LMFDB - Embedded newform 536.1.ba.a.35.1

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			35.1
Root			$0.723734 + 0.690079i$ of defining polynomial
Character	$\chi$	$=$	536.35
Dual form			536.1.ba.a.291.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.235759 - 0.971812i) q^{2} +(-0.279486 - 1.94387i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(-1.95496 - 0.186677i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-2.74102 + 0.804835i) q^{9} +O(q^{10})$	\(q+(0.235759 - 0.971812i) q^{2} +(-0.279486 - 1.94387i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(-1.95496 - 0.186677i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-2.74102 + 0.804835i) q^{9} +(1.30379 - 0.124497i) q^{11} +(-0.642315 + 1.85585i) q^{12} +(0.580057 + 0.814576i) q^{16} +(-0.0845850 + 0.0436066i) q^{17} +(0.135929 + 2.85350i) q^{18} +(0.839614 - 0.800570i) q^{19} +(0.186393 - 1.29639i) q^{22} +(1.65210 + 1.06174i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(1.51475 + 3.31685i) q^{27} +(0.928368 - 0.371662i) q^{32} +(-0.606397 - 2.49960i) q^{33} +(0.0224357 + 0.0924813i) q^{34} +(2.80511 + 0.540641i) q^{36} +(-0.580057 - 1.00469i) q^{38} +(-0.0913090 + 1.91681i) q^{41} +(-1.67489 - 1.07639i) q^{43} +(-1.21590 - 0.486774i) q^{44} +(1.42131 - 1.35522i) q^{48} +(0.0475819 + 0.998867i) q^{49} +(-0.888835 + 0.458227i) q^{50} +(0.108406 + 0.152235i) q^{51} +(3.58047 - 0.690079i) q^{54} +(-1.79086 - 1.40835i) q^{57} +(0.428368 - 0.494363i) q^{59} +(-0.142315 - 0.989821i) q^{64} -2.57211 q^{66} +(0.415415 - 0.909632i) q^{67} +0.0951638 q^{68} +(1.18673 - 2.59858i) q^{72} +(1.76962 + 0.168978i) q^{73} +(-1.28605 + 1.48418i) q^{75} +(-1.11312 + 0.326842i) q^{76} +(3.62093 - 2.32703i) q^{81} +(1.84125 + 0.540641i) q^{82} +(0.481929 + 0.676774i) q^{83} +(-1.44091 + 1.37391i) q^{86} +(-0.759713 + 1.06687i) q^{88} +(-0.0671040 + 0.466718i) q^{89} +(-0.981929 - 1.70075i) q^{96} +(0.888835 - 1.53951i) q^{97} +(0.981929 + 0.189251i) q^{98} +(-3.47351 + 1.39059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{33}\right)$

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 $

$2$	0.235759	−	0.971812i	0.235759	−	0.971812i
$2$	0.235759	−	0.971812i	0.235759	−	0.971812i
$3$	−0.279486	−	1.94387i	−0.279486	−	1.94387i	−0.327068	−	0.945001i	$-0.606061\pi$
$3$	−0.279486	−	1.94387i	−0.279486	−	1.94387i	0.0475819	−	0.998867i	$-0.484848\pi$
$4$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$5$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$5$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$6$	−1.95496	−	0.186677i	−1.95496	−	0.186677i
$7$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$7$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$8$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$9$	−2.74102	+	0.804835i	−2.74102	+	0.804835i
$10$		0			0
$11$	1.30379	−	0.124497i	1.30379	−	0.124497i	0.580057	−	0.814576i	$-0.303030\pi$
$11$	1.30379	−	0.124497i	1.30379	−	0.124497i	0.723734	+	0.690079i	$0.242424\pi$
$12$	−0.642315	+	1.85585i	−0.642315	+	1.85585i
$13$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$13$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$14$		0			0
$15$		0			0
$16$	0.580057	+	0.814576i	0.580057	+	0.814576i
$17$	−0.0845850	+	0.0436066i	−0.0845850	+	0.0436066i	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−0.0845850	+	0.0436066i	−0.0845850	+	0.0436066i	0.415415	+	0.909632i	$0.363636\pi$
$18$	0.135929	+	2.85350i	0.135929	+	2.85350i
$19$	0.839614	−	0.800570i	0.839614	−	0.800570i	−0.142315	−	0.989821i	$-0.545455\pi$
$19$	0.839614	−	0.800570i	0.839614	−	0.800570i	0.981929	+	0.189251i	$0.0606061\pi$
$20$		0			0
$21$		0			0
$22$	0.186393	−	1.29639i	0.186393	−	1.29639i
$23$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$23$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$24$	1.65210	+	1.06174i	1.65210	+	1.06174i
$25$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$26$		0			0
$27$	1.51475	+	3.31685i	1.51475	+	3.31685i
$28$		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		−0.981929	−	0.189251i	$-0.939394\pi$
$31$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$32$	0.928368	−	0.371662i	0.928368	−	0.371662i
$33$	−0.606397	−	2.49960i	−0.606397	−	2.49960i
$34$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i
$35$		0			0
$36$	2.80511	+	0.540641i	2.80511	+	0.540641i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−0.580057	−	1.00469i	−0.580057	−	1.00469i
$39$		0			0
$40$		0			0
$41$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	0.235759	+	0.971812i	$0.424242\pi$
$41$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	−0.327068	+	0.945001i	$0.606061\pi$
$42$		0			0
$43$	−1.67489	−	1.07639i	−1.67489	−	1.07639i	−0.888835	−	0.458227i	$-0.848485\pi$
$43$	−1.67489	−	1.07639i	−1.67489	−	1.07639i	−0.786053	−	0.618159i	$-0.787879\pi$
$44$	−1.21590	−	0.486774i	−1.21590	−	0.486774i
$45$		0			0
$46$		0			0
$47$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$47$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$48$	1.42131	−	1.35522i	1.42131	−	1.35522i
$49$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$50$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$51$	0.108406	+	0.152235i	0.108406	+	0.152235i
$52$		0			0
$53$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$53$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$54$	3.58047	−	0.690079i	3.58047	−	0.690079i
$55$		0			0
$56$		0			0
$57$	−1.79086	−	1.40835i	−1.79086	−	1.40835i
$58$		0			0
$59$	0.428368	−	0.494363i	0.428368	−	0.494363i	−0.500000	−	0.866025i	$-0.666667\pi$
