LMFDB - Embedded newform 536.1.ba.a.315.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [536,1,Mod(19,536)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(536, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 10]))

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

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

chi := DirichletCharacter("536.19");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 536 = 2^{3} \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	536.ba (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.267498846771$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{33}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{33} - \cdots)$

Embedding invariants

Embedding label			315.1
Root			$0.235759 + 0.971812i$ of defining polynomial
Character	$\chi$	$=$	536.315
Dual form			536.1.ba.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723734 - 0.690079i) q^{2} +(0.0930932 - 0.647478i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.379436 - 0.532843i) q^{6} +(-0.654861 - 0.755750i) q^{8} +(0.548932 + 0.161181i) q^{9} +O(q^{10})$	\(q+(0.723734 - 0.690079i) q^{2} +(0.0930932 - 0.647478i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.379436 - 0.532843i) q^{6} +(-0.654861 - 0.755750i) q^{8} +(0.548932 + 0.161181i) q^{9} +(-0.759713 + 1.06687i) q^{11} +(-0.642315 - 0.123796i) q^{12} +(-0.995472 - 0.0950560i) q^{16} +(-0.0845850 - 1.77566i) q^{17} +(0.508508 - 0.262154i) q^{18} +(-0.469383 + 1.93482i) q^{19} +(0.186393 + 1.29639i) q^{22} +(-0.550294 + 0.353653i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(0.427201 - 0.935439i) q^{27} +(-0.786053 + 0.618159i) q^{32} +(0.620049 + 0.591215i) q^{33} +(-1.28656 - 1.22673i) q^{34} +(0.187118 - 0.540641i) q^{36} +(0.995472 + 1.72421i) q^{38} +(1.70566 + 0.879330i) q^{41} +(0.975950 - 0.627205i) q^{43} +(1.02951 + 0.809616i) q^{44} +(-0.154218 + 0.635697i) q^{48} +(-0.888835 + 0.458227i) q^{49} +(0.0475819 + 0.998867i) q^{50} +(-1.15757 - 0.110535i) q^{51} +(-0.336347 - 0.971812i) q^{54} +(1.20906 + 0.484034i) q^{57} +(-1.28605 - 1.48418i) q^{59} +(-0.142315 + 0.989821i) q^{64} +0.856736 q^{66} +(0.415415 + 0.909632i) q^{67} -1.77767 q^{68} +(-0.237662 - 0.520406i) q^{72} +(0.0552004 + 0.0775182i) q^{73} +(0.428368 + 0.494363i) q^{75} +(1.91030 + 0.560914i) q^{76} +(-0.0846203 - 0.0543822i) q^{81} +(1.84125 - 0.540641i) q^{82} +(-0.827068 - 0.0789754i) q^{83} +(0.273507 - 1.12741i) q^{86} +(1.30379 - 0.124497i) q^{88} +(-0.205996 - 1.43273i) q^{89} +(0.327068 + 0.566498i) q^{96} +(-0.0475819 + 0.0824143i) q^{97} +(-0.327068 + 0.945001i) q^{98} +(-0.588989 + 0.463186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8}+O(q^{10}) $ 20 * q + q^2 + 2 * q^3 + q^4 - q^6 - 2 * q^8	$ 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8} + 2 q^{11} - 12 q^{12} + q^{16} - 12 q^{17} - q^{19} - 4 q^{22} + 2 q^{24} - 2 q^{25} - 2 q^{27} + q^{32} - 2 q^{33} - q^{34} - q^{38} + 2 q^{41} + 2 q^{43} + 2 q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23 q^{54} + q^{57} - 9 q^{59} - 2 q^{64} - 18 q^{66} - 2 q^{67} + 2 q^{68} - q^{73} - 9 q^{75} + 2 q^{76} + 2 q^{81} + 18 q^{82} - 9 q^{83} - q^{86} + 2 q^{88} + 2 q^{89} - q^{96} - q^{97} + q^{98}+O(q^{100}) $ 20 * q + q^2 + 2 * q^3 + q^4 - q^6 - 2 * q^8 + 2 * q^11 - 12 * q^12 + q^16 - 12 * q^17 - q^19 - 4 * q^22 + 2 * q^24 - 2 * q^25 - 2 * q^27 + q^32 - 2 * q^33 - q^34 - q^38 + 2 * q^41 + 2 * q^43 + 2 * q^44 - q^48 + q^49 + q^50 + q^51 + 23 * q^54 + q^57 - 9 * q^59 - 2 * q^64 - 18 * q^66 - 2 * q^67 + 2 * q^68 - q^73 - 9 * q^75 + 2 * q^76 + 2 * q^81 + 18 * q^82 - 9 * q^83 - q^86 + 2 * q^88 + 2 * q^89 - q^96 - q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{25}{33}\right)$

Coefficient data

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

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

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

$2$	0.723734	−	0.690079i	0.723734	−	0.690079i
$2$	0.723734	−	0.690079i	0.723734	−	0.690079i
$3$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	−0.888835	−	0.458227i	$-0.848485\pi$
$3$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	0.981929	−	0.189251i	$-0.0606061\pi$
$4$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$5$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$5$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$6$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$7$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$7$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$8$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$9$	0.548932	+	0.161181i	0.548932	+	0.161181i
$10$		0			0
$11$	−0.759713	+	1.06687i	−0.759713	+	1.06687i	0.235759	+	0.971812i	$0.424242\pi$
$11$	−0.759713	+	1.06687i	−0.759713	+	1.06687i	−0.995472	+	0.0950560i	$0.969697\pi$
$12$	−0.642315	−	0.123796i	−0.642315	−	0.123796i
$13$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$13$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$14$		0			0
$15$		0			0
$16$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$17$	−0.0845850	−	1.77566i	−0.0845850	−	1.77566i	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−0.0845850	−	1.77566i	−0.0845850	−	1.77566i	0.415415	−	0.909632i	$-0.363636\pi$
$18$	0.508508	−	0.262154i	0.508508	−	0.262154i
$19$	−0.469383	+	1.93482i	−0.469383	+	1.93482i	−0.142315	+	0.989821i	$0.545455\pi$
$19$	−0.469383	+	1.93482i	−0.469383	+	1.93482i	−0.327068	+	0.945001i	$0.606061\pi$
$20$		0			0
$21$		0			0
$22$	0.186393	+	1.29639i	0.186393	+	1.29639i
$23$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$23$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$24$	−0.550294	+	0.353653i	−0.550294	+	0.353653i
$25$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$26$		0			0
$27$	0.427201	−	0.935439i	0.427201	−	0.935439i
$28$		0			0
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$		0			0
$31$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$31$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$32$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$33$	0.620049	+	0.591215i	0.620049	+	0.591215i
