LMFDB - Embedded newform 2717.1.db.c.142.4

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			142.4
Root			$-0.374607 - 0.927184i$ of defining polynomial
Character	$\chi$	$=$	2717.142
Dual form			2717.1.db.c.2430.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.213817 + 1.21262i) q^{2} +(0.0534691 - 0.0448659i) q^{3} +(-0.485028 + 0.176536i) q^{4} +(0.0658378 + 0.0552444i) q^{6} +(0.559193 - 0.968551i) q^{7} +(0.297884 + 0.515950i) q^{8} +(-0.172802 + 0.980010i) q^{9} +O(q^{10})$	\(q+(0.213817 + 1.21262i) q^{2} +(0.0534691 - 0.0448659i) q^{3} +(-0.485028 + 0.176536i) q^{4} +(0.0658378 + 0.0552444i) q^{6} +(0.559193 - 0.968551i) q^{7} +(0.297884 + 0.515950i) q^{8} +(-0.172802 + 0.980010i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.0180136 + 0.0312005i) q^{12} +(-0.766044 - 0.642788i) q^{13} +(1.29405 + 0.470994i) q^{14} +(-0.957356 + 0.803317i) q^{16} -1.22532 q^{18} +(-0.848048 + 0.529919i) q^{19} +(-0.0135554 - 0.0768763i) q^{21} +(-0.943248 + 0.791479i) q^{22} +(1.35192 - 0.492057i) q^{23} +(0.0390762 + 0.0142226i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.615661 - 1.06636i) q^{26} +(0.0696290 + 0.120601i) q^{27} +(-0.100240 + 0.568492i) q^{28} +(-0.722429 - 0.606190i) q^{32} +(0.0655896 + 0.0238727i) q^{33} +(-0.0891929 - 0.505838i) q^{36} +(-0.823916 - 0.915051i) q^{38} -0.0697990 q^{39} +(-0.671624 + 0.563559i) q^{41} +(0.0903231 - 0.0328749i) q^{42} +(-0.395399 - 0.331779i) q^{44} +(0.885740 + 1.53415i) q^{46} +(-0.0151474 + 0.0859053i) q^{48} +(-0.125393 - 0.217188i) q^{49} +(-0.615661 + 1.06636i) q^{50} +(0.485028 + 0.176536i) q^{52} +(1.65940 - 0.603972i) q^{53} +(-0.131355 + 0.110220i) q^{54} +0.666298 q^{56} +(-0.0215691 + 0.0663828i) q^{57} +(0.852559 + 0.715382i) q^{63} +(-0.0442611 + 0.0766625i) q^{64} +(-0.0149242 + 0.0846394i) q^{66} +(0.0502092 - 0.0869649i) q^{69} +(-0.557111 + 0.202772i) q^{72} +(-0.473442 + 0.397265i) q^{73} +0.0697990 q^{75} +(0.317777 - 0.406737i) q^{76} +1.11839 q^{77} +(-0.0149242 - 0.0846394i) q^{78} +(-0.925981 - 0.337029i) q^{81} +(-0.826986 - 0.693923i) q^{82} +(0.961262 - 1.66495i) q^{83} +(0.0201461 + 0.0348941i) q^{84} +(-0.297884 + 0.515950i) q^{88} +(-1.05094 + 0.382510i) q^{91} +(-0.568852 + 0.477323i) q^{92} -0.0658249 q^{96} +(0.236554 - 0.198493i) q^{98} +(-0.935115 + 0.340354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	0.213817	+	1.21262i	0.213817	+	1.21262i	0.882948	+	0.469472i	$0.155556\pi$
$2$	0.213817	+	1.21262i	0.213817	+	1.21262i	−0.669131	+	0.743145i	$0.733333\pi$
$3$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i	−0.615661	−	0.788011i	$-0.711111\pi$
$3$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i	0.669131	+	0.743145i	$0.266667\pi$
$4$	−0.485028	+	0.176536i	−0.485028	+	0.176536i
$5$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$5$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$6$	0.0658378	+	0.0552444i	0.0658378	+	0.0552444i
$7$	0.559193	−	0.968551i	0.559193	−	0.968551i	−0.438371	−	0.898794i	$-0.644444\pi$
$7$	0.559193	−	0.968551i	0.559193	−	0.968551i	0.997564	−	0.0697565i	$-0.0222222\pi$
$8$	0.297884	+	0.515950i	0.297884	+	0.515950i
$9$	−0.172802	+	0.980010i	−0.172802	+	0.980010i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	−0.0180136	+	0.0312005i	−0.0180136	+	0.0312005i
$13$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$13$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$14$	1.29405	+	0.470994i	1.29405	+	0.470994i
$15$		0			0
$16$	−0.957356	+	0.803317i	−0.957356	+	0.803317i
$17$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$17$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$18$	−1.22532			−1.22532
$19$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$19$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$20$		0			0
$21$	−0.0135554	−	0.0768763i	−0.0135554	−	0.0768763i
$22$	−0.943248	+	0.791479i	−0.943248	+	0.791479i
$23$	1.35192	−	0.492057i	1.35192	−	0.492057i	0.438371	−	0.898794i	$-0.355556\pi$
$23$	1.35192	−	0.492057i	1.35192	−	0.492057i	0.913545	+	0.406737i	$0.133333\pi$
$24$	0.0390762	+	0.0142226i	0.0390762	+	0.0142226i
$25$	0.766044	+	0.642788i	0.766044	+	0.642788i
$26$	0.615661	−	1.06636i	0.615661	−	1.06636i
$27$	0.0696290	+	0.120601i	0.0696290	+	0.120601i
$28$	−0.100240	+	0.568492i	−0.100240	+	0.568492i
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−0.722429	−	0.606190i	−0.722429	−	0.606190i
$33$	0.0655896	+	0.0238727i	0.0655896	+	0.0238727i
$34$		0			0
$35$		0			0
$36$	−0.0891929	−	0.505838i	−0.0891929	−	0.505838i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.823916	−	0.915051i	−0.823916	−	0.915051i
$39$	−0.0697990			−0.0697990
$40$		0			0
$41$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	−0.913545	−	0.406737i	$-0.866667\pi$
$41$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	0.241922	+	0.970296i	$0.422222\pi$
$42$	0.0903231	−	0.0328749i	0.0903231	−	0.0328749i
$43$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$43$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$44$	−0.395399	−	0.331779i	−0.395399	−	0.331779i
$45$		0			0
$46$	0.885740	+	1.53415i	0.885740	+	1.53415i
$47$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$47$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$48$	−0.0151474	+	0.0859053i	−0.0151474	+	0.0859053i
$49$	−0.125393	−	0.217188i	−0.125393	−	0.217188i
$50$	−0.615661	+	1.06636i	−0.615661	+	1.06636i
$51$		0			0
$52$	0.485028	+	0.176536i	0.485028	+	0.176536i
$53$	1.65940	−	0.603972i	1.65940	−	0.603972i	0.669131	−	0.743145i	$-0.266667\pi$
$53$	1.65940	−	0.603972i	1.65940	−	0.603972i	0.990268	+	0.139173i	$0.0444444\pi$
$54$	−0.131355	+	0.110220i	−0.131355	+	0.110220i
$55$		0			0
$56$	0.666298			0.666298
$57$	−0.0215691	+	0.0663828i	−0.0215691	+	0.0663828i
$58$		0			0
$59$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$59$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$60$		0			0
