LMFDB - Embedded newform 400.3.r.f.51.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(51,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.r (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			51.10
Character	$\chi$	$=$	400.51
Dual form			400.3.r.f.251.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.522340 - 1.93059i) q^{2} +(-3.58499 + 3.58499i) q^{3} +(-3.45432 - 2.01684i) q^{4} +(5.04854 + 8.79371i) q^{6} -10.0090 q^{7} +(-5.69802 + 5.61539i) q^{8} -16.7043i q^{9} +(-0.304644 - 0.304644i) q^{11} +(19.6141 - 5.15334i) q^{12} +(-6.87350 - 6.87350i) q^{13} +(-5.22809 + 19.3232i) q^{14} +(7.86468 + 13.9337i) q^{16} +25.8031 q^{17} +(-32.2490 - 8.72531i) q^{18} +(-10.2562 + 10.2562i) q^{19} +(35.8821 - 35.8821i) q^{21} +(-0.747270 + 0.429014i) q^{22} +33.7343 q^{23} +(0.296235 - 40.5584i) q^{24} +(-16.8602 + 9.67958i) q^{26} +(27.6197 + 27.6197i) q^{27} +(34.5743 + 20.1866i) q^{28} +(23.1650 + 23.1650i) q^{29} +7.31924i q^{31} +(31.0082 - 7.90534i) q^{32} +2.18429 q^{33} +(13.4780 - 49.8152i) q^{34} +(-33.6899 + 57.7020i) q^{36} +(-6.85014 + 6.85014i) q^{37} +(14.4433 + 25.1578i) q^{38} +49.2828 q^{39} -63.7855i q^{41} +(-50.5308 - 88.0161i) q^{42} +(-15.0257 - 15.0257i) q^{43} +(0.437920 + 1.66676i) q^{44} +(17.6208 - 65.1271i) q^{46} -41.8744i q^{47} +(-78.1468 - 21.7572i) q^{48} +51.1799 q^{49} +(-92.5039 + 92.5039i) q^{51} +(9.88051 + 37.6060i) q^{52} +(36.5375 - 36.5375i) q^{53} +(67.7491 - 38.8954i) q^{54} +(57.0314 - 56.2044i) q^{56} -73.5369i q^{57} +(56.8221 - 32.6221i) q^{58} +(58.1638 + 58.1638i) q^{59} +(-26.2928 - 26.2928i) q^{61} +(14.1304 + 3.82313i) q^{62} +167.193i q^{63} +(0.934849 - 63.9932i) q^{64} +(1.14094 - 4.21696i) q^{66} +(4.48091 - 4.48091i) q^{67} +(-89.1323 - 52.0409i) q^{68} +(-120.937 + 120.937i) q^{69} +11.5673 q^{71} +(93.8010 + 95.1813i) q^{72} +101.723i q^{73} +(9.64668 + 16.8029i) q^{74} +(56.1135 - 14.7431i) q^{76} +(3.04918 + 3.04918i) q^{77} +(25.7424 - 95.1447i) q^{78} -73.1288i q^{79} -47.6943 q^{81} +(-123.143 - 33.3177i) q^{82} +(-39.9292 + 39.9292i) q^{83} +(-196.317 + 51.5798i) q^{84} +(-36.8568 + 21.1598i) q^{86} -166.093 q^{87} +(3.44656 + 0.0251734i) q^{88} +37.2154i q^{89} +(68.7968 + 68.7968i) q^{91} +(-116.529 - 68.0369i) q^{92} +(-26.2394 - 26.2394i) q^{93} +(-80.8420 - 21.8726i) q^{94} +(-82.8233 + 139.504i) q^{96} +114.749 q^{97} +(26.7333 - 98.8071i) q^{98} +(-5.08886 + 5.08886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 12 q^{6} + 32 q^{11} + 60 q^{12} - 36 q^{14} + 48 q^{16} - 160 q^{18} - 32 q^{19} + 12 q^{22} + 128 q^{23} - 120 q^{24} - 48 q^{26} + 96 q^{27} + 180 q^{28} + 32 q^{29} + 160 q^{32} + 16 q^{34}+ \cdots + 608 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 12 * q^6 + 32 * q^11 + 60 * q^12 - 36 * q^14 + 48 * q^16 - 160 * q^18 - 32 * q^19 + 12 * q^22 + 128 * q^23 - 120 * q^24 - 48 * q^26 + 96 * q^27 + 180 * q^28 + 32 * q^29 + 160 * q^32 + 16 * q^34 - 84 * q^36 + 96 * q^37 - 140 * q^38 + 384 * q^39 - 20 * q^42 - 96 * q^43 + 8 * q^44 + 36 * q^46 - 280 * q^48 + 224 * q^49 - 256 * q^51 + 104 * q^52 + 160 * q^53 + 192 * q^54 + 304 * q^56 + 4 * q^58 - 352 * q^59 - 32 * q^61 - 552 * q^62 + 240 * q^64 - 576 * q^66 - 160 * q^67 - 16 * q^68 + 96 * q^69 + 256 * q^71 - 568 * q^72 + 136 * q^74 + 512 * q^76 - 224 * q^77 + 208 * q^78 - 288 * q^81 + 196 * q^82 + 480 * q^83 - 736 * q^84 - 188 * q^86 + 320 * q^88 - 384 * q^91 - 28 * q^92 - 96 * q^93 - 604 * q^94 + 232 * q^96 - 20 * q^98 + 608 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.522340	−	1.93059i	0.261170	−	0.965293i
$2$	0.522340	−	1.93059i	0.261170	−	0.965293i
$3$	−3.58499	+	3.58499i	−1.19500	+	1.19500i	−0.219350	+	0.975646i	$0.570394\pi$
$3$	−3.58499	+	3.58499i	−1.19500	+	1.19500i	−0.975646	+	0.219350i	$0.929606\pi$
$4$	−3.45432	−	2.01684i	−0.863581	−	0.504211i
$5$		0			0
$5$		0			0
$6$	5.04854	+	8.79371i	0.841424	+	1.46562i
$7$	−10.0090			−1.42986			−0.714928	−	0.699198i	$-0.753540\pi$
$7$	−10.0090			−1.42986			−0.714928	+	0.699198i	$0.753540\pi$
$8$	−5.69802	+	5.61539i	−0.712252	+	0.701923i
$9$		−	16.7043i		−	1.85603i
$10$		0			0
$11$	−0.304644	−	0.304644i	−0.0276949	−	0.0276949i	0.693124	−	0.720819i	$-0.256234\pi$
$11$	−0.304644	−	0.304644i	−0.0276949	−	0.0276949i	−0.720819	+	0.693124i	$0.756234\pi$
$12$	19.6141	−	5.15334i	1.63451	−	0.429445i
$13$	−6.87350	−	6.87350i	−0.528731	−	0.528731i	0.391463	−	0.920194i	$-0.371969\pi$
$13$	−6.87350	−	6.87350i	−0.528731	−	0.528731i	−0.920194	+	0.391463i	$0.871969\pi$
$14$	−5.22809	+	19.3232i	−0.373435	+	1.38023i
$15$		0			0
$16$	7.86468	+	13.9337i	0.491543	+	0.870853i
$17$	25.8031			1.51783			0.758916	−	0.651189i	$-0.225730\pi$
$17$	25.8031			1.51783			0.758916	+	0.651189i	$0.225730\pi$
$18$	−32.2490	−	8.72531i	−1.79161	−	0.484739i
$19$	−10.2562	+	10.2562i	−0.539802	+	0.539802i	−0.923471	−	0.383669i	$-0.874660\pi$
$19$	−10.2562	+	10.2562i	−0.539802	+	0.539802i	0.383669	+	0.923471i	$0.374660\pi$
$20$		0			0
$21$	35.8821	−	35.8821i	1.70867	−	1.70867i
$22$	−0.747270	+	0.429014i	−0.0339668	+	0.0195006i
$23$	33.7343			1.46671			0.733355	−	0.679845i	$-0.237953\pi$
$23$	33.7343			1.46671			0.733355	+	0.679845i	$0.237953\pi$
$24$	0.296235	−	40.5584i	0.0123431	−	1.68993i
$25$		0			0
$26$	−16.8602	+	9.67958i	−0.648468	+	0.372291i
$27$	27.6197	+	27.6197i	1.02295	+	1.02295i
$28$	34.5743	+	20.1866i	1.23480	+	0.720949i
$29$	23.1650	+	23.1650i	0.798794	+	0.798794i	0.982905	−	0.184111i	$-0.0589407\pi$
$29$	23.1650	+	23.1650i	0.798794	+	0.798794i	−0.184111	+	0.982905i	$0.558941\pi$
$30$		0			0
$31$			7.31924i			0.236104i	0.993007	+	0.118052i	$0.0376650\pi$
$31$			7.31924i			0.236104i	−0.993007	+	0.118052i	$0.962335\pi$
$32$	31.0082	−	7.90534i	0.969005	−	0.247042i
$33$	2.18429			0.0661907
$34$	13.4780	−	49.8152i	0.396412	−	1.46515i
$35$		0			0
$36$	−33.6899	+	57.7020i	−0.935831	+	1.60283i
$37$	−6.85014	+	6.85014i	−0.185139	+	0.185139i	−0.793591	−	0.608452i	$-0.791791\pi$
$37$	−6.85014	+	6.85014i	−0.185139	+	0.185139i	0.608452	+	0.793591i	$0.291791\pi$
$38$	14.4433	+	25.1578i	0.380087	+	0.662047i
$39$	49.2828			1.26366
$40$		0			0
$41$		−	63.7855i		−	1.55574i	−0.628423	−	0.777872i	$-0.716299\pi$
$41$		−	63.7855i		−	1.55574i	0.628423	−	0.777872i	$-0.283701\pi$
$42$	−50.5308	−	88.0161i	−1.20311	−	2.09562i
$43$	−15.0257	−	15.0257i	−0.349434	−	0.349434i	0.510465	−	0.859899i	$-0.329473\pi$
$43$	−15.0257	−	15.0257i	−0.349434	−	0.349434i	−0.859899	+	0.510465i	$0.829473\pi$
$44$	0.437920	+	1.66676i	0.00995272	+	0.0378809i
$45$		0			0
$46$	17.6208	−	65.1271i	0.383061	−	1.41581i
$47$		−	41.8744i		−	0.890944i	−0.895296	−	0.445472i	$-0.853036\pi$
$47$		−	41.8744i		−	0.890944i	0.895296	−	0.445472i	$-0.146964\pi$
$48$	−78.1468	−	21.7572i	−1.62806	−	0.453275i
$49$	51.1799			1.04449
$50$		0			0
$51$	−92.5039	+	92.5039i	−1.81380	+	1.81380i
$52$	9.88051	+	37.6060i	0.190010	+	0.723193i
$53$	36.5375	−	36.5375i	0.689388	−	0.689388i	−0.272709	−	0.962097i	$-0.587920\pi$
$53$	36.5375	−	36.5375i	0.689388	−	0.689388i	0.962097	+	0.272709i	$0.0879196\pi$
$54$	67.7491	−	38.8954i	1.25461	−	0.720285i
$55$		0			0
$56$	57.0314	−	56.2044i	1.01842	−	1.00365i
$57$		−	73.5369i		−	1.29012i
$58$	56.8221	−	32.6221i	0.979691	−	0.562449i
$59$	58.1638	+	58.1638i	0.985828	+	0.985828i	0.999901	−	0.0140734i	$-0.00447984\pi$
$59$	58.1638	+	58.1638i	0.985828	+	0.985828i	−0.0140734	+	0.999901i	$0.504480\pi$
$60$		0			0
$61$	−26.2928	−	26.2928i	−0.431030	−	0.431030i	0.457949	−	0.888979i	$-0.348584\pi$
$61$	−26.2928	−	26.2928i	−0.431030	−	0.431030i	−0.888979	+	0.457949i	$0.848584\pi$
$62$	14.1304	+	3.82313i	0.227910	+	0.0616634i
$63$			167.193i			2.65386i
$64$	0.934849	−	63.9932i	0.0146070	−	0.999893i
$65$		0			0
$66$	1.14094	−	4.21696i	0.0172870	−	0.0638934i
$67$	4.48091	−	4.48091i	0.0668793	−	0.0668793i	−0.672876	−	0.739755i	$-0.734941\pi$
$67$	4.48091	−	4.48091i	0.0668793	−	0.0668793i	0.739755	+	0.672876i	$0.234941\pi$
