LMFDB - Embedded newform 504.2.bk.a.19.4

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			19.4
Root			$1.09935 - 0.468876i$ of defining polynomial
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.a.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169938 + 1.40397i) q^{2} +(-1.94224 - 0.477176i) q^{4} +(-1.59713 + 2.76632i) q^{5} +(0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +O(q^{10})$	\(q+(-0.169938 + 1.40397i) q^{2} +(-1.94224 - 0.477176i) q^{4} +(-1.59713 + 2.76632i) q^{5} +(0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +(-3.61240 - 2.71243i) q^{10} +(-0.800840 - 1.38709i) q^{11} -1.38831 q^{13} +(-3.70238 + 0.540703i) q^{14} +(3.54461 + 1.85358i) q^{16} +(-3.48605 + 2.01267i) q^{17} +(-4.56957 - 2.63824i) q^{19} +(4.42204 - 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +(3.83044 + 2.21151i) q^{23} +(-2.60168 - 4.50624i) q^{25} +(0.235927 - 1.94913i) q^{26} +(-0.129952 - 5.28991i) q^{28} -5.10613i q^{29} +(-0.0579809 - 0.100426i) q^{31} +(-3.20473 + 4.66151i) q^{32} +(-2.23331 - 5.23632i) q^{34} +(-8.17125 - 2.15734i) q^{35} +(-4.63087 - 2.67363i) q^{37} +(4.48055 - 5.96719i) q^{38} +(5.72186 + 6.99194i) q^{40} -4.21689i q^{41} +(0.893536 + 3.07621i) q^{44} +(-3.75582 + 5.00199i) q^{46} +(-5.05821 + 8.76108i) q^{47} +(-6.03630 + 3.54444i) q^{49} +(6.76873 - 2.88689i) q^{50} +(2.69643 + 0.662466i) q^{52} +(-6.13514 + 3.54212i) q^{53} +5.11619 q^{55} +(7.44893 + 0.716511i) q^{56} +(7.16884 + 0.867728i) q^{58} +(4.38856 - 2.53374i) q^{59} +(-4.21321 + 7.29750i) q^{61} +(0.150848 - 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.21731 - 3.84050i) q^{65} +(5.01815 + 8.69169i) q^{67} +(7.73114 - 2.24564i) q^{68} +(4.41745 - 11.1055i) q^{70} +5.29150i q^{71} +(9.30504 - 5.37227i) q^{73} +(4.54066 - 6.04723i) q^{74} +(7.61631 + 7.30460i) q^{76} +(2.98544 - 3.00745i) q^{77} +(10.3349 + 5.96688i) q^{79} +(-10.7888 + 6.84509i) q^{80} +(5.92037 + 0.716612i) q^{82} +14.9789i q^{83} -12.8580i q^{85} +(-4.47075 + 0.731728i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-0.963697 - 3.54444i) q^{91} +(-6.38437 - 6.12307i) q^{92} +(-11.4407 - 8.59041i) q^{94} +(14.5965 - 8.42726i) q^{95} +2.87198i q^{97} +(-3.95047 - 9.07710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.169938	+	1.40397i	−0.120165	+	0.992754i
$2$	−0.169938	+	1.40397i	−0.120165	+	0.992754i
$3$		0			0
$3$		0			0
$4$	−1.94224	−	0.477176i	−0.971121	−	0.238588i
$5$	−1.59713	+	2.76632i	−0.714260	+	1.23714i	0.248984	+	0.968508i	$0.419903\pi$
$5$	−1.59713	+	2.76632i	−0.714260	+	1.23714i	−0.963244	+	0.268628i	$0.913430\pi$
$6$		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
$10$	−3.61240	−	2.71243i	−1.14234	−	0.857745i
$11$	−0.800840	−	1.38709i	−0.241462	−	0.418225i	0.719669	−	0.694318i	$-0.244294\pi$
$11$	−0.800840	−	1.38709i	−0.241462	−	0.418225i	−0.961131	+	0.276093i	$0.910960\pi$
$12$		0			0
$13$	−1.38831			−0.385047			−0.192523	−	0.981292i	$-0.561667\pi$
$13$	−1.38831			−0.385047			−0.192523	+	0.981292i	$0.561667\pi$
$14$	−3.70238	+	0.540703i	−0.989503	+	0.144509i
$15$		0			0
$16$	3.54461	+	1.85358i	0.886152	+	0.463395i
$17$	−3.48605	+	2.01267i	−0.845490	+	0.488144i	−0.859127	−	0.511763i	$-0.828993\pi$
$17$	−3.48605	+	2.01267i	−0.845490	+	0.488144i	0.0136363	+	0.999907i	$0.495659\pi$
$18$		0			0
$19$	−4.56957	−	2.63824i	−1.04833	−	0.605255i	−0.126150	−	0.992011i	$-0.540262\pi$
$19$	−4.56957	−	2.63824i	−1.04833	−	0.605255i	−0.922182	+	0.386756i	$0.873595\pi$
$20$	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	$-0.180777\pi$
$23$	3.83044	+	2.21151i	0.798702	+	0.461131i	−0.0443149	+	0.999018i	$0.514110\pi$
$24$		0			0
$25$	−2.60168	−	4.50624i	−0.520336	−	0.901248i
$26$	0.235927	−	1.94913i	0.0462690	−	0.382257i
$27$		0			0
$28$	−0.129952	−	5.28991i	−0.0245586	−	0.999698i
$29$		−	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	$-0.169982\pi$
$31$	−0.0579809	−	0.100426i	−0.0104137	−	0.0180370i	−0.871185	+	0.490954i	$0.836648\pi$
$32$	−3.20473	+	4.66151i	−0.566522	+	0.824047i
$33$		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	$-0.478193\pi$
$37$	−4.63087	−	2.67363i	−0.761310	−	0.439543i	−0.829766	+	0.558111i	$0.811526\pi$
$38$	4.48055	−	5.96719i	0.726842	−	0.968006i
$39$		0			0
$40$	5.72186	+	6.99194i	0.904705	+	1.10552i
$41$		−	4.21689i		−	0.658568i	−0.944231	−	0.329284i	$-0.893193\pi$
$41$		−	4.21689i		−	0.658568i	0.944231	−	0.329284i	$-0.106807\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	0.893536	+	3.07621i	0.134706	+	0.463757i
$45$		0			0
$46$	−3.75582	+	5.00199i	−0.553765	+	0.737503i
$47$	−5.05821	+	8.76108i	−0.737816	+	1.27794i	0.215660	+	0.976468i	$0.430810\pi$
$47$	−5.05821	+	8.76108i	−0.737816	+	1.27794i	−0.953477	+	0.301467i	$0.902524\pi$
$48$		0			0
$49$	−6.03630	+	3.54444i	−0.862329	+	0.506348i
$50$	6.76873	−	2.88689i	0.957244	−	0.408267i
$51$		0			0
$52$	2.69643	+	0.662466i	0.373927	+	0.0918675i
$53$	−6.13514	+	3.54212i	−0.842726	+	0.486548i	−0.858190	−	0.513332i	$-0.828411\pi$
$53$	−6.13514	+	3.54212i	−0.842726	+	0.486548i	0.0154638	+	0.999880i	$0.495078\pi$
$54$		0			0
$55$	5.11619			0.689868
$56$	7.44893	+	0.716511i	0.995406	+	0.0957478i
$57$		0			0
$58$	7.16884	+	0.867728i	0.941315	+	0.113938i
$59$	4.38856	−	2.53374i	0.571342	−	0.329865i	−0.186343	−	0.982485i	$-0.559664\pi$
$59$	4.38856	−	2.53374i	0.571342	−	0.329865i	0.757685	+	0.652620i	$0.226330\pi$
$60$		0			0
$61$	−4.21321	+	7.29750i	−0.539447	+	0.934349i	0.459487	+	0.888184i	$0.348033\pi$
$61$	−4.21321	+	7.29750i	−0.539447	+	0.934349i	−0.998934	+	0.0461646i	$0.985300\pi$
$62$	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	0.990721	+	0.135913i	$0.0433969\pi$
$67$	5.01815	+	8.69169i	0.613065	+	1.06186i	−0.377656	+	0.925946i	$0.623270\pi$
$68$	7.73114	−	2.24564i	0.937539	−	0.272323i
$69$		0			0
$70$	4.41745	−	11.1055i	0.527986	−	1.32737i
$71$			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	0.155743	−	0.987798i	$-0.450223\pi$
$73$	9.30504	−	5.37227i	1.08907	−	0.628776i	0.933329	+	0.359021i	$0.116890\pi$