$59$	0.428368	−	0.494363i	0.428368	−	0.494363i	0.928368	+	0.371662i	$0.121212\pi$
$60$		0			0
$61$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$61$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$62$		0			0
$63$		0			0
$64$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$65$		0			0
$66$	−2.57211			−2.57211
$67$	0.415415	−	0.909632i	0.415415	−	0.909632i
$67$	0.415415	−	0.909632i	0.415415	−	0.909632i
$68$	0.0951638			0.0951638
$69$		0			0
$70$		0			0
$71$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$71$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$72$	1.18673	−	2.59858i	1.18673	−	2.59858i
$73$	1.76962	+	0.168978i	1.76962	+	0.168978i	0.928368	−	0.371662i	$-0.121212\pi$
$73$	1.76962	+	0.168978i	1.76962	+	0.168978i	0.841254	+	0.540641i	$0.181818\pi$
$74$		0			0
$75$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$76$	−1.11312	+	0.326842i	−1.11312	+	0.326842i
$77$		0			0
$78$		0			0
$79$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$79$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$80$		0			0
$81$	3.62093	−	2.32703i	3.62093	−	2.32703i
$82$	1.84125	+	0.540641i	1.84125	+	0.540641i
$83$	0.481929	+	0.676774i	0.481929	+	0.676774i	0.981929	−	0.189251i	$-0.0606061\pi$
$83$	0.481929	+	0.676774i	0.481929	+	0.676774i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	−1.44091	+	1.37391i	−1.44091	+	1.37391i
$87$		0			0
$88$	−0.759713	+	1.06687i	−0.759713	+	1.06687i
$89$	−0.0671040	+	0.466718i	−0.0671040	+	0.466718i	0.928368	+	0.371662i	$0.121212\pi$
$89$	−0.0671040	+	0.466718i	−0.0671040	+	0.466718i	−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
$96$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$97$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$97$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$98$	0.981929	+	0.189251i	0.981929	+	0.189251i
$99$	−3.47351	+	1.39059i	−3.47351	+	1.39059i
$100$	0.235759	+	0.971812i	0.235759	+	0.971812i
$101$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$101$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$102$	0.173501	−	0.0694593i	0.173501	−	0.0694593i
$103$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$103$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$107$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$108$	0.173501	−	3.64223i	0.173501	−	3.64223i
$109$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$109$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.379436	+	0.532843i	−0.379436	+	0.532843i	−0.959493	−	0.281733i	$-0.909091\pi$
$113$	−0.379436	+	0.532843i	−0.379436	+	0.532843i	0.580057	+	0.814576i	$0.303030\pi$
$114$	−1.79086	+	1.40835i	−1.79086	+	1.40835i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$119$		0			0
$120$		0			0
$121$	0.702443	−	0.135385i	0.702443	−	0.135385i
$122$		0			0
$123$	3.75155	−	0.358230i	3.75155	−	0.358230i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$127$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$128$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$129$	−1.62424	+	3.55660i	−1.62424	+	3.55660i
$130$		0			0
$131$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$131$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$132$	−0.606397	+	2.49960i	−0.606397	+	2.49960i
$133$		0			0
$134$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$135$		0			0
$136$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$137$	0.223734	+	1.55610i	0.223734	+	1.55610i	0.723734	+	0.690079i	$0.242424\pi$
$137$	0.223734	+	1.55610i	0.223734	+	1.55610i	−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	0.580057	+	0.814576i	$0.303030\pi$
$139$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	−0.995472	+	0.0950560i	$0.969697\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−2.24555	−	1.76592i	−2.24555	−	1.76592i
$145$		0			0
$146$	0.581419	−	1.67990i	0.581419	−	1.67990i
$147$	1.92837	−	0.371662i	1.92837	−	0.371662i
$148$		0			0
$149$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$149$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$150$	1.13915	+	1.59971i	1.13915	+	1.59971i
$151$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$151$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$152$	0.0552004	+	1.15880i	0.0552004	+	1.15880i
$153$	0.196753	−	0.187603i	0.196753	−	0.187603i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$157$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.40777	−	4.06748i	−1.40777	−	4.06748i
$163$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$163$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$164$	0.959493	−	1.66189i	0.959493	−	1.66189i
$165$		0			0
$166$	0.771316	−	0.308788i	0.771316	−	0.308788i
$167$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$167$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$168$		0			0
$169$	0.928368	−	0.371662i	0.928368	−	0.371662i
$170$		0			0
$171$	−1.65707	+	2.87013i	−1.65707	+	2.87013i
$172$	0.995472	+	1.72421i	0.995472	+	1.72421i
$173$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$173$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$174$		0			0
$175$		0			0
$176$	0.857685	+	0.989821i	0.857685	+	0.989821i
$177$	−1.08070	−	0.694523i	−1.08070	−	0.694523i
$178$	0.437742	+	0.175245i	0.437742	+	0.175245i
$179$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$179$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$180$		0			0
