LMFDB - Embedded newform 432.2.y.c.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.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(3.73205 + 1.00000i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(3.73205 + 1.00000i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.46410i q^{10} +(0.767949 + 2.86603i) q^{11} +(-1.63397 + 6.09808i) q^{13} +(-0.267949 + 1.00000i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 - 0.633975i) q^{19} +(-7.46410 + 2.00000i) q^{20} +(3.63397 - 2.09808i) q^{22} +(1.09808 - 0.633975i) q^{23} +(8.59808 + 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(2.36603 - 0.633975i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-0.830127 - 3.09808i) q^{34} +(-2.00000 - 2.00000i) q^{35} +(1.26795 - 1.26795i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(5.46410 + 9.46410i) q^{40} +(2.59808 - 1.50000i) q^{41} +(0.330127 + 1.23205i) q^{43} +(-4.19615 - 4.19615i) q^{44} +(-1.26795 - 1.26795i) q^{46} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(3.63397 - 13.5622i) q^{50} +(-3.26795 - 12.1962i) q^{52} +(0.535898 - 0.535898i) q^{53} +11.4641i q^{55} +(-0.535898 - 2.00000i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(-4.96410 - 1.33013i) q^{59} +(-3.00000 + 0.803848i) q^{61} +(-7.46410 + 7.46410i) q^{62} +8.00000i q^{64} +(-12.1962 + 21.1244i) q^{65} +(1.40192 - 5.23205i) q^{67} +(-3.92820 + 2.26795i) q^{68} +(-2.00000 + 3.46410i) q^{70} +10.9282i q^{71} -9.73205i q^{73} +(-2.19615 - 1.26795i) q^{74} +(1.73205 + 0.464102i) q^{76} +(0.562178 - 2.09808i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(10.9282 - 10.9282i) q^{80} +(-3.00000 - 3.00000i) q^{82} +(1.36603 - 0.366025i) q^{83} +(8.46410 + 2.26795i) q^{85} +(1.56218 - 0.901924i) q^{86} +(-4.19615 + 7.26795i) q^{88} +2.00000i q^{89} +(3.26795 - 3.26795i) q^{91} +(-1.26795 + 2.19615i) q^{92} +(-13.1962 - 3.53590i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(-6.46410 + 6.46410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 8 q^{5} - 6 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 8 * q^5 - 6 * q^7 + 8 * q^8	$ 4 q + 2 q^{2} + 8 q^{5} - 6 q^{7} + 8 q^{8} + 10 q^{11} - 10 q^{13} - 8 q^{14} + 8 q^{16} + 16 q^{17} - 6 q^{19} - 16 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} + 14 q^{34} - 8 q^{35} + 12 q^{37} - 6 q^{38} + 8 q^{40} - 16 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{47} - 6 q^{49} + 18 q^{50} - 20 q^{52} + 16 q^{53} - 16 q^{56} - 6 q^{59} - 12 q^{61} - 16 q^{62} - 28 q^{65} + 16 q^{67} + 12 q^{68} - 8 q^{70} + 12 q^{74} - 22 q^{77} - 24 q^{79} + 16 q^{80} - 12 q^{82} + 2 q^{83} + 20 q^{85} - 18 q^{86} + 4 q^{88} + 20 q^{91} - 12 q^{92} - 32 q^{94} - 20 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 8 * q^5 - 6 * q^7 + 8 * q^8 + 10 * q^11 - 10 * q^13 - 8 * q^14 + 8 * q^16 + 16 * q^17 - 6 * q^19 - 16 * 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 + 14 * q^34 - 8 * q^35 + 12 * q^37 - 6 * q^38 + 8 * q^40 - 16 * q^43 + 4 * q^44 - 12 * q^46 + 2 * q^47 - 6 * q^49 + 18 * q^50 - 20 * q^52 + 16 * q^53 - 16 * q^56 - 6 * q^59 - 12 * q^61 - 16 * q^62 - 28 * q^65 + 16 * q^67 + 12 * q^68 - 8 * q^70 + 12 * q^74 - 22 * q^77 - 24 * q^79 + 16 * q^80 - 12 * q^82 + 2 * q^83 + 20 * q^85 - 18 * q^86 + 4 * q^88 + 20 * q^91 - 12 * q^92 - 32 * 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
$5$	3.73205	+	1.00000i	1.66902	+	0.447214i	0.964847	−	0.262811i	$-0.0846497\pi$
$5$	3.73205	+	1.00000i	1.66902	+	0.447214i	0.704177	+	0.710025i	$0.251316\pi$
$6$		0			0
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	0.375382	−	0.926870i	$-0.377511\pi$
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	−0.615002	+	0.788526i	$0.710845\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		0			0
$10$		−	5.46410i		−	1.72790i
$11$	0.767949	+	2.86603i	0.231545	+	0.864139i	0.979676	+	0.200587i	$0.0642851\pi$
$11$	0.767949	+	2.86603i	0.231545	+	0.864139i	−0.748130	+	0.663552i	$0.769048\pi$
$12$		0			0
$13$	−1.63397	+	6.09808i	−0.453183	+	1.69130i	0.240192	+	0.970725i	$0.422790\pi$
$13$	−1.63397	+	6.09808i	−0.453183	+	1.69130i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−0.267949	+	1.00000i	−0.0716124	+	0.267261i
$15$		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	0.630635	−	0.776079i	$-0.282794\pi$
$19$	−0.633975	−	0.633975i	−0.145444	−	0.145444i	−0.776079	+	0.630635i	$0.782794\pi$
$20$	−7.46410	+	2.00000i	−1.66902	+	0.447214i
$21$		0			0
$22$	3.63397	−	2.09808i	0.774766	−	0.447311i
$23$	1.09808	−	0.633975i	0.228965	−	0.132193i	−0.381130	−	0.924522i	$-0.624465\pi$
$23$	1.09808	−	0.633975i	0.228965	−	0.132193i	0.610094	+	0.792329i	$0.291132\pi$
$24$		0			0
$25$	8.59808	+	4.96410i	1.71962	+	0.992820i
$26$	8.92820			1.75096
$27$		0			0
$28$	1.46410			0.276689
$29$	2.36603	−	0.633975i	0.439360	−	0.117726i	−0.0323566	−	0.999476i	$-0.510301\pi$
$29$	2.36603	−	0.633975i	0.439360	−	0.117726i	0.471717	+	0.881750i	$0.343635\pi$
$30$		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	$-0.400500\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		0			0
$34$	−0.830127	−	3.09808i	−0.142366	−	0.531316i
$35$	−2.00000	−	2.00000i	−0.338062	−	0.338062i
$36$		0			0
$37$	1.26795	−	1.26795i	0.208450	−	0.208450i	−0.595159	−	0.803608i	$-0.702911\pi$
$37$	1.26795	−	1.26795i	0.208450	−	0.208450i	0.803608	+	0.595159i	$0.202911\pi$
$38$	−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	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$		0			0
$43$	0.330127	+	1.23205i	0.0503439	+	0.187886i	0.986519	−	0.163649i	$-0.0523265\pi$
$43$	0.330127	+	1.23205i	0.0503439	+	0.187886i	−0.936175	+	0.351535i	$0.885660\pi$
$44$	−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
$50$	3.63397	−	13.5622i	0.513922	−	1.91798i
$51$		0			0
