LMFDB - Embedded newform 504.2.bk.a.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.1
Root			$2.00233 - 0.854000i$ of defining polynomial
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +(0.542829 - 4.48465i) q^{10} +(-0.800840 + 1.38709i) q^{11} +1.38831 q^{13} +(2.95297 - 2.29782i) q^{14} +(-3.37755 + 2.14293i) q^{16} +(-3.48605 - 2.01267i) q^{17} +(-4.56957 + 2.63824i) q^{19} +(-4.42204 + 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +(-3.83044 + 2.21151i) q^{23} +(-2.60168 + 4.50624i) q^{25} +(-1.57004 - 1.17889i) q^{26} +(-5.29072 + 0.0910883i) q^{28} -5.10613i q^{29} +(0.0579809 - 0.100426i) q^{31} +(5.63935 + 0.444621i) q^{32} +(2.23331 + 5.23632i) q^{34} +(-8.17125 + 2.15734i) q^{35} +(4.63087 - 2.67363i) q^{37} +(7.40801 + 0.896678i) q^{38} +(8.91613 - 1.45930i) q^{40} +4.21689i q^{41} +(-3.11085 - 0.764282i) q^{44} +(6.20976 + 0.751640i) q^{46} +(5.05821 + 8.76108i) q^{47} +(-6.03630 - 3.54444i) q^{49} +(6.76873 - 2.88689i) q^{50} +(0.774501 + 2.66641i) q^{52} +(6.13514 + 3.54212i) q^{53} -5.11619 q^{55} +(6.06063 + 4.38962i) q^{56} +(-4.33589 + 5.77453i) q^{58} +(4.38856 + 2.53374i) q^{59} +(4.21321 + 7.29750i) q^{61} +(-0.150848 + 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.21731 + 3.84050i) q^{65} +(5.01815 - 8.69169i) q^{67} +(1.92079 - 7.81818i) q^{68} +(11.0728 + 4.49891i) q^{70} +5.29150i q^{71} +(9.30504 + 5.37227i) q^{73} +(-7.50738 - 0.908707i) q^{74} +(-7.61631 - 7.30460i) q^{76} +(-2.98544 - 3.00745i) q^{77} +(-10.3349 + 5.96688i) q^{79} +(-11.3224 - 5.92084i) q^{80} +(3.58079 - 4.76889i) q^{82} -14.9789i q^{83} -12.8580i q^{85} +(2.86907 + 3.50592i) q^{88} +(-1.50000 + 0.866025i) q^{89} +(-0.963697 + 3.54444i) q^{91} +(-6.38437 - 6.12307i) q^{92} +(1.71917 - 14.2031i) q^{94} +(-14.5965 - 8.42726i) q^{95} -2.87198i q^{97} +(3.81669 + 9.13416i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58}+ \cdots + 6 q^{98}+O(q^{100}) $ 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.13090	−	0.849154i	−0.799668	−	0.600443i
$2$	−1.13090	−	0.849154i	−0.799668	−	0.600443i
$3$		0			0
$3$		0			0
$4$	0.557875	+	1.92062i	0.278937	+	0.960309i
$5$	1.59713	+	2.76632i	0.714260	+	1.23714i	0.963244	+	0.268628i	$0.0865701\pi$
$5$	1.59713	+	2.76632i	0.714260	+	1.23714i	−0.248984	+	0.968508i	$0.580097\pi$
$6$		0			0
$7$	−0.694153	+	2.55307i	−0.262365	+	0.964969i
$7$	−0.694153	+	2.55307i	−0.262365	+	0.964969i
$8$	1.00000	−	2.64575i	0.353553	−	0.935414i
$9$		0			0
$10$	0.542829	−	4.48465i	0.171658	−	1.41817i
$11$	−0.800840	+	1.38709i	−0.241462	+	0.418225i	−0.961131	−	0.276093i	$-0.910960\pi$
$11$	−0.800840	+	1.38709i	−0.241462	+	0.418225i	0.719669	+	0.694318i	$0.244294\pi$
$12$		0			0
$13$	1.38831			0.385047			0.192523	−	0.981292i	$-0.438333\pi$
$13$	1.38831			0.385047			0.192523	+	0.981292i	$0.438333\pi$
$14$	2.95297	−	2.29782i	0.789213	−	0.614119i
$15$		0			0
$16$	−3.37755	+	2.14293i	−0.844388	+	0.535732i
$17$	−3.48605	−	2.01267i	−0.845490	−	0.488144i	0.0136363	−	0.999907i	$-0.495659\pi$
$17$	−3.48605	−	2.01267i	−0.845490	−	0.488144i	−0.859127	+	0.511763i	$0.828993\pi$
$18$		0			0
$19$	−4.56957	+	2.63824i	−1.04833	+	0.605255i	−0.922182	−	0.386756i	$-0.873595\pi$
$19$	−4.56957	+	2.63824i	−1.04833	+	0.605255i	−0.126150	+	0.992011i	$0.540262\pi$
$20$	−4.42204	+	4.61075i	−0.988799	+	1.03099i
$21$		0			0
$22$	2.08353	−	0.888631i	0.444210	−	0.189457i
$23$	−3.83044	+	2.21151i	−0.798702	+	0.461131i	−0.843017	−	0.537887i	$-0.819223\pi$
$23$	−3.83044	+	2.21151i	−0.798702	+	0.461131i	0.0443149	+	0.999018i	$0.485890\pi$
$24$		0			0
$25$	−2.60168	+	4.50624i	−0.520336	+	0.901248i
$26$	−1.57004	−	1.17889i	−0.307910	−	0.231199i
$27$		0			0
$28$	−5.29072	+	0.0910883i	−0.999852	+	0.0172141i
$29$		−	5.10613i		−	0.948185i	−0.880475	−	0.474093i	$-0.842776\pi$
$29$		−	5.10613i		−	0.948185i	0.880475	−	0.474093i	$-0.157224\pi$
$30$		0			0
$31$	0.0579809	−	0.100426i	0.0104137	−	0.0180370i	−0.860772	−	0.508991i	$-0.830018\pi$
$31$	0.0579809	−	0.100426i	0.0104137	−	0.0180370i	0.871185	+	0.490954i	$0.163352\pi$
$32$	5.63935	+	0.444621i	0.996906	+	0.0785986i
$33$		0			0
$34$	2.23331	+	5.23632i	0.383009	+	0.898022i
$35$	−8.17125	+	2.15734i	−1.38119	+	0.364658i
$36$		0			0
$37$	4.63087	−	2.67363i	0.761310	−	0.439543i	−0.0684556	−	0.997654i	$-0.521807\pi$
$37$	4.63087	−	2.67363i	0.761310	−	0.439543i	0.829766	+	0.558111i	$0.188474\pi$
$38$	7.40801	+	0.896678i	1.20174	+	0.145460i
$39$		0			0
$40$	8.91613	−	1.45930i	1.40976	−	0.230736i
$41$			4.21689i			0.658568i	0.944231	+	0.329284i	$0.106807\pi$
$41$			4.21689i			0.658568i	−0.944231	+	0.329284i	$0.893193\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−3.11085	−	0.764282i	−0.468978	−	0.115220i
$45$		0			0
$46$	6.20976	+	0.751640i	0.915579	+	0.110823i
$47$	5.05821	+	8.76108i	0.737816	+	1.27794i	0.953477	+	0.301467i	$0.0974763\pi$
$47$	5.05821	+	8.76108i	0.737816	+	1.27794i	−0.215660	+	0.976468i	$0.569190\pi$
$48$		0			0
$49$	−6.03630	−	3.54444i	−0.862329	−	0.506348i
$50$	6.76873	−	2.88689i	0.957244	−	0.408267i
$51$		0			0
$52$	0.774501	+	2.66641i	0.107404	+	0.369764i
$53$	6.13514	+	3.54212i	0.842726	+	0.486548i	0.858190	−	0.513332i	$-0.171589\pi$
$53$	6.13514	+	3.54212i	0.842726	+	0.486548i	−0.0154638	+	0.999880i	$0.504922\pi$
$54$		0			0
$55$	−5.11619			−0.689868
$56$	6.06063	+	4.38962i	0.809885	+	0.586588i
$57$		0			0
$58$	−4.33589	+	5.77453i	−0.569331	+	0.758233i
$59$	4.38856	+	2.53374i	0.571342	+	0.329865i	0.757685	−	0.652620i	$-0.226330\pi$
$59$	4.38856	+	2.53374i	0.571342	+	0.329865i	−0.186343	+	0.982485i	$0.559664\pi$
$60$		0			0
$61$	4.21321	+	7.29750i	0.539447	+	0.934349i	0.998934	+	0.0461646i	$0.0146999\pi$
$61$	4.21321	+	7.29750i	0.539447	+	0.934349i	−0.459487	+	0.888184i	$0.651967\pi$
$62$	−0.150848	+	0.0643370i	−0.0191577	+	0.00817081i
$63$		0			0
$64$	−6.00000	−	5.29150i	−0.750000	−	0.661438i
$65$	2.21731	+	3.84050i	0.275024	+	0.476355i
$66$		0			0
$67$	5.01815	−	8.69169i	0.613065	−	1.06186i	−0.377656	−	0.925946i	$-0.623270\pi$
$67$	5.01815	−	8.69169i	0.613065	−	1.06186i	0.990721	−	0.135913i	$-0.0433969\pi$
$68$	1.92079	−	7.81818i	0.232930	−	0.948094i
$69$		0			0
$70$	11.0728	+	4.49891i	1.32345	+	0.537723i
$71$			5.29150i			0.627986i	0.949425	+	0.313993i	$0.101667\pi$
$71$			5.29150i			0.627986i	−0.949425	+	0.313993i	$0.898333\pi$
$72$		0			0
$73$	9.30504	+	5.37227i	1.08907	+	0.628776i	0.933329	−	0.359021i	$-0.116890\pi$
$73$	9.30504	+	5.37227i	1.08907	+	0.628776i	0.155743	+	0.987798i	$0.450223\pi$
$74$	−7.50738	−	0.908707i	−0.872716	−	0.105635i
$75$		0			0
$76$	−7.61631	−	7.30460i	−0.873651	−	0.837895i
$77$	−2.98544	−	3.00745i	−0.340223	−	0.342731i
$78$		0			0
$79$	−10.3349	+	5.96688i	−1.16277	+	0.671327i	−0.951967	−	0.306201i	$-0.900942\pi$
$79$	−10.3349	+	5.96688i	−1.16277	+	0.671327i	−0.210805	+	0.977528i	$0.567609\pi$
$80$	−11.3224	−	5.92084i	−1.26589	−	0.661970i
$81$		0			0
$82$	3.58079	−	4.76889i	0.395432	−	0.526636i
$83$		−	14.9789i		−	1.64415i	−0.569382	−	0.822073i	$-0.692818\pi$
$83$		−	14.9789i		−	1.64415i	0.569382	−	0.822073i	$-0.307182\pi$
$84$		0			0
$85$		−	12.8580i		−	1.39465i
$86$		0			0
$87$		0			0
$88$	2.86907	+	3.50592i	0.305844	+	0.373732i
$89$	−1.50000	+	0.866025i	−0.159000	+	0.0917985i	−0.577389	−	0.816469i	$-0.695928\pi$
$89$	−1.50000	+	0.866025i	−0.159000	+	0.0917985i	0.418389	+	0.908268i	$0.362595\pi$
$90$		0			0
$91$	−0.963697	+	3.54444i	−0.101023	+	0.371558i
