LMFDB - Embedded newform 280.2.bl.a.261.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(221,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("280.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bl (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:	$2.23581125660$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			261.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.261
Dual form			280.2.bl.a.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.366025 - 1.36603i) q^{10} +(-2.59808 + 1.50000i) q^{11} -1.00000i q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-4.09808 - 1.09808i) q^{18} +(0.866025 + 0.500000i) q^{19} +2.00000 q^{20} +(-3.00000 - 3.00000i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{25} +(1.36603 - 0.366025i) q^{26} +(1.73205 - 5.00000i) q^{28} -10.0000i q^{29} +(5.46410 + 1.46410i) q^{32} +(-6.00000 + 6.00000i) q^{34} +(2.59808 - 0.500000i) q^{35} -6.00000i q^{36} +(4.33013 + 2.50000i) q^{37} +(-0.366025 + 1.36603i) q^{38} +(0.732051 + 2.73205i) q^{40} +9.00000 q^{41} +6.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(2.59808 - 1.50000i) q^{45} +(-4.09808 - 1.09808i) q^{46} +(-2.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-1.00000 + 1.00000i) q^{50} +(1.00000 + 1.73205i) q^{52} +(-7.79423 + 4.50000i) q^{53} +3.00000 q^{55} +(7.46410 + 0.535898i) q^{56} +(13.6603 - 3.66025i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(6.92820 + 4.00000i) q^{61} +(-1.50000 - 7.79423i) q^{63} +8.00000i q^{64} +(-0.500000 + 0.866025i) q^{65} +(1.73205 - 1.00000i) q^{67} +(-10.3923 - 6.00000i) q^{68} +(1.63397 + 3.36603i) q^{70} -10.0000 q^{71} +(8.19615 - 2.19615i) q^{72} +(4.00000 + 6.92820i) q^{73} +(-1.83013 + 6.83013i) q^{74} -2.00000 q^{76} +(2.59808 - 7.50000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-3.46410 + 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.29423 + 12.2942i) q^{82} +16.0000i q^{83} -6.00000i q^{85} +(-8.19615 + 2.19615i) q^{86} +(8.19615 + 2.19615i) q^{88} +(1.00000 - 1.73205i) q^{89} +(3.00000 + 3.00000i) q^{90} +(1.73205 + 2.00000i) q^{91} -6.00000i q^{92} +(-6.83013 - 1.83013i) q^{94} +(-0.500000 - 0.866025i) q^{95} +8.00000 q^{97} +(9.83013 - 1.16987i) q^{98} -9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 8 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} - 8 q^{7} - 8 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{14} + 8 q^{16} + 12 q^{17} - 6 q^{18} + 8 q^{20} - 12 q^{22} - 6 q^{23} + 2 q^{25} + 2 q^{26} + 8 q^{32} - 24 q^{34} + 2 q^{38} - 4 q^{40} + 36 q^{41} + 12 q^{44} - 6 q^{46} - 10 q^{47} + 4 q^{49} - 4 q^{50} + 4 q^{52} + 12 q^{55} + 16 q^{56} + 20 q^{58} - 6 q^{63} - 2 q^{65} + 10 q^{70} - 40 q^{71} + 12 q^{72} + 16 q^{73} + 10 q^{74} - 8 q^{76} + 8 q^{79} - 18 q^{81} - 18 q^{82} - 12 q^{86} + 12 q^{88} + 4 q^{89} + 12 q^{90} - 10 q^{94} - 2 q^{95} + 32 q^{97} + 22 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 8 * q^7 - 8 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^14 + 8 * q^16 + 12 * q^17 - 6 * q^18 + 8 * q^20 - 12 * q^22 - 6 * q^23 + 2 * q^25 + 2 * q^26 + 8 * q^32 - 24 * q^34 + 2 * q^38 - 4 * q^40 + 36 * q^41 + 12 * q^44 - 6 * q^46 - 10 * q^47 + 4 * q^49 - 4 * q^50 + 4 * q^52 + 12 * q^55 + 16 * q^56 + 20 * q^58 - 6 * q^63 - 2 * q^65 + 10 * q^70 - 40 * q^71 + 12 * q^72 + 16 * q^73 + 10 * q^74 - 8 * q^76 + 8 * q^79 - 18 * q^81 - 18 * q^82 - 12 * q^86 + 12 * q^88 + 4 * q^89 + 12 * q^90 - 10 * q^94 - 2 * q^95 + 32 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	0.366025	−	1.36603i	0.115747	−	0.431975i
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	−3.09808	−	2.09808i	−0.827996	−	0.560734i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	−4.09808	−	1.09808i	−0.965926	−	0.258819i
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−3.00000	−	3.00000i	−0.639602	−	0.639602i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.36603	−	0.366025i	0.267900	−	0.0717835i
$27$		0			0
$28$	1.73205	−	5.00000i	0.327327	−	0.944911i
$29$		−	10.0000i		−	1.85695i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$		−	10.0000i		−	1.85695i	0.371391	−	0.928477i	$-0.378881\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$		0			0
$34$	−6.00000	+	6.00000i	−1.02899	+	1.02899i
$35$	2.59808	−	0.500000i	0.439155	−	0.0845154i
$36$		−	6.00000i		−	1.00000i
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	0.811752	−	0.584002i	$-0.198514\pi$
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	−0.0998840	+	0.994999i	$0.531847\pi$
$38$	−0.366025	+	1.36603i	−0.0593772	+	0.221599i
$39$		0			0
$40$	0.732051	+	2.73205i	0.115747	+	0.431975i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$	2.59808	−	1.50000i	0.387298	−	0.223607i
$46$	−4.09808	−	1.09808i	−0.604228	−	0.161903i
$47$	−2.50000	+	4.33013i	−0.364662	+	0.631614i	−0.988722	−	0.149763i	$-0.952149\pi$
$47$	−2.50000	+	4.33013i	−0.364662	+	0.631614i	0.624059	+	0.781377i	$0.285482\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−1.00000	+	1.00000i	−0.141421	+	0.141421i
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−7.79423	+	4.50000i	−1.07062	+	0.618123i	−0.928351	−	0.371706i	$-0.878773\pi$
$53$	−7.79423	+	4.50000i	−1.07062	+	0.618123i	−0.142269	+	0.989828i	$0.545440\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$	7.46410	+	0.535898i	0.997433	+	0.0716124i
$57$		0			0
$58$	13.6603	−	3.66025i	1.79368	−	0.480615i
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.877841	−	0.478953i	$-0.841016\pi$
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.0241347	+	0.999709i	$0.507683\pi$
$60$		0			0
$61$	6.92820	+	4.00000i	0.887066	+	0.512148i	0.872982	−	0.487753i	$-0.162183\pi$
$61$	6.92820	+	4.00000i	0.887066	+	0.512148i	0.0140840	+	0.999901i	$0.495517\pi$
$62$		0			0
$63$	−1.50000	−	7.79423i	−0.188982	−	0.981981i
$64$			8.00000i			1.00000i
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	−10.3923	−	6.00000i	−1.26025	−	0.727607i
$69$		0			0
$70$	1.63397	+	3.36603i	0.195297	+	0.402317i
$71$	−10.0000			−1.18678			−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000			−1.18678			−0.593391	+	0.804914i	$0.702211\pi$
$72$	8.19615	−	2.19615i	0.965926	−	0.258819i
$73$	4.00000	+	6.92820i	0.468165	+	0.810885i	0.999338	−	0.0363782i	$-0.0115821\pi$
$73$	4.00000	+	6.92820i	0.468165	+	0.810885i	−0.531174	+	0.847263i	$0.678249\pi$
$74$	−1.83013	+	6.83013i	−0.212748	+	0.793986i
$75$		0			0
$76$	−2.00000			−0.229416
$77$	2.59808	−	7.50000i	0.296078	−	0.854704i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−3.46410	+	2.00000i	−0.387298	+	0.223607i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	3.29423	+	12.2942i	0.363787	+	1.35767i
$83$			16.0000i			1.75623i	0.478451	+	0.878114i	$0.341198\pi$
$83$			16.0000i			1.75623i	−0.478451	+	0.878114i	$0.658802\pi$
$84$		0			0
$85$		−	6.00000i		−	0.650791i
$86$	−8.19615	+	2.19615i	−0.883814	+	0.236817i
$87$		0			0
$88$	8.19615	+	2.19615i	0.873713	+	0.234111i