$181$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$181$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.104852	+	0.0673845i	−0.104852	+	0.0673845i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$191$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$192$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$193$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$193$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$194$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$195$		0			0
$196$	0.415415	−	0.909632i	0.415415	−	0.909632i
$197$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$197$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$198$	0.532475	+	3.70344i	0.532475	+	3.70344i
$199$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$199$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$200$	1.00000			1.00000
$201$	−1.88431	−	0.553283i	−1.88431	−	0.553283i
$202$		0			0
$203$		0			0
$204$	−0.0265970	−	0.184986i	−0.0265970	−	0.184986i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.995012	−	1.14831i	0.995012	−	1.14831i
$210$		0			0
$211$	−0.370638	−	0.291473i	−0.370638	−	0.291473i	0.415415	−	0.909632i	$-0.363636\pi$
$211$	−0.370638	−	0.291473i	−0.370638	−	0.291473i	−0.786053	+	0.618159i	$0.787879\pi$
$212$		0			0
$213$		0			0
$214$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i
$215$		0			0
$216$	−3.49866	−	1.02730i	−3.49866	−	1.02730i
$217$		0			0
$218$		0			0
$219$	−0.166113	−	3.48714i	−0.166113	−	3.48714i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$223$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$224$		0			0
$225$	2.40324	+	1.54447i	2.40324	+	1.54447i
$226$	0.428368	+	0.494363i	0.428368	+	0.494363i
$227$	0.0688733	−	1.44583i	0.0688733	−	1.44583i	−0.654861	−	0.755750i	$-0.727273\pi$
$227$	0.0688733	−	1.44583i	0.0688733	−	1.44583i	0.723734	−	0.690079i	$-0.242424\pi$
$228$	0.946439	+	2.07241i	0.946439	+	2.07241i
$229$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$229$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.928368	+	0.371662i	−0.928368	+	0.371662i	−0.786053	−	0.618159i	$-0.787879\pi$
$233$	−0.928368	+	0.371662i	−0.928368	+	0.371662i	−0.142315	+	0.989821i	$0.545455\pi$
$234$		0			0
$235$		0			0
$236$	−0.607279	+	0.243118i	−0.607279	+	0.243118i
$237$		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	1.00000			$0$
$241$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$242$	0.0340387	−	0.714560i	0.0340387	−	0.714560i
$243$	−3.14757	−	3.63249i	−3.14757	−	3.63249i
$244$		0			0
$245$		0			0
$246$	0.536330	−	3.73026i	0.536330	−	3.73026i
$247$		0			0
$248$		0			0
$249$	1.18087	−	1.12595i	1.18087	−	1.12595i
$250$		0			0
$251$	−1.28656	+	0.663268i	−1.28656	+	0.663268i	−0.959493	−	0.281733i	$-0.909091\pi$
$251$	−1.28656	+	0.663268i	−1.28656	+	0.663268i	−0.327068	+	0.945001i	$0.606061\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$257$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.888835	−	0.458227i	$-0.848485\pi$
$257$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.786053	+	0.618159i	$0.787879\pi$
$258$	3.07341	+	2.41696i	3.07341	+	2.41696i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.91030	+	0.182411i	1.91030	+	0.182411i
$263$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$263$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$264$	2.28618	+	1.17861i	2.28618	+	1.17861i
$265$		0			0
$266$		0			0
$267$	0.925994			0.925994
$268$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$271$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$272$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$273$		0			0
$274$	1.56499	+	0.149438i	1.56499	+	0.149438i
$275$	−0.947890	−	0.903811i	−0.947890	−	0.903811i
$276$		0			0
$277$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$277$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$278$	0.786053	+	0.618159i	0.786053	+	0.618159i
$279$		0			0
$280$		0			0
$281$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i	−0.142315	−	0.989821i	$-0.545455\pi$
$281$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i	0.235759	+	0.971812i	$0.424242\pi$
$282$		0			0
$283$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$283$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.24555	+	1.76592i	−2.24555	+	1.76592i
$289$	−0.574804	+	0.807199i	−0.574804	+	0.807199i
$290$		0			0
$291$	−3.24102	−	1.29751i	−3.24102	−	1.29751i
$292$	−1.49547	−	0.961081i	−1.49547	−	0.961081i
$293$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$293$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$294$	0.0934441	−	1.96163i	0.0934441	−	1.96163i
$295$		0			0
$296$		0			0
$297$	2.38786	+	4.13590i	2.38786	+	4.13590i
$298$		0			0
$299$		0			0
$300$	1.82318	−	0.729892i	1.82318	−	0.729892i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.13915	+	0.219553i	1.13915	+	0.219553i
$305$		0			0
$306$	−0.135929	−	0.235436i	−0.135929	−	0.235436i
$307$	0.651174	+	1.88144i	0.651174	+	1.88144i	0.415415	+	0.909632i	$0.363636\pi$
$307$	0.651174	+	1.88144i	0.651174	+	1.88144i	0.235759	+	0.971812i	$0.424242\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$311$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$312$		0			0
$313$	−0.165101	+	1.14831i	−0.165101	+	1.14831i	0.723734	+	0.690079i	$0.242424\pi$
$313$	−0.165101	+	1.14831i	−0.165101	+	1.14831i	−0.888835	+	0.458227i	$0.848485\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$317$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.470237	+	0.302203i	−0.470237	+	0.302203i
$322$		0			0
$323$	−0.0361086	+	0.104329i	−0.0361086	+	0.104329i
$324$	−4.28471	+	0.409141i	−4.28471	+	0.409141i
$325$		0			0
$326$	−1.38884	+	0.407799i	−1.38884	+	0.407799i
$327$		0			0
$328$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$329$		0			0
$330$		0			0
