LMFDB - Embedded newform 536.1.ba.a.155.1

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			155.1
Root			$-0.327068 + 0.945001i$ of defining polynomial
Character	$\chi$	$=$	536.155
Dual form			536.1.ba.a.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.981929 - 0.189251i) q^{2} +(-0.738471 + 1.61703i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-0.419102 + 1.72756i) q^{6} +(0.841254 - 0.540641i) q^{8} +(-1.41457 - 1.63251i) q^{9} +O(q^{10})$	\(q+(0.981929 - 0.189251i) q^{2} +(-0.738471 + 1.61703i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-0.419102 + 1.72756i) q^{6} +(0.841254 - 0.540641i) q^{8} +(-1.41457 - 1.63251i) q^{9} +(0.396666 + 1.63508i) q^{11} +(-0.0845850 + 1.77566i) q^{12} +(0.723734 - 0.690079i) q^{16} +(-1.45949 - 0.584293i) q^{17} +(-1.69796 - 1.33529i) q^{18} +(-0.473420 - 1.36786i) q^{19} +(0.698939 + 1.53046i) q^{22} +(0.252989 + 1.75958i) q^{24} +(0.841254 + 0.540641i) q^{25} +(1.97876 - 0.581017i) q^{27} +(0.580057 - 0.814576i) q^{32} +(-2.93689 - 0.566040i) q^{33} +(-1.54370 - 0.297523i) q^{34} +(-1.91999 - 0.989821i) q^{36} +(-0.723734 - 1.25354i) q^{38} +(1.02951 - 0.809616i) q^{41} +(-0.0671040 - 0.466718i) q^{43} +(0.975950 + 1.37053i) q^{44} +(0.581419 + 1.67990i) q^{48} +(-0.786053 - 0.618159i) q^{49} +(0.928368 + 0.371662i) q^{50} +(2.02261 - 1.92856i) q^{51} +(1.83305 - 0.945001i) q^{54} +(2.56147 + 0.244591i) q^{57} +(0.0800569 - 0.0514495i) q^{59} +(0.415415 - 0.909632i) q^{64} -2.99094 q^{66} +(-0.959493 - 0.281733i) q^{67} -1.57211 q^{68} +(-2.07261 - 0.608574i) q^{72} +(0.437742 - 1.80440i) q^{73} +(-1.49547 + 0.961081i) q^{75} +(-0.947890 - 1.09392i) q^{76} +(-0.214323 + 1.49065i) q^{81} +(0.857685 - 0.989821i) q^{82} +(-1.38884 + 1.32425i) q^{83} +(-0.154218 - 0.445585i) q^{86} +(1.21769 + 1.16106i) q^{88} +(0.815816 + 1.78639i) q^{89} +(0.888835 + 1.53951i) q^{96} +(-0.928368 + 1.60798i) q^{97} +(-0.888835 - 0.458227i) q^{98} +(2.10816 - 2.96050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{31}{33}\right)$

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 $

$2$	0.981929	−	0.189251i	0.981929	−	0.189251i
$2$	0.981929	−	0.189251i	0.981929	−	0.189251i
$3$	−0.738471	+	1.61703i	−0.738471	+	1.61703i	0.0475819	+	0.998867i	$0.484848\pi$
$3$	−0.738471	+	1.61703i	−0.738471	+	1.61703i	−0.786053	+	0.618159i	$0.787879\pi$
$4$	0.928368	−	0.371662i	0.928368	−	0.371662i
$5$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$5$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$6$	−0.419102	+	1.72756i	−0.419102	+	1.72756i
$7$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$7$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$8$	0.841254	−	0.540641i	0.841254	−	0.540641i
$9$	−1.41457	−	1.63251i	−1.41457	−	1.63251i
$10$		0			0
$11$	0.396666	+	1.63508i	0.396666	+	1.63508i	0.723734	+	0.690079i	$0.242424\pi$
$11$	0.396666	+	1.63508i	0.396666	+	1.63508i	−0.327068	+	0.945001i	$0.606061\pi$
$12$	−0.0845850	+	1.77566i	−0.0845850	+	1.77566i
$13$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$13$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$14$		0			0
$15$		0			0
$16$	0.723734	−	0.690079i	0.723734	−	0.690079i
$17$	−1.45949	−	0.584293i	−1.45949	−	0.584293i	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−1.45949	−	0.584293i	−1.45949	−	0.584293i	−0.959493	+	0.281733i	$0.909091\pi$
$18$	−1.69796	−	1.33529i	−1.69796	−	1.33529i
$19$	−0.473420	−	1.36786i	−0.473420	−	1.36786i	−0.888835	−	0.458227i	$-0.848485\pi$
$19$	−0.473420	−	1.36786i	−0.473420	−	1.36786i	0.415415	−	0.909632i	$-0.363636\pi$
$20$		0			0
$21$		0			0
$22$	0.698939	+	1.53046i	0.698939	+	1.53046i
$23$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$23$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$24$	0.252989	+	1.75958i	0.252989	+	1.75958i
$25$	0.841254	+	0.540641i	0.841254	+	0.540641i
$26$		0			0
$27$	1.97876	−	0.581017i	1.97876	−	0.581017i
$28$		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		−0.888835	−	0.458227i	$-0.848485\pi$
$31$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$32$	0.580057	−	0.814576i	0.580057	−	0.814576i
$33$	−2.93689	−	0.566040i	−2.93689	−	0.566040i
$34$	−1.54370	−	0.297523i	−1.54370	−	0.297523i
$35$		0			0
$36$	−1.91999	−	0.989821i	−1.91999	−	0.989821i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−0.723734	−	1.25354i	−0.723734	−	1.25354i
$39$		0			0
$40$		0			0
$41$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.0475819	−	0.998867i	$-0.484848\pi$
$41$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.981929	+	0.189251i	$0.0606061\pi$
$42$		0			0
$43$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i	−0.995472	−	0.0950560i	$-0.969697\pi$
$43$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i	0.928368	−	0.371662i	$-0.121212\pi$
$44$	0.975950	+	1.37053i	0.975950	+	1.37053i
$45$		0			0
$46$		0			0
$47$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$47$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$48$	0.581419	+	1.67990i	0.581419	+	1.67990i
$49$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$50$	0.928368	+	0.371662i	0.928368	+	0.371662i
$51$	2.02261	−	1.92856i	2.02261	−	1.92856i
$52$		0			0
$53$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$53$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$54$	1.83305	−	0.945001i	1.83305	−	0.945001i
$55$		0			0
$56$		0			0