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	−0.808146	−	0.588982i	$-0.799529\pi$
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	0.914146	+	0.405385i	$0.132862\pi$
$90$	3.00000	+	3.00000i	0.316228	+	0.316228i
$91$	1.73205	+	2.00000i	0.181568	+	0.209657i
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$	−6.83013	−	1.83013i	−0.704474	−	0.188763i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	9.83013	−	1.16987i	0.992993	−	0.118175i
$99$		−	9.00000i		−	0.904534i
$100$	−1.73205	−	1.00000i	−0.173205	−	0.100000i
$101$	−5.19615	+	3.00000i	−0.517036	+	0.298511i	−0.735721	−	0.677284i	$-0.763157\pi$
$101$	−5.19615	+	3.00000i	−0.517036	+	0.298511i	0.218685	+	0.975796i	$0.429823\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	−2.00000	+	2.00000i	−0.196116	+	0.196116i
$105$		0			0
$106$	−9.00000	−	9.00000i	−0.874157	−	0.874157i
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$		0			0
$109$	1.73205	−	1.00000i	0.165900	−	0.0957826i	−0.414751	−	0.909935i	$-0.636131\pi$
$109$	1.73205	−	1.00000i	0.165900	−	0.0957826i	0.580651	+	0.814152i	$0.302798\pi$
$110$	1.09808	+	4.09808i	0.104697	+	0.390736i
$111$		0			0
$112$	2.00000	+	10.3923i	0.188982	+	0.981981i
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$	2.59808	−	1.50000i	0.242272	−	0.139876i
$116$	10.0000	+	17.3205i	0.928477	+	1.60817i
$117$	2.59808	+	1.50000i	0.240192	+	0.138675i
$118$	−8.00000	−	8.00000i	−0.736460	−	0.736460i
$119$	−15.0000	−	5.19615i	−1.37505	−	0.476331i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−2.92820	+	10.9282i	−0.265107	+	0.989393i
$123$		0			0
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$	10.0981	−	4.90192i	0.899608	−	0.436698i
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$		0			0
$130$	−1.36603	−	0.366025i	−0.119808	−	0.0321026i
$131$	−12.9904	−	7.50000i	−1.13497	−	0.655278i	−0.189794	−	0.981824i	$-0.560782\pi$
$131$	−12.9904	−	7.50000i	−1.13497	−	0.655278i	−0.945181	+	0.326546i	$0.894115\pi$
$132$		0			0
$133$	−2.59808	+	0.500000i	−0.225282	+	0.0433555i
$134$	2.00000	+	2.00000i	0.172774	+	0.172774i
$135$		0			0
$136$	4.39230	−	16.3923i	0.376637	−	1.40563i
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$		−	20.0000i		−	1.69638i	−0.529694	−	0.848189i	$-0.677693\pi$
$139$		−	20.0000i		−	1.69638i	0.529694	−	0.848189i	$-0.322307\pi$
$140$	−4.00000	+	3.46410i	−0.338062	+	0.292770i
$141$		0			0
$142$	−3.66025	−	13.6603i	−0.307162	−	1.14634i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$	−5.00000	+	8.66025i	−0.415227	+	0.719195i
$146$	−8.00000	+	8.00000i	−0.662085	+	0.662085i
$147$		0			0
$148$	−10.0000			−0.821995
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	−0.732051	−	2.73205i	−0.0593772	−	0.221599i
$153$	−18.0000			−1.45521
$154$	11.1962	+	0.803848i	0.902212	+	0.0647759i
$155$		0			0
$156$		0			0
$157$	−0.866025	+	0.500000i	−0.0691164	+	0.0399043i	−0.534160	−	0.845383i	$-0.679372\pi$
$157$	−0.866025	+	0.500000i	−0.0691164	+	0.0399043i	0.465044	+	0.885288i	$0.346039\pi$
$158$	5.46410	+	1.46410i	0.434701	+	0.116478i
$159$		0			0
$160$	−4.00000	−	4.00000i	−0.316228	−	0.316228i
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$	9.00000	−	9.00000i	0.707107	−	0.707107i
$163$	−1.73205	−	1.00000i	−0.135665	−	0.0783260i	0.430632	−	0.902528i	$-0.358291\pi$
$163$	−1.73205	−	1.00000i	−0.135665	−	0.0783260i	−0.566296	+	0.824202i	$0.691624\pi$
$164$	−15.5885	+	9.00000i	−1.21725	+	0.702782i
$165$		0			0
$166$	−21.8564	+	5.85641i	−1.69639	+	0.454545i
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	8.19615	−	2.19615i	0.628616	−	0.168437i
$171$	−2.59808	+	1.50000i	−0.198680	+	0.114708i
$172$	−6.00000	−	10.3923i	−0.457496	−	0.792406i
$173$	−11.2583	−	6.50000i	−0.855955	−	0.494186i	0.00670064	−	0.999978i	$-0.497867\pi$
$173$	−11.2583	−	6.50000i	−0.855955	−	0.494186i	−0.862656	+	0.505792i	$0.831200\pi$
$174$		0			0
$175$	−2.50000	−	0.866025i	−0.188982	−	0.0654654i
$176$			12.0000i			0.904534i
$177$		0			0
$178$	2.73205	+	0.732051i	0.204776	+	0.0548695i
$179$	21.6506	−	12.5000i	1.61824	−	0.934294i	0.630870	−	0.775888i	$-0.282698\pi$
$179$	21.6506	−	12.5000i	1.61824	−	0.934294i	0.987374	−	0.158406i	$-0.0506353\pi$
$180$	−3.00000	+	5.19615i	−0.223607	+	0.387298i
$181$			20.0000i			1.48659i	0.668965	+	0.743294i	$0.266738\pi$
$181$			20.0000i			1.48659i	−0.668965	+	0.743294i	$0.733262\pi$
$182$	−2.09808	+	3.09808i	−0.155520	+	0.229645i
$183$		0			0
$184$	8.19615	−	2.19615i	0.604228	−	0.161903i
$185$	−2.50000	−	4.33013i	−0.183804	−	0.318357i
$186$		0			0
$187$	−15.5885	−	9.00000i	−1.13994	−	0.658145i
$188$		−	10.0000i		−	0.729325i
$189$		0			0
$190$	1.00000	−	1.00000i	0.0725476	−	0.0725476i
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$		0			0
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	0.737620	−	0.675216i	$-0.235950\pi$
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	−0.953564	+	0.301189i	$0.902616\pi$
$194$	2.92820	+	10.9282i	0.210233	+	0.784599i
$195$		0			0
$196$	5.19615	+	13.0000i	0.371154	+	0.928571i
$197$			17.0000i			1.21120i	0.795769	+	0.605600i	$0.207067\pi$
$197$			17.0000i			1.21120i	−0.795769	+	0.605600i	$0.792933\pi$
$198$	12.2942	−	3.29423i	0.873713	−	0.234111i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	0.732051	−	2.73205i	0.0517638	−	0.193185i
$201$		0			0
$202$	−6.00000	−	6.00000i	−0.422159	−	0.422159i
$203$	17.3205	+	20.0000i	1.21566	+	1.40372i
$204$		0			0
$205$	−7.79423	−	4.50000i	−0.544373	−	0.314294i
$206$	21.8564	+	5.85641i	1.52281	+	0.408035i
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$	−3.46410	−	2.00000i	−0.240192	−	0.138675i
$209$	−3.00000			−0.207514
$210$		0			0
$211$			11.0000i			0.757271i	0.925546	+	0.378636i	$0.123607\pi$
$211$			11.0000i			0.757271i	−0.925546	+	0.378636i	$0.876393\pi$
$212$	9.00000	−	15.5885i	0.618123	−	1.07062i
$213$		0			0
$214$	−2.19615	+	8.19615i	−0.150126	+	0.560277i
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$		0			0
$217$		0			0
$218$	2.00000	+	2.00000i	0.135457	+	0.135457i
$219$		0			0
$220$	−5.19615	+	3.00000i	−0.350325	+	0.202260i
$221$	5.19615	−	3.00000i	0.349531	−	0.201802i
$222$		0			0
$223$	28.0000			1.87502			0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000			1.87502			0.937509	+	0.347960i	$0.113126\pi$
$224$	−13.4641	+	6.53590i	−0.899608	+	0.436698i
$225$	−3.00000			−0.200000
$226$	−1.46410	−	5.46410i	−0.0973906	−	0.363467i
$227$	−12.1244	+	7.00000i	−0.804722	+	0.464606i	−0.845120	−	0.534577i	$-0.820471\pi$
$227$	−12.1244	+	7.00000i	−0.804722	+	0.464606i	0.0403978	+	0.999184i	$0.487137\pi$
$228$		0			0
$229$	17.3205	+	10.0000i	1.14457	+	0.660819i	0.947559	−	0.319582i	$-0.103543\pi$
$229$	17.3205	+	10.0000i	1.14457	+	0.660819i	0.197013	+	0.980401i	$0.436876\pi$
$230$	3.00000	+	3.00000i	0.197814	+	0.197814i
$231$		0			0
$232$	−20.0000	+	20.0000i	−1.31306	+	1.31306i
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$	−1.09808	+	4.09808i	−0.0717835	+	0.267900i