$74$	4.54066	−	6.04723i	0.527840	−	0.702976i
$75$		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	$-0.0990581\pi$
$79$	10.3349	+	5.96688i	1.16277	+	0.671327i	0.210805	+	0.977528i	$0.432391\pi$
$80$	−10.7888	+	6.84509i	−1.20623	+	0.765305i
$81$		0			0
$82$	5.92037	+	0.716612i	0.653796	+	0.0791366i
$83$			14.9789i			1.64415i	0.569382	+	0.822073i	$0.307182\pi$
$83$			14.9789i			1.64415i	−0.569382	+	0.822073i	$0.692818\pi$
$84$		0			0
$85$		−	12.8580i		−	1.39465i
$86$		0			0
$87$		0			0
$88$	−4.47075	+	0.731728i	−0.476583	+	0.0780024i
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	0.418389	−	0.908268i	$-0.362595\pi$
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	−0.577389	+	0.816469i	$0.695928\pi$
$90$		0			0
$91$	−0.963697	−	3.54444i	−0.101023	−	0.371558i
$92$	−6.38437	−	6.12307i	−0.665616	−	0.638375i
$93$		0			0
$94$	−11.4407	−	8.59041i	−1.18002	−	0.886033i
$95$	14.5965	−	8.42726i	1.49756	−	0.864619i
$96$		0			0
$97$			2.87198i			0.291606i	0.989314	+	0.145803i	$0.0465765\pi$
$97$			2.87198i			0.291606i	−0.989314	+	0.145803i	$0.953423\pi$
$98$	−3.95047	−	9.07710i	−0.399058	−	0.916926i
$99$		0			0
$100$	2.90282	+	9.99367i	0.290282	+	0.999367i
$101$	3.40310	+	5.89434i	0.338621	+	0.586509i	0.984174	−	0.177207i	$-0.0567062\pi$
$101$	3.40310	+	5.89434i	0.338621	+	0.586509i	−0.645553	+	0.763716i	$0.723373\pi$
$102$		0			0
$103$	−7.02471	+	12.1672i	−0.692165	+	1.19887i	0.278962	+	0.960302i	$0.410010\pi$
$103$	−7.02471	+	12.1672i	−0.692165	+	1.19887i	−0.971127	+	0.238563i	$0.923324\pi$
$104$	−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	−0.963085	−	0.269198i	$-0.913241\pi$
$107$	−2.56957	+	4.45063i	−0.248410	+	0.430259i	0.714675	+	0.699457i	$0.246575\pi$
$108$		0			0
$109$	−2.45182	+	1.41556i	−0.234842	+	0.135586i	−0.612804	−	0.790235i	$-0.709958\pi$
$109$	−2.45182	+	1.41556i	−0.234842	+	0.135586i	0.377962	+	0.925821i	$0.376625\pi$
$110$	−0.869438	+	7.18296i	−0.0828977	+	0.684869i
$111$		0			0
$112$	−2.27182	+	10.3363i	−0.214667	+	0.976687i
$113$	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
$116$	−2.43652	+	9.91735i	−0.226225	+	0.920803i
$117$		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
$122$	−9.52946	−	7.15533i	−0.862756	−	0.647814i
$123$		0			0
$124$	0.0646922	+	0.222719i	0.00580953	+	0.0200007i
$125$	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	$0.929941\pi$
$128$	8.44872	−	7.52457i	0.746769	−	0.665084i
$129$		0			0
$130$	5.01512	+	3.76568i	0.439855	+	0.330272i
$131$	3.41647	+	1.97250i	0.298499	+	0.172338i	0.641768	−	0.766899i	$-0.278201\pi$
$131$	3.41647	+	1.97250i	0.298499	+	0.172338i	−0.343270	+	0.939237i	$0.611534\pi$
$132$		0			0
$133$	3.56363	−	13.4978i	0.309006	−	1.17041i
$134$	−13.0556	+	5.56826i	−1.12783	+	0.481025i
$135$		0			0
$136$	1.83898	+	11.2359i	0.157691	+	0.963469i
$137$	−0.0514223	−	0.0890661i	−0.00439331	−	0.00760943i	0.863820	−	0.503800i	$-0.168065\pi$
$137$	−0.0514223	−	0.0890661i	−0.00439331	−	0.00760943i	−0.868214	+	0.496190i	$0.834732\pi$
$138$		0			0
$139$			14.9789i			1.27049i	0.772310	+	0.635246i	$0.219101\pi$
$139$			14.9789i			1.27049i	−0.772310	+	0.635246i	$0.780899\pi$
$140$	14.8411	+	8.08921i	1.25430	+	0.683663i
$141$		0			0
$142$	−7.42909	−	0.899230i	−0.623435	−	0.0754617i
$143$	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	$-0.486607\pi$
$149$	−9.79164	−	5.65320i	−0.802162	−	0.463129i	−0.844227	+	0.535986i	$0.819940\pi$
$150$		0			0
$151$	12.8351	−	7.41032i	1.04450	−	0.603044i	0.123397	−	0.992357i	$-0.460621\pi$
$151$	12.8351	−	7.41032i	1.04450	−	0.603044i	0.921105	+	0.389314i	$0.127288\pi$
$152$	−11.5497	+	9.45171i	−0.936805	+	0.766635i
$153$		0			0
$154$	3.71502	+	4.70254i	0.299365	+	0.378941i
$155$	0.370413			0.0297523
$156$		0			0
$157$	−0.369362	−	0.639755i	−0.0294783	−	0.0510580i	0.850910	−	0.525312i	$-0.176051\pi$
$157$	−0.369362	−	0.639755i	−0.0294783	−	0.0510580i	−0.880388	+	0.474254i	$0.842718\pi$
$158$	−10.1336	+	13.4959i	−0.806186	+	1.07368i
$159$		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	−0.643704	−	0.765275i	$-0.722603\pi$
$163$	4.35226	−	7.53834i	0.340895	−	0.590448i	0.984599	+	0.174826i	$0.0559364\pi$
$164$	−2.01220	+	8.19022i	−0.157126	+	0.639549i
$165$		0			0
$166$	−21.0298	−	2.54549i	−1.63223	−	0.197568i
$167$	1.38831			0.107430			0.0537152	−	0.998556i	$-0.482894\pi$
$167$	1.38831			0.107430			0.0537152	+	0.998556i	$0.482894\pi$
$168$		0			0
$169$	−11.0726			−0.851739
$170$	18.0522	+	2.18507i	1.38454	+	0.167587i
$171$		0			0
$172$		0			0
$173$	−0.485324	+	0.840606i	−0.0368985	+	0.0639101i	−0.883885	−	0.467704i	$-0.845081\pi$
$173$	−0.485324	+	0.840606i	−0.0368985	+	0.0639101i	0.846986	+	0.531615i	$0.178414\pi$
$174$		0			0
$175$	9.69877	−	9.77028i	0.733158	−	0.738564i
$176$	−0.267569	−	6.40113i	−0.0201688	−	0.482503i
$177$		0			0
$178$	1.47078	−	1.95878i	0.110239	−	0.146817i
$179$	−7.13495	−	12.3581i	−0.533291	−	0.923687i	−0.999244	−	0.0388779i	$-0.987622\pi$
$179$	−7.13495	−	12.3581i	−0.533291	−	0.923687i	0.465953	−	0.884810i	$-0.345712\pi$
$180$		0			0
$181$	−15.3218			−1.13886			−0.569429	−	0.822041i	$-0.692836\pi$
$181$	−15.3218			−1.13886			−0.569429	+	0.822041i	$0.692836\pi$
$182$	5.14004	−	0.750661i	0.381005	−	0.0556427i
$183$		0			0
$184$	9.68154	−	7.92289i	0.713732	−	0.584083i
$185$	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	$-0.362171\pi$
$191$	−2.16564	−	1.25033i	−0.156700	−	0.0904709i	−0.576300	+	0.817238i	$0.695504\pi$
$192$		0			0
$193$	1.55026	+	2.68512i	0.111590	+	0.193279i	0.916411	−	0.400237i	$-0.131072\pi$
$193$	1.55026	+	2.68512i	0.111590	+	0.193279i	−0.804822	+	0.593517i	$0.797739\pi$
$194$	−4.03217	−	0.488061i	−0.289493	−	0.0350407i
$195$		0			0
$196$	13.4153	−	4.00378i	0.958234	−	0.285984i
$197$		−	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	$-0.304340\pi$
$199$	−5.91290	−	10.2414i	−0.419154	−	0.725997i	−0.995855	+	0.0909591i	$0.971007\pi$
$200$	−14.5241	+	2.37716i	−1.02701	+	0.168090i
$201$		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
$206$	−15.8885	−	11.9301i	−1.10700	−	0.831211i
