LMFDB - Embedded newform 567.2.e.f.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.4
Root			$0.920620 + 1.59456i$ of defining polynomial
Character	$\chi$	$=$	567.487
Dual form			567.2.e.f.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.920620 + 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 - 1.15593i) q^{5} +(0.640804 - 2.56698i) q^{7} +1.12285 q^{8} +O(q^{10})$	\(q+(0.920620 + 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 - 1.15593i) q^{5} +(0.640804 - 2.56698i) q^{7} +1.12285 q^{8} +(1.22880 - 2.12835i) q^{10} +(-0.756508 + 1.31031i) q^{11} +5.17599 q^{13} +(4.68314 - 1.34141i) q^{14} +(2.42388 + 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(-1.25211 - 2.16872i) q^{19} +1.85553 q^{20} -2.78583 q^{22} +(3.68039 + 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +(4.76513 + 8.25344i) q^{26} +(2.64502 + 2.55574i) q^{28} +0.0619427 q^{29} +(1.92388 - 3.33227i) q^{31} +(-3.34011 + 5.78523i) q^{32} +2.85195 q^{34} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(2.30543 - 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} -9.02376 q^{41} -10.1998 q^{43} +(-1.05167 - 1.82155i) q^{44} +(-6.77649 + 11.7372i) q^{46} +(4.75925 + 8.24327i) q^{47} +(-6.17874 - 3.28986i) q^{49} +5.92591 q^{50} +(-3.59775 + 6.23148i) q^{52} +(0.755374 - 1.30835i) q^{53} +2.01950 q^{55} +(0.719526 - 2.88233i) q^{56} +(0.0570257 + 0.0987714i) q^{58} +(4.22166 - 7.31212i) q^{59} +(-1.61958 - 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(-3.45434 - 5.98309i) q^{65} +(-3.46670 + 6.00449i) q^{67} +(1.07663 + 1.86478i) q^{68} +(-4.67599 - 4.51816i) q^{70} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(0.518508 - 0.898083i) q^{74} +3.48128 q^{76} +(2.87876 + 2.78159i) q^{77} +(2.95969 + 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(-8.30746 - 14.3889i) q^{82} -5.60222 q^{83} -2.06744 q^{85} +(-9.39010 - 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +(0.703287 + 1.21813i) q^{89} +(3.31680 - 13.2867i) q^{91} -10.2327 q^{92} +(-8.76293 + 15.1778i) q^{94} +(-1.67126 + 2.89470i) q^{95} +12.1943 q^{97} +(-0.442393 - 12.8811i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 5 * q^7 - 6 * q^8	$ 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29} - 3 q^{31} - 2 q^{32} - 6 q^{34} + 5 q^{35} + 20 q^{38} - 3 q^{40} - 10 q^{41} + 14 q^{43} - 10 q^{44} + 3 q^{46} + 27 q^{47} - 17 q^{49} - 38 q^{50} - 10 q^{52} - 21 q^{53} + 4 q^{55} + 27 q^{56} - 10 q^{58} + 30 q^{59} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} - 2 q^{67} + 27 q^{68} - 11 q^{70} - 6 q^{71} + 15 q^{73} - 36 q^{74} - 10 q^{76} + 20 q^{77} - 4 q^{79} + 20 q^{80} - 5 q^{82} - 18 q^{83} + 12 q^{85} - 8 q^{86} - 18 q^{88} + 28 q^{89} - 4 q^{91} - 54 q^{92} - 3 q^{94} - 14 q^{95} + 24 q^{97} + 59 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 5 * q^7 - 6 * q^8 - 7 * q^10 + 4 * q^11 + 16 * q^13 + 4 * q^14 + 2 * q^16 + 12 * q^17 + q^19 - 10 * q^20 + 2 * q^22 + 3 * q^23 - q^25 + 11 * q^26 - 2 * q^28 - 14 * q^29 - 3 * q^31 - 2 * q^32 - 6 * q^34 + 5 * q^35 + 20 * q^38 - 3 * q^40 - 10 * q^41 + 14 * q^43 - 10 * q^44 + 3 * q^46 + 27 * q^47 - 17 * q^49 - 38 * q^50 - 10 * q^52 - 21 * q^53 + 4 * q^55 + 27 * q^56 - 10 * q^58 + 30 * q^59 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 - 2 * q^67 + 27 * q^68 - 11 * q^70 - 6 * q^71 + 15 * q^73 - 36 * q^74 - 10 * q^76 + 20 * q^77 - 4 * q^79 + 20 * q^80 - 5 * q^82 - 18 * q^83 + 12 * q^85 - 8 * q^86 - 18 * q^88 + 28 * q^89 - 4 * q^91 - 54 * q^92 - 3 * q^94 - 14 * q^95 + 24 * q^97 + 59 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.920620	+	1.59456i	0.650977	+	1.12753i	0.982886	+	0.184214i	$0.0589739\pi$
$2$	0.920620	+	1.59456i	0.650977	+	1.12753i	−0.331909	+	0.943311i	$0.607693\pi$
$3$		0			0
$3$		0			0
$4$	−0.695084	+	1.20392i	−0.347542	+	0.601960i
$5$	−0.667377	−	1.15593i	−0.298460	−	0.516948i	0.677324	−	0.735685i	$-0.263140\pi$
$5$	−0.667377	−	1.15593i	−0.298460	−	0.516948i	−0.975784	+	0.218737i	$0.929806\pi$
$6$		0			0
$7$	0.640804	−	2.56698i	0.242201	−	0.970226i
$7$	0.640804	−	2.56698i	0.242201	−	0.970226i
$8$	1.12285			0.396987
$9$		0			0
$10$	1.22880	−	2.12835i	0.388581	−	0.673042i
$11$	−0.756508	+	1.31031i	−0.228096	+	0.395073i	−0.957244	−	0.289283i	$-0.906583\pi$
$11$	−0.756508	+	1.31031i	−0.228096	+	0.395073i	0.729148	+	0.684356i	$0.239917\pi$
$12$		0			0
$13$	5.17599			1.43556			0.717781	−	0.696269i	$-0.245158\pi$
$13$	5.17599			1.43556			0.717781	+	0.696269i	$0.245158\pi$
$14$	4.68314	−	1.34141i	1.25162	−	0.358507i
$15$		0			0
$16$	2.42388	+	4.19829i	0.605971	+	1.04957i
$17$	0.774463	−	1.34141i	0.187835	−	0.325340i	−0.756693	−	0.653770i	$-0.773186\pi$
$17$	0.774463	−	1.34141i	0.187835	−	0.325340i	0.944528	+	0.328430i	$0.106520\pi$
$18$		0			0
$19$	−1.25211	−	2.16872i	−0.287254	−	0.497538i	0.685900	−	0.727696i	$-0.259409\pi$
$19$	−1.25211	−	2.16872i	−0.287254	−	0.497538i	−0.973153	+	0.230158i	$0.926076\pi$
$20$	1.85553			0.414909
$21$		0			0
$22$	−2.78583			−0.593940
$23$	3.68039	+	6.37463i	0.767415	+	1.32920i	0.938960	+	0.344025i	$0.111791\pi$
$23$	3.68039	+	6.37463i	0.767415	+	1.32920i	−0.171545	+	0.985176i	$0.554876\pi$
$24$		0			0
$25$	1.60922	−	2.78725i	0.321843	−	0.557449i
$26$	4.76513	+	8.25344i	0.934518	+	1.61863i
$27$		0			0
$28$	2.64502	+	2.55574i	0.499862	+	0.482990i
$29$	0.0619427			0.0115025			0.00575123	−	0.999983i	$-0.498169\pi$
$29$	0.0619427			0.0115025			0.00575123	+	0.999983i	$0.498169\pi$
$30$		0			0
$31$	1.92388	−	3.33227i	0.345540	−	0.598493i	−0.639912	−	0.768448i	$-0.721029\pi$
$31$	1.92388	−	3.33227i	0.345540	−	0.598493i	0.985452	+	0.169956i	$0.0543625\pi$
$32$	−3.34011	+	5.78523i	−0.590453	+	1.02269i
$33$		0			0
$34$	2.85195			0.489105
$35$	−3.39490	+	0.972416i	−0.573844	+	0.164368i
$36$		0			0
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	0.841949	−	0.539557i	$-0.181408\pi$
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	−0.888245	+	0.459370i	$0.848075\pi$
$38$	2.30543	−	3.99313i	0.373991	−	0.647771i
$39$		0			0
$40$	−0.749363	−	1.29794i	−0.118485	−	0.205222i
$41$	−9.02376			−1.40928			−0.704638	−	0.709567i	$-0.748890\pi$
$41$	−9.02376			−1.40928			−0.704638	+	0.709567i	$0.748890\pi$
$42$		0			0
$43$	−10.1998			−1.55545			−0.777724	−	0.628606i	$-0.783626\pi$
$43$	−10.1998			−1.55545			−0.777724	+	0.628606i	$0.783626\pi$
$44$	−1.05167	−	1.82155i	−0.158546	−	0.274609i
$45$		0			0
$46$	−6.77649	+	11.7372i	−0.999139	+	1.73056i
$47$	4.75925	+	8.24327i	0.694209	+	1.20240i	0.970447	+	0.241315i	$0.0775788\pi$
$47$	4.75925	+	8.24327i	0.694209	+	1.20240i	−0.276238	+	0.961089i	$0.589088\pi$
$48$		0			0
$49$	−6.17874	−	3.28986i	−0.882677	−	0.469980i
$50$	5.92591			0.838050
$51$		0			0
$52$	−3.59775	+	6.23148i	−0.498918	+	0.864151i
$53$	0.755374	−	1.30835i	0.103759	−	0.179715i	−0.809472	−	0.587159i	$-0.800246\pi$
$53$	0.755374	−	1.30835i	0.103759	−	0.179715i	0.913230	+	0.407444i	$0.133580\pi$
$54$		0			0
$55$	2.01950			0.272310
$56$	0.719526	−	2.88233i	0.0961507	−	0.385167i
$57$		0			0
$58$	0.0570257	+	0.0987714i	0.00748784	+	0.0129693i
$59$	4.22166	−	7.31212i	0.549613	−	0.951957i	−0.448688	−	0.893688i	$-0.648109\pi$
$59$	4.22166	−	7.31212i	0.549613	−	0.951957i	0.998301	−	0.0582689i	$-0.0185581\pi$
$60$		0			0
$61$	−1.61958	−	2.80520i	−0.207367	−	0.359169i	0.743518	−	0.668716i	$-0.233156\pi$
$61$	−1.61958	−	2.80520i	−0.207367	−	0.359169i	−0.950884	+	0.309547i	$0.899823\pi$
$62$	7.08467			0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	−3.45434	−	5.98309i	−0.428458	−	0.742111i
$66$		0			0
$67$	−3.46670	+	6.00449i	−0.423524	+	0.733566i	−0.996281	−	0.0861595i	$-0.972541\pi$
