LMFDB - Embedded newform 980.1.bq.a.879.1

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			879.1
Root			$0.955573 - 0.294755i$ of defining polynomial
Character	$\chi$	$=$	980.879
Dual form			980.1.bq.a.359.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.365341 + 0.930874i) q^{2} +(-0.123490 + 1.64786i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(0.826239 + 0.563320i) q^{5} +(-1.48883 - 0.716983i) q^{6} +(0.733052 + 0.680173i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-1.71135 - 0.257945i) q^{9} +(-0.826239 + 0.563320i) q^{10} +(1.21135 - 1.12397i) q^{12} +(-0.900969 + 0.433884i) q^{14} +(-1.03030 + 1.29196i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(0.865341 - 1.49881i) q^{18} +(-0.222521 - 0.974928i) q^{20} +(-1.21135 + 1.12397i) q^{21} +(-0.142820 + 0.0440542i) q^{23} +(0.603718 + 1.53825i) q^{24} +(0.365341 + 0.930874i) q^{25} +(0.268680 - 1.17716i) q^{27} +(-0.0747301 - 0.997204i) q^{28} +(-0.425270 - 1.86323i) q^{29} +(-0.826239 - 1.43109i) q^{30} +(-0.955573 - 0.294755i) q^{32} +(0.222521 + 0.974928i) q^{35} +(1.07906 + 1.35310i) q^{36} +(0.988831 + 0.149042i) q^{40} +(1.78181 - 0.858075i) q^{41} +(-0.603718 - 1.53825i) q^{42} +(-1.78181 - 0.858075i) q^{43} +(-1.26868 - 1.17716i) q^{45} +(0.0111692 - 0.149042i) q^{46} +(0.658322 - 1.67738i) q^{47} -1.65248 q^{48} +(0.0747301 + 0.997204i) q^{49} -1.00000 q^{50} +(0.997630 + 0.680173i) q^{54} +(0.955573 + 0.294755i) q^{56} +(1.88980 + 0.284841i) q^{58} +(1.63402 - 0.246289i) q^{60} +(-0.109562 + 0.101659i) q^{61} +(-1.07906 - 1.35310i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.500000 + 0.866025i) q^{67} +(-0.0549581 - 0.240787i) q^{69} +(-0.988831 - 0.149042i) q^{70} +(-1.65379 + 0.510127i) q^{72} +(-1.57906 + 0.487076i) q^{75} +(-0.500000 + 0.866025i) q^{80} +(0.252824 + 0.0779858i) q^{81} +(0.147791 + 1.97213i) q^{82} +(0.914101 - 1.14625i) q^{83} +1.65248 q^{84} +(1.44973 - 1.34515i) q^{86} +(3.12285 - 0.470694i) q^{87} +(-1.88980 - 0.284841i) q^{89} +(1.55929 - 0.750915i) q^{90} +(0.134659 + 0.0648483i) q^{92} +(1.32091 + 1.22563i) q^{94} +(0.603718 - 1.53825i) q^{96} +(-0.955573 - 0.294755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 8 q^{3} + q^{4} + q^{5} - 5 q^{6} - q^{7} + 2 q^{8} - 7 q^{9} - 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}+ \cdots - 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

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$-1$	$-1$

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 $

$2$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$2$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$3$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$4$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$5$	0.826239	+	0.563320i	0.826239	+	0.563320i
$5$	0.826239	+	0.563320i	0.826239	+	0.563320i
$6$	−1.48883	−	0.716983i	−1.48883	−	0.716983i
$7$	0.733052	+	0.680173i	0.733052	+	0.680173i
$7$	0.733052	+	0.680173i	0.733052	+	0.680173i
$8$	0.900969	−	0.433884i	0.900969	−	0.433884i
$9$	−1.71135	−	0.257945i	−1.71135	−	0.257945i
$10$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$11$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$11$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$12$	1.21135	−	1.12397i	1.21135	−	1.12397i
$13$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$13$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$14$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$15$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$16$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$17$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$17$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$18$	0.865341	−	1.49881i	0.865341	−	1.49881i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$21$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$22$		0			0
$23$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i	−0.365341	−	0.930874i	$-0.619048\pi$
$23$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i	0.222521	+	0.974928i	$0.428571\pi$
$24$	0.603718	+	1.53825i	0.603718	+	1.53825i
$25$	0.365341	+	0.930874i	0.365341	+	0.930874i
$26$		0			0
$27$	0.268680	−	1.17716i	0.268680	−	1.17716i
$28$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$29$	−0.425270	−	1.86323i	−0.425270	−	1.86323i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−0.425270	−	1.86323i	−0.425270	−	1.86323i	0.0747301	−	0.997204i	$-0.476190\pi$
$30$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$33$		0			0
$34$		0			0
$35$	0.222521	+	0.974928i	0.222521	+	0.974928i
$36$	1.07906	+	1.35310i	1.07906	+	1.35310i
$37$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$37$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$38$		0			0
$39$		0			0
$40$	0.988831	+	0.149042i	0.988831	+	0.149042i
$41$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.826239	−	0.563320i	$-0.190476\pi$
$41$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.955573	−	0.294755i	$-0.0952381\pi$
$42$	−0.603718	−	1.53825i	−0.603718	−	1.53825i
$43$	−1.78181	−	0.858075i	−1.78181	−	0.858075i	−0.955573	−	0.294755i	$-0.904762\pi$
$43$	−1.78181	−	0.858075i	−1.78181	−	0.858075i	−0.826239	−	0.563320i	$-0.809524\pi$
$44$		0			0
$45$	−1.26868	−	1.17716i	−1.26868	−	1.17716i
$46$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$47$	0.658322	−	1.67738i	0.658322	−	1.67738i	−0.0747301	−	0.997204i	$-0.523810\pi$
$47$	0.658322	−	1.67738i	0.658322	−	1.67738i	0.733052	−	0.680173i	$-0.238095\pi$
$48$	−1.65248			−1.65248
$49$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$50$	−1.00000			−1.00000
$51$		0			0
$52$		0			0
$53$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$53$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$54$	0.997630	+	0.680173i	0.997630	+	0.680173i
$55$		0			0
$56$	0.955573	+	0.294755i	0.955573	+	0.294755i
$57$		0			0
$58$	1.88980	+	0.284841i	1.88980	+	0.284841i
$59$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$59$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$60$	1.63402	−	0.246289i	1.63402	−	0.246289i
$61$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	−0.733052	−	0.680173i	$-0.761905\pi$