$61$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$61$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$62$		0			0
$63$	0.852559	+	0.715382i	0.852559	+	0.715382i
$64$	−0.0442611	+	0.0766625i	−0.0442611	+	0.0766625i
$65$		0			0
$66$	−0.0149242	+	0.0846394i	−0.0149242	+	0.0846394i
$67$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$67$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$68$		0			0
$69$	0.0502092	−	0.0869649i	0.0502092	−	0.0869649i
$70$		0			0
$71$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$71$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$72$	−0.557111	+	0.202772i	−0.557111	+	0.202772i
$73$	−0.473442	+	0.397265i	−0.473442	+	0.397265i	−0.848048	−	0.529919i	$-0.822222\pi$
$73$	−0.473442	+	0.397265i	−0.473442	+	0.397265i	0.374607	+	0.927184i	$0.377778\pi$
$74$		0			0
$75$	0.0697990			0.0697990
$76$	0.317777	−	0.406737i	0.317777	−	0.406737i
$77$	1.11839			1.11839
$78$	−0.0149242	−	0.0846394i	−0.0149242	−	0.0846394i
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$		0			0
$81$	−0.925981	−	0.337029i	−0.925981	−	0.337029i
$82$	−0.826986	−	0.693923i	−0.826986	−	0.693923i
$83$	0.961262	−	1.66495i	0.961262	−	1.66495i	0.241922	−	0.970296i	$-0.422222\pi$
$83$	0.961262	−	1.66495i	0.961262	−	1.66495i	0.719340	−	0.694658i	$-0.244444\pi$
$84$	0.0201461	+	0.0348941i	0.0201461	+	0.0348941i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.297884	+	0.515950i	−0.297884	+	0.515950i
$89$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$89$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$90$		0			0
$91$	−1.05094	+	0.382510i	−1.05094	+	0.382510i
$92$	−0.568852	+	0.477323i	−0.568852	+	0.477323i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0658249			−0.0658249
$97$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$97$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$98$	0.236554	−	0.198493i	0.236554	−	0.198493i
$99$	−0.935115	+	0.340354i	−0.935115	+	0.340354i
$100$	−0.485028	−	0.176536i	−0.485028	−	0.176536i
$101$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$101$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$102$		0			0
$103$	0.241922	+	0.419021i	0.241922	+	0.419021i	0.961262	−	0.275637i	$-0.0888889\pi$
$103$	0.241922	+	0.419021i	0.241922	+	0.419021i	−0.719340	+	0.694658i	$0.755556\pi$
$104$	0.103454	−	0.586717i	0.103454	−	0.586717i
$105$		0			0
$106$	1.08719	+	1.88307i	1.08719	+	1.88307i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−0.0550624	−	0.0462028i	−0.0550624	−	0.0462028i
$109$	−1.83832	−	0.669092i	−1.83832	−	0.669092i	−0.990268	−	0.139173i	$-0.955556\pi$
$109$	−1.83832	−	0.669092i	−1.83832	−	0.669092i	−0.848048	−	0.529919i	$-0.822222\pi$
$110$		0			0
$111$		0			0
$112$	0.242706	+	1.37646i	0.242706	+	1.37646i
$113$	−0.749213			−0.749213			−0.374607	−	0.927184i	$-0.622222\pi$
$113$	−0.749213			−0.749213			−0.374607	+	0.927184i	$0.622222\pi$
$114$	−0.0851087	−	0.0119612i	−0.0851087	−	0.0119612i
$115$		0			0
$116$		0			0
$117$	0.762312	−	0.639656i	0.762312	−	0.639656i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	−0.0106265	+	0.0602660i	−0.0106265	+	0.0602660i
$124$		0			0
$125$		0			0
$126$	−0.685193	+	1.18679i	−0.685193	+	1.18679i
$127$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$127$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$128$	−0.988617	−	0.359827i	−0.988617	−	0.359827i
$129$		0			0
$130$		0			0
$131$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$131$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$132$	−0.0360272			−0.0360272
$133$	0.0390311	+	1.11770i	0.0390311	+	1.11770i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$137$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$138$	0.116191	+	0.0422899i	0.116191	+	0.0422899i
$139$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$139$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.173648	−	0.984808i	0.173648	−	0.984808i
$144$	−0.621825	−	1.07703i	−0.621825	−	1.07703i
$145$		0			0
$146$	−0.582959	−	0.489161i	−0.582959	−	0.489161i
$147$	−0.0164490	−	0.00598695i	−0.0164490	−	0.00598695i
$148$		0			0
$149$	0.160147	−	0.134379i	0.160147	−	0.134379i	−0.559193	−	0.829038i	$-0.688889\pi$
$149$	0.160147	−	0.134379i	0.160147	−	0.134379i	0.719340	+	0.694658i	$0.244444\pi$
$150$	0.0149242	+	0.0846394i	0.0149242	+	0.0846394i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	−0.526032	−	0.279696i	−0.526032	−	0.279696i
$153$		0			0
$154$	0.239130	+	1.35617i	0.239130	+	1.35617i
$155$		0			0
$156$	0.0338545	−	0.0123220i	0.0338545	−	0.0123220i
$157$	−1.71690	−	0.624902i	−1.71690	−	0.624902i	−0.719340	−	0.694658i	$-0.755556\pi$
$157$	−1.71690	−	0.624902i	−1.71690	−	0.624902i	−0.997564	+	0.0697565i	$0.977778\pi$
$158$		0			0
$159$	0.0616289	−	0.106744i	0.0616289	−	0.106744i
$160$		0			0
$161$	0.279400	−	1.58455i	0.279400	−	1.58455i
$162$	0.210697	−	1.19492i	0.210697	−	1.19492i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	0.226268	−	0.391908i	0.226268	−	0.391908i
$165$		0			0
$166$	2.22448	+	0.809646i	2.22448	+	0.809646i
$167$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.669131	−	0.743145i	$-0.733333\pi$
$167$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.0348995	+	0.999391i	$0.511111\pi$
$168$	0.0356264	−	0.0298941i	0.0356264	−	0.0298941i
$169$	0.173648	+	0.984808i	0.173648	+	0.984808i
$170$		0			0
$171$	−0.372782	−	0.922667i	−0.372782	−	0.922667i
$172$		0			0
$173$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$173$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$174$		0			0
$175$	1.05094	−	0.382510i	1.05094	−	0.382510i
$176$	−1.17437	−	0.427436i	−1.17437	−	0.427436i
$177$		0			0
$178$		0			0
$179$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$180$		0			0
$181$	0.343916	−	1.95045i	0.343916	−	1.95045i	0.0348995	−	0.999391i	$-0.488889\pi$
$181$	0.343916	−	1.95045i	0.343916	−	1.95045i	0.309017	−	0.951057i	$-0.400000\pi$