$67$	−3.46670	+	6.00449i	−0.423524	+	0.733566i	0.572757	+	0.819725i	$0.305874\pi$
$68$	1.07663	+	1.86478i	0.130561	+	0.226138i
$69$		0			0
$70$	−4.67599	−	4.51816i	−0.558888	−	0.540023i
$71$	−12.3304			−1.46335			−0.731673	−	0.681656i	$-0.761260\pi$
$71$	−12.3304			−1.46335			−0.731673	+	0.681656i	$0.761260\pi$
$72$		0			0
$73$	−1.37936	+	2.38912i	−0.161442	+	0.279625i	−0.935386	−	0.353629i	$-0.884948\pi$
$73$	−1.37936	+	2.38912i	−0.161442	+	0.279625i	0.773944	+	0.633254i	$0.218281\pi$
$74$	0.518508	−	0.898083i	0.0602754	−	0.104400i
$75$		0			0
$76$	3.48128			0.399331
$77$	2.87876	+	2.78159i	0.328065	+	0.316992i
$78$		0			0
$79$	2.95969	+	5.12633i	0.332991	+	0.576758i	0.983097	−	0.183086i	$-0.0586087\pi$
$79$	2.95969	+	5.12633i	0.332991	+	0.576758i	−0.650106	+	0.759844i	$0.725275\pi$
$80$	3.23529	−	5.60368i	0.361716	−	0.626511i
$81$		0			0
$82$	−8.30746	−	14.3889i	−0.917406	−	1.58899i
$83$	−5.60222			−0.614924			−0.307462	−	0.951560i	$-0.599480\pi$
$83$	−5.60222			−0.614924			−0.307462	+	0.951560i	$0.599480\pi$
$84$		0			0
$85$	−2.06744			−0.224245
$86$	−9.39010	−	16.2641i	−1.01256	−	1.75381i
$87$		0			0
$88$	−0.849444	+	1.47128i	−0.0905511	+	0.156839i
$89$	0.703287	+	1.21813i	0.0745483	+	0.129121i	0.900890	−	0.434048i	$-0.142915\pi$
$89$	0.703287	+	1.21813i	0.0745483	+	0.129121i	−0.826341	+	0.563169i	$0.809582\pi$
$90$		0			0
$91$	3.31680	−	13.2867i	0.347695	−	1.39282i
$92$	−10.2327			−1.06684
$93$		0			0
$94$	−8.76293	+	15.1778i	−0.903827	+	1.56548i
$95$	−1.67126	+	2.89470i	−0.171467	+	0.296990i
$96$		0			0
$97$	12.1943			1.23814			0.619070	−	0.785336i	$-0.287510\pi$
$97$	12.1943			1.23814			0.619070	+	0.785336i	$0.287510\pi$
$98$	−0.442393	−	12.8811i	−0.0446885	−	1.30119i
$99$		0			0
$100$	2.23708	+	3.87474i	0.223708	+	0.387474i
$101$	−0.559336	+	0.968798i	−0.0556560	+	0.0963990i	−0.892511	−	0.451025i	$-0.851058\pi$
$101$	−0.559336	+	0.968798i	−0.0556560	+	0.0963990i	0.836855	+	0.547425i	$0.184392\pi$
$102$		0			0
$103$	−0.965224	−	1.67182i	−0.0951063	−	0.164729i	0.814547	−	0.580098i	$-0.196986\pi$
$103$	−0.965224	−	1.67182i	−0.0951063	−	0.164729i	−0.909653	+	0.415369i	$0.863652\pi$
$104$	5.81186			0.569900
$105$		0			0
$106$	2.78165			0.270178
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	0.971225	−	0.238163i	$-0.0765454\pi$
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	−0.691868	+	0.722024i	$0.743212\pi$
$108$		0			0
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	−0.993066	−	0.117557i	$-0.962494\pi$
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	0.598340	+	0.801242i	$0.295827\pi$
$110$	1.85920	+	3.22022i	0.177267	+	0.307036i
$111$		0			0
$112$	12.3302	−	3.53177i	1.16509	−	0.333721i
$113$	−14.5021			−1.36424			−0.682121	−	0.731239i	$-0.738942\pi$
$113$	−14.5021			−1.36424			−0.682121	+	0.731239i	$0.738942\pi$
$114$		0			0
$115$	4.91242	−	8.50856i	0.458085	−	0.793427i
$116$	−0.0430553	+	0.0745740i	−0.00399759	+	0.00692403i
$117$		0			0
$118$	15.5462			1.43114
$119$	−2.94709	−	2.84761i	−0.270159	−	0.261040i
$120$		0			0
$121$	4.35539	+	7.54376i	0.395945	+	0.685796i
$122$	2.98204	−	5.16505i	0.269982	−	0.467622i
$123$		0			0
$124$	2.67452	+	4.63241i	0.240179	+	0.416002i
$125$	−10.9696			−0.981149
$126$		0			0
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	4.28260	+	7.41769i	0.378532	+	0.655637i
$129$		0			0
$130$	6.36027	−	11.0163i	0.557832	−	0.966194i
$131$	1.00673	+	1.74371i	0.0879585	+	0.152349i	0.906648	−	0.421888i	$-0.138632\pi$
$131$	1.00673	+	1.74371i	0.0879585	+	0.152349i	−0.818690	+	0.574236i	$0.805299\pi$
$132$		0			0
$133$	−6.36940	+	1.82441i	−0.552297	+	0.158197i
$134$	−12.7660			−1.10282
$135$		0			0
$136$	0.869605	−	1.50620i	0.0745680	−	0.129156i
$137$	−1.10870	+	1.92032i	−0.0947225	+	0.164064i	−0.909493	−	0.415720i	$-0.863530\pi$
$137$	−1.10870	+	1.92032i	−0.0947225	+	0.164064i	0.814770	+	0.579784i	$0.196863\pi$
$138$		0			0
$139$	−0.755339			−0.0640670			−0.0320335	−	0.999487i	$-0.510198\pi$
$139$	−0.755339			−0.0640670			−0.0320335	+	0.999487i	$0.510198\pi$
$140$	1.18903	−	4.76310i	0.100492	−	0.402556i
$141$		0			0
$142$	−11.3516	−	19.6615i	−0.952604	−	1.64996i
$143$	−3.91568	+	6.78216i	−0.327446	+	0.567153i
$144$		0			0
$145$	−0.0413391	−	0.0716014i	−0.00343303	−	0.00594618i
$146$	−5.07946			−0.420379
$147$		0			0
$148$	0.782965			0.0643593
$149$	−3.29249	−	5.70277i	−0.269732	−	0.467189i	0.699061	−	0.715062i	$-0.253602\pi$
$149$	−3.29249	−	5.70277i	−0.269732	−	0.467189i	−0.968792	+	0.247873i	$0.920268\pi$
$150$		0			0
$151$	−6.33356	+	10.9700i	−0.515417	+	0.892729i	0.484422	+	0.874834i	$0.339030\pi$
$151$	−6.33356	+	10.9700i	−0.515417	+	0.892729i	−0.999840	+	0.0178950i	$0.994304\pi$
$152$	−1.40593	−	2.43514i	−0.114036	−	0.197516i
$153$		0			0
$154$	−1.78517	+	7.15115i	−0.143853	+	0.576256i
$155$	−5.13582			−0.412519
$156$		0			0
$157$	8.65372	−	14.9887i	0.690642	−	1.19623i	−0.280986	−	0.959712i	$-0.590662\pi$
$157$	8.65372	−	14.9887i	0.690642	−	1.19623i	0.971628	−	0.236515i	$-0.0760052\pi$
$158$	−5.44950	+	9.43882i	−0.433539	+	0.750912i
$159$		0			0
$160$	8.91644			0.704906
$161$	18.7219	−	5.36260i	1.47549	−	0.422632i
$162$		0			0
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	0.999697	−	0.0246014i	$-0.00783167\pi$
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	−0.521154	+	0.853463i	$0.674498\pi$
$164$	6.27227	−	10.8639i	0.489782	−	0.848327i
$165$		0			0
$166$	−5.15752	−	8.93309i	−0.400301	−	0.693342i
$167$	−3.52495			−0.272769			−0.136385	−	0.990656i	$-0.543548\pi$
$167$	−3.52495			−0.272769			−0.136385	+	0.990656i	$0.543548\pi$
$168$		0			0
$169$	13.7909			1.06084
$170$	−1.90332	−	3.29665i	−0.145978	−	0.252842i
$171$		0			0
$172$	7.08968	−	12.2797i	0.540583	−	0.936318i
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	0.606339	−	0.795206i	$-0.292638\pi$
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	−0.991838	+	0.127502i	$0.959304\pi$
$174$		0			0
$175$	−6.12360	−	5.91690i	−0.462901	−	0.447276i
$176$	−7.33475			−0.552878
$177$		0			0
$178$	−1.29492	+	2.24287i	−0.0970584	+	0.168110i
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	−0.832486	−	0.554046i	$-0.813083\pi$
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	0.896061	+	0.443931i	$0.146416\pi$
$180$		0			0
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$	24.2399	−	6.94313i	1.79678	−	0.514659i
$183$		0			0
$184$	4.13252	+	7.15774i	0.304654	+	0.527676i
$185$	−0.375877	+	0.651039i	−0.0276351	+	0.0478653i
$186$		0			0
$187$	1.17178	+	2.02957i	0.0856887	+	0.148417i
$188$	−13.2323			−0.965066
$189$		0			0
$190$	−6.15437			−0.446485
$191$	−11.3470	−	19.6535i	−0.821038	−	1.42208i	−0.904910	−	0.425603i	$-0.860062\pi$
$191$	−11.3470	−	19.6535i	−0.821038	−	1.42208i	0.0838717	−	0.996477i	$-0.473271\pi$
$192$		0			0
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	−0.955619	−	0.294605i	$-0.904812\pi$
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	0.732945	+	0.680288i	$0.238145\pi$
$194$	11.2263	+	19.4445i	0.806001	+	1.39603i
$195$		0			0
$196$	8.25547	−	5.15198i	0.589676	−	0.367999i
$197$	9.77010			0.696091			0.348045	−	0.937478i	$-0.386846\pi$
$197$	9.77010			0.696091			0.348045	+	0.937478i	$0.386846\pi$
$198$		0			0
$199$	−4.33973	+	7.51664i	−0.307636	+	0.532840i	−0.977845	−	0.209332i	$-0.932871\pi$
$199$	−4.33973	+	7.51664i	−0.307636	+	0.532840i	0.670209	+	0.742172i	$0.266204\pi$
$200$	1.80691	−	3.12965i	0.127768	−	0.221300i
$201$		0			0
$202$	−2.05974			−0.144923
$203$	0.0396931	−	0.159005i	0.00278591	−	0.0111600i
$204$		0			0
$205$	6.02225	+	10.4308i	0.420612	+	0.728522i