$57$	2.56147	+	0.244591i	2.56147	+	0.244591i
$58$		0			0
$59$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	−0.500000	−	0.866025i	$-0.666667\pi$
$59$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	0.580057	+	0.814576i	$0.303030\pi$
$60$		0			0
$61$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$61$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$62$		0			0
$63$		0			0
$64$	0.415415	−	0.909632i	0.415415	−	0.909632i
$65$		0			0
$66$	−2.99094			−2.99094
$67$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$67$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$68$	−1.57211			−1.57211
$69$		0			0
$70$		0			0
$71$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$71$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$72$	−2.07261	−	0.608574i	−2.07261	−	0.608574i
$73$	0.437742	−	1.80440i	0.437742	−	1.80440i	−0.142315	−	0.989821i	$-0.545455\pi$
$73$	0.437742	−	1.80440i	0.437742	−	1.80440i	0.580057	−	0.814576i	$-0.303030\pi$
$74$		0			0
$75$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$76$	−0.947890	−	1.09392i	−0.947890	−	1.09392i
$77$		0			0
$78$		0			0
$79$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$79$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$80$		0			0
$81$	−0.214323	+	1.49065i	−0.214323	+	1.49065i
$82$	0.857685	−	0.989821i	0.857685	−	0.989821i
$83$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.500000	+	0.866025i	$0.666667\pi$
$83$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.888835	+	0.458227i	$0.848485\pi$
$84$		0			0
$85$		0			0
$86$	−0.154218	−	0.445585i	−0.154218	−	0.445585i
$87$		0			0
$88$	1.21769	+	1.16106i	1.21769	+	1.16106i
$89$	0.815816	+	1.78639i	0.815816	+	1.78639i	0.580057	+	0.814576i	$0.303030\pi$
$89$	0.815816	+	1.78639i	0.815816	+	1.78639i	0.235759	+	0.971812i	$0.424242\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.888835	+	1.53951i	0.888835	+	1.53951i
$97$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$97$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$98$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$99$	2.10816	−	2.96050i	2.10816	−	2.96050i
$100$	0.981929	+	0.189251i	0.981929	+	0.189251i
$101$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$101$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$102$	1.62108	−	2.27649i	1.62108	−	2.27649i
$103$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$103$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$104$		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	$0.545455\pi$
$108$	1.62108	−	1.27483i	1.62108	−	1.27483i
$109$		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
$113$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i	0.723734	−	0.690079i	$-0.242424\pi$
$113$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i	−0.654861	+	0.755750i	$0.727273\pi$
$114$	2.56147	−	0.244591i	2.56147	−	0.244591i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i
$119$		0			0
$120$		0			0
$121$	−1.62731	+	0.838935i	−1.62731	+	0.838935i
$122$		0			0
$123$	0.548907	+	2.26262i	0.548907	+	2.26262i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$127$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$128$	0.235759	−	0.971812i	0.235759	−	0.971812i
$129$	0.804250	+	0.236149i	0.804250	+	0.236149i
$130$		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	$0.909091\pi$
$132$	−2.93689	+	0.566040i	−2.93689	+	0.566040i
$133$		0			0
$134$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$135$		0			0
$136$	−1.54370	+	0.297523i	−1.54370	+	0.297523i
$137$	−0.827068	+	1.81103i	−0.827068	+	1.81103i	−0.327068	+	0.945001i	$0.606061\pi$
$137$	−0.827068	+	1.81103i	−0.827068	+	1.81103i	−0.500000	+	0.866025i	$0.666667\pi$
$138$		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
$144$	−2.15033	−	0.205332i	−2.15033	−	0.205332i
$145$		0			0
$146$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$147$	1.58006	−	0.814576i	1.58006	−	0.814576i
$148$		0			0
$149$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$149$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$150$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$151$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$151$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$152$	−1.13779	−	0.894765i	−1.13779	−	0.894765i
$153$	1.11070	+	3.20916i	1.11070	+	3.20916i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$157$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.0716573	+	1.50427i	0.0716573	+	1.50427i
$163$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$163$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$164$	0.654861	−	1.13425i	0.654861	−	1.13425i
$165$		0			0
$166$	−1.11312	+	1.56316i	−1.11312	+	1.56316i
$167$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$167$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$168$		0			0
$169$	0.580057	−	0.814576i	0.580057	−	0.814576i
$170$		0			0
$171$	−1.56335	+	2.70780i	−1.56335	+	2.70780i
$172$	−0.235759	−	0.408346i	−0.235759	−	0.408346i
$173$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$173$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$174$		0			0
$175$		0			0
$176$	1.41542	+	0.909632i	1.41542	+	0.909632i
$177$	0.0240754	+	0.167448i	0.0240754	+	0.167448i
$178$	1.13915	+	1.59971i	1.13915	+	1.59971i
$179$	−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		0.995472	−	0.0950560i	$-0.0303030\pi$