$34$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$35$		0			0
$36$	0.187118	−	0.540641i	0.187118	−	0.540641i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	0.995472	+	1.72421i	0.995472	+	1.72421i
$39$		0			0
$40$		0			0
$41$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.981929	+	0.189251i	$0.0606061\pi$
$41$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.723734	+	0.690079i	$0.242424\pi$
$42$		0			0
$43$	0.975950	−	0.627205i	0.975950	−	0.627205i	0.0475819	−	0.998867i	$-0.484848\pi$
$43$	0.975950	−	0.627205i	0.975950	−	0.627205i	0.928368	+	0.371662i	$0.121212\pi$
$44$	1.02951	+	0.809616i	1.02951	+	0.809616i
$45$		0			0
$46$		0			0
$47$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$47$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$48$	−0.154218	+	0.635697i	−0.154218	+	0.635697i
$49$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$50$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$51$	−1.15757	−	0.110535i	−1.15757	−	0.110535i
$52$		0			0
$53$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$53$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$54$	−0.336347	−	0.971812i	−0.336347	−	0.971812i
$55$		0			0
$56$		0			0
$57$	1.20906	+	0.484034i	1.20906	+	0.484034i
$58$		0			0
$59$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.786053	−	0.618159i	$-0.787879\pi$
$59$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.500000	−	0.866025i	$-0.666667\pi$
$60$		0			0
$61$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$61$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$62$		0			0
$63$		0			0
$64$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$65$		0			0
$66$	0.856736			0.856736
$67$	0.415415	+	0.909632i	0.415415	+	0.909632i
$67$	0.415415	+	0.909632i	0.415415	+	0.909632i
$68$	−1.77767			−1.77767
$69$		0			0
$70$		0			0
$71$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$71$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$72$	−0.237662	−	0.520406i	−0.237662	−	0.520406i
$73$	0.0552004	+	0.0775182i	0.0552004	+	0.0775182i	0.841254	−	0.540641i	$-0.181818\pi$
$73$	0.0552004	+	0.0775182i	0.0552004	+	0.0775182i	−0.786053	+	0.618159i	$0.787879\pi$
$74$		0			0
$75$	0.428368	+	0.494363i	0.428368	+	0.494363i
$76$	1.91030	+	0.560914i	1.91030	+	0.560914i
$77$		0			0
$78$		0			0
$79$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$79$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$80$		0			0
$81$	−0.0846203	−	0.0543822i	−0.0846203	−	0.0543822i
$82$	1.84125	−	0.540641i	1.84125	−	0.540641i
$83$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i	−0.327068	−	0.945001i	$-0.606061\pi$
$83$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.273507	−	1.12741i	0.273507	−	1.12741i
$87$		0			0
$88$	1.30379	−	0.124497i	1.30379	−	0.124497i
$89$	−0.205996	−	1.43273i	−0.205996	−	1.43273i	−0.786053	−	0.618159i	$-0.787879\pi$
$89$	−0.205996	−	1.43273i	−0.205996	−	1.43273i	0.580057	−	0.814576i	$-0.303030\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.327068	+	0.566498i	0.327068	+	0.566498i
$97$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$97$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$98$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$99$	−0.588989	+	0.463186i	−0.588989	+	0.463186i
$100$	0.723734	+	0.690079i	0.723734	+	0.690079i
$101$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$101$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$102$	−0.914053	+	0.718819i	−0.914053	+	0.718819i
$103$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$103$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$107$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$108$	−0.914053	−	0.471227i	−0.914053	−	0.471227i
$109$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$109$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.95496	+	0.186677i	−1.95496	+	0.186677i	−0.995472	−	0.0950560i	$-0.969697\pi$
$113$	−1.95496	+	0.186677i	−1.95496	+	0.186677i	−0.959493	+	0.281733i	$0.909091\pi$
$114$	1.20906	−	0.484034i	1.20906	−	0.484034i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.95496	−	0.186677i	−1.95496	−	0.186677i
$119$		0			0
$120$		0			0
$121$	−0.233975	−	0.676026i	−0.233975	−	0.676026i
$122$		0			0
$123$	0.728132	−	1.02252i	0.728132	−	1.02252i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$127$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$128$	0.580057	+	0.814576i	0.580057	+	0.814576i
$129$	−0.315247	−	0.690294i	−0.315247	−	0.690294i
$130$		0			0
$131$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$131$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$132$	0.620049	−	0.591215i	0.620049	−	0.591215i
$133$		0			0
$134$	0.928368	+	0.371662i	0.928368	+	0.371662i
$135$		0			0
$136$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$137$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	0.235759	+	0.971812i	$0.424242\pi$
$137$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$139$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.531125	−	0.212630i	−0.531125	−	0.212630i
$145$		0			0
$146$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i
$147$	0.213947	+	0.618159i	0.213947	+	0.618159i
$148$		0			0
$149$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$149$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$150$	0.651174	+	0.0621796i	0.651174	+	0.0621796i
$151$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$151$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$152$	1.76962	−	0.912303i	1.76962	−	0.912303i
$153$	0.239771	−	0.988348i	0.239771	−	0.988348i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$157$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.0987706	+	0.0190365i	−0.0987706	+	0.0190365i
$163$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$163$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$164$	0.959493	−	1.66189i	0.959493	−	1.66189i
$165$		0			0
$166$	−0.653077	+	0.513585i	−0.653077	+	0.513585i
