LMFDB - Embedded newform 177.4.e.a.4.15

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			4.15
Character	$\chi$	$=$	177.4
Dual form			177.4.e.a.133.15

$q$-expansion

$f(q)$	$=$	$q+(5.10094 + 0.554760i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(17.8988 + 3.93983i) q^{4} +(10.4418 + 7.93765i) q^{5} +(-11.1753 + 10.5858i) q^{6} +(11.7316 - 29.4442i) q^{7} +(50.2158 + 16.9197i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(5.10094 + 0.554760i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(17.8988 + 3.93983i) q^{4} +(10.4418 + 7.93765i) q^{5} +(-11.1753 + 10.5858i) q^{6} +(11.7316 - 29.4442i) q^{7} +(50.2158 + 16.9197i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(48.8595 + 46.2821i) q^{10} +(-44.4824 + 20.5797i) q^{11} +(-43.7708 + 33.2737i) q^{12} +(-5.27989 + 32.2059i) q^{13} +(76.1769 - 143.685i) q^{14} +(-38.4290 + 8.45885i) q^{15} +(113.694 + 52.6005i) q^{16} +(-30.1864 - 75.7621i) q^{17} +(-2.50009 - 46.1114i) q^{18} +(61.3215 + 90.4424i) q^{19} +(155.623 + 183.214i) q^{20} +(44.5391 + 84.0096i) q^{21} +(-238.319 + 80.2989i) q^{22} +(1.97683 - 36.4606i) q^{23} +(-136.214 + 81.9571i) q^{24} +(12.5838 + 45.3229i) q^{25} +(-44.7990 + 161.351i) q^{26} +(23.1351 + 13.9200i) q^{27} +(325.988 - 480.797i) q^{28} +(-187.001 + 20.3376i) q^{29} +(-200.716 + 21.8292i) q^{30} +(-51.0180 + 75.2459i) q^{31} +(187.529 + 112.833i) q^{32} +(39.3366 - 141.677i) q^{33} +(-111.949 - 403.204i) q^{34} +(356.217 - 214.329i) q^{35} +(8.92999 - 164.704i) q^{36} +(-43.3789 + 14.6161i) q^{37} +(262.623 + 495.360i) q^{38} +(-63.3840 - 74.6214i) q^{39} +(390.041 + 575.268i) q^{40} +(-22.6595 - 417.930i) q^{41} +(180.586 + 453.236i) q^{42} +(193.018 + 89.2997i) q^{43} +(-877.264 + 193.100i) q^{44} +(55.2941 - 104.296i) q^{45} +(30.3106 - 184.886i) q^{46} +(-24.1749 + 18.3773i) q^{47} +(-341.082 + 157.801i) q^{48} +(-480.314 - 454.978i) q^{49} +(39.0460 + 238.170i) q^{50} +(231.856 + 78.1213i) q^{51} +(-221.390 + 555.647i) q^{52} +(287.990 - 272.798i) q^{53} +(110.289 + 83.8393i) q^{54} +(-627.831 - 138.196i) q^{55} +(1087.30 - 1280.07i) q^{56} +(-325.891 - 35.4428i) q^{57} -965.162 q^{58} +(-68.6496 - 447.958i) q^{59} -721.160 q^{60} +(-131.559 - 14.3079i) q^{61} +(-301.983 + 355.522i) q^{62} +(-278.589 - 61.3220i) q^{63} +(96.1518 + 73.0927i) q^{64} +(-310.771 + 294.378i) q^{65} +(279.250 - 700.866i) q^{66} +(127.246 + 42.8741i) q^{67} +(-241.811 - 1474.98i) q^{68} +(79.5272 + 75.3322i) q^{69} +(1935.94 - 895.663i) q^{70} +(-334.901 + 254.585i) q^{71} +(77.1550 - 470.625i) q^{72} +(-404.824 + 763.580i) q^{73} +(-229.382 + 50.4907i) q^{74} +(-128.070 - 59.2515i) q^{75} +(741.255 + 1860.41i) q^{76} +(84.1027 + 1551.18i) q^{77} +(-281.921 - 415.802i) q^{78} +(893.664 + 1052.10i) q^{79} +(769.647 + 1451.71i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(116.266 - 2144.41i) q^{82} +(1084.81 - 652.708i) q^{83} +(466.214 + 1679.15i) q^{84} +(286.173 - 1030.70i) q^{85} +(935.034 + 562.591i) q^{86} +(316.684 - 467.074i) q^{87} +(-2581.92 + 280.801i) q^{88} +(-1232.08 + 133.997i) q^{89} +(339.911 - 501.331i) q^{90} +(886.337 + 533.291i) q^{91} +(179.032 - 644.813i) q^{92} +(-72.9637 - 262.791i) q^{93} +(-133.510 + 80.3301i) q^{94} +(-77.5936 + 1431.13i) q^{95} +(-622.201 + 209.644i) q^{96} +(209.325 + 394.829i) q^{97} +(-2197.65 - 2587.27i) q^{98} +(247.546 + 365.103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + O(q^{10}) $	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + 854q^{10} + 32q^{11} + 192q^{12} - 22q^{13} - 884q^{14} - 42q^{15} - 268q^{16} - 56q^{17} - 18q^{18} - 112q^{19} - 250q^{20} + 243q^{21} + 108q^{22} + 16q^{23} - 54q^{24} - 197q^{25} - 328q^{26} + 405q^{27} + 236q^{28} - 54q^{29} - 126q^{30} + 66q^{31} + 857q^{32} - 96q^{33} + 112q^{34} + 532q^{35} - 576q^{36} + 110q^{37} + 56q^{38} + 66q^{39} - 6044q^{40} + 304q^{41} - 306q^{42} - 324q^{43} - 568q^{44} + 126q^{45} + 5842q^{46} + 4082q^{47} + 804q^{48} + 739q^{49} + 576q^{50} + 168q^{51} - 1372q^{52} - 1498q^{53} + 54q^{54} - 4422q^{55} - 12036q^{56} + 336q^{57} + 6298q^{58} - 3305q^{59} + 750q^{60} - 1718q^{61} - 4333q^{62} + 54q^{63} - 6250q^{64} - 5884q^{65} - 324q^{66} + 382q^{67} + 734q^{68} + 3780q^{69} + 8082q^{70} + 8638q^{71} + 162q^{72} + 8894q^{73} + 12428q^{74} + 243q^{75} - 15468q^{76} - 9916q^{77} + 984q^{78} - 578q^{79} + 24570q^{80} - 1215q^{81} - 1382q^{82} - 32q^{83} + 7557q^{84} + 708q^{85} + 2296q^{86} - 5928q^{87} - 17646q^{88} - 2284q^{89} + 378q^{90} + 11124q^{91} + 762q^{92} - 198q^{93} - 1232q^{94} + 24184q^{95} - 396q^{96} - 658q^{97} - 4356q^{98} + 288q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	5.10094	+	0.554760i	1.80345	+	0.196137i	0.947249	−	0.320499i	$-0.103851\pi$
$2$	5.10094	+	0.554760i	1.80345	+	0.196137i	0.856205	+	0.516636i	$0.172816\pi$
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$4$	17.8988	+	3.93983i	2.23736	+	0.492479i
$5$	10.4418	+	7.93765i	0.933943	+	0.709965i	0.957097	−	0.289767i	$-0.0935778\pi$
$5$	10.4418	+	7.93765i	0.933943	+	0.709965i	−0.0231544	+	0.999732i	$0.507371\pi$
$6$	−11.1753	+	10.5858i	−0.760382	+	0.720272i
$7$	11.7316	−	29.4442i	0.633450	−	1.58984i	−0.164005	−	0.986459i	$-0.552441\pi$
$7$	11.7316	−	29.4442i	0.633450	−	1.58984i	0.797455	−	0.603379i	$-0.206179\pi$
$8$	50.2158	+	16.9197i	2.21925	+	0.747752i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	48.8595	+	46.2821i	1.54507	+	1.46357i
$11$	−44.4824	+	20.5797i	−1.21927	+	0.564093i	−0.920691	−	0.390292i	$-0.872374\pi$
$11$	−44.4824	+	20.5797i	−1.21927	+	0.564093i	−0.298577	+	0.954386i	$0.596512\pi$
$12$	−43.7708	+	33.2737i	−1.05296	+	0.800440i
$13$	−5.27989	+	32.2059i	−0.112645	+	0.687101i	0.868772	+	0.495212i	$0.164910\pi$
$13$	−5.27989	+	32.2059i	−0.112645	+	0.687101i	−0.981417	+	0.191889i	$0.938539\pi$
$14$	76.1769	−	143.685i	1.45422	−	2.74296i
$15$	−38.4290	+	8.45885i	−0.661488	+	0.145604i
$16$	113.694	+	52.6005i	1.77647	+	0.821883i
$17$	−30.1864	−	75.7621i	−0.430663	−	1.08088i	−0.970925	−	0.239386i	$-0.923054\pi$
$17$	−30.1864	−	75.7621i	−0.430663	−	1.08088i	0.540261	−	0.841497i	$-0.318325\pi$
$18$	−2.50009	−	46.1114i	−0.0327376	−	0.603809i
$19$	61.3215	+	90.4424i	0.740427	+	1.09205i	0.992248	+	0.124274i	$0.0396601\pi$
$19$	61.3215	+	90.4424i	0.740427	+	1.09205i	−0.251821	+	0.967774i	$0.581030\pi$
$20$	155.623	+	183.214i	1.73992	+	2.04839i
$21$	44.5391	+	84.0096i	0.462820	+	0.872971i
$22$	−238.319	+	80.2989i	−2.30953	+	0.778172i
$23$	1.97683	−	36.4606i	0.0179217	−	0.330546i	−0.975800	−	0.218665i	$-0.929830\pi$
$23$	1.97683	−	36.4606i	0.0179217	−	0.330546i	0.993722	−	0.111881i	$-0.0356874\pi$
$24$	−136.214	+	81.9571i	−1.15852	+	0.697059i
$25$	12.5838	+	45.3229i	0.100671	+	0.362583i
$26$	−44.7990	+	161.351i	−0.337916	+	1.21706i
$27$	23.1351	+	13.9200i	0.164902	+	0.0992184i
$28$	325.988	−	480.797i	2.20021	−	3.24507i
$29$	−187.001	+	20.3376i	−1.19742	+	0.130227i	−0.685023	−	0.728521i	$-0.740208\pi$
$29$	−187.001	+	20.3376i	−1.19742	+	0.130227i	−0.512397	+	0.858749i	$0.671242\pi$
$30$	−200.716	+	21.8292i	−1.22152	+	0.132848i
$31$	−51.0180	+	75.2459i	−0.295584	+	0.435954i	−0.946262	−	0.323400i	$-0.895174\pi$
$31$	−51.0180	+	75.2459i	−0.295584	+	0.435954i	0.650679	+	0.759353i	$0.274485\pi$
$32$	187.529	+	112.833i	1.03596	+	0.623318i
$33$	39.3366	−	141.677i	0.207504	−	0.747360i
$34$	−111.949	−	403.204i	−0.564680	−	2.03379i
$35$	356.217	−	214.329i	1.72033	−	1.03509i
$36$	8.92999	−	164.704i	0.0413426	−	0.762519i
$37$	−43.3789	+	14.6161i	−0.192742	+	0.0649423i	−0.414017	−	0.910269i	$-0.635875\pi$
$37$	−43.3789	+	14.6161i	−0.192742	+	0.0649423i	0.221275	+	0.975211i	$0.428978\pi$
$38$	262.623	+	495.360i	1.12113	+	2.11468i
