LMFDB - Embedded newform 980.1.bq.b.599.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,1,Mod(39,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 21, 34]))

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

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

chi := DirichletCharacter("980.39");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	980.bq (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:	$0.489083712380$
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			599.1
Root			$0.826239 + 0.563320i$ of defining polynomial
Character	$\chi$	$=$	980.599
Dual form			980.1.bq.b.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733052 + 0.680173i) q^{2} +(-0.722521 + 0.108903i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.365341 - 0.930874i) q^{5} +(0.455573 - 0.571270i) q^{6} +(0.0747301 - 0.997204i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.445396 + 0.137386i) q^{9} +O(q^{10})$	\(q+(-0.733052 + 0.680173i) q^{2} +(-0.722521 + 0.108903i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.365341 - 0.930874i) q^{5} +(0.455573 - 0.571270i) q^{6} +(0.0747301 - 0.997204i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.445396 + 0.137386i) q^{9} +(0.365341 + 0.930874i) q^{10} +(0.0546039 + 0.728639i) q^{12} +(0.623490 + 0.781831i) q^{14} +(-0.162592 + 0.712362i) q^{15} +(-0.988831 - 0.149042i) q^{16} +(0.233052 - 0.403658i) q^{18} +(-0.900969 - 0.433884i) q^{20} +(0.0546039 + 0.728639i) q^{21} +(-1.63402 - 1.11406i) q^{23} +(-0.535628 - 0.496990i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(0.965168 - 0.464800i) q^{27} +(-0.988831 - 0.149042i) q^{28} +(-1.48883 - 0.716983i) q^{29} +(-0.365341 - 0.632789i) q^{30} +(0.826239 - 0.563320i) q^{32} +(-0.900969 - 0.433884i) q^{35} +(0.103718 + 0.454418i) q^{36} +(0.955573 - 0.294755i) q^{40} +(1.19158 + 1.49419i) q^{41} +(-0.535628 - 0.496990i) q^{42} +(1.19158 - 1.49419i) q^{43} +(-0.0348320 + 0.464800i) q^{45} +(1.95557 - 0.294755i) q^{46} +(-0.914101 + 0.848162i) q^{47} +0.730682 q^{48} +(-0.988831 - 0.149042i) q^{49} +1.00000 q^{50} +(-0.391374 + 0.997204i) q^{54} +(0.826239 - 0.563320i) q^{56} +(1.57906 - 0.487076i) q^{58} +(0.698220 + 0.215372i) q^{60} +(-0.147791 - 1.97213i) q^{61} +(0.103718 + 0.454418i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.500000 - 0.866025i) q^{67} +(1.30194 + 0.626980i) q^{69} +(0.955573 - 0.294755i) q^{70} +(-0.385113 - 0.262566i) q^{72} +(0.603718 + 0.411608i) q^{75} +(-0.500000 + 0.866025i) q^{80} +(-0.261623 + 0.178372i) q^{81} +(-1.88980 - 0.284841i) q^{82} +(-0.0332580 + 0.145713i) q^{83} +0.730682 q^{84} +(0.142820 + 1.90580i) q^{86} +(1.15379 + 0.355898i) q^{87} +(1.57906 - 0.487076i) q^{89} +(-0.290611 - 0.364415i) q^{90} +(-1.23305 + 1.54620i) q^{92} +(0.0931869 - 1.24349i) q^{94} +(-0.535628 + 0.496990i) q^{96} +(0.826239 - 0.563320i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 8 q^{3} + q^{4} + q^{5} - 5 q^{6} + q^{7} - 2 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q + q^2 - 8 * q^3 + q^4 + q^5 - 5 * q^6 + q^7 - 2 * q^8 - 7 * q^9	$ 12 q + q^{2} - 8 q^{3} + q^{4} + q^{5} - 5 q^{6} + q^{7} - 2 q^{8} - 7 q^{9} + q^{10} - q^{12} - 2 q^{14} + 2 q^{15} + q^{16} - 7 q^{18} - 2 q^{20} - q^{21} - q^{23} - q^{24} + q^{25} + 12 q^{27} + q^{28} - 5 q^{29} - q^{30} + q^{32} - 2 q^{35} - 7 q^{36} + q^{40} + 2 q^{41} - q^{42} + 2 q^{43} + 13 q^{46} + 2 q^{47} + 2 q^{48} + q^{49} + 12 q^{50} + 15 q^{54} + q^{56} - q^{58} - q^{60} - q^{61} - 7 q^{63} - 2 q^{64} + 6 q^{67} - 2 q^{69} + q^{70} - q^{75} - 6 q^{80} - 8 q^{81} - q^{82} + 2 q^{83} + 2 q^{84} - q^{86} - 6 q^{87} - q^{89} - 5 q^{92} + 2 q^{94} - q^{96} + q^{98}+O(q^{100}) $ 12 * q + q^2 - 8 * q^3 + q^4 + q^5 - 5 * q^6 + q^7 - 2 * q^8 - 7 * q^9 + q^10 - q^12 - 2 * q^14 + 2 * q^15 + q^16 - 7 * q^18 - 2 * q^20 - q^21 - q^23 - q^24 + q^25 + 12 * q^27 + q^28 - 5 * q^29 - q^30 + q^32 - 2 * q^35 - 7 * q^36 + q^40 + 2 * q^41 - q^42 + 2 * q^43 + 13 * q^46 + 2 * q^47 + 2 * q^48 + q^49 + 12 * q^50 + 15 * q^54 + q^56 - q^58 - q^60 - q^61 - 7 * q^63 - 2 * q^64 + 6 * q^67 - 2 * q^69 + q^70 - q^75 - 6 * q^80 - 8 * q^81 - q^82 + 2 * q^83 + 2 * q^84 - q^86 - 6 * q^87 - q^89 - 5 * q^92 + 2 * q^94 - q^96 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$2$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$3$	−0.722521	+	0.108903i	−0.722521	+	0.108903i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−0.722521	+	0.108903i	−0.722521	+	0.108903i	−0.222521	+	0.974928i	$0.571429\pi$
$4$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$5$	0.365341	−	0.930874i	0.365341	−	0.930874i
$5$	0.365341	−	0.930874i	0.365341	−	0.930874i
$6$	0.455573	−	0.571270i	0.455573	−	0.571270i
$7$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$7$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$8$	0.623490	+	0.781831i	0.623490	+	0.781831i
$9$	−0.445396	+	0.137386i	−0.445396	+	0.137386i
$10$	0.365341	+	0.930874i	0.365341	+	0.930874i
$11$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$11$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$12$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$13$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$13$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$14$	0.623490	+	0.781831i	0.623490	+	0.781831i
$15$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$16$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$17$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$17$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$18$	0.233052	−	0.403658i	0.233052	−	0.403658i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$21$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$22$		0			0
$23$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.900969	−	0.433884i	$-0.857143\pi$
$23$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.733052	−	0.680173i	$-0.761905\pi$
$24$	−0.535628	−	0.496990i	−0.535628	−	0.496990i
$25$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$26$		0			0
$27$	0.965168	−	0.464800i	0.965168	−	0.464800i
$28$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$29$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.988831	+	0.149042i	$0.952381\pi$
$30$	−0.365341	−	0.632789i	−0.365341	−	0.632789i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.826239	−	0.563320i	0.826239	−	0.563320i
$33$		0			0
$34$		0			0