$182$	−0.688547	−	1.19260i	−0.688547	−	1.19260i
$183$		0			0
$184$	0.656591	+	0.550946i	0.656591	+	0.550946i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.155744			0.155744
$190$		0			0
$191$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$191$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$192$	0.00107293	+	0.00608489i	0.00107293	+	0.00608489i
$193$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.104528	−	0.994522i	$-0.466667\pi$
$193$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.997564	+	0.0697565i	$0.0222222\pi$
$194$		0			0
$195$		0			0
$196$	0.0991608	+	0.0832058i	0.0991608	+	0.0832058i
$197$	0.990268	−	1.71519i	0.990268	−	1.71519i	0.374607	−	0.927184i	$-0.377778\pi$
$197$	0.990268	−	1.71519i	0.990268	−	1.71519i	0.615661	−	0.788011i	$-0.288889\pi$
$198$	−0.612662	−	1.06116i	−0.612662	−	1.06116i
$199$	0.294524	−	1.67033i	0.294524	−	1.67033i	−0.374607	−	0.927184i	$-0.622222\pi$
$199$	0.294524	−	1.67033i	0.294524	−	1.67033i	0.669131	−	0.743145i	$-0.266667\pi$
$200$	−0.103454	+	0.586717i	−0.103454	+	0.586717i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.456385	+	0.382952i	−0.456385	+	0.382952i
$207$	0.248607	+	1.40992i	0.248607	+	1.40992i
$208$	1.24974			1.24974
$209$	−0.882948	−	0.469472i	−0.882948	−	0.469472i
$210$		0			0
$211$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$211$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$212$	−0.698232	+	0.585887i	−0.698232	+	0.585887i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−0.0414827	+	0.0718502i	−0.0414827	+	0.0718502i
$217$		0			0
$218$	0.418289	−	2.37224i	0.418289	−	2.37224i
$219$	−0.00749086	+	0.0424828i	−0.00749086	+	0.0424828i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$223$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$224$	−0.991103	+	0.360732i	−0.991103	+	0.360732i
$225$	−0.762312	+	0.639656i	−0.762312	+	0.639656i
$226$	−0.160195	−	0.908508i	−0.160195	−	0.908508i
$227$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$227$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$228$	−0.00125733	−	0.0360052i	−0.00125733	−	0.0360052i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	0.0597991	−	0.0501774i	0.0597991	−	0.0501774i
$232$		0			0
$233$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$233$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$234$	0.938653	+	0.787623i	0.938653	+	0.787623i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.848048	+	1.46886i	0.848048	+	1.46886i	0.882948	+	0.469472i	$0.155556\pi$
$239$	0.848048	+	1.46886i	0.848048	+	1.46886i	−0.0348995	+	0.999391i	$0.511111\pi$
$240$		0			0
$241$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.913545	−	0.406737i	$-0.866667\pi$
$241$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.559193	−	0.829038i	$-0.688889\pi$
$242$	−1.15707	−	0.421137i	−1.15707	−	0.421137i
$243$	−0.195492	+	0.0711533i	−0.195492	+	0.0711533i
$244$		0			0
$245$		0			0
$246$	−0.0753517			−0.0753517
$247$	0.990268	+	0.139173i	0.990268	+	0.139173i
$248$		0			0
$249$	−0.0233019	−	0.132152i	−0.0233019	−	0.132152i
$250$		0			0
$251$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.559193	−	0.829038i	$-0.311111\pi$
$251$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.961262	+	0.275637i	$0.0888889\pi$
$252$	−0.539806	−	0.196473i	−0.539806	−	0.196473i
$253$	1.10209	+	0.924765i	1.10209	+	0.924765i
$254$		0			0
$255$		0			0
$256$	0.209577	−	1.18857i	0.209577	−	1.18857i
$257$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	0.438371	+	0.898794i	$0.355556\pi$
$257$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	−0.719340	+	0.694658i	$0.755556\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$263$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$264$	0.00722099	+	0.0409522i	0.00722099	+	0.0409522i
$265$		0			0
$266$	−1.34700	+	0.286314i	−1.34700	+	0.286314i
$267$		0			0
$268$		0			0
$269$	0.671624	−	0.563559i	0.671624	−	0.563559i	−0.241922	−	0.970296i	$-0.577778\pi$
$269$	0.671624	−	0.563559i	0.671624	−	0.563559i	0.913545	+	0.406737i	$0.133333\pi$
$270$		0			0
$271$	1.86110	+	0.677383i	1.86110	+	0.677383i	0.978148	+	0.207912i	$0.0666667\pi$
$271$	1.86110	+	0.677383i	1.86110	+	0.677383i	0.882948	+	0.469472i	$0.155556\pi$
$272$		0			0
$273$	−0.0390311	+	0.0676039i	−0.0390311	+	0.0676039i
$274$		0			0
$275$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$276$	−0.00900046	+	0.0510441i	−0.00900046	+	0.0510441i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.86110	−	0.677383i	1.86110	−	0.677383i	0.882948	−	0.469472i	$-0.155556\pi$
$281$	1.86110	−	0.677383i	1.86110	−	0.677383i	0.978148	−	0.207912i	$-0.0666667\pi$
$282$		0			0
$283$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$283$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$284$		0			0
$285$		0			0
$286$	1.23132			1.23132
$287$	0.170268	+	0.965640i	0.170268	+	0.965640i
$288$	0.718910	−	0.603237i	0.718910	−	0.603237i
$289$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$290$		0			0
$291$		0			0
$292$	0.159501	−	0.276264i	0.159501	−	0.276264i
$293$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$293$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$294$	0.00374280	−	0.0212264i	0.00374280	−	0.0212264i
$295$		0			0
$296$		0			0
$297$	−0.0696290	+	0.120601i	−0.0696290	+	0.120601i
$298$	0.197193	+	0.165464i	0.197193	+	0.165464i
$299$	−1.35192	−	0.492057i	−1.35192	−	0.492057i
$300$	−0.0338545	+	0.0123220i	−0.0338545	+	0.0123220i
$301$		0			0
$302$	0.213817	+	1.21262i	0.213817	+	1.21262i
$303$		0			0
$304$	0.386191	−	1.18857i	0.386191	−	1.18857i
$305$		0			0
$306$		0			0
$307$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$307$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$308$	−0.542449	+	0.197435i	−0.542449	+	0.197435i
$309$	0.0317351	+	0.0115506i	0.0317351	+	0.0115506i
$310$		0			0