$39$	−63.3840	−	74.6214i	−0.260245	−	0.306384i
$40$	390.041	+	575.268i	1.54177	+	2.27395i
$41$	−22.6595	−	417.930i	−0.0863128	−	1.59195i	−0.646063	−	0.763284i	$-0.723586\pi$
$41$	−22.6595	−	417.930i	−0.0863128	−	1.59195i	0.559750	−	0.828661i	$-0.310897\pi$
$42$	180.586	+	453.236i	0.663452	+	1.66514i
$43$	193.018	+	89.2997i	0.684535	+	0.316699i	0.731153	−	0.682213i	$-0.238982\pi$
$43$	193.018	+	89.2997i	0.684535	+	0.316699i	−0.0466186	+	0.998913i	$0.514845\pi$
$44$	−877.264	+	193.100i	−3.00574	+	0.661613i
$45$	55.2941	−	104.296i	0.183172	−	0.345500i
$46$	30.3106	−	184.886i	0.0971533	−	0.592609i
$47$	−24.1749	+	18.3773i	−0.0750271	+	0.0570341i	−0.642015	−	0.766692i	$-0.721902\pi$
$47$	−24.1749	+	18.3773i	−0.0750271	+	0.0570341i	0.566988	+	0.823726i	$0.308108\pi$
$48$	−341.082	+	157.801i	−1.02565	+	0.474514i
$49$	−480.314	−	454.978i	−1.40033	−	1.32647i
$50$	39.0460	+	238.170i	0.110439	+	0.673647i
$51$	231.856	+	78.1213i	0.636594	+	0.214494i
$52$	−221.390	+	555.647i	−0.590409	+	1.48182i
$53$	287.990	−	272.798i	0.746386	−	0.707014i	−0.216691	−	0.976240i	$-0.569527\pi$
$53$	287.990	−	272.798i	0.746386	−	0.707014i	0.963077	+	0.269226i	$0.0867679\pi$
$54$	110.289	+	83.8393i	0.277933	+	0.211279i
$55$	−627.831	−	138.196i	−1.53921	−	0.338806i
$56$	1087.30	−	1280.07i	2.59459	−	3.05458i
$57$	−325.891	−	35.4428i	−0.757287	−	0.0823599i
$58$	−965.162			−2.18503
$59$	−68.6496	−	447.958i	−0.151482	−	0.988460i
$59$	−68.6496	−	447.958i	−0.151482	−	0.988460i
$60$	−721.160			−1.55169
$61$	−131.559	−	14.3079i	−0.276139	−	0.0300319i	−0.0309981	−	0.999519i	$-0.509869\pi$
$61$	−131.559	−	14.3079i	−0.276139	−	0.0300319i	−0.245141	+	0.969488i	$0.578834\pi$
$62$	−301.983	+	355.522i	−0.618579	+	0.728247i
$63$	−278.589	−	61.3220i	−0.557125	−	0.122633i
$64$	96.1518	+	73.0927i	0.187797	+	0.142759i
$65$	−310.771	+	294.378i	−0.593021	+	0.561740i
$66$	279.250	−	700.866i	0.520808	−	1.30713i
$67$	127.246	+	42.8741i	0.232023	+	0.0781778i	0.432912	−	0.901436i	$-0.357486\pi$
$67$	127.246	+	42.8741i	0.232023	+	0.0781778i	−0.200888	+	0.979614i	$0.564383\pi$
$68$	−241.811	−	1474.98i	−0.431234	−	2.63041i
$69$	79.5272	+	75.3322i	0.138753	+	0.131434i
$70$	1935.94	−	895.663i	3.30556	−	1.52932i
$71$	−334.901	+	254.585i	−0.559795	+	0.425545i	−0.846434	−	0.532493i	$-0.821255\pi$
$71$	−334.901	+	254.585i	−0.559795	+	0.425545i	0.286639	+	0.958039i	$0.407462\pi$
$72$	77.1550	−	470.625i	0.126289	−	0.770329i
$73$	−404.824	+	763.580i	−0.649056	+	1.22425i	0.312572	+	0.949894i	$0.398810\pi$
$73$	−404.824	+	763.580i	−0.649056	+	1.22425i	−0.961628	+	0.274356i	$0.911535\pi$
$74$	−229.382	+	50.4907i	−0.360339	+	0.0793165i
$75$	−128.070	−	59.2515i	−0.197177	−	0.0912236i
$76$	741.255	+	1860.41i	1.11879	+	2.80794i
$77$	84.1027	+	1551.18i	0.124473	+	2.29576i
$78$	−281.921	−	415.802i	−0.409247	−	0.603594i
$79$	893.664	+	1052.10i	1.27272	+	1.49836i	0.776421	+	0.630215i	$0.217033\pi$
$79$	893.664	+	1052.10i	1.27272	+	1.49836i	0.496302	+	0.868150i	$0.334691\pi$
$80$	769.647	+	1451.71i	1.07561	+	2.02882i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	116.266	−	2144.41i	0.156579	−	2.88793i
$83$	1084.81	−	652.708i	1.43462	−	0.863181i	0.435307	−	0.900282i	$-0.356640\pi$
$83$	1084.81	−	652.708i	1.43462	−	0.863181i	0.999312	+	0.0371012i	$0.0118124\pi$
$84$	466.214	+	1679.15i	0.605573	+	2.18108i
$85$	286.173	−	1030.70i	0.365174	−	1.31524i
$86$	935.034	+	562.591i	1.17241	+	0.705416i
$87$	316.684	−	467.074i	0.390254	−	0.575581i
$88$	−2581.92	+	280.801i	−3.12766	+	0.340153i
$89$	−1232.08	+	133.997i	−1.46742	+	0.159591i	−0.806664	−	0.591010i	$-0.798729\pi$
$89$	−1232.08	+	133.997i	−1.46742	+	0.159591i	−0.660755	+	0.750601i	$0.729764\pi$
$90$	339.911	−	501.331i	0.398108	−	0.587166i
$91$	886.337	+	533.291i	1.02103	+	0.614331i
$92$	179.032	−	644.813i	0.202884	−	0.730722i
$93$	−72.9637	−	262.791i	−0.0813546	−	0.293013i
$94$	−133.510	+	80.3301i	−0.146494	+	0.0881427i
$95$	−77.5936	+	1431.13i	−0.0837993	+	1.54559i
$96$	−622.201	+	209.644i	−0.661491	+	0.222882i
$97$	209.325	+	394.829i	0.219111	+	0.413286i	0.968562	−	0.248773i	$-0.0800274\pi$
$97$	209.325	+	394.829i	0.219111	+	0.413286i	−0.749451	+	0.662060i	$0.769683\pi$
$98$	−2197.65	−	2587.27i	−2.26527	−	2.66688i
$99$	247.546	+	365.103i	0.251306	+	0.370648i
$100$	46.6715	+	860.805i	0.0466715	+	0.860805i
$101$	−257.145	−	645.385i	−0.253335	−	0.635824i	0.746218	−	0.665701i	$-0.231868\pi$
$101$	−257.145	−	645.385i	−0.253335	−	0.635824i	−0.999554	+	0.0298776i	$0.990488\pi$
$102$	1139.34	+	527.116i	1.10600	+	0.511689i
$103$	1819.82	−	400.573i	1.74090	−	0.383201i	0.772973	−	0.634439i	$-0.218769\pi$
$103$	1819.82	−	400.573i	1.74090	−	0.383201i	0.967925	+	0.251238i	$0.0808377\pi$
$104$	−810.049	+	1527.91i	−0.763767	+	1.44062i
$105$	−201.771	+	1230.75i	−0.187531	+	1.14389i
$106$	1620.36	−	1231.76i	1.48474	−	1.12867i
$107$	−1344.74	+	622.143i	−1.21496	+	0.562101i	−0.919438	−	0.393235i	$-0.871356\pi$
$107$	−1344.74	+	622.143i	−1.21496	+	0.562101i	−0.295523	+	0.955336i	$0.595494\pi$
$108$	359.250	+	340.300i	0.320082	+	0.303198i
$109$	−104.602	−	638.043i	−0.0919178	−	0.560674i	−0.992129	−	0.125220i	$-0.960036\pi$
$109$	−104.602	−	638.043i	−0.0919178	−	0.560674i	0.900211	−	0.435454i	$-0.143412\pi$
$110$	−3125.86	−	1053.22i	−2.70945	−	0.912919i
$111$	50.8293	−	127.572i	0.0434640	−	0.109086i
$112$	2882.60	−	2730.54i	2.43196	−	2.30368i
$113$	1614.68	+	1227.45i	1.34422	+	1.02185i	0.996443	+	0.0842694i	$0.0268556\pi$
$113$	1614.68	+	1227.45i	1.34422	+	1.02185i	0.347775	+	0.937578i	$0.386937\pi$
$114$	−1642.69	−	361.583i	−1.34958	−	0.297065i
$115$	310.053	−	365.022i	0.251414	−	0.295987i
$116$	−3427.23	−	372.733i	−2.74319	−	0.298340i
$117$	293.723			0.232091
$118$	−101.668	−	2323.09i	−0.0793163	−	1.81235i
$119$	−2584.89			−1.99123
$120$	−2072.86	−	225.438i	−1.57688	−	0.171496i
$121$	693.485	−	816.434i	0.521026	−	0.613399i
$122$	−663.139	−	145.968i	−0.492113	−	0.108322i
$123$	999.601	+	759.877i	0.732772	+	0.557039i
$124$	−1209.62	+	1145.81i	−0.876025	+	0.829814i
$125$	378.496	−	949.954i	0.270830	−	0.679732i
$126$	−1387.04	−	467.350i	−0.980697	−	0.330435i
$127$	15.5662	+	94.9497i	0.0108762	+	0.0663419i	0.991707	−	0.128520i	$-0.0410225\pi$
$127$	15.5662	+	94.9497i	0.0108762	+	0.0663419i	−0.980831	+	0.194862i	$0.937574\pi$
$128$	−821.198	−	777.880i	−0.567065	−	0.537152i
$129$	−579.054	+	267.899i	−0.395216	+	0.182847i
$130$	−1748.53	+	1329.20i	−1.17967	+	0.896758i
$131$	−83.5869	+	509.858i	−0.0557483	+	0.340049i	0.944195	+	0.329387i	$0.106842\pi$
$131$	−83.5869	+	509.858i	−0.0557483	+	0.340049i	−0.999943	+	0.0106621i	$0.996606\pi$
$132$	1262.26	−	2380.88i	0.832318	−	1.56992i
$133$	3382.41	−	744.524i	2.20520	−	0.485402i
$134$	625.289	+	289.289i	0.403110	+	0.186498i
$135$	131.081	+	328.988i	0.0835677	+	0.209739i
$136$	−233.964	−	4315.20i	−0.147516	−	2.72078i
$137$	903.810	+	1333.02i	0.563633	+	0.831296i	0.997572	−	0.0696459i	$-0.0221869\pi$
$137$	903.810	+	1333.02i	0.563633	+	0.831296i	−0.433939	+	0.900942i	$0.642877\pi$
$138$	363.872	+	428.383i	0.224455	+	0.264249i
$139$	1099.55	+	2073.97i	0.670955	+	1.26556i	0.952070	+	0.305881i	$0.0989510\pi$
$139$	1099.55	+	2073.97i	0.670955	+	1.26556i	−0.281115	+	0.959674i	$0.590704\pi$
$140$	7220.30	−	2432.80i	4.35876	−	1.46864i
$141$	4.93210	−	90.9672i	0.00294580	−	0.0543320i
$142$	−1849.54	+	1112.83i	−1.09303	+	0.657655i
$143$	−427.927	−	1541.26i	−0.250245	−	0.901302i
$144$	301.625	−	1086.36i	0.174552	−	0.628678i
$145$	−2114.06	−	1271.99i	−1.21078	−	0.728501i
$146$	−2488.59	+	3670.39i	−1.41066	+	2.08057i
$147$	1973.15	−	214.593i	1.10709	−	0.120403i
$148$	−834.017	+	90.7048i	−0.463215	+	0.0503776i