$206$	1.77721	−	3.07822i	0.123824	−	0.214470i
$207$		0			0
$208$	12.5460	+	21.7303i	0.869909	+	1.50673i
$209$	3.78892			0.262085
$210$		0			0
$211$	5.68439			0.391330			0.195665	−	0.980671i	$-0.437314\pi$
$211$	5.68439			0.391330			0.195665	+	0.980671i	$0.437314\pi$
$212$	1.05010	+	1.81882i	0.0721209	+	0.124917i
$213$		0			0
$214$	−5.32062	+	9.21558i	−0.363710	+	0.629964i
$215$	6.80708	+	11.7902i	0.464239	+	0.804086i
$216$		0			0
$217$	−7.32102	−	7.07390i	−0.496983	−	0.480207i
$218$	−15.1757			−1.02783
$219$		0			0
$220$	−1.40372	+	2.43132i	−0.0946390	+	0.163920i
$221$	4.00862	−	6.94313i	0.269649	−	0.467045i
$222$		0			0
$223$	−11.7227			−0.785007			−0.392503	−	0.919751i	$-0.628391\pi$
$223$	−11.7227			−0.785007			−0.392503	+	0.919751i	$0.628391\pi$
$224$	12.7102	+	12.2812i	0.849236	+	0.820571i
$225$		0			0
$226$	−13.3509	−	23.1245i	−0.888091	−	1.53822i
$227$	−5.59154	+	9.68482i	−0.371123	+	0.642804i	−0.989739	−	0.142890i	$-0.954361\pi$
$227$	−5.59154	+	9.68482i	−0.371123	+	0.642804i	0.618615	+	0.785694i	$0.287694\pi$
$228$		0			0
$229$	4.82824	+	8.36275i	0.319059	+	0.552626i	0.980292	−	0.197554i	$-0.0632999\pi$
$229$	4.82824	+	8.36275i	0.319059	+	0.552626i	−0.661233	+	0.750181i	$0.729967\pi$
$230$	18.0899			1.19281
$231$		0			0
$232$	0.0695523			0.00456633
$233$	−9.64492	−	16.7055i	−0.631860	−	1.09441i	−0.987171	−	0.159666i	$-0.948958\pi$
$233$	−9.64492	−	16.7055i	−0.631860	−	1.09441i	0.355311	−	0.934748i	$-0.384375\pi$
$234$		0			0
$235$	6.35243	−	11.0027i	0.414387	−	0.717739i
$236$	5.86881	+	10.1651i	0.382027	+	0.661690i
$237$		0			0
$238$	1.82754	−	7.32088i	0.118462	−	0.474542i
$239$	0.389282			0.0251806			0.0125903	−	0.999921i	$-0.495992\pi$
$239$	0.389282			0.0251806			0.0125903	+	0.999921i	$0.495992\pi$
$240$		0			0
$241$	−5.31807	+	9.21117i	−0.342567	+	0.593344i	−0.984909	−	0.173075i	$-0.944630\pi$
$241$	−5.31807	+	9.21117i	−0.342567	+	0.593344i	0.642342	+	0.766419i	$0.277963\pi$
$242$	−8.01932	+	13.8899i	−0.515502	+	0.892875i
$243$		0			0
$244$	4.50299			0.288274
$245$	0.320700	+	9.33777i	0.0204888	+	0.596568i
$246$		0			0
$247$	−6.48091	−	11.2253i	−0.412370	−	0.714247i
$248$	2.16023	−	3.74163i	0.137175	−	0.237594i
$249$		0			0
$250$	−10.0988	−	17.4917i	−0.638705	−	1.10627i
$251$	−3.26628			−0.206166			−0.103083	−	0.994673i	$-0.532871\pi$
$251$	−3.26628			−0.206166			−0.103083	+	0.994673i	$0.532871\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	7.82531	+	13.5538i	0.491004	+	0.850443i
$255$		0			0
$256$	−10.4896	+	18.1686i	−0.655603	+	1.13554i
$257$	2.34787	+	4.06663i	0.146456	+	0.253669i	0.929915	−	0.367774i	$-0.119880\pi$
$257$	2.34787	+	4.06663i	0.146456	+	0.253669i	−0.783459	+	0.621443i	$0.786547\pi$
$258$		0			0
$259$	−1.43252	+	0.410323i	−0.0890127	+	0.0254962i
$260$	9.60421			0.595628
$261$		0			0
$262$	−1.85363	+	3.21059i	−0.114518	+	0.198351i
$263$	−9.77491	+	16.9306i	−0.602747	+	1.04399i	0.389656	+	0.920960i	$0.372594\pi$
$263$	−9.77491	+	16.9306i	−0.602747	+	1.04399i	−0.992403	+	0.123028i	$0.960740\pi$
$264$		0			0
$265$	−2.01648			−0.123871
$266$	−8.77294	−	8.47681i	−0.537903	−	0.519747i
$267$		0			0
$268$	−4.81929	−	8.34725i	−0.294385	−	0.509890i
$269$	7.88365	−	13.6549i	0.480675	−	0.832553i	−0.519079	−	0.854726i	$-0.673725\pi$
$269$	7.88365	−	13.6549i	0.480675	−	0.832553i	0.999754	+	0.0221730i	$0.00705846\pi$
$270$		0			0
$271$	7.39882	+	12.8151i	0.449446	+	0.778464i	0.998350	−	0.0574218i	$-0.0182880\pi$
$271$	7.39882	+	12.8151i	0.449446	+	0.778464i	−0.548904	+	0.835886i	$0.684955\pi$
$272$	7.50884			0.455290
$273$		0			0
$274$	−4.08276			−0.246649
$275$	2.43477	+	4.21715i	0.146822	+	0.254304i
$276$		0			0
$277$	3.72561	−	6.45295i	0.223850	−	0.387720i	−0.732124	−	0.681172i	$-0.761471\pi$
$277$	3.72561	−	6.45295i	0.223850	−	0.387720i	0.955974	+	0.293452i	$0.0948040\pi$
$278$	−0.695380	−	1.20443i	−0.0417061	−	0.0722371i
$279$		0			0
$280$	−3.81196	+	1.09188i	−0.227808	+	0.0652521i
$281$	25.9876			1.55029			0.775146	−	0.631782i	$-0.217676\pi$
$281$	25.9876			1.55029			0.775146	+	0.631782i	$0.217676\pi$
$282$		0			0
$283$	−9.37768	+	16.2426i	−0.557445	+	0.965524i	0.440263	+	0.897869i	$0.354885\pi$
$283$	−9.37768	+	16.2426i	−0.557445	+	0.965524i	−0.997709	+	0.0676550i	$0.978448\pi$
$284$	8.57064	−	14.8448i	0.508574	−	0.880876i
$285$		0			0
$286$	−14.4194			−0.852638
$287$	−5.78246	+	23.1638i	−0.341328	+	1.36732i
$288$		0			0
$289$	7.30041	+	12.6447i	0.429436	+	0.743805i
$290$	0.0761152	−	0.131835i	0.00446964	−	0.00774165i
$291$		0			0
$292$	−1.91754	−	3.32127i	−0.112215	−	0.194363i
$293$	2.46178			0.143819			0.0719093	−	0.997411i	$-0.477091\pi$
$293$	2.46178			0.143819			0.0719093	+	0.997411i	$0.477091\pi$
$294$		0			0
$295$	−11.2697			−0.656150
$296$	−0.316203	−	0.547680i	−0.0183790	−	0.0318333i
$297$		0			0
$298$	6.06227	−	10.5002i	0.351178	−	0.608258i
$299$	19.0497	+	32.9950i	1.10167	+	1.90815i
$300$		0			0
$301$	−6.53605	+	26.1825i	−0.376731	+	1.50914i
$302$	−23.3232			−1.34210
$303$		0			0
$304$	6.06994	−	10.5134i	0.348135	−	0.602987i
$305$	−2.16175	+	3.74425i	−0.123781	+	0.214395i
$306$		0			0
$307$	−4.66277			−0.266118			−0.133059	−	0.991108i	$-0.542480\pi$
$307$	−4.66277			−0.266118			−0.133059	+	0.991108i	$0.542480\pi$
$308$	−5.34979	+	1.53236i	−0.304833	+	0.0873145i
$309$		0			0
$310$	−4.72814	−	8.18938i	−0.268541	−	0.465126i
$311$	−13.7410	+	23.8002i	−0.779183	+	1.34958i	0.153231	+	0.988190i	$0.451032\pi$
$311$	−13.7410	+	23.8002i	−0.779183	+	1.34958i	−0.932413	+	0.361393i	$0.882301\pi$
$312$		0			0
$313$	−2.74666	−	4.75735i	−0.155250	−	0.268901i	0.777900	−	0.628388i	$-0.216285\pi$
$313$	−2.74666	−	4.75735i	−0.155250	−	0.268901i	−0.933150	+	0.359487i	$0.882952\pi$
$314$	31.8671			1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	−4.93879	−	8.55424i	−0.277390	−	0.480454i	0.693345	−	0.720606i	$-0.256136\pi$
$317$	−4.93879	−	8.55424i	−0.277390	−	0.480454i	−0.970735	+	0.240152i	$0.922803\pi$
$318$		0			0
$319$	−0.0468601	+	0.0811641i	−0.00262366	+	0.00454432i
$320$	1.73808	+	3.01044i	0.0971614	+	0.168288i
$321$		0			0
$322$	25.7868	+	24.9164i	1.43704	+	1.38853i
$323$	−3.87885			−0.215825
$324$		0			0
$325$	8.32930	−	14.4268i	0.462026	−	0.800253i
$326$	−11.2493	+	19.4844i	−0.623041	+	1.07914i
$327$		0			0
$328$	−10.1323			−0.559464
$329$	24.2100	−	6.93457i	1.33474	−	0.382315i
$330$		0			0
$331$	10.3471	+	17.9217i	0.568729	+	0.985067i	0.996692	+	0.0812710i	$0.0258979\pi$
$331$	10.3471	+	17.9217i	0.568729	+	0.985067i	−0.427963	+	0.903796i	$0.640769\pi$
$332$	3.89401	−	6.74463i	0.213712	−	0.370160i
$333$		0			0
$334$	−3.24514	−	5.62076i	−0.177566	−	0.307554i
$335$	9.25437			0.505620
$336$		0			0
$337$	−1.49749			−0.0815737			−0.0407869	−	0.999168i	$-0.512986\pi$
$337$	−1.49749			−0.0815737			−0.0407869	+	0.999168i	$0.512986\pi$
$338$	12.6962	+	21.9905i	0.690582	+	1.19612i
$339$		0			0
$340$	1.43704	−	2.48903i	0.0779344	−	0.134986i
$341$	2.91087	+	5.04177i	0.157632	+	0.273027i
$342$		0			0
$343$	−12.4044	+	13.7525i	−0.669772	+	0.742567i
$344$	−11.4528			−0.617493
$345$		0			0
$346$	9.33593	−	16.1703i	0.501903	−	0.869321i
$347$	14.7694	−	25.5813i	0.792862	−	1.37328i	−0.131326	−	0.991339i	$-0.541923\pi$
$347$	14.7694	−	25.5813i	0.792862	−	1.37328i	0.924188	−	0.381938i	$-0.124743\pi$
$348$		0			0
$349$	−36.0013			−1.92710			−0.963551	−	0.267523i	$-0.913795\pi$
$349$	−36.0013			−1.92710			−0.963551	+	0.267523i	$0.913795\pi$
$350$	3.79735	−	15.2117i	0.202977	−	0.813098i
$351$		0			0
$352$	−5.05363	−	8.75315i	−0.269360	−	0.466545i
$353$	14.7465	−	25.5417i	0.784877	−	1.35945i	−0.144196	−	0.989549i	$-0.546060\pi$
