0.294755	−	0.0444272i	0.294755	−	0.0444272i
$151$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$151$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$152$		0			0
$153$	−0.568090	+	0.712362i	−0.568090	+	0.712362i
$154$	−0.590232	+	1.22563i	−0.590232	+	1.22563i
$155$		0			0
$156$	0.417607	−	0.128815i	0.417607	−	0.128815i
$157$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$157$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$158$	0.563320	+	0.173761i	0.563320	+	0.173761i
$159$	0.0162766	+	0.217196i	0.0162766	+	0.217196i
$160$		0			0
$161$	1.94440	−	0.145713i	1.94440	−	0.145713i
$162$	0.164962	−	0.722745i	0.164962	−	0.722745i
$163$		0			0		0.149042	−	0.988831i	$-0.452381\pi$
$163$		0			0		−0.149042	+	0.988831i	$0.547619\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.01507	−	0.488831i	−1.01507	−	0.488831i	−0.149042	−	0.988831i	$-0.547619\pi$
$167$	−1.01507	−	0.488831i	−1.01507	−	0.488831i	−0.866025	+	0.500000i	$0.833333\pi$
$168$	−0.297251	−	0.0222759i	−0.297251	−	0.0222759i
$169$	−1.03563	+	0.498732i	−1.03563	+	0.498732i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$173$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$174$		0			0
$175$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$176$	−1.22563	−	0.590232i	−1.22563	−	0.590232i
$177$		0			0
$178$	0.988831	−	1.71271i	0.988831	−	1.71271i
$179$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$179$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$	1.46200	−	0.109562i	1.46200	−	0.109562i
$183$		0			0
$184$	0.145713	+	1.94440i	0.145713	+	1.94440i
$185$		0			0
$186$	0.170287	+	0.433884i	0.170287	+	0.433884i
$187$	1.29991	−	0.400969i	1.29991	−	0.400969i
$188$		0			0
$189$	−0.247176	+	0.513267i	−0.247176	+	0.513267i
$190$		0			0
$191$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$191$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$192$	0.0222759	−	0.297251i	0.0222759	−	0.297251i
$193$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$193$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$194$		0			0
$195$		0			0
$196$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.908598	+	0.843056i	−0.908598	+	0.843056i
$199$	1.84095	−	0.277479i	1.84095	−	0.277479i	0.866025	−	0.500000i	$-0.166667\pi$
$199$	1.84095	−	0.277479i	1.84095	−	0.277479i	0.974928	+	0.222521i	$0.0714286\pi$
$200$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$201$		0			0
$202$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$203$		0			0
$204$	0.185853	+	0.233052i	0.185853	+	0.233052i
$205$		0			0
$206$		0			0
$207$	1.69767	+	0.523663i	1.69767	+	0.523663i
$208$	0.109562	+	1.46200i	0.109562	+	1.46200i
$209$		0			0
$210$		0			0
$211$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$211$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$212$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$213$	0.458528	−	0.312619i	0.458528	−	0.312619i
$214$	−0.997204	+	1.72721i	−0.997204	+	1.72721i
$215$		0			0
$216$	−0.513267	−	0.247176i	−0.513267	−	0.247176i
$217$	0.233052	+	1.54620i	0.233052	+	1.54620i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$222$		0			0
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	0.294755	−	0.955573i	0.294755	−	0.955573i
$225$	0.820914	+	0.395331i	0.820914	+	0.395331i
$226$		0			0
$227$	0.930874	−	1.61232i	0.930874	−	1.61232i	0.149042	−	0.988831i	$-0.452381\pi$
$227$	0.930874	−	1.61232i	0.930874	−	1.61232i	0.781831	−	0.623490i	$-0.214286\pi$
$228$		0			0
$229$	−1.78181	−	0.268565i	−1.78181	−	0.268565i	−0.826239	−	0.563320i	$-0.809524\pi$
$229$	−1.78181	−	0.268565i	−1.78181	−	0.268565i	−0.955573	+	0.294755i	$0.904762\pi$
$230$		0			0
$231$	0.351172	−	0.202749i	0.351172	−	0.202749i
$232$		0			0
$233$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$233$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$234$	1.27649	+	0.393744i	1.27649	+	0.393744i
$235$		0			0
$236$		0			0
$237$	−0.109562	−	0.137386i	−0.109562	−	0.137386i
$238$	0.433884	+	0.900969i	0.433884	+	0.900969i
$239$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$239$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$240$		0			0
$241$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$241$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$242$	0.841040	−	0.126766i	0.841040	−	0.126766i
$243$	−0.579597	+	0.537787i	−0.579597	+	0.537787i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.54620	+	0.233052i	−1.54620	+	0.233052i
$249$		0			0
$250$		0			0
$251$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$251$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$252$	−0.712362	−	0.568090i	−0.712362	−	0.568090i