$61$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	0.623490	+	0.781831i	$0.285714\pi$
$62$		0			0
$63$	−1.07906	−	1.35310i	−1.07906	−	1.35310i
$64$	0.623490	−	0.781831i	0.623490	−	0.781831i
$65$		0			0
$66$		0			0
$67$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$67$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$68$		0			0
$69$	−0.0549581	−	0.240787i	−0.0549581	−	0.240787i
$70$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$71$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$71$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$72$	−1.65379	+	0.510127i	−1.65379	+	0.510127i
$73$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$73$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$74$		0			0
$75$	−1.57906	+	0.487076i	−1.57906	+	0.487076i
$76$		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
$81$	0.252824	+	0.0779858i	0.252824	+	0.0779858i
$82$	0.147791	+	1.97213i	0.147791	+	1.97213i
$83$	0.914101	−	1.14625i	0.914101	−	1.14625i	−0.0747301	−	0.997204i	$-0.523810\pi$
$83$	0.914101	−	1.14625i	0.914101	−	1.14625i	0.988831	−	0.149042i	$-0.0476190\pi$
$84$	1.65248			1.65248
$85$		0			0
$86$	1.44973	−	1.34515i	1.44973	−	1.34515i
$87$	3.12285	−	0.470694i	3.12285	−	0.470694i
$88$		0			0
$89$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.900969	−	0.433884i	$-0.857143\pi$
$89$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.988831	+	0.149042i	$0.952381\pi$
$90$	1.55929	−	0.750915i	1.55929	−	0.750915i
$91$		0			0
$92$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$93$		0			0
$94$	1.32091	+	1.22563i	1.32091	+	1.22563i
$95$		0			0
$96$	0.603718	−	1.53825i	0.603718	−	1.53825i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$99$		0			0
$100$	0.365341	−	0.930874i	0.365341	−	0.930874i
$101$	−0.109562	+	1.46200i	−0.109562	+	1.46200i	0.623490	+	0.781831i	$0.285714\pi$
$101$	−0.109562	+	1.46200i	−0.109562	+	1.46200i	−0.733052	+	0.680173i	$0.761905\pi$
$102$		0			0
$103$	0.826239	+	0.563320i	0.826239	+	0.563320i	0.900969	−	0.433884i	$-0.142857\pi$
$103$	0.826239	+	0.563320i	0.826239	+	0.563320i	−0.0747301	+	0.997204i	$0.523810\pi$
$104$		0			0
$105$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$106$		0			0
$107$	−1.44973	−	0.218511i	−1.44973	−	0.218511i	−0.623490	−	0.781831i	$-0.714286\pi$
$107$	−1.44973	−	0.218511i	−1.44973	−	0.218511i	−0.826239	+	0.563320i	$0.809524\pi$
$108$	−0.997630	+	0.680173i	−0.997630	+	0.680173i
$109$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.365341	−	0.930874i	$-0.380952\pi$
$109$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.623490	+	0.781831i	$0.285714\pi$
$110$		0			0
$111$		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
$115$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i
$116$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.367711	+	1.61105i	−0.367711	+	1.61105i
$121$	0.955573	−	0.294755i	0.955573	−	0.294755i
$122$	−0.0546039	−	0.139129i	−0.0546039	−	0.139129i
$123$	1.19395	+	3.04213i	1.19395	+	3.04213i
$124$		0			0
$125$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$126$	1.65379	−	0.510127i	1.65379	−	0.510127i
$127$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$127$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$	1.63402	−	2.83021i	1.63402	−	2.83021i
$130$		0			0
$131$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$131$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$132$		0			0
$133$		0			0
$134$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$135$	0.885113	−	0.821265i	0.885113	−	0.821265i
$136$		0			0
$137$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$137$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$138$	0.244221	+	0.0368104i	0.244221	+	0.0368104i
$139$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$139$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$140$	0.500000	−	0.866025i	0.500000	−	0.866025i
$141$	2.68278	+	1.29196i	2.68278	+	1.29196i
$142$		0			0
$143$		0			0
$144$	0.129334	−	1.72584i	0.129334	−	1.72584i
$145$	0.698220	−	1.77904i	0.698220	−	1.77904i
$146$		0			0
$147$	−1.65248			−1.65248
$148$		0			0
$149$	−0.535628	+	1.36476i	−0.535628	+	1.36476i	0.365341	+	0.930874i	$0.380952\pi$
$149$	−0.535628	+	1.36476i	−0.535628	+	1.36476i	−0.900969	+	0.433884i	$0.857143\pi$
$150$	0.123490	−	1.64786i	0.123490	−	1.64786i
$151$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$151$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$157$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$158$		0			0
$159$		0			0
$160$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$161$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i
$162$	−0.164962	+	0.206856i	−0.164962	+	0.206856i
$163$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	0.988831	+	0.149042i	$0.0476190\pi$
$163$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	−0.955573	+	0.294755i	$0.904762\pi$
$164$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$165$		0			0
$166$	0.733052	+	1.26968i	0.733052	+	1.26968i
$167$	0.162592	+	0.712362i	0.162592	+	0.712362i	0.988831	+	0.149042i	$0.0476190\pi$
$167$	0.162592	+	0.712362i	0.162592	+	0.712362i	−0.826239	+	0.563320i	$0.809524\pi$
$168$	−0.603718	+	1.53825i	−0.603718	+	1.53825i
$169$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$170$		0			0
$171$		0			0
$172$	0.722521	+	1.84095i	0.722521	+	1.84095i
$173$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$173$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$174$	−0.702749	+	3.07894i	−0.702749	+	3.07894i
$175$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$176$		0			0
$177$		0			0
$178$	0.955573	−	1.65510i	0.955573	−	1.65510i
$179$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$179$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$180$	0.129334	+	1.72584i	0.129334	+	1.72584i
$181$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$181$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$182$		0			0
$183$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$184$	−0.109562	+	0.101659i	−0.109562	+	0.101659i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$189$	0.997630	−	0.680173i	0.997630	−	0.680173i
