LMFDB - Embedded newform 536.1.ba.a.475.1

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			475.1
Root			$0.981929 - 0.189251i$ of defining polynomial
Character	$\chi$	$=$	536.475
Dual form			536.1.ba.a.123.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(0.0395325 - 0.0865641i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.0688733 + 0.0656706i) q^{6} +(0.841254 - 0.540641i) q^{8} +(0.648930 + 0.748905i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(0.0395325 - 0.0865641i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.0688733 + 0.0656706i) q^{6} +(0.841254 - 0.540641i) q^{8} +(0.648930 + 0.748905i) q^{9} +(1.21769 - 1.16106i) q^{11} +(-0.0845850 + 0.0436066i) q^{12} +(0.235759 + 0.971812i) q^{16} +(-1.45949 + 1.14776i) q^{17} +(-0.919960 + 0.368297i) q^{18} +(0.462997 + 0.0892353i) q^{19} +(0.698939 + 1.53046i) q^{22} +(-0.0135432 - 0.0941952i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.181791 - 0.0533787i) q^{27} +(-0.995472 - 0.0950560i) q^{32} +(-0.0523681 - 0.151308i) q^{33} +(-0.607279 - 1.75462i) q^{34} +(-0.0471510 - 0.989821i) q^{36} +(-0.235759 + 0.408346i) q^{38} +(-1.21590 - 0.486774i) q^{41} +(-0.205996 - 1.43273i) q^{43} +(-1.67489 + 0.159932i) q^{44} +(0.0934441 + 0.0180099i) q^{48} +(0.928368 - 0.371662i) q^{49} +(-0.786053 + 0.618159i) q^{50} +(0.0416572 + 0.171713i) q^{51} +(-0.00901515 + 0.189251i) q^{54} +(0.0260280 - 0.0365512i) q^{57} +(-1.49547 + 0.961081i) q^{59} +(0.415415 - 0.909632i) q^{64} +0.160114 q^{66} +(-0.959493 - 0.281733i) q^{67} +1.85674 q^{68} +(0.950804 + 0.279181i) q^{72} +(-1.13779 - 1.08488i) q^{73} +(0.0800569 - 0.0514495i) q^{75} +(-0.308779 - 0.356349i) q^{76} +(-0.138460 + 0.963011i) q^{81} +(0.857685 - 0.989821i) q^{82} +(-0.452418 - 1.86489i) q^{83} +(1.42131 + 0.273935i) q^{86} +(0.396666 - 1.63508i) q^{88} +(-0.271738 - 0.595023i) q^{89} +(-0.0475819 + 0.0824143i) q^{96} +(0.786053 + 1.36148i) q^{97} +(0.0475819 + 0.998867i) q^{98} +(1.65972 + 0.158484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{20}{33}\right)$

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 $

$2$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$2$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$3$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i	−0.888835	−	0.458227i	$-0.848485\pi$
$3$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i	0.928368	+	0.371662i	$0.121212\pi$
$4$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$5$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$5$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$6$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i
$7$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$7$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$8$	0.841254	−	0.540641i	0.841254	−	0.540641i
$9$	0.648930	+	0.748905i	0.648930	+	0.748905i
$10$		0			0
$11$	1.21769	−	1.16106i	1.21769	−	1.16106i	0.235759	−	0.971812i	$-0.424242\pi$
$11$	1.21769	−	1.16106i	1.21769	−	1.16106i	0.981929	−	0.189251i	$-0.0606061\pi$
$12$	−0.0845850	+	0.0436066i	−0.0845850	+	0.0436066i
$13$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$13$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$14$		0			0
$15$		0			0
$16$	0.235759	+	0.971812i	0.235759	+	0.971812i
$17$	−1.45949	+	1.14776i	−1.45949	+	1.14776i	−0.500000	+	0.866025i	$0.666667\pi$
$17$	−1.45949	+	1.14776i	−1.45949	+	1.14776i	−0.959493	+	0.281733i	$0.909091\pi$
$18$	−0.919960	+	0.368297i	−0.919960	+	0.368297i
$19$	0.462997	+	0.0892353i	0.462997	+	0.0892353i	0.415415	−	0.909632i	$-0.363636\pi$
$19$	0.462997	+	0.0892353i	0.462997	+	0.0892353i	0.0475819	+	0.998867i	$0.484848\pi$
$20$		0			0
$21$		0			0
$22$	0.698939	+	1.53046i	0.698939	+	1.53046i
$23$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$23$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$24$	−0.0135432	−	0.0941952i	−0.0135432	−	0.0941952i
$25$	0.841254	+	0.540641i	0.841254	+	0.540641i
$26$		0			0
$27$	0.181791	−	0.0533787i	0.181791	−	0.0533787i
$28$		0			0
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$31$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$32$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$33$	−0.0523681	−	0.151308i	−0.0523681	−	0.151308i
$34$	−0.607279	−	1.75462i	−0.607279	−	1.75462i
$35$		0			0
$36$	−0.0471510	−	0.989821i	−0.0471510	−	0.989821i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	−0.235759	+	0.408346i	−0.235759	+	0.408346i
$39$		0			0
$40$		0			0
$41$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.327068	−	0.945001i	$-0.606061\pi$
$41$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.888835	+	0.458227i	$0.848485\pi$
$42$		0			0
$43$	−0.205996	−	1.43273i	−0.205996	−	1.43273i	−0.786053	−	0.618159i	$-0.787879\pi$
$43$	−0.205996	−	1.43273i	−0.205996	−	1.43273i	0.580057	−	0.814576i	$-0.303030\pi$
$44$	−1.67489	+	0.159932i	−1.67489	+	0.159932i
$45$		0			0
$46$		0			0
$47$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$47$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$48$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i
$49$	0.928368	−	0.371662i	0.928368	−	0.371662i
$50$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$51$	0.0416572	+	0.171713i	0.0416572	+	0.171713i
$52$		0			0
$53$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$53$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$54$	−0.00901515	+	0.189251i	−0.00901515	+	0.189251i
$55$		0			0
$56$		0			0
$57$	0.0260280	−	0.0365512i	0.0260280	−	0.0365512i
$58$		0			0
$59$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.500000	+	0.866025i	$0.666667\pi$
$59$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.995472	+	0.0950560i	$0.969697\pi$
