LMFDB - Embedded newform 177.4.e.b.7.4

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	177.7
Dual form			177.4.e.b.76.4

$q$-expansion

$f(q)$	$=$	$q+(-2.02689 - 2.98944i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-1.86736 + 4.68671i) q^{4} +(-15.6898 + 7.25888i) q^{5} +(-9.28436 + 5.58622i) q^{6} +(-2.35079 + 8.46678i) q^{7} +(-10.4232 + 2.29432i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})$	\(q+(-2.02689 - 2.98944i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-1.86736 + 4.68671i) q^{4} +(-15.6898 + 7.25888i) q^{5} +(-9.28436 + 5.58622i) q^{6} +(-2.35079 + 8.46678i) q^{7} +(-10.4232 + 2.29432i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(53.5015 + 32.1908i) q^{10} +(23.4623 - 22.2246i) q^{11} +(13.7362 + 6.35506i) q^{12} +(27.9911 - 3.04421i) q^{13} +(30.0757 - 10.1337i) q^{14} +(19.1964 + 48.1794i) q^{15} +(57.2868 + 54.2649i) q^{16} +(4.60003 + 16.5678i) q^{17} +(15.2261 + 28.7195i) q^{18} +(4.49473 - 3.41680i) q^{19} +(-4.72181 - 87.0886i) q^{20} +(24.9813 + 8.41717i) q^{21} +(-113.995 - 25.0921i) q^{22} +(13.1382 - 24.7813i) q^{23} +(5.17997 + 31.5964i) q^{24} +(112.556 - 132.511i) q^{25} +(-65.8353 - 77.5074i) q^{26} +(-4.36811 + 26.6443i) q^{27} +(-35.2916 - 26.8280i) q^{28} +(-129.276 + 190.668i) q^{29} +(105.120 - 155.041i) q^{30} +(176.872 + 134.455i) q^{31} +(32.2944 - 196.987i) q^{32} +(-62.7654 - 73.8932i) q^{33} +(40.2047 - 47.3326i) q^{34} +(-24.5759 - 149.906i) q^{35} +(21.2682 - 40.1161i) q^{36} +(193.114 + 42.5077i) q^{37} +(-19.3247 - 6.51123i) q^{38} +(-4.57303 - 84.3445i) q^{39} +(146.884 - 111.658i) q^{40} +(-188.025 - 354.653i) q^{41} +(-25.4717 - 91.7407i) q^{42} +(-7.88009 - 7.46442i) q^{43} +(60.3481 + 151.462i) q^{44} +(147.444 - 49.6797i) q^{45} +(-100.712 + 10.9531i) q^{46} +(457.602 + 211.709i) q^{47} +(171.860 - 162.795i) q^{48} +(227.742 + 137.028i) q^{49} +(-624.271 - 67.8935i) q^{50} +(50.3776 - 11.0890i) q^{51} +(-38.0020 + 136.871i) q^{52} +(-300.866 + 181.025i) q^{53} +(88.5052 - 40.9469i) q^{54} +(-206.792 + 519.010i) q^{55} +(5.07726 - 93.6446i) q^{56} +(-9.50536 - 14.0194i) q^{57} +832.021 q^{58} +(15.9221 + 452.908i) q^{59} -261.650 q^{60} +(92.1707 + 135.942i) q^{61} +(43.4437 - 801.272i) q^{62} +(29.2719 - 73.4669i) q^{63} +(-81.4196 + 37.6687i) q^{64} +(-417.077 + 250.947i) q^{65} +(-93.6805 + 337.407i) q^{66} +(-361.289 + 79.5258i) q^{67} +(-86.2384 - 9.37899i) q^{68} +(-72.1010 - 43.3817i) q^{69} +(-398.323 + 377.312i) q^{70} +(510.678 + 236.265i) q^{71} +(95.4916 - 10.3853i) q^{72} +(-829.146 + 279.372i) q^{73} +(-264.348 - 663.462i) q^{74} +(-378.668 - 358.694i) q^{75} +(7.62032 + 27.4459i) q^{76} +(133.016 + 250.895i) q^{77} +(-242.874 + 184.628i) q^{78} +(43.1425 + 795.717i) q^{79} +(-1292.72 - 435.569i) q^{80} +(79.1063 + 17.4126i) q^{81} +(-679.107 + 1280.93i) q^{82} +(169.395 + 1033.27i) q^{83} +(-86.0979 + 101.362i) q^{84} +(-192.437 - 226.555i) q^{85} +(-6.34235 + 38.6866i) q^{86} +(550.170 + 418.228i) q^{87} +(-193.562 + 285.482i) q^{88} +(324.052 - 477.940i) q^{89} +(-447.367 - 340.080i) q^{90} +(-40.0265 + 244.151i) q^{91} +(91.6092 + 107.851i) q^{92} +(431.499 - 508.000i) q^{93} +(-294.617 - 1797.08i) q^{94} +(-45.7193 + 86.2357i) q^{95} +(-584.850 - 128.735i) q^{96} +(146.874 + 49.4876i) q^{97} +(-51.9716 - 958.560i) q^{98} +(-231.549 + 176.019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} + O(q^{10}) $	\( 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} - 754q^{10} + 64q^{11} - 168q^{12} + 90q^{13} + 1024q^{14} - 42q^{15} - 172q^{16} + 96q^{17} + 18q^{18} + 16q^{19} - 178q^{20} - 243q^{21} - 604q^{22} + 48q^{23} + 198q^{24} - 173q^{25} + 156q^{26} - 405q^{27} + 84q^{28} - 50q^{29} + 174q^{30} + 222q^{31} - 45q^{32} + 192q^{33} - 64q^{34} - 132q^{35} - 504q^{36} + 30q^{37} - 108q^{38} + 270q^{39} + 6984q^{40} + 400q^{41} + 114q^{42} + 1220q^{43} + 1180q^{44} - 126q^{45} + 4938q^{46} + 370q^{47} - 516q^{48} + 771q^{49} + 1048q^{50} + 288q^{51} - 1964q^{52} - 822q^{53} + 54q^{54} - 2342q^{55} - 13824q^{56} + 48q^{57} - 13150q^{58} - 3423q^{59} - 534q^{60} - 2182q^{61} + 845q^{62} + 54q^{63} - 8018q^{64} + 4140q^{65} - 1812q^{66} + 506q^{67} + 4826q^{68} - 3684q^{69} + 6882q^{70} + 5874q^{71} + 594q^{72} + 206q^{73} + 11124q^{74} - 867q^{75} + 16940q^{76} + 9940q^{77} + 468q^{78} - 1762q^{79} - 28954q^{80} - 1215q^{81} + 3770q^{82} - 1216q^{83} - 8013q^{84} - 420q^{85} - 2256q^{86} + 5940q^{87} + 13458q^{88} - 1580q^{89} + 522q^{90} - 12204q^{91} + 4562q^{92} + 666q^{93} + 176q^{94} - 28456q^{95} + 2040q^{96} + 2574q^{97} + 50690q^{98} + 576q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.02689	−	2.98944i	−0.716614	−	1.05693i	−0.995328	−	0.0965522i	$-0.969219\pi$
$2$	−2.02689	−	2.98944i	−0.716614	−	1.05693i	0.278714	−	0.960374i	$-0.410092\pi$
$3$	0.162417	−	2.99560i	0.0312571	−	0.576504i
$3$	0.162417	−	2.99560i	0.0312571	−	0.576504i
$4$	−1.86736	+	4.68671i	−0.233420	+	0.585839i
$5$	−15.6898	+	7.25888i	−1.40334	+	0.649254i	−0.967986	−	0.251005i	$-0.919239\pi$
$5$	−15.6898	+	7.25888i	−1.40334	+	0.649254i	−0.435354	+	0.900259i	$0.643377\pi$
$6$	−9.28436	+	5.58622i	−0.631721	+	0.380094i
$7$	−2.35079	+	8.46678i	−0.126931	+	0.457163i	−0.999510	−	0.0313098i	$-0.990032\pi$
$7$	−2.35079	+	8.46678i	−0.126931	+	0.457163i	0.872579	+	0.488473i	$0.162446\pi$
$8$	−10.4232	+	2.29432i	−0.460645	+	0.101396i
$9$	−8.94724	−	0.973071i	−0.331379	−	0.0360397i
$10$	53.5015	+	32.1908i	1.69187	+	1.01796i
$11$	23.4623	−	22.2246i	0.643103	−	0.609180i	−0.295016	−	0.955492i	$-0.595325\pi$
$11$	23.4623	−	22.2246i	0.643103	−	0.609180i	0.938119	+	0.346313i	$0.112566\pi$
$12$	13.7362	+	6.35506i	0.330442	+	0.152879i
$13$	27.9911	−	3.04421i	0.597179	−	0.0649472i	0.195463	−	0.980711i	$-0.437379\pi$
$13$	27.9911	−	3.04421i	0.597179	−	0.0649472i	0.401717	+	0.915764i	$0.368414\pi$
$14$	30.0757	−	10.1337i	0.574148	−	0.193453i
$15$	19.1964	+	48.1794i	0.330433	+	0.829324i
$16$	57.2868	+	54.2649i	0.895106	+	0.847890i
$17$	4.60003	+	16.5678i	0.0656277	+	0.236369i	0.989088	−	0.147324i	$-0.0470659\pi$
$17$	4.60003	+	16.5678i	0.0656277	+	0.236369i	−0.923461	+	0.383693i	$0.874652\pi$
$18$	15.2261	+	28.7195i	0.199380	+	0.376070i
$19$	4.49473	−	3.41680i	0.0542717	−	0.0412563i	−0.577687	−	0.816259i	$-0.696044\pi$
$19$	4.49473	−	3.41680i	0.0542717	−	0.0412563i	0.631958	+	0.775002i	$0.282251\pi$
$20$	−4.72181	−	87.0886i	−0.0527914	−	0.973680i
$21$	24.9813	+	8.41717i	0.259589	+	0.0874656i
$22$	−113.995	−	25.0921i	−1.10471	−	0.243166i
$23$	13.1382	−	24.7813i	0.119109	−	0.224663i	−0.816787	−	0.576939i	$-0.804247\pi$
$23$	13.1382	−	24.7813i	0.119109	−	0.224663i	0.935896	+	0.352275i	$0.114592\pi$
$24$	5.17997	+	31.5964i	0.0440565	+	0.268733i
$25$	112.556	−	132.511i	0.900445	−	1.06009i
$26$	−65.8353	−	77.5074i	−0.496591	−	0.584632i
$27$	−4.36811	+	26.6443i	−0.0311350	+	0.189915i
$28$	−35.2916	−	26.8280i	−0.238196	−	0.181072i
$29$	−129.276	+	190.668i	−0.827794	+	1.22090i	0.145046	+	0.989425i	$0.453667\pi$
$29$	−129.276	+	190.668i	−0.827794	+	1.22090i	−0.972840	+	0.231480i	$0.925643\pi$
$30$	105.120	−	155.041i	0.639742	−	0.943548i
$31$	176.872	+	134.455i	1.02475	+	0.778992i	0.975546	−	0.219797i	$-0.0705396\pi$
$31$	176.872	+	134.455i	1.02475	+	0.778992i	0.0492005	+	0.998789i	$0.484333\pi$
$32$	32.2944	−	196.987i	0.178403	−	1.08821i
$33$	−62.7654	−	73.8932i	−0.331093	−	0.389793i
$34$	40.2047	−	47.3326i	0.202795	−	0.238749i
$35$	−24.5759	−	149.906i	−0.118688	−	0.723966i
$36$	21.2682	−	40.1161i	0.0984639	−	0.185723i
$37$	193.114	+	42.5077i	0.858049	+	0.188871i	0.622142	−	0.782905i	$-0.286263\pi$
$37$	193.114	+	42.5077i	0.858049	+	0.188871i	0.235908	+	0.971776i	$0.424194\pi$
$38$	−19.3247	−	6.51123i	−0.0824966	−	0.0277964i
