LMFDB - Embedded newform 177.4.e.a.4.11

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			4.11
Character	$\chi$	$=$	177.4
Dual form			177.4.e.a.133.11

$q$-expansion

$f(q)$	$=$	$q+(2.45810 + 0.267335i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-1.84216 - 0.405491i) q^{4} +(7.30295 + 5.55156i) q^{5} +(-5.38528 + 5.10121i) q^{6} +(-2.79914 + 7.02531i) q^{7} +(-23.1651 - 7.80525i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(2.45810 + 0.267335i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-1.84216 - 0.405491i) q^{4} +(7.30295 + 5.55156i) q^{5} +(-5.38528 + 5.10121i) q^{6} +(-2.79914 + 7.02531i) q^{7} +(-23.1651 - 7.80525i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(16.4673 + 15.5986i) q^{10} +(-29.6784 + 13.7307i) q^{11} +(4.50492 - 3.42455i) q^{12} +(-9.95264 + 60.7084i) q^{13} +(-8.75869 + 16.5206i) q^{14} +(-26.8771 + 5.91609i) q^{15} +(-41.1603 - 19.0428i) q^{16} +(12.2307 + 30.6967i) q^{17} +(-1.20477 - 22.2207i) q^{18} +(-79.9088 - 117.857i) q^{19} +(-11.2021 - 13.1882i) q^{20} +(-10.6269 - 20.0445i) q^{21} +(-76.6233 + 25.8174i) q^{22} +(-9.44781 + 174.255i) q^{23} +(62.8370 - 37.8078i) q^{24} +(-10.9277 - 39.3582i) q^{25} +(-40.6941 + 146.567i) q^{26} +(23.1351 + 13.9200i) q^{27} +(8.00518 - 11.8068i) q^{28} +(-86.9923 + 9.46098i) q^{29} +(-67.6481 + 7.35718i) q^{30} +(-124.267 + 183.281i) q^{31} +(71.4799 + 43.0080i) q^{32} +(26.2451 - 94.5265i) q^{33} +(21.8580 + 78.7252i) q^{34} +(-59.4434 + 35.7659i) q^{35} +(-0.919082 + 16.9515i) q^{36} +(142.006 - 47.8474i) q^{37} +(-164.917 - 311.066i) q^{38} +(-119.479 - 140.662i) q^{39} +(-125.843 - 185.604i) q^{40} +(4.32733 + 79.8129i) q^{41} +(-20.7634 - 52.1123i) q^{42} +(275.947 + 127.667i) q^{43} +(60.2402 - 13.2599i) q^{44} +(38.6725 - 72.9440i) q^{45} +(-69.8080 + 425.810i) q^{46} +(263.317 - 200.168i) q^{47} +(123.481 - 57.1283i) q^{48} +(207.497 + 196.551i) q^{49} +(-16.3397 - 99.6678i) q^{50} +(-93.9414 - 31.6525i) q^{51} +(42.9511 - 107.799i) q^{52} +(534.609 - 506.409i) q^{53} +(53.1473 + 40.4015i) q^{54} +(-292.967 - 64.4869i) q^{55} +(119.677 - 140.894i) q^{56} +(424.673 + 46.1860i) q^{57} -216.365 q^{58} +(-395.079 + 222.017i) q^{59} +51.9109 q^{60} +(203.036 + 22.0815i) q^{61} +(-354.460 + 417.302i) q^{62} +(66.4705 + 14.6313i) q^{63} +(453.042 + 344.394i) q^{64} +(-409.710 + 388.098i) q^{65} +(89.7835 - 225.339i) q^{66} +(129.930 + 43.7786i) q^{67} +(-10.0837 - 61.5077i) q^{68} +(-380.082 - 360.032i) q^{69} +(-155.680 + 72.0250i) q^{70} +(609.418 - 463.267i) q^{71} +(-35.5925 + 217.105i) q^{72} +(-340.622 + 642.481i) q^{73} +(361.857 - 79.6507i) q^{74} +(111.215 + 51.4537i) q^{75} +(99.4154 + 249.514i) q^{76} +(-13.3884 - 246.934i) q^{77} +(-256.089 - 377.702i) q^{78} +(-664.206 - 781.963i) q^{79} +(-194.874 - 367.572i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-10.6997 + 197.345i) q^{82} +(-343.457 + 206.652i) q^{83} +(11.4487 + 41.2343i) q^{84} +(-81.0944 + 292.076i) q^{85} +(644.176 + 387.588i) q^{86} +(147.320 - 217.281i) q^{87} +(794.676 - 86.4262i) q^{88} +(-251.325 + 27.3333i) q^{89} +(114.561 - 168.965i) q^{90} +(-398.637 - 239.852i) q^{91} +(88.0631 - 317.175i) q^{92} +(-177.722 - 640.096i) q^{93} +(700.771 - 421.640i) q^{94} +(70.7182 - 1304.32i) q^{95} +(-237.163 + 79.9094i) q^{96} +(817.476 + 1541.92i) q^{97} +(457.503 + 538.614i) q^{98} +(165.161 + 243.595i) 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 $

$2$	2.45810	+	0.267335i	0.869071	+	0.0945171i	0.531779	−	0.846883i	$-0.321524\pi$
$2$	2.45810	+	0.267335i	0.869071	+	0.0945171i	0.337291	+	0.941400i	$0.390489\pi$
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$4$	−1.84216	−	0.405491i	−0.230271	−	0.0506864i
$5$	7.30295	+	5.55156i	0.653196	+	0.496547i	0.878500	−	0.477742i	$-0.158545\pi$
$5$	7.30295	+	5.55156i	0.653196	+	0.496547i	−0.225304	+	0.974288i	$0.572338\pi$
$6$	−5.38528	+	5.10121i	−0.366422	+	0.347093i
$7$	−2.79914	+	7.02531i	−0.151139	+	0.379331i	−0.984979	−	0.172676i	$-0.944759\pi$
$7$	−2.79914	+	7.02531i	−0.151139	+	0.379331i	0.833839	+	0.552007i	$0.186138\pi$
$8$	−23.1651	−	7.80525i	−1.02376	−	0.344946i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	16.4673	+	15.5986i	0.520741	+	0.493272i
$11$	−29.6784	+	13.7307i	−0.813489	+	0.376360i	−0.782104	−	0.623147i	$-0.785854\pi$
$11$	−29.6784	+	13.7307i	−0.813489	+	0.376360i	−0.0313844	+	0.999507i	$0.509992\pi$
$12$	4.50492	−	3.42455i	0.108372	−	0.0823820i
$13$	−9.95264	+	60.7084i	−0.212336	+	1.29519i	0.638444	+	0.769668i	$0.279578\pi$
$13$	−9.95264	+	60.7084i	−0.212336	+	1.29519i	−0.850780	+	0.525523i	$0.823870\pi$
$14$	−8.75869	+	16.5206i	−0.167204	+	0.315380i
$15$	−26.8771	+	5.91609i	−0.462642	+	0.101835i
$16$	−41.1603	−	19.0428i	−0.643129	−	0.297543i
$17$	12.2307	+	30.6967i	0.174493	+	0.437943i	0.990047	−	0.140737i	$-0.0449472\pi$
$17$	12.2307	+	30.6967i	0.174493	+	0.437943i	−0.815554	+	0.578680i	$0.803568\pi$
$18$	−1.20477	−	22.2207i	−0.0157760	−	0.290971i
$19$	−79.9088	−	117.857i	−0.964860	−	1.42306i	−0.905269	−	0.424840i	$-0.860330\pi$
$19$	−79.9088	−	117.857i	−0.964860	−	1.42306i	−0.0595917	−	0.998223i	$-0.518980\pi$
$20$	−11.2021	−	13.1882i	−0.125244	−	0.147448i
$21$	−10.6269	−	20.0445i	−0.110428	−	0.208289i
$22$	−76.6233	+	25.8174i	−0.742552	+	0.250195i
$23$	−9.44781	+	174.255i	−0.0856524	+	1.57977i	0.568037	+	0.823003i	$0.307703\pi$
$23$	−9.44781	+	174.255i	−0.0856524	+	1.57977i	−0.653690	+	0.756763i	$0.726780\pi$
$24$	62.8370	−	37.8078i	0.534439	−	0.321561i
$25$	−10.9277	−	39.3582i	−0.0874220	−	0.314866i
$26$	−40.6941	+	146.567i	−0.306953	+	1.10554i
$27$	23.1351	+	13.9200i	0.164902	+	0.0992184i
$28$	8.00518	−	11.8068i	0.0540299	−	0.0796881i
$29$	−86.9923	+	9.46098i	−0.557037	+	0.0605814i	−0.382308	−	0.924035i	$-0.624871\pi$
$29$	−86.9923	+	9.46098i	−0.557037	+	0.0605814i	−0.174729	+	0.984617i	$0.555905\pi$
$30$	−67.6481	+	7.35718i	−0.411693	+	0.0447744i
$31$	−124.267	+	183.281i	−0.719971	+	1.06188i	0.274974	+	0.961452i	$0.411331\pi$
$31$	−124.267	+	183.281i	−0.719971	+	1.06188i	−0.994945	+	0.100426i	$0.967979\pi$
$32$	71.4799	+	43.0080i	0.394874	+	0.237588i
$33$	26.2451	−	94.5265i	0.138445	−	0.498635i
$34$	21.8580	+	78.7252i	0.110253	+	0.397096i
$35$	−59.4434	+	35.7659i	−0.287079	+	0.172730i
$36$	−0.919082	+	16.9515i	−0.00425501	+	0.0784791i
$37$	142.006	−	47.8474i	0.630964	−	0.212596i	0.0143936	−	0.999896i	$-0.495418\pi$
$37$	142.006	−	47.8474i	0.630964	−	0.212596i	0.616570	+	0.787300i	$0.288522\pi$
$38$	−164.917	−	311.066i	−0.704028	−	1.32794i
$39$	−119.479	−	140.662i	−0.490564	−	0.577537i
$40$	−125.843	−	185.604i	−0.497437	−	0.733664i
$41$	4.32733	+	79.8129i	0.0164833	+	0.304016i	0.995137	+	0.0985003i	$0.0314046\pi$
$41$	4.32733	+	79.8129i	0.0164833	+	0.304016i	−0.978654	+	0.205516i	$0.934113\pi$
$42$	−20.7634	−	52.1123i	−0.0762826	−	0.191455i
$43$	275.947	+	127.667i	0.978639	+	0.452767i	0.842954	−	0.537985i	$-0.180814\pi$
$43$	275.947	+	127.667i	0.978639	+	0.452767i	0.135685	+	0.990752i	$0.456676\pi$
$44$	60.2402	−	13.2599i	0.206399	−	0.0454318i
$45$	38.6725	−	72.9440i	0.128110	−	0.241641i
$46$	−69.8080	+	425.810i	−0.223753	+	1.36483i
$47$	263.317	−	200.168i	0.817206	−	0.621224i	−0.110777	−	0.993845i	$-0.535334\pi$
$47$	263.317	−	200.168i	0.817206	−	0.621224i	0.927984	+	0.372621i	$0.121541\pi$
$48$	123.481	−	57.1283i	0.371311	−	0.171787i
$49$	207.497	+	196.551i	0.604946	+	0.573036i
$50$	−16.3397	−	99.6678i	−0.0462157	−	0.281903i