$68$	−89.1323	−	52.0409i	−1.31077	−	0.765307i
$69$	−120.937	+	120.937i	−1.75271	+	1.75271i
$70$		0			0
$71$	11.5673			0.162919			0.0814595	−	0.996677i	$-0.474042\pi$
$71$	11.5673			0.162919			0.0814595	+	0.996677i	$0.474042\pi$
$72$	93.8010	+	95.1813i	1.30279	+	1.32196i
$73$			101.723i			1.39346i	0.717332	+	0.696732i	$0.245363\pi$
$73$			101.723i			1.39346i	−0.717332	+	0.696732i	$0.754637\pi$
$74$	9.64668	+	16.8029i	0.130361	+	0.227066i
$75$		0			0
$76$	56.1135	−	14.7431i	0.738336	−	0.193988i
$77$	3.04918	+	3.04918i	0.0395998	+	0.0395998i
$78$	25.7424	−	95.1447i	0.330030	−	1.21980i
$79$		−	73.1288i		−	0.925681i	−0.886442	−	0.462840i	$-0.846830\pi$
$79$		−	73.1288i		−	0.925681i	0.886442	−	0.462840i	$-0.153170\pi$
$80$		0			0
$81$	−47.6943			−0.588819
$82$	−123.143	−	33.3177i	−1.50175	−	0.406313i
$83$	−39.9292	+	39.9292i	−0.481075	+	0.481075i	−0.905475	−	0.424400i	$-0.860485\pi$
$83$	−39.9292	+	39.9292i	−0.481075	+	0.481075i	0.424400	+	0.905475i	$0.360485\pi$
$84$	−196.317	+	51.5798i	−2.33711	+	0.614045i
$85$		0			0
$86$	−36.8568	+	21.1598i	−0.428568	+	0.246045i
$87$	−166.093			−1.90911
$88$	3.44656	+	0.0251734i	0.0391655	+	0.000286061i
$89$			37.2154i			0.418151i	0.977899	+	0.209076i	$0.0670455\pi$
$89$			37.2154i			0.418151i	−0.977899	+	0.209076i	$0.932955\pi$
$90$		0			0
$91$	68.7968	+	68.7968i	0.756008	+	0.756008i
$92$	−116.529	−	68.0369i	−1.26662	−	0.739532i
$93$	−26.2394	−	26.2394i	−0.282144	−	0.282144i
$94$	−80.8420	−	21.8726i	−0.860022	−	0.232688i
$95$		0			0
$96$	−82.8233	+	139.504i	−0.862743	+	1.45317i
$97$	114.749			1.18298			0.591490	−	0.806312i	$-0.298540\pi$
$97$	114.749			1.18298			0.591490	+	0.806312i	$0.298540\pi$
$98$	26.7333	−	98.8071i	0.272789	−	1.00824i
$99$	−5.08886	+	5.08886i	−0.0514026	+	0.0514026i
$100$		0			0
$101$	3.86189	−	3.86189i	0.0382366	−	0.0382366i	−0.687730	−	0.725967i	$-0.741393\pi$
$101$	3.86189	−	3.86189i	0.0382366	−	0.0382366i	0.725967	+	0.687730i	$0.241393\pi$
$102$	130.268	+	226.905i	1.27714	+	2.22456i
$103$	−82.3074			−0.799101			−0.399551	−	0.916711i	$-0.630834\pi$
$103$	−82.3074			−0.799101			−0.399551	+	0.916711i	$0.630834\pi$
$104$	77.7627	+	0.567971i	0.747718	+	0.00546126i
$105$		0			0
$106$	−51.4538	−	89.6239i	−0.485414	−	0.845508i
$107$	109.631	+	109.631i	1.02459	+	1.02459i	0.999690	+	0.0248967i	$0.00792568\pi$
$107$	109.631	+	109.631i	1.02459	+	1.02459i	0.0248967	+	0.999690i	$0.492074\pi$
$108$	−39.7028	−	151.112i	−0.367618	−	1.39919i
$109$	−2.99231	−	2.99231i	−0.0274524	−	0.0274524i	0.693247	−	0.720700i	$-0.256179\pi$
$109$	−2.99231	−	2.99231i	−0.0274524	−	0.0274524i	−0.720700	+	0.693247i	$0.756179\pi$
$110$		0			0
$111$		−	49.1153i		−	0.442480i
$112$	−78.7175	−	139.462i	−0.702835	−	1.24519i
$113$	−73.3488			−0.649105			−0.324552	−	0.945868i	$-0.605214\pi$
$113$	−73.3488			−0.649105			−0.324552	+	0.945868i	$0.605214\pi$
$114$	−141.969	−	38.4113i	−1.24535	−	0.336941i
$115$		0			0
$116$	−33.2992	−	126.740i	−0.287062	−	1.09258i
$117$	−114.817	+	114.817i	−0.981340	+	0.981340i
$118$	142.672	−	81.9090i	1.20908	−	0.694144i
$119$	−258.263			−2.17028
$120$		0			0
$121$		−	120.814i		−	0.998466i
$122$	−64.4943	+	37.0267i	−0.528642	+	0.303498i
$123$	228.670	+	228.670i	1.85911	+	1.85911i
$124$	14.7618	−	25.2830i	0.119046	−	0.203895i
$125$		0			0
$126$	322.780	+	87.3315i	2.56175	+	0.693107i
$127$		−	212.909i		−	1.67645i	−0.545323	−	0.838226i	$-0.683593\pi$
$127$		−	212.909i		−	1.67645i	0.545323	−	0.838226i	$-0.316407\pi$
$128$	−123.056	−	35.2310i	−0.961375	−	0.275242i
$129$	107.734			0.835145
$130$		0			0
$131$	34.5741	−	34.5741i	0.263924	−	0.263924i	−0.562722	−	0.826646i	$-0.690246\pi$
$131$	34.5741	−	34.5741i	0.263924	−	0.263924i	0.826646	+	0.562722i	$0.190246\pi$
$132$	−7.54525	−	4.40538i	−0.0571610	−	0.0333741i
$133$	102.655	−	102.655i	0.771838	−	0.771838i
$134$	−6.31023	−	10.9913i	−0.0470912	−	0.0820249i
$135$		0			0
$136$	−147.027	+	144.895i	−1.08108	+	1.06540i
$137$			156.675i			1.14362i	0.820388	+	0.571808i	$0.193758\pi$
$137$			156.675i			1.14362i	−0.820388	+	0.571808i	$0.806242\pi$
$138$	170.309	+	296.650i	1.23413	+	2.14964i
$139$	150.961	+	150.961i	1.08605	+	1.08605i	0.995931	+	0.0901190i	$0.0287247\pi$
$139$	150.961	+	150.961i	1.08605	+	1.08605i	0.0901190	+	0.995931i	$0.471275\pi$
$140$		0			0
$141$	150.119	+	150.119i	1.06467	+	1.06467i
$142$	6.04204	−	22.3316i	0.0425496	−	0.157265i
$143$			4.18794i			0.0292863i
$144$	232.752	−	131.374i	1.61633	−	0.912318i
$145$		0			0
$146$	196.385	+	53.1339i	1.34510	+	0.363931i
$147$	−183.479	+	183.479i	−1.24816	+	1.24816i
$148$	37.4782	−	9.84693i	0.253231	−	0.0665333i
$149$	96.4520	−	96.4520i	0.647329	−	0.647329i	−0.305018	−	0.952347i	$-0.598662\pi$
$149$	96.4520	−	96.4520i	0.647329	−	0.647329i	0.952347	+	0.305018i	$0.0986624\pi$
$150$		0			0
$151$	29.4114			0.194777			0.0973886	−	0.995246i	$-0.468951\pi$
$151$	29.4114			0.194777			0.0973886	+	0.995246i	$0.468951\pi$
$152$	0.847493	−	116.033i	0.00557561	−	0.763374i
$153$		−	431.023i		−	2.81714i
$154$	7.47941	−	4.29400i	0.0485676	−	0.0278831i
$155$		0			0
$156$	−170.239	−	99.3957i	−1.09127	−	0.637152i
$157$	117.658	+	117.658i	0.749415	+	0.749415i	0.974369	−	0.224954i	$-0.0722232\pi$
$157$	117.658	+	117.658i	0.749415	+	0.749415i	−0.224954	+	0.974369i	$0.572223\pi$
$158$	−141.181	−	38.1981i	−0.893553	−	0.241760i
$159$			261.973i			1.64763i
$160$		0			0
$161$	−337.647			−2.09718
$162$	−24.9127	+	92.0780i	−0.153782	+	0.568383i
$163$	7.81267	−	7.81267i	0.0479305	−	0.0479305i	−0.682735	−	0.730666i	$-0.739210\pi$
$163$	7.81267	−	7.81267i	0.0479305	−	0.0479305i	0.730666	+	0.682735i	$0.239210\pi$
$164$	−128.645	+	220.336i	−0.784423	+	1.34351i
$165$		0			0
$166$	56.2302	+	97.9434i	0.338736	+	0.590021i
$167$	255.372			1.52918			0.764588	−	0.644520i	$-0.222943\pi$
$167$	255.372			1.52918			0.764588	+	0.644520i	$0.222943\pi$
$168$	−2.96501	+	405.949i	−0.0176489	+	2.41636i
$169$		−	74.5100i		−	0.440888i
$170$		0			0
$171$	171.323	+	171.323i	1.00189	+	1.00189i
$172$	21.5991	+	82.2079i	0.125576	+	0.477953i
$173$	−27.0161	−	27.0161i	−0.156162	−	0.156162i	0.624701	−	0.780864i	$-0.285221\pi$
$173$	−27.0161	−	27.0161i	−0.156162	−	0.156162i	−0.780864	+	0.624701i	$0.785221\pi$
$174$	−86.7568	+	320.656i	−0.498602	+	1.84285i
$175$		0			0
$176$	1.84888	−	6.64074i	0.0105050	−	0.0377315i
$177$	−417.033			−2.35612
$178$	71.8476	+	19.4391i	0.403638	+	0.109208i
$179$	50.8893	−	50.8893i	0.284298	−	0.284298i	−0.550523	−	0.834820i	$-0.685572\pi$
$179$	50.8893	−	50.8893i	0.284298	−	0.284298i	0.834820	+	0.550523i	$0.185572\pi$
$180$		0			0
$181$	−13.6488	+	13.6488i	−0.0754079	+	0.0754079i	−0.743805	−	0.668397i	$-0.766981\pi$
$181$	−13.6488	+	13.6488i	−0.0754079	+	0.0754079i	0.668397	+	0.743805i	$0.266981\pi$
$182$	168.753	−	96.8828i	0.927216	−	0.532323i
$183$	188.519			1.03016
$184$	−192.219	+	189.431i	−1.04467	+	1.02952i
$185$		0			0
$186$	−64.3632	+	36.9515i	−0.346039	+	0.198664i
$187$	−7.86078	−	7.86078i	−0.0420362	−	0.0420362i
$188$	−84.4540	+	144.648i	−0.449224	+	0.769402i
$189$	−276.446	−	276.446i	−1.46268	−	1.46268i
$190$		0			0
$191$		−	263.019i		−	1.37706i	−0.725206	−	0.688532i	$-0.758255\pi$
$191$		−	263.019i		−	1.37706i	0.725206	−	0.688532i	$-0.241745\pi$
$192$	226.063	+	232.766i	1.17741	+	1.21232i
$193$	58.9456			0.305418			0.152709	−	0.988271i	$-0.451200\pi$
$193$	58.9456			0.305418			0.152709	+	0.988271i	$0.451200\pi$
$194$	59.9381	−	221.533i	0.308959	−	1.14192i
$195$		0			0
$196$	−176.792	−	103.222i	−0.901999	−	0.526642i
$197$	−9.54461	+	9.54461i	−0.0484498	+	0.0484498i	−0.730917	−	0.682467i	$-0.760907\pi$
$197$	−9.54461	+	9.54461i	−0.0484498	+	0.0484498i	0.682467	+	0.730917i	$0.260907\pi$
$198$	7.16637	+	12.4826i	0.0361938	+	0.0630434i
$199$	103.151			0.518348			0.259174	−	0.965831i	$-0.416550\pi$
$199$	103.151			0.518348			0.259174	+	0.965831i	$0.416550\pi$
$200$		0			0
$201$			32.1280i			0.159841i