$190$		0			0
$191$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$191$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$192$	1.21135	+	1.12397i	1.21135	+	1.12397i
$193$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$193$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$194$		0			0
$195$		0			0
$196$	0.623490	−	0.781831i	0.623490	−	0.781831i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$199$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$200$	0.733052	+	0.680173i	0.733052	+	0.680173i
$201$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$202$	−1.32091	−	0.636119i	−1.32091	−	0.636119i
$203$	0.955573	−	1.65510i	0.955573	−	1.65510i
$204$		0			0
$205$	1.95557	+	0.294755i	1.95557	+	0.294755i
$206$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$207$	0.255779	−	0.0385525i	0.255779	−	0.0385525i
$208$		0			0
$209$		0			0
$210$	0.367711	−	1.61105i	0.367711	−	1.61105i
$211$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$211$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$212$		0			0
$213$		0			0
$214$	0.733052	−	1.26968i	0.733052	−	1.26968i
$215$	−0.988831	−	1.71271i	−0.988831	−	1.71271i
$216$	−0.268680	−	1.17716i	−0.268680	−	1.17716i
$217$		0			0
$218$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$223$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$224$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$225$	−0.385113	−	1.68729i	−0.385113	−	1.68729i
$226$		0			0
$227$	0.623490	−	1.07992i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$227$	0.623490	−	1.07992i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$228$		0			0
$229$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	−0.988831	−	0.149042i	$-0.952381\pi$
$229$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	0.955573	−	0.294755i	$-0.0952381\pi$
$230$	0.0931869	−	0.116853i	0.0931869	−	0.116853i
$231$		0			0
$232$	−1.19158	−	1.49419i	−1.19158	−	1.49419i
$233$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$233$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$234$		0			0
$235$	1.48883	−	1.01507i	1.48883	−	1.01507i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$241$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	0.0747301	−	0.997204i	$-0.476190\pi$
$241$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$242$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$243$	0.281395	−	0.716983i	0.281395	−	0.716983i
$244$	0.149460			0.149460
$245$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$246$	−3.26804			−3.26804
$247$		0			0
$248$		0			0
$249$	1.77597	+	1.64786i	1.77597	+	1.64786i
$250$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$251$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$251$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$252$	−0.129334	+	1.72584i	−0.129334	+	1.72584i
$253$		0			0
$254$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$257$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$257$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$258$	2.03759	+	2.55506i	2.03759	+	2.55506i
$259$		0			0
$260$		0			0
$261$	0.247176	+	3.29834i	0.247176	+	3.29834i
$262$		0			0
$263$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.222521	−	0.974928i	$-0.428571\pi$
$263$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.733052	−	0.680173i	$-0.238095\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.702749	−	3.07894i	0.702749	−	3.07894i
$268$	0.955573	−	0.294755i	0.955573	−	0.294755i
$269$	0.266948	+	0.680173i	0.266948	+	0.680173i	1.00000			$0$
$269$	0.266948	+	0.680173i	0.266948	+	0.680173i	−0.733052	+	0.680173i	$0.761905\pi$
$270$	0.441126	+	1.12397i	0.441126	+	1.12397i
$271$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$271$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.123490	+	0.213891i	−0.123490	+	0.213891i
$277$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$277$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$278$		0			0
$279$		0			0
$280$	0.623490	+	0.781831i	0.623490	+	0.781831i
$281$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$281$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$282$	−2.18278	+	2.02532i	−2.18278	+	2.02532i
$283$	−1.78181	+	0.268565i	−1.78181	+	0.268565i	−0.955573	−	0.294755i	$-0.904762\pi$
$283$	−1.78181	+	0.268565i	−1.78181	+	0.268565i	−0.826239	+	0.563320i	$0.809524\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.88980	+	0.582926i	1.88980	+	0.582926i
$288$	1.55929	+	0.750915i	1.55929	+	0.750915i
$289$	0.826239	+	0.563320i	0.826239	+	0.563320i
$290$	1.40097	+	1.29991i	1.40097	+	1.29991i
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.603718	−	1.53825i	0.603718	−	1.53825i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$299$		0			0
$300$	1.48883	+	0.716983i	1.48883	+	0.716983i
$301$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$302$		0			0
$303$	−2.39564	−	0.361085i	−2.39564	−	0.361085i
$304$		0			0
$305$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i
$306$		0			0
$307$	−0.455573	−	0.571270i	−0.455573	−	0.571270i	0.500000	−	0.866025i	$-0.333333\pi$
$307$	−0.455573	−	0.571270i	−0.455573	−	0.571270i	−0.955573	+	0.294755i	$0.904762\pi$
$308$		0			0
$309$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$310$		0			0
$311$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$311$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$312$		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
$315$	−0.129334	−	1.72584i	−0.129334	−	1.72584i
$316$		0			0
$317$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$317$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$318$		0			0
$319$		0			0
$320$	0.955573	−	0.294755i	0.955573	−	0.294755i
$321$	0.539102	−	2.36196i	0.539102	−	2.36196i
$322$	0.109562	−	0.101659i	0.109562	−	0.101659i
$323$		0			0
$324$	−0.132289	−	0.229132i	−0.132289	−	0.229132i
$325$		0			0
$326$	−0.425270	−	0.131178i	−0.425270	−	0.131178i
$327$	0.123490	+	1.64786i	0.123490	+	1.64786i
$328$	1.23305	−	1.54620i	1.23305	−	1.54620i
$329$	1.62349	−	0.781831i	1.62349	−	0.781831i
