LMFDB - Embedded newform 177.3.g.a.10.13

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.g (of order $58$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$20$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			10.13
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.13

$q$-expansion

$f(q)$	$=$	$q+(0.819309 + 0.326442i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.33928 - 2.21588i) q^{4} +(1.32036 - 1.55445i) q^{5} +(1.34963 + 0.715530i) q^{6} +(7.54931 + 4.54227i) q^{7} +(-2.67451 - 5.78087i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(0.819309 + 0.326442i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.33928 - 2.21588i) q^{4} +(1.32036 - 1.55445i) q^{5} +(1.34963 + 0.715530i) q^{6} +(7.54931 + 4.54227i) q^{7} +(-2.67451 - 5.78087i) q^{8} +(2.92986 + 0.644911i) q^{9} +(1.58922 - 0.842551i) q^{10} +(8.00405 + 0.433967i) q^{11} +(-3.61304 - 4.25360i) q^{12} +(-2.74300 - 12.4616i) q^{13} +(4.70243 + 6.18594i) q^{14} +(2.56462 - 2.42934i) q^{15} +(0.393646 + 7.26038i) q^{16} +(21.3238 - 12.8301i) q^{17} +(2.18993 + 1.48481i) q^{18} +(5.94855 - 21.4248i) q^{19} +(-6.53316 + 0.710524i) q^{20} +(12.1485 + 9.23507i) q^{21} +(6.41612 + 2.96841i) q^{22} +(-34.7776 + 23.5798i) q^{23} +(-3.52267 - 10.4549i) q^{24} +(3.37159 + 20.5658i) q^{25} +(1.82062 - 11.1053i) q^{26} +(4.92415 + 1.65914i) q^{27} +(-7.59481 - 27.3540i) q^{28} +(11.4284 + 28.6832i) q^{29} +(2.89426 - 1.15318i) q^{30} +(-39.5754 + 10.9880i) q^{31} +(-10.1828 + 30.2216i) q^{32} +(13.7009 + 2.24615i) q^{33} +(21.6591 - 3.55083i) q^{34} +(17.0285 - 5.73758i) q^{35} +(-5.42472 - 8.00086i) q^{36} +(-20.3901 + 44.0726i) q^{37} +(11.8677 - 15.6116i) q^{38} +(-2.38952 - 21.9712i) q^{39} +(-12.5174 - 3.47543i) q^{40} +(24.0953 - 35.5378i) q^{41} +(6.93867 + 11.5322i) q^{42} +(-78.3897 + 4.25017i) q^{43} +(-17.7621 - 18.7512i) q^{44} +(4.87095 - 3.70280i) q^{45} +(-36.1910 + 7.96624i) q^{46} +(42.9177 - 36.4546i) q^{47} +(-0.681816 + 12.5753i) q^{48} +(13.4079 + 25.2900i) q^{49} +(-3.95118 + 17.9504i) q^{50} +(39.1201 - 18.0989i) q^{51} +(-21.1968 + 35.2293i) q^{52} +(8.86078 - 16.7132i) q^{53} +(3.49279 + 2.96680i) q^{54} +(11.2428 - 11.8689i) q^{55} +(6.06752 - 55.7900i) q^{56} +(14.2550 - 35.7773i) q^{57} +27.2311i q^{58} +(-8.63189 + 58.3651i) q^{59} -11.3825 q^{60} +(-90.9224 - 36.2268i) q^{61} +(-36.0114 - 3.91648i) q^{62} +(19.1891 + 18.1769i) q^{63} +(0.620203 - 0.730159i) q^{64} +(-22.9926 - 12.1899i) q^{65} +(10.4920 + 6.31284i) q^{66} +(-6.38717 - 13.8056i) q^{67} +(-78.3125 - 17.2379i) q^{68} +(-64.2991 + 34.0893i) q^{69} +(15.8246 + 0.857985i) q^{70} +(66.1839 + 77.9177i) q^{71} +(-4.10781 - 18.6620i) q^{72} +(49.5119 + 65.1318i) q^{73} +(-31.0930 + 29.4528i) q^{74} +(1.95423 + 36.0436i) q^{75} +(-61.3901 + 36.9372i) q^{76} +(58.4539 + 39.6327i) q^{77} +(5.21460 - 18.7813i) q^{78} +(-91.2954 + 9.92898i) q^{79} +(11.8056 + 8.97441i) q^{80} +(8.16818 + 3.77900i) q^{81} +(31.3425 - 21.2507i) q^{82} +(-2.10729 - 6.25421i) q^{83} +(-7.95496 - 48.5231i) q^{84} +(8.21138 - 50.0872i) q^{85} +(-65.6128 - 22.1075i) q^{86} +(14.3071 + 51.5297i) q^{87} +(-18.8982 - 47.4310i) q^{88} +(7.81364 - 3.11324i) q^{89} +(5.19956 - 1.44365i) q^{90} +(35.8961 - 106.536i) q^{91} +(133.605 + 21.9034i) q^{92} +(-70.2024 + 11.5091i) q^{93} +(47.0632 - 15.8574i) q^{94} +(-25.4494 - 37.5351i) q^{95} +(-23.1933 + 50.1316i) q^{96} +(71.2408 - 93.7156i) q^{97} +(2.72948 + 25.0972i) q^{98} +(23.1709 + 6.43337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) $	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{7}{58}\right)$	$1$

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 $

$2$	0.819309	+	0.326442i	0.409654	+	0.163221i	0.565856	−	0.824504i	$-0.308546\pi$
$2$	0.819309	+	0.326442i	0.409654	+	0.163221i	−0.156202	+	0.987725i	$0.549925\pi$
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$4$	−2.33928	−	2.21588i	−0.584820	−	0.553971i
$5$	1.32036	−	1.55445i	0.264072	−	0.310889i	−0.614106	−	0.789223i	$-0.710483\pi$
$5$	1.32036	−	1.55445i	0.264072	−	0.310889i	0.878178	+	0.478334i	$0.158759\pi$
$6$	1.34963	+	0.715530i	0.224939	+	0.119255i
$7$	7.54931	+	4.54227i	1.07847	+	0.648896i	0.939898	−	0.341456i	$-0.110920\pi$
$7$	7.54931	+	4.54227i	1.07847	+	0.648896i	0.138576	+	0.990352i	$0.455748\pi$
$8$	−2.67451	−	5.78087i	−0.334314	−	0.722609i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	1.58922	−	0.842551i	0.158922	−	0.0842551i
$11$	8.00405	+	0.433967i	0.727641	+	0.0394515i	0.414238	−	0.910169i	$-0.364048\pi$
$11$	8.00405	+	0.433967i	0.727641	+	0.0394515i	0.313403	+	0.949620i	$0.398531\pi$
$12$	−3.61304	−	4.25360i	−0.301086	−	0.354466i
$13$	−2.74300	−	12.4616i	−0.211000	−	0.958584i	−0.956421	−	0.291990i	$-0.905683\pi$
$13$	−2.74300	−	12.4616i	−0.211000	−	0.958584i	0.745421	−	0.666594i	$-0.232248\pi$
$14$	4.70243	+	6.18594i	0.335888	+	0.441853i
$15$	2.56462	−	2.42934i	0.170975	−	0.161956i
$16$	0.393646	+	7.26038i	0.0246029	+	0.453774i
$17$	21.3238	−	12.8301i	1.25434	−	0.754714i	0.275892	−	0.961189i	$-0.411027\pi$
$17$	21.3238	−	12.8301i	1.25434	−	0.754714i	0.978452	+	0.206475i	$0.0661992\pi$
$18$	2.18993	+	1.48481i	0.121663	+	0.0824896i
$19$	5.94855	−	21.4248i	0.313082	−	1.12762i	−0.624835	−	0.780757i	$-0.714834\pi$
$19$	5.94855	−	21.4248i	0.313082	−	1.12762i	0.937916	−	0.346862i	$-0.112753\pi$
$20$	−6.53316	+	0.710524i	−0.326658	+	0.0355262i
$21$	12.1485	+	9.23507i	0.578501	+	0.439765i
$22$	6.41612	+	2.96841i	0.291642	+	0.134928i
$23$	−34.7776	+	23.5798i	−1.51207	+	1.02521i	−0.527631	+	0.849474i	$0.676920\pi$
$23$	−34.7776	+	23.5798i	−1.51207	+	1.02521i	−0.984438	+	0.175734i	$0.943770\pi$
$24$	−3.52267	−	10.4549i	−0.146778	−	0.435621i
$25$	3.37159	+	20.5658i	0.134864	+	0.822632i
$26$	1.82062	−	11.1053i	0.0700240	−	0.427128i
$27$	4.92415	+	1.65914i	0.182376	+	0.0614496i
$28$	−7.59481	−	27.3540i	−0.271243	−	0.976930i
$29$	11.4284	+	28.6832i	0.394084	+	0.989076i	0.983445	+	0.181206i	$0.0580001\pi$
$29$	11.4284	+	28.6832i	0.394084	+	0.989076i	−0.589361	+	0.807869i	$0.700621\pi$
$30$	2.89426	−	1.15318i	0.0964752	−	0.0384392i
$31$	−39.5754	+	10.9880i	−1.27662	+	0.354453i	−0.838717	−	0.544567i	$-0.816694\pi$
$31$	−39.5754	+	10.9880i	−1.27662	+	0.354453i	−0.437907	+	0.899020i	$0.644280\pi$
$32$	−10.1828	+	30.2216i	−0.318214	+	0.944424i
$33$	13.7009	+	2.24615i	0.415178	+	0.0680650i
$34$	21.6591	−	3.55083i	0.637033	−	0.104436i
$35$	17.0285	−	5.73758i	0.486529	−	0.163931i
$36$	−5.42472	−	8.00086i	−0.150687	−	0.222246i
$37$	−20.3901	+	44.0726i	−0.551085	+	1.19115i	0.409281	+	0.912408i	$0.365780\pi$
$37$	−20.3901	+	44.0726i	−0.551085	+	1.19115i	−0.960366	+	0.278742i	$0.910083\pi$
$38$	11.8677	−	15.6116i	0.312307	−	0.410832i
$39$	−2.38952	−	21.9712i	−0.0612697	−	0.563365i
$40$	−12.5174	−	3.47543i	−0.312934	−	0.0868858i
$41$	24.0953	−	35.5378i	0.587689	−	0.866776i	−0.411311	−	0.911495i	$-0.634929\pi$
$41$	24.0953	−	35.5378i	0.587689	−	0.866776i	0.999000	+	0.0447188i	$0.0142392\pi$
$42$	6.93867	+	11.5322i	0.165206	+	0.274575i
$43$	−78.3897	+	4.25017i	−1.82302	+	0.0988411i	−0.933613	−	0.358283i	$-0.883362\pi$
