LMFDB - Embedded newform 1176.1.ck.b.485.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,1,Mod(53,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 21, 10]))

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

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

chi := DirichletCharacter("1176.53");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1176.ck (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:	$0.586900454856$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{21}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{21} + \cdots)$

Embedding invariants

Embedding label			485.1
Root			$0.365341 + 0.930874i$ of defining polynomial
Character	$\chi$	$=$	1176.485
Dual form			1176.1.ck.b.725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988831 + 0.149042i) q^{2} +(0.826239 + 0.563320i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.0546039 - 0.728639i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(0.0747301 + 0.997204i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.988831 + 0.149042i) q^{2} +(0.826239 + 0.563320i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.0546039 - 0.728639i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(0.0747301 + 0.997204i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.365341 + 0.930874i) q^{9} +(0.0546039 + 0.728639i) q^{10} +(0.698220 - 1.77904i) q^{11} +(0.955573 + 0.294755i) q^{12} +(-0.222521 - 0.974928i) q^{14} +(0.455573 - 0.571270i) q^{15} +(0.826239 - 0.563320i) q^{16} +(-0.500000 - 0.866025i) q^{18} +(-0.162592 - 0.712362i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(-0.425270 + 1.86323i) q^{22} +(-0.988831 - 0.149042i) q^{24} +(0.460898 + 0.0694692i) q^{25} +(-0.222521 + 0.974928i) q^{27} +(0.365341 + 0.930874i) q^{28} +(0.440071 + 1.92808i) q^{29} +(-0.365341 + 0.632789i) q^{30} +(-0.826239 - 1.43109i) q^{31} +(-0.733052 + 0.680173i) q^{32} +(1.57906 - 1.07659i) q^{33} +0.730682 q^{35} +(0.623490 + 0.781831i) q^{36} +(0.266948 + 0.680173i) q^{40} +(0.365341 - 0.930874i) q^{42} +(0.142820 - 1.90580i) q^{44} +(0.698220 - 0.215372i) q^{45} +1.00000 q^{48} +(-0.988831 + 0.149042i) q^{49} -0.466104 q^{50} +(-0.955573 + 0.294755i) q^{53} +(0.0747301 - 0.997204i) q^{54} +(-1.25815 - 0.605893i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.722521 - 1.84095i) q^{58} +(-0.0747301 - 0.997204i) q^{59} +(0.266948 - 0.680173i) q^{60} +(1.03030 + 1.29196i) q^{62} +(-0.900969 + 0.433884i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-1.40097 + 1.29991i) q^{66} +(-0.722521 + 0.108903i) q^{70} +(-0.733052 - 0.680173i) q^{72} +(1.78181 + 0.268565i) q^{73} +(0.341678 + 0.317031i) q^{75} +(1.82624 + 0.563320i) q^{77} +(-0.0747301 + 0.129436i) q^{79} +(-0.365341 - 0.632789i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-1.23305 + 1.54620i) q^{83} +(-0.222521 + 0.974928i) q^{84} +(-0.722521 + 1.84095i) q^{87} +(0.142820 + 1.90580i) q^{88} +(-0.658322 + 0.317031i) q^{90} +(0.123490 - 1.64786i) q^{93} +(-0.988831 + 0.149042i) q^{96} -1.46610 q^{97} +(0.955573 - 0.294755i) q^{98} +1.91115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 12 * q + q^2 + q^3 + q^4 - q^5 - 2 * q^6 + q^7 - 2 * q^8 + q^9	$ 12 q + q^{2} + q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{7} - 2 q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 2 q^{14} - 5 q^{15} + q^{16} - 6 q^{18} + 2 q^{20} - 6 q^{21} - 5 q^{22} + q^{24} - 2 q^{27} + q^{28} + 2 q^{29} - q^{30} - q^{31} + q^{32} - q^{33} + 2 q^{35} - 2 q^{36} + 13 q^{40} + q^{42} - q^{44} - q^{45} + 12 q^{48} + q^{49} + 14 q^{50} - q^{53} + q^{54} - 9 q^{55} - 6 q^{56} - 8 q^{58} - q^{59} + 13 q^{60} + 2 q^{62} - 2 q^{63} - 2 q^{64} - 8 q^{66} - 8 q^{70} + q^{72} + 2 q^{73} + 14 q^{75} + 13 q^{77} - q^{79} - q^{80} + q^{81} - 5 q^{83} - 2 q^{84} - 8 q^{87} - q^{88} + 2 q^{90} - 8 q^{93} + q^{96} + 2 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) $ 12 * q + q^2 + q^3 + q^4 - q^5 - 2 * q^6 + q^7 - 2 * q^8 + q^9 - q^10 - q^11 + q^12 - 2 * q^14 - 5 * q^15 + q^16 - 6 * q^18 + 2 * q^20 - 6 * q^21 - 5 * q^22 + q^24 - 2 * q^27 + q^28 + 2 * q^29 - q^30 - q^31 + q^32 - q^33 + 2 * q^35 - 2 * q^36 + 13 * q^40 + q^42 - q^44 - q^45 + 12 * q^48 + q^49 + 14 * q^50 - q^53 + q^54 - 9 * q^55 - 6 * q^56 - 8 * q^58 - q^59 + 13 * q^60 + 2 * q^62 - 2 * q^63 - 2 * q^64 - 8 * q^66 - 8 * q^70 + q^72 + 2 * q^73 + 14 * q^75 + 13 * q^77 - q^79 - q^80 + q^81 - 5 * q^83 - 2 * q^84 - 8 * q^87 - q^88 + 2 * q^90 - 8 * 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 $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$2$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$3$	0.826239	+	0.563320i	0.826239	+	0.563320i
$3$	0.826239	+	0.563320i	0.826239	+	0.563320i
$4$	0.955573	−	0.294755i	0.955573	−	0.294755i
$5$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$5$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$6$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$7$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$7$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$8$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$9$	0.365341	+	0.930874i	0.365341	+	0.930874i
$10$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$11$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.0747301	−	0.997204i	$-0.476190\pi$
$11$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.623490	−	0.781831i	$-0.285714\pi$
$12$	0.955573	+	0.294755i	0.955573	+	0.294755i
$13$		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
$15$	0.455573	−	0.571270i	0.455573	−	0.571270i
$16$	0.826239	−	0.563320i	0.826239	−	0.563320i
$17$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$17$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$18$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$21$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$22$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$23$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$23$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$24$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$25$	0.460898	+	0.0694692i	0.460898	+	0.0694692i
$26$		0			0
$27$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$28$	0.365341	+	0.930874i	0.365341	+	0.930874i
$29$	0.440071	+	1.92808i	0.440071	+	1.92808i	0.365341	+	0.930874i	$0.380952\pi$
$29$	0.440071	+	1.92808i	0.440071	+	1.92808i	0.0747301	+	0.997204i	$0.476190\pi$
$30$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$31$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$31$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$32$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$33$	1.57906	−	1.07659i	1.57906	−	1.07659i