$60$		0			0
$61$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$61$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$62$		0			0
$63$		0			0
$64$	0.415415	−	0.909632i	0.415415	−	0.909632i
$65$		0			0
$66$	0.160114			0.160114
$67$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$67$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$68$	1.85674			1.85674
$69$		0			0
$70$		0			0
$71$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$71$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$72$	0.950804	+	0.279181i	0.950804	+	0.279181i
$73$	−1.13779	−	1.08488i	−1.13779	−	1.08488i	−0.995472	−	0.0950560i	$-0.969697\pi$
$73$	−1.13779	−	1.08488i	−1.13779	−	1.08488i	−0.142315	−	0.989821i	$-0.545455\pi$
$74$		0			0
$75$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$76$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$77$		0			0
$78$		0			0
$79$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$79$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$80$		0			0
$81$	−0.138460	+	0.963011i	−0.138460	+	0.963011i
$82$	0.857685	−	0.989821i	0.857685	−	0.989821i
$83$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$84$		0			0
$85$		0			0
$86$	1.42131	+	0.273935i	1.42131	+	0.273935i
$87$		0			0
$88$	0.396666	−	1.63508i	0.396666	−	1.63508i
$89$	−0.271738	−	0.595023i	−0.271738	−	0.595023i	0.723734	−	0.690079i	$-0.242424\pi$
$89$	−0.271738	−	0.595023i	−0.271738	−	0.595023i	−0.995472	+	0.0950560i	$0.969697\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i
$97$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$97$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$98$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$99$	1.65972	+	0.158484i	1.65972	+	0.158484i
$100$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$101$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$101$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$102$	−0.175894	−	0.0167958i	−0.175894	−	0.0167958i
$103$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$103$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$107$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$108$	−0.175894	−	0.0704173i	−0.175894	−	0.0704173i
$109$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$109$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.419102	+	1.72756i	−0.419102	+	1.72756i	0.235759	+	0.971812i	$0.424242\pi$
$113$	−0.419102	+	1.72756i	−0.419102	+	1.72756i	−0.654861	+	0.755750i	$0.727273\pi$
$114$	0.0260280	+	0.0365512i	0.0260280	+	0.0365512i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.419102	−	1.72756i	−0.419102	−	1.72756i
$119$		0			0
$120$		0			0
$121$	0.0871144	−	1.82876i	0.0871144	−	1.82876i
$122$		0			0
$123$	−0.0902048	+	0.0860101i	−0.0902048	+	0.0860101i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$127$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$128$	0.723734	+	0.690079i	0.723734	+	0.690079i
$129$	−0.132167	−	0.0388077i	−0.132167	−	0.0388077i
$130$		0			0
$131$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$131$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$132$	−0.0523681	+	0.151308i	−0.0523681	+	0.151308i
$133$		0			0
$134$	0.580057	−	0.814576i	0.580057	−	0.814576i
$135$		0			0
$136$	−0.607279	+	1.75462i	−0.607279	+	1.75462i
$137$	0.481929	−	1.05528i	0.481929	−	1.05528i	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	0.481929	−	1.05528i	0.481929	−	1.05528i	0.981929	−	0.189251i	$-0.0606061\pi$
$138$		0			0
$139$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$139$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.574804	+	0.807199i	−0.574804	+	0.807199i
$145$		0			0
$146$	1.39734	−	0.720381i	1.39734	−	0.720381i
$147$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i
$148$		0			0
$149$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$149$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$150$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i
$151$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$151$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$152$	0.437742	−	0.175245i	0.437742	−	0.175245i
$153$	−1.80667	−	0.348207i	−1.80667	−	0.348207i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$157$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.864760	−	0.445815i	−0.864760	−	0.445815i
$163$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$163$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$164$	0.654861	+	1.13425i	0.654861	+	1.13425i
$165$		0			0
$166$	1.91030	+	0.182411i	1.91030	+	0.182411i
$167$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$167$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$168$		0			0
$169$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$170$		0			0
$171$	0.233624	+	0.404648i	0.233624	+	0.404648i
$172$	−0.723734	+	1.25354i	−0.723734	+	1.25354i
$173$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$173$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$174$		0			0
$175$		0			0
$176$	1.41542	+	0.909632i	1.41542	+	0.909632i
$177$	0.0240754	+	0.167448i	0.0240754	+	0.167448i
$178$	0.651174	−	0.0621796i	0.651174	−	0.0621796i
$179$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$179$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$180$		0			0
$181$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$181$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.444587	+	3.09217i	−0.444587	+	3.09217i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$191$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$192$	−0.0623191	−	0.0719200i	−0.0623191	−	0.0719200i