$181$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.376434	−	2.61816i	0.376434	−	2.61816i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$191$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$192$	1.16413	+	1.34347i	1.16413	+	1.34347i
$193$	−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	$0.363636\pi$
$194$	−0.607279	+	1.75462i	−0.607279	+	1.75462i
$195$		0			0
$196$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$197$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$197$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$198$	1.50979	−	3.30597i	1.50979	−	3.30597i
$199$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$199$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$200$	1.00000			1.00000
$201$	1.16413	−	1.34347i	1.16413	−	1.34347i
$202$		0			0
$203$		0			0
$204$	1.16096	−	2.54214i	1.16096	−	2.54214i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.04877	−	1.31666i	2.04877	−	1.31666i
$210$		0			0
$211$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.959493	−	0.281733i	$-0.909091\pi$
$211$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.995472	+	0.0950560i	$0.969697\pi$
$212$		0			0
$213$		0			0
$214$	−0.738471	+	0.380708i	−0.738471	+	0.380708i
$215$		0			0
$216$	1.35052	−	1.55858i	1.35052	−	1.55858i
$217$		0			0
$218$		0			0
$219$	2.59450	+	2.04034i	2.59450	+	2.04034i
$220$		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
$225$	−0.307416	−	2.13813i	−0.307416	−	2.13813i
$226$	0.0800569	+	0.0514495i	0.0800569	+	0.0514495i
$227$	0.514186	−	0.404360i	0.514186	−	0.404360i	−0.327068	−	0.945001i	$-0.606061\pi$
$227$	0.514186	−	0.404360i	0.514186	−	0.404360i	0.841254	+	0.540641i	$0.181818\pi$
$228$	2.46889	−	0.724932i	2.46889	−	0.724932i
$229$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$229$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	−0.995472	−	0.0950560i	$-0.969697\pi$
$233$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	0.415415	+	0.909632i	$0.363636\pi$
$234$		0			0
$235$		0			0
$236$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i
$237$		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
$241$	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			$0$
$242$	−1.43913	+	1.13174i	−1.43913	+	1.13174i
$243$	−0.517230	−	0.332404i	−0.517230	−	0.332404i
$244$		0			0
$245$		0			0
$246$	0.967192	+	2.11785i	0.967192	+	2.11785i
$247$		0			0
$248$		0			0
$249$	−1.11574	−	3.22371i	−1.11574	−	3.22371i
$250$		0			0
$251$	−0.607279	−	0.243118i	−0.607279	−	0.243118i	0.0475819	−	0.998867i	$-0.484848\pi$
$251$	−0.607279	−	0.243118i	−0.607279	−	0.243118i	−0.654861	+	0.755750i	$0.727273\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$257$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	0.928368	−	0.371662i	$-0.121212\pi$
$257$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	−0.995472	+	0.0950560i	$0.969697\pi$
$258$	0.834408	+	0.0796763i	0.834408	+	0.0796763i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.308779	+	1.27280i	−0.308779	+	1.27280i
$263$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$263$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$264$	−2.77670	+	1.11162i	−2.77670	+	1.11162i
$265$		0			0
$266$		0			0
$267$	−3.49109			−3.49109
$268$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$269$		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	+	0.584293i	−1.45949	+	0.584293i
$273$		0			0
$274$	−0.469383	+	1.93482i	−0.469383	+	1.93482i
$275$	−0.550294	+	1.58997i	−0.550294	+	1.58997i
$276$		0			0
$277$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$277$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$278$	0.995472	+	0.0950560i	0.995472	+	0.0950560i
$279$		0			0
$280$		0			0
$281$	1.39734	−	0.720381i	1.39734	−	0.720381i	0.415415	−	0.909632i	$-0.363636\pi$
$281$	1.39734	−	0.720381i	1.39734	−	0.720381i	0.981929	+	0.189251i	$0.0606061\pi$
$282$		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
$288$	−2.15033	+	0.205332i	−2.15033	+	0.205332i
$289$	1.06499	+	1.01546i	1.06499	+	1.01546i
$290$		0			0
$291$	−1.91457	−	2.68864i	−1.91457	−	2.68864i
$292$	−0.264241	−	1.83784i	−0.264241	−	1.83784i
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$	1.39734	−	1.09888i	1.39734	−	1.09888i
$295$		0			0
$296$		0			0
$297$	1.73492	+	3.00497i	1.73492	+	3.00497i
$298$		0			0
$299$		0			0
$300$	−1.03115	+	1.44805i	−1.03115	+	1.44805i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.28656	−	0.663268i	−1.28656	−	0.663268i
$305$		0			0
$306$	1.69796	+	2.94096i	1.69796	+	2.94096i
$307$	0.0224357	+	0.470984i	0.0224357	+	0.470984i	0.981929	+	0.189251i	$0.0606061\pi$
$307$	0.0224357	+	0.470984i	0.0224357	+	0.470984i	−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
$313$	0.601300	+	1.31666i	0.601300	+	1.31666i	0.928368	+	0.371662i	$0.121212\pi$
$313$	0.601300	+	1.31666i	0.601300	+	1.31666i	−0.327068	+	0.945001i	$0.606061\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$317$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.210191	−	1.46191i	0.210191	−	1.46191i
$322$		0			0
$323$	−0.108276	+	2.27300i	−0.108276	+	2.27300i
$324$	0.355048	+	1.46353i	0.355048	+	1.46353i
$325$		0			0
$326$	0.428368	+	0.494363i	0.428368	+	0.494363i
$327$		0			0
$328$	0.428368	−	1.23769i	0.428368	−	1.23769i
$329$		0			0
$330$		0			0
$331$	1.34378	−	0.537970i	1.34378	−	0.537970i	0.415415	−	0.909632i	$-0.363636\pi$