$149$	−405.155	+	597.559i	−0.222762	+	0.328550i	−0.922604	−	0.385748i	$-0.873943\pi$
$149$	−405.155	+	597.559i	−0.222762	+	0.328550i	0.699842	+	0.714298i	$0.253254\pi$
$150$	−620.407	−	373.286i	−0.337707	−	0.203191i
$151$	−488.974	+	1761.12i	−0.263524	+	0.949128i	0.706819	+	0.707395i	$0.250130\pi$
$151$	−488.974	+	1761.12i	−0.263524	+	0.949128i	−0.970343	+	0.241733i	$0.922284\pi$
$152$	1549.05	+	5579.18i	0.826610	+	2.97718i
$153$	−628.924	+	378.411i	−0.332324	+	0.199952i
$154$	−431.532	+	7959.15i	−0.225804	+	4.16472i
$155$	−1130.00	+	380.740i	−0.585570	+	0.197302i
$156$	−840.505	−	1585.36i	−0.431373	−	0.813656i
$157$	−1902.34	−	2239.61i	−0.967029	−	1.13847i	−0.990328	−	0.138746i	$-0.955693\pi$
$157$	−1902.34	−	2239.61i	−0.967029	−	1.13847i	0.0232989	−	0.999729i	$-0.492583\pi$
$158$	3974.86	+	5862.48i	2.00141	+	2.95186i
$159$	64.4279	+	1188.30i	0.0321350	+	0.592695i
$160$	1062.52	+	2666.71i	0.524995	+	1.31764i
$161$	−1050.36	−	485.949i	−0.514162	−	0.237877i
$162$	−405.896	+	89.3444i	−0.196853	+	0.0433306i
$163$	−1682.90	+	3174.28i	−0.808678	+	1.52533i	0.0416834	+	0.999131i	$0.486728\pi$
$163$	−1682.90	+	3174.28i	−0.808678	+	1.52533i	−0.850362	+	0.526198i	$0.823617\pi$
$164$	1241.00	−	7569.75i	0.590888	−	3.60426i
$165$	1535.33	−	1167.13i	0.724396	−	0.550671i
$166$	5895.64	−	2727.61i	2.75657	−	1.27533i
$167$	−2980.46	−	2823.24i	−1.38105	−	1.30820i	−0.902858	−	0.429940i	$-0.858535\pi$
$167$	−2980.46	−	2823.24i	−1.38105	−	1.30820i	−0.478189	−	0.878257i	$-0.658706\pi$
$168$	815.151	+	4972.20i	0.374347	+	2.28341i
$169$	1072.65	+	361.418i	0.488234	+	0.164505i
$170$	2031.54	−	5098.79i	0.916542	−	2.30035i
$171$	713.972	−	676.310i	0.319291	−	0.302449i
$172$	3102.98	+	2358.82i	1.37558	+	1.04569i
$173$	3340.95	+	735.398i	1.46825	+	0.323187i	0.875900	−	0.482493i	$-0.160269\pi$
$173$	3340.95	+	735.398i	1.46825	+	0.323187i	0.592352	+	0.805679i	$0.298200\pi$
$174$	1874.50	−	2206.83i	0.816697	−	0.961490i
$175$	1482.13	+	161.191i	0.640218	+	0.0696279i
$176$	−6139.89			−2.62961
$177$	1157.58	+	713.039i	0.491576	+	0.302798i
$178$	−6359.11			−2.67773
$179$	1787.56	+	194.409i	0.746416	+	0.0811776i	0.473419	−	0.880837i	$-0.343020\pi$
$179$	1787.56	+	194.409i	0.746416	+	0.0811776i	0.272997	+	0.962015i	$0.411985\pi$
$180$	1400.61	−	1648.92i	0.579973	−	0.682797i
$181$	1295.39	+	285.137i	0.531965	+	0.117094i	0.472827	−	0.881155i	$-0.343234\pi$
$181$	1295.39	+	285.137i	0.531965	+	0.117094i	0.0591382	+	0.998250i	$0.481165\pi$
$182$	4225.30	+	3211.99i	1.72088	+	1.30818i
$183$	288.224	−	273.020i	0.116427	−	0.110286i
$184$	716.170	−	1797.45i	0.286939	−	0.720162i
$185$	−568.971	−	191.709i	−0.226117	−	0.0761876i
$186$	−226.397	−	1380.96i	−0.0892485	−	0.544392i
$187$	2901.93	+	2748.85i	1.13481	+	1.07495i
$188$	−505.106	+	233.687i	−0.195950	+	0.0906563i
$189$	681.276	−	517.892i	0.262198	−	0.199318i
$190$	−1189.73	+	7257.06i	−0.454276	+	2.77096i
$191$	−1171.43	+	2209.56i	−0.443780	+	0.837057i	0.556202	+	0.831047i	$0.312258\pi$
$191$	−1171.43	+	2209.56i	−0.443780	+	0.837057i	−0.999982	+	0.00601030i	$0.998087\pi$
$192$	−353.868	+	77.8921i	−0.133011	+	0.0292780i
$193$	781.236	+	361.438i	0.291371	+	0.134803i	0.560130	−	0.828405i	$-0.310751\pi$
$193$	781.236	+	361.438i	0.291371	+	0.134803i	−0.268759	+	0.963208i	$0.586613\pi$
$194$	848.718	+	2130.12i	0.314095	+	0.788319i
$195$	−69.5244	−	1282.30i	−0.0255320	−	0.470911i
$196$	−6804.53	−	10035.9i	−2.47979	−	3.65741i
$197$	−958.280	−	1128.17i	−0.346572	−	0.408016i	0.561065	−	0.827771i	$-0.310392\pi$
$197$	−958.280	−	1128.17i	−0.346572	−	0.408016i	−0.907637	+	0.419756i	$0.862116\pi$
$198$	1060.17	+	1999.69i	0.380521	+	0.717738i
$199$	877.133	−	295.541i	0.312454	−	0.105278i	−0.158706	−	0.987326i	$-0.550732\pi$
$199$	877.133	−	295.541i	0.312454	−	0.105278i	0.471160	+	0.882048i	$0.343836\pi$
$200$	−134.941	+	2488.84i	−0.0477089	+	0.879938i
$201$	−345.163	+	207.678i	−0.121124	+	0.0728779i
$202$	−953.646	−	3434.72i	−0.332170	−	1.19637i
$203$	−1595.00	+	5744.69i	−0.551465	+	1.98620i
$204$	3842.17	+	2311.75i	1.31865	+	0.793408i
$205$	3080.78	−	4543.81i	1.04961	−	1.54807i
$206$	9505.03	−	1033.73i	3.21479	−	0.349630i
$207$	−326.700	+	35.5308i	−0.109697	+	0.0119303i
$208$	−2294.34	+	3383.90i	−0.764826	+	1.12803i
$209$	−4589.01	−	2761.11i	−1.51879	−	0.913829i
$210$	−1711.99	+	6166.03i	−0.562564	+	2.02617i
$211$	−407.408	−	1467.35i	−0.132925	−	0.478752i	0.866880	−	0.498517i	$-0.166122\pi$
$211$	−407.408	−	1467.35i	−0.132925	−	0.478752i	−0.999805	+	0.0197653i	$0.993708\pi$
$212$	6229.46	−	3748.14i	2.01812	−	1.21426i
$213$	68.3256	−	1260.19i	0.0219793	−	0.405385i
$214$	−7204.57	+	2427.50i	−2.30138	+	0.775424i
$215$	1306.63	+	2464.56i	0.414471	+	0.781775i
$216$	926.230	+	1090.44i	0.291768	+	0.343496i
$217$	1617.03	+	2384.94i	0.505858	+	0.746085i
$218$	−179.607	−	3312.65i	−0.0558004	−	1.02918i
$219$	−959.681	−	2408.62i	−0.296115	−	0.743194i
$220$	−10693.0	−	4947.10i	−3.27691	−	1.51606i
$221$	2599.37	−	572.165i	0.791188	−	0.174154i
$222$	330.049	−	622.539i	0.0997813	−	0.188207i
$223$	92.6028	−	564.852i	0.0278078	−	0.169620i	−0.969271	−	0.245994i	$-0.920886\pi$
$223$	92.6028	−	564.852i	0.0278078	−	0.169620i	0.997079	+	0.0763733i	$0.0243341\pi$
$224$	5522.29	−	4197.94i	1.64720	−	1.25217i
$225$	384.210	−	177.754i	0.113840	−	0.0526680i
$226$	7555.46	+	7156.91i	2.22381	+	2.10651i
$227$	173.828	+	1060.30i	0.0508254	+	0.310021i	0.999989	−	0.00476289i	$-0.00151608\pi$
$227$	173.828	+	1060.30i	0.0508254	+	0.310021i	−0.949163	+	0.314784i	$0.898068\pi$
$228$	−5693.44	−	1918.34i	−1.65376	−	0.557216i
$229$	−674.677	+	1693.31i	−0.194690	+	0.488634i	−0.993619	−	0.112791i	$-0.964021\pi$
$229$	−674.677	+	1693.31i	−0.194690	+	0.488634i	0.798929	+	0.601425i	$0.205400\pi$
$230$	1784.06	−	1689.95i	0.511467	−	0.484487i
$231$	−3710.10	−	2820.34i	−1.05674	−	0.803312i
$232$	−9734.51	−	2142.73i	−2.75475	−	0.606366i
$233$	−1700.37	+	2001.83i	−0.478091	+	0.562852i	−0.947346	−	0.320210i	$-0.896246\pi$
$233$	−1700.37	+	2001.83i	−0.478091	+	0.562852i	0.469256	+	0.883062i	$0.344522\pi$
$234$	1498.26	+	162.946i	0.418566	+	0.0455218i
$235$	−398.302			−0.110563
$236$	536.130	−	8288.40i	0.147877	−	2.28614i
$237$	−4141.26			−1.13504
$238$	−13185.4	−	1434.00i	−3.59110	−	0.390555i
$239$	−768.216	+	904.414i	−0.207915	+	0.244777i	−0.856229	−	0.516597i	$-0.827199\pi$
$239$	−768.216	+	904.414i	−0.207915	+	0.244777i	0.648314	+	0.761373i	$0.275475\pi$
$240$	−4814.08	−	1059.66i	−1.29478	−	0.285003i
$241$	−4229.19	−	3214.95i	−1.13040	−	0.859307i	−0.139014	−	0.990290i	$-0.544393\pi$
$241$	−4229.19	−	3214.95i	−1.13040	−	0.859307i	−0.991385	+	0.130983i	$0.958187\pi$
$242$	3990.35	−	3779.86i	1.05996	−	1.00404i
$243$	89.9436	−	225.741i	0.0237444	−	0.0595939i
$244$	−2298.39	−	774.418i	−0.603030	−	0.203185i
$245$	−1403.89	−	8563.35i	−0.366087	−	2.23303i
$246$	4677.35	+	4430.62i	1.21226	+	1.14832i
$247$	−3236.55	+	1497.39i	−0.833753	+	0.385735i
$248$	−3835.05	+	2915.33i	−0.981959	+	0.746466i
$249$	−614.464	+	3748.06i	−0.156386	+	0.953911i
$250$	2457.68	−	4635.68i	0.621750	−	1.17275i
$251$	−761.267	+	167.568i	−0.191437	+	0.0421385i	−0.309654	−	0.950849i	$-0.600213\pi$
$251$	−761.267	+	167.568i	−0.191437	+	0.0421385i	0.118217	+	0.992988i	$0.462282\pi$
$252$	−4744.82	−	2195.19i	−1.18609	−	0.548745i
$253$	662.414	+	1662.53i	0.164607	+	0.413133i
$254$	26.7280	+	492.968i	0.00660260	+	0.121778i
$255$	1800.89	+	2656.12i	0.442260	+	0.652284i
$256$	−4382.87	−	5159.91i	−1.07004	−	1.25974i
$257$	−195.869	−	369.449i	−0.0475408	−	0.0896715i	0.858603	−	0.512641i	$-0.171333\pi$
$257$	−195.869	−	369.449i	−0.0475408	−	0.0896715i	−0.906144	+	0.422969i	$0.860988\pi$
$258$	−3102.34	+	1045.30i	−0.748617	+	0.252239i