$52$	−3.26795	−	12.1962i	−0.453183	−	1.69130i
$53$	0.535898	−	0.535898i	0.0736113	−	0.0736113i	−0.669343	−	0.742954i	$-0.733424\pi$
$53$	0.535898	−	0.535898i	0.0736113	−	0.0736113i	0.742954	+	0.669343i	$0.233424\pi$
$54$		0			0
$55$			11.4641i			1.54582i
$56$	−0.535898	−	2.00000i	−0.0716124	−	0.267261i
$57$		0			0
$58$	−1.73205	−	3.00000i	−0.227429	−	0.393919i
$59$	−4.96410	−	1.33013i	−0.646271	−	0.173168i	−0.0792287	−	0.996856i	$-0.525246\pi$
$59$	−4.96410	−	1.33013i	−0.646271	−	0.173168i	−0.567042	+	0.823689i	$0.691912\pi$
$60$		0			0
$61$	−3.00000	+	0.803848i	−0.384111	+	0.102922i	−0.445707	−	0.895179i	$-0.647048\pi$
$61$	−3.00000	+	0.803848i	−0.384111	+	0.102922i	0.0615961	+	0.998101i	$0.480381\pi$
$62$	−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
$67$	1.40192	−	5.23205i	0.171272	−	0.639197i	−0.825884	−	0.563840i	$-0.809324\pi$
$67$	1.40192	−	5.23205i	0.171272	−	0.639197i	0.997157	−	0.0753572i	$-0.0240097\pi$
$68$	−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	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$		0			0
$73$		−	9.73205i		−	1.13905i	−0.821974	−	0.569525i	$-0.807127\pi$
$73$		−	9.73205i		−	1.13905i	0.821974	−	0.569525i	$-0.192873\pi$
$74$	−2.19615	−	1.26795i	−0.255298	−	0.147396i
$75$		0			0
$76$	1.73205	+	0.464102i	0.198680	+	0.0532361i
$77$	0.562178	−	2.09808i	0.0640661	−	0.239098i
$78$		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
$83$	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
$85$	8.46410	+	2.26795i	0.918061	+	0.245994i
$86$	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	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$		0			0
$91$	3.26795	−	3.26795i	0.342574	−	0.342574i
$92$	−1.26795	+	2.19615i	−0.132193	+	0.228965i
$93$		0			0
$94$	−13.1962	−	3.53590i	−1.36108	−	0.364700i
$95$	−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
$101$	2.00000	+	7.46410i	0.199007	+	0.742706i	0.991193	+	0.132426i	$0.0422765\pi$
$101$	2.00000	+	7.46410i	0.199007	+	0.742706i	−0.792186	+	0.610280i	$0.791057\pi$
$102$		0			0
$103$	−7.90192	+	4.56218i	−0.778600	+	0.449525i	−0.835934	−	0.548830i	$-0.815073\pi$
$103$	−7.90192	+	4.56218i	−0.778600	+	0.449525i	0.0573341	+	0.998355i	$0.481740\pi$
$104$	−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	0.378607	−	0.925558i	$-0.376403\pi$
$107$	13.4904	−	13.4904i	1.30416	−	1.30416i	0.925558	−	0.378607i	$-0.123597\pi$
$108$		0			0
$109$	7.26795	+	7.26795i	0.696143	+	0.696143i	0.963576	−	0.267433i	$-0.0861754\pi$
$109$	7.26795	+	7.26795i	0.696143	+	0.696143i	−0.267433	+	0.963576i	$0.586175\pi$
$110$	15.6603	−	4.19615i	1.49315	−	0.400087i
$111$		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
$115$	4.73205	−	1.26795i	0.441266	−	0.118237i
$116$	−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	$0.588648\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$		0			0
$130$	33.3205	+	8.92820i	2.92240	+	0.783055i
$131$	−0.830127	+	3.09808i	−0.0725285	+	0.270680i	−0.992662	−	0.120926i	$-0.961414\pi$
$131$	−0.830127	+	3.09808i	−0.0725285	+	0.270680i	0.920133	+	0.391606i	$0.128080\pi$
$132$		0			0
$133$	0.169873	+	0.633975i	0.0147299	+	0.0549726i
$134$	−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	−0.253645	−	0.967297i	$-0.581629\pi$
$137$	−14.2583	−	8.23205i	−1.21817	−	0.703312i	−0.964527	+	0.263986i	$0.914963\pi$
$138$		0			0
$139$	−9.06218	−	2.42820i	−0.768644	−	0.205958i	−0.146872	−	0.989156i	$-0.546920\pi$
$139$	−9.06218	−	2.42820i	−0.768644	−	0.205958i	−0.621772	+	0.783198i	$0.713587\pi$
$140$	5.46410	+	1.46410i	0.461801	+	0.123739i
$141$		0			0
$142$	14.9282	−	4.00000i	1.25275	−	0.335673i
$143$	−18.7321			−1.56645
$144$		0			0
$145$	9.46410			0.785951
$146$	−13.2942	+	3.56218i	−1.10024	+	0.294808i
$147$		0			0
$148$	−0.928203	+	3.46410i	−0.0762978	+	0.284747i
$149$	−3.09808	−	0.830127i	−0.253804	−	0.0680067i	0.129674	−	0.991557i	$-0.458607\pi$
$149$	−3.09808	−	0.830127i	−0.253804	−	0.0680067i	−0.383478	+	0.923550i	$0.625274\pi$
$150$		0			0
$151$	−2.36603	−	1.36603i	−0.192544	−	0.111166i	0.400629	−	0.916240i	$-0.368792\pi$
$151$	−2.36603	−	1.36603i	−0.192544	−	0.111166i	−0.593173	+	0.805075i	$0.702125\pi$
$152$		−	2.53590i		−	0.205689i
$153$		0			0
$154$	−3.07180			−0.247532
$155$	−7.46410	−	27.8564i	−0.599531	−	2.23748i
$156$		0			0
$157$	−1.26795	+	4.73205i	−0.101193	+	0.377659i	−0.997886	−	0.0649959i	$-0.979297\pi$
$157$	−1.26795	+	4.73205i	−0.101193	+	0.377659i	0.896692	+	0.442655i	$0.145963\pi$
$158$	16.3923	+	4.39230i	1.30410	+	0.349433i
$159$		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	0.377661	−	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
$167$	−0.464102	+	0.267949i	−0.0359133	+	0.0207345i	−0.517849	−	0.855472i	$-0.673267\pi$
$167$	−0.464102	+	0.267949i	−0.0359133	+	0.0207345i	0.481936	+	0.876206i	$0.339934\pi$
$168$		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
$173$	12.5622	−	3.36603i	0.955085	−	0.255914i	0.252566	−	0.967580i	$-0.418725\pi$
$173$	12.5622	−	3.36603i	0.955085	−	0.255914i	0.702519	+	0.711665i	$0.252059\pi$
$174$		0			0
$175$	−3.63397	−	6.29423i	−0.274703	−	0.475799i
$176$	11.4641	+	3.07180i	0.864139	+	0.231545i
$177$		0			0
$178$	2.73205	−	0.732051i	0.204776	−	0.0548695i
$179$	−11.9282	−	11.9282i	−0.891556	−	0.891556i	0.103114	−	0.994670i	$-0.467119\pi$
$179$	−11.9282	−	11.9282i	−0.891556	−	0.891556i	−0.994670	+	0.103114i	$0.967119\pi$
$180$		0			0
$181$	13.3923	−	13.3923i	0.995442	−	0.995442i	−0.00454748	−	0.999990i	$-0.501448\pi$
$181$	13.3923	−	13.3923i	0.995442	−	0.995442i	0.999990	+	0.00454748i	$0.00144751\pi$
$182$	−5.66025	−	3.26795i	−0.419566	−	0.242237i
$183$		0			0
$184$	3.46410	+	0.928203i	0.255377	+	0.0684280i
$185$	6.00000	−	3.46410i	0.441129	−	0.254686i
$186$		0			0
$187$	1.74167	+	6.50000i	0.127364	+	0.475327i