$202$	−5.43849	−	9.47293i	−0.0269232	−	0.0468957i
$203$	−231.859	−	231.859i	−1.14216	−	1.14216i
$204$	506.104	−	132.972i	2.48090	−	0.651825i
$205$		0			0
$206$	−42.9924	+	158.902i	−0.208701	+	0.771367i
$207$		−	563.508i		−	2.72226i
$208$	41.7151	−	149.831i	0.200553	−	0.720341i
$209$	6.24900			0.0298995
$210$		0			0
$211$	4.93870	−	4.93870i	0.0234062	−	0.0234062i	−0.695307	−	0.718713i	$-0.744732\pi$
$211$	4.93870	−	4.93870i	0.0234062	−	0.0234062i	0.718713	+	0.695307i	$0.244732\pi$
$212$	−199.903	+	52.5219i	−0.942938	+	0.247745i
$213$	−41.4685	+	41.4685i	−0.194688	+	0.194688i
$214$	268.916	−	154.387i	1.25662	−	0.721435i
$215$		0			0
$216$	−312.473	−	2.28227i	−1.44664	−	0.0105661i
$217$		−	73.2582i		−	0.337595i
$218$	−7.33992	+	4.21391i	−0.0336693	+	0.0193299i
$219$	−364.675	−	364.675i	−1.66518	−	1.66518i
$220$		0			0
$221$	−177.358	−	177.358i	−0.802524	−	0.802524i
$222$	−94.8213	−	25.6549i	−0.427123	−	0.115563i
$223$		−	177.151i		−	0.794401i	−0.917732	−	0.397200i	$-0.869982\pi$
$223$		−	177.151i		−	0.794401i	0.917732	−	0.397200i	$-0.130018\pi$
$224$	−310.360	+	79.1245i	−1.38554	+	0.353234i
$225$		0			0
$226$	−38.3130	+	141.606i	−0.169527	+	0.626576i
$227$	239.268	−	239.268i	1.05404	−	1.05404i	0.0555894	−	0.998454i	$-0.482296\pi$
$227$	239.268	−	239.268i	1.05404	−	1.05404i	0.998454	−	0.0555894i	$-0.0177038\pi$
$228$	−148.312	+	254.020i	−0.650493	+	1.11412i
$229$	−106.699	+	106.699i	−0.465933	+	0.465933i	−0.900594	−	0.434661i	$-0.856868\pi$
$229$	−106.699	+	106.699i	−0.465933	+	0.465933i	0.434661	+	0.900594i	$0.356868\pi$
$230$		0			0
$231$	−21.8626			−0.0946431
$232$	−262.075	−	1.91417i	−1.12964	−	0.00825074i
$233$		−	132.961i		−	0.570649i	−0.958431	−	0.285324i	$-0.907899\pi$
$233$		−	132.961i		−	0.570649i	0.958431	−	0.285324i	$-0.0921013\pi$
$234$	161.690	+	281.637i	0.690984	+	1.20358i
$235$		0			0
$236$	−83.6093	−	318.224i	−0.354277	−	1.34841i
$237$	262.166	+	262.166i	1.10618	+	1.10618i
$238$	−134.901	+	498.599i	−0.566812	+	2.09496i
$239$		−	89.6649i		−	0.375167i	−0.982249	−	0.187584i	$-0.939934\pi$
$239$		−	89.6649i		−	0.375167i	0.982249	−	0.187584i	$-0.0600655\pi$
$240$		0			0
$241$	259.019			1.07477			0.537383	−	0.843338i	$-0.319413\pi$
$241$	259.019			1.07477			0.537383	+	0.843338i	$0.319413\pi$
$242$	−233.243	−	63.1062i	−0.963812	−	0.260769i
$243$	−77.5940	+	77.5940i	−0.319317	+	0.319317i
$244$	37.7954	+	143.852i	0.154899	+	0.589559i
$245$		0			0
$246$	560.911	−	322.024i	2.28013	−	1.30904i
$247$	140.992			0.570819
$248$	−41.1004	−	41.7052i	−0.165727	−	0.168166i
$249$		−	286.292i		−	1.14977i
$250$		0			0
$251$	85.2338	+	85.2338i	0.339577	+	0.339577i	0.856208	−	0.516631i	$-0.172814\pi$
$251$	85.2338	+	85.2338i	0.339577	+	0.339577i	−0.516631	+	0.856208i	$0.672814\pi$
$252$	337.202	−	577.538i	1.33810	−	2.29182i
$253$	−10.2770	−	10.2770i	−0.0406205	−	0.0406205i
$254$	−411.040	−	111.211i	−1.61827	−	0.437839i
$255$		0			0
$256$	−132.293	+	219.168i	−0.516771	+	0.856123i
$257$	−451.683			−1.75752			−0.878760	−	0.477264i	$-0.841628\pi$
$257$	−451.683			−1.75752			−0.878760	+	0.477264i	$0.841628\pi$
$258$	56.2736	−	207.989i	0.218115	−	0.806159i
$259$	68.5629	−	68.5629i	0.264722	−	0.264722i
$260$		0			0
$261$	386.955	−	386.955i	1.48259	−	1.48259i
$262$	−48.6888	−	84.8077i	−0.185835	−	0.323694i
$263$	0.939393			0.00357184			0.00178592	−	0.999998i	$-0.499432\pi$
$263$	0.939393			0.00357184			0.00178592	+	0.999998i	$0.499432\pi$
$264$	−12.4461	+	12.2656i	−0.0471445	+	0.0464608i
$265$		0			0
$266$	−144.563	−	251.804i	−0.543469	−	0.946631i
$267$	−133.417	−	133.417i	−0.499689	−	0.499689i
$268$	−24.5158	+	6.44121i	−0.0914769	+	0.0240344i
$269$	141.098	+	141.098i	0.524527	+	0.524527i	0.918935	−	0.394408i	$-0.129050\pi$
$269$	141.098	+	141.098i	0.524527	+	0.524527i	−0.394408	+	0.918935i	$0.629050\pi$
$270$		0			0
$271$			237.677i			0.877037i	0.898722	+	0.438518i	$0.144497\pi$
$271$			237.677i			0.877037i	−0.898722	+	0.438518i	$0.855503\pi$
$272$	202.933	+	359.532i	0.746079	+	1.32181i
$273$	−493.271			−1.80685
$274$	302.475	+	81.8378i	1.10392	+	0.298678i
$275$		0			0
$276$	661.668	−	173.845i	2.39735	−	0.629872i
$277$	301.681	−	301.681i	1.08910	−	1.08910i	0.0934800	−	0.995621i	$-0.470201\pi$
$277$	301.681	−	301.681i	1.08910	−	1.08910i	0.995621	−	0.0934800i	$-0.0297991\pi$
$278$	370.296	−	212.590i	1.33200	−	0.764713i
$279$	122.263			0.438217
$280$		0			0
$281$			209.865i			0.746850i	0.927660	+	0.373425i	$0.121817\pi$
$281$			209.865i			0.746850i	−0.927660	+	0.373425i	$0.878183\pi$
$282$	368.231	−	211.405i	1.30578	−	0.749661i
$283$	−87.1403	−	87.1403i	−0.307916	−	0.307916i	0.536184	−	0.844101i	$-0.319865\pi$
$283$	−87.1403	−	87.1403i	−0.307916	−	0.307916i	−0.844101	+	0.536184i	$0.819865\pi$
$284$	−39.9570	−	23.3293i	−0.140694	−	0.0821456i
$285$		0			0
$286$	8.08518	+	2.18753i	0.0282699	+	0.00764871i
$287$			638.428i			2.22449i
$288$	−132.053	−	517.969i	−0.458518	−	1.79850i
$289$	376.801			1.30381
$290$		0			0
$291$	−411.374	+	411.374i	−1.41366	+	1.41366i
$292$	205.159	−	351.383i	0.702599	−	1.20337i
$293$	−210.545	+	210.545i	−0.718583	+	0.718583i	−0.968315	−	0.249732i	$-0.919657\pi$
$293$	−210.545	+	210.545i	−0.718583	+	0.718583i	0.249732	+	0.968315i	$0.419657\pi$
$294$	258.384	+	450.061i	0.878856	+	1.53082i
$295$		0			0
$296$	0.566040	−	77.4984i	0.00191230	−	0.261819i
$297$		−	16.8284i		−	0.0566612i
$298$	−135.828	−	236.590i	−0.455799	−	0.793925i
$299$	−231.873	−	231.873i	−0.775495	−	0.775495i
$300$		0			0
$301$	150.392	+	150.392i	0.499640	+	0.499640i
$302$	15.3627	−	56.7812i	0.0508699	−	0.188017i
$303$			27.6897i			0.0913851i
$304$	−223.569	−	62.2448i	−0.735424	−	0.204753i
$305$		0			0
$306$	−832.126	−	225.140i	−2.71937	−	0.735752i
$307$	−345.339	+	345.339i	−1.12488	+	1.12488i	−0.133888	+	0.990996i	$0.542746\pi$
$307$	−345.339	+	345.339i	−1.12488	+	1.12488i	−0.990996	+	0.133888i	$0.957254\pi$
$308$	−4.38313	−	16.6826i	−0.0142310	−	0.0541642i
$309$	295.071	−	295.071i	0.954923	−	0.954923i
$310$		0			0
$311$	−99.7096			−0.320610			−0.160305	−	0.987068i	$-0.551248\pi$
$311$	−99.7096			−0.320610			−0.160305	+	0.987068i	$0.551248\pi$
$312$	−280.814	+	276.742i	−0.900046	+	0.886994i
$313$			311.334i			0.994678i	0.867556	+	0.497339i	$0.165689\pi$
$313$			311.334i			0.994678i	−0.867556	+	0.497339i	$0.834311\pi$
$314$	288.607	−	165.692i	0.919130	−	0.527680i
$315$		0			0
$316$	−147.489	+	252.610i	−0.466738	+	0.799400i
$317$	−19.2419	−	19.2419i	−0.0607000	−	0.0607000i	0.676105	−	0.736805i	$-0.263666\pi$
$317$	−19.2419	−	19.2419i	−0.0607000	−	0.0607000i	−0.736805	+	0.676105i	$0.763666\pi$
$318$	505.762	+	136.839i	1.59045	+	0.430312i
$319$		−	14.1142i		−	0.0442451i
$320$		0			0
$321$	−786.050			−2.44875
$322$	−176.366	+	651.856i	−0.547722	+	2.02440i
$323$	−264.643	+	264.643i	−0.819328	+	0.819328i
$324$	164.752	+	96.1920i	0.508493	+	0.296889i
$325$		0			0
$326$	−11.0022	−	19.1639i	−0.0337490	−	0.0587850i
$327$	21.4548			0.0656110
$328$	358.180	+	363.451i	1.09201	+	1.10808i
$329$			419.120i			1.27392i
$330$		0			0
$331$	194.214	+	194.214i	0.586750	+	0.586750i	0.936750	−	0.350000i	$-0.113818\pi$
$331$	194.214	+	194.214i	0.586750	+	0.586750i	−0.350000	+	0.936750i	$0.613818\pi$
$332$	218.459	−	57.3974i	0.658010	−	0.172884i
$333$	114.427	+	114.427i	0.343623	+	0.343623i
$334$	133.391	−	493.018i	0.399375	−	1.47610i
$335$		0			0
$336$	782.170	+	217.767i	2.32789	+	0.648117i
$337$	552.303			1.63888			0.819441	−	0.573164i	$-0.194284\pi$
$337$	552.303			1.63888			0.819441	+	0.573164i	$0.194284\pi$
$338$	−143.848	−	38.9196i	−0.425586	−	0.115147i
$339$	262.955	−	262.955i	0.775677	−	0.775677i
$340$		0			0
$341$	2.22976	−	2.22976i	0.00653890	−	0.00653890i
$342$	420.242	−	241.265i	1.22878	−	0.705453i
$343$	−21.8182			−0.0636099
$344$	169.991	+	1.24160i	0.494161	+	0.00360930i
$345$		0			0
$346$	−66.2685	+	38.0453i	−0.191527	+	0.109958i
$347$	−119.162	−	119.162i	−0.343407	−	0.343407i	0.514239	−	0.857647i	$-0.328074\pi$