$39$	−4.57303	−	84.3445i	−0.0187762	−	0.346306i
$40$	146.884	−	111.658i	0.580610	−	0.441368i
$41$	−188.025	−	354.653i	−0.716209	−	1.35091i	−0.927623	−	0.373517i	$-0.878152\pi$
$41$	−188.025	−	354.653i	−0.716209	−	1.35091i	0.211414	−	0.977397i	$-0.432193\pi$
$42$	−25.4717	−	91.7407i	−0.0935801	−	0.337045i
$43$	−7.88009	−	7.46442i	−0.0279466	−	0.0264724i	0.673599	−	0.739097i	$-0.264748\pi$
$43$	−7.88009	−	7.46442i	−0.0279466	−	0.0264724i	−0.701545	+	0.712625i	$0.747506\pi$
$44$	60.3481	+	151.462i	0.206768	+	0.518950i
$45$	147.444	−	49.6797i	0.488437	−	0.164573i
$46$	−100.712	+	10.9531i	−0.322808	+	0.0351075i
$47$	457.602	+	211.709i	1.42017	+	0.657042i	0.971584	−	0.236697i	$-0.0760647\pi$
$47$	457.602	+	211.709i	1.42017	+	0.657042i	0.448589	+	0.893738i	$0.351927\pi$
$48$	171.860	−	162.795i	0.516790	−	0.489529i
$49$	227.742	+	137.028i	0.663970	+	0.399498i
$50$	−624.271	−	67.8935i	−1.76570	−	0.192032i
$51$	50.3776	−	11.0890i	0.138319	−	0.0304464i
$52$	−38.0020	+	136.871i	−0.101345	+	0.365011i
$53$	−300.866	+	181.025i	−0.779756	+	0.469164i	−0.848972	−	0.528438i	$-0.822778\pi$
$53$	−300.866	+	181.025i	−0.779756	+	0.469164i	0.0692160	+	0.997602i	$0.477950\pi$
$54$	88.5052	−	40.9469i	0.223038	−	0.103188i
$55$	−206.792	+	519.010i	−0.506980	+	1.27242i
$56$	5.07726	−	93.6446i	0.0121157	−	0.223460i
$57$	−9.50536	−	14.0194i	−0.0220880	−	0.0325774i
$58$	832.021			1.88361
$59$	15.9221	+	452.908i	0.0351336	+	0.999383i
$59$	15.9221	+	452.908i	0.0351336	+	0.999383i
$60$	−261.650			−0.562980
$61$	92.1707	+	135.942i	0.193463	+	0.285337i	0.912032	−	0.410119i	$-0.134513\pi$
$61$	92.1707	+	135.942i	0.193463	+	0.285337i	−0.718569	+	0.695456i	$0.755202\pi$
$62$	43.4437	−	801.272i	0.0889896	−	1.64132i
$63$	29.2719	−	73.4669i	0.0585382	−	0.146920i
$64$	−81.4196	+	37.6687i	−0.159023	+	0.0735717i
$65$	−417.077	+	250.947i	−0.795878	+	0.478864i
$66$	−93.6805	+	337.407i	−0.174716	+	0.629271i
$67$	−361.289	+	79.5258i	−0.658784	+	0.145009i	−0.531766	−	0.846891i	$-0.678471\pi$
$67$	−361.289	+	79.5258i	−0.658784	+	0.145009i	−0.127018	+	0.991900i	$0.540540\pi$
$68$	−86.2384	−	9.37899i	−0.153793	−	0.0167260i
$69$	−72.1010	−	43.3817i	−0.125796	−	0.0756891i
$70$	−398.323	+	377.312i	−0.680125	+	0.644248i
$71$	510.678	+	236.265i	0.853611	+	0.394922i	0.797367	−	0.603495i	$-0.206226\pi$
$71$	510.678	+	236.265i	0.853611	+	0.394922i	0.0562436	+	0.998417i	$0.482088\pi$
$72$	95.4916	−	10.3853i	0.156303	−	0.0169989i
$73$	−829.146	+	279.372i	−1.32937	+	0.447918i	−0.892273	−	0.451496i	$-0.850891\pi$
$73$	−829.146	+	279.372i	−1.32937	+	0.447918i	−0.437099	+	0.899413i	$0.643994\pi$
$74$	−264.348	−	663.462i	−0.415267	−	1.04224i
$75$	−378.668	−	358.694i	−0.582998	−	0.552245i
$76$	7.62032	+	27.4459i	0.0115015	+	0.0414245i
$77$	133.016	+	250.895i	0.196865	+	0.371327i
$78$	−242.874	+	184.628i	−0.352565	+	0.268013i
$79$	43.1425	+	795.717i	0.0614419	+	1.13323i	0.852923	+	0.522036i	$0.174827\pi$
$79$	43.1425	+	795.717i	0.0614419	+	1.13323i	−0.791481	+	0.611193i	$0.790690\pi$
$80$	−1292.72	−	435.569i	−1.80663	−	0.608726i
$81$	79.1063	+	17.4126i	0.108513	+	0.0238856i
$82$	−679.107	+	1280.93i	−0.914571	+	1.72506i
$83$	169.395	+	1033.27i	0.224019	+	1.36645i	0.824068	+	0.566490i	$0.191699\pi$
$83$	169.395	+	1033.27i	0.224019	+	1.36645i	−0.600050	+	0.799963i	$0.704853\pi$
$84$	−86.0979	+	101.362i	−0.111834	+	0.131661i
$85$	−192.437	−	226.555i	−0.245562	−	0.289098i
$86$	−6.34235	+	38.6866i	−0.00795248	+	0.0485080i
$87$	550.170	+	418.228i	0.677981	+	0.515388i
$88$	−193.562	+	285.482i	−0.234474	+	0.345824i
$89$	324.052	−	477.940i	0.385948	−	0.569231i	−0.584241	−	0.811580i	$-0.698608\pi$
$89$	324.052	−	477.940i	0.385948	−	0.569231i	0.970189	+	0.242349i	$0.0779179\pi$
$90$	−447.367	−	340.080i	−0.523962	−	0.398306i
$91$	−40.0265	+	244.151i	−0.0461090	+	0.281252i
$92$	91.6092	+	107.851i	0.103814	+	0.122220i
$93$	431.499	−	508.000i	0.481122	−	0.566421i
$94$	−294.617	−	1797.08i	−0.323270	−	1.97186i
$95$	−45.7193	+	86.2357i	−0.0493758	+	0.0931326i
$96$	−584.850	−	128.735i	−0.621781	−	0.136864i
$97$	146.874	+	49.4876i	0.153740	+	0.0518011i	0.395119	−	0.918630i	$-0.370703\pi$
$97$	146.874	+	49.4876i	0.153740	+	0.0518011i	−0.241379	+	0.970431i	$0.577600\pi$
$98$	−51.9716	−	958.560i	−0.0535707	−	0.988053i
$99$	−231.549	+	176.019i	−0.235066	+	0.178692i
$100$	410.858	+	774.961i	0.410858	+	0.774961i
$101$	131.728	+	474.440i	0.129776	+	0.467412i	0.999666	−	0.0258340i	$-0.00822414\pi$
$101$	131.728	+	474.440i	0.129776	+	0.467412i	−0.869890	+	0.493246i	$0.835810\pi$
$102$	−135.260	−	128.125i	−0.131301	−	0.124375i
$103$	−111.183	−	279.047i	−0.106361	−	0.266945i	0.866158	−	0.499770i	$-0.166582\pi$
$103$	−111.183	−	279.047i	−0.106361	−	0.266945i	−0.972519	+	0.232825i	$0.925203\pi$
$104$	−284.773	+	95.9511i	−0.268502	+	0.0904690i
$105$	−453.051	+	49.2723i	−0.421079	+	0.0457951i
$106$	1150.98	+	532.502i	1.05466	+	0.487935i
$107$	511.089	−	484.129i	0.461765	−	0.437407i	−0.421114	−	0.907008i	$-0.638361\pi$
$107$	511.089	−	484.129i	0.461765	−	0.437407i	0.882879	+	0.469601i	$0.155602\pi$
$108$	−116.717	−	70.2266i	−0.103992	−	0.0625699i
$109$	1103.71	+	120.036i	0.969876	+	0.105480i	0.579321	−	0.815099i	$-0.303318\pi$
$109$	1103.71	+	120.036i	0.969876	+	0.105480i	0.390555	+	0.920580i	$0.372283\pi$
$110$	1970.69	−	433.783i	1.70817	−	0.375996i
$111$	158.701	−	571.590i	0.135705	−	0.488765i
$112$	−594.119	+	357.469i	−0.501240	+	0.301586i
$113$	419.783	−	194.212i	0.349468	−	0.161681i	−0.237300	−	0.971437i	$-0.576262\pi$
$113$	419.783	−	194.212i	0.349468	−	0.161681i	0.586768	+	0.809755i	$0.300400\pi$
$114$	−22.6437	+	56.8314i	−0.0186033	+	0.0466908i
$115$	−26.2516	+	484.183i	−0.0212868	+	0.392611i
$116$	−652.203	−	961.928i	−0.522030	−	0.769937i
$117$	−253.405			−0.200234
$118$	1321.67	−	965.592i	1.03110	−	0.753305i
$119$	−151.090			−0.116390
$120$	−310.627	−	458.141i	−0.236302	−	0.348520i
$121$	−15.5156	+	286.168i	−0.0116571	+	0.215002i
$122$	219.569	−	551.078i	0.162942	−	0.408953i
$123$	−1092.94	+	505.646i	−0.801193	+	0.370671i
$124$	−960.433	+	577.873i	−0.695560	+	0.418504i
$125$	−225.981	+	813.911i	−0.161699	+	0.582387i
$126$	−278.956	+	61.4028i	−0.197233	+	0.0434142i
$127$	−1962.42	−	213.426i	−1.37115	−	0.149122i	−0.607280	−	0.794488i	$-0.707739\pi$
$127$	−1962.42	−	213.426i	−1.37115	−	0.149122i	−0.763874	+	0.645366i	$0.776705\pi$
$128$	−1090.71	−	656.258i	−0.753171	−	0.453168i
$129$	−23.6403	+	22.3933i	−0.0161350	+	0.0152838i
$130$	1595.56	+	738.185i	1.07646	+	0.498024i
$131$	2091.91	−	227.509i	1.39520	−	0.151737i	0.620568	−	0.784153i	$-0.286902\pi$
$131$	2091.91	−	227.509i	1.39520	−	0.151737i	0.774629	+	0.632416i	$0.217937\pi$
$132$	463.522	−	156.179i	0.305639	−	0.102982i
$133$	18.3632	+	46.0881i	0.0119721	+	0.0300477i
$134$	970.031	+	918.862i	0.625358	+	0.592370i
$135$	−124.873	−	449.752i	−0.0796101	−	0.286730i
$136$	−85.9590	−	162.136i	−0.0541979	−	0.102228i
$137$	−1259.58	+	957.505i	−0.785495	+	0.597118i	−0.919149	−	0.393910i	$-0.871122\pi$
$137$	−1259.58	+	957.505i	−0.785495	+	0.597118i	0.133654	+	0.991028i	$0.457329\pi$
$138$	16.4538	+	303.472i	0.0101495	+	0.187197i
$139$	1002.34	+	337.727i	0.611634	+	0.206084i	0.608035	−	0.793910i	$-0.291958\pi$
$139$	1002.34	+	337.727i	0.611634	+	0.206084i	0.00359897	+	0.999994i	$0.498854\pi$
$140$	748.460	+	164.749i	0.451832	+	0.0994556i
$141$	708.518	−	1336.41i	0.423177	−	0.798197i
$142$	−328.789	−	2005.52i	−0.194305	−	1.18521i
$143$	589.077	−	693.516i	0.344483	−	0.405557i
$144$	−459.755	−	541.266i	−0.266062	−	0.313232i
$145$	644.283	−	3929.95i	0.368999	−	2.25079i
$146$	2515.75	+	1912.42i	1.42606	+	1.08406i
$147$	447.469	−	659.968i	0.251066	−	0.370294i
$148$	−559.835	+	825.695i	−0.310934	+	0.458593i
