LMFDB - Embedded newform 432.2.y.b.181.1

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			181.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	432.181
Dual form			432.2.y.b.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-1.00000 + 3.73205i) q^{5} +(0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-1.00000 + 3.73205i) q^{5} +(0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +5.46410i q^{10} +(-2.86603 + 0.767949i) q^{11} +(6.09808 + 1.63397i) q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 + 0.633975i) q^{19} +(2.00000 + 7.46410i) q^{20} +(-3.63397 + 2.09808i) q^{22} +(-1.09808 + 0.633975i) q^{23} +(-8.59808 - 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(-0.633975 - 2.36603i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(1.46410 - 5.46410i) q^{32} +(3.09808 - 0.830127i) q^{34} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(5.46410 + 9.46410i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(-1.23205 + 0.330127i) q^{43} +(-4.19615 + 4.19615i) q^{44} +(-1.26795 + 1.26795i) q^{46} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(-13.5622 - 3.63397i) q^{50} +(12.1962 - 3.26795i) q^{52} +(0.535898 + 0.535898i) q^{53} -11.4641i q^{55} +(2.00000 - 0.535898i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(1.33013 - 4.96410i) q^{59} +(0.803848 + 3.00000i) q^{61} +(-7.46410 - 7.46410i) q^{62} -8.00000i q^{64} +(-12.1962 + 21.1244i) q^{65} +(-5.23205 - 1.40192i) q^{67} +(3.92820 - 2.26795i) q^{68} +(-2.00000 + 3.46410i) q^{70} -10.9282i q^{71} +9.73205i q^{73} +(2.19615 + 1.26795i) q^{74} +(-0.464102 + 1.73205i) q^{76} +(-2.09808 - 0.562178i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(10.9282 + 10.9282i) q^{80} +(-3.00000 + 3.00000i) q^{82} +(-0.366025 - 1.36603i) q^{83} +(-2.26795 + 8.46410i) q^{85} +(-1.56218 + 0.901924i) q^{86} +(-4.19615 + 7.26795i) q^{88} -2.00000i q^{89} +(3.26795 + 3.26795i) q^{91} +(-1.26795 + 2.19615i) q^{92} +(3.53590 - 13.1962i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(-6.46410 - 6.46410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	−1.00000	+	3.73205i	−0.447214	+	1.66902i	0.262811	+	0.964847i	$0.415350\pi$
$5$	−1.00000	+	3.73205i	−0.447214	+	1.66902i	−0.710025	+	0.704177i	$0.751316\pi$
$6$		0			0
$7$	0.633975	+	0.366025i	0.239620	+	0.138345i	0.615002	−	0.788526i	$-0.289155\pi$
$7$	0.633975	+	0.366025i	0.239620	+	0.138345i	−0.375382	+	0.926870i	$0.622489\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$			5.46410i			1.72790i
$11$	−2.86603	+	0.767949i	−0.864139	+	0.231545i	−0.663552	−	0.748130i	$-0.730952\pi$
$11$	−2.86603	+	0.767949i	−0.864139	+	0.231545i	−0.200587	+	0.979676i	$0.564285\pi$
$12$		0			0
$13$	6.09808	+	1.63397i	1.69130	+	0.453183i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	6.09808	+	1.63397i	1.69130	+	0.453183i	0.720577	+	0.693375i	$0.243877\pi$
$14$	1.00000	+	0.267949i	0.267261	+	0.0716124i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	2.26795			0.550058			0.275029	−	0.961436i	$-0.411312\pi$
$17$	2.26795			0.550058			0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	−0.633975	+	0.633975i	−0.145444	+	0.145444i	−0.776079	−	0.630635i	$-0.782794\pi$
$19$	−0.633975	+	0.633975i	−0.145444	+	0.145444i	0.630635	+	0.776079i	$0.282794\pi$
$20$	2.00000	+	7.46410i	0.447214	+	1.66902i
$21$		0			0
$22$	−3.63397	+	2.09808i	−0.774766	+	0.447311i
$23$	−1.09808	+	0.633975i	−0.228965	+	0.132193i	−0.610094	−	0.792329i	$-0.708868\pi$
$23$	−1.09808	+	0.633975i	−0.228965	+	0.132193i	0.381130	+	0.924522i	$0.375535\pi$
$24$		0			0
$25$	−8.59808	−	4.96410i	−1.71962	−	0.992820i
$26$	8.92820			1.75096
$27$		0			0
$28$	1.46410			0.276689
$29$	−0.633975	−	2.36603i	−0.117726	−	0.439360i	0.881750	−	0.471717i	$-0.156365\pi$
$29$	−0.633975	−	2.36603i	−0.117726	−	0.439360i	−0.999476	+	0.0323566i	$0.989699\pi$
$30$		0			0
$31$	−3.73205	−	6.46410i	−0.670296	−	1.16099i	−0.977820	−	0.209447i	$-0.932834\pi$
$31$	−3.73205	−	6.46410i	−0.670296	−	1.16099i	0.307524	−	0.951540i	$-0.400500\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$		0			0
$34$	3.09808	−	0.830127i	0.531316	−	0.142366i
$35$	−2.00000	+	2.00000i	−0.338062	+	0.338062i
$36$		0			0
$37$	1.26795	+	1.26795i	0.208450	+	0.208450i	0.803608	−	0.595159i	$-0.202911\pi$
$37$	1.26795	+	1.26795i	0.208450	+	0.208450i	−0.595159	+	0.803608i	$0.702911\pi$
$38$	−0.633975	+	1.09808i	−0.102844	+	0.178131i
$39$		0			0
$40$	5.46410	+	9.46410i	0.863950	+	1.49641i
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$		0			0
$43$	−1.23205	+	0.330127i	−0.187886	+	0.0503439i	−0.351535	−	0.936175i	$-0.614340\pi$
$43$	−1.23205	+	0.330127i	−0.187886	+	0.0503439i	0.163649	+	0.986519i	$0.447674\pi$
$44$	−4.19615	+	4.19615i	−0.632594	+	0.632594i
$45$		0			0
$46$	−1.26795	+	1.26795i	−0.186949	+	0.186949i
$47$	4.83013	−	8.36603i	0.704546	−	1.22031i	−0.262309	−	0.964984i	$-0.584484\pi$
$47$	4.83013	−	8.36603i	0.704546	−	1.22031i	0.966855	−	0.255326i	$-0.0821828\pi$
$48$		0			0
$49$	−3.23205	−	5.59808i	−0.461722	−	0.799725i
$50$	−13.5622	−	3.63397i	−1.91798	−	0.513922i
$51$		0			0
$52$	12.1962	−	3.26795i	1.69130	−	0.453183i
$53$	0.535898	+	0.535898i	0.0736113	+	0.0736113i	0.742954	−	0.669343i	$-0.233424\pi$
$53$	0.535898	+	0.535898i	0.0736113	+	0.0736113i	−0.669343	+	0.742954i	$0.733424\pi$
$54$		0			0
$55$		−	11.4641i		−	1.54582i
$56$	2.00000	−	0.535898i	0.267261	−	0.0716124i
$57$		0			0
$58$	−1.73205	−	3.00000i	−0.227429	−	0.393919i
$59$	1.33013	−	4.96410i	0.173168	−	0.646271i	−0.823689	−	0.567042i	$-0.808088\pi$
$59$	1.33013	−	4.96410i	0.173168	−	0.646271i	0.996856	−	0.0792287i	$-0.0252457\pi$
$60$		0			0
$61$	0.803848	+	3.00000i	0.102922	+	0.384111i	0.998101	−	0.0615961i	$-0.0196191\pi$
$61$	0.803848	+	3.00000i	0.102922	+	0.384111i	−0.895179	+	0.445707i	$0.852952\pi$
$62$	−7.46410	−	7.46410i	−0.947942	−	0.947942i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−12.1962	+	21.1244i	−1.51275	+	2.62015i
$66$		0			0
$67$	−5.23205	−	1.40192i	−0.639197	−	0.171272i	−0.0753572	−	0.997157i	$-0.524010\pi$
$67$	−5.23205	−	1.40192i	−0.639197	−	0.171272i	−0.563840	+	0.825884i	$0.690676\pi$
$68$	3.92820	−	2.26795i	0.476365	−	0.275029i
$69$		0			0
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$		−	10.9282i		−	1.29694i	−0.761241	−	0.648470i	$-0.775409\pi$
$71$		−	10.9282i		−	1.29694i	0.761241	−	0.648470i	$-0.224591\pi$
$72$		0			0
$73$			9.73205i			1.13905i	0.821974	+	0.569525i	$0.192873\pi$
$73$			9.73205i			1.13905i	−0.821974	+	0.569525i	$0.807127\pi$
$74$	2.19615	+	1.26795i	0.255298	+	0.147396i
$75$		0			0
$76$	−0.464102	+	1.73205i	−0.0532361	+	0.198680i
$77$	−2.09808	−	0.562178i	−0.239098	−	0.0640661i
$78$		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	$0.930788\pi$
$80$	10.9282	+	10.9282i	1.22181	+	1.22181i
$81$		0			0
$82$	−3.00000	+	3.00000i	−0.331295	+	0.331295i
$83$	−0.366025	−	1.36603i	−0.0401765	−	0.149941i	0.942924	−	0.333009i	$-0.108064\pi$
$83$	−0.366025	−	1.36603i	−0.0401765	−	0.149941i	−0.983100	+	0.183068i	$0.941397\pi$
$84$		0			0
$85$	−2.26795	+	8.46410i	−0.245994	+	0.918061i
$86$	−1.56218	+	0.901924i	−0.168454	+	0.0972569i
$87$		0			0
$88$	−4.19615	+	7.26795i	−0.447311	+	0.774766i
$89$		−	2.00000i		−	0.212000i	−0.994366	−	0.106000i	$-0.966196\pi$
$89$		−	2.00000i		−	0.212000i	0.994366	−	0.106000i	$-0.0338043\pi$