$193$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$193$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$194$	−1.54370	+	0.297523i	−1.54370	+	0.297523i
$195$		0			0
$196$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$197$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$197$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$198$	−0.692609	+	1.51660i	−0.692609	+	1.51660i
$199$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$199$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$200$	1.00000			1.00000
$201$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$202$		0			0
$203$		0			0
$204$	0.0734014	−	0.160727i	0.0734014	−	0.160727i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.667393	−	0.428908i	0.667393	−	0.428908i
$210$		0			0
$211$	−0.379436	+	0.532843i	−0.379436	+	0.532843i	−0.959493	−	0.281733i	$-0.909091\pi$
$211$	−0.379436	+	0.532843i	−0.379436	+	0.532843i	0.580057	+	0.814576i	$0.303030\pi$
$212$		0			0
$213$		0			0
$214$	0.0395325	−	0.829889i	0.0395325	−	0.829889i
$215$		0			0
$216$	0.124074	−	0.143189i	0.124074	−	0.143189i
$217$		0			0
$218$		0			0
$219$	−0.138891	+	0.0556035i	−0.138891	+	0.0556035i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$223$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$224$		0			0
$225$	0.141026	+	0.980857i	0.141026	+	0.980857i
$226$	−1.49547	−	0.961081i	−1.49547	−	0.961081i
$227$	1.82318	+	0.729892i	1.82318	+	0.729892i	0.981929	+	0.189251i	$0.0606061\pi$
$227$	1.82318	+	0.729892i	1.82318	+	0.729892i	0.841254	+	0.540641i	$0.181818\pi$
$228$	−0.0430538	+	0.0126417i	−0.0430538	+	0.0126417i
$229$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$229$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.580057	−	0.814576i	$-0.303030\pi$
$233$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.415415	+	0.909632i	$0.363636\pi$
$234$		0			0
$235$		0			0
$236$	1.76962	+	0.168978i	1.76962	+	0.168978i
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$		0			0
$241$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$241$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$242$	1.69968	+	0.680451i	1.69968	+	0.680451i
$243$	0.237277	+	0.152489i	0.237277	+	0.152489i
$244$		0			0
$245$		0			0
$246$	−0.0517765	−	0.113375i	−0.0517765	−	0.113375i
$247$		0			0
$248$		0			0
$249$	−0.179318	−	0.0345607i	−0.179318	−	0.0345607i
$250$		0			0
$251$	−1.54370	+	1.21398i	−1.54370	+	1.21398i	−0.654861	+	0.755750i	$0.727273\pi$
$251$	−1.54370	+	1.21398i	−1.54370	+	1.21398i	−0.888835	+	0.458227i	$0.848485\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$257$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	−0.786053	−	0.618159i	$-0.787879\pi$
$257$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	0.580057	+	0.814576i	$0.303030\pi$
$258$	0.0799009	−	0.112205i	0.0799009	−	0.112205i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.947890	−	0.903811i	−0.947890	−	0.903811i
$263$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$263$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$264$	−0.125858	−	0.0989758i	−0.125858	−	0.0989758i
$265$		0			0
$266$		0			0
$267$	−0.0622501			−0.0622501
$268$	0.580057	+	0.814576i	0.580057	+	0.814576i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$	−1.45949	−	1.14776i	−1.45949	−	1.14776i
$273$		0			0
$274$	0.839614	+	0.800570i	0.839614	+	0.800570i
$275$	1.65210	−	0.318417i	1.65210	−	0.318417i
$276$		0			0
$277$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$277$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$278$	−0.580057	+	0.814576i	−0.580057	+	0.814576i
$279$		0			0
$280$		0			0
$281$	0.0883470	−	1.85463i	0.0883470	−	1.85463i	−0.327068	−	0.945001i	$-0.606061\pi$
$281$	0.0883470	−	1.85463i	0.0883470	−	1.85463i	0.415415	−	0.909632i	$-0.363636\pi$
$282$		0			0
$283$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$283$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.574804	−	0.807199i	−0.574804	−	0.807199i
$289$	0.577012	−	2.37848i	0.577012	−	2.37848i
$290$		0			0
$291$	0.148930	−	0.0142211i	0.148930	−	0.0142211i
$292$	0.223734	+	1.55610i	0.223734	+	1.55610i
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i
$295$		0			0
$296$		0			0
$297$	0.159389	−	0.276070i	0.159389	−	0.276070i
$298$		0			0
$299$		0			0
$300$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.0224357	+	0.470984i	0.0224357	+	0.470984i
$305$		0			0
$306$	0.919960	−	1.59342i	0.919960	−	1.59342i
$307$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.327068	−	0.945001i	$-0.606061\pi$
$307$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.959493	+	0.281733i	$0.909091\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$311$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$312$		0			0
$313$	0.195876	+	0.428908i	0.195876	+	0.428908i	0.981929	−	0.189251i	$-0.0606061\pi$
$313$	0.195876	+	0.428908i	0.195876	+	0.428908i	−0.786053	+	0.618159i	$0.787879\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$317$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.0112521	+	0.0782602i	−0.0112521	+	0.0782602i
$322$		0			0
$323$	−0.778161	+	0.401170i	−0.778161	+	0.401170i
$324$	0.704131	−	0.671387i	0.704131	−	0.671387i
$325$		0			0
$326$	−1.28605	−	1.48418i	−1.28605	−	1.48418i
$327$		0			0
$328$	−1.28605	+	0.247866i	−1.28605	+	0.247866i
$329$		0			0
$330$		0			0
$331$	−0.370638	−	0.291473i	−0.370638	−	0.291473i	0.415415	−	0.909632i	$-0.363636\pi$
$331$	−0.370638	−	0.291473i	−0.370638	−	0.291473i	−0.786053	+	0.618159i	$0.787879\pi$
$332$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0930932	−	0.268975i	0.0930932	−	0.268975i	−0.888835	−	0.458227i	$-0.848485\pi$