$51$	−93.9414	−	31.6525i	−0.257930	−	0.0869067i
$52$	42.9511	−	107.799i	0.114543	−	0.287482i
$53$	534.609	−	506.409i	1.38555	−	1.31246i	0.487130	−	0.873330i	$-0.338044\pi$
$53$	534.609	−	506.409i	1.38555	−	1.31246i	0.898422	−	0.439134i	$-0.144715\pi$
$54$	53.1473	+	40.4015i	0.133934	+	0.101814i
$55$	−292.967	−	64.4869i	−0.718248	−	0.158098i
$56$	119.677	−	140.894i	0.285580	−	0.336211i
$57$	424.673	+	46.1860i	0.986831	+	0.107324i
$58$	−216.365			−0.489830
$59$	−395.079	+	222.017i	−0.871778	+	0.489901i
$59$	−395.079	+	222.017i	−0.871778	+	0.489901i
$60$	51.9109			0.111694
$61$	203.036	+	22.0815i	0.426166	+	0.0463484i	0.318689	−	0.947859i	$-0.396757\pi$
$61$	203.036	+	22.0815i	0.426166	+	0.0463484i	0.107477	+	0.994208i	$0.465723\pi$
$62$	−354.460	+	417.302i	−0.726071	+	0.854797i
$63$	66.4705	+	14.6313i	0.132929	+	0.0292598i
$64$	453.042	+	344.394i	0.884848	+	0.672644i
$65$	−409.710	+	388.098i	−0.781820	+	0.740579i
$66$	89.7835	−	225.339i	0.167448	−	0.420263i
$67$	129.930	+	43.7786i	0.236918	+	0.0798269i	0.435256	−	0.900307i	$-0.356658\pi$
$67$	129.930	+	43.7786i	0.236918	+	0.0798269i	−0.198338	+	0.980134i	$0.563554\pi$
$68$	−10.0837	−	61.5077i	−0.0179827	−	0.109690i
$69$	−380.082	−	360.032i	−0.663137	−	0.628157i
$70$	−155.680	+	72.0250i	−0.265818	+	0.122981i
$71$	609.418	−	463.267i	1.01866	−	0.774362i	0.0442191	−	0.999022i	$-0.485920\pi$
$71$	609.418	−	463.267i	1.01866	−	0.774362i	0.974437	+	0.224659i	$0.0721269\pi$
$72$	−35.5925	+	217.105i	−0.0582585	+	0.355361i
$73$	−340.622	+	642.481i	−0.546120	+	1.03009i	0.444798	+	0.895631i	$0.353275\pi$
$73$	−340.622	+	642.481i	−0.546120	+	1.03009i	−0.990919	+	0.134462i	$0.957070\pi$
$74$	361.857	−	79.6507i	0.568446	−	0.125124i
$75$	111.215	+	51.4537i	0.171227	+	0.0792182i
$76$	99.4154	+	249.514i	0.150049	+	0.376595i
$77$	−13.3884	−	246.934i	−0.0198149	−	0.365465i
$78$	−256.089	−	377.702i	−0.371748	−	0.548287i
$79$	−664.206	−	781.963i	−0.945936	−	1.11364i	−0.993392	−	0.114769i	$-0.963387\pi$
$79$	−664.206	−	781.963i	−0.945936	−	1.11364i	0.0474559	−	0.998873i	$-0.484889\pi$
$80$	−194.874	−	367.572i	−0.272345	−	0.513698i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	−10.6997	+	197.345i	−0.0144096	+	0.265770i
$83$	−343.457	+	206.652i	−0.454209	+	0.273289i	−0.724220	−	0.689569i	$-0.757800\pi$
$83$	−343.457	+	206.652i	−0.454209	+	0.273289i	0.270011	+	0.962857i	$0.412973\pi$
$84$	11.4487	+	41.2343i	0.0148708	+	0.0535599i
$85$	−81.0944	+	292.076i	−0.103481	+	0.372706i
$86$	644.176	+	387.588i	0.807712	+	0.485984i
$87$	147.320	−	217.281i	0.181545	−	0.267759i
$88$	794.676	−	86.4262i	0.962645	−	0.104694i
$89$	−251.325	+	27.3333i	−0.299331	+	0.0325542i	−0.256552	−	0.966530i	$-0.582587\pi$
$89$	−251.325	+	27.3333i	−0.299331	+	0.0325542i	−0.0427786	+	0.999085i	$0.513621\pi$
$90$	114.561	−	168.965i	0.134176	−	0.197895i
$91$	−398.637	−	239.852i	−0.459214	−	0.276300i
$92$	88.0631	−	317.175i	0.0997958	−	0.359432i
$93$	−177.722	−	640.096i	−0.198160	−	0.713709i
$94$	700.771	−	421.640i	0.768926	−	0.462647i
$95$	70.7182	−	1304.32i	0.0763741	−	1.40864i
$96$	−237.163	+	79.9094i	−0.252139	+	0.0849554i
$97$	817.476	+	1541.92i	0.855691	+	1.61401i	0.787485	+	0.616334i	$0.211383\pi$
$97$	817.476	+	1541.92i	0.855691	+	1.61401i	0.0682065	+	0.997671i	$0.478272\pi$
$98$	457.503	+	538.614i	0.471579	+	0.555186i
$99$	165.161	+	243.595i	0.167670	+	0.247295i
$100$	4.17131	+	76.9353i	0.00417131	+	0.0769353i
$101$	307.730	+	772.343i	0.303171	+	0.760901i	0.999085	+	0.0427761i	$0.0136202\pi$
$101$	307.730	+	772.343i	0.303171	+	0.760901i	−0.695914	+	0.718125i	$0.745000\pi$
$102$	−222.456	−	102.919i	−0.215945	−	0.0999069i
$103$	−1935.27	+	425.985i	−1.85134	+	0.407510i	−0.994197	−	0.107571i	$-0.965693\pi$
$103$	−1935.27	+	425.985i	−1.85134	+	0.407510i	−0.857141	+	0.515082i	$0.827762\pi$
$104$	704.398	−	1328.64i	0.664153	−	1.25273i
$105$	33.6703	−	205.380i	0.0312941	−	0.190886i
$106$	1449.50	−	1101.88i	1.32819	−	1.00967i
$107$	350.807	−	162.301i	0.316951	−	0.146637i	−0.254963	−	0.966951i	$-0.582063\pi$
$107$	350.807	−	162.301i	0.316951	−	0.146637i	0.571914	+	0.820314i	$0.306201\pi$
$108$	−36.9743	−	35.0239i	−0.0329431	−	0.0312054i
$109$	−25.0319	−	152.688i	−0.0219965	−	0.134173i	0.973545	−	0.228494i	$-0.0733801\pi$
$109$	−25.0319	−	152.688i	−0.0219965	−	0.134173i	−0.995542	+	0.0943214i	$0.969932\pi$
$110$	−702.903	−	236.836i	−0.609265	−	0.205285i
$111$	−166.396	+	417.622i	−0.142285	+	0.357108i
$112$	248.995	−	235.860i	0.210070	−	0.198988i
$113$	−31.5856	−	24.0108i	−0.0262949	−	0.0199889i	0.591944	−	0.805979i	$-0.298361\pi$
$113$	−31.5856	−	24.0108i	−0.0262949	−	0.0199889i	−0.618239	+	0.785990i	$0.712154\pi$
$114$	1031.54	+	227.060i	0.847482	+	0.186545i
$115$	−1036.38	+	1220.12i	−0.840375	+	0.989366i
$116$	164.090	+	17.8459i	0.131340	+	0.0142841i
$117$	553.669			0.437494
$118$	−1030.50	+	440.122i	−0.803941	+	0.343360i
$119$	−249.889			−0.192498
$120$	668.787	+	72.7350i	0.508764	+	0.0553314i
$121$	−169.395	+	199.427i	−0.127269	+	0.149833i
$122$	493.181	+	108.557i	0.365988	+	0.0805601i
$123$	−190.895	−	145.115i	−0.139939	−	0.106379i
$124$	303.240	−	287.244i	0.219611	−	0.208026i
$125$	563.127	−	1413.34i	0.402941	−	1.01131i
$126$	159.480	+	53.7351i	0.112759	+	0.0379929i
$127$	217.848	+	1328.81i	0.152211	+	0.928449i	0.946923	+	0.321461i	$0.104174\pi$
$127$	217.848	+	1328.81i	0.152211	+	0.928449i	−0.794711	+	0.606988i	$0.792378\pi$
$128$	537.049	+	508.720i	0.370851	+	0.351288i
$129$	−827.840	+	383.000i	−0.565018	+	0.261405i
$130$	−1110.86	+	844.455i	−0.749454	+	0.569720i
$131$	79.9286	−	487.543i	0.0533084	−	0.325167i	−0.946687	−	0.322154i	$-0.895593\pi$
$131$	79.9286	−	487.543i	0.0533084	−	0.325167i	0.999995	−	0.00301208i	$-0.000958777\pi$
$132$	−86.6775	+	163.491i	−0.0571538	+	0.107804i
$133$	1051.66	−	231.487i	0.685640	−	0.150921i
$134$	307.678	+	142.347i	0.198353	+	0.0917680i
$135$	91.6774	+	230.093i	0.0584469	+	0.146691i
$136$	−43.7302	−	806.556i	−0.0275723	−	0.508541i
$137$	−1547.46	−	2282.34i	−0.965027	−	1.42331i	−0.905145	−	0.425102i	$-0.860238\pi$
$137$	−1547.46	−	2282.34i	−0.965027	−	1.42331i	−0.0598814	−	0.998206i	$-0.519072\pi$
$138$	−838.031	−	986.606i	−0.516941	−	0.608590i
$139$	680.212	+	1283.02i	0.415071	+	0.782907i	0.999595	−	0.0284697i	$-0.00906343\pi$
$139$	680.212	+	1283.02i	0.415071	+	0.782907i	−0.584524	+	0.811377i	$0.698719\pi$
$140$	124.007	−	41.7829i	0.0748609	−	0.0252236i
$141$	−53.7212	+	990.828i	−0.0320861	+	0.591793i
$142$	1621.86	−	975.840i	0.958475	−	0.576695i
$143$	−538.190	−	1938.39i	−0.314725	−	1.13354i
$144$	−109.196	+	393.289i	−0.0631923	+	0.227598i
$145$	−687.824	−	413.850i	−0.393936	−	0.237023i
$146$	−1009.04	+	1488.22i	−0.571978	+	0.843605i
$147$	−852.403	+	92.7044i	−0.478265	+	0.0520145i
$148$	−281.000	+	30.5606i	−0.156068	+	0.0169734i
$149$	−833.465	+	1229.27i	−0.458256	+	0.675877i	−0.984685	−	0.174342i	$-0.944220\pi$
$149$	−833.465	+	1229.27i	−0.458256	+	0.675877i	0.526429	+	0.850219i	$0.323531\pi$
$150$	259.623	+	156.210i	0.141321	+	0.0850301i
$151$	−118.764	+	427.749i	−0.0640058	+	0.230528i	−0.988634	−	0.150343i	$-0.951962\pi$
$151$	−118.764	+	427.749i	−0.0640058	+	0.230528i	0.924628	+	0.380871i	$0.124376\pi$
$152$	931.199	+	3353.88i	0.496909	+	1.78971i
$153$	254.822	−	153.321i	0.134648	−	0.0810151i
$154$	33.1041	−	610.569i	0.0173221	−	0.319487i
$155$	−1925.01	+	648.613i	−0.997554	+	0.336115i
$156$	163.063	+	307.570i	0.0836892	+	0.157855i
