LMFDB - Embedded newform 1340.1.bl.a.1279.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1340,1,Mod(19,1340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1340, 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("1340.19");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1340 = 2^{2} \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1340.bl (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:	$0.668747116928$
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			1279.1
Root			$0.580057 - 0.814576i$ of defining polynomial
Character	$\chi$	$=$	1340.1279
Dual form			1340.1.bl.a.659.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(0.653077 - 1.43004i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.13779 - 1.08488i) q^{6} +(1.95496 - 0.376789i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.963639 - 1.11210i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(0.653077 - 1.43004i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.13779 - 1.08488i) q^{6} +(1.95496 - 0.376789i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.963639 - 1.11210i) q^{9} +(-0.580057 + 0.814576i) q^{10} +(-1.39734 + 0.720381i) q^{12} +(0.283341 - 1.97068i) q^{14} +(-1.02951 + 1.18812i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-1.36611 + 0.546908i) q^{18} +(0.580057 + 0.814576i) q^{20} +(0.737920 - 3.04175i) q^{21} +(-0.995472 + 0.0950560i) q^{23} +(0.223734 + 1.55610i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.711249 + 0.208842i) q^{27} +(-1.76962 - 0.912303i) q^{28} +(-0.580057 + 1.00469i) q^{29} +(0.786053 + 1.36148i) q^{30} +(0.995472 + 0.0950560i) q^{32} +(-1.98193 - 0.189251i) q^{35} +(0.0700176 + 1.46985i) q^{36} +(0.959493 - 0.281733i) q^{40} +(0.0883470 + 0.0353688i) q^{41} +(-2.63310 - 1.69219i) q^{42} +(0.264241 + 1.83784i) q^{43} +(0.611291 + 1.33854i) q^{45} +(-0.235759 + 0.971812i) q^{46} +(1.03115 + 1.44805i) q^{47} +(1.54370 + 0.297523i) q^{48} +(2.75155 - 1.10155i) q^{49} +(0.786053 - 0.618159i) q^{50} +(-0.0352713 + 0.740437i) q^{54} +(-1.44091 + 1.37391i) q^{56} +(0.759713 + 0.876756i) q^{58} +(1.54370 - 0.297523i) q^{60} +(-1.38884 - 1.32425i) q^{61} +(-2.30291 - 1.81103i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.928368 + 0.371662i) q^{67} +(-0.514186 + 1.48564i) q^{69} +(-0.827068 + 1.81103i) q^{70} +(1.41191 + 0.414574i) q^{72} +(1.32254 - 0.849945i) q^{75} +(0.0475819 - 0.998867i) q^{80} +(0.0435701 - 0.303037i) q^{81} +(0.0623191 - 0.0719200i) q^{82} +(-0.462997 - 1.90850i) q^{83} +(-2.46033 + 1.93482i) q^{84} +(1.82318 + 0.351390i) q^{86} +(1.05792 + 1.48564i) q^{87} +(-0.544078 - 1.19136i) q^{89} +(1.46485 - 0.139877i) q^{90} +(0.841254 + 0.540641i) q^{92} +(1.70566 - 0.500828i) q^{94} +(0.786053 - 1.36148i) q^{96} +(-0.141026 - 2.96050i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8	$ 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{10} + q^{12} + 2 q^{14} - 2 q^{15} + q^{16} + q^{20} - 10 q^{21} + q^{23} - 9 q^{24} - 2 q^{25} + 2 q^{27} + q^{28} - q^{29} - q^{30} - q^{32} - 21 q^{35} + 2 q^{40} - q^{41} - 20 q^{42} + 9 q^{43} - q^{46} + q^{47} + q^{48} - q^{50} + q^{54} - q^{56} - 2 q^{58} + q^{60} - 9 q^{61} + 11 q^{63} - 2 q^{64} - q^{67} + q^{69} - 9 q^{70} + 11 q^{72} - 2 q^{75} + q^{80} + 2 q^{81} - 2 q^{82} + q^{83} + q^{84} - q^{86} - q^{87} - 4 q^{89} - 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) $ 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8 - q^10 + q^12 + 2 * q^14 - 2 * q^15 + q^16 + q^20 - 10 * q^21 + q^23 - 9 * q^24 - 2 * q^25 + 2 * q^27 + q^28 - q^29 - q^30 - q^32 - 21 * q^35 + 2 * q^40 - q^41 - 20 * q^42 + 9 * q^43 - q^46 + q^47 + q^48 - q^50 + q^54 - q^56 - 2 * q^58 + q^60 - 9 * q^61 + 11 * q^63 - 2 * q^64 - q^67 + q^69 - 9 * q^70 + 11 * q^72 - 2 * q^75 + q^80 + 2 * q^81 - 2 * q^82 + q^83 + q^84 - q^86 - q^87 - 4 * q^89 - 2 * q^92 + 2 * q^94 - q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{20}{33}\right)$

Coefficient data

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

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

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

$2$	0.327068	−	0.945001i	0.327068	−	0.945001i
$2$	0.327068	−	0.945001i	0.327068	−	0.945001i
$3$	0.653077	−	1.43004i	0.653077	−	1.43004i	−0.235759	−	0.971812i	$-0.575758\pi$
$3$	0.653077	−	1.43004i	0.653077	−	1.43004i	0.888835	−	0.458227i	$-0.151515\pi$
$4$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$5$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$5$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$6$	−1.13779	−	1.08488i	−1.13779	−	1.08488i
$7$	1.95496	−	0.376789i	1.95496	−	0.376789i	0.959493	−	0.281733i	$-0.0909091\pi$
$7$	1.95496	−	0.376789i	1.95496	−	0.376789i	0.995472	−	0.0950560i	$-0.0303030\pi$
$8$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$9$	−0.963639	−	1.11210i	−0.963639	−	1.11210i
$10$	−0.580057	+	0.814576i	−0.580057	+	0.814576i
$11$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$11$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$12$	−1.39734	+	0.720381i	−1.39734	+	0.720381i
$13$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$13$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$14$	0.283341	−	1.97068i	0.283341	−	1.97068i
$15$	−1.02951	+	1.18812i	−1.02951	+	1.18812i
$16$	0.235759	+	0.971812i	0.235759	+	0.971812i
$17$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$17$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$18$	−1.36611	+	0.546908i	−1.36611	+	0.546908i
$19$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$19$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$20$	0.580057	+	0.814576i	0.580057	+	0.814576i
$21$	0.737920	−	3.04175i	0.737920	−	3.04175i
$22$		0			0
$23$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i	−0.580057	−	0.814576i	$-0.696970\pi$
$23$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i	−0.415415	+	0.909632i	$0.636364\pi$
$24$	0.223734	+	1.55610i	0.223734	+	1.55610i
$25$	0.841254	+	0.540641i	0.841254	+	0.540641i
$26$		0			0
$27$	−0.711249	+	0.208842i	−0.711249	+	0.208842i
$28$	−1.76962	−	0.912303i	−1.76962	−	0.912303i
$29$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$29$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$30$	0.786053	+	1.36148i	0.786053	+	1.36148i
$31$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$31$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$32$	0.995472	+	0.0950560i	0.995472	+	0.0950560i
$33$		0			0
$34$		0			0
$35$	−1.98193	−	0.189251i	−1.98193	−	0.189251i
$36$	0.0700176	+	1.46985i	0.0700176	+	1.46985i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$		0			0