$43$	−78.3897	+	4.25017i	−1.82302	+	0.0988411i	−0.889403	+	0.457124i	$0.848880\pi$
$44$	−17.7621	−	18.7512i	−0.403684	−	0.426164i
$45$	4.87095	−	3.70280i	0.108243	−	0.0822845i
$46$	−36.1910	+	7.96624i	−0.786761	+	0.173179i
$47$	42.9177	−	36.4546i	0.913142	−	0.775630i	−0.0617998	−	0.998089i	$-0.519684\pi$
$47$	42.9177	−	36.4546i	0.913142	−	0.775630i	0.974942	+	0.222458i	$0.0714082\pi$
$48$	−0.681816	+	12.5753i	−0.0142045	+	0.261986i
$49$	13.4079	+	25.2900i	0.273630	+	0.516122i
$50$	−3.95118	+	17.9504i	−0.0790235	+	0.359007i
$51$	39.1201	−	18.0989i	0.767062	−	0.354881i
$52$	−21.1968	+	35.2293i	−0.407630	+	0.677487i
$53$	8.86078	−	16.7132i	0.167185	−	0.315343i	−0.785737	−	0.618561i	$-0.787716\pi$
$53$	8.86078	−	16.7132i	0.167185	−	0.315343i	0.952921	+	0.303217i	$0.0980608\pi$
$54$	3.49279	+	2.96680i	0.0646812	+	0.0549407i
$55$	11.2428	−	11.8689i	0.204415	−	0.215798i
$56$	6.06752	−	55.7900i	0.108349	−	0.996249i
$57$	14.2550	−	35.7773i	0.250087	−	0.627671i
$58$			27.2311i			0.469502i
$59$	−8.63189	+	58.3651i	−0.146303	+	0.989240i
$59$	−8.63189	+	58.3651i	−0.146303	+	0.989240i
$60$	−11.3825			−0.189708
$61$	−90.9224	−	36.2268i	−1.49053	−	0.593882i	−0.524294	−	0.851537i	$-0.675671\pi$
$61$	−90.9224	−	36.2268i	−1.49053	−	0.593882i	−0.966237	+	0.257655i	$0.917050\pi$
$62$	−36.0114	−	3.91648i	−0.580829	−	0.0631690i
$63$	19.1891	+	18.1769i	0.304589	+	0.288522i
$64$	0.620203	−	0.730159i	0.00969067	−	0.0114087i
$65$	−22.9926	−	12.1899i	−0.353733	−	0.187537i
$66$	10.4920	+	6.31284i	0.158970	+	0.0956491i
$67$	−6.38717	−	13.8056i	−0.0953309	−	0.206054i	0.854043	−	0.520202i	$-0.174143\pi$
$67$	−6.38717	−	13.8056i	−0.0953309	−	0.206054i	−0.949374	+	0.314148i	$0.898281\pi$
$68$	−78.3125	−	17.2379i	−1.15165	−	0.253498i
$69$	−64.2991	+	34.0893i	−0.931872	+	0.494047i
$70$	15.8246	+	0.857985i	0.226066	+	0.0122569i
$71$	66.1839	+	77.9177i	0.932168	+	1.09743i	0.995046	+	0.0994117i	$0.0316961\pi$
$71$	66.1839	+	77.9177i	0.932168	+	1.09743i	−0.0628785	+	0.998021i	$0.520028\pi$
$72$	−4.10781	−	18.6620i	−0.0570529	−	0.259194i
$73$	49.5119	+	65.1318i	0.678245	+	0.892216i	0.998480	−	0.0551224i	$-0.0175549\pi$
$73$	49.5119	+	65.1318i	0.678245	+	0.892216i	−0.320235	+	0.947338i	$0.603762\pi$
$74$	−31.0930	+	29.4528i	−0.420175	+	0.398011i
$75$	1.95423	+	36.0436i	0.0260564	+	0.480581i
$76$	−61.3901	+	36.9372i	−0.807764	+	0.486016i
$77$	58.4539	+	39.6327i	0.759141	+	0.514711i
$78$	5.21460	−	18.7813i	0.0668538	−	0.240786i
$79$	−91.2954	+	9.92898i	−1.15564	+	0.125683i	−0.665800	−	0.746130i	$-0.731910\pi$
$79$	−91.2954	+	9.92898i	−1.15564	+	0.125683i	−0.489838	+	0.871813i	$0.662944\pi$
$80$	11.8056	+	8.97441i	0.147570	+	0.112180i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	31.3425	−	21.2507i	0.382226	−	0.259155i
$83$	−2.10729	−	6.25421i	−0.0253890	−	0.0753520i	0.934209	−	0.356725i	$-0.116107\pi$
$83$	−2.10729	−	6.25421i	−0.0253890	−	0.0753520i	−0.959598	+	0.281373i	$0.909210\pi$
$84$	−7.95496	−	48.5231i	−0.0947019	−	0.577656i
$85$	8.21138	−	50.0872i	0.0966044	−	0.589261i
$86$	−65.6128	−	22.1075i	−0.762939	−	0.257064i
$87$	14.3071	+	51.5297i	0.164450	+	0.592295i
$88$	−18.8982	−	47.4310i	−0.214753	−	0.538989i
$89$	7.81364	−	3.11324i	0.0877937	−	0.0349802i	−0.325828	−	0.945429i	$-0.605643\pi$
$89$	7.81364	−	3.11324i	0.0877937	−	0.0349802i	0.413622	+	0.910449i	$0.364264\pi$
$90$	5.19956	−	1.44365i	0.0577729	−	0.0160406i
$91$	35.8961	−	106.536i	0.394463	−	1.17072i
$92$	133.605	+	21.9034i	1.45222	+	0.238080i
$93$	−70.2024	+	11.5091i	−0.754865	+	0.123754i
$94$	47.0632	−	15.8574i	0.500672	−	0.168696i
$95$	−25.4494	−	37.5351i	−0.267889	−	0.395106i
$96$	−23.1933	+	50.1316i	−0.241597	+	0.522204i
$97$	71.2408	−	93.7156i	0.734441	−	0.966141i	−0.265557	−	0.964095i	$-0.585556\pi$
$97$	71.2408	−	93.7156i	0.734441	−	0.966141i	0.999998	−	0.00204544i	$-0.000651084\pi$
$98$	2.72948	+	25.0972i	0.0278519	+	0.256094i
$99$	23.1709	+	6.43337i	0.234049	+	0.0649835i
$100$	37.6843	−	55.5802i	0.376843	−	0.555802i
$101$	−59.5896	−	99.0387i	−0.589996	−	0.980581i	−0.997721	−	0.0674761i	$-0.978505\pi$
$101$	−59.5896	−	99.0387i	−0.589996	−	0.980581i	0.407725	−	0.913105i	$-0.366322\pi$
$102$	37.9597	−	2.05812i	0.372154	−	0.0201776i
$103$	125.135	+	132.104i	1.21491	+	1.28256i	0.947789	+	0.318898i	$0.103313\pi$
$103$	125.135	+	132.104i	1.21491	+	1.28256i	0.267118	+	0.963664i	$0.413929\pi$
$104$	−64.7026	+	49.1856i	−0.622140	+	0.472939i
$105$	30.3958	−	6.69063i	0.289484	−	0.0637203i
$106$	12.7156	−	10.8007i	0.119959	−	0.101894i
$107$	1.44307	−	26.6159i	0.0134866	−	0.248747i	−0.984014	−	0.178091i	$-0.943008\pi$
$107$	1.44307	−	26.6159i	0.0134866	−	0.248747i	0.997501	−	0.0706560i	$-0.0225093\pi$
$108$	−7.84251	−	14.7925i	−0.0726158	−	0.136968i
$109$	−2.91454	+	13.2409i	−0.0267389	+	0.121476i	−0.988099	−	0.153816i	$-0.950844\pi$
$109$	−2.91454	+	13.2409i	−0.0267389	+	0.121476i	0.961361	+	0.275292i	$0.0887746\pi$
$110$	13.0858	−	6.05415i	0.118962	−	0.0550377i
$111$	−43.3631	+	72.0700i	−0.390659	+	0.649280i
$112$	−30.0069	+	56.5989i	−0.267918	+	0.505348i
$113$	−3.25897	−	2.76819i	−0.0288404	−	0.0244973i	0.632850	−	0.774274i	$-0.281885\pi$
$113$	−3.25897	−	2.76819i	−0.0288404	−	0.0244973i	−0.661691	+	0.749777i	$0.730161\pi$
$114$	23.3584	−	24.6592i	0.204899	−	0.216309i
$115$	−9.26537	+	85.1937i	−0.0805685	+	0.740815i
$116$	36.8243	−	92.4221i	0.317451	−	0.796742i
$117$		−	38.2797i		−	0.327177i
$118$	−26.1250	+	45.0013i	−0.221399	+	0.381367i
$119$	219.258			1.84251
$120$	−20.9028	−	8.32844i	−0.174190	−	0.0694036i
$121$	−56.4142	−	6.13541i	−0.466233	−	0.0507059i
$122$	−62.6676	−	59.3619i	−0.513669	−	0.486573i
$123$	48.1446	−	56.6802i	0.391420	−	0.460815i
$124$	116.926	+	61.9903i	0.942952	+	0.499922i
$125$	80.1097	+	48.2004i	0.640877	+	0.385603i
$126$	9.78808	+	21.1566i	0.0776832	+	0.167909i
$127$	87.6442	+	19.2919i	0.690112	+	0.151905i	0.546161	−	0.837680i	$-0.316088\pi$
$127$	87.6442	+	19.2919i	0.690112	+	0.151905i	0.143950	+	0.989585i	$0.454020\pi$
$128$	113.451	−	60.1478i	0.886334	−	0.469904i
$129$	−135.775	−	7.36150i	−1.05252	−	0.0570659i
$130$	−14.8588	−	17.4931i	−0.114298	−	0.134562i
$131$	13.2832	+	60.3461i	0.101398	+	0.460657i	0.999771	+	0.0214223i	$0.00681944\pi$
$131$	13.2832	+	60.3461i	0.101398	+	0.460657i	−0.898372	+	0.439235i	$0.855250\pi$
$132$	−27.0730	−	35.6139i	−0.205099	−	0.269803i
$133$	142.225	−	134.722i	1.06936	−	1.01295i
$134$	−0.726317	−	13.3961i	−0.00542027	−	0.0999711i
$135$	9.08069	−	5.46367i	0.0672644	−	0.0404716i
$136$	−131.200	−	88.9560i	−0.964708	−	0.654088i
$137$	−48.7574	+	175.608i	−0.355893	+	1.28181i	0.541545	+	0.840672i	$0.317840\pi$
$137$	−48.7574	+	175.608i	−0.355893	+	1.28181i	−0.897438	+	0.441140i	$0.854574\pi$
$138$	−63.8090	+	6.93965i	−0.462384	+	0.0502873i
$139$	−137.731	−	104.700i	−0.990871	−	0.753241i	−0.0217343	−	0.999764i	$-0.506919\pi$
$139$	−137.731	−	104.700i	−0.990871	−	0.753241i	−0.969137	+	0.246523i	$0.920712\pi$
$140$	−52.5483	−	24.3114i	−0.375345	−	0.173653i
$141$	80.7266	−	54.7340i	0.572529	−	0.388184i
$142$	28.7894	+	85.4439i	0.202742	+	0.601718i
$143$	−16.5472	−	100.934i	−0.115715	−	0.705829i
$144$	−3.52897	+	21.5258i	−0.0245068	+	0.149485i