$311$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i	−0.882948	−	0.469472i	$-0.844444\pi$
$311$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i	0.848048	+	0.529919i	$0.177778\pi$
$312$	−0.0207920	−	0.0360128i	−0.0207920	−	0.0360128i
$313$	−0.0363024	+	0.205881i	−0.0363024	+	0.205881i	−0.997564	−	0.0697565i	$-0.977778\pi$
$313$	−0.0363024	+	0.205881i	−0.0363024	+	0.205881i	0.961262	+	0.275637i	$0.0888889\pi$
$314$	0.390663	−	2.21556i	0.390663	−	2.21556i
$315$		0			0
$316$		0			0
$317$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$317$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$318$	0.142617	+	0.0519084i	0.142617	+	0.0519084i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	1.98120			1.98120
$323$		0			0
$324$	0.508624			0.508624
$325$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$326$		0			0
$327$	−0.128313	+	0.0467020i	−0.128313	+	0.0467020i
$328$	−0.490834	−	0.178649i	−0.490834	−	0.178649i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−0.172315	+	0.977247i	−0.172315	+	0.977247i
$333$		0			0
$334$	−0.461262	−	0.798929i	−0.461262	−	0.798929i
$335$		0			0
$336$	0.0747333	+	0.0627087i	0.0747333	+	0.0627087i
$337$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$337$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$338$	−1.15707	+	0.421137i	−1.15707	+	0.421137i
$339$	−0.0400598	+	0.0336141i	−0.0400598	+	0.0336141i
$340$		0			0
$341$		0			0
$342$	1.03913	−	0.649323i	1.03913	−	0.649323i
$343$	0.837909			0.837909
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$347$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$348$		0			0
$349$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	−0.961262	−	0.275637i	$-0.911111\pi$
$349$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	0.719340	+	0.694658i	$0.244444\pi$
$350$	0.688547	+	1.19260i	0.688547	+	1.19260i
$351$	0.0241819	−	0.137142i	0.0241819	−	0.137142i
$352$	0.163761	−	0.928737i	0.163761	−	0.928737i
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.44514	−	1.21262i	1.44514	−	1.21262i
$359$	0.249824	+	1.41682i	0.249824	+	1.41682i	0.809017	+	0.587785i	$0.200000\pi$
$359$	0.249824	+	1.41682i	0.249824	+	1.41682i	−0.559193	+	0.829038i	$0.688889\pi$
$360$		0			0
$361$	0.438371	−	0.898794i	0.438371	−	0.898794i
$362$	2.43868			2.43868
$363$	0.0121205	+	0.0687386i	0.0121205	+	0.0687386i
$364$	0.442208	−	0.371057i	0.442208	−	0.371057i
$365$		0			0
$366$		0			0
$367$	0.473442	+	0.397265i	0.473442	+	0.397265i	0.848048	−	0.529919i	$-0.177778\pi$
$367$	0.473442	+	0.397265i	0.473442	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$368$	−0.898987	+	1.55709i	−0.898987	+	1.55709i
$369$	−0.436235	−	0.755582i	−0.436235	−	0.755582i
$370$		0			0
$371$	0.342947	−	1.94495i	0.342947	−	1.94495i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.0333007	+	0.188858i	0.0333007	+	0.188858i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	−0.418289	−	2.37224i	−0.418289	−	2.37224i
$383$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$383$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$384$	−0.0690044	+	0.0251156i	−0.0690044	+	0.0251156i
$385$		0			0
$386$	1.35703	+	1.13868i	1.35703	+	1.13868i
$387$		0			0
$388$		0			0
$389$	0.232387	−	1.31793i	0.232387	−	1.31793i	−0.615661	−	0.788011i	$-0.711111\pi$
$389$	0.232387	−	1.31793i	0.232387	−	1.31793i	0.848048	−	0.529919i	$-0.177778\pi$
$390$		0			0
$391$		0			0
$392$	0.0747054	−	0.129394i	0.0747054	−	0.129394i
$393$		0			0
$394$	2.29161	+	0.834078i	2.29161	+	0.834078i
$395$		0			0
$396$	0.393472	−	0.330162i	0.393472	−	0.330162i
$397$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$397$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$398$	2.08844			2.08844
$399$	0.0522338	+	0.0580115i	0.0522338	+	0.0580115i
$400$	−1.24974			−1.24974
$401$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$401$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$409$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−0.191311	−	0.160529i	−0.191311	−	0.160529i
$413$		0			0
$414$	−1.65654	+	0.602930i	−1.65654	+	0.602930i
$415$		0			0
$416$	0.163761	+	0.928737i	0.163761	+	0.928737i
$417$		0			0
$418$	0.380500	−	1.17106i	0.380500	−	1.17106i
$419$	−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		0.766044	−	0.642788i	$-0.222222\pi$
$421$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$422$		0			0
$423$		0			0
$424$	0.805928	+	0.676254i	0.805928	+	0.676254i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i
$430$		0			0
$431$	0.370646	+	0.311009i	0.370646	+	0.311009i	0.809017	−	0.587785i	$-0.200000\pi$
$431$	0.370646	+	0.311009i	0.370646	+	0.311009i	−0.438371	+	0.898794i	$0.644444\pi$
$432$	−0.163540	−	0.0595238i	−0.163540	−	0.0595238i
$433$	−1.59381	+	0.580099i	−1.59381	+	0.580099i	−0.978148	−	0.207912i	$-0.933333\pi$
$433$	−1.59381	+	0.580099i	−1.59381	+	0.580099i	−0.615661	+	0.788011i	$0.711111\pi$
$434$		0			0
$435$		0			0
$436$	1.00975			1.00975
$437$	−0.885740	+	1.13369i	−0.885740	+	1.13369i
$438$	−0.0531170			−0.0531170
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	0.234514	−	0.0853563i	0.234514	−	0.0853563i
$442$		0			0
$443$	1.47274	+	1.23577i	1.47274	+	1.23577i	0.913545	+	0.406737i	$0.133333\pi$
$443$	1.47274	+	1.23577i	1.47274	+	1.23577i	0.559193	+	0.829038i	$0.311111\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.00253387	−	0.0143703i	0.00253387	−	0.0143703i
$448$	0.0495010	+	0.0857383i	0.0495010	+	0.0857383i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.938653	−	0.787623i	−0.938653	−	0.787623i
$451$	−0.823868	−	0.299864i	−0.823868	−	0.299864i
$452$	0.363390	−	0.132263i	0.363390	−	0.132263i
$453$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i
$454$	−0.132146	−	0.749438i	−0.132146	−	0.749438i
$455$		0			0
$456$	−0.0406753	+	0.00864580i	−0.0406753	+	0.00864580i
$457$	−1.69610			−1.69610			−0.848048	−	0.529919i	$-0.822222\pi$