$92$	−6.38437	−	6.12307i	−0.665616	−	0.638375i
$93$		0			0
$94$	1.71917	−	14.2031i	0.177319	−	1.46494i
$95$	−14.5965	−	8.42726i	−1.49756	−	0.864619i
$96$		0			0
$97$		−	2.87198i		−	0.291606i	−0.989314	−	0.145803i	$-0.953423\pi$
$97$		−	2.87198i		−	0.291606i	0.989314	−	0.145803i	$-0.0465765\pi$
$98$	3.81669	+	9.13416i	0.385544	+	0.922690i
$99$		0			0
$100$	−10.1062	−	2.48292i	−1.01062	−	0.248292i
$101$	−3.40310	+	5.89434i	−0.338621	+	0.586509i	−0.984174	−	0.177207i	$-0.943294\pi$
$101$	−3.40310	+	5.89434i	−0.338621	+	0.586509i	0.645553	+	0.763716i	$0.276627\pi$
$102$		0			0
$103$	7.02471	+	12.1672i	0.692165	+	1.19887i	0.971127	+	0.238563i	$0.0766765\pi$
$103$	7.02471	+	12.1672i	0.692165	+	1.19887i	−0.278962	+	0.960302i	$0.589990\pi$
$104$	1.38831	−	3.67311i	0.136135	−	0.360178i
$105$		0			0
$106$	−3.93043	−	9.21547i	−0.381757	−	0.895086i
$107$	−2.56957	−	4.45063i	−0.248410	−	0.430259i	0.714675	−	0.699457i	$-0.246575\pi$
$107$	−2.56957	−	4.45063i	−0.248410	−	0.430259i	−0.963085	+	0.269198i	$0.913241\pi$
$108$		0			0
$109$	2.45182	+	1.41556i	0.234842	+	0.135586i	0.612804	−	0.790235i	$-0.290042\pi$
$109$	2.45182	+	1.41556i	0.234842	+	0.135586i	−0.377962	+	0.925821i	$0.623375\pi$
$110$	5.78591	+	4.34444i	0.551665	+	0.414226i
$111$		0			0
$112$	−3.12650	−	10.1106i	−0.295427	−	0.955365i
$113$	1.43695			0.135177			0.0675887	−	0.997713i	$-0.478469\pi$
$113$	1.43695			0.135177			0.0675887	+	0.997713i	$0.478469\pi$
$114$		0			0
$115$	−12.2355	−	7.06415i	−1.14096	−	0.658735i
$116$	9.80694	−	2.84858i	0.910551	−	0.264484i
$117$		0			0
$118$	−2.81150	−	6.59198i	−0.258819	−	0.606841i
$119$	7.55833	−	7.50301i	0.692871	−	0.687800i
$120$		0			0
$121$	4.21731	+	7.30460i	0.383392	+	0.664054i
$122$	1.43197	−	11.8304i	0.129645	−	1.07108i
$123$		0			0
$124$	0.225226	+	0.0553342i	0.0202259	+	0.00496916i
$125$	−0.649581			−0.0581003
$126$		0			0
$127$			4.92077i			0.436647i	0.975876	+	0.218324i	$0.0700589\pi$
$127$			4.92077i			0.436647i	−0.975876	+	0.218324i	$0.929941\pi$
$128$	2.29211	+	11.0791i	0.202595	+	0.979263i
$129$		0			0
$130$	0.753613	−	6.22606i	0.0660962	−	0.546062i
$131$	3.41647	−	1.97250i	0.298499	−	0.172338i	−0.343270	−	0.939237i	$-0.611534\pi$
$131$	3.41647	−	1.97250i	0.298499	−	0.172338i	0.641768	+	0.766899i	$0.278201\pi$
$132$		0			0
$133$	−3.56363	−	13.4978i	−0.309006	−	1.17041i
$134$	−13.0556	+	5.56826i	−1.12783	+	0.481025i
$135$		0			0
$136$	−8.81107	+	7.21054i	−0.755543	+	0.618299i
$137$	−0.0514223	+	0.0890661i	−0.00439331	+	0.00760943i	−0.868214	−	0.496190i	$-0.834732\pi$
$137$	−0.0514223	+	0.0890661i	−0.00439331	+	0.00760943i	0.863820	+	0.503800i	$0.168065\pi$
$138$		0			0
$139$		−	14.9789i		−	1.27049i	−0.772310	−	0.635246i	$-0.780899\pi$
$139$		−	14.9789i		−	1.27049i	0.772310	−	0.635246i	$-0.219101\pi$
$140$	−8.70197	−	14.4903i	−0.735451	−	1.22466i
$141$		0			0
$142$	4.49330	−	5.98417i	0.377069	−	0.502180i
$143$	−1.11181	+	1.92571i	−0.0929743	+	0.161036i
$144$		0			0
$145$	14.1252	−	8.15518i	1.17303	−	0.677251i
$146$	−5.96120	−	13.9769i	−0.493352	−	1.15674i
$147$		0			0
$148$	7.71848	+	7.40258i	0.634455	+	0.608489i
$149$	9.79164	−	5.65320i	0.802162	−	0.463129i	−0.0420645	−	0.999115i	$-0.513393\pi$
$149$	9.79164	−	5.65320i	0.802162	−	0.463129i	0.844227	+	0.535986i	$0.180060\pi$
$150$		0			0
$151$	−12.8351	−	7.41032i	−1.04450	−	0.603044i	−0.123397	−	0.992357i	$-0.539379\pi$
$151$	−12.8351	−	7.41032i	−1.04450	−	0.603044i	−0.921105	+	0.389314i	$0.872712\pi$
$152$	2.41057	+	14.7282i	0.195523	+	1.19461i
$153$		0			0
$154$	0.822447	+	5.93623i	0.0662747	+	0.478355i
$155$	0.370413			0.0297523
$156$		0			0
$157$	0.369362	−	0.639755i	0.0294783	−	0.0510580i	−0.850910	−	0.525312i	$-0.823949\pi$
$157$	0.369362	−	0.639755i	0.0294783	−	0.0510580i	0.880388	+	0.474254i	$0.157282\pi$
$158$	16.7546	+	2.02801i	1.33292	+	0.161339i
$159$		0			0
$160$	7.77685	+	16.3104i	0.614814	+	1.28945i
$161$	−2.98721	−	11.3145i	−0.235425	−	0.891707i
$162$		0			0
$163$	4.35226	+	7.53834i	0.340895	+	0.590448i	0.984599	−	0.174826i	$-0.0559364\pi$
$163$	4.35226	+	7.53834i	0.340895	+	0.590448i	−0.643704	+	0.765275i	$0.722603\pi$
$164$	−8.09904	+	2.35250i	−0.632429	+	0.183699i
$165$		0			0
$166$	−12.7194	+	16.9396i	−0.987215	+	1.31477i
$167$	−1.38831			−0.107430			−0.0537152	−	0.998556i	$-0.517106\pi$
$167$	−1.38831			−0.107430			−0.0537152	+	0.998556i	$0.517106\pi$
$168$		0			0
$169$	−11.0726			−0.851739
$170$	−10.9184	+	14.5411i	−0.837406	+	1.11526i
$171$		0			0
$172$		0			0
$173$	0.485324	+	0.840606i	0.0368985	+	0.0639101i	0.883885	−	0.467704i	$-0.154919\pi$
$173$	0.485324	+	0.840606i	0.0368985	+	0.0639101i	−0.846986	+	0.531615i	$0.821586\pi$
$174$		0			0
$175$	−9.69877	−	9.77028i	−0.733158	−	0.738564i
$176$	−0.267569	−	6.40113i	−0.0201688	−	0.482503i
$177$		0			0
$178$	2.43174	+	0.294342i	0.182267	+	0.0220619i
$179$	−7.13495	+	12.3581i	−0.533291	+	0.923687i	0.465953	+	0.884810i	$0.345712\pi$
$179$	−7.13495	+	12.3581i	−0.533291	+	0.923687i	−0.999244	+	0.0388779i	$0.987622\pi$
$180$		0			0
$181$	15.3218			1.13886			0.569429	−	0.822041i	$-0.307164\pi$
$181$	15.3218			1.13886			0.569429	+	0.822041i	$0.307164\pi$
$182$	4.09962	−	3.19008i	0.303884	−	0.236465i
$183$		0			0
$184$	2.02065	+	12.3459i	0.148965	+	0.910152i
$185$	14.7922	+	8.54031i	1.08755	+	0.627896i
$186$		0			0
$187$	5.58353	−	3.22365i	0.408308	−	0.235737i
$188$	−14.0049	+	14.6025i	−1.02141	+	1.06500i
$189$		0			0
$190$	9.35110	+	21.9250i	0.678400	+	1.59061i
$191$	2.16564	−	1.25033i	0.156700	−	0.0904709i	−0.419599	−	0.907709i	$-0.637829\pi$
$191$	2.16564	−	1.25033i	0.156700	−	0.0904709i	0.576300	+	0.817238i	$0.304496\pi$
$192$		0			0
$193$	1.55026	−	2.68512i	0.111590	−	0.193279i	−0.804822	−	0.593517i	$-0.797739\pi$
$193$	1.55026	−	2.68512i	0.111590	−	0.193279i	0.916411	+	0.400237i	$0.131072\pi$
$194$	−2.43876	+	3.24793i	−0.175093	+	0.233188i
$195$		0			0
$196$	3.44001	−	13.5708i	0.245715	−	0.969342i
$197$		−	15.6891i		−	1.11780i	−0.829233	−	0.558902i	$-0.811223\pi$
$197$		−	15.6891i		−	1.11780i	0.829233	−	0.558902i	$-0.188777\pi$
$198$		0			0
$199$	5.91290	−	10.2414i	0.419154	−	0.725997i	−0.576700	−	0.816956i	$-0.695660\pi$
$199$	5.91290	−	10.2414i	0.419154	−	0.725997i	0.995855	+	0.0909591i	$0.0289933\pi$
$200$	9.32071	+	11.3896i	0.659074	+	0.805369i
$201$		0			0
$202$	8.85377	−	3.77616i	0.622949	−	0.265690i
$203$	13.0363	+	3.54444i	0.914969	+	0.248771i
$204$		0			0
$205$	−11.6653	+	6.73495i	−0.814738	+	0.470389i
$206$	2.38754	−	19.7249i	0.166348	−	1.37430i
$207$		0			0
$208$	−4.68908	+	2.97504i	−0.325129	+	0.206282i
$209$		−	8.45124i		−	0.584585i
$210$		0			0
$211$	10.0726			0.693427			0.346713	−	0.937971i	$-0.387298\pi$
$211$	10.0726			0.693427			0.346713	+	0.937971i	$0.387298\pi$
$212$	−3.38043	+	13.7593i	−0.232169	+	0.944994i
$213$		0			0
$214$	−0.873339	+	7.21519i	−0.0597002	+	0.493220i
$215$		0			0
$216$		0			0
$217$	0.216146	+	0.217740i	0.0146730	+	0.0147812i
$218$	−1.57074	−	3.68283i	−0.106384	−	0.249433i
$219$		0			0
$220$	−2.85420	−	9.82626i	−0.192430	−	0.662486i
$221$	−4.83970	−	2.79420i	−0.325553	−	0.187958i
$222$		0			0
$223$	24.3086			1.62783			0.813913	−	0.580987i	$-0.197333\pi$
$223$	24.3086			1.62783			0.813913	+	0.580987i	$0.197333\pi$
$224$	−5.04972	+	14.0890i	−0.337399	+	0.941362i
$225$		0			0
$226$	−1.62505	−	1.22020i	−0.108097	−	0.0811662i