$145$	59.6761	+	20.1072i	0.411560	+	0.138671i
$146$	19.3037	+	69.5258i	0.132217	+	0.476204i
$147$	18.3510	+	46.0576i	0.124837	+	0.313317i
$148$	145.358	−	57.9159i	0.982148	−	0.391324i
$149$	234.819	−	65.1972i	1.57597	−	0.437565i	0.634017	−	0.773319i	$-0.281405\pi$
$149$	234.819	−	65.1972i	1.57597	−	0.437565i	0.941950	+	0.335754i	$0.108991\pi$
$150$	−10.1650	+	30.1688i	−0.0677670	+	0.201125i
$151$	−21.5206	−	3.52813i	−0.142521	−	0.0233651i	0.0900992	−	0.995933i	$-0.471282\pi$
$151$	−21.5206	−	3.52813i	−0.142521	−	0.0233651i	−0.232620	+	0.972568i	$0.574730\pi$
$152$	−139.763	+	22.9130i	−0.919495	+	0.150743i
$153$	70.7502	−	23.8385i	0.462420	−	0.155807i
$154$	34.9540	+	51.5533i	0.226974	+	0.334761i
$155$	−35.1734	+	76.0260i	−0.226925	+	0.490490i
$156$	−43.0960	+	56.6918i	−0.276256	+	0.363409i
$157$	−8.91544	−	81.9761i	−0.0567862	−	0.522141i	−0.987639	−	0.156746i	$-0.949900\pi$
$157$	−8.91544	−	81.9761i	−0.0567862	−	0.522141i	0.930853	−	0.365395i	$-0.119066\pi$
$158$	−78.0404	−	21.6678i	−0.493926	−	0.137138i
$159$	18.3872	−	27.1191i	0.115643	−	0.170560i
$160$	33.5329	+	55.7320i	0.209580	+	0.348325i
$161$	−369.653	+	20.0420i	−2.29598	+	0.124484i
$162$	5.45863	+	5.76261i	0.0336953	+	0.0355717i
$163$	−8.59461	+	6.53345i	−0.0527277	+	0.0400825i	−0.631206	−	0.775615i	$-0.717440\pi$
$163$	−8.59461	+	6.53345i	−0.0527277	+	0.0400825i	0.578478	+	0.815698i	$0.303647\pi$
$164$	−135.113	+	29.7407i	−0.823861	+	0.181346i
$165$	21.5816	−	18.3316i	0.130798	−	0.111101i
$166$	0.315120	−	5.81204i	0.00189831	−	0.0350123i
$167$	−16.8111	−	31.7092i	−0.100665	−	0.189875i	0.828064	−	0.560634i	$-0.189442\pi$
$167$	−16.8111	−	31.7092i	−0.100665	−	0.189875i	−0.928729	+	0.370759i	$0.879098\pi$
$168$	20.8953	−	94.9283i	0.124377	−	0.565050i
$169$	5.61317	−	2.59693i	0.0332140	−	0.0153664i
$170$	23.0782	−	38.3563i	0.135754	−	0.225625i
$171$	31.2455	−	58.9353i	0.182722	−	0.344651i
$172$	192.793	+	163.760i	1.12089	+	0.952094i
$173$	−26.5719	+	28.0516i	−0.153595	+	0.162148i	−0.798252	−	0.602324i	$-0.794242\pi$
$173$	−26.5719	+	28.0516i	−0.153595	+	0.162148i	0.644657	+	0.764472i	$0.277000\pi$
$174$	−5.09951	+	46.8892i	−0.0293075	+	0.269478i
$175$	−67.9622	+	170.572i	−0.388356	+	0.974699i
$176$			58.2833i			0.331155i
$177$	−25.7931	+	98.8823i	−0.145724	+	0.558657i
$178$	7.41807			0.0416746
$179$	−64.5880	−	25.7342i	−0.360827	−	0.143766i	0.182678	−	0.983173i	$-0.441524\pi$
$179$	−64.5880	−	25.7342i	−0.360827	−	0.143766i	−0.543504	+	0.839406i	$0.682903\pi$
$180$	−19.5995	−	2.13157i	−0.108886	−	0.0118421i
$181$	−168.881	−	159.973i	−0.933045	−	0.883827i	0.0603955	−	0.998175i	$-0.480764\pi$
$181$	−168.881	−	159.973i	−0.933045	−	0.883827i	−0.993441	+	0.114347i	$0.963522\pi$
$182$	64.1878	−	75.5678i	0.352680	−	0.415207i
$183$	−149.775	−	79.4057i	−0.818442	−	0.433911i
$184$	229.325	+	137.980i	1.24633	+	0.749892i
$185$	41.5862	+	89.8870i	0.224790	+	0.485876i
$186$	−61.2745	−	13.4875i	−0.329433	−	0.0725136i
$187$	176.245	−	93.4392i	0.942487	−	0.499675i
$188$	−181.176	−	9.82306i	−0.963700	−	0.0522503i
$189$	29.6377	+	34.8922i	0.156813	+	0.184615i
$190$	−8.59789	−	39.0606i	−0.0452520	−	0.205582i
$191$	13.0643	+	17.1858i	0.0683995	+	0.0899779i	0.829021	−	0.559218i	$-0.188899\pi$
$191$	13.0643	+	17.1858i	0.0683995	+	0.0899779i	−0.760621	+	0.649196i	$0.775105\pi$
$192$	1.20466	−	1.14112i	0.00627428	−	0.00594331i
$193$	−8.12766	−	149.906i	−0.0421122	−	0.776715i	−0.940973	−	0.338481i	$-0.890087\pi$
$193$	−8.12766	−	149.906i	−0.0421122	−	0.776715i	0.898861	−	0.438234i	$-0.144396\pi$
$194$	88.9610	−	53.5260i	0.458562	−	0.275907i
$195$	−37.3082	−	25.2956i	−0.191324	−	0.129721i
$196$	24.6748	−	88.8706i	0.125892	−	0.453421i
$197$	−186.144	+	20.2444i	−0.944893	+	0.102763i	−0.567576	−	0.823321i	$-0.692119\pi$
$197$	−186.144	+	20.2444i	−0.944893	+	0.102763i	−0.377317	+	0.926084i	$0.623153\pi$
$198$	16.8840	+	12.8349i	0.0852727	+	0.0648226i
$199$	179.941	+	83.2495i	0.904225	+	0.418339i	0.816194	−	0.577778i	$-0.196080\pi$
$199$	179.941	+	83.2495i	0.904225	+	0.418339i	0.0880318	+	0.996118i	$0.471942\pi$
$200$	109.871	−	74.4943i	0.549354	−	0.372471i
$201$	−8.41270	−	24.9680i	−0.0418542	−	0.124219i
$202$	−16.4918	−	100.596i	−0.0816428	−	0.497999i
$203$	−44.0100	+	268.449i	−0.216798	+	1.32241i
$204$	−131.618	−	44.3473i	−0.645186	−	0.217389i
$205$	−23.4273	−	84.3775i	−0.114280	−	0.411598i
$206$	59.4002	+	149.083i	0.288351	+	0.723706i
$207$	−117.100	+	46.6570i	−0.565702	+	0.225396i
$208$	89.3961	−	24.8207i	0.429789	−	0.119330i
$209$	56.9102	−	168.903i	0.272297	−	0.808150i
$210$	27.0877	+	4.44080i	0.128989	+	0.0211467i
$211$	55.2994	−	9.06587i	0.262082	−	0.0429662i	−0.0293081	−	0.999570i	$-0.509330\pi$
$211$	55.2994	−	9.06587i	0.262082	−	0.0429662i	0.291390	+	0.956604i	$0.405882\pi$
$212$	−57.7624	+	19.4624i	−0.272464	+	0.0918038i
$213$	99.3705	+	146.560i	0.466528	+	0.688077i
$214$	9.87088	−	21.3355i	0.0461256	−	0.0996988i
$215$	−96.8959	+	127.464i	−0.450679	+	0.592858i
$216$	−3.57845	−	32.9033i	−0.0165669	−	0.152330i
$217$	−348.677	−	96.8098i	−1.60681	−	0.446128i
$218$	−6.71029	+	9.89694i	−0.0307812	+	0.0453988i
$219$	73.0573	+	121.422i	0.333595	+	0.554439i
$220$	−52.6001	+	2.85190i	−0.239091	+	0.0129632i
$221$	−218.375	−	230.536i	−0.988123	−	1.04315i
$222$	−59.0545	+	44.8921i	−0.266011	+	0.202216i
$223$	−177.549	+	39.0815i	−0.796185	+	0.175254i	−0.594393	−	0.804175i	$-0.702608\pi$
$223$	−177.549	+	39.0815i	−0.796185	+	0.175254i	−0.201792	+	0.979428i	$0.564677\pi$
$224$	−214.148	+	181.899i	−0.956018	+	0.812049i
$225$	−3.38482	+	62.4293i	−0.0150436	+	0.277464i
$226$	−1.76645	−	3.33187i	−0.00781613	−	0.0147428i
$227$	22.5902	−	102.628i	0.0995163	−	0.452107i	−0.900341	−	0.435186i	$-0.856683\pi$
$227$	22.5902	−	102.628i	0.0995163	−	0.452107i	0.999857	−	0.0169210i	$-0.00538637\pi$
$228$	−112.625	+	52.1057i	−0.493967	+	0.228534i
$229$	−100.488	+	167.013i	−0.438814	+	0.729315i	−0.994797	−	0.101879i	$-0.967515\pi$
$229$	−100.488	+	167.013i	−0.438814	+	0.729315i	0.555982	+	0.831194i	$0.312342\pi$
$230$	−35.4020	+	66.7753i	−0.153922	+	0.290328i
$231$	93.2297	+	79.1900i	0.403592	+	0.342814i
$232$	135.248	−	142.780i	0.582967	−	0.615430i
$233$	−1.11447	+	10.2474i	−0.00478312	+	0.0439800i	−0.996286	−	0.0861025i	$-0.972559\pi$
$233$	−1.11447	+	10.2474i	−0.00478312	+	0.0439800i	0.991503	+	0.130083i	$0.0415242\pi$
$234$	12.4961	−	31.3629i	0.0534022	−	0.134030i
$235$		−	114.846i		−	0.488708i
$236$	149.523	−	117.405i	0.633571	−	0.497479i
$237$	−159.061			−0.671142
$238$	179.640	+	71.5752i	0.754791	+	0.300736i
$239$	−54.3324	−	5.90900i	−0.227332	−	0.0247239i	−0.00625613	−	0.999980i	$-0.501991\pi$
$239$	−54.3324	−	5.90900i	−0.227332	−	0.0247239i	−0.221076	+	0.975257i	$0.570957\pi$
$240$	18.6475	+	17.6638i	0.0776978	+	0.0735993i
$241$	18.6218	−	21.9233i	0.0772688	−	0.0909679i	−0.722169	−	0.691716i	$-0.756855\pi$
$241$	18.6218	−	21.9233i	0.0772688	−	0.0909679i	0.799438	+	0.600749i	$0.205131\pi$
$242$	−44.2178	−	23.4428i	−0.182718	−	0.0968710i
$243$	13.3571	+	8.03669i	0.0549674	+	0.0330728i
$244$	132.419	+	286.218i	0.542699	+	1.17303i
$245$	57.0151	+	12.5500i	0.232715	+	0.0512244i