$188$			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	$-0.395043\pi$
$194$	11.2942	+	3.02628i	0.810878	+	0.217274i
$195$		0			0
$196$	11.1962	+	6.46410i	0.799725	+	0.461722i
$197$	3.66025	−	3.66025i	0.260782	−	0.260782i	−0.564590	−	0.825372i	$-0.690966\pi$
$197$	3.66025	−	3.66025i	0.260782	−	0.260782i	0.825372	+	0.564590i	$0.190966\pi$
$198$		0			0
$199$			0.875644i			0.0620728i	0.999518	+	0.0310364i	$0.00988078\pi$
$199$			0.875644i			0.0620728i	−0.999518	+	0.0310364i	$0.990119\pi$
$200$	7.26795	+	27.1244i	0.513922	+	1.91798i
$201$		0			0
$202$	9.46410	−	5.46410i	0.665892	−	0.384453i
$203$	−1.73205	−	0.464102i	−0.121566	−	0.0325735i
$204$		0			0
$205$	11.1962	−	3.00000i	0.781973	−	0.209529i
$206$	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
$211$	−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	$0.129985\pi$
$212$	−0.392305	+	1.46410i	−0.0269436	+	0.100555i
$213$		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
$221$	−3.70577	+	13.8301i	−0.249277	+	0.930315i
$222$		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
$227$	14.4282	−	3.86603i	0.957633	−	0.256597i	0.254035	−	0.967195i	$-0.418242\pi$
$227$	14.4282	−	3.86603i	0.957633	−	0.256597i	0.703598	+	0.710598i	$0.251575\pi$
$228$		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
$233$		−	7.19615i		−	0.471436i	−0.971822	−	0.235718i	$-0.924256\pi$
$233$		−	7.19615i		−	0.471436i	0.971822	−	0.235718i	$-0.0757441\pi$
$234$		0			0
$235$	26.3923	−	26.3923i	1.72164	−	1.72164i
$236$	9.92820	−	2.66025i	0.646271	−	0.173168i
$237$		0			0
$238$	−0.607695	+	2.26795i	−0.0393910	+	0.147009i
$239$	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
$245$	−6.46410	−	24.1244i	−0.412976	−	1.54125i
$246$		0			0
$247$	4.90192	−	2.83013i	0.311902	−	0.180077i
$248$	5.46410	−	20.3923i	0.346971	−	1.29491i
$249$		0			0
$250$	13.4641	−	23.3205i	0.851545	−	1.47492i
$251$	−2.83013	+	2.83013i	−0.178636	+	0.178636i	−0.790761	−	0.612125i	$-0.790315\pi$
$251$	−2.83013	+	2.83013i	−0.178636	+	0.178636i	0.612125	+	0.790761i	$0.290315\pi$
$252$		0			0
$253$	2.66025	+	2.66025i	0.167249	+	0.167249i
$254$	2.26795	+	8.46410i	0.142304	+	0.531085i
$255$		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
$259$	−1.26795	+	0.339746i	−0.0787865	+	0.0211108i
$260$		−	48.7846i		−	3.02549i
$261$		0			0
$262$	4.53590			0.280229
$263$	23.4904	+	13.5622i	1.44848	+	0.836280i	0.998391	−	0.0567045i	$-0.0180593\pi$
$263$	23.4904	+	13.5622i	1.44848	+	0.836280i	0.450088	+	0.892984i	$0.351393\pi$
$264$		0			0
$265$	2.53590	−	1.46410i	0.155779	−	0.0899390i
$266$	0.803848	−	0.464102i	0.0492871	−	0.0284559i
$267$		0			0
$268$	2.80385	+	10.4641i	0.171272	+	0.639197i
$269$	−4.73205	−	4.73205i	−0.288518	−	0.288518i	0.547976	−	0.836494i	$-0.315399\pi$
$269$	−4.73205	−	4.73205i	−0.288518	−	0.288518i	−0.836494	+	0.547976i	$0.815399\pi$
$270$		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
$274$	−6.02628	+	22.4904i	−0.364061	+	1.35869i
$275$	−7.62436	+	28.4545i	−0.459766	+	1.71587i
$276$		0			0
$277$	−4.22243	−	15.7583i	−0.253701	−	0.946826i	−0.968808	−	0.247811i	$-0.920289\pi$
$277$	−4.22243	−	15.7583i	−0.253701	−	0.946826i	0.715107	−	0.699015i	$-0.246378\pi$
$278$			13.2679i			0.795759i
$279$		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
$283$	27.7583	+	7.43782i	1.65006	+	0.442133i	0.959630	−	0.281265i	$-0.0907541\pi$
$283$	27.7583	+	7.43782i	1.65006	+	0.442133i	0.690431	+	0.723398i	$0.257421\pi$
$284$	−10.9282	−	18.9282i	−0.648470	−	1.12318i
$285$		0			0
$286$	6.85641	+	25.5885i	0.405428	+	1.51308i
$287$	−2.19615			−0.129635
$288$		0			0
$289$	−11.8564			−0.697436
$290$	−3.46410	−	12.9282i	−0.203419	−	0.759170i
$291$		0			0
$292$	9.73205	+	16.8564i	0.569525	+	0.986447i
$293$	−13.5622	−	3.63397i	−0.792311	−	0.212299i	−0.160106	−	0.987100i	$-0.551183\pi$
$293$	−13.5622	−	3.63397i	−0.792311	−	0.212299i	−0.632205	+	0.774801i	$0.717850\pi$
$294$		0			0
$295$	−17.1962	−	9.92820i	−1.00120	−	0.578042i
$296$	5.07180			0.294792
$297$		0			0
$298$			4.53590i			0.262758i
$299$	2.07180	+	7.73205i	0.119815	+	0.447156i
$300$		0			0
$301$	0.241670	−	0.901924i	0.0139296	−	0.0519860i
$302$	−1.00000	+	3.73205i	−0.0575435	+	0.214755i
$303$		0			0
$304$	−3.46410	+	0.928203i	−0.198680	+	0.0532361i
$305$	−12.0000			−0.687118
$306$		0			0
$307$	−16.0263	−	16.0263i	−0.914668	−	0.914668i	0.0819670	−	0.996635i	$-0.473880\pi$
$307$	−16.0263	−	16.0263i	−0.914668	−	0.914668i	−0.996635	+	0.0819670i	$0.973880\pi$
$308$	1.12436	+	4.19615i	0.0640661	+	0.239098i
$309$		0			0
$310$	−35.3205	+	20.3923i	−2.00607	+	1.15821i
$311$	−13.9019	+	8.02628i	−0.788306	+	0.455129i	−0.839366	−	0.543567i	$-0.817073\pi$
$311$	−13.9019	+	8.02628i	−0.788306	+	0.455129i	0.0510600	+	0.998696i	$0.483740\pi$
$312$		0			0
$313$	24.6506	+	14.2321i	1.39334	+	0.804443i	0.993683	−	0.112223i	$-0.0357972\pi$
$313$	24.6506	+	14.2321i	1.39334	+	0.804443i	0.399653	+	0.916666i	$0.369131\pi$
$314$	6.92820			0.390981
$315$		0			0
$316$		−	24.0000i		−	1.35011i
$317$	−31.4904	+	8.43782i	−1.76868	+	0.473915i	−0.988445	−	0.151577i	$-0.951565\pi$
$317$	−31.4904	+	8.43782i	−1.76868	+	0.473915i	−0.780231	+	0.625492i	$0.784898\pi$
$318$		0			0
$319$	3.63397	+	6.29423i	0.203464	+	0.352409i
$320$	−8.00000	+	29.8564i	−0.447214	+	1.66902i
$321$		0			0
$322$	0.339746	+	1.26795i	0.0189333	+	0.0706600i
$323$	−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
$328$	8.19615	+	2.19615i	0.452557	+	0.121262i
$329$	−6.12436	+	3.53590i	−0.337647	+	0.194940i
$330$		0			0
$331$	5.09808	+	19.0263i	0.280216	+	1.04578i	0.952265	+	0.305273i	$0.0987476\pi$
$331$	5.09808	+	19.0263i	0.280216	+	1.04578i	−0.672049	+	0.740506i	$0.734586\pi$
$332$	−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	$-0.390984\pi$
$338$	−9.83013	+	36.6865i	−0.534688	+	1.99548i
