LMFDB - Embedded newform 2717.1.db.c.1715.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2717,1,Mod(142,2717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2717, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 8]))

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

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

chi := DirichletCharacter("2717.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2717 = 11 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2717.db (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35595963932$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			1715.2
Root			$0.990268 - 0.139173i$ of defining polynomial
Character	$\chi$	$=$	2717.1715
Dual form			2717.1.db.c.1429.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.704030 + 0.256246i) q^{2} +(0.294524 - 1.67033i) q^{3} +(-0.336048 + 0.281978i) q^{4} +(0.220661 + 1.25143i) q^{6} +(-0.997564 - 1.72783i) q^{7} +(0.538939 - 0.933469i) q^{8} +(-1.76356 - 0.641884i) q^{9} +O(q^{10})$	\(q+(-0.704030 + 0.256246i) q^{2} +(0.294524 - 1.67033i) q^{3} +(-0.336048 + 0.281978i) q^{4} +(0.220661 + 1.25143i) q^{6} +(-0.997564 - 1.72783i) q^{7} +(0.538939 - 0.933469i) q^{8} +(-1.76356 - 0.641884i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.372021 + 0.644360i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(1.14507 + 0.960824i) q^{14} +(-0.0640554 + 0.363276i) q^{16} +1.40608 q^{18} +(0.882948 - 0.469472i) q^{19} +(-3.17985 + 1.15737i) q^{21} +(-0.130100 + 0.737831i) q^{22} +(1.47274 - 1.23577i) q^{23} +(-1.40047 - 1.17513i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.374607 + 0.648838i) q^{26} +(-0.743520 + 1.28781i) q^{27} +(0.822440 + 0.299344i) q^{28} +(0.139180 + 0.789331i) q^{32} +(-1.29929 - 1.09023i) q^{33} +(0.773638 - 0.281581i) q^{36} +(-0.501321 + 0.556774i) q^{38} -1.69610 q^{39} +(-0.194206 + 1.10140i) q^{41} +(1.94214 - 1.62965i) q^{42} +(0.0761759 + 0.432015i) q^{44} +(-0.720190 + 1.24741i) q^{46} +(0.587925 + 0.213987i) q^{48} +(-1.49027 + 2.58122i) q^{49} +(-0.374607 - 0.648838i) q^{50} +(0.336048 + 0.281978i) q^{52} +(0.0534691 - 0.0448659i) q^{53} +(0.193463 - 1.09718i) q^{54} -2.15050 q^{56} +(-0.524123 - 1.61308i) q^{57} +(0.650198 + 3.68746i) q^{63} +(-0.484690 - 0.839508i) q^{64} +(1.19410 + 0.434618i) q^{66} +(-1.63039 - 2.82392i) q^{69} +(-1.54963 + 1.30029i) q^{72} +(-0.107320 + 0.608645i) q^{73} +1.69610 q^{75} +(-0.164332 + 0.406737i) q^{76} -1.99513 q^{77} +(1.19410 - 0.434618i) q^{78} +(0.494420 + 0.414868i) q^{81} +(-0.145501 - 0.825180i) q^{82} +(-0.241922 - 0.419021i) q^{83} +(0.742230 - 1.28558i) q^{84} +(-0.538939 - 0.933469i) q^{88} +(-1.52836 + 1.28244i) q^{91} +(-0.146450 + 0.830559i) q^{92} +1.35943 q^{96} +(0.387766 - 2.19913i) q^{98} +(-1.43767 + 1.20635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * q^78 + 6 * q^81 + 3 * q^82 - 12 * q^84 - 3 * q^88 - 6 * q^91 - 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.669131	−	0.743145i	$-0.733333\pi$
$2$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.0348995	+	0.999391i	$0.511111\pi$
$3$	0.294524	−	1.67033i	0.294524	−	1.67033i	−0.374607	−	0.927184i	$-0.622222\pi$
$3$	0.294524	−	1.67033i	0.294524	−	1.67033i	0.669131	−	0.743145i	$-0.266667\pi$
$4$	−0.336048	+	0.281978i	−0.336048	+	0.281978i
$5$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$5$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$6$	0.220661	+	1.25143i	0.220661	+	1.25143i
$7$	−0.997564	−	1.72783i	−0.997564	−	1.72783i	−0.559193	−	0.829038i	$-0.688889\pi$
$7$	−0.997564	−	1.72783i	−0.997564	−	1.72783i	−0.438371	−	0.898794i	$-0.644444\pi$
$8$	0.538939	−	0.933469i	0.538939	−	0.933469i
$9$	−1.76356	−	0.641884i	−1.76356	−	0.641884i
$10$		0			0
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$12$	0.372021	+	0.644360i	0.372021	+	0.644360i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$14$	1.14507	+	0.960824i	1.14507	+	0.960824i
$15$		0			0
$16$	−0.0640554	+	0.363276i	−0.0640554	+	0.363276i
$17$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$17$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$18$	1.40608			1.40608
$19$	0.882948	−	0.469472i	0.882948	−	0.469472i
$19$	0.882948	−	0.469472i	0.882948	−	0.469472i
$20$		0			0
$21$	−3.17985	+	1.15737i	−3.17985	+	1.15737i
$22$	−0.130100	+	0.737831i	−0.130100	+	0.737831i
$23$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.559193	−	0.829038i	$-0.311111\pi$
$23$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.913545	−	0.406737i	$-0.133333\pi$
$24$	−1.40047	−	1.17513i	−1.40047	−	1.17513i
$25$	0.173648	+	0.984808i	0.173648	+	0.984808i
$26$	0.374607	+	0.648838i	0.374607	+	0.648838i
$27$	−0.743520	+	1.28781i	−0.743520	+	1.28781i
$28$	0.822440	+	0.299344i	0.822440	+	0.299344i
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	0.139180	+	0.789331i	0.139180	+	0.789331i
$33$	−1.29929	−	1.09023i	−1.29929	−	1.09023i
$34$		0			0
$35$		0			0
$36$	0.773638	−	0.281581i	0.773638	−	0.281581i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.501321	+	0.556774i	−0.501321	+	0.556774i
$39$	−1.69610			−1.69610
$40$		0			0
$41$	−0.194206	+	1.10140i	−0.194206	+	1.10140i	0.719340	+	0.694658i	$0.244444\pi$
$41$	−0.194206	+	1.10140i	−0.194206	+	1.10140i	−0.913545	+	0.406737i	$0.866667\pi$
$42$	1.94214	−	1.62965i	1.94214	−	1.62965i
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	0.0761759	+	0.432015i	0.0761759	+	0.432015i
$45$		0			0
$46$	−0.720190	+	1.24741i	−0.720190	+	1.24741i
$47$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$47$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$48$	0.587925	+	0.213987i	0.587925	+	0.213987i
$49$	−1.49027	+	2.58122i	−1.49027	+	2.58122i
$50$	−0.374607	−	0.648838i	−0.374607	−	0.648838i
$51$		0			0