$35$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$36$	0.103718	+	0.454418i	0.103718	+	0.454418i
$37$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$37$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$38$		0			0
$39$		0			0
$40$	0.955573	−	0.294755i	0.955573	−	0.294755i
$41$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.826239	+	0.563320i	$0.190476\pi$
$41$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.365341	+	0.930874i	$0.380952\pi$
$42$	−0.535628	−	0.496990i	−0.535628	−	0.496990i
$43$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.365341	−	0.930874i	$-0.380952\pi$
$43$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.826239	−	0.563320i	$-0.190476\pi$
$44$		0			0
$45$	−0.0348320	+	0.464800i	−0.0348320	+	0.464800i
$46$	1.95557	−	0.294755i	1.95557	−	0.294755i
$47$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$47$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$48$	0.730682			0.730682
$49$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$50$	1.00000			1.00000
$51$		0			0
$52$		0			0
$53$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$53$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$54$	−0.391374	+	0.997204i	−0.391374	+	0.997204i
$55$		0			0
$56$	0.826239	−	0.563320i	0.826239	−	0.563320i
$57$		0			0
$58$	1.57906	−	0.487076i	1.57906	−	0.487076i
$59$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$59$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$60$	0.698220	+	0.215372i	0.698220	+	0.215372i
$61$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	−0.222521	−	0.974928i	$-0.571429\pi$
$61$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	0.0747301	−	0.997204i	$-0.476190\pi$
$62$		0			0
$63$	0.103718	+	0.454418i	0.103718	+	0.454418i
$64$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$65$		0			0
$66$		0			0
$67$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$67$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$68$		0			0
$69$	1.30194	+	0.626980i	1.30194	+	0.626980i
$70$	0.955573	−	0.294755i	0.955573	−	0.294755i
$71$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$71$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$72$	−0.385113	−	0.262566i	−0.385113	−	0.262566i
$73$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$73$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$74$		0			0
$75$	0.603718	+	0.411608i	0.603718	+	0.411608i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$81$	−0.261623	+	0.178372i	−0.261623	+	0.178372i
$82$	−1.88980	−	0.284841i	−1.88980	−	0.284841i
$83$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$83$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$84$	0.730682			0.730682
$85$		0			0
$86$	0.142820	+	1.90580i	0.142820	+	1.90580i
$87$	1.15379	+	0.355898i	1.15379	+	0.355898i
$88$		0			0
$89$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.623490	−	0.781831i	$-0.285714\pi$
$89$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.955573	+	0.294755i	$0.0952381\pi$
$90$	−0.290611	−	0.364415i	−0.290611	−	0.364415i
$91$		0			0
$92$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$93$		0			0
$94$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$95$		0			0
$96$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	0.826239	−	0.563320i	0.826239	−	0.563320i
$99$		0			0
$100$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$101$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i	−0.222521	−	0.974928i	$-0.571429\pi$
$101$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i	0.0747301	+	0.997204i	$0.476190\pi$
$102$		0			0
$103$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$103$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	−0.988831	+	0.149042i	$0.952381\pi$
$104$		0			0
$105$	0.698220	+	0.215372i	0.698220	+	0.215372i
$106$		0			0
$107$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	−0.222521	−	0.974928i	$-0.571429\pi$
$107$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	0.365341	+	0.930874i	$0.380952\pi$
$108$	−0.391374	−	0.997204i	−0.391374	−	0.997204i
$109$	−0.955573	−	0.294755i	−0.955573	−	0.294755i	−0.222521	−	0.974928i	$-0.571429\pi$
$109$	−0.955573	−	0.294755i	−0.955573	−	0.294755i	−0.733052	+	0.680173i	$0.761905\pi$
$110$		0			0
$111$		0			0
$112$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$116$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$121$	0.826239	+	0.563320i	0.826239	+	0.563320i
$122$	1.44973	+	1.34515i	1.44973	+	1.34515i
$123$	−1.02366	−	0.949820i	−1.02366	−	0.949820i
$124$		0			0
$125$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$126$	−0.385113	−	0.262566i	−0.385113	−	0.262566i
$127$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$127$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$128$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$129$	−0.698220	+	1.20935i	−0.698220	+	1.20935i
$130$		0			0
$131$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$131$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$132$		0			0
$133$		0			0
$134$	0.222521	+	0.974928i	0.222521	+	0.974928i
$135$	−0.0800550	−	1.06826i	−0.0800550	−	1.06826i
$136$		0			0
$137$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$137$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$138$	−1.38084	+	0.425934i	−1.38084	+	0.425934i
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$141$	0.568090	−	0.712362i	0.568090	−	0.712362i
$142$		0			0
$143$		0			0
$144$	0.460898	−	0.0694692i	0.460898	−	0.0694692i
$145$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$146$		0			0
$147$	0.730682			0.730682
$148$		0			0
$149$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	−0.733052	−	0.680173i	$-0.761905\pi$
$149$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	0.623490	+	0.781831i	$0.285714\pi$
$150$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$151$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$151$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$157$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$158$		0			0
$159$		0			0
$160$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$161$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$162$	0.0704598	−	0.308705i	0.0704598	−	0.308705i
$163$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$163$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$164$	1.57906	−	1.07659i	1.57906	−	1.07659i
$165$		0			0
$166$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$167$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.955573	−	0.294755i	$-0.0952381\pi$