$235$	4.33013	−	2.50000i	0.282466	−	0.163082i
$236$	8.00000	−	13.8564i	0.520756	−	0.901975i
$237$		0			0
$238$	1.60770	−	22.3923i	0.104211	−	1.45148i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	2.50000	+	4.33013i	0.161039	+	0.278928i	0.935242	−	0.354010i	$-0.115182\pi$
$241$	2.50000	+	4.33013i	0.161039	+	0.278928i	−0.774202	+	0.632938i	$0.781849\pi$
$242$	−2.73205	−	0.732051i	−0.175623	−	0.0470580i
$243$		0			0
$244$	−16.0000			−1.02430
$245$	−4.33013	+	5.50000i	−0.276642	+	0.351382i
$246$		0			0
$247$	0.500000	−	0.866025i	0.0318142	−	0.0551039i
$248$		0			0
$249$		0			0
$250$	1.36603	−	0.366025i	0.0863950	−	0.0231495i
$251$		−	25.0000i		−	1.57799i	−0.614402	−	0.788993i	$-0.710603\pi$
$251$		−	25.0000i		−	1.57799i	0.614402	−	0.788993i	$-0.289397\pi$
$252$	10.3923	+	12.0000i	0.654654	+	0.755929i
$253$		−	9.00000i		−	0.565825i
$254$	−1.83013	−	6.83013i	−0.114832	−	0.428560i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	2.00000	−	3.46410i	0.124757	−	0.216085i	−0.796881	−	0.604136i	$-0.793518\pi$
$257$	2.00000	−	3.46410i	0.124757	−	0.216085i	0.921638	+	0.388051i	$0.126852\pi$
$258$		0			0
$259$	−12.9904	+	2.50000i	−0.807183	+	0.155342i
$260$		−	2.00000i		−	0.124035i
$261$	25.9808	+	15.0000i	1.60817	+	0.928477i
$262$	5.49038	−	20.4904i	0.339197	−	1.26590i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	−1.63397	−	3.36603i	−0.100185	−	0.206384i
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	8.66025	−	5.00000i	0.528025	−	0.304855i	−0.212187	−	0.977229i	$-0.568059\pi$
$269$	8.66025	−	5.00000i	0.528025	−	0.304855i	0.740212	+	0.672374i	$0.234725\pi$
$270$		0			0
$271$	9.00000	−	15.5885i	0.546711	−	0.946931i	−0.451786	−	0.892126i	$-0.649213\pi$
$271$	9.00000	−	15.5885i	0.546711	−	0.946931i	0.998497	−	0.0548050i	$-0.0174537\pi$
$272$	24.0000			1.45521
$273$		0			0
$274$	18.0000	−	18.0000i	1.08742	−	1.08742i
$275$	−2.59808	−	1.50000i	−0.156670	−	0.0904534i
$276$		0			0
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.947604	−	0.319447i	$-0.896503\pi$
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.197153	+	0.980373i	$0.563170\pi$
$278$	27.3205	−	7.32051i	1.63858	−	0.439055i
$279$		0			0
$280$	−6.19615	−	4.19615i	−0.370291	−	0.250768i
$281$	15.0000			0.894825			0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000			0.894825			0.447412	+	0.894328i	$0.352346\pi$
$282$		0			0
$283$	22.5167	−	13.0000i	1.33848	−	0.772770i	0.351895	−	0.936039i	$-0.385537\pi$
$283$	22.5167	−	13.0000i	1.33848	−	0.772770i	0.986581	+	0.163270i	$0.0522041\pi$
$284$	17.3205	−	10.0000i	1.02778	−	0.593391i
$285$		0			0
$286$	−3.00000	+	3.00000i	−0.177394	+	0.177394i
$287$	−18.0000	+	15.5885i	−1.06251	+	0.920158i
$288$	−12.0000	+	12.0000i	−0.707107	+	0.707107i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−13.6603	−	3.66025i	−0.802158	−	0.214938i
$291$		0			0
$292$	−13.8564	−	8.00000i	−0.810885	−	0.468165i
$293$			13.0000i			0.759468i	0.925096	+	0.379734i	$0.123985\pi$
$293$			13.0000i			0.759468i	−0.925096	+	0.379734i	$0.876015\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$	−3.66025	−	13.6603i	−0.212748	−	0.793986i
$297$		0			0
$298$	2.19615	−	8.19615i	0.127220	−	0.474790i
$299$	2.59808	+	1.50000i	0.150251	+	0.0867472i
$300$		0			0
$301$	−10.3923	−	12.0000i	−0.599002	−	0.691669i
$302$	−8.00000	+	8.00000i	−0.460348	+	0.460348i
$303$		0			0
$304$	3.46410	−	2.00000i	0.198680	−	0.114708i
$305$	−4.00000	−	6.92820i	−0.229039	−	0.396708i
$306$	−6.58846	−	24.5885i	−0.376637	−	1.40563i
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$	3.00000	+	15.5885i	0.170941	+	0.888235i
$309$		0			0
$310$		0			0
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	0.972250	−	0.233944i	$-0.0751631\pi$
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	−0.688726	+	0.725022i	$0.741830\pi$
$312$		0			0
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	−0.956647	−	0.291250i	$-0.905929\pi$
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	0.730554	+	0.682855i	$0.239262\pi$
$314$	−1.00000	−	1.00000i	−0.0564333	−	0.0564333i
$315$	−2.59808	+	7.50000i	−0.146385	+	0.422577i
$316$			8.00000i			0.450035i
$317$	1.73205	+	1.00000i	0.0972817	+	0.0561656i	0.547852	−	0.836576i	$-0.315446\pi$
$317$	1.73205	+	1.00000i	0.0972817	+	0.0561656i	−0.450570	+	0.892741i	$0.648779\pi$
$318$		0			0
$319$	15.0000	+	25.9808i	0.839839	+	1.45464i
$320$	4.00000	−	6.92820i	0.223607	−	0.387298i
$321$		0			0
$322$	10.0981	−	4.90192i	0.562744	−	0.273174i
$323$			6.00000i			0.333849i
$324$	15.5885	+	9.00000i	0.866025	+	0.500000i
$325$	0.866025	−	0.500000i	0.0480384	−	0.0277350i
$326$	0.732051	−	2.73205i	0.0405445	−	0.151314i
$327$		0			0
$328$	−18.0000	−	18.0000i	−0.993884	−	0.993884i
$329$	−2.50000	−	12.9904i	−0.137829	−	0.716183i
$330$		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	$0.728286\pi$
$332$	−16.0000	−	27.7128i	−0.878114	−	1.52094i
$333$	−12.9904	+	7.50000i	−0.711868	+	0.410997i
$334$	7.68653	+	28.6865i	0.420588	+	1.56966i
$335$	−2.00000			−0.109272
$336$		0			0
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	4.39230	+	16.3923i	0.238910	+	0.891624i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$		0			0
$342$	−3.00000	−	3.00000i	−0.162221	−	0.162221i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	12.0000	−	12.0000i	0.646997	−	0.646997i
$345$		0			0
$346$	4.75833	−	17.7583i	0.255809	−	0.954694i
$347$	20.7846	−	12.0000i	1.11578	−	0.644194i	0.175457	−	0.984487i	$-0.443860\pi$
$347$	20.7846	−	12.0000i	1.11578	−	0.644194i	0.940319	+	0.340293i	$0.110526\pi$
$348$		0			0
$349$		−	12.0000i		−	0.642345i	−0.947021	−	0.321173i	$-0.895923\pi$
$349$		−	12.0000i		−	0.642345i	0.947021	−	0.321173i	$-0.104077\pi$
$350$	0.267949	−	3.73205i	0.0143225	−	0.199487i
$351$		0			0
$352$	−16.3923	+	4.39230i	−0.873713	+	0.234111i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	8.66025	+	5.00000i	0.459639	+	0.265372i
$356$			4.00000i			0.212000i
$357$		0			0
$358$	25.0000	+	25.0000i	1.32129	+	1.32129i
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	−0.989479	−	0.144677i	$-0.953786\pi$
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	0.620033	+	0.784576i	$0.287119\pi$
$360$	−8.19615	−	2.19615i	−0.431975	−	0.115747i
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	−27.3205	+	7.32051i	−1.43593	+	0.384757i
$363$		0			0
$364$	−5.00000	−	1.73205i	−0.262071	−	0.0907841i
$365$		−	8.00000i		−	0.418739i
$366$		0			0
$367$	−4.50000	−	7.79423i	−0.234898	−	0.406855i	0.724345	−	0.689438i	$-0.242142\pi$
$367$	−4.50000	−	7.79423i	−0.234898	−	0.406855i	−0.959243	+	0.282582i	$0.908809\pi$
$368$	6.00000	+	10.3923i	0.312772	+	0.541736i
$369$	−13.5000	+	23.3827i	−0.702782	+	1.21725i
$370$	5.00000	−	5.00000i	0.259938	−	0.259938i
$371$	7.79423	−	22.5000i	0.404656	−	1.16814i
$372$		0			0
$373$	−19.0526	−	11.0000i	−0.986504	−	0.569558i	−0.0822766	−	0.996610i	$-0.526219\pi$