$34$		0			0
$35$	0.730682			0.730682
$36$	0.623490	+	0.781831i	0.623490	+	0.781831i
$37$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$37$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$38$		0			0
$39$		0			0
$40$	0.266948	+	0.680173i	0.266948	+	0.680173i
$41$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$41$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$42$	0.365341	−	0.930874i	0.365341	−	0.930874i
$43$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$43$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$44$	0.142820	−	1.90580i	0.142820	−	1.90580i
$45$	0.698220	−	0.215372i	0.698220	−	0.215372i
$46$		0			0
$47$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$47$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$48$	1.00000			1.00000
$49$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$50$	−0.466104			−0.466104
$51$		0			0
$52$		0			0
$53$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.733052	−	0.680173i	$-0.761905\pi$
$53$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.222521	+	0.974928i	$0.571429\pi$
$54$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$55$	−1.25815	−	0.605893i	−1.25815	−	0.605893i
$56$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$57$		0			0
$58$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$59$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i	0.826239	−	0.563320i	$-0.190476\pi$
$60$	0.266948	−	0.680173i	0.266948	−	0.680173i
$61$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$61$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$62$	1.03030	+	1.29196i	1.03030	+	1.29196i
$63$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$64$	0.623490	−	0.781831i	0.623490	−	0.781831i
$65$		0			0
$66$	−1.40097	+	1.29991i	−1.40097	+	1.29991i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$		0			0
$70$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$71$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$71$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$72$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$73$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$73$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$74$		0			0
$75$	0.341678	+	0.317031i	0.341678	+	0.317031i
$76$		0			0
$77$	1.82624	+	0.563320i	1.82624	+	0.563320i
$78$		0			0
$79$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	−0.900969	−	0.433884i	$-0.857143\pi$
$79$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	0.826239	+	0.563320i	$0.190476\pi$
$80$	−0.365341	−	0.632789i	−0.365341	−	0.632789i
$81$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$82$		0			0
$83$	−1.23305	+	1.54620i	−1.23305	+	1.54620i	−0.500000	+	0.866025i	$0.666667\pi$
$83$	−1.23305	+	1.54620i	−1.23305	+	1.54620i	−0.733052	+	0.680173i	$0.761905\pi$
$84$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$85$		0			0
$86$		0			0
$87$	−0.722521	+	1.84095i	−0.722521	+	1.84095i
$88$	0.142820	+	1.90580i	0.142820	+	1.90580i
$89$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$89$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$90$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$91$		0			0
$92$		0			0
$93$	0.123490	−	1.64786i	0.123490	−	1.64786i
$94$		0			0
$95$		0			0
$96$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$97$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$97$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$98$	0.955573	−	0.294755i	0.955573	−	0.294755i
$99$	1.91115			1.91115
$100$	0.460898	−	0.0694692i	0.460898	−	0.0694692i
$101$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	0.365341	−	0.930874i	$-0.380952\pi$
$101$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$102$		0			0
$103$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$103$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$104$		0			0
$105$	0.603718	+	0.411608i	0.603718	+	0.411608i
$106$	0.900969	−	0.433884i	0.900969	−	0.433884i
$107$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	0.955573	−	0.294755i	$-0.0952381\pi$
$107$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	−0.900969	+	0.433884i	$0.857143\pi$
$108$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$109$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$109$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$110$	1.33440	+	0.411608i	1.33440	+	0.411608i
$111$		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
$116$	0.988831	+	1.71271i	0.988831	+	1.71271i
$117$		0			0
$118$	0.222521	+	0.974928i	0.222521	+	0.974928i
$119$		0			0
$120$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$121$	−1.94440	−	1.80414i	−1.94440	−	1.80414i
$122$		0			0
$123$		0			0
$124$	−1.21135	−	1.12397i	−1.21135	−	1.12397i
$125$	0.238377	−	1.04440i	0.238377	−	1.04440i
$126$	0.826239	−	0.563320i	0.826239	−	0.563320i
$127$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	−0.733052	−	0.680173i	$-0.761905\pi$
$127$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	0.365341	−	0.930874i	$-0.380952\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$	0.123490	−	0.0841939i	0.123490	−	0.0841939i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.123490	−	0.0841939i	0.123490	−	0.0841939i	0.623490	+	0.781831i	$0.285714\pi$
$132$	1.19158	−	1.49419i	1.19158	−	1.49419i
$133$		0			0
$134$		0			0
$135$	0.698220	+	0.215372i	0.698220	+	0.215372i
$136$		0			0
$137$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$137$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$138$		0			0
$139$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$139$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$140$	0.698220	−	0.215372i	0.698220	−	0.215372i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.826239	+	0.563320i	0.826239	+	0.563320i
$145$	1.42890	−	0.215372i	1.42890	−	0.215372i
$146$	−1.80194			−1.80194
$147$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$148$		0			0
$149$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.826239	−	0.563320i	$-0.190476\pi$
$149$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.955573	+	0.294755i	$0.0952381\pi$
$150$	−0.385113	−	0.262566i	−0.385113	−	0.262566i
$151$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.733052	−	0.680173i	$-0.761905\pi$
$151$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.222521	+	0.974928i	$0.571429\pi$
$152$		0			0
$153$		0			0
$154$	−1.88980	−	0.284841i	−1.88980	−	0.284841i
$155$	−1.08786	+	0.523887i	−1.08786	+	0.523887i
$156$		0			0
$157$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$157$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$158$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$159$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$160$	0.455573	+	0.571270i	0.455573	+	0.571270i