$331$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.142315	−	0.989821i	$-0.545455\pi$
$331$	−1.03115	−	0.531595i	−1.03115	−	0.531595i	−0.888835	+	0.458227i	$0.848485\pi$
$332$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.396666	−	1.63508i	0.396666	−	1.63508i	−0.327068	−	0.945001i	$-0.606061\pi$
$337$	0.396666	−	1.63508i	0.396666	−	1.63508i	0.723734	−	0.690079i	$-0.242424\pi$
$338$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$339$	1.14182	+	0.588651i	1.14182	+	0.588651i
$340$		0			0
$341$		0			0
$342$	2.39856	+	2.28702i	2.39856	+	2.28702i
$343$		0			0
$344$	1.91030	−	0.560914i	1.91030	−	0.560914i
$345$		0			0
$346$		0			0
$347$	0.327068	−	0.945001i	0.327068	−	0.945001i	−0.654861	−	0.755750i	$-0.727273\pi$
$347$	0.327068	−	0.945001i	0.327068	−	0.945001i	0.981929	−	0.189251i	$-0.0606061\pi$
$348$		0			0
$349$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$349$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$350$		0			0
$351$		0			0
$352$	1.16413	−	0.600149i	1.16413	−	0.600149i
$353$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	−0.995472	−	0.0950560i	$-0.969697\pi$
$353$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i	0.981929	−	0.189251i	$-0.0606061\pi$
$354$	−0.929730	+	0.886496i	−0.929730	+	0.886496i
$355$		0			0
$356$	0.273507	−	0.384087i	0.273507	−	0.384087i
$357$		0			0
$358$	0.771316	+	0.308788i	0.771316	+	0.308788i
$359$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$359$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$360$		0			0
$361$	0.0164569	−	0.345472i	0.0164569	−	0.345472i
$362$		0			0
$363$	−0.459493	−	1.32762i	−0.459493	−	1.32762i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$367$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$368$		0			0
$369$	−1.29244	−	5.32751i	−1.29244	−	5.32751i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$	0.0407651	+	0.117783i	0.0407651	+	0.117783i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.995472	−	0.0950560i	$-0.969697\pi$
$379$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.786053	−	0.618159i	$-0.787879\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$383$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$384$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$385$		0			0
$386$	0.975950	+	1.37053i	0.975950	+	1.37053i
$387$	5.45721	+	1.60238i	5.45721	+	1.60238i
$388$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$389$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$389$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$390$		0			0
$391$		0			0
$392$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$393$	3.61596	−	1.06174i	3.61596	−	1.06174i
$394$		0			0
$395$		0			0
$396$	3.72459	+	0.355655i	3.72459	+	0.355655i
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$		0			0
$399$		0			0
$400$	0.235759	−	0.971812i	0.235759	−	0.971812i
$401$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$401$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$402$	−0.981929	+	1.70075i	−0.981929	+	1.70075i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.186042	−	0.0177649i	−0.186042	−	0.0177649i
$409$	−0.205996	−	0.196417i	−0.205996	−	0.196417i	0.580057	−	0.814576i	$-0.303030\pi$
$409$	−0.205996	−	0.196417i	−0.205996	−	0.196417i	−0.786053	+	0.618159i	$0.787879\pi$
$410$		0			0
$411$	2.96233	−	0.869819i	2.96233	−	0.869819i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.88431	+	0.553283i	1.88431	+	0.553283i
$418$	−0.881354	−	1.23769i	−0.881354	−	1.23769i
$419$	1.58006	−	0.814576i	1.58006	−	0.814576i	0.580057	−	0.814576i	$-0.303030\pi$
$419$	1.58006	−	0.814576i	1.58006	−	0.814576i	1.00000			$0$
$420$		0			0
$421$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$421$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$422$	−0.370638	+	0.291473i	−0.370638	+	0.291473i
$423$		0			0
$424$		0			0
$425$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i
$426$		0			0
$427$		0			0
$428$	−0.0135432	+	0.284307i	−0.0135432	+	0.284307i
$429$		0			0
$430$		0			0
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−1.82318	+	3.15784i	−1.82318	+	3.15784i
$433$	−1.54370	−	0.297523i	−1.54370	−	0.297523i	−0.654861	−	0.755750i	$-0.727273\pi$
$433$	−1.54370	−	0.297523i	−1.54370	−	0.297523i	−0.888835	+	0.458227i	$0.848485\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−3.42800	−	0.660694i	−3.42800	−	0.660694i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−0.934347	−	2.69962i	−0.934347	−	2.69962i
$442$		0			0
$443$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i	−0.995472	−	0.0950560i	$-0.969697\pi$
$443$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.0475819	−	0.998867i	$-0.484848\pi$
$449$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.981929	+	0.189251i	$0.0606061\pi$
$450$	2.06752	−	1.97137i	2.06752	−	1.97137i
$451$	0.119589	+	2.51049i	0.119589	+	2.51049i
$452$	0.581419	−	0.299742i	0.581419	−	0.299742i
$453$		0			0
$454$	−1.38884	−	0.407799i	−1.38884	−	0.407799i
$455$		0			0
$456$	2.23713	−	0.431171i	2.23713	−	0.431171i
$457$	−0.154218	+	0.445585i	−0.154218	+	0.445585i	−0.995472	−	0.0950560i	$-0.969697\pi$
$457$	−0.154218	+	0.445585i	−0.154218	+	0.445585i	0.841254	+	0.540641i	$0.181818\pi$
$458$		0			0
$459$	−0.272762	−	0.214502i	−0.272762	−	0.214502i
$460$		0			0
$461$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$461$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$462$		0			0
$463$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$463$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$464$		0			0
$465$		0			0
$466$	0.142315	+	0.989821i	0.142315	+	0.989821i