$339$		0			0
$340$	−16.9282	+	4.53590i	−0.918061	+	0.245994i
$341$	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
$347$	24.7224	+	6.62436i	1.32717	+	0.355614i	0.851659	−	0.524096i	$-0.175597\pi$
$347$	24.7224	+	6.62436i	1.32717	+	0.355614i	0.475510	+	0.879710i	$0.342263\pi$
$348$		0			0
$349$	−7.73205	+	2.07180i	−0.413887	+	0.110901i	−0.459753	−	0.888047i	$-0.652062\pi$
$349$	−7.73205	+	2.07180i	−0.413887	+	0.110901i	0.0458657	+	0.998948i	$0.485395\pi$
$350$	−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
$355$	−10.9282	+	40.7846i	−0.580009	+	2.16462i
$356$	−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	$-0.872902\pi$
$359$		−	14.7321i		−	0.777528i	0.921337	−	0.388764i	$-0.127098\pi$
$360$		0			0
$361$		−	18.1962i		−	0.957692i
$362$	−23.1962	−	13.3923i	−1.21916	−	0.703884i
$363$		0			0
$364$	−2.39230	+	8.92820i	−0.125391	+	0.467965i
$365$	9.73205	−	36.3205i	0.509399	−	1.90110i
$366$		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
$371$	−0.535898	+	0.143594i	−0.0278225	+	0.00745501i
$372$		0			0
$373$	−5.63397	−	1.50962i	−0.291716	−	0.0781651i	0.109993	−	0.993932i	$-0.464917\pi$
$373$	−5.63397	−	1.50962i	−0.291716	−	0.0781651i	−0.401709	+	0.915767i	$0.631584\pi$
$374$	8.24167	−	4.75833i	0.426167	−	0.246047i
$375$		0			0
$376$	26.3923	−	7.07180i	1.36108	−	0.364700i
$377$			15.4641i			0.796442i
$378$		0			0
$379$	−18.7583	+	18.7583i	−0.963551	+	0.963551i	−0.999359	−	0.0358080i	$-0.988600\pi$
$379$	−18.7583	+	18.7583i	−0.963551	+	0.963551i	0.0358080	+	0.999359i	$0.488600\pi$
$380$	6.00000	+	3.46410i	0.307794	+	0.177705i
$381$		0			0
$382$	19.1962	+	5.14359i	0.982161	+	0.263169i
$383$	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
$389$	2.75833	+	10.2942i	0.139853	+	0.521938i	0.999931	+	0.0117752i	$0.00374824\pi$
$389$	2.75833	+	10.2942i	0.139853	+	0.521938i	−0.860078	+	0.510163i	$0.829585\pi$
$390$		0			0
$391$	2.49038	−	1.43782i	0.125944	−	0.0727138i
$392$	4.73205	−	17.6603i	0.239005	−	0.891978i
$393$		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	0.311306	−	0.950310i	$-0.399233\pi$
$397$	−12.7321	−	12.7321i	−0.639003	−	0.639003i	−0.950310	+	0.311306i	$0.899233\pi$
$398$	1.19615	−	0.320508i	0.0599577	−	0.0160656i
$399$		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
$403$	45.5167	−	12.1962i	2.26735	−	0.607534i
$404$	−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	−0.979051	−	0.203614i	$-0.934731\pi$
$409$	−26.1340	+	15.0885i	−1.29224	+	0.746076i	−0.313191	+	0.949690i	$0.601398\pi$
$410$	−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
$418$	−3.63397	−	0.973721i	−0.177744	−	0.0476262i
$419$	8.36603	−	31.2224i	0.408707	−	1.52532i	−0.388408	−	0.921488i	$-0.626975\pi$
$419$	8.36603	−	31.2224i	0.408707	−	1.52532i	0.797115	−	0.603828i	$-0.206359\pi$
$420$		0			0
$421$	0.588457	+	2.19615i	0.0286797	+	0.107034i	0.978782	−	0.204905i	$-0.0656884\pi$
$421$	0.588457	+	2.19615i	0.0286797	+	0.107034i	−0.950102	+	0.311938i	$0.899022\pi$
$422$	6.00000			0.292075
$423$		0			0
$424$	2.14359			0.104102
$425$	19.5000	+	11.2583i	0.945889	+	0.546109i
$426$		0			0
$427$	2.19615	+	0.588457i	0.106279	+	0.0284774i
$428$	−9.87564	+	36.8564i	−0.477357	+	1.78152i
$429$		0			0
$430$	6.73205	−	1.80385i	0.324648	−	0.0869893i
$431$	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	$0.517355\pi$
$434$	7.46410	−	2.00000i	0.358288	−	0.0960031i
$435$		0			0
$436$	−19.8564	−	5.32051i	−0.950949	−	0.254806i
$437$	−1.09808	−	0.294229i	−0.0525281	−	0.0140749i
$438$		0			0
$439$	−4.85641	−	2.80385i	−0.231784	−	0.133820i	0.379611	−	0.925146i	$-0.376058\pi$
$439$	−4.85641	−	2.80385i	−0.231784	−	0.133820i	−0.611395	+	0.791326i	$0.709391\pi$
$440$	−22.9282	+	22.9282i	−1.09306	+	1.09306i
$441$		0			0
$442$	20.2487			0.963133
$443$	5.25833	+	19.6244i	0.249831	+	0.932381i	0.970894	+	0.239511i	$0.0769873\pi$
$443$	5.25833	+	19.6244i	0.249831	+	0.932381i	−0.721063	+	0.692870i	$0.756346\pi$
$444$		0			0
$445$	−2.00000	+	7.46410i	−0.0948091	+	0.353832i
$446$	−30.1244	−	8.07180i	−1.42643	−	0.382211i
$447$		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	0.892348	−	0.451347i	$-0.149056\pi$
$457$	20.2583	+	11.6962i	0.947645	+	0.547123i	0.0552962	+	0.998470i	$0.482390\pi$
$458$		−	10.0000i		−	0.467269i
$459$		0			0
$460$	−6.92820	+	6.92820i	−0.323029	+	0.323029i
$461$	−2.56218	+	0.686533i	−0.119333	+	0.0319751i	−0.317991	−	0.948094i	$-0.603008\pi$
$461$	−2.56218	+	0.686533i	−0.119333	+	0.0319751i	0.198659	+	0.980069i	$0.436342\pi$
$462$		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	$0.973897\pi$
$464$	2.53590	−	9.46410i	0.117726	−	0.439360i
$465$		0			0
$466$	−9.83013	+	2.63397i	−0.455372	+	0.122017i
$467$	−4.36603	−	4.36603i	−0.202036	−	0.202036i	0.598836	−	0.800872i	$-0.295630\pi$
$467$	−4.36603	−	4.36603i	−0.202036	−	0.202036i	−0.800872	+	0.598836i	$0.795630\pi$
$468$		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
$475$	−2.30385	−	8.59808i	−0.105708	−	0.394507i
$476$	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
$482$	17.4904	+	4.68653i	0.796665	+	0.213466i
$483$		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	$0.119601\pi$
$487$			16.1962i			0.733918i	−0.930237	+	0.366959i	$0.880399\pi$
$488$	−7.60770	−	4.39230i	−0.344384	−	0.198830i
$489$		0			0
$490$	−30.5885	+	17.6603i	−1.38185	+	0.797809i
$491$	25.7224	+	6.89230i	1.16084	+	0.311045i	0.787300	−	0.616570i	$-0.211478\pi$
$491$	25.7224	+	6.89230i	1.16084	+	0.311045i	0.373537	+	0.927615i	$0.378145\pi$
$492$		0			0
$493$	5.36603	−	1.43782i	0.241674	−	0.0647563i
$494$	−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
$499$	−1.69615	+	6.33013i	−0.0759302	+	0.283375i	−0.993443	−	0.114332i	$-0.963527\pi$
$499$	−1.69615	+	6.33013i	−0.0759302	+	0.283375i	0.917512	+	0.397707i	$0.130194\pi$