$347$	−119.162	−	119.162i	−0.343407	−	0.343407i	−0.857647	+	0.514239i	$0.828074\pi$
$348$	573.738	+	334.983i	1.64867	+	0.962595i
$349$	−170.249	−	170.249i	−0.487821	−	0.487821i	0.419797	−	0.907618i	$-0.362101\pi$
$349$	−170.249	−	170.249i	−0.487821	−	0.487821i	−0.907618	+	0.419797i	$0.862101\pi$
$350$		0			0
$351$		−	379.688i		−	1.08173i
$352$	−11.8548	−	7.03814i	−0.0336783	−	0.0199947i
$353$	551.816			1.56322			0.781609	−	0.623769i	$-0.214399\pi$
$353$	551.816			1.56322			0.781609	+	0.623769i	$0.214399\pi$
$354$	−217.833	+	805.118i	−0.615348	+	2.27435i
$355$		0			0
$356$	75.0577	−	128.554i	0.210836	−	0.361107i
$357$	925.871	−	925.871i	2.59347	−	2.59347i
$358$	−71.6646	−	124.828i	−0.200180	−	0.348680i
$359$	432.275			1.20411			0.602054	−	0.798456i	$-0.294349\pi$
$359$	432.275			1.20411			0.602054	+	0.798456i	$0.294349\pi$
$360$		0			0
$361$			150.619i			0.417228i
$362$	19.2209	+	33.4796i	0.0530964	+	0.0924850i
$363$	433.118	+	433.118i	1.19316	+	1.19316i
$364$	−98.8939	−	376.399i	−0.271687	−	1.03406i
$365$		0			0
$366$	98.4709	−	363.952i	0.269046	−	0.994404i
$367$		−	223.982i		−	0.610306i	−0.952303	−	0.305153i	$-0.901292\pi$
$367$		−	223.982i		−	0.610306i	0.952303	−	0.305153i	$-0.0987076\pi$
$368$	265.310	+	470.043i	0.720951	+	1.27729i
$369$	−1065.49			−2.88751
$370$		0			0
$371$	−365.704	+	365.704i	−0.985725	+	0.985725i
$372$	37.7185	+	143.560i	0.101394	+	0.385914i
$373$	348.716	−	348.716i	0.934897	−	0.934897i	−0.0631100	−	0.998007i	$-0.520102\pi$
$373$	348.716	−	348.716i	0.934897	−	0.934897i	0.998007	+	0.0631100i	$0.0201019\pi$
$374$	−19.2819	+	11.0699i	−0.0515559	+	0.0295987i
$375$		0			0
$376$	235.141	+	238.601i	0.625374	+	0.634577i
$377$		−	318.450i		−	0.844694i
$378$	−678.100	+	389.303i	−1.79392	+	1.02990i
$379$	−374.578	−	374.578i	−0.988332	−	0.988332i	0.0116005	−	0.999933i	$-0.496307\pi$
$379$	−374.578	−	374.578i	−0.988332	−	0.988332i	−0.999933	+	0.0116005i	$0.996307\pi$
$380$		0			0
$381$	763.278	+	763.278i	2.00335	+	2.00335i
$382$	−507.781	−	137.385i	−1.32927	−	0.359648i
$383$		−	431.347i		−	1.12623i	−0.826378	−	0.563116i	$-0.809602\pi$
$383$		−	431.347i		−	1.12623i	0.826378	−	0.563116i	$-0.190398\pi$
$384$	567.457	−	314.852i	1.47775	−	0.819926i
$385$		0			0
$386$	30.7896	−	113.800i	0.0797659	−	0.294817i
$387$	−250.993	+	250.993i	−0.648560	+	0.648560i
$388$	−396.381	−	231.431i	−1.02160	−	0.596472i
$389$	55.8528	−	55.8528i	0.143580	−	0.143580i	−0.631663	−	0.775243i	$-0.717627\pi$
$389$	55.8528	−	55.8528i	0.143580	−	0.143580i	0.775243	+	0.631663i	$0.217627\pi$
$390$		0			0
$391$	870.452			2.22622
$392$	−291.624	+	287.395i	−0.743938	+	0.733150i
$393$			247.895i			0.630777i
$394$	13.4412	+	23.4122i	0.0341146	+	0.0594219i
$395$		0			0
$396$	27.8420	−	7.31513i	0.0703081	−	0.0184726i
$397$	104.083	+	104.083i	0.262173	+	0.262173i	0.825936	−	0.563763i	$-0.190647\pi$
$397$	104.083	+	104.083i	0.262173	+	0.262173i	−0.563763	+	0.825936i	$0.690647\pi$
$398$	53.8800	−	199.142i	0.135377	−	0.500358i
$399$			736.030i			1.84469i
$400$		0			0
$401$	32.9517			0.0821738			0.0410869	−	0.999156i	$-0.486918\pi$
$401$	32.9517			0.0821738			0.0410869	+	0.999156i	$0.486918\pi$
$402$	62.0259	+	16.7817i	0.154293	+	0.0417456i
$403$	50.3088	−	50.3088i	0.124836	−	0.124836i
$404$	−21.1291	+	5.55139i	−0.0522996	+	0.0137411i
$405$		0			0
$406$	−568.732	+	326.514i	−1.40082	+	0.804221i
$407$	4.17371			0.0102548
$408$	7.64378	−	1046.53i	0.0187348	−	2.56503i
$409$			559.822i			1.36876i	0.729126	+	0.684379i	$0.239927\pi$
$409$			559.822i			1.36876i	−0.729126	+	0.684379i	$0.760073\pi$
$410$		0			0
$411$	−561.679	−	561.679i	−1.36662	−	1.36662i
$412$	284.316	+	166.001i	0.690088	+	0.402916i
$413$	−582.161	−	582.161i	−1.40959	−	1.40959i
$414$	−1087.90	−	294.343i	−2.62778	−	0.710972i
$415$		0			0
$416$	−267.472	−	158.797i	−0.642961	−	0.381724i
$417$	−1082.39			−2.59565
$418$	3.26410	−	12.0642i	0.00780886	−	0.0288618i
$419$	168.614	−	168.614i	0.402420	−	0.402420i	−0.476665	−	0.879085i	$-0.658155\pi$
$419$	168.614	−	168.614i	0.402420	−	0.402420i	0.879085	+	0.476665i	$0.158155\pi$
$420$		0			0
$421$	409.607	−	409.607i	0.972937	−	0.972937i	−0.0267062	−	0.999643i	$-0.508502\pi$
$421$	409.607	−	409.607i	0.972937	−	0.972937i	0.999643	+	0.0267062i	$0.00850184\pi$
$422$	−6.95491	−	12.1143i	−0.0164808	−	0.0287068i
$423$	−699.481			−1.65362
$424$	−3.01917	+	413.364i	−0.00712068	+	0.974915i
$425$		0			0
$426$	58.3978	+	101.719i	0.137084	+	0.238777i
$427$	263.164	+	263.164i	0.616310	+	0.616310i
$428$	−157.592	−	599.808i	−0.368205	−	1.40142i
$429$	−15.0137	−	15.0137i	−0.0349970	−	0.0349970i
$430$		0			0
$431$		−	307.273i		−	0.712930i	−0.934309	−	0.356465i	$-0.883982\pi$
$431$		−	307.273i		−	0.712930i	0.934309	−	0.356465i	$-0.116018\pi$
$432$	−167.623	+	602.064i	−0.388017	+	1.39367i
$433$	573.906			1.32542			0.662709	−	0.748877i	$-0.269407\pi$
$433$	573.906			1.32542			0.662709	+	0.748877i	$0.269407\pi$
$434$	−141.431	−	38.2657i	−0.325878	−	0.0881697i
$435$		0			0
$436$	4.30138	+	16.3714i	0.00986556	+	0.0375492i
$437$	−345.987	+	345.987i	−0.791733	+	0.791733i
$438$	−894.521	+	513.552i	−2.04228	+	1.17249i
$439$	−491.449			−1.11947			−0.559737	−	0.828670i	$-0.689098\pi$
$439$	−491.449			−1.11947			−0.559737	+	0.828670i	$0.689098\pi$
$440$		0			0
$441$		−	854.922i		−	1.93860i
$442$	−435.045	+	249.763i	−0.984266	+	0.565075i
$443$	−343.974	−	343.974i	−0.776466	−	0.776466i	0.202762	−	0.979228i	$-0.435008\pi$
$443$	−343.974	−	343.974i	−0.776466	−	0.776466i	−0.979228	+	0.202762i	$0.935008\pi$
$444$	−99.0579	+	169.660i	−0.223103	+	0.382117i
$445$		0			0
$446$	−342.006	−	92.5332i	−0.766829	−	0.207474i
$447$			691.558i			1.54711i
$448$	−9.35690	+	640.507i	−0.0208859	+	1.42970i
$449$	−153.260			−0.341337			−0.170668	−	0.985329i	$-0.554593\pi$
$449$	−153.260			−0.341337			−0.170668	+	0.985329i	$0.554593\pi$
$450$		0			0
$451$	−19.4319	+	19.4319i	−0.0430862	+	0.0430862i
$452$	253.370	+	147.933i	0.560554	+	0.327286i
$453$	−105.439	+	105.439i	−0.232758	+	0.232758i
$454$	−336.948	−	586.906i	−0.742176	−	1.29274i
$455$		0			0
$456$	412.938	+	419.015i	0.905567	+	0.918892i
$457$			708.281i			1.54985i	0.632054	+	0.774924i	$0.282212\pi$
$457$			708.281i			1.54985i	−0.632054	+	0.774924i	$0.717788\pi$
$458$	150.258	+	261.724i	0.328074	+	0.571450i
$459$	712.676	+	712.676i	1.55267	+	1.55267i
$460$		0			0
$461$	20.0249	+	20.0249i	0.0434379	+	0.0434379i	0.728492	−	0.685054i	$-0.240221\pi$
$461$	20.0249	+	20.0249i	0.0434379	+	0.0434379i	−0.685054	+	0.728492i	$0.740221\pi$
$462$	−11.4197	+	42.2075i	−0.0247179	+	0.0913583i
$463$			30.9338i			0.0668117i	0.999442	+	0.0334059i	$0.0106354\pi$
$463$			30.9338i			0.0668117i	−0.999442	+	0.0334059i	$0.989365\pi$
$464$	−140.588	+	504.959i	−0.302991	+	1.08827i
$465$		0			0
$466$	−256.693	−	69.4509i	−0.550843	−	0.149036i
$467$	−89.9400	+	89.9400i	−0.192591	+	0.192591i	−0.796815	−	0.604224i	$-0.793483\pi$
$467$	−89.9400	+	89.9400i	−0.192591	+	0.192591i	0.604224	+	0.796815i	$0.293483\pi$
$468$	628.182	−	165.047i	1.34227	−	0.352664i
$469$	−44.8494	+	44.8494i	−0.0956277	+	0.0956277i
$470$		0			0
$471$	−843.606			−1.79110
$472$	−658.031	−	4.80619i	−1.39413	−	0.0101826i
$473$			9.15497i			0.0193551i
$474$	643.073	−	369.194i	1.35669	−	0.778890i
$475$		0			0
$476$	892.124	+	520.877i	1.87421	+	1.09428i
$477$	−610.333	−	610.333i	−1.27952	−	1.27952i
$478$	−173.106	−	46.8356i	−0.362146	−	0.0979824i
$479$		−	424.069i		−	0.885322i	−0.896689	−	0.442661i	$-0.854035\pi$
$479$		−	424.069i		−	0.885322i	0.896689	−	0.442661i	$-0.145965\pi$
$480$		0			0
$481$	94.1688			0.195777
$482$	135.296	−	500.058i	0.280697	−	1.03746i
$483$	1210.46	−	1210.46i	2.50613	−	2.50613i
$484$	−243.664	+	417.332i	−0.503437	+	0.862256i
$485$		0			0
$486$	109.271	+	190.332i	0.224838	+	0.391630i
$487$	−509.544			−1.04629			−0.523146	−	0.852243i	$-0.675242\pi$
$487$	−509.544			−1.04629			−0.523146	+	0.852243i	$0.675242\pi$