$207$		0			0
$208$	−4.92100	−	2.57334i	−0.341210	−	0.178429i
$209$			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	$0.387298\pi$
$212$	13.6061	−	3.95212i	0.934473	−	0.271433i
$213$		0			0
$214$	−5.81187	−	4.36393i	−0.397291	−	0.298312i
$215$		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
$220$	−9.93689	−	2.44132i	−0.669945	−	0.164594i
$221$	4.83970	−	2.79420i	0.325553	−	0.187958i
$222$		0			0
$223$	−24.3086			−1.62783			−0.813913	−	0.580987i	$-0.802667\pi$
$223$	−24.3086			−1.62783			−0.813913	+	0.580987i	$0.802667\pi$
$224$	−14.1257	−	4.94609i	−0.943815	−	0.330474i
$225$		0			0
$226$	−0.244194	+	2.01744i	−0.0162435	+	0.134198i
$227$	12.4048	−	7.16194i	0.823339	−	0.475355i	−0.0282277	−	0.999602i	$-0.508986\pi$
$227$	12.4048	−	7.16194i	0.823339	−	0.475355i	0.851566	+	0.524247i	$0.175653\pi$
$228$		0			0
$229$	−5.32502	+	9.22321i	−0.351887	+	0.609487i	−0.986580	−	0.163278i	$-0.947793\pi$
$229$	−5.32502	+	9.22321i	−0.351887	+	0.609487i	0.634693	+	0.772765i	$0.281127\pi$
$230$	−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	−0.876285	−	0.481793i	$-0.839986\pi$
$233$	−0.318991	+	0.552509i	−0.0208978	+	0.0361961i	0.855387	+	0.517989i	$0.173319\pi$
$234$		0			0
$235$	−16.1573	−	27.9853i	−1.05399	−	1.82556i
$236$	−9.73269	+	2.82702i	−0.633544	+	0.184023i
$237$		0			0
$238$	11.8184	−	9.33659i	0.766075	−	0.605201i
$239$			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	−0.789622	−	0.613594i	$-0.789723\pi$
$241$	−10.1380	+	5.85317i	−0.653045	+	0.377036i	0.136577	+	0.990629i	$0.456390\pi$
$242$	9.53873	+	7.16230i	0.613173	+	0.460410i
$243$		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
$248$	−0.323683	+	0.0529772i	−0.0205539	+	0.00336406i
$249$		0			0
$250$	−0.110389	+	0.911990i	−0.00698160	+	0.0576793i
$251$		−	11.5631i		−	0.729858i	−0.931035	−	0.364929i	$-0.881093\pi$
$251$		−	11.5631i		−	0.729858i	0.931035	−	0.364929i	$-0.118907\pi$
$252$		0			0
$253$		−	7.08425i		−	0.445383i
$254$	−6.90859	−	0.836227i	−0.433483	−	0.0524696i
$255$		0			0
$256$	9.12847	+	13.1404i	0.570530	+	0.821277i
$257$	20.4302	+	11.7954i	1.27440	+	0.735777i	0.975813	−	0.218605i	$-0.0701506\pi$
$257$	20.4302	+	11.7954i	1.27440	+	0.735777i	0.298589	+	0.954382i	$0.403484\pi$
$258$		0			0
$259$	3.61144	−	13.6788i	0.224404	−	0.849961i
$260$	−6.13915	+	6.40113i	−0.380734	+	0.396981i
$261$		0			0
$262$	−3.34991	+	4.46141i	−0.206958	+	0.275627i
$263$	9.24833	−	5.33953i	0.570277	−	0.329249i	−0.186983	−	0.982363i	$-0.559871\pi$
$263$	9.24833	−	5.33953i	0.570277	−	0.329249i	0.757260	+	0.653114i	$0.226538\pi$
$264$		0			0
$265$		−	22.6290i		−	1.39009i
$266$	18.3448	+	7.29701i	1.12479	+	0.447408i
$267$		0			0
$268$	−5.59900	−	19.2759i	−0.342013	−	1.17746i
$269$	11.6690	+	20.2113i	0.711471	+	1.23230i	0.964305	+	0.264794i	$0.0853040\pi$
$269$	11.6690	+	20.2113i	0.711471	+	1.23230i	−0.252834	+	0.967510i	$0.581363\pi$
$270$		0			0
$271$	6.81961	−	11.8119i	0.414262	−	0.717522i	−0.581089	−	0.813840i	$-0.697373\pi$
$271$	6.81961	−	11.8119i	0.414262	−	0.717522i	0.995351	+	0.0963179i	$0.0307066\pi$
$272$	−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	$-0.671041\pi$
$277$	−0.396180	+	0.228735i	−0.0238042	+	0.0137433i	0.488051	+	0.872815i	$0.337708\pi$
$278$	−21.0298	−	2.54549i	−1.26129	−	0.152668i
$279$		0			0
$280$	−13.8790	+	19.4618i	−0.829432	+	1.16306i
$281$	−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	0.617609	−	0.786486i	$-0.288102\pi$
$283$	27.0428	−	15.6132i	1.60753	−	0.928108i	0.989921	−	0.141622i	$-0.0452318\pi$
$284$	2.52498	−	10.2774i	0.149830	−	0.609850i
$285$		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
$290$	−13.8500	+	18.4454i	−0.813301	+	1.08315i
$291$		0			0
$292$	−20.6361	+	5.99410i	−1.20764	+	0.350778i
$293$	−31.3006			−1.82860			−0.914299	−	0.405040i	$-0.867258\pi$
$293$	−31.3006			−1.82860			−0.914299	+	0.405040i	$0.867258\pi$
$294$		0			0
$295$			16.1869i			0.942437i
$296$	−11.7046	+	9.57850i	−0.680319	+	0.556739i
$297$		0			0
$298$	9.60088	−	12.7864i	0.556164	−	0.740698i
$299$	−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
$304$	−11.3071	−	17.8216i	−0.648509	−	1.02214i
$305$	−13.4581	−	23.3102i	−0.770611	−	1.33474i
$306$		0			0
$307$			14.7215i			0.840202i	0.907477	+	0.420101i	$0.138005\pi$
$307$			14.7215i			0.840202i	−0.907477	+	0.420101i	$0.861995\pi$
$308$	−7.23353	+	4.41662i	−0.412169	+	0.251660i
$309$		0			0
$310$	−0.0629475	+	0.520048i	−0.00357518	+	0.0295367i
$311$	−7.79025	−	13.4931i	−0.441745	−	0.765124i	0.556074	−	0.831133i	$-0.312307\pi$
$311$	−7.79025	−	13.4931i	−0.441745	−	0.765124i	−0.997819	+	0.0660082i	$0.978974\pi$
$312$		0			0
$313$	11.3329	+	6.54308i	0.640576	+	0.369837i	0.784836	−	0.619703i	$-0.212747\pi$
$313$	11.3329	+	6.54308i	0.640576	+	0.369837i	−0.144260	+	0.989540i	$0.546080\pi$
$314$	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	$-0.103287\pi$
$317$	20.3971	+	11.7763i	1.14562	+	0.661422i	0.197801	+	0.980242i	$0.436620\pi$
$318$		0			0
$319$	−7.08269	+	4.08919i	−0.396555	+	0.228951i
$320$	24.2208	−	8.14667i	1.35398	−	0.455413i
$321$		0			0
$322$	−15.3775	−	6.11671i	−0.856956	−	0.340871i
$323$	21.2397			1.18181
$324$		0			0
$325$	3.61193	+	6.25604i	0.200354	+	0.347023i
$326$	9.84396	+	7.39148i	0.545206	+	0.409376i
$327$		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	−0.0922207	+	0.995739i	$0.529397\pi$
$331$	−16.5277	+	28.6268i	−0.908445	+	1.57347i	−0.816225	+	0.577735i	$0.803937\pi$
$332$	7.14756	−	29.0926i	0.392273	−	1.59666i
$333$		0			0
$334$	−0.235927	+	1.94913i	−0.0129093	+	0.106652i
$335$	−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	$0.638823\pi$
$338$	1.88166	−	15.5456i	0.102349	−	0.845567i
$339$		0			0
$340$	−6.13553	+	24.9734i	−0.332746	+	1.35437i
$341$	−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
$346$	−1.09771	−	0.824230i	−0.0590131	−	0.0443109i
$347$	11.2494	+	19.4846i	0.603900	+	1.04599i	0.992224	+	0.124463i	$0.0397209\pi$
$347$	11.2494	+	19.4846i	0.603900	+	1.04599i	−0.388324	+	0.921523i	$0.626946\pi$
$348$		0			0