$90$		0			0
$91$	3.26795	+	3.26795i	0.342574	+	0.342574i
$92$	−1.26795	+	2.19615i	−0.132193	+	0.228965i
$93$		0			0
$94$	3.53590	−	13.1962i	0.364700	−	1.36108i
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$		0			0
$97$	−4.13397	+	7.16025i	−0.419742	+	0.727014i	−0.995913	−	0.0903150i	$-0.971213\pi$
$97$	−4.13397	+	7.16025i	−0.419742	+	0.727014i	0.576172	+	0.817329i	$0.304546\pi$
$98$	−6.46410	−	6.46410i	−0.652973	−	0.652973i
$99$		0			0
$100$	−19.8564			−1.98564
$101$	−7.46410	+	2.00000i	−0.742706	+	0.199007i	−0.610280	−	0.792186i	$-0.708943\pi$
$101$	−7.46410	+	2.00000i	−0.742706	+	0.199007i	−0.132426	+	0.991193i	$0.542277\pi$
$102$		0			0
$103$	7.90192	−	4.56218i	0.778600	−	0.449525i	−0.0573341	−	0.998355i	$-0.518260\pi$
$103$	7.90192	−	4.56218i	0.778600	−	0.449525i	0.835934	+	0.548830i	$0.184927\pi$
$104$	15.4641	−	8.92820i	1.51638	−	0.875482i
$105$		0			0
$106$	0.928203	+	0.535898i	0.0901551	+	0.0520511i
$107$	13.4904	+	13.4904i	1.30416	+	1.30416i	0.925558	+	0.378607i	$0.123597\pi$
$107$	13.4904	+	13.4904i	1.30416	+	1.30416i	0.378607	+	0.925558i	$0.376403\pi$
$108$		0			0
$109$	7.26795	−	7.26795i	0.696143	−	0.696143i	−0.267433	−	0.963576i	$-0.586175\pi$
$109$	7.26795	−	7.26795i	0.696143	−	0.696143i	0.963576	+	0.267433i	$0.0861754\pi$
$110$	−4.19615	−	15.6603i	−0.400087	−	1.49315i
$111$		0			0
$112$	2.53590	−	1.46410i	0.239620	−	0.138345i
$113$	−6.92820	−	12.0000i	−0.651751	−	1.12887i	−0.982698	−	0.185216i	$-0.940702\pi$
$113$	−6.92820	−	12.0000i	−0.651751	−	1.12887i	0.330947	−	0.943649i	$-0.392632\pi$
$114$		0			0
$115$	−1.26795	−	4.73205i	−0.118237	−	0.441266i
$116$	−3.46410	−	3.46410i	−0.321634	−	0.321634i
$117$		0			0
$118$		−	7.26795i		−	0.669069i
$119$	1.43782	+	0.830127i	0.131805	+	0.0760976i
$120$		0			0
$121$	−1.90192	+	1.09808i	−0.172902	+	0.0998251i
$122$	2.19615	+	3.80385i	0.198830	+	0.344384i
$123$		0			0
$124$	−12.9282	−	7.46410i	−1.16099	−	0.670296i
$125$	13.4641	−	13.4641i	1.20427	−	1.20427i
$126$		0			0
$127$	−6.19615			−0.549820			−0.274910	−	0.961470i	$-0.588648\pi$
$127$	−6.19615			−0.549820			−0.274910	+	0.961470i	$0.588648\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$		0			0
$130$	−8.92820	+	33.3205i	−0.783055	+	2.92240i
$131$	3.09808	+	0.830127i	0.270680	+	0.0725285i	0.391606	−	0.920133i	$-0.371920\pi$
$131$	3.09808	+	0.830127i	0.270680	+	0.0725285i	−0.120926	+	0.992662i	$0.538586\pi$
$132$		0			0
$133$	−0.633975	+	0.169873i	−0.0549726	+	0.0147299i
$134$	−7.66025			−0.661745
$135$		0			0
$136$	4.53590	−	4.53590i	0.388950	−	0.388950i
$137$	14.2583	+	8.23205i	1.21817	+	0.703312i	0.964527	−	0.263986i	$-0.0850372\pi$
$137$	14.2583	+	8.23205i	1.21817	+	0.703312i	0.253645	+	0.967297i	$0.418371\pi$
$138$		0			0
$139$	2.42820	−	9.06218i	0.205958	−	0.768644i	−0.783198	−	0.621772i	$-0.786413\pi$
$139$	2.42820	−	9.06218i	0.205958	−	0.768644i	0.989156	−	0.146872i	$-0.0469204\pi$
$140$	−1.46410	+	5.46410i	−0.123739	+	0.461801i
$141$		0			0
$142$	−4.00000	−	14.9282i	−0.335673	−	1.25275i
$143$	−18.7321			−1.56645
$144$		0			0
$145$	9.46410			0.785951
$146$	3.56218	+	13.2942i	0.294808	+	1.10024i
$147$		0			0
$148$	3.46410	+	0.928203i	0.284747	+	0.0762978i
$149$	0.830127	−	3.09808i	0.0680067	−	0.253804i	−0.923550	−	0.383478i	$-0.874726\pi$
$149$	0.830127	−	3.09808i	0.0680067	−	0.253804i	0.991557	+	0.129674i	$0.0413929\pi$
$150$		0			0
$151$	2.36603	+	1.36603i	0.192544	+	0.111166i	0.593173	−	0.805075i	$-0.297875\pi$
$151$	2.36603	+	1.36603i	0.192544	+	0.111166i	−0.400629	+	0.916240i	$0.631208\pi$
$152$			2.53590i			0.205689i
$153$		0			0
$154$	−3.07180			−0.247532
$155$	27.8564	−	7.46410i	2.23748	−	0.599531i
$156$		0			0
$157$	4.73205	+	1.26795i	0.377659	+	0.101193i	0.442655	−	0.896692i	$-0.354037\pi$
$157$	4.73205	+	1.26795i	0.377659	+	0.101193i	−0.0649959	+	0.997886i	$0.520703\pi$
$158$	−4.39230	+	16.3923i	−0.349433	+	1.30410i
$159$		0			0
$160$	18.9282	+	10.9282i	1.49641	+	0.863950i
$161$	−0.928203			−0.0731527
$162$		0			0
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	−0.925944	−	0.377661i	$-0.876728\pi$
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	0.377661	+	0.925944i	$0.376728\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	0.464102	−	0.267949i	0.0359133	−	0.0207345i	−0.481936	−	0.876206i	$-0.660066\pi$
$167$	0.464102	−	0.267949i	0.0359133	−	0.0207345i	0.517849	+	0.855472i	$0.326733\pi$
$168$		0			0
$169$	23.2583	+	13.4282i	1.78910	+	1.03294i
$170$			12.3923i			0.950446i
$171$		0			0
$172$	−1.80385	+	1.80385i	−0.137542	+	0.137542i
$173$	−3.36603	−	12.5622i	−0.255914	−	0.955085i	−0.967580	−	0.252566i	$-0.918725\pi$
$173$	−3.36603	−	12.5622i	−0.255914	−	0.955085i	0.711665	−	0.702519i	$-0.247941\pi$
$174$		0			0
$175$	−3.63397	−	6.29423i	−0.274703	−	0.475799i
$176$	−3.07180	+	11.4641i	−0.231545	+	0.864139i
$177$		0			0
$178$	−0.732051	−	2.73205i	−0.0548695	−	0.204776i
$179$	−11.9282	+	11.9282i	−0.891556	+	0.891556i	−0.994670	−	0.103114i	$-0.967119\pi$
$179$	−11.9282	+	11.9282i	−0.891556	+	0.891556i	0.103114	+	0.994670i	$0.467119\pi$
$180$		0			0
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	0.999990	−	0.00454748i	$-0.00144751\pi$
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	−0.00454748	+	0.999990i	$0.501448\pi$
$182$	5.66025	+	3.26795i	0.419566	+	0.242237i
$183$		0			0
$184$	−0.928203	+	3.46410i	−0.0684280	+	0.255377i
$185$	−6.00000	+	3.46410i	−0.441129	+	0.254686i
$186$		0			0
$187$	−6.50000	+	1.74167i	−0.475327	+	0.127364i
$188$		−	19.3205i		−	1.40909i
$189$		0			0
$190$	−3.46410	−	3.46410i	−0.251312	−	0.251312i
$191$	−7.02628	+	12.1699i	−0.508404	+	0.880581i	0.491549	+	0.870850i	$0.336431\pi$
$191$	−7.02628	+	12.1699i	−0.508404	+	0.880581i	−0.999953	+	0.00973114i	$0.996902\pi$
$192$		0			0
$193$	−9.13397	−	15.8205i	−0.657478	−	1.13879i	−0.981266	−	0.192656i	$-0.938290\pi$
$193$	−9.13397	−	15.8205i	−0.657478	−	1.13879i	0.323789	−	0.946129i	$-0.395043\pi$
$194$	−3.02628	+	11.2942i	−0.217274	+	0.810878i
$195$		0			0
$196$	−11.1962	−	6.46410i	−0.799725	−	0.461722i
$197$	3.66025	+	3.66025i	0.260782	+	0.260782i	0.825372	−	0.564590i	$-0.190966\pi$
$197$	3.66025	+	3.66025i	0.260782	+	0.260782i	−0.564590	+	0.825372i	$0.690966\pi$
$198$		0			0
$199$		−	0.875644i		−	0.0620728i	−0.999518	−	0.0310364i	$-0.990119\pi$
$199$		−	0.875644i		−	0.0620728i	0.999518	−	0.0310364i	$-0.00988078\pi$
$200$	−27.1244	+	7.26795i	−1.91798	+	0.513922i
$201$		0			0
$202$	−9.46410	+	5.46410i	−0.665892	+	0.384453i
$203$	0.464102	−	1.73205i	0.0325735	−	0.121566i
$204$		0			0
$205$	−3.00000	−	11.1962i	−0.209529	−	0.781973i
$206$	9.12436	−	9.12436i	0.635724	−	0.635724i
$207$		0			0
$208$	17.8564	−	17.8564i	1.23812	−	1.23812i
$209$	1.33013	−	2.30385i	0.0920068	−	0.159360i
$210$		0			0
$211$	4.09808	+	1.09808i	0.282123	+	0.0755947i	0.397106	−	0.917773i	$-0.370015\pi$
$211$	4.09808	+	1.09808i	0.282123	+	0.0755947i	−0.114983	+	0.993367i	$0.536681\pi$
$212$	1.46410	+	0.392305i	0.100555	+	0.0269436i
$213$		0			0
$214$	23.3660	+	13.4904i	1.59727	+	0.922183i
$215$		−	4.92820i		−	0.336101i
$216$		0			0
$217$		−	5.46410i		−	0.370927i
$218$	7.26795	−	12.5885i	0.492248	−	0.852598i
$219$		0			0
$220$	−11.4641	−	19.8564i	−0.772910	−	1.33872i
$221$	13.8301	+	3.70577i	0.930315	+	0.249277i
$222$		0			0