$330$		0			0
$331$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$331$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$332$	−1.44973	+	0.218511i	−1.44973	+	0.218511i
$333$		0			0
$334$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$335$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$336$	−1.21135	−	1.12397i	−1.21135	−	1.12397i
$337$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$337$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$338$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$344$	−1.97766			−1.97766
$345$	0.0902318	−	0.229907i	0.0902318	−	0.229907i
$346$		0			0
$347$	−1.44973	−	1.34515i	−1.44973	−	1.34515i	−0.826239	−	0.563320i	$-0.809524\pi$
$347$	−1.44973	−	1.34515i	−1.44973	−	1.34515i	−0.623490	−	0.781831i	$-0.714286\pi$
$348$	−2.60937	−	1.77904i	−2.60937	−	1.77904i
$349$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.955573	+	0.294755i	$0.0952381\pi$
$349$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.826239	+	0.563320i	$0.190476\pi$
$350$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$351$		0			0
$352$		0			0
$353$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$353$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$354$		0			0
$355$		0			0
$356$	1.19158	+	1.49419i	1.19158	+	1.49419i
$357$		0			0
$358$		0			0
$359$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$359$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$360$	−1.65379	−	0.510127i	−1.65379	−	0.510127i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$363$	0.367711	+	1.61105i	0.367711	+	1.61105i
$364$		0			0
$365$		0			0
$366$	0.236007	−	0.0727985i	0.236007	−	0.0727985i
$367$	−0.266948	−	0.680173i	−0.266948	−	0.680173i	0.733052	−	0.680173i	$-0.238095\pi$
$367$	−0.266948	−	0.680173i	−0.266948	−	0.680173i	−1.00000			$\pi$
$368$	−0.0546039	−	0.139129i	−0.0546039	−	0.139129i
$369$	−3.27064	+	1.00886i	−3.27064	+	1.00886i
$370$		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
$375$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$376$	−0.134659	−	1.79690i	−0.134659	−	1.79690i
$377$		0			0
$378$	0.268680	+	1.17716i	0.268680	+	1.17716i
$379$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$379$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$380$		0			0
$381$	−2.03759	+	0.307117i	−2.03759	+	0.307117i
$382$		0			0
$383$	1.88980	+	0.284841i	1.88980	+	0.284841i	0.988831	−	0.149042i	$-0.0476190\pi$
$383$	1.88980	+	0.284841i	1.88980	+	0.284841i	0.900969	+	0.433884i	$0.142857\pi$
$384$	−1.48883	+	0.716983i	−1.48883	+	0.716983i
$385$		0			0
$386$		0			0
$387$	2.82797	+	1.92808i	2.82797	+	1.92808i
$388$		0			0
$389$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$389$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$390$		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		−0.826239	−	0.563320i	$-0.809524\pi$
$397$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$398$		0			0
$399$		0			0
$400$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$401$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.733052	−	0.680173i	$-0.761905\pi$
$401$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.900969	+	0.433884i	$0.857143\pi$
$402$	1.36534	−	0.930874i	1.36534	−	0.930874i
$403$		0			0
$404$	1.07473	−	0.997204i	1.07473	−	0.997204i
$405$	0.164962	+	0.206856i	0.164962	+	0.206856i
$406$	1.19158	+	1.49419i	1.19158	+	1.49419i
$407$		0			0
$408$		0			0
$409$	0.698220	+	0.215372i	0.698220	+	0.215372i	0.623490	−	0.781831i	$-0.285714\pi$
$409$	0.698220	+	0.215372i	0.698220	+	0.215372i	0.0747301	+	0.997204i	$0.476190\pi$
$410$	−0.988831	+	1.71271i	−0.988831	+	1.71271i
$411$		0			0
$412$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$413$		0			0
$414$	−0.0575591	+	0.252183i	−0.0575591	+	0.252183i
$415$	1.40097	−	0.432142i	1.40097	−	0.432142i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$419$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$420$	1.36534	+	0.930874i	1.36534	+	0.930874i
$421$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	−0.733052	−	0.680173i	$-0.761905\pi$
$421$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	0.365341	−	0.930874i	$-0.380952\pi$
$422$		0			0
$423$	−1.55929	+	2.70077i	−1.55929	+	2.70077i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.149460			−0.149460
$428$	0.914101	+	1.14625i	0.914101	+	1.14625i
$429$		0			0
$430$	1.95557	−	0.294755i	1.95557	−	0.294755i
$431$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$431$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$432$	1.19395	+	0.179959i	1.19395	+	0.179959i
$433$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$433$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$434$		0			0
$435$	2.84537	+	1.37026i	2.84537	+	1.37026i
$436$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$437$		0			0
$438$		0			0
$439$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$439$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$440$		0			0
$441$	0.129334	−	1.72584i	0.129334	−	1.72584i
$442$		0			0
$443$	−0.698220	+	1.77904i	−0.698220	+	1.77904i	−0.0747301	+	0.997204i	$0.523810\pi$
$443$	−0.698220	+	1.77904i	−0.698220	+	1.77904i	−0.623490	+	0.781831i	$0.714286\pi$
$444$		0			0
$445$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$446$	1.03030	+	0.702449i	1.03030	+	0.702449i
$447$	−2.18278	−	1.05117i	−2.18278	−	1.05117i
$448$	0.988831	−	0.149042i	0.988831	−	0.149042i
$449$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i	0.365341	+	0.930874i	$0.380952\pi$
$450$	1.71135	+	0.257945i	1.71135	+	0.257945i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.777479	+	0.974928i	0.777479	+	0.974928i
$455$		0			0
$456$		0			0
$457$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$457$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$458$	0.425270	+	0.131178i	0.425270	+	0.131178i
$459$		0			0
$460$	0.0747301	+	0.129436i	0.0747301	+	0.129436i
$461$	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	$0.571429\pi$
$462$		0			0
$463$	−0.326239	+	1.42935i	−0.326239	+	1.42935i	0.500000	+	0.866025i	$0.333333\pi$
$463$	−0.326239	+	1.42935i	−0.326239	+	1.42935i	−0.826239	+	0.563320i	$0.809524\pi$