$40$	0.959493	−	0.281733i	0.959493	−	0.281733i
$41$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	0.415415	−	0.909632i	$-0.363636\pi$
$41$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	−0.327068	+	0.945001i	$0.606061\pi$
$42$	−2.63310	−	1.69219i	−2.63310	−	1.69219i
$43$	0.264241	+	1.83784i	0.264241	+	1.83784i	0.500000	+	0.866025i	$0.333333\pi$
$43$	0.264241	+	1.83784i	0.264241	+	1.83784i	−0.235759	+	0.971812i	$0.575758\pi$
$44$		0			0
$45$	0.611291	+	1.33854i	0.611291	+	1.33854i
$46$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$47$	1.03115	+	1.44805i	1.03115	+	1.44805i	0.888835	+	0.458227i	$0.151515\pi$
$47$	1.03115	+	1.44805i	1.03115	+	1.44805i	0.142315	+	0.989821i	$0.454545\pi$
$48$	1.54370	+	0.297523i	1.54370	+	0.297523i
$49$	2.75155	−	1.10155i	2.75155	−	1.10155i
$50$	0.786053	−	0.618159i	0.786053	−	0.618159i
$51$		0			0
$52$		0			0
$53$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$53$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$54$	−0.0352713	+	0.740437i	−0.0352713	+	0.740437i
$55$		0			0
$56$	−1.44091	+	1.37391i	−1.44091	+	1.37391i
$57$		0			0
$58$	0.759713	+	0.876756i	0.759713	+	0.876756i
$59$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$59$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$60$	1.54370	−	0.297523i	1.54370	−	0.297523i
$61$	−1.38884	−	1.32425i	−1.38884	−	1.32425i	−0.888835	−	0.458227i	$-0.848485\pi$
$61$	−1.38884	−	1.32425i	−1.38884	−	1.32425i	−0.500000	−	0.866025i	$-0.666667\pi$
$62$		0			0
$63$	−2.30291	−	1.81103i	−2.30291	−	1.81103i
$64$	0.415415	−	0.909632i	0.415415	−	0.909632i
$65$		0			0
$66$		0			0
$67$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$67$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$68$		0			0
$69$	−0.514186	+	1.48564i	−0.514186	+	1.48564i
$70$	−0.827068	+	1.81103i	−0.827068	+	1.81103i
$71$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$71$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$72$	1.41191	+	0.414574i	1.41191	+	0.414574i
$73$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$73$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$74$		0			0
$75$	1.32254	−	0.849945i	1.32254	−	0.849945i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$79$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$80$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$81$	0.0435701	−	0.303037i	0.0435701	−	0.303037i
$82$	0.0623191	−	0.0719200i	0.0623191	−	0.0719200i
$83$	−0.462997	−	1.90850i	−0.462997	−	1.90850i	−0.415415	−	0.909632i	$-0.636364\pi$
$83$	−0.462997	−	1.90850i	−0.462997	−	1.90850i	−0.0475819	−	0.998867i	$-0.515152\pi$
$84$	−2.46033	+	1.93482i	−2.46033	+	1.93482i
$85$		0			0
$86$	1.82318	+	0.351390i	1.82318	+	0.351390i
$87$	1.05792	+	1.48564i	1.05792	+	1.48564i
$88$		0			0
$89$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$89$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$90$	1.46485	−	0.139877i	1.46485	−	0.139877i
$91$		0			0
$92$	0.841254	+	0.540641i	0.841254	+	0.540641i
$93$		0			0
$94$	1.70566	−	0.500828i	1.70566	−	0.500828i
$95$		0			0
$96$	0.786053	−	1.36148i	0.786053	−	1.36148i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	−0.141026	−	2.96050i	−0.141026	−	2.96050i
$99$		0			0
$100$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$101$	0.428368	+	1.23769i	0.428368	+	1.23769i	0.928368	+	0.371662i	$0.121212\pi$
$101$	0.428368	+	1.23769i	0.428368	+	1.23769i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	0.0311250	+	0.653395i	0.0311250	+	0.653395i	0.959493	+	0.281733i	$0.0909091\pi$
$103$	0.0311250	+	0.653395i	0.0311250	+	0.653395i	−0.928368	+	0.371662i	$0.878788\pi$
$104$		0			0
$105$	−1.56499	+	2.71064i	−1.56499	+	2.71064i
$106$		0			0
$107$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$107$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$108$	0.688177	+	0.275505i	0.688177	+	0.275505i
$109$	−0.550294	−	0.353653i	−0.550294	−	0.353653i	0.235759	−	0.971812i	$-0.424242\pi$
$109$	−0.550294	−	0.353653i	−0.550294	−	0.353653i	−0.786053	+	0.618159i	$0.787879\pi$
$110$		0			0
$111$		0			0
$112$	0.827068	+	1.81103i	0.827068	+	1.81103i
$113$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$113$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$114$		0			0
$115$	0.981929	+	0.189251i	0.981929	+	0.189251i
$116$	1.07701	−	0.431171i	1.07701	−	0.431171i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.223734	−	1.55610i	0.223734	−	1.55610i
$121$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$122$	−1.70566	+	0.879330i	−1.70566	+	0.879330i
$123$	0.108276	−	0.103241i	0.108276	−	0.103241i
$124$		0			0
$125$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$126$	−2.46463	+	1.58392i	−2.46463	+	1.58392i
$127$	−1.42131	+	0.273935i	−1.42131	+	0.273935i	−0.841254	−	0.540641i	$-0.818182\pi$
$127$	−1.42131	+	0.273935i	−1.42131	+	0.273935i	−0.580057	+	0.814576i	$0.696970\pi$
$128$	−0.723734	−	0.690079i	−0.723734	−	0.690079i
$129$	2.80075	+	0.822373i	2.80075	+	0.822373i
$130$		0			0
$131$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$131$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$132$		0			0
$133$		0			0
$134$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$135$	0.741276			0.741276
$136$		0			0
$137$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$137$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$138$	1.23576	+	0.971812i	1.23576	+	0.971812i
$139$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$139$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$140$	1.44091	+	1.37391i	1.44091	+	1.37391i
$141$	2.74418	−	0.528898i	2.74418	−	0.528898i
$142$		0			0
$143$		0			0
$144$	0.853564	−	1.19866i	0.853564	−	1.19866i
$145$	0.839614	−	0.800570i	0.839614	−	0.800570i
$146$		0			0
$147$	0.221708	−	4.65422i	0.221708	−	4.65422i
$148$		0			0
$149$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i	−0.786053	−	0.618159i	$-0.787879\pi$
$149$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i	0.723734	+	0.690079i	$0.242424\pi$
$150$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$151$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$151$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$157$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$158$		0			0
$159$		0			0
$160$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$161$	−1.91030	+	0.560914i	−1.91030	+	0.560914i
$162$	−0.272120	−	0.140287i	−0.272120	−	0.140287i
$163$	−0.142315	+	0.246497i	−0.142315	+	0.246497i	−0.928368	−	0.371662i	$-0.878788\pi$
$163$	−0.142315	+	0.246497i	−0.142315	+	0.246497i	0.786053	+	0.618159i	$0.212121\pi$
$164$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i