$223$	11.0263	−	19.0981i	0.738374	−	1.27890i	−0.214853	−	0.976646i	$-0.568927\pi$
$223$	11.0263	−	19.0981i	0.738374	−	1.27890i	0.953227	−	0.302255i	$-0.0977395\pi$
$224$	2.92820	−	2.92820i	0.195649	−	0.195649i
$225$		0			0
$226$	−13.8564	−	13.8564i	−0.921714	−	0.921714i
$227$	−3.86603	−	14.4282i	−0.256597	−	0.957633i	−0.967195	−	0.254035i	$-0.918242\pi$
$227$	−3.86603	−	14.4282i	−0.256597	−	0.957633i	0.710598	−	0.703598i	$-0.248425\pi$
$228$		0			0
$229$	−1.83013	+	6.83013i	−0.120938	+	0.451347i	−0.999662	−	0.0259823i	$-0.991729\pi$
$229$	−1.83013	+	6.83013i	−0.120938	+	0.451347i	0.878724	+	0.477330i	$0.158395\pi$
$230$	−3.46410	−	6.00000i	−0.228416	−	0.395628i
$231$		0			0
$232$	−6.00000	−	3.46410i	−0.393919	−	0.227429i
$233$			7.19615i			0.471436i	0.971822	+	0.235718i	$0.0757441\pi$
$233$			7.19615i			0.471436i	−0.971822	+	0.235718i	$0.924256\pi$
$234$		0			0
$235$	26.3923	+	26.3923i	1.72164	+	1.72164i
$236$	−2.66025	−	9.92820i	−0.173168	−	0.646271i
$237$		0			0
$238$	2.26795	+	0.607695i	0.147009	+	0.0393910i
$239$	13.0981	+	22.6865i	0.847244	+	1.46747i	0.883658	+	0.468133i	$0.155073\pi$
$239$	13.0981	+	22.6865i	0.847244	+	1.46747i	−0.0364139	+	0.999337i	$0.511593\pi$
$240$		0			0
$241$	−6.40192	+	11.0885i	−0.412384	+	0.714270i	−0.995150	−	0.0983699i	$-0.968637\pi$
$241$	−6.40192	+	11.0885i	−0.412384	+	0.714270i	0.582766	+	0.812640i	$0.301971\pi$
$242$	−2.19615	+	2.19615i	−0.141174	+	0.141174i
$243$		0			0
$244$	4.39230	+	4.39230i	0.281189	+	0.281189i
$245$	24.1244	−	6.46410i	1.54125	−	0.412976i
$246$		0			0
$247$	−4.90192	+	2.83013i	−0.311902	+	0.180077i
$248$	−20.3923	−	5.46410i	−1.29491	−	0.346971i
$249$		0			0
$250$	13.4641	−	23.3205i	0.851545	−	1.47492i
$251$	−2.83013	−	2.83013i	−0.178636	−	0.178636i	0.612125	−	0.790761i	$-0.290315\pi$
$251$	−2.83013	−	2.83013i	−0.178636	−	0.178636i	−0.790761	+	0.612125i	$0.790315\pi$
$252$		0			0
$253$	2.66025	−	2.66025i	0.167249	−	0.167249i
$254$	−8.46410	+	2.26795i	−0.531085	+	0.142304i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	4.42820	+	7.66987i	0.276224	+	0.478434i	0.970443	−	0.241330i	$-0.0775836\pi$
$257$	4.42820	+	7.66987i	0.276224	+	0.478434i	−0.694219	+	0.719763i	$0.744250\pi$
$258$		0			0
$259$	0.339746	+	1.26795i	0.0211108	+	0.0787865i
$260$			48.7846i			3.02549i
$261$		0			0
$262$	4.53590			0.280229
$263$	−23.4904	−	13.5622i	−1.44848	−	0.836280i	−0.450088	−	0.892984i	$-0.648607\pi$
$263$	−23.4904	−	13.5622i	−1.44848	−	0.836280i	−0.998391	+	0.0567045i	$0.981941\pi$
$264$		0			0
$265$	−2.53590	+	1.46410i	−0.155779	+	0.0899390i
$266$	−0.803848	+	0.464102i	−0.0492871	+	0.0284559i
$267$		0			0
$268$	−10.4641	+	2.80385i	−0.639197	+	0.171272i
$269$	−4.73205	+	4.73205i	−0.288518	+	0.288518i	−0.836494	−	0.547976i	$-0.815399\pi$
$269$	−4.73205	+	4.73205i	−0.288518	+	0.288518i	0.547976	+	0.836494i	$0.315399\pi$
$270$		0			0
$271$	20.3923			1.23874			0.619372	−	0.785098i	$-0.287387\pi$
$271$	20.3923			1.23874			0.619372	+	0.785098i	$0.287387\pi$
$272$	4.53590	−	7.85641i	0.275029	−	0.476365i
$273$		0			0
$274$	22.4904	+	6.02628i	1.35869	+	0.364061i
$275$	28.4545	+	7.62436i	1.71587	+	0.459766i
$276$		0			0
$277$	15.7583	−	4.22243i	0.946826	−	0.253701i	0.247811	−	0.968808i	$-0.420289\pi$
$277$	15.7583	−	4.22243i	0.946826	−	0.253701i	0.699015	+	0.715107i	$0.253622\pi$
$278$		−	13.2679i		−	0.795759i
$279$		0			0
$280$			8.00000i			0.478091i
$281$	−8.66025	−	5.00000i	−0.516627	−	0.298275i	0.218926	−	0.975741i	$-0.429745\pi$
$281$	−8.66025	−	5.00000i	−0.516627	−	0.298275i	−0.735554	+	0.677466i	$0.763078\pi$
$282$		0			0
$283$	−7.43782	+	27.7583i	−0.442133	+	1.65006i	0.281265	+	0.959630i	$0.409246\pi$
$283$	−7.43782	+	27.7583i	−0.442133	+	1.65006i	−0.723398	+	0.690431i	$0.757421\pi$
$284$	−10.9282	−	18.9282i	−0.648470	−	1.12318i
$285$		0			0
$286$	−25.5885	+	6.85641i	−1.51308	+	0.405428i
$287$	−2.19615			−0.129635
$288$		0			0
$289$	−11.8564			−0.697436
$290$	12.9282	−	3.46410i	0.759170	−	0.203419i
$291$		0			0
$292$	9.73205	+	16.8564i	0.569525	+	0.986447i
$293$	3.63397	−	13.5622i	0.212299	−	0.792311i	−0.774801	−	0.632205i	$-0.782150\pi$
$293$	3.63397	−	13.5622i	0.212299	−	0.792311i	0.987100	−	0.160106i	$-0.0511834\pi$
$294$		0			0
$295$	17.1962	+	9.92820i	1.00120	+	0.578042i
$296$	5.07180			0.294792
$297$		0			0
$298$		−	4.53590i		−	0.262758i
$299$	−7.73205	+	2.07180i	−0.447156	+	0.119815i
$300$		0			0
$301$	−0.901924	−	0.241670i	−0.0519860	−	0.0139296i
$302$	3.73205	+	1.00000i	0.214755	+	0.0575435i
$303$		0			0
$304$	0.928203	+	3.46410i	0.0532361	+	0.198680i
$305$	−12.0000			−0.687118
$306$		0			0
$307$	−16.0263	+	16.0263i	−0.914668	+	0.914668i	−0.996635	−	0.0819670i	$-0.973880\pi$
$307$	−16.0263	+	16.0263i	−0.914668	+	0.914668i	0.0819670	+	0.996635i	$0.473880\pi$
$308$	−4.19615	+	1.12436i	−0.239098	+	0.0640661i
$309$		0			0
$310$	35.3205	−	20.3923i	2.00607	−	1.15821i
$311$	13.9019	−	8.02628i	0.788306	−	0.455129i	−0.0510600	−	0.998696i	$-0.516260\pi$
$311$	13.9019	−	8.02628i	0.788306	−	0.455129i	0.839366	+	0.543567i	$0.182927\pi$
$312$		0			0
$313$	−24.6506	−	14.2321i	−1.39334	−	0.804443i	−0.399653	−	0.916666i	$-0.630869\pi$
$313$	−24.6506	−	14.2321i	−1.39334	−	0.804443i	−0.993683	+	0.112223i	$0.964203\pi$
$314$	6.92820			0.390981
$315$		0			0
$316$			24.0000i			1.35011i
$317$	8.43782	+	31.4904i	0.473915	+	1.76868i	0.625492	+	0.780231i	$0.284898\pi$
$317$	8.43782	+	31.4904i	0.473915	+	1.76868i	−0.151577	+	0.988445i	$0.548435\pi$
$318$		0			0
$319$	3.63397	+	6.29423i	0.203464	+	0.352409i
$320$	29.8564	+	8.00000i	1.66902	+	0.447214i
$321$		0			0
$322$	−1.26795	+	0.339746i	−0.0706600	+	0.0189333i
$323$	−1.43782	+	1.43782i	−0.0800026	+	0.0800026i
$324$		0			0
$325$	−44.3205	−	44.3205i	−2.45846	−	2.45846i
$326$	−7.00000	+	12.1244i	−0.387694	+	0.671506i
$327$		0			0
$328$	−2.19615	+	8.19615i	−0.121262	+	0.452557i
$329$	6.12436	−	3.53590i	0.337647	−	0.194940i
$330$		0			0
$331$	−19.0263	+	5.09808i	−1.04578	+	0.280216i	−0.740506	−	0.672049i	$-0.765414\pi$
$331$	−19.0263	+	5.09808i	−1.04578	+	0.280216i	−0.305273	+	0.952265i	$0.598748\pi$
$332$	−2.00000	−	2.00000i	−0.109764	−	0.109764i
$333$		0			0
$334$	0.535898	−	0.535898i	0.0293231	−	0.0293231i
$335$	10.4641	−	18.1244i	0.571715	−	0.990239i
$336$		0			0
$337$	−11.8923	−	20.5981i	−0.647815	−	1.12205i	−0.983644	−	0.180126i	$-0.942350\pi$
$337$	−11.8923	−	20.5981i	−0.647815	−	1.12205i	0.335829	−	0.941923i	$-0.390984\pi$
$338$	36.6865	+	9.83013i	1.99548	+	0.534688i
$339$		0			0
$340$	4.53590	+	16.9282i	0.245994	+	0.918061i
$341$	15.6603	+	15.6603i	0.848050	+	0.848050i
$342$		0			0
$343$		−	9.85641i		−	0.532196i
$344$	−1.80385	+	3.12436i	−0.0972569	+	0.168454i
$345$		0			0
$346$	−9.19615	−	15.9282i	−0.494388	−	0.856306i
$347$	−6.62436	+	24.7224i	−0.355614	+	1.32717i	0.524096	+	0.851659i	$0.324403\pi$
$347$	−6.62436	+	24.7224i	−0.355614	+	1.32717i	−0.879710	+	0.475510i	$0.842263\pi$
$348$		0			0
$349$	2.07180	+	7.73205i	0.110901	+	0.413887i	0.998948	−	0.0458657i	$-0.0146046\pi$
$349$	2.07180	+	7.73205i	0.110901	+	0.413887i	−0.888047	+	0.459753i	$0.847938\pi$
$350$	−7.26795	−	7.26795i	−0.388488	−	0.388488i
$351$		0			0
$352$			16.7846i			0.894623i
$353$	10.1603	−	17.5981i	0.540776	−	0.936651i	−0.458084	−	0.888909i	$-0.651464\pi$
$353$	10.1603	−	17.5981i	0.540776	−	0.936651i	0.998860	−	0.0477421i	$-0.0152026\pi$