$157$	207.584	+	244.386i	0.105522	+	0.124230i	0.812388	−	0.583118i	$-0.198167\pi$
$157$	207.584	+	244.386i	0.105522	+	0.124230i	−0.706866	+	0.707348i	$0.749891\pi$
$158$	−1423.64	−	2099.71i	−0.716827	−	1.05724i
$159$	119.601	+	2205.90i	0.0596537	+	1.10025i
$160$	283.253	+	710.910i	0.139957	+	0.351265i
$161$	−1197.75	−	554.137i	−0.586309	−	0.271255i
$162$	−195.598	+	43.0544i	−0.0948619	+	0.0208807i
$163$	−1169.66	+	2206.21i	−0.562053	+	1.06014i	0.425809	+	0.904813i	$0.359989\pi$
$163$	−1169.66	+	2206.21i	−0.562053	+	1.06014i	−0.987862	+	0.155332i	$0.950355\pi$
$164$	24.3917	−	148.783i	0.0116139	−	0.0708415i
$165$	716.436	−	544.621i	0.338027	−	0.256962i
$166$	−899.499	+	416.152i	−0.420570	+	0.194576i
$167$	−954.191	−	903.858i	−0.442141	−	0.418818i	0.433970	−	0.900927i	$-0.357112\pi$
$167$	−954.191	−	903.858i	−0.442141	−	0.418818i	−0.876111	+	0.482109i	$0.839871\pi$
$168$	89.7218	+	547.279i	0.0412035	+	0.251330i
$169$	−1504.46	−	506.912i	−0.684780	−	0.230729i
$170$	−277.420	+	696.273i	−0.125160	+	0.314127i
$171$	−930.387	+	881.309i	−0.416073	+	0.394125i
$172$	−456.572	−	347.077i	−0.202403	−	0.153863i
$173$	1228.99	+	270.521i	0.540107	+	0.118887i	0.476642	−	0.879098i	$-0.341854\pi$
$173$	1228.99	+	270.521i	0.540107	+	0.118887i	0.0634650	+	0.997984i	$0.479785\pi$
$174$	420.216	−	494.716i	0.183083	−	0.215542i
$175$	307.092	+	33.3983i	0.132651	+	0.0144267i
$176$	1483.04			0.635162
$177$	259.668	−	1334.54i	0.110270	−	0.566722i
$178$	−625.091			−0.263216
$179$	−2797.34	−	304.229i	−1.16806	−	0.127034i	−0.496536	−	0.868016i	$-0.665395\pi$
$179$	−2797.34	−	304.229i	−1.16806	−	0.127034i	−0.671525	+	0.740982i	$0.734360\pi$
$180$	−100.819	+	118.693i	−0.0417479	+	0.0491494i
$181$	−2118.46	−	466.309i	−0.869967	−	0.191494i	−0.242513	−	0.970148i	$-0.577972\pi$
$181$	−2118.46	−	466.309i	−0.869967	−	0.191494i	−0.627454	+	0.778654i	$0.715903\pi$
$182$	−915.769	−	696.150i	−0.372974	−	0.283528i
$183$	−444.818	+	421.354i	−0.179683	+	0.170204i
$184$	1578.96	−	3962.89i	0.632622	−	1.58776i
$185$	1302.69	+	438.928i	0.517707	+	0.174436i
$186$	−265.739	−	1620.93i	−0.104758	−	0.638993i
$187$	−784.473	−	743.093i	−0.306772	−	0.290590i
$188$	−566.239	+	261.970i	−0.219666	+	0.101628i
$189$	−162.551	+	123.568i	−0.0625599	+	0.0475568i
$190$	522.523	−	3187.25i	0.199515	−	1.21699i
$191$	344.489	−	649.775i	0.130504	−	0.246157i	−0.809645	−	0.586920i	$-0.800340\pi$
$191$	344.489	−	649.775i	0.130504	−	0.246157i	0.940149	+	0.340762i	$0.110685\pi$
$192$	−1667.33	+	367.007i	−0.626715	+	0.137950i
$193$	1667.46	+	771.448i	0.621897	+	0.287720i	0.705424	−	0.708785i	$-0.250756\pi$
$193$	1667.46	+	771.448i	0.621897	+	0.287720i	−0.0835272	+	0.996506i	$0.526619\pi$
$194$	1597.23	+	4008.74i	0.591105	+	1.48356i
$195$	−91.6586	−	1690.54i	−0.0336606	−	0.620833i
$196$	−302.543	−	446.218i	−0.110256	−	0.162616i
$197$	3425.95	+	4033.34i	1.23903	+	1.45870i	0.840742	+	0.541436i	$0.182119\pi$
$197$	3425.95	+	4033.34i	1.23903	+	1.45870i	0.398287	+	0.917261i	$0.369605\pi$
$198$	340.862	+	642.934i	0.122343	+	0.230764i
$199$	−3295.95	+	1110.54i	−1.17409	+	0.395597i	−0.837702	−	0.546127i	$-0.816102\pi$
$199$	−3295.95	+	1110.54i	−1.17409	+	0.395597i	−0.336387	+	0.941724i	$0.609205\pi$
$200$	−54.0575	+	997.032i	−0.0191122	+	0.352504i
$201$	−352.444	+	212.059i	−0.123679	+	0.0744152i
$202$	549.957	+	1980.77i	0.191559	+	0.689932i
$203$	177.037	−	637.631i	0.0612098	−	0.220458i
$204$	160.221	+	96.4016i	0.0549887	+	0.0330856i
$205$	−411.484	+	606.893i	−0.140192	+	0.206767i
$206$	−4870.97	+	529.750i	−1.64746	+	0.179172i
$207$	1561.39	−	169.811i	0.524270	−	0.0570178i
$208$	1565.71	−	2309.25i	0.521935	−	0.769796i
$209$	3989.82	+	2400.60i	1.32049	+	0.794511i
$210$	137.670	−	495.843i	0.0452388	−	0.162935i
$211$	676.636	+	2437.02i	0.220765	+	0.795125i	0.988091	+	0.153868i	$0.0491731\pi$
$211$	676.636	+	2437.02i	0.220765	+	0.795125i	−0.767326	+	0.641257i	$0.778413\pi$
$212$	−1190.18	+	716.109i	−0.385576	+	0.231993i
$213$	−124.332	+	2293.16i	−0.0399956	+	0.737676i
$214$	905.708	−	305.168i	0.289313	−	0.0974808i
$215$	1306.48	+	2464.28i	0.414423	+	0.781686i
$216$	−427.280	−	503.033i	−0.134596	−	0.158459i
$217$	−939.763	−	1386.05i	−0.293987	−	0.433599i
$218$	−20.7122	−	382.014i	−0.00643489	−	0.118684i
$219$	−807.482	−	2026.63i	−0.249153	−	0.625328i
$220$	513.544	+	237.591i	0.157378	+	0.0728108i
$221$	−1985.27	+	436.992i	−0.604271	+	0.133010i
$222$	−520.663	+	982.075i	−0.157408	+	0.296903i
$223$	939.643	−	5731.57i	0.282167	−	1.72114i	−0.341872	−	0.939747i	$-0.611061\pi$
$223$	939.643	−	5731.57i	0.282167	−	1.72114i	0.624038	−	0.781394i	$-0.285491\pi$
$224$	−502.227	+	381.783i	−0.149806	+	0.113879i
$225$	−333.646	+	154.361i	−0.0988581	+	0.0457366i
$226$	−71.2218	−	67.4648i	−0.0209628	−	0.0198571i
$227$	−7.59538	−	46.3298i	−0.00222081	−	0.0135463i	0.985693	−	0.168551i	$-0.0539089\pi$
$227$	−7.59538	−	46.3298i	−0.00222081	−	0.0135463i	−0.987914	+	0.155005i	$0.950461\pi$
$228$	−763.590	−	257.283i	−0.221798	−	0.0747325i
$229$	419.525	−	1052.93i	0.121061	−	0.303840i	−0.855940	−	0.517075i	$-0.827021\pi$
$229$	419.525	−	1052.93i	0.121061	−	0.303840i	0.977001	+	0.213235i	$0.0684000\pi$
$230$	−2873.71	+	2722.13i	−0.823857	+	0.780399i
$231$	590.614	+	448.973i	0.168223	+	0.127880i
$232$	2089.03	+	459.831i	0.591172	+	0.130127i
$233$	2482.23	−	2922.31i	0.697924	−	0.821659i	−0.292996	−	0.956114i	$-0.594652\pi$
$233$	2482.23	−	2922.31i	0.697924	−	0.821659i	0.990920	+	0.134454i	$0.0429282\pi$
$234$	1360.98	+	148.015i	0.380213	+	0.0413506i
$235$	3034.23			0.842262
$236$	817.826	−	248.791i	0.225576	−	0.0686224i
$237$	3077.94			0.843602
$238$	−614.253	−	66.8040i	−0.167295	−	0.0181944i
$239$	617.803	−	727.334i	0.167207	−	0.196851i	−0.672177	−	0.740391i	$-0.734640\pi$
$239$	617.803	−	727.334i	0.167207	−	0.196851i	0.839383	+	0.543540i	$0.182916\pi$
$240$	1218.93	+	268.306i	0.327839	+	0.0721628i
$241$	−2458.85	−	1869.17i	−0.657214	−	0.499601i	0.222606	−	0.974909i	$-0.428544\pi$
$241$	−2458.85	−	1869.17i	−0.657214	−	0.499601i	−0.879820	+	0.475307i	$0.842337\pi$
$242$	−469.705	+	444.928i	−0.124768	+	0.118186i
$243$	89.9436	−	225.741i	0.0237444	−	0.0595939i
$244$	−365.073	−	123.007i	−0.0957843	−	0.0322735i
$245$	424.172	+	2587.33i	0.110610	+	0.674689i
$246$	−430.446	−	407.740i	−0.111562	−	0.105677i
$247$	7950.20	−	3678.15i	2.04801	−	0.947511i
$248$	4309.23	−	3275.79i	1.10337	−	0.838761i
$249$	194.543	−	1186.66i	0.0495127	−	0.302014i
$250$	1762.06	−	3323.60i	0.445770	−	0.840811i
$251$	7264.01	−	1598.93i	1.82669	−	0.402086i	0.837228	−	0.546853i	$-0.184174\pi$
$251$	7264.01	−	1598.93i	1.82669	−	0.402086i	0.989466	+	0.144768i	$0.0462434\pi$
$252$	−116.517	−	53.9064i	−0.0291265	−	0.0134753i
$253$	−2112.24	−	5301.33i	−0.524883	−	1.31736i
$254$	180.254	+	3324.59i	0.0445282	+	0.821274i
$255$	−510.329	−	752.679i	−0.125326	−	0.184841i
$256$	−1763.20	−	2075.80i	−0.430469	−	0.506788i
$257$	478.384	+	902.329i	0.116112	+	0.219011i	0.934756	−	0.355291i	$-0.115618\pi$
$257$	478.384	+	902.329i	0.116112	+	0.219011i	−0.818644	+	0.574302i	$0.805274\pi$
$258$	−2137.31	+	720.142i	−0.515748	+	0.173776i
$259$	−61.3519	+	1131.57i	−0.0147190	+	0.271476i
$260$	912.123	−	548.806i	0.217567	−	0.130906i
$261$	210.691	+	758.841i	0.0499673	+	0.179966i
$262$	326.810	−	1177.06i	0.0770625	−	0.277554i
$263$	−5432.38	−	3268.55i	−1.27367	−	0.766341i	−0.291905	−	0.956447i	$-0.594289\pi$
$263$	−5432.38	−	3268.55i	−1.27367	−	0.766341i	−0.981764	+	0.190106i	$0.939117\pi$