$167$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$167$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$168$		0			0
$169$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$170$		0			0
$171$	−0.569516	+	0.986430i	−0.569516	+	0.986430i
$172$	−0.580057	−	1.00469i	−0.580057	−	1.00469i
$173$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$173$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$174$		0			0
$175$		0			0
$176$	0.857685	−	0.989821i	0.857685	−	0.989821i
$177$	−1.08070	+	0.694523i	−1.08070	+	0.694523i
$178$	−1.13779	−	0.894765i	−1.13779	−	0.894765i
$179$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$179$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$180$		0			0
$181$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$181$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.95865	+	1.25875i	1.95865	+	1.25875i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$191$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$192$	0.627639	+	0.184291i	0.627639	+	0.184291i
$193$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$193$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$194$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i
$195$		0			0
$196$	0.415415	+	0.909632i	0.415415	+	0.909632i
$197$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$197$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$198$	−0.106636	+	0.741673i	−0.106636	+	0.741673i
$199$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$199$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$200$	1.00000			1.00000
$201$	0.627639	−	0.184291i	0.627639	−	0.184291i
$202$		0			0
$203$		0			0
$204$	−0.165489	+	1.15100i	−0.165489	+	1.15100i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.70760	−	1.97068i	−1.70760	−	1.97068i
$210$		0			0
$211$	1.34378	+	0.537970i	1.34378	+	0.537970i	0.928368	−	0.371662i	$-0.121212\pi$
$211$	1.34378	+	0.537970i	1.34378	+	0.537970i	0.415415	+	0.909632i	$0.363636\pi$
$212$		0			0
$213$		0			0
$214$	0.0930932	+	0.268975i	0.0930932	+	0.268975i
$215$		0			0
$216$	−0.986715	+	0.289726i	−0.986715	+	0.289726i
$217$		0			0
$218$		0			0
$219$	0.0553301	−	0.0285246i	0.0553301	−	0.0285246i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$223$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$224$		0			0
$225$	−0.481286	+	0.309304i	−0.481286	+	0.309304i
$226$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$227$	−0.419102	−	0.216062i	−0.419102	−	0.216062i	0.235759	−	0.971812i	$-0.424242\pi$
$227$	−0.419102	−	0.216062i	−0.419102	−	0.216062i	−0.654861	+	0.755750i	$0.727273\pi$
$228$	0.541015	−	1.18466i	0.541015	−	1.18466i
$229$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$229$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.786053	−	0.618159i	0.786053	−	0.618159i	−0.142315	−	0.989821i	$-0.545455\pi$
$233$	0.786053	−	0.618159i	0.786053	−	0.618159i	0.928368	+	0.371662i	$0.121212\pi$
$234$		0			0
$235$		0			0
$236$	−1.54370	+	1.21398i	−1.54370	+	1.21398i
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$		0			0
$241$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$241$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$242$	−0.635847	−	0.327802i	−0.635847	−	0.327802i
$243$	0.630351	−	0.727464i	0.630351	−	0.727464i
$244$		0			0
$245$		0			0
$246$	−0.178645	−	1.24250i	−0.178645	−	1.24250i
$247$		0			0
$248$		0			0
$249$	−0.128129	+	0.528156i	−0.128129	+	0.528156i
$250$		0			0
$251$	0.0224357	+	0.470984i	0.0224357	+	0.470984i	0.981929	+	0.189251i	$0.0606061\pi$
$251$	0.0224357	+	0.470984i	0.0224357	+	0.470984i	−0.959493	+	0.281733i	$0.909091\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.981929	+	0.189251i	0.981929	+	0.189251i
$257$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.0475819	−	0.998867i	$-0.484848\pi$
$257$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.928368	−	0.371662i	$-0.121212\pi$
$258$	−0.704513	−	0.282044i	−0.704513	−	0.282044i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.11312	−	1.56316i	−1.11312	−	1.56316i
$263$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$263$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$264$	0.0407651	−	0.855765i	0.0407651	−	0.855765i
$265$		0			0
$266$		0			0
$267$	−0.946841			−0.946841
$268$	0.928368	−	0.371662i	0.928368	−	0.371662i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$271$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$272$	−0.0845850	+	1.77566i	−0.0845850	+	1.77566i
$273$		0			0
$274$	1.07701	+	1.51245i	1.07701	+	1.51245i
$275$	−0.308779	−	1.27280i	−0.308779	−	1.27280i
$276$		0			0
$277$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$277$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$278$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$279$		0			0
$280$		0			0
$281$	0.581419	+	1.67990i	0.581419	+	1.67990i	0.723734	+	0.690079i	$0.242424\pi$
$281$	0.581419	+	1.67990i	0.581419	+	1.67990i	−0.142315	+	0.989821i	$0.545455\pi$
$282$		0			0
$283$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$283$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.531125	+	0.212630i	−0.531125	+	0.212630i
$289$	−2.15033	+	0.205332i	−2.15033	+	0.205332i
$290$		0			0
$291$	0.0489319	+	0.0384804i	0.0489319	+	0.0384804i
$292$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$293$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$293$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$294$	0.581419	+	0.299742i	0.581419	+	0.299742i
$295$		0			0
$296$		0			0
$297$	0.673440	+	1.16643i	0.673440	+	1.16643i
$298$		0			0
$299$		0			0
$300$	0.514186	−	0.404360i	0.514186	−	0.404360i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.651174	−	1.88144i	0.651174	−	1.88144i
$305$		0			0
$306$	−0.508508	−	0.880762i	−0.508508	−	0.880762i
$307$	1.13915	−	0.219553i	1.13915	−	0.219553i	0.415415	−	0.909632i	$-0.363636\pi$
$307$	1.13915	−	0.219553i	1.13915	−	0.219553i	0.723734	+	0.690079i	$0.242424\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$311$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$312$		0			0
$313$	0.283341	+	1.97068i	0.283341	+	1.97068i	0.235759	+	0.971812i	$0.424242\pi$