$354$		0			0
$355$	40.7846	+	10.9282i	2.16462	+	0.580009i
$356$	−2.00000	−	3.46410i	−0.106000	−	0.183597i
$357$		0			0
$358$	−11.9282	+	20.6603i	−0.630425	+	1.09193i
$359$			14.7321i			0.777528i	0.921337	+	0.388764i	$0.127098\pi$
$359$			14.7321i			0.777528i	−0.921337	+	0.388764i	$0.872902\pi$
$360$		0			0
$361$			18.1962i			0.957692i
$362$	23.1962	+	13.3923i	1.21916	+	0.703884i
$363$		0			0
$364$	8.92820	+	2.39230i	0.467965	+	0.125391i
$365$	−36.3205	−	9.73205i	−1.90110	−	0.509399i
$366$		0			0
$367$	−10.1244	+	17.5359i	−0.528487	+	0.915366i	0.470961	+	0.882154i	$0.343907\pi$
$367$	−10.1244	+	17.5359i	−0.528487	+	0.915366i	−0.999448	+	0.0332125i	$0.989426\pi$
$368$			5.07180i			0.264386i
$369$		0			0
$370$	−6.92820	+	6.92820i	−0.360180	+	0.360180i
$371$	0.143594	+	0.535898i	0.00745501	+	0.0278225i
$372$		0			0
$373$	1.50962	−	5.63397i	0.0781651	−	0.291716i	−0.915767	−	0.401709i	$-0.868416\pi$
$373$	1.50962	−	5.63397i	0.0781651	−	0.291716i	0.993932	+	0.109993i	$0.0350829\pi$
$374$	−8.24167	+	4.75833i	−0.426167	+	0.246047i
$375$		0			0
$376$	−7.07180	−	26.3923i	−0.364700	−	1.36108i
$377$		−	15.4641i		−	0.796442i
$378$		0			0
$379$	−18.7583	−	18.7583i	−0.963551	−	0.963551i	0.0358080	−	0.999359i	$-0.488600\pi$
$379$	−18.7583	−	18.7583i	−0.963551	−	0.963551i	−0.999359	+	0.0358080i	$0.988600\pi$
$380$	−6.00000	−	3.46410i	−0.307794	−	0.177705i
$381$		0			0
$382$	−5.14359	+	19.1962i	−0.263169	+	0.982161i
$383$	3.26795	+	5.66025i	0.166984	+	0.289225i	0.937358	−	0.348367i	$-0.113264\pi$
$383$	3.26795	+	5.66025i	0.166984	+	0.289225i	−0.770374	+	0.637593i	$0.779930\pi$
$384$		0			0
$385$	4.19615	−	7.26795i	0.213856	−	0.370409i
$386$	−18.2679	−	18.2679i	−0.929814	−	0.929814i
$387$		0			0
$388$			16.5359i			0.839483i
$389$	−10.2942	+	2.75833i	−0.521938	+	0.139853i	−0.510163	−	0.860078i	$-0.670415\pi$
$389$	−10.2942	+	2.75833i	−0.521938	+	0.139853i	−0.0117752	+	0.999931i	$0.503748\pi$
$390$		0			0
$391$	−2.49038	+	1.43782i	−0.125944	+	0.0727138i
$392$	−17.6603	−	4.73205i	−0.891978	−	0.239005i
$393$		0			0
$394$	6.33975	+	3.66025i	0.319392	+	0.184401i
$395$	−32.7846	−	32.7846i	−1.64957	−	1.64957i
$396$		0			0
$397$	−12.7321	+	12.7321i	−0.639003	+	0.639003i	−0.950310	−	0.311306i	$-0.899233\pi$
$397$	−12.7321	+	12.7321i	−0.639003	+	0.639003i	0.311306	+	0.950310i	$0.399233\pi$
$398$	−0.320508	−	1.19615i	−0.0160656	−	0.0599577i
$399$		0			0
$400$	−34.3923	+	19.8564i	−1.71962	+	0.992820i
$401$	−13.7942	−	23.8923i	−0.688851	−	1.19312i	−0.972210	−	0.234111i	$-0.924782\pi$
$401$	−13.7942	−	23.8923i	−0.688851	−	1.19312i	0.283359	−	0.959014i	$-0.408551\pi$
$402$		0			0
$403$	−12.1962	−	45.5167i	−0.607534	−	2.26735i
$404$	−10.9282	+	10.9282i	−0.543698	+	0.543698i
$405$		0			0
$406$		−	2.53590i		−	0.125855i
$407$	−4.60770	−	2.66025i	−0.228395	−	0.131864i
$408$		0			0
$409$	26.1340	−	15.0885i	1.29224	−	0.746076i	0.313191	−	0.949690i	$-0.398602\pi$
$409$	26.1340	−	15.0885i	1.29224	−	0.746076i	0.979051	+	0.203614i	$0.0652688\pi$
$410$	−8.19615	−	14.1962i	−0.404779	−	0.701098i
$411$		0			0
$412$	9.12436	−	15.8038i	0.449525	−	0.778600i
$413$	2.66025	−	2.66025i	0.130903	−	0.130903i
$414$		0			0
$415$	5.46410			0.268222
$416$	17.8564	−	30.9282i	0.875482	−	1.51638i
$417$		0			0
$418$	0.973721	−	3.63397i	0.0476262	−	0.177744i
$419$	−31.2224	−	8.36603i	−1.52532	−	0.408707i	−0.603828	−	0.797115i	$-0.706359\pi$
$419$	−31.2224	−	8.36603i	−1.52532	−	0.408707i	−0.921488	+	0.388408i	$0.873025\pi$
$420$		0			0
$421$	−2.19615	+	0.588457i	−0.107034	+	0.0286797i	−0.311938	−	0.950102i	$-0.600978\pi$
$421$	−2.19615	+	0.588457i	−0.107034	+	0.0286797i	0.204905	+	0.978782i	$0.434312\pi$
$422$	6.00000			0.292075
$423$		0			0
$424$	2.14359			0.104102
$425$	−19.5000	−	11.2583i	−0.945889	−	0.546109i
$426$		0			0
$427$	−0.588457	+	2.19615i	−0.0284774	+	0.106279i
$428$	36.8564	+	9.87564i	1.78152	+	0.477357i
$429$		0			0
$430$	−1.80385	−	6.73205i	−0.0869893	−	0.324648i
$431$	5.80385			0.279562			0.139781	−	0.990182i	$-0.455360\pi$
$431$	5.80385			0.279562			0.139781	+	0.990182i	$0.455360\pi$
$432$		0			0
$433$	−2.26795			−0.108991			−0.0544953	−	0.998514i	$-0.517355\pi$
$433$	−2.26795			−0.108991			−0.0544953	+	0.998514i	$0.517355\pi$
$434$	−2.00000	−	7.46410i	−0.0960031	−	0.358288i
$435$		0			0
$436$	5.32051	−	19.8564i	0.254806	−	0.950949i
$437$	0.294229	−	1.09808i	0.0140749	−	0.0525281i
$438$		0			0
$439$	4.85641	+	2.80385i	0.231784	+	0.133820i	0.611395	−	0.791326i	$-0.290609\pi$
$439$	4.85641	+	2.80385i	0.231784	+	0.133820i	−0.379611	+	0.925146i	$0.623942\pi$
$440$	−22.9282	−	22.9282i	−1.09306	−	1.09306i
$441$		0			0
$442$	20.2487			0.963133
$443$	−19.6244	+	5.25833i	−0.932381	+	0.249831i	−0.692870	−	0.721063i	$-0.743654\pi$
$443$	−19.6244	+	5.25833i	−0.932381	+	0.249831i	−0.239511	+	0.970894i	$0.576987\pi$
$444$		0			0
$445$	7.46410	+	2.00000i	0.353832	+	0.0948091i
$446$	8.07180	−	30.1244i	0.382211	−	1.42643i
$447$		0			0
$448$	2.92820	−	5.07180i	0.138345	−	0.239620i
$449$	20.6603			0.975018			0.487509	−	0.873118i	$-0.337906\pi$
$449$	20.6603			0.975018			0.487509	+	0.873118i	$0.337906\pi$
$450$		0			0
$451$	6.29423	−	6.29423i	0.296384	−	0.296384i
$452$	−24.0000	−	13.8564i	−1.12887	−	0.651751i
$453$		0			0
$454$	−10.5622	−	18.2942i	−0.495708	−	0.858591i
$455$	−15.4641	+	8.92820i	−0.724968	+	0.418561i
$456$		0			0
$457$	−20.2583	−	11.6962i	−0.947645	−	0.547123i	−0.0552962	−	0.998470i	$-0.517610\pi$
$457$	−20.2583	−	11.6962i	−0.947645	−	0.547123i	−0.892348	+	0.451347i	$0.850944\pi$
$458$			10.0000i			0.467269i
$459$		0			0
$460$	−6.92820	−	6.92820i	−0.323029	−	0.323029i
$461$	0.686533	+	2.56218i	0.0319751	+	0.119333i	0.980069	−	0.198659i	$-0.0636585\pi$
$461$	0.686533	+	2.56218i	0.0319751	+	0.119333i	−0.948094	+	0.317991i	$0.896992\pi$
$462$		0			0
$463$	−9.19615	−	15.9282i	−0.427381	−	0.740246i	0.569258	−	0.822159i	$-0.307231\pi$
$463$	−9.19615	−	15.9282i	−0.427381	−	0.740246i	−0.996640	+	0.0819125i	$0.973897\pi$
$464$	−9.46410	−	2.53590i	−0.439360	−	0.117726i
$465$		0			0
$466$	2.63397	+	9.83013i	0.122017	+	0.455372i
$467$	−4.36603	+	4.36603i	−0.202036	+	0.202036i	−0.800872	−	0.598836i	$-0.795630\pi$
$467$	−4.36603	+	4.36603i	−0.202036	+	0.202036i	0.598836	+	0.800872i	$0.295630\pi$
$468$		0			0
$469$	−2.80385	−	2.80385i	−0.129470	−	0.129470i
$470$	45.7128	+	26.3923i	2.10857	+	1.21739i
$471$		0			0
$472$	−7.26795	−	12.5885i	−0.334534	−	0.579431i
$473$	3.27757	−	1.89230i	0.150703	−	0.0870083i
$474$		0			0
$475$	8.59808	−	2.30385i	0.394507	−	0.105708i
$476$	3.32051			0.152195
$477$		0			0
$478$	26.1962	+	26.1962i	1.19818	+	1.19818i
$479$	−12.8301	+	22.2224i	−0.586223	+	1.01537i	0.408498	+	0.912759i	$0.366053\pi$
$479$	−12.8301	+	22.2224i	−0.586223	+	1.01537i	−0.994722	+	0.102610i	$0.967281\pi$
$480$		0			0
$481$	5.66025	+	9.80385i	0.258085	+	0.447017i
$482$	−4.68653	+	17.4904i	−0.213466	+	0.796665i
$483$		0			0
$484$	−2.19615	+	3.80385i	−0.0998251	+	0.172902i
$485$	−22.5885	−	22.5885i	−1.02569	−	1.02569i
$486$		0			0
$487$		−	16.1962i		−	0.733918i	−0.930237	−	0.366959i	$-0.880399\pi$
$487$		−	16.1962i		−	0.733918i	0.930237	−	0.366959i	$-0.119601\pi$
$488$	7.60770	+	4.39230i	0.344384	+	0.198830i
$489$		0			0
$490$	30.5885	−	17.6603i	1.38185	−	0.797809i
$491$	−6.89230	+	25.7224i	−0.311045	+	1.16084i	0.616570	+	0.787300i	$0.288522\pi$