$52$	0.336048	+	0.281978i	0.336048	+	0.281978i
$53$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i	−0.615661	−	0.788011i	$-0.711111\pi$
$53$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i	0.669131	+	0.743145i	$0.266667\pi$
$54$	0.193463	−	1.09718i	0.193463	−	1.09718i
$55$		0			0
$56$	−2.15050			−2.15050
$57$	−0.524123	−	1.61308i	−0.524123	−	1.61308i
$58$		0			0
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$		0			0
$61$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$61$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$62$		0			0
$63$	0.650198	+	3.68746i	0.650198	+	3.68746i
$64$	−0.484690	−	0.839508i	−0.484690	−	0.839508i
$65$		0			0
$66$	1.19410	+	0.434618i	1.19410	+	0.434618i
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$		0			0
$69$	−1.63039	−	2.82392i	−1.63039	−	2.82392i
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	−1.54963	+	1.30029i	−1.54963	+	1.30029i
$73$	−0.107320	+	0.608645i	−0.107320	+	0.608645i	0.882948	+	0.469472i	$0.155556\pi$
$73$	−0.107320	+	0.608645i	−0.107320	+	0.608645i	−0.990268	+	0.139173i	$0.955556\pi$
$74$		0			0
$75$	1.69610			1.69610
$76$	−0.164332	+	0.406737i	−0.164332	+	0.406737i
$77$	−1.99513			−1.99513
$78$	1.19410	−	0.434618i	1.19410	−	0.434618i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$		0			0
$81$	0.494420	+	0.414868i	0.494420	+	0.414868i
$82$	−0.145501	−	0.825180i	−0.145501	−	0.825180i
$83$	−0.241922	−	0.419021i	−0.241922	−	0.419021i	0.719340	−	0.694658i	$-0.244444\pi$
$83$	−0.241922	−	0.419021i	−0.241922	−	0.419021i	−0.961262	+	0.275637i	$0.911111\pi$
$84$	0.742230	−	1.28558i	0.742230	−	1.28558i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.538939	−	0.933469i	−0.538939	−	0.933469i
$89$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$89$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$90$		0			0
$91$	−1.52836	+	1.28244i	−1.52836	+	1.28244i
$92$	−0.146450	+	0.830559i	−0.146450	+	0.830559i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.35943			1.35943
$97$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$97$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$98$	0.387766	−	2.19913i	0.387766	−	2.19913i
$99$	−1.43767	+	1.20635i	−1.43767	+	1.20635i
$100$	−0.336048	−	0.281978i	−0.336048	−	0.281978i
$101$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$101$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$102$		0			0
$103$	0.719340	−	1.24593i	0.719340	−	1.24593i	−0.241922	−	0.970296i	$-0.577778\pi$
$103$	0.719340	−	1.24593i	0.719340	−	1.24593i	0.961262	−	0.275637i	$-0.0888889\pi$
$104$	−1.01287	−	0.368656i	−1.01287	−	0.368656i
$105$		0			0
$106$	−0.0261472	+	0.0452882i	−0.0261472	+	0.0452882i
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	−0.113277	−	0.642423i	−0.113277	−	0.642423i
$109$	1.49861	+	1.25748i	1.49861	+	1.25748i	0.882948	+	0.469472i	$0.155556\pi$
$109$	1.49861	+	1.25748i	1.49861	+	1.25748i	0.615661	+	0.788011i	$0.288889\pi$
$110$		0			0
$111$		0			0
$112$	0.691580	−	0.251715i	0.691580	−	0.251715i
$113$	1.98054			1.98054			0.990268	−	0.139173i	$-0.0444444\pi$
$113$	1.98054			1.98054			0.990268	+	0.139173i	$0.0444444\pi$
$114$	0.782344	+	1.00135i	0.782344	+	1.00135i
$115$		0			0
$116$		0			0
$117$	−0.325893	+	1.84823i	−0.325893	+	1.84823i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$	1.78249	+	0.648775i	1.78249	+	0.648775i
$124$		0			0
$125$		0			0
$126$	−1.40265	−	2.42947i	−1.40265	−	2.42947i
$127$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$127$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$128$	−0.0576332	−	0.0483600i	−0.0576332	−	0.0483600i
$129$		0			0
$130$		0			0
$131$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$131$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$132$	0.744043			0.744043
$133$	−1.69196	−	1.05726i	−1.69196	−	1.05726i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$137$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$138$	1.87146	+	1.57034i	1.87146	+	1.57034i
$139$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$139$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$144$	0.346147	−	0.599544i	0.346147	−	0.599544i
$145$		0			0
$146$	−0.0804059	−	0.456005i	−0.0804059	−	0.456005i
$147$	3.87257	+	3.24947i	3.87257	+	3.24947i
$148$		0			0
$149$	0.0363024	−	0.205881i	0.0363024	−	0.205881i	−0.961262	−	0.275637i	$-0.911111\pi$
$149$	0.0363024	−	0.205881i	0.0363024	−	0.205881i	0.997564	+	0.0697565i	$0.0222222\pi$
$150$	−1.19410	+	0.434618i	−1.19410	+	0.434618i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	0.0376174	−	1.07722i	0.0376174	−	1.07722i
$153$		0			0
$154$	1.40463	−	0.511244i	1.40463	−	0.511244i
$155$		0			0
$156$	0.569970	−	0.478261i	0.569970	−	0.478261i
$157$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.961262	+	0.275637i	$0.0888889\pi$
$157$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.438371	+	0.898794i	$0.355556\pi$
$158$		0			0
$159$	−0.0591929	−	0.102525i	−0.0591929	−	0.102525i
$160$		0			0
$161$	−3.60436	−	1.31188i	−3.60436	−	1.31188i
$162$	−0.454395	−	0.165386i	−0.454395	−	0.165386i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	−0.245307	−	0.424883i	−0.245307	−	0.424883i
$165$		0			0
$166$	0.277693	+	0.233012i	0.277693	+	0.233012i
$167$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.669131	+	0.743145i	$0.733333\pi$
$167$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.848048	+	0.529919i	$0.822222\pi$
$168$	−0.633375	+	3.59205i	−0.633375	+	3.59205i
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$		0			0
$171$	−1.85848	+	0.261192i	−1.85848	+	0.261192i
$172$		0			0
$173$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$173$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$174$		0			0
$175$	1.52836	−	1.28244i	1.52836	−	1.28244i