$313$	0.283341	+	1.97068i	0.283341	+	1.97068i	0.0475819	+	0.998867i	$0.484848\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$317$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.156630	+	0.100660i	0.156630	+	0.100660i
$322$		0			0
$323$	3.47528	+	0.669806i	3.47528	+	0.669806i
$324$	−0.0583469	+	0.0819368i	−0.0583469	+	0.0819368i
$325$		0			0
$326$	−0.452418	−	0.132842i	−0.452418	−	0.132842i
$327$		0			0
$328$	−0.452418	−	1.86489i	−0.452418	−	1.86489i
$329$		0			0
$330$		0			0
$331$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i	0.0475819	+	0.998867i	$0.484848\pi$
$331$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i	−0.142315	+	0.989821i	$0.545455\pi$
$332$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.21769	−	1.16106i	1.21769	−	1.16106i	0.235759	−	0.971812i	$-0.424242\pi$
$337$	1.21769	−	1.16106i	1.21769	−	1.16106i	0.981929	−	0.189251i	$-0.0606061\pi$
$338$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$339$	−0.0611251	+	1.28317i	−0.0611251	+	1.28317i
$340$		0			0
$341$		0			0
$342$	0.268537	+	1.10692i	0.268537	+	1.10692i
$343$		0			0
$344$	−1.11312	−	0.326842i	−1.11312	−	0.326842i
$345$		0			0
$346$		0			0
$347$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.327068	−	0.945001i	$-0.606061\pi$
$347$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.654861	+	0.755750i	$0.727273\pi$
$348$		0			0
$349$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$349$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$350$		0			0
$351$		0			0
$352$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i
$353$	0.252989	−	0.130425i	0.252989	−	0.130425i	−0.327068	−	0.945001i	$-0.606061\pi$
$353$	0.252989	−	0.130425i	0.252989	−	0.130425i	0.580057	+	0.814576i	$0.303030\pi$
$354$	−0.302863	+	1.24842i	−0.302863	+	1.24842i
$355$		0			0
$356$	−1.44091	+	0.137591i	−1.44091	+	0.137591i
$357$		0			0
$358$	−0.653077	−	0.513585i	−0.653077	−	0.513585i
$359$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$359$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$360$		0			0
$361$	−2.63438	−	1.35812i	−2.63438	−	1.35812i
$362$		0			0
$363$	−0.459493	+	0.0885600i	−0.459493	+	0.0885600i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$367$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$368$		0			0
$369$	0.794561	+	0.757613i	0.794561	+	0.757613i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$	2.28618	−	0.440625i	2.28618	−	0.440625i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.50842	+	1.18624i	1.50842	+	1.18624i	0.928368	+	0.371662i	$0.121212\pi$
$379$	1.50842	+	1.18624i	1.50842	+	1.18624i	0.580057	+	0.814576i	$0.303030\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$383$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$384$	0.581419	−	0.299742i	0.581419	−	0.299742i
$385$		0			0
$386$	−1.67489	−	0.159932i	−1.67489	−	0.159932i
$387$	0.636823	−	0.186988i	0.636823	−	0.186988i
$388$	0.0800569	+	0.0514495i	0.0800569	+	0.0514495i
$389$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$389$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$390$		0			0
$391$		0			0
$392$	0.928368	+	0.371662i	0.928368	+	0.371662i
$393$	−1.20443	−	0.353653i	−1.20443	−	0.353653i
$394$		0			0
$395$		0			0
$396$	0.434637	+	0.610362i	0.434637	+	0.610362i
$397$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$397$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$398$		0			0
$399$		0			0
$400$	0.723734	−	0.690079i	0.723734	−	0.690079i
$401$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$401$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$402$	0.327068	−	0.566498i	0.327068	−	0.566498i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.674512	+	0.947220i	0.674512	+	0.947220i
$409$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	0.928368	−	0.371662i	$-0.121212\pi$
$409$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	−0.995472	+	0.0950560i	$0.969697\pi$
$410$		0			0
$411$	1.16536	+	0.342180i	1.16536	+	0.342180i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.627639	+	0.184291i	−0.627639	+	0.184291i
$418$	−2.59577	−	0.247866i	−2.59577	−	0.247866i
$419$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i	1.00000			$0$
$419$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i	−0.995472	+	0.0950560i	$0.969697\pi$
$420$		0			0
$421$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$421$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$422$	1.34378	−	0.537970i	1.34378	−	0.537970i
$423$		0			0
$424$		0			0
$425$	1.39734	+	1.09888i	1.39734	+	1.09888i
$426$		0			0
$427$		0			0
$428$	0.252989	+	0.130425i	0.252989	+	0.130425i
$429$		0			0
$430$		0			0
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−0.514186	+	0.890596i	−0.514186	+	0.890596i
$433$	−0.607279	+	1.75462i	−0.607279	+	1.75462i	0.0475819	+	0.998867i	$0.484848\pi$
$433$	−0.607279	+	1.75462i	−0.607279	+	1.75462i	−0.654861	+	0.755750i	$0.727273\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.0203600	−	0.0588264i	0.0203600	−	0.0588264i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−0.561767	+	0.108272i	−0.561767	+	0.108272i
$442$		0			0
$443$	1.58006	+	0.814576i	1.58006	+	0.814576i	1.00000			$0$
$443$	1.58006	+	0.814576i	1.58006	+	0.814576i	0.580057	+	0.814576i	$0.303030\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.888835	−	0.458227i	$-0.848485\pi$
$449$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.327068	+	0.945001i	$0.606061\pi$
$450$	−0.134879	+	0.555979i	−0.134879	+	0.555979i
$451$	−2.23394	+	1.15168i	−2.23394	+	1.15168i
$452$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$453$		0			0
$454$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$455$		0			0
$456$	−0.425956	−	1.23072i	−0.425956	−	1.23072i
$457$	1.42131	+	0.273935i	1.42131	+	0.273935i	0.841254	−	0.540641i	$-0.181818\pi$
$457$	1.42131	+	0.273935i	1.42131	+	0.273935i	0.580057	+	0.814576i	$0.303030\pi$
$458$		0			0
$459$	−1.69715	−	0.679438i	−1.69715	−	0.679438i
$460$		0			0