$491$	−6.89230	+	25.7224i	−0.311045	+	1.16084i	−0.927615	+	0.373537i	$0.878145\pi$
$492$		0			0
$493$	−1.43782	−	5.36603i	−0.0647563	−	0.241674i
$494$	−5.66025	+	5.66025i	−0.254667	+	0.254667i
$495$		0			0
$496$	−29.8564			−1.34059
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$		0			0
$499$	6.33013	+	1.69615i	0.283375	+	0.0759302i	0.397707	−	0.917512i	$-0.369806\pi$
$499$	6.33013	+	1.69615i	0.283375	+	0.0759302i	−0.114332	+	0.993443i	$0.536473\pi$
$500$	9.85641	−	36.7846i	0.440792	−	1.64506i
$501$		0			0
$502$	−4.90192	−	2.83013i	−0.218784	−	0.126315i
$503$			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
$505$		−	29.8564i		−	1.32859i
$506$	2.66025	−	4.60770i	0.118263	−	0.204837i
$507$		0			0
$508$	−10.7321	+	6.19615i	−0.476158	+	0.274910i
$509$	−16.9282	−	4.53590i	−0.750329	−	0.201050i	−0.136665	−	0.990617i	$-0.543638\pi$
$509$	−16.9282	−	4.53590i	−0.750329	−	0.201050i	−0.613664	+	0.789567i	$0.710305\pi$
$510$		0			0
$511$	−3.56218	+	6.16987i	−0.157581	+	0.272939i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	8.85641	+	8.85641i	0.390639	+	0.390639i
$515$	9.12436	+	34.0526i	0.402067	+	1.50054i
$516$		0			0
$517$	−7.41858	+	27.6865i	−0.326269	+	1.21765i
$518$	0.928203	+	1.60770i	0.0407829	+	0.0706381i
$519$		0			0
$520$	17.8564	+	66.6410i	0.783055	+	2.92240i
$521$			13.0000i			0.569540i	0.958596	+	0.284770i	$0.0919173\pi$
$521$			13.0000i			0.569540i	−0.958596	+	0.284770i	$0.908083\pi$
$522$		0			0
$523$	−14.4641	−	14.4641i	−0.632471	−	0.632471i	0.316216	−	0.948687i	$-0.397588\pi$
$523$	−14.4641	−	14.4641i	−0.632471	−	0.632471i	−0.948687	+	0.316216i	$0.897588\pi$
$524$	6.19615	−	1.66025i	0.270680	−	0.0725285i
$525$		0			0
$526$	−37.0526	−	9.92820i	−1.61557	−	0.432890i
$527$	−8.46410	−	14.6603i	−0.368702	−	0.638611i
$528$		0			0
$529$	−10.6962	+	18.5263i	−0.465050	+	0.805490i
$530$	−2.92820	+	2.92820i	−0.127193	+	0.127193i
$531$		0			0
$532$	−0.928203	+	0.928203i	−0.0402427	+	0.0402427i
$533$	−18.2942	+	4.90192i	−0.792411	+	0.212326i
$534$		0			0
$535$	−63.8372	+	36.8564i	−2.75992	+	1.59344i
$536$	−13.2679	+	7.66025i	−0.573088	+	0.330873i
$537$		0			0
$538$	−4.73205	+	8.19615i	−0.204013	+	0.353361i
$539$	13.5622	+	13.5622i	0.584164	+	0.584164i
$540$		0			0
$541$	−8.19615	+	8.19615i	−0.352380	+	0.352380i	−0.860994	−	0.508614i	$-0.830158\pi$
$541$	−8.19615	+	8.19615i	−0.352380	+	0.352380i	0.508614	+	0.860994i	$0.330158\pi$
$542$	27.8564	−	7.46410i	1.19654	−	0.320611i
$543$		0			0
$544$	3.32051	−	12.3923i	0.142366	−	0.531316i
$545$	19.8564	+	34.3923i	0.850555	+	1.47320i
$546$		0			0
$547$	8.37564	+	31.2583i	0.358117	+	1.33651i	0.876517	+	0.481371i	$0.159861\pi$
$547$	8.37564	+	31.2583i	0.358117	+	1.33651i	−0.518400	+	0.855138i	$0.673472\pi$
$548$	32.9282			1.40662
$549$		0			0
$550$	41.6603			1.77640
$551$	1.90192	+	1.09808i	0.0810247	+	0.0467796i
$552$		0			0
$553$	−7.60770	+	4.39230i	−0.323512	+	0.186780i
$554$	19.9808	−	11.5359i	0.848901	−	0.490113i
$555$		0			0
$556$	−4.85641	−	18.1244i	−0.205958	−	0.768644i
$557$	25.1962	−	25.1962i	1.06760	−	1.06760i	0.0700519	−	0.997543i	$-0.477684\pi$
$557$	25.1962	−	25.1962i	1.06760	−	1.06760i	0.997543	−	0.0700519i	$-0.0223165\pi$
$558$		0			0
$559$	−8.05256			−0.340587
$560$	2.92820	+	10.9282i	0.123739	+	0.461801i
$561$		0			0
$562$	−13.6603	−	3.66025i	−0.576223	−	0.154398i
$563$	3.76795	+	1.00962i	0.158800	+	0.0425504i	0.337343	−	0.941382i	$-0.390472\pi$
$563$	3.76795	+	1.00962i	0.158800	+	0.0425504i	−0.178543	+	0.983932i	$0.557138\pi$
$564$		0			0
$565$	51.7128	−	13.8564i	2.17557	−	0.582943i
$566$			40.6410i			1.70827i
$567$		0			0
$568$	−21.8564	−	21.8564i	−0.917074	−	0.917074i
$569$	23.5981	+	13.6244i	0.989283	+	0.571163i	0.905060	−	0.425284i	$-0.139826\pi$
$569$	23.5981	+	13.6244i	0.989283	+	0.571163i	0.0842230	+	0.996447i	$0.473159\pi$
$570$		0			0
$571$	5.33013	−	19.8923i	0.223059	−	0.832467i	−0.760114	−	0.649790i	$-0.774857\pi$
$571$	5.33013	−	19.8923i	0.223059	−	0.832467i	0.983173	−	0.182677i	$-0.0584764\pi$
$572$	−32.4449	+	18.7321i	−1.35659	+	0.783226i
$573$		0			0
$574$	−3.00000	+	0.803848i	−0.125218	+	0.0335519i
$575$	12.5885			0.524975
$576$		0			0
$577$	35.7846			1.48973			0.744866	−	0.667214i	$-0.232513\pi$
$577$	35.7846			1.48973			0.744866	+	0.667214i	$0.232513\pi$
$578$	−16.1962	+	4.33975i	−0.673671	+	0.180510i
$579$		0			0
$580$	16.3923	−	9.46410i	0.680653	−	0.392975i
$581$	0.267949	−	1.00000i	0.0111164	−	0.0414870i
$582$		0			0
$583$	−1.94744	−	1.12436i	−0.0806548	−	0.0465661i
$584$	19.4641	+	19.4641i	0.805430	+	0.805430i
$585$		0			0
$586$		−	19.8564i		−	0.820261i
$587$	−3.76795	+	1.00962i	−0.155520	+	0.0416714i	−0.335739	−	0.941955i	$-0.608986\pi$
$587$	−3.76795	+	1.00962i	−0.155520	+	0.0416714i	0.180219	+	0.983626i	$0.442319\pi$
$588$		0			0
$589$	6.46410	+	1.73205i	0.266349	+	0.0713679i
$590$	27.1244	+	7.26795i	1.11669	+	0.299217i
$591$		0			0
$592$	6.92820	−	1.85641i	0.284747	−	0.0762978i
$593$	−10.5359			−0.432657			−0.216329	−	0.976321i	$-0.569408\pi$
$593$	−10.5359			−0.432657			−0.216329	+	0.976321i	$0.569408\pi$
$594$		0			0
$595$	−4.53590	+	4.53590i	−0.185954	+	0.185954i
$596$	−1.66025	−	6.19615i	−0.0680067	−	0.253804i
$597$		0			0
$598$	−9.80385	+	5.66025i	−0.400909	+	0.231465i
$599$	23.3205	−	13.4641i	0.952850	−	0.550128i	0.0588850	−	0.998265i	$-0.481245\pi$
$599$	23.3205	−	13.4641i	0.952850	−	0.550128i	0.893965	+	0.448136i	$0.147912\pi$
$600$		0			0
$601$	17.5526	+	10.1340i	0.715984	+	0.413373i	0.813273	−	0.581883i	$-0.197684\pi$
$601$	17.5526	+	10.1340i	0.715984	+	0.413373i	−0.0972889	+	0.995256i	$0.531017\pi$
$602$	−1.32051			−0.0538199
$603$		0			0
$604$	5.46410			0.222331
$605$	−2.19615	−	8.19615i	−0.0892863	−	0.333221i
$606$		0			0
$607$	22.5885	+	39.1244i	0.916837	+	1.58801i	0.804189	+	0.594374i	$0.202600\pi$
$607$	22.5885	+	39.1244i	0.916837	+	1.58801i	0.112648	+	0.993635i	$0.464067\pi$
$608$	2.53590	+	4.39230i	0.102844	+	0.178131i
$609$		0			0
$610$	−16.3923	+	4.39230i	−0.663705	+	0.177839i
$611$	43.1244	−	43.1244i	1.74462	−	1.74462i
$612$		0			0
$613$	1.66025	+	1.66025i	0.0670570	+	0.0670570i	0.739840	−	0.672783i	$-0.234901\pi$
$613$	1.66025	+	1.66025i	0.0670570	+	0.0670570i	−0.672783	+	0.739840i	$0.734901\pi$
$614$	−16.0263	+	27.7583i	−0.646768	+	1.12024i
$615$		0			0
$616$	−5.32051	+	3.07180i	−0.214369	+	0.123766i
$617$	3.91154	−	2.25833i	0.157473	−	0.0909170i	−0.419193	−	0.907897i	$-0.637687\pi$
$617$	3.91154	−	2.25833i	0.157473	−	0.0909170i	0.576666	+	0.816980i	$0.304354\pi$
$618$		0			0
$619$	38.8205	−	10.4019i	1.56033	−	0.418089i	0.627561	−	0.778568i	$-0.284053\pi$
$619$	38.8205	−	10.4019i	1.56033	−	0.418089i	0.932767	+	0.360479i	$0.117387\pi$
$620$	40.7846	−	40.7846i	1.63795	−	1.63795i
$621$		0			0
$622$	16.0526	−	16.0526i	0.643649	−	0.643649i
$623$	0.732051	−	1.26795i	0.0293290	−	0.0507993i
$624$		0			0
$625$	11.9641	+	20.7224i	0.478564	+	0.828897i
$626$	−38.8827	−	10.4186i	−1.55406	−	0.416410i
$627$		0			0
$628$	9.46410	−	2.53590i	0.377659	−	0.101193i
$629$	2.87564	+	2.87564i	0.114659	+	0.114659i
$630$		0			0
$631$		−	38.3923i		−	1.52837i	−0.644995	−	0.764187i	$-0.723141\pi$
$631$		−	38.3923i		−	1.52837i	0.644995	−	0.764187i	$-0.276859\pi$
$632$	8.78461	+	32.7846i	0.349433	+	1.30410i
$633$		0			0
