LMFDB - Embedded newform 432.2.y.b.397.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	432.397
Dual form			432.2.y.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.00000 - 0.267949i) q^{5} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.00000 - 0.267949i) q^{5} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.46410i q^{10} +(-1.13397 - 4.23205i) q^{11} +(0.901924 - 3.36603i) q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +5.73205 q^{17} +(-2.36603 - 2.36603i) q^{19} +(2.00000 - 0.535898i) q^{20} +(-5.36603 + 3.09808i) q^{22} +(4.09808 - 2.36603i) q^{23} +(-3.40192 - 1.96410i) q^{25} -4.92820 q^{26} -5.46410 q^{28} +(-2.36603 + 0.633975i) q^{29} +(-0.267949 - 0.464102i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-2.09808 - 7.83013i) q^{34} +(-2.00000 - 2.00000i) q^{35} +(4.73205 - 4.73205i) q^{37} +(-2.36603 + 4.09808i) q^{38} +(-1.46410 - 2.53590i) q^{40} +(2.59808 - 1.50000i) q^{41} +(2.23205 + 8.33013i) q^{43} +(6.19615 + 6.19615i) q^{44} +(-4.73205 - 4.73205i) q^{46} +(-3.83013 + 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(-1.43782 + 5.36603i) q^{50} +(1.80385 + 6.73205i) q^{52} +(7.46410 - 7.46410i) q^{53} +4.53590i q^{55} +(2.00000 + 7.46410i) q^{56} +(1.73205 + 3.00000i) q^{58} +(-7.33013 - 1.96410i) q^{59} +(11.1962 - 3.00000i) q^{61} +(-0.535898 + 0.535898i) q^{62} +8.00000i q^{64} +(-1.80385 + 3.12436i) q^{65} +(-1.76795 + 6.59808i) q^{67} +(-9.92820 + 5.73205i) q^{68} +(-2.00000 + 3.46410i) q^{70} -2.92820i q^{71} -6.26795i q^{73} +(-8.19615 - 4.73205i) q^{74} +(6.46410 + 1.73205i) q^{76} +(3.09808 - 11.5622i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(-2.92820 + 2.92820i) q^{80} +(-3.00000 - 3.00000i) q^{82} +(1.36603 - 0.366025i) q^{83} +(-5.73205 - 1.53590i) q^{85} +(10.5622 - 6.09808i) q^{86} +(6.19615 - 10.7321i) q^{88} +2.00000i q^{89} +(6.73205 - 6.73205i) q^{91} +(-4.73205 + 8.19615i) q^{92} +(10.4641 + 2.80385i) q^{94} +(1.73205 + 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +(0.464102 - 0.464102i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{5} + 6 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^5 + 6 * q^7 + 8 * q^8	$ 4 q + 2 q^{2} - 4 q^{5} + 6 q^{7} + 8 q^{8} - 8 q^{11} + 14 q^{13} + 4 q^{14} + 8 q^{16} + 16 q^{17} - 6 q^{19} + 8 q^{20} - 18 q^{22} + 6 q^{23} - 24 q^{25} + 8 q^{26} - 8 q^{28} - 6 q^{29} - 8 q^{31} - 8 q^{32} + 2 q^{34} - 8 q^{35} + 12 q^{37} - 6 q^{38} + 8 q^{40} + 2 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{47} - 6 q^{49} - 30 q^{50} + 28 q^{52} + 16 q^{53} + 8 q^{56} - 12 q^{59} + 24 q^{61} - 16 q^{62} - 28 q^{65} - 14 q^{67} - 12 q^{68} - 8 q^{70} - 12 q^{74} + 12 q^{76} + 2 q^{77} - 24 q^{79} + 16 q^{80} - 12 q^{82} + 2 q^{83} - 16 q^{85} + 18 q^{86} + 4 q^{88} + 20 q^{91} - 12 q^{92} + 28 q^{94} - 20 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^5 + 6 * q^7 + 8 * q^8 - 8 * q^11 + 14 * q^13 + 4 * q^14 + 8 * q^16 + 16 * q^17 - 6 * q^19 + 8 * q^20 - 18 * q^22 + 6 * q^23 - 24 * q^25 + 8 * q^26 - 8 * q^28 - 6 * q^29 - 8 * q^31 - 8 * q^32 + 2 * q^34 - 8 * q^35 + 12 * q^37 - 6 * q^38 + 8 * q^40 + 2 * q^43 + 4 * q^44 - 12 * q^46 + 2 * q^47 - 6 * q^49 - 30 * q^50 + 28 * q^52 + 16 * q^53 + 8 * q^56 - 12 * q^59 + 24 * q^61 - 16 * q^62 - 28 * q^65 - 14 * q^67 - 12 * q^68 - 8 * q^70 - 12 * q^74 + 12 * q^76 + 2 * q^77 - 24 * q^79 + 16 * q^80 - 12 * q^82 + 2 * q^83 - 16 * q^85 + 18 * q^86 + 4 * q^88 + 20 * q^91 - 12 * q^92 + 28 * q^94 - 20 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$		0			0
$3$		0			0
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	−1.00000	−	0.267949i	−0.447214	−	0.119831i	0.0281817	−	0.999603i	$-0.491028\pi$
$5$	−1.00000	−	0.267949i	−0.447214	−	0.119831i	−0.475395	+	0.879772i	$0.657695\pi$
$6$		0			0
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.875338	−	0.483512i	$-0.160639\pi$
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.0189356	+	0.999821i	$0.493972\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		0			0
$10$			1.46410i			0.462990i
$11$	−1.13397	−	4.23205i	−0.341906	−	1.27601i	−0.896185	−	0.443680i	$-0.853673\pi$
$11$	−1.13397	−	4.23205i	−0.341906	−	1.27601i	0.554279	−	0.832331i	$-0.312994\pi$
$12$		0			0
$13$	0.901924	−	3.36603i	0.250149	−	0.933567i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	0.901924	−	3.36603i	0.250149	−	0.933567i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	1.00000	−	3.73205i	0.267261	−	0.997433i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	5.73205			1.39023			0.695113	−	0.718900i	$-0.255354\pi$
$17$	5.73205			1.39023			0.695113	+	0.718900i	$0.255354\pi$
$18$		0			0
$19$	−2.36603	−	2.36603i	−0.542803	−	0.542803i	0.381546	−	0.924350i	$-0.375392\pi$
$19$	−2.36603	−	2.36603i	−0.542803	−	0.542803i	−0.924350	+	0.381546i	$0.875392\pi$
$20$	2.00000	−	0.535898i	0.447214	−	0.119831i
$21$		0			0
$22$	−5.36603	+	3.09808i	−1.14404	+	0.660512i
$23$	4.09808	−	2.36603i	0.854508	−	0.493350i	−0.00766135	−	0.999971i	$-0.502439\pi$
$23$	4.09808	−	2.36603i	0.854508	−	0.493350i	0.862169	+	0.506620i	$0.169105\pi$
$24$		0			0
$25$	−3.40192	−	1.96410i	−0.680385	−	0.392820i
$26$	−4.92820			−0.966500
$27$		0			0
$28$	−5.46410			−1.03262
$29$	−2.36603	+	0.633975i	−0.439360	+	0.117726i	−0.471717	−	0.881750i	$-0.656365\pi$
$29$	−2.36603	+	0.633975i	−0.439360	+	0.117726i	0.0323566	+	0.999476i	$0.489699\pi$
$30$		0			0
$31$	−0.267949	−	0.464102i	−0.0481251	−	0.0833551i	0.840959	−	0.541098i	$-0.181991\pi$
$31$	−0.267949	−	0.464102i	−0.0481251	−	0.0833551i	−0.889085	+	0.457743i	$0.848658\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		0			0
$34$	−2.09808	−	7.83013i	−0.359817	−	1.34286i
$35$	−2.00000	−	2.00000i	−0.338062	−	0.338062i
$36$		0			0
$37$	4.73205	−	4.73205i	0.777944	−	0.777944i	−0.201537	−	0.979481i	$-0.564594\pi$
$37$	4.73205	−	4.73205i	0.777944	−	0.777944i	0.979481	+	0.201537i	$0.0645935\pi$
$38$	−2.36603	+	4.09808i	−0.383820	+	0.664796i
$39$		0			0
$40$	−1.46410	−	2.53590i	−0.231495	−	0.400961i
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$		0			0
$43$	2.23205	+	8.33013i	0.340385	+	1.27033i	0.897912	+	0.440174i	$0.145083\pi$
$43$	2.23205	+	8.33013i	0.340385	+	1.27033i	−0.557528	+	0.830158i	$0.688250\pi$
$44$	6.19615	+	6.19615i	0.934105	+	0.934105i
$45$		0			0
$46$	−4.73205	−	4.73205i	−0.697703	−	0.697703i
$47$	−3.83013	+	6.63397i	−0.558681	+	0.967665i	0.438925	+	0.898523i	$0.355359\pi$
$47$	−3.83013	+	6.63397i	−0.558681	+	0.967665i	−0.997607	+	0.0691412i	$0.977974\pi$
$48$		0			0
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$	−1.43782	+	5.36603i	−0.203339	+	0.758871i
$51$		0			0
$52$	1.80385	+	6.73205i	0.250149	+	0.933567i
$53$	7.46410	−	7.46410i	1.02527	−	1.02527i	0.0256010	−	0.999672i	$-0.491850\pi$
$53$	7.46410	−	7.46410i	1.02527	−	1.02527i	0.999672	−	0.0256010i	$-0.00814993\pi$
$54$		0			0
$55$			4.53590i			0.611620i
$56$	2.00000	+	7.46410i	0.267261	+	0.997433i
$57$		0			0
$58$	1.73205	+	3.00000i	0.227429	+	0.393919i
$59$	−7.33013	−	1.96410i	−0.954301	−	0.255704i	−0.252115	−	0.967697i	$-0.581126\pi$
$59$	−7.33013	−	1.96410i	−0.954301	−	0.255704i	−0.702186	+	0.711993i	$0.747793\pi$
$60$		0			0
$61$	11.1962	−	3.00000i	1.43352	−	0.384111i	0.543261	−	0.839564i	$-0.317189\pi$
$61$	11.1962	−	3.00000i	1.43352	−	0.384111i	0.890260	+	0.455453i	$0.150523\pi$
$62$	−0.535898	+	0.535898i	−0.0680592	+	0.0680592i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−1.80385	+	3.12436i	−0.223740	+	0.387529i
$66$		0			0
$67$	−1.76795	+	6.59808i	−0.215989	+	0.806083i	0.769827	+	0.638253i	$0.220343\pi$
$67$	−1.76795	+	6.59808i	−0.215989	+	0.806083i	−0.985816	+	0.167830i	$0.946324\pi$