$373$	−19.0526	−	11.0000i	−0.986504	−	0.569558i	−0.904227	+	0.427051i	$0.859552\pi$
$374$	6.58846	−	24.5885i	0.340681	−	1.27144i
$375$		0			0
$376$	13.6603	−	3.66025i	0.704474	−	0.188763i
$377$	−10.0000			−0.515026
$378$		0			0
$379$			13.0000i			0.667765i	0.942615	+	0.333883i	$0.108359\pi$
$379$			13.0000i			0.667765i	−0.942615	+	0.333883i	$0.891641\pi$
$380$	1.73205	+	1.00000i	0.0888523	+	0.0512989i
$381$		0			0
$382$	−32.7846	−	8.78461i	−1.67741	−	0.449460i
$383$	9.50000	−	16.4545i	0.485427	−	0.840785i	−0.514432	−	0.857531i	$-0.671997\pi$
$383$	9.50000	−	16.4545i	0.485427	−	0.840785i	0.999860	+	0.0167461i	$0.00533070\pi$
$384$		0			0
$385$	−6.00000	+	5.19615i	−0.305788	+	0.264820i
$386$	6.00000	−	6.00000i	0.305392	−	0.305392i
$387$	−15.5885	−	9.00000i	−0.792406	−	0.457496i
$388$	−13.8564	+	8.00000i	−0.703452	+	0.406138i
$389$	−17.3205	+	10.0000i	−0.878185	+	0.507020i	−0.870059	−	0.492947i	$-0.835920\pi$
$389$	−17.3205	+	10.0000i	−0.878185	+	0.507020i	−0.00812520	+	0.999967i	$0.502586\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$	−15.8564	+	11.8564i	−0.800869	+	0.598839i
$393$		0			0
$394$	−23.2224	+	6.22243i	−1.16993	+	0.313482i
$395$	−3.46410	+	2.00000i	−0.174298	+	0.100631i
$396$	9.00000	+	15.5885i	0.452267	+	0.783349i
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	0.837267	−	0.546795i	$-0.184152\pi$
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	−0.0549046	+	0.998492i	$0.517485\pi$
$398$	−10.0000	+	10.0000i	−0.501255	+	0.501255i
$399$		0			0
$400$	4.00000			0.200000
$401$	9.50000	−	16.4545i	0.474407	−	0.821698i	−0.525163	−	0.851002i	$-0.675996\pi$
$401$	9.50000	−	16.4545i	0.474407	−	0.821698i	0.999571	+	0.0293039i	$0.00932905\pi$
$402$		0			0
$403$		0			0
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$			9.00000i			0.447214i
$406$	−20.9808	+	30.9808i	−1.04126	+	1.53755i
$407$	−15.0000			−0.743522
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	3.29423	−	12.2942i	0.162690	−	0.607169i
$411$		0			0
$412$			32.0000i			1.57653i
$413$	6.92820	−	20.0000i	0.340915	−	0.984136i
$414$	9.00000	−	9.00000i	0.442326	−	0.442326i
$415$	8.00000	−	13.8564i	0.392705	−	0.680184i
$416$	1.46410	−	5.46410i	0.0717835	−	0.267900i
$417$		0			0
$418$	−1.09808	−	4.09808i	−0.0537087	−	0.200443i
$419$			31.0000i			1.51445i	0.653155	+	0.757225i	$0.273445\pi$
$419$			31.0000i			1.51445i	−0.653155	+	0.757225i	$0.726555\pi$
$420$		0			0
$421$			22.0000i			1.07221i	0.844150	+	0.536107i	$0.180106\pi$
$421$			22.0000i			1.07221i	−0.844150	+	0.536107i	$0.819894\pi$
$422$	−15.0263	+	4.02628i	−0.731468	+	0.195996i
$423$	−7.50000	−	12.9904i	−0.364662	−	0.631614i
$424$	24.5885	+	6.58846i	1.19412	+	0.319964i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	−20.7846	+	4.00000i	−1.00584	+	0.193574i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	8.19615	+	2.19615i	0.395254	+	0.105908i
$431$	7.00000	+	12.1244i	0.337178	+	0.584010i	0.983901	−	0.178716i	$-0.0571942\pi$
$431$	7.00000	+	12.1244i	0.337178	+	0.584010i	−0.646723	+	0.762725i	$0.723861\pi$
$432$		0			0
$433$	6.00000			0.288342			0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000			0.288342			0.144171	+	0.989553i	$0.453949\pi$
$434$		0			0
$435$		0			0
$436$	−2.00000	+	3.46410i	−0.0957826	+	0.165900i
$437$	−2.59808	+	1.50000i	−0.124283	+	0.0717547i
$438$		0			0
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$	−6.00000	−	6.00000i	−0.286039	−	0.286039i
$441$	16.5000	+	12.9904i	0.785714	+	0.618590i
$442$	6.00000	+	6.00000i	0.285391	+	0.285391i
$443$	−6.92820	−	4.00000i	−0.329169	−	0.190046i	0.326303	−	0.945265i	$-0.394197\pi$
$443$	−6.92820	−	4.00000i	−0.329169	−	0.190046i	−0.655472	+	0.755219i	$0.727530\pi$
$444$		0			0
$445$	−1.73205	+	1.00000i	−0.0821071	+	0.0474045i
$446$	10.2487	+	38.2487i	0.485291	+	1.81113i
$447$		0			0
$448$	−13.8564	−	16.0000i	−0.654654	−	0.755929i
$449$	13.0000			0.613508			0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000			0.613508			0.306754	+	0.951789i	$0.400757\pi$
$450$	−1.09808	−	4.09808i	−0.0517638	−	0.193185i
$451$	−23.3827	+	13.5000i	−1.10105	+	0.635690i
$452$	6.92820	−	4.00000i	0.325875	−	0.188144i
$453$		0			0
$454$	−14.0000	−	14.0000i	−0.657053	−	0.657053i
$455$	−0.500000	−	2.59808i	−0.0234404	−	0.121800i
$456$		0			0
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$	−7.32051	+	27.3205i	−0.342065	+	1.27660i
$459$		0			0
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$		−	24.0000i		−	1.11779i	−0.829238	−	0.558896i	$-0.811225\pi$
$461$		−	24.0000i		−	1.11779i	0.829238	−	0.558896i	$-0.188775\pi$
$462$		0			0
$463$	−17.0000			−0.790057			−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000			−0.790057			−0.395029	+	0.918669i	$0.629265\pi$
$464$	−34.6410	−	20.0000i	−1.60817	−	0.928477i
$465$		0			0
$466$	−32.7846	−	8.78461i	−1.51872	−	0.406939i
$467$	17.3205	+	10.0000i	0.801498	+	0.462745i	0.843995	−	0.536352i	$-0.180198\pi$
$467$	17.3205	+	10.0000i	0.801498	+	0.462745i	−0.0424970	+	0.999097i	$0.513531\pi$
$468$	−6.00000			−0.277350
$469$	−1.73205	+	5.00000i	−0.0799787	+	0.230879i
$470$	5.00000	+	5.00000i	0.230633	+	0.230633i
$471$		0			0
$472$	21.8564	+	5.85641i	1.00602	+	0.269563i
$473$	−9.00000	−	15.5885i	−0.413820	−	0.716758i
$474$		0			0
$475$			1.00000i			0.0458831i
$476$	31.1769	−	6.00000i	1.42899	−	0.275010i
$477$		−	27.0000i		−	1.23625i
$478$	4.39230	+	16.3923i	0.200899	+	0.749767i
$479$	−19.0000	−	32.9090i	−0.868132	−	1.50365i	−0.863903	−	0.503658i	$-0.831987\pi$
$479$	−19.0000	−	32.9090i	−0.868132	−	1.50365i	−0.00422900	−	0.999991i	$-0.501346\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$	−5.00000	+	5.00000i	−0.227744	+	0.227744i
$483$		0			0
$484$		−	4.00000i		−	0.181818i
$485$	−6.92820	−	4.00000i	−0.314594	−	0.181631i
$486$		0			0
$487$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$487$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$488$	−5.85641	−	21.8564i	−0.265107	−	0.989393i
$489$		0			0
$490$	−9.09808	−	3.90192i	−0.411009	−	0.176271i
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$		0			0
$493$	51.9615	−	30.0000i	2.34023	−	1.35113i
$494$	1.36603	+	0.366025i	0.0614604	+	0.0164683i
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$		0			0
$497$	20.0000	−	17.3205i	0.897123	−	0.776931i
$498$		0			0
$499$	−3.46410	−	2.00000i	−0.155074	−	0.0895323i	0.420455	−	0.907314i	$-0.361871\pi$
$499$	−3.46410	−	2.00000i	−0.155074	−	0.0895323i	−0.575529	+	0.817781i	$0.695204\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$		0			0
$502$	34.1506	−	9.15064i	1.52422	−	0.408413i
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$	−12.5885	+	18.5885i	−0.560734	+	0.827996i
$505$	6.00000			0.266996
$506$	12.2942	−	3.29423i	0.546545	−	0.146446i
$507$		0			0
$508$	8.66025	−	5.00000i	0.384237	−	0.221839i
$509$	12.1244	+	7.00000i	0.537403	+	0.310270i	0.744026	−	0.668151i	$-0.232914\pi$
$509$	12.1244	+	7.00000i	0.537403	+	0.310270i	−0.206623	+	0.978421i	$0.566247\pi$