$337$	0.0930932	−	0.268975i	0.0930932	−	0.268975i	0.981929	+	0.189251i	$0.0606061\pi$
$338$	0.415415	−	0.909632i	0.415415	−	0.909632i
$339$	0.132977	+	0.104574i	0.132977	+	0.104574i
$340$		0			0
$341$		0			0
$342$	−0.458804	+	0.0884272i	−0.458804	+	0.0884272i
$343$		0			0
$344$	−0.947890	−	1.09392i	−0.947890	−	1.09392i
$345$		0			0
$346$		0			0
$347$	0.888835	−	0.458227i	0.888835	−	0.458227i	0.0475819	−	0.998867i	$-0.484848\pi$
$347$	0.888835	−	0.458227i	0.888835	−	0.458227i	0.841254	+	0.540641i	$0.181818\pi$
$348$		0			0
$349$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$349$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$350$		0			0
$351$		0			0
$352$	−1.32254	+	1.04006i	−1.32254	+	1.04006i
$353$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.0475819	−	0.998867i	$-0.484848\pi$
$353$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.723734	+	0.690079i	$0.242424\pi$
$354$	−0.166113	−	0.0320156i	−0.166113	−	0.0320156i
$355$		0			0
$356$	−0.154218	+	0.635697i	−0.154218	+	0.635697i
$357$		0			0
$358$	1.91030	−	0.182411i	1.91030	−	0.182411i
$359$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$		0			0
$361$	−0.721965	−	0.289031i	−0.721965	−	0.289031i
$362$		0			0
$363$	−0.154861	−	0.0798363i	−0.154861	−	0.0798363i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$367$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$368$		0			0
$369$	−0.424489	−	1.22648i	−0.424489	−	1.22648i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$	−2.77670	−	1.43149i	−2.77670	−	1.43149i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.30379	−	0.124497i	1.30379	−	0.124497i	0.580057	−	0.814576i	$-0.303030\pi$
$379$	1.30379	−	0.124497i	1.30379	−	0.124497i	0.723734	+	0.690079i	$0.242424\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$383$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$384$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i
$385$		0			0
$386$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i
$387$	0.939306	−	1.08402i	0.939306	−	1.08402i
$388$	0.223734	−	1.55610i	0.223734	−	1.55610i
$389$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$389$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$390$		0			0
$391$		0			0
$392$	0.580057	−	0.814576i	0.580057	−	0.814576i
$393$	0.0816206	+	0.0941952i	0.0816206	+	0.0941952i
$394$		0			0
$395$		0			0
$396$	−1.20666	−	1.15055i	−1.20666	−	1.15055i
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$		0			0
$399$		0			0
$400$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$401$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$401$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$402$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.127880	+	0.121933i	0.127880	+	0.121933i
$409$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.235759	−	0.971812i	$-0.424242\pi$
$409$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.580057	+	0.814576i	$0.303030\pi$
$410$		0			0
$411$	−0.0722972	−	0.0834354i	−0.0722972	−	0.0834354i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.0623191	−	0.0719200i	0.0623191	−	0.0719200i
$418$	0.187035	+	0.770969i	0.187035	+	0.770969i
$419$	1.23576	−	0.971812i	1.23576	−	0.971812i	0.235759	−	0.971812i	$-0.424242\pi$
$419$	1.23576	−	0.971812i	1.23576	−	0.971812i	1.00000			$0$
$420$		0			0
$421$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$421$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$422$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$423$		0			0
$424$		0			0
$425$	−1.84833	+	0.176494i	−1.84833	+	0.176494i
$426$		0			0
$427$		0			0
$428$	0.771316	+	0.308788i	0.771316	+	0.308788i
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	0.0947329	+	0.164082i	0.0947329	+	0.164082i
$433$	0.0552004	+	1.15880i	0.0552004	+	1.15880i	0.841254	+	0.540641i	$0.181818\pi$
$433$	0.0552004	+	1.15880i	0.0552004	+	1.15880i	−0.786053	+	0.618159i	$0.787879\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.00711862	−	0.149438i	−0.00711862	−	0.149438i
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	0.880786	+	0.454077i	0.880786	+	0.454077i
$442$		0			0
$443$	1.72373	+	0.690079i	1.72373	+	0.690079i	1.00000			$0$
$443$	1.72373	+	0.690079i	1.72373	+	0.690079i	0.723734	+	0.690079i	$0.242424\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.975950	+	1.37053i	0.975950	+	1.37053i	0.928368	+	0.371662i	$0.121212\pi$
$449$	0.975950	+	1.37053i	0.975950	+	1.37053i	0.0475819	+	0.998867i	$0.484848\pi$
$450$	−0.973036	−	0.187537i	−0.973036	−	0.187537i
$451$	−2.04577	+	0.819001i	−2.04577	+	0.819001i
$452$	1.39734	−	1.09888i	1.39734	−	1.09888i
$453$		0			0
$454$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$455$		0			0
$456$	0.00213507	−	0.0448206i	0.00213507	−	0.0448206i
$457$	0.581419	−	0.299742i	0.581419	−	0.299742i	−0.142315	−	0.989821i	$-0.545455\pi$
$457$	0.581419	−	0.299742i	0.581419	−	0.299742i	0.723734	+	0.690079i	$0.242424\pi$
$458$		0			0
$459$	−0.204057	+	0.286558i	−0.204057	+	0.286558i
$460$		0			0
$461$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$461$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$462$		0			0
$463$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$463$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$464$		0			0
$465$		0			0
$466$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$467$	−0.550294	+	1.58997i	−0.550294	+	1.58997i	0.235759	+	0.971812i	$0.424242\pi$
$467$	−0.550294	+	1.58997i	−0.550294	+	1.58997i	−0.786053	+	0.618159i	$0.787879\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.738471	+	1.61703i	−0.738471	+	1.61703i
$473$	−1.91433	−	1.50545i	−1.91433	−	1.50545i
$474$		0			0