$253$	−1.65379	−	2.07379i	−1.65379	−	2.07379i
$254$		0			0
$255$		0			0
$256$	0.955573	+	0.294755i	0.955573	+	0.294755i
$257$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	0.900969	+	0.433884i	$0.142857\pi$
$257$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	−0.826239	+	0.563320i	$0.809524\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.61105	−	1.09839i	1.61105	−	1.09839i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	0.202749	+	0.351172i	0.202749	+	0.351172i
$265$		0			0
$266$		0			0
$267$	−0.531130	+	0.255779i	−0.531130	+	0.255779i
$268$		0			0
$269$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$269$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$270$		0			0
$271$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$271$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$272$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$273$	−0.378473	−	0.218511i	−0.378473	−	0.218511i
$274$	1.78181	+	0.858075i	1.78181	+	0.858075i
$275$	−0.680173	−	1.17809i	−0.680173	−	1.17809i
$276$	0.290611	−	0.503353i	0.290611	−	0.503353i
$277$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$277$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$278$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i
$279$	−0.317031	+	1.38900i	−0.317031	+	1.38900i
$280$		0			0
$281$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$281$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$282$		0			0
$283$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.433884	−	0.900969i	$-0.642857\pi$
$283$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.866025	+	0.500000i	$0.833333\pi$
$284$	0.680173	+	1.73305i	0.680173	+	1.73305i
$285$		0			0
$286$	−1.24349	−	1.55929i	−1.24349	−	1.55929i
$287$		0			0
$288$	0.568090	−	0.712362i	0.568090	−	0.712362i
$289$	0.365341	−	0.930874i	0.365341	−	0.930874i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$293$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$294$	0.185853	+	0.233052i	0.185853	+	0.233052i
$295$		0			0
$296$		0			0
$297$	0.766310	−	0.115503i	0.766310	−	0.115503i
$298$	0.147791	−	1.97213i	0.147791	−	1.97213i
$299$	−1.04440	+	2.66108i	−1.04440	+	2.66108i
$300$	0.185853	−	0.233052i	0.185853	−	0.233052i
$301$		0			0
$302$		0			0
$303$	0.126766	−	0.0391023i	0.126766	−	0.0391023i
$304$		0			0
$305$		0			0
$306$	0.0680900	+	0.908598i	0.0680900	+	0.908598i
$307$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$307$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$308$	0.400969	+	1.29991i	0.400969	+	1.29991i
$309$		0			0
$310$		0			0
$311$	1.43109	−	0.975699i	1.43109	−	0.975699i	0.433884	−	0.900969i	$-0.357143\pi$
$311$	1.43109	−	0.975699i	1.43109	−	0.975699i	0.997204	−	0.0747301i	$-0.0238095\pi$
$312$	0.218511	−	0.378473i	0.218511	−	0.378473i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	1.72188	+	0.829215i	1.72188	+	0.829215i
$315$		0			0
$316$	0.531130	−	0.255779i	0.531130	−	0.255779i
$317$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$317$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$318$	0.159662	+	0.148145i	0.159662	+	0.148145i
$319$		0			0
$320$		0			0
$321$	0.535628	−	0.257945i	0.535628	−	0.257945i
$322$	1.32624	−	1.42935i	1.32624	−	1.42935i
$323$		0			0
$324$	−0.370666	−	0.642012i	−0.370666	−	0.642012i
$325$	−0.733052	+	1.26968i	−0.733052	+	1.26968i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$331$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$332$		0			0
$333$		0			0
$334$	−1.07659	+	0.332083i	−1.07659	+	0.332083i
$335$		0			0
$336$	−0.233052	+	0.185853i	−0.233052	+	0.185853i
$337$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$337$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$338$	−0.419945	+	1.07000i	−0.419945	+	1.07000i
$339$		0			0
$340$		0			0
$341$	1.55929	−	1.44681i	1.55929	−	1.44681i
$342$		0			0
$343$	0.433884	+	0.900969i	0.433884	+	0.900969i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.0648483	−	0.865341i	0.0648483	−	0.865341i	−0.866025	−	0.500000i	$-0.833333\pi$
$347$	0.0648483	−	0.865341i	0.0648483	−	0.865341i	0.930874	−	0.365341i	$-0.119048\pi$
$348$		0			0
$349$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$349$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$350$	0.781831	−	0.623490i	0.781831	−	0.623490i
$351$	−0.520748	−	0.652997i	−0.520748	−	0.652997i
$352$	−1.29991	+	0.400969i	−1.29991	+	0.400969i
$353$	−0.365341	−	0.930874i	−0.365341	−	0.930874i	−0.988831	−	0.149042i	$-0.952381\pi$
$353$	−0.365341	−	0.930874i	−0.365341	−	0.930874i	0.623490	−	0.781831i	$-0.285714\pi$