$264$	−1345.77	+	1984.87i	−0.313737	+	0.462728i
$265$	6715.58	−	730.364i	1.55674	−	0.169305i
$266$	2646.96	−	287.875i	0.610135	−	0.0663561i
$267$	425.617	−	627.738i	0.0975555	−	0.143884i
$268$	−221.601	−	133.333i	−0.0505091	−	0.0303903i
$269$	−352.023	+	1267.87i	−0.0797890	+	0.287374i	−0.992671	−	0.120850i	$-0.961438\pi$
$269$	−352.023	+	1267.87i	−0.0797890	+	0.287374i	0.912882	+	0.408224i	$0.133852\pi$
$270$	163.841	+	590.101i	0.0369297	+	0.133009i
$271$	3807.95	−	2291.17i	0.853566	−	0.513574i	−0.0202699	−	0.999795i	$-0.506453\pi$
$271$	3807.95	−	2291.17i	0.853566	−	0.513574i	0.873836	+	0.486221i	$0.161625\pi$
$272$	81.1319	−	1496.39i	0.0180858	−	0.333573i
$273$	1322.63	−	445.647i	0.293221	−	0.0987978i
$274$	−3193.67	−	6023.91i	−0.704149	−	1.32817i
$275$	864.733	+	1018.04i	0.189620	+	0.223237i
$276$	554.183	+	817.359i	0.120862	+	0.178258i
$277$	438.178	+	8081.71i	0.0950453	+	1.75301i	0.525864	+	0.850569i	$0.323742\pi$
$277$	438.178	+	8081.71i	0.0950453	+	1.75301i	−0.430819	+	0.902438i	$0.641775\pi$
$278$	1329.04	+	3335.63i	0.286728	+	0.719633i
$279$	1808.74	+	836.810i	0.388122	+	0.179565i
$280$	1656.18	−	364.552i	0.353484	−	0.0778077i
$281$	2792.87	−	5267.91i	0.592913	−	1.11835i	−0.387587	−	0.921833i	$-0.626691\pi$
$281$	2792.87	−	5267.91i	0.592913	−	1.11835i	0.980500	−	0.196519i	$-0.0629638\pi$
$282$	−396.935	+	2421.20i	−0.0838196	+	0.511277i
$283$	1081.79	−	822.353i	0.227228	−	0.172734i	−0.485366	−	0.874311i	$-0.661313\pi$
$283$	1081.79	−	822.353i	0.227228	−	0.172734i	0.712594	+	0.701577i	$0.247520\pi$
$284$	−1310.50	+	606.301i	−0.273816	+	0.126681i
$285$	2844.97	+	2694.89i	0.591303	+	0.560111i
$286$	−804.729	−	4908.63i	−0.166380	−	1.01487i
$287$	−572.823	−	193.007i	−0.117814	−	0.0396962i
$288$	277.896	−	697.466i	0.0568582	−	0.142703i
$289$	2774.12	−	2627.79i	0.564649	−	0.534864i
$290$	−1580.11	−	1201.16i	−0.319955	−	0.243224i
$291$	−5113.25	−	1125.51i	−1.03005	−	0.226731i
$292$	888.002	−	1045.44i	0.177967	−	0.209519i
$293$	1799.70	+	195.729i	0.358839	+	0.0390260i	0.285763	−	0.958300i	$-0.407753\pi$
$293$	1799.70	+	195.729i	0.358839	+	0.0390260i	0.0730757	+	0.997326i	$0.476719\pi$
$294$	−2120.08			−0.420563
$295$	−4117.78	−	571.926i	−0.812701	−	0.112877i
$296$	−3663.05			−0.719293
$297$	−877.745	−	95.4605i	−0.171488	−	0.0186504i
$298$	−2377.37	+	2798.86i	−0.462139	+	0.544072i
$299$	−10484.7	−	2307.86i	−2.02791	−	0.446377i
$300$	−184.013	−	139.883i	−0.0354133	−	0.0269205i
$301$	−1669.31	+	1581.26i	−0.319660	+	0.302798i
$302$	−406.286	+	1019.70i	−0.0774144	+	0.194295i
$303$	−2363.61	−	796.394i	−0.448139	−	0.150995i
$304$	1044.75	+	6372.70i	0.197107	+	1.20230i
$305$	1360.18	+	1288.43i	0.255356	+	0.241886i
$306$	667.367	−	308.757i	0.124676	−	0.0576813i
$307$	−7166.11	+	5447.53i	−1.33222	+	1.01273i	−0.334700	+	0.942325i	$0.608635\pi$
$307$	−7166.11	+	5447.53i	−1.33222	+	1.01273i	−0.997519	+	0.0704020i	$0.977572\pi$
$308$	−75.4660	+	460.322i	−0.0139613	+	0.0851600i
$309$	2784.59	−	5252.30i	0.512654	−	0.966967i
$310$	−4905.28	+	1079.73i	−0.898713	+	0.197822i
$311$	−1117.21	−	516.877i	−0.203702	−	0.0942425i	0.315386	−	0.948964i	$-0.397866\pi$
$311$	−1117.21	−	516.877i	−0.203702	−	0.0942425i	−0.519088	+	0.854721i	$0.673728\pi$
$312$	1669.85	+	4191.02i	0.303003	+	0.760480i
$313$	34.9588	+	644.778i	0.00631307	+	0.116438i	0.999991	+	0.00417201i	$0.00132800\pi$
$313$	34.9588	+	644.778i	0.00631307	+	0.116438i	−0.993678	+	0.112266i	$0.964189\pi$
$314$	444.929	+	656.221i	0.0799643	+	0.117939i
$315$	404.205	+	475.867i	0.0722996	+	0.0851176i
$316$	906.497	+	1709.83i	0.161375	+	0.304385i
$317$	1861.26	−	627.132i	0.329775	−	0.111114i	−0.149543	−	0.988755i	$-0.547780\pi$
$317$	1861.26	−	627.132i	0.329775	−	0.111114i	0.479319	+	0.877641i	$0.340884\pi$
$318$	−295.724	+	5454.31i	−0.0521490	+	0.961831i
$319$	2451.89	−	1475.25i	0.430343	−	0.258929i
$320$	1396.62	+	5030.18i	0.243980	+	0.878736i
$321$	−310.225	+	1117.33i	−0.0539410	+	0.194278i
$322$	−2796.05	−	1682.33i	−0.483906	−	0.291156i
$323$	2640.47	−	3894.40i	0.454860	−	0.670868i
$324$	151.892	−	16.5192i	0.0260445	−	0.00283251i
$325$	2498.13	−	271.688i	0.426374	−	0.0463710i
$326$	−3464.93	+	5110.40i	−0.588666	+	0.868217i
$327$	397.734	+	239.308i	0.0672622	+	0.0404703i
$328$	522.716	−	1882.65i	0.0879944	−	0.316927i
$329$	669.183	+	2410.18i	0.112138	+	0.403883i
$330$	1906.67	−	1147.21i	0.318057	−	0.191368i
$331$	−11.2874	+	208.184i	−0.00187435	+	0.0345704i	−0.999321	−	0.0368456i	$-0.988269\pi$
$331$	−11.2874	+	208.184i	−0.00187435	+	0.0345704i	0.997447	+	0.0714160i	$0.0227518\pi$
$332$	716.500	−	241.417i	0.118443	−	0.0399081i
$333$	−631.720	−	1191.55i	−0.103958	−	0.196086i
$334$	−2103.87	−	2476.86i	−0.344666	−	0.405772i
$335$	705.834	+	1041.03i	0.115116	+	0.169783i
$336$	55.7041	+	1027.40i	0.00904437	+	0.166814i
$337$	1887.58	+	4737.47i	0.305113	+	0.765775i	0.998957	+	0.0456505i	$0.0145361\pi$
$337$	1887.58	+	4737.47i	0.305113	+	0.765775i	−0.693845	+	0.720125i	$0.744085\pi$
$338$	−3562.61	−	1648.24i	−0.573315	−	0.265244i
$339$	116.245	−	25.5874i	0.0186240	−	0.00409945i
$340$	267.823	−	505.168i	0.0427199	−	0.0805782i
$341$	1171.49	−	7145.76i	0.186040	−	1.13479i
$342$	−2522.59	+	1917.62i	−0.398848	+	0.303197i
$343$	−4315.82	+	1996.71i	−0.679394	+	0.314321i
$344$	−5395.88	−	5111.25i	−0.845716	−	0.801105i
$345$	−776.976	−	4739.35i	−0.121249	−	0.739588i
$346$	2948.67	+	993.522i	0.458154	+	0.154370i
$347$	−3857.46	+	9681.51i	−0.596771	+	1.49778i	0.251305	+	0.967908i	$0.419140\pi$
$347$	−3857.46	+	9681.51i	−0.596771	+	1.49778i	−0.848076	+	0.529875i	$0.822239\pi$
$348$	−359.494	+	340.531i	−0.0553762	+	0.0524551i
$349$	3180.07	+	2417.43i	0.487752	+	0.370779i	0.819954	−	0.572429i	$-0.193999\pi$
$349$	3180.07	+	2417.43i	0.487752	+	0.370779i	−0.332203	+	0.943208i	$0.607792\pi$
$350$	745.935	+	164.193i	0.113920	+	0.0250756i
$351$	−1075.31	+	1265.96i	−0.163521	+	0.192512i
$352$	−2711.94	−	294.941i	−0.410644	−	0.0446603i
$353$	−1065.42			−0.160642			−0.0803210	−	0.996769i	$-0.525595\pi$
$353$	−1065.42			−0.160642			−0.0803210	+	0.996769i	$0.525595\pi$
$354$	995.057	−	3211.01i	0.149397	−	0.482099i
$355$	7022.41			1.04989
$356$	474.066	+	51.5578i	0.0705771	+	0.00767572i
$357$	485.324	−	571.368i	0.0719498	−	0.0847059i
$358$	−6794.81	−	1495.65i	−1.00312	−	0.220803i
$359$	1453.96	+	1105.27i	0.213753	+	0.162491i	0.706572	−	0.707641i	$-0.250241\pi$
$359$	1453.96	+	1105.27i	0.213753	+	0.162491i	−0.492819	+	0.870132i	$0.664034\pi$
$360$	−1465.20	+	1387.91i	−0.214508	+	0.203192i
$361$	−4966.01	+	12463.7i	−0.724013	+	1.81714i
$362$	−5082.73	−	1712.57i	−0.737963	−	0.248649i
$363$	−126.996	−	774.640i	−0.0183624	−	0.112006i
$364$	637.097	+	603.490i	0.0917388	+	0.0868996i
$365$	−6054.32	+	2801.03i	−0.868212	+	0.401678i
$366$	−1206.05	+	916.816i	−0.172244	+	0.130937i
$367$	−412.563	+	2516.52i	−0.0586801	+	0.357933i	0.941123	+	0.338066i	$0.109773\pi$
$367$	−412.563	+	2516.52i	−0.0586801	+	0.357933i	−0.999803	+	0.0198671i	$0.993676\pi$
$368$	3707.17	−	6992.46i	0.525134	−	0.990508i
$369$	702.552	−	154.643i	0.0991149	−	0.0218168i
$370$	3084.81	+	1427.18i	0.433437	+	0.200529i
$371$	2061.23	+	5173.31i	0.288447	+	0.723948i
$372$	67.8396	+	1251.23i	0.00945516	+	0.174390i
$373$	−3431.42	−	5060.97i	−0.476333	−	0.702539i	0.511286	−	0.859411i	$-0.329169\pi$
$373$	−3431.42	−	5060.97i	−0.476333	−	0.702539i	−0.987619	+	0.156872i	$0.949859\pi$
