LMFDB - Embedded newform 567.2.ba.a.341.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			341.22
Character	$\chi$	$=$	567.341
Dual form			567.2.ba.a.143.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63361 + 1.94686i) q^{2} +(-0.774283 + 4.39118i) q^{4} +(0.356523 + 0.299159i) q^{5} +(-2.41592 + 1.07857i) q^{7} +(-5.41196 + 3.12460i) q^{8} +1.18281i q^{10} +(-1.58990 - 1.89477i) q^{11} +(2.13324 + 5.86102i) q^{13} +(-6.04649 - 2.94150i) q^{14} +(-6.54413 - 2.38187i) q^{16} -0.673165 q^{17} +0.725344i q^{19} +(-1.58971 + 1.33392i) q^{20} +(1.09157 - 6.19062i) q^{22} +(1.10753 + 3.04291i) q^{23} +(-0.830628 - 4.71072i) q^{25} +(-7.92569 + 13.7277i) q^{26} +(-2.86558 - 11.4439i) q^{28} +(1.84864 - 5.07909i) q^{29} +(6.82052 + 1.20264i) q^{31} +(-1.77867 - 4.88687i) q^{32} +(-1.09969 - 1.31055i) q^{34} +(-1.18400 - 0.338210i) q^{35} +(3.70433 + 6.41609i) q^{37} +(-1.41214 + 1.18493i) q^{38} +(-2.86424 - 0.505043i) q^{40} +(3.54917 - 1.29179i) q^{41} +(-1.41606 - 8.03089i) q^{43} +(9.55132 - 5.51446i) q^{44} +(-4.11484 + 7.12711i) q^{46} +(1.58499 + 8.98890i) q^{47} +(4.67338 - 5.21148i) q^{49} +(7.81418 - 9.31258i) q^{50} +(-27.3885 + 4.82933i) q^{52} +(11.5438 - 6.66480i) q^{53} -1.15116i q^{55} +(9.70479 - 13.3860i) q^{56} +(12.9082 - 4.69821i) q^{58} +(-10.2419 + 3.72774i) q^{59} +(0.919898 - 0.162203i) q^{61} +(8.80068 + 15.2432i) q^{62} +(-0.355740 + 0.616160i) q^{64} +(-0.992826 + 2.72777i) q^{65} +(-0.0184408 - 0.0154737i) q^{67} +(0.521220 - 2.95599i) q^{68} +(-1.27574 - 2.85757i) q^{70} +(-8.62973 - 4.98238i) q^{71} +(-2.49239 - 1.43898i) q^{73} +(-6.43979 + 17.6932i) q^{74} +(-3.18511 - 0.561622i) q^{76} +(5.88473 + 2.86281i) q^{77} +(0.843560 - 0.707831i) q^{79} +(-1.62058 - 2.80692i) q^{80} +(8.31288 + 4.79945i) q^{82} +(4.97140 + 1.80944i) q^{83} +(-0.239999 - 0.201383i) q^{85} +(13.3217 - 15.8762i) q^{86} +(14.5249 + 5.28663i) q^{88} -10.2028 q^{89} +(-11.4753 - 11.8589i) q^{91} +(-14.2195 + 2.50728i) q^{92} +(-14.9109 + 17.7701i) q^{94} +(-0.216993 + 0.258602i) q^{95} +(18.3280 - 3.23172i) q^{97} +(17.7805 + 0.584889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	1.63361	+	1.94686i	1.15513	+	1.37664i	0.913786	+	0.406197i	$0.133145\pi$
$2$	1.63361	+	1.94686i	1.15513	+	1.37664i	0.241348	+	0.970439i	$0.422410\pi$
$3$		0			0
$3$		0			0
$4$	−0.774283	+	4.39118i	−0.387142	+	2.19559i
$5$	0.356523	+	0.299159i	0.159442	+	0.133788i	0.719018	−	0.694991i	$-0.244592\pi$
$5$	0.356523	+	0.299159i	0.159442	+	0.133788i	−0.559576	+	0.828779i	$0.689036\pi$
$6$		0			0
$7$	−2.41592	+	1.07857i	−0.913133	+	0.407661i
$7$	−2.41592	+	1.07857i	−0.913133	+	0.407661i
$8$	−5.41196	+	3.12460i	−1.91342	+	1.10471i
$9$		0			0
$10$			1.18281i			0.374036i
$11$	−1.58990	−	1.89477i	−0.479374	−	0.571295i	0.471108	−	0.882075i	$-0.343854\pi$
$11$	−1.58990	−	1.89477i	−0.479374	−	0.571295i	−0.950482	+	0.310780i	$0.899410\pi$
$12$		0			0
$13$	2.13324	+	5.86102i	0.591653	+	1.62555i	0.767436	+	0.641125i	$0.221532\pi$
$13$	2.13324	+	5.86102i	0.591653	+	1.62555i	−0.175783	+	0.984429i	$0.556246\pi$
$14$	−6.04649	−	2.94150i	−1.61599	−	0.786149i
$15$		0			0
$16$	−6.54413	−	2.38187i	−1.63603	−	0.595467i
$17$	−0.673165			−0.163266			−0.0816332	−	0.996662i	$-0.526014\pi$
$17$	−0.673165			−0.163266			−0.0816332	+	0.996662i	$0.526014\pi$
$18$		0			0
$19$			0.725344i			0.166405i	0.996533	+	0.0832027i	$0.0265149\pi$
$19$			0.725344i			0.166405i	−0.996533	+	0.0832027i	$0.973485\pi$
$20$	−1.58971	+	1.33392i	−0.355470	+	0.298274i
$21$		0			0
$22$	1.09157	−	6.19062i	0.232724	−	1.31985i
$23$	1.10753	+	3.04291i	0.230935	+	0.634490i	0.999989	−	0.00469449i	$-0.00149431\pi$
$23$	1.10753	+	3.04291i	0.230935	+	0.634490i	−0.769054	+	0.639184i	$0.779272\pi$
$24$		0			0
$25$	−0.830628	−	4.71072i	−0.166126	−	0.942145i
$26$	−7.92569	+	13.7277i	−1.55436	+	2.69222i
$27$		0			0
$28$	−2.86558	−	11.4439i	−0.541543	−	2.16269i
$29$	1.84864	−	5.07909i	0.343284	−	0.943164i	−0.641151	−	0.767415i	$-0.721543\pi$
$29$	1.84864	−	5.07909i	0.343284	−	0.943164i	0.984435	−	0.175750i	$-0.0562349\pi$
$30$		0			0
$31$	6.82052	+	1.20264i	1.22500	+	0.216001i	0.748478	−	0.663160i	$-0.230785\pi$
$31$	6.82052	+	1.20264i	1.22500	+	0.216001i	0.476525	+	0.879161i	$0.341896\pi$
$32$	−1.77867	−	4.88687i	−0.314428	−	0.863884i
$33$		0			0
$34$	−1.09969	−	1.31055i	−0.188595	−	0.224758i
$35$	−1.18400	−	0.338210i	−0.200132	−	0.0571678i
$36$		0			0
$37$	3.70433	+	6.41609i	0.608988	+	1.05480i	0.991407	+	0.130810i	$0.0417578\pi$
$37$	3.70433	+	6.41609i	0.608988	+	1.05480i	−0.382419	+	0.923989i	$0.624909\pi$
$38$	−1.41214	+	1.18493i	−0.229079	+	0.192220i
$39$		0			0
$40$	−2.86424	−	0.505043i	−0.452876	−	0.0798543i
$41$	3.54917	−	1.29179i	0.554287	−	0.201744i	−0.0496629	−	0.998766i	$-0.515815\pi$
$41$	3.54917	−	1.29179i	0.554287	−	0.201744i	0.603950	+	0.797022i	$0.293592\pi$
$42$		0			0
$43$	−1.41606	−	8.03089i	−0.215948	−	1.22470i	−0.879254	−	0.476352i	$-0.841959\pi$
$43$	−1.41606	−	8.03089i	−0.215948	−	1.22470i	0.663307	−	0.748348i	$-0.269152\pi$
$44$	9.55132	−	5.51446i	1.43992	−	0.831335i
$45$		0			0
$46$	−4.11484	+	7.12711i	−0.606700	+	1.05083i
$47$	1.58499	+	8.98890i	0.231194	+	1.31117i	0.850483	+	0.526003i	$0.176310\pi$
$47$	1.58499	+	8.98890i	0.231194	+	1.31117i	−0.619289	+	0.785163i	$0.712579\pi$
$48$		0			0
$49$	4.67338	−	5.21148i	0.667626	−	0.744497i
$50$	7.81418	−	9.31258i	1.10509	−	1.31700i
$51$		0			0
$52$	−27.3885	+	4.82933i	−3.79810	+	0.669708i
$53$	11.5438	−	6.66480i	1.58566	−	0.915480i	0.591647	−	0.806197i	$-0.298478\pi$
$53$	11.5438	−	6.66480i	1.58566	−	0.915480i	0.994011	−	0.109283i	$-0.0348555\pi$
$54$		0			0
$55$		−	1.15116i		−	0.155223i
$56$	9.70479	−	13.3860i	1.29686	−	1.78877i
$57$		0			0
$58$	12.9082	−	4.69821i	1.69493	−	0.616905i
$59$	−10.2419	+	3.72774i	−1.33338	+	0.485310i	−0.907721	−	0.419574i	$-0.862180\pi$
$59$	−10.2419	+	3.72774i	−1.33338	+	0.485310i	−0.425658	+	0.904884i	$0.639957\pi$
$60$		0			0
$61$	0.919898	−	0.162203i	0.117781	−	0.0207680i	−0.114447	−	0.993429i	$-0.536510\pi$
$61$	0.919898	−	0.162203i	0.117781	−	0.0207680i	0.232228	+	0.972661i	$0.425398\pi$
$62$	8.80068	+	15.2432i	1.11769	+	1.93589i
$63$		0			0
$64$	−0.355740	+	0.616160i	−0.0444675	+	0.0770200i
$65$	−0.992826	+	2.72777i	−0.123145	+	0.338338i
$66$		0			0
$67$	−0.0184408	−	0.0154737i	−0.00225290	−	0.00189041i	0.641660	−	0.766989i	$-0.278246\pi$
$67$	−0.0184408	−	0.0154737i	−0.00225290	−	0.00189041i	−0.643913	+	0.765098i	$0.722690\pi$
$68$	0.521220	−	2.95599i	0.0632072	−	0.358466i
$69$		0			0
$70$	−1.27574	−	2.85757i	−0.152480	−	0.341545i
$71$	−8.62973	−	4.98238i	−1.02416	−	0.591300i	−0.108854	−	0.994058i	$-0.534718\pi$
$71$	−8.62973	−	4.98238i	−1.02416	−	0.591300i	−0.915306	+	0.402758i	$0.868052\pi$
$72$		0			0
$73$	−2.49239	−	1.43898i	−0.291712	−	0.168420i	0.347002	−	0.937865i	$-0.387200\pi$
$73$	−2.49239	−	1.43898i	−0.291712	−	0.168420i	−0.638714	+	0.769444i	$0.720533\pi$
$74$	−6.43979	+	17.6932i	−0.748610	+	2.05679i
$75$		0			0
$76$	−3.18511	−	0.561622i	−0.365358	−	0.0644224i
$77$	5.88473	+	2.86281i	0.670627	+	0.326247i
$78$		0			0
$79$	0.843560	−	0.707831i	0.0949080	−	0.0796372i	−0.594099	−	0.804392i	$-0.702491\pi$
$79$	0.843560	−	0.707831i	0.0949080	−	0.0796372i	0.689007	+	0.724755i	$0.258047\pi$
$80$	−1.62058	−	2.80692i	−0.181186	−	0.313824i
$81$		0			0
$82$	8.31288	+	4.79945i	0.918004	+	0.530010i
$83$	4.97140	+	1.80944i	0.545682	+	0.198612i	0.600127	−	0.799905i	$-0.295117\pi$