$457$	−1.69610			−1.69610			−0.848048	+	0.529919i	$0.822222\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.882948	−	0.469472i	$-0.155556\pi$
$461$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.374607	+	0.927184i	$0.377778\pi$
$462$	0.0736320	+	0.0617846i	0.0736320	+	0.0617846i
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$468$	−0.256821	+	0.444827i	−0.256821	+	0.444827i
$469$		0			0
$470$		0			0
$471$	−0.119838	+	0.0436175i	−0.119838	+	0.0436175i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.990268	−	0.139173i	−0.990268	−	0.139173i
$476$		0			0
$477$	0.305151	+	1.73059i	0.305151	+	1.73059i
$478$	−1.59984	+	1.34242i	−1.59984	+	1.34242i
$479$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$479$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$480$		0			0
$481$		0			0
$482$	1.18362	−	2.05010i	1.18362	−	2.05010i
$483$	−0.0561532	−	0.0972603i	−0.0561532	−	0.0972603i
$484$	0.0896296	−	0.508315i	0.0896296	−	0.508315i
$485$		0			0
$486$	−0.128081	−	0.221843i	−0.128081	−	0.221843i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$491$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$492$	−0.00548495	−	0.0311067i	−0.00548495	−	0.0311067i
$493$		0			0
$494$	0.0429726	+	1.23057i	0.0429726	+	1.23057i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.155267	−	0.0565125i	0.155267	−	0.0565125i
$499$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$499$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$500$		0			0
$501$	−0.0261472	+	0.0452882i	−0.0261472	+	0.0452882i
$502$	0.996161	+	1.72540i	0.996161	+	1.72540i
$503$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$503$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$504$	−0.115138	+	0.652979i	−0.115138	+	0.652979i
$505$		0			0
$506$	−0.885740	+	1.53415i	−0.885740	+	1.53415i
$507$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i
$508$		0			0
$509$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$509$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$510$		0			0
$511$	0.120026	+	0.680700i	0.120026	+	0.680700i
$512$	0.434030			0.434030
$513$	−0.122957	−	0.0653776i	−0.122957	−	0.0653776i
$514$	−1.99232			−1.99232
$515$		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	−0.809017	−	0.587785i	$-0.800000\pi$
$521$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$522$		0			0
$523$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$523$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$524$		0			0
$525$	0.0390311	−	0.0676039i	0.0390311	−	0.0676039i
$526$		0			0
$527$		0			0
$528$	−0.0819699	+	0.0298346i	−0.0819699	+	0.0298346i
$529$	0.819514	−	0.687654i	0.819514	−	0.687654i
$530$		0			0
$531$		0			0
$532$	−0.216246	−	0.535228i	−0.216246	−	0.535228i
$533$	0.876742			0.876742
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.100489	−	0.0365750i	−0.100489	−	0.0365750i
$538$	0.826986	+	0.693923i	0.826986	+	0.693923i
$539$	0.125393	−	0.217188i	0.125393	−	0.217188i
$540$		0			0
$541$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.104528	−	0.994522i	$-0.466667\pi$
$541$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.241922	−	0.970296i	$-0.422222\pi$
$542$	−0.423472	+	2.40163i	−0.423472	+	2.40163i
$543$	−0.0691197	−	0.119719i	−0.0691197	−	0.119719i
$544$		0			0
$545$		0			0
$546$	−0.0903231	−	0.0328749i	−0.0903231	−	0.0328749i
$547$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$547$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$548$		0			0
$549$		0			0
$550$	−1.23132			−1.23132
$551$		0			0
$552$	0.0598261			0.0598261
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.671624	−	0.563559i	−0.671624	−	0.563559i	0.241922	−	0.970296i	$-0.422222\pi$
$557$	−0.671624	−	0.563559i	−0.671624	−	0.563559i	−0.913545	+	0.406737i	$0.866667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.21934	+	2.11196i	1.21934	+	2.11196i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.844232	+	0.708395i	−0.844232	+	0.708395i
$568$		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			$\pi$
$572$	0.0896296	+	0.508315i	0.0896296	+	0.508315i
$573$	−0.104601	+	0.0877710i	−0.104601	+	0.0877710i
$574$	−1.13454	+	0.412940i	−1.13454	+	0.412940i
$575$	1.35192	+	0.492057i	1.35192	+	0.492057i
$576$	−0.0674816	−	0.0566238i	−0.0674816	−	0.0566238i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	−0.615661	−	1.06636i	−0.615661	−	1.06636i
$579$	0.0174375	−	0.0988928i	0.0174375	−	0.0988928i
$580$		0			0
$581$	−1.07506	−	1.86206i	−1.07506	−	1.86206i
$582$		0			0
$583$	1.35275	+	1.13510i	1.35275	+	1.13510i
$584$	−0.345999	−	0.125933i	−0.345999	−	0.125933i
$585$		0			0
$586$	1.77273	−	1.48749i	1.77273	−	1.48749i
$587$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$587$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$588$	0.00903514			0.00903514
$589$		0			0
$590$		0			0
$591$	−0.0240050	−	0.136139i	−0.0240050	−	0.136139i
$592$		0			0
$593$	1.71690	−	0.624902i	1.71690	−	0.624902i	0.719340	−	0.694658i	$-0.244444\pi$
$593$	1.71690	−	0.624902i	1.71690	−	0.624902i	0.997564	+	0.0697565i	$0.0222222\pi$
$594$	−0.161130	−	0.0586467i	−0.161130	−	0.0586467i
$595$		0			0
$596$	−0.0539530	+	0.0934494i	−0.0539530	+	0.0934494i
$597$	−0.0591929	−	0.102525i	−0.0591929	−	0.102525i
$598$	0.307614	−	1.74457i	0.307614	−	1.74457i
$599$	−0.213817	+	1.21262i	−0.213817	+	1.21262i	0.669131	+	0.743145i	$0.266667\pi$
$599$	−0.213817	+	1.21262i	−0.213817	+	1.21262i	−0.882948	+	0.469472i	$0.844444\pi$
$600$	0.0207920	+	0.0360128i	0.0207920	+	0.0360128i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	−0.485028	+	0.176536i	−0.485028	+	0.176536i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	0.933886	+	0.131249i	0.933886	+	0.131249i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.0348995	−	0.999391i	$-0.511111\pi$
$613$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.669131	+	0.743145i	$0.733333\pi$
$614$	−1.44514	−	1.21262i	−1.44514	−	1.21262i