$227$	12.4048	+	7.16194i	0.823339	+	0.475355i	0.851566	−	0.524247i	$-0.175653\pi$
$227$	12.4048	+	7.16194i	0.823339	+	0.475355i	−0.0282277	+	0.999602i	$0.508986\pi$
$228$		0			0
$229$	5.32502	+	9.22321i	0.351887	+	0.609487i	0.986580	−	0.163278i	$-0.0522066\pi$
$229$	5.32502	+	9.22321i	0.351887	+	0.609487i	−0.634693	+	0.772765i	$0.718873\pi$
$230$	7.83855	+	18.3786i	0.516859	+	1.21185i
$231$		0			0
$232$	−13.5096	−	5.10613i	−0.886946	−	0.335234i
$233$	−0.318991	−	0.552509i	−0.0208978	−	0.0361961i	0.855387	−	0.517989i	$-0.173319\pi$
$233$	−0.318991	−	0.552509i	−0.0208978	−	0.0361961i	−0.876285	+	0.481793i	$0.839986\pi$
$234$		0			0
$235$	−16.1573	+	27.9853i	−1.05399	+	1.82556i
$236$	−2.41808	+	9.84227i	−0.157403	+	0.640677i
$237$		0			0
$238$	−14.9189	+	2.06697i	−0.967051	+	0.133982i
$239$			4.73540i			0.306307i	0.988202	+	0.153154i	$0.0489430\pi$
$239$			4.73540i			0.306307i	−0.988202	+	0.153154i	$0.951057\pi$
$240$		0			0
$241$	−10.1380	−	5.85317i	−0.653045	−	0.377036i	0.136577	−	0.990629i	$-0.456390\pi$
$241$	−10.1380	−	5.85317i	−0.653045	−	0.377036i	−0.789622	+	0.613594i	$0.789723\pi$
$242$	1.43337	−	11.8419i	0.0921403	−	0.761228i
$243$		0			0
$244$	−11.6653	+	12.1631i	−0.746792	+	0.778661i
$245$	0.164257	−	22.3593i	0.0104940	−	1.42848i
$246$		0			0
$247$	−6.34397	+	3.66269i	−0.403657	+	0.233051i
$248$	−0.207721	−	0.253829i	−0.0131903	−	0.0161182i
$249$		0			0
$250$	0.734612	+	0.551594i	0.0464609	+	0.0348859i
$251$			11.5631i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$251$			11.5631i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$252$		0			0
$253$		−	7.08425i		−	0.445383i
$254$	4.17849	−	5.56490i	0.262182	−	0.349173i
$255$		0			0
$256$	6.81571	−	14.4757i	0.425982	−	0.904732i
$257$	20.4302	−	11.7954i	1.27440	−	0.735777i	0.298589	−	0.954382i	$-0.403484\pi$
$257$	20.4302	−	11.7954i	1.27440	−	0.735777i	0.975813	+	0.218605i	$0.0701506\pi$
$258$		0			0
$259$	3.61144	+	13.6788i	0.224404	+	0.849961i
$260$	−6.13915	+	6.40113i	−0.380734	+	0.396981i
$261$		0			0
$262$	−5.53865	−	0.670408i	−0.342179	−	0.0414179i
$263$	−9.24833	−	5.33953i	−0.570277	−	0.329249i	0.186983	−	0.982363i	$-0.440129\pi$
$263$	−9.24833	−	5.33953i	−0.570277	−	0.329249i	−0.757260	+	0.653114i	$0.773462\pi$
$264$		0			0
$265$			22.6290i			1.39009i
$266$	−7.43157	+	18.2907i	−0.455659	+	1.12148i
$267$		0			0
$268$	19.4929	+	4.78908i	1.19072	+	0.292540i
$269$	−11.6690	+	20.2113i	−0.711471	+	1.23230i	0.252834	+	0.967510i	$0.418637\pi$
$269$	−11.6690	+	20.2113i	−0.711471	+	1.23230i	−0.964305	+	0.264794i	$0.914696\pi$
$270$		0			0
$271$	−6.81961	−	11.8119i	−0.414262	−	0.717522i	0.581089	−	0.813840i	$-0.302627\pi$
$271$	−6.81961	−	11.8119i	−0.414262	−	0.717522i	−0.995351	+	0.0963179i	$0.969293\pi$
$272$	16.0873	−	0.672454i	0.975436	−	0.0407735i
$273$		0			0
$274$	0.133784	−	0.0570595i	0.00808221	−	0.00344709i
$275$	−4.16706	−	7.21755i	−0.251283	−	0.435235i
$276$		0			0
$277$	0.396180	+	0.228735i	0.0238042	+	0.0137433i	0.511855	−	0.859072i	$-0.328959\pi$
$277$	0.396180	+	0.228735i	0.0238042	+	0.0137433i	−0.488051	+	0.872815i	$0.662292\pi$
$278$	−12.7194	+	16.9396i	−0.762858	+	1.01597i
$279$		0			0
$280$	−2.46346	+	23.7764i	−0.147220	+	1.42091i
$281$	−1.43695			−0.0857215			−0.0428608	−	0.999081i	$-0.513647\pi$
$281$	−1.43695			−0.0857215			−0.0428608	+	0.999081i	$0.513647\pi$
$282$		0			0
$283$	27.0428	+	15.6132i	1.60753	+	0.928108i	0.989921	+	0.141622i	$0.0452318\pi$
$283$	27.0428	+	15.6132i	1.60753	+	0.928108i	0.617609	+	0.786486i	$0.288102\pi$
$284$	−10.1630	+	2.95200i	−0.603061	+	0.175169i
$285$		0			0
$286$	2.89257	−	1.23369i	0.171041	−	0.0729497i
$287$	−10.7660	−	2.92717i	−0.635497	−	0.172785i
$288$		0			0
$289$	−0.398321	−	0.689912i	−0.0234306	−	0.0405831i
$290$	−22.8992	−	2.77176i	−1.34469	−	0.162763i
$291$		0			0
$292$	−5.12703	+	20.8685i	−0.300037	+	1.22124i
$293$	31.3006			1.82860			0.914299	−	0.405040i	$-0.132742\pi$
$293$	31.3006			1.82860			0.914299	+	0.405040i	$0.132742\pi$
$294$		0			0
$295$			16.1869i			0.942437i
$296$	−2.44290	−	14.9258i	−0.141991	−	0.867543i
$297$		0			0
$298$	−15.8738	−	1.92139i	−0.919545	−	0.111303i
$299$	−5.31783	+	3.07025i	−0.307538	+	0.177557i
$300$		0			0
$301$		0			0
$302$	8.22268	+	19.2793i	0.473162	+	1.10940i
$303$		0			0
$304$	9.78040	−	18.7031i	0.560944	−	1.07270i
$305$	−13.4581	+	23.3102i	−0.770611	+	1.33474i
$306$		0			0
$307$		−	14.7215i		−	0.840202i	−0.907477	−	0.420101i	$-0.861995\pi$
$307$		−	14.7215i		−	0.840202i	0.907477	−	0.420101i	$-0.138005\pi$
$308$	4.11067	−	7.41168i	0.234227	−	0.422319i
$309$		0			0
$310$	−0.418901	−	0.314538i	−0.0237920	−	0.0178646i
$311$	7.79025	−	13.4931i	0.441745	−	0.765124i	−0.556074	−	0.831133i	$-0.687693\pi$
$311$	7.79025	−	13.4931i	0.441745	−	0.765124i	0.997819	+	0.0660082i	$0.0210263\pi$
$312$		0			0
$313$	11.3329	−	6.54308i	0.640576	−	0.369837i	−0.144260	−	0.989540i	$-0.546080\pi$
$313$	11.3329	−	6.54308i	0.640576	−	0.369837i	0.784836	+	0.619703i	$0.212747\pi$
$314$	−0.960963	+	0.409854i	−0.0542303	+	0.0231294i
$315$		0			0
$316$	−17.2257	−	16.5207i	−0.969022	−	0.929363i
$317$	−20.3971	+	11.7763i	−1.14562	+	0.661422i	−0.947815	−	0.318821i	$-0.896713\pi$
$317$	−20.3971	+	11.7763i	−1.14562	+	0.661422i	−0.197801	+	0.980242i	$0.563380\pi$
$318$		0			0
$319$	7.08269	+	4.08919i	0.396555	+	0.228951i
$320$	5.05517	−	25.0492i	0.282593	−	1.40029i
$321$		0			0
$322$	−6.22951	+	15.3322i	−0.347157	+	0.854429i
$323$	21.2397			1.18181
$324$		0			0
$325$	−3.61193	+	6.25604i	−0.200354	+	0.347023i
$326$	1.47923	−	12.2209i	0.0819272	−	0.676851i
$327$		0			0
$328$	11.1568	+	4.21689i	0.616034	+	0.232839i
$329$	−25.8788	+	6.83243i	−1.42674	+	0.376684i
$330$		0			0
$331$	−16.5277	−	28.6268i	−0.908445	−	1.57347i	−0.816225	−	0.577735i	$-0.803937\pi$
$331$	−16.5277	−	28.6268i	−0.908445	−	1.57347i	−0.0922207	−	0.995739i	$-0.529397\pi$
$332$	28.7687	−	8.35634i	1.57889	−	0.458614i
$333$		0			0
$334$	1.57004	+	1.17889i	0.0859086	+	0.0645058i
$335$	32.0587			1.75155
$336$		0			0
$337$	−15.5096			−0.844860			−0.422430	−	0.906396i	$-0.638823\pi$
$337$	−15.5096			−0.844860			−0.422430	+	0.906396i	$0.638823\pi$
$338$	12.5220	+	9.40235i	0.681108	+	0.511420i
$339$		0			0
$340$	24.6954	−	7.17316i	1.33929	−	0.389019i
$341$	0.0928668	+	0.160850i	0.00502902	+	0.00871052i
$342$		0			0
$343$	13.2393	−	12.9507i	0.714855	−	0.699272i
$344$		0			0
$345$		0			0
$346$	0.164951	−	1.36276i	0.00886780	−	0.0732623i
$347$	11.2494	−	19.4846i	0.603900	−	1.04599i	−0.388324	−	0.921523i	$-0.626946\pi$
$347$	11.2494	−	19.4846i	0.603900	−	1.04599i	0.992224	−	0.124463i	$-0.0397209\pi$
$348$		0			0
$349$	−28.4735			−1.52415			−0.762077	−	0.647486i	$-0.775820\pi$
$349$	−28.4735			−1.52415			−0.762077	+	0.647486i	$0.775820\pi$
$350$	2.67188	+	19.2850i	0.142818	+	1.03083i
$351$		0			0
$352$	−5.13295	+	7.46625i	−0.273587	+	0.397952i
$353$	8.29108	+	4.78686i	0.441290	+	0.254779i	0.704145	−	0.710057i	$-0.251331\pi$
$353$	8.29108	+	4.78686i	0.441290	+	0.254779i	−0.262855	+	0.964835i	$0.584664\pi$
$354$		0			0
$355$	−14.6380	+	8.45124i	−0.776903	+	0.448545i
$356$	−2.50012	−	2.39779i	−0.132506	−	0.127083i
$357$		0			0
$358$	18.5629	−	7.91711i	0.981077	−	0.418432i
$359$	3.25225	−	1.87769i	0.171647	−	0.0991006i	−0.411715	−	0.911313i	$-0.635070\pi$
$359$	3.25225	−	1.87769i	0.171647	−	0.0991006i	0.583362	+	0.812212i	$0.301737\pi$
$360$		0			0
$361$	4.42067	−	7.65683i	0.232667	−	0.402991i
