LMFDB - Embedded newform 252.2.bf.e.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	252.19
Dual form			252.2.bf.e.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.36603 + 0.633975i) q^{10} +(-0.866025 + 0.500000i) q^{11} +3.46410i q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.50000 - 0.866025i) q^{17} +(-2.59808 + 4.50000i) q^{19} +3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(1.26795 + 4.73205i) q^{26} +(-5.00000 - 1.73205i) q^{28} -4.00000 q^{29} +(-0.866025 - 1.50000i) q^{31} +(1.46410 - 5.46410i) q^{32} +(1.73205 - 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(4.73205 - 1.26795i) q^{40} +3.46410i q^{41} -2.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.36603 - 0.366025i) q^{46} +(-4.33013 + 7.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-2.00000 - 2.00000i) q^{50} +(3.46410 + 6.00000i) q^{52} +(-0.500000 - 0.866025i) q^{53} -1.73205 q^{55} +(-7.46410 - 0.535898i) q^{56} +(-5.46410 + 1.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-4.50000 - 2.59808i) q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +(-3.00000 + 5.19615i) q^{65} +(2.59808 - 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} +(-2.83013 - 5.83013i) q^{70} -14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-1.09808 + 4.09808i) q^{74} +10.3923i q^{76} +(2.50000 + 0.866025i) q^{77} +(7.79423 + 4.50000i) q^{79} +(6.00000 - 3.46410i) q^{80} +(1.26795 + 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(-0.732051 - 2.73205i) q^{86} +(-0.732051 + 2.73205i) q^{88} +(-13.5000 - 7.79423i) q^{89} +(6.92820 - 6.00000i) q^{91} -2.00000 q^{92} +(-3.16987 + 11.8301i) q^{94} +(-7.79423 + 4.50000i) q^{95} -17.3205i q^{97} +(1.16987 + 9.83013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{5} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^5 + 8 * q^8	$ 4 q + 2 q^{2} + 6 q^{5} + 8 q^{8} + 6 q^{10} - 2 q^{14} + 8 q^{16} + 6 q^{17} - 4 q^{22} - 4 q^{25} + 12 q^{26} - 20 q^{28} - 16 q^{29} - 8 q^{32} - 6 q^{37} - 18 q^{38} + 12 q^{40} - 4 q^{44} - 2 q^{46} - 4 q^{49} - 8 q^{50} - 2 q^{53} - 16 q^{56} - 8 q^{58} - 18 q^{61} - 12 q^{65} + 6 q^{70} + 30 q^{73} + 6 q^{74} + 10 q^{77} + 24 q^{80} + 12 q^{82} + 12 q^{85} + 4 q^{86} + 4 q^{88} - 54 q^{89} - 8 q^{92} - 30 q^{94} + 22 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^5 + 8 * q^8 + 6 * q^10 - 2 * q^14 + 8 * q^16 + 6 * q^17 - 4 * q^22 - 4 * q^25 + 12 * q^26 - 20 * q^28 - 16 * q^29 - 8 * q^32 - 6 * q^37 - 18 * q^38 + 12 * q^40 - 4 * q^44 - 2 * q^46 - 4 * q^49 - 8 * q^50 - 2 * q^53 - 16 * q^56 - 8 * q^58 - 18 * q^61 - 12 * q^65 + 6 * q^70 + 30 * q^73 + 6 * q^74 + 10 * q^77 + 24 * q^80 + 12 * q^82 + 12 * q^85 + 4 * q^86 + 4 * q^88 - 54 * q^89 - 8 * q^92 - 30 * q^94 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.36603	−	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
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	2.36603	+	0.633975i	0.748203	+	0.200480i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i	−0.624844	−	0.780750i	$-0.714837\pi$
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i	0.363727	+	0.931505i	$0.381504\pi$
$12$		0			0
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	−3.09808	−	2.09808i	−0.827996	−	0.560734i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	−0.306944	−	0.951727i	$-0.599307\pi$
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	0.670748	+	0.741685i	$0.265973\pi$
$18$		0			0
$19$	−2.59808	+	4.50000i	−0.596040	+	1.03237i	0.397360	+	0.917663i	$0.369927\pi$
$19$	−2.59808	+	4.50000i	−0.596040	+	1.03237i	−0.993399	+	0.114708i	$0.963407\pi$
$20$	3.46410			0.774597
$21$		0			0
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	0.406986	−	0.913434i	$-0.366580\pi$
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	−0.587565	+	0.809177i	$0.699913\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	1.26795	+	4.73205i	0.248665	+	0.928032i
$27$		0			0
$28$	−5.00000	−	1.73205i	−0.944911	−	0.327327i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−0.866025	−	1.50000i	−0.155543	−	0.269408i	0.777714	−	0.628619i	$-0.216379\pi$
$31$	−0.866025	−	1.50000i	−0.155543	−	0.269408i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$		0			0
$34$	1.73205	−	1.73205i	0.297044	−	0.297044i
$35$	−0.866025	−	4.50000i	−0.146385	−	0.760639i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	−1.90192	+	7.09808i	−0.308533	+	1.15146i
$39$		0			0
$40$	4.73205	−	1.26795i	0.748203	−	0.200480i
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$		0			0
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−1.36603	−	0.366025i	−0.201409	−	0.0539675i
$47$	−4.33013	+	7.50000i	−0.631614	+	1.09399i	0.355608	+	0.934635i	$0.384274\pi$
$47$	−4.33013	+	7.50000i	−0.631614	+	1.09399i	−0.987222	+	0.159352i	$0.949059\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$	−2.00000	−	2.00000i	−0.282843	−	0.282843i
$51$		0			0
$52$	3.46410	+	6.00000i	0.480384	+	0.832050i
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$		0			0
$55$	−1.73205			−0.233550
$56$	−7.46410	−	0.535898i	−0.997433	−	0.0716124i
$57$		0			0
$58$	−5.46410	+	1.46410i	−0.717472	+	0.192246i
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	0.984102	−	0.177605i	$-0.0568349\pi$
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	−0.645861	+	0.763455i	$0.723502\pi$
$60$		0			0
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	0.183442	−	0.983030i	$-0.441276\pi$
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	−0.759608	+	0.650381i	$0.774609\pi$
$62$	−1.73205	−	1.73205i	−0.219971	−	0.219971i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608004\pi$
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$68$	1.73205	−	3.00000i	0.210042	−	0.363803i
$69$		0			0
$70$	−2.83013	−	5.83013i	−0.338265	−	0.696833i
$71$		−	14.0000i		−	1.66149i	−0.556650	−	0.830747i	$-0.687914\pi$
$71$		−	14.0000i		−	1.66149i	0.556650	−	0.830747i	$-0.312086\pi$
$72$		0			0
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.00787336	−	0.999969i	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$	−1.09808	+	4.09808i	−0.127649	+	0.476392i
$75$		0			0
$76$			10.3923i			1.19208i
$77$	2.50000	+	0.866025i	0.284901	+	0.0986928i
$78$		0			0
$79$	7.79423	+	4.50000i	0.876919	+	0.506290i	0.869641	−	0.493684i	$-0.164350\pi$
$79$	7.79423	+	4.50000i	0.876919	+	0.506290i	0.00727784	+	0.999974i	$0.497683\pi$
$80$	6.00000	−	3.46410i	0.670820	−	0.387298i
$81$		0			0
$82$	1.26795	+	4.73205i	0.140022	+	0.522568i
$83$	13.8564			1.52094			0.760469	−	0.649374i	$-0.224969\pi$
$83$	13.8564			1.52094			0.760469	+	0.649374i	$0.224969\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$	−0.732051	−	2.73205i	−0.0789391	−	0.294605i
$87$		0			0
$88$	−0.732051	+	2.73205i	−0.0780369	+	0.291238i
$89$	−13.5000	−	7.79423i	−1.43100	−	0.826187i	−0.433800	−	0.901009i	$-0.642828\pi$
$89$	−13.5000	−	7.79423i	−1.43100	−	0.826187i	−0.997197	+	0.0748225i	$0.976161\pi$
$90$		0			0
$91$	6.92820	−	6.00000i	0.726273	−	0.628971i
$92$	−2.00000			−0.208514
$93$		0			0
$94$	−3.16987	+	11.8301i	−0.326947	+	1.22018i
$95$	−7.79423	+	4.50000i	−0.799671	+	0.461690i
$96$		0			0
$97$		−	17.3205i		−	1.75863i	−0.476240	−	0.879316i	$-0.658000\pi$