$165$		0			0
$166$	−1.95496	−	0.186677i	−1.95496	−	0.186677i
$167$	0.271738	+	0.785135i	0.271738	+	0.785135i	0.995472	+	0.0950560i	$0.0303030\pi$
$167$	0.271738	+	0.785135i	0.271738	+	0.785135i	−0.723734	+	0.690079i	$0.757576\pi$
$168$	1.02371	+	2.95783i	1.02371	+	2.95783i
$169$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$170$		0			0
$171$		0			0
$172$	0.928368	−	1.60798i	0.928368	−	1.60798i
$173$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$173$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$174$	1.74994	−	0.513830i	1.74994	−	0.513830i
$175$	1.84833	+	0.739959i	1.84833	+	0.739959i
$176$		0			0
$177$		0			0
$178$	−1.30379	+	0.124497i	−1.30379	+	0.124497i
$179$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$179$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$180$	0.346923	−	1.43004i	0.346923	−	1.43004i
$181$	−0.165101	−	0.231852i	−0.165101	−	0.231852i	0.723734	−	0.690079i	$-0.242424\pi$
$181$	−0.165101	−	0.231852i	−0.165101	−	0.231852i	−0.888835	+	0.458227i	$0.848485\pi$
$182$		0			0
$183$	−2.80075	+	1.12125i	−2.80075	+	1.12125i
$184$	0.786053	−	0.618159i	0.786053	−	0.618159i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.0845850	−	1.77566i	0.0845850	−	1.77566i
$189$	−1.31178	+	0.676269i	−1.31178	+	0.676269i
$190$		0			0
$191$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$191$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$192$	−1.02951	−	1.18812i	−1.02951	−	1.18812i
$193$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$193$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$194$		0			0
$195$		0			0
$196$	−2.84380	−	0.835015i	−2.84380	−	0.835015i
$197$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$197$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$198$		0			0
$199$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$199$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$200$	−1.00000			−1.00000
$201$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i
$202$	1.30972			1.30972
$203$	−0.755436	+	2.18269i	−0.755436	+	2.18269i
$204$		0			0
$205$	−0.0748038	−	0.0588264i	−0.0748038	−	0.0588264i
$206$	0.627639	+	0.184291i	0.627639	+	0.184291i
$207$	1.06499	+	1.01546i	1.06499	+	1.01546i
$208$		0			0
$209$		0			0
$210$	2.04970	+	2.36548i	2.04970	+	2.36548i
$211$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$211$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$212$		0			0
$213$		0			0
$214$	0.0800569	−	1.68060i	0.0800569	−	1.68060i
$215$	0.264241	−	1.83784i	0.264241	−	1.83784i
$216$	0.485433	−	0.560219i	0.485433	−	0.560219i
$217$		0			0
$218$	−0.514186	+	0.404360i	−0.514186	+	0.404360i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$223$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$224$	1.98193	−	0.189251i	1.98193	−	0.189251i
$225$	−0.209419	−	1.45654i	−0.209419	−	1.45654i
$226$		0			0
$227$	1.21590	+	0.486774i	1.21590	+	0.486774i	0.888835	−	0.458227i	$-0.151515\pi$
$227$	1.21590	+	0.486774i	1.21590	+	0.486774i	0.327068	+	0.945001i	$0.393939\pi$
$228$		0			0
$229$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.327068	−	0.945001i	$-0.606061\pi$
$229$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.959493	+	0.281733i	$0.909091\pi$
$230$	0.500000	−	0.866025i	0.500000	−	0.866025i
$231$		0			0
$232$	−0.0552004	−	1.15880i	−0.0552004	−	1.15880i
$233$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$233$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$234$		0			0
$235$	−0.581419	−	1.67990i	−0.581419	−	1.67990i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	−1.39734	−	0.720381i	−1.39734	−	0.720381i
$241$	0.627639	−	0.184291i	0.627639	−	0.184291i	0.0475819	−	0.998867i	$-0.484848\pi$
$241$	0.627639	−	0.184291i	0.627639	−	0.184291i	0.580057	+	0.814576i	$0.303030\pi$
$242$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$243$	−1.02850	−	0.660977i	−1.02850	−	0.660977i
$244$	0.273100	+	1.89945i	0.273100	+	1.89945i
$245$	−2.95044	+	0.281733i	−2.95044	+	0.281733i
$246$	−0.0621493	−	0.136088i	−0.0621493	−	0.136088i
$247$		0			0
$248$		0			0
$249$	−3.03160	−	0.584293i	−3.03160	−	0.584293i
$250$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$251$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$251$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$252$	0.690705	+	2.84713i	0.690705	+	2.84713i
$253$		0			0
$254$	−0.205996	+	1.43273i	−0.205996	+	1.43273i
$255$		0			0
$256$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$257$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$257$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$258$	1.69318	−	2.37774i	1.69318	−	2.37774i
$259$		0			0
$260$		0			0
$261$	1.67628	−	0.323076i	1.67628	−	0.323076i
$262$		0			0
$263$	0.452418	+	0.132842i	0.452418	+	0.132842i	0.500000	−	0.866025i	$-0.333333\pi$
$263$	0.452418	+	0.132842i	0.452418	+	0.132842i	−0.0475819	+	0.998867i	$0.515152\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.05902			−2.05902
$268$	0.959493	+	0.281733i	0.959493	+	0.281733i
$269$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$269$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$270$	0.242448	−	0.700507i	0.242448	−	0.700507i
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	1.32254	−	0.849945i	1.32254	−	0.849945i
$277$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$277$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$278$		0			0
$279$		0			0
$280$	1.76962	−	0.912303i	1.76962	−	0.912303i
$281$	−0.0845850	+	1.77566i	−0.0845850	+	1.77566i	0.415415	+	0.909632i	$0.363636\pi$
$281$	−0.0845850	+	1.77566i	−0.0845850	+	1.77566i	−0.500000	+	0.866025i	$0.666667\pi$
$282$	0.397725	−	2.76624i	0.397725	−	2.76624i
$283$	0.308779	−	0.356349i	0.308779	−	0.356349i	−0.580057	−	0.814576i	$-0.696970\pi$
$283$	0.308779	−	0.356349i	0.308779	−	0.356349i	0.888835	+	0.458227i	$0.151515\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.186042	+	0.0358566i	0.186042	+	0.0358566i
$288$	−0.853564	−	1.19866i	−0.853564	−	1.19866i
$289$	0.235759	−	0.971812i	0.235759	−	0.971812i
$290$	−0.481929	−	1.05528i	−0.481929	−	1.05528i
$291$		0			0
$292$		0			0
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$	−4.32573	−	1.73176i	−4.32573	−	1.73176i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.0475819	+	0.0824143i	0.0475819	+	0.0824143i
$299$		0			0
$300$	−1.56499	−	0.149438i	−1.56499	−	0.149438i
$301$	1.20906	+	3.49334i	1.20906	+	3.49334i
$302$		0			0
$303$	2.04970	+	0.195722i	2.04970	+	0.195722i
$304$		0			0
$305$	0.959493	+	1.66189i	0.959493	+	1.66189i
$306$		0			0
$307$	1.49547	+	0.770969i	1.49547	+	0.770969i	0.995472	−	0.0950560i	$-0.0303030\pi$