$362$	−17.3274	−	13.0105i	−0.910708	−	0.683819i
$363$		0			0
$364$	−7.34514	+	0.126458i	−0.384990	+	0.00662822i
$365$			34.3209i			1.79644i
$366$		0			0
$367$	−8.41302	+	14.5718i	−0.439156	+	0.760640i	−0.997625	−	0.0688852i	$-0.978056\pi$
$367$	−8.41302	+	14.5718i	−0.439156	+	0.760640i	0.558469	+	0.829526i	$0.311389\pi$
$368$	8.19841	−	15.6778i	0.427372	−	0.817264i
$369$		0			0
$370$	−9.47653	−	22.2191i	−0.492661	−	1.15512i
$371$	−13.3020	+	13.2046i	−0.690606	+	0.685551i
$372$		0			0
$373$	−11.1354	+	6.42901i	−0.576568	+	0.332882i	−0.759768	−	0.650194i	$-0.774688\pi$
$373$	−11.1354	+	6.42901i	−0.576568	+	0.332882i	0.183200	+	0.983076i	$0.441354\pi$
$374$	−9.05179	−	1.09564i	−0.468057	−	0.0566544i
$375$		0			0
$376$	28.2379	−	4.62169i	1.45626	−	0.238346i
$377$		−	7.08888i		−	0.365096i
$378$		0			0
$379$	25.5822			1.31407			0.657034	−	0.753861i	$-0.271811\pi$
$379$	25.5822			1.31407			0.657034	+	0.753861i	$0.271811\pi$
$380$	8.04257	−	32.7356i	0.412575	−	1.67930i
$381$		0			0
$382$	−3.51085	−	0.424959i	−0.179631	−	0.0217428i
$383$	−13.4846	−	23.3561i	−0.689033	−	1.19344i	−0.972151	−	0.234355i	$-0.924702\pi$
$383$	−13.4846	−	23.3561i	−0.689033	−	1.19344i	0.283118	−	0.959085i	$-0.408631\pi$
$384$		0			0
$385$	3.55142	−	13.0620i	0.180997	−	0.665701i
$386$	−4.03327	+	1.72020i	−0.205288	+	0.0875560i
$387$		0			0
$388$	5.51599	−	1.60221i	0.280032	−	0.0813398i
$389$	−27.7043	−	15.9951i	−1.40466	−	0.810983i	−0.409796	−	0.912177i	$-0.634400\pi$
$389$	−27.7043	−	15.9951i	−1.40466	−	0.810983i	−0.994867	+	0.101195i	$0.967734\pi$
$390$		0			0
$391$	17.8041			0.900394
$392$	−15.4140	+	12.4261i	−0.778525	+	0.627614i
$393$		0			0
$394$	−13.3225	+	17.7429i	−0.671178	+	0.893873i
$395$	−33.0126	−	19.0598i	−1.66104	−	0.959004i
$396$		0			0
$397$	−8.51929	−	14.7558i	−0.427571	−	0.740575i	0.569086	−	0.822278i	$-0.307297\pi$
$397$	−8.51929	−	14.7558i	−0.427571	−	0.740575i	−0.996657	+	0.0817035i	$0.973964\pi$
$398$	−15.3835	+	6.56110i	−0.771104	+	0.328878i
$399$		0			0
$400$	−0.869248	−	20.7953i	−0.0434624	−	1.03976i
$401$	−2.94858	−	5.10709i	−0.147245	−	0.255036i	0.782963	−	0.622068i	$-0.213707\pi$
$401$	−2.94858	−	5.10709i	−0.147245	−	0.255036i	−0.930208	+	0.367032i	$0.880374\pi$
$402$		0			0
$403$	0.0804953	−	0.139422i	0.00400976	−	0.00694510i
$404$	−13.2193	−	3.24775i	−0.657684	−	0.161582i
$405$		0			0
$406$	−11.7330	−	15.0782i	−0.582299	−	0.748320i
$407$			8.56461i			0.424532i
$408$		0			0
$409$	−0.207751	−	0.119945i	−0.0102726	−	0.00593090i	0.494855	−	0.868976i	$-0.335221\pi$
$409$	−0.207751	−	0.119945i	−0.0102726	−	0.00593090i	−0.505128	+	0.863045i	$0.668555\pi$
$410$	18.9113	+	2.28905i	0.933961	+	0.113048i
$411$		0			0
$412$	−19.4496	+	20.2795i	−0.958211	+	0.999101i
$413$	−9.51514	+	9.44550i	−0.468210	+	0.464783i
$414$		0			0
$415$	41.4364	−	23.9233i	2.03403	−	1.17435i
$416$	7.82915	+	0.617270i	0.383856	+	0.0302641i
$417$		0			0
$418$	−7.17641	+	9.55752i	−0.351010	+	0.467474i
$419$		−	29.4140i		−	1.43697i	−0.695544	−	0.718484i	$-0.744837\pi$
$419$		−	29.4140i		−	1.43697i	0.695544	−	0.718484i	$-0.255163\pi$
$420$		0			0
$421$			32.1265i			1.56575i	0.622180	+	0.782874i	$0.286247\pi$
$421$			32.1265i			1.56575i	−0.622180	+	0.782874i	$0.713753\pi$
$422$	−11.3911	−	8.55319i	−0.554511	−	0.416363i
$423$		0			0
$424$	15.5067	−	12.6899i	0.753073	−	0.616277i
$425$	18.1391	−	10.4726i	0.879878	−	0.507998i
$426$		0			0
$427$	−21.5556	+	5.69103i	−1.04315	+	0.275408i
$428$	7.11447	−	7.41807i	0.343891	−	0.358566i
$429$		0			0
$430$		0			0
$431$	32.7662	+	18.9176i	1.57829	+	0.911228i	0.995098	+	0.0988962i	$0.0315312\pi$
$431$	32.7662	+	18.9176i	1.57829	+	0.911228i	0.583196	+	0.812332i	$0.301802\pi$
$432$		0			0
$433$			25.4835i			1.22466i	0.790602	+	0.612330i	$0.209768\pi$
$433$			25.4835i			1.22466i	−0.790602	+	0.612330i	$0.790232\pi$
$434$	−0.0595453	−	0.429784i	−0.00285827	−	0.0206303i
$435$		0			0
$436$	−1.35094	+	5.49872i	−0.0646984	+	0.263341i
$437$	11.6690	−	20.2113i	0.558204	−	0.966837i
$438$		0			0
$439$	−11.9804	−	20.7506i	−0.571792	−	0.990373i	−0.996382	−	0.0849871i	$-0.972915\pi$
$439$	−11.9804	−	20.7506i	−0.571792	−	0.990373i	0.424590	−	0.905386i	$-0.360418\pi$
$440$	−5.11619	+	13.5362i	−0.243905	+	0.645312i
$441$		0			0
$442$	3.10051	+	7.26962i	0.147476	+	0.345780i
$443$	5.13495	+	8.89399i	0.243969	+	0.422566i	0.961841	−	0.273608i	$-0.0882172\pi$
$443$	5.13495	+	8.89399i	0.243969	+	0.422566i	−0.717872	+	0.696175i	$0.754884\pi$
$444$		0			0
$445$	−4.79140	−	2.76632i	−0.227134	−	0.131136i
$446$	−27.4907	−	20.6418i	−1.30172	−	0.977416i
$447$		0			0
$448$	17.6745	−	11.6453i	0.835041	−	0.550188i
$449$	−11.5096			−0.543170			−0.271585	−	0.962414i	$-0.587548\pi$
$449$	−11.5096			−0.543170			−0.271585	+	0.962414i	$0.587548\pi$
$450$		0			0
$451$	−5.84923	−	3.37705i	−0.275429	−	0.159019i
$452$	0.801641	+	2.75984i	0.0377060	+	0.129812i
$453$		0			0
$454$	−7.94707	−	18.6331i	−0.372974	−	0.874494i
$455$	−11.3442	+	2.99505i	−0.531824	+	0.140410i
$456$		0			0
$457$	−15.3050	−	26.5091i	−0.715939	−	1.24004i	−0.962596	−	0.270941i	$-0.912665\pi$
$457$	−15.3050	−	26.5091i	−0.715939	−	1.24004i	0.246657	−	0.969103i	$-0.420668\pi$
$458$	1.80985	−	14.9523i	0.0845689	−	0.698675i
$459$		0			0
$460$	6.74168	−	27.4406i	0.314332	−	1.27942i
$461$	−17.3671			−0.808866			−0.404433	−	0.914568i	$-0.632531\pi$
$461$	−17.3671			−0.808866			−0.404433	+	0.914568i	$0.632531\pi$
$462$		0			0
$463$		−	21.7288i		−	1.00983i	−0.863171	−	0.504913i	$-0.831525\pi$
$463$		−	21.7288i		−	1.00983i	0.863171	−	0.504913i	$-0.168475\pi$
$464$	10.9421	+	17.2462i	0.507973	+	0.800636i
$465$		0			0
$466$	−0.108418	+	0.895705i	−0.00502235	+	0.0414928i
$467$	0.585859	−	0.338246i	0.0271103	−	0.0156521i	−0.486384	−	0.873745i	$-0.661684\pi$
$467$	0.585859	−	0.338246i	0.0271103	−	0.0156521i	0.513494	+	0.858093i	$0.328351\pi$
$468$		0			0
$469$	18.7071	+	18.8450i	0.863814	+	0.870183i
$470$	42.0361	−	17.9285i	1.93898	−	0.826981i
$471$		0			0
$472$	11.0922	−	9.07731i	0.510560	−	0.417817i
$473$		0			0
$474$		0			0
$475$		−	27.4555i		−	1.25974i
$476$	18.6270	+	10.3309i	0.853768	+	0.473517i
$477$		0			0
$478$	4.02108	−	5.35527i	0.183920	−	0.244944i
$479$	−14.3839	+	24.9136i	−0.657217	+	1.13833i	0.324116	+	0.946017i	$0.394933\pi$
$479$	−14.3839	+	24.9136i	−0.657217	+	1.13833i	−0.981333	+	0.192316i	$0.938400\pi$
$480$		0			0
$481$	6.42907	−	3.71182i	0.293140	−	0.169245i
$482$	6.49482	+	15.2281i	0.295831	+	0.693619i
$483$		0			0
$484$	−11.6766	+	12.1749i	−0.530755	+	0.553404i
$485$	7.94483	−	4.58695i	0.360756	−	0.208283i
$486$		0			0
$487$	−1.58745	−	0.916514i	−0.0719342	−	0.0415312i	0.463602	−	0.886044i	$-0.346557\pi$
$487$	−1.58745	−	0.916514i	−0.0719342	−	0.0415312i	−0.535536	+	0.844513i	$0.679890\pi$
$488$	23.5206	−	3.84962i	1.06473	−	0.174264i
$489$		0			0
$490$	−19.1722	+	25.1467i	−0.866113	+	1.13601i
$491$	−13.4370			−0.606401			−0.303201	−	0.952927i	$-0.598055\pi$
$491$	−13.4370			−0.606401			−0.303201	+	0.952927i	$0.598055\pi$
$492$		0			0
$493$	−10.2770	+	17.8002i	−0.462851	+	0.801682i
$494$	10.2846	+	1.24486i	0.462726	+	0.0560091i
$495$		0			0
$496$	0.0193720	+	0.463443i	0.000869830	+	0.0208092i
$497$	−13.5096	−	3.67311i	−0.605987	−	0.164762i
$498$		0			0
$499$	5.68404	+	9.84505i	0.254453	+	0.440725i	0.964747	−	0.263180i	$-0.0847714\pi$
$499$	5.68404	+	9.84505i	0.254453	+	0.440725i	−0.710294	+	0.703905i	$0.751438\pi$