$149$	1699.31	+	1291.78i	0.934315	+	0.710248i	0.957181	−	0.289491i	$-0.0934860\pi$
$149$	1699.31	+	1291.78i	0.934315	+	0.710248i	−0.0228660	+	0.999739i	$0.507279\pi$
$150$	−304.774	+	1859.04i	−0.165898	+	1.01193i
$151$	−615.385	−	724.487i	−0.331651	−	0.390450i	0.570909	−	0.821013i	$-0.306591\pi$
$151$	−615.385	−	724.487i	−0.331651	−	0.390450i	−0.902560	+	0.430563i	$0.858315\pi$
$152$	−39.0103	+	45.9265i	−0.0208168	+	0.0245074i
$153$	−25.0359	−	152.712i	−0.0132290	−	0.0806932i
$154$	480.427	−	906.181i	0.251389	−	0.474170i
$155$	−3751.08	−	825.674i	−1.94383	−	0.427869i
$156$	403.838	+	136.069i	0.207262	+	0.0698348i
$157$	−202.777	−	3740.00i	−0.103079	−	1.90117i	−0.357241	−	0.934012i	$-0.616283\pi$
$157$	−202.777	−	3740.00i	−0.103079	−	1.90117i	0.254163	−	0.967161i	$-0.418200\pi$
$158$	2291.30	−	1741.80i	1.15371	−	0.877028i
$159$	493.412	+	930.674i	0.246102	+	0.464197i
$160$	923.214	+	3325.12i	0.456165	+	1.64296i
$161$	178.933	+	169.494i	0.0875893	+	0.0829690i
$162$	−108.286	−	271.777i	−0.0525169	−	0.131807i
$163$	−1884.82	+	635.070i	−0.905709	+	0.305169i	−0.733339	−	0.679863i	$-0.762039\pi$
$163$	−1884.82	+	635.070i	−0.905709	+	0.305169i	−0.172370	+	0.985032i	$0.555142\pi$
$164$	2013.27	−	218.956i	0.958596	−	0.104254i
$165$	1521.16	+	703.764i	0.717710	+	0.332048i
$166$	2745.54	−	2600.71i	1.28371	−	1.21599i
$167$	−2112.63	−	1271.12i	−0.978921	−	0.588997i	−0.0662984	−	0.997800i	$-0.521119\pi$
$167$	−2112.63	−	1271.12i	−0.978921	−	0.588997i	−0.912623	+	0.408802i	$0.865947\pi$
$168$	−279.697	−	30.4189i	−0.128447	−	0.0139695i
$169$	−1371.40	+	301.868i	−0.624216	+	0.137400i
$170$	−287.222	+	1034.48i	−0.129582	+	0.466712i
$171$	−43.5402	+	26.1973i	−0.0194714	+	0.0117155i
$172$	49.6985	−	22.9930i	0.0220319	−	0.0101930i
$173$	−674.488	+	1692.84i	−0.296418	+	0.743954i	0.703043	+	0.711147i	$0.251824\pi$
$173$	−674.488	+	1692.84i	−0.296418	+	0.743954i	−0.999462	+	0.0328069i	$0.989555\pi$
$174$	135.134	−	2492.40i	0.0588764	−	1.08591i
$175$	857.345	+	1264.49i	0.370338	+	0.546208i
$176$	2550.10			1.09216
$177$	1359.32	+	25.8635i	0.577246	+	0.0109832i
$178$	−2085.59			−0.878211
$179$	1671.91	+	2465.89i	0.698126	+	1.02966i	0.997152	+	0.0754144i	$0.0240280\pi$
$179$	1671.91	+	2465.89i	0.698126	+	1.02966i	−0.299026	+	0.954245i	$0.596662\pi$
$180$	−42.4963	+	783.797i	−0.0175971	+	0.324560i
$181$	−410.276	+	1029.71i	−0.168484	+	0.422862i	−0.988838	−	0.148993i	$-0.952397\pi$
$181$	−410.276	+	1029.71i	−0.168484	+	0.422862i	0.820355	+	0.571855i	$0.193776\pi$
$182$	811.003	−	375.210i	0.330305	−	0.152815i
$183$	422.197	−	254.027i	0.170545	−	0.102613i
$184$	−80.0861	+	288.444i	−0.0320871	+	0.115567i
$185$	−3338.49	+	734.857i	−1.32676	+	0.292042i
$186$	−2393.24	−	260.280i	−0.943444	−	0.102606i
$187$	476.140	+	286.484i	0.186197	+	0.112031i
$188$	−1846.73	+	1749.31i	−0.716417	+	0.678626i
$189$	−215.323	−	99.6191i	−0.0828701	−	0.0383398i
$190$	350.464	−	38.1153i	0.133818	−	0.0145536i
$191$	−1064.03	+	358.512i	−0.403090	+	0.135817i	−0.513542	−	0.858065i	$-0.671667\pi$
$191$	−1064.03	+	358.512i	−0.403090	+	0.135817i	0.110452	+	0.993882i	$0.464770\pi$
$192$	99.6166	+	250.019i	0.0374438	+	0.0939768i
$193$	1166.97	+	1105.41i	0.435235	+	0.412276i	0.873695	−	0.486474i	$-0.161717\pi$
$193$	1166.97	+	1105.41i	0.435235	+	0.412276i	−0.438460	+	0.898751i	$0.644476\pi$
$194$	−149.757	−	539.377i	−0.0554224	−	0.199614i
$195$	683.997	+	1290.15i	0.251190	+	0.473794i
$196$	−1067.49	+	811.481i	−0.389025	+	0.295729i
$197$	−87.1158	−	1606.76i	−0.0315063	−	0.581100i	−0.971080	−	0.238754i	$-0.923261\pi$
$197$	−87.1158	−	1606.76i	−0.0315063	−	0.581100i	0.939574	−	0.342346i	$-0.111222\pi$
$198$	995.521	+	335.430i	0.357316	+	0.120394i
$199$	−3076.58	−	677.207i	−1.09595	−	0.241236i	−0.370030	−	0.929020i	$-0.620653\pi$
$199$	−3076.58	−	677.207i	−1.09595	−	0.241236i	−0.725915	+	0.687784i	$0.758584\pi$
$200$	−869.169	+	1639.43i	−0.307298	+	0.579625i
$201$	179.548	+	1095.19i	0.0630067	+	0.384324i
$202$	1151.31	−	1355.43i	0.401020	−	0.472118i
$203$	−1310.45	−	1542.78i	−0.453080	−	0.533407i
$204$	−42.1023	+	256.813i	−0.0144498	+	0.0881396i
$205$	5524.46	+	4199.59i	1.88217	+	1.43079i
$206$	−608.840	+	897.971i	−0.205922	+	0.303712i
$207$	−141.665	+	208.940i	−0.0475671	+	0.0701562i
$208$	1768.71	+	1344.54i	0.589607	+	0.448207i
$209$	29.5193	−	180.060i	0.00976982	−	0.0595932i
$210$	1065.58	+	1254.50i	0.350153	+	0.412232i
$211$	895.598	−	1054.38i	0.292206	−	0.344012i	−0.596396	−	0.802690i	$-0.703401\pi$
$211$	895.598	−	1054.38i	0.292206	−	0.344012i	0.888602	+	0.458679i	$0.151677\pi$
$212$	−286.588	−	1748.11i	−0.0928440	−	0.566324i
$213$	790.698	−	1491.41i	0.254355	−	0.479765i
$214$	−2483.19	−	546.592i	−0.793214	−	0.174599i
$215$	177.821	+	59.9147i	0.0564059	+	0.0190053i
$216$	−15.6009	−	287.741i	−0.00491438	−	0.0906404i
$217$	−1554.19	+	1181.46i	−0.486198	+	0.369598i
$218$	−1878.26	−	3542.78i	−0.583542	−	1.10068i
$219$	702.219	+	2529.16i	0.216674	+	0.780388i
$220$	−2046.30	−	1938.35i	−0.627097	−	0.594017i
$221$	179.196	+	449.747i	0.0545430	+	0.136893i
$222$	−2030.40	+	684.122i	−0.613837	+	0.206826i
$223$	1739.55	−	189.187i	0.522371	−	0.0568113i	0.156865	−	0.987620i	$-0.449861\pi$
$223$	1739.55	−	189.187i	0.522371	−	0.0568113i	0.365506	+	0.930809i	$0.380896\pi$
$224$	1591.93	+	736.506i	0.474845	+	0.219687i
$225$	−1136.00	+	1076.08i	−0.336594	+	0.318839i
$226$	−1431.44	−	861.269i	−0.421319	−	0.253499i
$227$	−1803.87	−	196.182i	−0.527431	−	0.0573615i	−0.159470	−	0.987203i	$-0.550978\pi$
$227$	−1803.87	−	196.182i	−0.527431	−	0.0573615i	−0.367961	+	0.929841i	$0.619944\pi$
$228$	83.4546	−	18.3698i	0.0242409	−	0.00533582i
$229$	179.245	−	645.580i	0.0517241	−	0.186293i	−0.933175	−	0.359422i	$-0.882974\pi$
$229$	179.245	−	645.580i	0.0517241	−	0.186293i	0.984899	+	0.173129i	$0.0553877\pi$
$230$	1500.64	−	902.908i	0.430215	−	0.258852i
$231$	773.186	−	357.714i	0.220225	−	0.101887i
$232$	910.021	−	2283.98i	0.257525	−	0.646339i
$233$	−44.5482	+	821.644i	−0.0125255	+	0.231020i	0.985567	+	0.169285i	$0.0541460\pi$
$233$	−44.5482	+	821.644i	−0.0125255	+	0.231020i	−0.998093	+	0.0617345i	$0.980337\pi$
$234$	513.625	+	757.539i	0.143490	+	0.211632i
$235$	−8716.46			−2.41957
$236$	−2152.38	−	771.118i	−0.593678	−	0.212693i
$237$	2390.66			0.655231
$238$	306.242	+	451.673i	0.0834064	+	0.123015i
$239$	−101.861	+	1878.71i	−0.0275683	+	0.508468i	0.951842	+	0.306589i	$0.0991876\pi$
$239$	−101.861	+	1878.71i	−0.0275683	+	0.508468i	−0.979410	+	0.201879i	$0.935295\pi$
$240$	−1514.75	+	3801.73i	−0.407403	+	1.02250i
$241$	386.105	−	178.631i	0.103200	−	0.0477454i	−0.367610	−	0.929980i	$-0.619824\pi$
$241$	386.105	−	178.631i	0.103200	−	0.0477454i	0.470810	+	0.882235i	$0.343962\pi$
$242$	886.931	−	533.648i	0.235595	−	0.141753i
$243$	65.0094	−	234.143i	0.0171620	−	0.0618118i
$244$	−809.235	+	178.126i	−0.212320	+	0.0467351i
$245$	−4567.89	−	496.789i	−1.19115	−	0.129546i
$246$	3726.86	+	2242.38i	0.965918	+	0.581174i
$247$	115.411	−	109.323i	0.0297304	−	0.0281622i
$248$	−2152.06	−	995.647i	−0.551031	−	0.254934i
$249$	3122.76	−	339.621i	0.794767	−	0.0864361i
$250$	2891.18	−	974.151i	0.731416	−	0.246443i
$251$	−1603.91	−	4025.51i	−0.403338	−	1.01230i	−0.980648	−	0.195778i	$-0.937277\pi$
$251$	−1603.91	−	4025.51i	−0.403338	−	1.01230i	0.577310	−	0.816525i	$-0.304103\pi$
$252$	289.657	+	274.378i	0.0724075	+	0.0685880i
$253$	−242.503	−	873.417i	−0.0602610	−	0.217041i
$254$	3339.58	+	6299.12i	0.824977	+	1.55607i
$255$	−709.922	+	539.669i	−0.174341	+	0.132531i
$256$	287.759	+	5307.41i	0.0702537	+	1.29575i
$257$	−5604.83	−	1888.49i	−1.36039	−	0.458368i	−0.457869	−	0.889020i	$-0.651387\pi$
$257$	−5604.83	−	1888.49i	−1.36039	−	0.458368i	−0.902518	+	0.430652i	$0.858284\pi$