$374$	−1729.66	−	2036.32i	−0.239141	−	0.281538i
$375$	2137.90	+	4032.52i	0.294402	+	0.555302i
$376$	−7662.13	+	2581.67i	−1.05092	+	0.354095i
$377$	291.442	−	5375.33i	0.0398144	−	0.734333i
$378$	−432.600	+	260.287i	−0.0588639	+	0.0354172i
$379$	1701.69	+	6128.94i	0.230633	+	0.830666i	0.984757	+	0.173934i	$0.0556480\pi$
$379$	1701.69	+	6128.94i	0.230633	+	0.830666i	−0.754124	+	0.656732i	$0.771938\pi$
$380$	−659.165	+	2374.10i	−0.0889854	+	0.320496i
$381$	−3461.40	−	2082.66i	−0.465441	−	0.280047i
$382$	1020.50	−	1505.12i	0.136684	−	0.201593i
$383$	12668.5	−	1377.78i	1.69016	−	0.183816i	0.788135	−	0.615503i	$-0.211047\pi$
$383$	12668.5	−	1377.78i	1.69016	−	0.183816i	0.902024	+	0.431687i	$0.142081\pi$
$384$	−2206.22	+	239.940i	−0.293191	+	0.0318865i
$385$	1273.10	−	1877.68i	0.168527	−	0.248559i
$386$	3892.54	+	2342.07i	0.513278	+	0.308829i
$387$	732.074	−	2636.69i	0.0961587	−	0.346332i
$388$	−880.688	−	3171.95i	−0.115232	−	0.415030i
$389$	5861.51	−	3526.76i	0.763986	−	0.459675i	−0.0794943	−	0.996835i	$-0.525331\pi$
$389$	5861.51	−	3526.76i	0.763986	−	0.459675i	0.843480	+	0.537160i	$0.180503\pi$
$390$	226.635	−	4180.03i	0.0294259	−	0.542729i
$391$	−5464.59	+	1841.23i	−0.706793	+	0.238146i
$392$	−3272.56	−	6172.70i	−0.421656	−	0.795328i
$393$	959.526	+	1129.64i	0.123160	+	0.144995i
$394$	7343.08	+	10830.2i	0.938931	+	1.38482i
$395$	−509.546	−	9398.02i	−0.0649064	−	1.19713i
$396$	−205.479	−	515.712i	−0.0260750	−	0.0654433i
$397$	272.377	+	126.015i	0.0344338	+	0.0159308i	0.437030	−	0.899447i	$-0.356030\pi$
$397$	272.377	+	126.015i	0.0344338	+	0.0159308i	−0.402597	+	0.915377i	$0.631892\pi$
$398$	−8398.67	+	1848.69i	−1.05776	+	0.232830i
$399$	−1513.19	+	2854.18i	−0.189861	+	0.358115i
$400$	−299.700	+	1828.09i	−0.0374625	+	0.228511i
$401$	−2945.56	+	2239.16i	−0.366819	+	0.278848i	−0.772304	−	0.635253i	$-0.780896\pi$
$401$	−2945.56	+	2239.16i	−0.366819	+	0.278848i	0.405485	+	0.914102i	$0.367103\pi$
$402$	−923.034	+	427.041i	−0.114519	+	0.0529823i
$403$	−9889.90	−	9368.21i	−1.22246	−	1.15797i
$404$	−253.710	−	1547.56i	−0.0312440	−	0.190580i
$405$	−704.156	−	237.258i	−0.0863946	−	0.0291097i
$406$	605.637	−	1520.03i	0.0740326	−	0.185808i
$407$	−3557.54	+	3369.88i	−0.433269	+	0.410414i
$408$	1929.11	+	1466.47i	0.234081	+	0.177944i
$409$	2102.40	+	462.773i	0.254173	+	0.0559478i	0.340229	−	0.940343i	$-0.389495\pi$
$409$	2102.40	+	462.773i	0.254173	+	0.0559478i	−0.0860559	+	0.996290i	$0.527426\pi$
$410$	−1173.71	+	1381.80i	−0.141379	+	0.166445i
$411$	8223.95	+	894.408i	0.987001	+	0.107343i
$412$	3737.82			0.446964
$413$	−453.857	−	3397.01i	−0.0540747	−	0.404736i
$414$	3883.45			0.461017
$415$	−3655.49	−	397.559i	−0.432388	−	0.0470250i
$416$	−3322.36	+	3911.39i	−0.391568	+	0.460989i
$417$	−4254.68	−	936.526i	−0.499647	−	0.109981i
$418$	9165.63	+	6967.53i	1.07250	+	0.815294i
$419$	3703.49	−	3508.14i	0.431808	−	0.409030i	−0.440681	−	0.897664i	$-0.645263\pi$
$419$	3703.49	−	3508.14i	0.431808	−	0.409030i	0.872489	+	0.488634i	$0.162504\pi$
$420$	−145.306	+	364.690i	−0.0168814	+	0.0423692i
$421$	−2238.04	−	754.084i	−0.259087	−	0.0872965i	0.186761	−	0.982405i	$-0.440201\pi$
$421$	−2238.04	−	754.084i	−0.259087	−	0.0872965i	−0.445848	+	0.895109i	$0.647098\pi$
$422$	1011.74	+	6171.34i	0.116708	+	0.711886i
$423$	−2161.18	−	2047.18i	−0.248417	−	0.235313i
$424$	−16336.9	+	7558.27i	−1.87121	+	0.865713i
$425$	1074.51	−	816.823i	0.122639	−	0.0932276i
$426$	−918.663	+	5603.60i	−0.104482	+	0.637312i
$427$	−723.457	+	1364.59i	−0.0819919	+	0.154653i
$428$	−712.055	+	156.735i	−0.0804170	+	0.0177011i
$429$	5477.34	+	2534.09i	0.616430	+	0.285191i
$430$	2552.67	+	6406.72i	0.286281	+	0.718510i
$431$	−198.114	−	3654.00i	−0.0221411	−	0.408368i	−0.988505	−	0.151189i	$-0.951690\pi$
$431$	−198.114	−	3654.00i	−0.0221411	−	0.408368i	0.966364	−	0.257179i	$-0.0827930\pi$
$432$	−687.174	−	1013.51i	−0.0765317	−	0.112876i
$433$	−10.0472	−	11.8285i	−0.00111510	−	0.00131280i	0.761604	−	0.648042i	$-0.224412\pi$
$433$	−10.0472	−	11.8285i	−0.00111510	−	0.00131280i	−0.762719	+	0.646730i	$0.776136\pi$
$434$	−1939.50	−	3658.28i	−0.214513	−	0.404615i
$435$	2282.13	−	768.938i	0.251539	−	0.0847534i
$436$	−15.8006	+	291.426i	−0.00173558	+	0.0320109i
$437$	21292.0	−	12811.0i	2.33075	−	1.40236i
$438$	−1443.09	−	5197.53i	−0.157428	−	0.567003i
$439$	−2888.76	+	10404.4i	−0.314061	+	1.13115i	0.623069	+	0.782167i	$0.285885\pi$
$439$	−2888.76	+	10404.4i	−0.314061	+	1.13115i	−0.937130	+	0.348979i	$0.886528\pi$
$440$	6283.28	+	3780.52i	0.680781	+	0.409612i
$441$	1443.53	−	2129.05i	0.155872	−	0.229895i
$442$	−4996.83	+	543.438i	−0.537726	+	0.0584812i
$443$	−17809.6	+	1936.91i	−1.91007	+	0.207732i	−0.985059	−	0.172219i	$-0.944906\pi$
$443$	−17809.6	+	1936.91i	−1.91007	+	0.207732i	−0.925007	+	0.379951i	$0.875941\pi$
$444$	475.871	−	701.857i	0.0508645	−	0.0750195i
$445$	−1987.16	−	1195.63i	−0.211686	−	0.127367i
$446$	3841.99	−	13837.6i	0.407900	−	1.46912i
$447$	−1191.99	−	4293.14i	−0.126127	−	0.454270i
$448$	−3687.60	+	2218.76i	−0.388890	+	0.233987i
$449$	6.96801	−	128.517i	0.000732384	−	0.0135080i	−0.998144	−	0.0608917i	$-0.980606\pi$
$449$	6.96801	−	128.517i	0.000732384	−	0.0135080i	0.998877	+	0.0473837i	$0.0150883\pi$
$450$	−861.403	+	290.240i	−0.0902376	+	0.0304046i
$451$	−1224.31	−	2309.30i	−0.127829	−	0.241110i
$452$	48.4497	+	57.0394i	0.00504178	+	0.00593564i
$453$	−747.384	−	1102.31i	−0.0775169	−	0.114329i
$454$	−6.28467	−	115.914i	−0.000649678	−	0.0119826i
$455$	−1579.67	−	3964.68i	−0.162761	−	0.408499i
$456$	−9477.13	−	4384.59i	−0.973261	−	0.450279i
$457$	15755.9	−	3468.13i	1.61275	−	0.354994i	0.685104	−	0.728445i	$-0.259757\pi$
$457$	15755.9	−	3468.13i	1.61275	−	0.354994i	0.927650	+	0.373451i	$0.121826\pi$
$458$	1312.72	−	2476.05i	0.133929	−	0.252616i
$459$	−144.338	+	880.422i	−0.0146778	+	0.0895307i
$460$	2403.93	−	1827.42i	0.243661	−	0.185226i
$461$	7792.25	−	3605.08i	0.787248	−	0.364220i	0.0152816	−	0.999883i	$-0.495136\pi$
$461$	7792.25	−	3605.08i	0.787248	−	0.364220i	0.771966	+	0.635664i	$0.219273\pi$
$462$	1331.76	+	1261.51i	0.134111	+	0.127037i
$463$	−1323.59	−	8073.54i	−0.132856	−	0.810387i	−0.966231	−	0.257678i	$-0.917043\pi$
$463$	−1323.59	−	8073.54i	−0.132856	−	0.810387i	0.833375	−	0.552709i	$-0.186406\pi$
$464$	3760.79	+	1267.16i	0.376272	+	0.126781i
$465$	2255.64	−	5661.23i	0.224952	−	0.564587i
$466$	6882.81	−	6519.74i	0.684206	−	0.648114i
$467$	6249.92	+	4751.06i	0.619297	+	0.470777i	0.867168	−	0.498016i	$-0.165938\pi$
$467$	6249.92	+	4751.06i	0.619297	+	0.470777i	−0.247871	+	0.968793i	$0.579731\pi$
$468$	−1019.95	−	224.508i	−0.100742	−	0.0221750i
$469$	−671.251	+	790.258i	−0.0660885	+	0.0778054i
$470$	7458.46	+	811.156i	0.731985	+	0.0796082i
$471$	−961.946			−0.0941065
$472$	10885.0	−	2059.37i	1.06148	−	0.200826i
$473$	−9942.61			−0.966516
$474$	7565.89	+	822.841i	0.733150	+	0.0797349i
$475$	−3765.40	+	4432.98i	−0.363723	+	0.428208i
$476$	460.337	+	101.328i	0.0443267	+	0.00975704i
$477$	−5276.05	−	4010.75i	−0.506444	−	0.384989i
$478$	1713.07	−	1622.70i	0.163920	−	0.155273i
$479$	−3309.50	+	8306.22i	−0.315689	+	0.792319i	0.682427	+	0.730954i	$0.260925\pi$
$479$	−3309.50	+	8306.22i	−0.315689	+	0.792319i	−0.998115	+	0.0613650i	$0.980455\pi$
$480$	−2175.61	−	733.048i	−0.206880	−	0.0697060i
$481$	1491.41	+	9097.17i	0.141377	+	0.862360i
$482$	−5544.42	−	5251.95i	−0.523944	−	0.496307i
$483$	3593.24	−	1662.41i	0.338506	−	0.156609i
$484$	392.920	−	298.690i	0.0369008	−	0.0280513i