$461$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$461$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$462$		0			0
$463$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$463$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$464$		0			0
$465$		0			0
$466$	0.142315	−	0.989821i	0.142315	−	0.989821i
$467$	−0.947890	+	0.903811i	−0.947890	+	0.903811i	−0.995472	−	0.0950560i	$-0.969697\pi$
$467$	−0.947890	+	0.903811i	−0.947890	+	0.903811i	0.0475819	+	0.998867i	$0.484848\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.279486	+	1.94387i	−0.279486	+	1.94387i
$473$	−0.0722972	+	1.51770i	−0.0722972	+	1.51770i
$474$		0			0
$475$	−1.15486	−	1.62177i	−1.15486	−	1.62177i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$479$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$480$		0			0
$481$		0			0
$482$	−0.271738	−	0.785135i	−0.271738	−	0.785135i
$483$		0			0
$484$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$485$		0			0
$486$	−0.0458011	−	0.961482i	−0.0458011	−	0.961482i
$487$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$487$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$488$		0			0
$489$	−0.286343	+	0.114634i	−0.286343	+	0.114634i
$490$		0			0
$491$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$491$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$492$	−0.986715	−	0.775961i	−0.986715	−	0.775961i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.271738	+	0.470664i	0.271738	+	0.470664i
$499$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$499$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$500$		0			0
$501$		0			0
$502$	0.341254	+	0.325385i	0.341254	+	0.325385i
$503$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$503$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.327068	+	0.566498i	0.327068	+	0.566498i
$508$		0			0
$509$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$509$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$510$		0			0
$511$		0			0
$512$	0.841254	−	0.540641i	0.841254	−	0.540641i
$513$	1.60939	+	1.26564i	1.60939	+	1.26564i
$514$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$515$		0			0
$516$	−0.704513	+	0.282044i	−0.704513	+	0.282044i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.580057	−	0.814576i	$-0.303030\pi$
$521$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.928368	+	0.371662i	$0.121212\pi$
$522$		0			0
$523$	−0.607279	−	1.75462i	−0.607279	−	1.75462i	−0.654861	−	0.755750i	$-0.727273\pi$
$523$	−0.607279	−	1.75462i	−0.607279	−	1.75462i	0.0475819	−	0.998867i	$-0.484848\pi$
$524$	−1.88431	−	0.363170i	−1.88431	−	0.363170i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.561043	−	0.647478i	−0.561043	−	0.647478i
$529$	0.235759	+	0.971812i	0.235759	+	0.971812i
$530$		0			0
$531$	−0.466733	−	1.02200i	−0.466733	−	1.02200i
$532$		0			0
$533$		0			0
$534$	−0.685261	+	0.653395i	−0.685261	+	0.653395i
$535$		0			0
$536$	0.415415	−	0.909632i	0.415415	−	0.909632i
$537$	−0.543476			−0.543476
$538$		0			0
$539$	0.186393	−	1.29639i	0.186393	−	1.29639i
$540$		0			0
$541$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$541$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$542$		0			0
$543$		0			0
$544$	1.16413	+	1.34347i	1.16413	+	1.34347i
$545$		0			0
$546$		0			0
$547$	0.481929	−	0.676774i	0.481929	−	0.676774i	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	0.481929	−	0.676774i	0.481929	−	0.676774i	0.981929	+	0.189251i	$0.0606061\pi$
$548$	1.82318	+	0.351390i	1.82318	+	0.351390i
$549$		0			0
$550$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$557$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$557$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.997349	−	1.15100i	0.997349	−	1.15100i
$562$	1.58006	+	0.814576i	1.58006	+	0.814576i
$563$	−0.653077	+	1.43004i	−0.653077	+	1.43004i	0.235759	+	0.971812i	$0.424242\pi$
$563$	−0.653077	+	1.43004i	−0.653077	+	1.43004i	−0.888835	+	0.458227i	$0.848485\pi$
$564$		0			0
$565$		0			0
$566$	0.500000	−	0.866025i	0.500000	−	0.866025i
$567$		0			0
$568$		0			0
$569$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i	0.723734	−	0.690079i	$-0.242424\pi$
$569$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i	−0.654861	+	0.755750i	$0.727273\pi$
$570$		0			0
$571$	1.39734	−	1.09888i	1.39734	−	1.09888i	0.415415	−	0.909632i	$-0.363636\pi$
$571$	1.39734	−	1.09888i	1.39734	−	1.09888i	0.981929	−	0.189251i	$-0.0606061\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.237662	+	0.520406i	−0.237662	+	0.520406i
$577$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.327068	−	0.945001i	$-0.606061\pi$
$577$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.959493	+	0.281733i	$0.909091\pi$
$578$	−1.41457	+	1.63251i	−1.41457	+	1.63251i
$579$	−0.925874	+	0.595023i	−0.925874	+	0.595023i
$580$		0			0
$581$		0			0
$582$	0.0619682	−	0.00591725i	0.0619682	−	0.00591725i
$583$		0			0
$584$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$585$		0			0
$586$		0			0
$587$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i	0.0475819	−	0.998867i	$-0.484848\pi$
$587$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i	−0.142315	+	0.989821i	$0.545455\pi$
$588$	0.627639	−	0.184291i	0.627639	−	0.184291i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	0.415415	−	0.909632i	$-0.363636\pi$
$593$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	−0.327068	+	0.945001i	$0.606061\pi$
$594$	1.29232	+	0.379460i	1.29232	+	0.379460i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$599$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$600$	0.0930932	−	0.647478i	0.0930932	−	0.647478i
$601$	0.341254	−	0.325385i	0.341254	−	0.325385i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	0.341254	−	0.325385i	0.341254	−	0.325385i	0.841254	+	0.540641i	$0.181818\pi$
$602$		0			0
$603$	0.0814192	+	0.566283i	0.0814192	+	0.566283i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$607$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$608$	−0.827068	−	1.81103i	−0.827068	−	1.81103i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.975820	−	0.286527i	−0.975820	−	0.286527i