$467$	−0.308779	+	1.27280i	−0.308779	+	1.27280i	0.580057	+	0.814576i	$0.303030\pi$
$467$	−0.308779	+	1.27280i	−0.308779	+	1.27280i	−0.888835	+	0.458227i	$0.848485\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.0930932	+	0.647478i	0.0930932	+	0.647478i
$473$	−2.31771	−	1.19486i	−2.31771	−	1.19486i
$474$		0			0
$475$	−1.15486	−	0.110276i	−1.15486	−	0.110276i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$479$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$480$		0			0
$481$		0			0
$482$	0.815816	−	0.157236i	0.815816	−	0.157236i
$483$		0			0
$484$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$485$		0			0
$486$	−4.27217	+	2.20246i	−4.27217	+	2.20246i
$487$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$487$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$488$		0			0
$489$	−2.23445	+	1.75719i	−2.23445	+	1.75719i
$490$		0			0
$491$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$491$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$492$	−3.49866	−	1.40065i	−3.49866	−	1.40065i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.815816	−	1.41303i	−0.815816	−	1.41303i
$499$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$499$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$500$		0			0
$501$		0			0
$502$	0.341254	+	1.40667i	0.341254	+	1.40667i
$503$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$503$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$508$		0			0
$509$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$509$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$510$		0			0
$511$		0			0
$512$	0.841254	+	0.540641i	0.841254	+	0.540641i
$513$	3.92718	+	1.57221i	3.92718	+	1.57221i
$514$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$515$		0			0
$516$	3.07341	−	2.41696i	3.07341	−	2.41696i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.786053	−	0.618159i	$-0.787879\pi$
$521$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.995472	+	0.0950560i	$0.969697\pi$
$522$		0			0
$523$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.888835	−	0.458227i	$-0.848485\pi$
$523$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.654861	+	0.755750i	$0.727273\pi$
$524$	0.627639	−	1.81344i	0.627639	−	1.81344i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.68437	−	1.94387i	1.68437	−	1.94387i
$529$	0.723734	+	0.690079i	0.723734	+	0.690079i
$530$		0			0
$531$	−0.776283	+	1.69982i	−0.776283	+	1.69982i
$532$		0			0
$533$		0			0
$534$	0.218311	−	0.899892i	0.218311	−	0.899892i
$535$		0			0
$536$	0.415415	+	0.909632i	0.415415	+	0.909632i
$537$	1.63163			1.63163
$538$		0			0
$539$	0.186393	+	1.29639i	0.186393	+	1.29639i
$540$		0			0
$541$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$541$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$542$		0			0
$543$		0			0
$544$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$545$		0			0
$546$		0			0
$547$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i	−0.327068	+	0.945001i	$0.606061\pi$
$548$	0.514186	−	1.48564i	0.514186	−	1.48564i
$549$		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
$556$	0.786053	−	0.618159i	0.786053	−	0.618159i
$557$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$557$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.160291	+	0.184986i	0.160291	+	0.184986i
$562$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i
$563$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.723734	+	0.690079i	$0.242424\pi$
$563$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.0475819	+	0.998867i	$0.484848\pi$
$564$		0			0
$565$		0			0
$566$	0.500000	−	0.866025i	0.500000	−	0.866025i
$567$		0			0
$568$		0			0
$569$	−0.419102	−	1.72756i	−0.419102	−	1.72756i	−0.654861	−	0.755750i	$-0.727273\pi$
$569$	−0.419102	−	1.72756i	−0.419102	−	1.72756i	0.235759	−	0.971812i	$-0.424242\pi$
$570$		0			0
$571$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i	−0.327068	−	0.945001i	$-0.606061\pi$
$571$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i	0.415415	+	0.909632i	$0.363636\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.18673	+	2.59858i	1.18673	+	2.59858i
$577$	0.0224357	−	0.470984i	0.0224357	−	0.470984i	−0.959493	−	0.281733i	$-0.909091\pi$
$577$	0.0224357	−	0.470984i	0.0224357	−	0.470984i	0.981929	−	0.189251i	$-0.0606061\pi$
$578$	0.648930	+	0.748905i	0.648930	+	0.748905i
$579$	2.77967	+	1.78639i	2.77967	+	1.78639i
$580$		0			0
$581$		0			0
$582$	−2.02503	+	2.84376i	−2.02503	+	2.84376i
$583$		0			0
$584$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$585$		0			0
$586$		0			0
$587$	−1.03115	−	1.44805i	−1.03115	−	1.44805i	−0.888835	−	0.458227i	$-0.848485\pi$
$587$	−1.03115	−	1.44805i	−1.03115	−	1.44805i	−0.142315	−	0.989821i	$-0.545455\pi$
$588$	−1.88431	−	0.553283i	−1.88431	−	0.553283i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.981929	+	0.189251i	$0.0606061\pi$
$593$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.415415	+	0.909632i	$0.363636\pi$
$594$	4.58227	−	1.34548i	4.58227	−	1.34548i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$599$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$600$	−0.279486	−	1.94387i	−0.279486	−	1.94387i
$601$	0.341254	−	1.40667i	0.341254	−	1.40667i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	0.341254	−	1.40667i	0.341254	−	1.40667i	0.841254	−	0.540641i	$-0.181818\pi$
$602$		0			0
$603$	−0.406556	+	2.82766i	−0.406556	+	2.82766i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$607$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$608$	0.481929	−	1.05528i	0.481929	−	1.05528i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.260846	+	0.0765912i	−0.260846	+	0.0765912i