$353$	14.7465	−	25.5417i	0.784877	−	1.35945i	0.929073	−	0.369897i	$-0.120607\pi$
$354$		0			0
$355$	8.22900	+	14.2530i	0.436750	+	0.756473i
$356$	−1.95537			−0.103635
$357$		0			0
$358$	3.13224			0.165544
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	0.928544	−	0.371224i	$-0.121062\pi$
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	−0.785761	+	0.618531i	$0.787728\pi$
$360$		0			0
$361$	6.36444	−	11.0235i	0.334971	−	0.580186i
$362$	−15.6451	−	27.0981i	−0.822289	−	1.42425i
$363$		0			0
$364$	13.6906	+	13.2285i	0.717584	+	0.693362i
$365$	3.68220			0.192735
$366$		0			0
$367$	11.5422	−	19.9916i	0.602496	−	1.04355i	−0.389946	−	0.920838i	$-0.627506\pi$
$367$	11.5422	−	19.9916i	0.602496	−	1.04355i	0.992442	−	0.122715i	$-0.0391602\pi$
$368$	−17.8417	+	30.9027i	−0.930063	+	1.61092i
$369$		0			0
$370$	−1.38416			−0.0719591
$371$	−2.87445	−	2.77742i	−0.149234	−	0.144196i
$372$		0			0
$373$	−10.7515	−	18.6222i	−0.556692	−	0.964219i	−0.997770	−	0.0667498i	$-0.978737\pi$
$373$	−10.7515	−	18.6222i	−0.556692	−	0.964219i	0.441078	−	0.897469i	$-0.354596\pi$
$374$	−2.15752	+	3.73694i	−0.111563	+	0.193232i
$375$		0			0
$376$	5.34392	+	9.25595i	0.275592	+	0.477339i
$377$	0.320615			0.0165125
$378$		0			0
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	−2.32333	−	4.02412i	−0.119184	−	0.206433i
$381$		0			0
$382$	20.8925	−	36.1869i	1.06895	−	1.85148i
$383$	17.4604	+	30.2424i	0.892187	+	1.54531i	0.837248	+	0.546823i	$0.184163\pi$
$383$	17.4604	+	30.2424i	0.892187	+	1.54531i	0.0549390	+	0.998490i	$0.482504\pi$
$384$		0			0
$385$	1.29411	−	5.18402i	0.0659538	−	0.264202i
$386$	−11.3917			−0.579823
$387$		0			0
$388$	−8.47603	+	14.6809i	−0.430305	+	0.745311i
$389$	14.4411	−	25.0127i	0.732192	−	1.26819i	−0.223752	−	0.974646i	$-0.571831\pi$
$389$	14.4411	−	25.0127i	0.732192	−	1.26819i	0.955944	−	0.293548i	$-0.0948361\pi$
$390$		0			0
$391$	11.4013			0.576589
$392$	−6.93779	−	3.69401i	−0.350411	−	0.186576i
$393$		0			0
$394$	8.99455	+	15.5790i	0.453139	+	0.784860i
$395$	3.95046	−	6.84239i	0.198769	−	0.344278i
$396$		0			0
$397$	5.59226	+	9.68607i	0.280667	+	0.486130i	0.971549	−	0.236838i	$-0.0761109\pi$
$397$	5.59226	+	9.68607i	0.280667	+	0.486130i	−0.690882	+	0.722968i	$0.742778\pi$
$398$	−15.9810			−0.801055
$399$		0			0
$400$	15.6022			0.780111
$401$	0.541061	+	0.937146i	0.0270193	+	0.0467988i	0.879219	−	0.476418i	$-0.158065\pi$
$401$	0.541061	+	0.937146i	0.0270193	+	0.0467988i	−0.852200	+	0.523217i	$0.824732\pi$
$402$		0			0
$403$	9.95802	−	17.2478i	0.496044	−	0.859174i
$404$	−0.777570	−	1.34679i	−0.0386856	−	0.0670054i
$405$		0			0
$406$	0.290086	−	0.0830905i	0.0143967	−	0.00412371i
$407$	0.852155			0.0422398
$408$		0			0
$409$	10.8674	−	18.8229i	0.537360	−	0.930735i	−0.461685	−	0.887044i	$-0.652755\pi$
$409$	10.8674	−	18.8229i	0.537360	−	0.930735i	0.999045	−	0.0436908i	$-0.0139116\pi$
$410$	−11.0884	+	19.2057i	−0.547618	+	0.948501i
$411$		0			0
$412$	2.68365			0.132214
$413$	−16.0648	−	15.5225i	−0.790497	−	0.763814i
$414$		0			0
$415$	3.73879	+	6.47578i	0.183530	+	0.317884i
$416$	−17.2884	+	29.9443i	−0.847632	+	1.46814i
$417$		0			0
$418$	3.48816	+	6.04167i	0.170611	+	0.295508i
$419$	−25.1811			−1.23018			−0.615090	−	0.788457i	$-0.710880\pi$
$419$	−25.1811			−1.23018			−0.615090	+	0.788457i	$0.710880\pi$
$420$		0			0
$421$	29.6607			1.44558			0.722788	−	0.691070i	$-0.242860\pi$
$421$	29.6607			1.44558			0.722788	+	0.691070i	$0.242860\pi$
$422$	5.23316	+	9.06411i	0.254746	+	0.441234i
$423$		0			0
$424$	0.848171	−	1.46907i	0.0411908	−	0.0713446i
$425$	−2.49256	−	4.31724i	−0.120907	−	0.209417i
$426$		0			0
$427$	−8.23873	+	2.35985i	−0.398700	+	0.114201i
$428$	−8.03431			−0.388353
$429$		0			0
$430$	−12.5335	+	21.7086i	−0.604418	+	1.04688i
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	−0.801108	−	0.598520i	$-0.795756\pi$
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	0.918887	+	0.394520i	$0.129089\pi$
$432$		0			0
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$	4.53989	−	18.1862i	0.217921	−	0.872965i
$435$		0			0
$436$	−5.72896	−	9.92285i	−0.274367	−	0.475218i
$437$	9.21651	−	15.9635i	0.440885	−	0.763636i
$438$		0			0
$439$	7.41176	+	12.8375i	0.353744	+	0.612703i	0.986902	−	0.161320i	$-0.0515751\pi$
$439$	7.41176	+	12.8375i	0.353744	+	0.612703i	−0.633158	+	0.774022i	$0.718242\pi$
$440$	2.26760			0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	10.9510	+	18.9676i	0.520297	+	0.901180i	0.999722	+	0.0235972i	$0.00751192\pi$
$443$	10.9510	+	18.9676i	0.520297	+	0.901180i	−0.479425	+	0.877583i	$0.659155\pi$
$444$		0			0
$445$	0.938715	−	1.62590i	0.0444994	−	0.0770751i
$446$	−10.7921	−	18.6925i	−0.511021	−	0.885115i
$447$		0			0
$448$	−1.66887	+	6.68528i	−0.0788468	+	0.315850i
$449$	21.4952			1.01442			0.507212	−	0.861822i	$-0.330676\pi$
$449$	21.4952			1.01442			0.507212	+	0.861822i	$0.330676\pi$
$450$		0			0
$451$	6.82655	−	11.8239i	0.321450	−	0.556767i
$452$	10.0802	−	17.4594i	0.474131	−	0.821220i
$453$		0			0
$454$	−20.5907			−0.966371
$455$	−17.5720	+	5.03322i	−0.823788	+	0.235961i
$456$		0			0
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.745009	−	0.667054i	$-0.767555\pi$
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.205181	−	0.978724i	$-0.565778\pi$
$458$	−8.88995	+	15.3978i	−0.415400	+	0.719494i
$459$		0			0
$460$	6.82908	+	11.8283i	0.318408	+	0.551498i
$461$	−2.83081			−0.131844			−0.0659220	−	0.997825i	$-0.520999\pi$
$461$	−2.83081			−0.131844			−0.0659220	+	0.997825i	$0.520999\pi$
$462$		0			0
$463$	27.8648			1.29499			0.647494	−	0.762070i	$-0.275817\pi$
$463$	27.8648			1.29499			0.647494	+	0.762070i	$0.275817\pi$
$464$	0.150142	+	0.260053i	0.00697016	+	0.0120727i
$465$		0			0
$466$	17.7586	−	30.7588i	0.822653	−	1.42488i
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	−0.990126	−	0.140182i	$-0.955231\pi$
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	0.373661	−	0.927565i	$-0.378102\pi$
$468$		0			0
$469$	13.1919	+	12.7466i	0.609146	+	0.588585i
$470$	23.3927			1.07903
$471$		0			0
$472$	4.74028	−	8.21041i	0.218189	−	0.377915i
$473$	7.71620	−	13.3648i	0.354791	−	0.614516i
$474$		0			0
$475$	−8.05966			−0.369803
$476$	5.47677	−	1.56873i	0.251027	−	0.0719027i
$477$		0			0
$478$	0.358381	+	0.620734i	0.0163920	+	0.0283917i
$479$	15.7895	−	27.3483i	0.721443	−	1.24958i	−0.238979	−	0.971025i	$-0.576813\pi$
$479$	15.7895	−	27.3483i	0.721443	−	1.24958i	0.960422	−	0.278551i	$-0.0898540\pi$
$480$		0			0
$481$	−1.45760	−	2.52464i	−0.0664609	−	0.115114i
$482$	−19.5837			−0.892013
$483$		0			0
$484$	−12.1094			−0.550429
$485$	−8.13817	−	14.0957i	−0.369535	−	0.640054i
$486$		0			0
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	−0.869473	−	0.493980i	$-0.835541\pi$
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	0.862536	+	0.505996i	$0.168875\pi$
$488$	−1.81855	−	3.14982i	−0.0823218	−	0.142586i
$489$		0			0
$490$	−14.5944	+	9.10792i	−0.659308	+	0.411454i
$491$	18.1396			0.818629			0.409315	−	0.912393i	$-0.365768\pi$
$491$	18.1396			0.818629			0.409315	+	0.912393i	$0.365768\pi$
$492$		0			0
$493$	0.0479723	−	0.0830905i	0.00216057	−	0.00374221i
$494$	11.9329	−	20.6684i	0.536887	−	0.929916i
$495$		0			0
$496$	18.6531			0.837549
$497$	−7.90135	+	31.6518i	−0.354424	+	1.41978i
$498$		0			0
$499$	10.6546	+	18.4543i	0.476964	+	0.826126i	0.999652	−	0.0263983i	$-0.00840381\pi$
$499$	10.6546	+	18.4543i	0.476964	+	0.826126i	−0.522687	+	0.852524i	$0.675070\pi$
$500$	7.62478	−	13.2065i	0.340990	−	0.590613i
$501$		0			0
$502$	−3.00701	−	5.20829i	−0.134209	−	0.232457i
$503$	−17.0738			−0.761285			−0.380642	−	0.924722i	$-0.624297\pi$