$349$	28.4735			1.52415			0.762077	−	0.647486i	$-0.224180\pi$
$349$	28.4735			1.52415			0.762077	+	0.647486i	$0.224180\pi$
$350$	12.0690	+	15.2771i	0.645113	+	0.816595i
$351$		0			0
$352$	9.03244	+	0.712140i	0.481430	+	0.0379572i
$353$	8.29108	−	4.78686i	0.441290	−	0.254779i	−0.262855	−	0.964835i	$-0.584664\pi$
$353$	8.29108	−	4.78686i	0.441290	−	0.254779i	0.704145	+	0.710057i	$0.251331\pi$
$354$		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	$-0.364930\pi$
$359$	−3.25225	−	1.87769i	−0.171647	−	0.0991006i	−0.583362	+	0.812212i	$0.698263\pi$
$360$		0			0
$361$	4.42067	+	7.65683i	0.232667	+	0.402991i
$362$	2.60376	−	21.5112i	0.136850	−	1.13061i
$363$		0			0
$364$	0.180413	+	7.34401i	0.00945620	+	0.384931i
$365$			34.3209i			1.79644i
$366$		0			0
$367$	8.41302	+	14.5718i	0.439156	+	0.760640i	0.997625	−	0.0688852i	$-0.0219442\pi$
$367$	8.41302	+	14.5718i	0.439156	+	0.760640i	−0.558469	+	0.829526i	$0.688611\pi$
$368$	9.47820	+	14.9390i	0.494086	+	0.778747i
$369$		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	$-0.225312\pi$
$373$	11.1354	+	6.42901i	0.576568	+	0.332882i	−0.183200	+	0.983076i	$0.558646\pi$
$374$	−5.47475	+	7.29126i	−0.283093	+	0.377022i
$375$		0			0
$376$	18.1214	+	22.1439i	0.934542	+	1.14198i
$377$			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	$0.271811\pi$
$380$	−32.3711	+	9.40272i	−1.66060	+	0.482349i
$381$		0			0
$382$	2.12345	−	2.82801i	0.108645	−	0.144693i
$383$	13.4846	−	23.3561i	0.689033	−	1.19344i	−0.283118	−	0.959085i	$-0.591369\pi$
$383$	13.4846	−	23.3561i	0.689033	−	1.19344i	0.972151	−	0.234355i	$-0.0752978\pi$
$384$		0			0
$385$	3.55142	+	13.0620i	0.180997	+	0.665701i
$386$	−4.03327	+	1.72020i	−0.205288	+	0.0875560i
$387$		0			0
$388$	1.37044	−	5.57809i	0.0695736	−	0.283185i
$389$	27.7043	−	15.9951i	1.40466	−	0.810983i	0.409796	−	0.912177i	$-0.365600\pi$
$389$	27.7043	−	15.9951i	1.40466	−	0.810983i	0.994867	+	0.101195i	$0.0322665\pi$
$390$		0			0
$391$	−17.8041			−0.900394
$392$	3.34140	+	19.5150i	0.168766	+	0.985656i
$393$		0			0
$394$	22.0270	+	2.66619i	1.10971	+	0.134321i
$395$	−33.0126	+	19.0598i	−1.66104	+	0.959004i
$396$		0			0
$397$	8.51929	−	14.7558i	0.427571	−	0.740575i	−0.569086	−	0.822278i	$-0.692703\pi$
$397$	8.51929	−	14.7558i	0.427571	−	0.740575i	0.996657	+	0.0817035i	$0.0260360\pi$
$398$	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	−0.930208	−	0.367032i	$-0.880374\pi$
$401$	−2.94858	+	5.10709i	−0.147245	+	0.255036i	0.782963	+	0.622068i	$0.213707\pi$
$402$		0			0
$403$	0.0804953	+	0.139422i	0.00400976	+	0.00694510i
$404$	−3.79700	−	13.0721i	−0.188908	−	0.650362i
$405$		0			0
$406$	2.76090	+	18.9049i	0.137021	+	0.938233i
$407$			8.56461i			0.424532i
$408$		0			0
$409$	−0.207751	+	0.119945i	−0.0102726	+	0.00593090i	−0.505128	−	0.863045i	$-0.668555\pi$
$409$	−0.207751	+	0.119945i	−0.0102726	+	0.00593090i	0.494855	+	0.868976i	$0.335221\pi$
$410$	−11.4380	+	15.2331i	−0.564883	+	0.752310i
$411$		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
$416$	4.44915	−	6.47161i	0.218137	−	0.317297i
$417$		0			0
$418$	−11.8653	−	1.43619i	−0.580349	−	0.0702464i
$419$			29.4140i			1.43697i	0.695544	+	0.718484i	$0.255163\pi$
$419$			29.4140i			1.43697i	−0.695544	+	0.718484i	$0.744837\pi$
$420$		0			0
$421$			32.1265i			1.56575i	0.622180	+	0.782874i	$0.286247\pi$
$421$			32.1265i			1.56575i	−0.622180	+	0.782874i	$0.713753\pi$
$422$	−1.71172	+	14.1416i	−0.0833254	+	0.688402i
$423$		0			0
$424$	3.23644	+	19.7742i	0.157175	+	0.960319i
$425$	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	−0.583196	+	0.812332i	$0.698198\pi$
$431$	−32.7662	+	18.9176i	−1.57829	+	0.911228i	−0.995098	+	0.0988962i	$0.968469\pi$
$432$		0			0
$433$		−	25.4835i		−	1.22466i	−0.790602	−	0.612330i	$-0.790232\pi$
$433$		−	25.4835i		−	1.22466i	0.790602	−	0.612330i	$-0.209768\pi$
$434$	0.268968	+	0.340465i	0.0129109	+	0.0163428i
$435$		0			0
$436$	5.43750	−	1.57941i	0.260409	−	0.0756400i
$437$	−11.6690	−	20.2113i	−0.558204	−	0.966837i
$438$		0			0
$439$	11.9804	−	20.7506i	0.571792	−	0.990373i	−0.424590	−	0.905386i	$-0.639582\pi$
$439$	11.9804	−	20.7506i	0.571792	−	0.990373i	0.996382	−	0.0849871i	$-0.0270849\pi$
$440$	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	−0.717872	−	0.696175i	$-0.754884\pi$
$443$	5.13495	−	8.89399i	0.243969	−	0.422566i	0.961841	+	0.273608i	$0.0882172\pi$
$444$		0			0
$445$	4.79140	−	2.76632i	0.227134	−	0.131136i
$446$	4.13097	−	34.1285i	0.195607	−	1.61603i
$447$		0			0
$448$	9.34464	−	18.9915i	0.441493	−	0.897265i
$449$	−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
$452$	−2.79091	−	0.685680i	−0.131274	−	0.0322517i
$453$		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	0.246657	+	0.969103i	$0.420668\pi$
$457$	−15.3050	+	26.5091i	−0.715939	+	1.24004i	−0.962596	+	0.270941i	$0.912665\pi$
$458$	−12.0442	−	9.04353i	−0.562786	−	0.422576i
$459$		0			0
$460$	27.1351	−	7.88182i	1.26518	−	0.367492i
$461$	17.3671			0.808866			0.404433	−	0.914568i	$-0.367469\pi$
$461$	17.3671			0.808866			0.404433	+	0.914568i	$0.367469\pi$
$462$		0			0
$463$		−	21.7288i		−	1.00983i	−0.863171	−	0.504913i	$-0.831525\pi$
$463$		−	21.7288i		−	1.00983i	0.863171	−	0.504913i	$-0.168475\pi$
$464$	9.46463	−	18.0992i	0.439385	−	0.840236i
$465$		0			0
$466$	−0.721495	−	0.541745i	−0.0334226	−	0.0250959i
$467$	0.585859	+	0.338246i	0.0271103	+	0.0156521i	0.513494	−	0.858093i	$-0.328351\pi$
$467$	0.585859	+	0.338246i	0.0271103	+	0.0156521i	−0.486384	+	0.873745i	$0.661684\pi$
$468$		0			0
$469$	−18.7071	+	18.8450i	−0.863814	+	0.870183i
$470$	42.0361	−	17.9285i	1.93898	−	0.826981i
$471$		0			0
$472$	−2.31508	−	14.1448i	−0.106560	−	0.651067i
$473$		0			0
$474$		0			0
$475$			27.4555i			1.25974i
$476$	11.0999	+	18.1793i	0.508761	+	0.833247i
$477$		0			0
$478$	−6.64834	−	0.804726i	−0.304088	−	0.0368073i
$479$	14.3839	+	24.9136i	0.657217	+	1.13833i	0.981333	+	0.192316i	$0.0615999\pi$
$479$	14.3839	+	24.9136i	0.657217	+	1.13833i	−0.324116	+	0.946017i	$0.605067\pi$
$480$		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	$-0.653443\pi$