$68$	−9.92820	+	5.73205i	−1.20397	+	0.695113i
$69$		0			0
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$		0			0
$73$		−	6.26795i		−	0.733608i	−0.930298	−	0.366804i	$-0.880452\pi$
$73$		−	6.26795i		−	0.733608i	0.930298	−	0.366804i	$-0.119548\pi$
$74$	−8.19615	−	4.73205i	−0.952783	−	0.550090i
$75$		0			0
$76$	6.46410	+	1.73205i	0.741483	+	0.198680i
$77$	3.09808	−	11.5622i	0.353059	−	1.31763i
$78$		0			0
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	0.301401	+	0.953498i	$0.402546\pi$
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	−0.976453	+	0.215728i	$0.930788\pi$
$80$	−2.92820	+	2.92820i	−0.327383	+	0.327383i
$81$		0			0
$82$	−3.00000	−	3.00000i	−0.331295	−	0.331295i
$83$	1.36603	−	0.366025i	0.149941	−	0.0401765i	−0.183068	−	0.983100i	$-0.558603\pi$
$83$	1.36603	−	0.366025i	0.149941	−	0.0401765i	0.333009	+	0.942924i	$0.391936\pi$
$84$		0			0
$85$	−5.73205	−	1.53590i	−0.621728	−	0.166592i
$86$	10.5622	−	6.09808i	1.13895	−	0.657572i
$87$		0			0
$88$	6.19615	−	10.7321i	0.660512	−	1.14404i
$89$			2.00000i			0.212000i	0.994366	+	0.106000i	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$		0			0
$91$	6.73205	−	6.73205i	0.705711	−	0.705711i
$92$	−4.73205	+	8.19615i	−0.493350	+	0.854508i
$93$		0			0
$94$	10.4641	+	2.80385i	1.07929	+	0.289195i
$95$	1.73205	+	3.00000i	0.177705	+	0.307794i
$96$		0			0
$97$	−5.86603	+	10.1603i	−0.595605	+	1.03162i	0.397857	+	0.917448i	$0.369754\pi$
$97$	−5.86603	+	10.1603i	−0.595605	+	1.03162i	−0.993461	+	0.114170i	$0.963579\pi$
$98$	0.464102	−	0.464102i	0.0468813	−	0.0468813i
$99$		0			0
$100$	7.85641			0.785641
$101$	−0.535898	−	2.00000i	−0.0533239	−	0.199007i	0.934125	−	0.356946i	$-0.116182\pi$
$101$	−0.535898	−	2.00000i	−0.0533239	−	0.199007i	−0.987449	+	0.157938i	$0.949515\pi$
$102$		0			0
$103$	13.0981	−	7.56218i	1.29059	−	0.745124i	0.311833	−	0.950137i	$-0.399057\pi$
$103$	13.0981	−	7.56218i	1.29059	−	0.745124i	0.978759	+	0.205014i	$0.0657238\pi$
$104$	8.53590	−	4.92820i	0.837014	−	0.483250i
$105$		0			0
$106$	−12.9282	−	7.46410i	−1.25570	−	0.724978i
$107$	−12.4904	+	12.4904i	−1.20749	+	1.20749i	−0.235654	+	0.971837i	$0.575723\pi$
$107$	−12.4904	+	12.4904i	−1.20749	+	1.20749i	−0.971837	+	0.235654i	$0.924277\pi$
$108$		0			0
$109$	10.7321	+	10.7321i	1.02794	+	1.02794i	0.999598	+	0.0283459i	$0.00902398\pi$
$109$	10.7321	+	10.7321i	1.02794	+	1.02794i	0.0283459	+	0.999598i	$0.490976\pi$
$110$	6.19615	−	1.66025i	0.590780	−	0.158299i
$111$		0			0
$112$	9.46410	−	5.46410i	0.894274	−	0.516309i
$113$	6.92820	+	12.0000i	0.651751	+	1.12887i	0.982698	+	0.185216i	$0.0592984\pi$
$113$	6.92820	+	12.0000i	0.651751	+	1.12887i	−0.330947	+	0.943649i	$0.607368\pi$
$114$		0			0
$115$	−4.73205	+	1.26795i	−0.441266	+	0.118237i
$116$	3.46410	−	3.46410i	0.321634	−	0.321634i
$117$		0			0
$118$			10.7321i			0.987965i
$119$	13.5622	+	7.83013i	1.24324	+	0.717787i
$120$		0			0
$121$	−7.09808	+	4.09808i	−0.645280	+	0.372552i
$122$	−8.19615	−	14.1962i	−0.742045	−	1.28526i
$123$		0			0
$124$	0.928203	+	0.535898i	0.0833551	+	0.0481251i
$125$	6.53590	+	6.53590i	0.584589	+	0.584589i
$126$		0			0
$127$	4.19615			0.372348			0.186174	−	0.982517i	$-0.440391\pi$
$127$	4.19615			0.372348			0.186174	+	0.982517i	$0.440391\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$		0			0
$130$	4.92820	+	1.32051i	0.432232	+	0.115816i
$131$	−2.09808	+	7.83013i	−0.183310	+	0.684121i	0.811676	+	0.584108i	$0.198555\pi$
$131$	−2.09808	+	7.83013i	−0.183310	+	0.684121i	−0.994986	+	0.100014i	$0.968111\pi$
$132$		0			0
$133$	−2.36603	−	8.83013i	−0.205160	−	0.765669i
$134$	9.66025			0.834519
$135$		0			0
$136$	11.4641	+	11.4641i	0.983039	+	0.983039i
$137$	−8.25833	−	4.76795i	−0.705557	−	0.407353i	0.103857	−	0.994592i	$-0.466882\pi$
$137$	−8.25833	−	4.76795i	−0.705557	−	0.407353i	−0.809414	+	0.587239i	$0.800215\pi$
$138$		0			0
$139$	−11.4282	−	3.06218i	−0.969328	−	0.259731i	−0.260784	−	0.965397i	$-0.583981\pi$
$139$	−11.4282	−	3.06218i	−0.969328	−	0.259731i	−0.708544	+	0.705667i	$0.750648\pi$
$140$	5.46410	+	1.46410i	0.461801	+	0.123739i
$141$		0			0
$142$	−4.00000	+	1.07180i	−0.335673	+	0.0899432i
$143$	−15.2679			−1.27677
$144$		0			0
$145$	2.53590			0.210595
$146$	−8.56218	+	2.29423i	−0.708611	+	0.189872i
$147$		0			0
$148$	−3.46410	+	12.9282i	−0.284747	+	1.06269i
$149$	−7.83013	−	2.09808i	−0.641469	−	0.171881i	−0.0766003	−	0.997062i	$-0.524407\pi$
$149$	−7.83013	−	2.09808i	−0.641469	−	0.171881i	−0.564869	+	0.825181i	$0.691073\pi$
$150$		0			0
$151$	0.633975	+	0.366025i	0.0515921	+	0.0297867i	0.525574	−	0.850748i	$-0.323851\pi$
$151$	0.633975	+	0.366025i	0.0515921	+	0.0297867i	−0.473982	+	0.880534i	$0.657184\pi$
$152$		−	9.46410i		−	0.767640i
$153$		0			0
$154$	−16.9282			−1.36411
$155$	0.143594	+	0.535898i	0.0115337	+	0.0430444i
$156$		0			0
$157$	1.26795	−	4.73205i	0.101193	−	0.377659i	−0.896692	−	0.442655i	$-0.854037\pi$
$157$	1.26795	−	4.73205i	0.101193	−	0.377659i	0.997886	+	0.0649959i	$0.0207034\pi$
$158$	16.3923	+	4.39230i	1.30410	+	0.349433i
$159$		0			0
$160$	5.07180	+	2.92820i	0.400961	+	0.231495i
$161$	12.9282			1.01889
$162$		0			0
$163$	−7.00000	−	7.00000i	−0.548282	−	0.548282i	0.377661	−	0.925944i	$-0.376728\pi$
$163$	−7.00000	−	7.00000i	−0.548282	−	0.548282i	−0.925944	+	0.377661i	$0.876728\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	−6.46410	+	3.73205i	−0.500207	+	0.288795i	−0.728799	−	0.684728i	$-0.759921\pi$
$167$	−6.46410	+	3.73205i	−0.500207	+	0.288795i	0.228592	+	0.973522i	$0.426588\pi$
$168$		0			0
$169$	0.741670	+	0.428203i	0.0570515	+	0.0329387i
$170$			8.39230i			0.643660i
$171$		0			0
$172$	−12.1962	−	12.1962i	−0.929948	−	0.929948i
$173$	−1.63397	+	0.437822i	−0.124229	+	0.0332870i	−0.320398	−	0.947283i	$-0.603817\pi$
$173$	−1.63397	+	0.437822i	−0.124229	+	0.0332870i	0.196169	+	0.980570i	$0.437150\pi$
$174$		0			0
$175$	−5.36603	−	9.29423i	−0.405633	−	0.702578i
$176$	−16.9282	−	4.53590i	−1.27601	−	0.341906i
$177$		0			0
$178$	2.73205	−	0.732051i	0.204776	−	0.0548695i
$179$	1.92820	+	1.92820i	0.144121	+	0.144121i	0.775486	−	0.631365i	$-0.217505\pi$
$179$	1.92820	+	1.92820i	0.144121	+	0.144121i	−0.631365	+	0.775486i	$0.717505\pi$
$180$		0			0
$181$	−7.39230	+	7.39230i	−0.549466	+	0.549466i	−0.926286	−	0.376821i	$-0.877017\pi$
$181$	−7.39230	+	7.39230i	−0.549466	+	0.549466i	0.376821	+	0.926286i	$0.377017\pi$
$182$	−11.6603	−	6.73205i	−0.864316	−	0.499013i
$183$		0			0
$184$	12.9282	+	3.46410i	0.953080	+	0.255377i
$185$	−6.00000	+	3.46410i	−0.441129	+	0.254686i
$186$		0			0
$187$	−6.50000	−	24.2583i	−0.475327	−	1.77394i
$188$		−	15.3205i		−	1.11736i
$189$		0			0
$190$	3.46410	−	3.46410i	0.251312	−	0.251312i
$191$	12.0263	−	20.8301i	0.870191	−	1.50722i	0.00839227	−	0.999965i	$-0.497329\pi$
$191$	12.0263	−	20.8301i	0.870191	−	1.50722i	0.861799	−	0.507250i	$-0.169338\pi$
$192$		0			0
$193$	−10.8660	−	18.8205i	−0.782154	−	1.35473i	−0.930685	−	0.365822i	$-0.880788\pi$
$193$	−10.8660	−	18.8205i	−0.782154	−	1.35473i	0.148531	−	0.988908i	$-0.452545\pi$
$194$	16.0263	+	4.29423i	1.15062	+	0.308308i
$195$		0			0
$196$	−0.803848	−	0.464102i	−0.0574177	−	0.0331501i
$197$	−13.6603	+	13.6603i	−0.973253	+	0.973253i	−0.999651	−	0.0263987i	$-0.991596\pi$
$197$	−13.6603	+	13.6603i	−0.973253	+	0.973253i	0.0263987	+	0.999651i	$0.491596\pi$
$198$		0			0
$199$			25.1244i			1.78102i	0.454965	+	0.890509i	$0.349652\pi$
$199$			25.1244i			1.78102i	−0.454965	+	0.890509i	$0.650348\pi$
$200$	−2.87564	−	10.7321i	−0.203339	−	0.758871i
$201$		0			0
$202$	−2.53590	+	1.46410i	−0.178425	+	0.103014i
$203$	−6.46410	−	1.73205i	−0.453691	−	0.121566i
$204$		0			0
$205$	−3.00000	+	0.803848i	−0.209529	+	0.0561432i
$206$	−15.1244	−	15.1244i	−1.05376	−	1.05376i