$161$		0			0
$162$	0.623490	−	0.781831i	0.623490	−	0.781831i
$163$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$163$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$164$		0			0
$165$	−0.698220	−	1.20935i	−0.698220	−	1.20935i
$166$	0.988831	−	1.71271i	0.988831	−	1.71271i
$167$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$167$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$168$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$169$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	0.0747301	−	0.997204i	$-0.476190\pi$
$173$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$174$	0.440071	−	1.92808i	0.440071	−	1.92808i
$175$	−0.0348320	+	0.464800i	−0.0348320	+	0.464800i
$176$	−0.425270	−	1.86323i	−0.425270	−	1.86323i
$177$	0.500000	−	0.866025i	0.500000	−	0.866025i
$178$		0			0
$179$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$179$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$180$	0.603718	−	0.411608i	0.603718	−	0.411608i
$181$		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
$186$	0.123490	+	1.64786i	0.123490	+	1.64786i
$187$		0			0
$188$		0			0
$189$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$190$		0			0
$191$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$191$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$192$	0.955573	−	0.294755i	0.955573	−	0.294755i
$193$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	0.623490	−	0.781831i	$-0.285714\pi$
$193$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	−0.500000	+	0.866025i	$0.666667\pi$
$194$	1.44973	−	0.218511i	1.44973	−	0.218511i
$195$		0			0
$196$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$197$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$197$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$198$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$199$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.988831	−	0.149042i	$-0.952381\pi$
$199$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.500000	−	0.866025i	$-0.666667\pi$
$200$	−0.445396	+	0.137386i	−0.445396	+	0.137386i
$201$		0			0
$202$	0.400969	+	0.193096i	0.400969	+	0.193096i
$203$	−1.88980	+	0.582926i	−1.88980	+	0.582926i
$204$		0			0
$205$		0			0
$206$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$211$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$211$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$212$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$213$		0			0
$214$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$215$		0			0
$216$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$217$	1.36534	−	0.930874i	1.36534	−	0.930874i
$218$		0			0
$219$	1.32091	+	1.22563i	1.32091	+	1.22563i
$220$	−1.38084	−	0.208129i	−1.38084	−	0.208129i
$221$		0			0
$222$		0			0
$223$	0.326239	−	1.42935i	0.326239	−	1.42935i	−0.500000	−	0.866025i	$-0.666667\pi$
$223$	0.326239	−	1.42935i	0.326239	−	1.42935i	0.826239	−	0.563320i	$-0.190476\pi$
$224$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$225$	0.103718	+	0.454418i	0.103718	+	0.454418i
$226$		0			0
$227$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$227$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$228$		0			0
$229$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$229$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$230$		0			0
$231$	1.19158	+	1.49419i	1.19158	+	1.49419i
$232$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$233$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$233$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$234$		0			0
$235$		0			0
$236$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$237$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$238$		0			0
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$241$	−1.88980	+	0.582926i	−1.88980	+	0.582926i	−0.900969	+	0.433884i	$0.857143\pi$
$241$	−1.88980	+	0.582926i	−1.88980	+	0.582926i	−0.988831	+	0.149042i	$0.952381\pi$
$242$	2.19158	+	1.49419i	2.19158	+	1.49419i
$243$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$244$		0			0
$245$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$246$		0			0
$247$		0			0
$248$	1.36534	+	0.930874i	1.36534	+	0.930874i
$249$	−1.88980	+	0.582926i	−1.88980	+	0.582926i
$250$	−0.0800550	+	1.06826i	−0.0800550	+	1.06826i
$251$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.988831	+	0.149042i	$0.952381\pi$
$252$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$253$		0			0
$254$	0.603718	+	1.53825i	0.603718	+	1.53825i
$255$		0			0
$256$	0.365341	−	0.930874i	0.365341	−	0.930874i
$257$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$257$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$262$	−0.109562	+	0.101659i	−0.109562	+	0.101659i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$265$	0.162592	+	0.712362i	0.162592	+	0.712362i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.95557	+	0.294755i	1.95557	+	0.294755i	1.00000			$0$
$269$	1.95557	+	0.294755i	1.95557	+	0.294755i	0.955573	+	0.294755i	$0.0952381\pi$
$270$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$271$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$271$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.445396	−	0.771449i	0.445396	−	0.771449i
$276$		0			0
$277$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$277$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$278$		0			0
$279$	1.03030	−	1.29196i	1.03030	−	1.29196i
$280$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$281$		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		0.365341	−	0.930874i	$-0.380952\pi$
$283$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$289$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$290$	−1.38084	+	0.425934i	−1.38084	+	0.425934i
$291$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$292$	1.78181	−	0.268565i	1.78181	−	0.268565i
$293$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$293$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$294$	0.955573	+	0.294755i	0.955573	+	0.294755i
$295$	−0.730682			−0.730682
$296$		0			0
$297$	1.57906	+	1.07659i	1.57906	+	1.07659i
$298$	−1.72188	+	0.531130i	−1.72188	+	0.531130i
$299$		0			0
$300$	0.419945	+	0.202235i	0.419945	+	0.202235i
$301$		0			0
$302$	0.900969	−	0.433884i	0.900969	−	0.433884i
$303$	−0.162592	−	0.414278i	−0.162592	−	0.414278i
$304$		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	$0.285714\pi$
$308$	1.91115			1.91115
$309$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$310$	0.997630	−	0.680173i	0.997630	−	0.680173i