$176$	0.282579	+	0.237112i	0.282579	+	0.237112i
$177$		0			0
$178$		0			0
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$180$		0			0
$181$	1.15707	+	0.421137i	1.15707	+	0.421137i	0.848048	−	0.529919i	$-0.177778\pi$
$181$	1.15707	+	0.421137i	1.15707	+	0.421137i	0.309017	+	0.951057i	$0.400000\pi$
$182$	0.747388	−	1.29451i	0.747388	−	1.29451i
$183$		0			0
$184$	−0.359842	−	2.04076i	−0.359842	−	2.04076i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.96683			2.96683
$190$		0			0
$191$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$191$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$192$	−1.54501	+	0.562337i	−1.54501	+	0.562337i
$193$	−0.333843	+	1.89332i	−0.333843	+	1.89332i	0.104528	+	0.994522i	$0.466667\pi$
$193$	−0.333843	+	1.89332i	−0.333843	+	1.89332i	−0.438371	+	0.898794i	$0.644444\pi$
$194$		0			0
$195$		0			0
$196$	−0.227045	−	1.28764i	−0.227045	−	1.28764i
$197$	−0.615661	−	1.06636i	−0.615661	−	1.06636i	−0.990268	−	0.139173i	$-0.955556\pi$
$197$	−0.615661	−	1.06636i	−0.615661	−	1.06636i	0.374607	−	0.927184i	$-0.377778\pi$
$198$	0.703040	−	1.21770i	0.703040	−	1.21770i
$199$	1.65940	+	0.603972i	1.65940	+	0.603972i	0.990268	−	0.139173i	$-0.0444444\pi$
$199$	1.65940	+	0.603972i	1.65940	+	0.603972i	0.669131	+	0.743145i	$0.266667\pi$
$200$	1.01287	+	0.368656i	1.01287	+	0.368656i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.187172	+	1.06150i	−0.187172	+	1.06150i
$207$	−3.39049	+	1.23404i	−3.39049	+	1.23404i
$208$	0.368881			0.368881
$209$	0.0348995	−	0.999391i	0.0348995	−	0.999391i
$210$		0			0
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$	−0.00531700	+	0.0301542i	−0.00531700	+	0.0301542i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.801423	+	1.38811i	0.801423	+	1.38811i
$217$		0			0
$218$	−1.37729	−	0.501293i	−1.37729	−	0.501293i
$219$	0.985028	+	0.358521i	0.985028	+	0.358521i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$223$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$224$	1.22499	−	1.02789i	1.22499	−	1.02789i
$225$	0.325893	−	1.84823i	0.325893	−	1.84823i
$226$	−1.39436	+	0.507504i	−1.39436	+	0.507504i
$227$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$227$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$228$	0.630984	+	0.394283i	0.630984	+	0.394283i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	−0.587613	+	3.33252i	−0.587613	+	3.33252i
$232$		0			0
$233$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$233$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$234$	−0.244163	−	1.38472i	−0.244163	−	1.38472i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.882948	+	1.52931i	−0.882948	+	1.52931i	−0.0348995	+	0.999391i	$0.511111\pi$
$239$	−0.882948	+	1.52931i	−0.882948	+	1.52931i	−0.848048	+	0.529919i	$0.822222\pi$
$240$		0			0
$241$	0.0840186	+	0.476493i	0.0840186	+	0.476493i	0.997564	+	0.0697565i	$0.0222222\pi$
$241$	0.0840186	+	0.476493i	0.0840186	+	0.476493i	−0.913545	+	0.406737i	$0.866667\pi$
$242$	0.573931	+	0.481585i	0.573931	+	0.481585i
$243$	−0.300554	+	0.252195i	−0.300554	+	0.252195i
$244$		0			0
$245$		0			0
$246$	−1.42117			−1.42117
$247$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$248$		0			0
$249$	−0.771155	+	0.280677i	−0.771155	+	0.280677i
$250$		0			0
$251$	−1.23949	+	1.04005i	−1.23949	+	1.04005i	−0.241922	+	0.970296i	$0.577778\pi$
$251$	−1.23949	+	1.04005i	−1.23949	+	1.04005i	−0.997564	+	0.0697565i	$0.977778\pi$
$252$	−1.25828	−	1.05582i	−1.25828	−	1.05582i
$253$	−0.333843	−	1.89332i	−0.333843	−	1.89332i
$254$		0			0
$255$		0			0
$256$	0.963887	+	0.350826i	0.963887	+	0.350826i
$257$	1.52045	+	0.553400i	1.52045	+	0.553400i	0.961262	−	0.275637i	$-0.0888889\pi$
$257$	1.52045	+	0.553400i	1.52045	+	0.553400i	0.559193	+	0.829038i	$0.311111\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$263$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$264$	−1.71793	+	0.625276i	−1.71793	+	0.625276i
$265$		0			0
$266$	1.46211	+	0.310781i	1.46211	+	0.310781i
$267$		0			0
$268$		0			0
$269$	0.194206	−	1.10140i	0.194206	−	1.10140i	−0.719340	−	0.694658i	$-0.755556\pi$
$269$	0.194206	−	1.10140i	0.194206	−	1.10140i	0.913545	−	0.406737i	$-0.133333\pi$
$270$		0			0
$271$	0.943248	+	0.791479i	0.943248	+	0.791479i	0.978148	−	0.207912i	$-0.0666667\pi$
$271$	0.943248	+	0.791479i	0.943248	+	0.791479i	−0.0348995	+	0.999391i	$0.511111\pi$
$272$		0			0
$273$	1.69196	+	2.93057i	1.69196	+	2.93057i
$274$		0			0
$275$	0.939693	+	0.342020i	0.939693	+	0.342020i
$276$	1.34417	+	0.489239i	1.34417	+	0.489239i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.943248	−	0.791479i	0.943248	−	0.791479i	−0.0348995	−	0.999391i	$-0.511111\pi$
$281$	0.943248	−	0.791479i	0.943248	−	0.791479i	0.978148	+	0.207912i	$0.0666667\pi$
$282$		0			0
$283$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$283$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$284$		0			0
$285$		0			0
$286$	0.749213			0.749213
$287$	2.09676	−	0.763157i	2.09676	−	0.763157i
$288$	0.261206	−	1.48137i	0.261206	−	1.48137i
$289$	0.766044	−	0.642788i	0.766044	−	0.642788i
$290$		0			0
$291$		0			0
$292$	−0.135559	−	0.234796i	−0.135559	−	0.234796i
$293$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$293$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$294$	−3.55907	−	1.29539i	−3.55907	−	1.29539i
$295$		0			0
$296$		0			0
$297$	0.743520	+	1.28781i	0.743520	+	1.28781i
$298$	0.0271982	+	0.154249i	0.0271982	+	0.154249i
$299$	−1.47274	−	1.23577i	−1.47274	−	1.23577i
$300$	−0.569970	+	0.478261i	−0.569970	+	0.478261i
$301$		0			0
$302$	−0.704030	+	0.256246i	−0.704030	+	0.256246i
$303$		0			0
$304$	0.113990	+	0.350826i	0.113990	+	0.350826i
$305$		0			0
$306$		0			0