$615$		0			0
$616$	0.333149	+	0.577031i	0.333149	+	0.577031i
$617$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$617$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$618$	−0.00722099	+	0.0409522i	−0.00722099	+	0.0409522i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	0.153475	+	0.128781i	0.153475	+	0.128781i
$622$	−0.0807620	−	0.0293950i	−0.0807620	−	0.0293950i
$623$		0			0
$624$	0.0668225	−	0.0560707i	0.0668225	−	0.0560707i
$625$	0.173648	+	0.984808i	0.173648	+	0.984808i
$626$	−0.257417			−0.257417
$627$	−0.0682737	+	0.0145120i	−0.0682737	+	0.0145120i
$628$	0.943064			0.943064
$629$		0			0
$630$		0			0
$631$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$631$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.0110475	+	0.0626537i	−0.0110475	+	0.0626537i
$637$	−0.0435487	+	0.246977i	−0.0435487	+	0.246977i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$641$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$642$		0			0
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$	0.144214	+	0.817878i	0.144214	+	0.817878i
$645$		0			0
$646$		0			0
$647$	1.98054			1.98054			0.990268	−	0.139173i	$-0.0444444\pi$
$647$	1.98054			1.98054			0.990268	+	0.139173i	$0.0444444\pi$
$648$	−0.101944	−	0.578156i	−0.101944	−	0.578156i
$649$		0			0
$650$	1.15707	−	0.421137i	1.15707	−	0.421137i
$651$		0			0
$652$		0			0
$653$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$653$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$654$	−0.0840670	−	0.145608i	−0.0840670	−	0.145608i
$655$		0			0
$656$	0.190266	−	1.07905i	0.190266	−	1.07905i
$657$	−0.307511	−	0.532626i	−0.307511	−	0.532626i
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$		0			0
$661$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$661$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$	1.14538			1.14538
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.296238	−	0.248573i	0.296238	−	0.248573i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.0368088	+	0.0637548i	−0.0368088	+	0.0637548i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−0.0241819	+	0.137142i	−0.0241819	+	0.137142i
$676$	−0.258078	−	0.447004i	−0.258078	−	0.447004i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.0493265	−	0.0413899i	−0.0493265	−	0.0413899i
$679$		0			0
$680$		0			0
$681$	−0.0330457	+	0.0277287i	−0.0330457	+	0.0277287i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.343693	+	0.381710i	0.343693	+	0.381710i
$685$		0			0
$686$	0.179159	+	1.01606i	0.179159	+	1.01606i
$687$		0			0
$688$		0			0
$689$	−1.65940	−	0.603972i	−1.65940	−	0.603972i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−0.193260	+	1.09603i	−0.193260	+	1.09603i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.559839	−	0.203765i	−0.559839	−	0.203765i
$699$		0			0
$700$	−0.442208	+	0.371057i	−0.442208	+	0.371057i
$701$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$701$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$702$	0.171471			0.171471
$703$		0			0
$704$	−0.0885222			−0.0885222
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$709$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.605786	+	0.508315i	0.605786	+	0.508315i
$717$	0.111246	+	0.0404903i	0.111246	+	0.0404903i
$718$	−1.66465	+	0.605882i	−1.66465	+	0.605882i
$719$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$719$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$720$		0			0
$721$	0.541124			0.541124
$722$	1.18362	+	0.339399i	1.18362	+	0.339399i
$723$	−0.134190			−0.134190
$724$	0.177515	+	1.00674i	0.177515	+	1.00674i
$725$		0			0
$726$	−0.0807620	+	0.0293950i	−0.0807620	+	0.0293950i
$727$	−1.05094	−	0.382510i	−1.05094	−	0.382510i	−0.241922	−	0.970296i	$-0.577778\pi$
$727$	−1.05094	−	0.382510i	−1.05094	−	0.382510i	−0.809017	+	0.587785i	$0.800000\pi$
$728$	−0.510414	−	0.428288i	−0.510414	−	0.428288i
$729$	0.485444	−	0.840813i	0.485444	−	0.840813i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.961262	+	1.66495i	0.961262	+	1.66495i	0.719340	+	0.694658i	$0.244444\pi$
$733$	0.961262	+	1.66495i	0.961262	+	1.66495i	0.241922	+	0.970296i	$0.422222\pi$
$734$	−0.380500	+	0.659045i	−0.380500	+	0.659045i
$735$		0			0
$736$	−1.27494	−	0.464042i	−1.27494	−	0.464042i
$737$		0			0
$738$	0.822957	−	0.690543i	0.822957	−	0.690543i
$739$	−0.152245	−	0.863423i	−0.152245	−	0.863423i	−0.961262	−	0.275637i	$-0.911111\pi$
$739$	−0.152245	−	0.863423i	−0.152245	−	0.863423i	0.809017	−	0.587785i	$-0.200000\pi$
$740$		0			0
$741$	0.0591929	−	0.0369878i	0.0591929	−	0.0369878i
$742$	2.43180			2.43180
$743$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$743$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.46556	+	1.22975i	1.46556	+	1.22975i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.232387	−	1.31793i	0.232387	−	1.31793i	−0.615661	−	0.788011i	$-0.711111\pi$
$751$	0.232387	−	1.31793i	0.232387	−	1.31793i	0.848048	−	0.529919i	$-0.177778\pi$
$752$		0			0
$753$	0.0564686	−	0.0978064i	0.0564686	−	0.0978064i
$754$		0			0
$755$		0			0
$756$	−0.0755403	+	0.0274944i	−0.0755403	+	0.0274944i
$757$	−1.23949	+	1.04005i	−1.23949	+	1.04005i	−0.241922	+	0.970296i	$0.577778\pi$
$757$	−1.23949	+	1.04005i	−1.23949	+	1.04005i	−0.997564	+	0.0697565i	$0.977778\pi$
$758$		0			0
$759$	0.100418			0.100418
$760$		0			0
$761$	1.99513			1.99513			0.997564	−	0.0697565i	$-0.0222222\pi$
$761$	1.99513			1.99513			0.997564	+	0.0697565i	$0.0222222\pi$
$762$		0			0
$763$	−1.67602	+	1.40635i	−1.67602	+	1.40635i
$764$	0.948858	−	0.345356i	0.948858	−	0.345356i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.0421205	−	0.0729548i	−0.0421205	−	0.0729548i
$769$	−0.152245	+	0.863423i	−0.152245	+	0.863423i	0.809017	+	0.587785i	$0.200000\pi$
$769$	−0.152245	+	0.863423i	−0.152245	+	0.863423i	−0.961262	+	0.275637i	$0.911111\pi$
$770$		0			0
$771$	0.0564686	+	0.0978064i	0.0564686	+	0.0978064i