$503$	−17.0738			−0.761285			−0.380642	+	0.924722i	$0.624297\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	−10.2529	−	17.7586i	−0.455799	−	0.789466i
$507$		0			0
$508$	−5.90824	+	10.2334i	−0.262136	+	0.454032i
$509$	−18.3868	−	31.8468i	−0.814979	−	1.41159i	−0.909343	−	0.416048i	$-0.863415\pi$
$509$	−18.3868	−	31.8468i	−0.814979	−	1.41159i	0.0943635	−	0.995538i	$-0.469918\pi$
$510$		0			0
$511$	5.24891	+	5.07173i	0.232198	+	0.224360i
$512$	−21.4975			−0.950065
$513$		0			0
$514$	−4.32299	+	7.48764i	−0.190679	+	0.330265i
$515$	−1.28834	+	2.23146i	−0.0567709	+	0.0983300i
$516$		0			0
$517$	−14.4017			−0.633384
$518$	−1.97310	−	1.90649i	−0.0866929	−	0.0837666i
$519$		0			0
$520$	−3.87870	−	6.71810i	−0.170092	−	0.294608i
$521$	−9.57535	+	16.5850i	−0.419504	+	0.726602i	−0.995890	−	0.0905758i	$-0.971129\pi$
$521$	−9.57535	+	16.5850i	−0.419504	+	0.726602i	0.576386	+	0.817178i	$0.304463\pi$
$522$		0			0
$523$	−20.9715	−	36.3236i	−0.917018	−	1.58832i	−0.803920	−	0.594737i	$-0.797256\pi$
$523$	−20.9715	−	36.3236i	−0.917018	−	1.58832i	−0.113097	−	0.993584i	$-0.536077\pi$
$524$	−2.79905			−0.122277
$525$		0			0
$526$	−35.9959			−1.56950
$527$	−2.97996	−	5.16144i	−0.129809	−	0.224836i
$528$		0			0
$529$	−15.5906	+	27.0037i	−0.677851	+	1.17407i
$530$	−1.85641	−	3.21539i	−0.0806372	−	0.139668i
$531$		0			0
$532$	2.23082	−	8.93637i	0.0967183	−	0.387441i
$533$	−46.7069			−2.02310
$534$		0			0
$535$	3.85702	−	6.68056i	0.166754	−	0.288826i
$536$	−3.89258	+	6.74214i	−0.168134	+	0.291216i
$537$		0			0
$538$	29.0314			1.25163
$539$	8.98500	−	5.60726i	0.387011	−	0.241522i
$540$		0			0
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	0.833344	−	0.552754i	$-0.186423\pi$
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	−0.895371	+	0.445320i	$0.853090\pi$
$542$	−13.6230	+	23.5957i	−0.585158	+	1.01352i
$543$		0			0
$544$	5.17358	+	8.96090i	0.221815	+	0.384196i
$545$	11.0012			0.471239
$546$		0			0
$547$	−2.77476			−0.118640			−0.0593201	−	0.998239i	$-0.518893\pi$
$547$	−2.77476			−0.118640			−0.0593201	+	0.998239i	$0.518893\pi$
$548$	−1.54128	−	2.66957i	−0.0658401	−	0.114038i
$549$		0			0
$550$	−4.48300	+	7.76478i	−0.191156	+	0.331091i
$551$	−0.0775590	−	0.134336i	−0.00330413	−	0.00572291i
$552$		0			0
$553$	15.0558	−	4.31248i	0.640236	−	0.183385i
$554$	13.7195			0.582886
$555$		0			0
$556$	0.525024	−	0.909368i	0.0222660	−	0.0385658i
$557$	15.5344	−	26.9064i	0.658214	−	1.14006i	−0.322864	−	0.946445i	$-0.604646\pi$
$557$	15.5344	−	26.9064i	0.658214	−	1.14006i	0.981078	−	0.193614i	$-0.0620211\pi$
$558$		0			0
$559$	−52.7939			−2.23294
$560$	−12.3113	−	11.8958i	−0.520249	−	0.502688i
$561$		0			0
$562$	23.9248	+	41.4389i	1.00920	+	1.74799i
$563$	−0.144020	+	0.249451i	−0.00606973	+	0.0105131i	−0.869044	−	0.494734i	$-0.835265\pi$
$563$	−0.144020	+	0.249451i	−0.00606973	+	0.0105131i	0.862975	+	0.505247i	$0.168599\pi$
$564$		0			0
$565$	9.67836	+	16.7634i	0.407172	+	0.705242i
$566$	−34.5331			−1.45154
$567$		0			0
$568$	−13.8451			−0.580929
$569$	8.04004	+	13.9258i	0.337056	+	0.583798i	0.983878	−	0.178843i	$-0.0572354\pi$
$569$	8.04004	+	13.9258i	0.337056	+	0.583798i	−0.646821	+	0.762641i	$0.723902\pi$
$570$		0			0
$571$	7.64289	−	13.2379i	0.319845	−	0.553988i	−0.660610	−	0.750729i	$-0.729702\pi$
$571$	7.64289	−	13.2379i	0.319845	−	0.553988i	0.980456	+	0.196741i	$0.0630358\pi$
$572$	−5.44345	−	9.42834i	−0.227602	−	0.394218i
$573$		0			0
$574$	−42.2595	+	12.1046i	−1.76388	+	0.505235i
$575$	23.6902			0.987950
$576$		0			0
$577$	12.0812	−	20.9253i	0.502949	−	0.871133i	−0.497045	−	0.867725i	$-0.665582\pi$
$577$	12.0812	−	20.9253i	0.502949	−	0.871133i	0.999994	−	0.00340833i	$-0.00108491\pi$
$578$	−13.4418	+	23.2819i	−0.559106	+	0.968400i
$579$		0			0
$580$	0.114937			0.00477248
$581$	−3.58993	+	14.3808i	−0.148935	+	0.596615i
$582$		0			0
$583$	1.14289	+	1.97955i	0.0473338	+	0.0819845i
$584$	−1.54881	+	2.68262i	−0.0640902	+	0.111007i
$585$		0			0
$586$	2.26636	+	3.92546i	0.0936226	+	0.162159i
$587$	−36.0289			−1.48707			−0.743537	−	0.668695i	$-0.766853\pi$
$587$	−36.0289			−1.48707			−0.743537	+	0.668695i	$0.766853\pi$
$588$		0			0
$589$	−9.63566			−0.397030
$590$	−10.3752	−	17.9703i	−0.427138	−	0.739825i
$591$		0			0
$592$	1.36517	−	2.36455i	0.0561082	−	0.0971823i
$593$	12.4668	+	21.5932i	0.511951	+	0.886726i	0.999904	+	0.0138558i	$0.00441057\pi$
$593$	12.4668	+	21.5932i	0.511951	+	0.886726i	−0.487953	+	0.872870i	$0.662256\pi$
$594$		0			0
$595$	−1.32482	+	5.30706i	−0.0543124	+	0.217568i
$596$	9.15424			0.374972
$597$		0			0
$598$	−35.0751	+	60.7518i	−1.43433	+	2.48433i
$599$	−19.7642	+	34.2325i	−0.807542	+	1.39870i	0.107019	+	0.994257i	$0.465869\pi$
$599$	−19.7642	+	34.2325i	−0.807542	+	1.39870i	−0.914561	+	0.404447i	$0.867464\pi$
$600$		0			0
$601$	−3.72895			−0.152107			−0.0760534	−	0.997104i	$-0.524232\pi$
$601$	−3.72895			−0.152107			−0.0760534	+	0.997104i	$0.524232\pi$
$602$	−47.7669	+	13.6821i	−1.94683	+	0.557639i
$603$		0			0
$604$	−8.80470	−	15.2502i	−0.358258	−	0.620521i
$605$	5.81337	−	10.0691i	0.236347	−	0.409365i
$606$		0			0
$607$	−11.8264	−	20.4839i	−0.480018	−	0.831415i	0.519719	−	0.854337i	$-0.326036\pi$
$607$	−11.8264	−	20.4839i	−0.480018	−	0.831415i	−0.999737	+	0.0229218i	$0.992703\pi$
$608$	16.7287			0.678439
$609$		0			0
$610$	−7.96059			−0.322315
$611$	24.6339	+	42.6671i	0.996580	+	1.72613i
$612$		0			0
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	−0.825113	−	0.564968i	$-0.808888\pi$
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	0.901833	+	0.432084i	$0.142222\pi$
$614$	−4.29264	−	7.43507i	−0.173237	−	0.300055i
$615$		0			0
$616$	3.23242	+	3.12331i	0.130238	+	0.125842i
$617$	35.1230			1.41400			0.706999	−	0.707214i	$-0.250048\pi$
$617$	35.1230			1.41400			0.706999	+	0.707214i	$0.250048\pi$
$618$		0			0
$619$	10.5816	−	18.3279i	0.425311	−	0.736660i	−0.571138	−	0.820854i	$-0.693498\pi$
$619$	10.5816	−	18.3279i	0.425311	−	0.736660i	0.996449	+	0.0841934i	$0.0268314\pi$
$620$	3.56983	−	6.18312i	0.143368	−	0.248320i
$621$		0			0
$622$	−50.6011			−2.02892
$623$	3.57758	−	1.02474i	0.143333	−	0.0410553i
$624$		0			0
$625$	−0.725240	−	1.25615i	−0.0290096	−	0.0502461i
$626$	5.05726	−	8.75943i	0.202129	−	0.350097i
$627$		0			0
$628$	12.0301	+	20.8368i	0.480054	+	0.831477i
$629$	−0.872381			−0.0347841
$630$		0			0
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	3.32329	+	5.75610i	0.132193	+	0.228965i
$633$		0			0
$634$	9.09350	−	15.7504i	0.361149	−	0.625529i
$635$	−5.67273	−	9.82546i	−0.225115	−	0.389911i
$636$		0			0
$637$	−31.9811	−	17.0283i	−1.26714	−	0.674685i
$638$	−0.172562			−0.00683178
$639$		0			0
$640$	5.71622	−	9.90078i	0.225953	−	0.391363i
$641$	4.93735	−	8.55174i	0.195013	−	0.337773i	−0.751891	−	0.659287i	$-0.770858\pi$
$641$	4.93735	−	8.55174i	0.195013	−	0.337773i	0.946905	+	0.321514i	$0.104192\pi$
$642$		0			0
$643$	−43.9496			−1.73320			−0.866602	−	0.499000i	$-0.833701\pi$
$643$	−43.9496			−1.73320			−0.866602	+	0.499000i	$0.833701\pi$
$644$	−6.55717	+	26.2672i	−0.258389	+	1.03507i
$645$		0			0
$646$	−3.57095	−	6.18507i	−0.140497	−	0.243348i
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.0131398	−	0.999914i	$-0.495817\pi$
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.859381	−	0.511336i	$-0.170849\pi$
$648$		0			0
$649$	6.38743	+	11.0634i	0.250729	+	0.434275i
$650$	30.6725			1.20307
$651$		0			0
$652$	−16.9868			−0.665255
$653$	−20.9956	−	36.3655i	−0.821622	−	1.42309i	−0.904474	−	0.426529i	$-0.859736\pi$
$653$	−20.9956	−	36.3655i	−0.821622	−	1.42309i	0.0828523	−	0.996562i	$-0.473597\pi$
$654$		0			0