$500$	−36.7846	−	9.85641i	−1.64506	−	0.440792i
$501$		0			0
$502$	4.90192	+	2.83013i	0.218784	+	0.126315i
$503$		−	27.7128i		−	1.23565i	−0.786314	−	0.617827i	$-0.788013\pi$
$503$		−	27.7128i		−	1.23565i	0.786314	−	0.617827i	$-0.211987\pi$
$504$		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
$509$	4.53590	−	16.9282i	0.201050	−	0.750329i	−0.789567	−	0.613664i	$-0.789695\pi$
$509$	4.53590	−	16.9282i	0.201050	−	0.750329i	0.990617	−	0.136665i	$-0.0436385\pi$
$510$		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
$515$	−34.0526	+	9.12436i	−1.50054	+	0.402067i
$516$		0			0
$517$	27.6865	+	7.41858i	1.21765	+	0.326269i
$518$	0.928203	+	1.60770i	0.0407829	+	0.0706381i
$519$		0			0
$520$	−66.6410	+	17.8564i	−2.92240	+	0.783055i
$521$		−	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
$523$	−14.4641	+	14.4641i	−0.632471	+	0.632471i	−0.948687	−	0.316216i	$-0.897588\pi$
$523$	−14.4641	+	14.4641i	−0.632471	+	0.632471i	0.316216	+	0.948687i	$0.397588\pi$
$524$	−1.66025	−	6.19615i	−0.0725285	−	0.270680i
$525$		0			0
$526$	9.92820	−	37.0526i	0.432890	−	1.61557i
$527$	−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
$533$	4.90192	+	18.2942i	0.212326	+	0.792411i
$534$		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	0.508614	−	0.860994i	$-0.330158\pi$
$541$	−8.19615	−	8.19615i	−0.352380	−	0.352380i	−0.860994	+	0.508614i	$0.830158\pi$
$542$	−7.46410	−	27.8564i	−0.320611	−	1.19654i
$543$		0			0
$544$	−12.3923	−	3.32051i	−0.531316	−	0.142366i
$545$	19.8564	+	34.3923i	0.850555	+	1.47320i
$546$		0			0
$547$	−31.2583	+	8.37564i	−1.33651	+	0.358117i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−31.2583	+	8.37564i	−1.33651	+	0.358117i	−0.481371	+	0.876517i	$0.659861\pi$
$548$	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
$556$	18.1244	−	4.85641i	0.768644	−	0.205958i
$557$	25.1962	+	25.1962i	1.06760	+	1.06760i	0.997543	+	0.0700519i	$0.0223165\pi$
$557$	25.1962	+	25.1962i	1.06760	+	1.06760i	0.0700519	+	0.997543i	$0.477684\pi$
$558$		0			0
$559$	−8.05256			−0.340587
$560$	−10.9282	+	2.92820i	−0.461801	+	0.123739i
$561$		0			0
$562$	3.66025	−	13.6603i	0.154398	−	0.576223i
$563$	−1.00962	+	3.76795i	−0.0425504	+	0.158800i	−0.983932	−	0.178543i	$-0.942862\pi$
$563$	−1.00962	+	3.76795i	−0.0425504	+	0.158800i	0.941382	+	0.337343i	$0.109528\pi$
$564$		0			0
$565$	−13.8564	−	51.7128i	−0.582943	−	2.17557i
$566$		−	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	−0.0842230	−	0.996447i	$-0.526841\pi$
$569$	−23.5981	−	13.6244i	−0.989283	−	0.571163i	−0.905060	+	0.425284i	$0.860174\pi$
$570$		0			0
$571$	−19.8923	−	5.33013i	−0.832467	−	0.223059i	−0.182677	−	0.983173i	$-0.558476\pi$
$571$	−19.8923	−	5.33013i	−0.832467	−	0.223059i	−0.649790	+	0.760114i	$0.725143\pi$
$572$	32.4449	−	18.7321i	1.35659	−	0.783226i
$573$		0			0
$574$	0.803848	+	3.00000i	0.0335519	+	0.125218i
$575$	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	$0.232513\pi$
$578$	4.33975	+	16.1962i	0.180510	+	0.673671i
$579$		0			0
$580$	−16.3923	+	9.46410i	−0.680653	+	0.392975i
$581$	−1.00000	−	0.267949i	−0.0414870	−	0.0111164i
$582$		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
$587$	1.00962	+	3.76795i	0.0416714	+	0.155520i	0.983626	−	0.180219i	$-0.0576807\pi$
$587$	1.00962	+	3.76795i	0.0416714	+	0.155520i	−0.941955	+	0.335739i	$0.891014\pi$
$588$		0			0
$589$	−1.73205	+	6.46410i	−0.0713679	+	0.266349i
$590$	−7.26795	+	27.1244i	−0.299217	+	1.11669i
$591$		0			0
$592$	−1.85641	−	6.92820i	−0.0762978	−	0.284747i
$593$	−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
$596$	6.19615	−	1.66025i	0.253804	−	0.0680067i
$597$		0			0
$598$	9.80385	−	5.66025i	0.400909	−	0.231465i
$599$	−23.3205	+	13.4641i	−0.952850	+	0.550128i	−0.893965	−	0.448136i	$-0.852088\pi$
$599$	−23.3205	+	13.4641i	−0.952850	+	0.550128i	−0.0588850	+	0.998265i	$0.518755\pi$
$600$		0			0
$601$	−17.5526	−	10.1340i	−0.715984	−	0.413373i	0.0972889	−	0.995256i	$-0.468983\pi$
$601$	−17.5526	−	10.1340i	−0.715984	−	0.413373i	−0.813273	+	0.581883i	$0.802316\pi$
$602$	−1.32051			−0.0538199
$603$		0			0
$604$	5.46410			0.222331
$605$	8.19615	−	2.19615i	0.333221	−	0.0892863i
$606$		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
$610$	4.39230	+	16.3923i	0.177839	+	0.663705i
$611$	43.1244	+	43.1244i	1.74462	+	1.74462i
$612$		0			0
$613$	1.66025	−	1.66025i	0.0670570	−	0.0670570i	−0.672783	−	0.739840i	$-0.734901\pi$
$613$	1.66025	−	1.66025i	0.0670570	−	0.0670570i	0.739840	+	0.672783i	$0.234901\pi$
$614$	−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	−0.576666	−	0.816980i	$-0.695646\pi$
$617$	−3.91154	+	2.25833i	−0.157473	+	0.0909170i	0.419193	+	0.907897i	$0.362313\pi$
$618$		0			0
$619$	−10.4019	−	38.8205i	−0.418089	−	1.56033i	−0.778568	−	0.627561i	$-0.784053\pi$
$619$	−10.4019	−	38.8205i	−0.418089	−	1.56033i	0.360479	−	0.932767i	$-0.382613\pi$
$620$	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
$626$	10.4186	−	38.8827i	0.416410	−	1.55406i
$627$		0			0
$628$	−2.53590	−	9.46410i	−0.101193	−	0.377659i
$629$	2.87564	−	2.87564i	0.114659	−	0.114659i
$630$		0			0
$631$			38.3923i			1.52837i	0.644995	+	0.764187i	$0.276859\pi$
$631$			38.3923i			1.52837i	−0.644995	+	0.764187i	$0.723141\pi$
$632$	−32.7846	+	8.78461i	−1.30410	+	0.349433i
$633$		0			0
$634$	23.0526	+	39.9282i	0.915534	+	1.58575i
$635$	−23.1244	−	6.19615i	−0.917662	−	0.245887i
$636$		0			0
$637$	39.4186	−	10.5622i	1.56182	−	0.418489i
$638$	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
$643$	12.2321	−	45.6506i	0.482385	−	1.80029i	−0.109173	−	0.994023i	$-0.534820\pi$
$643$	12.2321	−	45.6506i	0.482385	−	1.80029i	0.591558	−	0.806263i	$-0.298513\pi$
$644$	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	$-0.916011\pi$
$647$		−	13.2679i		−	0.521617i	0.965391	−	0.260808i	$-0.0839891\pi$