$331$	1.34378	−	0.537970i	1.34378	−	0.537970i	0.928368	+	0.371662i	$0.121212\pi$
$332$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i	−0.327068	−	0.945001i	$-0.606061\pi$
$337$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i	0.0475819	+	0.998867i	$0.484848\pi$
$338$	0.415415	−	0.909632i	0.415415	−	0.909632i
$339$	−0.157052	+	0.0628741i	−0.157052	+	0.0628741i
$340$		0			0
$341$		0			0
$342$	−1.02264	+	2.95473i	−1.02264	+	2.95473i
$343$		0			0
$344$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$345$		0			0
$346$		0			0
$347$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	0.841254	+	0.540641i	$0.181818\pi$
$347$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	−0.888835	+	0.458227i	$0.848485\pi$
$348$		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
$352$	1.56199	+	0.625325i	1.56199	+	0.625325i
$353$	−0.653077	−	0.513585i	−0.653077	−	0.513585i	0.235759	−	0.971812i	$-0.424242\pi$
$353$	−0.653077	−	0.513585i	−0.653077	−	0.513585i	−0.888835	+	0.458227i	$0.848485\pi$
$354$	0.0553301	+	0.159866i	0.0553301	+	0.159866i
$355$		0			0
$356$	1.42131	+	1.35522i	1.42131	+	1.35522i
$357$		0			0
$358$	−1.11312	−	1.56316i	−1.11312	−	1.56316i
$359$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$		0			0
$361$	−0.860857	+	0.676985i	−0.860857	+	0.676985i
$362$		0			0
$363$	−0.154861	−	3.25093i	−0.154861	−	3.25093i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$367$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$368$		0			0
$369$	−2.77802	−	0.535420i	−2.77802	−	0.535420i
$370$		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	$0.333333\pi$
$374$	−0.125858	−	2.64208i	−0.125858	−	2.64208i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.759713	−	1.06687i	−0.759713	−	1.06687i	−0.995472	−	0.0950560i	$-0.969697\pi$
$379$	−0.759713	−	1.06687i	−0.759713	−	1.06687i	0.235759	−	0.971812i	$-0.424242\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$383$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$384$	1.39734	+	1.09888i	1.39734	+	1.09888i
$385$		0			0
$386$	−0.205996	+	0.196417i	−0.205996	+	0.196417i
$387$	−0.666997	+	0.769755i	−0.666997	+	0.769755i
$388$	−0.264241	+	1.83784i	−0.264241	+	1.83784i
$389$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$389$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$390$		0			0
$391$		0			0
$392$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$393$	−1.52468	−	1.75958i	−1.52468	−	1.75958i
$394$		0			0
$395$		0			0
$396$	0.856844	−	3.53196i	0.856844	−	3.53196i
$397$		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
$400$	0.981929	−	0.189251i	0.981929	−	0.189251i
$401$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$401$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$402$	0.888835	−	1.53951i	0.888835	−	1.53951i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.658873	−	2.71591i	0.658873	−	2.71591i
$409$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	0.723734	+	0.690079i	$0.242424\pi$
$409$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	−0.995472	+	0.0950560i	$0.969697\pi$
$410$		0			0
$411$	−2.31771	−	2.67478i	−2.31771	−	2.67478i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.16413	+	1.34347i	−1.16413	+	1.34347i
$418$	1.76256	−	1.68060i	1.76256	−	1.68060i
$419$	1.72373	+	0.690079i	1.72373	+	0.690079i	1.00000			$0$
$419$	1.72373	+	0.690079i	1.72373	+	0.690079i	0.723734	+	0.690079i	$0.242424\pi$
$420$		0			0
$421$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$421$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$422$	−1.95496	+	0.186677i	−1.95496	+	0.186677i
$423$		0			0
$424$		0			0
$425$	−0.911911	−	1.28060i	−0.911911	−	1.28060i
$426$		0			0
$427$		0			0
$428$	−0.653077	+	0.513585i	−0.653077	+	0.513585i
$429$		0			0
$430$		0			0
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	1.03115	−	1.78600i	1.03115	−	1.78600i
$433$	1.76962	+	0.912303i	1.76962	+	0.912303i	0.928368	+	0.371662i	$0.121212\pi$
$433$	1.76962	+	0.912303i	1.76962	+	0.912303i	0.841254	+	0.540641i	$0.181818\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	2.93375	+	1.51245i	2.93375	+	1.51245i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	0.102782	+	2.15767i	0.102782	+	2.15767i
$442$		0			0
$443$	1.23576	−	0.971812i	1.23576	−	0.971812i	0.235759	−	0.971812i	$-0.424242\pi$
$443$	1.23576	−	0.971812i	1.23576	−	0.971812i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.888835	−	0.458227i	$-0.848485\pi$
$449$	−1.67489	+	0.159932i	−1.67489	+	0.159932i	−0.786053	+	0.618159i	$0.787879\pi$
$450$	−0.706504	−	2.04131i	−0.706504	−	2.04131i
$451$	1.73216	+	1.36218i	1.73216	+	1.36218i
$452$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i
$453$		0			0
$454$	0.428368	−	0.494363i	0.428368	−	0.494363i
$455$		0			0
$456$	2.28708	−	1.17907i	2.28708	−	1.17907i
$457$	0.0934441	−	1.96163i	0.0934441	−	1.96163i	−0.142315	−	0.989821i	$-0.545455\pi$
$457$	0.0934441	−	1.96163i	0.0934441	−	1.96163i	0.235759	−	0.971812i	$-0.424242\pi$
$458$		0			0
$459$	−3.22747	−	0.308186i	−3.22747	−	0.308186i
$460$		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		0.235759	−	0.971812i	$-0.424242\pi$
$463$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$464$		0			0
$465$		0			0
$466$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$467$	1.65210	−	0.318417i	1.65210	−	0.318417i	0.723734	−	0.690079i	$-0.242424\pi$