$655$	1.34374	−	2.32742i	0.0525042	−	0.0909399i
$656$	−21.8726	−	37.8844i	−0.853980	−	1.47914i
$657$		0			0
$658$	33.3459	+	32.2203i	1.29996	+	1.25608i
$659$	39.2729			1.52986			0.764928	−	0.644115i	$-0.222774\pi$
$659$	39.2729			1.52986			0.764928	+	0.644115i	$0.222774\pi$
$660$		0			0
$661$	0.0933694	−	0.161721i	0.00363165	−	0.00629020i	−0.864204	−	0.503142i	$-0.832177\pi$
$661$	0.0933694	−	0.161721i	0.00363165	−	0.00629020i	0.867836	+	0.496852i	$0.165511\pi$
$662$	−19.0515	+	32.9982i	−0.740459	+	1.28251i
$663$		0			0
$664$	−6.29045			−0.244117
$665$	6.35969	+	6.14502i	0.246618	+	0.238293i
$666$		0			0
$667$	0.227973	+	0.394862i	0.00882717	+	0.0152891i
$668$	2.45014	−	4.24376i	0.0947987	−	0.164196i
$669$		0			0
$670$	8.51976	+	14.7567i	0.329147	+	0.570099i
$671$	4.90091			0.189198
$672$		0			0
$673$	10.8676			0.418917			0.209458	−	0.977818i	$-0.432830\pi$
$673$	10.8676			0.418917			0.209458	+	0.977818i	$0.432830\pi$
$674$	−1.37862	−	2.38785i	−0.0531026	−	0.0919764i
$675$		0			0
$676$	−9.58584	+	16.6032i	−0.368686	+	0.638583i
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	−0.998571	−	0.0534326i	$-0.982984\pi$
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	0.453012	−	0.891505i	$-0.350350\pi$
$678$		0			0
$679$	7.81414	−	31.3024i	0.299879	−	1.20128i
$680$	−2.32142			−0.0890223
$681$		0			0
$682$	−5.35961	+	9.28312i	−0.205230	+	0.355469i
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	−0.730243	−	0.683187i	$-0.760593\pi$
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	0.956779	+	0.290816i	$0.0939267\pi$
$684$		0			0
$685$	2.95968			0.113083
$686$	−33.3489	−	7.11864i	−1.27327	−	0.271791i
$687$		0			0
$688$	−24.7230	−	42.8216i	−0.942557	−	1.63256i
$689$	3.90981	−	6.77199i	0.148952	−	0.257992i
$690$		0			0
$691$	−5.95416	−	10.3129i	−0.226507	−	0.392321i	0.730264	−	0.683165i	$-0.239397\pi$
$691$	−5.95416	−	10.3129i	−0.226507	−	0.392321i	−0.956770	+	0.290844i	$0.906064\pi$
$692$	14.0976			0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	0.504096	+	0.873119i	0.0191214	+	0.0331193i
$696$		0			0
$697$	−6.98857	+	12.1046i	−0.264711	+	0.458493i
$698$	−33.1435	−	57.4062i	−1.25450	−	2.17286i
$699$		0			0
$700$	11.3799	−	3.25959i	0.430119	−	0.123201i
$701$	−31.3902			−1.18559			−0.592795	−	0.805353i	$-0.701976\pi$
$701$	−31.3902			−1.18559			−0.592795	+	0.805353i	$0.701976\pi$
$702$		0			0
$703$	−0.705208	+	1.22146i	−0.0265974	+	0.0460681i
$704$	1.97020	−	3.41249i	0.0742549	−	0.128613i
$705$		0			0
$706$	54.3037			2.04375
$707$	2.12846	+	2.05661i	0.0800489	+	0.0773469i
$708$		0			0
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	0.860096	−	0.510133i	$-0.170404\pi$
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	−0.871836	+	0.489798i	$0.837070\pi$
$710$	−15.1516	+	26.2433i	−0.568628	+	0.984893i
$711$		0			0
$712$	0.789685	+	1.36777i	0.0295947	+	0.0512595i
$713$	28.3226			1.06069
$714$		0			0
$715$	10.4529			0.390918
$716$	1.18245	+	2.04806i	0.0441901	+	0.0765395i
$717$		0			0
$718$	−4.98119	+	8.62768i	−0.185897	+	0.321982i
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	0.998681	−	0.0513506i	$-0.0163526\pi$
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	−0.543811	+	0.839208i	$0.683019\pi$
$720$		0			0
$721$	−4.91003	+	1.40640i	−0.182859	+	0.0523771i
$722$	23.4369			0.872233
$723$		0			0
$724$	11.8123	−	20.4595i	0.439002	−	0.760373i
$725$	0.0996792	−	0.172649i	0.00370199	−	0.00641204i
$726$		0			0
$727$	37.8506			1.40380			0.701900	−	0.712275i	$-0.252335\pi$
$727$	37.8506			1.40380			0.701900	+	0.712275i	$0.252335\pi$
$728$	3.72426	−	14.9189i	0.138030	−	0.552932i
$729$		0			0
$730$	3.38991	+	5.87150i	0.125466	+	0.217314i
$731$	−7.89934	+	13.6821i	−0.292168	+	0.506049i
$732$		0			0
$733$	−1.20077	−	2.07980i	−0.0443516	−	0.0768193i	0.842997	−	0.537918i	$-0.180789\pi$
$733$	−1.20077	−	2.07980i	−0.0443516	−	0.0768193i	−0.887349	+	0.461098i	$0.847456\pi$
$734$	42.5038			1.56884
$735$		0			0
$736$	−49.1716			−1.81249
$737$	−5.24517	−	9.08490i	−0.193208	−	0.334646i
$738$		0			0
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	0.438667	+	0.898650i	$0.355451\pi$
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	−0.997587	+	0.0694277i	$0.977883\pi$
$740$	−0.522533	−	0.905053i	−0.0192087	−	0.0332704i
$741$		0			0
$742$	1.78249	−	7.14043i	0.0654374	−	0.262133i
$743$	5.09570			0.186943			0.0934715	−	0.995622i	$-0.470204\pi$
$743$	5.09570			0.186943			0.0934715	+	0.995622i	$0.470204\pi$
$744$		0			0
$745$	−4.39467	+	7.61179i	−0.161008	+	0.278874i
$746$	19.7961	−	34.2879i	0.724787	−	1.25537i
$747$		0			0
$748$	−3.25793			−0.119122
$749$	14.6997	−	4.21049i	0.537115	−	0.153848i
$750$		0			0
$751$	0.487506	+	0.844384i	0.0177893	+	0.0308120i	0.874783	−	0.484515i	$-0.161004\pi$
$751$	0.487506	+	0.844384i	0.0177893	+	0.0308120i	−0.856994	+	0.515327i	$0.827671\pi$
$752$	−23.0718	+	39.9615i	−0.841341	+	1.45724i
$753$		0			0
$754$	0.295165	+	0.511240i	0.0107493	+	0.0186183i
$755$	16.9075			0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	5.26750	+	9.12357i	0.191324	+	0.331383i
$759$		0			0
$760$	−1.87657	+	3.25031i	−0.0680703	+	0.117901i
$761$	27.0875	+	46.9169i	0.981920	+	1.70073i	0.654897	+	0.755718i	$0.272712\pi$
$761$	27.0875	+	46.9169i	0.981920	+	1.70073i	0.327023	+	0.945016i	$0.393955\pi$
$762$		0			0
$763$	15.6820	+	15.1526i	0.567726	+	0.548562i
$764$	31.5484			1.14138
$765$		0			0
$766$	−32.1489	+	55.6835i	−1.16159	+	2.01193i
$767$	21.8513	−	37.8475i	0.789004	−	1.36659i
$768$		0			0
$769$	20.8652			0.752417			0.376208	−	0.926535i	$-0.377228\pi$
$769$	20.8652			0.752417			0.376208	+	0.926535i	$0.377228\pi$
$770$	9.45762	−	2.70898i	0.340829	−	0.0976249i
$771$		0			0
$772$	−4.30047	−	7.44863i	−0.154777	−	0.268082i
$773$	−27.4972	+	47.6266i	−0.989007	+	1.71301i	−0.366447	+	0.930439i	$0.619426\pi$
$773$	−27.4972	+	47.6266i	−0.989007	+	1.71301i	−0.622561	+	0.782572i	$0.713908\pi$
$774$		0			0
$775$	−6.19189	−	10.7247i	−0.222419	−	0.385242i
$776$	13.6923			0.491526
$777$		0			0
$778$	53.1790			1.90656
$779$	11.2987	+	19.5700i	0.404819	+	0.701168i
$780$		0			0
$781$	9.32802	−	16.1566i	0.333783	−	0.578129i
$782$	10.4963	+	18.1801i	0.375346	+	0.650119i
$783$		0			0
$784$	−1.16477	−	33.9144i	−0.0415989	−	1.21123i
$785$	−23.1012			−0.824516
$786$		0			0
$787$	−4.59475	+	7.95833i	−0.163785	+	0.283684i	−0.936223	−	0.351406i	$-0.885704\pi$
$787$	−4.59475	+	7.95833i	−0.163785	+	0.283684i	0.772438	+	0.635090i	$0.219037\pi$
$788$	−6.79103	+	11.7624i	−0.241921	+	0.419019i
$789$		0			0
$790$	14.5475			0.517576
$791$	−9.29301	+	37.2266i	−0.330421	+	1.32362i
$792$		0			0
$793$	−8.38296	−	14.5197i	−0.297688	−	0.515610i
$794$	−10.2967	+	17.8344i	−0.365416	+	0.632919i
$795$		0			0
$796$	−6.03296	−	10.4494i	−0.213832	−	0.370369i
$797$	−7.07547			−0.250626			−0.125313	−	0.992117i	$-0.539994\pi$
$797$	−7.07547			−0.250626			−0.125313	+	0.992117i	$0.539994\pi$
$798$		0			0
$799$	14.7435			0.521586
$800$	10.7499	+	18.6194i	0.380067	+	0.658295i
$801$		0			0
$802$	−0.996224	+	1.72551i	−0.0351779	+	0.0609299i
$803$	−2.08699	−	3.61477i	−0.0736483	−	0.127563i
$804$		0			0
$805$	−18.6934	−	18.0624i	−0.658855	−	0.636615i
$806$	36.6702			1.29165
$807$		0			0
$808$	−0.628050	+	1.08781i	−0.0220947	+	0.0382692i
$809$	−2.97060	+	5.14522i	−0.104441	+	0.180896i	−0.913510	−	0.406817i	$-0.866639\pi$
$809$	−2.97060	+	5.14522i	−0.104441	+	0.180896i	0.809069	+	0.587714i	$0.199972\pi$
$810$		0			0
$811$	44.4139			1.55958			0.779791	−	0.626039i	$-0.215325\pi$
$811$	44.4139			1.55958			0.779791	+	0.626039i	$0.215325\pi$
$812$	0.163840	+	0.158309i	0.00574965	+	0.00555557i