$634$	23.0526	+	39.9282i	0.915534	+	1.58575i
$635$	6.19615	−	23.1244i	0.245887	−	0.917662i
$636$		0			0
$637$	−10.5622	−	39.4186i	−0.418489	−	1.56182i
$638$	7.26795	+	7.26795i	0.287741	+	0.287741i
$639$		0			0
$640$	43.7128			1.72790
$641$	4.20577	−	7.28461i	0.166118	−	0.287725i	−0.770934	−	0.636915i	$-0.780210\pi$
$641$	4.20577	−	7.28461i	0.166118	−	0.287725i	0.937052	+	0.349191i	$0.113543\pi$
$642$		0			0
$643$	−45.6506	−	12.2321i	−1.80029	−	0.482385i	−0.806263	−	0.591558i	$-0.798513\pi$
$643$	−45.6506	−	12.2321i	−1.80029	−	0.482385i	−0.994023	+	0.109173i	$0.965180\pi$
$644$	−1.60770	+	0.928203i	−0.0633521	+	0.0365763i
$645$		0			0
$646$	−1.43782	+	2.49038i	−0.0565704	+	0.0979827i
$647$			13.2679i			0.521617i	0.965391	+	0.260808i	$0.0839891\pi$
$647$			13.2679i			0.521617i	−0.965391	+	0.260808i	$0.916011\pi$
$648$		0			0
$649$			15.2487i			0.598564i
$650$	−76.7654	−	44.3205i	−3.01099	−	1.73839i
$651$		0			0
$652$	−5.12436	+	19.1244i	−0.200685	+	0.748968i
$653$	−5.63397	−	1.50962i	−0.220474	−	0.0590760i	0.146891	−	0.989153i	$-0.453073\pi$
$653$	−5.63397	−	1.50962i	−0.220474	−	0.0590760i	−0.367365	+	0.930077i	$0.619740\pi$
$654$		0			0
$655$	−6.19615	+	10.7321i	−0.242104	+	0.419336i
$656$			12.0000i			0.468521i
$657$		0			0
$658$	7.07180	−	7.07180i	0.275687	−	0.275687i
$659$	−4.02628	−	15.0263i	−0.156842	−	0.585341i	−0.998941	−	0.0460178i	$-0.985347\pi$
$659$	−4.02628	−	15.0263i	−0.156842	−	0.585341i	0.842099	−	0.539323i	$-0.181320\pi$
$660$		0			0
$661$	2.19615	−	8.19615i	0.0854204	−	0.318793i	−0.909973	−	0.414667i	$-0.863898\pi$
$661$	2.19615	−	8.19615i	0.0854204	−	0.318793i	0.995393	+	0.0958740i	$0.0305646\pi$
$662$	−24.1244	+	13.9282i	−0.937620	+	0.541335i
$663$		0			0
$664$	−3.46410	−	2.00000i	−0.134433	−	0.0776151i
$665$		−	2.53590i		−	0.0983379i
$666$		0			0
$667$	2.19615	+	2.19615i	0.0850354	+	0.0850354i
$668$	0.535898	−	0.928203i	0.0207345	−	0.0359133i
$669$		0			0
$670$	7.66025	−	28.5885i	0.295941	−	1.10447i
$671$	−4.60770	−	7.98076i	−0.177878	−	0.308094i
$672$		0			0
$673$	8.80385	−	15.2487i	0.339363	−	0.587795i	−0.644950	−	0.764225i	$-0.723122\pi$
$673$	8.80385	−	15.2487i	0.339363	−	0.587795i	0.984313	+	0.176430i	$0.0564550\pi$
$674$	−23.7846	−	23.7846i	−0.916149	−	0.916149i
$675$		0			0
$676$	53.7128			2.06588
$677$	−4.73205	+	1.26795i	−0.181867	+	0.0487312i	−0.348603	−	0.937270i	$-0.613344\pi$
$677$	−4.73205	+	1.26795i	−0.181867	+	0.0487312i	0.166736	+	0.986002i	$0.446677\pi$
$678$		0			0
$679$	−5.24167	+	3.02628i	−0.201157	+	0.116138i
$680$	12.3923	+	21.4641i	0.475223	+	0.823111i
$681$		0			0
$682$	27.1244	+	15.6603i	1.03865	+	0.599662i
$683$	4.70577	+	4.70577i	0.180061	+	0.180061i	0.791383	−	0.611321i	$-0.209362\pi$
$683$	4.70577	+	4.70577i	0.180061	+	0.180061i	−0.611321	+	0.791383i	$0.709362\pi$
$684$		0			0
$685$	−44.9808	+	44.9808i	−1.71863	+	1.71863i
$686$	−3.60770	−	13.4641i	−0.137742	−	0.514062i
$687$		0			0
$688$	−1.32051	+	4.92820i	−0.0503439	+	0.187886i
$689$	2.39230	+	4.14359i	0.0911396	+	0.157858i
$690$		0			0
$691$	−6.29423	−	23.4904i	−0.239444	−	0.893616i	−0.976095	−	0.217344i	$-0.930261\pi$
$691$	−6.29423	−	23.4904i	−0.239444	−	0.893616i	0.736651	−	0.676273i	$-0.236406\pi$
$692$	−18.3923	−	18.3923i	−0.699171	−	0.699171i
$693$		0			0
$694$			36.1962i			1.37399i
$695$	31.3923	+	18.1244i	1.19078	+	0.687496i
$696$		0			0
$697$	−5.89230	+	3.40192i	−0.223187	+	0.128857i
$698$	5.66025	+	9.80385i	0.214244	+	0.371081i
$699$		0			0
$700$	−12.5885	−	7.26795i	−0.475799	−	0.274703i
$701$	−10.6603	+	10.6603i	−0.402632	+	0.402632i	−0.879160	−	0.476527i	$-0.841895\pi$
$701$	−10.6603	+	10.6603i	−0.402632	+	0.402632i	0.476527	+	0.879160i	$0.341895\pi$
$702$		0			0
$703$	−1.60770			−0.0606354
$704$	6.14359	+	22.9282i	0.231545	+	0.864139i
$705$		0			0
$706$	7.43782	−	27.7583i	0.279926	−	1.04470i
$707$	−5.46410	−	1.46410i	−0.205499	−	0.0550632i
$708$		0			0
$709$	−20.1962	+	5.41154i	−0.758482	+	0.203235i	−0.617277	−	0.786746i	$-0.711764\pi$
$709$	−20.1962	+	5.41154i	−0.758482	+	0.203235i	−0.141205	+	0.989980i	$0.545098\pi$
$710$	59.7128			2.24098
$711$		0			0
$712$	−4.00000	−	4.00000i	−0.149906	−	0.149906i
$713$	8.19615	+	4.73205i	0.306948	+	0.177217i
$714$		0			0
$715$	18.7321	−	69.9090i	0.700539	−	2.61445i
$716$	−8.73205	+	32.5885i	−0.326332	+	1.21789i
$717$		0			0
$718$	5.39230	+	20.1244i	0.201239	+	0.751034i
$719$	16.3923			0.611330			0.305665	−	0.952139i	$-0.401121\pi$
$719$	16.3923			0.611330			0.305665	+	0.952139i	$0.401121\pi$
$720$		0			0
$721$	6.67949			0.248757
$722$	6.66025	+	24.8564i	0.247869	+	0.925060i
$723$		0			0
$724$	36.5885	+	9.80385i	1.35980	+	0.364357i
$725$	−6.29423	+	23.4904i	−0.233762	+	0.872411i
$726$		0			0
$727$	31.8109	+	18.3660i	1.17980	+	0.681158i	0.955968	−	0.293470i	$-0.0948099\pi$
$727$	31.8109	+	18.3660i	1.17980	+	0.681158i	0.223832	+	0.974628i	$0.428143\pi$
$728$	13.0718			0.484473
$729$		0			0
$730$	−53.1769			−1.96817
$731$	−2.79423	+	0.748711i	−0.103348	+	0.0276921i
$732$		0			0
$733$	−29.9545	−	8.02628i	−1.10639	−	0.296457i	−0.341028	−	0.940053i	$-0.610775\pi$
$733$	−29.9545	−	8.02628i	−1.10639	−	0.296457i	−0.765366	+	0.643596i	$0.777442\pi$
$734$	−7.41154	+	27.6603i	−0.273565	+	1.02096i
$735$		0			0
$736$	1.85641	+	6.92820i	0.0684280	+	0.255377i
$737$	16.0718			0.592012
$738$		0			0
$739$	21.2224	−	21.2224i	0.780680	−	0.780680i	−0.199266	−	0.979945i	$-0.563856\pi$
$739$	21.2224	−	21.2224i	0.780680	−	0.780680i	0.979945	+	0.199266i	$0.0638557\pi$
$740$	−6.92820	+	12.0000i	−0.254686	+	0.441129i
$741$		0			0
$742$	0.392305	+	0.679492i	0.0144020	+	0.0249449i
$743$	−2.24167	+	1.29423i	−0.0822389	+	0.0474806i	−0.540556	−	0.841308i	$-0.681786\pi$
$743$	−2.24167	+	1.29423i	−0.0822389	+	0.0474806i	0.458317	+	0.888789i	$0.348453\pi$
$744$		0			0
$745$	10.7321	+	6.19615i	0.393192	+	0.227009i
$746$		−	8.24871i		−	0.302007i
$747$		0			0
$748$	−9.51666	+	9.51666i	−0.347964	+	0.347964i
$749$	3.61474	+	13.4904i	0.132080	+	0.492928i
$750$		0			0
$751$	18.8564	+	32.6603i	0.688080	+	1.19179i	0.972458	+	0.233077i	$0.0748796\pi$
$751$	18.8564	+	32.6603i	0.688080	+	1.19179i	−0.284378	+	0.958712i	$0.591787\pi$
$752$	−19.3205	−	33.4641i	−0.704546	−	1.22031i
$753$		0			0
$754$	−5.66025	−	21.1244i	−0.206134	−	0.769304i
$755$	−7.46410	+	7.46410i	−0.271646	+	0.271646i
$756$		0			0
$757$	−6.07180	−	6.07180i	−0.220683	−	0.220683i	0.588103	−	0.808786i	$-0.299875\pi$
$757$	−6.07180	−	6.07180i	−0.220683	−	0.220683i	−0.808786	+	0.588103i	$0.799875\pi$
$758$	−32.4904	−	18.7583i	−1.18010	−	0.681333i
$759$		0			0
$760$	−9.46410	−	2.53590i	−0.343299	−	0.0919867i
$761$	27.3731	−	15.8038i	0.992273	−	0.572889i	0.0863200	−	0.996267i	$-0.472489\pi$
$761$	27.3731	−	15.8038i	0.992273	−	0.572889i	0.905953	+	0.423378i	$0.139156\pi$
$762$		0			0
$763$	7.26795	−	1.94744i	0.263117	−	0.0705021i
$764$			28.1051i			1.01681i
$765$		0			0
$766$	6.53590	+	6.53590i	0.236152	+	0.236152i
$767$	16.2224	−	28.0981i	0.585758	−	1.01456i
$768$		0			0
$769$	10.1244	+	17.5359i	0.365094	+	0.632361i	0.988791	−	0.149305i	$-0.0477036\pi$
$769$	10.1244	+	17.5359i	0.365094	+	0.632361i	−0.623698	+	0.781666i	$0.714370\pi$
$770$	3.07180	−	11.4641i	0.110700	−	0.413138i
$771$		0			0
$772$	−31.6410	−	18.2679i	−1.13879	−	0.657478i
$773$	−4.41154	−	4.41154i	−0.158672	−	0.158672i	0.623306	−	0.781978i	$-0.285789\pi$