$467$	1.65210	−	0.318417i	1.65210	−	0.318417i	0.928368	+	0.371662i	$0.121212\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i
$473$	0.736504	−	0.294852i	0.736504	−	0.294852i
$474$		0			0
$475$	0.341254	−	1.40667i	0.341254	−	1.40667i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$479$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$480$		0			0
$481$		0			0
$482$	1.70566	−	0.879330i	1.70566	−	0.879330i
$483$		0			0
$484$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$485$		0			0
$486$	−0.570791	−	0.228510i	−0.570791	−	0.228510i
$487$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$487$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$488$		0			0
$489$	−1.15757	+	0.110535i	−1.15757	+	0.110535i
$490$		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	$-0.303030\pi$
$492$	1.35052	+	1.89654i	1.35052	+	1.89654i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.70566	−	2.95429i	−1.70566	−	2.95429i
$499$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$499$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$500$		0			0
$501$		0			0
$502$	−0.642315	−	0.123796i	−0.642315	−	0.123796i
$503$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$503$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.888835	+	1.53951i	0.888835	+	1.53951i
$508$		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
$513$	−1.73154	−	2.43160i	−1.73154	−	2.43160i
$514$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$515$		0			0
$516$	0.834408	−	0.0796763i	0.834408	−	0.0796763i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.759713	+	0.876756i	−0.759713	+	0.876756i	−0.995472	−	0.0950560i	$-0.969697\pi$
$521$	−0.759713	+	0.876756i	−0.759713	+	0.876756i	0.235759	+	0.971812i	$0.424242\pi$
$522$		0			0
$523$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.841254	−	0.540641i	$-0.181818\pi$
$523$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.928368	−	0.371662i	$-0.121212\pi$
$524$	−0.0623191	+	1.30824i	−0.0623191	+	1.30824i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−2.51614	+	1.61703i	−2.51614	+	1.61703i
$529$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$530$		0			0
$531$	−0.197238	−	0.0579143i	−0.197238	−	0.0579143i
$532$		0			0
$533$		0			0
$534$	−3.42800	+	0.660694i	−3.42800	+	0.660694i
$535$		0			0
$536$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$537$	3.41133			3.41133
$538$		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
$544$	−1.32254	+	0.849945i	−1.32254	+	0.849945i
$545$		0			0
$546$		0			0
$547$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$548$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i
$549$		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
$556$	0.995472	−	0.0950560i	0.995472	−	0.0950560i
$557$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$557$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	3.95564	+	2.54214i	3.95564	+	2.54214i
$562$	1.23576	−	0.971812i	1.23576	−	0.971812i
$563$	−1.11312	+	0.326842i	−1.11312	+	0.326842i	−0.786053	−	0.618159i	$-0.787879\pi$
$563$	−1.11312	+	0.326842i	−1.11312	+	0.326842i	−0.327068	+	0.945001i	$0.606061\pi$
$564$		0			0
$565$		0			0
$566$	0.500000	−	0.866025i	0.500000	−	0.866025i
$567$		0			0
$568$		0			0
$569$	1.82318	+	0.351390i	1.82318	+	0.351390i	0.981929	−	0.189251i	$-0.0606061\pi$
$569$	1.82318	+	0.351390i	1.82318	+	0.351390i	0.841254	+	0.540641i	$0.181818\pi$
$570$		0			0
$571$	−0.911911	+	1.28060i	−0.911911	+	1.28060i	0.0475819	+	0.998867i	$0.484848\pi$
$571$	−0.911911	+	1.28060i	−0.911911	+	1.28060i	−0.959493	+	0.281733i	$0.909091\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−2.07261	+	0.608574i	−2.07261	+	0.608574i
$577$	−1.54370	+	1.21398i	−1.54370	+	1.21398i	−0.654861	+	0.755750i	$0.727273\pi$
$577$	−1.54370	+	1.21398i	−1.54370	+	1.21398i	−0.888835	+	0.458227i	$0.848485\pi$
$578$	1.23792	+	0.795563i	1.23792	+	0.795563i
$579$	−0.0720082	−	0.500828i	−0.0720082	−	0.500828i
$580$		0			0
$581$		0			0
$582$	−2.38880	−	2.27772i	−2.38880	−	2.27772i
$583$		0			0
$584$	−0.607279	−	1.75462i	−0.607279	−	1.75462i
$585$		0			0
$586$		0			0
$587$	1.34378	−	1.28129i	1.34378	−	1.28129i	0.415415	−	0.909632i	$-0.363636\pi$
$587$	1.34378	−	1.28129i	1.34378	−	1.28129i	0.928368	−	0.371662i	$-0.121212\pi$
$588$	1.16413	−	1.34347i	1.16413	−	1.34347i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.84833	−	0.176494i	−1.84833	−	0.176494i	−0.888835	−	0.458227i	$-0.848485\pi$
$593$	−1.84833	−	0.176494i	−1.84833	−	0.176494i	−0.959493	+	0.281733i	$0.909091\pi$
$594$	2.27226	+	2.62233i	2.27226	+	2.62233i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$599$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$600$	−0.738471	+	1.61703i	−0.738471	+	1.61703i
$601$	−0.642315	+	0.123796i	−0.642315	+	0.123796i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−0.642315	+	0.123796i	−0.642315	+	0.123796i	−0.142315	+	0.989821i	$0.545455\pi$
$602$		0			0
$603$	0.897344	+	1.96491i	0.897344	+	1.96491i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$607$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$608$	−1.38884	−	0.407799i	−1.38884	−	0.407799i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	2.22386	+	2.56647i	2.22386	+	2.56647i
$613$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$613$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$614$	0.111165	+	0.458227i	0.111165	+	0.458227i