$83$	4.97140	+	1.80944i	0.545682	+	0.198612i	−0.0544449	+	0.998517i	$0.517339\pi$
$84$		0			0
$85$	−0.239999	−	0.201383i	−0.0260315	−	0.0218431i
$86$	13.3217	−	15.8762i	1.43652	−	1.71197i
$87$		0			0
$88$	14.5249	+	5.28663i	1.54836	+	0.563557i
$89$	−10.2028			−1.08150			−0.540749	−	0.841184i	$-0.681859\pi$
$89$	−10.2028			−1.08150			−0.540749	+	0.841184i	$0.681859\pi$
$90$		0			0
$91$	−11.4753	−	11.8589i	−1.20293	−	1.24315i
$92$	−14.2195	+	2.50728i	−1.48248	+	0.261402i
$93$		0			0
$94$	−14.9109	+	17.7701i	−1.53794	+	1.83284i
$95$	−0.216993	+	0.258602i	−0.0222630	+	0.0265320i
$96$		0			0
$97$	18.3280	−	3.23172i	1.86092	−	0.328131i	0.873575	−	0.486690i	$-0.161796\pi$
$97$	18.3280	−	3.23172i	1.86092	−	0.328131i	0.987349	+	0.158559i	$0.0506848\pi$
$98$	17.7805	+	0.584889i	1.79610	+	0.0590828i
$99$		0			0
$100$	21.3288			2.13288
$101$	1.00210	+	0.364734i	0.0997124	+	0.0362924i	0.391395	−	0.920223i	$-0.371993\pi$
$101$	1.00210	+	0.364734i	0.0997124	+	0.0362924i	−0.291682	+	0.956515i	$0.594215\pi$
$102$		0			0
$103$	3.63501	−	4.33204i	0.358169	−	0.426849i	−0.556629	−	0.830761i	$-0.687906\pi$
$103$	3.63501	−	4.33204i	0.358169	−	0.426849i	0.914798	+	0.403912i	$0.132350\pi$
$104$	−29.8583	−	25.0541i	−2.92785	−	2.45676i
$105$		0			0
$106$	31.8334	+	11.5864i	3.09193	+	1.12537i
$107$	2.29684	+	1.32608i	0.222044	+	0.128197i	0.606897	−	0.794781i	$-0.292414\pi$
$107$	2.29684	+	1.32608i	0.222044	+	0.128197i	−0.384852	+	0.922978i	$0.625748\pi$
$108$		0			0
$109$	5.69975	+	9.87226i	0.545937	+	0.945591i	0.998547	+	0.0538826i	$0.0171597\pi$
$109$	5.69975	+	9.87226i	0.545937	+	0.945591i	−0.452610	+	0.891709i	$0.649507\pi$
$110$	2.24115	−	1.88055i	0.213685	−	0.179303i
$111$		0			0
$112$	18.3791	−	1.30388i	1.73666	−	0.123205i
$113$	6.99660	+	1.23369i	0.658184	+	0.116056i	0.492758	−	0.870166i	$-0.335989\pi$
$113$	6.99660	+	1.23369i	0.658184	+	0.116056i	0.165427	+	0.986222i	$0.447100\pi$
$114$		0			0
$115$	−0.515452	+	1.41619i	−0.0480662	+	0.132061i
$116$	20.8718	+	12.0504i	1.93790	+	1.11885i
$117$		0			0
$118$	−23.9886	−	13.8498i	−2.20833	−	1.27498i
$119$	1.62631	−	0.726054i	0.149084	−	0.0665573i
$120$		0			0
$121$	0.847758	−	4.80788i	0.0770689	−	0.437080i
$122$	1.81854	+	1.52593i	0.164643	+	0.138152i
$123$		0			0
$124$	−10.5620	+	29.0189i	−0.948498	+	2.60598i
$125$	2.27664	−	3.94325i	0.203628	−	0.352695i
$126$		0			0
$127$	−4.69551	−	8.13286i	−0.416659	−	0.721675i	0.578942	−	0.815369i	$-0.303466\pi$
$127$	−4.69551	−	8.13286i	−0.416659	−	0.721675i	−0.995601	+	0.0936941i	$0.970132\pi$
$128$	−12.0237	+	2.12010i	−1.06275	+	0.187392i
$129$		0			0
$130$	−6.93245	+	2.52321i	−0.608016	+	0.221300i
$131$	−7.67063	+	2.79188i	−0.670186	+	0.243928i	−0.654628	−	0.755951i	$-0.727175\pi$
$131$	−7.67063	+	2.79188i	−0.670186	+	0.243928i	−0.0155582	+	0.999879i	$0.504953\pi$
$132$		0			0
$133$	−0.782333	−	1.75238i	−0.0678369	−	0.151950i
$134$		−	0.0611794i		−	0.00528510i
$135$		0			0
$136$	3.64314	−	2.10337i	0.312397	−	0.180362i
$137$	−20.1527	+	3.55346i	−1.72176	+	0.303593i	−0.945210	−	0.326464i	$-0.894143\pi$
$137$	−20.1527	+	3.55346i	−1.72176	+	0.303593i	−0.776549	+	0.630056i	$0.783032\pi$
$138$		0			0
$139$	0.533744	−	0.636091i	0.0452715	−	0.0539525i	−0.742934	−	0.669365i	$-0.766566\pi$
$139$	0.533744	−	0.636091i	0.0452715	−	0.0539525i	0.788205	+	0.615413i	$0.211011\pi$
$140$	2.40189	−	4.93727i	0.202996	−	0.417275i
$141$		0			0
$142$	−4.39761	−	24.9401i	−0.369039	−	2.09293i
$143$	7.71366	−	13.3605i	0.645049	−	1.11726i
$144$		0			0
$145$	2.17854	−	1.25778i	0.180918	−	0.104453i
$146$	−1.27009	−	7.20305i	−0.105114	−	0.596129i
$147$		0			0
$148$	−31.0424	+	11.2985i	−2.55167	+	0.928732i
$149$	−2.20568	−	0.388921i	−0.180696	−	0.0318616i	0.0825677	−	0.996585i	$-0.473688\pi$
$149$	−2.20568	−	0.388921i	−0.180696	−	0.0318616i	−0.263264	+	0.964724i	$0.584799\pi$
$150$		0			0
$151$	−2.25469	+	1.89191i	−0.183484	+	0.153961i	−0.729903	−	0.683550i	$-0.760435\pi$
$151$	−2.25469	+	1.89191i	−0.183484	+	0.153961i	0.546419	+	0.837512i	$0.315991\pi$
$152$	−2.26641	−	3.92553i	−0.183830	−	0.318403i
$153$		0			0
$154$	4.03985	+	16.1334i	0.325541	+	1.30007i
$155$	2.07189	+	2.46919i	0.166419	+	0.198330i
$156$		0			0
$157$	3.04333	+	8.36148i	0.242884	+	0.667319i	0.999903	+	0.0139259i	$0.00443289\pi$
$157$	3.04333	+	8.36148i	0.242884	+	0.667319i	−0.757019	+	0.653393i	$0.773345\pi$
$158$	2.75609	+	0.485973i	0.219263	+	0.0386620i
$159$		0			0
$160$	0.827810	−	2.27439i	0.0654441	−	0.179806i
$161$	−5.95769	−	6.15689i	−0.469531	−	0.485231i
$162$		0			0
$163$	0.888889	−	1.53960i	0.0696232	−	0.120591i	−0.829112	−	0.559082i	$-0.811154\pi$
$163$	0.888889	−	1.53960i	0.0696232	−	0.120591i	0.898735	+	0.438491i	$0.144487\pi$
$164$	2.92443	+	16.5853i	0.228359	+	1.29509i
$165$		0			0
$166$	4.59859	+	12.6345i	0.356920	+	0.980629i
$167$	−1.50485	+	8.53440i	−0.116448	+	0.660412i	0.869574	+	0.493802i	$0.164393\pi$
$167$	−1.50485	+	8.53440i	−0.116448	+	0.660412i	−0.986023	+	0.166610i	$0.946718\pi$
$168$		0			0
$169$	−19.8423	+	16.6496i	−1.52633	+	1.28074i
$170$		−	0.796224i		−	0.0610676i
$171$		0			0
$172$	36.3615			2.77254
$173$	−8.75822	−	3.18773i	−0.665875	−	0.242359i	−0.0131042	−	0.999914i	$-0.504171\pi$
$173$	−8.75822	−	3.18773i	−0.665875	−	0.242359i	−0.652771	+	0.757555i	$0.726394\pi$
$174$		0			0
$175$	7.08757	+	10.4849i	0.535770	+	0.792581i
$176$	5.89143	+	16.1866i	0.444083	+	1.22011i
$177$		0			0
$178$	−16.6674	−	19.8634i	−1.24928	−	1.48883i
$179$		−	11.4773i		−	0.857853i	−0.903339	−	0.428926i	$-0.858892\pi$
$179$		−	11.4773i		−	0.857853i	0.903339	−	0.428926i	$-0.141108\pi$
$180$		0			0
$181$	4.44357	−	2.56549i	0.330288	−	0.190692i	−0.325681	−	0.945480i	$-0.605594\pi$
$181$	4.44357	−	2.56549i	0.330288	−	0.190692i	0.655969	+	0.754788i	$0.272260\pi$
$182$	4.34160	−	41.7135i	0.321821	−	3.09201i
$183$		0			0
$184$	−15.5018	−	13.0075i	−1.14280	−	0.958927i
$185$	−0.598748	+	3.39567i	−0.0440208	+	0.249655i
$186$		0			0
$187$	1.07027	+	1.27549i	0.0782656	+	0.0932734i
$188$	−40.6991			−2.96829
$189$		0			0
$190$	−0.857942			−0.0622416
$191$	−11.2629	−	13.4226i	−0.814956	−	0.971227i	0.184977	−	0.982743i	$-0.440779\pi$
$191$	−11.2629	−	13.4226i	−0.814956	−	0.971227i	−0.999934	+	0.0115156i	$0.996334\pi$
$192$		0			0
$193$	−1.28928	+	7.31187i	−0.0928044	+	0.526320i	0.902594	+	0.430493i	$0.141660\pi$
$193$	−1.28928	+	7.31187i	−0.0928044	+	0.526320i	−0.995398	+	0.0958263i	$0.969451\pi$
$194$	36.2324	+	30.4026i	2.60133	+	2.18278i
$195$		0			0
$196$	19.2660	+	24.5568i	1.37614	+	1.75406i
$197$	−4.10505	+	2.37005i	−0.292473	+	0.168859i	−0.639057	−	0.769160i	$-0.720675\pi$
$197$	−4.10505	+	2.37005i	−0.292473	+	0.168859i	0.346584	+	0.938019i	$0.387342\pi$
$198$		0			0
$199$		−	6.70536i		−	0.475330i	−0.971347	−	0.237665i	$-0.923618\pi$
$199$		−	6.70536i		−	0.475330i	0.971347	−	0.237665i	$-0.0763821\pi$
$200$	19.2144	+	22.8989i	1.35867	+	1.61920i
$201$		0			0
$202$	0.926949	+	2.54677i	0.0652199	+	0.179190i
$203$	1.01198	+	14.2646i	0.0710271	+	1.00118i
$204$		0			0
$205$	1.65181	+	0.601211i	0.115368	+	0.0419904i
$206$	14.3720			1.00135
$207$		0			0
$208$		−	43.4364i		−	3.01177i
$209$	1.37436	−	1.15323i	0.0950666	−	0.0797704i
$210$		0			0
$211$	1.74430	−	9.89241i	0.120082	−	0.681021i	−0.864025	−	0.503449i	$-0.832064\pi$
$211$	1.74430	−	9.89241i	0.120082	−	0.681021i	0.984108	−	0.177573i	$-0.0568245\pi$
$212$	20.3282	+	55.8512i	1.39614	+	3.83587i
$213$		0			0
$214$	1.17045	+	6.63793i	0.0800100	+	0.453759i