$311$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$311$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$312$		0			0
$313$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	−0.900969	−	0.433884i	$-0.857143\pi$
$313$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	0.826239	+	0.563320i	$0.190476\pi$
$314$		0			0
$315$	0.266948	+	0.680173i	0.266948	+	0.680173i
$316$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$317$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$317$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$318$	0.988831	+	0.149042i	0.988831	+	0.149042i
$319$	3.73738	+	0.563320i	3.73738	+	0.563320i
$320$	−0.535628	−	0.496990i	−0.535628	−	0.496990i
$321$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	0.870666	+	1.09178i	0.870666	+	1.09178i
$331$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$331$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$332$	−0.722521	+	1.84095i	−0.722521	+	1.84095i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$337$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$337$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$338$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$339$		0			0
$340$		0			0
$341$	−3.12285	+	0.470694i	−3.12285	+	0.470694i
$342$		0			0
$343$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$344$		0			0
$345$		0			0
$346$	1.03030	+	0.702449i	1.03030	+	0.702449i
$347$	1.19158	−	0.367554i	1.19158	−	0.367554i	0.365341	−	0.930874i	$-0.380952\pi$
$347$	1.19158	−	0.367554i	1.19158	−	0.367554i	0.826239	+	0.563320i	$0.190476\pi$
$348$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$349$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$349$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$350$	−0.0348320	−	0.464800i	−0.0348320	−	0.464800i
$351$		0			0
$352$	0.698220	+	1.77904i	0.698220	+	1.77904i
$353$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$353$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$354$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.777479	−	0.974928i	0.777479	−	0.974928i
$359$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$359$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$360$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	−0.590232	−	2.58597i	−0.590232	−	2.58597i
$364$		0			0
$365$	0.292981	−	1.28363i	0.292981	−	1.28363i
$366$		0			0
$367$	0.988831	+	0.149042i	0.988831	+	0.149042i	0.623490	−	0.781831i	$-0.285714\pi$
$367$	0.988831	+	0.149042i	0.988831	+	0.149042i	0.365341	+	0.930874i	$0.380952\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$372$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	0.785286	−	0.728639i	0.785286	−	0.728639i
$376$		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
$381$	0.603718	−	1.53825i	0.603718	−	1.53825i
$382$		0			0
$383$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$383$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$384$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$385$	0.510177	−	1.29991i	0.510177	−	1.29991i
$386$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i
$387$		0			0
$388$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$389$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.955573	−	0.294755i	$-0.0952381\pi$
$389$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.0747301	+	0.997204i	$0.476190\pi$
$390$		0			0
$391$		0			0
$392$	0.826239	−	0.563320i	0.826239	−	0.563320i
$393$	0.149460			0.149460
$394$	0.440071	−	0.0663300i	0.440071	−	0.0663300i
$395$	0.0902318	+	0.0615190i	0.0902318	+	0.0615190i
$396$	1.82624	−	0.563320i	1.82624	−	0.563320i
$397$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$397$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$398$	1.62349	+	0.781831i	1.62349	+	0.781831i
$399$		0			0
$400$	0.419945	−	0.202235i	0.419945	−	0.202235i
$401$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$401$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$402$		0			0
$403$		0			0
$404$	−0.425270	−	0.131178i	−0.425270	−	0.131178i
$405$	0.455573	+	0.571270i	0.455573	+	0.571270i
$406$	1.78181	−	0.858075i	1.78181	−	0.858075i
$407$		0			0
$408$		0			0
$409$	0.733052	−	0.680173i	0.733052	−	0.680173i	−0.222521	−	0.974928i	$-0.571429\pi$
$409$	0.733052	−	0.680173i	0.733052	−	0.680173i	0.955573	+	0.294755i	$0.0952381\pi$
$410$		0			0
$411$		0			0
$412$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$413$	0.988831	−	0.149042i	0.988831	−	0.149042i
$414$		0			0
$415$	1.05929	+	0.982878i	1.05929	+	0.982878i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$419$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$420$	0.698220	+	0.215372i	0.698220	+	0.215372i
$421$		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
$424$	0.733052	−	0.680173i	0.733052	−	0.680173i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$429$		0			0
$430$		0			0
$431$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$431$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$432$	0.365341	+	0.930874i	0.365341	+	0.930874i
$433$	−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	$0.571429\pi$
$434$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$435$	1.30194	+	0.626980i	1.30194	+	0.626980i
$436$		0			0
$437$		0			0
$438$	−1.48883	−	1.01507i	−1.48883	−	1.01507i
$439$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.988831	−	0.149042i	$-0.952381\pi$
$439$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.900969	+	0.433884i	$0.857143\pi$
$440$	1.39644			1.39644
$441$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$442$		0			0
$443$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$443$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$444$		0			0
$445$		0			0
$446$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$447$	1.62349	+	0.781831i	1.62349	+	0.781831i
$448$	0.826239	+	0.563320i	0.826239	+	0.563320i
$449$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$449$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$450$	−0.170287	−	0.433884i	−0.170287	−	0.433884i
$451$		0			0
$452$		0			0
$453$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$454$	1.19158	+	1.49419i	1.19158	+	1.49419i
$455$		0			0
$456$		0			0
$457$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.733052	+	0.680173i	$0.761905\pi$
$457$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−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	$0.285714\pi$
$461$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$462$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$463$	−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	$0.857143\pi$
$464$	1.44973	+	1.34515i	1.44973	+	1.34515i