$487$	1.58745	−	0.916514i	0.0719342	−	0.0415312i	0.535536	+	0.844513i	$0.320110\pi$
$488$	15.0942	+	18.4446i	0.683280	+	0.834948i
$489$		0			0
$490$	31.4196	+	3.56909i	1.41939	+	0.161235i
$491$	−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
$494$	−6.22038	+	8.28428i	−0.279868	+	0.372728i
$495$		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	−0.710294	−	0.703905i	$-0.751438\pi$
$499$	5.68404	−	9.84505i	0.254453	−	0.440725i	0.964747	+	0.263180i	$0.0847714\pi$
$500$	−1.26164	−	0.309964i	−0.0564224	−	0.0138620i
$501$		0			0
$502$	16.2342	+	1.96502i	0.724569	+	0.0877031i
$503$	−13.2022			−0.588656			−0.294328	−	0.955704i	$-0.595096\pi$
$503$	−13.2022			−0.588656			−0.294328	+	0.955704i	$0.595096\pi$
$504$		0			0
$505$	−21.7408			−0.967454
$506$	9.94604	+	1.20389i	0.442156	+	0.0535193i
$507$		0			0
$508$	2.34807	−	9.55732i	0.104179	−	0.424037i
$509$	−13.2178	+	22.8940i	−0.585870	+	1.01476i	0.408896	+	0.912581i	$0.365914\pi$
$509$	−13.2178	+	22.8940i	−0.585870	+	1.01476i	−0.994766	+	0.102176i	$0.967420\pi$
$510$		0			0
$511$	20.1749	+	20.0272i	0.892484	+	0.885952i
$512$	−20.0000	+	10.5830i	−0.883883	+	0.467707i
$513$		0			0
$514$	−20.0322	+	26.6789i	−0.883583	+	1.17675i
$515$	−22.4388	−	38.8652i	−0.988773	−	1.71260i
$516$		0			0
$517$	16.2033			0.712619
$518$	18.5909	+	7.39489i	0.816837	+	0.324913i
$519$		0			0
$520$	−7.94369	−	9.70695i	−0.348354	−	0.425678i
$521$	10.4163	−	6.01384i	0.456345	−	0.263471i	−0.254161	−	0.967162i	$-0.581799\pi$
$521$	10.4163	−	6.01384i	0.456345	−	0.263471i	0.710506	+	0.703691i	$0.248466\pi$
$522$		0			0
$523$	2.43276	+	1.40455i	0.106377	+	0.0614168i	0.552245	−	0.833682i	$-0.313771\pi$
$523$	2.43276	+	1.40455i	0.106377	+	0.0614168i	−0.445868	+	0.895099i	$0.647105\pi$
$524$	−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
$530$	31.7703	+	3.84554i	1.38002	+	0.167039i
$531$		0			0
$532$	−13.3622	+	24.5155i	−0.579327	+	1.06288i
$533$			5.85434i			0.253580i
$534$		0			0
$535$	−8.20791	−	14.2165i	−0.354859	−	0.614634i
$536$	28.0142	−	4.58509i	1.21003	−	0.198046i
$537$		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	$-0.346661\pi$
$541$	−1.68628	−	0.973573i	−0.0724988	−	0.0418572i	−0.535811	+	0.844338i	$0.679994\pi$
$542$	15.4246	+	11.5818i	0.662543	+	0.497481i
$543$		0			0
$544$	1.78975	−	22.7003i	0.0767349	−	0.973268i
$545$		−	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	$0.291833\pi$
$548$	0.0573744	+	0.197525i	0.00245091	+	0.00843786i
$549$		0			0
$550$	−9.42505	−	7.07694i	−0.401886	−	0.301762i
$551$	−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
$556$	7.14756	−	29.0926i	0.303124	−	1.23380i
$557$	7.96630	−	4.59935i	0.337543	−	0.194881i	−0.321642	−	0.946861i	$-0.604235\pi$
$557$	7.96630	−	4.59935i	0.337543	−	0.194881i	0.659185	+	0.751981i	$0.270901\pi$
$558$		0			0
$559$		0			0
$560$	−24.9651	−	22.7930i	−1.05497	−	0.963181i
$561$		0			0
$562$	0.244194	−	2.01744i	0.0103007	−	0.0851004i
$563$	23.5533	−	13.5985i	0.992653	−	0.573108i	0.0865866	−	0.996244i	$-0.472404\pi$
$563$	23.5533	−	13.5985i	0.992653	−	0.573108i	0.906066	+	0.423136i	$0.139071\pi$
$564$		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	−0.999971	−	0.00758149i	$-0.997587\pi$
$569$	−11.7699	+	20.3861i	−0.493420	+	0.854628i	0.506551	+	0.862210i	$0.330920\pi$
$570$		0			0
$571$	−15.1713	−	26.2774i	−0.634897	−	1.09967i	−0.986537	−	0.163539i	$-0.947709\pi$
$571$	−15.1713	−	26.2774i	−0.634897	−	1.09967i	0.351640	−	0.936135i	$-0.385624\pi$
$572$	−1.24050	−	4.27073i	−0.0518680	−	0.178568i
$573$		0			0
$574$	2.28009	+	15.6126i	0.0951690	+	0.651655i
$575$		−	23.0145i		−	0.959772i
$576$		0			0
$577$	24.7760	−	14.3044i	1.03144	−	0.595500i	0.114041	−	0.993476i	$-0.463620\pi$
$577$	24.7760	−	14.3044i	1.03144	−	0.595500i	0.917396	+	0.397976i	$0.130287\pi$
$578$	−0.900923	−	0.676472i	−0.0374735	−	0.0281375i
$579$		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
$584$	−4.90864	−	29.9911i	−0.203121	−	1.24104i
$585$		0			0
$586$	5.31917	−	43.9449i	0.219733	−	1.81535i
$587$		−	15.2362i		−	0.628867i	−0.949280	−	0.314433i	$-0.898186\pi$
$587$		−	15.2362i		−	0.628867i	0.949280	−	0.314433i	$-0.101814\pi$
$588$		0			0
$589$			0.611872i			0.0252117i
$590$	−22.7258	−	2.75078i	−0.935608	−	0.113248i
$591$		0			0
$592$	−11.4588	−	18.0607i	−0.470955	−	0.742289i
$593$	−18.2934	−	10.5617i	−0.751221	−	0.433717i	0.0749142	−	0.997190i	$-0.476132\pi$
$593$	−18.2934	−	10.5617i	−0.751221	−	0.433717i	−0.826135	+	0.563473i	$0.809465\pi$
$594$		0			0
$595$	32.8274	−	8.92543i	1.34579	−	0.365907i
$596$	16.3202	+	15.6522i	0.668500	+	0.641140i
$597$		0			0
$598$	5.21423	−	6.94429i	0.213226	−	0.283973i
$599$	29.1795	−	16.8468i	1.19224	−	0.688341i	0.233427	−	0.972374i	$-0.425006\pi$
$599$	29.1795	−	16.8468i	1.19224	−	0.688341i	0.958814	+	0.284033i	$0.0916726\pi$
$600$		0			0
$601$			24.3960i			0.995132i	0.867426	+	0.497566i	$0.165773\pi$
$601$			24.3960i			0.995132i	−0.867426	+	0.497566i	$0.834227\pi$
$602$		0			0
$603$		0			0
$604$	−28.4648	+	8.26807i	−1.15822	+	0.336423i
$605$	13.4712	+	23.3329i	0.547683	+	0.948616i
$606$		0			0
$607$	−4.08757	+	7.07987i	−0.165909	+	0.287363i	−0.936978	−	0.349389i	$-0.886389\pi$
$607$	−4.08757	+	7.07987i	−0.165909	+	0.287363i	0.771069	+	0.636752i	$0.219723\pi$
$608$	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	$-0.555121\pi$
$613$	14.7221	−	8.49981i	0.594620	−	0.343304i	0.766922	+	0.641740i	$0.221787\pi$
$614$	−20.6685	−	2.50175i	−0.834114	−	0.100963i
$615$		0			0
$616$	−4.97153	−	10.9062i	−0.200309	−	0.439423i
$617$	−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	−0.729245	−	0.684252i	$-0.760129\pi$
$619$	−12.4719	+	7.20065i	−0.501288	+	0.289419i	0.227957	+	0.973671i	$0.426795\pi$
$620$	−0.719432	−	0.176752i	−0.0288931	−	0.00709854i
$621$		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
$626$	−11.1122	+	14.7992i	−0.444131	+	0.591493i
$627$		0			0
$628$	0.412116	+	1.41881i	0.0164452	+	0.0566166i
$629$	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	$0.739566\pi$
$632$	26.1218	−	21.3768i	1.03907	−	0.850324i