$215$	1.89765	−	3.28683i	0.129419	−	0.224160i
$216$		0			0
$217$	−17.7750	+	4.45091i	−1.20665	+	0.302148i
$218$	−9.90872	+	27.2240i	−0.671103	+	1.84384i
$219$		0			0
$220$	5.05496	+	0.891326i	0.340806	+	0.0600932i
$221$	−1.43602	−	3.94543i	−0.0965971	−	0.265398i
$222$		0			0
$223$	−18.4562	−	21.9953i	−1.23592	−	1.47291i	−0.828806	−	0.559536i	$-0.810979\pi$
$223$	−18.4562	−	21.9953i	−1.23592	−	1.47291i	−0.407114	−	0.913377i	$-0.633465\pi$
$224$	9.56797	+	9.88788i	0.639287	+	0.660662i
$225$		0			0
$226$	9.02787	+	15.6367i	0.600525	+	1.04014i
$227$	−1.78346	+	1.49650i	−0.118373	+	0.0993265i	−0.700053	−	0.714091i	$-0.746840\pi$
$227$	−1.78346	+	1.49650i	−0.118373	+	0.0993265i	0.581680	+	0.813418i	$0.302396\pi$
$228$		0			0
$229$	11.0964	+	1.95659i	0.733268	+	0.129295i	0.527800	−	0.849369i	$-0.323017\pi$
$229$	11.0964	+	1.95659i	0.733268	+	0.129295i	0.205468	+	0.978664i	$0.434128\pi$
$230$	−3.59917	+	1.30999i	−0.237322	+	0.0863782i
$231$		0			0
$232$	5.86536	+	33.2641i	0.385080	+	2.18390i
$233$	11.5914	−	6.69231i	0.759379	−	0.438428i	−0.0696935	−	0.997568i	$-0.522202\pi$
$233$	11.5914	−	6.69231i	0.759379	−	0.438428i	0.829073	+	0.559141i	$0.188869\pi$
$234$		0			0
$235$	−2.12402	+	3.67892i	−0.138556	+	0.239986i
$236$	−8.43905	−	47.8602i	−0.549335	−	3.11544i
$237$		0			0
$238$	4.07028	+	1.98011i	0.263837	+	0.128352i
$239$	15.7161	−	18.7297i	1.01659	−	1.21152i	0.0393838	−	0.999224i	$-0.487461\pi$
$239$	15.7161	−	18.7297i	1.01659	−	1.21152i	0.977205	−	0.212299i	$-0.0680950\pi$
$240$		0			0
$241$	12.5428	−	2.21163i	0.807953	−	0.142464i	0.245611	−	0.969369i	$-0.421011\pi$
$241$	12.5428	−	2.21163i	0.807953	−	0.142464i	0.562342	+	0.826905i	$0.309900\pi$
$242$	10.7451	−	6.20371i	0.690724	−	0.398790i
$243$		0			0
$244$			4.16503i			0.266639i
$245$	3.22523	−	0.459933i	0.206052	−	0.0293840i
$246$		0			0
$247$	−4.25126	+	1.54733i	−0.270501	+	0.0984543i
$248$	−40.6702	+	14.8027i	−2.58256	+	0.939975i
$249$		0			0
$250$	11.3961	−	2.00943i	0.720750	−	0.127088i
$251$	2.40624	+	4.16774i	0.151881	+	0.263065i	0.931919	−	0.362667i	$-0.118134\pi$
$251$	2.40624	+	4.16774i	0.151881	+	0.263065i	−0.780038	+	0.625732i	$0.784800\pi$
$252$		0			0
$253$	4.00475	−	6.93644i	0.251777	−	0.436090i
$254$	8.16290	−	22.4274i	0.512186	−	1.40722i
$255$		0			0
$256$	−22.6795	−	19.0303i	−1.41747	−	1.18940i
$257$	0.124550	−	0.706359i	0.00776923	−	0.0440615i	−0.980677	−	0.195635i	$-0.937323\pi$
$257$	0.124550	−	0.706359i	0.00776923	−	0.0440615i	0.988446	+	0.151574i	$0.0484342\pi$
$258$		0			0
$259$	−15.8696	−	11.5054i	−0.986088	−	0.714912i
$260$	−11.2094	−	6.47174i	−0.695176	−	0.401360i
$261$		0			0
$262$	−17.9662	−	10.3728i	−1.10995	−	0.640833i
$263$	5.52218	−	15.1721i	0.340512	−	0.935550i	−0.644734	−	0.764407i	$-0.723032\pi$
$263$	5.52218	−	15.1721i	0.340512	−	0.935550i	0.985246	−	0.171143i	$-0.0547459\pi$
$264$		0			0
$265$	6.10945	+	1.07726i	0.375301	+	0.0661756i
$266$	2.13360	−	4.38578i	0.130819	−	0.268910i
$267$		0			0
$268$	0.0822259	−	0.0689958i	0.00502275	−	0.00421459i
$269$	−8.30293	−	14.3811i	−0.506238	−	0.876831i	−0.999974	−	0.00721846i	$-0.997702\pi$
$269$	−8.30293	−	14.3811i	−0.506238	−	0.876831i	0.493736	−	0.869612i	$-0.335631\pi$
$270$		0			0
$271$	−12.6238	−	7.28836i	−0.766842	−	0.442736i	0.0649049	−	0.997891i	$-0.479326\pi$
$271$	−12.6238	−	7.28836i	−0.766842	−	0.442736i	−0.831747	+	0.555155i	$0.812659\pi$
$272$	4.40528	+	1.60339i	0.267109	+	0.0972198i
$273$		0			0
$274$	−39.8396	−	33.4294i	−2.40680	−	2.01954i
$275$	−7.60513	+	9.06345i	−0.458607	+	0.546546i
$276$		0			0
$277$	−16.7060	−	6.08048i	−1.00377	−	0.365341i	−0.212730	−	0.977111i	$-0.568236\pi$
$277$	−16.7060	−	6.08048i	−1.00377	−	0.365341i	−0.791036	+	0.611770i	$0.790458\pi$
$278$	2.11030			0.126568
$279$		0			0
$280$	7.46451	−	1.86913i	0.446090	−	0.111702i
$281$	25.4750	−	4.49194i	1.51971	−	0.267967i	0.649393	−	0.760453i	$-0.275023\pi$
$281$	25.4750	−	4.49194i	1.51971	−	0.267967i	0.870320	+	0.492486i	$0.163912\pi$
$282$		0			0
$283$	1.54832	−	1.84522i	0.0920382	−	0.109687i	−0.718060	−	0.695982i	$-0.754970\pi$
$283$	1.54832	−	1.84522i	0.0920382	−	0.109687i	0.810098	+	0.586295i	$0.199414\pi$
$284$	28.5604	−	34.0369i	1.69475	−	2.01972i
$285$		0			0
$286$	38.6120	−	6.80833i	2.28317	−	0.402585i
$287$	−7.18124	+	6.94890i	−0.423895	+	0.410181i
$288$		0			0
$289$	−16.5468			−0.973344
$290$	6.00759	+	2.18658i	0.352778	+	0.128401i
$291$		0			0
$292$	8.24864	−	9.83035i	0.482715	−	0.575278i
$293$	−14.1349	−	11.8606i	−0.825772	−	0.692905i	0.128544	−	0.991704i	$-0.458970\pi$
$293$	−14.1349	−	11.8606i	−0.825772	−	0.692905i	−0.954316	+	0.298799i	$0.903414\pi$
$294$		0			0
$295$	−4.76665	−	1.73492i	−0.277525	−	0.101011i
$296$	−40.0954	−	23.1491i	−2.33050	−	1.34551i
$297$		0			0
$298$	−2.84604	−	4.92948i	−0.164867	−	0.285557i
$299$	−15.4719	+	12.9825i	−0.894764	+	0.750796i
$300$		0			0
$301$	12.0830	+	17.8747i	0.696451	+	1.03028i
$302$	−7.36655	−	1.29892i	−0.423897	−	0.0747446i
$303$		0			0
$304$	1.72767	−	4.74674i	0.0990889	−	0.272244i
$305$	0.376490	+	0.217366i	0.0215577	+	0.0124464i
$306$		0			0
$307$	−8.85587	−	5.11294i	−0.505431	−	0.291811i	0.225522	−	0.974238i	$-0.427591\pi$
$307$	−8.85587	−	5.11294i	−0.505431	−	0.291811i	−0.730954	+	0.682427i	$0.760924\pi$
$308$	−17.1275	+	23.6243i	−0.975932	+	1.34612i
$309$		0			0
$310$	−1.42249	+	8.06736i	−0.0807922	+	0.458195i
$311$	19.0106	+	15.9518i	1.07799	+	0.904542i	0.995752	−	0.0920711i	$-0.0293487\pi$
$311$	19.0106	+	15.9518i	1.07799	+	0.904542i	0.0822383	+	0.996613i	$0.473793\pi$
$312$		0			0
$313$	5.68370	−	15.6158i	0.321262	−	0.882659i	−0.668978	−	0.743283i	$-0.733268\pi$
$313$	5.68370	−	15.6158i	0.321262	−	0.882659i	0.990239	−	0.139377i	$-0.0445100\pi$
$314$	−11.3070	+	19.5843i	−0.638091	+	1.10521i
$315$		0			0
$316$	2.45506	+	4.25229i	0.138108	+	0.239210i
$317$	6.28264	−	1.10780i	0.352868	−	0.0622202i	0.00559547	−	0.999984i	$-0.498219\pi$
$317$	6.28264	−	1.10780i	0.352868	−	0.0622202i	0.347273	+	0.937764i	$0.387108\pi$
$318$		0			0
$319$	−12.5629	+	4.57252i	−0.703387	+	0.256012i
$320$	−0.311159	+	0.113253i	−0.0173943	+	0.00633102i
$321$		0			0
$322$	2.25406	−	21.6567i	0.125614	−	1.20688i
$323$		−	0.488276i		−	0.0271684i
$324$		0			0
$325$	25.8377	−	14.9174i	1.43322	−	0.827469i
$326$	4.44948	−	0.784563i	0.246434	−	0.0434529i
$327$		0			0
$328$	−15.1716	+	18.0809i	−0.837714	+	0.998349i
$329$	−13.5244	−	20.0070i	−0.745622	−	1.10302i
$330$		0			0
$331$	1.59919	+	9.06946i	0.0878994	+	0.498502i	0.996693	+	0.0812569i	$0.0258934\pi$
$331$	1.59919	+	9.06946i	0.0878994	+	0.498502i	−0.908794	+	0.417246i	$0.862995\pi$
$332$	−11.7949	+	20.4293i	−0.647327	+	1.12120i
$333$		0			0
$334$	−19.0736	+	11.0121i	−1.04366	+	0.602557i
$335$	−0.00194549	−	0.0110334i	−0.000106294	−	0.000602821i
$336$		0			0
$337$	−4.60865	+	1.67741i	−0.251049	+	0.0913745i	−0.464480	−	0.885584i	$-0.653759\pi$
$337$	−4.60865	+	1.67741i	−0.251049	+	0.0913745i	0.213430	+	0.976958i	$0.431536\pi$
$338$	−64.8289	−	11.4311i	−3.52623	−	0.621769i
$339$		0			0
$340$	1.07014	−	0.897950i	0.0580362	−	0.0486982i
$341$	−8.56524	−	14.8354i	−0.463834	−	0.803383i
$342$		0			0
$343$	−5.66959	+	17.6311i	−0.306129	+	0.951990i
$344$	32.7570	+	39.0383i	1.76614	+	2.10480i
$345$		0			0
$346$	−8.10143	−	22.2585i	−0.435535	−	1.19662i
$347$	−5.56398	−	0.981080i	−0.298690	−	0.0526671i	0.0222948	−	0.999751i	$-0.492903\pi$
$347$	−5.56398	−	0.981080i	−0.298690	−	0.0526671i	−0.320985	+	0.947084i	$0.604014\pi$
$348$		0			0