$167$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.365341	+	0.930874i	$0.380952\pi$
$168$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$169$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$170$		0			0
$171$		0			0
$172$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$173$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$173$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$174$	−1.08786	+	0.523887i	−1.08786	+	0.523887i
$175$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$176$		0			0
$177$		0			0
$178$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$179$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$179$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$180$	0.460898	+	0.0694692i	0.460898	+	0.0694692i
$181$	0.222521	−	0.974928i	0.222521	−	0.974928i	−0.733052	−	0.680173i	$-0.761905\pi$
$181$	0.222521	−	0.974928i	0.222521	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$182$		0			0
$183$	0.321552	+	1.40881i	0.321552	+	1.40881i
$184$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.777479	+	0.974928i	0.777479	+	0.974928i
$189$	−0.391374	−	0.997204i	−0.391374	−	0.997204i
$190$		0			0
$191$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$191$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$192$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$193$		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
$196$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$199$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$200$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$201$	−0.266948	+	0.680173i	−0.266948	+	0.680173i
$202$	0.0931869	−	0.116853i	0.0931869	−	0.116853i
$203$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$204$		0			0
$205$	1.82624	−	0.563320i	1.82624	−	0.563320i
$206$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$207$	0.880843	+	0.271704i	0.880843	+	0.271704i
$208$		0			0
$209$		0			0
$210$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$211$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$211$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$212$		0			0
$213$		0			0
$214$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i
$215$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$216$	0.965168	+	0.464800i	0.965168	+	0.464800i
$217$		0			0
$218$	0.900969	−	0.433884i	0.900969	−	0.433884i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$223$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$224$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$225$	0.419945	+	0.202235i	0.419945	+	0.202235i
$226$		0			0
$227$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$227$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$228$		0			0
$229$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$229$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$230$	0.440071	−	1.92808i	0.440071	−	1.92808i
$231$		0			0
$232$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$233$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$233$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$234$		0			0
$235$	0.455573	+	1.16078i	0.455573	+	1.16078i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$239$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$240$	0.266948	−	0.680173i	0.266948	−	0.680173i
$241$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$241$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$242$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$243$	−0.615683	+	0.571270i	−0.615683	+	0.571270i
$244$	−1.97766			−1.97766
$245$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$246$	1.39644			1.39644
$247$		0			0
$248$		0			0
$249$	0.00816111	−	0.108903i	0.00816111	−	0.108903i
$250$	0.365341	−	0.930874i	0.365341	−	0.930874i
$251$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$251$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$252$	0.460898	−	0.0694692i	0.460898	−	0.0694692i
$253$		0			0
$254$	−0.425270	+	0.131178i	−0.425270	+	0.131178i
$255$		0			0
$256$	0.955573	+	0.294755i	0.955573	+	0.294755i
$257$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$257$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$258$	−0.310737	−	1.36143i	−0.310737	−	1.36143i
$259$		0			0
$260$		0			0
$261$	0.761623	+	0.114796i	0.761623	+	0.114796i
$262$		0			0
$263$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	0.0747301	+	0.997204i	$0.476190\pi$
$263$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	−0.900969	+	0.433884i	$0.857143\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.08786	+	0.523887i	−1.08786	+	0.523887i
$268$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$269$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$269$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$270$	0.785286	+	0.728639i	0.785286	+	0.728639i
$271$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$271$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.722521	−	1.25144i	0.722521	−	1.25144i
$277$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$277$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$278$		0			0
$279$		0			0
$280$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$281$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$281$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$282$	0.0680900	+	0.908598i	0.0680900	+	0.908598i
$283$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.826239	−	0.563320i	$-0.190476\pi$
$283$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.365341	+	0.930874i	$0.380952\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.57906	−	1.07659i	1.57906	−	1.07659i
$288$	−0.290611	+	0.364415i	−0.290611	+	0.364415i
$289$	0.365341	−	0.930874i	0.365341	−	0.930874i
$290$	0.123490	−	1.64786i	0.123490	−	1.64786i
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$299$		0			0
$300$	0.455573	−	0.571270i	0.455573	−	0.571270i
$301$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$302$		0			0
$303$	0.104356	−	0.0321896i	0.104356	−	0.0321896i
$304$		0			0
$305$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$306$		0			0
$307$	0.326239	+	1.42935i	0.326239	+	1.42935i	0.826239	+	0.563320i	$0.190476\pi$
$307$	0.326239	+	1.42935i	0.326239	+	1.42935i	−0.500000	+	0.866025i	$0.666667\pi$
$308$		0			0
$309$	0.162592	−	0.712362i	0.162592	−	0.712362i
$310$		0			0