$307$	1.49547	+	0.770969i	1.49547	+	0.770969i	0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$	0.954707	+	0.382207i	0.954707	+	0.382207i
$310$		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			0		−0.415415	−	0.909632i	$-0.636364\pi$
$313$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$314$		0			0
$315$	1.69940	+	2.38647i	1.69940	+	2.38647i
$316$		0			0
$317$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$317$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$318$		0			0
$319$		0			0
$320$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$321$	0.376434	−	2.61816i	0.376434	−	2.61816i
$322$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i
$323$		0			0
$324$	−0.221573	+	0.211270i	−0.221573	+	0.211270i
$325$		0			0
$326$	0.186393	+	0.215109i	0.186393	+	0.215109i
$327$	−0.865121	+	0.555979i	−0.865121	+	0.555979i
$328$	−0.0934441	+	0.0180099i	−0.0934441	+	0.0180099i
$329$	2.56147	+	2.44236i	2.56147	+	2.44236i
$330$		0			0
$331$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$331$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$332$	−0.815816	+	1.78639i	−0.815816	+	1.78639i
$333$		0			0
$334$	0.830830			0.830830
$335$	0.995472	−	0.0950560i	0.995472	−	0.0950560i
$336$	3.12998			3.12998
$337$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$337$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$338$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	3.28924	−	2.11387i	3.28924	−	2.11387i
$344$	−1.21590	−	1.40323i	−1.21590	−	1.40323i
$345$	0.911911	−	1.28060i	0.911911	−	1.28060i
$346$		0			0
$347$	−1.70566	+	0.879330i	−1.70566	+	0.879330i	−0.723734	+	0.690079i	$0.757576\pi$
$347$	−1.70566	+	0.879330i	−1.70566	+	0.879330i	−0.981929	+	0.189251i	$0.939394\pi$
$348$	0.0867810	−	1.82176i	0.0867810	−	1.82176i
$349$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	0.235759	+	0.971812i	$0.424242\pi$
$349$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	−0.500000	+	0.866025i	$0.666667\pi$
$350$	1.30379	−	1.50465i	1.30379	−	1.50465i
$351$		0			0
$352$		0			0
$353$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$353$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$354$		0			0
$355$		0			0
$356$	−0.308779	+	1.27280i	−0.308779	+	1.27280i
$357$		0			0
$358$		0			0
$359$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$	−1.23792	−	0.795563i	−1.23792	−	0.795563i
$361$	0.928368	+	0.371662i	0.928368	+	0.371662i
$362$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$363$	−1.39734	−	0.720381i	−1.39734	−	0.720381i
$364$		0			0
$365$		0			0
$366$	0.143547	+	3.01343i	0.143547	+	3.01343i
$367$	−0.651174	−	0.0621796i	−0.651174	−	0.0621796i	−0.235759	−	0.971812i	$-0.575758\pi$
$367$	−0.651174	−	0.0621796i	−0.651174	−	0.0621796i	−0.415415	+	0.909632i	$0.636364\pi$
$368$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$369$	−0.0458011	−	0.132333i	−0.0458011	−	0.132333i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−1.50842	+	0.442913i	−1.50842	+	0.442913i
$376$	−1.65033	−	0.660694i	−1.65033	−	0.660694i
$377$		0			0
$378$	0.210034	+	1.46082i	0.210034	+	1.46082i
$379$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$379$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$380$		0			0
$381$	−0.536487	+	2.21143i	−0.536487	+	2.21143i
$382$		0			0
$383$	1.74555	+	0.336426i	1.74555	+	0.336426i	0.959493	−	0.281733i	$-0.0909091\pi$
$383$	1.74555	+	0.336426i	1.74555	+	0.336426i	0.786053	+	0.618159i	$0.212121\pi$
$384$	−1.45949	+	0.584293i	−1.45949	+	0.584293i
$385$		0			0
$386$		0			0
$387$	1.78922	−	2.06487i	1.78922	−	2.06487i
$388$		0			0
$389$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i	0.928368	+	0.371662i	$0.121212\pi$
$389$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i	−0.959493	+	0.281733i	$0.909091\pi$
$390$		0			0
$391$		0			0
$392$	−1.71921	+	2.41429i	−1.71921	+	2.41429i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$		0			0
$399$		0			0
$400$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$401$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$401$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$402$	1.45949	+	0.584293i	1.45949	+	0.584293i
$403$		0			0
$404$	0.428368	−	1.23769i	0.428368	−	1.23769i
$405$	−0.127181	+	0.278487i	−0.127181	+	0.278487i
$406$	1.81556	+	1.42778i	1.81556	+	1.42778i
$407$		0			0
$408$		0			0
$409$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i	−0.327068	−	0.945001i	$-0.606061\pi$
$409$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i	0.0475819	+	0.998867i	$0.484848\pi$
$410$	−0.0800569	+	0.0514495i	−0.0800569	+	0.0514495i
$411$		0			0
$412$	0.379436	−	0.532843i	0.379436	−	0.532843i
$413$		0			0
$414$	1.30794	−	0.674289i	1.30794	−	0.674289i
$415$	−0.0934441	+	1.96163i	−0.0934441	+	1.96163i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$419$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$420$	2.90577	−	1.16329i	2.90577	−	1.16329i
$421$	0.815816	+	0.157236i	0.815816	+	0.157236i	0.580057	−	0.814576i	$-0.303030\pi$
$421$	0.815816	+	0.157236i	0.815816	+	0.157236i	0.235759	+	0.971812i	$0.424242\pi$
$422$		0			0
$423$	0.616716	−	2.54214i	0.616716	−	2.54214i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.21409	−	2.06557i	−3.21409	−	2.06557i
$428$	−1.56199	−	0.625325i	−1.56199	−	0.625325i
$429$		0			0
$430$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.370638	−	0.641964i	−0.370638	−	0.641964i
$433$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$433$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$434$		0			0
$435$	−0.596514	−	1.72351i	−0.596514	−	1.72351i
$436$	0.213947	+	0.618159i	0.213947	+	0.618159i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	−3.87654	−	1.99850i	−3.87654	−	1.99850i
$442$		0			0
$443$	−1.07701	−	0.431171i	−1.07701	−	0.431171i	−0.235759	−	0.971812i	$-0.575758\pi$
$443$	−1.07701	−	0.431171i	−1.07701	−	0.431171i	−0.841254	+	0.540641i	$0.818182\pi$
$444$		0			0
$445$	0.186393	+	1.29639i	0.186393	+	1.29639i
$446$	1.91030	−	0.182411i	1.91030	−	0.182411i
$447$	0.0621493	+	0.136088i	0.0621493	+	0.136088i
$448$	0.469383	−	1.93482i	0.469383	−	1.93482i
$449$	−1.03115	−	1.44805i	−1.03115	−	1.44805i	−0.888835	−	0.458227i	$-0.848485\pi$
$449$	−1.03115	−	1.44805i	−1.03115	−	1.44805i	−0.142315	−	0.989821i	$-0.545455\pi$
$450$	−1.44493	−	0.278487i	−1.44493	−	0.278487i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.857685	−	0.989821i	0.857685	−	0.989821i
$455$		0			0
$456$		0			0
$457$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$457$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$458$	−1.04758	+	0.998867i	−1.04758	+	0.998867i