$349$	−1.55645	+	4.27631i	−0.0833149	+	0.228906i	−0.974354	−	0.225021i	$-0.927755\pi$
$349$	−1.55645	+	4.27631i	−0.0833149	+	0.228906i	0.891039	+	0.453927i	$0.149977\pi$
$350$	−8.83422	+	30.9266i	−0.472209	+	1.65310i
$351$		0			0
$352$	−6.43158	+	11.1398i	−0.342805	+	0.593755i
$353$	1.73370	+	9.83232i	0.0922758	+	0.523322i	0.995548	+	0.0942543i	$0.0300467\pi$
$353$	1.73370	+	9.83232i	0.0922758	+	0.523322i	−0.903272	+	0.429068i	$0.858842\pi$
$354$		0			0
$355$	−1.58618	−	4.35799i	−0.0841857	−	0.231298i
$356$	7.89988	−	44.8024i	0.418693	−	2.37452i
$357$		0			0
$358$	22.3446	−	18.7494i	1.18095	−	0.990935i
$359$			14.3758i			0.758725i	0.925248	+	0.379363i	$0.123857\pi$
$359$			14.3758i			0.758725i	−0.925248	+	0.379363i	$0.876143\pi$
$360$		0			0
$361$	18.4739			0.972309
$362$	12.2537	+	4.45998i	0.644039	+	0.234411i
$363$		0			0
$364$	60.9598	−	41.2077i	3.19516	−	2.15987i
$365$	−0.458111	−	1.25865i	−0.0239786	−	0.0658808i
$366$		0			0
$367$	22.8297	+	27.2074i	1.19170	+	1.42022i	0.883202	+	0.468992i	$0.155383\pi$
$367$	22.8297	+	27.2074i	1.19170	+	1.42022i	0.308501	+	0.951224i	$0.400173\pi$
$368$		−	22.5512i		−	1.17556i
$369$		0			0
$370$	−7.58900	+	4.38151i	−0.394533	+	0.227784i
$371$	−20.7004	+	28.5524i	−1.07471	+	1.48237i
$372$		0			0
$373$	−2.61050	−	2.19047i	−0.135167	−	0.113418i	0.572698	−	0.819767i	$-0.305897\pi$
$373$	−2.61050	−	2.19047i	−0.135167	−	0.113418i	−0.707865	+	0.706348i	$0.750341\pi$
$374$	−0.734809	+	4.16731i	−0.0379961	+	0.215486i
$375$		0			0
$376$	−36.6646	−	43.6952i	−1.89083	−	2.25341i
$377$	33.7123			1.73627
$378$		0			0
$379$	1.03172			0.0529960			0.0264980	−	0.999649i	$-0.491564\pi$
$379$	1.03172			0.0529960			0.0264980	+	0.999649i	$0.491564\pi$
$380$	−0.967553	−	1.15309i	−0.0496344	−	0.0591520i
$381$		0			0
$382$	7.73274	−	43.8546i	0.395642	−	2.24380i
$383$	2.52649	+	2.11998i	0.129098	+	0.108326i	0.705050	−	0.709157i	$-0.250924\pi$
$383$	2.52649	+	2.11998i	0.129098	+	0.108326i	−0.575953	+	0.817483i	$0.695369\pi$
$384$		0			0
$385$	1.24161	+	2.78112i	0.0632783	+	0.141739i
$386$	−16.3413	+	9.43467i	−0.831752	+	0.480212i
$387$		0			0
$388$			82.9837i			4.21286i
$389$	12.3070	+	14.6669i	0.623989	+	0.743641i	0.981751	−	0.190172i	$-0.0609045\pi$
$389$	12.3070	+	14.6669i	0.623989	+	0.743641i	−0.357762	+	0.933813i	$0.616460\pi$
$390$		0			0
$391$	−0.745548	−	2.04838i	−0.0377040	−	0.103591i
$392$	−9.00837	+	42.8068i	−0.454991	+	2.16207i
$393$		0			0
$394$	−11.3202	−	4.12021i	−0.570303	−	0.207573i
$395$	0.512503			0.0257868
$396$		0			0
$397$			15.7797i			0.791958i	0.918260	+	0.395979i	$0.129595\pi$
$397$			15.7797i			0.791958i	−0.918260	+	0.395979i	$0.870405\pi$
$398$	13.0544	−	10.9539i	0.654357	−	0.549070i
$399$		0			0
$400$	−5.78459	+	32.8060i	−0.289229	+	1.64030i
$401$	9.81387	+	26.9634i	0.490081	+	1.34649i	0.900606	+	0.434637i	$0.143123\pi$
$401$	9.81387	+	26.9634i	0.490081	+	1.34649i	−0.410525	+	0.911850i	$0.634654\pi$
$402$		0			0
$403$	7.50108	+	42.5407i	0.373655	+	2.11911i
$404$	−2.37752	+	4.11798i	−0.118286	+	0.204877i
$405$		0			0
$406$	−26.1179	+	25.2729i	−1.29621	+	1.25427i
$407$	6.26751	−	17.2198i	0.310669	−	0.853555i
$408$		0			0
$409$	−0.828634	−	0.146111i	−0.0409733	−	0.00722470i	0.153124	−	0.988207i	$-0.451067\pi$
$409$	−0.828634	−	0.146111i	−0.0409733	−	0.00722470i	−0.194097	+	0.980982i	$0.562178\pi$
$410$	1.52794	+	4.19798i	0.0754596	+	0.207324i
$411$		0			0
$412$	16.2082	+	19.3162i	0.798522	+	0.951642i
$413$	20.7230	−	20.0525i	1.01971	−	0.986719i
$414$		0			0
$415$	1.23111	+	2.13235i	0.0604328	+	0.104673i
$416$	24.8477	−	20.8497i	1.21826	−	1.02224i
$417$		0			0
$418$	4.49033	+	0.791767i	0.219629	+	0.0387266i
$419$	14.6826	−	5.34404i	0.717294	−	0.261073i	0.0425171	−	0.999096i	$-0.486462\pi$
$419$	14.6826	−	5.34404i	0.717294	−	0.261073i	0.674776	+	0.738022i	$0.264240\pi$
$420$		0			0
$421$	−5.15879	−	29.2570i	−0.251424	−	1.42590i	−0.805088	−	0.593156i	$-0.797882\pi$
$421$	−5.15879	−	29.2570i	−0.251424	−	1.42590i	0.553663	−	0.832740i	$-0.313229\pi$
$422$	22.1086	−	12.7644i	1.07623	−	0.621361i
$423$		0			0
$424$	−41.6496	+	72.1392i	−2.02268	+	3.50339i
$425$	0.559149	+	3.17109i	0.0271227	+	0.153821i
$426$		0			0
$427$	−2.04746	+	1.38404i	−0.0990834	+	0.0669786i
$428$	−7.60148	+	9.05909i	−0.367431	+	0.437888i
$429$		0			0
$430$	9.49900	−	1.67493i	0.458082	−	0.0807723i
$431$	−31.9989	+	18.4746i	−1.54133	+	0.889889i	−0.542577	+	0.840006i	$0.682551\pi$
$431$	−31.9989	+	18.4746i	−1.54133	+	0.889889i	−0.998755	+	0.0498828i	$0.984115\pi$
$432$		0			0
$433$			9.86033i			0.473857i	0.971527	+	0.236929i	$0.0761407\pi$
$433$			9.86033i			0.473857i	−0.971527	+	0.236929i	$0.923859\pi$
$434$	−37.7026	−	27.3343i	−1.80978	−	1.31209i
$435$		0			0
$436$	−47.7641	+	17.3847i	−2.28748	+	0.832576i
$437$	−2.20715	+	0.803338i	−0.105582	+	0.0384289i
$438$		0			0
$439$	−35.0476	+	6.17984i	−1.67273	+	0.294948i	−0.928045	−	0.372467i	$-0.878512\pi$
$439$	−35.0476	+	6.17984i	−1.67273	+	0.294948i	−0.744686	+	0.667415i	$0.767401\pi$
$440$	3.59692	+	6.23005i	0.171477	+	0.297006i
$441$		0			0
$442$	5.33530	−	9.24101i	0.253774	−	0.439550i
$443$	4.55230	−	12.5073i	0.216286	−	0.594241i	−0.783340	−	0.621594i	$-0.786485\pi$
$443$	4.55230	−	12.5073i	0.216286	−	0.594241i	0.999626	+	0.0273526i	$0.00870769\pi$
$444$		0			0
$445$	−3.63755	−	3.05226i	−0.172436	−	0.144691i
$446$	12.6714	−	71.8633i	0.600010	−	3.40282i
$447$		0			0
$448$	0.194870	−	1.87229i	0.00920676	−	0.0884572i
$449$	6.46903	+	3.73490i	0.305293	+	0.176261i	0.644818	−	0.764336i	$-0.276933\pi$
$449$	6.46903	+	3.73490i	0.305293	+	0.176261i	−0.339525	+	0.940597i	$0.610266\pi$
$450$		0			0
$451$	−8.09049	−	4.67105i	−0.380966	−	0.219951i
$452$	−10.8347	+	29.7681i	−0.509621	+	1.40017i
$453$		0			0
$454$	−5.82696	−	1.02745i	−0.273473	−	0.0482206i
$455$	−0.543492	−	7.66091i	−0.0254793	−	0.359149i
$456$		0			0
$457$	−19.8548	+	16.6602i	−0.928770	+	0.779331i	−0.975596	−	0.219572i	$-0.929534\pi$
$457$	−19.8548	+	16.6602i	−0.928770	+	0.779331i	0.0468260	+	0.998903i	$0.485089\pi$
$458$	14.3179	+	24.7993i	0.669031	+	1.15880i
$459$		0			0
$460$	−5.81965	−	3.35998i	−0.271343	−	0.156660i
$461$	23.7286	+	8.63651i	1.10515	+	0.402242i	0.829213	−	0.558933i	$-0.188789\pi$
$461$	23.7286	+	8.63651i	1.10515	+	0.402242i	0.275939	+	0.961175i	$0.411011\pi$
$462$		0			0
$463$	15.4294	+	12.9468i	0.717064	+	0.601688i	0.926571	−	0.376119i	$-0.122742\pi$
$463$	15.4294	+	12.9468i	0.717064	+	0.601688i	−0.209508	+	0.977807i	$0.567186\pi$
$464$	−24.1955	+	28.8350i	−1.12325	+	1.33863i
$465$		0			0
$466$	31.9648	+	11.6342i	1.48074	+	0.538945i
$467$	−4.31501			−0.199675			−0.0998373	−	0.995004i	$-0.531832\pi$
$467$	−4.31501			−0.199675			−0.0998373	+	0.995004i	$0.531832\pi$
$468$		0			0
$469$	0.0612409	+	0.0174935i	0.00282784	+	0.000807776i
$470$	−10.6321	+	1.87473i	−0.490424	+	0.0864750i
$471$		0			0
$472$	43.7810	−	52.1761i	2.01518	−	2.40160i
$473$	−12.9653	+	15.4515i	−0.596146	+	0.710459i
$474$		0			0
$475$	3.41690	−	0.602491i	0.156778	−	0.0276442i
$476$	1.92901	+	7.70361i	0.0884158	+	0.353094i
$477$		0			0
$478$	62.1379			2.84212
$479$	−1.80247	−	0.656045i	−0.0823569	−	0.0299755i	0.300513	−	0.953778i	$-0.402842\pi$
$479$	−1.80247	−	0.656045i	−0.0823569	−	0.0299755i	−0.382870	+	0.923802i	$0.625064\pi$
$480$		0			0
$481$	−29.7026	+	35.3982i	−1.35432	+	1.61402i
$482$	24.7957	+	20.8061i	1.12941	+	0.947692i
$483$		0			0
$484$	20.4558	+	7.44531i	0.929811	+	0.338423i
$485$	7.50115	+	4.33079i	0.340610	+	0.196651i