$500$	−0.362385	−	1.24760i	−0.0162063	−	0.0557943i
$501$		0			0
$502$	9.81887	−	13.0767i	0.438238	−	0.583644i
$503$	13.2022			0.588656			0.294328	−	0.955704i	$-0.404904\pi$
$503$	13.2022			0.588656			0.294328	+	0.955704i	$0.404904\pi$
$504$		0			0
$505$	−21.7408			−0.967454
$506$	−6.01562	+	8.01158i	−0.267427	+	0.356158i
$507$		0			0
$508$	−9.45091	+	2.74517i	−0.419317	+	0.121797i
$509$	13.2178	+	22.8940i	0.585870	+	1.01476i	0.994766	+	0.102176i	$0.0325804\pi$
$509$	13.2178	+	22.8940i	0.585870	+	1.01476i	−0.408896	+	0.912581i	$0.634086\pi$
$510$		0			0
$511$	−20.1749	+	20.0272i	−0.892484	+	0.885952i
$512$	−20.0000	+	10.5830i	−0.883883	+	0.467707i
$513$		0			0
$514$	−33.1207	−	4.00898i	−1.46089	−	0.176829i
$515$	−22.4388	+	38.8652i	−0.988773	+	1.71260i
$516$		0			0
$517$	−16.2033			−0.712619
$518$	7.53126	−	18.5361i	0.330905	−	0.814428i
$519$		0			0
$520$	12.3783	−	2.02596i	0.542825	−	0.0888442i
$521$	10.4163	+	6.01384i	0.456345	+	0.263471i	0.710506	−	0.703691i	$-0.248466\pi$
$521$	10.4163	+	6.01384i	0.456345	+	0.263471i	−0.254161	+	0.967162i	$0.581799\pi$
$522$		0			0
$523$	2.43276	−	1.40455i	0.106377	−	0.0614168i	−0.445868	−	0.895099i	$-0.647105\pi$
$523$	2.43276	−	1.40455i	0.106377	−	0.0614168i	0.552245	+	0.833682i	$0.313771\pi$
$524$	5.69439	+	5.46133i	0.248760	+	0.238579i
$525$		0			0
$526$	5.92487	+	13.8917i	0.258337	+	0.605708i
$527$	−0.404248	+	0.233393i	−0.0176093	+	0.0101668i
$528$		0			0
$529$	−1.71848	+	2.97649i	−0.0747164	+	0.129413i
$530$	19.2155	−	25.5912i	0.834668	−	1.11161i
$531$		0			0
$532$	23.9360	−	14.3744i	1.03776	−	0.623211i
$533$			5.85434i			0.253580i
$534$		0			0
$535$	8.20791	−	14.2165i	0.354859	−	0.614634i
$536$	−17.9779	−	21.9685i	−0.776527	−	0.948894i
$537$		0			0
$538$	30.3590	−	12.9482i	1.30887	−	0.558236i
$539$	9.75058	−	5.53440i	0.419987	−	0.238383i
$540$		0			0
$541$	1.68628	−	0.973573i	0.0724988	−	0.0418572i	−0.463312	−	0.886195i	$-0.653339\pi$
$541$	1.68628	−	0.973573i	0.0724988	−	0.0418572i	0.535811	+	0.844338i	$0.320006\pi$
$542$	−2.31783	+	19.1490i	−0.0995592	+	0.822520i
$543$		0			0
$544$	−18.7642	−	12.9001i	−0.804507	−	0.553088i
$545$			9.04336i			0.387375i
$546$		0			0
$547$	28.4561			1.21669			0.608347	−	0.793671i	$-0.291833\pi$
$547$	28.4561			1.21669			0.608347	+	0.793671i	$0.291833\pi$
$548$	−0.199749	−	0.0490750i	−0.00853286	−	0.00209638i
$549$		0			0
$550$	−1.41629	+	11.7008i	−0.0603906	+	0.498924i
$551$	13.4712	+	23.3329i	0.573894	+	0.994013i
$552$		0			0
$553$	−8.05982	−	30.5277i	−0.342738	−	1.29817i
$554$	−0.253810	−	0.595095i	−0.0107833	−	0.0252832i
$555$		0			0
$556$	28.7687	−	8.35634i	1.22007	−	0.354388i
$557$	−7.96630	−	4.59935i	−0.337543	−	0.194881i	0.321642	−	0.946861i	$-0.395765\pi$
$557$	−7.96630	−	4.59935i	−0.337543	−	0.194881i	−0.659185	+	0.751981i	$0.729099\pi$
$558$		0			0
$559$		0			0
$560$	22.9758	−	24.7970i	0.970905	−	1.04786i
$561$		0			0
$562$	1.62505	+	1.22020i	0.0685488	+	0.0514709i
$563$	23.5533	+	13.5985i	0.992653	+	0.573108i	0.906066	−	0.423136i	$-0.139071\pi$
$563$	23.5533	+	13.5985i	0.992653	+	0.573108i	0.0865866	+	0.996244i	$0.472404\pi$
$564$		0			0
$565$	2.29501	+	3.97508i	0.0965518	+	0.167233i
$566$	−17.3248	−	40.6205i	−0.728214	−	1.70741i
$567$		0			0
$568$	14.0000	+	5.29150i	0.587427	+	0.222027i
$569$	−11.7699	−	20.3861i	−0.493420	−	0.854628i	0.506551	−	0.862210i	$-0.330920\pi$
$569$	−11.7699	−	20.3861i	−0.493420	−	0.854628i	−0.999971	+	0.00758149i	$0.997587\pi$
$570$		0			0
$571$	−15.1713	+	26.2774i	−0.634897	+	1.09967i	0.351640	+	0.936135i	$0.385624\pi$
$571$	−15.1713	+	26.2774i	−0.634897	+	1.09967i	−0.986537	+	0.163539i	$0.947709\pi$
$572$	−4.31881	−	1.06106i	−0.180579	−	0.0443651i
$573$		0			0
$574$	9.68967	+	12.4523i	0.404439	+	0.519751i
$575$		−	23.0145i		−	0.959772i
$576$		0			0
$577$	24.7760	+	14.3044i	1.03144	+	0.595500i	0.917396	−	0.397976i	$-0.130287\pi$
$577$	24.7760	+	14.3044i	1.03144	+	0.595500i	0.114041	+	0.993476i	$0.463620\pi$
$578$	−0.135380	+	1.11846i	−0.00563107	+	0.0465217i
$579$		0			0
$580$	23.5431	+	22.5795i	0.977574	+	0.937564i
$581$	38.2421	+	10.3976i	1.58655	+	0.431367i
$582$		0			0
$583$	−9.82652	+	5.67335i	−0.406973	+	0.234966i
$584$	23.5187	−	19.2465i	0.973211	−	0.796428i
$585$		0			0
$586$	−35.3978	−	26.5790i	−1.46227	−	1.09797i
$587$			15.2362i			0.628867i	0.949280	+	0.314433i	$0.101814\pi$
$587$			15.2362i			0.628867i	−0.949280	+	0.314433i	$0.898186\pi$
$588$		0			0
$589$			0.611872i			0.0252117i
$590$	13.7452	−	18.3058i	0.565880	−	0.753637i
$591$		0			0
$592$	−9.91160	+	18.9540i	−0.407364	+	0.779003i
$593$	−18.2934	+	10.5617i	−0.751221	+	0.433717i	−0.826135	−	0.563473i	$-0.809465\pi$
$593$	−18.2934	+	10.5617i	−0.751221	+	0.433717i	0.0749142	+	0.997190i	$0.476132\pi$
$594$		0			0
$595$	32.8274	+	8.92543i	1.34579	+	0.365907i
$596$	16.3202	+	15.6522i	0.668500	+	0.641140i
$597$		0			0
$598$	8.62105	+	1.04351i	0.352541	+	0.0426721i
$599$	−29.1795	−	16.8468i	−1.19224	−	0.688341i	−0.233427	−	0.972374i	$-0.574994\pi$
$599$	−29.1795	−	16.8468i	−1.19224	−	0.688341i	−0.958814	+	0.284033i	$0.908327\pi$
$600$		0			0
$601$		−	24.3960i		−	0.995132i	−0.867426	−	0.497566i	$-0.834227\pi$
$601$		−	24.3960i		−	0.995132i	0.867426	−	0.497566i	$-0.165773\pi$
$602$		0			0
$603$		0			0
$604$	7.07205	−	28.7853i	0.287758	−	1.17126i
$605$	−13.4712	+	23.3329i	−0.547683	+	0.948616i
$606$		0			0
$607$	4.08757	+	7.07987i	0.165909	+	0.287363i	0.936978	−	0.349389i	$-0.113611\pi$
$607$	4.08757	+	7.07987i	0.165909	+	0.287363i	−0.771069	+	0.636752i	$0.780277\pi$
$608$	−26.9425	+	12.8463i	−1.09266	+	0.520985i
$609$		0			0
$610$	35.0138	−	14.9335i	1.41767	−	0.604639i
$611$	7.02235	+	12.1631i	0.284094	+	0.492065i
$612$		0			0
$613$	−14.7221	−	8.49981i	−0.594620	−	0.343304i	0.172302	−	0.985044i	$-0.444879\pi$
$613$	−14.7221	−	8.49981i	−0.594620	−	0.343304i	−0.766922	+	0.641740i	$0.778213\pi$
$614$	−12.5009	+	16.6486i	−0.504493	+	0.671883i
$615$		0			0
$616$	−10.9424	+	4.89128i	−0.440882	+	0.197075i
$617$	−39.6548			−1.59644			−0.798221	−	0.602365i	$-0.794225\pi$
$617$	−39.6548			−1.59644			−0.798221	+	0.602365i	$0.794225\pi$
$618$		0			0
$619$	−12.4719	−	7.20065i	−0.501288	−	0.289419i	0.227957	−	0.973671i	$-0.426795\pi$
$619$	−12.4719	−	7.20065i	−0.501288	−	0.289419i	−0.729245	+	0.684252i	$0.760129\pi$
$620$	0.206644	+	0.711423i	0.00829903	+	0.0285714i
$621$		0			0
$622$	−20.2677	+	8.64425i	−0.812662	+	0.346603i
$623$	−1.16979	−	4.43075i	−0.0468667	−	0.177514i
$624$		0			0
$625$	11.9709	+	20.7343i	0.478837	+	0.829370i
$626$	−18.3725	−	2.22384i	−0.734314	−	0.0888826i
$627$		0			0
$628$	1.43478	+	0.352502i	0.0572541	+	0.0140663i
$629$	−21.5246			−0.858241
$630$		0			0
$631$			36.6698i			1.45980i	0.683553	+	0.729900i	$0.260434\pi$
$631$			36.6698i			1.45980i	−0.683553	+	0.729900i	$0.739566\pi$
$632$	5.45194	+	33.3106i	0.216867	+	1.32502i
$633$		0			0
$634$	33.0670	+	4.00248i	1.31326	+	0.158959i
$635$	−13.6124	+	7.85913i	−0.540192	+	0.311880i
$636$		0			0
$637$	−8.38024	−	4.92077i	−0.332037	−	0.194968i
$638$	−4.53747	−	10.6388i	−0.179640	−	0.421193i
$639$		0			0
$640$	−26.9875	+	24.0355i	−1.06677	+	0.950086i
$641$	9.13798	−	15.8274i	0.360929	−	0.625147i	−0.627185	−	0.778870i	$-0.715793\pi$
$641$	9.13798	−	15.8274i	0.360929	−	0.625147i	0.988114	+	0.153723i	$0.0491265\pi$
$642$		0			0
$643$			13.6340i			0.537671i	0.963186	+	0.268836i	$0.0866389\pi$