$613$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$613$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$614$	0.672932	−	0.945001i	0.672932	−	0.945001i
$615$		0			0
$616$		0			0
$617$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$617$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$618$		0			0
$619$	−1.84833	−	0.176494i	−1.84833	−	0.176494i	−0.888835	−	0.458227i	$-0.848485\pi$
$619$	−1.84833	−	0.176494i	−1.84833	−	0.176494i	−0.959493	+	0.281733i	$0.909091\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$626$	1.56499	+	1.23072i	1.56499	+	1.23072i
$627$	−1.43494	+	0.922178i	−1.43494	+	0.922178i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$631$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$632$		0			0
$633$	0.473420	−	0.819988i	0.473420	−	0.819988i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$641$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$642$	0.182822	−	0.0352360i	0.182822	−	0.0352360i
$643$	0.815816	−	1.78639i	0.815816	−	1.78639i	0.235759	−	0.971812i	$-0.424242\pi$
$643$	0.815816	−	1.78639i	0.815816	−	1.78639i	0.580057	−	0.814576i	$-0.303030\pi$
$644$		0			0
$645$		0			0
$646$	2.97740	−	1.91346i	2.97740	−	1.91346i
$647$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$647$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$648$	0.0143152	+	0.0995645i	0.0143152	+	0.0995645i
$649$	2.56046	−	0.244494i	2.56046	−	0.244494i
$650$		0			0
$651$		0			0
$652$	−0.419102	+	0.216062i	−0.419102	+	0.216062i
$653$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$653$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$654$		0			0
$655$		0			0
$656$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$657$	0.0178068	+	0.0514495i	0.0178068	+	0.0514495i
$658$		0			0
$659$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	−0.995472	−	0.0950560i	$-0.969697\pi$
$659$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	0.415415	+	0.909632i	$0.363636\pi$
$660$		0			0
$661$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$661$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$662$	1.30379	+	1.50465i	1.30379	+	1.50465i
$663$		0			0
$664$	0.481929	+	0.676774i	0.481929	+	0.676774i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.223734	−	1.55610i	0.223734	−	1.55610i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.223734	−	1.55610i	0.223734	−	1.55610i	0.723734	−	0.690079i	$-0.242424\pi$
$674$	0.0800569	−	1.68060i	0.0800569	−	1.68060i
$675$	0.427201	+	0.935439i	0.427201	+	0.935439i
$676$	0.580057	+	0.814576i	0.580057	+	0.814576i
$677$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$677$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$678$	0.841254	+	0.970858i	0.841254	+	0.970858i
$679$		0			0
$680$		0			0
$681$	−0.178911	+	0.251245i	−0.178911	+	0.251245i
$682$		0			0
$683$	−0.607279	−	1.75462i	−0.607279	−	1.75462i	−0.654861	−	0.755750i	$-0.727273\pi$
$683$	−0.607279	−	1.75462i	−0.607279	−	1.75462i	0.0475819	−	0.998867i	$-0.484848\pi$
$684$	0.958214	+	0.615807i	0.958214	+	0.615807i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.03115	+	0.531595i	−1.03115	+	0.531595i
$689$		0			0
$690$		0			0
$691$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.0475819	−	0.998867i	$-0.484848\pi$
$691$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.235759	+	0.971812i	$0.424242\pi$
$692$		0			0
$693$		0			0
$694$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$695$		0			0
$696$		0			0
$697$	1.41712	−	3.10305i	1.41712	−	3.10305i
$698$		0			0
$699$	−0.327068	−	0.566498i	−0.327068	−	0.566498i
$700$		0			0
$701$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$701$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$702$		0			0
$703$		0			0
$704$	−0.947890	−	0.903811i	−0.947890	−	0.903811i
$705$		0			0
$706$	0.0930932	−	0.268975i	0.0930932	−	0.268975i
$707$		0			0
$708$	0.642315	+	1.11252i	0.642315	+	1.11252i
$709$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$709$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$710$		0			0
$711$		0			0
$712$	−0.947890	+	1.09392i	−0.947890	+	1.09392i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i
$717$		0			0
$718$		0			0
$719$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$719$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$720$		0			0
$721$		0			0
$722$	−2.84380	+	0.835015i	−2.84380	+	0.835015i
$723$	−0.457201	−	0.293825i	−0.457201	−	0.293825i
$724$		0			0
$725$		0			0
$726$	−0.271437	+	0.381180i	−0.271437	+	0.381180i
$727$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$727$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$728$		0			0
$729$	−0.478207	−	0.551880i	−0.478207	−	0.551880i
$730$		0			0
$731$	−1.19625	−	1.67990i	−1.19625	−	1.67990i
$732$		0			0
$733$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$733$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.28605	−	0.247866i	−1.28605	−	0.247866i
$738$	1.09786			1.09786
$739$	1.42131	−	1.35522i	1.42131	−	1.35522i	0.580057	−	0.814576i	$-0.303030\pi$
$739$	1.42131	−	1.35522i	1.42131	−	1.35522i	0.841254	−	0.540641i	$-0.181818\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$743$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.441275	−	0.176660i	−0.441275	−	0.176660i
$748$	1.35052	−	1.89654i	1.35052	−	1.89654i
$749$		0			0
$750$		0			0
$751$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$751$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$752$		0			0
$753$	0.307040	+	0.0293188i	0.307040	+	0.0293188i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$757$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$758$	1.91030	−	0.182411i	1.91030	−	0.182411i
$759$		0			0
$760$		0			0
$761$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$761$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.213947	−	0.618159i	0.213947	−	0.618159i
$769$	−0.370638	+	0.291473i	−0.370638	+	0.291473i	−0.786053	−	0.618159i	$-0.787879\pi$
$769$	−0.370638	+	0.291473i	−0.370638	+	0.291473i	0.415415	+	0.909632i	$0.363636\pi$
$770$		0			0
$771$	−0.796533	−	0.759493i	−0.796533	−	0.759493i