$246$	57.9482	−	30.7222i	0.235562	−	0.124887i
$247$	−283.303	−	15.3603i	−1.14698	−	0.0621873i
$248$	169.365	+	199.392i	0.682925	+	0.804001i
$249$	−2.45732	−	11.1637i	−0.00986877	−	0.0448343i
$250$	49.8999	+	65.6422i	0.199600	+	0.262569i
$251$	−216.448	+	205.030i	−0.862343	+	0.816854i	−0.984450	−	0.175662i	$-0.943793\pi$
$251$	−216.448	+	205.030i	−0.862343	+	0.816854i	0.122108	+	0.992517i	$0.461035\pi$
$252$	−4.61082	−	85.0415i	−0.0182969	−	0.337466i
$253$	−288.594	+	173.641i	−1.14069	+	0.686330i
$254$	65.5099	+	44.4168i	0.257913	+	0.174869i
$255$	23.5189	−	84.7073i	0.0922308	−	0.332185i
$256$	108.776	−	11.8301i	0.424908	−	0.0462115i
$257$	−198.006	−	150.520i	−0.770452	−	0.585683i	0.144377	−	0.989523i	$-0.453882\pi$
$257$	−198.006	−	150.520i	−0.770452	−	0.585683i	−0.914830	+	0.403840i	$0.867675\pi$
$258$	−108.838	−	50.3540i	−0.421855	−	0.195171i
$259$	−354.121	+	240.100i	−1.36726	+	0.927027i
$260$	26.7747	+	79.4646i	0.102980	+	0.305633i
$261$	14.9856	+	91.4081i	0.0574161	+	0.350223i
$262$	−8.81650	+	53.7783i	−0.0336508	+	0.205261i
$263$	−139.883	−	47.1322i	−0.531876	−	0.179210i	0.0405332	−	0.999178i	$-0.487094\pi$
$263$	−139.883	−	47.1322i	−0.531876	−	0.179210i	−0.572409	+	0.819968i	$0.693991\pi$
$264$	−23.6585	−	85.2104i	−0.0896157	−	0.322767i
$265$	−14.2804	−	35.8411i	−0.0538882	−	0.135249i
$266$	160.505	−	63.9510i	0.603402	−	0.240417i
$267$	14.0373	−	3.89743i	0.0525741	−	0.0145971i
$268$	−15.6503	+	46.4485i	−0.0583967	+	0.173315i
$269$	−35.2447	−	5.77807i	−0.131021	−	0.0214798i	0.0959145	−	0.995390i	$-0.469422\pi$
$269$	−35.2447	−	5.77807i	−0.131021	−	0.0214798i	−0.226936	+	0.973910i	$0.572871\pi$
$270$	9.22347	−	1.51211i	0.0341610	−	0.00560041i
$271$	477.534	−	160.900i	1.76212	−	0.593726i	0.763476	−	0.645836i	$-0.223491\pi$
$271$	477.534	−	160.900i	1.76212	−	0.593726i	0.998641	+	0.0521096i	$0.0165945\pi$
$272$	101.546	+	149.769i	0.373330	+	0.550620i
$273$	81.7602	−	176.722i	0.299488	−	0.647332i
$274$	−97.2734	+	127.961i	−0.355012	+	0.467011i
$275$	18.0615	+	166.073i	0.0656782	+	0.603901i
$276$	225.952	+	62.7351i	0.818665	+	0.227301i
$277$	−41.8422	+	61.7126i	−0.151055	+	0.222789i	−0.895686	−	0.444687i	$-0.853315\pi$
$277$	−41.8422	+	61.7126i	−0.151055	+	0.222789i	0.744631	+	0.667476i	$0.232625\pi$
$278$	−78.6656	−	130.743i	−0.282970	−	0.470300i
$279$	−123.037	+	6.67085i	−0.440991	+	0.0239099i
$280$	−78.7112	−	83.0944i	−0.281112	−	0.296766i
$281$	373.261	−	283.746i	1.32833	−	1.00977i	0.330509	−	0.943803i	$-0.392780\pi$
$281$	373.261	−	283.746i	1.32833	−	1.00977i	0.997822	−	0.0659680i	$-0.0210135\pi$
$282$	84.0075	−	18.4915i	0.297899	−	0.0655725i
$283$	89.2486	−	75.8084i	0.315366	−	0.267874i	−0.475697	−	0.879609i	$-0.657804\pi$
$283$	89.2486	−	75.8084i	0.315366	−	0.267874i	0.791063	+	0.611735i	$0.209528\pi$
$284$	17.8339	−	328.927i	0.0627955	−	1.15819i
$285$	−36.7922	−	69.3974i	−0.129095	−	0.243500i
$286$	19.3917	−	88.0974i	0.0678032	−	0.308033i
$287$	343.325	−	158.839i	1.19625	−	0.553446i
$288$	−49.3245	+	81.9780i	−0.171266	+	0.284646i
$289$	154.724	−	291.841i	0.535378	−	1.00983i
$290$	42.3293	+	35.9549i	0.145963	+	0.123982i
$291$	140.219	−	148.028i	0.481853	−	0.508686i
$292$	28.5023	−	262.074i	0.0976105	−	0.897514i
$293$	137.987	−	346.320i	0.470944	−	1.18198i	−0.481277	−	0.876569i	$-0.659827\pi$
$293$	137.987	−	346.320i	0.470944	−	1.18198i	0.952221	−	0.305411i	$-0.0987938\pi$
$294$			43.7259i			0.148728i
$295$	79.3284	+	90.4808i	0.268910	+	0.306715i
$296$	309.311			1.04497
$297$	38.6931	+	15.4168i	0.130280	+	0.0519083i
$298$	213.672	+	23.2383i	0.717022	+	0.0779808i
$299$	389.236	+	368.704i	1.30179	+	1.23312i
$300$	75.2969	−	88.6464i	0.250990	−	0.295488i
$301$	−611.094	−	323.981i	−2.03021	−	1.07635i
$302$	−16.4803	−	9.91588i	−0.0545706	−	0.0328340i
$303$	−84.0604	−	181.694i	−0.277427	−	0.599649i
$304$	157.894	+	34.7550i	0.519387	+	0.114326i
$305$	−176.363	+	93.5017i	−0.578239	+	0.306563i
$306$	65.7482	+	3.56476i	0.214863	+	0.0116496i
$307$	−25.7497	−	30.3149i	−0.0838752	−	0.0987455i	0.718624	−	0.695399i	$-0.244772\pi$
$307$	−25.7497	−	30.3149i	−0.0838752	−	0.0987455i	−0.802499	+	0.596654i	$0.796497\pi$
$308$	−48.9185	−	222.239i	−0.158826	−	0.721555i
$309$	190.732	+	250.903i	0.617254	+	0.811984i
$310$	−53.6359	+	50.8067i	−0.173019	+	0.163892i
$311$	19.8752	+	366.577i	0.0639074	+	1.17870i	0.838014	+	0.545648i	$0.183716\pi$
$311$	19.8752	+	366.577i	0.0639074	+	1.17870i	−0.774107	+	0.633055i	$0.781801\pi$
$312$	−120.622	+	72.5759i	−0.386609	+	0.232615i
$313$	−52.4127	−	35.5367i	−0.167453	−	0.113536i	0.474582	−	0.880211i	$-0.342599\pi$
$313$	−52.4127	−	35.5367i	−0.167453	−	0.113536i	−0.642035	+	0.766675i	$0.721910\pi$
$314$	19.4560	−	70.0741i	0.0619617	−	0.223166i
$315$	53.5915	−	5.82842i	0.170132	−	0.0185029i
$316$	235.567	+	179.073i	0.745465	+	0.566688i
$317$	381.592	+	176.543i	1.20376	+	0.556919i	0.916153	−	0.400829i	$-0.131278\pi$
$317$	381.592	+	176.543i	1.20376	+	0.556919i	0.287608	+	0.957748i	$0.407140\pi$
$318$	23.9176	−	16.2165i	0.0752126	−	0.0509954i
$319$	79.0262	+	234.541i	0.247731	+	0.735239i
$320$	−0.316103	−	1.92815i	−0.000987823	−	0.00602545i
$321$	7.46912	−	45.5596i	0.0232683	−	0.141930i
$322$	−309.402	−	104.250i	−0.960876	−	0.323757i
$323$	−148.036	−	533.179i	−0.458317	−	1.65071i
$324$	−10.7338	−	26.9399i	−0.0331291	−	0.0831478i
$325$	247.034	−	98.4274i	0.760105	−	0.302854i
$326$	−9.17444	+	2.54727i	−0.0281424	+	0.00781371i
$327$	−7.49813	+	22.2536i	−0.0229301	+	0.0680540i
$328$	−269.883	−	44.2450i	−0.822813	−	0.134893i
$329$	489.586	−	80.2635i	1.48810	−	0.243962i
$330$	23.6662	−	7.97407i	0.0717158	−	0.0241639i
$331$	130.245	+	192.097i	0.393489	+	0.580353i	0.971900	−	0.235392i	$-0.0756375\pi$
$331$	130.245	+	192.097i	0.393489	+	0.580353i	−0.578411	+	0.815745i	$0.696327\pi$
$332$	−8.92907	+	19.2999i	−0.0268948	+	0.0581321i
$333$	−88.1632	+	115.977i	−0.264754	+	0.348278i
$334$	−3.42229	−	31.4674i	−0.0102464	−	0.0942139i
$335$	−29.8935	−	8.29989i	−0.0892343	−	0.0247758i
$336$	−62.2679	+	91.8382i	−0.185321	+	0.273328i
$337$	99.6933	+	165.692i	0.295826	+	0.491666i	0.968748	−	0.248047i	$-0.0797887\pi$
$337$	99.6933	+	165.692i	0.295826	+	0.491666i	−0.672922	+	0.739713i	$0.734961\pi$
$338$	5.44667	−	0.295310i	0.0161144	−	0.000873697i
$339$	−5.09322	−	5.37684i	−0.0150242	−	0.0158609i
$340$	−130.196	+	98.9725i	−0.382930	+	0.291096i
$341$	−321.532	+	70.7745i	−0.942908	+	0.207550i
$342$	44.8387	−	38.0863i	0.131107	−	0.111364i
$343$	9.71896	−	179.256i	0.0283352	−	0.522612i
$344$	234.224	+	441.793i	0.680884	+	1.28428i
$345$	−31.9080	+	144.960i	−0.0924871	+	0.420173i
$346$	−30.9278	+	14.3087i	−0.0893867	+	0.0413547i
$347$	46.3763	−	77.0779i	0.133649	−	0.222127i	−0.782804	−	0.622268i	$-0.786211\pi$
$347$	46.3763	−	77.0779i	0.133649	−	0.222127i	0.916453	+	0.400141i	$0.131039\pi$
$348$	80.7154	−	152.245i	0.231941	−	0.437487i
$349$	−215.168	−	182.765i	−0.616526	−	0.523682i	0.283808	−	0.958881i	$-0.408402\pi$
$349$	−215.168	−	182.765i	−0.616526	−	0.523682i	−0.900334	+	0.435199i	$0.856678\pi$
$350$	−111.364	+	117.566i	−0.318183	+	0.335902i
$351$	7.16855	−	65.9137i	0.0204232	−	0.187788i
$352$	−94.6191	+	237.476i	−0.268804	+	0.674648i