$465$	−1.19395	−	0.179959i	−1.19395	−	0.179959i
$466$		0			0
$467$	0.326239	+	0.302705i	0.326239	+	0.302705i	0.826239	−	0.563320i	$-0.190476\pi$
$467$	0.326239	+	0.302705i	0.326239	+	0.302705i	−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.500000	+	0.866025i	0.500000	+	0.866025i
$473$		0			0
$474$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$475$		0			0
$476$		0			0
$477$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$478$		0			0
$479$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$479$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$480$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$481$		0			0
$482$	1.78181	−	0.858075i	1.78181	−	0.858075i
$483$		0			0
$484$	−2.38980	−	1.15087i	−2.38980	−	1.15087i
$485$	−0.0800550	+	1.06826i	−0.0800550	+	1.06826i
$486$	0.955573	−	0.294755i	0.955573	−	0.294755i
$487$	1.36534	+	0.930874i	1.36534	+	0.930874i	1.00000			$0$
$487$	1.36534	+	0.930874i	1.36534	+	0.930874i	0.365341	+	0.930874i	$0.380952\pi$
$488$		0			0
$489$		0			0
$490$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$491$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$491$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.104356	−	1.39254i	0.104356	−	1.39254i
$496$	−1.48883	−	0.716983i	−1.48883	−	0.716983i
$497$		0			0
$498$	1.78181	−	0.858075i	1.78181	−	0.858075i
$499$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$499$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$500$	−0.0800550	−	1.06826i	−0.0800550	−	1.06826i
$501$		0			0
$502$	1.57906	+	0.487076i	1.57906	+	0.487076i
$503$		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
$505$	−0.202749	+	0.254239i	−0.202749	+	0.254239i
$506$		0			0
$507$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$508$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$509$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$509$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$510$		0			0
$511$	−0.134659	+	1.79690i	−0.134659	+	1.79690i
$512$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$513$		0			0
$514$		0			0
$515$	0.321552	+	0.0484662i	0.321552	+	0.0484662i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$	1.44973	−	1.34515i	1.44973	−	1.34515i
$523$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$523$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$524$	0.0931869	−	0.116853i	0.0931869	−	0.116853i
$525$	−0.290611	+	0.364415i	−0.290611	+	0.364415i
$526$		0			0
$527$		0			0
$528$	0.698220	−	1.77904i	0.698220	−	1.77904i
$529$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$530$	−0.266948	−	0.680173i	−0.266948	−	0.680173i
$531$	0.900969	−	0.433884i	0.900969	−	0.433884i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.104356	−	0.0321896i	0.104356	−	0.0321896i
$536$		0			0
$537$	−1.23305	+	0.185853i	−1.23305	+	0.185853i
$538$	−1.97766			−1.97766
$539$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$540$	0.730682			0.730682
$541$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$541$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$542$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$543$		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
$550$	−0.325443	+	0.829215i	−0.325443	+	0.829215i
$551$		0			0
$552$		0			0
$553$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$557$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$558$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$559$		0			0
$560$	0.603718	−	0.411608i	0.603718	−	0.411608i
$561$		0			0
$562$		0			0
$563$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	0.0747301	−	0.997204i	$-0.476190\pi$
$563$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	−0.222521	+	0.974928i	$0.571429\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$571$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.955573	+	0.294755i	0.955573	+	0.294755i
$577$	0.603718	−	1.53825i	0.603718	−	1.53825i	−0.222521	−	0.974928i	$-0.571429\pi$
$577$	0.603718	−	1.53825i	0.603718	−	1.53825i	0.826239	−	0.563320i	$-0.190476\pi$
$578$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$579$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$580$	1.30194	−	0.626980i	1.30194	−	0.626980i
$581$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$582$	1.32091	+	0.636119i	1.32091	+	0.636119i
$583$	−0.142820	+	1.90580i	−0.142820	+	1.90580i
$584$	−1.72188	+	0.531130i	−1.72188	+	0.531130i
$585$		0			0
$586$	1.44973	−	0.218511i	1.44973	−	0.218511i
$587$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$587$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$588$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$589$		0			0
$590$	0.722521	−	0.108903i	0.722521	−	0.108903i
$591$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$592$		0			0
$593$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$593$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$594$	−1.72188	−	0.829215i	−1.72188	−	0.829215i
$595$		0			0
$596$	1.62349	−	0.781831i	1.62349	−	0.781831i
$597$	−0.658322	−	1.67738i	−0.658322	−	1.67738i
$598$		0			0
$599$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$599$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$600$	−0.445396	−	0.137386i	−0.445396	−	0.137386i
$601$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.955573	+	0.294755i	$0.0952381\pi$
$601$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.0747301	+	0.997204i	$0.476190\pi$
$602$		0			0
$603$		0			0
$604$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$605$	−1.42074	+	1.31825i	−1.42074	+	1.31825i
$606$	0.222521	+	0.385418i	0.222521	+	0.385418i
$607$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.222521	+	0.974928i	$0.571429\pi$
$607$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.733052	+	0.680173i	$0.761905\pi$
$608$		0			0
$609$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$613$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$614$		0			0
$615$		0			0
$616$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$617$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$617$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$618$	0.222521	−	0.385418i	0.222521	−	0.385418i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$	−0.885113	+	0.821265i	−0.885113	+	0.821265i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.302576	−	0.0933323i	−0.302576	−	0.0933323i
$626$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.365341	−	0.632789i	−0.365341	−	0.632789i
$631$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.955573	−	0.294755i	$-0.0952381\pi$
$631$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.365341	+	0.930874i	$0.380952\pi$