$773$	−4.41154	−	4.41154i	−0.158672	−	0.158672i	−0.781978	+	0.623306i	$0.785789\pi$
$774$		0			0
$775$			74.1051i			2.66193i
$776$	6.05256	+	22.5885i	0.217274	+	0.810878i
$777$		0			0
$778$	−13.0526	+	7.53590i	−0.467957	+	0.270175i
$779$	0.696152	−	2.59808i	0.0249422	−	0.0930857i
$780$		0			0
$781$	8.39230	+	31.3205i	0.300300	+	1.12074i
$782$	−2.87564	+	2.87564i	−0.102833	+	0.102833i
$783$		0			0
$784$	−25.8564			−0.923443
$785$	−9.46410	+	16.3923i	−0.337788	+	0.585066i
$786$		0			0
$787$	49.8109	+	13.3468i	1.77557	+	0.475762i	0.989764	−	0.142716i	$-0.0455834\pi$
$787$	49.8109	+	13.3468i	1.77557	+	0.475762i	0.785803	+	0.618477i	$0.212250\pi$
$788$	10.0000	+	2.67949i	0.356235	+	0.0954529i
$789$		0			0
$790$	−56.7846	−	32.7846i	−2.02031	−	1.16642i
$791$		−	10.1436i		−	0.360665i
$792$		0			0
$793$			19.6077i			0.696290i
$794$	−12.7321	+	22.0526i	−0.451844	+	0.782616i
$795$		0			0
$796$	−0.875644	−	1.51666i	−0.0310364	−	0.0537566i
$797$	54.1769	+	14.5167i	1.91904	+	0.514206i	0.989275	+	0.146065i	$0.0466609\pi$
$797$	54.1769	+	14.5167i	1.91904	+	0.514206i	0.929770	+	0.368142i	$0.120006\pi$
$798$		0			0
$799$	10.9545	−	18.9737i	0.387542	−	0.671242i
$800$	−39.7128	+	39.7128i	−1.40406	+	1.40406i
$801$		0			0
$802$	−27.5885	−	27.5885i	−0.974182	−	0.974182i
$803$	−7.47372	−	27.8923i	−0.263742	−	0.984298i
$804$		0			0
$805$	0.928203	−	3.46410i	0.0327149	−	0.122094i
$806$	−33.3205	−	57.7128i	−1.17366	−	2.03285i
$807$		0			0
$808$	−10.9282	+	18.9282i	−0.384453	+	0.665892i
$809$			28.3205i			0.995696i	0.867264	+	0.497848i	$0.165876\pi$
$809$			28.3205i			0.995696i	−0.867264	+	0.497848i	$0.834124\pi$
$810$		0			0
$811$	5.02628	+	5.02628i	0.176497	+	0.176497i	0.789827	−	0.613330i	$-0.210170\pi$
$811$	5.02628	+	5.02628i	0.176497	+	0.176497i	−0.613330	+	0.789827i	$0.710170\pi$
$812$	−0.928203	−	3.46410i	−0.0325735	−	0.121566i
$813$		0			0
$814$	−7.26795	−	1.94744i	−0.254741	−	0.0682578i
$815$	−19.1244	−	33.1244i	−0.669897	−	1.16030i
$816$		0			0
$817$	0.571797	−	0.990381i	0.0200046	−	0.0346490i
$818$	30.1769	−	30.1769i	1.05511	−	1.05511i
$819$		0			0
$820$	−16.3923	−	16.3923i	−0.572444	−	0.572444i
$821$	−32.2224	+	8.63397i	−1.12457	+	0.301328i	−0.772732	−	0.634733i	$-0.781110\pi$
$821$	−32.2224	+	8.63397i	−1.12457	+	0.301328i	−0.351839	+	0.936061i	$0.614444\pi$
$822$		0			0
$823$	10.7321	−	6.19615i	0.374096	−	0.215984i	−0.301151	−	0.953577i	$-0.597371\pi$
$823$	10.7321	−	6.19615i	0.374096	−	0.215984i	0.675246	+	0.737592i	$0.264037\pi$
$824$	6.67949	−	24.9282i	0.232691	−	0.868415i
$825$		0			0
$826$	2.66025	−	4.60770i	0.0925621	−	0.160322i
$827$	−24.4641	−	24.4641i	−0.850700	−	0.850700i	0.139519	−	0.990219i	$-0.455444\pi$
$827$	−24.4641	−	24.4641i	−0.850700	−	0.850700i	−0.990219	+	0.139519i	$0.955444\pi$
$828$		0			0
$829$	24.5167	−	24.5167i	0.851499	−	0.851499i	−0.138819	−	0.990318i	$-0.544331\pi$
$829$	24.5167	−	24.5167i	0.851499	−	0.851499i	0.990318	+	0.138819i	$0.0443306\pi$
$830$	7.46410	−	2.00000i	0.259083	−	0.0694210i
$831$		0			0
$832$	13.0718	−	48.7846i	0.453183	−	1.69130i
$833$	−7.33013	−	12.6962i	−0.253974	−	0.439896i
$834$		0			0
$835$	0.535898	+	2.00000i	0.0185455	+	0.0692129i
$836$		−	5.32051i		−	0.184014i
$837$		0			0
$838$	−45.7128			−1.57912
$839$	35.4449	+	20.4641i	1.22369	+	0.706499i	0.965703	−	0.259649i	$-0.0836067\pi$
$839$	35.4449	+	20.4641i	1.22369	+	0.706499i	0.257989	+	0.966148i	$0.416940\pi$
$840$		0			0
$841$	19.9186	−	11.5000i	0.686848	−	0.396552i
$842$	−2.78461	+	1.60770i	−0.0959640	+	0.0554048i
$843$		0			0
$844$	8.19615	−	2.19615i	0.282123	−	0.0755947i
$845$	−73.3731	+	73.3731i	−2.52411	+	2.52411i
$846$		0			0
$847$	−1.60770			−0.0552411
$848$	2.92820	−	0.784610i	0.100555	−	0.0269436i
$849$		0			0
$850$	−30.7583	−	8.24167i	−1.05500	−	0.282687i
$851$	−2.19615	−	0.588457i	−0.0752831	−	0.0201721i
$852$		0			0
$853$	−12.5622	+	3.36603i	−0.430121	+	0.115251i	−0.467383	−	0.884055i	$-0.654803\pi$
$853$	−12.5622	+	3.36603i	−0.430121	+	0.115251i	0.0372621	+	0.999306i	$0.488136\pi$
$854$			3.21539i			0.110028i
$855$		0			0
$856$	53.9615			1.84437
$857$	−20.9090	−	12.0718i	−0.714237	−	0.412365i	0.0983911	−	0.995148i	$-0.468630\pi$
$857$	−20.9090	−	12.0718i	−0.714237	−	0.412365i	−0.812628	+	0.582783i	$0.801964\pi$
$858$		0			0
$859$	−8.25833	+	30.8205i	−0.281771	+	1.05158i	0.669396	+	0.742905i	$0.266553\pi$
$859$	−8.25833	+	30.8205i	−0.281771	+	1.05158i	−0.951167	+	0.308677i	$0.900114\pi$
$860$	−4.92820	−	8.53590i	−0.168050	−	0.291072i
$861$		0			0
$862$	7.92820	−	2.12436i	0.270036	−	0.0723558i
$863$	8.53590			0.290565			0.145283	−	0.989390i	$-0.453591\pi$
$863$	8.53590			0.290565			0.145283	+	0.989390i	$0.453591\pi$
$864$		0			0
$865$	50.2487			1.70851
$866$	−3.09808	+	0.830127i	−0.105277	+	0.0282089i
$867$		0			0
$868$	−5.46410	−	9.46410i	−0.185464	−	0.321233i
$869$	9.21539	−	34.3923i	0.312611	−	1.16668i
$870$		0			0
$871$	−29.6147	−	17.0981i	−1.00346	−	0.579346i
$872$		−	29.0718i		−	0.984495i
$873$		0			0
$874$		−	1.60770i		−	0.0543811i
$875$	13.4641	−	3.60770i	0.455170	−	0.121962i
$876$		0			0
$877$	−1.53590	−	0.411543i	−0.0518636	−	0.0138968i	0.232794	−	0.972526i	$-0.425213\pi$
$877$	−1.53590	−	0.411543i	−0.0518636	−	0.0138968i	−0.284658	+	0.958629i	$0.591880\pi$
$878$	7.66025	+	2.05256i	0.258521	+	0.0692705i
$879$		0			0
$880$	−39.7128	−	22.9282i	−1.33872	−	0.772910i
$881$	7.32051			0.246634			0.123317	−	0.992367i	$-0.460647\pi$
$881$	7.32051			0.246634			0.123317	+	0.992367i	$0.460647\pi$
$882$		0			0
$883$	−14.3660	+	14.3660i	−0.483455	+	0.483455i	−0.906233	−	0.422778i	$-0.861055\pi$
$883$	−14.3660	+	14.3660i	−0.483455	+	0.483455i	0.422778	+	0.906233i	$0.361055\pi$
$884$	27.6603	−	7.41154i	0.930315	−	0.249277i
$885$		0			0
$886$	−24.8827	+	14.3660i	−0.835950	+	0.482636i
$887$	−33.1244	+	19.1244i	−1.11221	+	0.642133i	−0.939400	−	0.342823i	$-0.888617\pi$
$887$	−33.1244	+	19.1244i	−1.11221	+	0.642133i	−0.172807	+	0.984956i	$0.555284\pi$
$888$		0			0
$889$	−3.92820	−	2.26795i	−0.131748	−	0.0760646i
$890$	10.9282			0.366314
$891$		0			0
$892$		−	44.1051i		−	1.47675i
$893$	2.24167	+	8.36603i	0.0750146	+	0.279958i
$894$		0			0
$895$	−32.5885	−	56.4449i	−1.08931	−	1.88674i
$896$	2.14359	−	8.00000i	0.0716124	−	0.267261i
$897$		0			0
$898$	28.2224	−	7.56218i	0.941795	−	0.252353i
$899$	−12.9282	+	12.9282i	−0.431180	+	0.431180i
$900$		0			0
$901$	1.21539	+	1.21539i	0.0404905	+	0.0404905i
$902$	6.29423	−	10.9019i	0.209575	−	0.362994i
$903$		0			0
$904$	−37.8564	−	10.1436i	−1.25909	−	0.337371i
$905$	−63.3731	+	36.5885i	−2.10659	+	1.21624i
$906$		0			0
$907$	−16.7942	+	4.50000i	−0.557643	+	0.149420i	−0.526623	−	0.850099i	$-0.676542\pi$
$907$	−16.7942	+	4.50000i	−0.557643	+	0.149420i	−0.0310198	+	0.999519i	$0.509876\pi$
$908$	−21.1244	−	21.1244i	−0.701036	−	0.701036i
$909$		0			0
$910$	−17.8564	+	17.8564i	−0.591934	+	0.591934i
$911$	4.46410	−	7.73205i	0.147902	−	0.256174i	−0.782550	−	0.622588i	$-0.786081\pi$
$911$	4.46410	−	7.73205i	0.147902	−	0.256174i	0.930452	+	0.366414i	$0.119415\pi$
$912$		0			0
$913$	2.09808	+	3.63397i	0.0694362	+	0.120267i
$914$	−31.9545	−	8.56218i	−1.05696	−	0.283212i
$915$		0			0
$916$	3.66025	+	13.6603i	0.120938	+	0.451347i
$917$	1.66025	+	1.66025i	0.0548264	+	0.0548264i
$918$		0			0
$919$			32.9808i			1.08793i	0.839106	+	0.543967i	$0.183079\pi$