$354$		0			0
$355$		0			0
$356$	−0.440071	−	1.92808i	−0.440071	−	1.92808i
$357$	0.0444272	−	0.294755i	0.0444272	−	0.294755i
$358$		0			0
$359$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$359$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	−0.228425	−	0.110004i	−0.228425	−	0.110004i
$364$	0.997204	−	1.07473i	0.997204	−	1.07473i
$365$		0			0
$366$		0			0
$367$	−1.46200	−	1.35654i	−1.46200	−	1.35654i	−0.781831	−	0.623490i	$-0.785714\pi$
$367$	−1.46200	−	1.35654i	−1.46200	−	1.35654i	−0.680173	−	0.733052i	$-0.738095\pi$
$368$	1.42935	+	1.32624i	1.42935	+	1.32624i
$369$		0			0
$370$		0			0
$371$	0.411608	+	0.603718i	0.411608	+	0.603718i
$372$	0.419945	+	0.202235i	0.419945	+	0.202235i
$373$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	−0.955573	−	0.294755i	$-0.904762\pi$
$373$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	0.222521	−	0.974928i	$-0.428571\pi$
$374$	0.680173	−	1.17809i	0.680173	−	1.17809i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.167917	+	0.544374i	0.167917	+	0.544374i
$379$	−0.385418	−	1.68862i	−0.385418	−	1.68862i	−0.680173	−	0.733052i	$-0.738095\pi$
$379$	−0.385418	−	1.68862i	−0.385418	−	1.68862i	0.294755	−	0.955573i	$-0.404762\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$383$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$384$	−0.185853	−	0.233052i	−0.185853	−	0.233052i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.63402	−	0.246289i	1.63402	−	0.246289i	0.733052	−	0.680173i	$-0.238095\pi$
$389$	1.63402	−	0.246289i	1.63402	−	0.246289i	0.900969	+	0.433884i	$0.142857\pi$
$390$		0			0
$391$	−1.94986			−1.94986
$392$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$393$	−0.581222			−0.581222
$394$		0			0
$395$		0			0
$396$	−0.0926259	+	1.23601i	−0.0926259	+	1.23601i
$397$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$397$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$398$	1.16078	−	1.45557i	1.16078	−	1.45557i
$399$		0			0
$400$	0.623490	+	0.781831i	0.623490	+	0.781831i
$401$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$401$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$402$		0			0
$403$	−2.19064	−	0.675724i	−2.19064	−	0.675724i
$404$	0.0332580	+	0.443797i	0.0332580	+	0.443797i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.294755	+	0.0444272i	0.294755	+	0.0444272i
$409$	0.603718	−	0.411608i	0.603718	−	0.411608i	−0.222521	−	0.974928i	$-0.571429\pi$
$409$	0.603718	−	0.411608i	0.603718	−	0.411608i	0.826239	+	0.563320i	$0.190476\pi$
$410$		0			0
$411$	−0.294755	−	0.510531i	−0.294755	−	0.510531i
$412$		0			0
$413$		0			0
$414$	1.60066	−	0.770839i	1.60066	−	0.770839i
$415$		0			0
$416$	1.07473	+	0.997204i	1.07473	+	0.997204i
$417$	0.128815	+	0.119523i	0.128815	+	0.119523i
$418$		0			0
$419$	0.531130	−	0.255779i	0.531130	−	0.255779i	−0.149042	−	0.988831i	$-0.547619\pi$
$419$	0.531130	−	0.255779i	0.531130	−	0.255779i	0.680173	+	0.733052i	$0.261905\pi$
$420$		0			0
$421$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$421$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$422$	0.433884	+	0.751509i	0.433884	+	0.751509i
$423$		0			0
$424$	−0.603718	+	0.411608i	−0.603718	+	0.411608i
$425$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$426$	0.123490	−	0.541044i	0.123490	−	0.541044i
$427$		0			0
$428$	0.443797	+	1.94440i	0.443797	+	1.94440i
$429$	0.0444272	+	0.592840i	0.0444272	+	0.592840i
$430$		0			0
$431$	0.632789	+	1.61232i	0.632789	+	1.61232i	0.781831	+	0.623490i	$0.214286\pi$
$431$	0.632789	+	1.61232i	0.632789	+	1.61232i	−0.149042	+	0.988831i	$0.547619\pi$
$432$	−0.544374	+	0.167917i	−0.544374	+	0.167917i
$433$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$433$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$434$	1.22252	+	0.974928i	1.22252	+	0.974928i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.432142	+	0.400969i	−0.432142	+	0.400969i	−0.866025	−	0.500000i	$-0.833333\pi$
$439$	−0.432142	+	0.400969i	−0.432142	+	0.400969i	0.433884	+	0.900969i	$0.357143\pi$
$440$		0			0
$441$	0.0680900	+	0.908598i	0.0680900	+	0.908598i
$442$	−1.46610			−1.46610
$443$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$443$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.367554	+	0.460898i	−0.367554	+	0.460898i
$448$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$449$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$449$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$450$	0.870666	−	0.268565i	0.870666	−	0.268565i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.414278	−	1.81507i	−0.414278	−	1.81507i
$455$		0			0