$613$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$613$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$614$	1.98193	−	0.189251i	1.98193	−	0.189251i
$615$		0			0
$616$		0			0
$617$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$617$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$618$		0			0
$619$	−0.911911	−	1.28060i	−0.911911	−	1.28060i	−0.959493	−	0.281733i	$-0.909091\pi$
$619$	−0.911911	−	1.28060i	−0.911911	−	1.28060i	0.0475819	−	0.998867i	$-0.484848\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$626$	1.07701	+	0.431171i	1.07701	+	0.431171i
$627$	−2.51025	−	1.61324i	−2.51025	−	1.61324i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$631$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$632$		0			0
$633$	−0.462997	+	0.801934i	−0.462997	+	0.801934i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$641$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$642$	0.182822	+	0.528229i	0.182822	+	0.528229i
$643$	−0.271738	−	0.595023i	−0.271738	−	0.595023i	0.723734	−	0.690079i	$-0.242424\pi$
$643$	−0.271738	−	0.595023i	−0.271738	−	0.595023i	−0.995472	+	0.0950560i	$0.969697\pi$
$644$		0			0
$645$		0			0
$646$	0.0928751	+	0.0596872i	0.0928751	+	0.0596872i
$647$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$647$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$648$	−0.612552	+	4.26039i	−0.612552	+	4.26039i
$649$	0.496956	−	0.697876i	0.496956	−	0.697876i
$650$		0			0
$651$		0			0
$652$	0.0688733	+	1.44583i	0.0688733	+	1.44583i
$653$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$653$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$654$		0			0
$655$		0			0
$656$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$657$	−4.98656	+	0.961081i	−4.98656	+	0.961081i
$658$		0			0
$659$	0.995472	−	0.0950560i	0.995472	−	0.0950560i	0.415415	−	0.909632i	$-0.363636\pi$
$659$	0.995472	−	0.0950560i	0.995472	−	0.0950560i	0.580057	+	0.814576i	$0.303030\pi$
$660$		0			0
$661$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$661$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$662$	−0.759713	+	0.876756i	−0.759713	+	0.876756i
$663$		0			0
$664$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	0.235759	−	0.971812i	$-0.424242\pi$
$674$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$675$	1.51475	−	3.31685i	1.51475	−	3.31685i
$676$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$677$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$677$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$678$	0.841254	−	0.970858i	0.841254	−	0.970858i
$679$		0			0
$680$		0			0
$681$	−2.82975	+	0.270208i	−2.82975	+	0.270208i
$682$		0			0
$683$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.888835	−	0.458227i	$-0.848485\pi$
$683$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.654861	+	0.755750i	$0.727273\pi$
$684$	2.78803	−	1.79176i	2.78803	−	1.79176i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.0947329	−	1.98869i	−0.0947329	−	1.98869i
$689$		0			0
$690$		0			0
$691$	−0.165101	+	0.231852i	−0.165101	+	0.231852i	−0.888835	−	0.458227i	$-0.848485\pi$
$691$	−0.165101	+	0.231852i	−0.165101	+	0.231852i	0.723734	+	0.690079i	$0.242424\pi$
$692$		0			0
$693$		0			0
$694$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$695$		0			0
$696$		0			0
$697$	−0.0758623	−	0.166115i	−0.0758623	−	0.166115i
$698$		0			0
$699$	0.981929	+	1.70075i	0.981929	+	1.70075i
$700$		0			0
$701$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$701$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$702$		0			0
$703$		0			0
$704$	−0.308779	−	1.27280i	−0.308779	−	1.27280i
$705$		0			0
$706$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i
$707$		0			0
$708$	0.642315	+	1.11252i	0.642315	+	1.11252i
$709$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$709$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$710$		0			0
$711$		0			0
$712$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.481929	−	0.676774i	0.481929	−	0.676774i
$717$		0			0
$718$		0			0
$719$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$719$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$720$		0			0
$721$		0			0
$722$	−0.331854	−	0.0974412i	−0.331854	−	0.0974412i
$723$	1.37262	−	0.882127i	1.37262	−	0.882127i
$724$		0			0
$725$		0			0
$726$	−1.39852	+	0.133543i	−1.39852	+	0.133543i
$727$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$727$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$728$		0			0
$729$	−3.36273	+	3.88080i	−3.36273	+	3.88080i
$730$		0			0
$731$	0.188608	+	0.0180099i	0.188608	+	0.0180099i
$732$		0			0
$733$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$733$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.428368	−	1.23769i	0.428368	−	1.23769i
$738$	−5.48204			−5.48204
$739$	−0.154218	+	0.635697i	−0.154218	+	0.635697i	0.841254	+	0.540641i	$0.181818\pi$
$739$	−0.154218	+	0.635697i	−0.154218	+	0.635697i	−0.995472	+	0.0950560i	$0.969697\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$743$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.86567	−	1.46718i	−1.86567	−	1.46718i
$748$	0.124074	−	0.0118476i	0.124074	−	0.0118476i
$749$		0			0
$750$		0			0
$751$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$751$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$752$		0			0
$753$	1.64888	+	2.31553i	1.64888	+	2.31553i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$757$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$758$	−1.11312	+	1.56316i	−1.11312	+	1.56316i
$759$		0			0
$760$		0			0