$353$		−	525.030i		−	1.48734i	−0.668549	−	0.743668i	$-0.733084\pi$
$353$		−	525.030i		−	1.48734i	0.668549	−	0.743668i	$-0.266916\pi$
$354$	−53.4119	+	72.5952i	−0.150881	+	0.205071i
$355$	208.506			0.587340
$356$	−25.1768	−	10.0314i	−0.0707215	−	0.0281780i
$357$	377.540	+	41.0600i	1.05754	+	0.115014i
$358$	−44.5168	−	42.1685i	−0.124348	−	0.117789i
$359$	−121.749	+	143.334i	−0.339135	+	0.399260i	−0.905121	−	0.425155i	$-0.860220\pi$
$359$	−121.749	+	143.334i	−0.339135	+	0.399260i	0.565986	+	0.824415i	$0.308496\pi$
$360$	−34.4328	−	18.2551i	−0.0956468	−	0.0507087i
$361$	−114.309	−	68.7777i	−0.316646	−	0.190520i
$362$	−86.1439	−	186.197i	−0.237967	−	0.514357i
$363$	−95.9905	−	21.1291i	−0.264437	−	0.0582069i
$364$	−320.042	+	169.676i	−0.879237	+	0.466142i
$365$	166.617	+	9.03373i	0.456486	+	0.0247499i
$366$	−96.7906	−	113.951i	−0.264455	−	0.311341i
$367$	125.273	+	569.120i	0.341343	+	1.55074i	0.764466	+	0.644664i	$0.223003\pi$
$367$	125.273	+	569.120i	0.341343	+	1.55074i	−0.423123	+	0.906072i	$0.639066\pi$
$368$	−184.888	−	243.216i	−0.502414	−	0.660914i
$369$	93.5145	−	88.5816i	0.253427	−	0.240059i
$370$	4.72897	+	87.2207i	0.0127810	+	0.235732i
$371$	142.809	−	85.9251i	0.384929	−	0.231604i
$372$	189.726	+	128.637i	0.510016	+	0.345799i
$373$	123.072	−	443.264i	0.329951	−	1.18838i	−0.593555	−	0.804793i	$-0.702276\pi$
$373$	123.072	−	443.264i	0.329951	−	1.18838i	0.923506	−	0.383583i	$-0.125310\pi$
$374$	174.902	−	19.0217i	0.467651	−	0.0508601i
$375$	128.914	+	97.9981i	0.343771	+	0.261328i
$376$	−325.523	−	150.603i	−0.865753	−	0.400540i
$377$	326.090	−	221.094i	0.864960	−	0.586457i
$378$	12.8921	+	38.2625i	0.0341062	+	0.101223i
$379$	20.7742	+	126.717i	0.0548131	+	0.334345i	0.999970	+	0.00772901i	$0.00246024\pi$
$379$	20.7742	+	126.717i	0.0548131	+	0.334345i	−0.945157	+	0.326616i	$0.894091\pi$
$380$	−23.6401	+	144.198i	−0.0622107	+	0.379469i
$381$	147.302	+	49.6317i	0.386618	+	0.130267i
$382$	5.09352	+	18.3452i	0.0133338	+	0.0480241i
$383$	−201.982	−	506.936i	−0.527368	−	1.32359i	−0.915622	−	0.402041i	$-0.868301\pi$
$383$	−201.982	−	506.936i	−0.527368	−	1.32359i	0.388254	−	0.921552i	$-0.373078\pi$
$384$	206.614	−	82.3226i	0.538058	−	0.214382i
$385$	138.787	−	38.5341i	0.360486	−	0.100088i
$386$	42.2766	−	125.472i	0.109525	−	0.325058i
$387$	−232.412	−	38.1020i	−0.600548	−	0.0984548i
$388$	−374.315	+	61.3658i	−0.964730	+	0.158159i
$389$	−539.133	+	181.655i	−1.38595	+	0.466980i	−0.910771	−	0.412911i	$-0.864512\pi$
$389$	−539.133	+	181.655i	−1.38595	+	0.466980i	−0.475175	+	0.879891i	$0.657615\pi$
$390$	−22.3094	−	32.9039i	−0.0572035	−	0.0843688i
$391$	−439.060	+	949.013i	−1.12292	+	2.42714i
$392$	110.338	−	145.148i	0.281475	−	0.370274i
$393$	11.5714	+	106.397i	0.0294438	+	0.270731i
$394$	−159.118	−	44.1789i	−0.403853	−	0.112129i
$395$	−105.109	+	155.024i	−0.266098	+	0.392465i
$396$	−39.9476	−	66.3934i	−0.100878	−	0.167660i
$397$	91.2267	−	4.94617i	0.229790	−	0.0124589i	0.0611158	−	0.998131i	$-0.480534\pi$
$397$	91.2267	−	4.94617i	0.229790	−	0.0124589i	0.168674	+	0.985672i	$0.446051\pi$
$398$	120.251	+	126.947i	0.302138	+	0.318963i
$399$	270.125	−	205.344i	0.677005	−	0.514646i
$400$	−147.988	+	32.5747i	−0.369971	+	0.0814368i
$401$	−29.5665	+	25.1140i	−0.0737319	+	0.0626284i	−0.683494	−	0.729956i	$-0.739541\pi$
$401$	−29.5665	+	25.1140i	−0.0737319	+	0.0626284i	0.609763	+	0.792584i	$0.291265\pi$
$402$	1.25802	−	23.2028i	0.00312940	−	0.0577183i
$403$	245.484	+	463.031i	0.609141	+	1.14896i
$404$	−80.0614	+	363.723i	−0.198172	+	0.900304i
$405$	16.6592	−	7.70736i	0.0411338	−	0.0190305i
$406$	−123.691	+	205.576i	−0.304658	+	0.506345i
$407$	−182.330	+	343.910i	−0.447985	+	0.844989i
$408$	−209.255	−	177.743i	−0.512879	−	0.435644i
$409$	−104.719	+	110.551i	−0.256038	+	0.270296i	−0.841324	−	0.540531i	$-0.818223\pi$
$409$	−104.719	+	110.551i	−0.256038	+	0.270296i	0.585287	+	0.810827i	$0.300982\pi$
$410$	8.35021	−	76.7789i	0.0203664	−	0.187266i
$411$	−116.841	+	293.249i	−0.284285	+	0.713501i
$412$		−	586.313i		−	1.42309i
$413$	−330.275	+	401.408i	−0.799698	+	0.971933i
$414$	−111.172			−0.268532
$415$	−12.5042	−	4.98214i	−0.0301307	−	0.0120052i
$416$	404.540	+	43.9964i	0.972453	+	0.105761i
$417$	−217.552	−	206.076i	−0.521707	−	0.494187i
$418$	101.764	−	119.806i	0.243455	−	0.286617i
$419$	−284.731	−	150.955i	−0.679550	−	0.360274i	0.0926104	−	0.995702i	$-0.470479\pi$
$419$	−284.731	−	150.955i	−0.679550	−	0.360274i	−0.772160	+	0.635428i	$0.780824\pi$
$420$	−85.9300	−	51.7024i	−0.204595	−	0.123101i
$421$	−63.7866	−	137.872i	−0.151512	−	0.327488i	0.816926	−	0.576743i	$-0.195676\pi$
$421$	−63.7866	−	137.872i	−0.151512	−	0.327488i	−0.968438	+	0.249255i	$0.919814\pi$
$422$	48.2667	+	10.6243i	0.114376	+	0.0251761i
$423$	149.253	−	79.1289i	0.352844	−	0.187066i
$424$	−120.315	−	6.52330i	−0.283762	−	0.0153851i
$425$	335.757	+	395.284i	0.790017	+	0.930080i
$426$	33.5715	+	152.517i	0.0788064	+	0.358021i
$427$	−521.850	−	686.482i	−1.22213	−	1.60769i
$428$	−62.3535	+	59.0643i	−0.145686	+	0.138001i
$429$	−9.59102	−	176.896i	−0.0223567	−	0.412345i
$430$	−120.997	+	72.8018i	−0.281389	+	0.169306i
$431$	−142.741	−	96.7808i	−0.331185	−	0.224549i	0.384248	−	0.923230i	$-0.374461\pi$
$431$	−142.741	−	96.7808i	−0.331185	−	0.224549i	−0.715434	+	0.698680i	$0.753771\pi$
$432$	−10.1076	+	36.4043i	−0.0233972	+	0.0842693i
$433$	−462.975	+	50.3515i	−1.06923	+	0.116285i	−0.625767	−	0.780010i	$-0.715214\pi$
$433$	−462.975	+	50.3515i	−1.06923	+	0.116285i	−0.443458	+	0.896295i	$0.646249\pi$
$434$	−254.072	−	193.140i	−0.585418	−	0.445024i
$435$	98.9908	+	45.7980i	0.227565	+	0.105283i
$436$	36.1582	−	24.5159i	0.0829316	−	0.0562290i
$437$	298.315	+	885.367i	0.682642	+	2.02601i
$438$	20.2191	+	123.331i	0.0461624	+	0.281578i
$439$	−66.4928	+	405.588i	−0.151464	+	0.923891i	0.796296	+	0.604907i	$0.206790\pi$
$439$	−66.4928	+	405.588i	−0.151464	+	0.923891i	−0.947760	+	0.318984i	$0.896658\pi$
$440$	−98.6815	−	33.2497i	−0.224276	−	0.0755674i
$441$	22.9735	+	82.7430i	0.0520940	+	0.187626i
$442$	−103.660	−	260.167i	−0.234525	−	0.588613i
$443$	283.050	−	112.778i	0.638940	−	0.254577i	−0.0280930	−	0.999605i	$-0.508943\pi$
$443$	283.050	−	112.778i	0.638940	−	0.254577i	0.667033	+	0.745029i	$0.267564\pi$
$444$	261.137	−	72.5044i	0.588147	−	0.163298i
$445$	5.47744	−	16.2565i	0.0123089	−	0.0365314i
$446$	−158.226	−	25.9398i	−0.354766	−	0.0581609i
$447$	416.544	−	68.2889i	0.931865	−	0.152772i
$448$	7.99869	−	2.69507i	0.0178542	−	0.00601578i
$449$	−118.935	−	175.416i	−0.264889	−	0.390682i	0.671863	−	0.740675i	$-0.265494\pi$
$449$	−118.935	−	175.416i	−0.264889	−	0.390682i	−0.936752	+	0.349993i	$0.886184\pi$
$450$	−23.1528	+	50.0440i	−0.0514507	+	0.111209i
$451$	208.282	−	273.990i	0.461822	−	0.607517i
$452$	1.48965	+	13.6971i	0.00329568	+	0.0303033i
$453$	−36.3956	−	10.1052i	−0.0803435	−	0.0223073i
$454$	52.0106	−	76.7099i	0.114561	−	0.168964i
$455$	−118.209	−	196.464i	−0.259799	−	0.431790i
$456$	−244.949	+	13.2807i	−0.537168	+	0.0291244i
$457$	−413.575	−	436.606i	−0.904979	−	0.955375i	0.0942135	−	0.995552i	$-0.469966\pi$
$457$	−413.575	−	436.606i	−0.904979	−	0.955375i	−0.999193	+	0.0401772i	$0.987208\pi$