$648$		0			0
$649$		−	15.2487i		−	0.598564i
$650$	76.7654	+	44.3205i	3.01099	+	1.73839i
$651$		0			0
$652$	19.1244	+	5.12436i	0.748968	+	0.200685i
$653$	1.50962	−	5.63397i	0.0590760	−	0.220474i	−0.930077	−	0.367365i	$-0.880260\pi$
$653$	1.50962	−	5.63397i	0.0590760	−	0.220474i	0.989153	+	0.146891i	$0.0469266\pi$
$654$		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
$659$	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	$0.636102\pi$
$662$	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
$670$	−28.5885	−	7.66025i	−1.10447	−	0.295941i
$671$	−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
$677$	1.26795	+	4.73205i	0.0487312	+	0.181867i	0.986002	−	0.166736i	$-0.0533227\pi$
$677$	1.26795	+	4.73205i	0.0487312	+	0.181867i	−0.937270	+	0.348603i	$0.886656\pi$
$678$		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	−0.611321	−	0.791383i	$-0.709362\pi$
$683$	4.70577	−	4.70577i	0.180061	−	0.180061i	0.791383	+	0.611321i	$0.209362\pi$
$684$		0			0
$685$	−44.9808	−	44.9808i	−1.71863	−	1.71863i
$686$	13.4641	−	3.60770i	0.514062	−	0.137742i
$687$		0			0
$688$	4.92820	+	1.32051i	0.187886	+	0.0503439i
$689$	2.39230	+	4.14359i	0.0911396	+	0.157858i
$690$		0			0
$691$	23.4904	−	6.29423i	0.893616	−	0.239444i	0.217344	−	0.976095i	$-0.430261\pi$
$691$	23.4904	−	6.29423i	0.893616	−	0.239444i	0.676273	+	0.736651i	$0.263594\pi$
$692$	−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	0.476527	−	0.879160i	$-0.341895\pi$
$701$	−10.6603	−	10.6603i	−0.402632	−	0.402632i	−0.879160	+	0.476527i	$0.841895\pi$
$702$		0			0
$703$	−1.60770			−0.0606354
$704$	−22.9282	+	6.14359i	−0.864139	+	0.231545i
$705$		0			0
$706$	−27.7583	−	7.43782i	−1.04470	−	0.279926i
$707$	1.46410	−	5.46410i	0.0550632	−	0.205499i
$708$		0			0
$709$	5.41154	+	20.1962i	0.203235	+	0.758482i	0.989980	+	0.141205i	$0.0450977\pi$
$709$	5.41154	+	20.1962i	0.203235	+	0.758482i	−0.786746	+	0.617277i	$0.788236\pi$
$710$	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
$715$	−69.9090	−	18.7321i	−2.61445	−	0.700539i
$716$	32.5885	+	8.73205i	1.21789	+	0.326332i
$717$		0			0
$718$	−20.1244	+	5.39230i	−0.751034	+	0.201239i
$719$	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
$722$	−24.8564	+	6.66025i	−0.925060	+	0.247869i
$723$		0			0
$724$	−9.80385	+	36.5885i	−0.364357	+	1.35980i
$725$	23.4904	+	6.29423i	0.872411	+	0.233762i
$726$		0			0
$727$	−31.8109	−	18.3660i	−1.17980	−	0.681158i	−0.223832	−	0.974628i	$-0.571857\pi$
$727$	−31.8109	−	18.3660i	−1.17980	−	0.681158i	−0.955968	+	0.293470i	$0.905190\pi$
$728$	13.0718			0.484473
$729$		0			0
$730$	−53.1769			−1.96817
$731$	0.748711	+	2.79423i	0.0276921	+	0.103348i
$732$		0			0
$733$	8.02628	−	29.9545i	0.296457	−	1.10639i	−0.643596	−	0.765366i	$-0.722558\pi$
$733$	8.02628	−	29.9545i	0.296457	−	1.10639i	0.940053	−	0.341028i	$-0.110775\pi$
$734$	27.6603	+	7.41154i	1.02096	+	0.273565i
$735$		0			0
$736$	−6.92820	+	1.85641i	−0.255377	+	0.0684280i
$737$	16.0718			0.592012
$738$		0			0
$739$	21.2224	+	21.2224i	0.780680	+	0.780680i	0.979945	−	0.199266i	$-0.0638557\pi$
$739$	21.2224	+	21.2224i	0.780680	+	0.780680i	−0.199266	+	0.979945i	$0.563856\pi$
$740$	−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	−0.458317	−	0.888789i	$-0.651547\pi$
$743$	2.24167	−	1.29423i	0.0822389	−	0.0474806i	0.540556	+	0.841308i	$0.318214\pi$
$744$		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
$749$	−13.4904	+	3.61474i	−0.492928	+	0.132080i
$750$		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
$754$	21.1244	−	5.66025i	0.769304	−	0.206134i
$755$	−7.46410	−	7.46410i	−0.271646	−	0.271646i
$756$		0			0
$757$	−6.07180	+	6.07180i	−0.220683	+	0.220683i	−0.808786	−	0.588103i	$-0.799875\pi$
$757$	−6.07180	+	6.07180i	−0.220683	+	0.220683i	0.588103	+	0.808786i	$0.299875\pi$
$758$	32.4904	+	18.7583i	1.18010	+	0.681333i
$759$		0			0
$760$	2.53590	−	9.46410i	0.0919867	−	0.343299i
$761$	−27.3731	+	15.8038i	−0.992273	+	0.572889i	−0.905953	−	0.423378i	$-0.860844\pi$
$761$	−27.3731	+	15.8038i	−0.992273	+	0.572889i	−0.0863200	+	0.996267i	$0.527511\pi$
$762$		0			0
$763$	−1.94744	−	7.26795i	−0.0705021	−	0.263117i
$764$		−	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	$0.714370\pi$
$770$	−11.4641	−	3.07180i	−0.413138	−	0.110700i
$771$		0			0
$772$	31.6410	+	18.2679i	1.13879	+	0.657478i
$773$	−4.41154	+	4.41154i	−0.158672	+	0.158672i	−0.781978	−	0.623306i	$-0.785789\pi$
$773$	−4.41154	+	4.41154i	−0.158672	+	0.158672i	0.623306	+	0.781978i	$0.285789\pi$
$774$		0			0
$775$		−	74.1051i		−	2.66193i
$776$	−22.5885	+	6.05256i	−0.810878	+	0.217274i
$777$		0			0
$778$	13.0526	−	7.53590i	0.467957	−	0.270175i
$779$	−2.59808	−	0.696152i	−0.0930857	−	0.0249422i
$780$		0			0
$781$	−31.3205	+	8.39230i	−1.12074	+	0.300300i
$782$	−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
$787$	−13.3468	+	49.8109i	−0.475762	+	1.77557i	0.142716	+	0.989764i	$0.454417\pi$
$787$	−13.3468	+	49.8109i	−0.475762	+	1.77557i	−0.618477	+	0.785803i	$0.712250\pi$
$788$	−2.67949	+	10.0000i	−0.0954529	+	0.356235i
$789$		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
$797$	−14.5167	+	54.1769i	−0.514206	+	1.91904i	−0.146065	+	0.989275i	$0.546661\pi$
$797$	−14.5167	+	54.1769i	−0.514206	+	1.91904i	−0.368142	+	0.929770i	$0.620006\pi$
$798$		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
$803$	27.8923	−	7.47372i	0.984298	−	0.263742i
$804$		0			0
$805$	−3.46410	−	0.928203i	−0.122094	−	0.0327149i
$806$	−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	$-0.834124\pi$
$809$		−	28.3205i		−	0.995696i	0.867264	−	0.497848i	$-0.165876\pi$
$810$		0			0
$811$	5.02628	−	5.02628i	0.176497	−	0.176497i	−0.613330	−	0.789827i	$-0.710170\pi$
$811$	5.02628	−	5.02628i	0.176497	−	0.176497i	0.789827	+	0.613330i	$0.210170\pi$