$459$		0			0
$460$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$461$	1.65210	−	1.06174i	1.65210	−	1.06174i	0.723734	−	0.690079i	$-0.242424\pi$
$461$	1.65210	−	1.06174i	1.65210	−	1.06174i	0.928368	−	0.371662i	$-0.121212\pi$
$462$		0			0
$463$	0.205996	+	0.196417i	0.205996	+	0.196417i	0.786053	−	0.618159i	$-0.212121\pi$
$463$	0.205996	+	0.196417i	0.205996	+	0.196417i	−0.580057	+	0.814576i	$0.696970\pi$
$464$	−1.11312	−	0.326842i	−1.11312	−	0.326842i
$465$		0			0
$466$		0			0
$467$	0.473420	−	1.36786i	0.473420	−	1.36786i	−0.415415	−	0.909632i	$-0.636364\pi$
$467$	0.473420	−	1.36786i	0.473420	−	1.36786i	0.888835	−	0.458227i	$-0.151515\pi$
$468$		0			0
$469$	−1.67489	+	1.07639i	−1.67489	+	1.07639i
$470$	−1.77767			−1.77767
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$479$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$480$	−1.13779	+	1.08488i	−1.13779	+	1.08488i
$481$		0			0
$482$	0.0311250	−	0.653395i	0.0311250	−	0.653395i
$483$	−0.445442	+	3.09812i	−0.445442	+	3.09812i
$484$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$485$		0			0
$486$	−0.961014	+	0.755750i	−0.961014	+	0.755750i
$487$	−1.82318	+	0.729892i	−1.82318	+	0.729892i	−0.841254	+	0.540641i	$0.818182\pi$
$487$	−1.82318	+	0.729892i	−1.82318	+	0.729892i	−0.981929	+	0.189251i	$0.939394\pi$
$488$	1.88431	+	0.363170i	1.88431	+	0.363170i
$489$	0.259557	+	0.364497i	0.259557	+	0.364497i
$490$	−0.698756	+	2.88031i	−0.698756	+	2.88031i
$491$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$491$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$492$	−0.148930	+	0.0142211i	−0.148930	+	0.0142211i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.54370	+	2.67376i	−1.54370	+	2.67376i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$501$	1.30024	+	0.124158i	1.30024	+	0.124158i
$502$		0			0
$503$	0.0311250	+	0.0899299i	0.0311250	+	0.0899299i	0.959493	−	0.281733i	$-0.0909091\pi$
$503$	0.0311250	+	0.0899299i	0.0311250	+	0.0899299i	−0.928368	+	0.371662i	$0.878788\pi$
$504$	2.91644	+	0.278487i	2.91644	+	0.278487i
$505$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i
$506$		0			0
$507$	−0.786053	+	1.36148i	−0.786053	+	1.36148i
$508$	1.28656	+	0.663268i	1.28656	+	0.663268i
$509$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$509$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$510$		0			0
$511$		0			0
$512$	0.142315	+	0.989821i	0.142315	+	0.989821i
$513$		0			0
$514$		0			0
$515$	0.154218	−	0.635697i	0.154218	−	0.635697i
$516$	−1.69318	−	2.37774i	−1.69318	−	2.37774i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$521$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$522$	0.242950	−	1.68975i	0.242950	−	1.68975i
$523$	−0.0883470	+	1.85463i	−0.0883470	+	1.85463i	0.327068	+	0.945001i	$0.393939\pi$
$523$	−0.0883470	+	1.85463i	−0.0883470	+	1.85463i	−0.415415	+	0.909632i	$0.636364\pi$
$524$		0			0
$525$	2.26527	−	2.15993i	2.26527	−	2.15993i
$526$	0.273507	−	0.384087i	0.273507	−	0.384087i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.673440	+	1.94578i	−0.673440	+	1.94578i
$535$	−1.68251			−1.68251
$536$	0.580057	−	0.814576i	0.580057	−	0.814576i
$537$		0			0
$538$	−0.0930932	+	0.268975i	−0.0930932	+	0.268975i
$539$		0			0
$540$	−0.582682	−	0.458227i	−0.582682	−	0.458227i
$541$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.786053	−	0.618159i	$-0.787879\pi$
$541$	−1.78153	−	0.523103i	−1.78153	−	0.523103i	−0.995472	+	0.0950560i	$0.969697\pi$
$542$		0			0
$543$	−0.439382	+	0.0846839i	−0.439382	+	0.0846839i
$544$		0			0
$545$	0.428368	+	0.494363i	0.428368	+	0.494363i
$546$		0			0
$547$	−1.04758	+	0.998867i	−1.04758	+	0.998867i	−0.0475819	+	0.998867i	$0.515152\pi$
$547$	−1.04758	+	0.998867i	−1.04758	+	0.998867i	−1.00000			$\pi$
$548$		0			0
$549$	−0.134363	+	2.82062i	−0.134363	+	2.82062i
$550$		0			0
$551$		0			0
$552$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$557$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$558$		0			0
$559$		0			0
$560$	−0.283341	−	1.97068i	−0.283341	−	1.97068i
$561$		0			0
$562$	1.65033	+	0.660694i	1.65033	+	0.660694i
$563$	1.78153	−	0.523103i	1.78153	−	0.523103i	0.786053	−	0.618159i	$-0.212121\pi$
$563$	1.78153	−	0.523103i	1.78153	−	0.523103i	0.995472	+	0.0950560i	$0.0303030\pi$
$564$	−2.48402	−	1.28060i	−2.48402	−	1.28060i
$565$		0			0
$566$	−0.235759	−	0.408346i	−0.235759	−	0.408346i
$567$	−0.0290028	−	0.608843i	−0.0290028	−	0.608843i
$568$		0			0
$569$	−0.271738	−	0.785135i	−0.271738	−	0.785135i	−0.995472	−	0.0950560i	$-0.969697\pi$
$569$	−0.271738	−	0.785135i	−0.271738	−	0.785135i	0.723734	−	0.690079i	$-0.242424\pi$
$570$		0			0
$571$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$571$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$572$		0			0
$573$		0			0
$574$	0.0947329	−	0.164082i	0.0947329	−	0.164082i
$575$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$576$	−1.41191	+	0.414574i	−1.41191	+	0.414574i
$577$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$577$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$578$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$579$		0			0
$580$	−1.15486	+	0.110276i	−1.15486	+	0.110276i
$581$	−1.62424	−	3.55660i	−1.62424	−	3.55660i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.396666	−	1.63508i	−0.396666	−	1.63508i	−0.723734	−	0.690079i	$-0.757576\pi$
$587$	−0.396666	−	1.63508i	−0.396666	−	1.63508i	0.327068	−	0.945001i	$-0.393939\pi$
$588$	−3.05132	+	3.52141i	−3.05132	+	3.52141i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$593$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$594$		0			0
$595$		0			0
$596$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i
$597$		0			0
$598$		0			0
$599$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$599$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$600$	−0.653077	+	1.43004i	−0.653077	+	1.43004i
$601$	−0.607279	+	1.75462i	−0.607279	+	1.75462i	0.0475819	+	0.998867i	$0.484848\pi$
$601$	−0.607279	+	1.75462i	−0.607279	+	1.75462i	−0.654861	+	0.755750i	$0.727273\pi$
$602$	3.69666			3.69666
$603$	1.30794	+	0.674289i	1.30794	+	0.674289i
$604$		0			0
$605$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$606$	0.855348	−	1.87295i	0.855348	−	1.87295i
$607$	−1.39734	−	1.09888i	−1.39734	−	1.09888i	−0.981929	−	0.189251i	$-0.939394\pi$
$607$	−1.39734	−	1.09888i	−1.39734	−	1.09888i	−0.415415	−	0.909632i	$-0.636364\pi$
$608$		0			0
$609$	2.62797	+	2.50576i	2.62797	+	2.50576i
$610$	1.88431	−	0.363170i	1.88431	−	0.363170i
$611$		0			0
$612$		0			0
$613$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$613$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$614$	1.21769	−	1.16106i	1.21769	−	1.16106i