$615$		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
$619$	−1.44091	+	1.37391i	−1.44091	+	1.37391i	−0.654861	+	0.755750i	$0.727273\pi$
$619$	−1.44091	+	1.37391i	−1.44091	+	1.37391i	−0.786053	+	0.618159i	$0.787879\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.415415	+	0.909632i	0.415415	+	0.909632i
$626$	0.839614	+	1.17907i	0.839614	+	1.17907i
$627$	0.616123	+	4.28523i	0.616123	+	4.28523i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$631$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$632$		0			0
$633$	1.74555	−	3.02337i	1.74555	−	3.02337i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$641$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$642$	−0.0702757	−	1.47527i	−0.0702757	−	1.47527i
$643$	−0.0913090	+	0.0268107i	−0.0913090	+	0.0268107i	−0.327068	−	0.945001i	$-0.606061\pi$
$643$	−0.0913090	+	0.0268107i	−0.0913090	+	0.0268107i	0.235759	+	0.971812i	$0.424242\pi$
$644$		0			0
$645$		0			0
$646$	0.323848	+	2.25241i	0.323848	+	2.25241i
$647$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$647$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$648$	0.625606	+	1.36989i	0.625606	+	1.36989i
$649$	0.115880	+	0.110491i	0.115880	+	0.110491i
$650$		0			0
$651$		0			0
$652$	0.514186	+	0.404360i	0.514186	+	0.404360i
$653$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$653$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$654$		0			0
$655$		0			0
$656$	0.186393	−	1.29639i	0.186393	−	1.29639i
$657$	−3.56491	+	1.83784i	−3.56491	+	1.83784i
$658$		0			0
$659$	−0.235759	−	0.971812i	−0.235759	−	0.971812i	−0.959493	−	0.281733i	$-0.909091\pi$
$659$	−0.235759	−	0.971812i	−0.235759	−	0.971812i	0.723734	−	0.690079i	$-0.242424\pi$
$660$		0			0
$661$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$661$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$662$	1.21769	−	0.782560i	1.21769	−	0.782560i
$663$		0			0
$664$	−0.452418	+	1.86489i	−0.452418	+	1.86489i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.481929	−	1.05528i	0.481929	−	1.05528i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.481929	−	1.05528i	0.481929	−	1.05528i	0.981929	−	0.189251i	$-0.0606061\pi$
$674$	−0.264241	+	0.105786i	−0.264241	+	0.105786i
$675$	1.97876	+	0.581017i	1.97876	+	0.581017i
$676$	0.235759	−	0.971812i	0.235759	−	0.971812i
$677$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$677$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$678$	−0.142315	+	0.0914602i	−0.142315	+	0.0914602i
$679$		0			0
$680$		0			0
$681$	0.274150	+	1.13006i	0.274150	+	1.13006i
$682$		0			0
$683$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.841254	−	0.540641i	$-0.181818\pi$
$683$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.928368	−	0.371662i	$-0.121212\pi$
$684$	−0.444975	+	3.09487i	−0.444975	+	3.09487i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.370638	−	0.291473i	−0.370638	−	0.291473i
$689$		0			0
$690$		0			0
$691$	0.601300	+	0.573338i	0.601300	+	0.573338i	0.928368	−	0.371662i	$-0.121212\pi$
$691$	0.601300	+	0.573338i	0.601300	+	0.573338i	−0.327068	+	0.945001i	$0.606061\pi$
$692$		0			0
$693$		0			0
$694$	0.142315	+	0.989821i	0.142315	+	0.989821i
$695$		0			0
$696$		0			0
$697$	−1.97562	+	0.580093i	−1.97562	+	0.580093i
$698$		0			0
$699$	−0.888835	−	1.53951i	−0.888835	−	1.53951i
$700$		0			0
$701$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$701$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$702$		0			0
$703$		0			0
$704$	1.65210	+	0.318417i	1.65210	+	0.318417i
$705$		0			0
$706$	−0.738471	−	0.380708i	−0.738471	−	0.380708i
$707$		0			0
$708$	0.0845850	+	0.146505i	0.0845850	+	0.146505i
$709$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$709$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$710$		0			0
$711$		0			0
$712$	1.65210	+	1.06174i	1.65210	+	1.06174i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$717$		0			0
$718$		0			0
$719$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$719$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$720$		0			0
$721$		0			0
$722$	−0.717180	+	0.827670i	−0.717180	+	0.827670i
$723$	−0.485482	+	3.37660i	−0.485482	+	3.37660i
$724$		0			0
$725$		0			0
$726$	−0.767304	−	3.16287i	−0.767304	−	3.16287i
$727$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$727$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$728$		0			0
$729$	−0.347444	+	0.223289i	−0.347444	+	0.223289i
$730$		0			0
$731$	−0.174762	+	0.720381i	−0.174762	+	0.720381i
$732$		0			0
$733$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$733$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.0800569	−	1.68060i	0.0800569	−	1.68060i
$738$	−2.82915			−2.82915
$739$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i	−0.142315	−	0.989821i	$-0.545455\pi$
$739$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i	0.235759	+	0.971812i	$0.424242\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$743$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.12646	+	0.394029i	4.12646	+	0.394029i
$748$	−0.623601	−	2.57052i	−0.623601	−	2.57052i
$749$		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
$753$	0.841586	−	0.802450i	0.841586	−	0.802450i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$757$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$758$	−0.947890	−	0.903811i	−0.947890	−	0.903811i