$311$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$311$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$		0			0
$315$	0.460898	+	0.0694692i	0.460898	+	0.0694692i
$316$		0			0
$317$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$317$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$318$		0			0
$319$		0			0
$320$	0.826239	+	0.563320i	0.826239	+	0.563320i
$321$	−0.0983929	+	0.0473835i	−0.0983929	+	0.0473835i
$322$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$323$		0			0
$324$	0.158322	+	0.274221i	0.158322	+	0.274221i
$325$		0			0
$326$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$327$	0.722521	+	0.108903i	0.722521	+	0.108903i
$328$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$329$	0.777479	+	0.974928i	0.777479	+	0.974928i
$330$		0			0
$331$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$331$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$332$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$333$		0			0
$334$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$335$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$336$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$337$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$337$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$338$	0.365341	−	0.930874i	0.365341	−	0.930874i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$344$	1.91115			1.91115
$345$	1.05929	−	0.982878i	1.05929	−	0.982878i
$346$		0			0
$347$	0.142820	−	1.90580i	0.142820	−	1.90580i	−0.222521	−	0.974928i	$-0.571429\pi$
$347$	0.142820	−	1.90580i	0.142820	−	1.90580i	0.365341	−	0.930874i	$-0.380952\pi$
$348$	0.441126	−	1.12397i	0.441126	−	1.12397i
$349$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.365341	−	0.930874i	$-0.380952\pi$
$349$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.826239	−	0.563320i	$-0.190476\pi$
$350$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$351$		0			0
$352$		0			0
$353$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$353$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$354$		0			0
$355$		0			0
$356$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$357$		0			0
$358$		0			0
$359$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$359$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$360$	−0.385113	+	0.262566i	−0.385113	+	0.262566i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	0.500000	+	0.866025i	0.500000	+	0.866025i
$363$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$364$		0			0
$365$		0			0
$366$	−1.19395	−	0.814021i	−1.19395	−	0.814021i
$367$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$367$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$368$	1.44973	+	1.34515i	1.44973	+	1.34515i
$369$	−0.736007	−	0.501801i	−0.736007	−	0.501801i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	0.603718	−	0.411608i	0.603718	−	0.411608i
$376$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$377$		0			0
$378$	0.965168	+	0.464800i	0.965168	+	0.464800i
$379$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$379$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$380$		0			0
$381$	−0.310737	−	0.0958497i	−0.310737	−	0.0958497i
$382$		0			0
$383$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.623490	−	0.781831i	$-0.285714\pi$
$383$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.955573	+	0.294755i	$0.0952381\pi$
$384$	0.455573	+	0.571270i	0.455573	+	0.571270i
$385$		0			0
$386$		0			0
$387$	−0.325443	+	0.829215i	−0.325443	+	0.829215i
$388$		0			0
$389$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.826239	−	0.563320i	$-0.190476\pi$
$389$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.955573	+	0.294755i	$0.0952381\pi$
$390$		0			0
$391$		0			0
$392$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$397$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$398$		0			0
$399$		0			0
$400$	0.623490	+	0.781831i	0.623490	+	0.781831i
$401$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.0747301	−	0.997204i	$-0.476190\pi$
$401$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.623490	+	0.781831i	$0.285714\pi$
$402$	−0.266948	−	0.680173i	−0.266948	−	0.680173i
$403$		0			0
$404$	0.0111692	+	0.149042i	0.0111692	+	0.149042i
$405$	0.0704598	+	0.308705i	0.0704598	+	0.308705i
$406$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$407$		0			0
$408$		0			0
$409$	−1.21135	+	0.825886i	−1.21135	+	0.825886i	−0.988831	−	0.149042i	$-0.952381\pi$
$409$	−1.21135	+	0.825886i	−1.21135	+	0.825886i	−0.222521	+	0.974928i	$0.571429\pi$
$410$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$411$		0			0
$412$	0.900969	+	0.433884i	0.900969	+	0.433884i
$413$		0			0
$414$	−0.830509	+	0.399952i	−0.830509	+	0.399952i
$415$	0.123490	+	0.0841939i	0.123490	+	0.0841939i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$	0.266948	−	0.680173i	0.266948	−	0.680173i
$421$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$421$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$422$		0			0
$423$	0.290611	−	0.503353i	0.290611	−	0.503353i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.97766			−1.97766
$428$	−0.0332580	−	0.145713i	−0.0332580	−	0.145713i
$429$		0			0
$430$	1.82624	+	0.563320i	1.82624	+	0.563320i
$431$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$431$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$432$	−1.02366	+	0.315758i	−1.02366	+	0.315758i
$433$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$433$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$434$		0			0
$435$	0.752824	−	0.944011i	0.752824	−	0.944011i
$436$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$437$		0			0
$438$		0			0
$439$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$439$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$440$		0			0
$441$	0.460898	−	0.0694692i	0.460898	−	0.0694692i
$442$		0			0
$443$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.222521	+	0.974928i	$0.571429\pi$
$443$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.988831	+	0.149042i	$0.952381\pi$
$444$		0			0
$445$	0.123490	−	1.64786i	0.123490	−	1.64786i
$446$	−0.162592	+	0.414278i	−0.162592	+	0.414278i
$447$	0.0680900	−	0.0853822i	0.0680900	−	0.0853822i
$448$	0.955573	+	0.294755i	0.955573	+	0.294755i
$449$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.733052	−	0.680173i	$-0.761905\pi$
$449$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.500000	−	0.866025i	$-0.666667\pi$