$488$	297.461	+	2.17263i	0.609552	+	0.00445210i
$489$			56.0166i			0.114553i
$490$		0			0
$491$	232.469	+	232.469i	0.473461	+	0.473461i	0.903033	−	0.429572i	$-0.141335\pi$
$491$	232.469	+	232.469i	0.473461	+	0.473461i	−0.429572	+	0.903033i	$0.641335\pi$
$492$	−328.708	−	1251.09i	−0.668107	−	2.54287i
$493$	597.730	+	597.730i	1.21243	+	1.21243i
$494$	73.6459	−	272.198i	0.149081	−	0.551008i
$495$		0			0
$496$	−101.984	+	57.5635i	−0.205612	+	0.116055i
$497$	−115.777			−0.232951
$498$	−552.710	−	149.541i	−1.10986	−	0.300284i
$499$	−609.443	+	609.443i	−1.22133	+	1.22133i	−0.254170	+	0.967160i	$0.581802\pi$
$499$	−609.443	+	609.443i	−1.22133	+	1.22133i	−0.967160	+	0.254170i	$0.918198\pi$
$500$		0			0
$501$	−915.506	+	915.506i	−1.82736	+	1.82736i
$502$	209.072	−	120.030i	0.416479	−	0.239104i
$503$	83.3154			0.165637			0.0828185	−	0.996565i	$-0.473608\pi$
$503$	83.3154			0.165637			0.0828185	+	0.996565i	$0.473608\pi$
$504$	−938.853	−	952.668i	−1.86280	−	1.89022i
$505$		0			0
$506$	−25.2087	+	14.4725i	−0.0498195	+	0.0286018i
$507$	267.118	+	267.118i	0.526859	+	0.526859i
$508$	−429.405	+	735.458i	−0.845285	+	1.44775i
$509$	534.566	+	534.566i	1.05023	+	1.05023i	0.998670	+	0.0515585i	$0.0164189\pi$
$509$	534.566	+	534.566i	1.05023	+	1.05023i	0.0515585	+	0.998670i	$0.483581\pi$
$510$		0			0
$511$		−	1018.14i		−	1.99245i
$512$	354.020	+	369.884i	0.691445	+	0.722429i
$513$	−566.549			−1.10438
$514$	−235.932	+	872.012i	−0.459011	+	1.69652i
$515$		0			0
$516$	−372.147	−	217.282i	−0.721215	−	0.421089i
$517$	−12.7568	+	12.7568i	−0.0246746	+	0.0246746i
$518$	−96.5535	−	168.180i	−0.186397	−	0.324671i
$519$	193.705			0.373227
$520$		0			0
$521$			513.800i			0.986181i	0.869978	+	0.493091i	$0.164133\pi$
$521$			513.800i			0.986181i	−0.869978	+	0.493091i	$0.835867\pi$
$522$	−544.928	−	949.172i	−1.04392	−	1.81834i
$523$	146.299	+	146.299i	0.279731	+	0.279731i	0.833001	−	0.553271i	$-0.186621\pi$
$523$	146.299	+	146.299i	0.279731	+	0.279731i	−0.553271	+	0.833001i	$0.686621\pi$
$524$	−189.161	+	49.6995i	−0.360994	+	0.0948464i
$525$		0			0
$526$	0.490682	−	1.81358i	0.000932856	−	0.00344787i
$527$			188.859i			0.358367i
$528$	17.1788	+	30.4352i	0.0325355	+	0.0576424i
$529$	609.006			1.15124
$530$		0			0
$531$	971.585	−	971.585i	1.82973	−	1.82973i
$532$	−561.640	+	147.564i	−1.05571	+	0.277375i
$533$	−438.429	+	438.429i	−0.822569	+	0.822569i
$534$	−327.262	+	187.884i	−0.612850	+	0.351842i
$535$		0			0
$536$	−0.370267	+	50.6944i	−0.000690796	+	0.0945791i
$537$			364.875i			0.679469i
$538$	346.102	−	198.700i	0.643313	−	0.369332i
$539$	−15.5917	−	15.5917i	−0.0289270	−	0.0289270i
$540$		0			0
$541$	−610.827	−	610.827i	−1.12907	−	1.12907i	−0.990328	−	0.138743i	$-0.955694\pi$
$541$	−610.827	−	610.827i	−1.12907	−	1.12907i	−0.138743	−	0.990328i	$-0.544306\pi$
$542$	458.856	+	124.148i	0.846597	+	0.229056i
$543$		−	97.8618i		−	0.180224i
$544$	800.107	−	203.983i	1.47079	−	0.374968i
$545$		0			0
$546$	−257.655	+	952.302i	−0.471896	+	1.74414i
$547$	392.410	−	392.410i	0.717386	−	0.717386i	−0.250683	−	0.968069i	$-0.580655\pi$
$547$	392.410	−	392.410i	0.717386	−	0.717386i	0.968069	+	0.250683i	$0.0806552\pi$
$548$	315.990	−	541.207i	0.576624	−	0.987604i
$549$	−439.202	+	439.202i	−0.800004	+	0.800004i
$550$		0			0
$551$	−475.172			−0.862381
$552$	9.99328	−	1368.21i	0.0181038	−	2.47865i
$553$			731.945i			1.32359i
$554$	−424.841	−	740.001i	−0.766861	−	1.33574i
$555$		0			0
$556$	−217.003	−	825.932i	−0.390293	−	1.48549i
$557$	587.051	+	587.051i	1.05395	+	1.05395i	0.998459	+	0.0554921i	$0.0176728\pi$
$557$	587.051	+	587.051i	1.05395	+	1.05395i	0.0554921	+	0.998459i	$0.482327\pi$
$558$	63.8626	−	236.038i	0.114449	−	0.423008i
$559$			206.558i			0.369513i
$560$		0			0
$561$	56.3616			0.100466
$562$	405.162	+	109.621i	0.720929	+	0.195055i
$563$	−168.514	+	168.514i	−0.299314	+	0.299314i	−0.840745	−	0.541431i	$-0.817883\pi$
$563$	−168.514	+	168.514i	−0.299314	+	0.299314i	0.541431	+	0.840745i	$0.317883\pi$
$564$	−215.793	−	821.326i	−0.382612	−	1.45625i
$565$		0			0
$566$	−213.749	+	122.715i	−0.377648	+	0.216811i
$567$	477.372			0.841926
$568$	−65.9104	+	64.9546i	−0.116040	+	0.114357i
$569$		−	550.627i		−	0.967711i	−0.875148	−	0.483855i	$-0.839236\pi$
$569$		−	550.627i		−	0.967711i	0.875148	−	0.483855i	$-0.160764\pi$
$570$		0			0
$571$	−163.518	−	163.518i	−0.286371	−	0.286371i	0.549272	−	0.835644i	$-0.314905\pi$
$571$	−163.518	−	163.518i	−0.286371	−	0.286371i	−0.835644	+	0.549272i	$0.814905\pi$
$572$	8.44643	−	14.4665i	0.0147665	−	0.0252911i
$573$	942.921	+	942.921i	1.64559	+	1.64559i
$574$	1232.54	+	333.476i	2.14728	+	0.580969i
$575$		0			0
$576$	−1068.96	−	15.6160i	−1.85583	−	0.0271111i
$577$	−15.6965			−0.0272037			−0.0136018	−	0.999907i	$-0.504330\pi$
$577$	−15.6965			−0.0272037			−0.0136018	+	0.999907i	$0.504330\pi$
$578$	196.818	−	727.447i	0.340516	−	1.25856i
$579$	−211.319	+	211.319i	−0.364973	+	0.364973i
$580$		0			0
$581$	399.651	−	399.651i	0.687868	−	0.687868i
$582$	579.316	+	1009.07i	0.995389	+	1.73380i
$583$	−22.2619			−0.0381851
$584$	−571.213	−	579.619i	−0.978104	−	0.992497i
$585$		0			0
$586$	296.499	+	516.451i	0.505971	+	0.881315i
$587$	−715.538	−	715.538i	−1.21897	−	1.21897i	−0.967992	−	0.250983i	$-0.919246\pi$
$587$	−715.538	−	715.538i	−1.21897	−	1.21897i	−0.250983	−	0.967992i	$-0.580754\pi$
$588$	1003.85	−	263.747i	1.70722	−	0.448550i
$589$	−75.0678	−	75.0678i	−0.127450	−	0.127450i
$590$		0			0
$591$		−	68.4346i		−	0.115795i
$592$	−149.322	−	41.5733i	−0.252232	−	0.0702251i
$593$	557.100			0.939460			0.469730	−	0.882810i	$-0.344351\pi$
$593$	557.100			0.939460			0.469730	+	0.882810i	$0.344351\pi$
$594$	−32.4886	−	8.79014i	−0.0546947	−	0.0147982i
$595$		0			0
$596$	−527.705	+	138.648i	−0.885411	+	0.232630i
$597$	−369.796	+	369.796i	−0.619424	+	0.619424i
$598$	−568.767	+	326.534i	−0.951116	+	0.546044i
$599$	524.845			0.876202			0.438101	−	0.898926i	$-0.355651\pi$
$599$	524.845			0.876202			0.438101	+	0.898926i	$0.355651\pi$
$600$		0			0
$601$		−	182.301i		−	0.303330i	−0.988432	−	0.151665i	$-0.951537\pi$
$601$		−	182.301i		−	0.303330i	0.988432	−	0.151665i	$-0.0484635\pi$
$602$	368.900	−	211.789i	0.612790	−	0.351808i
$603$	−74.8504	−	74.8504i	−0.124130	−	0.124130i
$604$	−101.596	−	59.3181i	−0.168206	−	0.0982088i
$605$		0			0
$606$	53.4573	+	14.4634i	0.0882133	+	0.0238670i
$607$		−	987.505i		−	1.62686i	−0.581662	−	0.813431i	$-0.697597\pi$
$607$		−	987.505i		−	1.62686i	0.581662	−	0.813431i	$-0.302403\pi$
$608$	−236.948	+	399.106i	−0.389717	+	0.656424i
$609$	1662.42			2.72975
$610$		0			0
$611$	−287.823	+	287.823i	−0.471069	+	0.471069i
$612$	−869.305	+	1488.89i	−1.42043	+	2.43283i
$613$	−768.517	+	768.517i	−1.25370	+	1.25370i	−0.299648	+	0.954050i	$0.596869\pi$
$613$	−768.517	+	768.517i	−1.25370	+	1.25370i	−0.954050	+	0.299648i	$0.903131\pi$
$614$	486.323	+	847.092i	0.792057	+	1.37963i
$615$		0			0
$616$	−34.4966	−	0.251960i	−0.0560010	−	0.000409026i
$617$		−	467.462i		−	0.757636i	−0.925471	−	0.378818i	$-0.876331\pi$
$617$		−	467.462i		−	0.757636i	0.925471	−	0.378818i	$-0.123669\pi$
$618$	−415.533	−	723.787i	−0.672383	−	1.17118i
$619$	−272.667	−	272.667i	−0.440496	−	0.440496i	0.451682	−	0.892179i	$-0.350824\pi$
$619$	−272.667	−	272.667i	−0.440496	−	0.440496i	−0.892179	+	0.451682i	$0.850824\pi$
$620$		0			0
$621$	931.734	+	931.734i	1.50038	+	1.50038i
$622$	−52.0823	+	192.498i	−0.0837336	+	0.309482i
$623$		−	372.489i		−	0.597896i
$624$	387.594	+	686.690i	0.621144	+	1.10046i
$625$		0			0
$626$	601.057	+	162.622i	0.960155	+	0.259780i
$627$	−22.4026	+	22.4026i	−0.0357298	+	0.0357298i
$628$	−169.131	−	643.727i	−0.269317	−	1.02504i
$629$	−176.755	+	176.755i	−0.281009	+	0.281009i
$630$		0			0
$631$	1107.18			1.75465			0.877324	−	0.479898i	$-0.159326\pi$
$631$	1107.18			1.75465			0.877324	+	0.479898i	$0.159326\pi$
$632$	410.646	+	416.689i	0.649757	+	0.659318i
$633$			35.4104i			0.0559405i