$475$	0.341254	+	0.325385i	0.341254	+	0.325385i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$479$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$480$		0			0
$481$		0			0
$482$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i
$483$		0			0
$484$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$485$		0			0
$486$	−0.221708	+	0.174353i	−0.221708	+	0.174353i
$487$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$487$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$488$		0			0
$489$	0.108406	+	0.152235i	0.108406	+	0.152235i
$490$		0			0
$491$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$491$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$492$	0.124074	−	0.0118476i	0.124074	−	0.0118476i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0913090	−	0.158152i	0.0913090	−	0.158152i
$499$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$499$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$500$		0			0
$501$		0			0
$502$	−0.642315	−	1.85585i	−0.642315	−	1.85585i
$503$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$503$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i
$508$		0			0
$509$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$509$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$510$		0			0
$511$		0			0
$512$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$513$	0.0889320	−	0.00849198i	0.0889320	−	0.00849198i
$514$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$515$		0			0
$516$	0.0799009	+	0.112205i	0.0799009	+	0.112205i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.30379	−	1.50465i	1.30379	−	1.50465i	0.580057	−	0.814576i	$-0.303030\pi$
$521$	1.30379	−	1.50465i	1.30379	−	1.50465i	0.723734	−	0.690079i	$-0.242424\pi$
$522$		0			0
$523$	0.0552004	−	1.15880i	0.0552004	−	1.15880i	−0.786053	−	0.618159i	$-0.787879\pi$
$523$	0.0552004	−	1.15880i	0.0552004	−	1.15880i	0.841254	−	0.540641i	$-0.181818\pi$
$524$	1.16413	−	0.600149i	1.16413	−	0.600149i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.134696	−	0.0865641i	0.134696	−	0.0865641i
$529$	0.981929	−	0.189251i	0.981929	−	0.189251i
$530$		0			0
$531$	−1.69022	−	0.496292i	−1.69022	−	0.496292i
$532$		0			0
$533$		0			0
$534$	0.0203600	−	0.0588264i	0.0203600	−	0.0588264i
$535$		0			0
$536$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$537$	−0.182618			−0.182618
$538$		0			0
$539$	0.698939	−	1.53046i	0.698939	−	1.53046i
$540$		0			0
$541$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$541$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$542$		0			0
$543$		0			0
$544$	1.56199	−	1.00383i	1.56199	−	1.00383i
$545$		0			0
$546$		0			0
$547$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.500000	+	0.866025i	$0.666667\pi$
$547$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.888835	+	0.458227i	$0.848485\pi$
$548$	−1.03115	+	0.531595i	−1.03115	+	0.531595i
$549$		0			0
$550$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.580057	−	0.814576i	−0.580057	−	0.814576i
$557$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$557$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.250095	+	0.160727i	0.250095	+	0.160727i
$562$	1.72373	+	0.690079i	1.72373	+	0.690079i
$563$	1.91030	−	0.560914i	1.91030	−	0.560914i	0.928368	−	0.371662i	$-0.121212\pi$
$563$	1.91030	−	0.560914i	1.91030	−	0.560914i	0.981929	−	0.189251i	$-0.0606061\pi$
$564$		0			0
$565$		0			0
$566$	0.500000	+	0.866025i	0.500000	+	0.866025i
$567$		0			0
$568$		0			0
$569$	0.514186	+	1.48564i	0.514186	+	1.48564i	0.841254	+	0.540641i	$0.181818\pi$
$569$	0.514186	+	1.48564i	0.514186	+	1.48564i	−0.327068	+	0.945001i	$0.606061\pi$
$570$		0			0
$571$	−1.84833	−	0.176494i	−1.84833	−	0.176494i	−0.888835	−	0.458227i	$-0.848485\pi$
$571$	−1.84833	−	0.176494i	−1.84833	−	0.176494i	−0.959493	+	0.281733i	$0.909091\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.950804	−	0.279181i	0.950804	−	0.279181i
$577$	−0.607279	−	0.243118i	−0.607279	−	0.243118i	0.0475819	−	0.998867i	$-0.484848\pi$
$577$	−0.607279	−	0.243118i	−0.607279	−	0.243118i	−0.654861	+	0.755750i	$0.727273\pi$
$578$	2.05894	+	1.32320i	2.05894	+	1.32320i
$579$	0.00385480	+	0.0268107i	0.00385480	+	0.0268107i
$580$		0			0
$581$		0			0
$582$	−0.0352713	+	0.145390i	−0.0352713	+	0.145390i
$583$		0			0
$584$	−1.54370	−	0.297523i	−1.54370	−	0.297523i
$585$		0			0
$586$		0			0
$587$	−0.370638	−	1.52779i	−0.370638	−	1.52779i	−0.786053	−	0.618159i	$-0.787879\pi$
$587$	−0.370638	−	1.52779i	−0.370638	−	1.52779i	0.415415	−	0.909632i	$-0.363636\pi$
$588$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.911911	+	1.28060i	−0.911911	+	1.28060i	0.0475819	+	0.998867i	$0.484848\pi$
$593$	−0.911911	+	1.28060i	−0.911911	+	1.28060i	−0.959493	+	0.281733i	$0.909091\pi$
$594$	0.208755	+	0.240916i	0.208755	+	0.240916i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$599$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$600$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i
$601$	−0.642315	+	1.85585i	−0.642315	+	1.85585i	−0.142315	+	0.989821i	$0.545455\pi$
$601$	−0.642315	+	1.85585i	−0.642315	+	1.85585i	−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	−0.411653	−	0.901394i	−0.411653	−	0.901394i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$607$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$608$	−0.452418	−	0.132842i	−0.452418	−	0.132842i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.20489	+	1.39052i	1.20489	+	1.39052i
$613$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$613$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$614$	1.04758	−	0.998867i	1.04758	−	0.998867i
$615$		0			0
$616$		0			0