$450$	−0.445396	+	0.137386i	−0.445396	+	0.137386i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$455$		0			0
$456$		0			0
$457$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$457$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$458$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$459$		0			0
$460$	0.988831	+	1.71271i	0.988831	+	1.71271i
$461$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$461$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$462$		0			0
$463$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i	0.365341	+	0.930874i	$0.380952\pi$
$464$	1.36534	+	0.930874i	1.36534	+	0.930874i
$465$		0			0
$466$		0			0
$467$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	0.0747301	−	0.997204i	$-0.476190\pi$
$467$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	−0.900969	+	0.433884i	$0.857143\pi$
$468$		0			0
$469$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$470$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$479$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$480$	0.266948	+	0.680173i	0.266948	+	0.680173i
$481$		0			0
$482$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$483$	0.722521	−	1.25144i	0.722521	−	1.25144i
$484$	0.623490	−	0.781831i	0.623490	−	0.781831i
$485$		0			0
$486$	0.0627651	−	0.837541i	0.0627651	−	0.837541i
$487$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.733052	−	0.680173i	$-0.761905\pi$
$487$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.500000	+	0.866025i	$0.666667\pi$
$488$	1.44973	−	1.34515i	1.44973	−	1.34515i
$489$	−1.31664			−1.31664
$490$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	−1.02366	+	0.949820i	−1.02366	+	0.949820i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0680900	+	0.0853822i	0.0680900	+	0.0853822i
$499$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$499$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$500$	0.365341	+	0.930874i	0.365341	+	0.930874i
$501$	−1.02366	−	0.315758i	−1.02366	−	0.315758i
$502$		0			0
$503$	−0.425270	−	1.86323i	−0.425270	−	1.86323i	−0.500000	−	0.866025i	$-0.666667\pi$
$503$	−0.425270	−	1.86323i	−0.425270	−	1.86323i	0.0747301	−	0.997204i	$-0.476190\pi$
$504$	−0.290611	+	0.364415i	−0.290611	+	0.364415i
$505$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$506$		0			0
$507$	0.603718	−	0.411608i	0.603718	−	0.411608i
$508$	0.222521	−	0.385418i	0.222521	−	0.385418i
$509$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$509$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$510$		0			0
$511$		0			0
$512$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$513$		0			0
$514$		0			0
$515$	0.733052	+	0.680173i	0.733052	+	0.680173i
$516$	1.15379	+	0.786643i	1.15379	+	0.786643i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$521$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$522$	−0.636391	+	0.433884i	−0.636391	+	0.433884i
$523$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$523$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$524$		0			0
$525$	0.455573	−	0.571270i	0.455573	−	0.571270i
$526$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$527$		0			0
$528$		0			0
$529$	1.06356	+	2.70991i	1.06356	+	2.70991i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.441126	−	1.12397i	0.441126	−	1.12397i
$535$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$536$	0.988831	−	0.149042i	0.988831	−	0.149042i
$537$		0			0
$538$	−1.46610			−1.46610
$539$		0			0
$540$	−1.07126			−1.07126
$541$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	−0.900969	−	0.433884i	$-0.857143\pi$
$541$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	0.365341	+	0.930874i	$0.380952\pi$
$542$		0			0
$543$	−0.0546039	+	0.728639i	−0.0546039	+	0.728639i
$544$		0			0
$545$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$546$		0			0
$547$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.733052	−	0.680173i	$-0.761905\pi$
$547$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.500000	−	0.866025i	$-0.666667\pi$
$548$		0			0
$549$	0.336770	+	0.858075i	0.336770	+	0.858075i
$550$		0			0
$551$		0			0
$552$	0.321552	+	1.40881i	0.321552	+	1.40881i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$	0.826239	+	0.563320i	0.826239	+	0.563320i
$561$		0			0
$562$	1.03030	+	0.702449i	1.03030	+	0.702449i
$563$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$563$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$564$	−0.667917	−	0.619736i	−0.667917	−	0.619736i
$565$		0			0
$566$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$567$	0.158322	+	0.274221i	0.158322	+	0.274221i
$568$		0			0
$569$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$569$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$570$		0			0
$571$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$571$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$572$		0			0
$573$		0			0
$574$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$575$	0.440071	+	1.92808i	0.440071	+	1.92808i
$576$	−0.0348320	−	0.464800i	−0.0348320	−	0.464800i
$577$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$577$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$578$	0.365341	+	0.930874i	0.365341	+	0.930874i
$579$		0			0
$580$	1.03030	+	1.29196i	1.03030	+	1.29196i
$581$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$587$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$588$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$593$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$594$		0			0
$595$		0			0
$596$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$597$		0			0
$598$		0			0
$599$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$599$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$600$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$601$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$601$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$602$	1.91115			1.91115
$603$	−0.103718	+	0.454418i	−0.103718	+	0.454418i
$604$		0			0
$605$	0.826239	−	0.563320i	0.826239	−	0.563320i
$606$	−0.0546039	+	0.0945768i	−0.0546039	+	0.0945768i
$607$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$607$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$608$		0			0
$609$	0.441126	−	1.12397i	0.441126	−	1.12397i
$610$	1.78181	−	0.858075i	1.78181	−	0.858075i
$611$		0			0
$612$		0			0