$207$		0			0
$208$	−9.85641	−	9.85641i	−0.683419	−	0.683419i
$209$	−7.33013	+	12.6962i	−0.507035	+	0.878211i
$210$		0			0
$211$	−1.09808	+	4.09808i	−0.0755947	+	0.282123i	−0.993367	−	0.114983i	$-0.963319\pi$
$211$	−1.09808	+	4.09808i	−0.0755947	+	0.282123i	0.917773	+	0.397106i	$0.129985\pi$
$212$	−5.46410	+	20.3923i	−0.375276	+	1.40055i
$213$		0			0
$214$	21.6340	+	12.4904i	1.47887	+	0.853825i
$215$		−	8.92820i		−	0.608898i
$216$		0			0
$217$		−	1.46410i		−	0.0993897i
$218$	10.7321	−	18.5885i	0.726866	−	1.25897i
$219$		0			0
$220$	−4.53590	−	7.85641i	−0.305810	−	0.529679i
$221$	5.16987	−	19.2942i	0.347763	−	1.29787i
$222$		0			0
$223$	−8.02628	+	13.9019i	−0.537479	+	0.930942i	0.461559	+	0.887109i	$0.347290\pi$
$223$	−8.02628	+	13.9019i	−0.537479	+	0.930942i	−0.999039	+	0.0438324i	$0.986043\pi$
$224$	−10.9282	−	10.9282i	−0.730171	−	0.730171i
$225$		0			0
$226$	13.8564	−	13.8564i	0.921714	−	0.921714i
$227$	−2.13397	+	0.571797i	−0.141637	+	0.0379515i	−0.328941	−	0.944351i	$-0.606692\pi$
$227$	−2.13397	+	0.571797i	−0.141637	+	0.0379515i	0.187304	+	0.982302i	$0.440025\pi$
$228$		0			0
$229$	6.83013	+	1.83013i	0.451347	+	0.120938i	0.477330	−	0.878724i	$-0.341605\pi$
$229$	6.83013	+	1.83013i	0.451347	+	0.120938i	−0.0259823	+	0.999662i	$0.508271\pi$
$230$	3.46410	+	6.00000i	0.228416	+	0.395628i
$231$		0			0
$232$	−6.00000	−	3.46410i	−0.393919	−	0.227429i
$233$			3.19615i			0.209387i	0.994505	+	0.104693i	$0.0333861\pi$
$233$			3.19615i			0.209387i	−0.994505	+	0.104693i	$0.966614\pi$
$234$		0			0
$235$	5.60770	−	5.60770i	0.365806	−	0.365806i
$236$	14.6603	−	3.92820i	0.954301	−	0.255704i
$237$		0			0
$238$	5.73205	−	21.3923i	0.371554	−	1.38666i
$239$	7.90192	+	13.6865i	0.511133	+	0.885308i	0.999917	+	0.0129033i	$0.00410736\pi$
$239$	7.90192	+	13.6865i	0.511133	+	0.885308i	−0.488784	+	0.872405i	$0.662559\pi$
$240$		0			0
$241$	−11.5981	+	20.0885i	−0.747098	+	1.29401i	0.202110	+	0.979363i	$0.435220\pi$
$241$	−11.5981	+	20.0885i	−0.747098	+	1.29401i	−0.949208	+	0.314649i	$0.898113\pi$
$242$	8.19615	+	8.19615i	0.526869	+	0.526869i
$243$		0			0
$244$	−16.3923	+	16.3923i	−1.04941	+	1.04941i
$245$	−0.124356	−	0.464102i	−0.00794479	−	0.0296504i
$246$		0			0
$247$	−10.0981	+	5.83013i	−0.642525	+	0.370962i
$248$	0.392305	−	1.46410i	0.0249114	−	0.0929705i
$249$		0			0
$250$	6.53590	−	11.3205i	0.413367	−	0.715972i
$251$	5.83013	−	5.83013i	0.367994	−	0.367994i	−0.498751	−	0.866745i	$-0.666208\pi$
$251$	5.83013	−	5.83013i	0.367994	−	0.367994i	0.866745	+	0.498751i	$0.166208\pi$
$252$		0			0
$253$	−14.6603	−	14.6603i	−0.921682	−	0.921682i
$254$	−1.53590	−	5.73205i	−0.0963708	−	0.359661i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.42820	−	16.3301i	−0.588115	−	1.01865i	−0.994479	−	0.104934i	$-0.966537\pi$
$257$	−9.42820	−	16.3301i	−0.588115	−	1.01865i	0.406364	−	0.913711i	$-0.366796\pi$
$258$		0			0
$259$	17.6603	−	4.73205i	1.09735	−	0.294035i
$260$		−	7.21539i		−	0.447480i
$261$		0			0
$262$	11.4641			0.708255
$263$	2.49038	+	1.43782i	0.153563	+	0.0886599i	0.574813	−	0.818285i	$-0.305075\pi$
$263$	2.49038	+	1.43782i	0.153563	+	0.0886599i	−0.421249	+	0.906945i	$0.638408\pi$
$264$		0			0
$265$	−9.46410	+	5.46410i	−0.581375	+	0.335657i
$266$	−11.1962	+	6.46410i	−0.686480	+	0.396339i
$267$		0			0
$268$	−3.53590	−	13.1962i	−0.215989	−	0.806083i
$269$	−1.26795	−	1.26795i	−0.0773082	−	0.0773082i	0.667395	−	0.744704i	$-0.267409\pi$
$269$	−1.26795	−	1.26795i	−0.0773082	−	0.0773082i	−0.744704	+	0.667395i	$0.767409\pi$
$270$		0			0
$271$	−0.392305			−0.0238308			−0.0119154	−	0.999929i	$-0.503793\pi$
$271$	−0.392305			−0.0238308			−0.0119154	+	0.999929i	$0.503793\pi$
$272$	11.4641	−	19.8564i	0.695113	−	1.20397i
$273$		0			0
$274$	−3.49038	+	13.0263i	−0.210862	+	0.786946i
$275$	−4.45448	+	16.6244i	−0.268615	+	1.00249i
$276$		0			0
$277$	−6.75833	−	25.2224i	−0.406069	−	1.51547i	−0.802076	−	0.597222i	$-0.796271\pi$
$277$	−6.75833	−	25.2224i	−0.406069	−	1.51547i	0.396007	−	0.918247i	$-0.370395\pi$
$278$			16.7321i			1.00352i
$279$		0			0
$280$		−	8.00000i		−	0.478091i
$281$	8.66025	+	5.00000i	0.516627	+	0.298275i	0.735554	−	0.677466i	$-0.236922\pi$
$281$	8.66025	+	5.00000i	0.516627	+	0.298275i	−0.218926	+	0.975741i	$0.570255\pi$
$282$		0			0
$283$	−19.5622	−	5.24167i	−1.16285	−	0.311585i	−0.374747	−	0.927127i	$-0.622270\pi$
$283$	−19.5622	−	5.24167i	−1.16285	−	0.311585i	−0.788104	+	0.615542i	$0.788937\pi$
$284$	2.92820	+	5.07180i	0.173757	+	0.300956i
$285$		0			0
$286$	5.58846	+	20.8564i	0.330452	+	1.23327i
$287$	8.19615			0.483804
$288$		0			0
$289$	15.8564			0.932730
$290$	−0.928203	−	3.46410i	−0.0545060	−	0.203419i
$291$		0			0
$292$	6.26795	+	10.8564i	0.366804	+	0.635323i
$293$	5.36603	+	1.43782i	0.313487	+	0.0839985i	0.412132	−	0.911124i	$-0.364784\pi$
$293$	5.36603	+	1.43782i	0.313487	+	0.0839985i	−0.0986454	+	0.995123i	$0.531451\pi$
$294$		0			0
$295$	6.80385	+	3.92820i	0.396135	+	0.228709i
$296$	18.9282			1.10018
$297$		0			0
$298$			11.4641i			0.664098i
$299$	−4.26795	−	15.9282i	−0.246822	−	0.921152i
$300$		0			0
$301$	−6.09808	+	22.7583i	−0.351487	+	1.31177i
$302$	0.267949	−	1.00000i	0.0154187	−	0.0575435i
$303$		0			0
$304$	−12.9282	+	3.46410i	−0.741483	+	0.198680i
$305$	−12.0000			−0.687118
$306$		0			0
$307$	3.02628	+	3.02628i	0.172719	+	0.172719i	0.788173	−	0.615454i	$-0.211027\pi$
$307$	3.02628	+	3.02628i	0.172719	+	0.172719i	−0.615454	+	0.788173i	$0.711027\pi$
$308$	6.19615	+	23.1244i	0.353059	+	1.31763i
$309$		0			0
$310$	0.679492	−	0.392305i	0.0385925	−	0.0222814i
$311$	19.0981	−	11.0263i	1.08295	−	0.625243i	0.151261	−	0.988494i	$-0.451667\pi$
$311$	19.0981	−	11.0263i	1.08295	−	0.625243i	0.931691	+	0.363251i	$0.118333\pi$
$312$		0			0
$313$	18.6506	+	10.7679i	1.05420	+	0.608640i	0.923821	−	0.382824i	$-0.125049\pi$
$313$	18.6506	+	10.7679i	1.05420	+	0.608640i	0.130375	+	0.991465i	$0.458382\pi$
$314$	−6.92820			−0.390981
$315$		0			0
$316$		−	24.0000i		−	1.35011i
$317$	20.5622	−	5.50962i	1.15489	−	0.309451i	0.369965	−	0.929046i	$-0.379370\pi$
$317$	20.5622	−	5.50962i	1.15489	−	0.309451i	0.784922	+	0.619595i	$0.212703\pi$
$318$		0			0
$319$	5.36603	+	9.29423i	0.300440	+	0.520377i
$320$	2.14359	−	8.00000i	0.119831	−	0.447214i
$321$		0			0
$322$	−4.73205	−	17.6603i	−0.263707	−	0.984167i
$323$	−13.5622	−	13.5622i	−0.754620	−	0.754620i
$324$		0			0
$325$	−9.67949	+	9.67949i	−0.536922	+	0.536922i
$326$	−7.00000	+	12.1244i	−0.387694	+	0.671506i
$327$		0			0
$328$	8.19615	+	2.19615i	0.452557	+	0.121262i
$329$	−18.1244	+	10.4641i	−0.999228	+	0.576905i
$330$		0			0
$331$	0.0262794	+	0.0980762i	0.00144445	+	0.00539076i	0.966644	−	0.256123i	$-0.0824451\pi$
$331$	0.0262794	+	0.0980762i	0.00144445	+	0.00539076i	−0.965200	+	0.261513i	$0.915778\pi$
$332$	−2.00000	+	2.00000i	−0.109764	+	0.109764i
$333$		0			0
$334$	7.46410	+	7.46410i	0.408417	+	0.408417i
$335$	3.53590	−	6.12436i	0.193187	−	0.334609i
$336$		0			0
$337$	8.89230	+	15.4019i	0.484395	+	0.838996i	0.999839	−	0.0179267i	$-0.00570654\pi$
$337$	8.89230	+	15.4019i	0.484395	+	0.838996i	−0.515445	+	0.856923i	$0.672373\pi$
$338$	0.313467	−	1.16987i	0.0170503	−	0.0636327i
$339$		0			0
$340$	11.4641	−	3.07180i	0.621728	−	0.166592i
$341$	−1.66025	+	1.66025i	−0.0899078	+	0.0899078i
$342$		0			0
$343$		−	17.8564i		−	0.964155i
$344$	−12.1962	+	21.1244i	−0.657572	+	1.13895i
$345$		0			0
$346$	1.19615	+	2.07180i	0.0643056	+	0.111380i
$347$	17.6244	+	4.72243i	0.946125	+	0.253513i	0.698717	−	0.715398i	$-0.253755\pi$
$347$	17.6244	+	4.72243i	0.946125	+	0.253513i	0.247408	+	0.968911i	$0.420421\pi$
$348$		0			0
$349$	15.9282	−	4.26795i	0.852617	−	0.228458i	0.194061	−	0.980989i	$-0.437834\pi$