$464$	1.82624	−	0.563320i	1.82624	−	0.563320i
$465$		0			0
$466$		0			0
$467$	0.955573	−	0.294755i	0.955573	−	0.294755i	0.222521	−	0.974928i	$-0.428571\pi$
$467$	0.955573	−	0.294755i	0.955573	−	0.294755i	0.733052	+	0.680173i	$0.238095\pi$
$468$		0			0
$469$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$470$	0.400969	+	1.75676i	0.400969	+	1.75676i
$471$		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		0.988831	−	0.149042i	$-0.0476190\pi$
$479$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$480$	1.36534	−	0.930874i	1.36534	−	0.930874i
$481$		0			0
$482$	1.12349	−	0.541044i	1.12349	−	0.541044i
$483$	0.123490	−	0.213891i	0.123490	−	0.213891i
$484$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$485$		0			0
$486$	0.564616	+	0.523887i	0.564616	+	0.523887i
$487$	0.134659	−	1.79690i	0.134659	−	1.79690i	−0.365341	−	0.930874i	$-0.619048\pi$
$487$	0.134659	−	1.79690i	0.134659	−	1.79690i	0.500000	−	0.866025i	$-0.333333\pi$
$488$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i
$489$	−0.735422			−0.735422
$490$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	1.19395	−	3.04213i	1.19395	−	3.04213i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−2.18278	+	1.05117i	−2.18278	+	1.05117i
$499$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$499$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$500$	0.826239	−	0.563320i	0.826239	−	0.563320i
$501$	−1.19395	+	0.179959i	−1.19395	+	0.179959i
$502$		0			0
$503$	1.23305	+	1.54620i	1.23305	+	1.54620i	0.733052	+	0.680173i	$0.238095\pi$
$503$	1.23305	+	1.54620i	1.23305	+	1.54620i	0.500000	+	0.866025i	$0.333333\pi$
$504$	−1.55929	−	0.750915i	−1.55929	−	0.750915i
$505$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$506$		0			0
$507$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$508$	0.623490	−	1.07992i	0.623490	−	1.07992i
$509$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	0.826239	−	0.563320i	$-0.190476\pi$
$509$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	−0.900969	+	0.433884i	$0.857143\pi$
$510$		0			0
$511$		0			0
$512$	0.222521	−	0.974928i	0.222521	−	0.974928i
$513$		0			0
$514$		0			0
$515$	0.365341	+	0.930874i	0.365341	+	0.930874i
$516$	−3.12285	+	0.963272i	−3.12285	+	0.963272i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$521$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$522$	−3.16064	−	0.974928i	−3.16064	−	0.974928i
$523$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	0.988831	+	0.149042i	$0.0476190\pi$
$523$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	−0.955573	+	0.294755i	$0.904762\pi$
$524$		0			0
$525$	−1.48883	−	0.716983i	−1.48883	−	0.716983i
$526$	1.19158	+	1.49419i	1.19158	+	1.49419i
$527$		0			0
$528$		0			0
$529$	−0.807782	+	0.550736i	−0.807782	+	0.550736i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	2.60937	+	1.77904i	2.60937	+	1.77904i
$535$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$536$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$537$		0			0
$538$	−0.730682			−0.730682
$539$		0			0
$540$	−1.20744			−1.20744
$541$	0.603718	−	1.53825i	0.603718	−	1.53825i	−0.222521	−	0.974928i	$-0.571429\pi$
$541$	0.603718	−	1.53825i	0.603718	−	1.53825i	0.826239	−	0.563320i	$-0.190476\pi$
$542$		0			0
$543$	−1.21135	−	1.12397i	−1.21135	−	1.12397i
$544$		0			0
$545$	0.900969	+	0.433884i	0.900969	+	0.433884i
$546$		0			0
$547$	0.134659	−	0.0648483i	0.134659	−	0.0648483i	−0.365341	−	0.930874i	$-0.619048\pi$
$547$	0.134659	−	0.0648483i	0.134659	−	0.0648483i	0.500000	+	0.866025i	$0.333333\pi$
$548$		0			0
$549$	0.213722	−	0.145713i	0.213722	−	0.145713i
$550$		0			0
$551$		0			0
$552$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$553$		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
$560$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$561$		0			0
$562$	1.72188	−	0.531130i	1.72188	−	0.531130i
$563$	−0.698220	−	1.77904i	−0.698220	−	1.77904i	−0.623490	−	0.781831i	$-0.714286\pi$
$563$	−0.698220	−	1.77904i	−0.698220	−	1.77904i	−0.0747301	−	0.997204i	$-0.523810\pi$
$564$	−1.08786	−	2.77183i	−1.08786	−	2.77183i
$565$		0			0
$566$	0.400969	−	1.75676i	0.400969	−	1.75676i
$567$	0.132289	+	0.229132i	0.132289	+	0.229132i
$568$		0			0
$569$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$569$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$570$		0			0
$571$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$571$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$572$		0			0
$573$		0			0
$574$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$575$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i
$576$	−1.26868	+	1.17716i	−1.26868	+	1.17716i
$577$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$577$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$578$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$579$		0			0
$580$	−1.72188	+	0.829215i	−1.72188	+	0.829215i
$581$	1.44973	−	0.218511i	1.44973	−	0.218511i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$587$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$588$	1.21135	+	1.12397i	1.21135	+	1.12397i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$593$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$594$		0			0
$595$		0			0
$596$	1.32091	−	0.636119i	1.32091	−	0.636119i
$597$		0			0
$598$		0			0
$599$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$599$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$600$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$601$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$601$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$602$	1.97766			1.97766
$603$	1.07906	−	1.35310i	1.07906	−	1.35310i
$604$		0			0
$605$	0.955573	+	0.294755i	0.955573	+	0.294755i
$606$	1.21135	−	2.09812i	1.21135	−	2.09812i
$607$	0.955573	+	1.65510i	0.955573	+	1.65510i	0.733052	+	0.680173i	$0.238095\pi$
$607$	0.955573	+	1.65510i	0.955573	+	1.65510i	0.222521	+	0.974928i	$0.428571\pi$
$608$		0			0
$609$	2.60937	+	1.77904i	2.60937	+	1.77904i
$610$	0.0332580	−	0.145713i	0.0332580	−	0.145713i
$611$		0			0
$612$		0			0