$632$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$633$		0			0
$634$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$635$	−1.19395	+	0.179959i	−1.19395	+	0.179959i
$636$	−1.00000			−1.00000
$637$		0			0
$638$	−3.77960			−3.77960
$639$		0			0
$640$	0.603718	+	0.411608i	0.603718	+	0.411608i
$641$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$641$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$642$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$643$		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		−0.0747301	−	0.997204i	$-0.523810\pi$
$647$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$648$	0.365341	−	0.930874i	0.365341	−	0.930874i
$649$	−1.82624	−	0.563320i	−1.82624	−	0.563320i
$650$		0			0
$651$	1.65248			1.65248
$652$		0			0
$653$	0.603718	−	0.411608i	0.603718	−	0.411608i	−0.222521	−	0.974928i	$-0.571429\pi$
$653$	0.603718	−	0.411608i	0.603718	−	0.411608i	0.826239	+	0.563320i	$0.190476\pi$
$654$		0			0
$655$	−0.0546039	−	0.0945768i	−0.0546039	−	0.0945768i
$656$		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	$-0.857143\pi$
$659$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$660$	−1.02366	−	0.949820i	−1.02366	−	0.949820i
$661$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$661$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$662$		0			0
$663$		0			0
$664$	0.440071	−	1.92808i	0.440071	−	1.92808i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	1.07473	−	0.997204i	1.07473	−	0.997204i
$670$		0			0
$671$		0			0
$672$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$673$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.826239	+	0.563320i	$0.190476\pi$
$673$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.365341	+	0.930874i	$0.380952\pi$
$674$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$675$	−0.170287	+	0.433884i	−0.170287	+	0.433884i
$676$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$677$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$677$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$678$		0			0
$679$	−0.109562	−	1.46200i	−0.109562	−	1.46200i
$680$		0			0
$681$	0.142820	−	1.90580i	0.142820	−	1.90580i
$682$	3.01782	−	0.930874i	3.01782	−	0.930874i
$683$	0.603718	+	0.411608i	0.603718	+	0.411608i	0.826239	−	0.563320i	$-0.190476\pi$
$683$	0.603718	+	0.411608i	0.603718	+	0.411608i	−0.222521	+	0.974928i	$0.571429\pi$
$684$		0			0
$685$		0			0
$686$	0.365341	+	0.930874i	0.365341	+	0.930874i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$691$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$692$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$693$	0.142820	+	1.90580i	0.142820	+	1.90580i
$694$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$695$		0			0
$696$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.103718	+	0.454418i	0.103718	+	0.454418i
$701$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.0747301	−	0.997204i	$-0.476190\pi$
$701$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.955573	−	0.294755i	$-0.0952381\pi$
$702$		0			0
$703$		0			0
$704$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$705$		0			0
$706$		0			0
$707$	0.222521	−	0.385418i	0.222521	−	0.385418i
$708$	0.222521	−	0.974928i	0.222521	−	0.974928i
$709$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$709$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$710$		0			0
$711$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$717$		0			0
$718$		0			0
$719$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$719$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$720$	0.455573	−	0.571270i	0.455573	−	0.571270i
$721$	−0.445042			−0.445042
$722$	0.623490	+	0.781831i	0.623490	+	0.781831i
$723$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$724$		0			0
$725$	0.0688859	+	0.919218i	0.0688859	+	0.919218i
$726$	0.969059	+	2.46912i	0.969059	+	2.46912i
$727$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.826239	−	0.563320i	$-0.190476\pi$
$727$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.955573	−	0.294755i	$-0.0952381\pi$
$728$		0			0
$729$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$730$	−0.0983929	+	1.31296i	−0.0983929	+	1.31296i
$731$		0			0
$732$		0			0
$733$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$733$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$734$	−1.00000			−1.00000
$735$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$739$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$740$		0			0
$741$		0			0
$742$	0.500000	+	0.866025i	0.500000	+	0.866025i
$743$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$743$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$744$	0.603718	+	1.53825i	0.603718	+	1.53825i
$745$	−0.0983929	−	1.31296i	−0.0983929	−	1.31296i
$746$		0			0
$747$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$748$		0			0
$749$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$750$	−0.667917	+	0.837541i	−0.667917	+	0.837541i
$751$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.623490	−	0.781831i	$-0.285714\pi$
$751$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.955573	−	0.294755i	$-0.0952381\pi$
$752$		0			0
$753$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$754$		0			0
$755$	0.162592	+	0.712362i	0.162592	+	0.712362i
$756$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$757$		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		−0.733052	−	0.680173i	$-0.761905\pi$
$761$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$762$	−0.367711	+	1.61105i	−0.367711	+	1.61105i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.826239	−	0.563320i	0.826239	−	0.563320i
$769$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	−0.733052	−	0.680173i	$-0.761905\pi$
$769$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	0.826239	+	0.563320i	$0.190476\pi$
$770$	−0.310737	+	1.36143i	−0.310737	+	1.36143i
$771$		0			0
$772$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$773$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	−0.988831	−	0.149042i	$-0.952381\pi$
$773$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	0.826239	+	0.563320i	$0.190476\pi$
$774$		0			0
$775$	−0.281395	−	0.716983i	−0.281395	−	0.716983i
$776$	1.32091	−	0.636119i	1.32091	−	0.636119i
$777$		0			0
$778$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.97766			−1.97766
$784$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$785$		0			0
$786$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i
$787$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$787$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$788$	−0.425270	+	0.131178i	−0.425270	+	0.131178i
$789$		0			0