$456$		0			0
$457$	−0.440071	−	0.0663300i	−0.440071	−	0.0663300i	−0.0747301	−	0.997204i	$-0.523810\pi$
$457$	−0.440071	−	0.0663300i	−0.440071	−	0.0663300i	−0.365341	+	0.930874i	$0.619048\pi$
$458$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$459$	0.284841	−	0.493360i	0.284841	−	0.493360i
$460$		0			0
$461$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$461$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$462$	0.119523	−	0.387483i	0.119523	−	0.387483i
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$467$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$468$	1.20354	−	0.579597i	1.20354	−	0.579597i
$469$		0			0
$470$		0			0
$471$	−0.284841	−	0.493360i	−0.284841	−	0.493360i
$472$		0			0
$473$		0			0
$474$	−0.173761	−	0.0261903i	−0.173761	−	0.0261903i
$475$		0			0
$476$	0.930874	+	0.365341i	0.930874	+	0.365341i
$477$	0.148145	+	0.649066i	0.148145	+	0.649066i
$478$		0			0
$479$	1.86323	+	0.574730i	1.86323	+	0.574730i	0.997204	+	0.0747301i	$0.0238095\pi$
$479$	1.86323	+	0.574730i	1.86323	+	0.574730i	0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.566649	+	0.129334i	−0.566649	+	0.129334i
$484$	0.530303	−	0.664979i	0.530303	−	0.664979i
$485$		0			0
$486$	−0.0590863	+	0.788452i	−0.0590863	+	0.788452i
$487$	1.71271	−	0.258149i	1.71271	−	0.258149i	0.781831	−	0.623490i	$-0.214286\pi$
$487$	1.71271	−	0.258149i	1.71271	−	0.258149i	0.930874	+	0.365341i	$0.119048\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$497$	0.807782	−	1.67738i	0.807782	−	1.67738i
$498$		0			0
$499$	0.563320	−	0.173761i	0.563320	−	0.173761i		−	1.00000i	$-0.5\pi$
$499$	0.563320	−	0.173761i	0.563320	−	0.173761i	0.563320	+	0.826239i	$0.309524\pi$
$500$		0			0
$501$	0.320914	+	0.0989888i	0.320914	+	0.0989888i
$502$		0			0
$503$	0.443797	+	1.94440i	0.443797	+	1.94440i	0.294755	+	0.955573i	$0.404762\pi$
$503$	0.443797	+	1.94440i	0.443797	+	1.94440i	0.149042	+	0.988831i	$0.452381\pi$
$504$	−0.908598	+	0.0680900i	−0.908598	+	0.0680900i
$505$		0			0
$506$	−2.62285	−	0.395331i	−2.62285	−	0.395331i
$507$	0.283099	−	0.193014i	0.283099	−	0.193014i
$508$		0			0
$509$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$509$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$510$		0			0
$511$		0			0
$512$	0.900969	−	0.433884i	0.900969	−	0.433884i
$513$		0			0
$514$	0.733052	+	0.680173i	0.733052	+	0.680173i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$523$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$524$	0.433884	−	1.90097i	0.433884	−	1.90097i
$525$	−0.297251	+	0.0222759i	−0.297251	+	0.0222759i
$526$		0			0
$527$	−0.116853	−	1.55929i	−0.116853	−	1.55929i
$528$	0.387483	+	0.119523i	0.387483	+	0.119523i
$529$	1.02366	+	2.60825i	1.02366	+	2.60825i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.215372	+	0.548760i	−0.215372	+	0.548760i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.680173	−	1.17809i	0.680173	−	1.17809i
$540$		0			0
$541$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$541$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$542$		0			0
$543$		0			0
$544$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$545$		0			0
$546$	−0.426066	+	0.0972467i	−0.426066	+	0.0972467i
$547$	0.702449	+	0.880843i	0.702449	+	0.880843i	0.997204	−	0.0747301i	$-0.0238095\pi$
$547$	0.702449	+	0.880843i	0.702449	+	0.880843i	−0.294755	+	0.955573i	$0.595238\pi$
$548$	1.88980	−	0.582926i	1.88980	−	0.582926i
$549$		0			0
$550$	−1.29991	−	0.400969i	−1.29991	−	0.400969i
$551$		0			0
$552$	−0.129334	−	0.566649i	−0.129334	−	0.566649i
$553$	−0.548760	−	0.215372i	−0.548760	−	0.215372i
$554$		0			0
$555$		0			0
$556$	−0.487076	+	0.332083i	−0.487076	+	0.332083i
$557$	0.365341	−	0.632789i	0.365341	−	0.632789i	−0.623490	−	0.781831i	$-0.714286\pi$
$557$	0.365341	−	0.632789i	0.365341	−	0.632789i	0.988831	+	0.149042i	$0.0476190\pi$
$558$	0.712362	+	1.23385i	0.712362	+	1.23385i
$559$		0			0
$560$		0			0
$561$	−0.365341	+	0.175939i	−0.365341	+	0.175939i
$562$	0.826239	+	0.563320i	0.826239	+	0.563320i
$563$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$563$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$564$		0			0
$565$		0			0
$566$	−1.22563	+	0.590232i	−1.22563	+	0.590232i
$567$	−0.218511	+	0.708397i	−0.218511	+	0.708397i
$568$	1.67738	+	0.807782i	1.67738	+	0.807782i
$569$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$569$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$	−1.29196	+	0.880843i	−1.29196	+	0.880843i	−0.997204	−	0.0747301i	$-0.976190\pi$
$571$	−1.29196	+	0.880843i	−1.29196	+	0.880843i	−0.294755	+	0.955573i	$0.595238\pi$
$572$	−1.97213	−	0.297251i	−1.97213	−	0.297251i