$761$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$761$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.92837	+	0.371662i	1.92837	+	0.371662i
$769$	1.34378	−	0.537970i	1.34378	−	0.537970i	0.415415	−	0.909632i	$-0.363636\pi$
$769$	1.34378	−	0.537970i	1.34378	−	0.537970i	0.928368	+	0.371662i	$0.121212\pi$
$770$		0			0
$771$	0.778996	+	3.21106i	0.778996	+	3.21106i
$772$	1.56199	−	0.625325i	1.56199	−	0.625325i
$773$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$773$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$774$	2.84380	−	4.92561i	2.84380	−	4.92561i
$775$		0			0
$776$	0.581419	+	1.67990i	0.581419	+	1.67990i
$777$		0			0
$778$		0			0
$779$	1.45788	+	1.68248i	1.45788	+	1.68248i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$785$		0			0
$786$	−0.179318	−	3.76435i	−0.179318	−	3.76435i
$787$	0.252989	−	0.130425i	0.252989	−	0.130425i	−0.327068	−	0.945001i	$-0.606061\pi$
$787$	0.252989	−	0.130425i	0.252989	−	0.130425i	0.580057	+	0.814576i	$0.303030\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.22373	−	3.53575i	1.22373	−	3.53575i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$797$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$798$		0			0
$799$		0			0
$800$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$801$	−0.191698	−	1.33329i	−0.191698	−	1.33329i
$802$	0.396666	−	1.63508i	0.396666	−	1.63508i
$803$	2.32825			2.32825
$804$	1.42131	+	1.35522i	1.42131	+	1.35522i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$809$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$810$		0			0
$811$	0.601300	+	0.573338i	0.601300	+	0.573338i	0.928368	−	0.371662i	$-0.121212\pi$
$811$	0.601300	+	0.573338i	0.601300	+	0.573338i	−0.327068	+	0.945001i	$0.606061\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.0611251	+	0.176609i	−0.0611251	+	0.176609i
$817$	−2.26798	+	0.437118i	−2.26798	+	0.437118i
$818$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$819$		0			0
$820$		0			0
$821$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$821$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$822$	−0.146904	−	3.08390i	−0.146904	−	3.08390i
$823$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$823$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$824$		0			0
$825$	−1.49197	+	2.09518i	−1.49197	+	2.09518i
$826$		0			0
$827$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.327068	−	0.945001i	$-0.606061\pi$
$827$	−1.21590	−	0.486774i	−1.21590	−	0.486774i	−0.888835	+	0.458227i	$0.848485\pi$
$828$		0			0
$829$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$829$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i
$834$	0.981929	−	1.70075i	0.981929	−	1.70075i
$835$		0			0
$836$	−1.41059	+	0.564714i	−1.41059	+	0.564714i
$837$		0			0
$838$	−0.419102	−	1.72756i	−0.419102	−	1.72756i
$839$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$839$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$840$		0			0
$841$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$842$		0			0
$843$	−0.0611251	−	0.176609i	−0.0611251	−	0.176609i
$844$	0.195876	+	0.428908i	0.195876	+	0.428908i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.279486	−	1.94387i	0.279486	−	1.94387i
$850$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i
$851$		0			0
$852$		0			0
$853$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$853$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$854$		0			0
$855$		0			0
$856$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$857$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$857$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$858$		0			0
$859$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i	−0.959493	−	0.281733i	$-0.909091\pi$
$859$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i	0.928368	+	0.371662i	$0.121212\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$863$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$864$	2.63900	+	2.51628i	2.63900	+	2.51628i
$865$		0			0
$866$	−0.653077	+	1.43004i	−0.653077	+	1.43004i
$867$	1.72974	+	0.891742i	1.72974	+	0.891742i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.19726	+	4.93519i	−1.19726	+	4.93519i
$874$		0			0
$875$		0			0
$876$	−1.45025	+	3.17561i	−1.45025	+	3.17561i
$877$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$877$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$881$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$882$	−2.84380	+	0.271550i	−2.84380	+	0.271550i
$883$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.0475819	−	0.998867i	$-0.484848\pi$
$883$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.580057	−	0.814576i	$-0.303030\pi$
$884$		0			0
$885$		0			0
$886$	−0.0913090	−	0.0268107i	−0.0913090	−	0.0268107i
$887$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$887$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.43122	−	3.48475i	4.43122	−	3.48475i
$892$		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
$900$	−1.42837	−	2.47401i	−1.42837	−	2.47401i
$901$		0			0
$902$	2.46792	+	0.475652i	2.46792	+	0.475652i
$903$		0			0
$904$	−0.154218	−	0.635697i	−0.154218	−	0.635697i
$905$		0			0
$906$		0			0
$907$	1.65210	+	0.318417i	1.65210	+	0.318417i	0.928368	−	0.371662i	$-0.121212\pi$
$907$	1.65210	+	0.318417i	1.65210	+	0.318417i	0.723734	+	0.690079i	$0.242424\pi$
$908$	−0.723734	+	1.25354i	−0.723734	+	1.25354i
$909$		0			0
$910$		0			0
$911$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$911$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$912$	0.108406	−	2.27572i	0.108406	−	2.27572i
$913$	0.712591	+	0.822373i	0.712591	+	0.822373i