$485$	−2590.09	+	15798.9i	−0.242495	+	1.47915i
$486$	281.439	−	530.850i	0.0262682	−	0.0495470i
$487$	2542.22	−	559.585i	0.236548	−	0.0520682i	−0.0951140	−	0.995466i	$-0.530322\pi$
$487$	2542.22	−	559.585i	0.236548	−	0.0520682i	0.331662	+	0.943398i	$0.392391\pi$
$488$	−4531.02	−	2096.27i	−0.420306	−	0.194454i
$489$	−2772.80	−	6959.21i	−0.256422	−	0.643572i
$490$	350.974	+	6473.33i	0.0323579	+	0.596807i
$491$	1528.22	+	2253.96i	0.140464	+	0.207169i	0.891414	−	0.453191i	$-0.149714\pi$
$491$	1528.22	+	2253.96i	0.140464	+	0.207169i	−0.750950	+	0.660359i	$0.770404\pi$
$492$	292.818	+	344.732i	0.0268318	+	0.0315888i
$493$	−1354.40	−	2554.66i	−0.123730	−	0.233380i
$494$	20525.7	−	6915.91i	1.86942	−	0.629882i
$495$	−146.165	+	2695.86i	−0.0132720	+	0.244788i
$496$	8605.06	−	5177.49i	0.778989	−	0.468702i
$497$	1548.75	+	5578.10i	0.139781	+	0.503445i
$498$	795.443	−	2864.93i	0.0715756	−	0.257792i
$499$	14958.1	+	9000.01i	1.34192	+	0.807406i	0.991615	−	0.129230i	$-0.0412504\pi$
$499$	14958.1	+	9000.01i	1.34192	+	0.807406i	0.350305	+	0.936636i	$0.386078\pi$
$500$	−1610.47	+	2375.26i	−0.144045	+	0.212450i
$501$	3919.85	−	426.309i	0.349553	−	0.0380162i
$502$	18283.1	−	1988.41i	1.62553	−	0.176787i
$503$	−11358.9	+	16753.1i	−1.00690	+	1.48506i	−0.137774	+	0.990464i	$0.543995\pi$
$503$	−11358.9	+	16753.1i	−1.00690	+	1.48506i	−0.869122	+	0.494597i	$0.835316\pi$
$504$	−1425.60	−	857.754i	−0.125994	−	0.0758084i
$505$	−2040.38	+	7348.77i	−0.179793	+	0.647556i
$506$	−3774.88	−	13595.9i	−0.331648	−	1.19449i
$507$	4080.95	−	2455.43i	0.357478	−	0.215088i
$508$	137.510	−	2536.22i	0.0120099	−	0.221509i
$509$	10261.1	−	3457.38i	0.893550	−	0.301072i	0.165186	−	0.986262i	$-0.447178\pi$
$509$	10261.1	−	3457.38i	0.893550	−	0.301072i	0.728364	+	0.685190i	$0.240281\pi$
$510$	−1053.22	−	1986.59i	−0.0914461	−	0.172486i
$511$	−3560.18	−	4191.37i	−0.308206	−	0.362848i
$512$	−7100.27	−	10472.1i	−0.612872	−	0.903918i
$513$	−208.142	−	3838.96i	−0.0179137	−	0.330398i
$514$	934.694	+	2345.90i	0.0802093	+	0.201310i
$515$	−16498.1	−	7632.82i	−1.41163	−	0.653092i
$516$	1680.32	−	369.867i	0.143357	−	0.0315552i
$517$	−5066.37	+	9556.19i	−0.430984	+	0.812922i
$518$	−453.317	+	2765.11i	−0.0384510	+	0.234541i
$519$	−3005.44	+	2284.68i	−0.254189	+	0.193230i
$520$	12520.2	−	5792.46i	1.05586	−	0.488492i
$521$	8960.71	+	8488.04i	0.753505	+	0.713758i	0.964603	−	0.263707i	$-0.0849453\pi$
$521$	8960.71	+	8488.04i	0.753505	+	0.713758i	−0.211098	+	0.977465i	$0.567704\pi$
$522$	315.036	+	1921.63i	0.0264152	+	0.161126i
$523$	−13179.6	−	4440.71i	−1.10192	−	0.371278i	−0.291166	−	0.956672i	$-0.594043\pi$
$523$	−13179.6	−	4440.71i	−1.10192	−	0.371278i	−0.810749	+	0.585394i	$0.800940\pi$
$524$	−344.936	+	865.724i	−0.0287569	+	0.0721743i
$525$	−672.786	+	637.297i	−0.0559291	+	0.0529789i
$526$	−12479.5	−	9486.70i	−1.03448	−	0.786388i
$527$	−7145.99	−	1572.95i	−0.590672	−	0.130017i
$528$	−2880.30	+	3390.95i	−0.237404	+	0.279493i
$529$	−18179.7	−	1977.17i	−1.49418	−	0.162502i
$530$	16702.8			1.36892
$531$	2547.08	+	3185.61i	0.208162	+	0.260346i
$532$	−2031.19			−0.165532
$533$	−4888.38	−	531.643i	−0.397259	−	0.0432046i
$534$	1214.03	−	1429.26i	0.0983821	−	0.115824i
$535$	3462.95	+	762.252i	0.279843	+	0.0615982i
$536$	−2668.15	−	2028.27i	−0.215012	−	0.163448i
$537$	6128.49	−	5805.21i	0.492484	−	0.466505i
$538$	−1204.26	+	3022.45i	−0.0965040	+	0.242207i
$539$	−8856.95	−	2984.26i	−0.707785	−	0.238480i
$540$	−75.5842	−	461.043i	−0.00602338	−	0.0367410i
$541$	−1271.35	−	1204.29i	−0.101034	−	0.0957049i	0.635515	−	0.772088i	$-0.280788\pi$
$541$	−1271.35	−	1204.29i	−0.101034	−	0.0957049i	−0.736550	+	0.676383i	$0.763546\pi$
$542$	9972.84	−	4613.93i	0.790350	−	0.365655i
$543$	5180.60	−	3938.19i	0.409430	−	0.311241i
$544$	−445.956	+	2720.21i	−0.0351474	+	0.214390i
$545$	664.848	−	1254.04i	0.0522549	−	0.0985633i
$546$	3370.31	−	741.861i	0.264168	−	0.0581478i
$547$	3073.83	+	1422.10i	0.240269	+	0.111160i	0.536329	−	0.844009i	$-0.319811\pi$
$547$	3073.83	+	1422.10i	0.240269	+	0.111160i	−0.296060	+	0.955169i	$0.595673\pi$
$548$	1925.21	+	4831.92i	0.150075	+	0.376660i
$549$	−99.5129	−	1835.41i	−0.00773608	−	0.142684i
$550$	1853.45	+	2733.63i	0.143693	+	0.211931i
$551$	8066.50	+	9496.61i	0.623674	+	0.734246i
$552$	5994.50	+	11306.8i	0.462216	+	0.871831i
$553$	7352.74	−	2477.43i	0.565408	−	0.190508i
$554$	−1083.44	+	19982.8i	−0.0830881	+	1.53247i
$555$	−3533.64	+	2126.12i	−0.270260	+	0.162610i
$556$	−732.811	−	2639.35i	−0.0558959	−	0.201319i
$557$	−389.175	+	1401.68i	−0.0296048	+	0.106627i	−0.976876	−	0.213805i	$-0.931414\pi$
$557$	−389.175	+	1401.68i	−0.0296048	+	0.106627i	0.947272	+	0.320432i	$0.103828\pi$
$558$	4222.35	+	2540.50i	0.320334	+	0.192738i
$559$	−10496.8	+	15481.7i	−0.794220	+	1.17139i
$560$	3127.79	−	340.168i	0.236024	−	0.0256691i
$561$	3222.64	−	350.484i	0.242531	−	0.0263769i
$562$	8273.45	−	12202.4i	0.620987	−	0.915887i
$563$	6362.25	+	3828.04i	0.476265	+	0.286559i	0.733376	−	0.679823i	$-0.237943\pi$
$563$	6362.25	+	3828.04i	0.476265	+	0.286559i	−0.257112	+	0.966382i	$0.582771\pi$
$564$	500.735	−	1803.48i	0.0373843	−	0.134646i
$565$	−97.3710	−	350.699i	−0.00725032	−	0.0261133i
$566$	2878.99	−	1732.23i	0.213804	−	0.128641i
$567$	33.1631	−	611.658i	0.00245630	−	0.0453037i
$568$	−17733.2	+	5975.00i	−1.30998	+	0.441383i
$569$	−8045.64	−	15175.7i	−0.592778	−	1.11810i	−0.980536	−	0.196337i	$-0.937095\pi$
$569$	−8045.64	−	15175.7i	−0.592778	−	1.11810i	0.387758	−	0.921761i	$-0.373250\pi$
$570$	6272.78	+	7384.89i	0.460943	+	0.542665i
$571$	−11263.4	−	16612.3i	−0.825500	−	1.21752i	−0.973535	−	0.228539i	$-0.926605\pi$
$571$	−11263.4	−	16612.3i	−0.825500	−	1.21752i	0.148035	−	0.988982i	$-0.452705\pi$
$572$	205.437	+	3789.06i	0.0150170	+	0.276973i
$573$	816.649	+	2049.63i	0.0595393	+	0.149432i
$574$	−1356.46	−	627.566i	−0.0986369	−	0.0456343i
$575$	6961.59	−	1532.36i	0.504902	−	0.111137i
$576$	2399.06	−	4525.11i	0.173543	−	0.327338i
$577$	525.698	−	3206.61i	0.0379291	−	0.231357i	−0.961058	−	0.276345i	$-0.910877\pi$
$577$	525.698	−	3206.61i	0.0379291	−	0.231357i	0.998988	+	0.0449880i	$0.0143250\pi$
$578$	7521.57	−	5717.75i	0.541273	−	0.411465i
$579$	−5002.37	+	2314.34i	−0.359052	+	0.166115i
$580$	1099.27	+	1041.29i	0.0786979	+	0.0745466i
$581$	−490.406	−	2991.34i	−0.0350180	−	0.213600i
$582$	−12268.0	−	4133.57i	−0.873755	−	0.294402i
$583$	−8913.01	+	22370.0i	−0.633171	+	1.58914i
$584$	12905.3	−	12224.5i	0.914425	−	0.866190i
$585$	4043.42	+	3073.73i	0.285769	+	0.217236i
$586$	4371.53	+	962.246i	0.308167	+	0.0678328i
$587$	−3913.42	+	4607.23i	−0.275169	+	0.323954i	−0.882336	−	0.470621i	$-0.844030\pi$
$587$	−3913.42	+	4607.23i	−0.275169	+	0.323954i	0.607167	+	0.794574i	$0.292306\pi$
$588$	1607.86	+	174.865i	0.112767	+	0.0122641i
$589$	31531.0			2.20579
$590$	−9969.04	−	2506.68i	−0.695625	−	0.174912i
$591$	−15875.9			−1.10499
$592$	−6756.16	−	734.776i	−0.469048	−	0.0510120i
$593$	−5314.87	+	6257.15i	−0.368053	+	0.433306i	−0.914747	−	0.404027i	$-0.867610\pi$
$593$	−5314.87	+	6257.15i	−0.368053	+	0.433306i	0.546694	+	0.837333i	$0.315886\pi$
$594$	−2132.07	−	469.303i	−0.147272	−	0.0324171i
$595$	−1824.93	−	1387.27i	−0.125739	−	0.0955844i
$596$	2033.84	−	1926.55i	0.139781	−	0.132407i
$597$	3862.04	−	9692.99i	0.264762	−	0.664502i
$598$	−25155.5	−	8475.87i	−1.72021	−	0.579605i
$599$	−784.913	−	4787.76i	−0.0535404	−	0.326582i	−0.999993	−	0.00373907i	$-0.998810\pi$