$790$	−0.0983929	−	0.0473835i	−0.0983929	−	0.0473835i
$791$		0			0
$792$	−1.72188	+	0.829215i	−1.72188	+	0.829215i
$793$		0			0
$794$		0			0
$795$	−0.266948	+	0.680173i	−0.266948	+	0.680173i
$796$	−1.72188	−	0.531130i	−1.72188	−	0.531130i
$797$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	−0.988831	−	0.149042i	$-0.952381\pi$
$797$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	0.0747301	−	0.997204i	$-0.476190\pi$
$798$		0			0
$799$		0			0
$800$	−0.385113	+	0.262566i	−0.385113	+	0.262566i
$801$		0			0
$802$		0			0
$803$	1.72188	−	2.98239i	1.72188	−	2.98239i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.44973	+	1.34515i	1.44973	+	1.34515i
$808$	0.440071	+	0.0663300i	0.440071	+	0.0663300i
$809$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$809$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$810$	−0.535628	−	0.496990i	−0.535628	−	0.496990i
$811$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$811$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$812$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$813$	0.326239	+	1.42935i	0.326239	+	1.42935i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$819$		0			0
$820$		0			0
$821$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	0.365341	−	0.930874i	$-0.380952\pi$
$821$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	−0.222521	+	0.974928i	$0.571429\pi$
$822$		0			0
$823$	−0.134659	−	1.79690i	−0.134659	−	1.79690i	−0.500000	−	0.866025i	$-0.666667\pi$
$823$	−0.134659	−	1.79690i	−0.134659	−	1.79690i	0.365341	−	0.930874i	$-0.380952\pi$
$824$	−0.162592	−	0.414278i	−0.162592	−	0.414278i
$825$	0.802576	−	0.386500i	0.802576	−	0.386500i
$826$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$827$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$827$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$828$		0			0
$829$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$829$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$830$	−1.19395	−	0.814021i	−1.19395	−	0.814021i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.57906	−	0.487076i	1.57906	−	0.487076i
$838$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$839$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$839$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$840$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$841$	−2.62285	+	1.26310i	−2.62285	+	1.26310i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.698220	+	0.215372i	0.698220	+	0.215372i
$846$		0			0
$847$	1.65379	−	2.07379i	1.65379	−	2.07379i
$848$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$849$		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
$856$	−0.109562	−	0.101659i	−0.109562	−	0.101659i
$857$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$857$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$858$		0			0
$859$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$859$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$865$	−0.667917	+	0.619736i	−0.667917	+	0.619736i
$866$	1.03030	−	0.702449i	1.03030	−	0.702449i
$867$	0.623490	−	0.781831i	0.623490	−	0.781831i
$868$	1.03030	−	1.29196i	1.03030	−	1.29196i
$869$	0.178094	+	0.223322i	0.178094	+	0.223322i
$870$	−1.38084	−	0.425934i	−1.38084	−	0.425934i
$871$		0			0
$872$		0			0
$873$	−0.535628	−	1.36476i	−0.535628	−	1.36476i
$874$		0			0
$875$	1.05929	+	0.159662i	1.05929	+	0.159662i
$876$	1.62349	+	0.781831i	1.62349	+	0.781831i
$877$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$877$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$878$	1.82624	−	0.563320i	1.82624	−	0.563320i
$879$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$880$	−1.38084	+	0.208129i	−1.38084	+	0.208129i
$881$		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
$885$	−0.603718	−	0.411608i	−0.603718	−	0.411608i
$886$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$887$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$887$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$888$		0			0
$889$	1.57906	−	0.487076i	1.57906	−	0.487076i
$890$		0			0
$891$	0.698220	+	1.77904i	0.698220	+	1.77904i
$892$	−0.109562	−	1.46200i	−0.109562	−	1.46200i
$893$		0			0
$894$	−1.72188	−	0.531130i	−1.72188	−	0.531130i
$895$	0.568090	+	0.712362i	0.568090	+	0.712362i
$896$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$897$		0			0
$898$		0			0
$899$	2.39564	−	2.22283i	2.39564	−	2.22283i
$900$	0.233052	+	0.403658i	0.233052	+	0.403658i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.988831	+	0.149042i	0.988831	+	0.149042i
$907$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$907$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$908$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$909$	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
$913$	1.88980	+	3.27323i	1.88980	+	3.27323i
$914$	1.44973	−	1.34515i	1.44973	−	1.34515i
$915$		0			0
$916$		0			0
$917$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$918$		0			0
$919$	−0.425270	−	0.131178i	−0.425270	−	0.131178i	0.0747301	−	0.997204i	$-0.476190\pi$
$919$	−0.425270	−	0.131178i	−0.425270	−	0.131178i	−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$		0			0
$922$	−0.658322	−	1.67738i	−0.658322	−	1.67738i
$923$		0			0
$924$	1.57906	+	1.07659i	1.57906	+	1.07659i
$925$		0			0
$926$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$927$	−0.425270	+	0.131178i	−0.425270	+	0.131178i
$928$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$929$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$929$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$930$	1.20744			1.20744
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$935$		0			0
$936$		0			0
$937$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.500000	−	0.866025i	$-0.666667\pi$
$937$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.988831	+	0.149042i	$0.952381\pi$
$938$		0			0
$939$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$940$		0			0
$941$	−0.109562	−	1.46200i	−0.109562	−	1.46200i	−0.733052	−	0.680173i	$-0.761905\pi$
$941$	−0.109562	−	1.46200i	−0.109562	−	1.46200i	0.623490	−	0.781831i	$-0.285714\pi$
$942$		0			0
$943$		0			0
$944$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$945$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$946$		0			0
$947$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.500000	+	0.866025i	$0.666667\pi$
$947$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$948$	−0.109562	+	0.101659i	−0.109562	+	0.101659i
$949$		0			0
$950$		0			0
$951$	0.326239	+	1.42935i	0.326239	+	1.42935i
$952$		0			0
$953$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$953$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$954$	0.733052	+	0.680173i	0.733052	+	0.680173i