$486$		0			0
$487$	−10.2277	−	17.7149i	−0.463461	−	0.802738i	0.535670	−	0.844428i	$-0.320059\pi$
$487$	−10.2277	−	17.7149i	−0.463461	−	0.802738i	−0.999131	+	0.0416897i	$0.986726\pi$
$488$	−4.47163	+	3.75215i	−0.202421	+	0.169852i
$489$		0			0
$490$	6.16417	+	5.52770i	0.278469	+	0.249716i
$491$	−27.9607	−	4.93023i	−1.26185	−	0.222498i	−0.497593	−	0.867411i	$-0.665783\pi$
$491$	−27.9607	−	4.93023i	−1.26185	−	0.222498i	−0.764256	+	0.644912i	$0.776894\pi$
$492$		0			0
$493$	−1.24444	+	3.41907i	−0.0560467	+	0.153987i
$494$	−9.95731	−	5.74885i	−0.448000	−	0.258653i
$495$		0			0
$496$	−41.7698	−	24.1158i	−1.87552	−	1.08283i
$497$	26.2226	+	2.72929i	1.17625	+	0.122425i
$498$		0			0
$499$	4.06570	−	23.0577i	0.182006	−	1.03220i	−0.747737	−	0.663995i	$-0.768860\pi$
$499$	4.06570	−	23.0577i	0.182006	−	1.03220i	0.929743	−	0.368210i	$-0.120029\pi$
$500$	15.5527	+	13.0503i	0.695540	+	0.583627i
$501$		0			0
$502$	−4.18313	+	11.4930i	−0.186702	+	0.512960i
$503$	−5.80401	+	10.0528i	−0.258788	+	0.448234i	−0.965918	−	0.258850i	$-0.916656\pi$
$503$	−5.80401	+	10.0528i	−0.258788	+	0.448234i	0.707129	+	0.707084i	$0.249990\pi$
$504$		0			0
$505$	0.248158	+	0.429822i	0.0110429	+	0.0191268i
$506$	20.0464	−	3.53473i	0.891173	−	0.157138i
$507$		0			0
$508$	39.3485	−	14.3217i	1.74581	−	0.635422i
$509$	−16.5581	+	6.02667i	−0.733926	+	0.267127i	−0.681826	−	0.731515i	$-0.738814\pi$
$509$	−16.5581	+	6.02667i	−0.733926	+	0.267127i	−0.0521003	+	0.998642i	$0.516592\pi$
$510$		0			0
$511$	7.57347	+	0.788257i	0.335030	+	0.0348705i
$512$		−	50.8234i		−	2.24610i
$513$		0			0
$514$	1.57865	−	0.911432i	0.0696311	−	0.0402015i
$515$	2.59193	−	0.457028i	0.114214	−	0.0201391i
$516$		0			0
$517$	14.5120	−	17.2947i	0.638235	−	0.760619i
$518$	−3.52526	−	49.6911i	−0.154891	−	2.18330i
$519$		0			0
$520$	−3.15004	−	17.8647i	−0.138138	−	0.783421i
$521$	−12.9686	+	22.4622i	−0.568164	+	0.984088i	0.428584	+	0.903502i	$0.359013\pi$
$521$	−12.9686	+	22.4622i	−0.568164	+	0.984088i	−0.996748	+	0.0805864i	$0.974321\pi$
$522$		0			0
$523$	3.19247	−	1.84317i	0.139597	−	0.0805962i	−0.428575	−	0.903506i	$-0.640984\pi$
$523$	3.19247	−	1.84317i	0.139597	−	0.0805962i	0.568172	+	0.822910i	$0.307651\pi$
$524$	−6.32041	−	35.8448i	−0.276108	−	1.56589i
$525$		0			0
$526$	38.5589	−	14.0343i	1.68125	−	0.611924i
$527$	−4.59134	−	0.809576i	−0.200002	−	0.0352657i
$528$		0			0
$529$	9.58636	−	8.04391i	0.416798	−	0.349735i
$530$	7.88317	+	13.6540i	0.342423	+	0.593094i
$531$		0			0
$532$	8.30074	−	2.07853i	0.359883	−	0.0901157i
$533$	15.1424	+	18.0461i	0.655892	+	0.781662i
$534$		0			0
$535$	0.422169	+	1.15990i	0.0182520	+	0.0501469i
$536$	0.148150	+	0.0261228i	0.00639909	+	0.00112833i
$537$		0			0
$538$	14.4342	−	39.6576i	0.622303	−	1.70976i
$539$	−17.3048	−	0.569242i	−0.745370	−	0.0245190i
$540$		0			0
$541$	−12.7616	+	22.1037i	−0.548663	+	0.950313i	0.449703	+	0.893178i	$0.351530\pi$
$541$	−12.7616	+	22.1037i	−0.548663	+	0.950313i	−0.998366	+	0.0571349i	$0.981803\pi$
$542$	−6.43295	−	36.4831i	−0.276319	−	1.56708i
$543$		0			0
$544$	1.19734	+	3.28967i	0.0513356	+	0.141043i
$545$	−0.921277	+	5.22482i	−0.0394632	+	0.223807i
$546$		0			0
$547$	−5.90120	+	4.95170i	−0.252317	+	0.211719i	−0.760169	−	0.649725i	$-0.774884\pi$
$547$	−5.90120	+	4.95170i	−0.252317	+	0.211719i	0.507852	+	0.861444i	$0.330440\pi$
$548$		−	91.2454i		−	3.89781i
$549$		0			0
$550$	−30.0690			−1.28215
$551$	3.68409	+	1.34090i	0.156948	+	0.0571242i
$552$		0			0
$553$	−1.27453	+	2.61990i	−0.0541987	+	0.111410i
$554$	−15.4532	−	42.4573i	−0.656543	−	1.80384i
$555$		0			0
$556$	2.37992	+	2.83628i	0.100931	+	0.120285i
$557$			1.54966i			0.0656610i	0.999461	+	0.0328305i	$0.0104522\pi$
$557$			1.54966i			0.0656610i	−0.999461	+	0.0328305i	$0.989548\pi$
$558$		0			0
$559$	44.0484	−	25.4314i	1.86305	−	1.07563i
$560$	6.94265	+	5.03341i	0.293381	+	0.212700i
$561$		0			0
$562$	50.3613	+	42.2582i	2.12437	+	1.78255i
$563$	4.28366	−	24.2938i	0.180535	−	1.02386i	−0.751025	−	0.660274i	$-0.770440\pi$
$563$	4.28366	−	24.2938i	0.180535	−	1.02386i	0.931559	−	0.363589i	$-0.118449\pi$
$564$		0			0
$565$	2.12538	+	2.53293i	0.0894154	+	0.106561i
$566$	6.12172			0.257315
$567$		0			0
$568$	62.2717			2.61286
$569$	17.4658	+	20.8149i	0.732204	+	0.872606i	0.995755	−	0.0920390i	$-0.0293384\pi$
$569$	17.4658	+	20.8149i	0.732204	+	0.872606i	−0.263552	+	0.964645i	$0.584894\pi$
$570$		0			0
$571$	2.74433	−	15.5639i	0.114847	−	0.651329i	−0.871979	−	0.489543i	$-0.837164\pi$
$571$	2.74433	−	15.5639i	0.114847	−	0.651329i	0.986826	−	0.161786i	$-0.0517253\pi$
$572$	52.6956	+	44.2168i	2.20331	+	1.84880i
$573$		0			0
$574$	−25.2598	−	2.62908i	−1.05432	−	0.109736i
$575$	13.4144	−	7.74478i	0.559417	−	0.322980i
$576$		0			0
$577$			16.3564i			0.680925i	0.940258	+	0.340463i	$0.110584\pi$
$577$			16.3564i			0.680925i	−0.940258	+	0.340463i	$0.889416\pi$
$578$	−27.0310	−	32.2143i	−1.12434	−	1.33994i
$579$		0			0
$580$	3.83633	+	10.5402i	0.159295	+	0.437659i
$581$	−13.9621	+	0.990523i	−0.579247	+	0.0410938i
$582$		0			0
$583$	−30.9817	−	11.2764i	−1.28313	−	0.467022i
$584$	17.9850			0.744223
$585$		0			0
$586$		−	46.8943i		−	1.93719i
$587$	2.06287	−	1.73095i	0.0851436	−	0.0714439i	−0.599222	−	0.800583i	$-0.704524\pi$
$587$	2.06287	−	1.73095i	0.0851436	−	0.0714439i	0.684366	+	0.729139i	$0.260079\pi$
$588$		0			0
$589$	−0.872329	+	4.94723i	−0.0359437	+	0.203847i
$590$	−4.40920	−	12.1142i	−0.181524	−	0.498732i
$591$		0			0
$592$	−8.95934	−	50.8110i	−0.368227	−	2.08832i
$593$	−3.92320	+	6.79519i	−0.161107	+	0.279045i	−0.935266	−	0.353946i	$-0.884840\pi$
$593$	−3.92320	+	6.79519i	−0.161107	+	0.279045i	0.774159	+	0.632991i	$0.218173\pi$
$594$		0			0
$595$	0.797025	+	0.227671i	0.0326748	+	0.00933359i
$596$	3.41564	−	9.38439i	0.139910	−	0.384400i
$597$		0			0
$598$	−50.5500	−	8.91334i	−2.06714	−	0.364493i
$599$	11.3767	+	31.2573i	0.464840	+	1.27714i	0.921805	+	0.387653i	$0.126714\pi$
$599$	11.3767	+	31.2573i	0.464840	+	1.27714i	−0.456965	+	0.889485i	$0.651064\pi$
$600$		0			0
$601$	21.4176	+	25.5245i	0.873642	+	1.04117i	0.998797	+	0.0490291i	$0.0156127\pi$
$601$	21.4176	+	25.5245i	0.873642	+	1.04117i	−0.125155	+	0.992137i	$0.539943\pi$
$602$	−15.0607	+	52.7241i	−0.613827	+	2.14887i
$603$		0			0
$604$	−6.56194	−	11.3656i	−0.267002	−	0.462460i
$605$	1.74056	−	1.46051i	0.0707639	−	0.0593780i
$606$		0			0
$607$	12.7757	+	2.25270i	0.518549	+	0.0914341i	0.426796	−	0.904348i	$-0.359642\pi$
$607$	12.7757	+	2.25270i	0.518549	+	0.0914341i	0.0917522	+	0.995782i	$0.470753\pi$
$608$	3.54466	−	1.29015i	0.143755	−	0.0523225i
$609$		0			0
$610$	0.191855	+	1.08806i	0.00776797	+	0.0440543i
$611$	−49.3030	+	28.4651i	−1.99459	+	1.15157i
$612$		0			0
$613$	20.5385	−	35.5738i	0.829543	−	1.43681i	−0.0688544	−	0.997627i	$-0.521934\pi$
$613$	20.5385	−	35.5738i	0.829543	−	1.43681i	0.898397	−	0.439184i	$-0.144732\pi$
$614$	−4.51285	−	25.5936i	−0.182124	−	1.03287i
$615$		0			0
$616$	−40.7930	+	2.89400i	−1.64360	+	0.116603i
$617$	14.4145	−	17.1786i	0.580307	−	0.691583i	−0.393405	−	0.919365i	$-0.628703\pi$
$617$	14.4145	−	17.1786i	0.580307	−	0.691583i	0.973712	+	0.227782i	$0.0731473\pi$
$618$		0			0
$619$	30.2635	−	5.33627i	1.21639	−	0.214483i	0.471621	−	0.881801i	$-0.343669\pi$
$619$	30.2635	−	5.33627i	1.21639	−	0.214483i	0.744772	+	0.667318i	$0.232558\pi$
$620$	−12.4469	+	7.18621i	−0.499879	+	0.288605i
$621$		0			0
$622$			63.0698i			2.52887i
$623$	24.6493	−	11.0045i	0.987552	−	0.440884i
$624$		0			0