$349$	15.9282	−	4.26795i	0.852617	−	0.228458i	0.658556	+	0.752531i	$0.271167\pi$
$350$	−10.7321	+	10.7321i	−0.573652	+	0.573652i
$351$		0			0
$352$			24.7846i			1.32102i
$353$	−7.16025	+	12.4019i	−0.381102	+	0.660088i	−0.991220	−	0.132223i	$-0.957789\pi$
$353$	−7.16025	+	12.4019i	−0.381102	+	0.660088i	0.610118	+	0.792310i	$0.291122\pi$
$354$		0			0
$355$	−0.784610	+	2.92820i	−0.0416428	+	0.155413i
$356$	−2.00000	−	3.46410i	−0.106000	−	0.183597i
$357$		0			0
$358$	1.92820	−	3.33975i	0.101909	−	0.176511i
$359$		−	11.2679i		−	0.594700i	−0.954769	−	0.297350i	$-0.903897\pi$
$359$		−	11.2679i		−	0.594700i	0.954769	−	0.297350i	$-0.0961028\pi$
$360$		0			0
$361$		−	7.80385i		−	0.410729i
$362$	12.8038	+	7.39230i	0.672955	+	0.388531i
$363$		0			0
$364$	−4.92820	+	18.3923i	−0.258308	+	0.964019i
$365$	−1.67949	+	6.26795i	−0.0879086	+	0.328079i
$366$		0			0
$367$	14.1244	−	24.4641i	0.737285	−	1.27702i	−0.216428	−	0.976299i	$-0.569441\pi$
$367$	14.1244	−	24.4641i	0.737285	−	1.27702i	0.953713	−	0.300717i	$-0.0972260\pi$
$368$		−	18.9282i		−	0.986701i
$369$		0			0
$370$	6.92820	+	6.92820i	0.360180	+	0.360180i
$371$	27.8564	−	7.46410i	1.44623	−	0.387517i
$372$		0			0
$373$	27.4904	+	7.36603i	1.42340	+	0.381398i	0.886688	−	0.462368i	$-0.153000\pi$
$373$	27.4904	+	7.36603i	1.42340	+	0.381398i	0.536710	+	0.843767i	$0.319667\pi$
$374$	−30.7583	+	17.7583i	−1.59048	+	0.918261i
$375$		0			0
$376$	−20.9282	+	5.60770i	−1.07929	+	0.289195i
$377$			8.53590i			0.439621i
$378$		0			0
$379$	3.75833	−	3.75833i	0.193052	−	0.193052i	−0.603961	−	0.797014i	$-0.706412\pi$
$379$	3.75833	−	3.75833i	0.193052	−	0.193052i	0.797014	+	0.603961i	$0.206412\pi$
$380$	−6.00000	−	3.46410i	−0.307794	−	0.177705i
$381$		0			0
$382$	−32.8564	−	8.80385i	−1.68108	−	0.450444i
$383$	6.73205	+	11.6603i	0.343992	+	0.595811i	0.985170	−	0.171581i	$-0.0548874\pi$
$383$	6.73205	+	11.6603i	0.343992	+	0.595811i	−0.641178	+	0.767392i	$0.721554\pi$
$384$		0			0
$385$	−6.19615	+	10.7321i	−0.315785	+	0.546956i
$386$	−21.7321	+	21.7321i	−1.10613	+	1.10613i
$387$		0			0
$388$		−	23.4641i		−	1.19121i
$389$	5.29423	+	19.7583i	0.268428	+	1.00179i	0.960119	+	0.279593i	$0.0901996\pi$
$389$	5.29423	+	19.7583i	0.268428	+	1.00179i	−0.691691	+	0.722194i	$0.743134\pi$
$390$		0			0
$391$	23.4904	−	13.5622i	1.18796	−	0.685869i
$392$	−0.339746	+	1.26795i	−0.0171598	+	0.0640411i
$393$		0			0
$394$	23.6603	+	13.6603i	1.19199	+	0.688194i
$395$	8.78461	−	8.78461i	0.442002	−	0.442002i
$396$		0			0
$397$	−9.26795	−	9.26795i	−0.465145	−	0.465145i	0.435192	−	0.900337i	$-0.356680\pi$
$397$	−9.26795	−	9.26795i	−0.465145	−	0.465145i	−0.900337	+	0.435192i	$0.856680\pi$
$398$	34.3205	−	9.19615i	1.72033	−	0.460961i
$399$		0			0
$400$	−13.6077	+	7.85641i	−0.680385	+	0.392820i
$401$	1.79423	+	3.10770i	0.0895995	+	0.155191i	0.907342	−	0.420393i	$-0.138108\pi$
$401$	1.79423	+	3.10770i	0.0895995	+	0.155191i	−0.817742	+	0.575584i	$0.804775\pi$
$402$		0			0
$403$	−1.80385	+	0.483340i	−0.0898560	+	0.0240769i
$404$	2.92820	+	2.92820i	0.145684	+	0.145684i
$405$		0			0
$406$			9.46410i			0.469695i
$407$	−25.3923	−	14.6603i	−1.25865	−	0.726682i
$408$		0			0
$409$	27.8660	−	16.0885i	1.37789	−	0.795523i	0.385981	−	0.922507i	$-0.373863\pi$
$409$	27.8660	−	16.0885i	1.37789	−	0.795523i	0.991905	+	0.126984i	$0.0405295\pi$
$410$	2.19615	+	3.80385i	0.108460	+	0.187859i
$411$		0			0
$412$	−15.1244	+	26.1962i	−0.745124	+	1.29059i
$413$	−14.6603	−	14.6603i	−0.721384	−	0.721384i
$414$		0			0
$415$	−1.46410			−0.0718699
$416$	−9.85641	+	17.0718i	−0.483250	+	0.837014i
$417$		0			0
$418$	20.0263	+	5.36603i	0.979517	+	0.262461i
$419$	−1.77757	+	6.63397i	−0.0868399	+	0.324091i	−0.995656	−	0.0931055i	$-0.970321\pi$
$419$	−1.77757	+	6.63397i	−0.0868399	+	0.324091i	0.908816	+	0.417196i	$0.136987\pi$
$420$		0			0
$421$	8.19615	+	30.5885i	0.399456	+	1.49079i	0.814056	+	0.580786i	$0.197255\pi$
$421$	8.19615	+	30.5885i	0.399456	+	1.49079i	−0.414600	+	0.910004i	$0.636078\pi$
$422$	6.00000			0.292075
$423$		0			0
$424$	29.8564			1.44996
$425$	−19.5000	−	11.2583i	−0.945889	−	0.546109i
$426$		0			0
$427$	30.5885	+	8.19615i	1.48028	+	0.396640i
$428$	9.14359	−	34.1244i	0.441972	−	1.64946i
$429$		0			0
$430$	−12.1962	+	3.26795i	−0.588151	+	0.157595i
$431$	16.1962			0.780141			0.390071	−	0.920785i	$-0.372451\pi$
$431$	16.1962			0.780141			0.390071	+	0.920785i	$0.372451\pi$
$432$		0			0
$433$	−5.73205			−0.275465			−0.137732	−	0.990469i	$-0.543981\pi$
$433$	−5.73205			−0.275465			−0.137732	+	0.990469i	$0.543981\pi$
$434$	−2.00000	+	0.535898i	−0.0960031	+	0.0257239i
$435$		0			0
$436$	−29.3205	−	7.85641i	−1.40420	−	0.376254i
$437$	−15.2942	−	4.09808i	−0.731622	−	0.196038i
$438$		0			0
$439$	−22.8564	−	13.1962i	−1.09088	−	0.629818i	−0.157067	−	0.987588i	$-0.550204\pi$
$439$	−22.8564	−	13.1962i	−1.09088	−	0.629818i	−0.933810	+	0.357770i	$0.883537\pi$
$440$	−9.07180	+	9.07180i	−0.432481	+	0.432481i
$441$		0			0
$442$	−28.2487			−1.34365
$443$	4.62436	+	17.2583i	0.219710	+	0.819968i	0.984455	+	0.175636i	$0.0561980\pi$
$443$	4.62436	+	17.2583i	0.219710	+	0.819968i	−0.764745	+	0.644332i	$0.777135\pi$
$444$		0			0
$445$	0.535898	−	2.00000i	0.0254040	−	0.0948091i
$446$	21.9282	+	5.87564i	1.03833	+	0.278220i
$447$		0			0
$448$	−10.9282	+	18.9282i	−0.516309	+	0.894274i
$449$	3.33975			0.157612			0.0788062	−	0.996890i	$-0.474889\pi$
$449$	3.33975			0.157612			0.0788062	+	0.996890i	$0.474889\pi$
$450$		0			0
$451$	−9.29423	−	9.29423i	−0.437648	−	0.437648i
$452$	−24.0000	−	13.8564i	−1.12887	−	0.651751i
$453$		0			0
$454$	1.56218	+	2.70577i	0.0733166	+	0.126988i
$455$	−8.53590	+	4.92820i	−0.400169	+	0.231038i
$456$		0			0
$457$	2.25833	+	1.30385i	0.105640	+	0.0609914i	0.551889	−	0.833917i	$-0.313907\pi$
$457$	2.25833	+	1.30385i	0.105640	+	0.0609914i	−0.446249	+	0.894909i	$0.647240\pi$
$458$		−	10.0000i		−	0.467269i
$459$		0			0
$460$	6.92820	−	6.92820i	0.323029	−	0.323029i
$461$	−35.6865	+	9.56218i	−1.66209	+	0.445355i	−0.962961	−	0.269642i	$-0.913094\pi$
$461$	−35.6865	+	9.56218i	−1.66209	+	0.445355i	−0.699127	+	0.714997i	$0.746428\pi$
$462$		0			0
$463$	1.19615	+	2.07180i	0.0555899	+	0.0962846i	0.892481	−	0.451085i	$-0.148963\pi$
$463$	1.19615	+	2.07180i	0.0555899	+	0.0962846i	−0.836891	+	0.547369i	$0.815629\pi$
$464$	−2.53590	+	9.46410i	−0.117726	+	0.439360i
$465$		0			0
$466$	4.36603	−	1.16987i	0.202252	−	0.0541933i
$467$	−2.63397	−	2.63397i	−0.121886	−	0.121886i	0.643533	−	0.765419i	$-0.277468\pi$
$467$	−2.63397	−	2.63397i	−0.121886	−	0.121886i	−0.765419	+	0.643533i	$0.777468\pi$
$468$		0			0
$469$	−13.1962	+	13.1962i	−0.609342	+	0.609342i
$470$	−9.71281	−	5.60770i	−0.448019	−	0.258664i
$471$		0			0
$472$	−10.7321	−	18.5885i	−0.493983	−	0.855603i
$473$	32.7224	−	18.8923i	1.50458	−	0.868669i
$474$		0			0
$475$	3.40192	+	12.6962i	0.156091	+	0.582539i
$476$	−31.3205			−1.43557
$477$		0			0
$478$	15.8038	−	15.8038i	0.722851	−	0.722851i
$479$	−4.16987	+	7.22243i	−0.190526	+	0.330001i	−0.945425	−	0.325840i	$-0.894353\pi$
$479$	−4.16987	+	7.22243i	−0.190526	+	0.330001i	0.754898	+	0.655842i	$0.227686\pi$
$480$		0			0
$481$	−11.6603	−	20.1962i	−0.531662	−	0.920865i
$482$	31.6865	+	8.49038i	1.44328	+	0.386726i
$483$		0			0
$484$	8.19615	−	14.1962i	0.372552	−	0.645280i
$485$	8.58846	−	8.58846i	0.389982	−	0.389982i
$486$		0			0
$487$			5.80385i			0.262997i	0.991316	+	0.131499i	$0.0419789\pi$
$487$			5.80385i			0.262997i	−0.991316	+	0.131499i	$0.958021\pi$
$488$	28.3923	+	16.3923i	1.28526	+	0.742045i
$489$		0			0
$490$	−0.588457	+	0.339746i	−0.0265838	+	0.0153482i
$491$	13.8923	+	3.72243i	0.626951	+	0.167991i	0.558286	−	0.829649i	$-0.311459\pi$