$634$	−47.1989	+	27.0973i	−0.0744462	+	0.0427402i
$635$		0			0
$636$	528.359	−	904.940i	0.830753	−	1.42286i
$637$	−351.785	−	351.785i	−0.552252	−	0.552252i
$638$	−27.2486	−	7.37240i	−0.0427095	−	0.0115555i
$639$		−	193.223i		−	0.302383i
$640$		0			0
$641$	−645.436			−1.00692			−0.503460	−	0.864018i	$-0.667940\pi$
$641$	−645.436			−1.00692			−0.503460	+	0.864018i	$0.667940\pi$
$642$	−410.585	+	1517.54i	−0.639541	+	2.36376i
$643$	−397.860	+	397.860i	−0.618756	+	0.618756i	−0.945212	−	0.326456i	$-0.894145\pi$
$643$	−397.860	+	397.860i	−0.618756	+	0.618756i	0.326456	+	0.945212i	$0.394145\pi$
$644$	1166.34	+	680.981i	1.81109	+	1.05742i
$645$		0			0
$646$	372.682	+	649.149i	0.576907	+	1.00487i
$647$	386.850			0.597913			0.298956	−	0.954267i	$-0.403361\pi$
$647$	386.850			0.597913			0.298956	+	0.954267i	$0.403361\pi$
$648$	271.763	−	267.822i	0.419388	−	0.413306i
$649$		−	35.4386i		−	0.0546049i
$650$		0			0
$651$	262.630	+	262.630i	0.403425	+	0.403425i
$652$	−42.7444	+	11.2305i	−0.0655589	+	0.0172248i
$653$	557.600	+	557.600i	0.853905	+	0.853905i	0.990612	−	0.136707i	$-0.0436517\pi$
$653$	557.600	+	557.600i	0.853905	+	0.853905i	−0.136707	+	0.990612i	$0.543652\pi$
$654$	11.2067	−	41.4203i	0.0171356	−	0.0633338i
$655$		0			0
$656$	888.765	−	501.653i	1.35482	−	0.764714i
$657$	1699.21			2.58631
$658$	809.147	+	218.923i	1.22971	+	0.332710i
$659$	85.5304	−	85.5304i	0.129788	−	0.129788i	−0.639229	−	0.769017i	$-0.720746\pi$
$659$	85.5304	−	85.5304i	0.129788	−	0.129788i	0.769017	+	0.639229i	$0.220746\pi$
$660$		0			0
$661$	−677.148	+	677.148i	−1.02443	+	1.02443i	−0.0247351	+	0.999694i	$0.507874\pi$
$661$	−677.148	+	677.148i	−1.02443	+	1.02443i	−0.999694	+	0.0247351i	$0.992126\pi$
$662$	476.393	−	273.501i	0.719627	−	0.413144i
$663$	1271.65			1.91803
$664$	3.29943	−	451.736i	0.00496902	−	0.680325i
$665$		0			0
$666$	280.680	−	161.141i	0.421441	−	0.241953i
$667$	781.457	+	781.457i	1.17160	+	1.17160i
$668$	−882.138	−	515.046i	−1.32057	−	0.771027i
$669$	635.086	+	635.086i	0.949306	+	0.949306i
$670$		0			0
$671$			16.0199i			0.0238747i
$672$	828.977	−	1396.30i	1.23360	−	2.07782i
$673$	−1077.92			−1.60167			−0.800836	−	0.598884i	$-0.795611\pi$
$673$	−1077.92			−1.60167			−0.800836	+	0.598884i	$0.795611\pi$
$674$	288.490	−	1066.27i	0.428027	−	1.58200i
$675$		0			0
$676$	−150.275	+	257.382i	−0.222300	+	0.380742i
$677$	−926.183	+	926.183i	−1.36807	+	1.36807i	−0.504881	+	0.863189i	$0.668464\pi$
$677$	−926.183	+	926.183i	−1.36807	+	1.36807i	−0.863189	+	0.504881i	$0.831536\pi$
$678$	−370.305	−	645.008i	−0.546172	−	0.951339i
$679$	−1148.52			−1.69149
$680$		0			0
$681$			1715.54i			2.51915i
$682$	−3.14006	−	5.46944i	−0.00460419	−	0.00801971i
$683$	−548.522	−	548.522i	−0.803107	−	0.803107i	0.180473	−	0.983580i	$-0.442237\pi$
$683$	−548.522	−	548.522i	−0.803107	−	0.803107i	−0.983580	+	0.180473i	$0.942237\pi$
$684$	−246.273	−	937.336i	−0.360048	−	1.37037i
$685$		0			0
$686$	−11.3965	+	42.1219i	−0.0166130	+	0.0614022i
$687$		−	765.027i		−	1.11358i
$688$	91.1903	−	327.535i	0.132544	−	0.476068i
$689$	−502.281			−0.729001
$690$		0			0
$691$	−21.6062	+	21.6062i	−0.0312680	+	0.0312680i	−0.722568	−	0.691300i	$-0.757038\pi$
$691$	−21.6062	+	21.6062i	−0.0312680	+	0.0312680i	0.691300	+	0.722568i	$0.257038\pi$
$692$	38.8351	+	147.810i	0.0561200	+	0.213598i
$693$	50.9344	−	50.9344i	0.0734984	−	0.0734984i
$694$	−292.296	+	167.810i	−0.421176	+	0.241801i
$695$		0			0
$696$	946.399	−	932.675i	1.35977	−	1.34005i
$697$		−	1645.86i		−	2.36136i
$698$	−417.609	+	239.753i	−0.598294	+	0.343486i
$699$	476.664	+	476.664i	0.681923	+	0.681923i
$700$		0			0
$701$	−462.868	−	462.868i	−0.660296	−	0.660296i	0.295153	−	0.955450i	$-0.404629\pi$
$701$	−462.868	−	462.868i	−0.660296	−	0.660296i	−0.955450	+	0.295153i	$0.904629\pi$
$702$	−733.021	−	198.326i	−1.04419	−	0.282516i
$703$		−	140.513i		−	0.199877i
$704$	−19.7800	+	19.2104i	−0.0280965	+	0.0272874i
$705$		0			0
$706$	288.235	−	1065.33i	0.408266	−	1.50896i
$707$	−38.6536	+	38.6536i	−0.0546728	+	0.0546728i
$708$	1440.57	+	841.091i	2.03470	+	1.18798i
$709$	−91.9564	+	91.9564i	−0.129699	+	0.129699i	−0.768976	−	0.639277i	$-0.779234\pi$
$709$	−91.9564	+	91.9564i	−0.129699	+	0.129699i	0.639277	+	0.768976i	$0.279234\pi$
$710$		0			0
$711$	−1221.56			−1.71809
$712$	−208.979	−	212.054i	−0.293510	−	0.297829i
$713$			246.910i			0.346297i
$714$	−1303.85	−	2271.09i	−1.82613	−	3.18080i
$715$		0			0
$716$	−278.424	+	73.1522i	−0.388860	+	0.102168i
$717$	321.448	+	321.448i	0.448323	+	0.448323i
$718$	225.794	−	834.543i	0.314477	−	1.16232i
$719$			463.016i			0.643972i	0.946744	+	0.321986i	$0.104350\pi$
$719$			463.016i			0.643972i	−0.946744	+	0.321986i	$0.895650\pi$
$720$		0			0
$721$	823.814			1.14260
$722$	290.784	+	78.6745i	0.402748	+	0.108967i
$723$	−928.579	+	928.579i	−1.28434	+	1.28434i
$724$	74.6750	−	19.6199i	0.103142	−	0.0270993i
$725$		0			0
$726$	1062.41	−	609.937i	1.46337	−	0.840133i
$727$	233.171			0.320730			0.160365	−	0.987058i	$-0.448733\pi$
$727$	233.171			0.320730			0.160365	+	0.987058i	$0.448733\pi$
$728$	−778.326	−	5.68481i	−1.06913	−	0.00780881i
$729$		−	985.596i		−	1.35198i
$730$		0			0
$731$	−387.709	−	387.709i	−0.530382	−	0.530382i
$732$	−651.205	−	380.213i	−0.889624	−	0.519417i
$733$	−873.035	−	873.035i	−1.19104	−	1.19104i	−0.976775	−	0.214269i	$-0.931263\pi$
$733$	−873.035	−	873.035i	−1.19104	−	1.19104i	−0.214269	−	0.976775i	$-0.568737\pi$
$734$	−432.417	−	116.995i	−0.589124	−	0.159394i
$735$		0			0
$736$	1046.04	−	266.682i	1.42125	−	0.362339i
$737$	−2.73017			−0.00370443
$738$	−556.548	+	2057.02i	−0.754130	+	2.78729i
$739$	−127.699	+	127.699i	−0.172799	+	0.172799i	−0.788208	−	0.615409i	$-0.788991\pi$
$739$	−127.699	+	127.699i	−0.172799	+	0.172799i	0.615409	+	0.788208i	$0.288991\pi$
$740$		0			0
$741$	−505.456	+	505.456i	−0.682127	+	0.682127i
$742$	515.001	+	897.044i	0.694071	+	1.20895i
$743$	−226.592			−0.304968			−0.152484	−	0.988306i	$-0.548727\pi$
$743$	−226.592			−0.304968			−0.152484	+	0.988306i	$0.548727\pi$
$744$	296.857	+	2.16821i	0.399001	+	0.00291426i
$745$		0			0
$746$	−491.078	−	855.375i	−0.658282	−	1.14662i
$747$	666.989	+	666.989i	0.892890	+	0.892890i
$748$	11.2997	+	43.0076i	0.0151065	+	0.0574968i
$749$	−1097.29	−	1097.29i	−1.46501	−	1.46501i
$750$		0			0
$751$			516.811i			0.688164i	0.938940	+	0.344082i	$0.111810\pi$
$751$			516.811i			0.688164i	−0.938940	+	0.344082i	$0.888190\pi$
$752$	583.463	−	329.329i	0.775881	−	0.437937i
$753$	−611.124			−0.811586
$754$	−614.794	−	166.339i	−0.815377	−	0.220609i
$755$		0			0
$756$	397.385	+	1512.48i	0.525641	+	2.00063i
$757$	−135.597	+	135.597i	−0.179124	+	0.179124i	−0.790974	−	0.611850i	$-0.790426\pi$
$757$	−135.597	+	135.597i	−0.179124	+	0.179124i	0.611850	+	0.790974i	$0.290426\pi$
$758$	−918.812	+	527.498i	−1.21215	+	0.695907i
$759$	73.6857			0.0970826
$760$		0			0
$761$			268.435i			0.352739i	0.984324	+	0.176370i	$0.0564354\pi$
$761$			268.435i			0.352739i	−0.984324	+	0.176370i	$0.943565\pi$
$762$	1872.26	−	1074.88i	2.45704	−	1.41061i
$763$	29.9500	+	29.9500i	0.0392530	+	0.0392530i
$764$	−530.469	+	908.553i	−0.694331	+	1.18921i
$765$		0			0
$766$	−832.752	−	225.310i	−1.08714	−	0.294138i
$767$		−	799.578i		−	1.04247i
$768$	−311.443	−	1259.98i	−0.405524	−	1.64060i
$769$	−826.424			−1.07467			−0.537337	−	0.843368i	$-0.680570\pi$
$769$	−826.424			−1.07467			−0.537337	+	0.843368i	$0.680570\pi$
$770$		0			0
$771$	1619.28	−	1619.28i	2.10023	−	2.10023i
$772$	−203.617	−	118.884i	−0.263753	−	0.153995i
$773$	1042.45	−	1042.45i	1.34857	−	1.34857i	0.461359	−	0.887213i	$-0.347362\pi$
$773$	1042.45	−	1042.45i	1.34857	−	1.34857i	0.887213	−	0.461359i	$-0.152638\pi$
$774$	353.460	+	615.667i	0.456666	+	0.795435i
$775$		0			0
$776$	−653.843	+	644.361i	−0.842581	+	0.830362i
$777$			491.595i			0.632683i
$778$	−78.6544	−	137.003i	−0.101098	−	0.176096i
$779$	654.199	+	654.199i	0.839793	+	0.839793i
$780$		0			0
$781$	−3.52390	−	3.52390i	−0.00451203	−	0.00451203i