$573$		0			0
$574$		0			0
$575$	0.433884	+	1.90097i	0.433884	+	1.90097i
$576$	−0.0680900	−	0.908598i	−0.0680900	−	0.908598i
$577$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i	0.222521	−	0.974928i	$-0.428571\pi$
$577$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i	−0.365341	+	0.930874i	$0.619048\pi$
$578$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.363142	−	0.925270i	0.363142	−	0.925270i
$584$		0			0
$585$		0			0
$586$	1.40097	−	1.29991i	1.40097	−	1.29991i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	0.294755	+	0.0444272i	0.294755	+	0.0444272i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	−0.900969	−	0.433884i	$-0.857143\pi$
$593$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	0.955573	+	0.294755i	$0.0952381\pi$
$594$	0.483183	−	0.605893i	0.483183	−	0.605893i
$595$		0			0
$596$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$597$	−0.530303	+	0.163577i	−0.530303	+	0.163577i
$598$	1.04440	+	2.66108i	1.04440	+	2.66108i
$599$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$599$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$600$	−0.0222759	−	0.297251i	−0.0222759	−	0.297251i
$601$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$601$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	0.0663300	−	0.114887i	0.0663300	−	0.114887i
$607$	0.866025	+	1.50000i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$607$	0.866025	+	1.50000i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.667917	+	0.619736i	0.667917	+	0.619736i
$613$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$613$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$614$		0			0
$615$		0			0
$616$	1.17809	+	0.680173i	1.17809	+	0.680173i
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$		0			0
$619$	−0.866025	+	1.50000i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$619$	−0.866025	+	1.50000i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$	−1.09839	−	0.165556i	−1.09839	−	0.165556i
$622$	0.385418	−	1.68862i	0.385418	−	1.68862i
$623$	−1.11406	+	1.63402i	−1.11406	+	1.63402i
$624$	−0.0972467	−	0.426066i	−0.0972467	−	0.426066i
$625$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$626$		0			0
$627$		0			0
$628$	1.82624	−	0.563320i	1.82624	−	0.563320i
$629$		0			0
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$	0.215372	−	0.548760i	0.215372	−	0.548760i
$633$	0.0193303	−	0.257945i	0.0193303	−	0.257945i
$634$		0			0
$635$		0			0
$636$	0.217805			0.217805
$637$	−1.46610			−1.46610
$638$		0			0
$639$	1.24349	−	1.15379i	1.24349	−	1.15379i
$640$		0			0
$641$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$641$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$642$	0.217196	−	0.553406i	0.217196	−	0.553406i
$643$	0.702449	−	0.880843i	0.702449	−	0.880843i	−0.294755	−	0.955573i	$-0.595238\pi$
$643$	0.702449	−	0.880843i	0.702449	−	0.880843i	0.997204	+	0.0747301i	$0.0238095\pi$
$644$		−	1.94986i		−	1.94986i
$645$		0			0
$646$		0			0
$647$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$647$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$648$	−0.708397	−	0.218511i	−0.708397	−	0.218511i
$649$		0			0
$650$	0.326239	+	1.42935i	0.326239	+	1.42935i
$651$	−0.137386	−	0.445396i	−0.137386	−	0.445396i
$652$		0			0
$653$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$653$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$659$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	0.0747301	−	0.997204i	$-0.476190\pi$
$661$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$662$		0			0
$663$	0.361085	+	0.246184i	0.361085	+	0.246184i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.563320	+	0.975699i	−0.563320	+	0.975699i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.0444272	+	0.294755i	−0.0444272	+	0.294755i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$		0			0
$675$	−0.544374	−	0.167917i	−0.544374	−	0.167917i
$676$	0.419945	+	1.07000i	0.419945	+	1.07000i
$677$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$677$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.202749	+	0.516596i	−0.202749	+	0.516596i
$682$	0.158960	−	2.12117i	0.158960	−	2.12117i
$683$	1.84095	−	0.277479i	1.84095	−	0.277479i	0.866025	−	0.500000i	$-0.166667\pi$
$683$	1.84095	−	0.277479i	1.84095	−	0.277479i	0.974928	+	0.222521i	$0.0714286\pi$
$684$		0			0
$685$		0			0
$686$	0.930874	+	0.365341i	0.930874	+	0.365341i
$687$	0.537130			0.537130
$688$		0			0
$689$	−1.05929	+	0.159662i	−1.05929	+	0.159662i
$690$		0			0
$691$	0.571270	−	1.45557i	0.571270	−	1.45557i	−0.294755	−	0.955573i	$-0.595238\pi$