$599$	−784.913	−	4787.76i	−0.0535404	−	0.326582i	0.946453	−	0.322843i	$-0.104638\pi$
$600$	−2174.71	−	2060.00i	−0.147970	−	0.140165i
$601$	4523.03	−	2092.57i	0.306985	−	0.142026i	−0.260348	−	0.965515i	$-0.583837\pi$
$601$	4523.03	−	2092.57i	0.306985	−	0.142026i	0.567333	+	0.823488i	$0.307975\pi$
$602$	−4526.06	+	3440.62i	−0.306426	+	0.232939i
$603$	199.633	−	1217.71i	0.0134821	−	0.0822371i
$604$	392.231	−	739.826i	0.0264233	−	0.0498396i
$605$	−2344.22	+	516.002i	−0.157531	+	0.0346751i
$606$	−5597.10	−	2589.49i	−0.375192	−	0.173582i
$607$	134.863	+	338.481i	0.00901800	+	0.0226335i	0.933417	−	0.358794i	$-0.116812\pi$
$607$	134.863	+	338.481i	0.00901800	+	0.0226335i	−0.924399	+	0.381427i	$0.875433\pi$
$608$	−643.091	−	11861.1i	−0.0428960	−	0.791170i
$609$	1114.10	+	1643.17i	0.0741307	+	0.109335i
$610$	2999.02	+	3530.72i	0.199060	+	0.234352i
$611$	9531.20	+	17977.7i	0.631082	+	1.19035i
$612$	−531.595	+	179.115i	−0.0351118	+	0.0118306i
$613$	−797.868	+	14715.8i	−0.0525703	+	0.969601i	0.846662	+	0.532131i	$0.178608\pi$
$613$	−797.868	+	14715.8i	−0.0525703	+	0.969601i	−0.899233	+	0.437471i	$0.855874\pi$
$614$	−19071.3	+	11474.8i	−1.25351	+	0.754213i
$615$	−588.486	−	2119.53i	−0.0385854	−	0.138972i
$616$	−1617.24	+	5824.77i	−0.105780	+	0.380985i
$617$	−17334.5	−	10429.8i	−1.13106	−	0.680534i	−0.178211	−	0.983992i	$-0.557031\pi$
$617$	−17334.5	−	10429.8i	−1.13106	−	0.680534i	−0.952845	+	0.303458i	$0.901859\pi$
$618$	8248.94	−	12166.3i	0.536927	−	0.791908i
$619$	17725.2	−	1927.73i	1.15094	−	0.125173i	0.487309	−	0.873230i	$-0.337979\pi$
$619$	17725.2	−	1927.73i	1.15094	−	0.125173i	0.663635	+	0.748057i	$0.269013\pi$
$620$	3809.20	−	414.275i	0.246744	−	0.0268350i
$621$	−2644.19	+	3899.89i	−0.170866	+	0.252009i
$622$	−2608.04	−	1569.21i	−0.168124	−	0.101157i
$623$	511.470	−	1842.15i	0.0328918	−	0.118466i
$624$	2239.21	+	8064.90i	0.143654	+	0.517395i
$625$	7583.73	−	4562.98i	0.485359	−	0.292031i
$626$	−86.4391	+	1594.28i	−0.00551885	+	0.101789i
$627$	−13237.8	+	4460.33i	−0.843169	+	0.284097i
$628$	−283.307	−	534.373i	−0.0180019	−	0.0339551i
$629$	3205.59	+	3773.91i	0.203204	+	0.239230i
$630$	866.361	+	1277.79i	0.0547883	+	0.0808068i
$631$	−1514.03	−	27924.7i	−0.0955193	−	1.76175i	−0.518003	−	0.855379i	$-0.673324\pi$
$631$	−1514.03	−	27924.7i	−0.0955193	−	1.76175i	0.422483	−	0.906371i	$-0.361158\pi$
$632$	9283.00	+	23298.6i	0.584269	+	1.46640i
$633$	−6886.35	−	3185.96i	−0.432398	−	0.200049i
$634$	4742.82	−	1043.97i	0.297100	−	0.0653967i
$635$	−5786.05	+	10913.6i	−0.361594	+	0.682039i
$636$	674.150	−	4112.13i	0.0420311	−	0.256378i
$637$	−13997.5	+	10640.6i	−0.870643	+	0.661845i
$638$	6421.38	−	2970.85i	0.398471	−	0.184352i
$639$	−5001.82	−	4737.97i	−0.309654	−	0.293320i
$640$	1097.85	+	6696.62i	0.0678071	+	0.413605i
$641$	−11842.1	−	3990.06i	−0.729694	−	0.245863i	−0.0701585	−	0.997536i	$-0.522351\pi$
$641$	−11842.1	−	3990.06i	−0.729694	−	0.245863i	−0.659536	+	0.751673i	$0.729247\pi$
$642$	−1061.26	+	2663.57i	−0.0652411	+	0.163743i
$643$	5105.15	−	4835.86i	0.313107	−	0.296590i	−0.514967	−	0.857210i	$-0.672196\pi$
$643$	5105.15	−	4835.86i	0.313107	−	0.296590i	0.828073	+	0.560620i	$0.189437\pi$
$644$	1981.75	+	1506.49i	0.121261	+	0.0921800i
$645$	−8171.93	−	1798.78i	−0.498867	−	0.109809i
$646$	7531.66	−	8866.95i	0.458714	−	0.540040i
$647$	−12355.2	−	1343.71i	−0.750746	−	0.0816485i	−0.275257	−	0.961371i	$-0.588763\pi$
$647$	−12355.2	−	1343.71i	−0.750746	−	0.0816485i	−0.475488	+	0.879722i	$0.657729\pi$
$648$	1980.02			0.120035
$649$	8676.87	−	12013.8i	0.524803	−	0.726631i
$650$	6213.30			0.374932
$651$	4994.35	+	543.168i	0.300682	+	0.0327011i
$652$	3049.30	−	3589.91i	0.183159	−	0.215632i
$653$	−8406.83	−	1850.48i	−0.503805	−	0.110896i	−0.0442061	−	0.999022i	$-0.514076\pi$
$653$	−8406.83	−	1850.48i	−0.503805	−	0.110896i	−0.459599	+	0.888127i	$0.652007\pi$
$654$	913.695	+	694.573i	0.0546304	+	0.0415290i
$655$	3290.34	−	3116.77i	0.196281	−	0.185927i
$656$	1341.74	−	3367.52i	0.0798572	−	0.200426i
$657$	6202.12	+	2089.74i	0.368292	+	0.124092i
$658$	1000.60	+	6103.37i	0.0592816	+	0.361602i
$659$	−7428.04	−	7036.21i	−0.439082	−	0.415921i	0.435961	−	0.899966i	$-0.356409\pi$
$659$	−7428.04	−	7036.21i	−0.439082	−	0.415921i	−0.875043	+	0.484045i	$0.839167\pi$
$660$	−1540.63	+	712.772i	−0.0908622	+	0.0420373i
$661$	−17692.3	+	13449.3i	−1.04107	+	0.791403i	−0.978419	−	0.206632i	$-0.933750\pi$
$661$	−17692.3	+	13449.3i	−1.04107	+	0.791403i	−0.0626544	+	0.998035i	$0.519957\pi$
$662$	−83.4003	+	508.719i	−0.00489644	+	0.0298670i
$663$	2856.54	−	5388.01i	0.167329	−	0.315615i
$664$	9569.21	−	2106.34i	0.559273	−	0.123105i
$665$	8965.31	+	4147.80i	0.522797	+	0.241872i
$666$	−1234.29	−	3097.83i	−0.0718135	−	0.180238i
$667$	−826.733	−	15248.2i	−0.0479929	−	0.885176i
$668$	1391.27	+	2051.97i	0.0805836	+	0.118852i
$669$	11280.2	+	13280.1i	0.651896	+	0.767471i
$670$	1456.71	+	2747.65i	0.0839965	+	0.158434i
$671$	−6328.99	+	2132.49i	−0.364125	+	0.122688i
$672$	102.463	−	1889.82i	0.00588184	−	0.108484i
$673$	11649.9	−	7009.50i	0.667266	−	0.401481i	−0.141234	−	0.989976i	$-0.545107\pi$
$673$	11649.9	−	7009.50i	0.667266	−	0.401481i	0.808500	+	0.588496i	$0.200280\pi$
$674$	3373.37	+	12149.8i	0.192786	+	0.694351i
$675$	295.049	−	1062.67i	0.0168244	−	0.0605959i
$676$	2565.92	+	1543.86i	0.145990	+	0.0878392i
$677$	565.792	−	834.480i	0.0321199	−	0.0473732i	−0.811290	−	0.584644i	$-0.801234\pi$
$677$	565.792	−	834.480i	0.0321199	−	0.0473732i	0.843410	+	0.537271i	$0.180545\pi$
$678$	292.581	−	31.8201i	0.0165730	−	0.00180243i
$679$	−13120.7	+	1426.96i	−0.741571	+	0.0806507i
$680$	4158.29	−	6133.01i	0.234504	−	0.345868i
$681$	120.684	+	72.6131i	0.00679092	+	0.00408596i
$682$	4789.95	−	17251.8i	0.268939	−	0.968632i
$683$	−1718.78	−	6190.50i	−0.0962920	−	0.346812i	0.899672	−	0.436567i	$-0.143806\pi$
$683$	−1718.78	−	6190.50i	−0.0962920	−	0.346812i	−0.995964	+	0.0897542i	$0.971392\pi$
$684$	2071.29	−	1246.25i	0.115786	−	0.0696662i
$685$	1369.48	−	25258.6i	0.0763872	−	1.40888i
$686$	−11142.5	+	3754.35i	−0.620150	+	0.208953i
$687$	1592.72	+	3004.19i	0.0884514	+	0.166837i
$688$	−8926.92	−	10509.6i	−0.494674	−	0.582375i
$689$	25422.5	+	37495.4i	1.40569	+	2.07324i
$690$	−642.896	−	11857.5i	−0.0354705	−	0.654214i
$691$	9956.30	+	24988.4i	0.548127	+	1.37569i	0.898454	+	0.439067i	$0.144691\pi$
$691$	9956.30	+	24988.4i	0.548127	+	1.37569i	−0.350328	+	0.936627i	$0.613930\pi$
$692$	−2154.31	−	996.690i	−0.118345	−	0.0547521i
$693$	−2173.64	+	478.454i	−0.119148	+	0.0262265i
$694$	−12070.2	+	22766.9i	−0.660202	+	1.24527i
$695$	−2155.19	+	13146.1i	−0.117627	+	0.717494i
$696$	−5108.63	+	3883.48i	−0.278222	+	0.211499i
$697$	−2397.06	+	1109.00i	−0.130266	+	0.0602674i
$698$	7170.68	+	6792.43i	0.388846	+	0.368334i
$699$	1860.93	+	11351.2i	0.100696	+	0.614221i
$700$	−552.171	−	186.048i	−0.0298144	−	0.0100457i
$701$	4392.02	−	11023.1i	0.236640	−	0.593921i	−0.761914	−	0.647678i	$-0.775740\pi$
$701$	4392.02	−	11023.1i	0.236640	−	0.593921i	0.998554	+	0.0537569i	$0.0171196\pi$
$702$	−2981.67	+	2824.38i	−0.160307	+	0.151851i
$703$	−16986.7	−	12912.9i	−0.911330	−	0.692775i
$704$	−18174.3	−	4000.47i	−0.972970	−	0.214167i
$705$	−5892.97	+	6937.74i	−0.314811	+	0.370624i
$706$	−2618.91	−	284.824i	−0.139609	−	0.0151834i
$707$	−6287.33			−0.334455
$708$	−1019.49	+	2353.14i	−0.0541170	+	0.124910i
$709$	−22317.9			−1.18218			−0.591091	−	0.806605i	$-0.701302\pi$