$258$	114.860	+	25.2825i	0.0277164	+	0.00610085i
$259$	−813.875	+	1535.13i	−0.195258	+	0.368295i
$260$	−397.285	−	2423.33i	−0.0947637	−	0.578033i
$261$	1342.20	−	1580.16i	0.318315	−	0.374749i
$262$	−4920.19	−	5792.49i	−1.16019	−	1.36588i
$263$	6.27707	−	38.2884i	0.00147171	−	0.00897706i	−0.986080	−	0.166269i	$-0.946828\pi$
$263$	6.27707	−	38.2884i	0.00147171	−	0.00897706i	0.987552	+	0.157292i	$0.0502763\pi$
$264$	823.753	+	626.200i	0.192040	+	0.145985i
$265$	3406.49	−	5024.19i	0.789656	−	1.16466i
$266$	100.557	−	148.311i	0.0231788	−	0.0341862i
$267$	−1379.09	−	1048.35i	−0.316100	−	0.240293i
$268$	301.942	−	1841.76i	0.0688210	−	0.419789i
$269$	4288.52	+	5048.83i	0.972028	+	1.14436i	0.989503	+	0.144513i	$0.0461614\pi$
$269$	4288.52	+	5048.83i	0.972028	+	1.14436i	−0.0174749	+	0.999847i	$0.505563\pi$
$270$	−1091.40	+	1284.90i	−0.246002	+	0.289616i
$271$	−1306.89	−	7971.68i	−0.292944	−	1.78688i	−0.565507	−	0.824743i	$-0.691320\pi$
$271$	−1306.89	−	7971.68i	−0.292944	−	1.78688i	0.272563	−	0.962138i	$-0.412129\pi$
$272$	−635.530	+	1198.74i	−0.141671	+	0.267221i
$273$	724.877	+	159.557i	0.160702	+	0.0353731i
$274$	5415.42	+	1824.67i	1.19401	+	0.402308i
$275$	−304.193	−	5610.51i	−0.0667037	−	1.23028i
$276$	337.956	−	256.908i	0.0737050	−	0.0560291i
$277$	446.094	+	841.422i	0.0967624	+	0.182513i	0.927168	−	0.374647i	$-0.122236\pi$
$277$	446.094	+	841.422i	0.0967624	+	0.182513i	−0.830405	+	0.557160i	$0.811891\pi$
$278$	−1022.01	−	3680.96i	−0.220490	−	0.794135i
$279$	−1451.68	−	1375.11i	−0.311505	−	0.295073i
$280$	600.093	+	1506.12i	0.128080	+	0.321457i
$281$	6635.02	−	2235.60i	1.40858	−	0.474608i	0.490656	−	0.871353i	$-0.336757\pi$
$281$	6635.02	−	2235.60i	1.40858	−	0.474608i	0.917929	+	0.396746i	$0.129861\pi$
$282$	−5431.20	+	590.678i	−1.14689	+	0.124732i
$283$	−5394.80	−	2495.90i	−1.13317	−	0.524261i	−0.238570	−	0.971125i	$-0.576679\pi$
$283$	−5394.80	−	2495.90i	−1.13317	−	0.524261i	−0.894602	+	0.446864i	$0.852541\pi$
$284$	−2060.92	+	1952.21i	−0.430610	+	0.407896i
$285$	250.902	+	150.963i	0.0521479	+	0.0313764i
$286$	−3267.22	−	355.331i	−0.675506	−	0.0734657i
$287$	3444.78	−	758.252i	0.708497	−	0.155952i
$288$	−480.629	+	1731.07i	−0.0983379	+	0.354181i
$289$	3956.41	−	2380.49i	0.805294	−	0.484529i
$290$	−13054.2	+	6039.54i	−2.64335	+	1.22294i
$291$	172.100	−	431.938i	0.0346690	−	0.0870126i
$292$	238.976	−	4407.66i	0.0478939	−	0.883351i
$293$	4880.66	+	7198.43i	0.973143	+	1.43528i	0.898958	+	0.438035i	$0.144325\pi$
$293$	4880.66	+	7198.43i	0.973143	+	1.43528i	0.0741854	+	0.997244i	$0.476364\pi$
$294$	−2879.90			−0.571291
$295$	−3537.42	−	6990.46i	−0.698158	−	1.37966i
$296$	−2110.40			−0.414407
$297$	489.674	+	722.215i	0.0956693	+	0.141102i
$298$	417.389	−	7698.28i	0.0811365	−	1.49648i
$299$	292.313	−	733.651i	0.0565382	−	0.141900i
$300$	2388.20	−	1104.90i	0.459610	−	0.212638i
$301$	81.7241	−	49.1717i	0.0156495	−	0.00941598i
$302$	−918.492	+	3308.11i	−0.175011	+	0.630332i
$303$	1442.63	−	317.547i	0.273521	−	0.0602065i
$304$	442.901	+	48.1684i	0.0835596	+	0.00908766i
$305$	−2432.93	−	1463.84i	−0.456751	−	0.274818i
$306$	−405.779	+	384.374i	−0.0758067	+	0.0718079i
$307$	−220.793	−	102.150i	−0.0410467	−	0.0189902i	0.399258	−	0.916838i	$-0.369268\pi$
$307$	−220.793	−	102.150i	−0.0410467	−	0.0189902i	−0.440305	+	0.897848i	$0.645130\pi$
$308$	−1424.26	+	154.898i	−0.263490	+	0.0286563i
$309$	−853.971	+	287.736i	−0.157219	+	0.0529733i
$310$	5134.72	+	12887.2i	0.940749	+	2.36110i
$311$	5878.34	+	5568.26i	1.07180	+	1.01526i	0.999841	+	0.0178567i	$0.00568426\pi$
$311$	5878.34	+	5568.26i	1.07180	+	1.01526i	0.0719608	+	0.997407i	$0.477074\pi$
$312$	241.179	+	868.649i	0.0437631	+	0.157620i
$313$	1991.23	+	3755.86i	0.359588	+	0.678254i	0.995629	−	0.0934010i	$-0.0297738\pi$
$313$	1991.23	+	3755.86i	0.359588	+	0.678254i	−0.636041	+	0.771655i	$0.719429\pi$
$314$	−10769.5	+	8186.75i	−1.93553	+	1.47135i
$315$	74.0169	+	1365.16i	0.0132393	+	0.244185i
$316$	−3809.86	−	1283.69i	−0.678232	−	0.228523i
$317$	199.221	+	43.8519i	0.0352977	+	0.00776962i	0.232584	−	0.972576i	$-0.425282\pi$
$317$	199.221	+	43.8519i	0.0352977	+	0.00776962i	−0.197286	+	0.980346i	$0.563213\pi$
$318$	1782.10	−	3361.40i	0.314262	−	0.592761i
$319$	1204.42	+	7346.63i	0.211393	+	1.28944i
$320$	1004.03	−	1182.03i	0.175396	−	0.206492i
$321$	−1367.25	−	1609.65i	−0.237733	−	0.279881i
$322$	144.015	−	878.454i	0.0249244	−	0.152032i
$323$	77.2848	+	58.7504i	0.0133134	+	0.0101206i
$324$	−229.328	+	338.233i	−0.0393223	+	0.0579960i
$325$	2747.16	−	4051.76i	0.468877	−	0.691542i
$326$	5718.83	+	4347.34i	0.971584	+	0.738579i
$327$	538.841	−	3286.79i	0.0911254	−	0.555840i
$328$	2773.51	+	3265.23i	0.466895	+	0.549672i
$329$	−2868.22	+	3376.73i	−0.480639	+	0.565852i
$330$	−979.366	−	5973.87i	−0.163371	−	0.996517i
$331$	16.9150	−	31.9051i	0.00280886	−	0.00529808i	−0.882104	−	0.471055i	$-0.843873\pi$
$331$	16.9150	−	31.9051i	0.00280886	−	0.00529808i	0.884913	+	0.465757i	$0.154218\pi$
$332$	−5158.94	−	1135.57i	−0.852812	−	0.187718i
$333$	−1686.48	−	568.241i	−0.277533	−	0.0935117i
$334$	482.110	+	8891.99i	0.0789817	+	1.45673i
$335$	5091.29	−	3870.30i	0.830349	−	0.631215i
$336$	974.340	+	1837.80i	0.158198	+	0.298394i
$337$	362.335	+	1305.01i	0.0585686	+	0.210945i	0.987044	−	0.160448i	$-0.0512940\pi$
$337$	362.335	+	1305.01i	0.0585686	+	0.210945i	−0.928476	+	0.371393i	$0.878880\pi$
$338$	3682.10	+	3487.87i	0.592544	+	0.561287i
$339$	−513.603	−	1289.05i	−0.0822864	−	0.206523i
$340$	1421.15	−	478.840i	0.226684	−	0.0763786i
$341$	7138.02	−	776.306i	1.13356	−	0.123282i
$342$	166.566	+	77.0618i	0.0263359	+	0.0121843i
$343$	−3883.68	+	3678.82i	−0.611368	+	0.579118i
$344$	99.2617	+	59.7238i	0.0155576	+	0.00936073i
$345$	1446.15	+	157.279i	0.225676	+	0.0245438i
$346$	6427.75	−	1414.85i	0.998722	−	0.219835i
$347$	−1824.69	+	6571.92i	−0.282289	+	1.01671i	0.677392	+	0.735622i	$0.263110\pi$
$347$	−1824.69	+	6571.92i	−0.282289	+	1.01671i	−0.959681	+	0.281091i	$0.909304\pi$
$348$	−2987.48	+	1797.51i	−0.460189	+	0.276886i
$349$	−2577.69	+	1192.57i	−0.395360	+	0.182913i	−0.607488	−	0.794329i	$-0.707823\pi$
$349$	−2577.69	+	1192.57i	−0.395360	+	0.182913i	0.212128	+	0.977242i	$0.431961\pi$
$350$	2042.37	−	5125.96i	0.311912	−	0.782840i
$351$	−41.1572	+	759.101i	−0.00625872	+	0.115435i
$352$	−3620.27	−	5339.50i	−0.548185	−	0.808512i
$353$	9708.30			1.46380			0.731899	−	0.681413i	$-0.238634\pi$
$353$	9708.30			1.46380			0.731899	+	0.681413i	$0.238634\pi$
$354$	−2677.87	−	4116.02i	−0.402054	−	0.617977i
$355$	−9727.46			−1.45431
$356$	1634.85	+	2411.22i	0.243390	+	0.358973i
$357$	−24.5395	+	452.604i	−0.00363800	+	0.0670990i
$358$	3982.84	−	9996.16i	0.587987	−	1.47574i
$359$	9365.54	−	4332.96i	1.37686	−	0.637005i	0.414821	−	0.909903i	$-0.363844\pi$
$359$	9365.54	−	4332.96i	1.37686	−	0.637005i	0.962043	+	0.272897i	$0.0879820\pi$
$360$	−1422.86	+	856.106i	−0.208309	+	0.125335i
$361$	−1826.45	+	6578.27i	−0.266285	+	0.959072i
$362$	3909.85	−	860.623i	0.567672	−	0.124954i
$363$	854.725	+	92.9570i	0.123585	+	0.0134407i
$364$	−1069.52	−	643.509i	−0.154006	−	0.0926622i
$365$	10981.2	−	10402.0i	1.57475	−	1.49168i
$366$	−1615.15	−	747.246i	−0.230670	−	0.106719i
$367$	6618.35	−	719.789i	0.941349	−	0.102378i	0.375441	−	0.926846i	$-0.377491\pi$
$367$	6618.35	−	719.789i	0.941349	−	0.102378i	0.565908	+	0.824468i	$0.308526\pi$
$368$	2097.40	−	706.697i	0.297105	−	0.100106i
$369$	1337.20	+	3356.13i	0.188650	+	0.473477i
$370$	8963.56	+	8490.73i	1.25944	+	1.19301i
$371$	−825.425	−	2972.91i	−0.115509	−	0.416027i
$372$	1575.09	+	2970.93i	0.219528	+	0.414074i
$373$	−6946.59	+	5280.66i	−0.964292	+	0.733036i	−0.963706	−	0.266964i	$-0.913980\pi$
$373$	−6946.59	+	5280.66i	−0.964292	+	0.733036i	−0.000585622		1.00000i	$0.500186\pi$