$259$	−78.5478	+	1448.73i	−0.0188445	+	0.347566i
$260$	−6722.24	+	4044.64i	−1.60345	+	0.964761i
$261$	452.907	+	1631.22i	0.107411	+	0.386859i
$262$	−709.221	+	2554.38i	−0.167236	+	0.602329i
$263$	3952.74	+	2378.28i	0.926753	+	0.557609i	0.897040	−	0.441950i	$-0.145713\pi$
$263$	3952.74	+	2378.28i	0.926753	+	0.557609i	0.0297134	+	0.999558i	$0.490541\pi$
$264$	4372.46	−	6448.89i	1.01934	−	1.50342i
$265$	5172.51	−	562.544i	1.19904	−	0.130403i
$266$	17666.5	−	1921.35i	4.07219	−	0.442877i
$267$	2086.52	−	3077.38i	0.478250	−	0.705365i
$268$	2108.64	+	1268.73i	0.480618	+	0.289178i
$269$	−147.023	+	529.530i	−0.0333241	+	0.120022i	−0.978341	−	0.206998i	$-0.933631\pi$
$269$	−147.023	+	529.530i	−0.0333241	+	0.120022i	0.945017	+	0.327020i	$0.106045\pi$
$270$	486.125	+	1750.87i	0.109573	+	0.394646i
$271$	−310.784	+	186.993i	−0.0696634	+	0.0419151i	−0.549959	−	0.835191i	$-0.685357\pi$
$271$	−310.784	+	186.993i	−0.0696634	+	0.0419151i	0.480296	+	0.877106i	$0.340529\pi$
$272$	553.111	−	10201.5i	0.123299	−	2.27411i
$273$	−2940.77	+	990.861i	−0.651954	+	0.219669i
$274$	3870.77	+	7301.05i	0.853438	+	1.60975i
$275$	−1492.49	−	1757.10i	−0.327275	−	0.385298i
$276$	1126.65	+	1661.68i	0.245711	+	0.362397i
$277$	−231.578	−	4271.21i	−0.0502317	−	0.926469i	−0.909696	−	0.415274i	$-0.863686\pi$
$277$	−231.578	−	4271.21i	−0.0502317	−	0.926469i	0.859465	−	0.511195i	$-0.170797\pi$
$278$	4458.19	+	11189.2i	0.961814	+	2.41397i
$279$	742.576	+	343.552i	0.159344	+	0.0737202i
$280$	21514.1	−	4735.62i	4.59184	−	1.01074i
$281$	1958.12	−	3693.40i	0.415699	−	0.784092i	−0.583917	−	0.811814i	$-0.698480\pi$
$281$	1958.12	−	3693.40i	0.415699	−	0.784092i	0.999616	+	0.0277220i	$0.00882531\pi$
$282$	75.6233	−	461.282i	0.0159692	−	0.0974076i
$283$	−2383.75	+	1812.08i	−0.500705	+	0.380626i	−0.824823	−	0.565390i	$-0.808725\pi$
$283$	−2383.75	+	1812.08i	−0.500705	+	0.380626i	0.324118	+	0.946017i	$0.394932\pi$
$284$	−6997.37	+	3237.33i	−1.46203	+	0.676409i
$285$	−3121.56	−	2956.90i	−0.648790	−	0.614566i
$286$	−1327.80	−	8099.25i	−0.274527	−	1.67454i
$287$	−12571.5	−	4235.82i	−2.58561	−	0.871194i
$288$	729.066	−	1829.82i	0.149169	−	0.374385i
$289$	−1261.86	+	1195.30i	−0.256842	+	0.243294i
$290$	−10078.0	−	7661.12i	−2.04070	−	1.55130i
$291$	−1309.31	−	288.202i	−0.263757	−	0.0580573i
$292$	−10254.3	+	12072.3i	−2.05509	+	2.41944i
$293$	−4281.09	−	465.597i	−0.853598	−	0.0928344i	−0.329151	−	0.944277i	$-0.606762\pi$
$293$	−4281.09	−	465.597i	−0.853598	−	0.0928344i	−0.524447	+	0.851443i	$0.675728\pi$
$294$	10183.9			2.02020
$295$	2838.91	−	5222.40i	0.560297	−	1.03071i
$296$	−2425.61			−0.476303
$297$	−1315.58	−	143.077i	−0.257028	−	0.0279535i
$298$	−2398.17	+	2823.35i	−0.466183	+	0.548833i
$299$	1163.81	+	256.174i	0.225100	+	0.0495482i
$300$	−2058.86	−	1565.11i	−0.396228	−	0.301205i
$301$	4893.78	−	4635.64i	0.937119	−	0.887686i
$302$	−3471.23	+	8712.12i	−0.661413	+	1.66002i
$303$	1975.08	+	665.482i	0.374473	+	0.126175i
$304$	2214.57	+	13508.3i	0.417811	+	2.54853i
$305$	−1260.15	−	1193.67i	−0.236576	−	0.224097i
$306$	−3418.03	+	1581.35i	−0.638548	+	0.295424i
$307$	7306.41	−	5554.19i	1.35830	−	1.03256i	0.363409	−	0.931630i	$-0.381613\pi$
$307$	7306.41	−	5554.19i	1.35830	−	1.03256i	0.994894	−	0.100925i	$-0.0321803\pi$
$308$	−4606.06	+	28095.7i	−0.852126	+	5.19774i
$309$	−2618.48	+	4938.98i	−0.482072	+	0.909284i
$310$	−5975.25	+	1315.25i	−1.09475	+	0.240972i
$311$	−1410.23	−	652.440i	−0.257127	−	0.118960i	0.287091	−	0.957903i	$-0.407312\pi$
$311$	−1410.23	−	652.440i	−0.257127	−	0.118960i	−0.544219	+	0.838944i	$0.683174\pi$
$312$	−1920.31	−	4819.62i	−0.348449	−	0.874542i
$313$	241.816	+	4460.04i	0.0436685	+	0.805419i	0.935560	+	0.353169i	$0.114896\pi$
$313$	241.816	+	4460.04i	0.0436685	+	0.805419i	−0.891891	+	0.452250i	$0.850621\pi$
$314$	−8461.29	−	12479.5i	−1.52069	−	2.24286i
$315$	−2422.21	−	2851.65i	−0.433258	−	0.510071i
$316$	11850.4	+	22352.3i	2.10962	+	3.97916i
$317$	32.4024	−	10.9176i	0.00574101	−	0.00193437i	−0.316430	−	0.948616i	$-0.602484\pi$
$317$	32.4024	−	10.9176i	0.00574101	−	0.00193437i	0.322171	+	0.946682i	$0.395588\pi$
$318$	−330.581	+	6097.20i	−0.0582957	+	1.07520i
$319$	7899.70	−	4753.09i	1.38651	−	0.834238i
$320$	423.814	+	1526.44i	0.0740372	+	0.266658i
$321$	1189.18	−	4283.03i	0.206771	−	0.744720i
$322$	−5088.24	−	3061.49i	−0.880611	−	0.529846i
$323$	5001.03	−	7375.97i	0.861501	−	1.27062i
$324$	−1475.81	+	160.504i	−0.253054	+	0.0275213i
$325$	−1526.11	+	165.974i	−0.260471	+	0.0283280i
$326$	−10345.3	+	15258.2i	−1.75759	+	2.59225i
$327$	1662.03	+	1000.01i	0.281072	+	0.169115i
$328$	5933.39	−	21370.1i	0.998831	−	3.59746i
$329$	257.493	+	927.407i	0.0431491	+	0.155409i
$330$	8479.10	−	5101.71i	1.41442	−	0.851029i
$331$	−120.046	+	2214.12i	−0.0199346	+	0.367671i	0.971498	+	0.237049i	$0.0761802\pi$
$331$	−120.046	+	2214.12i	−0.0199346	+	0.367671i	−0.991432	+	0.130622i	$0.958303\pi$
$332$	21988.4	−	7408.75i	3.63485	−	1.22472i
$333$	192.973	+	363.986i	0.0317563	+	0.0598988i
$334$	−13636.9	−	16054.6i	−2.23407	−	2.63015i
$335$	988.356	+	1457.72i	0.161193	+	0.237742i
$336$	644.883	+	11894.2i	0.104706	+	1.93119i
$337$	−2411.36	−	6052.06i	−0.389778	−	0.978269i	−0.984664	−	0.174459i	$-0.944182\pi$
$337$	−2411.36	−	6052.06i	−0.389778	−	0.978269i	0.594887	−	0.803810i	$-0.297197\pi$
$338$	5271.02	+	2438.63i	0.848241	+	0.392438i
$339$	−5942.52	+	1308.05i	−0.952075	+	0.209567i
$340$	9182.96	−	17320.9i	1.46475	−	2.76282i
$341$	720.860	−	4397.05i	0.114477	−	0.698281i
$342$	4017.12	−	3053.73i	0.635149	−	0.482827i
$343$	−9164.63	+	4240.01i	−1.44269	+	0.667461i
$344$	8181.65	+	7750.07i	1.28234	+	1.21470i
$345$	232.447	+	1417.86i	0.0362740	+	0.221261i
$346$	16634.0	+	5604.65i	2.58454	+	0.870831i
$347$	−2714.03	+	6811.70i	−0.419875	+	1.05381i	0.555158	+	0.831745i	$0.312658\pi$
$347$	−2714.03	+	6811.70i	−0.419875	+	1.05381i	−0.975033	+	0.222062i	$0.928721\pi$
$348$	7508.47	−	7112.40i	1.15660	−	1.09559i
$349$	6516.12	+	4953.43i	0.999427	+	0.759745i	0.970811	−	0.239846i	$-0.0770969\pi$
$349$	6516.12	+	4953.43i	0.999427	+	0.759745i	0.0286160	+	0.999590i	$0.490890\pi$
$350$	7470.81	+	1644.45i	1.14095	+	0.251142i
$351$	−570.456	+	671.593i	−0.0867484	+	0.102128i
$352$	−10663.8	−	1159.76i	−1.61472	−	0.175612i
$353$	8492.07			1.28042			0.640209	−	0.768201i	$-0.278848\pi$
$353$	8492.07			1.28042			0.640209	+	0.768201i	$0.278848\pi$
$354$	5509.17	+	4279.35i	0.827144	+	0.642499i
$355$	−5517.78			−0.824939
$356$	−22580.8	−	2455.80i	−3.36173	−	0.365611i
$357$	5020.27	−	5910.32i	0.744260	−	0.876211i
$358$	9010.38	+	1983.33i	1.33020	+	0.292800i
$359$	−958.771	−	728.839i	−0.140953	−	0.107149i	0.532322	−	0.846542i	$-0.321320\pi$
$359$	−958.771	−	728.839i	−0.140953	−	0.107149i	−0.673274	+	0.739393i	$0.735113\pi$
$360$	4541.29	−	4301.74i	0.664853	−	0.629782i
$361$	−1880.73	+	4720.27i	−0.274198	+	0.688186i
$362$	6449.52	+	2173.10i	0.936407	+	0.315512i
$363$	519.907	+	3171.29i	0.0751736	+	0.458539i
$364$	13763.3	+	13037.3i	1.98185	+	1.87731i
$365$	−10288.1	+	4759.79i	−1.47536	+	0.682572i
$366$	1621.67	−	1232.77i	0.231602	−	0.176059i
$367$	827.993	−	5050.53i	0.117768	−	0.718353i	−0.860256	−	0.509862i	$-0.829696\pi$
$367$	827.993	−	5050.53i	0.117768	−	0.718353i	0.978024	−	0.208491i	$-0.0668552\pi$
$368$	2142.60	−	4041.37i	0.303507	−	0.572475i
$369$	−3678.83	+	809.772i	−0.519003	+	0.114241i
$370$	−2795.93	−	1293.54i	−0.392848	−	0.181751i
$371$	−4653.74	−	11680.0i	−0.651240	−	1.63449i
$372$	−270.611	−	4991.13i	−0.0377165	−	0.695640i
$373$	−1392.15	−	2053.26i	−0.193251	−	0.285024i	0.718702	−	0.695318i	$-0.244736\pi$
$373$	−1392.15	−	2053.26i	−0.193251	−	0.285024i	−0.911953	+	0.410294i	$0.865426\pi$
$374$	13277.6	+	15631.6i	1.83574	+	2.16120i