$691$	0.571270	−	1.45557i	0.571270	−	1.45557i	0.866025	−	0.500000i	$-0.166667\pi$
$692$		0			0
$693$	0.969059	−	0.772799i	0.969059	−	0.772799i
$694$	−0.541044	−	0.678448i	−0.541044	−	0.678448i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.134659	+	1.79690i	0.134659	+	1.79690i
$699$		0			0
$700$	0.149042	−	0.988831i	0.149042	−	0.988831i
$701$	0.162592	−	0.712362i	0.162592	−	0.712362i	−0.826239	−	0.563320i	$-0.809524\pi$
$701$	0.162592	−	0.712362i	0.162592	−	0.712362i	0.988831	−	0.149042i	$-0.0476190\pi$
$702$	−0.825886	−	0.124482i	−0.825886	−	0.124482i
$703$		0			0
$704$	−0.680173	+	1.17809i	−0.680173	+	1.17809i
$705$		0			0
$706$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$707$	0.302705	−	0.326239i	0.302705	−	0.326239i
$708$		0			0
$709$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$709$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$710$		0			0
$711$	−0.393744	−	0.365341i	−0.393744	−	0.365341i
$712$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$713$	−2.74698	+	1.32288i	−2.74698	+	1.32288i
$714$	−0.167917	−	0.246289i	−0.167917	−	0.246289i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.34515	−	0.202749i	−1.34515	−	0.202749i	−0.563320	−	0.826239i	$-0.690476\pi$
$719$	−1.34515	−	0.202749i	−1.34515	−	0.202749i	−0.781831	+	0.623490i	$0.785714\pi$
$720$		0			0
$721$		0			0
$722$	0.222521	+	0.974928i	0.222521	+	0.974928i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.242269	+	0.0747301i	−0.242269	+	0.0747301i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		−	1.46610i		−	1.46610i
$729$	−0.315266	+	0.395331i	−0.315266	+	0.395331i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.733052	−	0.680173i	0.733052	−	0.680173i	−0.222521	−	0.974928i	$-0.571429\pi$
$733$	0.733052	−	0.680173i	0.733052	−	0.680173i	0.955573	+	0.294755i	$0.0952381\pi$
$734$	−1.99441			−1.99441
$735$		0			0
$736$	1.94986			1.94986
$737$		0			0
$738$		0			0
$739$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$739$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$740$		0			0
$741$		0			0
$742$	0.712362	+	0.162592i	0.712362	+	0.162592i
$743$	−0.185853	−	0.233052i	−0.185853	−	0.233052i	0.680173	−	0.733052i	$-0.261905\pi$
$743$	−0.185853	−	0.233052i	−0.185853	−	0.233052i	−0.866025	+	0.500000i	$0.833333\pi$
$744$	0.445396	−	0.137386i	0.445396	−	0.137386i
$745$		0			0
$746$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$747$		0			0
$748$	−0.302705	−	1.32624i	−0.302705	−	1.32624i
$749$	1.12349	−	1.64786i	1.12349	−	1.64786i
$750$		0			0
$751$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i	−0.149042	−	0.988831i	$-0.547619\pi$
$751$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i	−0.433884	+	0.900969i	$0.642857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.493360	+	0.284841i	0.493360	+	0.284841i
$757$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$757$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$758$	−1.43109	−	0.975699i	−1.43109	−	0.975699i
$759$	0.579597	+	0.537787i	0.579597	+	0.537787i
$760$		0			0
$761$	−1.36534	−	0.930874i	−1.36534	−	0.930874i	−0.365341	−	0.930874i	$-0.619048\pi$
$761$	−1.36534	−	0.930874i	−1.36534	−	0.930874i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.294755	−	0.0444272i	−0.294755	−	0.0444272i
$769$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$769$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$770$		0			0
$771$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i
$772$		0			0
$773$	−1.57906	−	0.487076i	−1.57906	−	0.487076i	−0.623490	−	0.781831i	$-0.714286\pi$
$773$	−1.57906	−	0.487076i	−1.57906	−	0.487076i	−0.955573	+	0.294755i	$0.904762\pi$
$774$		0			0
$775$	−1.49419	+	0.460898i	−1.49419	+	0.460898i
$776$		0			0
$777$		0			0
$778$	1.03030	−	1.29196i	1.03030	−	1.29196i
$779$		0			0
$780$		0			0
$781$	−2.50433	+	0.377467i	−2.50433	+	0.377467i
$782$	−1.42935	+	1.32624i	−1.42935	+	1.32624i
$783$		0			0
$784$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$785$		0			0
$786$	−0.426066	+	0.395331i	−0.426066	+	0.395331i
$787$	−0.858075	+	0.129334i	−0.858075	+	0.129334i	−0.563320	−	0.826239i	$-0.690476\pi$
$787$	−0.858075	+	0.129334i	−0.858075	+	0.129334i	−0.294755	+	0.955573i	$0.595238\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.772799	+	0.969059i	0.772799	+	0.969059i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.139129	−	1.85654i	−0.139129	−	1.85654i
$797$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	−0.988831	−	0.149042i	$-0.952381\pi$
$797$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	0.826239	−	0.563320i	$-0.190476\pi$
$798$		0			0