$491$	13.8923	+	3.72243i	0.626951	+	0.167991i	0.0686652	+	0.997640i	$0.478126\pi$
$492$		0			0
$493$	−13.5622	+	3.63397i	−0.610810	+	0.163666i
$494$	11.6603	+	11.6603i	0.524620	+	0.524620i
$495$		0			0
$496$	−2.14359			−0.0962502
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$		0			0
$499$	−2.33013	+	8.69615i	−0.104311	+	0.389293i	−0.998266	−	0.0588630i	$-0.981252\pi$
$499$	−2.33013	+	8.69615i	−0.104311	+	0.389293i	0.893955	+	0.448156i	$0.147919\pi$
$500$	−17.8564	−	4.78461i	−0.798563	−	0.213974i
$501$		0			0
$502$	−10.0981	−	5.83013i	−0.450699	−	0.260211i
$503$			27.7128i			1.23565i	0.786314	+	0.617827i	$0.211987\pi$
$503$			27.7128i			1.23565i	−0.786314	+	0.617827i	$0.788013\pi$
$504$		0			0
$505$			2.14359i			0.0953887i
$506$	−14.6603	+	25.3923i	−0.651728	+	1.12883i
$507$		0			0
$508$	−7.26795	+	4.19615i	−0.322463	+	0.186174i
$509$	−3.07180	+	11.4641i	−0.136155	+	0.508137i	0.863835	+	0.503774i	$0.168056\pi$
$509$	−3.07180	+	11.4641i	−0.136155	+	0.508137i	−0.999990	+	0.00436335i	$0.998611\pi$
$510$		0			0
$511$	8.56218	−	14.8301i	0.378768	−	0.656046i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−18.8564	+	18.8564i	−0.831720	+	0.831720i
$515$	−15.1244	+	4.05256i	−0.666459	+	0.178577i
$516$		0			0
$517$	32.4186	+	8.68653i	1.42577	+	0.382033i
$518$	−12.9282	−	22.3923i	−0.568033	−	0.983861i
$519$		0			0
$520$	−9.85641	+	2.64102i	−0.432232	+	0.115816i
$521$		−	13.0000i		−	0.569540i	−0.958596	−	0.284770i	$-0.908083\pi$
$521$		−	13.0000i		−	0.569540i	0.958596	−	0.284770i	$-0.0919173\pi$
$522$		0			0
$523$	−7.53590	+	7.53590i	−0.329522	+	0.329522i	−0.852405	−	0.522883i	$-0.824857\pi$
$523$	−7.53590	+	7.53590i	−0.329522	+	0.329522i	0.522883	+	0.852405i	$0.324857\pi$
$524$	−4.19615	−	15.6603i	−0.183310	−	0.684121i
$525$		0			0
$526$	1.05256	−	3.92820i	0.0458937	−	0.171278i
$527$	−1.53590	−	2.66025i	−0.0669048	−	0.115882i
$528$		0			0
$529$	−0.303848	+	0.526279i	−0.0132108	+	0.0228817i
$530$	10.9282	+	10.9282i	0.474691	+	0.474691i
$531$		0			0
$532$	12.9282	+	12.9282i	0.560509	+	0.560509i
$533$	−2.70577	−	10.0981i	−0.117200	−	0.437396i
$534$		0			0
$535$	15.8372	−	9.14359i	0.684701	−	0.395312i
$536$	−16.7321	+	9.66025i	−0.722715	+	0.417259i
$537$		0			0
$538$	−1.26795	+	2.19615i	−0.0546652	+	0.0946829i
$539$	1.43782	−	1.43782i	0.0619314	−	0.0619314i
$540$		0			0
$541$	2.19615	+	2.19615i	0.0944200	+	0.0944200i	0.752739	−	0.658319i	$-0.228732\pi$
$541$	2.19615	+	2.19615i	0.0944200	+	0.0944200i	−0.658319	+	0.752739i	$0.728732\pi$
$542$	0.143594	+	0.535898i	0.00616787	+	0.0230188i
$543$		0			0
$544$	−31.3205	−	8.39230i	−1.34286	−	0.359817i
$545$	−7.85641	−	13.6077i	−0.336531	−	0.582890i
$546$		0			0
$547$	32.6244	−	8.74167i	1.39492	−	0.373767i	0.518400	−	0.855138i	$-0.326528\pi$
$547$	32.6244	−	8.74167i	1.39492	−	0.373767i	0.876517	+	0.481371i	$0.159861\pi$
$548$	19.0718			0.814707
$549$		0			0
$550$	24.3397			1.03785
$551$	7.09808	+	4.09808i	0.302388	+	0.174584i
$552$		0			0
$553$	−28.3923	+	16.3923i	−1.20736	+	0.697072i
$554$	−31.9808	+	18.4641i	−1.35873	+	0.784465i
$555$		0			0
$556$	22.8564	−	6.12436i	0.969328	−	0.259731i
$557$	14.8038	+	14.8038i	0.627259	+	0.627259i	0.947378	−	0.320118i	$-0.103723\pi$
$557$	14.8038	+	14.8038i	0.627259	+	0.627259i	−0.320118	+	0.947378i	$0.603723\pi$
$558$		0			0
$559$	30.0526			1.27109
$560$	−10.9282	+	2.92820i	−0.461801	+	0.123739i
$561$		0			0
$562$	3.66025	−	13.6603i	0.154398	−	0.576223i
$563$	7.23205	−	26.9904i	0.304795	−	1.13751i	−0.628327	−	0.777949i	$-0.716260\pi$
$563$	7.23205	−	26.9904i	0.304795	−	1.13751i	0.933122	−	0.359560i	$-0.117073\pi$
$564$		0			0
$565$	−3.71281	−	13.8564i	−0.156199	−	0.582943i
$566$			28.6410i			1.20387i
$567$		0			0
$568$	5.85641	−	5.85641i	0.245729	−	0.245729i
$569$	18.4019	+	10.6244i	0.771449	+	0.445396i	0.833391	−	0.552684i	$-0.186396\pi$
$569$	18.4019	+	10.6244i	0.771449	+	0.445396i	−0.0619424	+	0.998080i	$0.519730\pi$
$570$		0			0
$571$	−3.33013	−	0.892305i	−0.139361	−	0.0373418i	0.188464	−	0.982080i	$-0.439649\pi$
$571$	−3.33013	−	0.892305i	−0.139361	−	0.0373418i	−0.327825	+	0.944738i	$0.606316\pi$
$572$	26.4449	−	15.2679i	1.10572	−	0.638385i
$573$		0			0
$574$	−3.00000	−	11.1962i	−0.125218	−	0.467318i
$575$	−18.5885			−0.775192
$576$		0			0
$577$	−5.78461			−0.240816			−0.120408	−	0.992724i	$-0.538420\pi$
$577$	−5.78461			−0.240816			−0.120408	+	0.992724i	$0.538420\pi$
$578$	−5.80385	−	21.6603i	−0.241408	−	0.900948i
$579$		0			0
$580$	−4.39230	+	2.53590i	−0.182381	+	0.105297i
$581$	3.73205	+	1.00000i	0.154832	+	0.0414870i
$582$		0			0
$583$	−40.0526	−	23.1244i	−1.65881	−	0.957713i
$584$	12.5359	−	12.5359i	0.518739	−	0.518739i
$585$		0			0
$586$		−	7.85641i		−	0.324545i
$587$	−7.23205	−	26.9904i	−0.298499	−	1.11401i	−0.938399	−	0.345554i	$-0.887691\pi$
$587$	−7.23205	−	26.9904i	−0.298499	−	1.11401i	0.639900	−	0.768458i	$-0.278976\pi$
$588$		0			0
$589$	−0.464102	+	1.73205i	−0.0191230	+	0.0713679i
$590$	2.87564	−	10.7321i	0.118388	−	0.441832i
$591$		0			0
$592$	−6.92820	−	25.8564i	−0.284747	−	1.06269i
$593$	−17.4641			−0.717165			−0.358582	−	0.933498i	$-0.616740\pi$
$593$	−17.4641			−0.717165			−0.358582	+	0.933498i	$0.616740\pi$
$594$		0			0
$595$	−11.4641	−	11.4641i	−0.469982	−	0.469982i
$596$	15.6603	−	4.19615i	0.641469	−	0.171881i
$597$		0			0
$598$	−20.1962	+	11.6603i	−0.825882	+	0.476823i
$599$	−11.3205	+	6.53590i	−0.462543	+	0.267050i	−0.713113	−	0.701049i	$-0.752715\pi$
$599$	−11.3205	+	6.53590i	−0.462543	+	0.267050i	0.250570	+	0.968099i	$0.419382\pi$
$600$		0			0
$601$	−20.5526	−	11.8660i	−0.838356	−	0.484025i	0.0183488	−	0.999832i	$-0.494159\pi$
$601$	−20.5526	−	11.8660i	−0.838356	−	0.484025i	−0.856705	+	0.515806i	$0.827492\pi$
$602$	33.3205			1.35804
$603$		0			0
$604$	−1.46410			−0.0595734
$605$	8.19615	−	2.19615i	0.333221	−	0.0892863i
$606$		0			0
$607$	−8.58846	−	14.8756i	−0.348595	−	0.603784i	0.637405	−	0.770529i	$-0.280008\pi$
$607$	−8.58846	−	14.8756i	−0.348595	−	0.603784i	−0.986000	+	0.166745i	$0.946674\pi$
$608$	9.46410	+	16.3923i	0.383820	+	0.664796i
$609$		0			0
$610$	4.39230	+	16.3923i	0.177839	+	0.663705i
$611$	18.8756	+	18.8756i	0.763627	+	0.763627i
$612$		0			0
$613$	−15.6603	+	15.6603i	−0.632512	+	0.632512i	−0.948697	−	0.316186i	$-0.897598\pi$
$613$	−15.6603	+	15.6603i	−0.632512	+	0.632512i	0.316186	+	0.948697i	$0.397598\pi$
$614$	3.02628	−	5.24167i	0.122131	−	0.211537i
$615$		0			0
$616$	29.3205	−	16.9282i	1.18136	−	0.682057i
$617$	35.0885	−	20.2583i	1.41261	−	0.815570i	0.416975	−	0.908918i	$-0.363090\pi$
$617$	35.0885	−	20.2583i	1.41261	−	0.815570i	0.995633	+	0.0933485i	$0.0297571\pi$
$618$		0			0
$619$	4.17949	+	15.5981i	0.167988	+	0.626940i	0.997640	+	0.0686590i	$0.0218721\pi$
$619$	4.17949	+	15.5981i	0.167988	+	0.626940i	−0.829652	+	0.558281i	$0.811461\pi$
$620$	−0.784610	−	0.784610i	−0.0315107	−	0.0315107i
$621$		0			0
$622$	−22.0526	−	22.0526i	−0.884227	−	0.884227i
$623$	−2.73205	+	4.73205i	−0.109457	+	0.189586i
$624$		0			0
$625$	5.03590	+	8.72243i	0.201436	+	0.348897i
$626$	7.88269	−	29.4186i	0.315055	−	1.17580i
$627$		0			0
$628$	2.53590	+	9.46410i	0.101193	+	0.377659i
$629$	27.1244	−	27.1244i	1.08152	−	1.08152i
$630$		0			0
$631$			17.6077i			0.700951i	0.936572	+	0.350476i	$0.113980\pi$
$631$			17.6077i			0.700951i	−0.936572	+	0.350476i	$0.886020\pi$
$632$	−32.7846	+	8.78461i	−1.30410	+	0.349433i
$633$		0			0
$634$	−15.0526	−	26.0718i	−0.597813	−	1.03544i
$635$	−4.19615	−	1.12436i	−0.166519	−	0.0446187i
$636$		0			0
$637$	1.56218	−	0.418584i	0.0618957	−	0.0165849i
$638$	10.7321	−	10.7321i	0.424886	−	0.424886i
$639$		0			0
$640$	−11.7128			−0.462990
$641$	19.7942	−	34.2846i	0.781825	−	1.35416i	−0.149053	−	0.988829i	$-0.547622\pi$