$458$	−136.851	+	104.032i	−0.298802	+	0.227143i
$459$	126.289	−	27.7983i	0.275139	−	0.0605627i
$460$	210.454	−	178.761i	0.457508	−	0.388611i
$461$	17.0765	−	314.957i	0.0370423	−	0.683205i	−0.919763	−	0.392475i	$-0.871619\pi$
$461$	17.0765	−	314.957i	0.0370423	−	0.683205i	0.956805	−	0.290730i	$-0.0938981\pi$
$462$	50.5329	+	95.3152i	0.109379	+	0.206310i
$463$	57.0114	−	259.006i	0.123135	−	0.559407i	−0.874143	−	0.485669i	$-0.838576\pi$
$463$	57.0114	−	259.006i	0.123135	−	0.559407i	0.997278	−	0.0737382i	$-0.0234929\pi$
$464$	−203.752	+	94.2658i	−0.439121	+	0.203159i
$465$	−74.8021	+	124.322i	−0.160865	+	0.267359i
$466$	−4.25826	+	8.03194i	−0.00913790	+	0.0172359i
$467$	582.475	+	494.759i	1.24727	+	1.05944i	0.995798	+	0.0915760i	$0.0291905\pi$
$467$	582.475	+	494.759i	1.24727	+	1.05944i	0.251472	+	0.967865i	$0.419085\pi$
$468$	−84.8234	+	89.5470i	−0.181247	+	0.191340i
$469$	14.4902	−	133.235i	0.0308960	−	0.284084i
$470$	37.4908	−	94.0947i	0.0797676	−	0.200202i
$471$		−	142.824i		−	0.303236i
$472$	360.487	−	106.199i	0.763744	−	0.224997i
$473$	−629.280			−1.33040
$474$	−130.320	−	51.9242i	−0.274936	−	0.109545i
$475$	460.673	+	50.1013i	0.969839	+	0.105476i
$476$	−512.907	−	485.851i	−1.07753	−	1.02070i
$477$	36.7394	−	43.2530i	0.0770218	−	0.0906771i
$478$	−42.5861	−	22.5777i	−0.0890922	−	0.0472337i
$479$	85.1234	+	51.2170i	0.177711	+	0.106925i	0.601630	−	0.798775i	$-0.294518\pi$
$479$	85.1234	+	51.2170i	0.177711	+	0.106925i	−0.423919	+	0.905700i	$0.639346\pi$
$480$	47.3033	+	102.244i	0.0985486	+	0.213009i
$481$	605.144	+	133.202i	1.25810	+	0.276928i
$482$	22.4137	−	11.8830i	0.0465014	−	0.0246535i
$483$	−640.257	−	34.7137i	−1.32558	−	0.0718711i
$484$	118.373	+	139.360i	0.244573	+	0.287933i
$485$	−51.6126	−	234.478i	−0.106418	−	0.483461i
$486$	8.32006	+	10.9448i	0.0171195	+	0.0225203i
$487$	−449.585	+	425.869i	−0.923172	+	0.874475i	−0.992391	−	0.123126i	$-0.960708\pi$
$487$	−449.585	+	425.869i	−0.923172	+	0.874475i	0.0692188	+	0.997602i	$0.477949\pi$
$488$	33.7509	+	622.500i	0.0691618	+	1.27561i
$489$	−16.0225	+	9.64044i	−0.0327659	+	0.0197146i
$490$	42.6161	+	28.8945i	0.0869717	+	0.0589683i
$491$	195.329	−	703.512i	0.397819	−	1.43282i	−0.445442	−	0.895311i	$-0.646953\pi$
$491$	195.329	−	703.512i	0.397819	−	1.43282i	0.843261	−	0.537504i	$-0.180633\pi$
$492$	−238.221	+	25.9081i	−0.484188	+	0.0526586i
$493$	611.707	+	465.008i	1.24079	+	0.943221i
$494$	−227.099	−	105.067i	−0.459714	−	0.212686i
$495$	40.5942	−	27.5236i	0.0820086	−	0.0556032i
$496$	−95.3561	−	283.007i	−0.192250	−	0.570578i
$497$	145.720	+	888.851i	0.293199	+	1.78843i
$498$	1.63101	−	9.94872i	0.00327512	−	0.0199774i
$499$	720.645	+	242.814i	1.44418	+	0.486601i	0.928871	−	0.370404i	$-0.120781\pi$
$499$	720.645	+	242.814i	1.44418	+	0.486601i	0.515308	+	0.857005i	$0.327677\pi$
$500$	−80.5925	−	290.268i	−0.161185	−	0.580536i
$501$	−23.0089	−	57.7481i	−0.0459260	−	0.115266i
$502$	−244.268	+	97.3254i	−0.486590	+	0.193875i
$503$	623.522	−	173.120i	1.23961	−	0.344175i	0.414969	−	0.909836i	$-0.363793\pi$
$503$	623.522	−	173.120i	1.23961	−	0.344175i	0.824638	+	0.565661i	$0.191379\pi$
$504$	53.7566	−	159.544i	0.106660	−	0.316555i
$505$	−232.630	−	38.1378i	−0.460654	−	0.0755203i
$506$	−293.132	+	48.0565i	−0.579312	+	0.0949734i
$507$	10.1516	−	3.42048i	0.0200229	−	0.00674651i
$508$	−162.276	−	239.339i	−0.319440	−	0.471139i
$509$	−26.0331	+	56.2696i	−0.0511455	+	0.110549i	−0.931463	−	0.363835i	$-0.881467\pi$
$509$	−26.0331	+	56.2696i	−0.0511455	+	0.110549i	0.880318	+	0.474384i	$0.157329\pi$
$510$	46.9213	−	61.7239i	0.0920025	−	0.121027i
$511$	77.9345	+	716.596i	0.152514	+	1.40234i
$512$	−401.930	−	111.595i	−0.785019	−	0.217960i
$513$	64.8382	−	95.6292i	0.126390	−	0.186412i
$514$	−113.092	−	187.960i	−0.220023	−	0.365682i
$515$	370.572	−	20.0918i	0.719558	−	0.0390133i
$516$	301.303	+	318.082i	0.583921	+	0.616438i
$517$	359.335	−	273.160i	0.695040	−	0.528355i
$518$	−368.513	+	81.1159i	−0.711416	+	0.156594i
$519$	−51.0072	+	43.3259i	−0.0982798	+	0.0834796i
$520$	−8.97421	+	165.519i	−0.0172581	+	0.318307i
$521$	170.281	+	321.185i	0.326836	+	0.616478i	0.991417	−	0.130738i	$-0.0417348\pi$
$521$	170.281	+	321.185i	0.326836	+	0.616478i	−0.664581	+	0.747216i	$0.731390\pi$
$522$	−17.5617	+	79.7834i	−0.0336430	+	0.152842i
$523$	−290.621	+	134.456i	−0.555681	+	0.257085i	−0.677570	−	0.735458i	$-0.736967\pi$
$523$	−290.621	+	134.456i	−0.555681	+	0.257085i	0.121889	+	0.992544i	$0.461105\pi$
$524$	102.647	−	170.600i	0.195891	−	0.325573i
$525$	−148.967	+	280.981i	−0.283746	+	0.535202i
$526$	−99.2216	−	84.2796i	−0.188634	−	0.160227i
$527$	−702.921	+	742.064i	−1.33382	+	1.40809i
$528$	−10.9146	+	100.358i	−0.0206715	+	0.190072i
$529$	457.671	−	1148.67i	0.865162	−	2.17139i
$530$		−	34.0266i		−	0.0642012i
$531$	−62.9306	+	165.435i	−0.118513	+	0.311554i
$532$	−631.232			−1.18653
$533$	−508.951	−	202.785i	−0.954880	−	0.380459i
$534$	12.7732	+	1.38916i	0.0239198	+	0.00260143i
$535$	−39.4676	−	37.3857i	−0.0737713	−	0.0698798i
$536$	−62.7260	+	73.8468i	−0.117026	+	0.137774i
$537$	−106.395	−	56.4069i	−0.198128	−	0.105041i
$538$	−26.9901	−	16.2394i	−0.0501674	−	0.0301847i
$539$	96.3424	+	208.241i	0.178743	+	0.386346i
$540$	−33.3491	−	7.34070i	−0.0617577	−	0.0135939i
$541$	515.798	−	273.459i	0.953417	−	0.505469i	0.0823333	−	0.996605i	$-0.473763\pi$
$541$	515.798	−	273.459i	0.953417	−	0.505469i	0.871083	+	0.491135i	$0.163418\pi$
$542$	443.772	+	24.0606i	0.818768	+	0.0443923i
$543$	−260.838	−	307.083i	−0.480365	−	0.565530i
$544$	170.610	+	775.088i	0.313621	+	1.42479i
$545$	16.7340	+	22.0132i	0.0307046	+	0.0403912i
$546$	124.676	−	118.100i	0.228345	−	0.216300i
$547$	−43.6691	−	805.429i	−0.0798338	−	1.47245i	−0.714486	−	0.699650i	$-0.753339\pi$
$547$	−43.6691	−	805.429i	−0.0798338	−	1.47245i	0.634652	−	0.772798i	$-0.281143\pi$
$548$	503.185	−	302.756i	0.918220	−	0.552475i
$549$	−243.027	−	164.776i	−0.442672	−	0.300139i
$550$	−39.4153	+	141.961i	−0.0716642	+	0.258111i
$551$	682.513	−	74.2278i	1.23868	−	0.134715i
$552$	369.034	+	280.533i	0.668541	+	0.508211i
$553$	−734.318	−	339.732i	−1.32788	−	0.614343i
$554$	−54.4273	+	36.9026i	−0.0982442	+	0.0666112i
$555$	54.7742	+	162.564i	0.0986922	+	0.292908i
$556$	90.1876	+	550.120i	0.162208	+	0.989424i
$557$	−57.7167	+	352.056i	−0.103621	+	0.632058i	0.883044	+	0.469291i	$0.155490\pi$
$557$	−57.7167	+	352.056i	−0.103621	+	0.632058i	−0.986664	+	0.162767i	$0.947958\pi$
$558$	−102.983	−	34.6989i	−0.184557	−	0.0621844i
$559$	267.987	+	965.202i	0.479404	+	1.72666i
$560$	48.3602	+	121.375i	0.0863575	+	0.216741i
$561$	320.974	−	127.888i	0.572146	−	0.227964i
$562$	398.443	−	110.627i	0.708973	−	0.196845i
$563$	191.951	−	569.689i	0.340943	−	1.01188i	−0.630822	−	0.775928i	$-0.717282\pi$
$563$	191.951	−	569.689i	0.340943	−	1.01188i	0.971764	−	0.235954i	$-0.0758214\pi$
$564$	−310.126	−	50.8426i	−0.549869	−	0.0901465i
$565$	−8.60602	+	1.41089i	−0.0152319	+	0.00249714i
$566$	97.8693	−	32.9760i	0.172914	−	0.0582615i
$567$	44.4989	+	65.6309i	0.0784813	+	0.115751i
$568$	273.422	−	590.993i	0.481377	−	1.04048i