$799$		0			0
$800$	0.988831	+	0.149042i	0.988831	+	0.149042i
$801$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−2.06546	+	0.994675i	−2.06546	+	0.994675i
$807$		0			0
$808$	0.326239	+	0.302705i	0.326239	+	0.302705i
$809$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$809$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$810$		0			0
$811$	−1.67738	+	0.807782i	−1.67738	+	0.807782i	−0.680173	+	0.733052i	$0.738095\pi$
$811$	−1.67738	+	0.807782i	−1.67738	+	0.807782i	−0.997204	+	0.0747301i	$0.976190\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.246289	−	0.167917i	0.246289	−	0.167917i
$817$		0			0
$818$	0.162592	−	0.712362i	0.162592	−	0.712362i
$819$	−1.24349	−	0.488035i	−1.24349	−	0.488035i
$820$		0			0
$821$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$821$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$822$	−0.563320	−	0.173761i	−0.563320	−	0.173761i
$823$	0.108903	+	0.277479i	0.108903	+	0.277479i	0.974928	−	0.222521i	$-0.0714286\pi$
$823$	0.108903	+	0.277479i	0.108903	+	0.277479i	−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$	0.252824	+	0.317031i	0.252824	+	0.317031i
$826$		0			0
$827$	1.24349	−	1.55929i	1.24349	−	1.55929i	0.563320	−	0.826239i	$-0.309524\pi$
$827$	1.24349	−	1.55929i	1.24349	−	1.55929i	0.680173	−	0.733052i	$-0.261905\pi$
$828$	0.649066	−	1.65379i	0.649066	−	1.65379i
$829$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	−0.988831	−	0.149042i	$-0.952381\pi$
$829$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	1.00000			$0$
$830$		0			0
$831$		0			0
$832$	1.46610			1.46610
$833$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$834$	0.175724			0.175724
$835$		0			0
$836$		0			0
$837$	0.0665690	−	0.888301i	0.0665690	−	0.888301i
$838$	0.215372	−	0.548760i	0.215372	−	0.548760i
$839$	0.541044	−	0.678448i	0.541044	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$839$	0.541044	−	0.678448i	0.541044	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$	1.19158	−	0.367554i	1.19158	−	0.367554i
$843$	−0.108903	−	0.277479i	−0.108903	−	0.277479i
$844$	0.829215	+	0.255779i	0.829215	+	0.255779i
$845$		0			0
$846$		0			0
$847$	−0.848162	+	0.0635609i	−0.848162	+	0.0635609i
$848$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$849$	0.400969	+	0.0604363i	0.400969	+	0.0604363i
$850$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$851$		0			0
$852$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$853$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$853$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$854$		0			0
$855$		0			0
$856$	1.64786	+	1.12349i	1.64786	+	1.12349i
$857$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$857$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$858$	0.435801	+	0.404364i	0.435801	+	0.404364i
$859$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$859$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$860$		0			0
$861$		0			0
$862$	1.56052	+	0.751509i	1.56052	+	0.751509i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	−0.284841	+	0.493360i	−0.284841	+	0.493360i
$865$		0			0
$866$	0.440071	+	0.0663300i	0.440071	+	0.0663300i
$867$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i
$868$	1.55929	−	0.116853i	1.55929	−	0.116853i
$869$	0.178448	+	0.781831i	0.178448	+	0.781831i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$877$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$878$	−0.0440542	+	0.587862i	−0.0440542	+	0.587862i
$879$	−0.563320	+	0.0849068i	−0.563320	+	0.0849068i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	0.667917	+	0.619736i	0.667917	+	0.619736i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−1.07473	+	0.997204i	−1.07473	+	0.997204i
$885$		0			0
$886$		0			0
$887$	0.496990	−	1.26631i	0.496990	−	1.26631i	−0.433884	−	0.900969i	$-0.642857\pi$
$887$	0.496990	−	1.26631i	0.496990	−	1.26631i	0.930874	−	0.365341i	$-0.119048\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.963664	−	0.297251i	0.963664	−	0.297251i
$892$		0			0
$893$		0			0
$894$	0.0440542	+	0.587862i	0.0440542	+	0.587862i
$895$		0			0
$896$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$897$	0.189617	−	0.830767i	0.189617	−	0.830767i
$898$		0			0
$899$		0			0
$900$	0.455573	−	0.789075i	0.455573	−	0.789075i
$901$	−0.365341	−	0.632789i	−0.365341	−	0.632789i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.14625	+	1.06356i	1.14625	+	1.06356i	0.997204	+	0.0747301i	$0.0238095\pi$
$907$	1.14625	+	1.06356i	1.14625	+	1.06356i	0.149042	+	0.988831i	$0.452381\pi$
$908$	−1.53825	−	1.04876i	−1.53825	−	1.04876i
$909$	0.365341	−	0.175939i	0.365341	−	0.175939i