$510$		0			0
$511$	−20.0000	−	6.92820i	−0.884748	−	0.306486i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	5.46410	+	1.46410i	0.241011	+	0.0645788i
$515$	−13.8564	+	8.00000i	−0.610586	+	0.352522i
$516$		0			0
$517$		−	15.0000i		−	0.659699i
$518$	−8.16987	−	16.8301i	−0.358964	−	0.739473i
$519$		0			0
$520$	2.73205	−	0.732051i	0.119808	−	0.0321026i
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$	−10.9808	+	40.9808i	−0.480615	+	1.79368i
$523$	−29.4449	−	17.0000i	−1.28753	−	0.743358i	−0.309320	−	0.950958i	$-0.600101\pi$
$523$	−29.4449	−	17.0000i	−1.28753	−	0.743358i	−0.978214	+	0.207600i	$0.933435\pi$
$524$	30.0000			1.31056
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	3.29423	+	12.2942i	0.143092	+	0.534027i
$531$		−	24.0000i		−	1.04151i
$532$	4.00000	−	3.46410i	0.173422	−	0.150188i
$533$		−	9.00000i		−	0.389833i
$534$		0			0
$535$	−3.00000	−	5.19615i	−0.129701	−	0.224649i
$536$	−5.46410	−	1.46410i	−0.236013	−	0.0632396i
$537$		0			0
$538$	10.0000	+	10.0000i	0.431131	+	0.431131i
$539$	7.79423	+	19.5000i	0.335721	+	0.839924i
$540$		0			0
$541$	24.2487	+	14.0000i	1.04253	+	0.601907i	0.920550	−	0.390625i	$-0.127741\pi$
$541$	24.2487	+	14.0000i	1.04253	+	0.601907i	0.121984	+	0.992532i	$0.461074\pi$
$542$	24.5885	+	6.58846i	1.05616	+	0.282998i
$543$		0			0
$544$	8.78461	+	32.7846i	0.376637	+	1.40563i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$			8.00000i			0.342055i	0.985266	+	0.171028i	$0.0547087\pi$
$547$			8.00000i			0.342055i	−0.985266	+	0.171028i	$0.945291\pi$
$548$	31.1769	+	18.0000i	1.33181	+	0.768922i
$549$	−20.7846	+	12.0000i	−0.887066	+	0.512148i
$550$	1.09808	−	4.09808i	0.0468221	−	0.174743i
$551$	5.00000	−	8.66025i	0.213007	−	0.368939i
$552$		0			0
$553$	2.00000	+	10.3923i	0.0850487	+	0.441926i
$554$	−22.0000	−	22.0000i	−0.934690	−	0.934690i
$555$		0			0
$556$	20.0000	+	34.6410i	0.848189	+	1.46911i
$557$	6.06218	−	3.50000i	0.256863	−	0.148300i	−0.366040	−	0.930599i	$-0.619287\pi$
$557$	6.06218	−	3.50000i	0.256863	−	0.148300i	0.622903	+	0.782299i	$0.285953\pi$
$558$		0			0
$559$	6.00000			0.253773
$560$	3.46410	−	10.0000i	0.146385	−	0.422577i
$561$		0			0
$562$	5.49038	+	20.4904i	0.231598	+	0.864335i
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.615673	−	0.788002i	$-0.288884\pi$
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.990266	−	0.139188i	$-0.0444492\pi$
$564$		0			0
$565$	3.46410	+	2.00000i	0.145736	+	0.0841406i
$566$	26.0000	+	26.0000i	1.09286	+	1.09286i
$567$	22.5000	+	7.79423i	0.944911	+	0.327327i
$568$	20.0000	+	20.0000i	0.839181	+	0.839181i
$569$	16.5000	−	28.5788i	0.691716	−	1.19809i	−0.279559	−	0.960128i	$-0.590188\pi$
$569$	16.5000	−	28.5788i	0.691716	−	1.19809i	0.971275	−	0.237959i	$-0.0764783\pi$
$570$		0			0
$571$	13.8564	−	8.00000i	0.579873	−	0.334790i	−0.181210	−	0.983444i	$-0.558001\pi$
$571$	13.8564	−	8.00000i	0.579873	−	0.334790i	0.761083	+	0.648655i	$0.224668\pi$
$572$	−5.19615	−	3.00000i	−0.217262	−	0.125436i
$573$		0			0
$574$	−27.8827	−	18.8827i	−1.16380	−	0.788148i
$575$	−3.00000			−0.125109
$576$	−20.7846	−	12.0000i	−0.866025	−	0.500000i
$577$	−9.00000	−	15.5885i	−0.374675	−	0.648956i	0.615603	−	0.788056i	$-0.288912\pi$
$577$	−9.00000	−	15.5885i	−0.374675	−	0.648956i	−0.990278	+	0.139100i	$0.955579\pi$
$578$	−25.9545	−	6.95448i	−1.07956	−	0.289268i
$579$		0			0
$580$		−	20.0000i		−	0.830455i
$581$	−27.7128	−	32.0000i	−1.14972	−	1.32758i
$582$		0			0
$583$	13.5000	−	23.3827i	0.559113	−	0.968412i
$584$	5.85641	−	21.8564i	0.242340	−	0.904425i
$585$	−1.50000	−	2.59808i	−0.0620174	−	0.107417i
$586$	−17.7583	+	4.75833i	−0.733590	+	0.196565i
$587$			30.0000i			1.23823i	0.785299	+	0.619116i	$0.212509\pi$
$587$			30.0000i			1.23823i	−0.785299	+	0.619116i	$0.787491\pi$
$588$		0			0
$589$		0			0
$590$	2.92820	+	10.9282i	0.120552	+	0.449907i
$591$		0			0
$592$	17.3205	−	10.0000i	0.711868	−	0.410997i
$593$	10.0000	−	17.3205i	0.410651	−	0.711268i	−0.584310	−	0.811530i	$-0.698635\pi$
$593$	10.0000	−	17.3205i	0.410651	−	0.711268i	0.994961	+	0.100262i	$0.0319682\pi$
$594$		0			0
$595$	10.3923	+	12.0000i	0.426043	+	0.491952i
$596$	12.0000			0.491539
$597$		0			0
$598$	−1.09808	+	4.09808i	−0.0449037	+	0.167583i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$	12.5885	−	18.5885i	0.513067	−	0.757609i
$603$			6.00000i			0.244339i
$604$	−13.8564	−	8.00000i	−0.563809	−	0.325515i
$605$	1.73205	−	1.00000i	0.0704179	−	0.0406558i
$606$		0			0
$607$	2.50000	−	4.33013i	0.101472	−	0.175754i	−0.810819	−	0.585296i	$-0.800978\pi$
$607$	2.50000	−	4.33013i	0.101472	−	0.175754i	0.912291	+	0.409542i	$0.134311\pi$
$608$	4.00000	+	4.00000i	0.162221	+	0.162221i
$609$		0			0
$610$	8.00000	−	8.00000i	0.323911	−	0.323911i
$611$	4.33013	+	2.50000i	0.175178	+	0.101139i
$612$	31.1769	−	18.0000i	1.26025	−	0.727607i
$613$	−7.79423	+	4.50000i	−0.314806	+	0.181753i	−0.649075	−	0.760724i	$-0.724844\pi$
$613$	−7.79423	+	4.50000i	−0.314806	+	0.181753i	0.334269	+	0.942478i	$0.391511\pi$
$614$	16.3923	−	4.39230i	0.661540	−	0.177259i
$615$		0			0
$616$	−20.1962	+	9.80385i	−0.813726	+	0.395008i
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$		0			0
$619$	−23.3827	+	13.5000i	−0.939829	+	0.542611i	−0.889907	−	0.456142i	$-0.849231\pi$
$619$	−23.3827	+	13.5000i	−0.939829	+	0.542611i	−0.0499226	+	0.998753i	$0.515897\pi$
$620$		0			0
$621$		0			0
$622$	−10.0000	+	10.0000i	−0.400963	+	0.400963i
$623$	1.00000	+	5.19615i	0.0400642	+	0.208179i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−10.9282	−	2.92820i	−0.436779	−	0.117035i
$627$		0			0
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$			30.0000i			1.19618i
$630$	−11.1962	−	0.803848i	−0.446065	−	0.0320261i
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$	−10.9282	+	2.92820i	−0.434701	+	0.116478i
$633$		0			0
$634$	−0.732051	+	2.73205i	−0.0290735	+	0.108504i
$635$	4.33013	+	2.50000i	0.171836	+	0.0992095i
$636$		0			0
$637$	−6.92820	−	1.00000i	−0.274505	−	0.0396214i
$638$	−30.0000	+	30.0000i	−1.18771	+	1.18771i
$639$	15.0000	−	25.9808i	0.593391	−	1.02778i
$640$	10.9282	+	2.92820i	0.431975	+	0.115747i
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$		0			0
$643$			8.00000i			0.315489i	0.987480	+	0.157745i	$0.0504223\pi$
$643$			8.00000i			0.315489i	−0.987480	+	0.157745i	$0.949578\pi$
$644$	10.3923	+	12.0000i	0.409514	+	0.472866i
$645$		0			0
$646$	−8.19615	+	2.19615i	−0.322473	+	0.0864065i
$647$	−5.50000	−	9.52628i	−0.216227	−	0.374517i	0.737424	−	0.675430i	$-0.236042\pi$
$647$	−5.50000	−	9.52628i	−0.216227	−	0.374517i	−0.953652	+	0.300913i	$0.902709\pi$
$648$	−6.58846	+	24.5885i	−0.258819	+	0.965926i
$649$	12.0000	−	20.7846i	0.471041	−	0.815867i
$650$	1.00000	+	1.00000i	0.0392232	+	0.0392232i
$651$		0			0
$652$	4.00000			0.156652
$653$	−33.7750	−	19.5000i	−1.32172	−	0.763094i	−0.337715	−	0.941248i	$-0.609654\pi$
$653$	−33.7750	−	19.5000i	−1.32172	−	0.763094i	−0.984003	+	0.178154i	$0.942987\pi$
$654$		0			0