$97$		−	17.3205i		−	1.75863i	0.476240	−	0.879316i	$-0.342000\pi$
$98$	1.16987	+	9.83013i	0.118175	+	0.992993i
$99$		0			0
$100$	−3.46410	−	2.00000i	−0.346410	−	0.200000i
$101$	7.50000	−	4.33013i	0.746278	−	0.430864i	−0.0780696	−	0.996948i	$-0.524876\pi$
$101$	7.50000	−	4.33013i	0.746278	−	0.430864i	0.824347	+	0.566084i	$0.191542\pi$
$102$		0			0
$103$	−4.33013	+	7.50000i	−0.426660	+	0.738997i	−0.996574	−	0.0827075i	$-0.973643\pi$
$103$	−4.33013	+	7.50000i	−0.426660	+	0.738997i	0.569914	+	0.821705i	$0.306977\pi$
$104$	6.92820	+	6.92820i	0.679366	+	0.679366i
$105$		0			0
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$	11.2583	+	6.50000i	1.08838	+	0.628379i	0.933146	−	0.359498i	$-0.117052\pi$
$107$	11.2583	+	6.50000i	1.08838	+	0.628379i	0.155238	+	0.987877i	$0.450386\pi$
$108$		0			0
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	0.565940	−	0.824447i	$-0.308513\pi$
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	−0.996962	+	0.0778949i	$0.975180\pi$
$110$	−2.36603	+	0.633975i	−0.225592	+	0.0604471i
$111$		0			0
$112$	−10.3923	+	2.00000i	−0.981981	+	0.188982i
$113$	16.0000			1.50515			0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000			1.50515			0.752577	+	0.658505i	$0.228811\pi$
$114$		0			0
$115$	−0.866025	−	1.50000i	−0.0807573	−	0.139876i
$116$	−6.92820	+	4.00000i	−0.643268	+	0.371391i
$117$		0			0
$118$	5.19615	+	5.19615i	0.478345	+	0.478345i
$119$	−4.33013	−	1.50000i	−0.396942	−	0.137505i
$120$		0			0
$121$	−5.00000	+	8.66025i	−0.454545	+	0.787296i
$122$	−7.09808	−	1.90192i	−0.642630	−	0.172192i
$123$		0			0
$124$	−3.00000	−	1.73205i	−0.269408	−	0.155543i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$		0			0
$130$	−2.19615	+	8.19615i	−0.192615	+	0.718850i
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	−0.956916	−	0.290365i	$-0.906223\pi$
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	0.729921	+	0.683531i	$0.239557\pi$
$132$		0			0
$133$	13.5000	−	2.59808i	1.17060	−	0.225282i
$134$	3.00000	−	3.00000i	0.259161	−	0.259161i
$135$		0			0
$136$	1.26795	−	4.73205i	0.108726	−	0.405770i
$137$	0.500000	+	0.866025i	0.0427179	+	0.0739895i	0.886594	−	0.462549i	$-0.153065\pi$
$137$	0.500000	+	0.866025i	0.0427179	+	0.0739895i	−0.843876	+	0.536538i	$0.819732\pi$
$138$		0			0
$139$	6.92820			0.587643			0.293821	−	0.955860i	$-0.405073\pi$
$139$	6.92820			0.587643			0.293821	+	0.955860i	$0.405073\pi$
$140$	−6.00000	−	6.92820i	−0.507093	−	0.585540i
$141$		0			0
$142$	−5.12436	−	19.1244i	−0.430026	−	1.60488i
$143$	−1.73205	−	3.00000i	−0.144841	−	0.250873i
$144$		0			0
$145$	−6.00000	−	3.46410i	−0.498273	−	0.287678i
$146$	8.66025	−	8.66025i	0.716728	−	0.716728i
$147$		0			0
$148$			6.00000i			0.493197i
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	−0.725956	−	0.687741i	$-0.758602\pi$
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	0.232623	+	0.972567i	$0.425269\pi$
$152$	3.80385	+	14.1962i	0.308533	+	1.15146i
$153$		0			0
$154$	3.73205	+	0.267949i	0.300737	+	0.0215920i
$155$		−	3.00000i		−	0.240966i
$156$		0			0
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	0.558661	+	0.829396i	$0.311315\pi$
$158$	12.2942	+	3.29423i	0.978076	+	0.262075i
$159$		0			0
$160$	6.92820	−	6.92820i	0.547723	−	0.547723i
$161$	0.500000	+	2.59808i	0.0394055	+	0.204757i
$162$		0			0
$163$	18.1865	+	10.5000i	1.42448	+	0.822423i	0.996678	−	0.0814491i	$-0.0259548\pi$
$163$	18.1865	+	10.5000i	1.42448	+	0.822423i	0.427802	+	0.903873i	$0.359288\pi$
$164$	3.46410	+	6.00000i	0.270501	+	0.468521i
$165$		0			0
$166$	18.9282	−	5.07180i	1.46911	−	0.393648i
$167$	−17.3205			−1.34030			−0.670151	−	0.742225i	$-0.733770\pi$
$167$	−17.3205			−1.34030			−0.670151	+	0.742225i	$0.733770\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	4.09808	−	1.09808i	0.314308	−	0.0842186i
$171$		0			0
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	10.5000	+	6.06218i	0.798300	+	0.460899i	0.842876	−	0.538107i	$-0.180860\pi$
$173$	10.5000	+	6.06218i	0.798300	+	0.460899i	−0.0445762	+	0.999006i	$0.514194\pi$
$174$		0			0
$175$	−1.73205	+	5.00000i	−0.130931	+	0.377964i
$176$			4.00000i			0.301511i
$177$		0			0
$178$	−21.2942	−	5.70577i	−1.59607	−	0.427666i
$179$	16.4545	−	9.50000i	1.22987	−	0.710063i	0.262864	−	0.964833i	$-0.415333\pi$
$179$	16.4545	−	9.50000i	1.22987	−	0.710063i	0.967002	+	0.254770i	$0.0819996\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	7.26795	−	10.7321i	0.538736	−	0.795513i
$183$		0			0
$184$	−2.73205	+	0.732051i	−0.201409	+	0.0539675i
$185$	−4.50000	+	2.59808i	−0.330847	+	0.191014i
$186$		0			0
$187$	−0.866025	+	1.50000i	−0.0633300	+	0.109691i
$188$			17.3205i			1.26323i
$189$		0			0
$190$	−9.00000	+	9.00000i	−0.652929	+	0.652929i
$191$	0.866025	+	0.500000i	0.0626634	+	0.0361787i	0.531004	−	0.847369i	$-0.321815\pi$
$191$	0.866025	+	0.500000i	0.0626634	+	0.0361787i	−0.468341	+	0.883548i	$0.655148\pi$
$192$		0			0
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	0.998911	+	0.0466572i	$0.0148568\pi$
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	−0.459049	+	0.888411i	$0.651810\pi$
$194$	−6.33975	−	23.6603i	−0.455167	−	1.69871i
$195$		0			0
$196$	5.19615	+	13.0000i	0.371154	+	0.928571i
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	−11.2583	−	19.5000i	−0.798082	−	1.38232i	−0.920864	−	0.389885i	$-0.872515\pi$
$199$	−11.2583	−	19.5000i	−0.798082	−	1.38232i	0.122782	−	0.992434i	$-0.460818\pi$
$200$	−5.46410	−	1.46410i	−0.386370	−	0.103528i
$201$		0			0
$202$	8.66025	−	8.66025i	0.609333	−	0.609333i
$203$	6.92820	+	8.00000i	0.486265	+	0.561490i
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	−3.16987	+	11.8301i	−0.220856	+	0.824244i
$207$		0			0
$208$	12.0000	+	6.92820i	0.832050	+	0.480384i
$209$		−	5.19615i		−	0.359425i
$210$		0			0
$211$		−	10.0000i		−	0.688428i	−0.938891	−	0.344214i	$-0.888145\pi$
$211$		−	10.0000i		−	0.688428i	0.938891	−	0.344214i	$-0.111855\pi$
$212$	−1.73205	−	1.00000i	−0.118958	−	0.0686803i
$213$		0			0
$214$	17.7583	+	4.75833i	1.21393	+	0.325273i
$215$	1.73205	−	3.00000i	0.118125	−	0.204598i
$216$		0			0
$217$	−1.50000	+	4.33013i	−0.101827	+	0.293948i
$218$	−9.00000	−	9.00000i	−0.609557	−	0.609557i
$219$		0			0
$220$	−3.00000	+	1.73205i	−0.202260	+	0.116775i
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$	−6.92820			−0.463947			−0.231973	−	0.972722i	$-0.574518\pi$
$223$	−6.92820			−0.463947			−0.231973	+	0.972722i	$0.574518\pi$
$224$	−13.4641	+	6.53590i	−0.899608	+	0.436698i
$225$		0			0
$226$	21.8564	−	5.85641i	1.45387	−	0.389562i
$227$	−9.52628	−	16.5000i	−0.632281	−	1.09514i	−0.987084	−	0.160202i	$-0.948785\pi$
$227$	−9.52628	−	16.5000i	−0.632281	−	1.09514i	0.354803	−	0.934941i	$-0.384548\pi$
$228$		0			0
$229$	−13.5000	−	7.79423i	−0.892105	−	0.515057i	−0.0174746	−	0.999847i	$-0.505563\pi$
$229$	−13.5000	−	7.79423i	−0.892105	−	0.515057i	−0.874630	+	0.484790i	$0.838896\pi$
$230$	−1.73205	−	1.73205i	−0.114208	−	0.114208i
$231$		0			0
$232$	−8.00000	+	8.00000i	−0.525226	+	0.525226i
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	−0.957599	−	0.288106i	$-0.906975\pi$
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	0.728306	+	0.685252i	$0.240308\pi$