$633$		0			0
$634$	−19.9998	+	26.6356i	−0.794292	+	1.05784i
$635$	−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
$640$	7.32160	+	35.3896i	0.289412	+	1.39890i
$641$	9.13798	+	15.8274i	0.360929	+	0.625147i	0.988114	−	0.153723i	$-0.0491265\pi$
$641$	9.13798	+	15.8274i	0.360929	+	0.625147i	−0.627185	+	0.778870i	$0.715793\pi$
$642$		0			0
$643$		−	13.6340i		−	0.537671i	−0.963186	−	0.268836i	$-0.913361\pi$
$643$		−	13.6340i		−	0.537671i	0.963186	−	0.268836i	$-0.0866389\pi$
$644$	11.2009	−	20.5501i	0.441377	−	0.809786i
$645$		0			0
$646$	−3.60943	+	29.8198i	−0.142011	+	1.17324i
$647$	8.74153	+	15.1408i	0.343665	+	0.595245i	0.985110	−	0.171923i	$-0.0549982\pi$
$647$	8.74153	+	15.1408i	0.343665	+	0.595245i	−0.641445	+	0.767169i	$0.721665\pi$
$648$		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	$-0.272518\pi$
$653$	8.40495	+	4.85260i	0.328911	+	0.189897i	−0.326446	+	0.945216i	$0.605851\pi$
$654$		0			0
$655$	−10.9131	+	6.30070i	−0.426411	+	0.246189i
$656$	7.81635	−	14.9472i	0.305177	−	0.583591i
$657$		0			0
$658$	13.9903	−	35.1719i	0.545399	−	1.37114i
$659$	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	$-0.247217\pi$
$661$	−6.43683	−	11.1489i	−0.250364	−	0.433643i	−0.963626	+	0.267254i	$0.913884\pi$
$662$	−37.3824	−	28.0691i	−1.45291	−	1.09094i
$663$		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
$668$	−2.69643	−	0.662466i	−0.104328	−	0.0256316i
$669$		0			0
$670$	5.44800	−	45.0093i	0.210475	−	1.73886i
$671$	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	$0.650687\pi$
$674$	2.63567	−	21.7749i	0.101522	−	0.838738i
$675$		0			0
$676$	21.5057	+	5.28358i	0.827142	+	0.203215i
$677$	1.80224	−	3.12157i	0.0692657	−	0.119972i	−0.829313	−	0.558785i	$-0.811268\pi$
$677$	1.80224	−	3.12157i	0.0692657	−	0.119972i	0.898578	+	0.438813i	$0.144601\pi$
$678$		0			0
$679$	−7.33237	+	1.99360i	−0.281391	+	0.0765072i
$680$	−34.0191	−	12.8580i	−1.30457	−	0.493083i
$681$		0			0
$682$	−0.210046	−	0.157717i	−0.00804309	−	0.00603928i
$683$	−3.80924	−	6.59779i	−0.145756	−	0.252457i	0.783899	−	0.620889i	$-0.213228\pi$
$683$	−3.80924	−	6.59779i	−0.145756	−	0.252457i	−0.929655	+	0.368432i	$0.879895\pi$
$684$		0			0
$685$	0.328514			0.0125519
$686$	20.4322	−	16.3867i	0.780106	−	0.625648i
$687$		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	−0.933526	−	0.358509i	$-0.883285\pi$
$691$	−44.9707	−	25.9639i	−1.71077	−	0.987712i	−0.777241	−	0.629203i	$-0.783381\pi$
$692$	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
$698$	−4.83875	+	39.9759i	−0.183149	+	1.51311i
$699$		0			0
$700$	−23.4995	+	14.3482i	−0.888198	+	0.542312i
$701$			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
$704$	−2.53478	+	12.5602i	−0.0955331	+	0.473381i
$705$		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	$-0.614565\pi$
$709$	−35.6491	−	20.5820i	−1.33883	−	0.772974i	−0.986634	+	0.162952i	$0.947898\pi$
$710$	14.3528	−	19.1150i	0.538652	−	0.717375i
$711$		0			0
$712$	−3.79129	+	3.10260i	−0.142085	+	0.116275i
$713$		−	0.512901i		−	0.0192083i
$714$		0			0
$715$	−7.10284			−0.265631
$716$	7.96082	+	27.4070i	0.297510	+	1.02425i
$717$		0			0
$718$	3.18889	−	4.24696i	0.119008	−	0.158495i
$719$	7.02471	−	12.1672i	0.261978	−	0.453758i	−0.704790	−	0.709416i	$-0.748959\pi$
$719$	7.02471	−	12.1672i	0.261978	−	0.453758i	0.966767	+	0.255658i	$0.0822920\pi$
$720$		0			0
$721$	−35.9398	−	9.48869i	−1.33847	−	0.353377i
$722$	−11.5012	+	4.90528i	−0.428029	+	0.182556i
$723$		0			0
$724$	29.7586	+	7.31117i	1.10597	+	0.271718i
$725$	−23.0095	+	13.2845i	−0.854550	+	0.493375i
$726$		0			0
$727$	−13.2022			−0.489642			−0.244821	−	0.969568i	$-0.578729\pi$
$727$	−13.2022			−0.489642			−0.244821	+	0.969568i	$0.578729\pi$
$728$	−10.3414	−	0.994736i	−0.383278	−	0.0368674i
$729$		0			0
$730$	−48.1854	−	5.83245i	−1.78342	−	0.215868i
$731$		0			0
$732$		0			0
$733$	−24.9797	+	43.2661i	−0.922646	+	1.59807i	−0.127342	+	0.991859i	$0.540644\pi$
$733$	−24.9797	+	43.2661i	−0.922646	+	1.59807i	−0.795304	+	0.606211i	$0.792689\pi$
$734$	−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	0.977297	+	0.211875i	$0.0679571\pi$
$739$	18.2718	+	31.6476i	0.672138	+	1.16418i	−0.305159	+	0.952301i	$0.598710\pi$
$740$	−32.8054	+	9.52884i	−1.20595	+	0.350287i
$741$		0			0
$742$	20.7994	−	16.4316i	0.763570	−	0.603223i
$743$			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
$746$	−10.9184	+	14.5411i	−0.399752	+	0.532389i
$747$		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	$-0.414688\pi$
$751$	−11.9997	−	6.92806i	−0.437877	−	0.252808i	−0.702697	+	0.711490i	$0.748021\pi$
$752$	−34.1688	+	21.6788i	−1.24601	+	0.790544i
$753$		0			0
$754$	−9.95254	−	1.20467i	−0.362450	−	0.0438716i
$755$			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	$-0.322560\pi$
$758$	−4.34739	+	35.9165i	−0.157904	+	1.30455i
$759$		0			0
$760$	−7.70000	−	47.0458i	−0.279308	−	1.70653i
$761$	−40.7899	−	23.5501i	−1.47863	−	0.853689i	−0.478925	−	0.877856i	$-0.658974\pi$
$761$	−40.7899	−	23.5501i	−1.47863	−	0.853689i	−0.999708	+	0.0241662i	$0.992307\pi$
$762$		0			0
$763$	−5.31596	−	5.27705i	−0.192451	−	0.191042i
$764$	3.60957	+	3.46184i	0.130590	+	0.125245i
$765$		0			0
$766$	30.4996	+	22.9011i	1.10199	+	0.827449i
$767$	−6.09267	+	3.51761i	−0.219994	+	0.127013i
$768$		0			0
$769$		−	17.3071i		−	0.624110i	−0.950064	−	0.312055i	$-0.898983\pi$
$769$		−	17.3071i		−	0.624110i	0.950064	−	0.312055i	$-0.101017\pi$
$770$	−18.9421	+	2.76634i	−0.682626	+	0.0996921i
$771$		0			0
$772$	−1.72970	−	5.95490i	−0.0622532	−	0.214322i
$773$	−13.5389	−	23.4501i	−0.486960	−	0.843440i	0.512927	−	0.858432i	$-0.328561\pi$
$773$	−13.5389	−	23.4501i	−0.486960	−	0.843440i	−0.999888	+	0.0149920i	$0.995228\pi$
$774$		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
$782$	3.02561	−	24.9964i	0.108195	−	0.893869i
$783$		0			0
$784$	−27.9662	+	1.37486i	−0.998794	+	0.0491023i
$785$	2.35969			0.0842208
$786$		0			0
$787$	−46.9684	+	27.1172i	−1.67424	+	0.966624i	−0.709023	+	0.705186i	$0.750864\pi$