$625$	−20.4833	+	7.45530i	−0.819331	+	0.298212i
$626$	39.6867	−	14.4448i	1.58620	−	0.577330i
$627$		0			0
$628$	−39.0732	+	6.88965i	−1.55919	+	0.274927i
$629$	−2.49363	−	4.31909i	−0.0994274	−	0.172213i
$630$		0			0
$631$	−1.19417	+	2.06836i	−0.0475391	+	0.0823402i	−0.888816	−	0.458265i	$-0.848471\pi$
$631$	−1.19417	+	2.06836i	−0.0475391	+	0.0823402i	0.841277	+	0.540605i	$0.181805\pi$
$632$	−2.35363	+	6.46654i	−0.0936223	+	0.257225i
$633$		0			0
$634$	12.4201	+	10.4217i	0.493265	+	0.413898i
$635$	0.758956	−	4.30426i	0.0301183	−	0.170809i
$636$		0			0
$637$	40.5140	+	16.2734i	1.60522	+	0.644777i
$638$	−29.4248	−	16.9884i	−1.16494	−	0.672579i
$639$		0			0
$640$	−4.92097	−	2.84113i	−0.194519	−	0.112305i
$641$	8.06378	−	22.1550i	0.318500	−	0.875072i	−0.672366	−	0.740219i	$-0.734722\pi$
$641$	8.06378	−	22.1550i	0.318500	−	0.875072i	0.990866	−	0.134852i	$-0.0430560\pi$
$642$		0			0
$643$	35.0530	+	6.18079i	1.38236	+	0.243746i	0.814873	−	0.579639i	$-0.196807\pi$
$643$	35.0530	+	6.18079i	1.38236	+	0.243746i	0.567482	+	0.823386i	$0.307918\pi$
$644$	31.6489	−	21.3941i	1.24714	−	0.843045i
$645$		0			0
$646$	0.950603	−	0.797651i	0.0374010	−	0.0313832i
$647$	−8.19674	−	14.1972i	−0.322247	−	0.558148i	0.658704	−	0.752402i	$-0.271105\pi$
$647$	−8.19674	−	14.1972i	−0.322247	−	0.558148i	−0.980951	+	0.194254i	$0.937772\pi$
$648$		0			0
$649$	23.3468	+	13.4793i	0.916443	+	0.529108i
$650$	71.2507	+	25.9331i	2.79468	+	1.01718i
$651$		0			0
$652$	6.07241	+	5.09536i	0.237814	+	0.199550i
$653$	−2.22308	+	2.64937i	−0.0869960	+	0.103678i	−0.807786	−	0.589475i	$-0.799335\pi$
$653$	−2.22308	+	2.64937i	−0.0869960	+	0.103678i	0.720790	+	0.693153i	$0.243779\pi$
$654$		0			0
$655$	−3.56997	−	1.29936i	−0.139490	−	0.0507704i
$656$	−26.3031			−1.02696
$657$		0			0
$658$	16.8573	−	59.0135i	0.657165	−	2.30059i
$659$	−22.4506	+	3.95865i	−0.874551	+	0.154207i	−0.592867	−	0.805300i	$-0.702004\pi$
$659$	−22.4506	+	3.95865i	−0.874551	+	0.154207i	−0.281684	+	0.959507i	$0.590893\pi$
$660$		0			0
$661$	−8.28313	+	9.87145i	−0.322176	+	0.383955i	−0.902687	−	0.430298i	$-0.858409\pi$
$661$	−8.28313	+	9.87145i	−0.322176	+	0.383955i	0.580511	+	0.814253i	$0.302853\pi$
$662$	−15.0445	+	17.9293i	−0.584720	+	0.696843i
$663$		0			0
$664$	−32.5588	+	5.74100i	−1.26353	+	0.222794i
$665$	0.245318	−	0.858805i	0.00951303	−	0.0333030i
$666$		0			0
$667$	17.5026			0.677704
$668$	−36.3109	−	13.2161i	−1.40491	−	0.511346i
$669$		0			0
$670$	0.0183023	−	0.0218119i	0.000707081	−	0.000842667i
$671$	−1.76989	−	1.48511i	−0.0683257	−	0.0573321i
$672$		0			0
$673$	−7.15895	−	2.60564i	−0.275957	−	0.100440i	0.200334	−	0.979728i	$-0.435797\pi$
$673$	−7.15895	−	2.60564i	−0.275957	−	0.100440i	−0.476292	+	0.879287i	$0.658019\pi$
$674$	−10.7944	−	6.23215i	−0.415785	−	0.240054i
$675$		0			0
$676$	−57.7480	−	100.022i	−2.22108	−	3.84702i
$677$	31.8604	−	26.7340i	1.22449	−	1.02747i	0.225917	−	0.974147i	$-0.427462\pi$
$677$	31.8604	−	26.7340i	1.22449	−	1.02747i	0.998577	−	0.0533258i	$-0.0169822\pi$
$678$		0			0
$679$	−40.7934	+	27.5756i	−1.56551	+	1.05825i
$680$	1.92811	+	0.339977i	0.0739395	+	0.0130375i
$681$		0			0
$682$	14.8902	−	40.9105i	0.570176	−	1.56655i
$683$	29.6444	+	17.1152i	1.13431	+	0.654896i	0.945016	−	0.327024i	$-0.106046\pi$
$683$	29.6444	+	17.1152i	1.13431	+	0.654896i	0.189297	+	0.981920i	$0.439379\pi$
$684$		0			0
$685$	−8.24795	−	4.76195i	−0.315138	−	0.181945i
$686$	−43.5871	+	17.7644i	−1.66416	+	0.678248i
$687$		0			0
$688$	−9.86163	+	55.9281i	−0.375971	+	2.13224i
$689$	63.6881	+	53.4406i	2.42632	+	2.03593i
$690$		0			0
$691$	−1.43134	+	3.93259i	−0.0544509	+	0.149603i	−0.963936	−	0.266134i	$-0.914254\pi$
$691$	−1.43134	+	3.93259i	−0.0544509	+	0.149603i	0.909485	+	0.415736i	$0.136476\pi$
$692$	20.7792	−	35.9907i	0.789908	−	1.36816i
$693$		0			0
$694$	−7.17933	−	12.4350i	−0.272524	−	0.472025i
$695$	0.380584	−	0.0671072i	0.0144364	−	0.00254552i
$696$		0			0
$697$	−2.38918	+	0.869589i	−0.0904965	+	0.0329380i
$698$	−10.8680	+	3.95563i	−0.411360	+	0.149723i
$699$		0			0
$700$	−51.5287	+	23.0045i	−1.94760	+	0.869490i
$701$			12.5933i			0.475643i	0.971309	+	0.237821i	$0.0764333\pi$
$701$			12.5933i			0.475643i	−0.971309	+	0.237821i	$0.923567\pi$
$702$		0			0
$703$	−4.65387	+	2.68692i	−0.175524	+	0.101339i
$704$	1.73308	−	0.305588i	0.0653178	−	0.0115173i
$705$		0			0
$706$	−16.3099	+	19.4374i	−0.613832	+	0.731537i
$707$	−2.81438	+	0.199662i	−0.105846	+	0.00750907i
$708$		0			0
$709$	−1.30698	−	7.41224i	−0.0490846	−	0.278373i	0.950380	−	0.311091i	$-0.100695\pi$
$709$	−1.30698	−	7.41224i	−0.0490846	−	0.278373i	−0.999465	+	0.0327188i	$0.989583\pi$
$710$	5.89319	−	10.2073i	0.221168	−	0.383073i
$711$		0			0
$712$	55.2173	−	31.8797i	2.06936	−	1.19474i
$713$	3.89439	+	22.0862i	0.145846	+	0.827134i
$714$		0			0
$715$	6.74699	−	2.45570i	0.252323	−	0.0918381i
$716$	50.3988	+	8.88667i	1.88349	+	0.332110i
$717$		0			0
$718$	−27.9876	+	23.4844i	−1.04449	+	0.876430i
$719$	18.9465	+	32.8163i	0.706585	+	1.22384i	0.966117	+	0.258106i	$0.0830985\pi$
$719$	18.9465	+	32.8163i	0.706585	+	1.22384i	−0.259532	+	0.965735i	$0.583568\pi$
$720$		0			0
$721$	−4.10951	+	14.3865i	−0.153046	+	0.535781i
$722$	30.1790	+	35.9660i	1.12315	+	1.33852i
$723$		0			0
$724$	7.82496	+	21.4989i	0.290812	+	0.799001i
$725$	−25.4617	−	4.48959i	−0.945626	−	0.166739i
$726$		0			0
$727$	−6.98614	+	19.1943i	−0.259102	+	0.711876i	0.740122	+	0.672473i	$0.234768\pi$
$727$	−6.98614	+	19.1943i	−0.259102	+	0.711876i	−0.999223	+	0.0394032i	$0.987454\pi$
$728$	99.1580	+	28.3246i	3.67504	+	1.04978i
$729$		0			0
$730$	1.70204	−	2.94802i	0.0629952	−	0.109111i
$731$	0.953244	+	5.40612i	0.0352570	+	0.199952i
$732$		0			0
$733$	−9.86692	−	27.1092i	−0.364443	−	1.00130i	−0.977440	−	0.211214i	$-0.932258\pi$
$733$	−9.86692	−	27.1092i	−0.364443	−	1.00130i	0.612997	−	0.790085i	$-0.289964\pi$
$734$	−15.6741	+	88.8925i	−0.578543	+	3.28108i
$735$		0			0
$736$	12.9004	−	10.8247i	0.475513	−	0.399003i
$737$			0.0595427i			0.00219328i
$738$		0			0
$739$	26.5104			0.975200			0.487600	−	0.873067i	$-0.337872\pi$
$739$	26.5104			0.975200			0.487600	+	0.873067i	$0.337872\pi$
$740$	−14.4474	−	5.25842i	−0.531096	−	0.193303i
$741$		0			0
$742$	−89.4037	+	6.34261i	−3.28211	+	0.232845i
$743$	−2.96176	−	8.13736i	−0.108656	−	0.298531i	0.873434	−	0.486943i	$-0.161888\pi$
$743$	−2.96176	−	8.13736i	−0.108656	−	0.298531i	−0.982090	+	0.188412i	$0.939666\pi$
$744$		0			0
$745$	−0.670027	−	0.798507i	−0.0245479	−	0.0292550i
$746$		−	8.66064i		−	0.317089i
$747$		0			0
$748$	−6.42961	+	3.71214i	−0.235090	+	0.135729i
$749$	−6.97928	−	0.726413i	−0.255017	−	0.0265426i
$750$		0			0
$751$	4.87548	+	4.09101i	0.177909	+	0.149283i	0.727394	−	0.686221i	$-0.240732\pi$
$751$	4.87548	+	4.09101i	0.177909	+	0.149283i	−0.549485	+	0.835504i	$0.685176\pi$
$752$	11.0380	−	62.5998i	0.402515	−	2.28278i
$753$		0			0
$754$	55.0726	+	65.6329i	2.00562	+	2.39021i
$755$	−1.36983			−0.0498532
$756$		0			0
$757$	19.8369			0.720983			0.360492	−	0.932762i	$-0.382609\pi$
$757$	19.8369			0.720983			0.360492	+	0.932762i	$0.382609\pi$
$758$	1.68543	+	2.00861i	0.0612174	+	0.0729561i
$759$		0			0
$760$	0.366330	−	2.07756i	0.0132882	−	0.0753610i
$761$	−38.5154	−	32.3183i	−1.39618	−	1.17154i	−0.962764	−	0.270344i	$-0.912863\pi$
$761$	−38.5154	−	32.3183i	−1.39618	−	1.17154i	−0.433419	−	0.901192i	$-0.642693\pi$
$762$		0			0
$763$	−24.4181	−	17.7031i	−0.883994	−	0.640894i
$764$	67.6618	−	39.0646i	2.44792	−	1.41331i
$765$		0			0