$812$	3.46410	−	0.928203i	0.121566	−	0.0325735i
$813$		0			0
$814$	1.94744	−	7.26795i	0.0682578	−	0.254741i
$815$	−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
$821$	8.63397	+	32.2224i	0.301328	+	1.12457i	0.936061	+	0.351839i	$0.114444\pi$
$821$	8.63397	+	32.2224i	0.301328	+	1.12457i	−0.634733	+	0.772732i	$0.718890\pi$
$822$		0			0
$823$	−10.7321	+	6.19615i	−0.374096	+	0.215984i	−0.675246	−	0.737592i	$-0.735963\pi$
$823$	−10.7321	+	6.19615i	−0.374096	+	0.215984i	0.301151	+	0.953577i	$0.402629\pi$
$824$	−24.9282	−	6.67949i	−0.868415	−	0.232691i
$825$		0			0
$826$	2.66025	−	4.60770i	0.0925621	−	0.160322i
$827$	−24.4641	+	24.4641i	−0.850700	+	0.850700i	−0.990219	−	0.139519i	$-0.955444\pi$
$827$	−24.4641	+	24.4641i	−0.850700	+	0.850700i	0.139519	+	0.990219i	$0.455444\pi$
$828$		0			0
$829$	24.5167	+	24.5167i	0.851499	+	0.851499i	0.990318	−	0.138819i	$-0.0443306\pi$
$829$	24.5167	+	24.5167i	0.851499	+	0.851499i	−0.138819	+	0.990318i	$0.544331\pi$
$830$	−2.00000	−	7.46410i	−0.0694210	−	0.259083i
$831$		0			0
$832$	−48.7846	−	13.0718i	−1.69130	−	0.453183i
$833$	−7.33013	−	12.6962i	−0.253974	−	0.439896i
$834$		0			0
$835$	−2.00000	+	0.535898i	−0.0692129	+	0.0185455i
$836$			5.32051i			0.184014i
$837$		0			0
$838$	−45.7128			−1.57912
$839$	−35.4449	−	20.4641i	−1.22369	−	0.706499i	−0.257989	−	0.966148i	$-0.583060\pi$
$839$	−35.4449	−	20.4641i	−1.22369	−	0.706499i	−0.965703	+	0.259649i	$0.916393\pi$
$840$		0			0
$841$	−19.9186	+	11.5000i	−0.686848	+	0.396552i
$842$	2.78461	−	1.60770i	0.0959640	−	0.0554048i
$843$		0			0
$844$	−2.19615	−	8.19615i	−0.0755947	−	0.282123i
$845$	−73.3731	−	73.3731i	−2.52411	−	2.52411i
$846$		0			0
$847$	−1.60770			−0.0552411
$848$	−0.784610	−	2.92820i	−0.0269436	−	0.100555i
$849$		0			0
$850$	8.24167	−	30.7583i	0.282687	−	1.05500i
$851$	0.588457	−	2.19615i	0.0201721	−	0.0752831i
$852$		0			0
$853$	3.36603	+	12.5622i	0.115251	+	0.430121i	0.999306	−	0.0372621i	$-0.0118636\pi$
$853$	3.36603	+	12.5622i	0.115251	+	0.430121i	−0.884055	+	0.467383i	$0.845197\pi$
$854$		−	3.21539i		−	0.110028i
$855$		0			0
$856$	53.9615			1.84437
$857$	20.9090	+	12.0718i	0.714237	+	0.412365i	0.812628	−	0.582783i	$-0.198036\pi$
$857$	20.9090	+	12.0718i	0.714237	+	0.412365i	−0.0983911	+	0.995148i	$0.531370\pi$
$858$		0			0
$859$	30.8205	+	8.25833i	1.05158	+	0.281771i	0.742905	−	0.669396i	$-0.233447\pi$
$859$	30.8205	+	8.25833i	1.05158	+	0.281771i	0.308677	+	0.951167i	$0.400114\pi$
$860$	−4.92820	−	8.53590i	−0.168050	−	0.291072i
$861$		0			0
$862$	−2.12436	−	7.92820i	−0.0723558	−	0.270036i
$863$	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
$866$	0.830127	+	3.09808i	0.0282089	+	0.105277i
$867$		0			0
$868$	−5.46410	−	9.46410i	−0.185464	−	0.321233i
$869$	−34.3923	−	9.21539i	−1.16668	−	0.312611i
$870$		0			0
$871$	29.6147	+	17.0981i	1.00346	+	0.579346i
$872$			29.0718i			0.984495i
$873$		0			0
$874$			1.60770i			0.0543811i
$875$	−3.60770	−	13.4641i	−0.121962	−	0.455170i
$876$		0			0
$877$	0.411543	−	1.53590i	0.0138968	−	0.0518636i	−0.958629	−	0.284658i	$-0.908120\pi$
$877$	0.411543	−	1.53590i	0.0138968	−	0.0518636i	0.972526	+	0.232794i	$0.0747868\pi$
$878$	−2.05256	+	7.66025i	−0.0692705	+	0.258521i
$879$		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	0.422778	−	0.906233i	$-0.361055\pi$
$883$	−14.3660	−	14.3660i	−0.483455	−	0.483455i	−0.906233	+	0.422778i	$0.861055\pi$
$884$	−7.41154	−	27.6603i	−0.249277	−	0.930315i
$885$		0			0
$886$	24.8827	−	14.3660i	0.835950	−	0.482636i
$887$	33.1244	−	19.1244i	1.11221	−	0.642133i	0.172807	−	0.984956i	$-0.444716\pi$
$887$	33.1244	−	19.1244i	1.11221	−	0.642133i	0.939400	+	0.342823i	$0.111383\pi$
$888$		0			0
$889$	3.92820	+	2.26795i	0.131748	+	0.0760646i
$890$	10.9282			0.366314
$891$		0			0
$892$			44.1051i			1.47675i
$893$	−8.36603	+	2.24167i	−0.279958	+	0.0750146i
$894$		0			0
$895$	−32.5885	−	56.4449i	−1.08931	−	1.88674i
$896$	−8.00000	−	2.14359i	−0.267261	−	0.0716124i
$897$		0			0
$898$	−7.56218	−	28.2224i	−0.252353	−	0.941795i
$899$	−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
$904$	10.1436	−	37.8564i	0.337371	−	1.25909i
$905$	63.3731	−	36.5885i	2.10659	−	1.21624i
$906$		0			0
$907$	4.50000	+	16.7942i	0.149420	+	0.557643i	0.999519	+	0.0310198i	$0.00987551\pi$
$907$	4.50000	+	16.7942i	0.149420	+	0.557643i	−0.850099	+	0.526623i	$0.823458\pi$
$908$	−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
$914$	8.56218	−	31.9545i	0.283212	−	1.05696i
$915$		0			0
$916$	−13.6603	+	3.66025i	−0.451347	+	0.120938i
$917$	1.66025	−	1.66025i	0.0548264	−	0.0548264i
$918$		0			0
$919$		−	32.9808i		−	1.08793i	−0.839106	−	0.543967i	$-0.816921\pi$
$919$		−	32.9808i		−	1.08793i	0.839106	−	0.543967i	$-0.183079\pi$
$920$	12.0000	+	6.92820i	0.395628	+	0.228416i
$921$		0			0
$922$	1.87564	+	3.24871i	0.0617711	+	0.106991i
$923$	−66.6410	−	17.8564i	−2.19352	−	0.587751i
$924$		0			0
$925$	17.1962	−	4.60770i	0.565406	−	0.151500i
$926$	−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
$931$	−1.50000	+	5.59808i	−0.0491605	+	0.183470i
$932$	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	$0.315076\pi$
$937$			51.1769i			1.67188i	−0.548823	+	0.835938i	$0.684924\pi$
$938$	4.85641	+	2.80385i	0.158567	+	0.0915489i
$939$		0			0
$940$	−19.3205	+	72.1051i	−0.630165	+	2.35181i
$941$	−3.26795	+	12.1962i	−0.106532	+	0.397583i	−0.998514	−	0.0544870i	$-0.982648\pi$
$941$	−3.26795	+	12.1962i	−0.106532	+	0.397583i	0.891982	+	0.452070i	$0.149314\pi$
$942$		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
$947$	−14.9904	+	4.01666i	−0.487122	+	0.130524i	−0.494017	−	0.869452i	$-0.664472\pi$
$947$	−14.9904	+	4.01666i	−0.487122	+	0.130524i	0.00689497	+	0.999976i	$0.497805\pi$
$948$		0			0
$949$	59.3468	+	15.9019i	1.92648	+	0.516198i
$950$	−10.9019	+	6.29423i	−0.353705	+	0.204212i
$951$		0			0