$234$		0			0
$235$	−12.9904	+	7.50000i	−0.847399	+	0.489246i
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$		0			0
$238$	−6.46410	−	0.464102i	−0.419005	−	0.0300832i
$239$			20.0000i			1.29369i	0.762620	+	0.646846i	$0.223912\pi$
$239$			20.0000i			1.29369i	−0.762620	+	0.646846i	$0.776088\pi$
$240$		0			0
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	−0.637883	−	0.770133i	$-0.720190\pi$
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	0.348013	+	0.937490i	$0.386857\pi$
$242$	−3.66025	+	13.6603i	−0.235290	+	0.878114i
$243$		0			0
$244$	−10.3923			−0.665299
$245$	−7.50000	+	9.52628i	−0.479157	+	0.608612i
$246$		0			0
$247$	−15.5885	−	9.00000i	−0.991870	−	0.572656i
$248$	−4.73205	−	1.26795i	−0.300486	−	0.0805149i
$249$		0			0
$250$	−4.43782	−	16.5622i	−0.280673	−	1.04748i
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$		0			0
$253$	1.00000			0.0628695
$254$	−2.19615	−	8.19615i	−0.137799	−	0.514272i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−4.50000	−	2.59808i	−0.280702	−	0.162064i	0.353039	−	0.935609i	$-0.385148\pi$
$257$	−4.50000	−	2.59808i	−0.280702	−	0.162064i	−0.633741	+	0.773545i	$0.718482\pi$
$258$		0			0
$259$	7.79423	−	1.50000i	0.484310	−	0.0932055i
$260$			12.0000i			0.744208i
$261$		0			0
$262$	−1.90192	+	7.09808i	−0.117501	+	0.438521i
$263$	−19.9186	+	11.5000i	−1.22823	+	0.709120i	−0.966660	−	0.256063i	$-0.917574\pi$
$263$	−19.9186	+	11.5000i	−1.22823	+	0.709120i	−0.261573	+	0.965184i	$0.584241\pi$
$264$		0			0
$265$		−	1.73205i		−	0.106399i
$266$	17.4904	−	8.49038i	1.07240	−	0.520579i
$267$		0			0
$268$	3.00000	−	5.19615i	0.183254	−	0.317406i
$269$	−19.5000	+	11.2583i	−1.18894	+	0.686433i	−0.958065	−	0.286552i	$-0.907491\pi$
$269$	−19.5000	+	11.2583i	−1.18894	+	0.686433i	−0.230871	+	0.972984i	$0.574158\pi$
$270$		0			0
$271$	−7.79423	+	13.5000i	−0.473466	+	0.820067i	−0.999539	−	0.0303728i	$-0.990331\pi$
$271$	−7.79423	+	13.5000i	−0.473466	+	0.820067i	0.526073	+	0.850439i	$0.323664\pi$
$272$		−	6.92820i		−	0.420084i
$273$		0			0
$274$	1.00000	+	1.00000i	0.0604122	+	0.0604122i
$275$	1.73205	+	1.00000i	0.104447	+	0.0603023i
$276$		0			0
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	0.992522	−	0.122068i	$-0.0389525\pi$
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	−0.601975	+	0.798515i	$0.705619\pi$
$278$	9.46410	−	2.53590i	0.567619	−	0.152093i
$279$		0			0
$280$	−10.7321	−	7.26795i	−0.641363	−	0.434343i
$281$	4.00000			0.238620			0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000			0.238620			0.119310	+	0.992857i	$0.461932\pi$
$282$		0			0
$283$	6.06218	+	10.5000i	0.360359	+	0.624160i	0.988020	−	0.154327i	$-0.0493208\pi$
$283$	6.06218	+	10.5000i	0.360359	+	0.624160i	−0.627661	+	0.778487i	$0.715988\pi$
$284$	−14.0000	−	24.2487i	−0.830747	−	1.43890i
$285$		0			0
$286$	−3.46410	−	3.46410i	−0.204837	−	0.204837i
$287$	6.92820	−	6.00000i	0.408959	−	0.354169i
$288$		0			0
$289$	−7.00000	+	12.1244i	−0.411765	+	0.713197i
$290$	−9.46410	−	2.53590i	−0.555751	−	0.148913i
$291$		0			0
$292$	8.66025	−	15.0000i	0.506803	−	0.877809i
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$		0			0
$295$			9.00000i			0.524000i
$296$	2.19615	+	8.19615i	0.127649	+	0.476392i
$297$		0			0
$298$	0.366025	−	1.36603i	0.0212033	−	0.0791317i
$299$	1.73205	−	3.00000i	0.100167	−	0.173494i
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$	−7.00000	+	7.00000i	−0.402805	+	0.402805i
$303$		0			0
$304$	10.3923	+	18.0000i	0.596040	+	1.03237i
$305$	−4.50000	−	7.79423i	−0.257669	−	0.446296i
$306$		0			0
$307$	−20.7846			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$307$	−20.7846			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$308$	5.19615	−	1.00000i	0.296078	−	0.0569803i
$309$		0			0
$310$	−1.09808	−	4.09808i	−0.0623665	−	0.232755i
$311$	−4.33013	−	7.50000i	−0.245539	−	0.425286i	0.716744	−	0.697336i	$-0.245632\pi$
$311$	−4.33013	−	7.50000i	−0.245539	−	0.425286i	−0.962283	+	0.272050i	$0.912298\pi$
$312$		0			0
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	0.541793	−	0.840512i	$-0.317746\pi$
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	−0.457008	+	0.889463i	$0.651079\pi$
$314$	1.73205	−	1.73205i	0.0977453	−	0.0977453i
$315$		0			0
$316$	18.0000			1.01258
$317$	5.50000	−	9.52628i	0.308911	−	0.535049i	−0.669214	−	0.743070i	$-0.733369\pi$
$317$	5.50000	−	9.52628i	0.308911	−	0.535049i	0.978124	+	0.208021i	$0.0667022\pi$
$318$		0			0
$319$	3.46410	−	2.00000i	0.193952	−	0.111979i
$320$	6.92820	−	12.0000i	0.387298	−	0.670820i
$321$		0			0
$322$	1.63397	+	3.36603i	0.0910578	+	0.187581i
$323$			9.00000i			0.500773i
$324$		0			0
$325$	6.00000	−	3.46410i	0.332820	−	0.192154i
$326$	28.6865	+	7.68653i	1.58880	+	0.425718i
$327$		0			0
$328$	6.92820	+	6.92820i	0.382546	+	0.382546i
$329$	22.5000	−	4.33013i	1.24047	−	0.238728i
$330$		0			0
$331$	−6.06218	−	3.50000i	−0.333207	−	0.192377i	0.324057	−	0.946038i	$-0.394953\pi$
$331$	−6.06218	−	3.50000i	−0.333207	−	0.192377i	−0.657264	+	0.753660i	$0.728286\pi$
$332$	24.0000	−	13.8564i	1.31717	−	0.760469i
$333$		0			0
$334$	−23.6603	+	6.33975i	−1.29463	+	0.346895i
$335$	5.19615			0.283896
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	1.36603	−	0.366025i	0.0743020	−	0.0199092i
$339$		0			0
$340$	5.19615	−	3.00000i	0.281801	−	0.162698i
$341$	1.50000	+	0.866025i	0.0812296	+	0.0468979i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−4.00000	−	4.00000i	−0.215666	−	0.215666i
$345$		0			0
$346$	16.5622	+	4.43782i	0.890388	+	0.238579i
$347$	11.2583	−	6.50000i	0.604379	−	0.348938i	−0.166383	−	0.986061i	$-0.553209\pi$
$347$	11.2583	−	6.50000i	0.604379	−	0.348938i	0.770762	+	0.637123i	$0.219876\pi$
$348$		0			0
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$	−0.535898	+	7.46410i	−0.0286450	+	0.398973i
$351$		0			0
$352$	1.46410	+	5.46410i	0.0780369	+	0.291238i
$353$	25.5000	−	14.7224i	1.35723	−	0.783596i	0.367979	−	0.929834i	$-0.380050\pi$
$353$	25.5000	−	14.7224i	1.35723	−	0.783596i	0.989249	+	0.146238i	$0.0467166\pi$
$354$		0			0
$355$	12.1244	−	21.0000i	0.643494	−	1.11456i
$356$	−31.1769			−1.65237
$357$		0			0
$358$	19.0000	−	19.0000i	1.00418	−	1.00418i
$359$	−19.9186	−	11.5000i	−1.05126	−	0.606947i	−0.128260	−	0.991741i	$-0.540939\pi$
$359$	−19.9186	−	11.5000i	−1.05126	−	0.606947i	−0.923003	+	0.384794i	$0.874273\pi$
$360$		0			0
$361$	−4.00000	−	6.92820i	−0.210526	−	0.364642i
$362$	2.53590	+	9.46410i	0.133284	+	0.497422i
$363$		0			0
$364$	6.00000	−	17.3205i	0.314485	−	0.907841i
$365$	15.0000			0.785136
$366$		0			0
$367$	0.866025	+	1.50000i	0.0452062	+	0.0782994i	0.887743	−	0.460339i	$-0.152272\pi$
$367$	0.866025	+	1.50000i	0.0452062	+	0.0782994i	−0.842537	+	0.538639i	$0.818939\pi$
$368$	−3.46410	+	2.00000i	−0.180579	+	0.104257i
$369$		0			0
$370$	−5.19615	+	5.19615i	−0.270135	+	0.270135i
$371$	−0.866025	+	2.50000i	−0.0449618	+	0.129794i
$372$		0			0
$373$	14.5000	−	25.1147i	0.750782	−	1.30039i	−0.196663	−	0.980471i	$-0.563010\pi$
$373$	14.5000	−	25.1147i	0.750782	−	1.30039i	0.947444	−	0.319921i	$-0.103656\pi$
$374$	−0.633975	+	2.36603i	−0.0327820	+	0.122344i
$375$		0			0
$376$	6.33975	+	23.6603i	0.326947	+	1.22018i