$613$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$613$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$614$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$615$	−1.25815	+	0.605893i	−1.25815	+	0.605893i
$616$		0			0
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$	0.365341	+	0.632789i	0.365341	+	0.632789i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−2.09492	−	0.315758i	−2.09492	−	0.315758i
$622$		0			0
$623$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$624$		0			0
$625$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.385113	+	0.262566i	−0.385113	+	0.262566i
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.326239	−	0.302705i	0.326239	−	0.302705i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$641$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$641$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$642$	0.0398981	−	0.101659i	0.0398981	−	0.101659i
$643$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$643$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$644$	1.44973	+	1.34515i	1.44973	+	1.34515i
$645$	0.870666	+	1.09178i	0.870666	+	1.09178i
$646$		0			0
$647$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$647$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$648$	−0.302576	−	0.0933323i	−0.302576	−	0.0933323i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.400969	−	1.75676i	0.400969	−	1.75676i
$653$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$653$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$654$	−0.603718	+	0.411608i	−0.603718	+	0.411608i
$655$		0			0
$656$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$657$		0			0
$658$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$659$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$659$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	0.623490	−	0.781831i	$-0.285714\pi$
$661$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	−0.733052	+	0.680173i	$0.761905\pi$
$662$		0			0
$663$		0			0
$664$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$665$		0			0
$666$		0			0
$667$	1.63402	+	2.83021i	1.63402	+	2.83021i
$668$	0.733052	−	1.26968i	0.733052	−	1.26968i
$669$	−0.268680	+	0.183183i	−0.268680	+	0.183183i
$670$	0.988831	+	0.149042i	0.988831	+	0.149042i
$671$		0			0
$672$	0.455573	+	0.571270i	0.455573	+	0.571270i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$		0			0
$675$	−1.02366	−	0.315758i	−1.02366	−	0.315758i
$676$	0.365341	+	0.930874i	0.365341	+	0.930874i
$677$		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
$681$	−0.118803	+	0.302705i	−0.118803	+	0.302705i
$682$		0			0
$683$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$683$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$684$		0			0
$685$		0			0
$686$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$687$	−1.31664			−1.31664
$688$	−1.40097	+	1.29991i	−1.40097	+	1.29991i
$689$		0			0
$690$	−0.107988	+	1.44100i	−0.107988	+	1.44100i
$691$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$691$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$692$		0			0
$693$		0			0
$694$	1.19158	+	1.49419i	1.19158	+	1.49419i
$695$		0			0
$696$	0.441126	+	1.12397i	0.441126	+	1.12397i
$697$		0			0
$698$	0.142820	+	1.90580i	0.142820	+	1.90580i
$699$		0			0
$700$	0.623490	+	0.781831i	0.623490	+	0.781831i
$701$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	0.826239	+	0.563320i	$0.190476\pi$
$701$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	−0.988831	+	0.149042i	$0.952381\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.455573	−	0.789075i	−0.455573	−	0.789075i
$706$		0			0
$707$	0.0111692	+	0.149042i	0.0111692	+	0.149042i
$708$		0			0
$709$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	0.623490	−	0.781831i	$-0.285714\pi$
$709$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	1.36534	+	0.930874i	1.36534	+	0.930874i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$719$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$720$	0.103718	−	0.454418i	0.103718	−	0.454418i
$721$	0.900969	+	0.433884i	0.900969	+	0.433884i
$722$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$723$	−0.0243010	−	0.324275i	−0.0243010	−	0.324275i
$724$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$725$	0.603718	+	1.53825i	0.603718	+	1.53825i
$726$	0.698220	−	0.215372i	0.698220	−	0.215372i
$727$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	0.826239	−	0.563320i	$-0.190476\pi$
$727$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	−0.733052	+	0.680173i	$0.761905\pi$
$728$		0			0
$729$	0.580055	−	0.727366i	0.580055	−	0.727366i
$730$		0			0
$731$		0			0
$732$	1.42890	−	0.215372i	1.42890	−	0.215372i
$733$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$733$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$734$	−1.46610			−1.46610
$735$	0.266948	−	0.680173i	0.266948	−	0.680173i
$736$	−1.97766			−1.97766
$737$		0			0
$738$	0.880843	−	0.132766i	0.880843	−	0.132766i
$739$		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			0
$743$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	−0.988831	−	0.149042i	$-0.952381\pi$
$743$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	0.0747301	−	0.997204i	$-0.476190\pi$
$744$		0			0
$745$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$746$		0			0
$747$	−0.00520599	−	0.0694692i	−0.00520599	−	0.0694692i
$748$		0			0
$749$	−0.0332580	−	0.145713i	−0.0332580	−	0.145713i
$750$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$751$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$751$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$752$	1.03030	−	0.702449i	1.03030	−	0.702449i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.02366	+	0.315758i	−1.02366	+	0.315758i
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	0.365341	−	0.930874i	$-0.380952\pi$
$761$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$762$	0.292981	−	0.141092i	0.292981	−	0.141092i
$763$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$764$		0			0
$765$		0			0
$766$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$767$		0			0
$768$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$769$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$769$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$773$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$774$	−0.325443	−	0.829215i	−0.325443	−	0.829215i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.77023			−1.77023
$784$	0.955573	+	0.294755i	0.955573	+	0.294755i