$782$	454.672	−	1680.48i	0.581421	−	2.14895i
$783$			1279.62i			1.63426i
$784$	402.513	+	713.123i	0.513410	+	0.909595i
$785$		0			0
$786$	478.583	+	129.486i	0.608885	+	0.164740i
$787$	924.222	−	924.222i	1.17436	−	1.17436i	0.193201	−	0.981159i	$-0.438113\pi$
$787$	924.222	−	924.222i	1.17436	−	1.17436i	0.981159	−	0.193201i	$-0.0618870\pi$
$788$	52.2201	−	13.7202i	0.0662692	−	0.0174114i
$789$	−3.36771	+	3.36771i	−0.00426833	+	0.00426833i
$790$		0			0
$791$	734.148			0.928126
$792$	0.420503	−	57.5724i	0.000530938	−	0.0726924i
$793$			361.447i			0.455797i
$794$	255.307	−	146.574i	0.321546	−	0.184602i
$795$		0			0
$796$	−356.318	−	208.040i	−0.447636	−	0.261357i
$797$	−761.055	−	761.055i	−0.954899	−	0.954899i	0.0441268	−	0.999026i	$-0.485949\pi$
$797$	−761.055	−	761.055i	−0.954899	−	0.954899i	−0.999026	+	0.0441268i	$0.985949\pi$
$798$	1420.97	+	384.458i	1.78066	+	0.481777i
$799$		−	1080.49i		−	1.35230i
$800$		0			0
$801$	621.657			0.776101
$802$	17.2120	−	63.6160i	0.0214613	−	0.0793217i
$803$	30.9893	−	30.9893i	0.0385919	−	0.0385919i
$804$	64.7972	−	110.981i	0.0805935	−	0.138036i
$805$		0			0
$806$	−70.8471	−	123.404i	−0.0878996	−	0.153106i
$807$	−1011.67			−1.25362
$808$	−0.319116	+	43.6912i	−0.000394945	+	0.0540732i
$809$		−	106.311i		−	0.131410i	−0.997839	−	0.0657052i	$-0.979070\pi$
$809$		−	106.311i		−	0.131410i	0.997839	−	0.0657052i	$-0.0209297\pi$
$810$		0			0
$811$	−602.747	−	602.747i	−0.743214	−	0.743214i	0.229981	−	0.973195i	$-0.426134\pi$
$811$	−602.747	−	602.747i	−0.743214	−	0.743214i	−0.973195	+	0.229981i	$0.926134\pi$
$812$	333.292	+	1268.54i	0.410458	+	1.56224i
$813$	−852.069	−	852.069i	−1.04806	−	1.04806i
$814$	2.18010	−	8.05771i	0.00267825	−	0.00989890i
$815$		0			0
$816$	−2016.43	−	561.403i	−2.47112	−	0.687994i
$817$	308.213			0.377250
$818$	1080.78	+	292.417i	1.32125	+	0.357479i
$819$	1149.20	−	1149.20i	1.40317	−	1.40317i
$820$		0			0
$821$	236.461	−	236.461i	0.288016	−	0.288016i	−0.548280	−	0.836295i	$-0.684717\pi$
$821$	236.461	−	236.461i	0.288016	−	0.288016i	0.836295	+	0.548280i	$0.184717\pi$
$822$	−1377.76	+	790.982i	−1.67610	+	0.962266i
$823$	412.888			0.501687			0.250843	−	0.968028i	$-0.419292\pi$
$823$	412.888			0.501687			0.250843	+	0.968028i	$0.419292\pi$
$824$	468.989	−	462.188i	0.569162	−	0.560908i
$825$		0			0
$826$	−1428.00	+	819.826i	−1.72881	+	0.992525i
$827$	772.140	+	772.140i	0.933664	+	0.933664i	0.997933	−	0.0642682i	$-0.0204713\pi$
$827$	772.140	+	772.140i	0.933664	+	0.933664i	−0.0642682	+	0.997933i	$0.520471\pi$
$828$	−1136.51	+	1946.54i	−1.37259	+	2.35089i
$829$	−163.360	−	163.360i	−0.197056	−	0.197056i	0.601681	−	0.798737i	$-0.294498\pi$
$829$	−163.360	−	163.360i	−0.197056	−	0.197056i	−0.798737	+	0.601681i	$0.794498\pi$
$830$		0			0
$831$			2163.05i			2.60294i
$832$	−446.283	+	433.431i	−0.536397	+	0.520951i
$833$	1320.60			1.58535
$834$	−565.373	+	2089.64i	−0.677906	+	2.50556i
$835$		0			0
$836$	−21.5861	−	12.6033i	−0.0258207	−	0.0150757i
$837$	−202.155	+	202.155i	−0.241524	+	0.241524i
$838$	−237.450	−	413.598i	−0.283353	−	0.493553i
$839$	156.751			0.186831			0.0934154	−	0.995627i	$-0.470222\pi$
$839$	156.751			0.186831			0.0934154	+	0.995627i	$0.470222\pi$
$840$		0			0
$841$			232.237i			0.276144i
$842$	−576.827	−	1004.73i	−0.685067	−	1.19327i
$843$	−752.363	−	752.363i	−0.892482	−	0.892482i
$844$	−27.0205	+	7.09928i	−0.0320148	+	0.00841147i
$845$		0			0
$846$	−365.367	+	1350.41i	−0.431875	+	1.59623i
$847$			1209.23i			1.42766i
$848$	796.458	+	221.745i	0.939219	+	0.261492i
$849$	624.794			0.735917
$850$		0			0
$851$	−231.085	+	231.085i	−0.271545	+	0.271545i
$852$	226.881	−	59.6100i	0.266292	−	0.0699648i
$853$	933.500	−	933.500i	1.09437	−	1.09437i	0.0993169	−	0.995056i	$-0.468334\pi$
$853$	933.500	−	933.500i	1.09437	−	1.09437i	0.995056	−	0.0993169i	$-0.0316657\pi$
$854$	645.523	−	370.600i	0.755881	−	0.433958i
$855$		0			0
$856$	−1240.30	−	9.05901i	−1.44895	−	0.0105830i
$857$		−	988.694i		−	1.15367i	−0.816861	−	0.576834i	$-0.804288\pi$
$857$		−	988.694i		−	1.15367i	0.816861	−	0.576834i	$-0.195712\pi$
$858$	−36.8276	+	21.1430i	−0.0429226	+	0.0246422i
$859$	868.729	+	868.729i	1.01133	+	1.01133i	0.999935	+	0.0113913i	$0.00362604\pi$
$859$	868.729	+	868.729i	1.01133	+	1.01133i	0.0113913	+	0.999935i	$0.496374\pi$
$860$		0			0
$861$	−2288.76	−	2288.76i	−2.65825	−	2.65825i
$862$	−593.216	−	160.501i	−0.688186	−	0.186196i
$863$			1065.18i			1.23428i	0.786854	+	0.617139i	$0.211709\pi$
$863$			1065.18i			1.23428i	−0.786854	+	0.617139i	$0.788291\pi$
$864$	1074.78	+	638.093i	1.24396	+	0.738534i
$865$		0			0
$866$	299.774	−	1107.97i	0.346159	−	1.27942i
$867$	−1350.83	+	1350.83i	−1.55805	+	1.55805i
$868$	−147.750	+	253.057i	−0.170219	+	0.291541i
$869$	−22.2783	+	22.2783i	−0.0256367	+	0.0256367i
$870$		0			0
$871$	−61.5991			−0.0707222
$872$	33.8532	+	0.247261i	0.0388225	+	0.000283556i
$873$		−	1916.80i		−	2.19565i
$874$	487.235	+	848.681i	0.557477	+	0.971031i
$875$		0			0
$876$	524.213	+	1995.20i	0.598416	+	2.27762i
$877$	107.637	+	107.637i	0.122733	+	0.122733i	0.765805	−	0.643072i	$-0.222341\pi$
$877$	107.637	+	107.637i	0.122733	+	0.122733i	−0.643072	+	0.765805i	$0.722341\pi$
$878$	−256.703	+	948.785i	−0.292373	+	1.08062i
$879$		−	1509.60i		−	1.71741i
$880$		0			0
$881$	1289.21			1.46334			0.731672	−	0.681657i	$-0.238740\pi$
$881$	1289.21			1.46334			0.731672	+	0.681657i	$0.238740\pi$
$882$	−1650.50	−	446.560i	−1.87132	−	0.506304i
$883$	89.1493	−	89.1493i	0.100962	−	0.100962i	−0.654822	−	0.755783i	$-0.727256\pi$
$883$	89.1493	−	89.1493i	0.100962	−	0.100962i	0.755783	+	0.654822i	$0.227256\pi$
$884$	254.948	+	970.354i	0.288403	+	1.09769i
$885$		0			0
$886$	−843.743	+	484.400i	−0.952306	+	0.546727i
$887$	−1235.62			−1.39303			−0.696516	−	0.717541i	$-0.745268\pi$
$887$	−1235.62			−1.39303			−0.696516	+	0.717541i	$0.745268\pi$
$888$	275.802	+	279.860i	0.310587	+	0.315158i
$889$			2131.01i			2.39708i
$890$		0			0
$891$	14.5298	+	14.5298i	0.0163073	+	0.0163073i
$892$	−357.287	+	611.938i	−0.400546	+	0.686029i
$893$	429.473	+	429.473i	0.480933	+	0.480933i
$894$	1335.11	+	361.229i	1.49341	+	0.404059i
$895$		0			0
$896$	1231.67	+	352.627i	1.37463	+	0.393556i
$897$	1662.52			1.85343
$898$	−80.0539	+	295.882i	−0.0891468	+	0.329490i
$899$	−169.550	+	169.550i	−0.188599	+	0.188599i
$900$		0			0
$901$	942.783	−	942.783i	1.04637	−	1.04637i
$902$	27.3649	+	47.6650i	0.0303380	+	0.0528436i
$903$	−1078.30			−1.19414
$904$	417.943	−	411.882i	0.462326	−	0.455622i
$905$		0			0
$906$	148.485	+	258.635i	0.163890	+	0.285469i
$907$	−1170.07	−	1170.07i	−1.29004	−	1.29004i	−0.934757	−	0.355287i	$-0.884383\pi$
$907$	−1170.07	−	1170.07i	−1.29004	−	1.29004i	−0.355287	−	0.934757i	$-0.615617\pi$
$908$	−1309.07	+	343.942i	−1.44171	+	0.378791i
$909$	−64.5101	−	64.5101i	−0.0709682	−	0.0709682i
$910$		0			0
$911$			174.325i			0.191356i	0.995412	+	0.0956781i	$0.0305019\pi$
$911$			174.325i			0.191356i	−0.995412	+	0.0956781i	$0.969498\pi$
$912$	1024.64	−	578.345i	1.12351	−	0.634150i
$913$	24.3284			0.0266467
$914$	1367.40	+	369.963i	1.49606	+	0.404774i
$915$		0			0
$916$	583.766	−	153.377i	0.637299	−	0.167442i
$917$	−346.052	+	346.052i	−0.377374	+	0.377374i
$918$	1748.14	−	1003.62i	1.90429	−	1.09327i
$919$	−1108.52			−1.20622			−0.603110	−	0.797658i	$-0.706072\pi$
$919$	−1108.52			−1.20622			−0.603110	+	0.797658i	$0.706072\pi$
$920$		0			0
$921$		−	2476.08i		−	2.68846i
$922$	49.1195	−	28.2000i	0.0532750	−	0.0305856i
$923$	−79.5075	−	79.5075i	−0.0861403	−	0.0861403i
$924$	75.5203	+	44.0934i	0.0817319	+	0.0477201i
$925$		0			0
$926$	59.7204	+	16.1580i	0.0644929	+	0.0174492i
$927$			1374.89i			1.48316i
$928$	901.432	+	535.177i	0.971371	+	0.576700i
$929$	−410.945			−0.442352			−0.221176	−	0.975234i	$-0.570990\pi$
$929$	−410.945			−0.442352			−0.221176	+	0.975234i	$0.570990\pi$
$930$		0			0
$931$	−524.912	+	524.912i	−0.563816	+	0.563816i