$617$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$617$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$618$		0			0
$619$	0.273507	+	1.12741i	0.273507	+	1.12741i	0.928368	+	0.371662i	$0.121212\pi$
$619$	0.273507	+	1.12741i	0.273507	+	1.12741i	−0.654861	+	0.755750i	$0.727273\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.415415	+	0.909632i	0.415415	+	0.909632i
$626$	−0.469383	+	0.0448206i	−0.469383	+	0.0448206i
$627$	−0.0107443	−	0.0747281i	−0.0107443	−	0.0747281i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$631$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$632$		0			0
$633$	0.0311250	+	0.0539102i	0.0311250	+	0.0539102i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$641$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$642$	−0.0702757	−	0.0362297i	−0.0702757	−	0.0362297i
$643$	1.70566	−	0.500828i	1.70566	−	0.500828i	0.723734	−	0.690079i	$-0.242424\pi$
$643$	1.70566	−	0.500828i	1.70566	−	0.500828i	0.981929	+	0.189251i	$0.0606061\pi$
$644$		0			0
$645$		0			0
$646$	−0.124594	−	0.866573i	−0.124594	−	0.866573i
$647$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$647$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$648$	0.404163	+	0.884993i	0.404163	+	0.884993i
$649$	−0.705142	+	2.90663i	−0.705142	+	2.90663i
$650$		0			0
$651$		0			0
$652$	1.82318	−	0.729892i	1.82318	−	0.729892i
$653$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$653$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$654$		0			0
$655$		0			0
$656$	0.186393	−	1.29639i	0.186393	−	1.29639i
$657$	0.0741264	−	1.55610i	0.0741264	−	1.55610i
$658$		0			0
$659$	−0.723734	+	0.690079i	−0.723734	+	0.690079i	−0.959493	−	0.281733i	$-0.909091\pi$
$659$	−0.723734	+	0.690079i	−0.723734	+	0.690079i	0.235759	+	0.971812i	$0.424242\pi$
$660$		0			0
$661$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$661$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$662$	0.396666	−	0.254922i	0.396666	−	0.254922i
$663$		0			0
$664$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.827068	+	1.81103i	−0.827068	+	1.81103i	−0.327068	+	0.945001i	$0.606061\pi$
$673$	−0.827068	+	1.81103i	−0.827068	+	1.81103i	−0.500000	+	0.866025i	$0.666667\pi$
$674$	0.223734	+	0.175946i	0.223734	+	0.175946i
$675$	0.181791	+	0.0533787i	0.181791	+	0.0533787i
$676$	0.723734	+	0.690079i	0.723734	+	0.690079i
$677$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$677$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$678$	−0.142315	+	0.0914602i	−0.142315	+	0.0914602i
$679$		0			0
$680$		0			0
$681$	0.135257	−	0.128968i	0.135257	−	0.128968i
$682$		0			0
$683$	0.0552004	−	1.15880i	0.0552004	−	1.15880i	−0.786053	−	0.618159i	$-0.787879\pi$
$683$	0.0552004	−	1.15880i	0.0552004	−	1.15880i	0.841254	−	0.540641i	$-0.181818\pi$
$684$	0.0664963	−	0.462492i	0.0664963	−	0.462492i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.34378	−	0.537970i	1.34378	−	0.537970i
$689$		0			0
$690$		0			0
$691$	0.195876	−	0.807410i	0.195876	−	0.807410i	−0.786053	−	0.618159i	$-0.787879\pi$
$691$	0.195876	−	0.807410i	0.195876	−	0.807410i	0.981929	−	0.189251i	$-0.0606061\pi$
$692$		0			0
$693$		0			0
$694$	0.142315	+	0.989821i	0.142315	+	0.989821i
$695$		0			0
$696$		0			0
$697$	2.33330	−	0.685119i	2.33330	−	0.685119i
$698$		0			0
$699$	0.0475819	−	0.0824143i	0.0475819	−	0.0824143i
$700$		0			0
$701$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$701$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$702$		0			0
$703$		0			0
$704$	−0.550294	−	1.58997i	−0.550294	−	1.58997i
$705$		0			0
$706$	0.0395325	+	0.829889i	0.0395325	+	0.829889i
$707$		0			0
$708$	0.0845850	−	0.146505i	0.0845850	−	0.146505i
$709$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$709$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$710$		0			0
$711$		0			0
$712$	−0.550294	−	0.353653i	−0.550294	−	0.353653i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.452418	+	1.86489i	−0.452418	+	1.86489i
$717$		0			0
$718$		0			0
$719$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$719$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$720$		0			0
$721$		0			0
$722$	0.509266	−	0.587724i	0.509266	−	0.587724i
$723$	0.0259893	−	0.180759i	0.0259893	−	0.180759i
$724$		0			0
$725$		0			0
$726$	0.126095	−	0.120232i	0.126095	−	0.120232i
$727$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$727$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$728$		0			0
$729$	−0.795887	+	0.511485i	−0.795887	+	0.511485i
$730$		0			0
$731$	1.94508	+	1.85463i	1.94508	+	1.85463i
$732$		0			0
$733$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$733$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.49547	+	0.770969i	−1.49547	+	0.770969i
$738$	1.29786			1.29786
$739$	0.581419	−	1.67990i	0.581419	−	1.67990i	−0.142315	−	0.989821i	$-0.545455\pi$
$739$	0.581419	−	1.67990i	0.581419	−	1.67990i	0.723734	−	0.690079i	$-0.242424\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$743$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.10304	−	1.54900i	1.10304	−	1.54900i
$748$	2.26092	−	2.15579i	2.26092	−	2.15579i
$749$		0			0
$750$		0			0
$751$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$751$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$752$		0			0
$753$	0.0440606	+	0.181620i	0.0440606	+	0.181620i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$757$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$758$	−0.308779	+	1.27280i	−0.308779	+	1.27280i
$759$		0			0
$760$		0			0
$761$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$761$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i
$769$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.959493	−	0.281733i	$-0.909091\pi$