$377$		−	13.8564i		−	0.713641i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	−9.00000	+	15.5885i	−0.461690	+	0.799671i
$381$		0			0
$382$	1.36603	+	0.366025i	0.0698919	+	0.0187275i
$383$	2.59808	−	4.50000i	0.132755	−	0.229939i	−0.791982	−	0.610544i	$-0.790951\pi$
$383$	2.59808	−	4.50000i	0.132755	−	0.229939i	0.924738	+	0.380605i	$0.124284\pi$
$384$		0			0
$385$	3.00000	+	3.46410i	0.152894	+	0.176547i
$386$	15.0000	+	15.0000i	0.763480	+	0.763480i
$387$		0			0
$388$	−17.3205	−	30.0000i	−0.879316	−	1.52302i
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$		0			0
$391$	−1.73205			−0.0875936
$392$	11.8564	+	15.8564i	0.598839	+	0.800869i
$393$		0			0
$394$	−21.8564	+	5.85641i	−1.10111	+	0.295041i
$395$	7.79423	+	13.5000i	0.392170	+	0.679259i
$396$		0			0
$397$	16.5000	+	9.52628i	0.828111	+	0.478110i	0.853206	−	0.521575i	$-0.174655\pi$
$397$	16.5000	+	9.52628i	0.828111	+	0.478110i	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−22.5167	−	22.5167i	−1.12866	−	1.12866i
$399$		0			0
$400$	−8.00000			−0.400000
$401$	−11.5000	+	19.9186i	−0.574283	+	0.994687i	0.421837	+	0.906672i	$0.361386\pi$
$401$	−11.5000	+	19.9186i	−0.574283	+	0.994687i	−0.996119	+	0.0880147i	$0.971948\pi$
$402$		0			0
$403$	5.19615	−	3.00000i	0.258839	−	0.149441i
$404$	8.66025	−	15.0000i	0.430864	−	0.746278i
$405$		0			0
$406$	12.3923	+	8.39230i	0.615020	+	0.416503i
$407$		−	3.00000i		−	0.148704i
$408$		0			0
$409$	22.5000	−	12.9904i	1.11255	−	0.642333i	0.173064	−	0.984911i	$-0.444633\pi$
$409$	22.5000	−	12.9904i	1.11255	−	0.642333i	0.939490	+	0.342578i	$0.111300\pi$
$410$	−2.19615	+	8.19615i	−0.108460	+	0.404779i
$411$		0			0
$412$			17.3205i			0.853320i
$413$	4.50000	−	12.9904i	0.221431	−	0.639215i
$414$		0			0
$415$	20.7846	+	12.0000i	1.02028	+	0.589057i
$416$	18.9282	+	5.07180i	0.928032	+	0.248665i
$417$		0			0
$418$	−1.90192	−	7.09808i	−0.0930261	−	0.347178i
$419$	−20.7846			−1.01539			−0.507697	−	0.861536i	$-0.669503\pi$
$419$	−20.7846			−1.01539			−0.507697	+	0.861536i	$0.669503\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	−3.66025	−	13.6603i	−0.178178	−	0.664971i
$423$		0			0
$424$	−2.73205	−	0.732051i	−0.132680	−	0.0355515i
$425$	−3.00000	−	1.73205i	−0.145521	−	0.0840168i
$426$		0			0
$427$	2.59808	+	13.5000i	0.125730	+	0.653311i
$428$	26.0000			1.25676
$429$		0			0
$430$	1.26795	−	4.73205i	0.0611459	−	0.228200i
$431$	19.9186	−	11.5000i	0.959444	−	0.553936i	0.0634424	−	0.997985i	$-0.479792\pi$
$431$	19.9186	−	11.5000i	0.959444	−	0.553936i	0.896002	+	0.444050i	$0.146459\pi$
$432$		0			0
$433$		−	10.3923i		−	0.499422i	−0.968320	−	0.249711i	$-0.919664\pi$
$433$		−	10.3923i		−	0.499422i	0.968320	−	0.249711i	$-0.0803357\pi$
$434$	−0.464102	+	6.46410i	−0.0222776	+	0.310287i
$435$		0			0
$436$	−15.5885	−	9.00000i	−0.746552	−	0.431022i
$437$	4.50000	−	2.59808i	0.215264	−	0.124283i
$438$		0			0
$439$	11.2583	−	19.5000i	0.537331	−	0.930684i	−0.461716	−	0.887028i	$-0.652766\pi$
$439$	11.2583	−	19.5000i	0.537331	−	0.930684i	0.999047	−	0.0436563i	$-0.0139007\pi$
$440$	−3.46410	+	3.46410i	−0.165145	+	0.165145i
$441$		0			0
$442$	6.00000	+	6.00000i	0.285391	+	0.285391i
$443$	14.7224	+	8.50000i	0.699484	+	0.403847i	0.807155	−	0.590339i	$-0.201006\pi$
$443$	14.7224	+	8.50000i	0.699484	+	0.403847i	−0.107671	+	0.994187i	$0.534339\pi$
$444$		0			0
$445$	−13.5000	−	23.3827i	−0.639961	−	1.10845i
$446$	−9.46410	+	2.53590i	−0.448138	+	0.120078i
$447$		0			0
$448$	−16.0000	+	13.8564i	−0.755929	+	0.654654i
$449$	−8.00000			−0.377543			−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000			−0.377543			−0.188772	+	0.982021i	$0.560451\pi$
$450$		0			0
$451$	−1.73205	−	3.00000i	−0.0815591	−	0.141264i
$452$	27.7128	−	16.0000i	1.30350	−	0.752577i
$453$		0			0
$454$	−19.0526	−	19.0526i	−0.894181	−	0.894181i
$455$	15.5885	−	3.00000i	0.730798	−	0.140642i
$456$		0			0
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	−0.986396	−	0.164386i	$-0.947436\pi$
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	0.635561	+	0.772051i	$0.280769\pi$
$458$	−21.2942	−	5.70577i	−0.995014	−	0.266613i
$459$		0			0
$460$	−3.00000	−	1.73205i	−0.139876	−	0.0807573i
$461$			17.3205i			0.806696i	0.915047	+	0.403348i	$0.132154\pi$
$461$			17.3205i			0.806696i	−0.915047	+	0.403348i	$0.867846\pi$
$462$		0			0
$463$			30.0000i			1.39422i	0.716965	+	0.697109i	$0.245531\pi$
$463$			30.0000i			1.39422i	−0.716965	+	0.697109i	$0.754469\pi$
$464$	−8.00000	+	13.8564i	−0.371391	+	0.643268i
$465$		0			0
$466$	−2.56218	+	9.56218i	−0.118691	+	0.442959i
$467$	4.33013	−	7.50000i	0.200374	−	0.347059i	−0.748275	−	0.663389i	$-0.769117\pi$
$467$	4.33013	−	7.50000i	0.200374	−	0.347059i	0.948649	+	0.316330i	$0.102451\pi$
$468$		0			0
$469$	−7.50000	−	2.59808i	−0.346318	−	0.119968i
$470$	−15.0000	+	15.0000i	−0.691898	+	0.691898i
$471$		0			0
$472$	14.1962	+	3.80385i	0.653431	+	0.175086i
$473$	1.00000	+	1.73205i	0.0459800	+	0.0796398i
$474$		0			0
$475$	10.3923			0.476832
$476$	−9.00000	+	1.73205i	−0.412514	+	0.0793884i
$477$		0			0
$478$	7.32051	+	27.3205i	0.334832	+	1.24961i
$479$	6.06218	+	10.5000i	0.276988	+	0.479757i	0.970635	−	0.240558i	$-0.0773304\pi$
$479$	6.06218	+	10.5000i	0.276988	+	0.479757i	−0.693647	+	0.720315i	$0.743997\pi$
$480$		0			0
$481$	−9.00000	−	5.19615i	−0.410365	−	0.236924i
$482$	−5.19615	+	5.19615i	−0.236678	+	0.236678i
$483$		0			0
$484$			20.0000i			0.909091i
$485$	15.0000	−	25.9808i	0.681115	−	1.17973i
$486$		0			0
$487$	26.8468	−	15.5000i	1.21654	−	0.702372i	0.252367	−	0.967632i	$-0.418791\pi$
$487$	26.8468	−	15.5000i	1.21654	−	0.702372i	0.964177	+	0.265260i	$0.0854576\pi$
$488$	−14.1962	+	3.80385i	−0.642630	+	0.172192i
$489$		0			0
$490$	−6.75833	+	15.7583i	−0.305310	+	0.711889i
$491$			32.0000i			1.44414i	0.691820	+	0.722070i	$0.256809\pi$
$491$			32.0000i			1.44414i	−0.691820	+	0.722070i	$0.743191\pi$
$492$		0			0
$493$	−6.00000	+	3.46410i	−0.270226	+	0.156015i
$494$	−24.5885	−	6.58846i	−1.10629	−	0.296429i
$495$		0			0
$496$	−6.92820			−0.311086
$497$	−28.0000	+	24.2487i	−1.25597	+	1.08770i
$498$		0			0
$499$	−30.3109	−	17.5000i	−1.35690	−	0.783408i	−0.367697	−	0.929946i	$-0.619854\pi$
$499$	−30.3109	−	17.5000i	−1.35690	−	0.783408i	−0.989205	+	0.146538i	$0.953187\pi$
$500$	−12.1244	−	21.0000i	−0.542218	−	0.939149i
$501$		0			0
$502$	−4.73205	+	1.26795i	−0.211202	+	0.0565913i
$503$	−6.92820			−0.308913			−0.154457	−	0.988000i	$-0.549363\pi$
$503$	−6.92820			−0.308913			−0.154457	+	0.988000i	$0.549363\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$	1.36603	−	0.366025i	0.0607272	−	0.0162718i
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−10.5000	−	6.06218i	−0.465404	−	0.268701i	0.248910	−	0.968527i	$-0.419928\pi$
$509$	−10.5000	−	6.06218i	−0.465404	−	0.268701i	−0.714314	+	0.699825i	$0.753261\pi$
$510$		0			0
$511$	−21.6506	−	7.50000i	−0.957768	−	0.331780i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−7.09808	−	1.90192i	−0.313083	−	0.0838903i
$515$	−12.9904	+	7.50000i	−0.572425	+	0.330489i
$516$		0			0
$517$		−	8.66025i		−	0.380878i
$518$	10.0981	−	4.90192i	0.443684	−	0.215378i
$519$		0			0
$520$	4.39230	+	16.3923i	0.192615	+	0.718850i
$521$	−1.50000	+	0.866025i	−0.0657162	+	0.0379413i	−0.532498	−	0.846431i	$-0.678747\pi$