$766$			8.38193i			0.302851i
$767$	−43.6967	−	52.0757i	−1.57780	−	1.88034i
$768$		0			0
$769$	−10.8973	−	29.9402i	−0.392968	−	1.07967i	−0.965640	−	0.259885i	$-0.916315\pi$
$769$	−10.8973	−	29.9402i	−0.392968	−	1.07967i	0.572672	−	0.819785i	$-0.305907\pi$
$770$	−3.38615	+	6.96050i	−0.122028	+	0.250839i
$771$		0			0
$772$	−31.1094	−	11.3229i	−1.11965	−	0.407520i
$773$	24.1518			0.868679			0.434339	−	0.900749i	$-0.356982\pi$
$773$	24.1518			0.868679			0.434339	+	0.900749i	$0.356982\pi$
$774$		0			0
$775$		−	33.1286i		−	1.19001i
$776$	−89.0925	+	74.7575i	−3.19823	+	2.68364i
$777$		0			0
$778$	−8.44957	+	47.9199i	−0.302932	+	1.71801i
$779$	0.936994	+	2.57437i	0.0335713	+	0.0922364i
$780$		0			0
$781$	4.27996	+	24.2729i	0.153149	+	0.868552i
$782$	2.76996	−	4.79772i	0.0990537	−	0.171566i
$783$		0			0
$784$	−42.9963	+	22.9732i	−1.53558	+	0.820472i
$785$	−1.41639	+	3.89150i	−0.0505532	+	0.138894i
$786$		0			0
$787$	9.90805	+	1.74706i	0.353184	+	0.0622758i	0.347425	−	0.937708i	$-0.387056\pi$
$787$	9.90805	+	1.74706i	0.353184	+	0.0622758i	0.00575824	+	0.999983i	$0.498167\pi$
$788$	−7.22885	−	19.8611i	−0.257517	−	0.707523i
$789$		0			0
$790$	0.837228	+	0.997769i	0.0297872	+	0.0354990i
$791$	−18.2339	+	4.56581i	−0.648322	+	0.162342i
$792$		0			0
$793$	2.91304	+	5.04552i	0.103445	+	0.179172i
$794$	−30.7207	+	25.7777i	−1.09024	+	0.914818i
$795$		0			0
$796$	29.4444	+	5.19185i	1.04363	+	0.184020i
$797$	−21.8937	+	7.96866i	−0.775515	+	0.282264i	−0.699301	−	0.714827i	$-0.746505\pi$
$797$	−21.8937	+	7.96866i	−0.775515	+	0.282264i	−0.0762137	+	0.997092i	$0.524283\pi$
$798$		0			0
$799$	−1.06696	−	6.05101i	−0.0377462	−	0.214069i
$800$	−21.5433	+	12.4380i	−0.761670	+	0.439750i
$801$		0			0
$802$	−36.4618	+	63.1537i	−1.28751	+	2.23004i
$803$	1.23611	+	7.01035i	0.0436215	+	0.247390i
$804$		0			0
$805$	−0.282168	−	3.97737i	−0.00994513	−	0.140184i
$806$	−70.5669	+	84.0983i	−2.48561	+	2.96224i
$807$		0			0
$808$	−6.56296	+	1.15723i	−0.230884	+	0.0407111i
$809$	36.9148	−	21.3128i	1.29786	−	0.749317i	0.317822	−	0.948150i	$-0.397049\pi$
$809$	36.9148	−	21.3128i	1.29786	−	0.749317i	0.980033	+	0.198833i	$0.0637153\pi$
$810$		0			0
$811$		−	33.7669i		−	1.18572i	−0.805307	−	0.592859i	$-0.797999\pi$
$811$		−	33.7669i		−	1.18572i	0.805307	−	0.592859i	$-0.202001\pi$
$812$	−63.4219	−	6.60105i	−2.22567	−	0.231651i
$813$		0			0
$814$	43.7632	−	15.9285i	1.53390	−	0.558293i
$815$	0.777495	−	0.282985i	0.0272344	−	0.00991253i
$816$		0			0
$817$	5.82516	−	1.02713i	0.203797	−	0.0359348i
$818$	−1.06921	−	1.85192i	−0.0373839	−	0.0647508i
$819$		0			0
$820$	−3.91899	+	6.78790i	−0.136857	+	0.237044i
$821$	−8.06058	+	22.1463i	−0.281316	+	0.772910i	0.715890	+	0.698213i	$0.246021\pi$
$821$	−8.06058	+	22.1463i	−0.281316	+	0.772910i	−0.997206	+	0.0746970i	$0.976201\pi$
$822$		0			0
$823$	−22.2555	−	18.6746i	−0.775777	−	0.650954i	0.166404	−	0.986058i	$-0.446784\pi$
$823$	−22.2555	−	18.6746i	−0.775777	−	0.650954i	−0.942181	+	0.335103i	$0.891229\pi$
$824$	−6.13667	+	34.8028i	−0.213781	+	1.21241i
$825$		0			0
$826$	72.8925	+	7.58676i	2.53626	+	0.263977i
$827$	28.8450	+	16.6537i	1.00304	+	0.579105i	0.909146	−	0.416478i	$-0.136736\pi$
$827$	28.8450	+	16.6537i	1.00304	+	0.579105i	0.0938928	+	0.995582i	$0.470069\pi$
$828$		0			0
$829$	−34.3451	−	19.8291i	−1.19285	−	0.688694i	−0.233901	−	0.972261i	$-0.575149\pi$
$829$	−34.3451	−	19.8291i	−1.19285	−	0.688694i	−0.958953	+	0.283566i	$0.908482\pi$
$830$	−2.14022	+	5.88021i	−0.0742881	+	0.204105i
$831$		0			0
$832$	−4.37020	−	0.770585i	−0.151510	−	0.0267152i
$833$	−3.14595	+	3.50818i	−0.109001	+	0.121551i
$834$		0			0
$835$	−3.08965	+	2.59253i	−0.106922	+	0.0897180i
$836$	3.99988	+	6.92799i	0.138339	+	0.239610i
$837$		0			0
$838$	34.3897	+	19.8549i	1.18797	+	0.685877i
$839$	−48.4005	−	17.6163i	−1.67097	−	0.608184i	−0.678942	−	0.734192i	$-0.737561\pi$
$839$	−48.4005	−	17.6163i	−1.67097	−	0.608184i	−0.992029	+	0.126008i	$0.959784\pi$
$840$		0			0
$841$	−0.164445	−	0.137985i	−0.00567050	−	0.00475812i
$842$	48.5316	−	57.8378i	1.67251	−	1.99322i
$843$		0			0
$844$	42.0887	+	15.3190i	1.44875	+	0.527303i
$845$	−12.0551			−0.414709
$846$		0			0
$847$	3.13751	+	12.5298i	0.107806	+	0.430530i
$848$	−91.4185	+	16.1196i	−3.13933	+	0.553548i
$849$		0			0
$850$	−5.26023	+	6.26890i	−0.180425	+	0.215022i
$851$	−15.4209	+	18.3779i	−0.528622	+	0.629987i
$852$		0			0
$853$	−37.1908	+	6.55774i	−1.27339	+	0.224533i	−0.769171	−	0.639044i	$-0.779330\pi$
$853$	−37.1908	+	6.55774i	−1.27339	+	0.224533i	−0.504218	+	0.863576i	$0.668219\pi$
$854$	−6.03927	−	1.72512i	−0.206660	−	0.0590325i
$855$		0			0
$856$	−16.5739			−0.566485
$857$	−41.7013	−	15.1780i	−1.42449	−	0.518472i	−0.489143	−	0.872204i	$-0.662690\pi$
$857$	−41.7013	−	15.1780i	−1.42449	−	0.518472i	−0.935347	+	0.353732i	$0.884912\pi$
$858$		0			0
$859$	−6.73029	+	8.02085i	−0.229635	+	0.273668i	−0.868542	−	0.495616i	$-0.834942\pi$
$859$	−6.73029	+	8.02085i	−0.229635	+	0.273668i	0.638907	+	0.769284i	$0.279387\pi$
$860$	12.9637	+	10.8779i	0.442059	+	0.370932i
$861$		0			0
$862$	−88.2409	−	32.1171i	−3.00550	−	1.09391i
$863$	−16.5153	−	9.53510i	−0.562187	−	0.324579i	0.191836	−	0.981427i	$-0.438556\pi$
$863$	−16.5153	−	9.53510i	−0.562187	−	0.324579i	−0.754023	+	0.656848i	$0.771889\pi$
$864$		0			0
$865$	−2.16887	−	3.75660i	−0.0737439	−	0.127728i
$866$	−19.1966	+	16.1079i	−0.652328	+	0.547368i
$867$		0			0
$868$	−5.78186	−	81.4994i	−0.196249	−	2.76627i
$869$	−2.68236	−	0.472972i	−0.0909928	−	0.0160445i
$870$		0			0
$871$	0.0513528	−	0.141091i	0.00174002	−	0.00478068i
$872$	−61.6937	−	35.6189i	−2.08921	−	1.20621i
$873$		0			0
$874$	−5.16960	−	2.98467i	−0.174864	−	0.100958i
$875$	−1.24711	+	11.9821i	−0.0421602	+	0.405069i
$876$		0			0
$877$	6.40894	−	36.3469i	0.216414	−	1.22735i	−0.662021	−	0.749485i	$-0.730301\pi$
$877$	6.40894	−	36.3469i	0.216414	−	1.22735i	0.878435	−	0.477862i	$-0.158588\pi$
$878$	−69.2853	−	58.1372i	−2.33826	−	1.96204i
$879$		0			0
$880$	−2.74192	+	7.53336i	−0.0924301	+	0.253950i
$881$	−14.1834	+	24.5664i	−0.477851	+	0.827662i	−0.999678	−	0.0253894i	$-0.991917\pi$
$881$	−14.1834	+	24.5664i	−0.477851	+	0.827662i	0.521827	+	0.853052i	$0.325251\pi$
$882$		0			0
$883$	−1.51080	−	2.61677i	−0.0508423	−	0.0880615i	0.839484	−	0.543384i	$-0.182857\pi$
$883$	−1.51080	−	2.61677i	−0.0508423	−	0.0880615i	−0.890327	+	0.455323i	$0.849524\pi$
$884$	18.4370	−	3.25094i	0.620103	−	0.109341i
$885$		0			0
$886$	31.7866	−	11.5694i	1.06789	−	0.388681i
$887$	−0.118237	+	0.0430349i	−0.00397003	+	0.00144497i	−0.344004	−	0.938968i	$-0.611784\pi$
$887$	−0.118237	+	0.0430349i	−0.00397003	+	0.00144497i	0.340034	+	0.940413i	$0.389561\pi$
$888$		0			0
$889$	20.1158	+	14.5839i	0.674664	+	0.489130i
$890$		−	12.0680i		−	0.404520i
$891$		0			0
$892$	110.876	−	64.0140i	3.71239	−	2.14335i
$893$	−6.52005	+	1.14966i	−0.218185	+	0.0384719i
$894$		0			0
$895$	3.43353	−	4.09192i	0.114770	−	0.136778i
$896$	26.7617	−	18.0904i	0.894044	−	0.604357i
$897$		0			0
$898$	3.29654	+	18.6956i	0.110007	+	0.623881i
$899$	18.7170	−	32.4188i	0.624248	−	1.08123i
$900$		0			0
$901$	−7.77086	+	4.48651i	−0.258885	+	0.149467i
$902$	−4.12282	−	23.3817i	−0.137275	−	0.778525i
$903$		0			0
$904$	−41.7201	+	15.1849i	−1.38759	+	0.505041i
$905$	2.35172	+	0.414672i	0.0781740	+	0.0137842i
$906$		0			0
$907$	−5.90765	+	4.95711i	−0.196160	+	0.164598i	−0.735577	−	0.677441i	$-0.763089\pi$
$907$	−5.90765	+	4.95711i	−0.196160	+	0.164598i	0.539417	+	0.842039i	$0.318645\pi$