$374$	−108.657	−	2004.06i	−0.0150228	−	0.277079i
$375$	2401.45	+	809.142i	0.330694	+	0.111424i
$376$	−5255.41	−	1156.80i	−0.720817	−	0.158664i
$377$	−3038.15	+	5730.56i	−0.415047	+	0.782862i
$378$	138.631	+	845.612i	0.0188635	+	0.115062i
$379$	−3168.71	+	3730.49i	−0.429461	+	0.505600i	−0.933746	−	0.357937i	$-0.883480\pi$
$379$	−3168.71	+	3730.49i	−0.429461	+	0.505600i	0.504285	+	0.863537i	$0.331756\pi$
$380$	−318.788	−	375.306i	−0.0430355	−	0.0506653i
$381$	−958.069	+	5843.96i	−0.128828	+	0.785814i
$382$	3228.41	+	2454.18i	0.432408	+	0.328708i
$383$	8118.03	−	11973.2i	1.08306	−	1.59739i	0.324382	−	0.945926i	$-0.394844\pi$
$383$	8118.03	−	11973.2i	1.08306	−	1.59739i	0.758677	−	0.651467i	$-0.225846\pi$
$384$	−2143.03	+	3160.74i	−0.284795	+	0.420041i
$385$	−3908.22	−	2970.95i	−0.517354	−	0.393282i
$386$	939.244	−	5729.14i	0.123850	−	0.755454i
$387$	63.2417	+	74.4539i	0.00830686	+	0.00977959i
$388$	−506.201	+	595.946i	−0.0662331	+	0.0779757i
$389$	2403.29	+	14659.4i	0.313243	+	1.91070i	0.403872	+	0.914815i	$0.367664\pi$
$389$	2403.29	+	14659.4i	0.313243	+	1.91070i	−0.0906290	+	0.995885i	$0.528888\pi$
$390$	2470.45	−	4659.77i	0.320760	−	0.605017i
$391$	471.008	+	103.677i	0.0609204	+	0.0134096i
$392$	−2688.19	−	905.756i	−0.346362	−	0.116703i
$393$	−341.764	−	6303.47i	−0.0438670	−	0.809079i
$394$	−4626.73	+	3517.15i	−0.591602	+	0.449724i
$395$	−6452.91	−	12171.5i	−0.821978	−	1.55041i
$396$	−392.565	−	1413.89i	−0.0498160	−	0.179421i
$397$	−9450.57	−	8952.05i	−1.19474	−	1.13171i	−0.988183	−	0.153279i	$-0.951017\pi$
$397$	−9450.57	−	8952.05i	−1.19474	−	1.13171i	−0.206554	−	0.978435i	$-0.566225\pi$
$398$	4211.42	+	10569.9i	0.530401	+	1.33121i
$399$	141.044	−	47.5232i	0.0176968	−	0.00596275i
$400$	13638.6	−	1483.29i	1.70483	−	0.185411i
$401$	6706.31	+	3102.67i	0.835155	+	0.386384i	0.790383	−	0.612613i	$-0.209882\pi$
$401$	6706.31	+	3102.67i	0.835155	+	0.386384i	0.0447722	+	0.998997i	$0.485744\pi$
$402$	2910.09	−	2756.59i	0.361050	−	0.342005i
$403$	5360.14	+	3225.09i	0.662550	+	0.398643i
$404$	−2469.55	−	268.580i	−0.304120	−	0.0330751i
$405$	−1367.56	+	301.022i	−0.167789	+	0.0369331i
$406$	−1955.91	+	7044.54i	−0.239089	+	0.861119i
$407$	5475.62	−	3294.57i	0.666871	−	0.401243i
$408$	−499.655	+	231.165i	−0.0606290	+	0.0280499i
$409$	1035.99	−	2600.15i	0.125248	−	0.314350i	−0.852960	−	0.521977i	$-0.825195\pi$
$409$	1035.99	−	2600.15i	0.125248	−	0.314350i	0.978208	+	0.207627i	$0.0665740\pi$
$410$	1356.93	−	25027.1i	0.163449	−	3.01464i
$411$	2663.73	+	3928.70i	0.319688	+	0.471505i
$412$	1515.43			0.181213
$413$	−3872.10	−	929.882i	−0.461341	−	0.110791i
$414$	911.752			0.108237
$415$	−10158.1	−	14982.1i	−1.20155	−	1.77215i
$416$	304.285	−	5612.20i	0.0358624	−	0.661444i
$417$	1174.49	−	2947.75i	0.137926	−	0.346168i
$418$	−598.110	+	276.715i	−0.0699868	+	0.0323794i
$419$	−11610.7	+	6985.94i	−1.35375	+	0.814524i	−0.992997	−	0.118137i	$-0.962308\pi$
$419$	−11610.7	+	6985.94i	−1.35375	+	0.814524i	−0.360753	+	0.932661i	$0.617480\pi$
$420$	615.083	−	2215.33i	0.0714595	−	0.257374i
$421$	9490.24	−	2088.96i	1.09864	−	0.241828i	0.371576	−	0.928402i	$-0.378817\pi$
$421$	9490.24	−	2088.96i	1.09864	−	0.241828i	0.727060	+	0.686574i	$0.240886\pi$
$422$	−4967.28	−	540.224i	−0.572994	−	0.0623168i
$423$	−3888.27	−	2339.49i	−0.446936	−	0.268913i
$424$	2720.66	−	2577.14i	0.311620	−	0.295182i
$425$	2713.17	+	1255.25i	0.309666	+	0.143267i
$426$	−6061.15	+	659.190i	−0.689351	+	0.0749715i
$427$	−1367.66	+	460.819i	−0.155002	+	0.0522262i
$428$	1314.59	+	3299.37i	0.148465	+	0.372619i
$429$	−1981.82	−	1877.28i	−0.223038	−	0.211272i
$430$	−181.311	−	653.024i	−0.0203340	−	0.0732363i
$431$	−7658.33	−	14445.1i	−0.855890	−	1.61438i	−0.787163	−	0.616745i	$-0.788451\pi$
$431$	−7658.33	−	14445.1i	−0.855890	−	1.61438i	−0.0687269	−	0.997636i	$-0.521894\pi$
$432$	−1696.09	+	1289.33i	−0.188896	+	0.143595i
$433$	658.001	+	12136.1i	0.0730289	+	1.34694i	0.773744	+	0.633498i	$0.218381\pi$
$433$	658.001	+	12136.1i	0.0730289	+	1.34694i	−0.700715	+	0.713441i	$0.747136\pi$
$434$	6682.07	+	2251.45i	0.739054	+	0.249016i
$435$	−11667.9	−	2568.31i	−1.28606	−	0.283082i
$436$	−2623.60	+	4948.64i	−0.288183	+	0.543570i
$437$	−25.6202	−	156.276i	−0.00280453	−	0.0171069i
$438$	6137.46	−	7225.58i	0.669542	−	0.788245i
$439$	6957.82	+	8191.38i	0.756443	+	0.890554i	0.996784	−	0.0801346i	$-0.0255350\pi$
$439$	6957.82	+	8191.38i	0.756443	+	0.890554i	−0.240341	+	0.970689i	$0.577259\pi$
$440$	964.666	−	5884.20i	0.104520	−	0.637542i
$441$	−1904.32	−	1447.63i	−0.205628	−	0.156315i
$442$	981.282	−	1447.28i	0.105599	−	0.155747i
$443$	−564.758	+	832.956i	−0.0605699	+	0.0893339i	−0.856768	−	0.515702i	$-0.827531\pi$
$443$	−564.758	+	832.956i	−0.0605699	+	0.0893339i	0.796198	+	0.605036i	$0.206841\pi$
$444$	2382.53	+	1811.15i	0.254661	+	0.193589i
$445$	−1615.00	+	9851.05i	−0.172041	+	1.04940i
$446$	−4091.44	−	4816.81i	−0.434384	−	0.511396i
$447$	4145.66	−	4880.65i	0.438664	−	0.516435i
$448$	−127.532	−	777.914i	−0.0134494	−	0.0820379i
$449$	5773.92	−	10890.8i	0.606878	−	1.14469i	−0.369624	−	0.929182i	$-0.620513\pi$
$449$	5773.92	−	10890.8i	0.606878	−	1.14469i	0.976501	−	0.215511i	$-0.0691417\pi$
$450$	5519.43	+	1214.92i	0.578197	+	0.127271i
$451$	−12293.5	−	4142.17i	−1.28355	−	0.432477i
$452$	126.333	+	2330.07i	0.0131464	+	0.242472i
$453$	−2270.22	+	1725.78i	−0.235462	+	0.178994i
$454$	3069.76	+	5790.19i	0.317337	+	0.598561i
$455$	−1144.25	−	4121.23i	−0.117898	−	0.424629i
$456$	131.241	+	124.318i	0.0134779	+	0.0127670i
$457$	−3750.90	−	9414.05i	−0.383938	−	0.963612i	−0.986236	−	0.165341i	$-0.947127\pi$
$457$	−3750.90	−	9414.05i	−0.383938	−	0.963612i	0.602298	−	0.798271i	$-0.294252\pi$
$458$	−2293.23	+	772.680i	−0.233964	+	0.0788318i
$459$	−461.531	+	50.1945i	−0.0469334	+	0.00510431i
$460$	−2220.21	−	1027.18i	−0.225038	−	0.104114i
$461$	5231.32	−	4955.37i	0.528518	−	0.500639i	−0.376265	−	0.926512i	$-0.622792\pi$
$461$	5231.32	−	4955.37i	0.528518	−	0.500639i	0.904783	+	0.425873i	$0.140033\pi$
$462$	−2636.53	−	1586.35i	−0.265503	−	0.159748i
$463$	15891.1	+	1728.26i	1.59508	+	0.173475i	0.862086	−	0.506762i	$-0.169158\pi$
$463$	15891.1	+	1728.26i	1.59508	+	0.173475i	0.732992	+	0.680238i	$0.238123\pi$
$464$	−17752.4	+	3907.61i	−1.77616	+	0.390961i
$465$	−3082.63	+	11102.6i	−0.307427	+	1.10725i
$466$	2546.55	−	1532.21i	0.253147	−	0.152314i
$467$	−4987.81	+	2307.60i	−0.494236	+	0.228658i	−0.651142	−	0.758956i	$-0.725710\pi$
$467$	−4987.81	+	2307.60i	−0.494236	+	0.228658i	0.156907	+	0.987613i	$0.449848\pi$
$468$	473.198	−	1187.64i	0.0467384	−	0.117305i
$469$	175.988	−	3245.91i	0.0173270	−	0.319578i
$470$	17667.3	+	26057.3i	1.73390	+	2.55731i
$471$	−11236.5			−1.09926
$472$	−1205.08	−	4684.23i	−0.117517	−	0.456799i
$473$	−350.779			−0.0340990
$474$	−4845.60	−	7146.72i	−0.469548	−	0.692531i
$475$	53.1438	−	980.180i	0.00513349	−	0.0946816i
$476$	282.138	−	708.114i	0.0271676	−	0.0681856i
$477$	2868.07	−	1326.91i	0.275303	−	0.127369i
$478$	5822.76	−	3503.44i	0.557169	−	0.335237i
$479$	−3662.02	+	13189.4i	−0.349315	+	1.25812i	0.555213	+	0.831708i	$0.312637\pi$
$479$	−3662.02	+	13189.4i	−0.349315	+	1.25812i	−0.904529	+	0.426412i	$0.859777\pi$
$480$	10110.7	−	2225.52i	0.961430	−	0.211627i
$481$	5534.89	+	601.955i	0.524676	+	0.0570619i
$482$	−1316.60	−	792.171i	−0.124418	−	0.0748597i
$483$	536.798	−	508.482i	0.0505697	−	0.0479022i
$484$	−1312.21	−	607.095i	−0.123236	−	0.0570150i
$485$	−2663.65	+	289.690i	−0.249382	+	0.0271219i
$486$	−831.722	+	280.240i	−0.0776290	+	0.0261562i
$487$	356.018	+	893.539i	0.0331268	+	0.0831419i	0.944610	−	0.328196i	$-0.106441\pi$
$487$	356.018	+	893.539i	0.0331268	+	0.0831419i	−0.911483	+	0.411338i	$0.865061\pi$