$375$	1436.96	+	2710.39i	0.197878	+	0.373237i
$376$	−1524.90	+	513.799i	−0.209151	+	0.0704712i
$377$	332.354	−	6129.92i	0.0454035	−	0.837418i
$378$	3762.45	−	2263.79i	0.511957	−	0.308034i
$379$	−1992.73	−	7177.16i	−0.270078	−	0.972733i	−0.966830	−	0.255421i	$-0.917786\pi$
$379$	−1992.73	−	7177.16i	−0.270078	−	0.972733i	0.696752	−	0.717312i	$-0.254628\pi$
$380$	−7027.25	+	25309.9i	−0.948658	+	3.41676i
$381$	−247.333	−	148.815i	−0.0332579	−	0.0200106i
$382$	−7201.18	+	10620.9i	−0.964514	+	1.42255i
$383$	9887.75	−	1075.36i	1.31917	−	0.143468i	0.578688	−	0.815549i	$-0.303565\pi$
$383$	9887.75	−	1075.36i	1.31917	−	0.143468i	0.740478	+	0.672081i	$0.234599\pi$
$384$	3373.51	−	366.891i	0.448317	−	0.0487574i
$385$	−11434.6	+	16864.7i	−1.51366	+	2.23248i
$386$	3784.53	+	2277.07i	0.499035	+	0.300259i
$387$	512.068	−	1844.30i	0.0672607	−	0.242251i
$388$	2191.12	+	7891.69i	0.286693	+	1.03258i
$389$	1268.93	−	763.491i	0.165392	−	0.0995130i	−0.430451	−	0.902614i	$-0.641646\pi$
$389$	1268.93	−	763.491i	0.165392	−	0.0995130i	0.595843	+	0.803101i	$0.296818\pi$
$390$	356.731	−	6579.51i	0.0463174	−	0.854273i
$391$	−2822.00	+	950.843i	−0.364999	+	0.122983i
$392$	−16421.3	−	30973.8i	−2.11582	−	3.99086i
$393$	−1003.44	−	1181.35i	−0.128797	−	0.151631i
$394$	−4262.26	−	6286.36i	−0.544999	−	0.803813i
$395$	980.239	+	18079.4i	0.124864	+	2.30298i
$396$	2992.34	+	7510.21i	0.379724	+	0.953035i
$397$	3882.13	+	1796.07i	0.490777	+	0.227058i	0.649639	−	0.760243i	$-0.274920\pi$
$397$	3882.13	+	1796.07i	0.490777	+	0.227058i	−0.158861	+	0.987301i	$0.550782\pi$
$398$	4638.16	−	1020.94i	0.584145	−	0.128580i
$399$	−4866.83	+	9179.81i	−0.610642	+	1.15179i
$400$	−953.298	+	5814.86i	−0.119162	+	0.726858i
$401$	509.226	−	387.104i	0.0634153	−	0.0482071i	−0.572986	−	0.819565i	$-0.694215\pi$
$401$	509.226	−	387.104i	0.0634153	−	0.0482071i	0.636402	+	0.771358i	$0.280422\pi$
$402$	−1875.87	+	867.868i	−0.232736	+	0.107675i
$403$	−2153.99	−	2040.37i	−0.266248	−	0.252204i
$404$	−2059.89	−	12564.8i	−0.253671	−	1.54733i
$405$	−1006.81	−	339.232i	−0.123527	−	0.0416212i
$406$	−11322.9	+	28418.4i	−1.38411	+	3.47385i
$407$	1628.80	−	1542.88i	0.198370	−	0.187906i
$408$	10321.0	+	7845.86i	1.25237	+	0.952029i
$409$	−12075.8	−	2658.09i	−1.45993	−	0.321354i	−0.587153	−	0.809476i	$-0.699751\pi$
$409$	−12075.8	−	2658.09i	−1.45993	−	0.321354i	−0.872775	+	0.488122i	$0.837682\pi$
$410$	18235.6	−	21468.6i	2.19656	−	2.58600i
$411$	−4803.28	−	522.388i	−0.576467	−	0.0626946i
$412$	34150.9			4.08373
$413$	−13995.1	−	3233.95i	−1.66745	−	0.385308i
$414$	−1686.19			−0.200173
$415$	16508.3	+	1795.39i	1.95268	+	0.212367i
$416$	−4624.01	+	5443.81i	−0.544978	+	0.641597i
$417$	−6877.62	−	1513.88i	−0.807670	−	0.177782i
$418$	−21876.5	−	16630.1i	−2.55984	−	1.94594i
$419$	10178.8	−	9641.87i	1.18679	−	1.12419i	0.197192	−	0.980365i	$-0.436818\pi$
$419$	10178.8	−	9641.87i	1.18679	−	1.12419i	0.989603	−	0.143827i	$-0.0459408\pi$
$420$	−8460.40	+	21234.0i	−0.982917	+	2.46694i
$421$	16.0890	+	5.42102i	0.00186254	+	0.000627564i	0.320233	−	0.947339i	$-0.396239\pi$
$421$	16.0890	+	5.42102i	0.00186254	+	0.000627564i	−0.318370	+	0.947966i	$0.603135\pi$
$422$	−1264.13	−	7710.88i	−0.145823	−	0.889478i
$423$	198.416	+	187.950i	0.0228069	+	0.0216039i
$424$	19077.3	−	8826.11i	2.18509	−	1.01093i
$425$	3053.90	−	2321.51i	0.348555	−	0.264964i
$426$	1047.63	−	6390.26i	0.119150	−	0.726782i
$427$	−1964.70	+	3705.81i	−0.222666	+	0.419992i
$428$	−26520.4	+	5837.59i	−2.99512	+	0.659276i
$429$	4355.16	+	2014.91i	0.490138	+	0.226762i
$430$	5297.78	+	13296.4i	0.594144	+	1.49119i
$431$	−92.9185	−	1713.78i	−0.0103845	−	0.191531i	−0.999123	−	0.0418762i	$-0.986666\pi$
$431$	−92.9185	−	1713.78i	−0.0103845	−	0.191531i	0.988738	−	0.149655i	$-0.0478163\pi$
$432$	1898.13	+	2799.54i	0.211398	+	0.311789i
$433$	−7457.13	−	8779.21i	−0.827637	−	0.974370i	0.172306	−	0.985043i	$-0.444878\pi$
$433$	−7457.13	−	8779.21i	−0.827637	−	0.974370i	−0.999943	+	0.0106738i	$0.996602\pi$
$434$	6925.31	+	13062.5i	0.765957	+	1.44475i
$435$	7014.21	−	2363.36i	0.773117	−	0.260493i
$436$	641.531	−	11832.3i	0.0704674	−	1.29969i
$437$	3418.80	−	2057.02i	0.374241	−	0.225174i
$438$	−3559.07	−	12818.6i	−0.388262	−	1.39839i
$439$	3339.21	−	12026.7i	0.363033	−	1.30753i	−0.526312	−	0.850291i	$-0.676426\pi$
$439$	3339.21	−	12026.7i	0.363033	−	1.30753i	0.889345	−	0.457236i	$-0.151161\pi$
$440$	−29188.8	−	17562.3i	−3.16255	−	1.90284i
$441$	−3341.50	+	4928.34i	−0.360814	+	0.532161i
$442$	13576.6	−	1476.55i	1.46103	−	0.158897i
$443$	−2003.08	+	217.848i	−0.214828	+	0.0233640i	−0.214900	−	0.976636i	$-0.568943\pi$
$443$	−2003.08	+	217.848i	−0.214828	+	0.0233640i	7.18525e−5		1.00000i	$0.499977\pi$
$444$	1412.40	−	2083.13i	0.150967	−	0.222660i
$445$	−13928.8	−	8380.66i	−1.48379	−	0.892767i
$446$	785.719	−	2829.90i	0.0834190	−	0.300448i
$447$	−579.435	−	2086.94i	−0.0613117	−	0.220825i
$448$	3280.18	−	1973.62i	0.345924	−	0.208135i
$449$	−215.495	+	3974.57i	−0.0226500	+	0.417754i	0.965117	+	0.261818i	$0.0843221\pi$
$449$	−215.495	+	3974.57i	−0.0226500	+	0.417754i	−0.987767	+	0.155936i	$0.950161\pi$
$450$	2058.44	−	693.570i	0.215635	−	0.0726560i
$451$	9608.85	+	18124.2i	1.00324	+	1.89232i
$452$	24065.0	+	28331.5i	2.50425	+	2.94824i
$453$	−3077.12	−	4538.42i	−0.319152	−	0.470714i
$454$	298.471	+	5504.98i	0.0308545	+	0.569078i
$455$	5021.87	+	12603.9i	0.517426	+	1.29864i
$456$	−15765.2	−	7293.77i	−1.61902	−	0.749040i
$457$	−3859.35	+	849.507i	−0.395039	+	0.0869546i	−0.408047	−	0.912961i	$-0.633790\pi$
$457$	−3859.35	+	849.507i	−0.395039	+	0.0869546i	0.0130086	+	0.999915i	$0.495859\pi$
$458$	−4380.87	+	8263.20i	−0.446953	+	0.843044i
$459$	356.239	−	2172.96i	0.0362262	−	0.220970i
$460$	6987.71	−	5311.92i	0.708269	−	0.538412i
$461$	4491.05	−	2077.78i	0.453729	−	0.209917i	−0.179695	−	0.983722i	$-0.557511\pi$
$461$	4491.05	−	2077.78i	0.453729	−	0.209917i	0.633424	+	0.773805i	$0.281649\pi$
$462$	−17360.4	−	16444.6i	−1.74822	−	1.65600i
$463$	−2609.29	−	15916.0i	−0.261910	−	1.59758i	−0.710405	−	0.703793i	$-0.751488\pi$
$463$	−2609.29	−	15916.0i	−0.261910	−	1.59758i	0.448495	−	0.893785i	$-0.351960\pi$
$464$	−22330.7	−	7524.07i	−2.23421	−	0.752794i
$465$	1324.07	−	3323.17i	0.132048	−	0.331416i
$466$	−9784.03	+	9267.93i	−0.972611	+	0.921306i
$467$	10814.1	+	8220.70i	1.07156	+	0.814579i	0.983386	−	0.181526i	$-0.0581036\pi$
$467$	10814.1	+	8220.70i	1.07156	+	0.814579i	0.0881744	+	0.996105i	$0.471897\pi$
$468$	5257.30	+	1157.22i	0.519271	+	0.114300i
$469$	2755.20	−	3243.67i	0.271265	−	0.319358i
$470$	−2031.71	−	220.962i	−0.199396	−	0.0216856i
$471$	8815.50			0.862413
$472$	4132.01	−	23656.1i	0.402947	−	2.30691i
$473$	−10423.7			−1.01328
$474$	−21124.3	−	2297.41i	−2.04699	−	0.222623i
$475$	−3327.45	+	3917.38i	−0.321419	+	0.378403i
$476$	−46266.6	−	10184.0i	−4.45510	−	0.980641i
$477$	−2842.17	−	2160.56i	−0.272817	−	0.207390i
$478$	−4420.35	+	4187.18i	−0.422976	+	0.400664i
$479$	2480.14	−	6224.68i	0.236577	−	0.593764i	−0.761972	−	0.647610i	$-0.775769\pi$
$479$	2480.14	−	6224.68i	0.236577	−	0.593764i	0.998549	+	0.0538459i	$0.0171480\pi$
$480$	−8160.98	−	2749.75i	−0.776034	−	0.261476i
$481$	−241.688	−	1474.23i	−0.0229106	−	0.139749i
$482$	−19789.3	−	18745.4i	−1.87008	−	1.77143i
$483$	3151.08	−	1457.85i	0.296851	−	0.137338i
$484$	15629.2	−	11881.0i	1.46781	−	1.11580i
$485$	−948.283	+	5784.27i	−0.0887821	+	0.541547i
$486$	584.029	−	1101.60i	0.0545105	−	0.102818i
$487$	−3347.70	+	736.884i	−0.311496	+	0.0685655i	−0.367967	−	0.929839i	$-0.619946\pi$
$487$	−3347.70	+	736.884i	−0.311496	+	0.0685655i	0.0564711	+	0.998404i	$0.482015\pi$
$488$	−6364.28	−	2944.43i	−0.590364	−	0.273131i