$772$	−0.371292	+	0.643096i	−0.371292	+	0.643096i
$773$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$773$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.64783			1.64783
$779$	0.270928	−	0.833831i	0.270928	−	0.833831i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.294517	+	0.107195i	0.294517	+	0.107195i
$785$		0			0
$786$		0			0
$787$	0.559193	+	0.968551i	0.559193	+	0.968551i	0.997564	+	0.0697565i	$0.0222222\pi$
$787$	0.559193	+	0.968551i	0.559193	+	0.968551i	−0.438371	+	0.898794i	$0.644444\pi$
$788$	−0.177515	+	1.00674i	−0.177515	+	1.00674i
$789$		0			0
$790$		0			0
$791$	−0.418955	+	0.725651i	−0.418955	+	0.725651i
$792$	−0.454161	−	0.381087i	−0.454161	−	0.381087i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.152020	+	0.862151i	0.152020	+	0.862151i
$797$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$797$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$798$	−0.0591772	+	0.0757434i	−0.0591772	+	0.0757434i
$799$		0			0
$800$	−0.163761	−	0.928737i	−0.163761	−	0.928737i
$801$		0			0
$802$		0			0
$803$	−0.580762	−	0.211380i	−0.580762	−	0.211380i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.0106265	−	0.0602660i	0.0106265	−	0.0602660i
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$	1.52836	+	1.28244i	1.52836	+	1.28244i	0.809017	+	0.587785i	$0.200000\pi$
$811$	1.52836	+	1.28244i	1.52836	+	1.28244i	0.719340	+	0.694658i	$0.244444\pi$
$812$		0			0
$813$	0.129903	−	0.0472807i	0.129903	−	0.0472807i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.427634			−0.427634
$819$	−0.193260	−	1.09603i	−0.193260	−	1.09603i
$820$		0			0
$821$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$821$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$822$		0			0
$823$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.997564	−	0.0697565i	$-0.977778\pi$
$823$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.241922	−	0.970296i	$-0.577778\pi$
$824$	−0.144129	+	0.249639i	−0.144129	+	0.249639i
$825$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i
$826$		0			0
$827$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	0.615661	+	0.788011i	$0.288889\pi$
$827$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	−0.848048	+	0.529919i	$0.822222\pi$
$828$	−0.369483	−	0.639963i	−0.369483	−	0.639963i
$829$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$829$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$830$		0			0
$831$		0			0
$832$	0.0831837	−	0.0302764i	0.0831837	−	0.0302764i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.511133	+	0.0718351i	0.511133	+	0.0718351i
$837$		0			0
$838$	−0.0446999	−	0.253506i	−0.0446999	−	0.253506i
$839$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$839$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$840$		0			0
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$	0.0691197	−	0.119719i	0.0691197	−	0.119719i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.559193	+	0.968551i	0.559193	+	0.968551i
$848$	−1.10345	+	1.91124i	−1.10345	+	1.91124i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.213817	+	1.21262i	0.213817	+	1.21262i	0.882948	+	0.469472i	$0.155556\pi$
$853$	0.213817	+	1.21262i	0.213817	+	1.21262i	−0.669131	+	0.743145i	$0.733333\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$857$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$858$	0.0658378	−	0.0552444i	0.0658378	−	0.0552444i
$859$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.882948	+	0.469472i	$0.844444\pi$
$859$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.978148	+	0.207912i	$0.933333\pi$
$860$		0			0
$861$	0.0524284	+	0.0439927i	0.0524284	+	0.0439927i
$862$	−0.297884	+	0.515950i	−0.297884	+	0.515950i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	0.0228051	−	0.129334i	0.0228051	−	0.129334i
$865$		0			0
$866$	−1.04422	−	1.80864i	−1.04422	−	1.80864i
$867$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.202387	−	1.14779i	−0.202387	−	1.14779i
$873$		0			0
$874$	−1.56412	−	0.831659i	−1.56412	−	0.831659i
$875$		0			0
$876$	−0.00386645	−	0.0219278i	−0.00386645	−	0.0219278i
$877$	−0.473442	+	0.397265i	−0.473442	+	0.397265i	−0.848048	−	0.529919i	$-0.822222\pi$
$877$	−0.473442	+	0.397265i	−0.473442	+	0.397265i	0.374607	+	0.927184i	$0.377778\pi$
$878$		0			0
$879$	−0.123268	−	0.0448659i	−0.123268	−	0.0448659i
$880$		0			0
$881$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.0348995	−	0.999391i	$-0.488889\pi$
$881$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.848048	−	0.529919i	$-0.177778\pi$
$882$	0.153648	+	0.266125i	0.153648	+	0.266125i
$883$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$883$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$884$		0			0
$885$		0			0
$886$	−1.18362	+	2.05010i	−1.18362	+	2.05010i
$887$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$887$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.171114	−	0.970437i	−0.171114	−	0.970437i
$892$		0			0
$893$		0			0
$894$	0.0179674			0.0179674
$895$		0			0
$896$	−0.901338	+	0.756312i	−0.901338	+	0.756312i
$897$	−0.0943624	+	0.0343451i	−0.0943624	+	0.0343451i
$898$		0			0
$899$		0			0
$900$	0.256821	−	0.444827i	0.256821	−	0.444827i
$901$		0			0
$902$	0.187462	−	1.06315i	0.187462	−	1.06315i
$903$		0			0
$904$	−0.223179	−	0.386557i	−0.223179	−	0.386557i
$905$		0			0
$906$	0.0658378	+	0.0552444i	0.0658378	+	0.0552444i
$907$	1.52045	+	0.553400i	1.52045	+	0.553400i	0.961262	−	0.275637i	$-0.0888889\pi$
$907$	1.52045	+	0.553400i	1.52045	+	0.553400i	0.559193	+	0.829038i	$0.311111\pi$
$908$	0.299764	−	0.109105i	0.299764	−	0.109105i
$909$		0			0
$910$		0			0
$911$	−1.43868			−1.43868			−0.719340	−	0.694658i	$-0.755556\pi$
$911$	−1.43868			−1.43868			−0.719340	+	0.694658i	$0.755556\pi$
$912$	−0.0326771	−	0.0808787i	−0.0326771	−	0.0808787i
$913$	1.92252			1.92252
$914$	−0.362654	−	2.05671i	−0.362654	−	2.05671i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−0.0185696	+	0.105314i	−0.0185696	+	0.105314i