$785$		0			0
$786$		0			0
$787$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.900969	−	0.433884i	$-0.857143\pi$
$787$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.733052	+	0.680173i	$0.761905\pi$
$788$		0			0
$789$	0.441126	−	1.12397i	0.441126	−	1.12397i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$797$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$798$		0			0
$799$		0			0
$800$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$801$	−0.636391	+	0.433884i	−0.636391	+	0.433884i
$802$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$803$		0			0
$804$	0.658322	+	0.317031i	0.658322	+	0.317031i
$805$	0.988831	+	1.71271i	0.988831	+	1.71271i
$806$		0			0
$807$	−0.885113	−	0.603460i	−0.885113	−	0.603460i
$808$	−0.109562	−	0.101659i	−0.109562	−	0.101659i
$809$	0.733052	+	0.680173i	0.733052	+	0.680173i	0.955573	−	0.294755i	$-0.0952381\pi$
$809$	0.733052	+	0.680173i	0.733052	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$810$	−0.261623	−	0.178372i	−0.261623	−	0.178372i
$811$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$811$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$812$	1.36534	+	0.930874i	1.36534	+	0.930874i
$813$		0			0
$814$		0			0
$815$	0.900969	−	1.56052i	0.900969	−	1.56052i
$816$		0			0
$817$		0			0
$818$	0.326239	−	1.42935i	0.326239	−	1.42935i
$819$		0			0
$820$	−0.425270	−	1.86323i	−0.425270	−	1.86323i
$821$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	−0.988831	−	0.149042i	$-0.952381\pi$
$821$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	0.955573	−	0.294755i	$-0.0952381\pi$
$822$		0			0
$823$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$823$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$824$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$825$		0			0
$826$		0			0
$827$	0.455573	−	0.571270i	0.455573	−	0.571270i	−0.500000	−	0.866025i	$-0.666667\pi$
$827$	0.455573	−	0.571270i	0.455573	−	0.571270i	0.955573	+	0.294755i	$0.0952381\pi$
$828$	0.336770	−	0.858075i	0.336770	−	0.858075i
$829$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	0.365341	+	0.930874i	$0.380952\pi$
$829$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	−0.500000	+	0.866025i	$0.666667\pi$
$830$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.07473	−	0.997204i	1.07473	−	0.997204i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$839$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$840$	0.266948	+	0.680173i	0.266948	+	0.680173i
$841$	1.07906	+	1.35310i	1.07906	+	1.35310i
$842$	0.698220	−	0.215372i	0.698220	−	0.215372i
$843$	0.332879	+	0.848162i	0.332879	+	0.848162i
$844$		0			0
$845$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$846$	0.129334	+	0.566649i	0.129334	+	0.566649i
$847$	0.623490	−	0.781831i	0.623490	−	0.781831i
$848$		0			0
$849$	−0.900969	−	0.135799i	−0.900969	−	0.135799i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$853$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$854$	1.44973	−	1.34515i	1.44973	−	1.34515i
$855$		0			0
$856$	0.123490	+	0.0841939i	0.123490	+	0.0841939i
$857$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$857$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$858$		0			0
$859$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$859$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$860$	−1.72188	+	0.829215i	−1.72188	+	0.829215i
$861$	−1.02366	+	0.949820i	−1.02366	+	0.949820i
$862$		0			0
$863$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$863$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$864$	0.535628	−	0.927735i	0.535628	−	0.927735i
$865$		0			0
$866$		0			0
$867$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$868$		0			0
$869$		0			0
$870$	0.0902318	+	1.20406i	0.0902318	+	1.20406i
$871$		0			0
$872$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$873$		0			0
$874$		0			0
$875$	0.365341	+	0.930874i	0.365341	+	0.930874i
$876$		0			0
$877$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$877$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$882$	−0.290611	+	0.364415i	−0.290611	+	0.364415i
$883$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$883$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$884$		0			0
$885$		0			0
$886$	0.123490	−	1.64786i	0.123490	−	1.64786i
$887$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.222521	+	0.974928i	$0.571429\pi$
$887$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	0.222521	−	0.385418i	0.222521	−	0.385418i
$890$	1.03030	+	1.29196i	1.03030	+	1.29196i
$891$		0			0
$892$	−0.162592	−	0.414278i	−0.162592	−	0.414278i
$893$		0			0
$894$	0.00816111	+	0.108903i	0.00816111	+	0.108903i
$895$		0			0
$896$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$897$		0			0
$898$	1.95557	+	0.294755i	1.95557	+	0.294755i
$899$		0			0
$900$	0.233052	−	0.403658i	0.233052	−	0.403658i
$901$		0			0
$902$		0			0
$903$	1.15379	+	0.786643i	1.15379	+	0.786643i
$904$		0			0
$905$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$906$		0			0
$907$	−0.535628	−	0.496990i	−0.535628	−	0.496990i	0.365341	−	0.930874i	$-0.380952\pi$
$907$	−0.535628	−	0.496990i	−0.535628	−	0.496990i	−0.900969	+	0.433884i	$0.857143\pi$
$908$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$909$	0.0627651	−	0.0302261i	0.0627651	−	0.0302261i
$910$		0			0
$911$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$911$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.42890	+	0.215372i	1.42890	+	0.215372i
$916$	0.400969	−	1.75676i	0.400969	−	1.75676i
$917$		0			0
$918$		0			0
$919$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$919$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$920$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$921$	−0.391374	−	0.997204i	−0.391374	−	0.997204i
$922$	1.19158	−	0.367554i	1.19158	−	0.367554i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$927$	0.0348320	−	0.464800i	0.0348320	−	0.464800i
$928$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$929$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$929$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.988831	−	0.149042i	0.988831	−	0.149042i
$935$		0			0
$936$		0			0
$937$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$937$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$938$	0.988831	−	0.149042i	0.988831	−	0.149042i
$939$		0			0
$940$	1.19158	−	0.367554i	1.19158	−	0.367554i
$941$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	−0.733052	−	0.680173i	$-0.761905\pi$