$521$	−1.50000	+	0.866025i	−0.0657162	+	0.0379413i	0.466782	+	0.884372i	$0.345413\pi$
$522$		0			0
$523$	−12.9904	+	22.5000i	−0.568030	+	0.983856i	0.428731	+	0.903432i	$0.358961\pi$
$523$	−12.9904	+	22.5000i	−0.568030	+	0.983856i	−0.996761	+	0.0804241i	$0.974373\pi$
$524$			10.3923i			0.453990i
$525$		0			0
$526$	−23.0000	+	23.0000i	−1.00285	+	1.00285i
$527$	−2.59808	−	1.50000i	−0.113174	−	0.0653410i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$	−0.633975	−	2.36603i	−0.0275381	−	0.102774i
$531$		0			0
$532$	20.7846	−	18.0000i	0.901127	−	0.780399i
$533$	−12.0000			−0.519778
$534$		0			0
$535$	11.2583	+	19.5000i	0.486740	+	0.843059i
$536$	2.19615	−	8.19615i	0.0948593	−	0.354020i
$537$		0			0
$538$	−22.5167	+	22.5167i	−0.970762	+	0.970762i
$539$	−2.59808	−	6.50000i	−0.111907	−	0.279975i
$540$		0			0
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	−0.586278	−	0.810110i	$-0.699407\pi$
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	0.994715	+	0.102677i	$0.0327407\pi$
$542$	−5.70577	+	21.2942i	−0.245084	+	0.914665i
$543$		0			0
$544$	−2.53590	−	9.46410i	−0.108726	−	0.405770i
$545$		−	15.5885i		−	0.667736i
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	1.73205	+	1.00000i	0.0739895	+	0.0427179i
$549$		0			0
$550$	2.73205	+	0.732051i	0.116495	+	0.0312148i
$551$	10.3923	−	18.0000i	0.442727	−	0.766826i
$552$		0			0
$553$	−4.50000	−	23.3827i	−0.191359	−	0.994333i
$554$	13.0000	+	13.0000i	0.552317	+	0.552317i
$555$		0			0
$556$	12.0000	−	6.92820i	0.508913	−	0.293821i
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	0.929672	+	0.368389i	$0.120091\pi$
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	−0.145802	+	0.989314i	$0.546576\pi$
$558$		0			0
$559$	6.92820			0.293032
$560$	−17.3205	−	6.00000i	−0.731925	−	0.253546i
$561$		0			0
$562$	5.46410	−	1.46410i	0.230489	−	0.0617594i
$563$	−11.2583	−	19.5000i	−0.474482	−	0.821827i	0.525091	−	0.851046i	$-0.324031\pi$
$563$	−11.2583	−	19.5000i	−0.474482	−	0.821827i	−0.999573	+	0.0292191i	$0.990698\pi$
$564$		0			0
$565$	24.0000	+	13.8564i	1.00969	+	0.582943i
$566$	12.1244	+	12.1244i	0.509625	+	0.509625i
$567$		0			0
$568$	−28.0000	−	28.0000i	−1.17485	−	1.17485i
$569$	−6.50000	+	11.2583i	−0.272494	+	0.471974i	−0.969500	−	0.245092i	$-0.921182\pi$
$569$	−6.50000	+	11.2583i	−0.272494	+	0.471974i	0.697006	+	0.717066i	$0.254515\pi$
$570$		0			0
$571$	18.1865	−	10.5000i	0.761083	−	0.439411i	−0.0686016	−	0.997644i	$-0.521854\pi$
$571$	18.1865	−	10.5000i	0.761083	−	0.439411i	0.829684	+	0.558233i	$0.188520\pi$
$572$	−6.00000	−	3.46410i	−0.250873	−	0.144841i
$573$		0			0
$574$	7.26795	−	10.7321i	0.303358	−	0.447947i
$575$			2.00000i			0.0834058i
$576$		0			0
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.228968	+	0.973434i	$0.573535\pi$
$578$	−5.12436	+	19.1244i	−0.213145	+	0.795468i
$579$		0			0
$580$	−13.8564			−0.575356
$581$	−24.0000	−	27.7128i	−0.995688	−	1.14972i
$582$		0			0
$583$	0.866025	+	0.500000i	0.0358671	+	0.0207079i
$584$	6.33975	−	23.6603i	0.262341	−	0.979068i
$585$		0			0
$586$	7.60770	+	28.3923i	0.314271	+	1.17288i
$587$	6.92820			0.285958			0.142979	−	0.989726i	$-0.454332\pi$
$587$	6.92820			0.285958			0.142979	+	0.989726i	$0.454332\pi$
$588$		0			0
$589$	9.00000			0.370839
$590$	3.29423	+	12.2942i	0.135621	+	0.506145i
$591$		0			0
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	13.5000	+	7.79423i	0.554379	+	0.320071i	0.750886	−	0.660432i	$-0.229627\pi$
$593$	13.5000	+	7.79423i	0.554379	+	0.320071i	−0.196508	+	0.980502i	$0.562960\pi$
$594$		0			0
$595$	−5.19615	−	6.00000i	−0.213021	−	0.245976i
$596$		−	2.00000i		−	0.0819232i
$597$		0			0
$598$	1.26795	−	4.73205i	0.0518503	−	0.193508i
$599$	14.7224	−	8.50000i	0.601542	−	0.347301i	−0.168106	−	0.985769i	$-0.553765\pi$
$599$	14.7224	−	8.50000i	0.601542	−	0.347301i	0.769648	+	0.638468i	$0.220432\pi$
$600$		0			0
$601$			38.1051i			1.55434i	0.629291	+	0.777170i	$0.283346\pi$
$601$			38.1051i			1.55434i	−0.629291	+	0.777170i	$0.716654\pi$
$602$	−4.19615	+	6.19615i	−0.171022	+	0.252536i
$603$		0			0
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$	−15.0000	+	8.66025i	−0.609837	+	0.352089i
$606$		0			0
$607$	7.79423	−	13.5000i	0.316358	−	0.547948i	−0.663367	−	0.748294i	$-0.730873\pi$
$607$	7.79423	−	13.5000i	0.316358	−	0.547948i	0.979725	+	0.200346i	$0.0642066\pi$
$608$	20.7846	+	20.7846i	0.842927	+	0.842927i
$609$		0			0
$610$	−9.00000	−	9.00000i	−0.364399	−	0.364399i
$611$	−25.9808	−	15.0000i	−1.05107	−	0.606835i
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	−28.3923	+	7.60770i	−1.14582	+	0.307022i
$615$		0			0
$616$	6.73205	−	3.26795i	0.271242	−	0.131669i
$617$	−20.0000			−0.805170			−0.402585	−	0.915383i	$-0.631888\pi$
$617$	−20.0000			−0.805170			−0.402585	+	0.915383i	$0.631888\pi$
$618$		0			0
$619$	7.79423	+	13.5000i	0.313276	+	0.542611i	0.979070	−	0.203526i	$-0.0652400\pi$
$619$	7.79423	+	13.5000i	0.313276	+	0.542611i	−0.665793	+	0.746136i	$0.731907\pi$
$620$	−3.00000	−	5.19615i	−0.120483	−	0.208683i
$621$		0			0
$622$	−8.66025	−	8.66025i	−0.347245	−	0.347245i
$623$	7.79423	+	40.5000i	0.312269	+	1.62260i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	2.36603	+	0.633975i	0.0945654	+	0.0253387i
$627$		0			0
$628$	1.73205	−	3.00000i	0.0691164	−	0.119713i
$629$			5.19615i			0.207184i
$630$		0			0
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$	24.5885	−	6.58846i	0.978076	−	0.262075i
$633$		0			0
$634$	4.02628	−	15.0263i	0.159904	−	0.596770i
$635$	5.19615	−	9.00000i	0.206203	−	0.357154i
$636$		0			0
$637$	−24.0000	−	3.46410i	−0.950915	−	0.137253i
$638$	4.00000	−	4.00000i	0.158362	−	0.158362i
$639$		0			0
$640$	5.07180	−	18.9282i	0.200480	−	0.748203i
$641$	−6.50000	−	11.2583i	−0.256735	−	0.444677i	0.708631	−	0.705580i	$-0.249313\pi$
$641$	−6.50000	−	11.2583i	−0.256735	−	0.444677i	−0.965365	+	0.260902i	$0.915980\pi$
$642$		0			0
$643$	13.8564			0.546443			0.273222	−	0.961951i	$-0.411911\pi$
$643$	13.8564			0.546443			0.273222	+	0.961951i	$0.411911\pi$
$644$	3.46410	+	4.00000i	0.136505	+	0.157622i
$645$		0			0
$646$	3.29423	+	12.2942i	0.129610	+	0.483710i
$647$	16.4545	+	28.5000i	0.646892	+	1.12045i	0.983861	+	0.178935i	$0.0572651\pi$
$647$	16.4545	+	28.5000i	0.646892	+	1.12045i	−0.336968	+	0.941516i	$0.609402\pi$
$648$		0			0
$649$	−4.50000	−	2.59808i	−0.176640	−	0.101983i
$650$	6.92820	−	6.92820i	0.271746	−	0.271746i
$651$		0			0
$652$	42.0000			1.64485
$653$	15.5000	−	26.8468i	0.606562	−	1.05060i	−0.385241	−	0.922816i	$-0.625882\pi$
$653$	15.5000	−	26.8468i	0.606562	−	1.05060i	0.991803	−	0.127780i	$-0.0407851\pi$
$654$		0			0
$655$	−7.79423	+	4.50000i	−0.304546	+	0.175830i
$656$	12.0000	+	6.92820i	0.468521	+	0.270501i
$657$		0			0
$658$	29.1506	−	14.1506i	1.13641	−	0.551649i
$659$		−	38.0000i		−	1.48027i	−0.672458	−	0.740135i	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$		0			0
$661$	−34.5000	+	19.9186i	−1.34189	+	0.774743i	−0.987085	−	0.160196i	$-0.948788\pi$
$661$	−34.5000	+	19.9186i	−1.34189	+	0.774743i	−0.354809	+	0.934939i	$0.615454\pi$
$662$	−9.56218	−	2.56218i	−0.371645	−	0.0995819i
$663$		0			0
$664$	27.7128	−	27.7128i	1.07547	−	1.07547i