$772$	−1.32254	+	1.04006i	−1.32254	+	1.04006i
$773$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$773$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$774$	0.331854	−	0.574788i	0.331854	−	0.574788i
$775$		0			0
$776$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i
$777$		0			0
$778$		0			0
$779$	−2.50196	+	2.88741i	−2.50196	+	2.88741i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.928368	−	0.371662i	0.928368	−	0.371662i
$785$		0			0
$786$	−1.11574	+	0.575202i	−1.11574	+	0.575202i
$787$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	−0.995472	−	0.0950560i	$-0.969697\pi$
$787$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	0.981929	−	0.189251i	$-0.0606061\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.735759	+	0.141806i	0.735759	+	0.141806i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$797$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$798$		0			0
$799$		0			0
$800$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$801$	0.117852	−	0.819677i	0.117852	−	0.819677i
$802$	1.21769	−	1.16106i	1.21769	−	1.16106i
$803$	−0.124638			−0.124638
$804$	−0.154218	−	0.635697i	−0.154218	−	0.635697i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$809$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$810$		0			0
$811$	0.195876	+	0.807410i	0.195876	+	0.807410i	0.981929	+	0.189251i	$0.0606061\pi$
$811$	0.195876	+	0.807410i	0.195876	+	0.807410i	−0.786053	+	0.618159i	$0.787879\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.14182	+	0.220069i	1.14182	+	0.220069i
$817$	0.755436	+	2.18269i	0.755436	+	2.18269i
$818$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$819$		0			0
$820$		0			0
$821$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$821$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$822$	1.07954	−	0.556543i	1.07954	−	0.556543i
$823$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$823$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$824$		0			0
$825$	−0.852856	+	0.0814379i	−0.852856	+	0.0814379i
$826$		0			0
$827$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$827$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$828$		0			0
$829$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$829$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.888835	+	1.53951i	0.888835	+	1.53951i
$834$	−0.327068	+	0.566498i	−0.327068	+	0.566498i
$835$		0			0
$836$	−2.04970	+	1.61190i	−2.04970	+	1.61190i
$837$		0			0
$838$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i
$839$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$839$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$840$		0			0
$841$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$842$		0			0
$843$	1.14182	−	0.220069i	1.14182	−	0.220069i
$844$	0.601300	−	1.31666i	0.601300	−	1.31666i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0930932	−	0.647478i	−0.0930932	−	0.647478i
$850$	1.76962	−	0.168978i	1.76962	−	0.168978i
$851$		0			0
$852$		0			0
$853$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$853$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$854$		0			0
$855$		0			0
$856$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$857$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$857$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$858$		0			0
$859$	−1.74555	−	0.336426i	−1.74555	−	0.336426i	−0.786053	−	0.618159i	$-0.787879\pi$
$859$	−1.74555	−	0.336426i	−1.74555	−	0.336426i	−0.959493	+	0.281733i	$0.909091\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$863$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$864$	0.242448	+	0.999383i	0.242448	+	0.999383i
$865$		0			0
$866$	0.771316	+	1.68895i	0.771316	+	1.68895i
$867$	−0.0672336	+	1.41141i	−0.0672336	+	1.41141i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0394028	+	0.0375705i	−0.0394028	+	0.0375705i
$874$		0			0
$875$		0			0
$876$	−0.0258596	−	0.0566247i	−0.0258596	−	0.0566247i
$877$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$877$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.327068	−	0.945001i	$-0.606061\pi$
$881$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.888835	+	0.458227i	$0.848485\pi$
$882$	−0.331854	+	0.466024i	−0.331854	+	0.466024i
$883$	−1.88431	−	0.363170i	−1.88431	−	0.363170i	−0.888835	−	0.458227i	$-0.848485\pi$
$883$	−1.88431	−	0.363170i	−1.88431	−	0.363170i	−0.995472	+	0.0950560i	$0.969697\pi$
$884$		0			0
$885$		0			0
$886$	1.70566	−	0.500828i	1.70566	−	0.500828i
$887$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$887$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.122306	−	0.0489638i	0.122306	−	0.0489638i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$899$		0			0
$900$	0.286053	+	0.495458i	0.286053	+	0.495458i
$901$		0			0
$902$	−0.822032	+	2.37511i	−0.822032	+	2.37511i
$903$		0			0
$904$	1.42131	+	1.35522i	1.42131	+	1.35522i
$905$		0			0
$906$		0			0
$907$	−0.550294	+	1.58997i	−0.550294	+	1.58997i	0.235759	+	0.971812i	$0.424242\pi$
$907$	−0.550294	+	1.58997i	−0.550294	+	1.58997i	−0.786053	+	0.618159i	$0.787879\pi$
$908$	−0.235759	+	0.408346i	−0.235759	+	0.408346i
$909$		0			0
$910$		0			0
$911$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$911$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$912$	−1.15757	−	0.596770i	−1.15757	−	0.596770i
$913$	0.712591	−	0.822373i	0.712591	−	0.822373i
$914$	1.21769	−	0.782560i	1.21769	−	0.782560i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.69715	+	0.679438i	−1.69715	+	0.679438i
$919$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$919$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$920$		0			0
$921$	−0.0361086	−	0.758013i	−0.0361086	−	0.758013i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.50842	+	0.442913i	1.50842	+	0.442913i	0.928368	−	0.371662i	$-0.121212\pi$
$929$	1.50842	+	0.442913i	1.50842	+	0.442913i	0.580057	+	0.814576i	$0.303030\pi$
$930$		0			0
$931$	−0.469383	−	1.93482i	−0.469383	−	1.93482i
$932$	−0.580057	−	0.814576i	−0.580057	−	0.814576i
$933$		0			0
$934$	−0.0623191	+	1.30824i	−0.0623191	+	1.30824i