$655$	7.50000	+	12.9904i	0.293049	+	0.507576i
$656$	18.0000	−	31.1769i	0.702782	−	1.21725i
$657$	−24.0000			−0.936329
$658$	16.8301	−	8.16987i	0.656107	−	0.318495i
$659$		−	4.00000i		−	0.155818i	−0.996960	−	0.0779089i	$-0.975176\pi$
$659$		−	4.00000i		−	0.155818i	0.996960	−	0.0779089i	$-0.0248243\pi$
$660$		0			0
$661$	3.46410	−	2.00000i	0.134738	−	0.0777910i	−0.431116	−	0.902297i	$-0.641880\pi$
$661$	3.46410	−	2.00000i	0.134738	−	0.0777910i	0.565854	+	0.824506i	$0.308547\pi$
$662$	2.56218	−	9.56218i	0.0995819	−	0.371645i
$663$		0			0
$664$	32.0000	−	32.0000i	1.24184	−	1.24184i
$665$	2.50000	+	0.866025i	0.0969458	+	0.0335830i
$666$	−15.0000	−	15.0000i	−0.581238	−	0.581238i
$667$	25.9808	+	15.0000i	1.00598	+	0.580802i
$668$	−36.3731	+	21.0000i	−1.40732	+	0.812514i
$669$		0			0
$670$	−0.732051	−	2.73205i	−0.0282816	−	0.105548i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	8.00000			0.308377			0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000			0.308377			0.154189	+	0.988041i	$0.450724\pi$
$674$	2.19615	+	8.19615i	0.0845926	+	0.315704i
$675$		0			0
$676$	−20.7846	+	12.0000i	−0.799408	+	0.461538i
$677$	23.3827	+	13.5000i	0.898670	+	0.518847i	0.876768	−	0.480913i	$-0.159695\pi$
$677$	23.3827	+	13.5000i	0.898670	+	0.518847i	0.0219013	+	0.999760i	$0.493028\pi$
$678$		0			0
$679$	−16.0000	+	13.8564i	−0.614024	+	0.531760i
$680$	−12.0000	+	12.0000i	−0.460179	+	0.460179i
$681$		0			0
$682$		0			0
$683$	−1.73205	+	1.00000i	−0.0662751	+	0.0382639i	−0.532771	−	0.846259i	$-0.678849\pi$
$683$	−1.73205	+	1.00000i	−0.0662751	+	0.0382639i	0.466496	+	0.884523i	$0.345516\pi$
$684$	3.00000	−	5.19615i	0.114708	−	0.198680i
$685$			18.0000i			0.687745i
$686$	−17.6340	+	19.3660i	−0.673268	+	0.739398i
$687$		0			0
$688$	20.7846	+	12.0000i	0.792406	+	0.457496i
$689$	4.50000	+	7.79423i	0.171436	+	0.296936i
$690$		0			0
$691$	38.1051	+	22.0000i	1.44959	+	0.836919i	0.998457	−	0.0555386i	$-0.0176876\pi$
$691$	38.1051	+	22.0000i	1.44959	+	0.836919i	0.451130	+	0.892458i	$0.351021\pi$
$692$	26.0000			0.988372
$693$	15.5885	+	18.0000i	0.592157	+	0.683763i
$694$	24.0000	+	24.0000i	0.911028	+	0.911028i
$695$	−10.0000	+	17.3205i	−0.379322	+	0.657004i
$696$		0			0
$697$	27.0000	+	46.7654i	1.02270	+	1.77136i
$698$	16.3923	−	4.39230i	0.620458	−	0.166251i
$699$		0			0
$700$	5.19615	−	1.00000i	0.196396	−	0.0377964i
$701$		−	26.0000i		−	0.982006i	−0.871158	−	0.491003i	$-0.836630\pi$
$701$		−	26.0000i		−	0.982006i	0.871158	−	0.491003i	$-0.163370\pi$
$702$		0			0
$703$	2.50000	+	4.33013i	0.0942893	+	0.163314i
$704$	−12.0000	−	20.7846i	−0.452267	−	0.783349i
$705$		0			0
$706$	−18.0000	+	18.0000i	−0.677439	+	0.677439i
$707$	5.19615	−	15.0000i	0.195421	−	0.564133i
$708$		0			0
$709$	12.1244	+	7.00000i	0.455340	+	0.262891i	0.710083	−	0.704118i	$-0.248658\pi$
$709$	12.1244	+	7.00000i	0.455340	+	0.262891i	−0.254743	+	0.967009i	$0.581991\pi$
$710$	−3.66025	+	13.6603i	−0.137367	+	0.512660i
$711$	6.00000	+	10.3923i	0.225018	+	0.389742i
$712$	−5.46410	+	1.46410i	−0.204776	+	0.0548695i
$713$		0			0
$714$		0			0
$715$		−	3.00000i		−	0.112194i
$716$	−25.0000	+	43.3013i	−0.934294	+	1.61824i
$717$		0			0
$718$	−19.1244	−	5.12436i	−0.713715	−	0.191239i
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	0.146920	+	0.989148i	$0.453064\pi$
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	−0.930087	+	0.367338i	$0.880269\pi$
$720$		−	12.0000i		−	0.447214i
$721$	8.00000	+	41.5692i	0.297936	+	1.54812i
$722$	18.0000	−	18.0000i	0.669891	−	0.669891i
$723$		0			0
$724$	−20.0000	−	34.6410i	−0.743294	−	1.28742i
$725$	8.66025	−	5.00000i	0.321634	−	0.185695i
$726$		0			0
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$	0.535898	−	7.46410i	0.0198617	−	0.276638i
$729$	27.0000			1.00000
$730$	10.9282	−	2.92820i	0.404471	−	0.108378i
$731$	−31.1769	+	18.0000i	−1.15312	+	0.665754i
$732$		0			0
$733$	−21.6506	−	12.5000i	−0.799684	−	0.461698i	0.0436764	−	0.999046i	$-0.486093\pi$
$733$	−21.6506	−	12.5000i	−0.799684	−	0.461698i	−0.843361	+	0.537348i	$0.819426\pi$
$734$	9.00000	−	9.00000i	0.332196	−	0.332196i
$735$		0			0
$736$	−12.0000	+	12.0000i	−0.442326	+	0.442326i
$737$	−3.00000	+	5.19615i	−0.110506	+	0.191403i
$738$	−36.8827	−	9.88269i	−1.35767	−	0.363787i
$739$	−32.0429	+	18.5000i	−1.17872	+	0.680534i	−0.955718	−	0.294285i	$-0.904919\pi$
$739$	−32.0429	+	18.5000i	−1.17872	+	0.680534i	−0.223001	+	0.974818i	$0.571585\pi$
$740$	8.66025	+	5.00000i	0.318357	+	0.183804i
$741$		0			0
$742$	33.5885	+	2.41154i	1.23307	+	0.0885305i
$743$	−3.00000			−0.110059			−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000			−0.110059			−0.0550297	+	0.998485i	$0.517525\pi$
$744$		0			0
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	8.05256	−	30.0526i	0.294825	−	1.10030i
$747$	−41.5692	−	24.0000i	−1.52094	−	0.878114i
$748$	36.0000			1.31629
$749$	−15.5885	+	3.00000i	−0.569590	+	0.109618i
$750$		0			0
$751$	7.00000	−	12.1244i	0.255434	−	0.442424i	−0.709580	−	0.704625i	$-0.751115\pi$
$751$	7.00000	−	12.1244i	0.255434	−	0.442424i	0.965013	+	0.262201i	$0.0844484\pi$
$752$	10.0000	+	17.3205i	0.364662	+	0.631614i
$753$		0			0
$754$	−3.66025	−	13.6603i	−0.133299	−	0.497477i
$755$		−	8.00000i		−	0.291150i
$756$		0			0
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	−17.7583	+	4.75833i	−0.645012	+	0.172830i
$759$		0			0
$760$	−0.732051	+	2.73205i	−0.0265543	+	0.0991019i
$761$	−19.5000	+	33.7750i	−0.706874	+	1.22434i	0.259136	+	0.965841i	$0.416562\pi$
$761$	−19.5000	+	33.7750i	−0.706874	+	1.22434i	−0.966011	+	0.258502i	$0.916771\pi$
$762$		0			0
$763$	−1.73205	+	5.00000i	−0.0627044	+	0.181012i
$764$		−	48.0000i		−	1.73658i
$765$	15.5885	+	9.00000i	0.563602	+	0.325396i
$766$	25.9545	+	6.95448i	0.937774	+	0.251276i
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	−41.0000			−1.47850			−0.739249	−	0.673432i	$-0.764819\pi$
$769$	−41.0000			−1.47850			−0.739249	+	0.673432i	$0.764819\pi$
$770$	−9.29423	−	6.29423i	−0.334941	−	0.226828i
$771$		0			0
$772$	10.3923	+	6.00000i	0.374027	+	0.215945i
$773$	23.3827	−	13.5000i	0.841017	−	0.485561i	−0.0165929	−	0.999862i	$-0.505282\pi$
$773$	23.3827	−	13.5000i	0.841017	−	0.485561i	0.857610	+	0.514301i	$0.171949\pi$
$774$	6.58846	−	24.5885i	0.236817	−	0.883814i
$775$		0			0
$776$	−16.0000	−	16.0000i	−0.574367	−	0.574367i
$777$		0			0
$778$	−20.0000	−	20.0000i	−0.717035	−	0.717035i
$779$	7.79423	+	4.50000i	0.279257	+	0.161229i
$780$		0			0
$781$	25.9808	−	15.0000i	0.929665	−	0.536742i
$782$	−6.58846	−	24.5885i	−0.235603	−	0.879281i
$783$		0			0
$784$	−22.0000	−	17.3205i	−0.785714	−	0.618590i
$785$	1.00000			0.0356915
$786$		0			0
$787$	19.0526	−	11.0000i	0.679150	−	0.392108i	−0.120384	−	0.992727i	$-0.538413\pi$
$787$	19.0526	−	11.0000i	0.679150	−	0.392108i	0.799535	+	0.600620i	$0.205079\pi$
$788$	−17.0000	−	29.4449i	−0.605600	−	1.04893i
$789$		0			0
$790$	−4.00000	−	4.00000i	−0.142314	−	0.142314i
$791$	8.00000	−	6.92820i	0.284447	−	0.246339i