$813$		0			0
$814$	0.784512	+	1.35881i	0.0274971	+	0.0476264i
$815$	8.15485	−	14.1246i	0.285652	−	0.494764i
$816$		0			0
$817$	12.7712	+	22.1204i	0.446808	+	0.773894i
$818$	40.0191			1.39924
$819$		0			0
$820$	−16.7439			−0.584721
$821$	−3.17761	−	5.50378i	−0.110899	−	0.192083i	0.805234	−	0.592958i	$-0.202040\pi$
$821$	−3.17761	−	5.50378i	−0.110899	−	0.192083i	−0.916133	+	0.400874i	$0.868706\pi$
$822$		0			0
$823$	4.73216	−	8.19635i	0.164953	−	0.285707i	−0.771686	−	0.636004i	$-0.780586\pi$
$823$	4.73216	−	8.19635i	0.164953	−	0.285707i	0.936639	+	0.350297i	$0.113919\pi$
$824$	−1.08380	−	1.87720i	−0.0377560	−	0.0653953i
$825$		0			0
$826$	9.96205	−	39.9067i	0.346624	−	1.38853i
$827$	−4.86261			−0.169090			−0.0845448	−	0.996420i	$-0.526944\pi$
$827$	−4.86261			−0.169090			−0.0845448	+	0.996420i	$0.526944\pi$
$828$		0			0
$829$	20.3926	−	35.3211i	0.708266	−	1.22675i	−0.257234	−	0.966349i	$-0.582811\pi$
$829$	20.3926	−	35.3211i	0.708266	−	1.22675i	0.965500	−	0.260403i	$-0.0838555\pi$
$830$	−6.88402	+	11.9235i	−0.238948	+	0.413870i
$831$		0			0
$832$	−13.4801			−0.467337
$833$	−9.19826	+	5.74035i	−0.318701	+	0.198891i
$834$		0			0
$835$	2.35247	+	4.07460i	0.0814107	+	0.141007i
$836$	−2.63362	+	4.56156i	−0.0910856	+	0.157765i
$837$		0			0
$838$	−23.1823	−	40.1529i	−0.800818	−	1.38706i
$839$	−19.2034			−0.662976			−0.331488	−	0.943459i	$-0.607551\pi$
$839$	−19.2034			−0.662976			−0.331488	+	0.943459i	$0.607551\pi$
$840$		0			0
$841$	−28.9962			−0.999868
$842$	27.3063	+	47.2959i	0.941036	+	1.62992i
$843$		0			0
$844$	−3.95113	+	6.84355i	−0.136003	+	0.235565i
$845$	−9.20374	−	15.9413i	−0.316618	−	0.548399i
$846$		0			0
$847$	22.1556	−	6.34612i	0.761276	−	0.218055i
$848$	7.32376			0.251499
$849$		0			0
$850$	4.58940	−	7.94907i	0.157415	−	0.272651i
$851$	2.07286	−	3.59029i	0.0710566	−	0.123074i
$852$		0			0
$853$	13.9011			0.475965			0.237982	−	0.971269i	$-0.423514\pi$
$853$	13.9011			0.475965			0.237982	+	0.971269i	$0.423514\pi$
$854$	−11.3477	−	10.9646i	−0.388309	−	0.375202i
$855$		0			0
$856$	3.24469	+	5.61996i	0.110901	+	0.192086i
$857$	−28.4919	+	49.3494i	−0.973265	+	1.68574i	−0.287718	+	0.957715i	$0.592897\pi$
$857$	−28.4919	+	49.3494i	−0.973265	+	1.68574i	−0.685547	+	0.728029i	$0.740437\pi$
$858$		0			0
$859$	10.0501	+	17.4073i	0.342905	+	0.593929i	0.984971	−	0.172721i	$-0.0552557\pi$
$859$	10.0501	+	17.4073i	0.342905	+	0.593929i	−0.642066	+	0.766650i	$0.721922\pi$
$860$	−18.9260			−0.645370
$861$		0			0
$862$	9.00429			0.306687
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	0.808650	−	0.588289i	$-0.200198\pi$
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	−0.913799	+	0.406167i	$0.866865\pi$
$864$		0			0
$865$	−6.76781	+	11.7222i	−0.230112	+	0.398566i
$866$	8.94318	+	15.4900i	0.303902	+	0.526373i
$867$		0			0
$868$	13.6051	−	3.89697i	0.461788	−	0.132272i
$869$	−8.95612			−0.303816
$870$		0			0
$871$	−17.9436	+	31.0792i	−0.607996	+	1.05308i
$872$	−4.62732	+	8.01476i	−0.156701	+	0.271414i
$873$		0			0
$874$	33.9396			1.14802
$875$	−7.02935	+	28.1587i	−0.237636	+	0.951937i
$876$		0			0
$877$	18.6287	+	32.2658i	0.629046	+	1.08954i	0.987743	+	0.156086i	$0.0498877\pi$
$877$	18.6287	+	32.2658i	0.629046	+	1.08954i	−0.358697	+	0.933454i	$0.616779\pi$
$878$	−13.6468	+	23.6370i	−0.460558	+	0.797710i
$879$		0			0
$880$	4.89504	+	8.47846i	0.165012	+	0.285809i
$881$	−11.7848			−0.397041			−0.198520	−	0.980097i	$-0.563614\pi$
$881$	−11.7848			−0.397041			−0.198520	+	0.980097i	$0.563614\pi$
$882$		0			0
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	5.57265	+	9.65211i	0.187428	+	0.324636i
$885$		0			0
$886$	−20.1634	+	34.9240i	−0.677402	+	1.17329i
$887$	−14.2581	−	24.6957i	−0.478739	−	0.829201i	0.520964	−	0.853579i	$-0.325573\pi$
$887$	−14.2581	−	24.6957i	−0.478739	−	0.829201i	−0.999703	+	0.0243782i	$0.992239\pi$
$888$		0			0
$889$	5.44686	−	21.8194i	0.182682	−	0.731800i
$890$	3.45680			0.115872
$891$		0			0
$892$	8.14822	−	14.1131i	0.272823	−	0.472543i
$893$	11.9182	−	20.6430i	0.398828	−	0.690790i
$894$		0			0
$895$	−2.27063			−0.0758986
$896$	21.7853	−	6.24006i	0.727797	−	0.208466i
$897$		0			0
$898$	19.7890	+	34.2755i	0.660366	+	1.14379i
$899$	0.119171	−	0.206410i	0.00397456	−	0.00688414i
$900$		0			0
$901$	−1.17002	−	2.02653i	−0.0389790	−	0.0675135i
$902$	25.1386			0.837025
$903$		0			0
$904$	−16.2837			−0.541587
$905$	11.3415	+	19.6440i	0.377003	+	0.652989i
$906$		0			0
$907$	3.94577	−	6.83428i	0.131017	−	0.226929i	−0.793052	−	0.609154i	$-0.791509\pi$
$907$	3.94577	−	6.83428i	0.131017	−	0.226929i	0.924069	+	0.382226i	$0.124842\pi$
$908$	−7.77317	−	13.4635i	−0.257962	−	0.446803i
$909$		0			0
$910$	−24.2029	−	23.3860i	−0.802319	−	0.775237i
$911$	28.4412			0.942299			0.471150	−	0.882053i	$-0.343839\pi$
$911$	28.4412			0.942299			0.471150	+	0.882053i	$0.343839\pi$
$912$		0			0
$913$	4.23813	−	7.34065i	0.140262	−	0.242940i
$914$	37.4007	−	64.7798i	1.23710	−	2.14273i
$915$		0			0
$916$	−13.4241			−0.443545
$917$	5.12118	−	1.46688i	0.169116	−	0.0484406i
$918$		0			0
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	0.924335	−	0.381582i	$-0.124621\pi$
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	−0.792627	+	0.609706i	$0.791287\pi$
$920$	5.51590	−	9.55382i	0.181854	−	0.314980i
$921$		0			0
$922$	−2.60610	−	4.51390i	−0.0858274	−	0.148657i
$923$	−63.8219			−2.10072
$924$		0			0
$925$	−1.81267			−0.0596004
$926$	25.6529	+	44.4322i	0.843008	+	1.46013i
$927$		0			0
$928$	−0.206895	+	0.358353i	−0.00679167	+	0.0117635i
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	0.669601	−	0.742721i	$-0.266465\pi$
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	−0.978016	+	0.208531i	$0.933132\pi$
$930$		0			0
$931$	0.601686	+	17.5192i	0.0197195	+	0.574169i
$932$	26.8161			0.878391
$933$		0			0
$934$	24.5288	−	42.4852i	0.802608	−	1.39016i
$935$	1.56403	−	2.70898i	0.0511493	−	0.0885932i
$936$		0			0
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$	−8.18053	+	32.7701i	−0.267104	+	1.06998i
$939$		0			0
$940$	8.83094	+	15.2956i	0.288034	+	0.498889i
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	−0.983272	−	0.182141i	$-0.941697\pi$
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	0.649375	+	0.760468i	$0.275031\pi$
$942$		0			0
$943$	−33.2110	−	57.5231i	−1.08150	−	1.87321i
$944$	40.9312			1.33220
$945$		0			0
$946$	28.4148			0.923843
$947$	7.42524	+	12.8609i	0.241288	+	0.417923i	0.961081	−	0.276265i	$-0.0890969\pi$
$947$	7.42524	+	12.8609i	0.241288	+	0.417923i	−0.719793	+	0.694188i	$0.755764\pi$
$948$		0			0
$949$	−7.13954	+	12.3661i	−0.231759	+	0.401419i
$950$	−7.41989	−	12.8516i	−0.240733	−	0.416962i
$951$		0			0
$952$	−3.30914	−	3.19744i	−0.107250	−	0.103629i
$953$	46.4678			1.50524			0.752620	−	0.658456i	$-0.228790\pi$
$953$	46.4678			1.50524			0.752620	+	0.658456i	$0.228790\pi$
$954$		0			0
$955$	−15.1454	+	26.2326i	−0.490094	+	0.848868i
$956$	−0.270584	+	0.468665i	−0.00875130	+	0.0151577i
$957$		0			0
$958$	58.1447			1.87857
$959$	4.21896	+	4.07655i	0.136237	+	0.131639i
$960$		0			0
$961$	8.09733	+	14.0250i	0.261204	+	0.452419i
$962$	2.68380	−	4.64847i	0.0865291	−	0.149873i
$963$		0			0
$964$	−7.39301	−	12.8051i	−0.238113	−	0.412423i
$965$	8.25809			0.265837
$966$		0			0
$967$	−1.72734			−0.0555475			−0.0277738	−	0.999614i	$-0.508842\pi$
$967$	−1.72734			−0.0555475			−0.0277738	+	0.999614i	$0.508842\pi$
$968$	4.89045	+	8.47050i	0.157185	+	0.272252i
$969$		0			0
$970$	14.9843	−	25.9536i	0.481118	−	0.833320i
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	0.798960	−	0.601384i	$-0.205384\pi$