$769$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.995472	+	0.0950560i	$0.969697\pi$
$770$		0			0
$771$	0.00885911	+	0.0255967i	0.00885911	+	0.0255967i
$772$	0.283341	+	0.0270558i	0.283341	+	0.0270558i
$773$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$773$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$774$	0.717180	+	1.24219i	0.717180	+	1.24219i
$775$		0			0
$776$	1.39734	+	0.720381i	1.39734	+	0.720381i
$777$		0			0
$778$		0			0
$779$	−0.519522	−	0.333877i	−0.519522	−	0.333877i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.580057	+	0.814576i	0.580057	+	0.814576i
$785$		0			0
$786$	−0.115710	+	0.0463233i	−0.115710	+	0.0463233i
$787$	−0.653077	+	0.513585i	−0.653077	+	0.513585i	−0.888835	−	0.458227i	$-0.848485\pi$
$787$	−0.653077	+	0.513585i	−0.653077	+	0.513585i	0.235759	+	0.971812i	$0.424242\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.48193	−	0.763987i	1.48193	−	0.763987i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$797$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$798$		0			0
$799$		0			0
$800$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$801$	0.269277	−	0.589634i	0.269277	−	0.589634i
$802$	0.0930932	−	0.268975i	0.0930932	−	0.268975i
$803$	−2.64508			−2.64508
$804$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$809$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$810$		0			0
$811$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.995472	−	0.0950560i	$-0.969697\pi$
$811$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.888835	+	0.458227i	$0.848485\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.157052	+	0.0809659i	−0.157052	+	0.0809659i
$817$	0.0324750	−	0.681734i	0.0324750	−	0.681734i
$818$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$819$		0			0
$820$		0			0
$821$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$821$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$822$	0.102493	−	0.0410319i	0.102493	−	0.0410319i
$823$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$823$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$824$		0			0
$825$	0.0377483	−	0.155600i	0.0377483	−	0.155600i
$826$		0			0
$827$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.888835	−	0.458227i	$-0.848485\pi$
$827$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.786053	+	0.618159i	$0.787879\pi$
$828$		0			0
$829$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$829$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.928368	+	1.60798i	−0.928368	+	1.60798i
$834$	0.0475819	+	0.0824143i	0.0475819	+	0.0824143i
$835$		0			0
$836$	−0.789740	−	0.0754110i	−0.789740	−	0.0754110i
$837$		0			0
$838$	0.514186	+	1.48564i	0.514186	+	1.48564i
$839$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$839$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$	−0.157052	−	0.0809659i	−0.157052	−	0.0809659i
$844$	0.627639	−	0.184291i	0.627639	−	0.184291i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0395325	−	0.0865641i	−0.0395325	−	0.0865641i
$850$	0.437742	−	1.80440i	0.437742	−	1.80440i
$851$		0			0
$852$		0			0
$853$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$853$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$854$		0			0
$855$		0			0
$856$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$857$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$857$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$858$		0			0
$859$	−1.65033	+	0.850806i	−1.65033	+	0.850806i	−0.654861	+	0.755750i	$0.727273\pi$
$859$	−1.65033	+	0.850806i	−1.65033	+	0.850806i	−0.995472	+	0.0950560i	$0.969697\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$863$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$864$	−0.186042	+	0.0358566i	−0.186042	+	0.0358566i
$865$		0			0
$866$	−1.11312	−	0.326842i	−1.11312	−	0.326842i
$867$	−0.183080	−	0.143976i	−0.183080	−	0.143976i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.509529	+	1.47219i	−0.509529	+	1.47219i
$874$		0			0
$875$		0			0
$876$	0.143547	+	0.0421493i	0.143547	+	0.0421493i
$877$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$877$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.0475819	−	0.998867i	$-0.484848\pi$
$881$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.928368	−	0.371662i	$-0.121212\pi$
$882$	−0.717180	+	0.683830i	−0.717180	+	0.683830i
$883$	1.16413	−	0.600149i	1.16413	−	0.600149i	0.235759	−	0.971812i	$-0.424242\pi$
$883$	1.16413	−	0.600149i	1.16413	−	0.600149i	0.928368	+	0.371662i	$0.121212\pi$
$884$		0			0
$885$		0			0
$886$	−1.21590	+	1.40323i	−1.21590	+	1.40323i
$887$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$887$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.949515	+	1.33341i	0.949515	+	1.33341i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$899$		0			0
$900$	0.495472	−	0.858183i	0.495472	−	0.858183i
$901$		0			0
$902$	−0.104852	−	2.20112i	−0.104852	−	2.20112i
$903$		0			0
$904$	0.581419	+	1.67990i	0.581419	+	1.67990i
$905$		0			0
$906$		0			0
$907$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	−0.995472	−	0.0950560i	$-0.969697\pi$
$907$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	0.981929	−	0.189251i	$-0.0606061\pi$
$908$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$909$		0			0
$910$		0			0
$911$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$911$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$912$	0.0416572	+	0.0166770i	0.0416572	+	0.0166770i
$913$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$914$	0.0930932	+	0.647478i	0.0930932	+	0.647478i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.204057	−	0.286558i	−0.204057	−	0.286558i