$665$	22.5000	+	7.79423i	0.872513	+	0.302247i
$666$		0			0
$667$	3.46410	+	2.00000i	0.134131	+	0.0774403i
$668$	−30.0000	+	17.3205i	−1.16073	+	0.670151i
$669$		0			0
$670$	7.09808	−	1.90192i	0.274223	−	0.0734777i
$671$	5.19615			0.200595
$672$		0			0
$673$	24.0000			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$674$		0			0
$675$		0			0
$676$	1.73205	−	1.00000i	0.0666173	−	0.0384615i
$677$	37.5000	+	21.6506i	1.44124	+	0.832102i	0.997933	−	0.0642672i	$-0.0204710\pi$
$677$	37.5000	+	21.6506i	1.44124	+	0.832102i	0.443309	+	0.896369i	$0.353804\pi$
$678$		0			0
$679$	−34.6410	+	30.0000i	−1.32940	+	1.15129i
$680$	6.00000	−	6.00000i	0.230089	−	0.230089i
$681$		0			0
$682$	2.36603	+	0.633975i	0.0905998	+	0.0242761i
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	−0.853318	−	0.521391i	$-0.825413\pi$
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	0.0248792	+	0.999690i	$0.492080\pi$
$684$		0			0
$685$			1.73205i			0.0661783i
$686$	17.6340	−	19.3660i	0.673268	−	0.739398i
$687$		0			0
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$	3.00000	−	1.73205i	0.114291	−	0.0659859i
$690$		0			0
$691$	6.06218	−	10.5000i	0.230616	−	0.399439i	−0.727373	−	0.686242i	$-0.759259\pi$
$691$	6.06218	−	10.5000i	0.230616	−	0.399439i	0.957990	+	0.286803i	$0.0925925\pi$
$692$	24.2487			0.921798
$693$		0			0
$694$	13.0000	−	13.0000i	0.493473	−	0.493473i
$695$	10.3923	+	6.00000i	0.394203	+	0.227593i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	3.80385	+	14.1962i	0.143978	+	0.537332i
$699$		0			0
$700$	2.00000	+	10.3923i	0.0755929	+	0.392792i
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$	−7.79423	−	13.5000i	−0.293965	−	0.509162i
$704$	4.00000	+	6.92820i	0.150756	+	0.261116i
$705$		0			0
$706$	29.4449	−	29.4449i	1.10817	−	1.10817i
$707$	−21.6506	−	7.50000i	−0.814256	−	0.282067i
$708$		0			0
$709$	4.50000	−	7.79423i	0.169001	−	0.292718i	−0.769068	−	0.639167i	$-0.779279\pi$
$709$	4.50000	−	7.79423i	0.169001	−	0.292718i	0.938069	+	0.346449i	$0.112613\pi$
$710$	8.87564	−	33.1244i	0.333097	−	1.24313i
$711$		0			0
$712$	−42.5885	+	11.4115i	−1.59607	+	0.427666i
$713$			1.73205i			0.0648658i
$714$		0			0
$715$		−	6.00000i		−	0.224387i
$716$	19.0000	−	32.9090i	0.710063	−	1.22987i
$717$		0			0
$718$	−31.4186	−	8.41858i	−1.17253	−	0.314179i
$719$	−12.9904	+	22.5000i	−0.484459	+	0.839108i	−0.999841	−	0.0178527i	$-0.994317\pi$
$719$	−12.9904	+	22.5000i	−0.484459	+	0.839108i	0.515381	+	0.856961i	$0.327650\pi$
$720$		0			0
$721$	22.5000	−	4.33013i	0.837944	−	0.161262i
$722$	−8.00000	−	8.00000i	−0.297729	−	0.297729i
$723$		0			0
$724$	6.92820	+	12.0000i	0.257485	+	0.445976i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	1.85641	−	25.8564i	0.0688030	−	0.958302i
$729$		0			0
$730$	20.4904	−	5.49038i	0.758383	−	0.203208i
$731$	−1.73205	−	3.00000i	−0.0640622	−	0.110959i
$732$		0			0
$733$	37.5000	+	21.6506i	1.38509	+	0.799684i	0.992757	−	0.120137i	$-0.0383334\pi$
$733$	37.5000	+	21.6506i	1.38509	+	0.799684i	0.392337	+	0.919822i	$0.371667\pi$
$734$	1.73205	+	1.73205i	0.0639312	+	0.0639312i
$735$		0			0
$736$	−4.00000	+	4.00000i	−0.147442	+	0.147442i
$737$	−1.50000	+	2.59808i	−0.0552532	+	0.0957014i
$738$		0			0
$739$	−44.1673	+	25.5000i	−1.62472	+	0.938033i	−0.639087	+	0.769135i	$0.720687\pi$
$739$	−44.1673	+	25.5000i	−1.62472	+	0.938033i	−0.985634	+	0.168898i	$0.945979\pi$
$740$	−5.19615	+	9.00000i	−0.191014	+	0.330847i
$741$		0			0
$742$	−0.267949	+	3.73205i	−0.00983672	+	0.137008i
$743$		−	34.0000i		−	1.24734i	−0.781688	−	0.623670i	$-0.785641\pi$
$743$		−	34.0000i		−	1.24734i	0.781688	−	0.623670i	$-0.214359\pi$
$744$		0			0
$745$	1.50000	−	0.866025i	0.0549557	−	0.0317287i
$746$	10.6147	−	39.6147i	0.388633	−	1.45040i
$747$		0			0
$748$			3.46410i			0.126660i
$749$	−6.50000	−	33.7750i	−0.237505	−	1.23411i
$750$		0			0
$751$	−21.6506	−	12.5000i	−0.790043	−	0.456131i	0.0499348	−	0.998752i	$-0.484099\pi$
$751$	−21.6506	−	12.5000i	−0.790043	−	0.456131i	−0.839978	+	0.542621i	$0.817432\pi$
$752$	17.3205	+	30.0000i	0.631614	+	1.09399i
$753$		0			0
$754$	−5.07180	−	18.9282i	−0.184704	−	0.689325i
$755$	−12.1244			−0.441250
$756$		0			0
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$	2.92820	+	10.9282i	0.106357	+	0.396930i
$759$		0			0
$760$	−6.58846	+	24.5885i	−0.238988	+	0.891917i
$761$	−16.5000	−	9.52628i	−0.598125	−	0.345327i	0.170179	−	0.985413i	$-0.445565\pi$
$761$	−16.5000	−	9.52628i	−0.598125	−	0.345327i	−0.768303	+	0.640086i	$0.778899\pi$
$762$		0			0
$763$	−7.79423	+	22.5000i	−0.282170	+	0.814555i
$764$	2.00000			0.0723575
$765$		0			0
$766$	1.90192	−	7.09808i	0.0687193	−	0.256464i
$767$	−15.5885	+	9.00000i	−0.562867	+	0.324971i
$768$		0			0
$769$		−	3.46410i		−	0.124919i	−0.998048	−	0.0624593i	$-0.980106\pi$
$769$		−	3.46410i		−	0.124919i	0.998048	−	0.0624593i	$-0.0198944\pi$
$770$	5.36603	+	3.63397i	0.193378	+	0.130959i
$771$		0			0
$772$	25.9808	+	15.0000i	0.935068	+	0.539862i
$773$	−22.5000	+	12.9904i	−0.809269	+	0.467232i	−0.846702	−	0.532068i	$-0.821415\pi$
$773$	−22.5000	+	12.9904i	−0.809269	+	0.467232i	0.0374331	+	0.999299i	$0.488082\pi$
$774$		0			0
$775$	−1.73205	+	3.00000i	−0.0622171	+	0.107763i
$776$	−34.6410	−	34.6410i	−1.24354	−	1.24354i
$777$		0			0
$778$	−19.0000	−	19.0000i	−0.681183	−	0.681183i
$779$	−15.5885	−	9.00000i	−0.558514	−	0.322458i
$780$		0			0
$781$	7.00000	+	12.1244i	0.250480	+	0.433844i
$782$	−2.36603	+	0.633975i	−0.0846089	+	0.0226709i
$783$		0			0
$784$	22.0000	+	17.3205i	0.785714	+	0.618590i
$785$	3.00000			0.107075
$786$		0			0
$787$	−2.59808	−	4.50000i	−0.0926114	−	0.160408i	0.815998	−	0.578055i	$-0.196188\pi$
$787$	−2.59808	−	4.50000i	−0.0926114	−	0.160408i	−0.908609	+	0.417647i	$0.862855\pi$
$788$	−27.7128	+	16.0000i	−0.987228	+	0.569976i
$789$		0			0
$790$	15.5885	+	15.5885i	0.554612	+	0.554612i
$791$	−27.7128	−	32.0000i	−0.985354	−	1.13779i
$792$		0			0
$793$	9.00000	−	15.5885i	0.319599	−	0.553562i
$794$	26.0263	+	6.97372i	0.923638	+	0.247488i
$795$		0			0
$796$	−39.0000	−	22.5167i	−1.38232	−	0.798082i
$797$			10.3923i			0.368114i	0.982916	+	0.184057i	$0.0589232\pi$
$797$			10.3923i			0.368114i	−0.982916	+	0.184057i	$0.941077\pi$
$798$		0			0
$799$			15.0000i			0.530662i
$800$	−10.9282	+	2.92820i	−0.386370	+	0.103528i
$801$		0			0
$802$	−8.41858	+	31.4186i	−0.297271	+	1.10943i
$803$	−4.33013	+	7.50000i	−0.152807	+	0.264669i
$804$		0			0
$805$	−1.50000	+	4.33013i	−0.0528681	+	0.152617i
$806$	6.00000	−	6.00000i	0.211341	−	0.211341i
$807$		0			0
$808$	6.33975	−	23.6603i	0.223031	−	0.832365i
$809$	21.5000	+	37.2391i	0.755900	+	1.30926i	0.944926	+	0.327285i	$0.106134\pi$
$809$	21.5000	+	37.2391i	0.755900	+	1.30926i	−0.189026	+	0.981972i	$0.560533\pi$
$810$		0			0
$811$	−13.8564			−0.486564			−0.243282	−	0.969956i	$-0.578224\pi$
$811$	−13.8564			−0.486564			−0.243282	+	0.969956i	$0.578224\pi$
$812$	20.0000	+	6.92820i	0.701862	+	0.243132i
$813$		0			0
$814$	−1.09808	−	4.09808i	−0.0384876	−	0.143637i
$815$	18.1865	+	31.5000i	0.637046	+	1.10340i
$816$		0			0
$817$	9.00000	+	5.19615i	0.314870	+	0.181790i
$818$	25.9808	−	25.9808i	0.908396	−	0.908396i
$819$		0			0
$820$			12.0000i			0.419058i