$643$			13.6340i			0.537671i	−0.963186	+	0.268836i	$0.913361\pi$
$644$	20.0643	−	12.0494i	0.790646	−	0.474812i
$645$		0			0
$646$	−24.0200	−	18.0357i	−0.945053	−	0.709607i
$647$	−8.74153	+	15.1408i	−0.343665	+	0.595245i	−0.985110	−	0.171923i	$-0.945002\pi$
$647$	−8.74153	+	15.1408i	−0.343665	+	0.595245i	0.641445	+	0.767169i	$0.278335\pi$
$648$		0			0
$649$	−7.02907	+	4.05824i	−0.275915	+	0.159300i
$650$	9.39708	−	4.00788i	0.368584	−	0.157202i
$651$		0			0
$652$	−12.0503	+	12.5645i	−0.471924	+	0.492063i
$653$	−8.40495	+	4.85260i	−0.328911	+	0.189897i	−0.655358	−	0.755319i	$-0.727482\pi$
$653$	−8.40495	+	4.85260i	−0.328911	+	0.189897i	0.326446	+	0.945216i	$0.394149\pi$
$654$		0			0
$655$	10.9131	+	6.30070i	0.426411	+	0.246189i
$656$	−9.03650	−	14.2428i	−0.352816	−	0.556087i
$657$		0			0
$658$	35.0682	+	14.2483i	1.36710	+	0.555456i
$659$	28.9465			1.12760			0.563798	−	0.825913i	$-0.309340\pi$
$659$	28.9465			1.12760			0.563798	+	0.825913i	$0.309340\pi$
$660$		0			0
$661$	6.43683	−	11.1489i	0.250364	−	0.433643i	−0.713262	−	0.700897i	$-0.752783\pi$
$661$	6.43683	−	11.1489i	0.250364	−	0.433643i	0.963626	+	0.267254i	$0.0861164\pi$
$662$	−5.61739	+	46.4087i	−0.218326	+	1.80373i
$663$		0			0
$664$	−39.6304	−	14.9789i	−1.53796	−	0.581293i
$665$	31.6475	−	31.4159i	1.22724	−	1.21826i
$666$		0			0
$667$	11.2922	+	19.5587i	0.437238	+	0.757318i
$668$	−0.774501	−	2.66641i	−0.0299663	−	0.103166i
$669$		0			0
$670$	−36.2552	−	27.2227i	−1.40066	−	1.05171i
$671$	−13.4964			−0.521024
$672$		0			0
$673$	−23.6548			−0.911825			−0.455912	−	0.890025i	$-0.650687\pi$
$673$	−23.6548			−0.911825			−0.455912	+	0.890025i	$0.650687\pi$
$674$	17.5398	+	13.1700i	0.675607	+	0.507290i
$675$		0			0
$676$	−6.17713	−	21.2663i	−0.237582	−	0.817933i
$677$	−1.80224	−	3.12157i	−0.0692657	−	0.119972i	0.829313	−	0.558785i	$-0.188732\pi$
$677$	−1.80224	−	3.12157i	−0.0692657	−	0.119972i	−0.898578	+	0.438813i	$0.855399\pi$
$678$		0			0
$679$	7.33237	+	1.99360i	0.281391	+	0.0765072i
$680$	−34.0191	−	12.8580i	−1.30457	−	0.493083i
$681$		0			0
$682$	0.0315633	−	0.260764i	0.00120862	−	0.00998516i
$683$	−3.80924	+	6.59779i	−0.145756	+	0.252457i	−0.929655	−	0.368432i	$-0.879895\pi$
$683$	−3.80924	+	6.59779i	−0.145756	+	0.252457i	0.783899	+	0.620889i	$0.213228\pi$
$684$		0			0
$685$	−0.328514			−0.0125519
$686$	−25.9695	+	3.40375i	−0.991520	+	0.129956i
$687$		0			0
$688$		0			0
$689$	8.51745	+	4.91755i	0.324489	+	0.187344i
$690$		0			0
$691$	−44.9707	+	25.9639i	−1.71077	+	0.987712i	−0.777241	+	0.629203i	$0.783381\pi$
$691$	−44.9707	+	25.9639i	−1.71077	+	0.987712i	−0.933526	+	0.358509i	$0.883285\pi$
$692$	−1.34373	+	1.40108i	−0.0510811	+	0.0532609i
$693$		0			0
$694$	−29.2674	+	12.4826i	−1.11097	+	0.473834i
$695$	41.4364	−	23.9233i	1.57177	−	0.907462i
$696$		0			0
$697$	8.48721	−	14.7003i	0.321476	−	0.556813i
$698$	32.2008	+	24.1784i	1.21882	+	0.915167i
$699$		0			0
$700$	13.3543	−	24.0782i	0.504745	−	0.910072i
$701$			0.741474i			0.0280051i	0.999902	+	0.0140025i	$0.00445729\pi$
$701$			0.741474i			0.0280051i	−0.999902	+	0.0140025i	$0.995543\pi$
$702$		0			0
$703$	−14.1074	+	24.4347i	−0.532071	+	0.921574i
$704$	12.1449	−	4.08492i	0.457726	−	0.153956i
$705$		0			0
$706$	−5.31161	−	12.4539i	−0.199905	−	0.468708i
$707$	−12.6864	−	12.7799i	−0.477120	−	0.480638i
$708$		0			0
$709$	35.6491	−	20.5820i	1.33883	−	0.772974i	0.352196	−	0.935926i	$-0.385435\pi$
$709$	35.6491	−	20.5820i	1.33883	−	0.772974i	0.986634	+	0.162952i	$0.0521016\pi$
$710$	23.7305	+	2.87238i	0.890590	+	0.107799i
$711$		0			0
$712$	0.791288	+	4.83465i	0.0296548	+	0.181186i
$713$			0.512901i			0.0192083i
$714$		0			0
$715$	−7.10284			−0.265631
$716$	−27.7156	−	6.80925i	−1.03578	−	0.254474i
$717$		0			0
$718$	−5.27242	−	0.638183i	−0.196765	−	0.0238168i
$719$	−7.02471	−	12.1672i	−0.261978	−	0.453758i	0.704790	−	0.709416i	$-0.251041\pi$
$719$	−7.02471	−	12.1672i	−0.261978	−	0.453758i	−0.966767	+	0.255658i	$0.917708\pi$
$720$		0			0
$721$	−35.9398	+	9.48869i	−1.33847	+	0.353377i
$722$	−11.5012	+	4.90528i	−0.428029	+	0.182556i
$723$		0			0
$724$	8.54763	+	29.4273i	0.317670	+	1.09366i
$725$	23.0095	+	13.2845i	0.854550	+	0.493375i
$726$		0			0
$727$	13.2022			0.489642			0.244821	−	0.969568i	$-0.421271\pi$
$727$	13.2022			0.489642			0.244821	+	0.969568i	$0.421271\pi$
$728$	8.41401	+	6.09414i	0.311844	+	0.225864i
$729$		0			0
$730$	29.1438	−	38.8136i	1.07866	−	1.43656i
$731$		0			0
$732$		0			0
$733$	24.9797	+	43.2661i	0.922646	+	1.59807i	0.795304	+	0.606211i	$0.207311\pi$
$733$	24.9797	+	43.2661i	0.922646	+	1.59807i	0.127342	+	0.991859i	$0.459356\pi$
$734$	21.8880	−	9.33529i	0.807900	−	0.344572i
$735$		0			0
$736$	−22.5845	+	10.7684i	−0.832476	+	0.396928i
$737$	8.03747	+	13.9213i	0.296064	+	0.512798i
$738$		0			0
$739$	18.2718	−	31.6476i	0.672138	−	1.16418i	−0.305159	−	0.952301i	$-0.598710\pi$
$739$	18.2718	−	31.6476i	0.672138	−	1.16418i	0.977297	−	0.211875i	$-0.0679571\pi$
$740$	−8.15045	+	33.1747i	−0.299617	+	1.21953i
$741$		0			0
$742$	26.2560	−	3.63770i	0.963889	−	0.133544i
$743$			15.1330i			0.555177i	0.960700	+	0.277589i	$0.0895352\pi$
$743$			15.1330i			0.555177i	−0.960700	+	0.277589i	$0.910465\pi$
$744$		0			0
$745$	31.2771	+	18.0579i	1.14591	+	0.661589i
$746$	18.0522	+	2.18507i	0.660939	+	0.0800012i
$747$		0			0
$748$	9.30631	+	8.92543i	0.340273	+	0.326346i
$749$	13.1464	−	3.47087i	0.480360	−	0.126823i
$750$		0			0
$751$	11.9997	−	6.92806i	0.437877	−	0.252808i	−0.264820	−	0.964298i	$-0.585312\pi$
$751$	11.9997	−	6.92806i	0.437877	−	0.252808i	0.702697	+	0.711490i	$0.251979\pi$
$752$	−35.8588	−	18.7516i	−1.30763	−	0.683801i
$753$		0			0
$754$	−6.01955	+	8.01682i	−0.219219	+	0.291955i
$755$		−	47.3412i		−	1.72292i
$756$		0			0
$757$		−	46.6967i		−	1.69722i	−0.529019	−	0.848610i	$-0.677440\pi$
$757$		−	46.6967i		−	1.69722i	0.529019	−	0.848610i	$-0.322560\pi$
$758$	−28.9309	−	21.7232i	−1.05082	−	0.789022i
$759$		0			0
$760$	−36.8929	+	30.1913i	−1.33825	+	1.09515i
$761$	−40.7899	+	23.5501i	−1.47863	+	0.853689i	−0.999708	−	0.0241662i	$-0.992307\pi$
$761$	−40.7899	+	23.5501i	−1.47863	+	0.853689i	−0.478925	+	0.877856i	$0.658974\pi$
$762$		0			0
$763$	−5.31596	+	5.27705i	−0.192451	+	0.191042i
$764$	3.60957	+	3.46184i	0.130590	+	0.125245i
$765$		0			0
$766$	−4.58312	+	37.8640i	−0.165595	+	1.36808i
$767$	6.09267	+	3.51761i	0.219994	+	0.127013i
$768$		0			0
$769$			17.3071i			0.624110i	0.950064	+	0.312055i	$0.101017\pi$
$769$			17.3071i			0.624110i	−0.950064	+	0.312055i	$0.898983\pi$
$770$	−15.1079	+	11.7561i	−0.544453	+	0.423661i
$771$		0			0
$772$	6.02195	+	1.47949i	0.216735	+	0.0532480i
$773$	13.5389	−	23.4501i	0.486960	−	0.843440i	−0.512927	−	0.858432i	$-0.671439\pi$
$773$	13.5389	−	23.4501i	0.486960	−	0.843440i	0.999888	+	0.0149920i	$0.00477229\pi$
$774$		0			0
$775$	0.301696	+	0.522552i	0.0108372	+	0.0187706i
$776$	−7.59856	−	2.87198i	−0.272772	−	0.103098i
$777$		0			0
$778$	17.7485	+	41.6141i	0.636315	+	1.49194i
$779$	−11.1252	−	19.2694i	−0.398601	−	0.690398i
$780$		0			0
$781$	−7.33982	−	4.23764i	−0.262639	−	0.151635i
$782$	−20.1347	−	15.1184i	−0.720016	−	0.540635i
$783$		0			0
$784$	27.9834	−	0.963845i	0.999407	−	0.0344230i
$785$	2.35969			0.0842208
$786$		0			0
$787$	−46.9684	−	27.1172i	−1.67424	−	0.966624i	−0.965220	−	0.261439i	$-0.915803\pi$
$787$	−46.9684	−	27.1172i	−1.67424	−	0.966624i	−0.709023	−	0.705186i	$-0.750864\pi$