$489$	−3989.49	−	10012.9i	−0.368939	−	0.925967i
$490$	−2410.55	−	44459.9i	−0.222240	−	4.09897i
$491$	9850.51	+	14528.4i	0.905392	+	1.33535i	0.941856	+	0.336018i	$0.109080\pi$
$491$	9850.51	+	14528.4i	0.905392	+	1.33535i	−0.0364642	+	0.999335i	$0.511609\pi$
$492$	14897.9	+	17539.2i	1.36514	+	1.60717i
$493$	7185.70	+	13553.7i	0.656445	+	1.23819i
$494$	−17340.1	+	5842.57i	−1.57929	+	0.532125i
$495$	−313.234	+	5777.26i	−0.0284421	+	0.524583i
$496$	−9758.42	+	5871.44i	−0.883399	+	0.531523i
$497$	3567.12	+	12847.6i	0.321946	+	1.15955i
$498$	−5213.62	+	18777.8i	−0.469132	+	1.68966i
$499$	7472.75	+	4496.20i	0.670393	+	0.403362i	0.809665	−	0.586892i	$-0.199649\pi$
$499$	7472.75	+	4496.20i	0.670393	+	0.403362i	−0.139272	+	0.990254i	$0.544476\pi$
$500$	10517.3	−	15511.9i	0.940697	−	1.38742i
$501$	12243.8	−	1331.60i	1.09184	−	0.118745i
$502$	−3976.14	+	432.431i	−0.353513	+	0.0384469i
$503$	265.975	−	392.283i	0.0235770	−	0.0347735i	−0.815718	−	0.578450i	$-0.803658\pi$
$503$	265.975	−	392.283i	0.0235770	−	0.0347735i	0.839295	+	0.543677i	$0.182968\pi$
$504$	−12952.0	−	7792.97i	−1.14470	−	0.688743i
$505$	2437.78	−	8780.10i	0.214812	−	0.773682i
$506$	2456.63	+	8847.97i	0.215831	+	0.777352i
$507$	−2909.63	+	1750.67i	−0.254874	+	0.153353i
$508$	−95.4688	+	1760.82i	−0.00833808	+	0.153787i
$509$	−3121.61	+	1051.79i	−0.271833	+	0.0915911i	−0.451917	−	0.892060i	$-0.649260\pi$
$509$	−3121.61	+	1051.79i	−0.271833	+	0.0915911i	0.180084	+	0.983651i	$0.442363\pi$
$510$	7712.73	+	14547.7i	0.669658	+	1.26311i
$511$	17733.8	+	20877.8i	1.53522	+	1.80740i
$512$	−14416.0	−	21262.0i	−1.24434	−	1.83527i
$513$	159.727	+	2945.99i	0.0137468	+	0.253545i
$514$	−794.162	−	1993.20i	−0.0681498	−	0.171043i
$515$	22181.8	+	10262.4i	1.89796	+	0.878089i
$516$	−11419.9	+	2513.71i	−0.974287	+	0.214457i
$517$	697.157	−	1314.98i	0.0593055	−	0.111862i
$518$	−1204.36	+	7346.30i	−0.102156	+	0.623123i
$519$	−8170.13	+	6210.77i	−0.691000	+	0.525284i
$520$	−20586.4	+	9524.29i	−1.73610	+	0.803207i
$521$	−5587.72	−	5292.97i	−0.469870	−	0.445085i	0.415761	−	0.909474i	$-0.363515\pi$
$521$	−5587.72	−	5292.97i	−0.469870	−	0.445085i	−0.885631	+	0.464389i	$0.846274\pi$
$522$	1405.31	+	8572.03i	0.117833	+	0.718750i
$523$	−6673.91	−	2248.70i	−0.557992	−	0.188009i	0.0261541	−	0.999658i	$-0.491674\pi$
$523$	−6673.91	−	2248.70i	−0.557992	−	0.188009i	−0.584146	+	0.811649i	$0.698570\pi$
$524$	−3504.86	+	8796.55i	−0.292196	+	0.733357i
$525$	−3247.08	+	3075.80i	−0.269932	+	0.255693i
$526$	18843.3	+	14324.3i	1.56199	+	1.18739i
$527$	7240.84	+	1593.83i	0.598512	+	0.131742i
$528$	11924.6	−	14038.8i	0.982866	−	1.15712i
$529$	10770.2	+	1171.33i	0.885199	+	0.0962712i
$530$	26696.7			2.18798
$531$	−3878.55	+	1261.95i	−0.316977	+	0.103134i
$532$	63474.5			5.17287
$533$	13579.5	+	1476.86i	1.10355	+	0.120018i
$534$	12350.4	−	14540.0i	1.00085	−	1.17829i
$535$	−18979.8	−	4177.78i	−1.53378	−	0.337610i
$536$	5664.34	+	4305.92i	0.456460	+	0.346992i
$537$	−3916.24	+	3709.66i	−0.314708	+	0.298107i
$538$	−1043.72	+	2619.54i	−0.0836393	+	0.209919i
$539$	30728.8	+	10353.7i	2.45563	+	0.827398i
$540$	1050.04	+	6404.94i	0.0836785	+	0.510416i
$541$	9424.75	+	8927.59i	0.748986	+	0.709477i	0.963637	−	0.267213i	$-0.0861029\pi$
$541$	9424.75	+	8927.59i	0.748986	+	0.709477i	−0.214651	+	0.976691i	$0.568861\pi$
$542$	−1689.03	+	781.427i	−0.133856	+	0.0619284i
$543$	−3167.82	+	2408.11i	−0.250357	+	0.190317i
$544$	2887.60	−	17613.6i	0.227583	−	1.38819i
$545$	3972.33	−	7492.61i	0.312213	−	0.588896i
$546$	−15550.4	+	3422.90i	−1.21885	+	0.268290i
$547$	−1213.16	−	561.269i	−0.0948283	−	0.0438723i	0.371902	−	0.928272i	$-0.378706\pi$
$547$	−1213.16	−	561.269i	−0.0948283	−	0.0438723i	−0.466730	+	0.884400i	$0.654568\pi$
$548$	10925.3	+	27420.4i	0.851651	+	2.13748i
$549$	64.4803	+	1189.27i	0.00501267	+	0.0924532i
$550$	−6638.34	−	9790.82i	−0.514654	−	0.759058i
$551$	−13306.5	−	15665.7i	−1.02882	−	1.21122i
$552$	2718.93	+	5128.45i	0.209647	+	0.395437i
$553$	41462.5	−	13970.3i	3.18836	−	1.07428i
$554$	1188.23	−	21915.6i	0.0911247	−	1.68070i
$555$	1543.37	−	928.615i	0.118040	−	0.0710226i
$556$	11509.6	+	41453.8i	0.877905	+	3.16193i
$557$	380.621	−	1370.87i	0.0289541	−	0.104283i	−0.947661	−	0.319278i	$-0.896560\pi$
$557$	380.621	−	1370.87i	0.0289541	−	0.104283i	0.976615	+	0.214995i	$0.0689734\pi$
$558$	3597.25	+	2164.39i	0.272910	+	0.164204i
$559$	−3895.10	+	5744.84i	−0.294714	+	0.434670i
$560$	51773.6	−	5630.72i	3.90685	−	0.424895i
$561$	−11921.2	+	1296.51i	−0.897173	+	0.0975734i
$562$	12037.2	−	17753.5i	0.903484	−	1.33254i
$563$	−1068.45	−	642.865i	−0.0799819	−	0.0481235i	0.475001	−	0.879985i	$-0.342448\pi$
$563$	−1068.45	−	642.865i	−0.0799819	−	0.0481235i	−0.554983	+	0.831862i	$0.687275\pi$
$564$	446.674	−	1608.78i	0.0333482	−	0.120109i
$565$	7117.13	+	25633.6i	0.529946	+	1.90869i
$566$	−13164.7	+	7920.91i	−0.977653	+	0.588235i
$567$	−138.992	+	2563.56i	−0.0102947	+	0.189875i
$568$	−21124.9	+	7117.79i	−1.56053	+	0.525803i
$569$	933.638	+	1761.03i	0.0687876	+	0.129747i	0.915521	−	0.402270i	$-0.131779\pi$
$569$	933.638	+	1761.03i	0.0687876	+	0.129747i	−0.846733	+	0.532018i	$0.821434\pi$
$570$	−14282.5	−	16814.7i	−1.04952	−	1.23559i
$571$	8631.88	+	12731.1i	0.632632	+	0.933063i	0.999996	+	0.00298545i	$0.000950298\pi$
$571$	8631.88	+	12731.1i	0.632632	+	0.933063i	−0.367363	+	0.930078i	$0.619739\pi$
$572$	−1587.12	−	29272.7i	−0.116015	−	2.13977i
$573$	−2777.01	−	6969.78i	−0.202463	−	0.508144i
$574$	−61776.4	−	28580.8i	−4.49216	−	2.07829i
$575$	1677.37	−	369.218i	0.121654	−	0.0267782i
$576$	509.168	−	960.392i	0.0368322	−	0.0694728i
$577$	2566.68	−	15656.1i	0.185186	−	1.12958i	−0.716627	−	0.697457i	$-0.754315\pi$
$577$	2566.68	−	15656.1i	0.185186	−	1.12958i	0.901813	−	0.432127i	$-0.142237\pi$
$578$	−7099.80	+	5397.13i	−0.510922	+	0.388393i
$579$	−2343.71	+	1084.32i	−0.168223	+	0.0778283i
$580$	−32827.8	−	31096.1i	−2.35017	−	2.22620i
$581$	−6491.88	−	39598.7i	−0.463560	−	2.82759i
$582$	−6518.84	−	2196.45i	−0.464286	−	0.156436i
$583$	−7196.35	+	18061.5i	−0.511222	+	1.28307i
$584$	−33248.1	+	31494.3i	−2.35585	+	2.23158i
$585$	3066.99	+	2331.47i	0.216760	+	0.164777i
$586$	−21579.3	−	4749.96i	−1.52122	−	0.334845i
$587$	516.489	−	608.058i	0.0363165	−	0.0427551i	−0.743704	−	0.668509i	$-0.766933\pi$
$587$	516.489	−	608.058i	0.0363165	−	0.0427551i	0.780020	+	0.625754i	$0.215209\pi$
$588$	36162.5	+	3932.91i	2.53625	+	0.275834i
$589$	−9933.92			−0.694940
$590$	17378.3	−	25064.2i	1.21263	−	1.74895i
$591$	4440.69			0.309079
$592$	−5700.74	−	619.993i	−0.395775	−	0.0430431i
$593$	5534.33	−	6515.52i	0.383251	−	0.451198i	−0.536383	−	0.843975i	$-0.680210\pi$
$593$	5534.33	−	6515.52i	0.383251	−	0.451198i	0.919634	+	0.392777i	$0.128486\pi$
$594$	−6631.29	−	1459.66i	−0.458056	−	0.100826i
$595$	−26990.9	−	20518.0i	−1.85970	−	1.41371i
$596$	−9606.09	+	9099.37i	−0.660203	+	0.625377i
$597$	−1027.78	+	2579.54i	−0.0704595	+	0.176840i
$598$	5794.40	+	1952.36i	0.396239	+	0.133508i
$599$	2131.86	+	13003.8i	0.145418	+	0.887010i	0.954259	+	0.298982i	$0.0966471\pi$
$599$	2131.86	+	13003.8i	0.145418	+	0.887010i	−0.808841	+	0.588028i	$0.799905\pi$
$600$	−5428.62	−	5142.27i	−0.369371	−	0.349887i
$601$	−13657.8	+	6318.77i	−0.926977	+	0.428865i	−0.824495	−	0.565870i	$-0.808541\pi$
$601$	−13657.8	+	6318.77i	−0.926977	+	0.428865i	−0.102482	+	0.994735i	$0.532679\pi$
$602$	27534.5	−	20931.2i	1.86416	−	1.41710i
$603$	195.509	−	1192.55i	0.0132036	−	0.0805382i
$604$	−15690.6	+	29595.6i	−1.05702	+	1.99376i
$605$	13721.8	−	3020.40i	0.922100	−	0.202970i
$606$	9705.58	+	4490.28i	0.650598	+	0.300998i
$607$	−3269.82	−	8206.64i	−0.218646	−	0.548760i	0.778209	−	0.628005i	$-0.216128\pi$