$821$	−5.50000	+	9.52628i	−0.191951	+	0.332469i	−0.945897	−	0.324468i	$-0.894815\pi$
$821$	−5.50000	+	9.52628i	−0.191951	+	0.332469i	0.753946	+	0.656937i	$0.228148\pi$
$822$		0			0
$823$	−7.79423	+	4.50000i	−0.271690	+	0.156860i	−0.629655	−	0.776875i	$-0.716804\pi$
$823$	−7.79423	+	4.50000i	−0.271690	+	0.156860i	0.357966	+	0.933735i	$0.383471\pi$
$824$	6.33975	+	23.6603i	0.220856	+	0.824244i
$825$		0			0
$826$	1.39230	−	19.3923i	0.0484445	−	0.674745i
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$		0			0
$829$	−7.50000	+	4.33013i	−0.260486	+	0.150392i	−0.624556	−	0.780980i	$-0.714720\pi$
$829$	−7.50000	+	4.33013i	−0.260486	+	0.150392i	0.364070	+	0.931371i	$0.381387\pi$
$830$	32.7846	+	8.78461i	1.13797	+	0.304918i
$831$		0			0
$832$	27.7128			0.960769
$833$	4.50000	+	11.2583i	0.155916	+	0.390078i
$834$		0			0
$835$	−25.9808	−	15.0000i	−0.899101	−	0.519096i
$836$	−5.19615	−	9.00000i	−0.179713	−	0.311272i
$837$		0			0
$838$	−28.3923	+	7.60770i	−0.980796	+	0.262803i
$839$	48.4974			1.67432			0.837158	−	0.546960i	$-0.184215\pi$
$839$	48.4974			1.67432			0.837158	+	0.546960i	$0.184215\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−27.3205	+	7.32051i	−0.941527	+	0.252281i
$843$		0			0
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	1.50000	+	0.866025i	0.0516016	+	0.0297922i
$846$		0			0
$847$	25.9808	−	5.00000i	0.892710	−	0.171802i
$848$	−4.00000			−0.137361
$849$		0			0
$850$	−4.73205	−	1.26795i	−0.162308	−	0.0434903i
$851$	2.59808	−	1.50000i	0.0890609	−	0.0514193i
$852$		0			0
$853$		−	24.2487i		−	0.830260i	−0.909762	−	0.415130i	$-0.863736\pi$
$853$		−	24.2487i		−	0.830260i	0.909762	−	0.415130i	$-0.136264\pi$
$854$	8.49038	+	17.4904i	0.290535	+	0.598509i
$855$		0			0
$856$	35.5167	−	9.51666i	1.21393	−	0.325273i
$857$	22.5000	−	12.9904i	0.768585	−	0.443743i	−0.0637844	−	0.997964i	$-0.520317\pi$
$857$	22.5000	−	12.9904i	0.768585	−	0.443743i	0.832370	+	0.554221i	$0.186984\pi$
$858$		0			0
$859$	25.1147	−	43.5000i	0.856904	−	1.48420i	−0.0179638	−	0.999839i	$-0.505718\pi$
$859$	25.1147	−	43.5000i	0.856904	−	1.48420i	0.874868	−	0.484362i	$-0.160948\pi$
$860$		−	6.92820i		−	0.236250i
$861$		0			0
$862$	23.0000	−	23.0000i	0.783383	−	0.783383i
$863$	30.3109	+	17.5000i	1.03179	+	0.595707i	0.917498	−	0.397740i	$-0.130205\pi$
$863$	30.3109	+	17.5000i	1.03179	+	0.595707i	0.114296	+	0.993447i	$0.463539\pi$
$864$		0			0
$865$	10.5000	+	18.1865i	0.357011	+	0.618361i
$866$	−3.80385	−	14.1962i	−0.129260	−	0.482405i
$867$		0			0
$868$	1.73205	+	9.00000i	0.0587896	+	0.305480i
$869$	−9.00000			−0.305304
$870$		0			0
$871$	5.19615	+	9.00000i	0.176065	+	0.304953i
$872$	−24.5885	−	6.58846i	−0.832670	−	0.223113i
$873$		0			0
$874$	5.19615	−	5.19615i	0.175762	−	0.175762i
$875$	−24.2487	+	21.0000i	−0.819756	+	0.709930i
$876$		0			0
$877$	−0.500000	+	0.866025i	−0.0168838	+	0.0292436i	−0.874344	−	0.485307i	$-0.838708\pi$
$877$	−0.500000	+	0.866025i	−0.0168838	+	0.0292436i	0.857460	+	0.514551i	$0.172041\pi$
$878$	8.24167	−	30.7583i	0.278143	−	1.03804i
$879$		0			0
$880$	−3.46410	+	6.00000i	−0.116775	+	0.202260i
$881$		−	13.8564i		−	0.466834i	−0.972377	−	0.233417i	$-0.925009\pi$
$881$		−	13.8564i		−	0.466834i	0.972377	−	0.233417i	$-0.0749907\pi$
$882$		0			0
$883$			10.0000i			0.336527i	0.985742	+	0.168263i	$0.0538159\pi$
$883$			10.0000i			0.336527i	−0.985742	+	0.168263i	$0.946184\pi$
$884$	10.3923	+	6.00000i	0.349531	+	0.201802i
$885$		0			0
$886$	23.2224	+	6.22243i	0.780173	+	0.209047i
$887$	12.9904	−	22.5000i	0.436174	−	0.755476i	−0.561216	−	0.827669i	$-0.689666\pi$
$887$	12.9904	−	22.5000i	0.436174	−	0.755476i	0.997391	+	0.0721931i	$0.0229998\pi$
$888$		0			0
$889$	−12.0000	+	10.3923i	−0.402467	+	0.348547i
$890$	−27.0000	−	27.0000i	−0.905042	−	0.905042i
$891$		0			0
$892$	−12.0000	+	6.92820i	−0.401790	+	0.231973i
$893$	−22.5000	−	38.9711i	−0.752934	−	1.30412i
$894$		0			0
$895$	32.9090			1.10003
$896$	−16.7846	+	24.7846i	−0.560734	+	0.827996i
$897$		0			0
$898$	−10.9282	+	2.92820i	−0.364679	+	0.0977154i
$899$	3.46410	+	6.00000i	0.115534	+	0.200111i
$900$		0			0
$901$	−1.50000	−	0.866025i	−0.0499722	−	0.0288515i
$902$	−3.46410	−	3.46410i	−0.115342	−	0.115342i
$903$		0			0
$904$	32.0000	−	32.0000i	1.06430	−	1.06430i
$905$	−6.00000	+	10.3923i	−0.199447	+	0.345452i
$906$		0			0
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	−0.395966	−	0.918265i	$-0.629590\pi$
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	0.597258	+	0.802049i	$0.296257\pi$
$908$	−33.0000	−	19.0526i	−1.09514	−	0.632281i
$909$		0			0
$910$	20.1962	−	9.80385i	0.669496	−	0.324994i
$911$		−	26.0000i		−	0.861418i	−0.902491	−	0.430709i	$-0.858263\pi$
$911$		−	26.0000i		−	0.861418i	0.902491	−	0.430709i	$-0.141737\pi$
$912$		0			0
$913$	−12.0000	+	6.92820i	−0.397142	+	0.229290i
$914$	−5.49038	+	20.4904i	−0.181606	+	0.677762i
$915$		0			0
$916$	−31.1769			−1.03011
$917$	13.5000	−	2.59808i	0.445809	−	0.0857960i
$918$		0			0
$919$	−0.866025	−	0.500000i	−0.0285675	−	0.0164935i	0.485648	−	0.874154i	$-0.338584\pi$
$919$	−0.866025	−	0.500000i	−0.0285675	−	0.0164935i	−0.514216	+	0.857661i	$0.671917\pi$
$920$	−4.73205	−	1.26795i	−0.156011	−	0.0418030i
$921$		0			0
$922$	6.33975	+	23.6603i	0.208788	+	0.779209i
$923$	48.4974			1.59631
$924$		0			0
$925$	6.00000			0.197279
$926$	10.9808	+	40.9808i	0.360850	+	1.34671i
$927$		0			0
$928$	−5.85641	+	21.8564i	−0.192246	+	0.717472i
$929$	−7.50000	−	4.33013i	−0.246067	−	0.142067i	0.371895	−	0.928275i	$-0.378708\pi$
$929$	−7.50000	−	4.33013i	−0.246067	−	0.142067i	−0.617962	+	0.786208i	$0.712041\pi$
$930$		0			0
$931$	−28.5788	−	22.5000i	−0.936634	−	0.737408i
$932$			14.0000i			0.458585i
$933$		0			0
$934$	3.16987	−	11.8301i	0.103721	−	0.387094i
$935$	−2.59808	+	1.50000i	−0.0849662	+	0.0490552i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−11.1962	−	0.803848i	−0.365567	−	0.0262466i
$939$		0			0
$940$	−15.0000	+	25.9808i	−0.489246	+	0.847399i
$941$	−49.5000	+	28.5788i	−1.61365	+	0.931644i	−0.625140	+	0.780513i	$0.714958\pi$
$941$	−49.5000	+	28.5788i	−1.61365	+	0.931644i	−0.988514	+	0.151131i	$0.951708\pi$
$942$		0			0
$943$	1.73205	−	3.00000i	0.0564033	−	0.0976934i
$944$	20.7846			0.676481
$945$		0			0
$946$	2.00000	+	2.00000i	0.0650256	+	0.0650256i
$947$	−25.1147	−	14.5000i	−0.816119	−	0.471187i	0.0329571	−	0.999457i	$-0.489508\pi$
$947$	−25.1147	−	14.5000i	−0.816119	−	0.471187i	−0.849076	+	0.528270i	$0.822841\pi$
$948$		0			0
$949$	15.0000	+	25.9808i	0.486921	+	0.843371i
$950$	14.1962	−	3.80385i	0.460584	−	0.123413i
$951$		0			0
$952$	−11.6603	+	5.66025i	−0.377911	+	0.183450i
$953$	8.00000			0.259145			0.129573	−	0.991570i	$-0.458639\pi$
$953$	8.00000			0.259145			0.129573	+	0.991570i	$0.458639\pi$
$954$		0			0
$955$	0.866025	+	1.50000i	0.0280239	+	0.0485389i
$956$	20.0000	+	34.6410i	0.646846	+	1.12037i
$957$		0			0
$958$	12.1244	+	12.1244i	0.391720	+	0.391720i
$959$	0.866025	−	2.50000i	0.0279654	−	0.0807292i
$960$		0			0
$961$	14.0000	−	24.2487i	0.451613	−	0.782216i
$962$	−14.1962	−	3.80385i	−0.457702	−	0.122641i
$963$		0			0
$964$	−5.19615	+	9.00000i	−0.167357	+	0.289870i
$965$			25.9808i			0.836350i
$966$		0			0
$967$			6.00000i			0.192947i	0.995336	+	0.0964735i	$0.0307563\pi$