$932$	−268.162	+	459.291i	−0.287727	+	0.492801i
$933$	357.458	−	357.458i	0.383127	−	0.383127i
$934$	126.658	+	220.616i	0.135608	+	0.236206i
$935$		0			0
$936$	9.48754	−	1298.97i	0.0101363	−	1.38779i
$937$			181.492i			0.193694i	0.995299	+	0.0968472i	$0.0308758\pi$
$937$			181.492i			0.193694i	−0.995299	+	0.0968472i	$0.969124\pi$
$938$	63.1590	+	110.012i	0.0673337	+	0.117284i
$939$	−1116.13	−	1116.13i	−1.18864	−	1.18864i
$940$		0			0
$941$	−363.737	−	363.737i	−0.386543	−	0.386543i	0.486910	−	0.873452i	$-0.338124\pi$
$941$	−363.737	−	363.737i	−0.386543	−	0.386543i	−0.873452	+	0.486910i	$0.838124\pi$
$942$	−440.649	+	1628.65i	−0.467780	+	1.72893i
$943$		−	2151.76i		−	2.28183i
$944$	−352.995	+	1267.87i	−0.373935	+	1.34309i
$945$		0			0
$946$	17.6744	+	4.78200i	0.0186833	+	0.00505497i
$947$	616.971	−	616.971i	0.651500	−	0.651500i	−0.301854	−	0.953354i	$-0.597605\pi$
$947$	616.971	−	616.971i	0.651500	−	0.651500i	0.953354	+	0.301854i	$0.0976055\pi$
$948$	−376.858	−	1434.35i	−0.397529	−	1.51303i
$949$	699.192	−	699.192i	0.736767	−	0.736767i
$950$		0			0
$951$	137.964			0.145072
$952$	1471.59	−	1450.25i	1.54579	−	1.52337i
$953$			602.419i			0.632129i	0.948738	+	0.316064i	$0.102362\pi$
$953$			602.419i			0.632129i	−0.948738	+	0.316064i	$0.897638\pi$
$954$	−1497.10	+	859.499i	−1.56929	+	0.900943i
$955$		0			0
$956$	−180.840	+	309.732i	−0.189163	+	0.323987i
$957$	50.5992	+	50.5992i	0.0528727	+	0.0528727i
$958$	−818.702	−	221.508i	−0.854595	−	0.231219i
$959$		−	1568.16i		−	1.63521i
$960$		0			0
$961$	907.429			0.944255
$962$	49.1881	−	181.801i	0.0511311	−	0.188982i
$963$	1831.30	−	1831.30i	1.90166	−	1.90166i
$964$	−894.734	−	522.400i	−0.928147	−	0.541909i
$965$		0			0
$966$	−1704.62	−	2969.17i	−1.76462	−	3.07367i
$967$	−1277.51			−1.32111			−0.660553	−	0.750779i	$-0.729678\pi$
$967$	−1277.51			−1.32111			−0.660553	+	0.750779i	$0.729678\pi$
$968$	678.420	+	688.403i	0.700847	+	0.711160i
$969$		−	1897.48i		−	1.95819i
$970$		0			0
$971$	122.966	+	122.966i	0.126639	+	0.126639i	0.767585	−	0.640947i	$-0.221458\pi$
$971$	122.966	+	122.966i	0.126639	+	0.126639i	−0.640947	+	0.767585i	$0.721458\pi$
$972$	424.530	−	111.540i	0.436759	−	0.114753i
$973$	−1510.97	−	1510.97i	−1.55289	−	1.55289i
$974$	−266.155	+	983.718i	−0.273260	+	1.00998i
$975$		0			0
$976$	159.570	−	573.140i	0.163494	−	0.587233i
$977$	−809.129			−0.828177			−0.414088	−	0.910237i	$-0.635900\pi$
$977$	−809.129			−0.828177			−0.414088	+	0.910237i	$0.635900\pi$
$978$	108.145	+	29.2597i	0.110578	+	0.0299179i
$979$	11.3375	−	11.3375i	0.0115807	−	0.0115807i
$980$		0			0
$981$	−49.9844	+	49.9844i	−0.0509525	+	0.0509525i
$982$	570.230	−	327.374i	0.580682	−	0.333375i
$983$	986.542			1.00360			0.501802	−	0.864983i	$-0.332671\pi$
$983$	986.542			1.00360			0.501802	+	0.864983i	$0.332671\pi$
$984$	−2587.04	−	18.8955i	−2.62910	−	0.0192027i
$985$		0			0
$986$	1466.19	−	841.751i	1.48701	−	0.853703i
$987$	−1502.54	−	1502.54i	−1.52233	−	1.52233i
$988$	−487.033	−	284.360i	−0.492948	−	0.287813i
$989$	−506.881	−	506.881i	−0.512519	−	0.512519i
$990$		0			0
$991$		−	674.433i		−	0.680558i	−0.940325	−	0.340279i	$-0.889479\pi$
$991$		−	674.433i		−	0.680558i	0.940325	−	0.340279i	$-0.110521\pi$
$992$	57.8611	+	226.956i	0.0583277	+	0.228786i
$993$	−1392.51			−1.40233
$994$	−60.4747	+	223.517i	−0.0608397	+	0.224866i
$995$		0			0
$996$	−577.405	+	988.943i	−0.579724	+	0.992915i
$997$	1315.09	−	1315.09i	1.31905	−	1.31905i	0.404519	−	0.914530i	$-0.367439\pi$
$997$	1315.09	−	1315.09i	1.31905	−	1.31905i	0.914530	−	0.404519i	$-0.132561\pi$
$998$	858.246	+	1494.92i	0.859966	+	1.49792i
$999$	−378.398			−0.378777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.r.f.51.10		32
5.2	odd	4		400.3.k.h.99.16		32
5.3	odd	4		400.3.k.g.99.1		32
5.4	even	2		80.3.r.a.51.7	yes	32
16.11	odd	4	inner	400.3.r.f.251.10		32
20.19	odd	2		320.3.r.a.111.2		32
40.19	odd	2		640.3.r.b.351.15		32
40.29	even	2		640.3.r.a.351.2		32
80.19	odd	4		640.3.r.a.31.2		32
80.27	even	4		400.3.k.g.299.1		32
80.29	even	4		640.3.r.b.31.15		32
80.43	even	4		400.3.k.h.299.16		32
80.59	odd	4		80.3.r.a.11.7	✓	32
80.69	even	4		320.3.r.a.271.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.7	✓	32	80.59	odd	4
80.3.r.a.51.7	yes	32	5.4	even	2
320.3.r.a.111.2		32	20.19	odd	2
320.3.r.a.271.2		32	80.69	even	4
400.3.k.g.99.1		32	5.3	odd	4
400.3.k.g.299.1		32	80.27	even	4
400.3.k.h.99.16		32	5.2	odd	4
400.3.k.h.299.16		32	80.43	even	4
400.3.r.f.51.10		32	1.1	even	1	trivial
400.3.r.f.251.10		32	16.11	odd	4	inner
640.3.r.a.31.2		32	80.19	odd	4
640.3.r.a.351.2		32	40.29	even	2
640.3.r.b.31.15		32	80.29	even	4
640.3.r.b.351.15		32	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.522340 - 1.93059i) q^{2} +(-3.58499 + 3.58499i) q^{3} +(-3.45432 - 2.01684i) q^{4} +(5.04854 + 8.79371i) q^{6} -10.0090 q^{7} +(-5.69802 + 5.61539i) q^{8} -16.7043i q^{9} +(-0.304644 - 0.304644i) q^{11} +(19.6141 - 5.15334i) q^{12} +(-6.87350 - 6.87350i) q^{13} +(-5.22809 + 19.3232i) q^{14} +(7.86468 + 13.9337i) q^{16} +25.8031 q^{17} +(-32.2490 - 8.72531i) q^{18} +(-10.2562 + 10.2562i) q^{19} +(35.8821 - 35.8821i) q^{21} +(-0.747270 + 0.429014i) q^{22} +33.7343 q^{23} +(0.296235 - 40.5584i) q^{24} +(-16.8602 + 9.67958i) q^{26} +(27.6197 + 27.6197i) q^{27} +(34.5743 + 20.1866i) q^{28} +(23.1650 + 23.1650i) q^{29} +7.31924i q^{31} +(31.0082 - 7.90534i) q^{32} +2.18429 q^{33} +(13.4780 - 49.8152i) q^{34} +(-33.6899 + 57.7020i) q^{36} +(-6.85014 + 6.85014i) q^{37} +(14.4433 + 25.1578i) q^{38} +49.2828 q^{39} -63.7855i q^{41} +(-50.5308 - 88.0161i) q^{42} +(-15.0257 - 15.0257i) q^{43} +(0.437920 + 1.66676i) q^{44} +(17.6208 - 65.1271i) q^{46} -41.8744i q^{47} +(-78.1468 - 21.7572i) q^{48} +51.1799 q^{49} +(-92.5039 + 92.5039i) q^{51} +(9.88051 + 37.6060i) q^{52} +(36.5375 - 36.5375i) q^{53} +(67.7491 - 38.8954i) q^{54} +(57.0314 - 56.2044i) q^{56} -73.5369i q^{57} +(56.8221 - 32.6221i) q^{58} +(58.1638 + 58.1638i) q^{59} +(-26.2928 - 26.2928i) q^{61} +(14.1304 + 3.82313i) q^{62} +167.193i q^{63} +(0.934849 - 63.9932i) q^{64} +(1.14094 - 4.21696i) q^{66} +(4.48091 - 4.48091i) q^{67} +(-89.1323 - 52.0409i) q^{68} +(-120.937 + 120.937i) q^{69} +11.5673 q^{71} +(93.8010 + 95.1813i) q^{72} +101.723i q^{73} +(9.64668 + 16.8029i) q^{74} +(56.1135 - 14.7431i) q^{76} +(3.04918 + 3.04918i) q^{77} +(25.7424 - 95.1447i) q^{78} -73.1288i q^{79} -47.6943 q^{81} +(-123.143 - 33.3177i) q^{82} +(-39.9292 + 39.9292i) q^{83} +(-196.317 + 51.5798i) q^{84} +(-36.8568 + 21.1598i) q^{86} -166.093 q^{87} +(3.44656 + 0.0251734i) q^{88} +37.2154i q^{89} +(68.7968 + 68.7968i) q^{91} +(-116.529 - 68.0369i) q^{92} +(-26.2394 - 26.2394i) q^{93} +(-80.8420 - 21.8726i) q^{94} +(-82.8233 + 139.504i) q^{96} +114.749 q^{97} +(26.7333 - 98.8071i) q^{98} +(-5.08886 + 5.08886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 12 q^{6} + 32 q^{11} + 60 q^{12} - 36 q^{14} + 48 q^{16} - 160 q^{18} - 32 q^{19} + 12 q^{22} + 128 q^{23} - 120 q^{24} - 48 q^{26} + 96 q^{27} + 180 q^{28} + 32 q^{29} + 160 q^{32} + 16 q^{34}+ \cdots + 608 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 12 * q^6 + 32 * q^11 + 60 * q^12 - 36 * q^14 + 48 * q^16 - 160 * q^18 - 32 * q^19 + 12 * q^22 + 128 * q^23 - 120 * q^24 - 48 * q^26 + 96 * q^27 + 180 * q^28 + 32 * q^29 + 160 * q^32 + 16 * q^34 - 84 * q^36 + 96 * q^37 - 140 * q^38 + 384 * q^39 - 20 * q^42 - 96 * q^43 + 8 * q^44 + 36 * q^46 - 280 * q^48 + 224 * q^49 - 256 * q^51 + 104 * q^52 + 160 * q^53 + 192 * q^54 + 304 * q^56 + 4 * q^58 - 352 * q^59 - 32 * q^61 - 552 * q^62 + 240 * q^64 - 576 * q^66 - 160 * q^67 - 16 * q^68 + 96 * q^69 + 256 * q^71 - 568 * q^72 + 136 * q^74 + 512 * q^76 - 224 * q^77 + 208 * q^78 - 288 * q^81 + 196 * q^82 + 480 * q^83 - 736 * q^84 - 188 * q^86 + 320 * q^88 - 384 * q^91 - 28 * q^92 - 96 * q^93 - 604 * q^94 + 232 * q^96 - 20 * q^98 + 608 * q^99

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