$307$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$307$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$308$	0.670459	−	0.562582i	0.670459	−	0.562582i
$309$	−1.86925	−	1.56849i	−1.86925	−	1.56849i
$310$		0			0
$311$	−0.848048	−	1.46886i	−0.848048	−	1.46886i	−0.882948	−	0.469472i	$-0.844444\pi$
$311$	−0.848048	−	1.46886i	−0.848048	−	1.46886i	0.0348995	−	0.999391i	$-0.488889\pi$
$312$	−0.914092	+	1.58325i	−0.914092	+	1.58325i
$313$	0.196449	+	0.0715017i	0.196449	+	0.0715017i	0.438371	−	0.898794i	$-0.355556\pi$
$313$	0.196449	+	0.0715017i	0.196449	+	0.0715017i	−0.241922	+	0.970296i	$0.577778\pi$
$314$	−1.28633	−	0.468185i	−1.28633	−	0.468185i
$315$		0			0
$316$		0			0
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$	0.0679452	+	0.0570128i	0.0679452	+	0.0570128i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	2.87374			2.87374
$323$		0			0
$324$	−0.283132			−0.283132
$325$	0.939693	−	0.342020i	0.939693	−	0.342020i
$326$		0			0
$327$	2.54179	−	2.13281i	2.54179	−	2.13281i
$328$	0.923454	+	0.774870i	0.923454	+	0.774870i
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	0.199452	+	0.0725946i	0.199452	+	0.0725946i
$333$		0			0
$334$	0.741922	−	1.28505i	0.741922	−	1.28505i
$335$		0			0
$336$	−0.216759	−	1.22930i	−0.216759	−	1.22930i
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	0.573931	−	0.481585i	0.573931	−	0.481585i
$339$	0.583315	−	3.30815i	0.583315	−	3.30815i
$340$		0			0
$341$		0			0
$342$	1.24150	−	0.660115i	1.24150	−	0.660115i
$343$	3.95142			3.95142
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$347$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$	−0.719340	−	1.24593i	−0.719340	−	1.24593i	−0.961262	−	0.275637i	$-0.911111\pi$
$349$	−0.719340	−	1.24593i	−0.719340	−	1.24593i	0.241922	−	0.970296i	$-0.422222\pi$
$350$	−0.747388	+	1.29451i	−0.747388	+	1.29451i
$351$	1.39736	+	0.508597i	1.39736	+	0.508597i
$352$	0.753171	+	0.274132i	0.753171	+	0.274132i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0451831	−	0.256246i	0.0451831	−	0.256246i
$359$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.809017	−	0.587785i	$-0.200000\pi$
$359$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.997564	−	0.0697565i	$-0.0222222\pi$
$360$		0			0
$361$	0.559193	−	0.829038i	0.559193	−	0.829038i
$362$	−0.922523			−0.922523
$363$	−1.59381	+	0.580099i	−1.59381	+	0.580099i
$364$	0.151981	−	0.861925i	0.151981	−	0.861925i
$365$		0			0
$366$		0			0
$367$	0.107320	+	0.608645i	0.107320	+	0.608645i	0.990268	+	0.139173i	$0.0444444\pi$
$367$	0.107320	+	0.608645i	0.107320	+	0.608645i	−0.882948	+	0.469472i	$0.844444\pi$
$368$	0.354591	+	0.614169i	0.354591	+	0.614169i
$369$	1.04946	−	1.81772i	1.04946	−	1.81772i
$370$		0			0
$371$	−0.130860	−	0.0476290i	−0.130860	−	0.0476290i
$372$		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			0
$376$		0			0
$377$		0			0
$378$	−2.08874	+	0.760239i	−2.08874	+	0.760239i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	1.37729	−	0.501293i	1.37729	−	0.501293i
$383$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$383$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$384$	−0.0977514	+	0.0820232i	−0.0977514	+	0.0820232i
$385$		0			0
$386$	−0.250119	−	1.41850i	−0.250119	−	1.41850i
$387$		0			0
$388$		0			0
$389$	−1.25755	−	0.457712i	−1.25755	−	0.457712i	−0.374607	−	0.927184i	$-0.622222\pi$
$389$	−1.25755	−	0.457712i	−1.25755	−	0.457712i	−0.882948	+	0.469472i	$0.844444\pi$
$390$		0			0
$391$		0			0
$392$	1.60633	+	2.78224i	1.60633	+	2.78224i
$393$		0			0
$394$	0.706694	+	0.592987i	0.706694	+	0.592987i
$395$		0			0
$396$	0.142963	−	0.810781i	0.142963	−	0.810781i
$397$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$397$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$398$	−1.32303			−1.32303
$399$	−2.26429	+	2.51475i	−2.26429	+	2.51475i
$400$	−0.368881			−0.368881
$401$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$401$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$409$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	0.109593	+	0.621531i	0.109593	+	0.621531i
$413$		0			0
$414$	2.07079	−	1.73760i	2.07079	−	1.73760i
$415$		0			0
$416$	0.753171	−	0.274132i	0.753171	−	0.274132i
$417$		0			0
$418$	0.231520	+	0.712544i	0.231520	+	0.712544i
$419$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$419$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$420$		0			0
$421$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$421$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$422$		0			0
$423$		0			0
$424$	−0.0130644	−	0.0740918i	−0.0130644	−	0.0740918i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.848048	+	1.46886i	−0.848048	+	1.46886i
$430$		0			0
$431$	0.249824	+	1.41682i	0.249824	+	1.41682i	0.809017	+	0.587785i	$0.200000\pi$
$431$	0.249824	+	1.41682i	0.249824	+	1.41682i	−0.559193	+	0.829038i	$0.688889\pi$
$432$	−0.420206	−	0.352595i	−0.420206	−	0.352595i
$433$	−1.35275	+	1.13510i	−1.35275	+	1.13510i	−0.374607	+	0.927184i	$0.622222\pi$
$433$	−1.35275	+	1.13510i	−1.35275	+	1.13510i	−0.978148	+	0.207912i	$0.933333\pi$
$434$		0			0
$435$		0			0
$436$	−0.858187			−0.858187
$437$	0.720190	−	1.78253i	0.720190	−	1.78253i
$438$	−0.785359			−0.785359
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	4.28502	−	3.59556i	4.28502	−	3.59556i
$442$		0			0
$443$	−0.0840186	−	0.476493i	−0.0840186	−	0.476493i	−0.997564	−	0.0697565i	$-0.977778\pi$
$443$	−0.0840186	−	0.476493i	−0.0840186	−	0.476493i	0.913545	−	0.406737i	$-0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.333197	−	0.121274i	−0.333197	−	0.121274i
$448$	−0.967019	+	1.67493i	−0.967019	+	1.67493i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	0.244163	+	1.38472i	0.244163	+	1.38472i
$451$	0.856733	+	0.718885i	0.856733	+	0.718885i
$452$	−0.665555	+	0.558467i	−0.665555	+	0.558467i