$788$	30.1329	−	8.75257i	1.07344	−	0.311798i
$789$		0			0
$790$	21.1492	+	49.5876i	0.752456	+	1.76425i
$791$	−0.997467	+	3.66864i	−0.0354658	+	0.130442i
$792$		0			0
$793$	5.84923	+	10.1312i	0.207712	+	0.359768i
$794$	−2.89551	+	23.9216i	−0.102758	+	0.848946i
$795$		0			0
$796$	22.9686	+	5.64298i	0.814099	+	0.200010i
$797$	−20.1437			−0.713527			−0.356763	−	0.934195i	$-0.616120\pi$
$797$	−20.1437			−0.713527			−0.356763	+	0.934195i	$0.616120\pi$
$798$		0			0
$799$		−	40.7221i		−	1.44064i
$800$	−16.6754	+	24.2555i	−0.589563	+	0.857562i
$801$		0			0
$802$	−1.00215	+	8.27941i	−0.0353873	+	0.292356i
$803$	−14.9037	+	8.60465i	−0.525940	+	0.303651i
$804$		0			0
$805$	26.5285	−	26.3344i	0.935008	−	0.928164i
$806$	−0.209423	+	0.0893195i	−0.00737661	+	0.00314615i
$807$		0			0
$808$	12.1919	+	14.8981i	0.428908	+	0.524113i
$809$	17.2771	−	29.9249i	0.607432	−	1.05210i	−0.384231	−	0.923237i	$-0.625533\pi$
$809$	17.2771	−	29.9249i	0.607432	−	1.05210i	0.991662	−	0.128865i	$-0.0411334\pi$
$810$		0			0
$811$		−	13.6340i		−	0.478754i	−0.970927	−	0.239377i	$-0.923057\pi$
$811$		−	13.6340i		−	0.478754i	0.970927	−	0.239377i	$-0.0769431\pi$
$812$	0.465109	+	27.0151i	0.0163221	+	0.948045i
$813$		0			0
$814$	7.27267	−	9.68573i	0.254907	−	0.339485i
$815$	−13.9023	+	24.0795i	−0.486976	+	0.843468i
$816$		0			0
$817$		0			0
$818$	0.133094	+	0.312058i	0.00465352	+	0.0109109i
$819$		0			0
$820$	−19.4430	−	18.6473i	−0.678980	−	0.651191i
$821$	27.7311	−	16.0106i	0.967822	−	0.558772i	0.0692505	−	0.997599i	$-0.477939\pi$
$821$	27.7311	−	16.0106i	0.967822	−	0.558772i	0.898572	+	0.438827i	$0.144606\pi$
$822$		0			0
$823$	−26.8399	−	15.4960i	−0.935580	−	0.540158i	−0.0470083	−	0.998894i	$-0.514969\pi$
$823$	−26.8399	−	15.4960i	−0.935580	−	0.540158i	−0.888572	+	0.458737i	$0.848302\pi$
$824$	39.2160	−	6.41848i	1.36615	−	0.223598i
$825$		0			0
$826$	18.7814	−	2.60210i	0.653487	−	0.0905387i
$827$	11.0191			0.383172			0.191586	−	0.981476i	$-0.438637\pi$
$827$	11.0191			0.383172			0.191586	+	0.981476i	$0.438637\pi$
$828$		0			0
$829$	−18.9836	+	32.8806i	−0.659328	+	1.14199i	0.321462	+	0.946922i	$0.395826\pi$
$829$	−18.9836	+	32.8806i	−0.659328	+	1.14199i	−0.980790	+	0.195067i	$0.937508\pi$
$830$	−67.1750	−	8.13097i	−2.33168	−	0.282230i
$831$		0			0
$832$	−8.32984	−	7.34623i	−0.288785	−	0.254685i
$833$	13.9090	+	24.5052i	0.481920	+	0.849054i
$834$		0			0
$835$	−2.21731	−	3.84050i	−0.0767332	−	0.132906i
$836$	16.2316	−	4.71473i	0.561382	−	0.163063i
$837$		0			0
$838$	−24.9770	+	33.2643i	−0.862816	+	1.14910i
$839$	8.32984			0.287578			0.143789	−	0.989608i	$-0.454071\pi$
$839$	8.32984			0.287578			0.143789	+	0.989608i	$0.454071\pi$
$840$		0			0
$841$	2.92739			0.100945
$842$	27.2803	−	36.3319i	0.940142	−	1.25208i
$843$		0			0
$844$	5.61925	+	19.3456i	0.193423	+	0.665904i
$845$	−17.6844	−	30.6304i	−0.608363	−	1.05372i
$846$		0			0
$847$	−21.5766	+	5.69657i	−0.741380	+	0.195736i
$848$	−28.3123	+	1.18346i	−0.972247	+	0.0406402i
$849$		0			0
$850$	−29.4065	−	3.55941i	−1.00863	−	0.122087i
$851$	−11.8255	+	20.4824i	−0.405374	+	0.702128i
$852$		0			0
$853$	−6.94153			−0.237673			−0.118837	−	0.992914i	$-0.537917\pi$
$853$	−6.94153			−0.237673			−0.118837	+	0.992914i	$0.537917\pi$
$854$	29.2098	+	11.8680i	0.999540	+	0.406116i
$855$		0			0
$856$	−14.3448	+	2.34782i	−0.490297	+	0.0802469i
$857$	−1.91744	−	1.10704i	−0.0654986	−	0.0378156i	0.466893	−	0.884314i	$-0.345373\pi$
$857$	−1.91744	−	1.10704i	−0.0654986	−	0.0378156i	−0.532392	+	0.846498i	$0.678707\pi$
$858$		0			0
$859$	5.26337	−	3.03881i	0.179584	−	0.103683i	−0.407513	−	0.913199i	$-0.633604\pi$
$859$	5.26337	−	3.03881i	0.179584	−	0.103683i	0.587097	+	0.809516i	$0.300271\pi$
$860$		0			0
$861$		0			0
$862$	−20.9914	−	49.2175i	−0.714970	−	1.67635i
$863$	7.64747	−	4.41527i	0.260323	−	0.150298i	−0.364159	−	0.931337i	$-0.618643\pi$
$863$	7.64747	−	4.41527i	0.260323	−	0.150298i	0.624482	+	0.781039i	$0.285310\pi$
$864$		0			0
$865$	−1.55026	+	2.68512i	−0.0527103	+	0.0912969i
$866$	21.6394	−	28.8193i	0.735338	−	0.979321i
$867$		0			0
$868$	−0.297613	+	0.536607i	−0.0101016	+	0.0182136i
$869$		−	19.1141i		−	0.648400i
$870$		0			0
$871$	6.96673	−	12.0667i	0.236059	−	0.408866i
$872$	6.19704	−	5.07135i	0.209858	−	0.171738i
$873$		0			0
$874$	−30.3590	+	12.9482i	−1.02691	+	0.437979i
$875$	0.450909	−	1.65842i	0.0152435	−	0.0560650i
$876$		0			0
$877$	−10.3059	+	5.95011i	−0.348005	+	0.200921i	−0.663806	−	0.747905i	$-0.731060\pi$
$877$	−10.3059	+	5.95011i	−0.348005	+	0.200921i	0.315801	+	0.948825i	$0.397727\pi$
$878$	−4.07185	+	33.6401i	−0.137418	+	1.13530i
$879$		0			0
$880$	17.2802	−	10.9636i	0.582516	−	0.369584i
$881$			53.9142i			1.81642i	0.418519	+	0.908208i	$0.362549\pi$
$881$			53.9142i			1.81642i	−0.418519	+	0.908208i	$0.637451\pi$
$882$		0			0
$883$	11.1987			0.376866			0.188433	−	0.982086i	$-0.439659\pi$
$883$	11.1987			0.376866			0.188433	+	0.982086i	$0.439659\pi$
$884$	2.66665	−	10.8540i	0.0896891	−	0.365061i
$885$		0			0
$886$	1.74525	−	14.4186i	0.0586328	−	0.484402i
$887$	−18.1832	−	31.4942i	−0.610531	−	1.05747i	−0.991151	−	0.132740i	$-0.957623\pi$
$887$	−18.1832	−	31.4942i	−0.610531	−	1.05747i	0.380620	−	0.924732i	$-0.375711\pi$
$888$		0			0
$889$	−12.5630	−	3.41576i	−0.421351	−	0.114561i
$890$	3.06957	+	7.19707i	0.102892	+	0.241246i
$891$		0			0
$892$	13.5612	+	46.6876i	0.454062	+	1.56322i
$893$	−46.2278	−	26.6896i	−1.54695	−	0.893134i
$894$		0			0
$895$	−45.5819			−1.52364
$896$	−29.8767	−	1.83868i	−0.998112	−	0.0614262i
$897$		0			0
$898$	13.0162	+	9.77339i	0.434355	+	0.326142i
$899$	−0.512788	−	0.296058i	−0.0171024	−	0.00987410i
$900$		0			0
$901$	−14.2583	−	24.6960i	−0.475011	−	0.822744i
$902$	3.74726	+	8.78601i	0.124770	+	0.292542i
$903$		0			0
$904$	1.43695	−	3.80183i	0.0477924	−	0.126447i
$905$	24.4709	+	42.3849i	0.813441	+	1.40892i
$906$		0			0
$907$	8.92370	−	15.4563i	0.296307	−	0.513218i	−0.678981	−	0.734156i	$-0.737578\pi$
$907$	8.92370	−	15.4563i	0.296307	−	0.513218i	0.975288	+	0.220937i	$0.0709116\pi$
$908$	−6.83501	+	27.8205i	−0.226828	+	0.923254i
$909$		0			0
$910$	15.3724	+	6.24586i	0.509591	+	0.207048i
$911$		−	11.1458i		−	0.369278i	−0.982806	−	0.184639i	$-0.940888\pi$
$911$		−	11.1458i		−	0.369278i	0.982806	−	0.184639i	$-0.0591116\pi$
$912$		0			0
$913$	20.7771	+	11.9957i	0.687623	+	0.396999i
$914$	−5.20183	+	42.9755i	−0.172061	+	1.42150i
$915$		0			0
$916$	−14.7436	+	15.3727i	−0.487141	+	0.507929i
$917$	2.66437	+	10.0917i	0.0879854	+	0.333257i
$918$		0			0
$919$	28.2802	−	16.3276i	0.932879	−	0.538598i	0.0451579	−	0.998980i	$-0.485621\pi$
$919$	28.2802	−	16.3276i	0.932879	−	0.538598i	0.887721	+	0.460382i	$0.152288\pi$
$920$	−30.9254	+	25.3078i	−1.01958	+	0.834375i
$921$		0			0
$922$	19.6405	+	14.7473i	0.646825	+	0.485678i
$923$			7.34623i			0.241804i
$924$		0			0
$925$			27.8238i			0.914839i
$926$	−18.4511	+	24.5732i	−0.606342	+	0.807525i
$927$		0			0
$928$	2.27029	−	28.7953i	0.0745260	−	0.945252i
$929$	23.3027	−	13.4538i	0.764537	−	0.441406i	−0.0663853	−	0.997794i	$-0.521147\pi$
$929$	23.3027	−	13.4538i	0.764537	−	0.441406i	0.830922	+	0.556388i	$0.187813\pi$
$930$		0			0
$931$	36.9344	+	0.271329i	1.21048	+	0.00889246i
$932$	0.883202	−	0.920891i	0.0289302	−	0.0301648i
$933$		0			0
$934$	−0.949771	−	0.114962i	−0.0310775	−	0.00376167i
$935$	17.8353	+	10.2972i	0.583276	+	0.336755i
$936$		0			0
$937$			32.6476i			1.06655i	0.845942	+	0.533275i	$0.179039\pi$