$709$	−22317.9			−1.18218			−0.591091	+	0.806605i	$0.701302\pi$
$710$	17261.8	+	1877.33i	0.912428	+	0.0992325i
$711$	−5977.85	+	7037.67i	−0.315312	+	0.371214i
$712$	6035.33	+	1328.48i	0.317674	+	0.0699252i
$713$	−30763.5	−	23385.8i	−1.61585	−	1.22834i
$714$	1345.72	−	1274.74i	0.0705356	−	0.0668149i
$715$	6830.69	−	17143.7i	0.357277	−	0.896698i
$716$	5029.79	+	1694.73i	0.262531	+	0.0884570i
$717$	463.168	+	2825.20i	0.0241246	+	0.147153i
$718$	3278.51	+	3105.57i	0.170408	+	0.161419i
$719$	11101.8	−	5136.25i	0.575839	−	0.266412i	−0.110280	−	0.993901i	$-0.535175\pi$
$719$	11101.8	−	5136.25i	0.575839	−	0.266412i	0.686119	+	0.727489i	$0.259313\pi$
$720$	−2980.82	+	2265.96i	−0.154290	+	0.117288i
$721$	2424.41	−	14788.3i	0.125229	−	0.763861i
$722$	−15538.9	+	29309.6i	−0.800969	+	1.51079i
$723$	9049.31	−	1991.90i	0.465488	−	0.102462i
$724$	3713.47	+	1718.03i	0.190622	+	0.0881909i
$725$	1323.00	+	3320.47i	0.0677722	+	0.170096i
$726$	−105.080	−	1938.09i	−0.00537176	−	0.0990763i
$727$	−17271.8	−	25474.0i	−0.881123	−	1.29956i	−0.953256	−	0.302165i	$-0.902291\pi$
$727$	−17271.8	−	25474.0i	−0.881123	−	1.29956i	0.0721324	−	0.997395i	$-0.477020\pi$
$728$	7362.38	+	8667.66i	0.374818	+	0.441270i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−15630.9	+	5266.68i	−0.792503	+	0.267025i
$731$	−543.924	+	10032.1i	−0.0275209	+	0.507593i
$732$	990.283	−	595.834i	0.0500026	−	0.0300856i
$733$	9400.80	+	33858.6i	0.473706	+	1.70613i	0.684854	+	0.728680i	$0.259866\pi$
$733$	9400.80	+	33858.6i	0.473706	+	1.70613i	−0.211148	+	0.977454i	$0.567720\pi$
$734$	−1686.87	+	6075.57i	−0.0848279	+	0.305522i
$735$	−6739.71	−	4055.15i	−0.338229	−	0.203505i
$736$	−8169.68	+	12049.4i	−0.409155	+	0.603459i
$737$	−4457.23	+	484.753i	−0.222774	+	0.0242281i
$738$	1768.29	−	192.313i	0.0881999	−	0.00959232i
$739$	12419.7	−	18317.7i	0.618223	−	0.911810i	−0.381699	−	0.924287i	$-0.624661\pi$
$739$	12419.7	−	18317.7i	0.618223	−	0.911810i	0.999922	+	0.0124762i	$0.00397139\pi$
$740$	−2221.79	−	1336.81i	−0.110371	−	0.0664081i
$741$	−7030.50	+	25321.6i	−0.348545	+	1.25535i
$742$	3683.72	+	13267.6i	0.182255	+	0.656425i
$743$	21204.1	−	12758.1i	1.04698	−	0.629945i	0.115336	−	0.993327i	$-0.463206\pi$
$743$	21204.1	−	12758.1i	1.04698	−	0.629945i	0.931640	+	0.363382i	$0.118378\pi$
$744$	−879.156	+	16215.1i	−0.0433218	+	0.799024i
$745$	−12911.1	+	4350.26i	−0.634935	+	0.213935i
$746$	−7081.81	−	13357.7i	−0.347565	−	0.655577i
$747$	2335.45	+	2749.50i	0.114390	+	0.134671i
$748$	1143.81	+	1687.00i	0.0559116	+	0.0824635i
$749$	158.254	+	2918.83i	0.00772028	+	0.142392i
$750$	4177.16	+	10483.9i	0.203371	+	0.510423i
$751$	−8437.88	−	3903.78i	−0.409990	−	0.189682i	0.204043	−	0.978962i	$-0.434592\pi$
$751$	−8437.88	−	3903.78i	−0.409990	−	0.189682i	−0.614033	+	0.789280i	$0.710454\pi$
$752$	−14649.9	+	3224.70i	−0.710410	+	0.156373i
$753$	−10451.9	+	19714.4i	−0.505829	+	0.954095i
$754$	2153.41	−	13135.2i	0.104008	−	0.634424i
$755$	−3242.00	+	2464.51i	−0.156276	+	0.118798i
$756$	349.550	−	161.719i	0.0168162	−	0.00777999i
$757$	19493.2	+	18464.9i	0.935919	+	0.886550i	0.993733	−	0.111777i	$-0.0356544\pi$
$757$	19493.2	+	18464.9i	0.935919	+	0.886550i	−0.0578138	+	0.998327i	$0.518413\pi$
$758$	2544.45	+	15520.5i	0.121924	+	0.743706i
$759$	16223.7	+	5466.41i	0.775868	+	0.261420i
$760$	−11818.7	+	29662.8i	−0.564093	+	1.41577i
$761$	16944.5	−	16050.7i	0.807145	−	0.764568i	−0.168082	−	0.985773i	$-0.553757\pi$
$761$	16944.5	−	16050.7i	0.807145	−	0.764568i	0.975227	+	0.221205i	$0.0709988\pi$
$762$	−7951.72	−	6044.74i	−0.378032	−	0.287373i
$763$	1142.75	+	251.537i	0.0542204	+	0.0119348i
$764$	−898.083	+	1057.30i	−0.0425281	+	0.0500680i
$765$	2712.13	+	294.962i	0.128179	+	0.0139403i
$766$	31508.8			1.48624
$767$	−9546.22	−	26194.3i	−0.449405	−	1.23314i
$768$	8170.71			0.383900
$769$	−17386.5	−	1890.90i	−0.815310	−	0.0886703i	−0.309044	−	0.951048i	$-0.600009\pi$
$769$	−17386.5	−	1890.90i	−0.815310	−	0.0886703i	−0.506266	+	0.862377i	$0.668975\pi$
$770$	3631.37	−	4275.18i	0.169955	−	0.200087i
$771$	−2992.26	&min

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)

\(f(q)\)	\(=\)	\(q+(2.45810 + 0.267335i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-1.84216 - 0.405491i) q^{4} +(7.30295 + 5.55156i) q^{5} +(-5.38528 + 5.10121i) q^{6} +(-2.79914 + 7.02531i) q^{7} +(-23.1651 - 7.80525i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(2.45810 + 0.267335i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-1.84216 - 0.405491i) q^{4} +(7.30295 + 5.55156i) q^{5} +(-5.38528 + 5.10121i) q^{6} +(-2.79914 + 7.02531i) q^{7} +(-23.1651 - 7.80525i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(16.4673 + 15.5986i) q^{10} +(-29.6784 + 13.7307i) q^{11} +(4.50492 - 3.42455i) q^{12} +(-9.95264 + 60.7084i) q^{13} +(-8.75869 + 16.5206i) q^{14} +(-26.8771 + 5.91609i) q^{15} +(-41.1603 - 19.0428i) q^{16} +(12.2307 + 30.6967i) q^{17} +(-1.20477 - 22.2207i) q^{18} +(-79.9088 - 117.857i) q^{19} +(-11.2021 - 13.1882i) q^{20} +(-10.6269 - 20.0445i) q^{21} +(-76.6233 + 25.8174i) q^{22} +(-9.44781 + 174.255i) q^{23} +(62.8370 - 37.8078i) q^{24} +(-10.9277 - 39.3582i) q^{25} +(-40.6941 + 146.567i) q^{26} +(23.1351 + 13.9200i) q^{27} +(8.00518 - 11.8068i) q^{28} +(-86.9923 + 9.46098i) q^{29} +(-67.6481 + 7.35718i) q^{30} +(-124.267 + 183.281i) q^{31} +(71.4799 + 43.0080i) q^{32} +(26.2451 - 94.5265i) q^{33} +(21.8580 + 78.7252i) q^{34} +(-59.4434 + 35.7659i) q^{35} +(-0.919082 + 16.9515i) q^{36} +(142.006 - 47.8474i) q^{37} +(-164.917 - 311.066i) q^{38} +(-119.479 - 140.662i) q^{39} +(-125.843 - 185.604i) q^{40} +(4.32733 + 79.8129i) q^{41} +(-20.7634 - 52.1123i) q^{42} +(275.947 + 127.667i) q^{43} +(60.2402 - 13.2599i) q^{44} +(38.6725 - 72.9440i) q^{45} +(-69.8080 + 425.810i) q^{46} +(263.317 - 200.168i) q^{47} +(123.481 - 57.1283i) q^{48} +(207.497 + 196.551i) q^{49} +(-16.3397 - 99.6678i) q^{50} +(-93.9414 - 31.6525i) q^{51} +(42.9511 - 107.799i) q^{52} +(534.609 - 506.409i) q^{53} +(53.1473 + 40.4015i) q^{54} +(-292.967 - 64.4869i) q^{55} +(119.677 - 140.894i) q^{56} +(424.673 + 46.1860i) q^{57} -216.365 q^{58} +(-395.079 + 222.017i) q^{59} +51.9109 q^{60} +(203.036 + 22.0815i) q^{61} +(-354.460 + 417.302i) q^{62} +(66.4705 + 14.6313i) q^{63} +(453.042 + 344.394i) q^{64} +(-409.710 + 388.098i) q^{65} +(89.7835 - 225.339i) q^{66} +(129.930 + 43.7786i) q^{67} +(-10.0837 - 61.5077i) q^{68} +(-380.082 - 360.032i) q^{69} +(-155.680 + 72.0250i) q^{70} +(609.418 - 463.267i) q^{71} +(-35.5925 + 217.105i) q^{72} +(-340.622 + 642.481i) q^{73} +(361.857 - 79.6507i) q^{74} +(111.215 + 51.4537i) q^{75} +(99.4154 + 249.514i) q^{76} +(-13.3884 - 246.934i) q^{77} +(-256.089 - 377.702i) q^{78} +(-664.206 - 781.963i) q^{79} +(-194.874 - 367.572i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-10.6997 + 197.345i) q^{82} +(-343.457 + 206.652i) q^{83} +(11.4487 + 41.2343i) q^{84} +(-81.0944 + 292.076i) q^{85} +(644.176 + 387.588i) q^{86} +(147.320 - 217.281i) q^{87} +(794.676 - 86.4262i) q^{88} +(-251.325 + 27.3333i) q^{89} +(114.561 - 168.965i) q^{90} +(-398.637 - 239.852i) q^{91} +(88.0631 - 317.175i) q^{92} +(-177.722 - 640.096i) q^{93} +(700.771 - 421.640i) q^{94} +(70.7182 - 1304.32i) q^{95} +(-237.163 + 79.9094i) q^{96} +(817.476 + 1541.92i) q^{97} +(457.503 + 538.614i) q^{98} +(165.161 + 243.595i) 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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