$453$	0.294524	−	1.67033i	0.294524	−	1.67033i
$454$	0.435115	−	0.158369i	0.435115	−	0.158369i
$455$		0			0
$456$	−1.78823	−	0.380101i	−1.78823	−	0.380101i
$457$	1.76590			1.76590			0.882948	−	0.469472i	$-0.155556\pi$
$457$	1.76590			1.76590			0.882948	+	0.469472i	$0.155556\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.02517	−	0.860218i	−1.02517	−	0.860218i	−0.0348995	−	0.999391i	$-0.511111\pi$
$461$	−1.02517	−	0.860218i	−1.02517	−	0.860218i	−0.990268	+	0.139173i	$0.955556\pi$
$462$	−0.440248	−	2.49677i	−0.440248	−	2.49677i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$468$	−0.411644	−	0.712989i	−0.411644	−	0.712989i
$469$		0			0
$470$		0			0
$471$	2.37391	−	1.99195i	2.37391	−	1.99195i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.615661	+	0.788011i	0.615661	+	0.788011i
$476$		0			0
$477$	−0.123095	+	0.0448028i	−0.123095	+	0.0448028i
$478$	0.229742	−	1.30293i	0.229742	−	1.30293i
$479$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$479$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	−0.181251	−	0.313936i	−0.181251	−	0.313936i
$483$	−3.25284	+	5.63409i	−3.25284	+	5.63409i
$484$	0.412224	+	0.150037i	0.412224	+	0.150037i
$485$		0			0
$486$	0.146975	−	0.254569i	0.146975	−	0.254569i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$491$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$492$	−0.781944	+	0.284604i	−0.781944	+	0.284604i
$493$		0			0
$494$	0.635369	+	0.397023i	0.635369	+	0.397023i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.470994	−	0.395211i	0.470994	−	0.395211i
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$		0			0
$501$	1.67959	+	2.90914i	1.67959	+	2.90914i
$502$	0.606126	−	1.04984i	0.606126	−	1.04984i
$503$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$503$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$504$	3.79254	+	1.38037i	3.79254	+	1.38037i
$505$		0			0
$506$	0.720190	+	1.24741i	0.720190	+	1.24741i
$507$	0.294524	+	1.67033i	0.294524	+	1.67033i
$508$		0			0
$509$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$509$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$510$		0			0
$511$	1.15869	−	0.421730i	1.15869	−	0.421730i
$512$	−0.693269			−0.693269
$513$	−0.0518969	+	1.48613i	−0.0518969	+	1.48613i
$514$	−1.21225			−1.21225
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.104528	+	0.994522i	$0.533333\pi$
$521$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.809017	+	0.587785i	$0.800000\pi$
$522$		0			0
$523$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$523$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$524$		0			0
$525$	−1.69196	−	2.93057i	−1.69196	−	2.93057i
$526$		0			0
$527$		0			0
$528$	0.479281	−	0.402165i	0.479281	−	0.402165i
$529$	0.468172	−	2.65514i	0.468172	−	2.65514i
$530$		0			0
$531$		0			0
$532$	0.866704	−	0.121807i	0.866704	−	0.121807i
$533$	1.11839			1.11839
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.451237	+	0.378633i	0.451237	+	0.378633i
$538$	0.145501	+	0.825180i	0.145501	+	0.825180i
$539$	1.49027	+	2.58122i	1.49027	+	2.58122i
$540$		0			0
$541$	0.823868	+	0.299864i	0.823868	+	0.299864i	0.719340	−	0.694658i	$-0.244444\pi$
$541$	0.823868	+	0.299864i	0.823868	+	0.299864i	0.104528	+	0.994522i	$0.466667\pi$
$542$	−0.866888	−	0.315522i	−0.866888	−	0.315522i
$543$	1.04422	−	1.80864i	1.04422	−	1.80864i
$544$		0			0
$545$		0			0
$546$	−1.94214	−	1.62965i	−1.94214	−	1.62965i
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$		0			0
$549$		0			0
$550$	−0.749213			−0.749213
$551$		0			0
$552$	−3.51473			−3.51473
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	−0.913545	−	0.406737i	$-0.866667\pi$
$557$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	0.719340	−	0.694658i	$-0.244444\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.461262	+	0.798929i	−0.461262	+	0.798929i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.223606	−	1.26813i	0.223606	−	1.26813i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	0.412224	−	0.150037i	0.412224	−	0.150037i
$573$	−0.576176	+	3.26766i	−0.576176	+	3.26766i
$574$	−1.28062	+	1.07457i	−1.28062	+	1.07457i
$575$	1.47274	+	1.23577i	1.47274	+	1.23577i
$576$	0.315914	+	1.79164i	0.315914	+	1.79164i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.374607	+	0.648838i	−0.374607	+	0.648838i
$579$	3.06414	+	1.11525i	3.06414	+	1.11525i
$580$		0			0
$581$	−0.482665	+	0.836001i	−0.482665	+	0.836001i
$582$		0			0
$583$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i
$584$	0.510312	+	0.428203i	0.510312	+	0.428203i
$585$		0			0
$586$	−0.199324	+	1.13042i	−0.199324	+	1.13042i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	−2.21765			−2.21765
$589$		0			0
$590$		0			0
$591$	−1.96249	+	0.714289i	−1.96249	+	0.714289i
$592$		0			0
$593$	−1.39963	+	1.17443i	−1.39963	+	1.17443i	−0.438371	+	0.898794i	$0.644444\pi$
$593$	−1.39963	+	1.17443i	−1.39963	+	1.17443i	−0.961262	+	0.275637i	$0.911111\pi$
$594$	−0.853457	−	0.716136i	−0.853457	−	0.716136i
$595$		0			0
$596$	0.0458545	+	0.0794223i	0.0458545	+	0.0794223i
$597$	1.49756	−	2.59386i	1.49756	−	2.59386i
$598$	1.35351	+	0.492639i	1.35351	+	0.492639i
$599$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.669131	−	0.743145i	$-0.266667\pi$
$599$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.0348995	+	0.999391i	$0.488889\pi$
$600$	0.914092	−	1.58325i	0.914092	−	1.58325i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	−0.336048	+	0.281978i	−0.336048	+	0.281978i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	0.493457	+	0.631597i	0.493457	+	0.631597i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.51718	−	1.27306i	−1.51718	−	1.27306i	−0.848048	−	0.529919i	$-0.822222\pi$
$613$	−1.51718	−	1.27306i	−1.51718	−	1.27306i	−0.669131	−	0.743145i	$-0.733333\pi$