$613$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$613$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$614$	0.698220	−	0.215372i	0.698220	−	0.215372i
$615$	−0.727208	+	3.18610i	−0.727208	+	3.18610i
$616$		0			0
$617$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$617$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$618$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	0.0134861	+	0.179959i	0.0134861	+	0.179959i
$622$		0			0
$623$	−1.19158	−	1.49419i	−1.19158	−	1.49419i
$624$		0			0
$625$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.65379	+	0.510127i	1.65379	+	0.510127i
$631$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$631$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.455573	+	1.16078i	−0.455573	+	1.16078i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$641$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$641$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$642$	2.00173	+	1.36476i	2.00173	+	1.36476i
$643$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$643$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$644$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$645$	2.94440	−	1.41795i	2.94440	−	1.41795i
$646$		0			0
$647$	−0.603718	+	0.411608i	−0.603718	+	0.411608i	−0.826239	−	0.563320i	$-0.809524\pi$
$647$	−0.603718	+	0.411608i	−0.603718	+	0.411608i	0.222521	+	0.974928i	$0.428571\pi$
$648$	0.261623	−	0.0394334i	0.261623	−	0.0394334i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.277479	−	0.347948i	0.277479	−	0.347948i
$653$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$653$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$654$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$655$		0			0
$656$	0.988831	+	1.71271i	0.988831	+	1.71271i
$657$		0			0
$658$	0.134659	+	1.79690i	0.134659	+	1.79690i
$659$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$659$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$660$		0			0
$661$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$661$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$662$		0			0
$663$		0			0
$664$	0.326239	−	1.42935i	0.326239	−	1.42935i
$665$		0			0
$666$		0			0
$667$	0.142820	+	0.247372i	0.142820	+	0.247372i
$668$	0.365341	−	0.632789i	0.365341	−	0.632789i
$669$	1.96906	+	0.607374i	1.96906	+	0.607374i
$670$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$671$		0			0
$672$	1.48883	−	0.716983i	1.48883	−	0.716983i
$673$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$673$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$674$		0			0
$675$	1.19395	−	0.179959i	1.19395	−	0.179959i
$676$	0.826239	−	0.563320i	0.826239	−	0.563320i
$677$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$677$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.70255	+	1.16078i	1.70255	+	1.16078i
$682$		0			0
$683$	−0.0546039	+	0.728639i	−0.0546039	+	0.728639i	0.900969	+	0.433884i	$0.142857\pi$
$683$	−0.0546039	+	0.728639i	−0.0546039	+	0.728639i	−0.955573	+	0.294755i	$0.904762\pi$
$684$		0			0
$685$		0			0
$686$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$687$	0.735422			0.735422
$688$	0.722521	−	1.84095i	0.722521	−	1.84095i
$689$		0			0
$690$	0.181049	+	0.167989i	0.181049	+	0.167989i
$691$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$691$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$692$		0			0
$693$		0			0
$694$	1.78181	−	0.858075i	1.78181	−	0.858075i
$695$		0			0
$696$	2.60937	−	1.77904i	2.60937	−	1.77904i
$697$		0			0
$698$	−1.44973	+	1.34515i	−1.44973	+	1.34515i
$699$		0			0
$700$	0.900969	−	0.433884i	0.900969	−	0.433884i
$701$	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			0
$705$	1.48883	+	2.57873i	1.48883	+	2.57873i
$706$		0			0
$707$	−1.07473	+	0.997204i	−1.07473	+	0.997204i
$708$		0			0
$709$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.900969	−	0.433884i	$-0.857143\pi$
$709$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	−1.82624	+	0.563320i	−1.82624	+	0.563320i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$719$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$720$	1.07906	−	1.35310i	1.07906	−	1.35310i
$721$	0.222521	+	0.974928i	0.222521	+	0.974928i
$722$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$723$	1.51053	−	1.40157i	1.51053	−	1.40157i
$724$	0.988831	−	0.149042i	0.988831	−	0.149042i
$725$	1.57906	−	1.07659i	1.57906	−	1.07659i
$726$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$727$	−1.32091	+	0.636119i	−1.32091	+	0.636119i	−0.955573	−	0.294755i	$-0.904762\pi$
$727$	−1.32091	+	0.636119i	−1.32091	+	0.636119i	−0.365341	+	0.930874i	$0.619048\pi$
$728$		0			0
$729$	1.38511	+	0.667035i	1.38511	+	0.667035i
$730$		0			0
$731$		0			0
$732$	−0.0184568	+	0.246289i	−0.0184568	+	0.246289i
$733$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$733$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$734$	0.730682			0.730682
$735$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$736$	0.149460			0.149460
$737$		0			0
$738$	0.255779	−	3.41313i	0.255779	−	3.41313i
$739$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$739$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.658322	−	0.317031i	0.658322	−	0.317031i	−0.0747301	−	0.997204i	$-0.523810\pi$
$743$	0.658322	−	0.317031i	0.658322	−	0.317031i	0.733052	+	0.680173i	$0.238095\pi$
$744$		0			0
$745$	−1.21135	+	0.825886i	−1.21135	+	0.825886i
$746$		0			0
$747$	−1.86002	+	1.72584i	−1.86002	+	1.72584i
$748$		0			0
$749$	−0.914101	−	1.14625i	−0.914101	−	1.14625i
$750$	1.03030	−	1.29196i	1.03030	−	1.29196i
$751$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$751$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$752$	1.72188	+	0.531130i	1.72188	+	0.531130i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.19395	−	0.179959i	−1.19395	−	0.179959i
$757$		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
$761$	1.19158	−	0.367554i	1.19158	−	0.367554i	0.365341	−	0.930874i	$-0.380952\pi$
$761$	1.19158	−	0.367554i	1.19158	−	0.367554i	0.826239	+	0.563320i	$0.190476\pi$
$762$	0.458528	−	2.00894i	0.458528	−	2.00894i
$763$	0.826239	+	0.563320i	0.826239	+	0.563320i
$764$		0			0
$765$		0			0