$569$	−87.8924	+	115.620i	−0.154468	+	0.203199i	−0.866817	−	0.498626i	$-0.833838\pi$
$569$	−87.8924	+	115.620i	−0.154468	+	0.203199i	0.712349	+	0.701825i	$0.247631\pi$
$570$	−7.48990	−	68.8685i	−0.0131402	−	0.120822i
$571$	826.888	+	229.584i	1.44814	+	0.402074i	0.900579	−	0.434692i	$-0.143143\pi$
$571$	826.888	+	229.584i	1.44814	+	0.402074i	0.547561	+	0.836766i	$0.315557\pi$
$572$	−184.948	+	272.779i	−0.323336	+	0.476885i
$573$	19.2770	+	32.0387i	0.0336423	+	0.0559139i
$574$	333.141	−	18.0624i	0.580385	−	0.0314676i
$575$	−602.193	−	635.727i	−1.04729	−	1.10561i
$576$	2.28800	−	1.73929i	0.00397222	−	0.00301960i
$577$	475.785	−	104.728i	0.824584	−	0.181505i	0.217417	−	0.976079i	$-0.430237\pi$
$577$	475.785	−	104.728i	0.824584	−	0.181505i	0.607167	+	0.794574i	$0.292306\pi$
$578$	222.036	−	188.599i	0.384145	−	0.326296i
$579$	14.0775	−	259.645i	0.0243135	−	0.448436i
$580$	−95.0439	−	179.272i	−0.163869	−	0.309089i
$581$	12.4997	−	56.7869i	0.0215142	−	0.0977399i
$582$	163.205	−	75.5068i	0.280422	−	0.129737i
$583$	78.1751	−	129.928i	0.134091	−	0.222861i
$584$	244.098	−	460.417i	0.417976	−	0.788386i
$585$	−59.5038	−	50.5430i	−0.101716	−	0.0863983i
$586$	226.107	−	238.698i	0.385848	−	0.407335i
$587$	92.6144	−	851.575i	0.157776	−	1.45072i	−0.600936	−	0.799297i	$-0.705205\pi$
$587$	92.6144	−	851.575i	0.157776	−	1.45072i	0.758711	−	0.651427i	$-0.225829\pi$
$588$	59.1301	−	148.405i	0.100561	−	0.252390i
$589$			913.255i			1.55052i
$590$	35.4576	+	100.028i	0.0600977	+	0.169539i
$591$	−324.312			−0.548751
$592$	−328.010	−	130.691i	−0.554071	−	0.220762i
$593$	−530.156	−	57.6580i	−0.894024	−	0.0972310i	−0.350440	−	0.936585i	$-0.613968\pi$
$593$	−530.156	−	57.6580i	−0.894024	−	0.0972310i	−0.543585	+	0.839354i	$0.682933\pi$
$594$	26.6689	+	25.2622i	0.0448972	+	0.0425289i
$595$	289.500	−	340.826i	0.486554	−	0.572816i
$596$	−693.777	−	367.817i	−1.16406	−	0.617143i
$597$	294.250	+	177.044i	0.492881	+	0.296556i
$598$	198.544	+	429.146i	0.332014	+	0.717635i
$599$	−315.160	−	69.3720i	−0.526144	−	0.115813i	−0.0560475	−	0.998428i	$-0.517850\pi$
$599$	−315.160	−	69.3720i	−0.526144	−	0.115813i	−0.470096	+	0.882615i	$0.655781\pi$
$600$	203.137	−	107.696i	0.338561	−	0.179494i
$601$	−475.497	−	25.7807i	−0.791177	−	0.0428963i	−0.345879	−	0.938279i	$-0.612419\pi$
$601$	−475.497	−	25.7807i	−0.791177	−	0.0428963i	−0.445297	+	0.895383i	$0.646902\pi$
$602$	−394.913	−	464.928i	−0.656002	−	0.772305i
$603$	−9.81011	−	44.5678i	−0.0162688	−	0.0739101i
$604$	42.5249	+	55.9405i	0.0704054	+	0.0926167i
$605$	−84.0242	+	79.5919i	−0.138883	+	0.131557i
$606$	−9.55893	−	176.304i	−0.0157738	−	0.290931i
$607$	−49.1221	+	29.5558i	−0.0809261	+	0.0486916i	−0.555442	−	0.831555i	$-0.687451\pi$
$607$	−49.1221	+	29.5558i	−0.0809261	+	0.0486916i	0.474516	+	0.880247i	$0.342623\pi$
$608$	586.917	+	397.940i	0.965324	+	0.654506i
$609$	−126.053	+	454.001i	−0.206983	+	0.745485i
$610$	−175.019	+	19.0344i	−0.286916	+	0.0312040i
$611$	−572.006	−	434.827i	−0.936179	−	0.711665i
$612$	−218.328	−	101.009i	−0.356745	−	0.165048i
$613$	512.289	−	347.340i	0.835707	−	0.566624i	−0.0665690	−	0.997782i	$-0.521205\pi$
$613$	512.289	−	347.340i	0.835707	−	0.566624i	0.902276	+	0.431158i	$0.141895\pi$
$614$	−11.2009	−	33.2430i	−0.0182425	−	0.0541417i
$615$	−24.5382	−	149.677i	−0.0398996	−	0.243377i
$616$	72.7758	−	443.913i	0.118142	−	0.720637i
$617$	468.600	+	157.890i	0.759481	+	0.255899i	0.672285	−	0.740292i	$-0.265313\pi$
$617$	468.600	+	157.890i	0.759481	+	0.255899i	0.0871960	+	0.996191i	$0.472209\pi$
$618$	74.3626	+	267.830i	0.120328	+	0.433382i
$619$	119.582	+	300.129i	0.193186	+	0.484861i	0.993379	−	0.114882i	$-0.0366489\pi$
$619$	119.582	+	300.129i	0.193186	+	0.484861i	−0.800193	+	0.599743i	$0.795270\pi$
$620$	250.745	−	99.9060i	0.404427	−	0.161139i
$621$	−210.372	+	58.4095i	−0.338764	+	0.0940572i
$622$	−103.382	+	306.828i	−0.166209	+	0.493292i
$623$	73.1287	+	11.9888i	0.117382	+	0.0192437i
$624$	158.579	−	25.9977i	0.254133	−	0.0416630i
$625$	−313.037	+	105.474i	−0.500859	+	0.168759i
$626$	−31.3415	−	46.2252i	−0.0500663	−	0.0738422i
$627$	129.624	−	280.177i	0.206736	−	0.446853i
$628$	−160.794	+	211.521i	−0.256041	+	0.336816i
$629$	130.661	+	1201.41i	0.207728	+	1.91002i
$630$	45.8106	+	12.7192i	0.0727152	+	0.0201893i
$631$	−548.626	+	809.163i	−0.869455	+	1.28235i	0.0886876	+	0.996059i	$0.471733\pi$
$631$	−548.626	+	809.163i	−0.869455	+	1.28235i	−0.958143	+	0.286291i	$0.907578\pi$
$632$	301.569	+	501.212i	0.477166	+	0.793056i
$633$	96.9176	−	5.25472i	0.153108	−	0.00830129i
$634$	255.010	+	269.211i	0.402225	+	0.424623i
$635$	145.710	−	110.766i	0.229465	−	0.174435i
$636$	−103.106	+	22.6952i	−0.162116	+	0.0356843i
$637$	278.375	−	236.454i	0.437010	−	0.371199i
$638$	−11.8174	+	217.959i	−0.0185226	+	0.341629i
$639$	143.660	+	270.971i	0.224820	+	0.424055i
$640$	56.2992	−	255.770i	0.0879675	−	0.399640i
$641$	628.468	−	290.760i	0.980449	−	0.453604i	0.136858	−	0.990591i	$-0.456300\pi$
$641$	628.468	−	290.760i	0.980449	−	0.453604i	0.843591	+	0.536987i	$0.180438\pi$
$642$	20.9921	−	34.8891i	0.0326980	−	0.0543444i
$643$	320.520	−	604.565i	0.498476	−	0.940226i	−0.498817	−	0.866707i	$-0.666232\pi$
$643$	320.520	−	604.565i	0.498476	−	0.940226i	0.997294	−	0.0735191i	$-0.0234230\pi$
$644$	909.131	+	772.223i	1.41169	+	1.19910i
$645$	−190.715	+	201.335i	−0.295682	+	0.312148i
$646$	52.7647	−	485.164i	0.0816791	−	0.751027i
$647$	−68.4056	+	171.685i	−0.105727	+	0.265356i	−0.972317	−	0.233666i	$-0.924928\pi$
$647$	−68.4056	+	171.685i	−0.105727	+	0.265356i	0.866590	+	0.499021i	$0.166307\pi$
$648$		−	57.3262i		−	0.0884663i
$649$	−94.4186	+	463.412i	−0.145483	+	0.714040i
$650$	234.528			0.360813
$651$	−582.257	−	231.993i	−0.894405	−	0.356363i
$652$	34.5826	+	3.76108i	0.0530408	+	0.00576853i
$653$	581.786	+	551.097i	0.890944	+	0.843947i	0.988490	−	0.151284i	$-0.0483408\pi$
$653$	581.786	+	551.097i	0.890944	+	0.843947i	−0.0975463	+	0.995231i	$0.531099\pi$
$654$	−13.4078	+	15.7849i	−0.0205012	+	0.0241359i
$655$	111.343	+	59.0306i	0.169990	+	0.0901230i
$656$	267.503	+	160.951i	0.407779	+	0.245353i
$657$	103.059	+	222.758i	0.156863	+	0.339053i
$658$	427.323	+	94.0610i	0.649428	+	0.142950i
$659$	634.409	−	336.342i	0.962684	−	0.510383i	0.0885524	−	0.996072i	$-0.471776\pi$
$659$	634.409	−	336.342i	0.962684	−	0.510383i	0.874132	+	0.485689i	$0.161431\pi$
$660$	−91.1061	−	4.93963i	−0.138040	−	0.00748429i
$661$	358.970	+	422.612i	0.543070	+	0.639352i	0.963415	−	0.268012i	$-0.0863668\pi$
$661$	358.970	+	422.612i	0.543070	+	0.639352i	−0.420345	+	0.907364i	$0.638091\pi$
$662$	44.0022	+	199.904i	0.0664686	+	0.301970i
$663$	−332.848	−	437.854i	−0.502033	−	0.660413i
$664$	−30.5188	+	28.9089i	−0.0459621	+	0.0435376i
$665$	−21.6311	−	398.962i	−0.0325280	−	0.599943i
$666$	−110.093	+	66.2405i	−0.165304	+	0.0994602i
$667$	−1073.80	−	728.052i	−1.60989	−	1.09153i
$668$	−30.9379	+	111.428i	−0.0463142	+	0.166808i
$669$	−313.040	+	34.0452i	−0.467923	+	0.0508897i
$670$	−21.7826	−	16.5587i	−0.0325113	−	0.0247144i
$671$	−712.026	−	329.418i	−1.06114	−	0.490937i
$672$	−402.805	+	273.108i	−0.599412	+	0.406411i
$673$	−91.3076	−	270.991i	−0.135673	−	0.402662i	0.858183	−	0.513343i	$-0.171593\pi$