$937$			32.6476i			1.06655i	−0.845942	+	0.533275i	$0.820961\pi$
$938$	−5.15355	−	37.1971i	−0.168269	−	1.21453i
$939$		0			0
$940$	−62.7628	−	15.4197i	−2.04710	−	0.502936i
$941$	6.32087	−	10.9481i	0.206055	−	0.356897i	−0.744414	−	0.667719i	$-0.767271\pi$
$941$	6.32087	−	10.9481i	0.206055	−	0.356897i	0.950468	+	0.310822i	$0.100604\pi$
$942$		0			0
$943$	−9.32569	−	16.1526i	−0.303686	−	0.526000i
$944$	−20.2522	+	0.846548i	−0.659154	+	0.0275528i
$945$		0			0
$946$		0			0
$947$	−21.1271	−	36.5931i	−0.686537	−	1.18912i	−0.972951	−	0.231011i	$-0.925797\pi$
$947$	−21.1271	−	36.5931i	−0.686537	−	1.18912i	0.286414	−	0.958106i	$-0.407537\pi$
$948$		0			0
$949$	12.9182	+	7.45835i	0.419344	+	0.242108i
$950$	−23.3139	+	31.0494i	−0.756403	+	1.00738i
$951$		0			0
$952$	−12.2928	−	27.5005i	−0.398411	−	0.891295i
$953$	44.4561			1.44007			0.720037	−	0.693936i	$-0.244125\pi$
$953$	44.4561			1.44007			0.720037	+	0.693936i	$0.244125\pi$
$954$		0			0
$955$	6.91764	+	3.99390i	0.223850	+	0.129240i
$956$	−9.09489	+	2.64176i	−0.294150	+	0.0854406i
$957$		0			0
$958$	37.4223	−	15.9607i	1.20906	−	0.515668i
$959$	−0.191697	−	0.193110i	−0.00619021	−	0.00623585i
$960$		0			0
$961$	15.4933	+	26.8351i	0.499783	+	0.865650i
$962$	−10.4225	−	1.26156i	−0.336036	−	0.0406744i
$963$		0			0
$964$	5.58598	−	22.7365i	0.179912	−	0.732294i
$965$	9.90388			0.318817
$966$		0			0
$967$			25.7160i			0.826972i	0.910510	+	0.413486i	$0.135689\pi$
$967$			25.7160i			0.826972i	−0.910510	+	0.413486i	$0.864311\pi$
$968$	23.5435	−	3.85336i	0.756716	−	0.123852i
$969$		0			0
$970$	−12.8798	−	1.55900i	−0.413547	−	0.0500564i
$971$	40.2746	−	23.2526i	1.29247	−	0.746210i	0.313381	−	0.949627i	$-0.398538\pi$
$971$	40.2746	−	23.2526i	1.29247	−	0.746210i	0.979092	+	0.203417i	$0.0652048\pi$
$972$		0			0
$973$	38.2421	+	10.3976i	1.22599	+	0.333333i
$974$	1.01699	+	2.38448i	0.0325863	+	0.0764035i
$975$		0			0
$976$	−29.8684	−	15.6191i	−0.956063	−	0.499954i
$977$	17.1348	−	29.6783i	0.548189	−	0.949492i	−0.450209	−	0.892923i	$-0.648651\pi$
$977$	17.1348	−	29.6783i	0.548189	−	0.949492i	0.998399	−	0.0565688i	$-0.0180160\pi$
$978$		0			0
$979$		−	2.77419i		−	0.0886635i
$980$	43.0353	−	12.1582i	1.37471	−	0.388380i
$981$		0			0
$982$	15.1959	+	11.4100i	0.484920	+	0.364109i
$983$	0.777334	−	1.34638i	0.0247931	−	0.0429429i	−0.853363	−	0.521318i	$-0.825441\pi$
$983$	0.777334	−	1.34638i	0.0247931	−	0.0429429i	0.878156	+	0.478375i	$0.158774\pi$
$984$		0			0
$985$	43.4012	−	25.0577i	1.38288	−	0.798404i
$986$	26.7374	−	11.4036i	0.851491	−	0.363163i
$987$		0			0
$988$	−10.5738	−	10.1410i	−0.336396	−	0.322629i
$989$		0			0
$990$		0			0
$991$	22.6482	+	13.0759i	0.719443	+	0.415371i	0.814548	−	0.580097i	$-0.196985\pi$
$991$	22.6482	+	13.0759i	0.719443	+	0.415371i	−0.0951047	+	0.995467i	$0.530319\pi$
$992$	0.371626	−	0.540558i	0.0117992	−	0.0171627i
$993$		0			0
$994$	12.1589	+	15.6256i	0.385658	+	0.495615i
$995$	37.7748			1.19754
$996$		0			0
$997$	18.1467	−	31.4310i	0.574711	−	0.995429i	−0.421362	−	0.906893i	$-0.638448\pi$
$997$	18.1467	−	31.4310i	0.574711	−	0.995429i	0.996073	−	0.0885360i	$-0.0282188\pi$
$998$	1.93187	−	15.9604i	0.0611524	−	0.505218i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.a.451.1		12
3.2	odd	2		56.2.m.a.3.6	yes	12
4.3	odd	2		2016.2.bs.a.1711.6		12
7.5	odd	6	inner	504.2.bk.a.19.4		12
8.3	odd	2	inner	504.2.bk.a.451.3		12
8.5	even	2		2016.2.bs.a.1711.1		12
12.11	even	2		224.2.q.a.143.3		12
21.2	odd	6		392.2.m.g.19.3		12
21.5	even	6		56.2.m.a.19.3	yes	12
21.11	odd	6		392.2.e.e.195.4		12
21.17	even	6		392.2.e.e.195.3		12
21.20	even	2		392.2.m.g.227.6		12
24.5	odd	2		224.2.q.a.143.4		12
24.11	even	2		56.2.m.a.3.4	✓	12
28.19	even	6		2016.2.bs.a.271.1		12
56.5	odd	6		2016.2.bs.a.271.6		12
56.19	even	6	inner	504.2.bk.a.19.2		12
84.11	even	6		1568.2.e.e.783.6		12
84.23	even	6		1568.2.q.g.1391.3		12
84.47	odd	6		224.2.q.a.47.4		12
84.59	odd	6		1568.2.e.e.783.7		12
84.83	odd	2		1568.2.q.g.815.4		12
168.5	even	6		224.2.q.a.47.3		12
168.11	even	6		392.2.e.e.195.2		12
168.53	odd	6		1568.2.e.e.783.5		12
168.59	odd	6		392.2.e.e.195.1		12
168.83	odd	2		392.2.m.g.227.4		12
168.101	even	6		1568.2.e.e.783.8		12
168.107	even	6		392.2.m.g.19.5		12
168.125	even	2		1568.2.q.g.815.3		12
168.131	odd	6		56.2.m.a.19.5	yes	12
168.149	odd	6		1568.2.q.g.1391.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.4	✓	12	24.11	even	2
56.2.m.a.3.6	yes	12	3.2	odd	2
56.2.m.a.19.3	yes	12	21.5	even	6
56.2.m.a.19.5	yes	12	168.131	odd	6
224.2.q.a.47.3		12	168.5	even	6
224.2.q.a.47.4		12	84.47	odd	6
224.2.q.a.143.3		12	12.11	even	2
224.2.q.a.143.4		12	24.5	odd	2
392.2.e.e.195.1		12	168.59	odd	6
392.2.e.e.195.2		12	168.11	even	6
392.2.e.e.195.3		12	21.17	even	6
392.2.e.e.195.4		12	21.11	odd	6
392.2.m.g.19.3		12	21.2	odd	6
392.2.m.g.19.5		12	168.107	even	6
392.2.m.g.227.4		12	168.83	odd	2
392.2.m.g.227.6		12	21.20	even	2
504.2.bk.a.19.2		12	56.19	even	6	inner
504.2.bk.a.19.4		12	7.5	odd	6	inner
504.2.bk.a.451.1		12	1.1	even	1	trivial
504.2.bk.a.451.3		12	8.3	odd	2	inner
1568.2.e.e.783.5		12	168.53	odd	6
1568.2.e.e.783.6		12	84.11	even	6
1568.2.e.e.783.7		12	84.59	odd	6
1568.2.e.e.783.8		12	168.101	even	6
1568.2.q.g.815.3		12	168.125	even	2
1568.2.q.g.815.4		12	84.83	odd	2
1568.2.q.g.1391.3		12	84.23	even	6
1568.2.q.g.1391.4		12	168.149	odd	6
2016.2.bs.a.271.1		12	28.19	even	6
2016.2.bs.a.271.6		12	56.5	odd	6
2016.2.bs.a.1711.1		12	8.5	even	2
2016.2.bs.a.1711.6		12	4.3	odd	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +(0.542829 - 4.48465i) q^{10} +(-0.800840 + 1.38709i) q^{11} +1.38831 q^{13} +(2.95297 - 2.29782i) q^{14} +(-3.37755 + 2.14293i) q^{16} +(-3.48605 - 2.01267i) q^{17} +(-4.56957 + 2.63824i) q^{19} +(-4.42204 + 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +(-3.83044 + 2.21151i) q^{23} +(-2.60168 + 4.50624i) q^{25} +(-1.57004 - 1.17889i) q^{26} +(-5.29072 + 0.0910883i) q^{28} -5.10613i q^{29} +(0.0579809 - 0.100426i) q^{31} +(5.63935 + 0.444621i) q^{32} +(2.23331 + 5.23632i) q^{34} +(-8.17125 + 2.15734i) q^{35} +(4.63087 - 2.67363i) q^{37} +(7.40801 + 0.896678i) q^{38} +(8.91613 - 1.45930i) q^{40} +4.21689i q^{41} +(-3.11085 - 0.764282i) q^{44} +(6.20976 + 0.751640i) q^{46} +(5.05821 + 8.76108i) q^{47} +(-6.03630 - 3.54444i) q^{49} +(6.76873 - 2.88689i) q^{50} +(0.774501 + 2.66641i) q^{52} +(6.13514 + 3.54212i) q^{53} -5.11619 q^{55} +(6.06063 + 4.38962i) q^{56} +(-4.33589 + 5.77453i) q^{58} +(4.38856 + 2.53374i) q^{59} +(4.21321 + 7.29750i) q^{61} +(-0.150848 + 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.21731 + 3.84050i) q^{65} +(5.01815 - 8.69169i) q^{67} +(1.92079 - 7.81818i) q^{68} +(11.0728 + 4.49891i) q^{70} +5.29150i q^{71} +(9.30504 + 5.37227i) q^{73} +(-7.50738 - 0.908707i) q^{74} +(-7.61631 - 7.30460i) q^{76} +(-2.98544 - 3.00745i) q^{77} +(-10.3349 + 5.96688i) q^{79} +(-11.3224 - 5.92084i) q^{80} +(3.58079 - 4.76889i) q^{82} -14.9789i q^{83} -12.8580i q^{85} +(2.86907 + 3.50592i) q^{88} +(-1.50000 + 0.866025i) q^{89} +(-0.963697 + 3.54444i) q^{91} +(-6.38437 - 6.12307i) q^{92} +(1.71917 - 14.2031i) q^{94} +(-14.5965 - 8.42726i) q^{95} -2.87198i q^{97} +(3.81669 + 9.13416i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58}+ \cdots + 6 q^{98}+O(q^{100}) \) 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

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