$792$	−18.0000	+	18.0000i	−0.639602	+	0.639602i
$793$	4.00000	−	6.92820i	0.142044	−	0.246028i
$794$	−6.58846	+	24.5885i	−0.233816	+	0.872612i
$795$		0			0
$796$	−17.3205	−	10.0000i	−0.613909	−	0.354441i
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$		0			0
$799$	−30.0000			−1.06132
$800$	1.46410	+	5.46410i	0.0517638	+	0.193185i
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	25.9545	+	6.95448i	0.916485	+	0.245571i
$803$	−20.7846	−	12.0000i	−0.733473	−	0.423471i
$804$		0			0
$805$	−2.59808	+	7.50000i	−0.0915702	+	0.264340i
$806$		0			0
$807$		0			0
$808$	16.3923	+	4.39230i	0.576679	+	0.154521i
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	0.891189	−	0.453632i	$-0.149872\pi$
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	−0.838452	+	0.544976i	$0.816539\pi$
$810$	−12.2942	+	3.29423i	−0.431975	+	0.115747i
$811$		−	35.0000i		−	1.22902i	−0.788911	−	0.614508i	$-0.789355\pi$
$811$		−	35.0000i		−	1.22902i	0.788911	−	0.614508i	$-0.210645\pi$
$812$	−50.0000	−	17.3205i	−1.75466	−	0.607831i
$813$		0			0
$814$	−5.49038	−	20.4904i	−0.192438	−	0.718187i
$815$	1.00000	+	1.73205i	0.0350285	+	0.0606711i
$816$		0			0
$817$	−3.00000	+	5.19615i	−0.104957	+	0.181790i
$818$	14.0000	−	14.0000i	0.489499	−	0.489499i
$819$	−7.79423	+	1.50000i	−0.272352	+	0.0524142i
$820$	18.0000			0.628587
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	0.997686	+	0.0679910i	$0.0216589\pi$
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	−0.439961	+	0.898017i	$0.645008\pi$
$824$	−43.7128	+	11.7128i	−1.52281	+	0.408035i
$825$		0			0
$826$	29.8564	+	2.14359i	1.03884	+	0.0745852i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	15.5885	+	9.00000i	0.541736	+	0.312772i
$829$	−32.9090	+	19.0000i	−1.14298	+	0.659897i	−0.947166	−	0.320745i	$-0.896067\pi$
$829$	−32.9090	+	19.0000i	−1.14298	+	0.659897i	−0.195810	+	0.980642i	$0.562734\pi$
$830$	21.8564	+	5.85641i	0.758647	+	0.203279i
$831$		0			0
$832$	8.00000			0.277350
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$		0			0
$835$	−18.1865	−	10.5000i	−0.629371	−	0.363367i
$836$	5.19615	−	3.00000i	0.179713	−	0.103757i
$837$		0			0
$838$	−42.3468	+	11.3468i	−1.46285	+	0.391968i
$839$	36.0000			1.24286			0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000			1.24286			0.621429	+	0.783470i	$0.286552\pi$
$840$		0			0
$841$	−71.0000			−2.44828
$842$	−30.0526	+	8.05256i	−1.03568	+	0.277510i
$843$		0			0
$844$	−11.0000	−	19.0526i	−0.378636	−	0.655816i
$845$	−10.3923	−	6.00000i	−0.357506	−	0.206406i
$846$	15.0000	−	15.0000i	0.515711	−	0.515711i
$847$	−1.00000	−	5.19615i	−0.0343604	−	0.178542i
$848$			36.0000i			1.23625i
$849$		0			0
$850$	−8.19615	−	2.19615i	−0.281126	−	0.0753274i
$851$	−12.9904	+	7.50000i	−0.445305	+	0.257097i
$852$		0			0
$853$			19.0000i			0.650548i	0.945620	+	0.325274i	$0.105456\pi$
$853$			19.0000i			0.650548i	−0.945620	+	0.325274i	$0.894544\pi$
$854$	−13.0718	−	26.9282i	−0.447308	−	0.921464i
$855$	3.00000			0.102598
$856$	−4.39230	−	16.3923i	−0.150126	−	0.560277i
$857$	14.0000	+	24.2487i	0.478231	+	0.828320i	0.999689	−	0.0249570i	$-0.00794488\pi$
$857$	14.0000	+	24.2487i	0.478231	+	0.828320i	−0.521458	+	0.853277i	$0.674612\pi$
$858$		0			0
$859$	−10.3923	−	6.00000i	−0.354581	−	0.204717i	0.312120	−	0.950043i	$-0.398961\pi$
$859$	−10.3923	−	6.00000i	−0.354581	−	0.204717i	−0.666701	+	0.745325i	$0.732294\pi$
$860$			12.0000i			0.409197i
$861$		0			0
$862$	−14.0000	+	14.0000i	−0.476842	+	0.476842i
$863$	−10.5000	+	18.1865i	−0.357424	+	0.619077i	−0.987530	−	0.157433i	$-0.949678\pi$
$863$	−10.5000	+	18.1865i	−0.357424	+	0.619077i	0.630106	+	0.776509i	$0.283012\pi$
$864$		0			0
$865$	6.50000	+	11.2583i	0.221007	+	0.382795i
$866$	2.19615	+	8.19615i	0.0746283	+	0.278517i
$867$		0			0
$868$		0			0
$869$			12.0000i			0.407072i
$870$		0			0
$871$	−1.00000	−	1.73205i	−0.0338837	−	0.0586883i
$872$	−5.46410	−	1.46410i	−0.185038	−	0.0495807i
$873$	−12.0000	+	20.7846i	−0.406138	+	0.703452i
$874$	−3.00000	−	3.00000i	−0.101477	−	0.101477i
$875$	1.73205	+	2.00000i	0.0585540	+	0.0676123i
$876$		0			0
$877$	−6.06218	−	3.50000i	−0.204705	−	0.118187i	0.394143	−	0.919049i	$-0.371041\pi$
$877$	−6.06218	−	3.50000i	−0.204705	−	0.118187i	−0.598848	+	0.800862i	$0.704375\pi$
$878$	5.46410	+	1.46410i	0.184404	+	0.0494110i
$879$		0			0
$880$	6.00000	−	10.3923i	0.202260	−	0.350325i
$881$	37.0000			1.24656			0.623281	−	0.781998i	$-0.285799\pi$
$881$	37.0000			1.24656			0.623281	+	0.781998i	$0.285799\pi$
$882$	−11.7058	+	27.2942i	−0.394154	+	0.919044i
$883$		−	44.0000i		−	1.48072i	−0.672212	−	0.740359i	$-0.734656\pi$
$883$		−	44.0000i		−	1.48072i	0.672212	−	0.740359i	$-0.265344\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	2.92820	−	10.9282i	0.0983749	−	0.367140i
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$		0			0
$889$	10.0000	−	8.66025i	0.335389	−	0.290456i
$890$	−2.00000	−	2.00000i	−0.0670402	−	0.0670402i
$891$	23.3827	+	13.5000i	0.783349	+	0.452267i
$892$	−48.4974	+	28.0000i	−1.62381	+	0.937509i
$893$	−4.33013	+	2.50000i	−0.144902	+	0.0836593i
$894$		0			0
$895$	−25.0000			−0.835658
$896$	16.7846	−	24.7846i	0.560734	−	0.827996i
$897$		0			0
$898$	4.75833	+	17.7583i	0.158788	+	0.592603i
$899$		0			0
$900$	5.19615	−	3.00000i	0.173205	−	0.100000i
$901$	−46.7654	−	27.0000i	−1.55798	−	0.899500i
$902$	−27.0000	−	27.0000i	−0.899002	−	0.899002i
$903$		0			0
$904$	8.00000	+	8.00000i	0.266076	+	0.266076i
$905$	10.0000	−	17.3205i	0.332411	−	0.575753i
$906$		0			0
$907$	48.4974	−	28.0000i	1.61033	−	0.929725i	0.621038	−	0.783781i	$-0.286711\pi$
$907$	48.4974	−	28.0000i	1.61033	−	0.929725i	0.989293	−	0.145944i	$-0.0466219\pi$
$908$	14.0000	−	24.2487i	0.464606	−	0.804722i
$909$		−	18.0000i		−	0.597022i
$910$	3.36603	−	1.63397i	0.111583	−	0.0541657i
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	−24.0000	−	41.5692i	−0.794284	−	1.37574i
$914$	−10.9282	−	2.92820i	−0.361473	−	0.0968564i
$915$		0			0
$916$	−40.0000			−1.32164
$917$	38.9711	−	7.50000i	1.28694	−	0.247672i
$918$		0			0
$919$	9.00000	−	15.5885i	0.296883	−	0.514216i	−0.678538	−	0.734565i	$-0.737386\pi$
$919$	9.00000	−	15.5885i	0.296883	−	0.514216i	0.975421	+	0.220349i	$0.0707197\pi$
$920$	−8.19615	−	2.19615i	−0.270219	−	0.0724050i
$921$		0			0
$922$	32.7846	−	8.78461i	1.07970	−	0.289306i
$923$			10.0000i			0.329154i
$924$		0			0
$925$			5.00000i			0.164399i
$926$	−6.22243	−	23.2224i	−0.204482	−	0.763136i
$927$	24.0000	+	41.5692i	0.788263	+	1.36531i
$928$	14.6410	−	54.6410i	0.480615	−	1.79368i
$929$	−20.5000	+	35.5070i	−0.672583	+	1.16495i	0.304586	+	0.952485i	$0.401482\pi$
$929$	−20.5000	+	35.5070i	−0.672583	+	1.16495i	−0.977169	+	0.212463i	$0.931851\pi$
$930$		0			0
$931$	4.33013	−	5.50000i	0.141914	−	0.180255i
$932$		−	48.0000i		−	1.57229i
$933$		0			0
$934$	−7.32051	+	27.3205i	−0.239534	+	0.893954i
$935$	9.00000	+	15.5885i	0.294331	+	0.509797i
$936$	−2.19615	−	8.19615i	−0.0717835	−	0.267900i