$488$	−1272.61	−	1205.48i	−0.118050	−	0.111823i
$489$	1596.29	+	5749.31i	0.147621	+	0.531683i
$490$	7773.50	+	14662.4i	0.716675	+	1.35179i
$491$	−11138.5	+	8467.28i	−1.02378	+	0.778254i	−0.975370	−	0.220573i	$-0.929207\pi$
$491$	−11138.5	+	8467.28i	−1.02378	+	0.778254i	−0.0484057	+	0.998828i	$0.515414\pi$
$492$	−328.916	−	6066.50i	−0.0301396	−	0.555892i
$493$	−3753.63	−	1264.75i	−0.342911	−	0.115540i
$494$	−560.740	−	123.428i	−0.0510706	−	0.0112415i
$495$	2355.26	−	4442.48i	0.213860	−	0.403383i
$496$	2836.26	+	17300.4i	0.256758	+	1.56615i
$497$	−3200.90	+	3768.39i	−0.288893	+	0.340112i
$498$	−7344.77	−	8646.93i	−0.660898	−	0.778069i
$499$	−2924.44	+	17838.3i	−0.262357	+	1.60031i	0.446387	+	0.894840i	$0.352710\pi$
$499$	−2924.44	+	17838.3i	−0.262357	+	1.60031i	−0.708744	+	0.705466i	$0.750738\pi$
$500$	−3392.58	−	2578.97i	−0.303442	−	0.230670i
$501$	−4150.91	+	6122.13i	−0.370157	+	0.545941i
$502$	−8783.07	+	12954.1i	−0.780892	+	1.15173i
$503$	−5062.12	−	3848.13i	−0.448726	−	0.341112i	0.356280	−	0.934379i	$-0.384045\pi$
$503$	−5062.12	−	3848.13i	−0.448726	−	0.341112i	−0.805006	+	0.593267i	$0.797838\pi$
$504$	−136.550	+	832.920i	−0.0120683	+	0.0736135i
$505$	−5510.69	−	6487.68i	−0.485589	−	0.571680i
$506$	−2119.50	+	2495.27i	−0.186212	+	0.219226i
$507$	681.538	+	4157.20i	0.0597006	+	0.364157i
$508$	4664.80	−	8798.76i	0.407416	−	0.768468i
$509$	−4253.16	−	936.191i	−0.370369	−	0.0815244i	0.0258859	−	0.999665i	$-0.491759\pi$
$509$	−4253.16	−	936.191i	−0.370369	−	0.0815244i	−0.396255	+	0.918141i	$0.629690\pi$
$510$	3052.24	+	1028.42i	0.265011	+	0.0892925i
$511$	−416.232	−	7676.94i	−0.0360333	−	0.664595i
$512$	7176.02	−	5455.07i	0.619411	−	0.470864i
$513$	71.4049	+	134.684i	0.00614543	+	0.0115915i
$514$	5714.85	+	20583.0i	0.490411	+	1.76630i
$515$	3770.00	+	3571.14i	0.322575	+	0.305559i
$516$	−60.8060	−	152.611i	−0.00518766	−	0.0130200i
$517$	15441.5	−	5202.86i	1.31357	−	0.442595i
$518$	6238.82	−	678.512i	0.529185	−	0.0575523i
$519$	4961.51	+	2295.44i	0.419627	+	0.194140i
$520$	3771.53	−	3572.59i	0.318063	−	0.301285i
$521$	−16669.7	−	10029.8i	−1.40175	−	0.843406i	−0.404291	−	0.914631i	$-0.632482\pi$
$521$	−16669.7	−	10029.8i	−1.40175	−	0.843406i	−0.997460	+	0.0712250i	$0.977309\pi$
$522$	−7444.29	−	809.615i	−0.624191	−	0.0678849i
$523$	−4271.20	+	940.162i	−0.357106	+	0.0786050i	−0.389900	−	0.920857i	$-0.627491\pi$
$523$	−4271.20	+	940.162i	−0.357106	+	0.0786050i	0.0327940	+	0.999462i	$0.489559\pi$
$524$	−2840.07	+	10229.0i	−0.236773	+	0.852779i
$525$	3927.15	−	2362.89i	0.326466	−	0.196428i
$526$	−127.184	+	58.8415i	−0.0105427	+	0.00487759i
$527$	−1414.00	+	3548.87i	−0.116878	+	0.293342i
$528$	414.178	−	7639.07i	0.0341379	−	0.629636i
$529$	6386.46	+	9419.33i	0.524900	+	0.774170i
$530$	−21924.1			−1.79683
$531$	298.253	−	4067.77i	0.0243749	−	0.332441i
$532$	−250.292			−0.0203976
$533$	−6342.66	−	9354.73i	−0.515443	−	0.760222i
$534$	−338.735	+	6247.60i	−0.0274504	+	0.506292i
$535$	−4504.65	+	11305.8i	−0.364025	+	0.913633i
$536$	3583.34	−	1657.83i	0.288762	−	0.133596i
$537$	7658.36	−	4607.88i	0.615424	−	0.370288i
$538$	6400.83	−	23053.7i	0.512935	−	1.84743i
$539$	8388.73	−	1846.50i	0.670367	−	0.147559i
$540$	2341.04	+	254.604i	0.186560	+	0.0202896i
$541$	−12291.1	−	7395.29i	−0.976773	−	0.587705i	−0.0647750	−	0.997900i	$-0.520633\pi$
$541$	−12291.1	−	7395.29i	−0.976773	−	0.587705i	−0.911998	+	0.410195i	$0.865461\pi$
$542$	−21181.9	+	20064.6i	−1.67867	+	1.59012i
$543$	3017.98	+	1396.26i	0.238515	+	0.110349i
$544$	3412.20	−	371.099i	0.268928	−	0.0292477i
$545$	−18188.4	+	6128.38i	−1.42955	+	0.481671i
$546$	−992.258	−	2490.38i	−0.0777742	−	0.195199i
$547$	5642.52	+	5344.88i	0.441055	+	0.417789i	0.875732	−	0.482797i	$-0.160379\pi$
$547$	5642.52	+	5344.88i	0.441055	+	0.417789i	−0.434678	+	0.900586i	$0.643138\pi$
$548$	−2135.47	−	7691.28i	−0.166465	−	0.599553i
$549$	−692.393	−	1305.99i	−0.0538262	−	0.101527i
$550$	−16155.7	+	12281.2i	−1.25251	+	0.952135i
$551$	70.4143	+	1298.72i	0.00544419	+	0.100412i
$552$	851.056	+	286.754i	0.0656220	+	0.0221106i
$553$	−6838.58	−	1505.29i	−0.525870	−	0.115753i
$554$	1611.20	−	3039.04i	0.123562	−	0.233062i
$555$	1659.11	+	10120.1i	0.126893	+	0.774010i
$556$	−3454.55	+	4067.01i	−0.263499	+	0.310215i
$557$	12392.5	+	14589.6i	0.942707	+	1.10984i	0.993804	+	0.111147i	$0.0354524\pi$
$557$	12392.5	+	14589.6i	0.942707	+	1.10984i	−0.0510968	+	0.998694i	$0.516272\pi$
$558$	−1168.40	+	7126.90i	−0.0886419	+	0.540691i
$559$	−243.296	−	184.949i	−0.0184084	−	0.0139937i
$560$	6726.78	−	9921.26i	0.507604	−	0.748660i
$561$	935.525	−	1379.80i	0.0704062	−	0.103841i
$562$	−20131.7	−	15303.7i	−1.51104	−	1.14866i
$563$	−2159.03	+	13169.5i	−0.161621	+	0.985842i	0.774090	+	0.633075i	$0.218208\pi$
$563$	−2159.03	+	13169.5i	−0.161621	+	0.985842i	−0.935711	+	0.352767i	$0.885241\pi$
$564$	4940.30	+	5816.17i	0.368837	+	0.434229i
$565$	−5176.56	+	6094.31i	−0.385450	+	0.453787i
$566$	3473.32	+	21186.3i	0.257941	+	1.57337i
$567$	−333.391	+	628.842i	−0.0246933	+	0.0465765i
$568$	−5864.98	−	1290.98i	−0.433255	−	0.0953667i
$569$	10552.7	+	3555.63i	0.777492	+	0.261968i	0.679945	−	0.733263i	$-0.262004\pi$
$569$	10552.7	+	3555.63i	0.777492	+	0.261968i	0.0975473	+	0.995231i	$0.468900\pi$
$570$	−57.2569	−	1056.04i	−0.00420742	−	0.0776013i
$571$	−13137.5	+	9986.90i	−0.962853	+	0.731942i	−0.963403	−	0.268058i	$-0.913618\pi$
$571$	−13137.5	+	9986.90i	−0.962853	+	0.731942i	0.000549434		1.00000i	$0.499825\pi$
$572$	2150.29	+	4055.88i	0.157182	+	0.296477i
$573$	901.143	+	3245.62i	0.0656995	+	0.236628i
$574$	−9248.93	−	8761.05i	−0.672548	−	0.637072i
$575$	−1805.01	−	4530.23i	−0.130911	−	0.328563i
$576$	765.135	−	257.804i	0.0553483	−	0.0186490i
$577$	−5127.53	+	557.653i	−0.369952	+	0.0402347i	−0.291207	−	0.956660i	$-0.594057\pi$
$577$	−5127.53	+	557.653i	−0.369952	+	0.0402347i	−0.0787448	+	0.996895i	$0.525091\pi$
$578$	−15135.5	−	7002.44i	−1.08920	−	0.503916i
$579$	3500.91	−	3316.24i	0.251283	−	0.238028i
$580$	17215.5	+	10358.2i	1.23247	+	0.741553i
$581$	−9146.64	−	994.757i	−0.653127	−	0.0710318i
$582$	−1640.08	+	361.009i	−0.116810	+	0.0257119i
$583$	−3035.78	+	10933.9i	−0.215659	+	0.776732i
$584$	8001.40	−	4814.28i	0.566952	−	0.341124i
$585$	3975.88	−	1839.44i	0.280996	−	0.130002i
$586$	11626.7	−	29180.9i	0.819616	−	2.05708i
$587$	952.822	−	17573.8i	0.0669969	−	1.23568i	−0.750938	−	0.660373i	$-0.770398\pi$
$587$	952.822	−	17573.8i	0.0669969	−	1.23568i	0.817934	−	0.575311i	$-0.195119\pi$
$588$	2257.50	+	3329.56i	0.158329	+	0.233518i
$589$	1254.40			0.0877530
$590$	−13727.6	+	24743.8i	−0.957892	+	1.72659i
$591$	−4827.35			−0.335991
$592$	8756.23	+	12914.5i	0.607904	+	0.896591i
$593$	1138.61	−	21000.5i	0.0788486	−	1.45428i	−0.644929	−	0.764243i	$-0.723113\pi$
$593$	1138.61	−	21000.5i	0.0788486	−	1.45428i	0.723777	−	0.690034i	$-0.242404\pi$
$594$	1166.50	−	2927.70i	0.0805761	−	0.202231i
$595$	2370.57	−	1096.74i	0.163334	−	0.0755664i
$596$	−9227.43	+	5551.96i	−0.634178	+	0.381572i
$597$	−2528.33	+	9106.22i	−0.173329	+	0.624276i
$598$	−2785.69	+	613.177i	−0.190494	+	0.0419309i
$599$	−15921.8	−	1731.60i	−1.08606	−	0.118116i	−0.452464	−	0.891783i	$-0.649455\pi$
$599$	−15921.8	−	1731.60i	−1.08606	−	0.118116i	−0.633593	+	0.773667i	$0.718421\pi$
$600$	4769.90	+	2869.95i	0.324551	+	0.195276i
$601$	15115.8	−	14318.4i	1.02593	−	0.971816i	0.0263216	−	0.999654i	$-0.491621\pi$
$601$	15115.8	−	14318.4i	1.02593	−	0.971816i	0.999612	+	0.0278371i	$0.00886198\pi$
$602$	−312.642	−	144.643i	−0.0211666	−	0.00979273i
$603$	3309.93	−	359.976i	0.223533	−	0.0243107i
$604$	4544.61	−	1531.26i	0.306155	−	0.103156i
$605$	−1833.82	−	4602.55i	−0.123232	−	0.309290i
$606$	−3873.34	−	3669.02i	−0.259643	−	0.245947i