$607$	−3269.82	−	8206.64i	−0.218646	−	0.548760i	−0.996855	+	0.0792452i	$0.974749\pi$
$608$	1294.72	+	23879.6i	0.0863613	+	1.59284i
$609$	−10037.4	−	14804.0i	−0.667875	−	0.985042i
$610$	−5765.72	−	6787.93i	−0.382700	−	0.450550i
$611$	−464.217	−	875.605i	−0.0307368	−	0.0579758i
$612$	−12747.9	+	4295.26i	−0.841998	+	0.283702i
$613$	−113.912	+	2100.98i	−0.00750546	+	0.138430i	0.992379	+	0.123224i	$0.0393233\pi$
$613$	−113.912	+	2100.98i	−0.00750546	+	0.138430i	−0.999884	+	0.0152063i	$0.995159\pi$
$614$	40350.8	−	24278.3i	2.65216	−	1.59575i
$615$	4405.99	+	15869.0i	0.288889	+	1.04048i
$616$	−22022.3	+	79317.0i	−1.44042	+	5.18794i
$617$	−20301.7	−	12215.2i	−1.32466	−	0.797024i	−0.335247	−	0.942130i	$-0.608820\pi$
$617$	−20301.7	−	12215.2i	−1.32466	−	0.797024i	−0.989416	+	0.145107i	$0.953647\pi$
$618$	−16096.7	+	23740.8i	−1.04774	+	1.54530i
$619$	−7231.91	+	786.518i	−0.469588	+	0.0510708i	−0.339854	−	0.940478i	$-0.610378\pi$
$619$	−7231.91	+	786.518i	−0.469588	+	0.0510708i	−0.129734	+	0.991549i	$0.541412\pi$
$620$	−21725.7	+	2362.81i	−1.40730	+	0.153053i
$621$	553.264	−	816.003i	0.0357515	−	0.0527296i
$622$	−6831.53	−	4110.39i	−0.440385	−	0.264971i
$623$	−10508.9	+	37849.7i	−0.675811	+	2.43405i
$624$	−3281.27	−	11818.0i	−0.210506	−	0.758174i
$625$	16530.6	−	9946.15i	1.05796	−	0.636553i
$626$	−1240.76	+	22884.5i	−0.0792186	+	1.46110i
$627$	15225.8	−	5130.18i	0.969794	−	0.326762i
$628$	−25226.1	−	47581.4i	−1.60291	−	3.02341i
$629$	2416.80	+	2845.27i	0.153202	+	0.180363i
$630$	−10773.6	−	15889.8i	−0.681317	−	1.00487i
$631$	−374.988	−	6916.24i	−0.0236577	−	0.436341i	−0.986237	−	0.165340i	$-0.947128\pi$
$631$	−374.988	−	6916.24i	−0.0236577	−	0.436341i	0.962579	−	0.271001i	$-0.0873548\pi$
$632$	27074.9	+	67952.8i	1.70408	+	4.27692i
$633$	4146.33	+	1918.30i	0.260350	+	0.120451i
$634$	171.339	−	37.7146i	0.0107330	−	0.00236252i
$635$	−591.138	+	1115.00i	−0.0369427	+	0.0696813i
$636$	−3528.53	+	21523.1i	−0.219993	+	1.34190i
$637$	17189.0	−	13066.7i	1.06916	−	0.812751i
$638$	42932.7	−	19862.8i	2.66414	−	1.23256i
$639$	2748.71	+	2603.72i	0.170168	+	0.161192i
$640$	−2400.24	−	14640.8i	−0.148247	−	0.904266i
$641$	−883.317	−	297.624i	−0.0544289	−	0.0183392i	0.291955	−	0.956432i	$-0.405694\pi$
$641$	−883.317	−	297.624i	−0.0544289	−	0.0183392i	−0.346384	+	0.938093i	$0.612591\pi$
$642$	8441.97	−	21187.7i	0.518969	−	1.30251i
$643$	−12732.7	+	12061.0i	−0.780915	+	0.739722i	−0.970228	−	0.242195i	$-0.922133\pi$
$643$	−12732.7	+	12061.0i	−0.780915	+	0.739722i	0.189312	+	0.981917i	$0.439374\pi$
$644$	−16885.7	−	12836.2i	−1.03321	−	0.785428i
$645$	−8172.86	−	1798.98i	−0.498924	−	0.109821i
$646$	29601.9	−	34850.0i	1.80289	−	2.12253i
$647$	−23763.3	−	2584.41i	−1.44394	−	0.157038i	−0.647645	−	0.761942i	$-0.724246\pi$
$647$	−23763.3	−	2584.41i	−1.44394	−	0.157038i	−0.796298	+	0.604904i	$0.793211\pi$
$648$	−4292.16			−0.260204
$649$	12272.6	+	18513.4i	0.742280	+	1.11975i
$650$	−7876.65			−0.475304
$651$	−8593.67	−	934.618i	−0.517377	−	0.0562682i
$652$	−42628.0	+	50185.6i	−2.56049	+	3.01445i
$653$	−28422.7	−	6256.30i	−1.70331	−	0.374928i	−0.746446	−	0.665446i	$-0.768241\pi$
$653$	−28422.7	−	6256.30i	−1.70331	−	0.374928i	−0.956869	+	0.290518i	$0.906172\pi$
$654$	7923.15	+	6023.02i	0.473730	+	0.360120i
$655$	−4919.87	+	4660.35i	−0.293489	+	0.278007i
$656$	19407.1	−	48708.1i	1.15506	−	2.89898i
$657$	7371.13	+	2483.62i	0.437709	+	0.147481i
$658$	798.968	+	4873.49i	0.0473359	+	0.288736i
$659$	−22946.0	−	21735.6i	−1.35637	−	1.28482i	−0.923621	−	0.383307i	$-0.874785\pi$
$659$	−22946.0	−	21735.6i	−1.35637	−	1.28482i	−0.432749	−	0.901515i	$-0.642456\pi$
$660$	32078.9	−	14841.3i	1.89193	−	0.875298i
$661$	−5788.42	+	4400.24i	−0.340611	+	0.258925i	−0.761470	−	0.648201i	$-0.775522\pi$
$661$	−5788.42	+	4400.24i	−0.340611	+	0.258925i	0.420859	+	0.907126i	$0.361729\pi$
$662$	−1840.66	+	11227.5i	−0.108065	+	0.659168i
$663$	−3740.14	+	7054.66i	−0.219088	+	0.413243i
$664$	65518.2	−	14421.7i	3.82922	−	0.842875i
$665$	41228.2	+	19074.2i	2.40415	+	1.11228i
$666$	782.418	+	1963.72i	0.0455227	+	0.114253i
$667$	371.849	+	6858.36i	0.0215863	+	0.398136i
$668$	−42223.7	−	62275.2i	−2.44563	−	3.60704i
$669$	1111.68	+	1308.77i	0.0642450	+	0.0756351i
$670$	4232.86	+	7984.02i	0.244074	+	0.460373i
$671$	6146.53	−	2071.01i	0.353628	−	0.119151i
$672$	−1126.64	+	20779.7i	−0.0646744	+	1.19285i
$673$	−2509.10	+	1509.67i	−0.143713	+	0.0864690i	−0.585594	−	0.810604i	$-0.699139\pi$
$673$	−2509.10	+	1509.67i	−0.143713	+	0.0864690i	0.441882	+	0.897073i	$0.354311\pi$
$674$	−8942.75	−	32208.9i	−0.511071	−	1.84071i
$675$	−339.764	+	1223.72i	−0.0193741	+	0.0697791i
$676$	17775.3	+	10695.0i	1.01134	+	0.608501i
$677$	−13922.8	+	20534.6i	−0.790393	+	1.16574i	0.192452	+	0.981306i	$0.438356\pi$
$677$	−13922.8	+	20534.6i	−0.790393	+	1.16574i	−0.982845	+	0.184436i	$0.940954\pi$
$678$	−31038.1	+	3375.59i	−1.75813	+	0.191208i
$679$	14081.2	−	1531.42i	0.795854	−	0.0865544i
$680$	31809.6	−	46915.6i	1.79388	−	2.64578i
$681$	−2761.97	−	1661.82i	−0.155417	−	0.0935114i
$682$	6116.38	−	22029.2i	0.343414	−	1.23686i
$683$	−3076.51	−	11080.6i	−0.172356	−	0.620771i	−0.998367	−	0.0571174i	$-0.981809\pi$
$683$	−3076.51	−	11080.6i	−0.172356	−	0.620771i	0.826011	−	0.563654i	$-0.190605\pi$
$684$	15443.8	−	9292.24i	0.863318	−	0.519441i
$685$	−1143.64	+	21093.3i	−0.0637903	+	1.17654i
$686$	−49100.4	+	16543.9i	−2.73274	+	0.920769i
$687$	−2561.41	−	4831.32i	−0.142247	−	0.268306i
$688$	17247.8	+	20305.7i	0.955766	+	1.12521i
$689$	7265.17	+	10715.3i	0.401714	+	0.592484i
$690$	399.122	+	7361.38i	0.0220208	+	0.406149i
$691$	6260.86	+	15713.6i	0.344681	+	0.865084i	0.994475	+	0.104973i	$0.0334758\pi$
$691$	6260.86	+	15713.6i	0.344681	+	0.865084i	−0.649794	+	0.760110i	$0.725145\pi$
$692$	56901.8	+	26325.6i	3.12584	+	1.44617i
$693$	13654.3	−	3005.53i	0.748461	−	0.164749i
$694$	−17622.9	+	33240.4i	−0.963916	+	1.81814i
$695$	−4981.18	+	30383.9i	−0.271866	+	1.65831i
$696$	23805.3	−	18096.3i	1.29646	−	0.985544i
$697$	−30979.3	+	14332.5i	−1.68354	+	0.778886i
$698$	30490.4	+	28882.0i	1.65341	+	1.56619i
$699$	−1274.77	−	7775.76i	−0.0689789	−	0.420753i
$700$	25893.3	+	8724.46i	1.39811	+	0.471077i
$701$	−3794.36	+	9523.12i	−0.204438	+	0.513100i	−0.995068	−	0.0991935i	$-0.968374\pi$
$701$	−3794.36	+	9523.12i	−0.204438	+	0.513100i	0.790630	+	0.612294i	$0.209753\pi$
$702$	−3282.44	+	3109.29i	−0.176478	+	0.167169i
$703$	−3981.97	−	3027.01i	−0.213631	−	0.162398i
$704$	−5781.29	−	1272.56i	−0.309504	−	0.0681269i
$705$	773.565	−	910.712i	0.0413250	−	0.0486516i
$706$	43317.5	+	4711.07i	2.30917	+	0.251138i
$707$	−22019.6			−1.17133
$708$	17910.1	+	17323.2i	0.950708	+	0.919558i
$709$	−16960.9			−0.898419			−0.449210	−	0.893426i	$-0.648294\pi$
$709$	−16960.9			−0.898419			−0.449210	+	0.893426i	$0.648294\pi$
$710$	−28145.9	−	3061.05i	−1.48774	−	0.161801i
$711$	8042.98	−	9468.93i	0.424241	−	0.499455i
$712$	−64137.2	−	14117.7i	−3.37590	−	0.743092i
$713$	2642.65	+	2008.89i	0.138805	+	0.105517i
$714$	28886.9	−	27363.1i	1.51410	−	1.43423i
$715$	7765.61	−	19490.2i	0.406178	−	1.01943i
$716$	31229.3	+	10522.4i	1.63002	+	0.549217i
$717$	−575.932	−	3513.03i	−0.0299980	−	0.182980i
$718$	−4486.30	−	4249.65i	−0.233186	−	0.220885i
$719$	9771.11	−	4520.60i	0.506816	−	0.234478i	−0.149781	−	0.988719i	$-0.547857\pi$
$719$	9771.11	−	4520.60i	0.506816	−	0.234478i	0.656598	+	0.754241i	$0.271995\pi$
$720$	11772.6	−	8949.31i	0.609360	−	0.463224i
$721$	9554.96	−	58282.7i	0.493544	−	3.01049i
$722$	−12212.1	+	23034.4i	−0.629483	+	1.18733i
$723$	15564.7	−	3426.05i	0.800632	−	0.176233i
$724$	22062.6	+	10207.2i	1.13253	+	0.523963i
$725$	−3274.94	−	8219.49i	−0.167763	−	0.421054i
$726$	892.705	+	16465.0i	0.0456355	+	0.841698i