$615$	−0.132977	+	0.0685542i	−0.132977	+	0.0685542i
$616$		0			0
$617$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$617$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$618$	0.673440	−	0.777191i	0.673440	−	0.777191i
$619$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$619$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$620$		0			0
$621$	0.688177	−	0.275505i	0.688177	−	0.275505i
$622$		0			0
$623$	−1.51255	−	2.12407i	−1.51255	−	2.12407i
$624$		0			0
$625$	0.415415	+	0.909632i	0.415415	+	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	2.81104	−	0.825395i	2.81104	−	0.825395i
$631$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$631$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.44091	+	0.137591i	1.44091	+	0.137591i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	+	0.866025i	0.500000	+	0.866025i
$641$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$641$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$642$	−2.35104	−	1.21205i	−2.35104	−	1.21205i
$643$	1.11312	−	0.326842i	1.11312	−	0.326842i	0.327068	−	0.945001i	$-0.393939\pi$
$643$	1.11312	−	0.326842i	1.11312	−	0.326842i	0.786053	+	0.618159i	$0.212121\pi$
$644$	1.84833	+	0.739959i	1.84833	+	0.739959i
$645$	−2.45561	−	1.57812i	−2.45561	−	1.57812i
$646$		0			0
$647$	−1.76962	+	0.168978i	−1.76962	+	0.168978i	−0.928368	−	0.371662i	$-0.878788\pi$
$647$	−1.76962	+	0.168978i	−1.76962	+	0.168978i	−0.841254	+	0.540641i	$0.818182\pi$
$648$	0.127181	+	0.278487i	0.127181	+	0.278487i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.264241	−	0.105786i	0.264241	−	0.105786i
$653$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$653$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$654$	0.242448	+	0.999383i	0.242448	+	0.999383i
$655$		0			0
$656$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i
$657$		0			0
$658$	3.14580	−	1.62177i	3.14580	−	1.62177i
$659$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$659$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$660$		0			0
$661$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$661$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$662$		0			0
$663$		0			0
$664$	1.42131	+	1.35522i	1.42131	+	1.35522i
$665$		0			0
$666$		0			0
$667$	0.481929	−	1.05528i	0.481929	−	1.05528i
$668$	0.271738	−	0.785135i	0.271738	−	0.785135i
$669$	3.01685			3.01685
$670$	0.235759	−	0.971812i	0.235759	−	0.971812i
$671$		0			0
$672$	1.02371	−	2.95783i	1.02371	−	2.95783i
$673$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$673$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$674$		0			0
$675$	−0.711249	−	0.208842i	−0.711249	−	0.208842i
$676$	0.723734	+	0.690079i	0.723734	+	0.690079i
$677$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$677$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.49018	−	1.42089i	1.49018	−	1.42089i
$682$		0			0
$683$	−0.0800569	+	1.68060i	−0.0800569	+	1.68060i	0.500000	+	0.866025i	$0.333333\pi$
$683$	−0.0800569	+	1.68060i	−0.0800569	+	1.68060i	−0.580057	+	0.814576i	$0.696970\pi$
$684$		0			0
$685$		0			0
$686$	−0.921801	−	3.79972i	−0.921801	−	3.79972i
$687$	−1.78872	+	1.40667i	−1.78872	+	1.40667i
$688$	−1.72373	+	0.690079i	−1.72373	+	0.690079i
$689$		0			0
$690$	−0.911911	−	1.28060i	−0.911911	−	1.28060i
$691$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$691$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$692$		0			0
$693$		0			0
$694$	0.273100	+	1.89945i	0.273100	+	1.89945i
$695$		0			0
$696$	−1.69318	−	0.677846i	−1.69318	−	0.677846i
$697$		0			0
$698$	1.65033	+	0.850806i	1.65033	+	0.850806i
$699$		0			0
$700$	−0.995472	−	1.72421i	−0.995472	−	1.72421i
$701$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i	−0.888835	−	0.458227i	$-0.848485\pi$
$701$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i	0.841254	−	0.540641i	$-0.181818\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−2.78203	−	0.265652i	−2.78203	−	0.265652i
$706$		0			0
$707$	1.30379	+	2.25823i	1.30379	+	2.25823i
$708$		0			0
$709$	0.888835	+	0.458227i	0.888835	+	0.458227i	0.841254	−	0.540641i	$-0.181818\pi$
$709$	0.888835	+	0.458227i	0.888835	+	0.458227i	0.0475819	+	0.998867i	$0.484848\pi$
$710$		0			0
$711$		0			0
$712$	1.10181	+	0.708089i	1.10181	+	0.708089i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$719$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$720$	−1.15669	+	0.909632i	−1.15669	+	0.909632i
$721$	0.307040	+	1.26564i	0.307040	+	1.26564i
$722$	0.654861	−	0.755750i	0.654861	−	0.755750i
$723$	0.146352	−	1.01790i	0.146352	−	1.01790i
$724$	−0.0135432	+	0.284307i	−0.0135432	+	0.284307i
$725$	−1.03115	+	0.531595i	−1.03115	+	0.531595i
$726$	−1.13779	+	1.08488i	−1.13779	+	1.08488i
$727$	−0.0552004	+	0.0775182i	−0.0552004	+	0.0775182i	−0.841254	−	0.540641i	$-0.818182\pi$
$727$	−0.0552004	+	0.0775182i	−0.0552004	+	0.0775182i	0.786053	+	0.618159i	$0.212121\pi$
$728$		0			0
$729$	−1.35936	+	0.873608i	−1.35936	+	0.873608i
$730$		0			0
$731$		0			0
$732$	2.89465	+	0.849945i	2.89465	+	0.849945i
$733$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$733$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$734$	−0.271738	+	0.595023i	−0.271738	+	0.595023i
$735$	−1.52397	+	4.40323i	−1.52397	+	4.40323i
$736$	−1.00000			−1.00000
$737$		0			0
$738$	−0.140035			−0.140035
$739$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$739$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.205996	+	0.196417i	0.205996	+	0.196417i	0.786053	−	0.618159i	$-0.212121\pi$
$743$	0.205996	+	0.196417i	0.205996	+	0.196417i	−0.580057	+	0.814576i	$0.696970\pi$
$744$		0			0
$745$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$746$		0			0
$747$	−1.67628	+	2.35400i	−1.67628	+	2.35400i
$748$		0			0
$749$	2.97740	−	1.53496i	2.97740	−	1.53496i
$750$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i
$751$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$751$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$752$	−1.16413	+	1.34347i	−1.16413	+	1.34347i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	1.44917	+	0.279304i	1.44917	+	0.279304i
$757$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$757$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$761$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$762$	1.91433	+	1.23027i	1.91433	+	1.23027i
$763$	−1.20906	−	0.484034i	−1.20906	−	0.484034i
$764$		0			0
$765$		0			0
$766$	0.888835	−	1.53951i	0.888835	−	1.53951i
$767$		0			0
$768$	0.0748038	+	1.57033i	0.0748038	+	1.57033i
$769$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.841254	−	0.540641i	$-0.181818\pi$