$607$	376.242	+	1355.10i	0.0251585	+	0.0906127i	0.975063	−	0.221926i	$-0.0712344\pi$
$607$	376.242	+	1355.10i	0.0251585	+	0.0906127i	−0.949905	+	0.312539i	$0.898821\pi$
$608$	−527.912	−	995.748i	−0.0352133	−	0.0664193i
$609$	−4834.38	+	3675.00i	−0.321673	+	0.244530i
$610$	555.204	+	10240.1i	0.0368517	+	0.679690i
$611$	13453.3	+	4532.93i	0.890770	+	0.300136i
$612$	762.470	+	167.832i	0.0503611	+	0.0110853i
$613$	−4129.21	+	7788.52i	−0.272068	+	0.513174i	−0.981467	−	0.191633i	$-0.938622\pi$
$613$	−4129.21	+	7788.52i	−0.272068	+	0.513174i	0.709399	+	0.704807i	$0.248966\pi$
$614$	142.153	+	867.095i	0.00934337	+	0.0569920i
$615$	13477.5	−	15867.0i	0.883686	−	1.04036i
$616$	−1962.09	−	2309.95i	−0.128336	−	0.151089i
$617$	4789.13	−	29212.4i	0.312485	−	1.90607i	−0.0997783	−	0.995010i	$-0.531813\pi$
$617$	4789.13	−	29212.4i	0.312485	−	1.90607i	0.412263	−	0.911065i	$-0.364738\pi$
$618$	2591.08	+	1969.69i	0.168654	+	0.128208i
$619$	11789.7	−	17388.6i	0.765541	−	1.12909i	−0.222506	−	0.974931i	$-0.571424\pi$
$619$	11789.7	−	17388.6i	0.765541	−	1.12909i	0.988046	−	0.154157i	$-0.0492661\pi$
$620$	10874.3	−	16038.4i	0.704391	−	1.03890i
$621$	602.892	+	458.306i	0.0389585	+	0.0296155i
$622$	4731.23	−	28859.2i	0.304992	−	1.86037i
$623$	3284.84	+	3867.21i	0.211243	+	0.248694i
$624$	4314.98	−	5079.98i	0.276823	−	0.325901i
$625$	1153.48	+	7035.92i	0.0738228	+	0.450299i
$626$	7191.90	−	13565.4i	0.459179	−	0.866104i
$627$	−534.592	−	117.673i	−0.0340503	−	0.00749505i
$628$	17907.0	+	6033.55i	1.13784	+	0.383384i
$629$	184.073	+	3395.02i	0.0116684	+	0.215212i
$630$	3931.04	−	2988.30i	0.248598	−	0.188979i
$631$	3973.03	+	7493.93i	0.250656	+	0.472787i	0.976628	−	0.214937i	$-0.0689547\pi$
$631$	3973.03	+	7493.93i	0.250656	+	0.472787i	−0.725972	+	0.687724i	$0.758610\pi$
$632$	−2275.32	−	8194.95i	−0.143208	−	0.515787i
$633$	−3013.04	−	2854.10i	−0.189190	−	0.179211i
$634$	−272.707	−	684.443i	−0.0170829	−	0.0428749i
$635$	32339.2	−	10896.4i	2.02101	−	0.680958i
$636$	−5283.18	+	574.581i	−0.329390	+	0.0358233i
$637$	6791.88	+	3142.26i	0.422456	+	0.195449i
$638$	19521.1	−	18491.4i	1.21136	−	1.14746i
$639$	−4339.26	−	2610.85i	−0.268636	−	0.161633i
$640$	21876.7	+	2379.24i	1.35118	+	0.146949i
$641$	1889.14	−	415.830i	0.116406	−	0.0256230i	−0.156385	−	0.987696i	$-0.549984\pi$
$641$	1889.14	−	415.830i	0.116406	−	0.0256230i	0.272791	+	0.962073i	$0.412053\pi$
$642$	−2040.68	+	7349.88i	−0.125451	+	0.451833i
$643$	−1146.51	+	689.829i	−0.0703169	+	0.0423083i	−0.550278	−	0.834981i	$-0.685478\pi$
$643$	−1146.51	+	689.829i	−0.0703169	+	0.0423083i	0.479961	+	0.877290i	$0.340651\pi$
$644$	−1128.50	+	522.100i	−0.0690515	+	0.0319466i
$645$	208.362	−	522.948i	0.0127197	−	0.0319241i
$646$	18.9829	−	350.119i	0.00115615	−	0.0213239i
$647$	5675.70	+	8371.03i	0.344876	+	0.508654i	0.960084	−	0.279710i	$-0.0902385\pi$
$647$	5675.70	+	8371.03i	0.344876	+	0.508654i	−0.615208	+	0.788365i	$0.710928\pi$
$648$	−864.492			−0.0524081
$649$	10439.3	+	10272.4i	0.631398	+	0.621304i
$650$	−17680.7			−1.06691
$651$	3286.76	+	4847.61i	0.197878	+	0.291848i
$652$	543.242	−	10019.5i	0.0326304	−	0.601832i
$653$	3352.36	−	8413.79i	0.200900	−	0.504222i	−0.793663	−	0.608358i	$-0.791828\pi$
$653$	3352.36	−	8413.79i	0.200900	−	0.504222i	0.994563	+	0.104136i	$0.0332077\pi$
$654$	−10917.8	+	5051.12i	−0.652784	+	0.302010i
$655$	−31170.2	+	18754.5i	−1.85942	+	1.11878i
$656$	8473.86	−	30520.1i	0.504342	−	1.81648i
$657$	7690.42	−	1692.79i	0.456669	−	0.100521i
$658$	15908.1	+	1730.11i	0.942496	+	0.102503i
$659$	−23568.2	−	14180.5i	−1.39315	−	0.838230i	−0.396344	−	0.918102i	$-0.629721\pi$
$659$	−23568.2	−	14180.5i	−1.39315	−	0.838230i	−0.996805	+	0.0798717i	$0.974549\pi$
$660$	−6138.89	+	5815.06i	−0.362054	+	0.342956i
$661$	8382.71	+	3878.25i	0.493267	+	0.228210i	0.650721	−	0.759317i	$-0.274467\pi$
$661$	8382.71	+	3878.25i	0.493267	+	0.228210i	−0.157454	+	0.987526i	$0.550329\pi$
$662$	−129.663	+	14.1017i	−0.00761255	+	0.000827914i
$663$	1376.37	−	463.752i	0.0806239	−	0.0271654i
$664$	−4136.29	−	10381.3i	−0.241746	−	0.606736i
$665$	−622.663	−	589.817i	−0.0363095	−	0.0343942i
$666$	1719.59	+	6193.39i	0.100049	+	0.360344i
$667$	3026.55	+	5708.68i	0.175695	+	0.331396i
$668$	9902.42	−	7527.63i	0.573557	−	0.436007i
$669$	−284.198	−	5241.72i	−0.0164241	−	0.302925i
$670$	−21889.5	−	7375.44i	−1.26219	−	0.425281i
$671$	5183.79	+	1141.04i	0.298238	+	0.0656472i
$672$	2464.83	−	4649.17i	0.141493	−	0.266883i
$673$	3021.23	+	18428.7i	0.173046	+	1.05553i	0.920363	+	0.391066i	$0.127894\pi$
$673$	3021.23	+	18428.7i	0.173046	+	1.05553i	−0.747316	+	0.664468i	$0.768658\pi$
$674$	3166.84	−	3728.29i	0.180982	−	0.213069i
$675$	3039.00	+	3577.79i	0.173291	+	0.204014i
$676$	1146.13	−	6991.06i	0.0652098	−	0.397762i
$677$	24719.0	+	18790.9i	1.40329	+	1.06675i	0.987556	+	0.157268i	$0.0502686\pi$
$677$	24719.0	+	18790.9i	1.40329	+	1.06675i	0.415735	+	0.909486i	$0.363524\pi$
$678$	−2812.51	+	4148.14i	−0.159312	+	0.234968i
$679$	−764.271	+	1127.22i	−0.0431959	+	0.0637092i
$680$	2525.60	+	1919.91i	0.142430	+	0.108273i
$681$	−880.661	+	5371.80i	−0.0495551	+	0.302273i
$682$	−16788.7	−	19765.2i	−0.942628	−	1.10975i
$683$	−4244.77	+	4997.33i	−0.237806	+	0.279967i	−0.868100	−	0.496390i	$-0.834659\pi$
$683$	−4244.77	+	4997.33i	−0.237806	+	0.279967i	0.630293	+	0.776357i	$0.282935\pi$
$684$	−41.4740	−	252.980i	−0.00231842	−	0.0141417i
$685$	12812.1	−	24166.2i	0.714635	−	1.34795i
$686$	18869.4	+	4153.47i	1.05020	+	0.231166i
$687$	−1904.79	−	641.798i	−0.105782	−	0.0356421i
$688$	−46.3690	−	855.225i	−0.00256948	−	0.0473912i
$689$	−7870.47	+	5982.98i	−0.435183	+	0.330818i
$690$	−2461.02	−	4641.98i	−0.135782	−	0.256112i
$691$	−731.524	−	2634.71i	−0.0402728	−	0.145049i	0.940680	−	0.339294i	$-0.110188\pi$
$691$	−731.524	−	2634.71i	−0.0402728	−	0.145049i	−0.980953	+	0.194245i	$0.937774\pi$
$692$	−6674.33	−	6322.26i	−0.366647	−	0.347307i
$693$	−945.989	−	2374.25i	−0.0518545	−	0.130145i
$694$	23344.8	−	7865.78i	1.27688	−	0.430232i
$695$	−18178.0	+	1976.98i	−0.992131	+	0.107901i
$696$	−6694.09	−	3097.01i	−0.364567	−	0.168667i
$697$	5010.90	−	4746.57i	0.272312	−	0.257947i
$698$	8789.81	+	5288.65i	0.476647	+	0.286789i
$699$	2454.08	+	266.897i	0.132792	+	0.0144420i
$700$	−7527.27	+	1656.88i	−0.406434	+	0.0894629i
$701$	−7928.54	+	28556.0i	−0.427185	+	1.53858i	0.366596	+	0.930380i	$0.380523\pi$
$701$	−7928.54	+	28556.0i	−0.427185	+	1.53858i	−0.793782	+	0.608203i	$0.791891\pi$
$702$	2352.71	−	1415.58i	0.126492	−	0.0761075i
$703$	1013.24	−	468.774i	0.0543599	−	0.0251496i
$704$	−1073.11	+	2693.31i	−0.0574496	+	0.144188i
$705$	−1415.70	+	26111.0i	−0.0756288	+	1.39489i
$706$	−19677.7	−	29022.4i	−1.04898	−	1.54713i
$707$	−4326.65			−0.230156
$708$	−2659.55	+	6322.43i	−0.141175	+	0.335610i
$709$	3186.27			0.168777			0.0843886	−	0.996433i	$-0.473106\pi$
$709$	3186.27			0.168777			0.0843886	+	0.996433i	$0.473106\pi$
$710$	19716.5	+	29079.7i	1.04218	+	1.53710i
$711$	388.283	−	7161.45i	0.0204806	−	0.377743i
$712$	−2281.11	+	5725.16i	−0.120068	+	0.301347i
$713$	5655.74	−	2616.62i	0.297068	−	0.137438i
$714$	1402.77	−	844.019i	0.0735258	−	0.0442390i
$715$	−4208.37	+	15157.2i	−0.220118	+	0.792792i
$716$	−14679.0	+	3231.08i	−0.766171	+	0.168647i
$717$	5611.33	+	610.268i	0.292272	+	0.0317865i
$718$	−31936.0	−	19215.3i	−1.65995	−	0.998758i
$719$	−2314.15	+	2192.08i	−0.120032	+	0.113701i	−0.745362	−	0.666660i	$-0.767723\pi$
$719$	−2314.15	+	2192.08i	−0.120032	+	0.113701i	0.625330	+	0.780361i	$0.284965\pi$
$720$	11142.5	+	5155.05i	0.576743	+	0.266830i
$721$	2624.00	−	285.377i	0.135538	−	0.0147406i
$722$	23367.4	−	7873.38i	1.20449	−	0.405841i
$723$	−472.397	−	1185.63i	−0.0242996	−	0.0609875i
$724$	−4059.84	−	3845.69i	−0.208402	−	0.197409i