$614$	−0.0451831	−	0.256246i	−0.0451831	−	0.256246i
$615$		0			0
$616$	−1.07525	+	1.86239i	−1.07525	+	1.86239i
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	1.71793	+	0.625276i	1.71793	+	0.625276i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	0.496437	+	2.81544i	0.496437	+	2.81544i
$622$	0.973442	+	0.816814i	0.973442	+	0.816814i
$623$		0			0
$624$	0.108644	−	0.616152i	0.108644	−	0.616152i
$625$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$626$	−0.156628			−0.156628
$627$	−1.65903	−	0.352638i	−1.65903	−	0.352638i
$628$	−0.801508			−0.801508
$629$		0			0
$630$		0			0
$631$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$631$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	0.0488015	+	0.0177623i	0.0488015	+	0.0177623i
$637$	2.80079	+	1.01940i	2.80079	+	1.01940i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.10209	−	0.924765i	−1.10209	−	0.924765i	−0.104528	−	0.994522i	$-0.533333\pi$
$641$	−1.10209	−	0.924765i	−1.10209	−	0.924765i	−0.997564	+	0.0697565i	$0.977778\pi$
$642$		0			0
$643$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$643$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$644$	1.58116	−	0.575495i	1.58116	−	0.575495i
$645$		0			0
$646$		0			0
$647$	−1.23132			−1.23132			−0.615661	−	0.788011i	$-0.711111\pi$
$647$	−1.23132			−1.23132			−0.615661	+	0.788011i	$0.711111\pi$
$648$	0.653728	−	0.237938i	0.653728	−	0.237938i
$649$		0			0
$650$	−0.573931	+	0.481585i	−0.573931	+	0.481585i
$651$		0			0
$652$		0			0
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$654$	−1.24297	+	2.15289i	−1.24297	+	2.15289i
$655$		0			0
$656$	−0.387671	−	0.141101i	−0.387671	−	0.141101i
$657$	0.579945	−	1.00449i	0.579945	−	1.00449i
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$		0			0
$664$	−0.521524			−0.521524
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.150869	−	0.855621i	0.150869	−	0.855621i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.35612	−	2.34887i	−1.35612	−	2.34887i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−1.39736	−	0.508597i	−1.39736	−	0.508597i
$676$	0.219340	−	0.379908i	0.219340	−	0.379908i
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$	0.437028	+	2.47851i	0.437028	+	2.47851i
$679$		0			0
$680$		0			0
$681$	−0.182026	+	1.03232i	−0.182026	+	1.03232i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.550888	−	0.611823i	0.550888	−	0.611823i
$685$		0			0
$686$	−2.78192	+	1.01254i	−2.78192	+	1.01254i
$687$		0			0
$688$		0			0
$689$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$	3.51853	+	1.28064i	3.51853	+	1.28064i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.825702	+	0.692846i	0.825702	+	0.692846i
$699$		0			0
$700$	−0.151981	+	0.861925i	−0.151981	+	0.861925i
$701$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$701$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$702$	−1.11411			−1.11411
$703$		0			0
$704$	−0.969381			−0.969381
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$709$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0264556	−	0.150037i	−0.0264556	−	0.150037i
$717$	2.29440	+	1.92523i	2.29440	+	1.92523i
$718$	−1.10340	+	0.925858i	−1.10340	+	0.925858i
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$720$		0			0
$721$	−2.87035			−2.87035
$722$	−0.181251	+	0.726958i	−0.181251	+	0.726958i
$723$	0.820646			0.820646
$724$	−0.507581	+	0.184744i	−0.507581	+	0.184744i
$725$		0			0
$726$	0.973442	−	0.816814i	0.973442	−	0.816814i
$727$	−1.52836	−	1.28244i	−1.52836	−	1.28244i	−0.809017	−	0.587785i	$-0.800000\pi$
$727$	−1.52836	−	1.28244i	−1.52836	−	1.28244i	−0.719340	−	0.694658i	$-0.755556\pi$
$728$	0.373431	+	2.11783i	0.373431	+	2.11783i
$729$	0.655438	+	1.13525i	0.655438	+	1.13525i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	−0.961262	−	0.275637i	$-0.911111\pi$
$733$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	0.719340	+	0.694658i	$0.244444\pi$
$734$	−0.231520	−	0.401004i	−0.231520	−	0.401004i
$735$		0			0
$736$	1.18041	+	0.990482i	1.18041	+	0.990482i
$737$		0			0
$738$	−0.273069	+	1.54865i	−0.273069	+	1.54865i
$739$	1.05094	−	0.382510i	1.05094	−	0.382510i	0.241922	−	0.970296i	$-0.422222\pi$
$739$	1.05094	−	0.382510i	1.05094	−	0.382510i	0.809017	+	0.587785i	$0.200000\pi$
$740$		0			0
$741$	−1.49756	+	0.796269i	−1.49756	+	0.796269i
$742$	0.104334			0.104334
$743$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$743$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.157681	+	0.894255i	0.157681	+	0.894255i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.25755	−	0.457712i	−1.25755	−	0.457712i	−0.374607	−	0.927184i	$-0.622222\pi$
$751$	−1.25755	−	0.457712i	−1.25755	−	0.457712i	−0.882948	+	0.469472i	$0.844444\pi$
$752$		0			0
$753$	1.37217	+	2.37667i	1.37217	+	2.37667i
$754$		0			0
$755$		0			0
$756$	−0.996999	+	0.836581i	−0.996999	+	0.836581i
$757$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	0.438371	+	0.898794i	$0.355556\pi$
$757$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	−0.719340	+	0.694658i	$0.755556\pi$
$758$		0			0
$759$	−3.26078			−3.26078
$760$		0			0
$761$	−0.876742			−0.876742			−0.438371	−	0.898794i	$-0.644444\pi$
$761$	−0.876742			−0.876742			−0.438371	+	0.898794i	$0.644444\pi$
$762$		0			0
$763$	0.677759	−	3.84376i	0.677759	−	3.84376i
$764$	0.657409	−	0.551632i	0.657409	−	0.551632i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.869883	−	1.50668i	0.869883	−	1.50668i
$769$	1.05094	+	0.382510i	1.05094	+	0.382510i	0.809017	−	0.587785i	$-0.200000\pi$
$769$	1.05094	+	0.382510i	1.05094	+	0.382510i	0.241922	+	0.970296i	$0.422222\pi$
$770$		0			0
$771$	1.37217	−	2.37667i	1.37217	−	2.37667i
$772$	−0.421686	−	0.730381i	−0.421686	−	0.730381i