$919$			32.9808i			1.08793i	−0.839106	+	0.543967i	$0.816921\pi$
$920$	−12.0000	−	6.92820i	−0.395628	−	0.228416i
$921$		0			0
$922$	1.87564	+	3.24871i	0.0617711	+	0.106991i
$923$	17.8564	−	66.6410i	0.587751	−	2.19352i
$924$		0			0
$925$	−4.60770	−	17.1962i	−0.151500	−	0.565406i
$926$	−18.3923	−	18.3923i	−0.604409	−	0.604409i
$927$		0			0
$928$	−13.8564			−0.454859
$929$	18.4641	−	31.9808i	0.605788	−	1.04925i	−0.386139	−	0.922441i	$-0.626191\pi$
$929$	18.4641	−	31.9808i	0.605788	−	1.04925i	0.991926	−	0.126814i	$-0.0404752\pi$
$930$		0			0
$931$	5.59808	+	1.50000i	0.183470	+	0.0491605i
$932$	7.19615	+	12.4641i	0.235718	+	0.408275i
$933$		0			0
$934$	−4.36603	+	7.56218i	−0.142861	+	0.247442i
$935$		−	26.0000i		−	0.850291i
$936$		0			0
$937$		−	51.1769i		−	1.67188i	−0.548823	−	0.835938i	$-0.684924\pi$
$937$		−	51.1769i		−	1.67188i	0.548823	−	0.835938i	$-0.315076\pi$
$938$	−4.85641	−	2.80385i	−0.158567	−	0.0915489i
$939$		0			0
$940$	72.1051	+	19.3205i	2.35181	+	0.630165i
$941$	12.1962	+	3.26795i	0.397583	+	0.106532i	0.452070	−	0.891982i	$-0.350686\pi$
$941$	12.1962	+	3.26795i	0.397583	+	0.106532i	−0.0544870	+	0.998514i	$0.517352\pi$
$942$		0			0
$943$	1.90192	−	3.29423i	0.0619352	−	0.107275i
$944$	−14.5359	−	14.5359i	−0.473103	−	0.473103i
$945$		0			0
$946$	3.78461	−	3.78461i	0.123048	−	0.123048i
$947$	4.01666	+	14.9904i	0.130524	+	0.487122i	0.999976	−	0.00689497i	$-0.00219475\pi$
$947$	4.01666	+	14.9904i	0.130524	+	0.487122i	−0.869452	+	0.494017i	$0.835528\pi$
$948$		0			0
$949$	−15.9019	+	59.3468i	−0.516198	+	1.92648i
$950$	10.9019	−	6.29423i	0.353705	−	0.204212i
$951$		0			0
$952$	4.53590	−	1.21539i	0.147009	−	0.0393910i
$953$		−	59.1051i		−	1.91460i	−0.289092	−	0.957301i	$-0.593353\pi$
$953$		−	59.1051i		−	1.91460i	0.289092	−	0.957301i	$-0.406647\pi$
$954$		0			0
$955$	−38.3923	−	38.3923i	−1.24235	−	1.24235i
$956$	45.3731	+	26.1962i	1.46747	+	0.847244i
$957$		0			0
$958$	−9.39230	+	35.0526i	−0.303452	+	1.13250i
$959$	6.02628	+	10.4378i	0.194599	+	0.337055i
$960$		0			0
$961$	−12.3564	+	21.4019i	−0.398594	+	0.690385i
$962$	11.3205	+	11.3205i	0.364988	+	0.364988i
$963$		0			0
$964$			25.6077i			0.824768i
$965$	68.1769	−	18.2679i	2.19469	−	0.588066i
$966$		0			0
$967$	9.16987	−	5.29423i	0.294883	−	0.170251i	−0.345259	−	0.938508i	$-0.612209\pi$
$967$	9.16987	−	5.29423i	0.294883	−	0.170251i	0.640142	+	0.768257i	$0.278876\pi$
$968$	−1.60770	+	6.00000i	−0.0516733	+	0.192847i
$969$		0			0
$970$	−39.1244	−	22.5885i	−1.25621	−	0.725272i
$971$	−22.4641	−	22.4641i	−0.720907	−	0.720907i	0.247883	−	0.968790i	$-0.420265\pi$
$971$	−22.4641	−	22.4641i	−0.720907	−	0.720907i	−0.968790	+	0.247883i	$0.920265\pi$
$972$		0			0
$973$	4.85641	−	4.85641i	0.155689	−	0.155689i
$974$	−5.92820	−	22.1244i	−0.189952	−	0.708910i
$975$		0			0
$976$	12.0000	+	3.21539i	0.384111	+	0.102922i
$977$	9.93782	+	17.2128i	0.317939	+	0.550687i	0.980058	−	0.198712i	$-0.0636759\pi$
$977$	9.93782	+	17.2128i	0.317939	+	0.550687i	−0.662119	+	0.749399i	$0.730343\pi$
$978$		0			0
$979$	1.53590	+	5.73205i	0.0490875	+	0.183197i
$980$	35.3205	−	35.3205i	1.12827	−	1.12827i
$981$		0			0
$982$			37.6603i			1.20179i
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	0.704425	−	0.709779i	$-0.251205\pi$
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	−0.262474	+	0.964939i	$0.584538\pi$
$984$		0			0
$985$	−17.3205	+	10.0000i	−0.551877	+	0.318626i
$986$	−3.92820	−	6.80385i	−0.125099	−	0.216679i
$987$		0			0
$988$	−5.66025	+	9.80385i	−0.180077	+	0.311902i
$989$	1.14359	−	1.14359i	0.0363642	−	0.0363642i
$990$		0			0
$991$	−32.6410			−1.03688			−0.518438	−	0.855115i	$-0.673486\pi$
$991$	−32.6410			−1.03688			−0.518438	+	0.855115i	$0.673486\pi$
$992$	−40.7846	+	10.9282i	−1.29491	+	0.346971i
$993$		0			0
$994$	2.92820	−	10.9282i	0.0928770	−	0.346622i
$995$	3.26795	+	0.875644i	0.103601	+	0.0277598i
$996$		0			0
$997$	32.1244	−	8.60770i	1.01739	−	0.272608i	0.288675	−	0.957427i	$-0.406785\pi$
$997$	32.1244	−	8.60770i	1.01739	−	0.272608i	0.728713	+	0.684819i	$0.240119\pi$
$998$	9.26795			0.293372
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.b.181.1		4
3.2	odd	2		144.2.x.c.133.1	yes	4
4.3	odd	2		1728.2.bc.a.1585.1		4
9.4	even	3		432.2.y.c.37.1		4
9.5	odd	6		144.2.x.b.85.1	yes	4
12.11	even	2		576.2.bb.c.241.1		4
16.3	odd	4		1728.2.bc.d.721.1		4
16.13	even	4		432.2.y.c.397.1		4
36.23	even	6		576.2.bb.d.49.1		4
36.31	odd	6		1728.2.bc.d.1009.1		4
48.29	odd	4		144.2.x.b.61.1	✓	4
48.35	even	4		576.2.bb.d.529.1		4
144.13	even	12	inner	432.2.y.b.253.1		4
144.67	odd	12		1728.2.bc.a.145.1		4
144.77	odd	12		144.2.x.c.13.1	yes	4
144.131	even	12		576.2.bb.c.337.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.b.61.1	✓	4	48.29	odd	4
144.2.x.b.85.1	yes	4	9.5	odd	6
144.2.x.c.13.1	yes	4	144.77	odd	12
144.2.x.c.133.1	yes	4	3.2	odd	2
432.2.y.b.181.1		4	1.1	even	1	trivial
432.2.y.b.253.1		4	144.13	even	12	inner
432.2.y.c.37.1		4	9.4	even	3
432.2.y.c.397.1		4	16.13	even	4
576.2.bb.c.241.1		4	12.11	even	2
576.2.bb.c.337.1		4	144.131	even	12
576.2.bb.d.49.1		4	36.23	even	6
576.2.bb.d.529.1		4	48.35	even	4
1728.2.bc.a.145.1		4	144.67	odd	12
1728.2.bc.a.1585.1		4	4.3	odd	2
1728.2.bc.d.721.1		4	16.3	odd	4
1728.2.bc.d.1009.1		4	36.31	odd	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-1.00000 + 3.73205i) q^{5} +(0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-1.00000 + 3.73205i) q^{5} +(0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +5.46410i q^{10} +(-2.86603 + 0.767949i) q^{11} +(6.09808 + 1.63397i) q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 + 0.633975i) q^{19} +(2.00000 + 7.46410i) q^{20} +(-3.63397 + 2.09808i) q^{22} +(-1.09808 + 0.633975i) q^{23} +(-8.59808 - 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(-0.633975 - 2.36603i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(1.46410 - 5.46410i) q^{32} +(3.09808 - 0.830127i) q^{34} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(5.46410 + 9.46410i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(-1.23205 + 0.330127i) q^{43} +(-4.19615 + 4.19615i) q^{44} +(-1.26795 + 1.26795i) q^{46} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(-13.5622 - 3.63397i) q^{50} +(12.1962 - 3.26795i) q^{52} +(0.535898 + 0.535898i) q^{53} -11.4641i q^{55} +(2.00000 - 0.535898i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(1.33013 - 4.96410i) q^{59} +(0.803848 + 3.00000i) q^{61} +(-7.46410 - 7.46410i) q^{62} -8.00000i q^{64} +(-12.1962 + 21.1244i) q^{65} +(-5.23205 - 1.40192i) q^{67} +(3.92820 - 2.26795i) q^{68} +(-2.00000 + 3.46410i) q^{70} -10.9282i q^{71} +9.73205i q^{73} +(2.19615 + 1.26795i) q^{74} +(-0.464102 + 1.73205i) q^{76} +(-2.09808 - 0.562178i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(10.9282 + 10.9282i) q^{80} +(-3.00000 + 3.00000i) q^{82} +(-0.366025 - 1.36603i) q^{83} +(-2.26795 + 8.46410i) q^{85} +(-1.56218 + 0.901924i) q^{86} +(-4.19615 + 7.26795i) q^{88} -2.00000i q^{89} +(3.26795 + 3.26795i) q^{91} +(-1.26795 + 2.19615i) q^{92} +(3.53590 - 13.1962i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(-6.46410 - 6.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{5} + 6 q^{7} + 8 q^{8}+O(q^{10}) \) 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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