$787$	−46.9684	+	27.1172i	−1.67424	+	0.966624i	−0.965220	+	0.261439i	$0.915803\pi$
$788$	−7.48648	+	30.4721i	−0.266695	+	1.08552i
$789$		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
$794$	19.2690	+	14.4684i	0.683830	+	0.513464i
$795$		0			0
$796$	6.59732	+	22.7129i	0.233836	+	0.805036i
$797$	20.1437			0.713527			0.356763	−	0.934195i	$-0.383880\pi$
$797$	20.1437			0.713527			0.356763	+	0.934195i	$0.383880\pi$
$798$		0			0
$799$		−	40.7221i		−	1.44064i
$800$	29.3436	+	2.31352i	1.03745	+	0.0817953i
$801$		0			0
$802$	−6.66910	−	5.00759i	−0.235494	−	0.176824i
$803$	−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
$808$	18.9981	−	3.10941i	0.668349	−	0.109389i
$809$	17.2771	+	29.9249i	0.607432	+	1.05210i	0.991662	+	0.128865i	$0.0411334\pi$
$809$	17.2771	+	29.9249i	0.607432	+	1.05210i	−0.384231	+	0.923237i	$0.625533\pi$
$810$		0			0
$811$			13.6340i			0.478754i	0.970927	+	0.239377i	$0.0769431\pi$
$811$			13.6340i			0.478754i	−0.970927	+	0.239377i	$0.923057\pi$
$812$	−27.0110	+	0.663551i	−0.947899	+	0.0232861i
$813$		0			0
$814$	−12.0244	−	1.45546i	−0.421456	−	0.0510137i
$815$	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	$-0.522061\pi$
$821$	−27.7311	−	16.0106i	−0.967822	−	0.558772i	−0.898572	+	0.438827i	$0.855394\pi$
$822$		0			0
$823$	26.8399	−	15.4960i	0.935580	−	0.540158i	0.0470083	−	0.998894i	$-0.485031\pi$
$823$	26.8399	−	15.4960i	0.935580	−	0.540158i	0.888572	+	0.458737i	$0.151698\pi$
$824$	25.1666	+	30.7528i	0.876719	+	1.07132i
$825$		0			0
$826$	−14.8781	+	11.7538i	−0.517677	+	0.408966i
$827$	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	0.980790	+	0.195067i	$0.0624924\pi$
$829$	18.9836	+	32.8806i	0.659328	+	1.14199i	−0.321462	+	0.946922i	$0.604174\pi$
$830$	40.6291	−	54.1098i	1.41026	−	1.87818i
$831$		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
$836$	4.03273	−	16.4144i	0.139475	−	0.567702i
$837$		0			0
$838$	−41.2962	−	4.99857i	−1.42655	−	0.172673i
$839$	−8.32984			−0.287578			−0.143789	−	0.989608i	$-0.545929\pi$
$839$	−8.32984			−0.287578			−0.143789	+	0.989608i	$0.545929\pi$
$840$		0			0
$841$	2.92739			0.100945
$842$	−45.1045	−	5.45952i	−1.55440	−	0.188148i
$843$		0			0
$844$	−19.5634	−	4.80640i	−0.673401	−	0.165443i
$845$	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
$850$	−17.7858	+	23.6870i	−0.610047	+	0.812459i
$851$	−11.8255	−	20.4824i	−0.405374	−	0.702128i
$852$		0			0
$853$	6.94153			0.237673			0.118837	−	0.992914i	$-0.462083\pi$
$853$	6.94153			0.237673			0.118837	+	0.992914i	$0.462083\pi$
$854$	11.6531	−	29.2962i	0.398763	−	1.00250i
$855$		0			0
$856$	9.20569	+	11.2491i	0.314644	+	0.384486i
$857$	−1.91744	+	1.10704i	−0.0654986	+	0.0378156i	−0.532392	−	0.846498i	$-0.678707\pi$
$857$	−1.91744	+	1.10704i	−0.0654986	+	0.0378156i	0.466893	+	0.884314i	$0.345373\pi$
$858$		0			0
$859$	5.26337	+	3.03881i	0.179584	+	0.103683i	0.587097	−	0.809516i	$-0.300271\pi$
$859$	5.26337	+	3.03881i	0.179584	+	0.103683i	−0.407513	+	0.913199i	$0.633604\pi$
$860$		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	$-0.381357\pi$
$863$	−7.64747	−	4.41527i	−0.260323	−	0.150298i	−0.624482	+	0.781039i	$0.714690\pi$
$864$		0			0
$865$	−1.55026	−	2.68512i	−0.0527103	−	0.0912969i
$866$	35.7780	+	4.33063i	1.21579	+	0.147161i
$867$		0			0
$868$	−0.523709	+	0.319764i	−0.0177758	+	0.0108535i
$869$		−	19.1141i		−	0.648400i
$870$		0			0
$871$	−6.96673	−	12.0667i	−0.236059	−	0.408866i
$872$	1.29340	+	7.90247i	0.0438000	+	0.267611i
$873$		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	$-0.268940\pi$
$877$	10.3059	+	5.95011i	0.348005	+	0.200921i	−0.315801	+	0.948825i	$0.602273\pi$
$878$	27.0972	+	20.3464i	0.914487	+	0.686657i
$879$		0			0
$880$	18.1349	+	9.48328i	0.611327	+	0.319681i
$881$		−	53.9142i		−	1.81642i	−0.418519	−	0.908208i	$-0.637451\pi$
$881$		−	53.9142i		−	1.81642i	0.418519	−	0.908208i	$-0.362549\pi$
$882$		0			0
$883$	11.1987			0.376866			0.188433	−	0.982086i	$-0.439659\pi$
$883$	11.1987			0.376866			0.188433	+	0.982086i	$0.439659\pi$
$884$	−10.7332	+	3.11763i	−0.360996	+	0.104857i
$885$		0			0
$886$	11.6142	+	8.72073i	0.390188	+	0.292979i
$887$	18.1832	−	31.4942i	0.610531	−	1.05747i	−0.380620	−	0.924732i	$-0.624289\pi$
$887$	18.1832	−	31.4942i	0.610531	−	1.05747i	0.991151	−	0.132740i	$-0.0423774\pi$
$888$		0			0
$889$	−12.5630	+	3.41576i	−0.421351	+	0.114561i
$890$	3.06957	+	7.19707i	0.102892	+	0.241246i
$891$		0			0
$892$	47.2132	+	11.5995i	1.58082	+	0.388380i
$893$	46.2278	−	26.6896i	1.54695	−	0.893134i
$894$		0			0
$895$	45.5819			1.52364
$896$	25.0754	+	16.3470i	0.837711	+	0.546113i
$897$		0			0
$898$	1.95592	−	16.1590i	0.0652698	−	0.539234i
$899$	−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	0.975288	−	0.220937i	$-0.0709116\pi$
$907$	8.92370	+	15.4563i	0.296307	+	0.513218i	−0.678981	+	0.734156i	$0.737578\pi$
$908$	−27.5107	+	7.99093i	−0.912975	+	0.265188i
$909$		0			0
$910$	−6.13277	+	15.4179i	−0.203299	+	0.511098i
$911$		−	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
$914$	−34.6170	−	25.9927i	−1.14503	−	0.859761i
$915$		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	$-0.514379\pi$
$919$	−28.2802	−	16.3276i	−0.932879	−	0.538598i	−0.887721	+	0.460382i	$0.847712\pi$
$920$	6.45452	+	39.4361i	0.212799	+	1.30017i
$921$		0			0
$922$	−2.95134	+	24.3828i	−0.0971971	+	0.803005i
$923$		−	7.34623i		−	0.241804i
$924$		0			0
$925$			27.8238i			0.914839i
$926$	30.5066	+	3.69257i	1.00251	+	0.121345i
$927$		0			0
$928$	23.8023	+	16.3638i	0.781349	+	0.537167i
$929$	23.3027	+	13.4538i	0.764537	+	0.441406i	0.830922	−	0.556388i	$-0.187813\pi$
$929$	23.3027	+	13.4538i	0.764537	+	0.441406i	−0.0663853	+	0.997794i	$0.521147\pi$
$930$		0			0
$931$	36.9344	−	0.271329i	1.21048	−	0.00889246i
$932$	0.883202	−	0.920891i	0.0289302	−	0.0301648i
$933$		0			0
$934$	−0.574445	+	0.765045i	−0.0187964	+	0.0250330i
$935$	−17.8353	+	10.2972i	−0.583276	+	0.336755i
$936$		0			0
$937$		−	32.6476i		−	1.06655i	−0.845942	−	0.533275i	$-0.820961\pi$
$937$		−	32.6476i		−	1.06655i	0.845942	−	0.533275i	$-0.179039\pi$
$938$	−23.2787	−	29.4666i	−0.760078	−	0.962120i