$773$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$773$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.00264			1.00264
$779$	0.345600	+	1.06365i	0.345600	+	1.06365i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.842237	−	0.706721i	−0.842237	−	0.706721i
$785$		0			0
$786$		0			0
$787$	−0.997564	+	1.72783i	−0.997564	+	1.72783i	−0.438371	+	0.898794i	$0.644444\pi$
$787$	−0.997564	+	1.72783i	−0.997564	+	1.72783i	−0.559193	+	0.829038i	$0.688889\pi$
$788$	0.507581	+	0.184744i	0.507581	+	0.184744i
$789$		0			0
$790$		0			0
$791$	−1.97571	−	3.42203i	−1.97571	−	3.42203i
$792$	0.351273	+	1.99217i	0.351273	+	1.99217i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.727944	+	0.264950i	−0.727944	+	0.264950i
$797$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$797$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$798$	0.949734	−	2.35067i	0.949734	−	2.35067i
$799$		0			0
$800$	−0.753171	+	0.274132i	−0.753171	+	0.274132i
$801$		0			0
$802$		0			0
$803$	0.473442	+	0.397265i	0.473442	+	0.397265i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.78249	−	0.648775i	−1.78249	−	0.648775i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	−0.152245	−	0.863423i	−0.152245	−	0.863423i	−0.961262	−	0.275637i	$-0.911111\pi$
$811$	−0.152245	−	0.863423i	−0.152245	−	0.863423i	0.809017	−	0.587785i	$-0.200000\pi$
$812$		0			0
$813$	1.59984	−	1.34242i	1.59984	−	1.34242i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.40806			1.40806
$819$	3.51853	−	1.28064i	3.51853	−	1.28064i
$820$		0			0
$821$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$821$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$822$		0			0
$823$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$823$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$824$	−0.775360	−	1.34296i	−0.775360	−	1.34296i
$825$	0.848048	−	1.46886i	0.848048	−	1.46886i
$826$		0			0
$827$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.882948	−	0.469472i	$-0.155556\pi$
$827$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.374607	+	0.927184i	$0.377778\pi$
$828$	0.791396	−	1.37074i	0.791396	−	1.37074i
$829$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$829$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$830$		0			0
$831$		0			0
$832$	−0.742589	+	0.623106i	−0.742589	+	0.623106i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.270078	+	0.345684i	0.270078	+	0.345684i
$837$		0			0
$838$	0.147182	−	0.0535700i	0.147182	−	0.0535700i
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$		0			0
$843$	−1.04422	−	1.80864i	−1.04422	−	1.80864i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.997564	+	1.72783i	−0.997564	+	1.72783i
$848$	0.0128737	+	0.0222980i	0.0128737	+	0.0222980i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.669131	−	0.743145i	$-0.733333\pi$
$853$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.0348995	+	0.999391i	$0.511111\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$857$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$858$	0.220661	−	1.25143i	0.220661	−	1.25143i
$859$	−0.943248	+	0.791479i	−0.943248	+	0.791479i	−0.978148	−	0.207912i	$-0.933333\pi$
$859$	−0.943248	+	0.791479i	−0.943248	+	0.791479i	0.0348995	+	0.999391i	$0.488889\pi$
$860$		0			0
$861$	−0.657178	−	3.72704i	−0.657178	−	3.72704i
$862$	−0.538939	−	0.933469i	−0.538939	−	0.933469i
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	−1.11999	−	0.407645i	−1.11999	−	0.407645i
$865$		0			0
$866$	0.661516	−	1.14578i	0.661516	−	1.14578i
$867$	−0.848048	−	1.46886i	−0.848048	−	1.46886i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.98148	−	0.721200i	1.98148	−	0.721200i
$873$		0			0
$874$	−0.0502685	+	1.43950i	−0.0502685	+	1.43950i
$875$		0			0
$876$	−0.432112	+	0.157276i	−0.432112	+	0.157276i
$877$	−0.107320	+	0.608645i	−0.107320	+	0.608645i	0.882948	+	0.469472i	$0.155556\pi$
$877$	−0.107320	+	0.608645i	−0.107320	+	0.608645i	−0.990268	+	0.139173i	$0.955556\pi$
$878$		0			0
$879$	−1.99062	−	1.67033i	−1.99062	−	1.67033i
$880$		0			0
$881$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	0.848048	−	0.529919i	$-0.177778\pi$
$881$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	−0.882948	+	0.469472i	$0.844444\pi$
$882$	−2.09544	+	3.62940i	−2.09544	+	3.62940i
$883$	−1.59381	−	0.580099i	−1.59381	−	0.580099i	−0.615661	−	0.788011i	$-0.711111\pi$
$883$	−1.59381	−	0.580099i	−1.59381	−	0.580099i	−0.978148	+	0.207912i	$0.933333\pi$
$884$		0			0
$885$		0			0
$886$	0.181251	+	0.313936i	0.181251	+	0.313936i
$887$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$887$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.606496	−	0.220746i	0.606496	−	0.220746i
$892$		0			0
$893$		0			0
$894$	0.265657			0.265657
$895$		0			0
$896$	−0.0260651	+	0.147823i	−0.0260651	+	0.147823i
$897$	−2.49791	+	2.09599i	−2.49791	+	2.09599i
$898$		0			0
$899$		0			0
$900$	0.411644	+	0.712989i	0.411644	+	0.712989i
$901$		0			0
$902$	−0.787377	−	0.286582i	−0.787377	−	0.286582i
$903$		0			0
$904$	1.06739	−	1.84877i	1.06739	−	1.84877i
$905$		0			0
$906$	0.220661	+	1.25143i	0.220661	+	1.25143i
$907$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.997564	−	0.0697565i	$-0.977778\pi$
$907$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.241922	−	0.970296i	$-0.577778\pi$
$908$	0.207689	−	0.174272i	0.207689	−	0.174272i
$909$		0			0
$910$		0			0
$911$	1.92252			1.92252			0.961262	−	0.275637i	$-0.0888889\pi$
$911$	1.92252			1.92252			0.961262	+	0.275637i	$0.0888889\pi$
$912$	0.619568	−	0.0870746i	0.619568	−	0.0870746i
$913$	−0.483844			−0.483844
$914$	−1.24324	+	0.452504i	−1.24324	+	0.452504i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	0.553524	+	0.201466i	0.553524	+	0.201466i
$922$	0.942176	+	0.342924i	0.942176	+	0.342924i
$923$		0			0