$952$	−1.21539	−	4.53590i	−0.0393910	−	0.147009i
$953$			59.1051i			1.91460i	0.289092	+	0.957301i	$0.406647\pi$
$953$			59.1051i			1.91460i	−0.289092	+	0.957301i	$0.593353\pi$
$954$		0			0
$955$	−38.3923	+	38.3923i	−1.24235	+	1.24235i
$956$	−45.3731	−	26.1962i	−1.46747	−	0.847244i
$957$		0			0
$958$	35.0526	+	9.39230i	1.13250	+	0.303452i
$959$	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
$965$	−18.2679	−	68.1769i	−0.588066	−	2.19469i
$966$		0			0
$967$	−9.16987	+	5.29423i	−0.294883	+	0.170251i	−0.640142	−	0.768257i	$-0.721124\pi$
$967$	−9.16987	+	5.29423i	−0.294883	+	0.170251i	0.345259	+	0.938508i	$0.387791\pi$
$968$	6.00000	+	1.60770i	0.192847	+	0.0516733i
$969$		0			0
$970$	39.1244	+	22.5885i	1.25621	+	0.725272i
$971$	−22.4641	+	22.4641i	−0.720907	+	0.720907i	−0.968790	−	0.247883i	$-0.920265\pi$
$971$	−22.4641	+	22.4641i	−0.720907	+	0.720907i	0.247883	+	0.968790i	$0.420265\pi$
$972$		0			0
$973$	4.85641	+	4.85641i	0.155689	+	0.155689i
$974$	22.1244	−	5.92820i	0.708910	−	0.189952i
$975$		0			0
$976$	−3.21539	+	12.0000i	−0.102922	+	0.384111i
$977$	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
$979$	−5.73205	+	1.53590i	−0.183197	+	0.0490875i
$980$	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	0.262474	−	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
$986$	−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	$0.673486\pi$
$992$	10.9282	+	40.7846i	0.346971	+	1.29491i
$993$		0			0
$994$	−10.9282	−	2.92820i	−0.346622	−	0.0928770i
$995$	−0.875644	+	3.26795i	−0.0277598	+	0.103601i
$996$		0			0
$997$	−8.60770	−	32.1244i	−0.272608	−	1.01739i	−0.957427	−	0.288675i	$-0.906785\pi$
$997$	−8.60770	−	32.1244i	−0.272608	−	1.01739i	0.684819	−	0.728713i	$-0.259881\pi$
$998$	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.c.397.1		4
3.2	odd	2		144.2.x.b.61.1	✓	4
4.3	odd	2		1728.2.bc.d.721.1		4
9.4	even	3		432.2.y.b.253.1		4
9.5	odd	6		144.2.x.c.13.1	yes	4
12.11	even	2		576.2.bb.d.529.1		4
16.5	even	4		432.2.y.b.181.1		4
16.11	odd	4		1728.2.bc.a.1585.1		4
36.23	even	6		576.2.bb.c.337.1		4
36.31	odd	6		1728.2.bc.a.145.1		4
48.5	odd	4		144.2.x.c.133.1	yes	4
48.11	even	4		576.2.bb.c.241.1		4
144.5	odd	12		144.2.x.b.85.1	yes	4
144.59	even	12		576.2.bb.d.49.1		4
144.85	even	12	inner	432.2.y.c.37.1		4
144.139	odd	12		1728.2.bc.d.1009.1		4

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

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)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(3.73205 + 1.00000i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(3.73205 + 1.00000i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.46410i q^{10} +(0.767949 + 2.86603i) q^{11} +(-1.63397 + 6.09808i) q^{13} +(-0.267949 + 1.00000i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 - 0.633975i) q^{19} +(-7.46410 + 2.00000i) q^{20} +(3.63397 - 2.09808i) q^{22} +(1.09808 - 0.633975i) q^{23} +(8.59808 + 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(2.36603 - 0.633975i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-0.830127 - 3.09808i) q^{34} +(-2.00000 - 2.00000i) q^{35} +(1.26795 - 1.26795i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(5.46410 + 9.46410i) q^{40} +(2.59808 - 1.50000i) q^{41} +(0.330127 + 1.23205i) q^{43} +(-4.19615 - 4.19615i) q^{44} +(-1.26795 - 1.26795i) q^{46} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(3.63397 - 13.5622i) q^{50} +(-3.26795 - 12.1962i) q^{52} +(0.535898 - 0.535898i) q^{53} +11.4641i q^{55} +(-0.535898 - 2.00000i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(-4.96410 - 1.33013i) q^{59} +(-3.00000 + 0.803848i) q^{61} +(-7.46410 + 7.46410i) q^{62} +8.00000i q^{64} +(-12.1962 + 21.1244i) q^{65} +(1.40192 - 5.23205i) q^{67} +(-3.92820 + 2.26795i) q^{68} +(-2.00000 + 3.46410i) q^{70} +10.9282i q^{71} -9.73205i q^{73} +(-2.19615 - 1.26795i) q^{74} +(1.73205 + 0.464102i) q^{76} +(0.562178 - 2.09808i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(10.9282 - 10.9282i) q^{80} +(-3.00000 - 3.00000i) q^{82} +(1.36603 - 0.366025i) q^{83} +(8.46410 + 2.26795i) q^{85} +(1.56218 - 0.901924i) q^{86} +(-4.19615 + 7.26795i) q^{88} +2.00000i q^{89} +(3.26795 - 3.26795i) q^{91} +(-1.26795 + 2.19615i) q^{92} +(-13.1962 - 3.53590i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(-6.46410 + 6.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 8 q^{5} - 6 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 8 * q^5 - 6 * q^7 + 8 * q^8	\( 4 q + 2 q^{2} + 8 q^{5} - 6 q^{7} + 8 q^{8} + 10 q^{11} - 10 q^{13} - 8 q^{14} + 8 q^{16} + 16 q^{17} - 6 q^{19} - 16 q^{20} + 18 q^{22} - 6 q^{23} + 24 q^{25} + 8 q^{26} - 8 q^{28} + 6 q^{29} - 8 q^{31} - 8 q^{32} + 14 q^{34} - 8 q^{35} + 12 q^{37} - 6 q^{38} + 8 q^{40} - 16 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{47} - 6 q^{49} + 18 q^{50} - 20 q^{52} + 16 q^{53} - 16 q^{56} - 6 q^{59} - 12 q^{61} - 16 q^{62} - 28 q^{65} + 16 q^{67} + 12 q^{68} - 8 q^{70} + 12 q^{74} - 22 q^{77} - 24 q^{79} + 16 q^{80} - 12 q^{82} + 2 q^{83} + 20 q^{85} - 18 q^{86} + 4 q^{88} + 20 q^{91} - 12 q^{92} - 32 q^{94} - 20 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 8 * q^5 - 6 * q^7 + 8 * q^8 + 10 * q^11 - 10 * q^13 - 8 * q^14 + 8 * q^16 + 16 * q^17 - 6 * q^19 - 16 * 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 + 14 * q^34 - 8 * q^35 + 12 * q^37 - 6 * q^38 + 8 * q^40 - 16 * q^43 + 4 * q^44 - 12 * q^46 + 2 * q^47 - 6 * q^49 + 18 * q^50 - 20 * q^52 + 16 * q^53 - 16 * q^56 - 6 * q^59 - 12 * q^61 - 16 * q^62 - 28 * q^65 + 16 * q^67 + 12 * q^68 - 8 * q^70 + 12 * q^74 - 22 * q^77 - 24 * q^79 + 16 * q^80 - 12 * q^82 + 2 * q^83 + 20 * q^85 - 18 * q^86 + 4 * q^88 + 20 * q^91 - 12 * q^92 - 32 * q^94 - 20 * q^97 - 12 * q^98

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