$919$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$919$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$920$		0			0
$921$	−0.108276	+	0.0851493i	−0.108276	+	0.0851493i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.30379	+	1.50465i	1.30379	+	1.50465i	0.723734	+	0.690079i	$0.242424\pi$
$929$	1.30379	+	1.50465i	1.30379	+	1.50465i	0.580057	+	0.814576i	$0.303030\pi$
$930$		0			0
$931$	0.462997	−	0.0892353i	0.462997	−	0.0892353i
$932$	−0.723734	−	0.690079i	−0.723734	−	0.690079i
$933$		0			0
$934$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$935$		0			0
$936$		0			0
$937$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$937$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$938$		0			0
$939$	0.0448714			0.0448714
$940$		0			0
$941$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$941$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$942$		0			0
$943$		0			0
$944$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$945$		0			0
$946$	2.04877	−	1.31666i	2.04877	−	1.31666i
$947$	0.428368	+	0.494363i	0.428368	+	0.494363i	0.928368	−	0.371662i	$-0.121212\pi$
$947$	0.428368	+	0.494363i	0.428368	+	0.494363i	−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$	−0.419102	+	0.216062i	−0.419102	+	0.216062i
$951$		0			0
$952$		0			0
$953$	−0.947890	+	1.09392i	−0.947890	+	1.09392i	0.0475819	+	0.998867i	$0.484848\pi$
$953$	−0.947890	+	1.09392i	−0.947890	+	1.09392i	−0.995472	+	0.0950560i	$0.969697\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$962$		0			0
$963$	−0.692609	−	0.445113i	−0.692609	−	0.445113i
$964$	−1.78153	−	0.713215i	−1.78153	−	0.713215i
$965$		0			0
$966$		0			0
$967$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$967$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$968$	−0.915415	−	1.58555i	−0.915415	−	1.58555i
$969$	0.00396426	+	0.0832201i	0.00396426	+	0.0832201i
$970$		0			0
$971$	−0.473420	−	1.36786i	−0.473420	−	1.36786i	−0.888835	−	0.458227i	$-0.848485\pi$
$971$	−0.473420	−	1.36786i	−0.473420	−	1.36786i	0.415415	−	0.909632i	$-0.363636\pi$
$972$	−0.0922502	−	0.266539i	−0.0922502	−	0.266539i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.981929	+	0.189251i	$0.0606061\pi$
$977$	1.70566	+	0.879330i	1.70566	+	0.879330i	0.723734	+	0.690079i	$0.242424\pi$
$978$	−0.179318	+	0.0526525i	−0.179318	+	0.0526525i
$979$	−1.02175	−	0.409047i	−1.02175	−	0.409047i
$980$		0			0
$981$		0			0
$982$	0.995472	−	0.0950560i	0.995472	−	0.0950560i
$983$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$983$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$984$	−0.0293845	+	0.121125i	−0.0293845	+	0.121125i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$991$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$992$		0			0
$993$	−0.0398833	+	0.0205613i	−0.0398833	+	0.0205613i
$994$		0			0
$995$		0			0
$996$	0.119589	+	0.138014i	0.119589	+	0.138014i
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$	−1.95496	+	0.376789i	−1.95496	+	0.376789i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.1.ba.a.475.1	yes	20
4.3	odd	2		2144.1.bu.a.207.1		20
8.3	odd	2	CM	536.1.ba.a.475.1	yes	20
8.5	even	2		2144.1.bu.a.207.1		20
67.56	even	33	inner	536.1.ba.a.123.1	✓	20
268.123	odd	66		2144.1.bu.a.1999.1		20
536.123	odd	66	inner	536.1.ba.a.123.1	✓	20
536.525	even	66		2144.1.bu.a.1999.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.1.ba.a.123.1	✓	20	67.56	even	33	inner
536.1.ba.a.123.1	✓	20	536.123	odd	66	inner
536.1.ba.a.475.1	yes	20	1.1	even	1	trivial
536.1.ba.a.475.1	yes	20	8.3	odd	2	CM
2144.1.bu.a.207.1		20	4.3	odd	2
2144.1.bu.a.207.1		20	8.5	even	2
2144.1.bu.a.1999.1		20	268.123	odd	66
2144.1.bu.a.1999.1		20	536.525	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)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.0395325 - 0.0865641i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.0688733 + 0.0656706i) q^{6} +(0.841254 - 0.540641i) q^{8} +(0.648930 + 0.748905i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.0395325 - 0.0865641i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.0688733 + 0.0656706i) q^{6} +(0.841254 - 0.540641i) q^{8} +(0.648930 + 0.748905i) q^{9} +(1.21769 - 1.16106i) q^{11} +(-0.0845850 + 0.0436066i) q^{12} +(0.235759 + 0.971812i) q^{16} +(-1.45949 + 1.14776i) q^{17} +(-0.919960 + 0.368297i) q^{18} +(0.462997 + 0.0892353i) q^{19} +(0.698939 + 1.53046i) q^{22} +(-0.0135432 - 0.0941952i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.181791 - 0.0533787i) q^{27} +(-0.995472 - 0.0950560i) q^{32} +(-0.0523681 - 0.151308i) q^{33} +(-0.607279 - 1.75462i) q^{34} +(-0.0471510 - 0.989821i) q^{36} +(-0.235759 + 0.408346i) q^{38} +(-1.21590 - 0.486774i) q^{41} +(-0.205996 - 1.43273i) q^{43} +(-1.67489 + 0.159932i) q^{44} +(0.0934441 + 0.0180099i) q^{48} +(0.928368 - 0.371662i) q^{49} +(-0.786053 + 0.618159i) q^{50} +(0.0416572 + 0.171713i) q^{51} +(-0.00901515 + 0.189251i) q^{54} +(0.0260280 - 0.0365512i) q^{57} +(-1.49547 + 0.961081i) q^{59} +(0.415415 - 0.909632i) q^{64} +0.160114 q^{66} +(-0.959493 - 0.281733i) q^{67} +1.85674 q^{68} +(0.950804 + 0.279181i) q^{72} +(-1.13779 - 1.08488i) q^{73} +(0.0800569 - 0.0514495i) q^{75} +(-0.308779 - 0.356349i) q^{76} +(-0.138460 + 0.963011i) q^{81} +(0.857685 - 0.989821i) q^{82} +(-0.452418 - 1.86489i) q^{83} +(1.42131 + 0.273935i) q^{86} +(0.396666 - 1.63508i) q^{88} +(-0.271738 - 0.595023i) q^{89} +(-0.0475819 + 0.0824143i) q^{96} +(0.786053 + 1.36148i) q^{97} +(0.0475819 + 0.998867i) q^{98} +(1.65972 + 0.158484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8}+O(q^{10}) \) 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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