$641$	19.7942	−	34.2846i	0.781825	−	1.35416i	0.930878	−	0.365331i	$-0.119044\pi$
$642$		0			0
$643$	−2.34936	+	8.76795i	−0.0926499	+	0.345774i	−0.996653	−	0.0817525i	$-0.973948\pi$
$643$	−2.34936	+	8.76795i	−0.0926499	+	0.345774i	0.904003	+	0.427527i	$0.140615\pi$
$644$	−22.3923	+	12.9282i	−0.882380	+	0.509443i
$645$		0			0
$646$	−13.5622	+	23.4904i	−0.533597	+	0.924217i
$647$		−	16.7321i		−	0.657805i	−0.944364	−	0.328902i	$-0.893321\pi$
$647$		−	16.7321i		−	0.657805i	0.944364	−	0.328902i	$-0.106679\pi$
$648$		0			0
$649$			33.2487i			1.30513i
$650$	16.7654	+	9.67949i	0.657592	+	0.379661i
$651$		0			0
$652$	19.1244	+	5.12436i	0.748968	+	0.200685i
$653$	−7.36603	+	27.4904i	−0.288255	+	1.07578i	0.658173	+	0.752867i	$0.271329\pi$
$653$	−7.36603	+	27.4904i	−0.288255	+	1.07578i	−0.946428	+	0.322915i	$0.895337\pi$
$654$		0			0
$655$	4.19615	−	7.26795i	0.163957	−	0.283982i
$656$		−	12.0000i		−	0.468521i
$657$		0			0
$658$	20.9282	+	20.9282i	0.815866	+	0.815866i
$659$	15.0263	−	4.02628i	0.585341	−	0.156842i	0.0460178	−	0.998941i	$-0.485347\pi$
$659$	15.0263	−	4.02628i	0.585341	−	0.156842i	0.539323	+	0.842099i	$0.318680\pi$
$660$		0			0
$661$	−8.19615	−	2.19615i	−0.318793	−	0.0854204i	0.0958740	−	0.995393i	$-0.469435\pi$
$661$	−8.19615	−	2.19615i	−0.318793	−	0.0854204i	−0.414667	+	0.909973i	$0.636102\pi$
$662$	0.124356	−	0.0717968i	0.00483322	−	0.00279046i
$663$		0			0
$664$	3.46410	+	2.00000i	0.134433	+	0.0776151i
$665$			9.46410i			0.367002i
$666$		0			0
$667$	−8.19615	+	8.19615i	−0.317356	+	0.317356i
$668$	7.46410	−	12.9282i	0.288795	−	0.500207i
$669$		0			0
$670$	−9.66025	−	2.58846i	−0.373208	−	0.100001i
$671$	−25.3923	−	43.9808i	−0.980259	−	1.69786i
$672$		0			0
$673$	19.1962	−	33.2487i	0.739957	−	1.28164i	−0.212557	−	0.977149i	$-0.568179\pi$
$673$	19.1962	−	33.2487i	0.739957	−	1.28164i	0.952514	−	0.304495i	$-0.0984877\pi$
$674$	17.7846	−	17.7846i	0.685038	−	0.685038i
$675$		0			0
$676$	−1.71281			−0.0658774
$677$	−1.26795	−	4.73205i	−0.0487312	−	0.181867i	0.937270	−	0.348603i	$-0.113344\pi$
$677$	−1.26795	−	4.73205i	−0.0487312	−	0.181867i	−0.986002	+	0.166736i	$0.946677\pi$
$678$		0			0
$679$	−27.7583	+	16.0263i	−1.06527	+	0.615032i
$680$	−8.39230	−	14.5359i	−0.321830	−	0.557426i
$681$		0			0
$682$	2.87564	+	1.66025i	0.110114	+	0.0635744i
$683$	20.2942	−	20.2942i	0.776537	−	0.776537i	−0.202703	−	0.979240i	$-0.564973\pi$
$683$	20.2942	−	20.2942i	0.776537	−	0.776537i	0.979240	+	0.202703i	$0.0649726\pi$
$684$		0			0
$685$	6.98076	+	6.98076i	0.266721	+	0.266721i
$686$	−24.3923	+	6.53590i	−0.931303	+	0.249542i
$687$		0			0
$688$	33.3205	+	8.92820i	1.27033	+	0.340385i
$689$	−18.3923	−	31.8564i	−0.700691	−	1.21363i
$690$		0			0
$691$	9.29423	−	2.49038i	0.353569	−	0.0947386i	−0.0776628	−	0.996980i	$-0.524746\pi$
$691$	9.29423	−	2.49038i	0.353569	−	0.0947386i	0.431232	+	0.902241i	$0.358079\pi$
$692$	2.39230	−	2.39230i	0.0909418	−	0.0909418i
$693$		0			0
$694$		−	25.8038i		−	0.979501i
$695$	10.6077	+	6.12436i	0.402373	+	0.232310i
$696$		0			0
$697$	14.8923	−	8.59808i	0.564086	−	0.325675i
$698$	−11.6603	−	20.1962i	−0.441347	−	0.764436i
$699$		0			0
$700$	18.5885	+	10.7321i	0.702578	+	0.405633i
$701$	6.66025	+	6.66025i	0.251554	+	0.251554i	0.821608	−	0.570053i	$-0.193077\pi$
$701$	6.66025	+	6.66025i	0.251554	+	0.251554i	−0.570053	+	0.821608i	$0.693077\pi$
$702$		0			0
$703$	−22.3923			−0.844542
$704$	33.8564	−	9.07180i	1.27601	−	0.341906i
$705$		0			0
$706$	19.5622	+	5.24167i	0.736232	+	0.197273i
$707$	1.46410	−	5.46410i	0.0550632	−	0.205499i
$708$		0			0
$709$	−9.80385	−	36.5885i	−0.368191	−	1.37411i	−0.863043	−	0.505131i	$-0.831444\pi$
$709$	−9.80385	−	36.5885i	−0.368191	−	1.37411i	0.494852	−	0.868978i	$-0.335222\pi$
$710$	4.28719			0.160895
$711$		0			0
$712$	−4.00000	+	4.00000i	−0.149906	+	0.149906i
$713$	−2.19615	−	1.26795i	−0.0822466	−	0.0474851i
$714$		0			0
$715$	15.2679	+	4.09103i	0.570989	+	0.152996i
$716$	−5.26795	−	1.41154i	−0.196873	−	0.0527518i
$717$		0			0
$718$	−15.3923	+	4.12436i	−0.574436	+	0.153920i
$719$	−4.39230			−0.163805			−0.0819027	−	0.996640i	$-0.526100\pi$
$719$	−4.39230			−0.163805			−0.0819027	+	0.996640i	$0.526100\pi$
$720$		0			0
$721$	41.3205			1.53886
$722$	−10.6603	+	2.85641i	−0.396734	+	0.106304i
$723$		0			0
$724$	5.41154	−	20.1962i	0.201118	−	0.750584i
$725$	9.29423	+	2.49038i	0.345179	+	0.0924904i
$726$		0			0
$727$	−28.8109	−	16.6340i	−1.06854	−	0.616920i	−0.140755	−	0.990044i	$-0.544953\pi$
$727$	−28.8109	−	16.6340i	−1.06854	−	0.616920i	−0.927781	+	0.373124i	$0.878286\pi$
$728$	26.9282			0.998026
$729$		0			0
$730$	9.17691			0.339653
$731$	12.7942	+	47.7487i	0.473212	+	1.76605i
$732$		0			0
$733$	2.95448	−	11.0263i	0.109126	−	0.407265i	−0.889654	−	0.456635i	$-0.849055\pi$
$733$	2.95448	−	11.0263i	0.109126	−	0.407265i	0.998781	+	0.0493698i	$0.0157213\pi$
$734$	−38.5885	−	10.3397i	−1.42433	−	0.381647i
$735$		0			0
$736$	−25.8564	+	6.92820i	−0.953080	+	0.255377i
$737$	29.9282			1.10242
$738$		0			0
$739$	−8.22243	−	8.22243i	−0.302467	−	0.302467i	0.539511	−	0.841978i	$-0.318609\pi$
$739$	−8.22243	−	8.22243i	−0.302467	−	0.302467i	−0.841978	+	0.539511i	$0.818609\pi$
$740$	6.92820	−	12.0000i	0.254686	−	0.441129i
$741$		0			0
$742$	−20.3923	−	35.3205i	−0.748625	−	1.29666i
$743$	−24.7583	+	14.2942i	−0.908295	+	0.524404i	−0.879882	−	0.475192i	$-0.842379\pi$
$743$	−24.7583	+	14.2942i	−0.908295	+	0.524404i	−0.0284129	+	0.999596i	$0.509045\pi$
$744$		0			0
$745$	7.26795	+	4.19615i	0.266277	+	0.153735i
$746$		−	40.2487i		−	1.47361i
$747$		0			0
$748$	35.5167	+	35.5167i	1.29862	+	1.29862i
$749$	−46.6147	+	12.4904i	−1.70327	+	0.456389i
$750$		0			0
$751$	−8.85641	−	15.3397i	−0.323175	−	0.559755i	0.657966	−	0.753047i	$-0.271417\pi$
$751$	−8.85641	−	15.3397i	−0.323175	−	0.559755i	−0.981141	+	0.193292i	$0.938084\pi$
$752$	15.3205	+	26.5359i	0.558681	+	0.967665i
$753$		0			0
$754$	11.6603	−	3.12436i	0.424641	−	0.113782i
$755$	−0.535898	−	0.535898i	−0.0195033	−	0.0195033i
$756$		0			0
$757$	−19.9282	+	19.9282i	−0.724303	+	0.724303i	−0.969479	−	0.245176i	$-0.921154\pi$
$757$	−19.9282	+	19.9282i	−0.724303	+	0.724303i	0.245176	+	0.969479i	$0.421154\pi$
$758$	−6.50962	−	3.75833i	−0.236440	−	0.136509i
$759$		0			0
$760$	−2.53590	+	9.46410i	−0.0919867	+	0.343299i
$761$	−45.3731	+	26.1962i	−1.64477	+	0.949610i	−0.665669	+	0.746247i	$0.731854\pi$
$761$	−45.3731	+	26.1962i	−1.64477	+	0.949610i	−0.979104	+	0.203363i	$0.934813\pi$
$762$		0			0
$763$	10.7321	+	40.0526i	0.388526	+	1.45000i
$764$			48.1051i			1.74038i
$765$		0			0
$766$	13.4641	−	13.4641i	0.486478	−	0.486478i
$767$	−13.2224	+	22.9019i	−0.477434	+	0.826941i
$768$		0			0
$769$	−14.1244	−	24.4641i	−0.509337	−	0.882198i	−0.999942	−	0.0108155i	$-0.996557\pi$
$769$	−14.1244	−	24.4641i	−0.509337	−	0.882198i	0.490604	−	0.871383i	$-0.336776\pi$
$770$	16.9282	+	4.53590i	0.610050	+	0.163462i
$771$		0			0
$772$	37.6410	+	21.7321i	1.35473	+	0.782154i
$773$	−35.5885	+	35.5885i	−1.28003	+	1.28003i	−0.339378	+	0.940650i	$0.610216\pi$
$773$	−35.5885	+	35.5885i	−1.28003	+	1.28003i	−0.940650	+	0.339378i	$0.889784\pi$
$774$		0			0
$775$			2.10512i			0.0756181i
$776$	−32.0526	+	8.58846i	−1.15062	+	0.308308i
$777$		0			0
$778$	25.0526	−	14.4641i	0.898178	−	0.518563i
$779$	−9.69615	−	2.59808i	−0.347401	−	0.0930857i
$780$		0			0
$781$	−12.3923	+	3.32051i	−0.443432	+	0.118817i
$782$	−27.1244	−	27.1244i	−0.969965	−	0.969965i
$783$		0			0
$784$	1.85641			0.0663002
$785$	−2.53590	+	4.39230i	−0.0905101	+	0.156768i
$786$		0			0
$787$	−10.8109	+	40.3468i	−0.385367	+	1.43821i	0.452222	+	0.891906i	$0.350632\pi$
$787$	−10.8109	+	40.3468i	−0.385367	+	1.43821i	−0.837588	+	0.546302i	$0.816035\pi$