$766$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$767$		0			0
$768$	−0.123490	−	1.64786i	−0.123490	−	1.64786i
$769$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$769$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$773$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$774$	−2.82797	+	1.92808i	−2.82797	+	1.92808i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.30759			−2.30759
$784$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$785$		0			0
$786$		0			0
$787$	−0.142820	+	1.90580i	−0.142820	+	1.90580i	0.222521	+	0.974928i	$0.428571\pi$
$787$	−0.142820	+	1.90580i	−0.142820	+	1.90580i	−0.365341	+	0.930874i	$0.619048\pi$
$788$		0			0
$789$	2.60937	+	1.77904i	2.60937	+	1.77904i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$797$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$798$		0			0
$799$		0			0
$800$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$801$	3.16064	+	0.974928i	3.16064	+	0.974928i
$802$	0.826239	−	1.43109i	0.826239	−	1.43109i
$803$		0			0
$804$	0.367711	+	1.61105i	0.367711	+	1.61105i
$805$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$806$		0			0
$807$	−1.15379	+	0.355898i	−1.15379	+	0.355898i
$808$	0.535628	+	1.36476i	0.535628	+	1.36476i
$809$	−0.365341	−	0.930874i	−0.365341	−	0.930874i	−0.988831	−	0.149042i	$-0.952381\pi$
$809$	−0.365341	−	0.930874i	−0.365341	−	0.930874i	0.623490	−	0.781831i	$-0.285714\pi$
$810$	−0.252824	+	0.0779858i	−0.252824	+	0.0779858i
$811$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$811$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$812$	−1.82624	+	0.563320i	−1.82624	+	0.563320i
$813$		0			0
$814$		0			0
$815$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$816$		0			0
$817$		0			0
$818$	−0.455573	+	0.571270i	−0.455573	+	0.571270i
$819$		0			0
$820$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$821$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$821$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$822$		0			0
$823$	−0.603718	+	0.411608i	−0.603718	+	0.411608i	−0.826239	−	0.563320i	$-0.809524\pi$
$823$	−0.603718	+	0.411608i	−0.603718	+	0.411608i	0.222521	+	0.974928i	$0.428571\pi$
$824$	0.988831	+	0.149042i	0.988831	+	0.149042i
$825$		0			0
$826$		0			0
$827$	1.48883	+	0.716983i	1.48883	+	0.716983i	0.988831	−	0.149042i	$-0.0476190\pi$
$827$	1.48883	+	0.716983i	1.48883	+	0.716983i	0.500000	+	0.866025i	$0.333333\pi$
$828$	−0.213722	−	0.145713i	−0.213722	−	0.145713i
$829$	0.326239	+	0.302705i	0.326239	+	0.302705i	0.826239	−	0.563320i	$-0.190476\pi$
$829$	0.326239	+	0.302705i	0.326239	+	0.302705i	−0.500000	+	0.866025i	$0.666667\pi$
$830$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.266948	+	0.680173i	−0.266948	+	0.680173i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$839$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$840$	−1.36534	+	0.930874i	−1.36534	+	0.930874i
$841$	−2.38980	+	1.15087i	−2.38980	+	1.15087i
$842$	1.63402	+	0.246289i	1.63402	+	0.246289i
$843$	2.46026	−	1.67738i	2.46026	−	1.67738i
$844$		0			0
$845$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$846$	−1.94440	−	2.43821i	−1.94440	−	2.43821i
$847$	0.900969	+	0.433884i	0.900969	+	0.433884i
$848$		0			0
$849$	−0.222521	−	2.96934i	−0.222521	−	2.96934i
$850$		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	$0.428571\pi$
$854$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$855$		0			0
$856$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$857$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$857$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$858$		0			0
$859$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$859$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$860$	−0.440071	+	1.92808i	−0.440071	+	1.92808i
$861$	−1.19395	+	3.04213i	−1.19395	+	3.04213i
$862$		0			0
$863$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$863$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$864$	−0.603718	+	1.04567i	−0.603718	+	1.04567i
$865$		0			0
$866$		0			0
$867$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$868$		0			0
$869$		0			0
$870$	−2.31507	+	2.14807i	−2.31507	+	2.14807i
$871$		0			0
$872$	0.826239	−	0.563320i	0.826239	−	0.563320i
$873$		0			0
$874$		0			0
$875$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$876$		0			0
$877$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$877$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$878$		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	$0.666667\pi$
$882$	1.55929	+	0.750915i	1.55929	+	0.750915i
$883$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$883$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$884$		0			0
$885$		0			0
$886$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$887$	−0.123490	−	0.0841939i	−0.123490	−	0.0841939i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	−0.123490	−	0.0841939i	−0.123490	−	0.0841939i	−0.623490	+	0.781831i	$0.714286\pi$
$888$		0			0
$889$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$890$	1.72188	−	0.829215i	1.72188	−	0.829215i
$891$		0			0
$892$	−1.03030	+	0.702449i	−1.03030	+	0.702449i
$893$		0			0
$894$	1.77597	−	1.64786i	1.77597	−	1.64786i
$895$		0			0
$896$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$897$		0			0
$898$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$899$		0			0
$900$	−0.865341	+	1.49881i	−0.865341	+	1.49881i
$901$		0			0
$902$		0			0
$903$	3.12285	−	0.963272i	3.12285	−	0.963272i
$904$		0			0
$905$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$906$		0			0
$907$	−0.603718	−	1.53825i	−0.603718	−	1.53825i	−0.826239	−	0.563320i	$-0.809524\pi$
$907$	−0.603718	−	1.53825i	−0.603718	−	1.53825i	0.222521	−	0.974928i	$-0.428571\pi$
$908$	−1.19158	+	0.367554i	−1.19158	+	0.367554i
$909$	0.564616	−	2.47374i	0.564616	−	2.47374i
$910$		0			0
$911$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$911$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.0184568	−	0.246289i	−0.0184568	−	0.246289i
$916$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$917$		0			0
$918$		0			0