$910$		0			0
$911$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$911$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$912$		0			0
$913$		0			0
$914$	−0.367711	+	0.250701i	−0.367711	+	0.250701i
$915$		0			0
$916$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$917$	−1.68862	+	0.974928i	−1.68862	+	0.974928i
$918$	−0.126766	−	0.555400i	−0.126766	−	0.555400i
$919$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$919$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$920$		0			0
$921$		0			0
$922$	−0.698220	+	0.215372i	−0.698220	+	0.215372i
$923$	1.70182	+	2.13402i	1.70182	+	2.13402i
$924$	−0.175939	−	0.365341i	−0.175939	−	0.365341i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$929$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.378473	+	0.351172i	−0.378473	+	0.351172i
$934$		0			0
$935$		0			0
$936$	0.488035	−	1.24349i	0.488035	−	1.24349i
$937$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$937$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$941$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$942$	−0.544374	−	0.167917i	−0.544374	−	0.167917i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.71271	−	0.258149i	−1.71271	−	0.258149i	−0.781831	−	0.623490i	$-0.785714\pi$
$947$	−1.71271	−	0.258149i	−1.71271	−	0.258149i	−0.930874	+	0.365341i	$0.880952\pi$
$948$	−0.145190	+	0.0989888i	−0.145190	+	0.0989888i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.930874	−	0.365341i	0.930874	−	0.365341i
$953$	1.48883	−	0.716983i	1.48883	−	0.716983i	0.500000	−	0.866025i	$-0.333333\pi$
$953$	1.48883	−	0.716983i	1.48883	−	0.716983i	0.988831	+	0.149042i	$0.0476190\pi$
$954$	0.550075	+	0.375035i	0.550075	+	0.375035i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	1.75676	−	0.846011i	1.75676	−	0.846011i
$959$	−1.71271	−	0.988831i	−1.71271	−	0.988831i
$960$		0			0
$961$	−0.722521	−	1.25144i	−0.722521	−	1.25144i
$962$		0			0
$963$	1.50144	−	1.02366i	1.50144	−	1.02366i
$964$		0			0
$965$		0			0
$966$	−0.327414	+	0.480228i	−0.327414	+	0.480228i
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	−0.0635609	−	0.848162i	−0.0635609	−	0.848162i
$969$		0			0
$970$		0			0
$971$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$971$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$972$	0.492970	+	0.618165i	0.492970	+	0.618165i
$973$	0.574730	+	0.131178i	0.574730	+	0.131178i
$974$	1.07992	−	1.35417i	1.07992	−	1.35417i
$975$	0.159662	−	0.406813i	0.159662	−	0.406813i
$976$		0			0
$977$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$977$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.365341	+	0.930874i	$0.380952\pi$
$978$		0			0
$979$	2.69030			2.69030
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.34515	−	0.202749i	1.34515	−	0.202749i	0.563320	−	0.826239i	$-0.309524\pi$
$983$	1.34515	−	0.202749i	1.34515	−	0.202749i	0.781831	+	0.623490i	$0.214286\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.781831	−	0.623490i	$-0.214286\pi$
$991$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.294755	+	0.955573i	$0.404762\pi$
$992$	0.116853	+	1.55929i	0.116853	+	1.55929i
$993$		0			0
$994$	−0.548760	−	1.77904i	−0.548760	−	1.77904i
$995$		0			0
$996$		0			0
$997$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$997$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$998$	0.294755	−	0.510531i	0.294755	−	0.510531i
$999$		0			0

Display

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

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a_p

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.cc.c.1971.1	yes	24
4.3	odd	2	inner	3332.1.cc.c.1971.2	yes	24
17.16	even	2	inner	3332.1.cc.c.1971.2	yes	24
49.9	even	21	inner	3332.1.cc.c.1087.1	✓	24
68.67	odd	2	CM	3332.1.cc.c.1971.1	yes	24
196.107	odd	42	inner	3332.1.cc.c.1087.2	yes	24
833.254	even	42	inner	3332.1.cc.c.1087.2	yes	24
3332.1087	odd	42	inner	3332.1.cc.c.1087.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.cc.c.1087.1	✓	24	49.9	even	21	inner
3332.1.cc.c.1087.1	✓	24	3332.1087	odd	42	inner
3332.1.cc.c.1087.2	yes	24	196.107	odd	42	inner
3332.1.cc.c.1087.2	yes	24	833.254	even	42	inner
3332.1.cc.c.1971.1	yes	24	1.1	even	1	trivial
3332.1.cc.c.1971.1	yes	24	68.67	odd	2	CM
3332.1.cc.c.1971.2	yes	24	4.3	odd	2	inner
3332.1.cc.c.1971.2	yes	24	17.16	even	2	inner

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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	3332.1.cc.c.1971.1

Level	$3332$
Weight	$1$
Character	3332.1971
Analytic conductor	$1.663$
Analytic rank	$0$
Dimension	$24$
Projective image	$D_{42}$
CM discriminant	-68
Inner twists	$8$