$788$	10.0000	−	37.3205i	0.356235	−	1.32949i
$789$		0			0
$790$	−15.2154	−	8.78461i	−0.541339	−	0.312542i
$791$			37.8564i			1.34602i
$792$		0			0
$793$		−	40.3923i		−	1.43437i
$794$	−9.26795	+	16.0526i	−0.328907	+	0.569684i
$795$		0			0
$796$	−25.1244	−	43.5167i	−0.890509	−	1.54241i
$797$	−8.17691	+	30.5167i	−0.289641	+	1.08096i	0.655740	+	0.754987i	$0.272357\pi$
$797$	−8.17691	+	30.5167i	−0.289641	+	1.08096i	−0.945381	+	0.325968i	$0.894310\pi$
$798$		0			0
$799$	−21.9545	+	38.0263i	−0.776694	+	1.34527i
$800$	15.7128	+	15.7128i	0.555532	+	0.555532i
$801$		0			0
$802$	3.58846	−	3.58846i	0.126713	−	0.126713i
$803$	−26.5263	+	7.10770i	−0.936092	+	0.250825i
$804$		0			0
$805$	−12.9282	−	3.46410i	−0.455659	−	0.122094i
$806$	1.32051	+	2.28719i	0.0465129	+	0.0805627i
$807$		0			0
$808$	2.92820	−	5.07180i	0.103014	−	0.178425i
$809$			6.32051i			0.222217i	0.993808	+	0.111109i	$0.0354401\pi$
$809$			6.32051i			0.222217i	−0.993808	+	0.111109i	$0.964560\pi$
$810$		0			0
$811$	−14.0263	+	14.0263i	−0.492529	+	0.492529i	−0.909102	−	0.416573i	$-0.863231\pi$
$811$	−14.0263	+	14.0263i	−0.492529	+	0.492529i	0.416573	+	0.909102i	$0.363231\pi$
$812$	12.9282	−	3.46410i	0.453691	−	0.121566i
$813$		0			0
$814$	−10.7321	+	40.0526i	−0.376158	+	1.40384i
$815$	5.12436	+	8.87564i	0.179498	+	0.310900i
$816$		0			0
$817$	14.4282	−	24.9904i	0.504779	−	0.874303i
$818$	−32.1769	−	32.1769i	−1.12504	−	1.12504i
$819$		0			0
$820$	4.39230	−	4.39230i	0.153386	−	0.153386i
$821$	−2.77757	−	10.3660i	−0.0969378	−	0.361777i	0.900368	−	0.435129i	$-0.143297\pi$
$821$	−2.77757	−	10.3660i	−0.0969378	−	0.361777i	−0.997306	+	0.0733518i	$0.976630\pi$
$822$		0			0
$823$	7.26795	−	4.19615i	0.253345	−	0.146269i	−0.367950	−	0.929846i	$-0.619940\pi$
$823$	7.26795	−	4.19615i	0.253345	−	0.146269i	0.621295	+	0.783577i	$0.286607\pi$
$824$	41.3205	+	11.0718i	1.43947	+	0.385704i
$825$		0			0
$826$	−14.6603	+	25.3923i	−0.510095	+	0.883511i
$827$	−17.5359	+	17.5359i	−0.609783	+	0.609783i	−0.942889	−	0.333106i	$-0.891903\pi$
$827$	−17.5359	+	17.5359i	−0.609783	+	0.609783i	0.333106	+	0.942889i	$0.391903\pi$
$828$		0			0
$829$	−20.5167	−	20.5167i	−0.712573	−	0.712573i	0.254500	−	0.967073i	$-0.418089\pi$
$829$	−20.5167	−	20.5167i	−0.712573	−	0.712573i	−0.967073	+	0.254500i	$0.918089\pi$
$830$	0.535898	+	2.00000i	0.0186013	+	0.0694210i
$831$		0			0
$832$	26.9282	+	7.21539i	0.933567	+	0.250149i
$833$	1.33013	+	2.30385i	0.0460862	+	0.0798236i
$834$		0			0
$835$	7.46410	−	2.00000i	0.258306	−	0.0692129i
$836$		−	29.3205i		−	1.01407i
$837$		0			0
$838$	9.71281			0.335524
$839$	−23.4449	−	13.5359i	−0.809407	−	0.467311i	0.0373432	−	0.999303i	$-0.488111\pi$
$839$	−23.4449	−	13.5359i	−0.809407	−	0.467311i	−0.846750	+	0.531991i	$0.821444\pi$
$840$		0			0
$841$	−19.9186	+	11.5000i	−0.686848	+	0.396552i
$842$	38.7846	−	22.3923i	1.33661	−	0.771690i
$843$		0			0
$844$	−2.19615	−	8.19615i	−0.0755947	−	0.282123i
$845$	−0.626933	−	0.626933i	−0.0215672	−	0.0215672i
$846$		0			0
$847$	−22.3923			−0.769409
$848$	−10.9282	−	40.7846i	−0.375276	−	1.40055i
$849$		0			0
$850$	−8.24167	+	30.7583i	−0.282687	+	1.05500i
$851$	8.19615	−	30.5885i	0.280960	−	1.04856i
$852$		0			0
$853$	−0.437822	−	1.63397i	−0.0149907	−	0.0559462i	0.958025	−	0.286684i	$-0.0925528\pi$
$853$	−0.437822	−	1.63397i	−0.0149907	−	0.0559462i	−0.973016	+	0.230737i	$0.925886\pi$
$854$		−	44.7846i		−	1.53250i
$855$		0			0
$856$	−49.9615			−1.70765
$857$	44.9090	+	25.9282i	1.53406	+	0.885691i	0.999169	+	0.0407704i	$0.0129812\pi$
$857$	44.9090	+	25.9282i	1.53406	+	0.885691i	0.534892	+	0.844920i	$0.320352\pi$
$858$		0			0
$859$	14.2583	+	3.82051i	0.486488	+	0.130354i	0.493722	−	0.869620i	$-0.335636\pi$
$859$	14.2583	+	3.82051i	0.486488	+	0.130354i	−0.00723407	+	0.999974i	$0.502303\pi$
$860$	8.92820	+	15.4641i	0.304449	+	0.527321i
$861$		0			0
$862$	−5.92820	−	22.1244i	−0.201915	−	0.753559i
$863$	15.4641			0.526404			0.263202	−	0.964741i	$-0.415221\pi$
$863$	15.4641			0.526404			0.263202	+	0.964741i	$0.415221\pi$
$864$		0			0
$865$	1.75129			0.0595456
$866$	2.09808	+	7.83013i	0.0712955	+	0.266079i
$867$		0			0
$868$	1.46410	+	2.53590i	0.0496948	+	0.0860740i
$869$	50.7846	+	13.6077i	1.72275	+	0.461609i
$870$		0			0
$871$	20.6147	+	11.9019i	0.698504	+	0.403281i
$872$			42.9282i			1.45373i
$873$		0			0
$874$			22.3923i			0.757431i
$875$	6.53590	+	24.3923i	0.220954	+	0.824610i
$876$		0			0
$877$	−8.46410	+	31.5885i	−0.285812	+	1.06667i	0.662431	+	0.749123i	$0.269525\pi$
$877$	−8.46410	+	31.5885i	−0.285812	+	1.06667i	−0.948244	+	0.317544i	$0.897142\pi$
$878$	−9.66025	+	36.0526i	−0.326018	+	1.21671i
$879$		0			0
$880$	15.7128	+	9.07180i	0.529679	+	0.305810i
$881$	−27.3205			−0.920451			−0.460226	−	0.887802i	$-0.652231\pi$
$881$	−27.3205			−0.920451			−0.460226	+	0.887802i	$0.652231\pi$
$882$		0			0
$883$	−12.6340	−	12.6340i	−0.425167	−	0.425167i	0.461811	−	0.886978i	$-0.347200\pi$
$883$	−12.6340	−	12.6340i	−0.425167	−	0.425167i	−0.886978	+	0.461811i	$0.847200\pi$
$884$	10.3397	+	38.5885i	0.347763	+	1.29787i
$885$		0			0
$886$	21.8827	−	12.6340i	0.735163	−	0.424447i
$887$	−8.87564	+	5.12436i	−0.298015	+	0.172059i	−0.641551	−	0.767081i	$-0.721709\pi$
$887$	−8.87564	+	5.12436i	−0.298015	+	0.172059i	0.343536	+	0.939140i	$0.388375\pi$
$888$		0			0
$889$	9.92820	+	5.73205i	0.332981	+	0.192247i
$890$	−2.92820			−0.0981536
$891$		0			0
$892$		−	32.1051i		−	1.07496i
$893$	24.7583	−	6.63397i	0.828506	−	0.221997i
$894$		0			0
$895$	−1.41154	−	2.44486i	−0.0471827	−	0.0817228i
$896$	29.8564	+	8.00000i	0.997433	+	0.267261i
$897$		0			0
$898$	−1.22243	−	4.56218i	−0.0407931	−	0.152242i
$899$	0.928203	+	0.928203i	0.0309573	+	0.0309573i
$900$		0			0
$901$	42.7846	−	42.7846i	1.42536	−	1.42536i
$902$	−9.29423	+	16.0981i	−0.309464	+	0.536007i
$903$		0			0
$904$	−10.1436	+	37.8564i	−0.337371	+	1.25909i
$905$	9.37307	−	5.41154i	0.311571	−	0.179886i
$906$		0			0
$907$	−1.20577	−	4.50000i	−0.0400370	−	0.149420i	0.943014	−	0.332754i	$-0.107978\pi$
$907$	−1.20577	−	4.50000i	−0.0400370	−	0.149420i	−0.983051	+	0.183334i	$0.941311\pi$
$908$	3.12436	−	3.12436i	0.103685	−	0.103685i
$909$		0			0
$910$	9.85641	+	9.85641i	0.326737	+	0.326737i
$911$	−2.46410	+	4.26795i	−0.0816393	+	0.141403i	−0.903954	−	0.427629i	$-0.859349\pi$
$911$	−2.46410	+	4.26795i	−0.0816393	+	0.141403i	0.822315	+	0.569033i	$0.192682\pi$
$912$		0			0
$913$	−3.09808	−	5.36603i	−0.102531	−	0.177590i
$914$	0.954483	−	3.56218i	0.0315715	−	0.117826i
$915$		0			0
$916$	−13.6603	+	3.66025i	−0.451347	+	0.120938i
$917$	−15.6603	+	15.6603i	−0.517147	+	0.517147i
$918$		0			0
$919$			18.9808i			0.626118i	0.949734	+	0.313059i	$0.101354\pi$
$919$			18.9808i			0.626118i	−0.949734	+	0.313059i	$0.898646\pi$
$920$	−12.0000	−	6.92820i	−0.395628	−	0.228416i
$921$		0			0
$922$	26.1244	+	45.2487i	0.860360	+	1.49019i
$923$	−9.85641	−	2.64102i	−0.324428	−	0.0869301i
$924$		0			0
$925$	−25.3923	+	6.80385i	−0.834894	+	0.223709i
$926$	2.39230	−	2.39230i	0.0786160	−	0.0786160i
$927$		0			0
$928$	13.8564			0.454859
$929$	11.5359	−	19.9808i	0.378481	−	0.655548i	−0.612361	−	0.790578i	$-0.709780\pi$
$929$	11.5359	−	19.9808i	0.378481	−	0.655548i	0.990841	+	0.135031i	$0.0431134\pi$
$930$		0			0
$931$	0.401924	−	1.50000i	0.0131725	−	0.0491605i
$932$	−3.19615	−	5.53590i	−0.104693	−	0.181334i
$933$		0			0
$934$	−2.63397	+	4.56218i	−0.0861863	+	0.149279i
$935$			26.0000i			0.850291i
$936$		0			0
$937$		−	11.1769i		−	0.365134i	−0.983193	−	0.182567i	$-0.941559\pi$
$937$		−	11.1769i		−	0.365134i	0.983193	−	0.182567i	$-0.0584406\pi$
$938$	22.8564	+	13.1962i	0.746288	+	0.430870i
$939$		0			0
$940$	−4.10512	+	15.3205i	−0.133894	+	0.499700i