$908$	−5.19051	−	8.99023i	−0.172253	−	0.298351i
$909$		0			0
$910$	14.0268	−	13.5730i	0.464985	−	0.449941i
$911$	−3.55791	−	4.24015i	−0.117879	−	0.140482i	0.703878	−	0.710321i	$-0.251450\pi$
$911$	−3.55791	−	4.24015i	−0.117879	−	0.140482i	−0.821757	+	0.569838i	$0.807006\pi$
$912$		0			0
$913$	−4.47556	−	12.2965i	−0.148120	−	0.406955i
$914$	−64.8700	−	11.4383i	−2.14571	−	0.378346i
$915$		0			0
$916$	−17.1834	+	47.2111i	−0.567757	+	1.55990i
$917$	15.5204	−	15.0183i	0.512530	−	0.495947i
$918$		0			0
$919$	0.511927	−	0.886684i	0.0168869	−	0.0292490i	−0.857458	−	0.514553i	$-0.827958\pi$
$919$	0.511927	−	0.886684i	0.0168869	−	0.0292490i	0.874345	+	0.485304i	$0.161291\pi$
$920$	−1.63543	−	9.27496i	−0.0539184	−	0.305786i
$921$		0			0
$922$	21.9492	+	60.3048i	0.722857	+	1.98603i
$923$	10.7926	−	61.2076i	0.355241	−	2.01467i
$924$		0			0
$925$	27.1475	−	22.7795i	0.892605	−	0.748984i
$926$			51.1887i			1.68216i
$927$		0			0
$928$	−28.1090			−0.922723
$929$	21.0190	+	7.65030i	0.689612	+	0.250998i	0.662969	−	0.748647i	$-0.269296\pi$
$929$	21.0190	+	7.65030i	0.689612	+	0.250998i	0.0266431	+	0.999645i	$0.491518\pi$
$930$		0			0
$931$	3.78012	+	3.38981i	0.123888	+	0.111096i
$932$	20.4121	+	56.0817i	0.668620	+	1.83702i
$933$		0			0
$934$	−7.04902	−	8.40070i	−0.230651	−	0.274879i
$935$			0.774923i			0.0253427i
$936$		0			0
$937$	−12.3038	+	7.10360i	−0.401947	+	0.232064i	−0.687324	−	0.726351i	$-0.741215\pi$
$937$	−12.3038	+	7.10360i	−0.401947	+	0.232064i	0.285377	+	0.958415i	$0.407881\pi$
$938$	0.0659862	+	0.147805i	0.00215453	+	0.00482600i
$939$		0			0
$940$	−14.5102	−	12.1755i	−0.473270	−	0.397120i
$941$	5.57685	−	31.6279i	0.181800	−	1.03104i	−0.748198	−	0.663475i	$-0.769081\pi$
$941$	5.57685	−	31.6279i	0.181800	−	1.03104i	0.929998	−	0.367564i	$-0.119808\pi$
$942$		0			0
$943$	7.86161	+	9.36910i	0.256009	+	0.305100i
$944$	75.9032			2.47044
$945$		0			0
$946$	−51.2620			−1.66667
$947$	26.6191	+	31.7234i	0.865004	+	1.03087i	0.999203	+	0.0399177i	$0.0127096\pi$
$947$	26.6191	+	31.7234i	0.865004	+	1.03087i	−0.134198	+	0.990954i	$0.542846\pi$
$948$		0			0
$949$	3.11704	−	17.6776i	0.101184	−	0.573840i
$950$	6.75483	+	5.66797i	0.219155	+	0.183893i
$951$		0			0
$952$	−6.53293	+	9.01096i	−0.211733	+	0.292047i
$953$	−29.7841	+	17.1959i	−0.964803	+	0.557029i	−0.897648	−	0.440713i	$-0.854726\pi$
$953$	−29.7841	+	17.1959i	−0.964803	+	0.557029i	−0.0671552	+	0.997743i	$0.521392\pi$
$954$		0			0
$955$		−	8.15488i		−	0.263886i
$956$	70.0767	+	83.5142i	2.26644	+	2.70104i
$957$		0			0
$958$	−1.66730	−	4.58087i	−0.0538680	−	0.148001i
$959$	44.8547	−	30.3209i	1.44843	−	0.979114i
$960$		0			0
$961$	15.9427	+	5.80268i	0.514281	+	0.187183i
$962$	−117.438			−3.78634
$963$		0			0
$964$			56.7901i			1.82909i
$965$	−2.64707	+	2.22115i	−0.0852121	+	0.0715014i
$966$		0			0
$967$	0.771534	−	4.37559i	0.0248109	−	0.140709i	−0.969886	−	0.243559i	$-0.921685\pi$
$967$	0.771534	−	4.37559i	0.0248109	−	0.140709i	0.994697	+	0.102850i	$0.0327961\pi$
$968$	10.4346	+	28.6689i	0.335382	+	0.921455i
$969$		0			0
$970$	3.82250	+	21.6785i	0.122733	+	0.696053i
$971$	−19.3649	+	33.5409i	−0.621448	+	1.07638i	0.367768	+	0.929918i	$0.380122\pi$
$971$	−19.3649	+	33.5409i	−0.621448	+	1.07638i	−0.989216	+	0.146462i	$0.953211\pi$
$972$		0			0
$973$	−0.603416	+	2.11243i	−0.0193446	+	0.0677213i
$974$	17.7803	−	48.8510i	0.569718	−	1.56529i
$975$		0			0
$976$	−6.40628	−	1.12960i	−0.205060	−	0.0361576i
$977$	6.19981	+	17.0338i	0.198349	+	0.544961i	0.998495	−	0.0548455i	$-0.0174666\pi$
$977$	6.19981	+	17.0338i	0.198349	+	0.544961i	−0.800145	+	0.599806i	$0.795244\pi$
$978$		0			0
$979$	16.2215	+	19.3320i	0.518442	+	0.617855i
$980$	−0.477592	+	14.5187i	−0.0152561	+	0.463782i
$981$		0			0
$982$	−36.0784	−	62.4895i	−1.15131	−	1.99412i
$983$	4.94956	−	4.15317i	0.157866	−	0.132466i	−0.560433	−	0.828200i	$-0.689365\pi$
$983$	4.94956	−	4.15317i	0.157866	−	0.132466i	0.718299	+	0.695734i	$0.244921\pi$
$984$		0			0
$985$	−2.17257	−	0.383082i	−0.0692238	−	0.0122060i
$986$	−8.68936	+	3.16267i	−0.276725	+	0.100720i
$987$		0			0
$988$	−3.50293	−	19.8661i	−0.111443	−	0.632024i
$989$	22.8689	−	13.2034i	0.727190	−	0.419843i
$990$		0			0
$991$	−18.8875	+	32.7141i	−0.599981	+	1.03920i	0.392842	+	0.919606i	$0.371492\pi$
$991$	−18.8875	+	32.7141i	−0.599981	+	1.03920i	−0.992823	+	0.119591i	$0.961842\pi$
$992$	−6.25434	−	35.4701i	−0.198575	−	1.12618i
$993$		0			0
$994$	37.5239	+	55.5102i	1.19019	+	1.76068i
$995$	2.00597	−	2.39062i	0.0635934	−	0.0757877i
$996$		0			0
$997$	42.1085	−	7.42486i	1.33359	−	0.235148i	0.539005	−	0.842302i	$-0.318800\pi$
$997$	42.1085	−	7.42486i	1.33359	−	0.235148i	0.794584	+	0.607155i	$0.207689\pi$
$998$	51.5318	−	29.7519i	1.63121	−	0.941780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.341.22		132
3.2	odd	2		189.2.ba.a.131.1	yes	132
7.3	odd	6		567.2.bd.a.17.1		132
21.17	even	6		189.2.bd.a.185.22	yes	132
27.7	even	9		189.2.bd.a.47.22	yes	132
27.20	odd	18		567.2.bd.a.467.1		132
189.101	even	18	inner	567.2.ba.a.143.22		132
189.115	odd	18		189.2.ba.a.101.1	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.1	✓	132	189.115	odd	18
189.2.ba.a.131.1	yes	132	3.2	odd	2
189.2.bd.a.47.22	yes	132	27.7	even	9
189.2.bd.a.185.22	yes	132	21.17	even	6
567.2.ba.a.143.22		132	189.101	even	18	inner
567.2.ba.a.341.22		132	1.1	even	1	trivial
567.2.bd.a.17.1		132	7.3	odd	6
567.2.bd.a.467.1		132	27.20	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.63361 + 1.94686i) q^{2} +(-0.774283 + 4.39118i) q^{4} +(0.356523 + 0.299159i) q^{5} +(-2.41592 + 1.07857i) q^{7} +(-5.41196 + 3.12460i) q^{8} +1.18281i q^{10} +(-1.58990 - 1.89477i) q^{11} +(2.13324 + 5.86102i) q^{13} +(-6.04649 - 2.94150i) q^{14} +(-6.54413 - 2.38187i) q^{16} -0.673165 q^{17} +0.725344i q^{19} +(-1.58971 + 1.33392i) q^{20} +(1.09157 - 6.19062i) q^{22} +(1.10753 + 3.04291i) q^{23} +(-0.830628 - 4.71072i) q^{25} +(-7.92569 + 13.7277i) q^{26} +(-2.86558 - 11.4439i) q^{28} +(1.84864 - 5.07909i) q^{29} +(6.82052 + 1.20264i) q^{31} +(-1.77867 - 4.88687i) q^{32} +(-1.09969 - 1.31055i) q^{34} +(-1.18400 - 0.338210i) q^{35} +(3.70433 + 6.41609i) q^{37} +(-1.41214 + 1.18493i) q^{38} +(-2.86424 - 0.505043i) q^{40} +(3.54917 - 1.29179i) q^{41} +(-1.41606 - 8.03089i) q^{43} +(9.55132 - 5.51446i) q^{44} +(-4.11484 + 7.12711i) q^{46} +(1.58499 + 8.98890i) q^{47} +(4.67338 - 5.21148i) q^{49} +(7.81418 - 9.31258i) q^{50} +(-27.3885 + 4.82933i) q^{52} +(11.5438 - 6.66480i) q^{53} -1.15116i q^{55} +(9.70479 - 13.3860i) q^{56} +(12.9082 - 4.69821i) q^{58} +(-10.2419 + 3.72774i) q^{59} +(0.919898 - 0.162203i) q^{61} +(8.80068 + 15.2432i) q^{62} +(-0.355740 + 0.616160i) q^{64} +(-0.992826 + 2.72777i) q^{65} +(-0.0184408 - 0.0154737i) q^{67} +(0.521220 - 2.95599i) q^{68} +(-1.27574 - 2.85757i) q^{70} +(-8.62973 - 4.98238i) q^{71} +(-2.49239 - 1.43898i) q^{73} +(-6.43979 + 17.6932i) q^{74} +(-3.18511 - 0.561622i) q^{76} +(5.88473 + 2.86281i) q^{77} +(0.843560 - 0.707831i) q^{79} +(-1.62058 - 2.80692i) q^{80} +(8.31288 + 4.79945i) q^{82} +(4.97140 + 1.80944i) q^{83} +(-0.239999 - 0.201383i) q^{85} +(13.3217 - 15.8762i) q^{86} +(14.5249 + 5.28663i) q^{88} -10.2028 q^{89} +(-11.4753 - 11.8589i) q^{91} +(-14.2195 + 2.50728i) q^{92} +(-14.9109 + 17.7701i) q^{94} +(-0.216993 + 0.258602i) q^{95} +(18.3280 - 3.23172i) q^{97} +(17.7805 + 0.584889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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