$769$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.723734	+	0.690079i	$0.242424\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$773$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$774$	−1.36611	−	2.36617i	−1.36611	−	2.36617i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.607279	+	0.243118i	0.607279	+	0.243118i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.202744	−	0.835724i	0.202744	−	0.835724i
$784$	1.71921	+	2.41429i	1.71921	+	2.41429i
$785$		0			0
$786$		0			0
$787$	1.13779	−	0.894765i	1.13779	−	0.894765i	0.142315	−	0.989821i	$-0.454545\pi$
$787$	1.13779	−	0.894765i	1.13779	−	0.894765i	0.995472	+	0.0950560i	$0.0303030\pi$
$788$		0			0
$789$	0.485433	−	0.560219i	0.485433	−	0.560219i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$797$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$798$		0			0
$799$		0			0
$800$	0.786053	+	0.618159i	0.786053	+	0.618159i
$801$	−0.800620	+	1.75311i	−0.800620	+	1.75311i
$802$	−0.651174	+	1.88144i	−0.651174	+	1.88144i
$803$		0			0
$804$	1.02951	−	1.18812i	1.02951	−	1.18812i
$805$	1.99094			1.99094
$806$		0			0
$807$	−0.185885	+	0.407031i	−0.185885	+	0.407031i
$808$	−1.02951	−	0.809616i	−1.02951	−	0.809616i
$809$	−1.38884	−	0.407799i	−1.38884	−	0.407799i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−1.38884	−	0.407799i	−1.38884	−	0.407799i	−0.888835	+	0.458227i	$0.848485\pi$
$810$	0.221573	+	0.211270i	0.221573	+	0.211270i
$811$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$811$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$812$	1.94306	−	1.24873i	1.94306	−	1.24873i
$813$		0			0
$814$		0			0
$815$	0.205996	−	0.196417i	0.205996	−	0.196417i
$816$		0			0
$817$		0			0
$818$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$819$		0			0
$820$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i
$821$	1.50842	−	1.18624i	1.50842	−	1.18624i	0.580057	−	0.814576i	$-0.303030\pi$
$821$	1.50842	−	1.18624i	1.50842	−	1.18624i	0.928368	−	0.371662i	$-0.121212\pi$
$822$		0			0
$823$	−1.13915	−	0.219553i	−1.13915	−	0.219553i	−0.415415	−	0.909632i	$-0.636364\pi$
$823$	−1.13915	−	0.219553i	−1.13915	−	0.219553i	−0.723734	+	0.690079i	$0.757576\pi$
$824$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$825$		0			0
$826$		0			0
$827$	0.0947329	−	0.00904590i	0.0947329	−	0.00904590i	−0.0475819	−	0.998867i	$-0.515152\pi$
$827$	0.0947329	−	0.00904590i	0.0947329	−	0.00904590i	0.142315	+	0.989821i	$0.454545\pi$
$828$	−0.209419	−	1.45654i	−0.209419	−	1.45654i
$829$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$829$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$830$	1.82318	+	0.729892i	1.82318	+	0.729892i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.0395325	−	0.829889i	−0.0395325	−	0.829889i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$839$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$840$	−0.148930	−	3.12643i	−0.148930	−	3.12643i
$841$	−0.172932	−	0.299527i	−0.172932	−	0.299527i
$842$	0.415415	−	0.719520i	0.415415	−	0.719520i
$843$	2.48402	+	1.28060i	2.48402	+	1.28060i
$844$		0			0
$845$	0.928368	+	0.371662i	0.928368	+	0.371662i
$846$	−2.20061	−	1.41425i	−2.20061	−	1.41425i
$847$	−0.283341	−	1.97068i	−0.283341	−	1.97068i
$848$		0			0
$849$	−0.307937	−	0.674289i	−0.307937	−	0.674289i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$853$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$854$	−3.00319	+	2.36173i	−3.00319	+	2.36173i
$855$		0			0
$856$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$857$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$857$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$858$		0			0
$859$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$859$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$860$	−1.34378	+	1.28129i	−1.34378	+	1.28129i
$861$	0.172776	−	0.242630i	0.172776	−	0.242630i
$862$		0			0
$863$	−0.396666	+	0.254922i	−0.396666	+	0.254922i	−0.723734	−	0.690079i	$-0.757576\pi$
$863$	−0.396666	+	0.254922i	−0.396666	+	0.254922i	0.327068	+	0.945001i	$0.393939\pi$
$864$	−0.727880	+	0.140287i	−0.727880	+	0.140287i
$865$		0			0
$866$		0			0
$867$	−1.23576	−	0.971812i	−1.23576	−	0.971812i
$868$		0			0
$869$		0			0
$870$	−1.82382			−1.82382
$871$		0			0
$872$	0.654136			0.654136
$873$		0			0
$874$		0			0
$875$	−1.56499	−	1.23072i	−1.56499	−	1.23072i
$876$		0			0
$877$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$877$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	−0.995472	−	0.0950560i	$-0.969697\pi$
$881$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	0.415415	+	0.909632i	$0.363636\pi$
$882$	−3.15647	+	3.00969i	−3.15647	+	3.00969i
$883$	1.49547	−	0.770969i	1.49547	−	0.770969i	0.500000	−	0.866025i	$-0.333333\pi$
$883$	1.49547	−	0.770969i	1.49547	−	0.770969i	0.995472	+	0.0950560i	$0.0303030\pi$
$884$		0			0
$885$		0			0
$886$	−0.759713	+	0.876756i	−0.759713	+	0.876756i
$887$	−0.273507	−	1.12741i	−0.273507	−	1.12741i	−0.928368	−	0.371662i	$-0.878788\pi$
$887$	−0.273507	−	1.12741i	−0.273507	−	1.12741i	0.654861	−	0.755750i	$-0.272727\pi$
$888$		0			0
$889$	−2.67540	+	1.07107i	−2.67540	+	1.07107i
$890$	1.28605	+	0.247866i	1.28605	+	0.247866i
$891$		0			0
$892$	0.452418	−	1.86489i	0.452418	−	1.86489i
$893$		0			0
$894$	0.148930	−	0.0142211i	0.148930	−	0.0142211i
$895$		0			0
$896$	−1.67489	−	1.07639i	−1.67489	−	1.07639i
$897$		0			0
$898$	−1.70566	+	0.500828i	−1.70566	+	0.500828i
$899$		0			0
$900$	−0.735759	+	1.27437i	−0.735759	+	1.27437i
$901$		0			0
$902$		0			0
$903$	5.78522	+	0.552422i	5.78522	+	0.552422i
$904$		0			0
$905$	0.0930932	+	0.268975i	0.0930932	+	0.268975i
$906$		0			0
$907$	0.0913090	+	1.91681i	0.0913090	+	1.91681i	0.327068	+	0.945001i	$0.393939\pi$
$907$	0.0913090	+	1.91681i	0.0913090	+	1.91681i	−0.235759	+	0.971812i	$0.575758\pi$
$908$	−0.654861	−	1.13425i	−0.654861	−	1.13425i
$909$	0.963639	−	1.66907i	0.963639	−	1.66907i
$910$		0			0
$911$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$911$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	3.00319	−	0.286770i	3.00319	−	0.286770i
$916$	0.601300	+	1.31666i	0.601300	+	1.31666i
$917$		0			0
$918$		0			0
$919$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$919$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$920$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$921$	2.07917	−	1.63508i	2.07917	−	1.63508i
$922$	−0.462997	−	1.90850i	−0.462997	−	1.90850i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.252989	−	0.130425i	0.252989	−	0.130425i
$927$	0.696647	−	0.664251i	0.696647	−	0.664251i
$928$	−0.672932	+	0.945001i	−0.672932	+	0.945001i