$941$	1.80385	−	6.73205i	0.0588038	−	0.219459i	−0.930271	−	0.366873i	$-0.880428\pi$
$941$	1.80385	−	6.73205i	0.0588038	−	0.219459i	0.989075	+	0.147414i	$0.0470951\pi$
$942$		0			0
$943$	7.09808	−	12.2942i	0.231145	−	0.400355i
$944$	−21.4641	+	21.4641i	−0.698597	+	0.698597i
$945$		0			0
$946$	−37.7846	−	37.7846i	−1.22848	−	1.22848i
$947$	−41.0167	+	10.9904i	−1.33286	+	0.357139i	−0.853782	−	0.520631i	$-0.825697\pi$
$947$	−41.0167	+	10.9904i	−1.33286	+	0.357139i	−0.479081	+	0.877771i	$0.659030\pi$
$948$		0			0
$949$	−21.0981	−	5.65321i	−0.684873	−	0.183511i
$950$	16.0981	−	9.29423i	0.522291	−	0.301545i
$951$		0			0
$952$	11.4641	+	42.7846i	0.371554	+	1.38666i
$953$		−	17.1051i		−	0.554089i	−0.960857	−	0.277045i	$-0.910645\pi$
$953$		−	17.1051i		−	0.554089i	0.960857	−	0.277045i	$-0.0893550\pi$
$954$		0			0
$955$	−17.6077	+	17.6077i	−0.569772	+	0.569772i
$956$	−27.3731	−	15.8038i	−0.885308	−	0.511133i
$957$		0			0
$958$	11.3923	+	3.05256i	0.368069	+	0.0986237i
$959$	−13.0263	−	22.5622i	−0.420641	−	0.728571i
$960$		0			0
$961$	15.3564	−	26.5981i	0.495368	−	0.858002i
$962$	−23.3205	+	23.3205i	−0.751883	+	0.751883i
$963$		0			0
$964$		−	46.3923i		−	1.49420i
$965$	5.82309	+	21.7321i	0.187452	+	0.699579i
$966$		0			0
$967$	17.8301	−	10.2942i	0.573378	−	0.331040i	−0.185119	−	0.982716i	$-0.559267\pi$
$967$	17.8301	−	10.2942i	0.573378	−	0.331040i	0.758497	+	0.651676i	$0.225934\pi$
$968$	−22.3923	−	6.00000i	−0.719716	−	0.192847i
$969$		0			0
$970$	−14.8756	−	8.58846i	−0.477628	−	0.275759i
$971$	−15.5359	+	15.5359i	−0.498571	+	0.498571i	−0.910993	−	0.412422i	$-0.864683\pi$
$971$	−15.5359	+	15.5359i	−0.498571	+	0.498571i	0.412422	+	0.910993i	$0.364683\pi$
$972$		0			0
$973$	−22.8564	−	22.8564i	−0.732743	−	0.732743i
$974$	7.92820	−	2.12436i	0.254036	−	0.0680687i
$975$		0			0
$976$	12.0000	−	44.7846i	0.384111	−	1.43352i
$977$	22.0622	+	38.2128i	0.705832	+	1.22254i	0.966391	+	0.257078i	$0.0827598\pi$
$977$	22.0622	+	38.2128i	0.705832	+	1.22254i	−0.260559	+	0.965458i	$0.583907\pi$
$978$		0			0
$979$	8.46410	−	2.26795i	0.270514	−	0.0724840i
$980$	0.679492	+	0.679492i	0.0217056	+	0.0217056i
$981$		0			0
$982$		−	20.3397i		−	0.649067i
$983$	−13.8564	−	8.00000i	−0.441951	−	0.255160i	0.262474	−	0.964939i	$-0.415462\pi$
$983$	−13.8564	−	8.00000i	−0.441951	−	0.255160i	−0.704425	+	0.709779i	$0.748795\pi$
$984$		0			0
$985$	17.3205	−	10.0000i	0.551877	−	0.318626i
$986$	9.92820	+	17.1962i	0.316178	+	0.547637i
$987$		0			0
$988$	11.6603	−	20.1962i	0.370962	−	0.642525i
$989$	28.8564	+	28.8564i	0.917580	+	0.917580i
$990$		0			0
$991$	36.6410			1.16394			0.581970	−	0.813210i	$-0.302282\pi$
$991$	36.6410			1.16394			0.581970	+	0.813210i	$0.302282\pi$
$992$	0.784610	+	2.92820i	0.0249114	+	0.0929705i
$993$		0			0
$994$	−10.9282	−	2.92820i	−0.346622	−	0.0928770i
$995$	6.73205	−	25.1244i	0.213420	−	0.796496i
$996$		0			0
$997$	7.87564	+	29.3923i	0.249424	+	0.930864i	0.971108	+	0.238641i	$0.0767018\pi$
$997$	7.87564	+	29.3923i	0.249424	+	0.930864i	−0.721684	+	0.692223i	$0.756632\pi$
$998$	12.7321			0.403026
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.b.397.1		4
3.2	odd	2		144.2.x.c.61.1	yes	4
4.3	odd	2		1728.2.bc.a.721.1		4
9.4	even	3		432.2.y.c.253.1		4
9.5	odd	6		144.2.x.b.13.1	✓	4
12.11	even	2		576.2.bb.c.529.1		4
16.5	even	4		432.2.y.c.181.1		4
16.11	odd	4		1728.2.bc.d.1585.1		4
36.23	even	6		576.2.bb.d.337.1		4
36.31	odd	6		1728.2.bc.d.145.1		4
48.5	odd	4		144.2.x.b.133.1	yes	4
48.11	even	4		576.2.bb.d.241.1		4
144.5	odd	12		144.2.x.c.85.1	yes	4
144.59	even	12		576.2.bb.c.49.1		4
144.85	even	12	inner	432.2.y.b.37.1		4
144.139	odd	12		1728.2.bc.a.1009.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.b.13.1	✓	4	9.5	odd	6
144.2.x.b.133.1	yes	4	48.5	odd	4
144.2.x.c.61.1	yes	4	3.2	odd	2
144.2.x.c.85.1	yes	4	144.5	odd	12
432.2.y.b.37.1		4	144.85	even	12	inner
432.2.y.b.397.1		4	1.1	even	1	trivial
432.2.y.c.181.1		4	16.5	even	4
432.2.y.c.253.1		4	9.4	even	3
576.2.bb.c.49.1		4	144.59	even	12
576.2.bb.c.529.1		4	12.11	even	2
576.2.bb.d.241.1		4	48.11	even	4
576.2.bb.d.337.1		4	36.23	even	6
1728.2.bc.a.721.1		4	4.3	odd	2
1728.2.bc.a.1009.1		4	144.139	odd	12
1728.2.bc.d.145.1		4	36.31	odd	6
1728.2.bc.d.1585.1		4	16.11	odd	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.00000 - 0.267949i) q^{5} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.00000 - 0.267949i) q^{5} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.46410i q^{10} +(-1.13397 - 4.23205i) q^{11} +(0.901924 - 3.36603i) q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +5.73205 q^{17} +(-2.36603 - 2.36603i) q^{19} +(2.00000 - 0.535898i) q^{20} +(-5.36603 + 3.09808i) q^{22} +(4.09808 - 2.36603i) q^{23} +(-3.40192 - 1.96410i) q^{25} -4.92820 q^{26} -5.46410 q^{28} +(-2.36603 + 0.633975i) q^{29} +(-0.267949 - 0.464102i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-2.09808 - 7.83013i) q^{34} +(-2.00000 - 2.00000i) q^{35} +(4.73205 - 4.73205i) q^{37} +(-2.36603 + 4.09808i) q^{38} +(-1.46410 - 2.53590i) q^{40} +(2.59808 - 1.50000i) q^{41} +(2.23205 + 8.33013i) q^{43} +(6.19615 + 6.19615i) q^{44} +(-4.73205 - 4.73205i) q^{46} +(-3.83013 + 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(-1.43782 + 5.36603i) q^{50} +(1.80385 + 6.73205i) q^{52} +(7.46410 - 7.46410i) q^{53} +4.53590i q^{55} +(2.00000 + 7.46410i) q^{56} +(1.73205 + 3.00000i) q^{58} +(-7.33013 - 1.96410i) q^{59} +(11.1962 - 3.00000i) q^{61} +(-0.535898 + 0.535898i) q^{62} +8.00000i q^{64} +(-1.80385 + 3.12436i) q^{65} +(-1.76795 + 6.59808i) q^{67} +(-9.92820 + 5.73205i) q^{68} +(-2.00000 + 3.46410i) q^{70} -2.92820i q^{71} -6.26795i q^{73} +(-8.19615 - 4.73205i) q^{74} +(6.46410 + 1.73205i) q^{76} +(3.09808 - 11.5622i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(-2.92820 + 2.92820i) q^{80} +(-3.00000 - 3.00000i) q^{82} +(1.36603 - 0.366025i) q^{83} +(-5.73205 - 1.53590i) q^{85} +(10.5622 - 6.09808i) q^{86} +(6.19615 - 10.7321i) q^{88} +2.00000i q^{89} +(6.73205 - 6.73205i) q^{91} +(-4.73205 + 8.19615i) q^{92} +(10.4641 + 2.80385i) q^{94} +(1.73205 + 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +(0.464102 - 0.464102i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{5} + 6 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^5 + 6 * q^7 + 8 * q^8	\( 4 q + 2 q^{2} - 4 q^{5} + 6 q^{7} + 8 q^{8} - 8 q^{11} + 14 q^{13} + 4 q^{14} + 8 q^{16} + 16 q^{17} - 6 q^{19} + 8 q^{20} - 18 q^{22} + 6 q^{23} - 24 q^{25} + 8 q^{26} - 8 q^{28} - 6 q^{29} - 8 q^{31} - 8 q^{32} + 2 q^{34} - 8 q^{35} + 12 q^{37} - 6 q^{38} + 8 q^{40} + 2 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{47} - 6 q^{49} - 30 q^{50} + 28 q^{52} + 16 q^{53} + 8 q^{56} - 12 q^{59} + 24 q^{61} - 16 q^{62} - 28 q^{65} - 14 q^{67} - 12 q^{68} - 8 q^{70} - 12 q^{74} + 12 q^{76} + 2 q^{77} - 24 q^{79} + 16 q^{80} - 12 q^{82} + 2 q^{83} - 16 q^{85} + 18 q^{86} + 4 q^{88} + 20 q^{91} - 12 q^{92} + 28 q^{94} - 20 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^5 + 6 * q^7 + 8 * q^8 - 8 * q^11 + 14 * q^13 + 4 * q^14 + 8 * q^16 + 16 * q^17 - 6 * q^19 + 8 * q^20 - 18 * q^22 + 6 * q^23 - 24 * q^25 + 8 * q^26 - 8 * q^28 - 6 * q^29 - 8 * q^31 - 8 * q^32 + 2 * q^34 - 8 * q^35 + 12 * q^37 - 6 * q^38 + 8 * q^40 + 2 * q^43 + 4 * q^44 - 12 * q^46 + 2 * q^47 - 6 * q^49 - 30 * q^50 + 28 * q^52 + 16 * q^53 + 8 * q^56 - 12 * q^59 + 24 * q^61 - 16 * q^62 - 28 * q^65 - 14 * q^67 - 12 * q^68 - 8 * q^70 - 12 * q^74 + 12 * q^76 + 2 * q^77 - 24 * q^79 + 16 * q^80 - 12 * q^82 + 2 * q^83 - 16 * q^85 + 18 * q^86 + 4 * q^88 + 20 * q^91 - 12 * q^92 + 28 * q^94 - 20 * q^97 - 12 * q^98

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