$939$		0			0
$940$	18.0275	+	62.0640i	0.587992	+	2.02431i
$941$	−6.32087	−	10.9481i	−0.206055	−	0.356897i	0.744414	−	0.667719i	$-0.232729\pi$
$941$	−6.32087	−	10.9481i	−0.206055	−	0.356897i	−0.950468	+	0.310822i	$0.899396\pi$
$942$		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	0.286414	+	0.958106i	$0.407537\pi$
$947$	−21.1271	+	36.5931i	−0.686537	+	1.18912i	−0.972951	+	0.231011i	$0.925797\pi$
$948$		0			0
$949$	−12.9182	+	7.45835i	−0.419344	+	0.242108i
$950$	−38.5465	−	4.66574i	−1.25061	−	0.151377i
$951$		0			0
$952$	−27.4094	+	12.4945i	−0.888345	+	0.404948i
$953$	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
$956$	2.25962	−	9.19729i	0.0730812	−	0.297462i
$957$		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
$962$	−6.30382	+	8.39541i	−0.203243	+	0.270679i
$963$		0			0
$964$	22.4834	−	6.53067i	0.724142	−	0.210339i
$965$	−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	$0.864311\pi$
$968$	−15.1088	−	18.4626i	−0.485616	−	0.593409i
$969$		0			0
$970$	7.79005	−	10.3748i	0.250123	−	0.333114i
$971$	40.2746	+	23.2526i	1.29247	+	0.746210i	0.979092	−	0.203417i	$-0.0652048\pi$
$971$	40.2746	+	23.2526i	1.29247	+	0.746210i	0.313381	+	0.949627i	$0.398538\pi$
$972$		0			0
$973$	−38.2421	+	10.3976i	−1.22599	+	0.333333i
$974$	1.01699	+	2.38448i	0.0325863	+	0.0764035i
$975$		0			0
$976$	−28.4607	+	18.0572i	−0.911004	+	0.577998i
$977$	17.1348	+	29.6783i	0.548189	+	0.949492i	0.998399	+	0.0565688i	$0.0180160\pi$
$977$	17.1348	+	29.6783i	0.548189	+	0.949492i	−0.450209	+	0.892923i	$0.648651\pi$
$978$		0			0
$979$			2.77419i			0.0886635i
$980$	−10.3503	+	43.5055i	−0.330628	+	1.38973i
$981$		0			0
$982$	2.28346	−	18.8650i	0.0728680	−	0.602007i
$983$	−0.777334	−	1.34638i	−0.0247931	−	0.0429429i	0.853363	−	0.521318i	$-0.174559\pi$
$983$	−0.777334	−	1.34638i	−0.0247931	−	0.0429429i	−0.878156	+	0.478375i	$0.841226\pi$
$984$		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	$-0.803015\pi$
$991$	−22.6482	+	13.0759i	−0.719443	+	0.415371i	0.0951047	+	0.995467i	$0.469681\pi$
$992$	0.653950	+	0.0515591i	0.0207629	+	0.00163700i
$993$		0			0
$994$	−2.86113	−	19.5912i	−0.0907496	−	0.621394i
$995$	37.7748			1.19754
$996$		0			0
$997$	−18.1467	−	31.4310i	−0.574711	−	0.995429i	−0.996073	−	0.0885360i	$-0.971781\pi$
$997$	−18.1467	−	31.4310i	−0.574711	−	0.995429i	0.421362	−	0.906893i	$-0.361552\pi$
$998$	12.8562	+	9.65325i	0.406955	+	0.305568i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.4	✓	12	168.59	odd	6
56.2.m.a.3.6	yes	12	21.17	even	6
56.2.m.a.19.3	yes	12	3.2	odd	2
56.2.m.a.19.5	yes	12	24.11	even	2
224.2.q.a.47.3		12	24.5	odd	2
224.2.q.a.47.4		12	12.11	even	2
224.2.q.a.143.3		12	84.59	odd	6
224.2.q.a.143.4		12	168.101	even	6
392.2.e.e.195.1		12	168.107	even	6
392.2.e.e.195.2		12	168.131	odd	6
392.2.e.e.195.3		12	21.2	odd	6
392.2.e.e.195.4		12	21.5	even	6
392.2.m.g.19.3		12	21.20	even	2
392.2.m.g.19.5		12	168.83	odd	2
392.2.m.g.227.4		12	168.11	even	6
392.2.m.g.227.6		12	21.11	odd	6
504.2.bk.a.19.2		12	8.3	odd	2	inner
504.2.bk.a.19.4		12	1.1	even	1	trivial
504.2.bk.a.451.1		12	7.3	odd	6	inner
504.2.bk.a.451.3		12	56.3	even	6	inner
1568.2.e.e.783.5		12	168.5	even	6
1568.2.e.e.783.6		12	84.47	odd	6
1568.2.e.e.783.7		12	84.23	even	6
1568.2.e.e.783.8		12	168.149	odd	6
1568.2.q.g.815.3		12	168.53	odd	6
1568.2.q.g.815.4		12	84.11	even	6
1568.2.q.g.1391.3		12	84.83	odd	2
1568.2.q.g.1391.4		12	168.125	even	2
2016.2.bs.a.271.1		12	4.3	odd	2
2016.2.bs.a.271.6		12	8.5	even	2
2016.2.bs.a.1711.1		12	56.45	odd	6
2016.2.bs.a.1711.6		12	28.3	even	6

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)

\(f(q)\)	\(=\)	\(q+(-0.169938 + 1.40397i) q^{2} +(-1.94224 - 0.477176i) q^{4} +(-1.59713 + 2.76632i) q^{5} +(0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +O(q^{10})\)	\(q+(-0.169938 + 1.40397i) q^{2} +(-1.94224 - 0.477176i) q^{4} +(-1.59713 + 2.76632i) q^{5} +(0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +(-3.61240 - 2.71243i) q^{10} +(-0.800840 - 1.38709i) q^{11} -1.38831 q^{13} +(-3.70238 + 0.540703i) q^{14} +(3.54461 + 1.85358i) q^{16} +(-3.48605 + 2.01267i) q^{17} +(-4.56957 - 2.63824i) q^{19} +(4.42204 - 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +(3.83044 + 2.21151i) q^{23} +(-2.60168 - 4.50624i) q^{25} +(0.235927 - 1.94913i) q^{26} +(-0.129952 - 5.28991i) q^{28} -5.10613i q^{29} +(-0.0579809 - 0.100426i) q^{31} +(-3.20473 + 4.66151i) q^{32} +(-2.23331 - 5.23632i) q^{34} +(-8.17125 - 2.15734i) q^{35} +(-4.63087 - 2.67363i) q^{37} +(4.48055 - 5.96719i) q^{38} +(5.72186 + 6.99194i) q^{40} -4.21689i q^{41} +(0.893536 + 3.07621i) q^{44} +(-3.75582 + 5.00199i) q^{46} +(-5.05821 + 8.76108i) q^{47} +(-6.03630 + 3.54444i) q^{49} +(6.76873 - 2.88689i) q^{50} +(2.69643 + 0.662466i) q^{52} +(-6.13514 + 3.54212i) q^{53} +5.11619 q^{55} +(7.44893 + 0.716511i) q^{56} +(7.16884 + 0.867728i) q^{58} +(4.38856 - 2.53374i) q^{59} +(-4.21321 + 7.29750i) q^{61} +(0.150848 - 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.21731 - 3.84050i) q^{65} +(5.01815 + 8.69169i) q^{67} +(7.73114 - 2.24564i) q^{68} +(4.41745 - 11.1055i) q^{70} +5.29150i q^{71} +(9.30504 - 5.37227i) q^{73} +(4.54066 - 6.04723i) q^{74} +(7.61631 + 7.30460i) q^{76} +(2.98544 - 3.00745i) q^{77} +(10.3349 + 5.96688i) q^{79} +(-10.7888 + 6.84509i) q^{80} +(5.92037 + 0.716612i) q^{82} +14.9789i q^{83} -12.8580i q^{85} +(-4.47075 + 0.731728i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-0.963697 - 3.54444i) q^{91} +(-6.38437 - 6.12307i) q^{92} +(-11.4407 - 8.59041i) q^{94} +(14.5965 - 8.42726i) q^{95} +2.87198i q^{97} +(-3.95047 - 9.07710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^8	\( 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58} - 42 q^{59} - 72 q^{64} + 12 q^{65} + 30 q^{67} + 36 q^{68} + 30 q^{70} + 18 q^{73} - 12 q^{74} - 36 q^{80} + 54 q^{82} + 6 q^{88} - 18 q^{89} - 72 q^{91} - 60 q^{92} - 12 q^{94} + 6 q^{98}+O(q^{100}) \) 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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