$941$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	0.0747301	−	0.997204i	$-0.476190\pi$
$942$		0			0
$943$	−0.282450	−	3.76903i	−0.282450	−	3.76903i
$944$		0			0
$945$	−1.07126			−1.07126
$946$		0			0
$947$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$947$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$953$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$	−0.0575591	+	0.0392431i	−0.0575591	+	0.0392431i
$964$	0.440071	+	0.0663300i	0.440071	+	0.0663300i
$965$		0			0
$966$	0.321552	+	1.40881i	0.321552	+	1.40881i
$967$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	−0.988831	−	0.149042i	$-0.952381\pi$
$967$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	0.826239	−	0.563320i	$-0.190476\pi$
$968$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$969$		0			0
$970$		0			0
$971$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$971$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$972$	0.523663	+	0.656652i	0.523663	+	0.656652i
$973$		0			0
$974$	0.777479	−	0.974928i	0.777479	−	0.974928i
$975$		0			0
$976$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$977$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$977$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$978$	0.965168	−	0.895545i	0.965168	−	0.895545i
$979$		0			0
$980$	0.826239	+	0.563320i	0.826239	+	0.563320i
$981$	0.466104			0.466104
$982$		0			0
$983$	1.95557	−	0.294755i	1.95557	−	0.294755i	0.955573	−	0.294755i	$-0.0952381\pi$
$983$	1.95557	−	0.294755i	1.95557	−	0.294755i	1.00000			$0$
$984$	0.104356	−	1.39254i	0.104356	−	1.39254i
$985$		0			0
$986$		0			0
$987$	−0.667917	−	0.619736i	−0.667917	−	0.619736i
$988$		0			0
$989$	−3.61168	+	1.11406i	−3.61168	+	1.11406i
$990$		0			0
$991$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$991$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.107988	−	0.0162766i	−0.107988	−	0.0162766i
$997$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$997$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.1.bq.b.599.1	yes	12
4.3	odd	2		980.1.bq.a.599.1	yes	12
5.4	even	2		980.1.bq.a.599.1	yes	12
20.19	odd	2	CM	980.1.bq.b.599.1	yes	12
49.9	even	21	inner	980.1.bq.b.499.1	yes	12
196.107	odd	42		980.1.bq.a.499.1	✓	12
245.9	even	42		980.1.bq.a.499.1	✓	12
980.499	odd	42	inner	980.1.bq.b.499.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.1.bq.a.499.1	✓	12	196.107	odd	42
980.1.bq.a.499.1	✓	12	245.9	even	42
980.1.bq.a.599.1	yes	12	4.3	odd	2
980.1.bq.a.599.1	yes	12	5.4	even	2
980.1.bq.b.499.1	yes	12	49.9	even	21	inner
980.1.bq.b.499.1	yes	12	980.499	odd	42	inner
980.1.bq.b.599.1	yes	12	1.1	even	1	trivial
980.1.bq.b.599.1	yes	12	20.19	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	980.bq (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733052 + 0.680173i) q^{2} +(-0.722521 + 0.108903i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.365341 - 0.930874i) q^{5} +(0.455573 - 0.571270i) q^{6} +(0.0747301 - 0.997204i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.445396 + 0.137386i) q^{9} +O(q^{10})\)	\(q+(-0.733052 + 0.680173i) q^{2} +(-0.722521 + 0.108903i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.365341 - 0.930874i) q^{5} +(0.455573 - 0.571270i) q^{6} +(0.0747301 - 0.997204i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.445396 + 0.137386i) q^{9} +(0.365341 + 0.930874i) q^{10} +(0.0546039 + 0.728639i) q^{12} +(0.623490 + 0.781831i) q^{14} +(-0.162592 + 0.712362i) q^{15} +(-0.988831 - 0.149042i) q^{16} +(0.233052 - 0.403658i) q^{18} +(-0.900969 - 0.433884i) q^{20} +(0.0546039 + 0.728639i) q^{21} +(-1.63402 - 1.11406i) q^{23} +(-0.535628 - 0.496990i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(0.965168 - 0.464800i) q^{27} +(-0.988831 - 0.149042i) q^{28} +(-1.48883 - 0.716983i) q^{29} +(-0.365341 - 0.632789i) q^{30} +(0.826239 - 0.563320i) q^{32} +(-0.900969 - 0.433884i) q^{35} +(0.103718 + 0.454418i) q^{36} +(0.955573 - 0.294755i) q^{40} +(1.19158 + 1.49419i) q^{41} +(-0.535628 - 0.496990i) q^{42} +(1.19158 - 1.49419i) q^{43} +(-0.0348320 + 0.464800i) q^{45} +(1.95557 - 0.294755i) q^{46} +(-0.914101 + 0.848162i) q^{47} +0.730682 q^{48} +(-0.988831 - 0.149042i) q^{49} +1.00000 q^{50} +(-0.391374 + 0.997204i) q^{54} +(0.826239 - 0.563320i) q^{56} +(1.57906 - 0.487076i) q^{58} +(0.698220 + 0.215372i) q^{60} +(-0.147791 - 1.97213i) q^{61} +(0.103718 + 0.454418i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.500000 - 0.866025i) q^{67} +(1.30194 + 0.626980i) q^{69} +(0.955573 - 0.294755i) q^{70} +(-0.385113 - 0.262566i) q^{72} +(0.603718 + 0.411608i) q^{75} +(-0.500000 + 0.866025i) q^{80} +(-0.261623 + 0.178372i) q^{81} +(-1.88980 - 0.284841i) q^{82} +(-0.0332580 + 0.145713i) q^{83} +0.730682 q^{84} +(0.142820 + 1.90580i) q^{86} +(1.15379 + 0.355898i) q^{87} +(1.57906 - 0.487076i) q^{89} +(-0.290611 - 0.364415i) q^{90} +(-1.23305 + 1.54620i) q^{92} +(0.0931869 - 1.24349i) q^{94} +(-0.535628 + 0.496990i) q^{96} +(0.826239 - 0.563320i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 8 q^{3} + q^{4} + q^{5} - 5 q^{6} + q^{7} - 2 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q + q^2 - 8 * q^3 + q^4 + q^5 - 5 * q^6 + q^7 - 2 * q^8 - 7 * q^9	\( 12 q + q^{2} - 8 q^{3} + q^{4} + q^{5} - 5 q^{6} + q^{7} - 2 q^{8} - 7 q^{9} + q^{10} - q^{12} - 2 q^{14} + 2 q^{15} + q^{16} - 7 q^{18} - 2 q^{20} - q^{21} - q^{23} - q^{24} + q^{25} + 12 q^{27} + q^{28} - 5 q^{29} - q^{30} + q^{32} - 2 q^{35} - 7 q^{36} + q^{40} + 2 q^{41} - q^{42} + 2 q^{43} + 13 q^{46} + 2 q^{47} + 2 q^{48} + q^{49} + 12 q^{50} + 15 q^{54} + q^{56} - q^{58} - q^{60} - q^{61} - 7 q^{63} - 2 q^{64} + 6 q^{67} - 2 q^{69} + q^{70} - q^{75} - 6 q^{80} - 8 q^{81} - q^{82} + 2 q^{83} + 2 q^{84} - q^{86} - 6 q^{87} - q^{89} - 5 q^{92} + 2 q^{94} - q^{96} + q^{98}+O(q^{100}) \) 12 * q + q^2 - 8 * q^3 + q^4 + q^5 - 5 * q^6 + q^7 - 2 * q^8 - 7 * q^9 + q^10 - q^12 - 2 * q^14 + 2 * q^15 + q^16 - 7 * q^18 - 2 * q^20 - q^21 - q^23 - q^24 + q^25 + 12 * q^27 + q^28 - 5 * q^29 - q^30 + q^32 - 2 * q^35 - 7 * q^36 + q^40 + 2 * q^41 - q^42 + 2 * q^43 + 13 * q^46 + 2 * q^47 + 2 * q^48 + q^49 + 12 * q^50 + 15 * q^54 + q^56 - q^58 - q^60 - q^61 - 7 * q^63 - 2 * q^64 + 6 * q^67 - 2 * q^69 + q^70 - q^75 - 6 * q^80 - 8 * q^81 - q^82 + 2 * q^83 + 2 * q^84 - q^86 - 6 * q^87 - q^89 - 5 * q^92 + 2 * q^94 - q^96 + q^98

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