$922$	−0.286143	+	1.62280i	−0.286143	+	1.62280i
$923$		0			0
$924$	−0.0201461	+	0.0348941i	−0.0201461	+	0.0348941i
$925$		0			0
$926$		0			0
$927$	−0.452449	+	0.164678i	−0.452449	+	0.164678i
$928$		0			0
$929$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$929$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$930$		0			0
$931$	0.221432	+	0.117737i	0.221432	+	0.117737i
$932$		0			0
$933$	0.000845996		0.00479788i	0.000845996		0.00479788i
$934$	0.327587	−	0.274878i	0.327587	−	0.274878i
$935$		0			0
$936$	0.557111	+	0.202772i	0.557111	+	0.202772i
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$	0.00729598	+	0.0126370i	0.00729598	+	0.0126370i
$940$		0			0
$941$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	0.615661	+	0.788011i	$0.288889\pi$
$941$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	−0.848048	+	0.529919i	$0.822222\pi$
$942$	−0.0785148	−	0.135992i	−0.0785148	−	0.135992i
$943$	−0.630676	+	1.09236i	−0.630676	+	1.09236i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$947$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$948$		0			0
$949$	0.618034			0.618034
$950$	−0.0429726	−	1.23057i	−0.0429726	−	1.23057i
$951$		0			0
$952$		0			0
$953$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$953$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$954$	−2.03330	+	0.740061i	−2.03330	+	0.740061i
$955$		0			0
$956$	−0.670634	−	0.562729i	−0.670634	−	0.562729i
$957$		0			0
$958$	−1.15707	−	2.00410i	−1.15707	−	2.00410i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	0.932478	+	0.339394i	0.932478	+	0.339394i
$965$		0			0
$966$	0.105933	−	0.0888883i	0.105933	−	0.0888883i
$967$	0.130100	+	0.737831i	0.130100	+	0.737831i	0.978148	+	0.207912i	$0.0666667\pi$
$967$	0.130100	+	0.737831i	0.130100	+	0.737831i	−0.848048	+	0.529919i	$0.822222\pi$
$968$	−0.595768			−0.595768
$969$		0			0
$970$		0			0
$971$	0.232387	+	1.31793i	0.232387	+	1.31793i	0.848048	+	0.529919i	$0.177778\pi$
$971$	0.232387	+	1.31793i	0.232387	+	1.31793i	−0.615661	+	0.788011i	$0.711111\pi$
$972$	0.0822581	−	0.0690227i	0.0822581	−	0.0690227i
$973$		0			0
$974$		0			0
$975$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i
$976$		0			0
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.973382	−	1.68595i	0.973382	−	1.68595i
$982$		0			0
$983$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$983$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$984$	−0.0342597	+	0.0124695i	−0.0342597	+	0.0124695i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.504877	+	0.107315i	−0.504877	+	0.107315i
$989$		0			0
$990$		0			0
$991$	−1.35275	+	1.13510i	−1.35275	+	1.13510i	−0.374607	+	0.927184i	$0.622222\pi$
$991$	−1.35275	+	1.13510i	−1.35275	+	1.13510i	−0.978148	+	0.207912i	$0.933333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.0346316	+	0.0599836i	0.0346316	+	0.0599836i
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$		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.142.4	✓	24
11.10	odd	2		2717.1.db.d.142.1	yes	24
13.12	even	2		2717.1.db.d.142.1	yes	24
19.17	even	9	inner	2717.1.db.c.2430.4	yes	24
143.142	odd	2	CM	2717.1.db.c.142.4	✓	24
209.131	odd	18		2717.1.db.d.2430.1	yes	24
247.207	even	18		2717.1.db.d.2430.1	yes	24
2717.2430	odd	18	inner	2717.1.db.c.2430.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.142.4	✓	24	1.1	even	1	trivial
2717.1.db.c.142.4	✓	24	143.142	odd	2	CM
2717.1.db.c.2430.4	yes	24	19.17	even	9	inner
2717.1.db.c.2430.4	yes	24	2717.2430	odd	18	inner
2717.1.db.d.142.1	yes	24	11.10	odd	2
2717.1.db.d.142.1	yes	24	13.12	even	2
2717.1.db.d.2430.1	yes	24	209.131	odd	18
2717.1.db.d.2430.1	yes	24	247.207	even	18

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)

\(f(q)\)	\(=\)	\(q+(0.213817 + 1.21262i) q^{2} +(0.0534691 - 0.0448659i) q^{3} +(-0.485028 + 0.176536i) q^{4} +(0.0658378 + 0.0552444i) q^{6} +(0.559193 - 0.968551i) q^{7} +(0.297884 + 0.515950i) q^{8} +(-0.172802 + 0.980010i) q^{9} +O(q^{10})\)	\(q+(0.213817 + 1.21262i) q^{2} +(0.0534691 - 0.0448659i) q^{3} +(-0.485028 + 0.176536i) q^{4} +(0.0658378 + 0.0552444i) q^{6} +(0.559193 - 0.968551i) q^{7} +(0.297884 + 0.515950i) q^{8} +(-0.172802 + 0.980010i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.0180136 + 0.0312005i) q^{12} +(-0.766044 - 0.642788i) q^{13} +(1.29405 + 0.470994i) q^{14} +(-0.957356 + 0.803317i) q^{16} -1.22532 q^{18} +(-0.848048 + 0.529919i) q^{19} +(-0.0135554 - 0.0768763i) q^{21} +(-0.943248 + 0.791479i) q^{22} +(1.35192 - 0.492057i) q^{23} +(0.0390762 + 0.0142226i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.615661 - 1.06636i) q^{26} +(0.0696290 + 0.120601i) q^{27} +(-0.100240 + 0.568492i) q^{28} +(-0.722429 - 0.606190i) q^{32} +(0.0655896 + 0.0238727i) q^{33} +(-0.0891929 - 0.505838i) q^{36} +(-0.823916 - 0.915051i) q^{38} -0.0697990 q^{39} +(-0.671624 + 0.563559i) q^{41} +(0.0903231 - 0.0328749i) q^{42} +(-0.395399 - 0.331779i) q^{44} +(0.885740 + 1.53415i) q^{46} +(-0.0151474 + 0.0859053i) q^{48} +(-0.125393 - 0.217188i) q^{49} +(-0.615661 + 1.06636i) q^{50} +(0.485028 + 0.176536i) q^{52} +(1.65940 - 0.603972i) q^{53} +(-0.131355 + 0.110220i) q^{54} +0.666298 q^{56} +(-0.0215691 + 0.0663828i) q^{57} +(0.852559 + 0.715382i) q^{63} +(-0.0442611 + 0.0766625i) q^{64} +(-0.0149242 + 0.0846394i) q^{66} +(0.0502092 - 0.0869649i) q^{69} +(-0.557111 + 0.202772i) q^{72} +(-0.473442 + 0.397265i) q^{73} +0.0697990 q^{75} +(0.317777 - 0.406737i) q^{76} +1.11839 q^{77} +(-0.0149242 - 0.0846394i) q^{78} +(-0.925981 - 0.337029i) q^{81} +(-0.826986 - 0.693923i) q^{82} +(0.961262 - 1.66495i) q^{83} +(0.0201461 + 0.0348941i) q^{84} +(-0.297884 + 0.515950i) q^{88} +(-1.05094 + 0.382510i) q^{91} +(-0.568852 + 0.477323i) q^{92} -0.0658249 q^{96} +(0.236554 - 0.198493i) q^{98} +(-0.935115 + 0.340354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more