$759$		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
$768$	1.58006	+	0.814576i	1.58006	+	0.814576i
$769$	−0.379436	+	0.532843i	−0.379436	+	0.532843i	−0.959493	−	0.281733i	$-0.909091\pi$
$769$	−0.379436	+	0.532843i	−0.379436	+	0.532843i	0.580057	+	0.814576i	$0.303030\pi$
$770$		0			0
$771$	0.496834	+	0.0957569i	0.496834	+	0.0957569i
$772$	−0.165101	+	0.231852i	−0.165101	+	0.231852i
$773$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$773$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$774$	−0.509266	+	0.882075i	−0.509266	+	0.882075i
$775$		0			0
$776$	0.0883470	+	1.85463i	0.0883470	+	1.85463i
$777$		0			0
$778$		0			0
$779$	−1.59483	−	1.02494i	−1.59483	−	1.02494i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$785$		0			0
$786$	−1.83013	−	1.43923i	−1.83013	−	1.43923i
$787$	0.771316	+	0.308788i	0.771316	+	0.308788i	0.723734	−	0.690079i	$-0.242424\pi$
$787$	0.771316	+	0.308788i	0.771316	+	0.308788i	0.0475819	+	0.998867i	$0.484848\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.172932	−	3.63029i	0.172932	−	3.63029i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$797$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$798$		0			0
$799$		0			0
$800$	0.928368	−	0.371662i	0.928368	−	0.371662i
$801$	1.76226	−	3.85880i	1.76226	−	3.85880i
$802$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i
$803$	3.12397			3.12397
$804$	0.581419	−	1.67990i	0.581419	−	1.67990i
$805$		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
$811$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.0475819	−	0.998867i	$-0.484848\pi$
$811$	0.627639	−	1.81344i	0.627639	−	1.81344i	0.580057	−	0.814576i	$-0.303030\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.132977	−	2.79152i	0.132977	−	2.79152i
$817$	−0.606636	+	0.312743i	−0.606636	+	0.312743i
$818$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$819$		0			0
$820$		0			0
$821$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$821$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$822$	−2.78203	−	2.18781i	−2.78203	−	2.18781i
$823$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$823$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$824$		0			0
$825$	−2.16465	−	2.06399i	−2.16465	−	2.06399i
$826$		0			0
$827$	0.975950	+	1.37053i	0.975950	+	1.37053i	0.928368	+	0.371662i	$0.121212\pi$
$827$	0.975950	+	1.37053i	0.975950	+	1.37053i	0.0475819	+	0.998867i	$0.484848\pi$
$828$		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
$833$	0.786053	+	1.36148i	0.786053	+	1.36148i
$834$	−0.888835	+	1.53951i	−0.888835	+	1.53951i
$835$		0			0
$836$	1.41266	−	1.98380i	1.41266	−	1.98380i
$837$		0			0
$838$	1.82318	+	0.351390i	1.82318	+	0.351390i
$839$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$839$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$840$		0			0
$841$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$842$		0			0
$843$	0.132977	+	2.79152i	0.132977	+	2.79152i
$844$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.738471	+	1.61703i	0.738471	+	1.61703i
$850$	−1.13779	−	1.08488i	−1.13779	−	1.08488i
$851$		0			0
$852$		0			0
$853$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$853$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$854$		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
$859$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i	0.580057	+	0.814576i	$0.303030\pi$
$859$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i	−0.654861	+	0.755750i	$0.727273\pi$
$860$		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	$0.818182\pi$
$864$	0.674512	−	1.94888i	0.674512	−	1.94888i
$865$		0			0
$866$	1.91030	+	0.560914i	1.91030	+	0.560914i
$867$	−2.42849	+	0.972222i	−2.42849	+	0.972222i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	3.93828	−	0.759041i	3.93828	−	0.759041i
$874$		0			0
$875$		0			0
$876$	3.16697	+	0.929905i	3.16697	+	0.929905i
$877$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$877$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.786053	−	0.618159i	$-0.787879\pi$
$881$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.888835	+	0.458227i	$0.848485\pi$
$882$	0.509266	+	2.09922i	0.509266	+	2.09922i
$883$	−0.0623191	+	1.30824i	−0.0623191	+	1.30824i	0.723734	+	0.690079i	$0.242424\pi$
$883$	−0.0623191	+	1.30824i	−0.0623191	+	1.30824i	−0.786053	+	0.618159i	$0.787879\pi$
$884$		0			0
$885$		0			0
$886$	1.02951	−	1.18812i	1.02951	−	1.18812i
$887$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$887$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.52235	+	0.240855i	−2.52235	+	0.240855i
$892$		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
$900$	−1.08006	−	1.87071i	−1.08006	−	1.87071i
$901$		0			0
$902$	1.95865	+	1.00976i	1.95865	+	1.00976i
$903$		0			0
$904$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i
$905$		0			0
$906$		0			0
$907$	0.252989	+	0.130425i	0.252989	+	0.130425i	0.580057	−	0.814576i	$-0.303030\pi$
$907$	0.252989	+	0.130425i	0.252989	+	0.130425i	−0.327068	+	0.945001i	$0.606061\pi$
$908$	0.327068	−	0.566498i	0.327068	−	0.566498i
$909$		0			0
$910$		0			0
$911$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$911$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$912$	2.02261	−	1.59060i	2.02261	−	1.59060i
$913$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$914$	−0.279486	−	1.94387i	−0.279486	−	1.94387i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−3.22747	+	0.308186i	−3.22747	+	0.308186i