$967$			6.00000i			0.192947i	−0.995336	+	0.0964735i	$0.969244\pi$
$968$	7.32051	+	27.3205i	0.235290	+	0.878114i
$969$		0			0
$970$	10.9808	−	40.9808i	0.352571	−	1.31581i
$971$	−30.3109	+	52.5000i	−0.972723	+	1.68481i	−0.285469	+	0.958388i	$0.592149\pi$
$971$	−30.3109	+	52.5000i	−0.972723	+	1.68481i	−0.687254	+	0.726417i	$0.741184\pi$
$972$		0			0
$973$	−12.0000	−	13.8564i	−0.384702	−	0.444216i
$974$	31.0000	−	31.0000i	0.993304	−	0.993304i
$975$		0			0
$976$	−18.0000	+	10.3923i	−0.576166	+	0.332650i
$977$	−15.5000	−	26.8468i	−0.495889	−	0.858905i	0.504100	−	0.863645i	$-0.331824\pi$
$977$	−15.5000	−	26.8468i	−0.495889	−	0.858905i	−0.999989	+	0.00474056i	$0.998491\pi$
$978$		0			0
$979$	15.5885			0.498209
$980$	−3.46410	+	24.0000i	−0.110657	+	0.766652i
$981$		0			0
$982$	11.7128	+	43.7128i	0.373771	+	1.39493i
$983$	−30.3109	−	52.5000i	−0.966767	−	1.67449i	−0.704790	−	0.709416i	$-0.748959\pi$
$983$	−30.3109	−	52.5000i	−0.966767	−	1.67449i	−0.261977	−	0.965074i	$-0.584374\pi$
$984$		0			0
$985$	−24.0000	−	13.8564i	−0.764704	−	0.441502i
$986$	−6.92820	+	6.92820i	−0.220639	+	0.220639i
$987$		0			0
$988$	−36.0000			−1.14531
$989$	−1.00000	+	1.73205i	−0.0317982	+	0.0550760i
$990$		0			0
$991$	19.9186	−	11.5000i	0.632735	−	0.365310i	−0.149076	−	0.988826i	$-0.547630\pi$
$991$	19.9186	−	11.5000i	0.632735	−	0.365310i	0.781810	+	0.623516i	$0.214296\pi$
$992$	−9.46410	+	2.53590i	−0.300486	+	0.0805149i
$993$		0			0
$994$	−29.3731	+	43.3731i	−0.931657	+	1.37571i
$995$		−	39.0000i		−	1.23638i
$996$		0			0
$997$	19.5000	−	11.2583i	0.617571	−	0.356555i	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	19.5000	−	11.2583i	0.617571	−	0.356555i	0.775923	+	0.630828i	$0.217285\pi$
$998$	−47.8109	−	12.8109i	−1.51343	−	0.405522i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.e.19.2		4
3.2	odd	2		28.2.f.a.19.1	yes	4
4.3	odd	2	inner	252.2.bf.e.19.1		4
7.2	even	3		1764.2.b.a.1567.1		4
7.3	odd	6	inner	252.2.bf.e.199.1		4
7.5	odd	6		1764.2.b.a.1567.2		4
12.11	even	2		28.2.f.a.19.2	yes	4
15.2	even	4		700.2.t.b.299.1		4
15.8	even	4		700.2.t.a.299.2		4
15.14	odd	2		700.2.p.a.551.2		4
21.2	odd	6		196.2.d.b.195.3		4
21.5	even	6		196.2.d.b.195.4		4
21.11	odd	6		196.2.f.a.31.2		4
21.17	even	6		28.2.f.a.3.2	yes	4
21.20	even	2		196.2.f.a.19.1		4
24.5	odd	2		448.2.p.d.383.1		4
24.11	even	2		448.2.p.d.383.2		4
28.3	even	6	inner	252.2.bf.e.199.2		4
28.19	even	6		1764.2.b.a.1567.4		4
28.23	odd	6		1764.2.b.a.1567.3		4
60.23	odd	4		700.2.t.b.299.2		4
60.47	odd	4		700.2.t.a.299.1		4
60.59	even	2		700.2.p.a.551.1		4
84.11	even	6		196.2.f.a.31.1		4
84.23	even	6		196.2.d.b.195.2		4
84.47	odd	6		196.2.d.b.195.1		4
84.59	odd	6		28.2.f.a.3.1	✓	4
84.83	odd	2		196.2.f.a.19.2		4
105.17	odd	12		700.2.t.b.199.2		4
105.38	odd	12		700.2.t.a.199.1		4
105.59	even	6		700.2.p.a.451.1		4
168.5	even	6		3136.2.f.e.3135.2		4
168.59	odd	6		448.2.p.d.255.1		4
168.101	even	6		448.2.p.d.255.2		4
168.107	even	6		3136.2.f.e.3135.1		4
168.131	odd	6		3136.2.f.e.3135.4		4
168.149	odd	6		3136.2.f.e.3135.3		4
420.59	odd	6		700.2.p.a.451.2		4
420.143	even	12		700.2.t.b.199.1		4
420.227	even	12		700.2.t.a.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.f.a.3.1	✓	4	84.59	odd	6
28.2.f.a.3.2	yes	4	21.17	even	6
28.2.f.a.19.1	yes	4	3.2	odd	2
28.2.f.a.19.2	yes	4	12.11	even	2
196.2.d.b.195.1		4	84.47	odd	6
196.2.d.b.195.2		4	84.23	even	6
196.2.d.b.195.3		4	21.2	odd	6
196.2.d.b.195.4		4	21.5	even	6
196.2.f.a.19.1		4	21.20	even	2
196.2.f.a.19.2		4	84.83	odd	2
196.2.f.a.31.1		4	84.11	even	6
196.2.f.a.31.2		4	21.11	odd	6
252.2.bf.e.19.1		4	4.3	odd	2	inner
252.2.bf.e.19.2		4	1.1	even	1	trivial
252.2.bf.e.199.1		4	7.3	odd	6	inner
252.2.bf.e.199.2		4	28.3	even	6	inner
448.2.p.d.255.1		4	168.59	odd	6
448.2.p.d.255.2		4	168.101	even	6
448.2.p.d.383.1		4	24.5	odd	2
448.2.p.d.383.2		4	24.11	even	2
700.2.p.a.451.1		4	105.59	even	6
700.2.p.a.451.2		4	420.59	odd	6
700.2.p.a.551.1		4	60.59	even	2
700.2.p.a.551.2		4	15.14	odd	2
700.2.t.a.199.1		4	105.38	odd	12
700.2.t.a.199.2		4	420.227	even	12
700.2.t.a.299.1		4	60.47	odd	4
700.2.t.a.299.2		4	15.8	even	4
700.2.t.b.199.1		4	420.143	even	12
700.2.t.b.199.2		4	105.17	odd	12
700.2.t.b.299.1		4	15.2	even	4
700.2.t.b.299.2		4	60.23	odd	4
1764.2.b.a.1567.1		4	7.2	even	3
1764.2.b.a.1567.2		4	7.5	odd	6
1764.2.b.a.1567.3		4	28.23	odd	6
1764.2.b.a.1567.4		4	28.19	even	6
3136.2.f.e.3135.1		4	168.107	even	6
3136.2.f.e.3135.2		4	168.5	even	6
3136.2.f.e.3135.3		4	168.149	odd	6
3136.2.f.e.3135.4		4	168.131	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.36603 + 0.633975i) q^{10} +(-0.866025 + 0.500000i) q^{11} +3.46410i q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.50000 - 0.866025i) q^{17} +(-2.59808 + 4.50000i) q^{19} +3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(1.26795 + 4.73205i) q^{26} +(-5.00000 - 1.73205i) q^{28} -4.00000 q^{29} +(-0.866025 - 1.50000i) q^{31} +(1.46410 - 5.46410i) q^{32} +(1.73205 - 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(4.73205 - 1.26795i) q^{40} +3.46410i q^{41} -2.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.36603 - 0.366025i) q^{46} +(-4.33013 + 7.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-2.00000 - 2.00000i) q^{50} +(3.46410 + 6.00000i) q^{52} +(-0.500000 - 0.866025i) q^{53} -1.73205 q^{55} +(-7.46410 - 0.535898i) q^{56} +(-5.46410 + 1.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-4.50000 - 2.59808i) q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +(-3.00000 + 5.19615i) q^{65} +(2.59808 - 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} +(-2.83013 - 5.83013i) q^{70} -14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-1.09808 + 4.09808i) q^{74} +10.3923i q^{76} +(2.50000 + 0.866025i) q^{77} +(7.79423 + 4.50000i) q^{79} +(6.00000 - 3.46410i) q^{80} +(1.26795 + 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(-0.732051 - 2.73205i) q^{86} +(-0.732051 + 2.73205i) q^{88} +(-13.5000 - 7.79423i) q^{89} +(6.92820 - 6.00000i) q^{91} -2.00000 q^{92} +(-3.16987 + 11.8301i) q^{94} +(-7.79423 + 4.50000i) q^{95} -17.3205i q^{97} +(1.16987 + 9.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{5} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^5 + 8 * q^8	\( 4 q + 2 q^{2} + 6 q^{5} + 8 q^{8} + 6 q^{10} - 2 q^{14} + 8 q^{16} + 6 q^{17} - 4 q^{22} - 4 q^{25} + 12 q^{26} - 20 q^{28} - 16 q^{29} - 8 q^{32} - 6 q^{37} - 18 q^{38} + 12 q^{40} - 4 q^{44} - 2 q^{46} - 4 q^{49} - 8 q^{50} - 2 q^{53} - 16 q^{56} - 8 q^{58} - 18 q^{61} - 12 q^{65} + 6 q^{70} + 30 q^{73} + 6 q^{74} + 10 q^{77} + 24 q^{80} + 12 q^{82} + 12 q^{85} + 4 q^{86} + 4 q^{88} - 54 q^{89} - 8 q^{92} - 30 q^{94} + 22 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^5 + 8 * q^8 + 6 * q^10 - 2 * q^14 + 8 * q^16 + 6 * q^17 - 4 * q^22 - 4 * q^25 + 12 * q^26 - 20 * q^28 - 16 * q^29 - 8 * q^32 - 6 * q^37 - 18 * q^38 + 12 * q^40 - 4 * q^44 - 2 * q^46 - 4 * q^49 - 8 * q^50 - 2 * q^53 - 16 * q^56 - 8 * q^58 - 18 * q^61 - 12 * q^65 + 6 * q^70 + 30 * q^73 + 6 * q^74 + 10 * q^77 + 24 * q^80 + 12 * q^82 + 12 * q^85 + 4 * q^86 + 4 * q^88 - 54 * q^89 - 8 * q^92 - 30 * q^94 + 22 * q^98

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