$919$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$919$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$920$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i
$921$	0.997630	−	0.680173i	0.997630	−	0.680173i
$922$	−1.78181	−	0.268565i	−1.78181	−	0.268565i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$927$	−1.26868	−	1.17716i	−1.26868	−	1.17716i
$928$	−0.142820	+	1.90580i	−0.142820	+	1.90580i
$929$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	−0.900969	−	0.433884i	$-0.857143\pi$
$929$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	0.955573	+	0.294755i	$0.0952381\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$935$		0			0
$936$		0			0
$937$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$937$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$938$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$939$		0			0
$940$	−1.78181	−	0.268565i	−1.78181	−	0.268565i
$941$	−0.367711	+	0.250701i	−0.367711	+	0.250701i	−0.733052	−	0.680173i	$-0.761905\pi$
$941$	−0.367711	+	0.250701i	−0.367711	+	0.250701i	0.365341	+	0.930874i	$0.380952\pi$
$942$		0			0
$943$	−0.216677	+	0.201047i	−0.216677	+	0.201047i
$944$		0			0
$945$	1.20744			1.20744
$946$		0			0
$947$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i	−0.955573	−	0.294755i	$-0.904762\pi$
$947$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i	0.900969	−	0.433884i	$-0.142857\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$953$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.367711	+	1.61105i	0.367711	+	1.61105i
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$	2.42463	+	0.747900i	2.42463	+	0.747900i
$964$	0.0931869	+	1.24349i	0.0931869	+	1.24349i
$965$		0			0
$966$	0.153989	+	0.193096i	0.153989	+	0.193096i
$967$	−1.03030	−	1.29196i	−1.03030	−	1.29196i	−0.955573	−	0.294755i	$-0.904762\pi$
$967$	−1.03030	−	1.29196i	−1.03030	−	1.29196i	−0.0747301	−	0.997204i	$-0.523810\pi$
$968$	0.733052	−	0.680173i	0.733052	−	0.680173i
$969$		0			0
$970$		0			0
$971$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$971$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$972$	−0.693950	+	0.334189i	−0.693950	+	0.334189i
$973$		0			0
$974$	1.62349	+	0.781831i	1.62349	+	0.781831i
$975$		0			0
$976$	−0.109562	−	0.101659i	−0.109562	−	0.101659i
$977$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$977$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$978$	0.268680	−	0.684585i	0.268680	−	0.684585i
$979$		0			0
$980$	0.955573	−	0.294755i	0.955573	−	0.294755i
$981$	−1.73068			−1.73068
$982$		0			0
$983$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i	0.988831	+	0.149042i	$0.0476190\pi$
$983$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i	−1.00000			$\pi$
$984$	2.39564	+	2.22283i	2.39564	+	2.22283i
$985$		0			0
$986$		0			0
$987$	1.08786	+	2.77183i	1.08786	+	2.77183i
$988$		0			0
$989$	0.292280	+	0.0440542i	0.292280	+	0.0440542i
$990$		0			0
$991$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$991$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.181049	−	2.41593i	−0.181049	−	2.41593i
$997$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$997$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.1.bq.a.879.1	yes	12
4.3	odd	2		980.1.bq.b.879.1	yes	12
5.4	even	2		980.1.bq.b.879.1	yes	12
20.19	odd	2	CM	980.1.bq.a.879.1	yes	12
49.16	even	21	inner	980.1.bq.a.359.1	✓	12
196.163	odd	42		980.1.bq.b.359.1	yes	12
245.114	even	42		980.1.bq.b.359.1	yes	12
980.359	odd	42	inner	980.1.bq.a.359.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.1.bq.a.359.1	✓	12	49.16	even	21	inner
980.1.bq.a.359.1	✓	12	980.359	odd	42	inner
980.1.bq.a.879.1	yes	12	1.1	even	1	trivial
980.1.bq.a.879.1	yes	12	20.19	odd	2	CM
980.1.bq.b.359.1	yes	12	196.163	odd	42
980.1.bq.b.359.1	yes	12	245.114	even	42
980.1.bq.b.879.1	yes	12	4.3	odd	2
980.1.bq.b.879.1	yes	12	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.365341 + 0.930874i) q^{2} +(-0.123490 + 1.64786i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(0.826239 + 0.563320i) q^{5} +(-1.48883 - 0.716983i) q^{6} +(0.733052 + 0.680173i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-1.71135 - 0.257945i) q^{9} +(-0.826239 + 0.563320i) q^{10} +(1.21135 - 1.12397i) q^{12} +(-0.900969 + 0.433884i) q^{14} +(-1.03030 + 1.29196i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(0.865341 - 1.49881i) q^{18} +(-0.222521 - 0.974928i) q^{20} +(-1.21135 + 1.12397i) q^{21} +(-0.142820 + 0.0440542i) q^{23} +(0.603718 + 1.53825i) q^{24} +(0.365341 + 0.930874i) q^{25} +(0.268680 - 1.17716i) q^{27} +(-0.0747301 - 0.997204i) q^{28} +(-0.425270 - 1.86323i) q^{29} +(-0.826239 - 1.43109i) q^{30} +(-0.955573 - 0.294755i) q^{32} +(0.222521 + 0.974928i) q^{35} +(1.07906 + 1.35310i) q^{36} +(0.988831 + 0.149042i) q^{40} +(1.78181 - 0.858075i) q^{41} +(-0.603718 - 1.53825i) q^{42} +(-1.78181 - 0.858075i) q^{43} +(-1.26868 - 1.17716i) q^{45} +(0.0111692 - 0.149042i) q^{46} +(0.658322 - 1.67738i) q^{47} -1.65248 q^{48} +(0.0747301 + 0.997204i) q^{49} -1.00000 q^{50} +(0.997630 + 0.680173i) q^{54} +(0.955573 + 0.294755i) q^{56} +(1.88980 + 0.284841i) q^{58} +(1.63402 - 0.246289i) q^{60} +(-0.109562 + 0.101659i) q^{61} +(-1.07906 - 1.35310i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.500000 + 0.866025i) q^{67} +(-0.0549581 - 0.240787i) q^{69} +(-0.988831 - 0.149042i) q^{70} +(-1.65379 + 0.510127i) q^{72} +(-1.57906 + 0.487076i) q^{75} +(-0.500000 + 0.866025i) q^{80} +(0.252824 + 0.0779858i) q^{81} +(0.147791 + 1.97213i) q^{82} +(0.914101 - 1.14625i) q^{83} +1.65248 q^{84} +(1.44973 - 1.34515i) q^{86} +(3.12285 - 0.470694i) q^{87} +(-1.88980 - 0.284841i) q^{89} +(1.55929 - 0.750915i) q^{90} +(0.134659 + 0.0648483i) q^{92} +(1.32091 + 1.22563i) q^{94} +(0.603718 - 1.53825i) q^{96} +(-0.955573 - 0.294755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 8 q^{3} + q^{4} + q^{5} - 5 q^{6} - q^{7} + 2 q^{8} - 7 q^{9} - q^{10} + q^{12} - 2 q^{14} - 2 q^{15} + q^{16} + 7 q^{18} - 2 q^{20} - q^{21} + q^{23} - q^{24} + q^{25} - 12 q^{27}+ \cdots - q^{98}+O(q^{100}) \) 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

Introduction

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