$914$	0.396666	+	0.254922i	0.396666	+	0.254922i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.272762	+	0.214502i	−0.272762	+	0.214502i
$919$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$919$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$920$		0			0
$921$	3.47528	−	1.79163i	3.47528	−	1.79163i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.78153	+	0.523103i	−1.78153	+	0.523103i	−0.995472	−	0.0950560i	$-0.969697\pi$
$929$	−1.78153	+	0.523103i	−1.78153	+	0.523103i	−0.786053	+	0.618159i	$0.787879\pi$
$930$		0			0
$931$	0.839614	+	0.800570i	0.839614	+	0.800570i
$932$	0.995472	+	0.0950560i	0.995472	+	0.0950560i
$933$		0			0
$934$	1.16413	+	0.600149i	1.16413	+	0.600149i
$935$		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
$939$	2.27830			2.27830
$940$		0			0
$941$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$941$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$942$		0			0
$943$		0			0
$944$	0.651174	+	0.0621796i	0.651174	+	0.0621796i
$945$		0			0
$946$	−1.70760	+	1.97068i	−1.70760	+	1.97068i
$947$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	0.0475819	+	0.998867i	$0.484848\pi$
$948$		0			0
$949$		0			0
$950$	−0.379436	+	1.09631i	−0.379436	+	1.09631i
$951$		0			0
$952$		0			0
$953$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.981929	+	0.189251i	$0.0606061\pi$
$953$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.928368	+	0.371662i	$0.121212\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.928368	+	0.371662i	0.928368	+	0.371662i
$962$		0			0
$963$	0.532475	+	0.614509i	0.532475	+	0.614509i
$964$	0.0395325	−	0.829889i	0.0395325	−	0.829889i
$965$		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
$969$	0.212894	+	0.0410319i	0.212894	+	0.0410319i
$970$		0			0
$971$	−0.469383	−	1.93482i	−0.469383	−	1.93482i	−0.327068	−	0.945001i	$-0.606061\pi$
$971$	−0.469383	−	1.93482i	−0.469383	−	1.93482i	−0.142315	−	0.989821i	$-0.545455\pi$
$972$	1.13317	+	4.67099i	1.13317	+	4.67099i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.271738	−	0.785135i	−0.271738	−	0.785135i	−0.995472	−	0.0950560i	$-0.969697\pi$
$977$	−0.271738	−	0.785135i	−0.271738	−	0.785135i	0.723734	−	0.690079i	$-0.242424\pi$
$978$	1.18087	+	2.58574i	1.18087	+	2.58574i
$979$	−0.0293845	+	0.616858i	−0.0293845	+	0.616858i
$980$		0			0
$981$		0			0
$982$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$983$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$983$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$984$	−2.18601	+	3.06982i	−2.18601	+	3.06982i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$991$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$992$		0			0
$993$	−0.745158	+	2.15299i	−0.745158	+	2.15299i
$994$		0			0
$995$		0			0
$996$	−1.56554	+	0.459684i	−1.56554	+	0.459684i
$997$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$997$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$998$	1.34378	+	1.28129i	1.34378	+	1.28129i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.1.ba.a.35.1	✓	20
4.3	odd	2		2144.1.bu.a.303.1		20
8.3	odd	2	CM	536.1.ba.a.35.1	✓	20
8.5	even	2		2144.1.bu.a.303.1		20
67.23	even	33	inner	536.1.ba.a.291.1	yes	20
268.23	odd	66		2144.1.bu.a.559.1		20
536.157	even	66		2144.1.bu.a.559.1		20
536.291	odd	66	inner	536.1.ba.a.291.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.1.ba.a.35.1	✓	20	1.1	even	1	trivial
536.1.ba.a.35.1	✓	20	8.3	odd	2	CM
536.1.ba.a.291.1	yes	20	67.23	even	33	inner
536.1.ba.a.291.1	yes	20	536.291	odd	66	inner
2144.1.bu.a.303.1		20	4.3	odd	2
2144.1.bu.a.303.1		20	8.5	even	2
2144.1.bu.a.559.1		20	268.23	odd	66
2144.1.bu.a.559.1		20	536.157	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)

\(f(q)\)	\(=\)	\(q+(0.235759 - 0.971812i) q^{2} +(-0.279486 - 1.94387i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(-1.95496 - 0.186677i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-2.74102 + 0.804835i) q^{9} +O(q^{10})\)	\(q+(0.235759 - 0.971812i) q^{2} +(-0.279486 - 1.94387i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(-1.95496 - 0.186677i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-2.74102 + 0.804835i) q^{9} +(1.30379 - 0.124497i) q^{11} +(-0.642315 + 1.85585i) q^{12} +(0.580057 + 0.814576i) q^{16} +(-0.0845850 + 0.0436066i) q^{17} +(0.135929 + 2.85350i) q^{18} +(0.839614 - 0.800570i) q^{19} +(0.186393 - 1.29639i) q^{22} +(1.65210 + 1.06174i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(1.51475 + 3.31685i) q^{27} +(0.928368 - 0.371662i) q^{32} +(-0.606397 - 2.49960i) q^{33} +(0.0224357 + 0.0924813i) q^{34} +(2.80511 + 0.540641i) q^{36} +(-0.580057 - 1.00469i) q^{38} +(-0.0913090 + 1.91681i) q^{41} +(-1.67489 - 1.07639i) q^{43} +(-1.21590 - 0.486774i) q^{44} +(1.42131 - 1.35522i) q^{48} +(0.0475819 + 0.998867i) q^{49} +(-0.888835 + 0.458227i) q^{50} +(0.108406 + 0.152235i) q^{51} +(3.58047 - 0.690079i) q^{54} +(-1.79086 - 1.40835i) q^{57} +(0.428368 - 0.494363i) q^{59} +(-0.142315 - 0.989821i) q^{64} -2.57211 q^{66} +(0.415415 - 0.909632i) q^{67} +0.0951638 q^{68} +(1.18673 - 2.59858i) q^{72} +(1.76962 + 0.168978i) q^{73} +(-1.28605 + 1.48418i) q^{75} +(-1.11312 + 0.326842i) q^{76} +(3.62093 - 2.32703i) q^{81} +(1.84125 + 0.540641i) q^{82} +(0.481929 + 0.676774i) q^{83} +(-1.44091 + 1.37391i) q^{86} +(-0.759713 + 1.06687i) q^{88} +(-0.0671040 + 0.466718i) q^{89} +(-0.981929 - 1.70075i) q^{96} +(0.888835 - 1.53951i) q^{97} +(0.981929 + 0.189251i) q^{98} +(-3.47351 + 1.39059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8}+O(q^{10}) \) 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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