$919$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$919$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$920$		0			0
$921$	−0.778161	−	0.311529i	−0.778161	−	0.311529i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.759713	−	0.876756i	−0.759713	−	0.876756i	0.235759	−	0.971812i	$-0.424242\pi$
$929$	−0.759713	−	0.876756i	−0.759713	−	0.876756i	−0.995472	+	0.0950560i	$0.969697\pi$
$930$		0			0
$931$	−0.473420	+	1.36786i	−0.473420	+	1.36786i
$932$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$933$		0			0
$934$	1.56199	−	0.625325i	1.56199	−	0.625325i
$935$		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
$939$	−2.57312			−2.57312
$940$		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
$944$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$945$		0			0
$946$	0.667393	−	0.428908i	0.667393	−	0.428908i
$947$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.786053	−	0.618159i	$-0.787879\pi$
$947$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.500000	−	0.866025i	$-0.666667\pi$
$948$		0			0
$949$		0			0
$950$	0.0688733	−	1.44583i	0.0688733	−	1.44583i
$951$		0			0
$952$		0			0
$953$	−0.308779	+	0.356349i	−0.308779	+	0.356349i	−0.888835	−	0.458227i	$-0.848485\pi$
$953$	−0.308779	+	0.356349i	−0.308779	+	0.356349i	0.580057	+	0.814576i	$0.303030\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.580057	+	0.814576i	0.580057	+	0.814576i
$962$		0			0
$963$	1.50979	+	0.970281i	1.50979	+	0.970281i
$964$	1.50842	−	1.18624i	1.50842	−	1.18624i
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.915415	+	1.58555i	−0.915415	+	1.58555i
$969$	−3.59554	−	1.85363i	−3.59554	−	1.85363i
$970$		0			0
$971$	0.462997	+	0.0892353i	0.462997	+	0.0892353i	0.415415	−	0.909632i	$-0.363636\pi$
$971$	0.462997	+	0.0892353i	0.462997	+	0.0892353i	0.0475819	+	0.998867i	$0.484848\pi$
$972$	−0.603722	−	0.116358i	−0.603722	−	0.116358i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i	−0.327068	−	0.945001i	$-0.606061\pi$
$977$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i	0.235759	−	0.971812i	$-0.424242\pi$
$978$	−1.11574	+	0.327609i	−1.11574	+	0.327609i
$979$	−2.59728	+	2.04252i	−2.59728	+	2.04252i
$980$		0			0
$981$		0			0
$982$	−0.580057	−	0.814576i	−0.580057	−	0.814576i
$983$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$983$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$984$	1.68504	+	1.60668i	1.68504	+	1.60668i
$985$		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
$993$	−0.122434	+	2.57021i	−0.122434	+	2.57021i
$994$		0			0
$995$		0			0
$996$	−2.23394	−	2.57811i	−2.23394	−	2.57811i
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$	−0.379436	+	1.09631i	−0.379436	+	1.09631i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.1.ba.a.155.1	yes	20
4.3	odd	2		2144.1.bu.a.2031.1		20
8.3	odd	2	CM	536.1.ba.a.155.1	yes	20
8.5	even	2		2144.1.bu.a.2031.1		20
67.16	even	33	inner	536.1.ba.a.83.1	✓	20
268.83	odd	66		2144.1.bu.a.1423.1		20
536.83	odd	66	inner	536.1.ba.a.83.1	✓	20
536.485	even	66		2144.1.bu.a.1423.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.1.ba.a.83.1	✓	20	67.16	even	33	inner
536.1.ba.a.83.1	✓	20	536.83	odd	66	inner
536.1.ba.a.155.1	yes	20	1.1	even	1	trivial
536.1.ba.a.155.1	yes	20	8.3	odd	2	CM
2144.1.bu.a.1423.1		20	268.83	odd	66
2144.1.bu.a.1423.1		20	536.485	even	66
2144.1.bu.a.2031.1		20	4.3	odd	2
2144.1.bu.a.2031.1		20	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.981929 - 0.189251i) q^{2} +(-0.738471 + 1.61703i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-0.419102 + 1.72756i) q^{6} +(0.841254 - 0.540641i) q^{8} +(-1.41457 - 1.63251i) q^{9} +O(q^{10})\)	\(q+(0.981929 - 0.189251i) q^{2} +(-0.738471 + 1.61703i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-0.419102 + 1.72756i) q^{6} +(0.841254 - 0.540641i) q^{8} +(-1.41457 - 1.63251i) q^{9} +(0.396666 + 1.63508i) q^{11} +(-0.0845850 + 1.77566i) q^{12} +(0.723734 - 0.690079i) q^{16} +(-1.45949 - 0.584293i) q^{17} +(-1.69796 - 1.33529i) q^{18} +(-0.473420 - 1.36786i) q^{19} +(0.698939 + 1.53046i) q^{22} +(0.252989 + 1.75958i) q^{24} +(0.841254 + 0.540641i) q^{25} +(1.97876 - 0.581017i) q^{27} +(0.580057 - 0.814576i) q^{32} +(-2.93689 - 0.566040i) q^{33} +(-1.54370 - 0.297523i) q^{34} +(-1.91999 - 0.989821i) q^{36} +(-0.723734 - 1.25354i) q^{38} +(1.02951 - 0.809616i) q^{41} +(-0.0671040 - 0.466718i) q^{43} +(0.975950 + 1.37053i) q^{44} +(0.581419 + 1.67990i) q^{48} +(-0.786053 - 0.618159i) q^{49} +(0.928368 + 0.371662i) q^{50} +(2.02261 - 1.92856i) q^{51} +(1.83305 - 0.945001i) q^{54} +(2.56147 + 0.244591i) q^{57} +(0.0800569 - 0.0514495i) q^{59} +(0.415415 - 0.909632i) q^{64} -2.99094 q^{66} +(-0.959493 - 0.281733i) q^{67} -1.57211 q^{68} +(-2.07261 - 0.608574i) q^{72} +(0.437742 - 1.80440i) q^{73} +(-1.49547 + 0.961081i) q^{75} +(-0.947890 - 1.09392i) q^{76} +(-0.214323 + 1.49065i) q^{81} +(0.857685 - 0.989821i) q^{82} +(-1.38884 + 1.32425i) q^{83} +(-0.154218 - 0.445585i) q^{86} +(1.21769 + 1.16106i) q^{88} +(0.815816 + 1.78639i) q^{89} +(0.888835 + 1.53951i) q^{96} +(-0.928368 + 1.60798i) q^{97} +(-0.888835 - 0.458227i) q^{98} +(2.10816 - 2.96050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8}+O(q^{10}) \) 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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