$924$	−0.742230	−	1.28558i	−0.742230	−	1.28558i
$925$		0			0
$926$		0			0
$927$	−2.06834	+	1.73555i	−2.06834	+	1.73555i
$928$		0			0
$929$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$929$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$930$		0			0
$931$	−0.104019	+	2.97872i	−0.104019	+	2.97872i
$932$		0			0
$933$	−2.70325	+	0.983904i	−2.70325	+	0.983904i
$934$	−0.244507	+	1.38667i	−0.244507	+	1.38667i
$935$		0			0
$936$	1.54963	+	1.30029i	1.54963	+	1.30029i
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$		0			0
$939$	0.177290	−	0.307076i	0.177290	−	0.307076i
$940$		0			0
$941$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.882948	−	0.469472i	$-0.155556\pi$
$941$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.374607	+	0.927184i	$0.377778\pi$
$942$	−1.16088	+	2.01070i	−1.16088	+	2.01070i
$943$	1.07506	+	1.86206i	1.07506	+	1.86206i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$947$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$	0.618034			0.618034
$950$	−0.635369	−	0.397023i	−0.635369	−	0.397023i
$951$		0			0
$952$		0			0
$953$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$953$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$954$	0.0751819	−	0.0630851i	0.0751819	−	0.0630851i
$955$		0			0
$956$	−0.134519	−	0.762893i	−0.134519	−	0.762893i
$957$		0			0
$958$	0.573931	−	0.994077i	0.573931	−	0.994077i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	−0.162595	−	0.136433i	−0.162595	−	0.136433i
$965$		0			0
$966$	0.846386	−	4.80009i	0.846386	−	4.80009i
$967$	1.86110	−	0.677383i	1.86110	−	0.677383i	0.882948	−	0.469472i	$-0.155556\pi$
$967$	1.86110	−	0.677383i	1.86110	−	0.677383i	0.978148	−	0.207912i	$-0.0666667\pi$
$968$	−1.07788			−1.07788
$969$		0			0
$970$		0			0
$971$	−1.25755	+	0.457712i	−1.25755	+	0.457712i	−0.882948	−	0.469472i	$-0.844444\pi$
$971$	−1.25755	+	0.457712i	−1.25755	+	0.457712i	−0.374607	+	0.927184i	$0.622222\pi$
$972$	0.0298873	−	0.169499i	0.0298873	−	0.169499i
$973$		0			0
$974$		0			0
$975$	−0.294524	−	1.67033i	−0.294524	−	1.67033i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.83573	−	3.17958i	−1.83573	−	3.17958i
$982$		0			0
$983$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$983$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$984$	1.56627	−	1.31425i	1.56627	−	1.31425i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.429093	+	0.0912066i	0.429093	+	0.0912066i
$989$		0			0
$990$		0			0
$991$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$991$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.180000	−	0.311770i	0.180000	−	0.311770i
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.c.1715.2	yes	24
11.10	odd	2		2717.1.db.d.1715.3	yes	24
13.12	even	2		2717.1.db.d.1715.3	yes	24
19.4	even	9	inner	2717.1.db.c.1429.2	✓	24
143.142	odd	2	CM	2717.1.db.c.1715.2	yes	24
209.175	odd	18		2717.1.db.d.1429.3	yes	24
247.194	even	18		2717.1.db.d.1429.3	yes	24
2717.1429	odd	18	inner	2717.1.db.c.1429.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.1429.2	✓	24	19.4	even	9	inner
2717.1.db.c.1429.2	✓	24	2717.1429	odd	18	inner
2717.1.db.c.1715.2	yes	24	1.1	even	1	trivial
2717.1.db.c.1715.2	yes	24	143.142	odd	2	CM
2717.1.db.d.1429.3	yes	24	209.175	odd	18
2717.1.db.d.1429.3	yes	24	247.194	even	18
2717.1.db.d.1715.3	yes	24	11.10	odd	2
2717.1.db.d.1715.3	yes	24	13.12	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:	\( N \)	\(=\)	\( 2717 = 11 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2717.db (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.704030 + 0.256246i) q^{2} +(0.294524 - 1.67033i) q^{3} +(-0.336048 + 0.281978i) q^{4} +(0.220661 + 1.25143i) q^{6} +(-0.997564 - 1.72783i) q^{7} +(0.538939 - 0.933469i) q^{8} +(-1.76356 - 0.641884i) q^{9} +O(q^{10})\)	\(q+(-0.704030 + 0.256246i) q^{2} +(0.294524 - 1.67033i) q^{3} +(-0.336048 + 0.281978i) q^{4} +(0.220661 + 1.25143i) q^{6} +(-0.997564 - 1.72783i) q^{7} +(0.538939 - 0.933469i) q^{8} +(-1.76356 - 0.641884i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.372021 + 0.644360i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(1.14507 + 0.960824i) q^{14} +(-0.0640554 + 0.363276i) q^{16} +1.40608 q^{18} +(0.882948 - 0.469472i) q^{19} +(-3.17985 + 1.15737i) q^{21} +(-0.130100 + 0.737831i) q^{22} +(1.47274 - 1.23577i) q^{23} +(-1.40047 - 1.17513i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.374607 + 0.648838i) q^{26} +(-0.743520 + 1.28781i) q^{27} +(0.822440 + 0.299344i) q^{28} +(0.139180 + 0.789331i) q^{32} +(-1.29929 - 1.09023i) q^{33} +(0.773638 - 0.281581i) q^{36} +(-0.501321 + 0.556774i) q^{38} -1.69610 q^{39} +(-0.194206 + 1.10140i) q^{41} +(1.94214 - 1.62965i) q^{42} +(0.0761759 + 0.432015i) q^{44} +(-0.720190 + 1.24741i) q^{46} +(0.587925 + 0.213987i) q^{48} +(-1.49027 + 2.58122i) q^{49} +(-0.374607 - 0.648838i) q^{50} +(0.336048 + 0.281978i) q^{52} +(0.0534691 - 0.0448659i) q^{53} +(0.193463 - 1.09718i) q^{54} -2.15050 q^{56} +(-0.524123 - 1.61308i) q^{57} +(0.650198 + 3.68746i) q^{63} +(-0.484690 - 0.839508i) q^{64} +(1.19410 + 0.434618i) q^{66} +(-1.63039 - 2.82392i) q^{69} +(-1.54963 + 1.30029i) q^{72} +(-0.107320 + 0.608645i) q^{73} +1.69610 q^{75} +(-0.164332 + 0.406737i) q^{76} -1.99513 q^{77} +(1.19410 - 0.434618i) q^{78} +(0.494420 + 0.414868i) q^{81} +(-0.145501 - 0.825180i) q^{82} +(-0.241922 - 0.419021i) q^{83} +(0.742230 - 1.28558i) q^{84} +(-0.538939 - 0.933469i) q^{88} +(-1.52836 + 1.28244i) q^{91} +(-0.146450 + 0.830559i) q^{92} +1.35943 q^{96} +(0.387766 - 2.19913i) q^{98} +(-1.43767 + 1.20635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * q^78 + 6 * q^81 + 3 * q^82 - 12 * q^84 - 3 * q^88 - 6 * q^91 - 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

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