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	−0.920294	+	0.391228i	$0.872050\pi$
$972$		0			0
$973$	−0.484024	+	1.93894i	−0.0155171	+	0.0621595i
$974$	−0.563740			−0.0180634
$975$		0			0
$976$	7.85137	−	13.5990i	0.251316	−	0.435293i
$977$	28.3101	−	49.0345i	0.905721	−	1.56875i	0.0857737	−	0.996315i	$-0.472664\pi$
$977$	28.3101	−	49.0345i	0.905721	−	1.56875i	0.819947	−	0.572440i	$-0.194003\pi$
$978$		0			0
$979$	−2.12817			−0.0680166
$980$	−11.4648	−	6.10443i	−0.366231	−	0.194999i
$981$		0			0
$982$	16.6997	+	28.9247i	0.532909	+	0.923025i
$983$	−16.1486	+	27.9702i	−0.515061	+	0.892112i	0.484786	+	0.874633i	$0.338897\pi$
$983$	−16.1486	+	27.9702i	−0.515061	+	0.892112i	−0.999847	+	0.0174790i	$0.994436\pi$
$984$		0			0
$985$	−6.52033	−	11.2936i	−0.207755	−	0.359842i
$986$	0.176657			0.00562591
$987$		0			0
$988$	18.0191			0.573264
$989$	−37.5391	−	65.0197i	−1.19367	−	2.06750i
$990$		0			0
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	−0.957003	−	0.290078i	$-0.906319\pi$
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	0.729716	+	0.683750i	$0.239652\pi$
$992$	12.8520	+	22.2602i	0.408050	+	0.706764i
$993$		0			0
$994$	−57.7448	+	16.5401i	−1.83155	+	0.524619i
$995$	11.5849			0.367268
$996$		0			0
$997$	−28.1262	+	48.7160i	−0.890765	+	1.54285i	−0.0518058	+	0.998657i	$0.516498\pi$
$997$	−28.1262	+	48.7160i	−0.890765	+	1.54285i	−0.838960	+	0.544194i	$0.816836\pi$
$998$	−19.6176	+	33.9787i	−0.620985	+	1.07558i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.f.487.4		10
3.2	odd	2		567.2.e.e.487.2		10
7.2	even	3	inner	567.2.e.f.163.4		10
7.3	odd	6		3969.2.a.ba.1.2		5
7.4	even	3		3969.2.a.z.1.2		5
9.2	odd	6		189.2.g.b.172.2		10
9.4	even	3		63.2.h.b.25.2	yes	10
9.5	odd	6		189.2.h.b.46.4		10
9.7	even	3		63.2.g.b.4.4	✓	10
21.2	odd	6		567.2.e.e.163.2		10
21.11	odd	6		3969.2.a.bc.1.4		5
21.17	even	6		3969.2.a.bb.1.4		5
36.7	odd	6		1008.2.t.i.193.5		10
36.11	even	6		3024.2.t.i.1873.2		10
36.23	even	6		3024.2.q.i.2881.4		10
36.31	odd	6		1008.2.q.i.529.2		10
63.2	odd	6		189.2.h.b.37.4		10
63.4	even	3		441.2.f.e.295.4		10
63.5	even	6		1323.2.g.f.667.2		10
63.11	odd	6		1323.2.f.e.442.2		10
63.13	odd	6		441.2.h.f.214.2		10
63.16	even	3		63.2.h.b.58.2	yes	10
63.20	even	6		1323.2.g.f.361.2		10
63.23	odd	6		189.2.g.b.100.2		10
63.25	even	3		441.2.f.e.148.4		10
63.31	odd	6		441.2.f.f.295.4		10
63.32	odd	6		1323.2.f.e.883.2		10
63.34	odd	6		441.2.g.f.67.4		10
63.38	even	6		1323.2.f.f.442.2		10
63.40	odd	6		441.2.g.f.79.4		10
63.41	even	6		1323.2.h.f.802.4		10
63.47	even	6		1323.2.h.f.226.4		10
63.52	odd	6		441.2.f.f.148.4		10
63.58	even	3		63.2.g.b.16.4	yes	10
63.59	even	6		1323.2.f.f.883.2		10
63.61	odd	6		441.2.h.f.373.2		10
252.23	even	6		3024.2.t.i.289.2		10
252.79	odd	6		1008.2.q.i.625.2		10
252.191	even	6		3024.2.q.i.2305.4		10
252.247	odd	6		1008.2.t.i.961.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	9.7	even	3
63.2.g.b.16.4	yes	10	63.58	even	3
63.2.h.b.25.2	yes	10	9.4	even	3
63.2.h.b.58.2	yes	10	63.16	even	3
189.2.g.b.100.2		10	63.23	odd	6
189.2.g.b.172.2		10	9.2	odd	6
189.2.h.b.37.4		10	63.2	odd	6
189.2.h.b.46.4		10	9.5	odd	6
441.2.f.e.148.4		10	63.25	even	3
441.2.f.e.295.4		10	63.4	even	3
441.2.f.f.148.4		10	63.52	odd	6
441.2.f.f.295.4		10	63.31	odd	6
441.2.g.f.67.4		10	63.34	odd	6
441.2.g.f.79.4		10	63.40	odd	6
441.2.h.f.214.2		10	63.13	odd	6
441.2.h.f.373.2		10	63.61	odd	6
567.2.e.e.163.2		10	21.2	odd	6
567.2.e.e.487.2		10	3.2	odd	2
567.2.e.f.163.4		10	7.2	even	3	inner
567.2.e.f.487.4		10	1.1	even	1	trivial
1008.2.q.i.529.2		10	36.31	odd	6
1008.2.q.i.625.2		10	252.79	odd	6
1008.2.t.i.193.5		10	36.7	odd	6
1008.2.t.i.961.5		10	252.247	odd	6
1323.2.f.e.442.2		10	63.11	odd	6
1323.2.f.e.883.2		10	63.32	odd	6
1323.2.f.f.442.2		10	63.38	even	6
1323.2.f.f.883.2		10	63.59	even	6
1323.2.g.f.361.2		10	63.20	even	6
1323.2.g.f.667.2		10	63.5	even	6
1323.2.h.f.226.4		10	63.47	even	6
1323.2.h.f.802.4		10	63.41	even	6
3024.2.q.i.2305.4		10	252.191	even	6
3024.2.q.i.2881.4		10	36.23	even	6
3024.2.t.i.289.2		10	252.23	even	6
3024.2.t.i.1873.2		10	36.11	even	6
3969.2.a.z.1.2		5	7.4	even	3
3969.2.a.ba.1.2		5	7.3	odd	6
3969.2.a.bb.1.4		5	21.17	even	6
3969.2.a.bc.1.4		5	21.11	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.920620 + 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 - 1.15593i) q^{5} +(0.640804 - 2.56698i) q^{7} +1.12285 q^{8} +O(q^{10})\)	\(q+(0.920620 + 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 - 1.15593i) q^{5} +(0.640804 - 2.56698i) q^{7} +1.12285 q^{8} +(1.22880 - 2.12835i) q^{10} +(-0.756508 + 1.31031i) q^{11} +5.17599 q^{13} +(4.68314 - 1.34141i) q^{14} +(2.42388 + 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(-1.25211 - 2.16872i) q^{19} +1.85553 q^{20} -2.78583 q^{22} +(3.68039 + 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +(4.76513 + 8.25344i) q^{26} +(2.64502 + 2.55574i) q^{28} +0.0619427 q^{29} +(1.92388 - 3.33227i) q^{31} +(-3.34011 + 5.78523i) q^{32} +2.85195 q^{34} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(2.30543 - 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} -9.02376 q^{41} -10.1998 q^{43} +(-1.05167 - 1.82155i) q^{44} +(-6.77649 + 11.7372i) q^{46} +(4.75925 + 8.24327i) q^{47} +(-6.17874 - 3.28986i) q^{49} +5.92591 q^{50} +(-3.59775 + 6.23148i) q^{52} +(0.755374 - 1.30835i) q^{53} +2.01950 q^{55} +(0.719526 - 2.88233i) q^{56} +(0.0570257 + 0.0987714i) q^{58} +(4.22166 - 7.31212i) q^{59} +(-1.61958 - 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(-3.45434 - 5.98309i) q^{65} +(-3.46670 + 6.00449i) q^{67} +(1.07663 + 1.86478i) q^{68} +(-4.67599 - 4.51816i) q^{70} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(0.518508 - 0.898083i) q^{74} +3.48128 q^{76} +(2.87876 + 2.78159i) q^{77} +(2.95969 + 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(-8.30746 - 14.3889i) q^{82} -5.60222 q^{83} -2.06744 q^{85} +(-9.39010 - 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +(0.703287 + 1.21813i) q^{89} +(3.31680 - 13.2867i) q^{91} -10.2327 q^{92} +(-8.76293 + 15.1778i) q^{94} +(-1.67126 + 2.89470i) q^{95} +12.1943 q^{97} +(-0.442393 - 12.8811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 5 * q^7 - 6 * q^8	\( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29} - 3 q^{31} - 2 q^{32} - 6 q^{34} + 5 q^{35} + 20 q^{38} - 3 q^{40} - 10 q^{41} + 14 q^{43} - 10 q^{44} + 3 q^{46} + 27 q^{47} - 17 q^{49} - 38 q^{50} - 10 q^{52} - 21 q^{53} + 4 q^{55} + 27 q^{56} - 10 q^{58} + 30 q^{59} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} - 2 q^{67} + 27 q^{68} - 11 q^{70} - 6 q^{71} + 15 q^{73} - 36 q^{74} - 10 q^{76} + 20 q^{77} - 4 q^{79} + 20 q^{80} - 5 q^{82} - 18 q^{83} + 12 q^{85} - 8 q^{86} - 18 q^{88} + 28 q^{89} - 4 q^{91} - 54 q^{92} - 3 q^{94} - 14 q^{95} + 24 q^{97} + 59 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 5 * q^7 - 6 * q^8 - 7 * q^10 + 4 * q^11 + 16 * q^13 + 4 * q^14 + 2 * q^16 + 12 * q^17 + q^19 - 10 * q^20 + 2 * q^22 + 3 * q^23 - q^25 + 11 * q^26 - 2 * q^28 - 14 * q^29 - 3 * q^31 - 2 * q^32 - 6 * q^34 + 5 * q^35 + 20 * q^38 - 3 * q^40 - 10 * q^41 + 14 * q^43 - 10 * q^44 + 3 * q^46 + 27 * q^47 - 17 * q^49 - 38 * q^50 - 10 * q^52 - 21 * q^53 + 4 * q^55 + 27 * q^56 - 10 * q^58 + 30 * q^59 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 - 2 * q^67 + 27 * q^68 - 11 * q^70 - 6 * q^71 + 15 * q^73 - 36 * q^74 - 10 * q^76 + 20 * q^77 - 4 * q^79 + 20 * q^80 - 5 * q^82 - 18 * q^83 + 12 * q^85 - 8 * q^86 - 18 * q^88 + 28 * q^89 - 4 * q^91 - 54 * q^92 - 3 * q^94 - 14 * q^95 + 24 * q^97 + 59 * q^98

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