$935$		0			0
$936$		0			0
$937$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$937$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$938$		0			0
$939$	1.30235			1.30235
$940$		0			0
$941$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$941$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$942$		0			0
$943$		0			0
$944$	1.13915	+	1.59971i	1.13915	+	1.59971i
$945$		0			0
$946$	0.995012	+	1.14831i	0.995012	+	1.14831i
$947$	−1.38884	−	0.407799i	−1.38884	−	0.407799i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	−1.38884	−	0.407799i	−1.38884	−	0.407799i	−0.888835	+	0.458227i	$0.848485\pi$
$948$		0			0
$949$		0			0
$950$	−1.95496	−	0.376789i	−1.95496	−	0.376789i
$951$		0			0
$952$		0			0
$953$	−1.11312	+	0.326842i	−1.11312	+	0.326842i	−0.786053	−	0.618159i	$-0.787879\pi$
$953$	−1.11312	+	0.326842i	−1.11312	+	0.326842i	−0.327068	+	0.945001i	$0.606061\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$962$		0			0
$963$	−0.106636	+	0.123065i	−0.106636	+	0.123065i
$964$	−0.738471	−	0.380708i	−0.738471	−	0.380708i
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.357685	+	0.619529i	−0.357685	+	0.619529i
$969$	0.757210	−	2.18781i	0.757210	−	2.18781i
$970$		0			0
$971$	0.839614	+	0.800570i	0.839614	+	0.800570i	0.981929	−	0.189251i	$-0.0606061\pi$
$971$	0.839614	+	0.800570i	0.839614	+	0.800570i	−0.142315	+	0.989821i	$0.545455\pi$
$972$	−0.696647	−	0.664251i	−0.696647	−	0.664251i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.235759	−	0.971812i	$-0.424242\pi$
$977$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.580057	+	0.814576i	$0.303030\pi$
$978$	−0.128129	+	0.280564i	−0.128129	+	0.280564i
$979$	1.68504	+	0.868697i	1.68504	+	0.868697i
$980$		0			0
$981$		0			0
$982$	0.786053	+	0.618159i	0.786053	+	0.618159i
$983$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$983$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$984$	−1.24959	+	0.119322i	−1.24959	+	0.119322i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$991$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$992$		0			0
$993$	1.27881	+	0.246471i	1.27881	+	0.246471i
$994$		0			0
$995$		0			0
$996$	0.521461	+	0.153115i	0.521461	+	0.153115i
$997$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$997$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$998$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.1.ba.a.315.1	yes	20
4.3	odd	2		2144.1.bu.a.47.1		20
8.3	odd	2	CM	536.1.ba.a.315.1	yes	20
8.5	even	2		2144.1.bu.a.47.1		20
67.10	even	33	inner	536.1.ba.a.211.1	✓	20
268.211	odd	66		2144.1.bu.a.1551.1		20
536.77	even	66		2144.1.bu.a.1551.1		20
536.211	odd	66	inner	536.1.ba.a.211.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.1.ba.a.211.1	✓	20	67.10	even	33	inner
536.1.ba.a.211.1	✓	20	536.211	odd	66	inner
536.1.ba.a.315.1	yes	20	1.1	even	1	trivial
536.1.ba.a.315.1	yes	20	8.3	odd	2	CM
2144.1.bu.a.47.1		20	4.3	odd	2
2144.1.bu.a.47.1		20	8.5	even	2
2144.1.bu.a.1551.1		20	268.211	odd	66
2144.1.bu.a.1551.1		20	536.77	even	66

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:	\( N \)	\(=\)	\( 536 = 2^{3} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	536.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.723734 - 0.690079i) q^{2} +(0.0930932 - 0.647478i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.379436 - 0.532843i) q^{6} +(-0.654861 - 0.755750i) q^{8} +(0.548932 + 0.161181i) q^{9} +O(q^{10})\)	\(q+(0.723734 - 0.690079i) q^{2} +(0.0930932 - 0.647478i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.379436 - 0.532843i) q^{6} +(-0.654861 - 0.755750i) q^{8} +(0.548932 + 0.161181i) q^{9} +(-0.759713 + 1.06687i) q^{11} +(-0.642315 - 0.123796i) q^{12} +(-0.995472 - 0.0950560i) q^{16} +(-0.0845850 - 1.77566i) q^{17} +(0.508508 - 0.262154i) q^{18} +(-0.469383 + 1.93482i) q^{19} +(0.186393 + 1.29639i) q^{22} +(-0.550294 + 0.353653i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(0.427201 - 0.935439i) q^{27} +(-0.786053 + 0.618159i) q^{32} +(0.620049 + 0.591215i) q^{33} +(-1.28656 - 1.22673i) q^{34} +(0.187118 - 0.540641i) q^{36} +(0.995472 + 1.72421i) q^{38} +(1.70566 + 0.879330i) q^{41} +(0.975950 - 0.627205i) q^{43} +(1.02951 + 0.809616i) q^{44} +(-0.154218 + 0.635697i) q^{48} +(-0.888835 + 0.458227i) q^{49} +(0.0475819 + 0.998867i) q^{50} +(-1.15757 - 0.110535i) q^{51} +(-0.336347 - 0.971812i) q^{54} +(1.20906 + 0.484034i) q^{57} +(-1.28605 - 1.48418i) q^{59} +(-0.142315 + 0.989821i) q^{64} +0.856736 q^{66} +(0.415415 + 0.909632i) q^{67} -1.77767 q^{68} +(-0.237662 - 0.520406i) q^{72} +(0.0552004 + 0.0775182i) q^{73} +(0.428368 + 0.494363i) q^{75} +(1.91030 + 0.560914i) q^{76} +(-0.0846203 - 0.0543822i) q^{81} +(1.84125 - 0.540641i) q^{82} +(-0.827068 - 0.0789754i) q^{83} +(0.273507 - 1.12741i) q^{86} +(1.30379 - 0.124497i) q^{88} +(-0.205996 - 1.43273i) q^{89} +(0.327068 + 0.566498i) q^{96} +(-0.0475819 + 0.0824143i) q^{97} +(-0.327068 + 0.945001i) q^{98} +(-0.588989 + 0.463186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8}+O(q^{10}) \) 20 * q + q^2 + 2 * q^3 + q^4 - q^6 - 2 * q^8	\( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8} + 2 q^{11} - 12 q^{12} + q^{16} - 12 q^{17} - q^{19} - 4 q^{22} + 2 q^{24} - 2 q^{25} - 2 q^{27} + q^{32} - 2 q^{33} - q^{34} - q^{38} + 2 q^{41} + 2 q^{43} + 2 q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23 q^{54} + q^{57} - 9 q^{59} - 2 q^{64} - 18 q^{66} - 2 q^{67} + 2 q^{68} - q^{73} - 9 q^{75} + 2 q^{76} + 2 q^{81} + 18 q^{82} - 9 q^{83} - q^{86} + 2 q^{88} + 2 q^{89} - q^{96} - q^{97} + q^{98}+O(q^{100}) \) 20 * q + q^2 + 2 * q^3 + q^4 - q^6 - 2 * q^8 + 2 * q^11 - 12 * q^12 + q^16 - 12 * q^17 - q^19 - 4 * q^22 + 2 * q^24 - 2 * q^25 - 2 * q^27 + q^32 - 2 * q^33 - q^34 - q^38 + 2 * q^41 + 2 * q^43 + 2 * q^44 - q^48 + q^49 + q^50 + q^51 + 23 * q^54 + q^57 - 9 * q^59 - 2 * q^64 - 18 * q^66 - 2 * q^67 + 2 * q^68 - q^73 - 9 * q^75 + 2 * q^76 + 2 * q^81 + 18 * q^82 - 9 * q^83 - q^86 + 2 * q^88 + 2 * q^89 - q^96 - q^97 + q^98

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