$725$	10714.8	+	38591.3i	0.548881	+	1.97689i
$726$	−1454.54	−	2743.56i	−0.0743571	−	0.140252i
$727$	24866.9	−	18903.3i	1.26859	−	0.964355i	0.268588	−	0.963255i	$-0.413443\pi$
$727$	24866.9	−	18903.3i	1.26859	−	0.964355i	0.999999	−	0.00110029i	$-0.000350233\pi$
$728$	−142.956	−	2636.67i	−0.00727789	−	0.134233i
$729$	−690.839	−	232.771i	−0.0350983	−	0.0118260i
$730$	−53353.7	−	11744.0i	−2.70508	−	0.595434i
$731$	87.4204	−	164.892i	0.00442320	−	0.00834304i
$732$	402.161	+	2453.08i	0.0203064	+	0.123864i
$733$	15353.8	−	18075.8i	0.773675	−	0.910841i	−0.224295	−	0.974521i	$-0.572008\pi$
$733$	15353.8	−	18075.8i	0.773675	−	0.910841i	0.997970	+	0.0636805i	$0.0202839\pi$
$734$	−15566.4	−	18326.2i	−0.782790	−	0.921571i
$735$	−2230.08	+	13602.9i	−0.111915	+	0.682654i
$736$	−4457.31	−	3388.36i	−0.223232	−	0.169696i
$737$	−6709.23	+	9895.37i	−0.335329	+	0.494574i
$738$	7322.57	−	10800.0i	0.365241	−	0.538690i
$739$	−11467.8	−	8717.60i	−0.570839	−	0.433941i	0.279523	−	0.960139i	$-0.409824\pi$
$739$	−11467.8	−	8717.60i	−0.570839	−	0.433941i	−0.850362	+	0.526198i	$0.823617\pi$
$740$	2790.09	−	17018.8i	0.138602	−	0.845436i
$741$	−308.743	−	363.481i	−0.0153063	−	0.0180200i
$742$	−7214.30	+	8493.33i	−0.356934	+	0.420215i
$743$	−1163.35	−	7096.10i	−0.0574415	−	0.350378i	−0.999872	−	0.0159767i	$-0.994914\pi$
$743$	−1163.35	−	7096.10i	−0.0574415	−	0.350378i	0.942431	−	0.334401i	$-0.108534\pi$
$744$	−3332.09	+	6284.99i	−0.164194	+	0.309703i
$745$	−36038.7	−	7932.73i	−1.77229	−	0.390111i
$746$	29866.2	+	10063.1i	1.46579	+	0.493882i
$747$	−510.180	−	9409.71i	−0.0249886	−	0.460888i
$748$	−2231.79	+	1696.56i	−0.109094	+	0.0829312i
$749$	2897.55	+	5465.36i	0.141354	+	0.266622i
$750$	−2448.59	−	8819.03i	−0.119213	−	0.429367i
$751$	−14483.1	−	13719.1i	−0.703724	−	0.666603i	0.249670	−	0.968331i	$-0.419678\pi$
$751$	−14483.1	−	13719.1i	−0.703724	−	0.666603i	−0.953394	+	0.301728i	$0.902436\pi$
$752$	14726.2	+	36959.9i	0.714106	+	1.79227i
$753$	−12319.3	+	4150.87i	−0.596204	+	0.200884i
$754$	23289.2	−	2532.85i	1.12486	−	0.122335i
$755$	14914.2	+	6900.06i	0.718920	+	0.332608i
$756$	868.971	−	823.133i	0.0418045	−	0.0395993i
$757$	10534.2	+	6338.22i	0.505775	+	0.304315i	0.745477	−	0.666532i	$-0.232222\pi$
$757$	10534.2	+	6338.22i	0.505775	+	0.304315i	−0.239701	+	0.970847i	$0.577050\pi$
$758$	17574.7	+	1911.36i	0.842140	+	0.0915882i
$759$	−2655.80	+	584.585i	−0.127008	+	0.0279566i
$760$	278.689	−	1003.75i	0.0133015	−	0.0479076i
$761$	22500.5	−	13538.1i	1.07181	−	0.644884i	0.133626	−	0.991032i	$-0.457338\pi$
$761$	22500.5	−	13538.1i	1.07181	−	0.644884i	0.938180	+	0.346148i	$0.112510\pi$
$762$	19412.1	−	8980.98i	0.922867	−	0.426964i
$763$	−3610.92	+	9062.72i	−0.171329	+	0.430003i
$764$	306.673	−	5656.25i	0.0145223	−	0.267848i
$765$	1501.33	+	2214.29i	0.0709551	+	0.104651i
$766$	−52247.5			−2.46446
$767$	1824.43	+	12628.9i	0.0858881	+	0.594529i
$768$	15945.6			0.749202
$769$	8394.99	+	12381.7i	0.393668	+	0.580618i	0.971941	−	0.235226i	$-0.0755832\pi$
$769$	8394.99	+	12381.7i	0.393668	+	0.580618i	−0.578272	+	0.815844i	$0.696273\pi$
$770$	−959.946	+	17705.2i	−0.0449274	+	0.828636i
$771$	−6567.47	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02689 - 2.98944i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-1.86736 + 4.68671i) q^{4} +(-15.6898 + 7.25888i) q^{5} +(-9.28436 + 5.58622i) q^{6} +(-2.35079 + 8.46678i) q^{7} +(-10.4232 + 2.29432i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})\)	\(q+(-2.02689 - 2.98944i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-1.86736 + 4.68671i) q^{4} +(-15.6898 + 7.25888i) q^{5} +(-9.28436 + 5.58622i) q^{6} +(-2.35079 + 8.46678i) q^{7} +(-10.4232 + 2.29432i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(53.5015 + 32.1908i) q^{10} +(23.4623 - 22.2246i) q^{11} +(13.7362 + 6.35506i) q^{12} +(27.9911 - 3.04421i) q^{13} +(30.0757 - 10.1337i) q^{14} +(19.1964 + 48.1794i) q^{15} +(57.2868 + 54.2649i) q^{16} +(4.60003 + 16.5678i) q^{17} +(15.2261 + 28.7195i) q^{18} +(4.49473 - 3.41680i) q^{19} +(-4.72181 - 87.0886i) q^{20} +(24.9813 + 8.41717i) q^{21} +(-113.995 - 25.0921i) q^{22} +(13.1382 - 24.7813i) q^{23} +(5.17997 + 31.5964i) q^{24} +(112.556 - 132.511i) q^{25} +(-65.8353 - 77.5074i) q^{26} +(-4.36811 + 26.6443i) q^{27} +(-35.2916 - 26.8280i) q^{28} +(-129.276 + 190.668i) q^{29} +(105.120 - 155.041i) q^{30} +(176.872 + 134.455i) q^{31} +(32.2944 - 196.987i) q^{32} +(-62.7654 - 73.8932i) q^{33} +(40.2047 - 47.3326i) q^{34} +(-24.5759 - 149.906i) q^{35} +(21.2682 - 40.1161i) q^{36} +(193.114 + 42.5077i) q^{37} +(-19.3247 - 6.51123i) q^{38} +(-4.57303 - 84.3445i) q^{39} +(146.884 - 111.658i) q^{40} +(-188.025 - 354.653i) q^{41} +(-25.4717 - 91.7407i) q^{42} +(-7.88009 - 7.46442i) q^{43} +(60.3481 + 151.462i) q^{44} +(147.444 - 49.6797i) q^{45} +(-100.712 + 10.9531i) q^{46} +(457.602 + 211.709i) q^{47} +(171.860 - 162.795i) q^{48} +(227.742 + 137.028i) q^{49} +(-624.271 - 67.8935i) q^{50} +(50.3776 - 11.0890i) q^{51} +(-38.0020 + 136.871i) q^{52} +(-300.866 + 181.025i) q^{53} +(88.5052 - 40.9469i) q^{54} +(-206.792 + 519.010i) q^{55} +(5.07726 - 93.6446i) q^{56} +(-9.50536 - 14.0194i) q^{57} +832.021 q^{58} +(15.9221 + 452.908i) q^{59} -261.650 q^{60} +(92.1707 + 135.942i) q^{61} +(43.4437 - 801.272i) q^{62} +(29.2719 - 73.4669i) q^{63} +(-81.4196 + 37.6687i) q^{64} +(-417.077 + 250.947i) q^{65} +(-93.6805 + 337.407i) q^{66} +(-361.289 + 79.5258i) q^{67} +(-86.2384 - 9.37899i) q^{68} +(-72.1010 - 43.3817i) q^{69} +(-398.323 + 377.312i) q^{70} +(510.678 + 236.265i) q^{71} +(95.4916 - 10.3853i) q^{72} +(-829.146 + 279.372i) q^{73} +(-264.348 - 663.462i) q^{74} +(-378.668 - 358.694i) q^{75} +(7.62032 + 27.4459i) q^{76} +(133.016 + 250.895i) q^{77} +(-242.874 + 184.628i) q^{78} +(43.1425 + 795.717i) q^{79} +(-1292.72 - 435.569i) q^{80} +(79.1063 + 17.4126i) q^{81} +(-679.107 + 1280.93i) q^{82} +(169.395 + 1033.27i) q^{83} +(-86.0979 + 101.362i) q^{84} +(-192.437 - 226.555i) q^{85} +(-6.34235 + 38.6866i) q^{86} +(550.170 + 418.228i) q^{87} +(-193.562 + 285.482i) q^{88} +(324.052 - 477.940i) q^{89} +(-447.367 - 340.080i) q^{90} +(-40.0265 + 244.151i) q^{91} +(91.6092 + 107.851i) q^{92} +(431.499 - 508.000i) q^{93} +(-294.617 - 1797.08i) q^{94} +(-45.7193 + 86.2357i) q^{95} +(-584.850 - 128.735i) q^{96} +(146.874 + 49.4876i) q^{97} +(-51.9716 - 958.560i) q^{98} +(-231.549 + 176.019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} + O(q^{10}) \)	\( 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} - 754q^{10} + 64q^{11} - 168q^{12} + 90q^{13} + 1024q^{14} - 42q^{15} - 172q^{16} + 96q^{17} + 18q^{18} + 16q^{19} - 178q^{20} - 243q^{21} - 604q^{22} + 48q^{23} + 198q^{24} - 173q^{25} + 156q^{26} - 405q^{27} + 84q^{28} - 50q^{29} + 174q^{30} + 222q^{31} - 45q^{32} + 192q^{33} - 64q^{34} - 132q^{35} - 504q^{36} + 30q^{37} - 108q^{38} + 270q^{39} + 6984q^{40} + 400q^{41} + 114q^{42} + 1220q^{43} + 1180q^{44} - 126q^{45} + 4938q^{46} + 370q^{47} - 516q^{48} + 771q^{49} + 1048q^{50} + 288q^{51} - 1964q^{52} - 822q^{53} + 54q^{54} - 2342q^{55} - 13824q^{56} + 48q^{57} - 13150q^{58} - 3423q^{59} - 534q^{60} - 2182q^{61} + 845q^{62} + 54q^{63} - 8018q^{64} + 4140q^{65} - 1812q^{66} + 506q^{67} + 4826q^{68} - 3684q^{69} + 6882q^{70} + 5874q^{71} + 594q^{72} + 206q^{73} + 11124q^{74} - 867q^{75} + 16940q^{76} + 9940q^{77} + 468q^{78} - 1762q^{79} - 28954q^{80} - 1215q^{81} + 3770q^{82} - 1216q^{83} - 8013q^{84} - 420q^{85} - 2256q^{86} + 5940q^{87} + 13458q^{88} - 1580q^{89} + 522q^{90} - 12204q^{91} + 4562q^{92} + 666q^{93} + 176q^{94} - 28456q^{95} + 2040q^{96} + 2574q^{97} + 50690q^{98} + 576q^{99} + O(q^{100}) \)

Introduction

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