$929$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.786053	−	0.618159i	$-0.787879\pi$
$929$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.500000	−	0.866025i	$-0.666667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.13779	−	0.894765i	−1.13779	−	0.894765i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	0.469383	+	1.93482i	0.469383	+	1.93482i
$939$		0			0
$940$	−0.581419	+	1.67990i	−0.581419	+	1.67990i
$941$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$941$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$942$		0			0
$943$	−0.0913090	−	0.0268107i	−0.0913090	−	0.0268107i
$944$		0			0
$945$	1.44917	−	0.279304i	1.44917	−	0.279304i
$946$		0			0
$947$	1.21590	+	1.40323i	1.21590	+	1.40323i	0.888835	+	0.458227i	$0.151515\pi$
$947$	1.21590	+	1.40323i	1.21590	+	1.40323i	0.327068	+	0.945001i	$0.393939\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$953$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.653077	+	1.43004i	0.653077	+	1.43004i
$961$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$962$		0			0
$963$	−2.08281	−	1.33854i	−2.08281	−	1.33854i
$964$	−0.607279	−	0.243118i	−0.607279	−	0.243118i
$965$		0			0
$966$	2.78203	+	1.43424i	2.78203	+	1.43424i
$967$	0.841254	−	1.45709i	0.841254	−	1.45709i	−0.0475819	−	0.998867i	$-0.515152\pi$
$967$	0.841254	−	1.45709i	0.841254	−	1.45709i	0.888835	−	0.458227i	$-0.151515\pi$
$968$	0.500000	+	0.866025i	0.500000	+	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$971$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$972$	0.399867	+	1.15534i	0.399867	+	1.15534i
$973$		0			0
$974$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$975$		0			0
$976$	0.959493	−	1.66189i	0.959493	−	1.66189i
$977$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$977$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$978$	0.429342	−	0.126066i	0.429342	−	0.126066i
$979$		0			0
$980$	2.49336	+	1.60238i	2.49336	+	1.60238i
$981$	0.136988	+	0.952775i	0.136988	+	0.952775i
$982$		0			0
$983$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$983$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$984$	−0.0352713	+	0.145390i	−0.0352713	+	0.145390i
$985$		0			0
$986$		0			0
$987$	5.16550	−	2.06795i	5.16550	−	2.06795i
$988$		0			0
$989$	−0.437742	−	1.80440i	−0.437742	−	1.80440i
$990$		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			0
$994$		0			0
$995$		0			0
$996$	2.02181	+	2.33330i	2.02181	+	2.33330i
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1340.1.bl.a.1279.1	yes	20
4.3	odd	2		1340.1.bl.b.1279.1	yes	20
5.4	even	2		1340.1.bl.b.1279.1	yes	20
20.19	odd	2	CM	1340.1.bl.a.1279.1	yes	20
67.56	even	33	inner	1340.1.bl.a.659.1	✓	20
268.123	odd	66		1340.1.bl.b.659.1	yes	20
335.324	even	66		1340.1.bl.b.659.1	yes	20
1340.659	odd	66	inner	1340.1.bl.a.659.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bl.a.659.1	✓	20	67.56	even	33	inner
1340.1.bl.a.659.1	✓	20	1340.659	odd	66	inner
1340.1.bl.a.1279.1	yes	20	1.1	even	1	trivial
1340.1.bl.a.1279.1	yes	20	20.19	odd	2	CM
1340.1.bl.b.659.1	yes	20	268.123	odd	66
1340.1.bl.b.659.1	yes	20	335.324	even	66
1340.1.bl.b.1279.1	yes	20	4.3	odd	2
1340.1.bl.b.1279.1	yes	20	5.4	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:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1340.bl (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.653077 - 1.43004i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.13779 - 1.08488i) q^{6} +(1.95496 - 0.376789i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.963639 - 1.11210i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.653077 - 1.43004i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.13779 - 1.08488i) q^{6} +(1.95496 - 0.376789i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.963639 - 1.11210i) q^{9} +(-0.580057 + 0.814576i) q^{10} +(-1.39734 + 0.720381i) q^{12} +(0.283341 - 1.97068i) q^{14} +(-1.02951 + 1.18812i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-1.36611 + 0.546908i) q^{18} +(0.580057 + 0.814576i) q^{20} +(0.737920 - 3.04175i) q^{21} +(-0.995472 + 0.0950560i) q^{23} +(0.223734 + 1.55610i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.711249 + 0.208842i) q^{27} +(-1.76962 - 0.912303i) q^{28} +(-0.580057 + 1.00469i) q^{29} +(0.786053 + 1.36148i) q^{30} +(0.995472 + 0.0950560i) q^{32} +(-1.98193 - 0.189251i) q^{35} +(0.0700176 + 1.46985i) q^{36} +(0.959493 - 0.281733i) q^{40} +(0.0883470 + 0.0353688i) q^{41} +(-2.63310 - 1.69219i) q^{42} +(0.264241 + 1.83784i) q^{43} +(0.611291 + 1.33854i) q^{45} +(-0.235759 + 0.971812i) q^{46} +(1.03115 + 1.44805i) q^{47} +(1.54370 + 0.297523i) q^{48} +(2.75155 - 1.10155i) q^{49} +(0.786053 - 0.618159i) q^{50} +(-0.0352713 + 0.740437i) q^{54} +(-1.44091 + 1.37391i) q^{56} +(0.759713 + 0.876756i) q^{58} +(1.54370 - 0.297523i) q^{60} +(-1.38884 - 1.32425i) q^{61} +(-2.30291 - 1.81103i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.928368 + 0.371662i) q^{67} +(-0.514186 + 1.48564i) q^{69} +(-0.827068 + 1.81103i) q^{70} +(1.41191 + 0.414574i) q^{72} +(1.32254 - 0.849945i) q^{75} +(0.0475819 - 0.998867i) q^{80} +(0.0435701 - 0.303037i) q^{81} +(0.0623191 - 0.0719200i) q^{82} +(-0.462997 - 1.90850i) q^{83} +(-2.46033 + 1.93482i) q^{84} +(1.82318 + 0.351390i) q^{86} +(1.05792 + 1.48564i) q^{87} +(-0.544078 - 1.19136i) q^{89} +(1.46485 - 0.139877i) q^{90} +(0.841254 + 0.540641i) q^{92} +(1.70566 - 0.500828i) q^{94} +(0.786053 - 1.36148i) q^{96} +(-0.141026 - 2.96050i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8	\( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{10} + q^{12} + 2 q^{14} - 2 q^{15} + q^{16} + q^{20} - 10 q^{21} + q^{23} - 9 q^{24} - 2 q^{25} + 2 q^{27} + q^{28} - q^{29} - q^{30} - q^{32} - 21 q^{35} + 2 q^{40} - q^{41} - 20 q^{42} + 9 q^{43} - q^{46} + q^{47} + q^{48} - q^{50} + q^{54} - q^{56} - 2 q^{58} + q^{60} - 9 q^{61} + 11 q^{63} - 2 q^{64} - q^{67} + q^{69} - 9 q^{70} + 11 q^{72} - 2 q^{75} + q^{80} + 2 q^{81} - 2 q^{82} + q^{83} + q^{84} - q^{86} - q^{87} - 4 q^{89} - 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) \) 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8 - q^10 + q^12 + 2 * q^14 - 2 * q^15 + q^16 + q^20 - 10 * q^21 + q^23 - 9 * q^24 - 2 * q^25 + 2 * q^27 + q^28 - q^29 - q^30 - q^32 - 21 * q^35 + 2 * q^40 - q^41 - 20 * q^42 + 9 * q^43 - q^46 + q^47 + q^48 - q^50 + q^54 - q^56 - 2 * q^58 + q^60 - 9 * q^61 + 11 * q^63 - 2 * q^64 - q^67 + q^69 - 9 * q^70 + 11 * q^72 - 2 * q^75 + q^80 + 2 * q^81 - 2 * q^82 + q^83 + q^84 - q^86 - q^87 - 4 * q^89 - 2 * q^92 + 2 * q^94 - q^96

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