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$	−7.46410	−	0.535898i	−0.243712	−	0.0174977i
$939$		0			0
$940$	−5.00000	+	8.66025i	−0.163082	+	0.282466i
$941$	−38.1051	+	22.0000i	−1.24219	+	0.717180i	−0.969540	−	0.244933i	$-0.921234\pi$
$941$	−38.1051	+	22.0000i	−1.24219	+	0.717180i	−0.272651	+	0.962113i	$0.587901\pi$
$942$		0			0
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$			32.0000i			1.04151i
$945$		0			0
$946$	18.0000	−	18.0000i	0.585230	−	0.585230i
$947$	34.6410	+	20.0000i	1.12568	+	0.649913i	0.942845	−	0.333231i	$-0.108139\pi$
$947$	34.6410	+	20.0000i	1.12568	+	0.649913i	0.182836	+	0.983143i	$0.441472\pi$
$948$		0			0
$949$	6.92820	−	4.00000i	0.224899	−	0.129845i
$950$	−1.36603	+	0.366025i	−0.0443197	+	0.0118754i
$951$		0			0
$952$	19.6077	+	40.3923i	0.635489	+	1.30912i
$953$	−50.0000			−1.61966			−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000			−1.61966			−0.809829	+	0.586665i	$0.800440\pi$
$954$	36.8827	−	9.88269i	1.19412	−	0.319964i
$955$	20.7846	−	12.0000i	0.672574	−	0.388311i
$956$	−20.7846	+	12.0000i	−0.672222	+	0.388108i
$957$		0			0
$958$	38.0000	−	38.0000i	1.22772	−	1.22772i
$959$	45.0000	+	15.5885i	1.45313	+	0.503378i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	6.83013	+	1.83013i	0.220212	+	0.0590057i
$963$	−15.5885	+	9.00000i	−0.502331	+	0.290021i
$964$	−8.66025	−	5.00000i	−0.278928	−	0.161039i
$965$			6.00000i			0.193147i
$966$		0			0
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$	5.46410	−	1.46410i	0.175623	−	0.0470580i
$969$		0			0
$970$	2.92820	−	10.9282i	0.0940189	−	0.350883i
$971$	−4.33013	−	2.50000i	−0.138960	−	0.0802288i	0.428908	−	0.903348i	$-0.358898\pi$
$971$	−4.33013	−	2.50000i	−0.138960	−	0.0802288i	−0.567868	+	0.823119i	$0.692232\pi$
$972$		0			0
$973$	34.6410	+	40.0000i	1.11054	+	1.28234i
$974$		0			0
$975$		0			0
$976$	27.7128	−	16.0000i	0.887066	−	0.512148i
$977$	4.00000	+	6.92820i	0.127971	+	0.221653i	0.922890	−	0.385063i	$-0.125820\pi$
$977$	4.00000	+	6.92820i	0.127971	+	0.221653i	−0.794919	+	0.606715i	$0.792487\pi$
$978$		0			0
$979$			6.00000i			0.191761i
$980$	2.00000	−	13.8564i	0.0638877	−	0.442627i
$981$			6.00000i			0.191565i
$982$	−27.3205	+	7.32051i	−0.871832	+	0.233607i
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	0.989122	+	0.147100i	$0.0469940\pi$
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	−0.367168	+	0.930155i	$0.619673\pi$
$984$		0			0
$985$	8.50000	−	14.7224i	0.270833	−	0.469096i
$986$	60.0000	+	60.0000i	1.91079	+	1.91079i
$987$		0			0
$988$			2.00000i			0.0636285i
$989$	−15.5885	−	9.00000i	−0.495684	−	0.286183i
$990$	−12.2942	−	3.29423i	−0.390736	−	0.104697i
$991$	15.0000	+	25.9808i	0.476491	+	0.825306i	0.999637	−	0.0269367i	$-0.00857526\pi$
$991$	15.0000	+	25.9808i	0.476491	+	0.825306i	−0.523146	+	0.852243i	$0.675242\pi$
$992$		0			0
$993$		0			0
$994$	30.9808	+	20.9808i	0.982650	+	0.665469i
$995$		−	10.0000i		−	0.317021i
$996$		0			0
$997$	−43.3013	+	25.0000i	−1.37136	+	0.791758i	−0.991100	−	0.133120i	$-0.957501\pi$
$997$	−43.3013	+	25.0000i	−1.37136	+	0.791758i	−0.380265	+	0.924878i	$0.624167\pi$
$998$	1.46410	−	5.46410i	0.0463453	−	0.172963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bl.a.261.2	yes	4
4.3	odd	2		1120.2.cb.a.401.1		4
7.4	even	3	inner	280.2.bl.a.221.1	✓	4
8.3	odd	2		1120.2.cb.a.401.2		4
8.5	even	2	inner	280.2.bl.a.261.1	yes	4
28.11	odd	6		1120.2.cb.a.81.2		4
56.11	odd	6		1120.2.cb.a.81.1		4
56.53	even	6	inner	280.2.bl.a.221.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bl.a.221.1	✓	4	7.4	even	3	inner
280.2.bl.a.221.2	yes	4	56.53	even	6	inner
280.2.bl.a.261.1	yes	4	8.5	even	2	inner
280.2.bl.a.261.2	yes	4	1.1	even	1	trivial
1120.2.cb.a.81.1		4	56.11	odd	6
1120.2.cb.a.81.2		4	28.11	odd	6
1120.2.cb.a.401.1		4	4.3	odd	2
1120.2.cb.a.401.2		4	8.3	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.366025 - 1.36603i) q^{10} +(-2.59808 + 1.50000i) q^{11} -1.00000i q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-4.09808 - 1.09808i) q^{18} +(0.866025 + 0.500000i) q^{19} +2.00000 q^{20} +(-3.00000 - 3.00000i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{25} +(1.36603 - 0.366025i) q^{26} +(1.73205 - 5.00000i) q^{28} -10.0000i q^{29} +(5.46410 + 1.46410i) q^{32} +(-6.00000 + 6.00000i) q^{34} +(2.59808 - 0.500000i) q^{35} -6.00000i q^{36} +(4.33013 + 2.50000i) q^{37} +(-0.366025 + 1.36603i) q^{38} +(0.732051 + 2.73205i) q^{40} +9.00000 q^{41} +6.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(2.59808 - 1.50000i) q^{45} +(-4.09808 - 1.09808i) q^{46} +(-2.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-1.00000 + 1.00000i) q^{50} +(1.00000 + 1.73205i) q^{52} +(-7.79423 + 4.50000i) q^{53} +3.00000 q^{55} +(7.46410 + 0.535898i) q^{56} +(13.6603 - 3.66025i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(6.92820 + 4.00000i) q^{61} +(-1.50000 - 7.79423i) q^{63} +8.00000i q^{64} +(-0.500000 + 0.866025i) q^{65} +(1.73205 - 1.00000i) q^{67} +(-10.3923 - 6.00000i) q^{68} +(1.63397 + 3.36603i) q^{70} -10.0000 q^{71} +(8.19615 - 2.19615i) q^{72} +(4.00000 + 6.92820i) q^{73} +(-1.83013 + 6.83013i) q^{74} -2.00000 q^{76} +(2.59808 - 7.50000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-3.46410 + 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.29423 + 12.2942i) q^{82} +16.0000i q^{83} -6.00000i q^{85} +(-8.19615 + 2.19615i) q^{86} +(8.19615 + 2.19615i) q^{88} +(1.00000 - 1.73205i) q^{89} +(3.00000 + 3.00000i) q^{90} +(1.73205 + 2.00000i) q^{91} -6.00000i q^{92} +(-6.83013 - 1.83013i) q^{94} +(-0.500000 - 0.866025i) q^{95} +8.00000 q^{97} +(9.83013 - 1.16987i) q^{98} -9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 8 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} - 8 q^{7} - 8 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{14} + 8 q^{16} + 12 q^{17} - 6 q^{18} + 8 q^{20} - 12 q^{22} - 6 q^{23} + 2 q^{25} + 2 q^{26} + 8 q^{32} - 24 q^{34} + 2 q^{38} - 4 q^{40} + 36 q^{41} + 12 q^{44} - 6 q^{46} - 10 q^{47} + 4 q^{49} - 4 q^{50} + 4 q^{52} + 12 q^{55} + 16 q^{56} + 20 q^{58} - 6 q^{63} - 2 q^{65} + 10 q^{70} - 40 q^{71} + 12 q^{72} + 16 q^{73} + 10 q^{74} - 8 q^{76} + 8 q^{79} - 18 q^{81} - 18 q^{82} - 12 q^{86} + 12 q^{88} + 4 q^{89} + 12 q^{90} - 10 q^{94} - 2 q^{95} + 32 q^{97} + 22 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 8 * q^7 - 8 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^14 + 8 * q^16 + 12 * q^17 - 6 * q^18 + 8 * q^20 - 12 * q^22 - 6 * q^23 + 2 * q^25 + 2 * q^26 + 8 * q^32 - 24 * q^34 + 2 * q^38 - 4 * q^40 + 36 * q^41 + 12 * q^44 - 6 * q^46 - 10 * q^47 + 4 * q^49 - 4 * q^50 + 4 * q^52 + 12 * q^55 + 16 * q^56 + 20 * q^58 - 6 * q^63 - 2 * q^65 + 10 * q^70 - 40 * q^71 + 12 * q^72 + 16 * q^73 + 10 * q^74 - 8 * q^76 + 8 * q^79 - 18 * q^81 - 18 * q^82 - 12 * q^86 + 12 * q^88 + 4 * q^89 + 12 * q^90 - 10 * q^94 - 2 * q^95 + 32 * q^97 + 22 * q^98

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