$955$		0			0
$956$		0			0
$957$	2.77064	+	2.57078i	2.77064	+	2.57078i
$958$		0			0
$959$		0			0
$960$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$961$	−0.865341	+	1.49881i	−0.865341	+	1.49881i
$962$		0			0
$963$	−0.109562	+	0.101659i	−0.109562	+	0.101659i
$964$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$965$	0.0680900	−	0.0853822i	0.0680900	−	0.0853822i
$966$		0			0
$967$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	0.826239	−	0.563320i	$-0.190476\pi$
$967$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	−0.733052	+	0.680173i	$0.761905\pi$
$968$	2.53464	+	0.781831i	2.53464	+	0.781831i
$969$		0			0
$970$	−0.0800550	−	1.06826i	−0.0800550	−	1.06826i
$971$	0.603718	+	1.53825i	0.603718	+	1.53825i	0.826239	+	0.563320i	$0.190476\pi$
$971$	0.603718	+	1.53825i	0.603718	+	1.53825i	−0.222521	+	0.974928i	$0.571429\pi$
$972$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$973$		0			0
$974$	−1.48883	−	0.716983i	−1.48883	−	0.716983i
$975$		0			0
$976$		0			0
$977$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$977$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$978$		0			0
$979$		0			0
$980$	0.266948	+	0.680173i	0.266948	+	0.680173i
$981$		0			0
$982$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$983$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$983$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$984$		0			0
$985$	−0.0243010	+	0.324275i	−0.0243010	+	0.324275i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.104356	+	1.39254i	0.104356	+	1.39254i
$991$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.0747301	−	0.997204i	$-0.476190\pi$
$991$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.623490	−	0.781831i	$-0.285714\pi$
$992$	1.57906	+	0.487076i	1.57906	+	0.487076i
$993$		0			0
$994$		0			0
$995$	−0.820914	+	1.02939i	−0.820914	+	1.02939i
$996$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$997$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$997$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.1.ck.b.485.1	yes	12
3.2	odd	2		1176.1.ck.a.485.1	✓	12
8.5	even	2		1176.1.ck.a.485.1	✓	12
24.5	odd	2	CM	1176.1.ck.b.485.1	yes	12
49.39	even	21	inner	1176.1.ck.b.725.1	yes	12
147.137	odd	42		1176.1.ck.a.725.1	yes	12
392.333	even	42		1176.1.ck.a.725.1	yes	12
1176.725	odd	42	inner	1176.1.ck.b.725.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.1.ck.a.485.1	✓	12	3.2	odd	2
1176.1.ck.a.485.1	✓	12	8.5	even	2
1176.1.ck.a.725.1	yes	12	147.137	odd	42
1176.1.ck.a.725.1	yes	12	392.333	even	42
1176.1.ck.b.485.1	yes	12	1.1	even	1	trivial
1176.1.ck.b.485.1	yes	12	24.5	odd	2	CM
1176.1.ck.b.725.1	yes	12	49.39	even	21	inner
1176.1.ck.b.725.1	yes	12	1176.725	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1176.ck (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988831 + 0.149042i) q^{2} +(0.826239 + 0.563320i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.0546039 - 0.728639i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(0.0747301 + 0.997204i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.988831 + 0.149042i) q^{2} +(0.826239 + 0.563320i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.0546039 - 0.728639i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(0.0747301 + 0.997204i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.365341 + 0.930874i) q^{9} +(0.0546039 + 0.728639i) q^{10} +(0.698220 - 1.77904i) q^{11} +(0.955573 + 0.294755i) q^{12} +(-0.222521 - 0.974928i) q^{14} +(0.455573 - 0.571270i) q^{15} +(0.826239 - 0.563320i) q^{16} +(-0.500000 - 0.866025i) q^{18} +(-0.162592 - 0.712362i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(-0.425270 + 1.86323i) q^{22} +(-0.988831 - 0.149042i) q^{24} +(0.460898 + 0.0694692i) q^{25} +(-0.222521 + 0.974928i) q^{27} +(0.365341 + 0.930874i) q^{28} +(0.440071 + 1.92808i) q^{29} +(-0.365341 + 0.632789i) q^{30} +(-0.826239 - 1.43109i) q^{31} +(-0.733052 + 0.680173i) q^{32} +(1.57906 - 1.07659i) q^{33} +0.730682 q^{35} +(0.623490 + 0.781831i) q^{36} +(0.266948 + 0.680173i) q^{40} +(0.365341 - 0.930874i) q^{42} +(0.142820 - 1.90580i) q^{44} +(0.698220 - 0.215372i) q^{45} +1.00000 q^{48} +(-0.988831 + 0.149042i) q^{49} -0.466104 q^{50} +(-0.955573 + 0.294755i) q^{53} +(0.0747301 - 0.997204i) q^{54} +(-1.25815 - 0.605893i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.722521 - 1.84095i) q^{58} +(-0.0747301 - 0.997204i) q^{59} +(0.266948 - 0.680173i) q^{60} +(1.03030 + 1.29196i) q^{62} +(-0.900969 + 0.433884i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-1.40097 + 1.29991i) q^{66} +(-0.722521 + 0.108903i) q^{70} +(-0.733052 - 0.680173i) q^{72} +(1.78181 + 0.268565i) q^{73} +(0.341678 + 0.317031i) q^{75} +(1.82624 + 0.563320i) q^{77} +(-0.0747301 + 0.129436i) q^{79} +(-0.365341 - 0.632789i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-1.23305 + 1.54620i) q^{83} +(-0.222521 + 0.974928i) q^{84} +(-0.722521 + 1.84095i) q^{87} +(0.142820 + 1.90580i) q^{88} +(-0.658322 + 0.317031i) q^{90} +(0.123490 - 1.64786i) q^{93} +(-0.988831 + 0.149042i) q^{96} -1.46610 q^{97} +(0.955573 - 0.294755i) q^{98} +1.91115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 12 * q + q^2 + q^3 + q^4 - q^5 - 2 * q^6 + q^7 - 2 * q^8 + q^9	\( 12 q + q^{2} + q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{7} - 2 q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 2 q^{14} - 5 q^{15} + q^{16} - 6 q^{18} + 2 q^{20} - 6 q^{21} - 5 q^{22} + q^{24} - 2 q^{27} + q^{28} + 2 q^{29} - q^{30} - q^{31} + q^{32} - q^{33} + 2 q^{35} - 2 q^{36} + 13 q^{40} + q^{42} - q^{44} - q^{45} + 12 q^{48} + q^{49} + 14 q^{50} - q^{53} + q^{54} - 9 q^{55} - 6 q^{56} - 8 q^{58} - q^{59} + 13 q^{60} + 2 q^{62} - 2 q^{63} - 2 q^{64} - 8 q^{66} - 8 q^{70} + q^{72} + 2 q^{73} + 14 q^{75} + 13 q^{77} - q^{79} - q^{80} + q^{81} - 5 q^{83} - 2 q^{84} - 8 q^{87} - q^{88} + 2 q^{90} - 8 q^{93} + q^{96} + 2 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + q^2 + q^3 + q^4 - q^5 - 2 * q^6 + q^7 - 2 * q^8 + q^9 - q^10 - q^11 + q^12 - 2 * q^14 - 5 * q^15 + q^16 - 6 * q^18 + 2 * q^20 - 6 * q^21 - 5 * q^22 + q^24 - 2 * q^27 + q^28 + 2 * q^29 - q^30 - q^31 + q^32 - q^33 + 2 * q^35 - 2 * q^36 + 13 * q^40 + q^42 - q^44 - q^45 + 12 * q^48 + q^49 + 14 * q^50 - q^53 + q^54 - 9 * q^55 - 6 * q^56 - 8 * q^58 - q^59 + 13 * q^60 + 2 * q^62 - 2 * q^63 - 2 * q^64 - 8 * q^66 - 8 * q^70 + q^72 + 2 * q^73 + 14 * q^75 + 13 * q^77 - q^79 - q^80 + q^81 - 5 * q^83 - 2 * q^84 - 8 * q^87 - q^88 + 2 * q^90 - 8 * q^93 + q^96 + 2 * q^97 + q^98 + 2 * q^99

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