$727$	−6777.12	−	9995.50i	−0.345735	−	0.509921i	0.614574	−	0.788859i	$-0.289328\pi$
$727$	−6777.12	−	9995.50i	−0.345735	−	0.509921i	−0.960309	+	0.278938i	$0.910018\pi$
$728$	35485.0	+	41776.2i	1.80654	+	2.12683i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−55119.6	+	18572.0i	−2.79461	+	0.941615i
$731$	939.014	−	17319.1i	0.0475112	−	0.876293i
$732$	6234.54	−	3751.20i	0.314802	−	0.189410i
$733$	−6477.08	−	23328.3i	−0.326380	−	1.17551i	−0.926715	−	0.375765i	$-0.877380\pi$
$733$	−6477.08	−	23328.3i	−0.326380	−	1.17551i	0.600335	−	0.799748i	$-0.295034\pi$
$734$	7025.37	−	25303.1i	0.353285	−	1.27242i
$735$	22306.6	+	13421.4i	1.11944	+	0.673546i
$736$	4484.65	−	6614.36i	0.224601	−	0.331262i
$737$	−6542.54	+	711.544i	−0.326998	+	0.0355632i
$738$	−19214.7	+	2089.73i	−0.958406	+	0.104233i
$739$	3106.95	−	4582.41i	0.154656	−	0.228101i	−0.742465	−	0.669884i	$-0.766344\pi$
$739$	3106.95	−	4582.41i	0.154656	−	0.228101i	0.897122	+	0.441783i	$0.145654\pi$
$740$	−9428.62	−	5673.01i	−0.468382	−	0.281816i
$741$	2862.14	−	10308.5i	0.141894	−	0.511055i
$742$	−17258.8	−	62160.7i	−0.853897	−	3.07546i
$743$	11487.6	−	6911.84i	0.567211	−	0.341280i	−0.202890	−	0.979202i	$-0.565033\pi$
$743$	11487.6	−	6911.84i	0.567211	−	0.341280i	0.770101	+	0.637922i	$0.220206\pi$
$744$	782.416	−	14430.8i	0.0385548	−	0.711101i
$745$	−8973.76	+	3023.61i	−0.441306	+	0.148693i
$746$	−5962.18	−	11245.9i	−0.292615	−	0.551931i
$747$	−7376.51	−	8684.30i	−0.361302	−	0.425357i
$748$	41111.1	+	60634.4i	2.00959	+	2.96392i
$749$	2542.49	+	46893.6i	0.124033	+	2.28765i
$750$	5826.21	+	14622.7i	0.283658	+	0.711927i
$751$	−1055.04	−	488.114i	−0.0512637	−	0.0237171i	0.394090	−	0.919072i	$-0.371060\pi$
$751$	−1055.04	−	488.114i	−0.0512637	−	0.0237171i	−0.445353	+	0.895355i	$0.646922\pi$
$752$	−3715.20	+	817.777i	−0.180159	+	0.0396559i
$753$	1095.36	−	2066.07i	0.0530108	−	0.0999890i
$754$	5095.95	−	31083.9i	0.246132	−	1.50134i
$755$	−19085.0	+	14508.0i	−0.919964	+	0.699338i
$756$	14234.5	−	6585.56i	0.684791	−	0.316818i
$757$	21719.0	+	20573.3i	1.04279	+	0.987780i	0.999936	−	0.0113016i	$-0.00359748\pi$
$757$	21719.0	+	20573.3i	1.04279	+	0.987780i	0.0428505	+	0.999081i	$0.486356\pi$
$758$	−6183.18	−	37715.7i	−0.296284	−	1.80725i
$759$	−5087.88	−	1714.31i	−0.243318	−	0.0819833i
$760$	−28110.7	+	70552.5i	−1.34169	+	3.36738i
$761$	10394.6	−	9846.27i	0.495142	−	0.469024i	−0.398908	−	0.916991i	$-0.630611\pi$
$761$	10394.6	−	9846.27i	0.495142	−	0.469024i	0.894050	+	0.447967i	$0.147852\pi$
$762$	−1179.07	−	896.309i	−0.0560543	−	0.0426114i
$763$	−20013.8	−	4405.38i	−0.949606	−	0.209024i
$764$	−29672.6	+	34933.3i	−1.40513	+	1.65424i
$765$	−9570.79	−	1040.89i	−0.452330	−	0.0491939i
$766$	51033.4			2.40719
$767$	14789.4	+	154.244i	0.696236	+	0.00726132i
$768$	20310.3			0.954277
$769$	3416.39	+	371.555i	0.160206	+	0.0174234i	0.187870	−	0.982194i	$-0.439841\pi$
$769$	3416.39	+	371.555i	0.160206	+	0.0174234i	−0.0276645	+	0.999617i	$0.508807\pi$
$770$	−67682.9	+	79682.4i	−3.16769	+	3.72929i
$771$	1225.15	+	269.676i	0.0572278	+	0.0125968i

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)

\(f(q)\)	\(=\)	\(q+(5.10094 + 0.554760i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(17.8988 + 3.93983i) q^{4} +(10.4418 + 7.93765i) q^{5} +(-11.1753 + 10.5858i) q^{6} +(11.7316 - 29.4442i) q^{7} +(50.2158 + 16.9197i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(5.10094 + 0.554760i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(17.8988 + 3.93983i) q^{4} +(10.4418 + 7.93765i) q^{5} +(-11.1753 + 10.5858i) q^{6} +(11.7316 - 29.4442i) q^{7} +(50.2158 + 16.9197i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(48.8595 + 46.2821i) q^{10} +(-44.4824 + 20.5797i) q^{11} +(-43.7708 + 33.2737i) q^{12} +(-5.27989 + 32.2059i) q^{13} +(76.1769 - 143.685i) q^{14} +(-38.4290 + 8.45885i) q^{15} +(113.694 + 52.6005i) q^{16} +(-30.1864 - 75.7621i) q^{17} +(-2.50009 - 46.1114i) q^{18} +(61.3215 + 90.4424i) q^{19} +(155.623 + 183.214i) q^{20} +(44.5391 + 84.0096i) q^{21} +(-238.319 + 80.2989i) q^{22} +(1.97683 - 36.4606i) q^{23} +(-136.214 + 81.9571i) q^{24} +(12.5838 + 45.3229i) q^{25} +(-44.7990 + 161.351i) q^{26} +(23.1351 + 13.9200i) q^{27} +(325.988 - 480.797i) q^{28} +(-187.001 + 20.3376i) q^{29} +(-200.716 + 21.8292i) q^{30} +(-51.0180 + 75.2459i) q^{31} +(187.529 + 112.833i) q^{32} +(39.3366 - 141.677i) q^{33} +(-111.949 - 403.204i) q^{34} +(356.217 - 214.329i) q^{35} +(8.92999 - 164.704i) q^{36} +(-43.3789 + 14.6161i) q^{37} +(262.623 + 495.360i) q^{38} +(-63.3840 - 74.6214i) q^{39} +(390.041 + 575.268i) q^{40} +(-22.6595 - 417.930i) q^{41} +(180.586 + 453.236i) q^{42} +(193.018 + 89.2997i) q^{43} +(-877.264 + 193.100i) q^{44} +(55.2941 - 104.296i) q^{45} +(30.3106 - 184.886i) q^{46} +(-24.1749 + 18.3773i) q^{47} +(-341.082 + 157.801i) q^{48} +(-480.314 - 454.978i) q^{49} +(39.0460 + 238.170i) q^{50} +(231.856 + 78.1213i) q^{51} +(-221.390 + 555.647i) q^{52} +(287.990 - 272.798i) q^{53} +(110.289 + 83.8393i) q^{54} +(-627.831 - 138.196i) q^{55} +(1087.30 - 1280.07i) q^{56} +(-325.891 - 35.4428i) q^{57} -965.162 q^{58} +(-68.6496 - 447.958i) q^{59} -721.160 q^{60} +(-131.559 - 14.3079i) q^{61} +(-301.983 + 355.522i) q^{62} +(-278.589 - 61.3220i) q^{63} +(96.1518 + 73.0927i) q^{64} +(-310.771 + 294.378i) q^{65} +(279.250 - 700.866i) q^{66} +(127.246 + 42.8741i) q^{67} +(-241.811 - 1474.98i) q^{68} +(79.5272 + 75.3322i) q^{69} +(1935.94 - 895.663i) q^{70} +(-334.901 + 254.585i) q^{71} +(77.1550 - 470.625i) q^{72} +(-404.824 + 763.580i) q^{73} +(-229.382 + 50.4907i) q^{74} +(-128.070 - 59.2515i) q^{75} +(741.255 + 1860.41i) q^{76} +(84.1027 + 1551.18i) q^{77} +(-281.921 - 415.802i) q^{78} +(893.664 + 1052.10i) q^{79} +(769.647 + 1451.71i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(116.266 - 2144.41i) q^{82} +(1084.81 - 652.708i) q^{83} +(466.214 + 1679.15i) q^{84} +(286.173 - 1030.70i) q^{85} +(935.034 + 562.591i) q^{86} +(316.684 - 467.074i) q^{87} +(-2581.92 + 280.801i) q^{88} +(-1232.08 + 133.997i) q^{89} +(339.911 - 501.331i) q^{90} +(886.337 + 533.291i) q^{91} +(179.032 - 644.813i) q^{92} +(-72.9637 - 262.791i) q^{93} +(-133.510 + 80.3301i) q^{94} +(-77.5936 + 1431.13i) q^{95} +(-622.201 + 209.644i) q^{96} +(209.325 + 394.829i) q^{97} +(-2197.65 - 2587.27i) q^{98} +(247.546 + 365.103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + O(q^{10}) \)	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + 854q^{10} + 32q^{11} + 192q^{12} - 22q^{13} - 884q^{14} - 42q^{15} - 268q^{16} - 56q^{17} - 18q^{18} - 112q^{19} - 250q^{20} + 243q^{21} + 108q^{22} + 16q^{23} - 54q^{24} - 197q^{25} - 328q^{26} + 405q^{27} + 236q^{28} - 54q^{29} - 126q^{30} + 66q^{31} + 857q^{32} - 96q^{33} + 112q^{34} + 532q^{35} - 576q^{36} + 110q^{37} + 56q^{38} + 66q^{39} - 6044q^{40} + 304q^{41} - 306q^{42} - 324q^{43} - 568q^{44} + 126q^{45} + 5842q^{46} + 4082q^{47} + 804q^{48} + 739q^{49} + 576q^{50} + 168q^{51} - 1372q^{52} - 1498q^{53} + 54q^{54} - 4422q^{55} - 12036q^{56} + 336q^{57} + 6298q^{58} - 3305q^{59} + 750q^{60} - 1718q^{61} - 4333q^{62} + 54q^{63} - 6250q^{64} - 5884q^{65} - 324q^{66} + 382q^{67} + 734q^{68} + 3780q^{69} + 8082q^{70} + 8638q^{71} + 162q^{72} + 8894q^{73} + 12428q^{74} + 243q^{75} - 15468q^{76} - 9916q^{77} + 984q^{78} - 578q^{79} + 24570q^{80} - 1215q^{81} - 1382q^{82} - 32q^{83} + 7557q^{84} + 708q^{85} + 2296q^{86} - 5928q^{87} - 17646q^{88} - 2284q^{89} + 378q^{90} + 11124q^{91} + 762q^{92} - 198q^{93} - 1232q^{94} + 24184q^{95} - 396q^{96} - 658q^{97} - 4356q^{98} + 288q^{99} + O(q^{100}) \)

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