$673$	−91.3076	−	270.991i	−0.135673	−	0.402662i	−0.993856	+	0.110681i	$0.964697\pi$
$674$	27.5908	+	168.297i	0.0409360	+	0.249698i
$675$	−17.5193	+	106.863i	−0.0259545	+	0.158316i
$676$	−18.8853	−	6.36319i	−0.0279368	−	0.00941300i
$677$	−247.658	−	891.984i	−0.365817	−	1.31755i	−0.886074	−	0.463544i	$-0.846577\pi$
$677$	−247.658	−	891.984i	−0.365817	−	1.31755i	0.520256	−	0.854010i	$-0.325836\pi$
$678$	−2.41769	−	6.06794i	−0.00356591	−	0.00894976i
$679$	963.501	−	383.894i	1.41900	−	0.565381i
$680$	−311.509	+	86.4900i	−0.458101	+	0.127191i
$681$	58.1170	−	172.485i	0.0853406	−	0.253282i
$682$	−286.537	−	46.9754i	−0.420143	−	0.0688789i
$683$	−1150.43	+	188.603i	−1.68437	+	0.276139i	−0.926508	−	0.376274i	$-0.877205\pi$
$683$	−1150.43	+	188.603i	−1.68437	+	0.276139i	−0.757864	+	0.652413i	$0.773757\pi$
$684$	−203.686	+	68.6297i	−0.297786	+	0.100336i
$685$	208.597	+	307.657i	0.304520	+	0.449134i
$686$	66.4795	−	143.693i	0.0969089	−	0.209465i
$687$	−204.307	+	268.761i	−0.297390	+	0.391210i
$688$	−61.7156	−	567.466i	−0.0897030	−	0.824805i
$689$	−232.578	−	64.5750i	−0.337559	−	0.0937228i
$690$	−73.4635	+	108.351i	−0.106469	+	0.157030i
$691$	217.948	+	362.232i	0.315409	+	0.524214i	0.973489	−	0.228734i	$-0.0734586\pi$
$691$	217.948	+	362.232i	0.315409	+	0.524214i	−0.658080	+	0.752948i	$0.728631\pi$
$692$	124.318	−	6.74033i	0.179650	−	0.00974036i
$693$	145.702	+	153.816i	0.210249	+	0.221957i
$694$	63.1580	−	48.0115i	0.0910057	−	0.0691808i
$695$	−344.606	+	75.8535i	−0.495836	+	0.109142i
$696$	259.622	−	220.525i	0.373020	−	0.316846i
$697$	57.8483	−	1066.95i	0.0829961	−	1.53077i
$698$	−116.626	−	219.981i	−0.167087	−	0.315159i
$699$	−3.83799	+	17.4362i	−0.00549069	+	0.0249445i
$700$	536.951	−	248.420i	0.767073	−	0.354886i
$701$	−504.454	+	838.409i	−0.719621	+	1.19602i	0.253858	+	0.967241i	$0.418300\pi$
$701$	−504.454	+	838.409i	−0.719621	+	1.19602i	−0.973479	+	0.228777i	$0.926527\pi$
$702$	27.3903	−	51.6636i	0.0390175	−	0.0735949i
$703$	822.952	+	699.022i	1.17063	+	0.994341i
$704$	5.28100	−	5.57508i	0.00750142	−	0.00791915i
$705$	21.5070	−	197.754i	0.0305064	−	0.280502i
$706$	171.392	−	430.162i	0.242765	−	0.609294i
$707$		−	1018.35i		−	1.44038i
$708$	279.449	−	174.159i	0.394702	−	0.245987i
$709$	326.694			0.460782			0.230391	−	0.973098i	$-0.426000\pi$
$709$	326.694			0.460782			0.230391	+	0.973098i	$0.426000\pi$
$710$	170.830	+	68.0651i	0.240606	+	0.0958663i
$711$	−273.886	−	29.7869i	−0.385213	−	0.0418944i
$712$	−38.8949	−	36.8432i	−0.0546277	−	0.0517461i
$713$	1117.24	−	1315.32i	1.56696	−	1.84476i
$714$	295.918	+	156.886i	0.414452	+	0.219728i
$715$	−178.744	−	107.547i	−0.249992	−	0.150415i
$716$	94.0653	+	203.319i	0.131376	+	0.283965i
$717$	−92.4483	−	20.3494i	−0.128938	−	0.0283813i
$718$	−146.541	+	77.6909i	−0.204096	+	0.108205i
$719$	574.104	+	31.1270i	0.798475	+	0.0432921i	0.448861	−	0.893602i	$-0.351830\pi$
$719$	574.104	+	31.1270i	0.798475	+	0.0432921i	0.349614	+	0.936894i	$0.386313\pi$
$720$	28.8012	+	33.9074i	0.0400016	+	0.0470936i
$721$	344.635	+	1565.69i	0.477996	+	2.17156i
$722$	−71.2027	−	93.6656i	−0.0986187	−	0.129731i
$723$	36.1703	−	34.2624i	0.0500281	−	0.0473891i
$724$	40.5794	+	748.442i	0.0560488	+	1.03376i
$725$	−551.361	+	331.743i	−0.760498	+	0.457576i
$726$	−71.7484	−	48.6466i	−0.0988270	−	0.0670064i
$727$	221.115	−	796.384i	0.304147	−	1.09544i	−0.640663	−	0.767822i	$-0.721341\pi$
$727$	221.115	−	796.384i	0.304147	−	1.09544i	0.944810	−	0.327617i	$-0.106246\pi$
$728$	−711.875	+	77.4210i	−0.977850	+	0.106348i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	133.562	+	61.7924i	0.182962	+	0.0846471i
$731$	−1617.04	+	1096.38i	−2.21209	+	1.49984i
$732$	174.412	+	517.636i	0.238268	+	0.707153i
$733$	40.0448	+	244.263i	0.0546314	+	0.333237i	0.999974	+	0.00715909i	$0.00227883\pi$
$733$	40.0448	+	244.263i	0.0546314	+	0.333237i	−0.945343	+	0.326078i	$0.894273\pi$
$734$	−83.1479	+	507.180i	−0.113280	+	0.690980i
$735$	95.8240	+	32.2869i	0.130373	+	0.0439277i
$736$	−358.484	−	1291.14i	−0.487071	−	1.75427i
$737$	−45.1320	−	113.273i	−0.0612375	−	0.153695i
$738$	105.534	−	42.0486i	0.143000	−	0.0569764i
$739$	123.832	−	34.3817i	0.167567	−	0.0465247i	−0.182732	−	0.983163i	$-0.558494\pi$
$739$	123.832	−	34.3817i	0.167567	−	0.0465247i	0.350298	+	0.936638i	$0.386080\pi$
$740$	101.898	−	302.421i	0.137699	−	0.408677i
$741$	−484.943	−	79.5023i	−0.654444	−	0.107291i
$742$	145.054	−	23.7804i	0.195491	−	0.0320491i
$743$	−866.287	+	291.886i	−1.16593	+	0.392848i	−0.834702	−	0.550702i	$-0.814360\pi$
$743$	−866.287	+	291.886i	−1.16593	+	0.392848i	−0.331229	+	0.943550i	$0.607463\pi$
$744$	254.290	+	375.050i	0.341788	+	0.504099i
$745$	208.700	−	451.098i	0.280134	−	0.605500i
$746$	245.534	−	322.994i	0.329134	−	0.432968i
$747$	−2.14065	−	19.6830i	−0.00286567	−	0.0263494i
$748$	−619.337	−	171.958i	−0.827990	−	0.229890i
$749$	131.791	−	194.377i	0.175956	−	0.259515i
$750$	73.6299	+	122.374i	0.0981731	+	0.163165i
$751$	−884.130	+	47.9362i	−1.17727	+	0.0638298i	−0.632367	−	0.774669i	$-0.717917\pi$
$751$	−884.130	+	47.9362i	−1.17727	+	0.0638298i	−0.544904	+	0.838499i	$0.683434\pi$
$752$	281.569	+	297.249i	0.374427	+	0.395277i
$753$	−411.097	+	312.508i	−0.545945	+	0.415017i
$754$	339.343	−	74.6950i	0.450057	−	0.0990650i
$755$	−33.8993	+	28.7943i	−0.0448997	+	0.0381381i
$756$	7.98617	−	147.296i	0.0105637	−	0.194836i
$757$	−235.285	−	443.795i	−0.310813	−	0.586255i	0.678062	−	0.735005i	$-0.262820\pi$
$757$	−235.285	−	443.795i	−0.310813	−	0.586255i	−0.988875	+	0.148749i	$0.952475\pi$
$758$	−24.3453	+	110.602i	−0.0321178	+	0.145913i
$759$	−529.447	+	244.948i	−0.697559	+	0.322725i
$760$	−148.921	+	247.508i	−0.195948	+	0.325668i
$761$	99.6153	−	187.894i	0.130900	−	0.246905i	−0.809394	−	0.587266i	$-0.800204\pi$
$761$	99.6153	−	187.894i	0.130900	−	0.246905i	0.940295	+	0.340361i	$0.110549\pi$
$762$	104.484	+	88.7491i	0.137118	+	0.116469i
$763$	−82.1465	+	86.7210i	−0.107662	+	0.113658i
$764$	7.52066	−	69.1513i	0.00984380	−	0.0905122i
$765$	56.3600	−	141.453i	0.0736732	−	0.184906i
$766$		−	481.273i		−	0.628293i
$767$	751.000	−	52.5287i	0.979139	−	0.0684860i
$768$	189.517			0.246767
$769$	−395.418	−	157.549i	−0.514198	−	0.204875i	0.0985818	−	0.995129i	$-0.468569\pi$
$769$	−395.418	−	157.549i	−0.514198	−	0.204875i	−0.612780	+	0.790254i	$0.709949\pi$
$770$	126.289	+	13.7347i	0.164011	+	0.0178373i
$771$	−312.759	−	296.261i	−0.405653	−	0.384255i
$772$	−313.161	+	368.682i	−0.405649	+	0.477567i
$773$	897.562	+	475.857i	1.16114	+	0.615598i	0.933652	−	0.358182i	$-0.116603\pi$
$773$	897.562	+	475.857i	1.16114	+	0.615598i

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.g (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819309 + 0.326442i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.33928 - 2.21588i) q^{4} +(1.32036 - 1.55445i) q^{5} +(1.34963 + 0.715530i) q^{6} +(7.54931 + 4.54227i) q^{7} +(-2.67451 - 5.78087i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(0.819309 + 0.326442i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.33928 - 2.21588i) q^{4} +(1.32036 - 1.55445i) q^{5} +(1.34963 + 0.715530i) q^{6} +(7.54931 + 4.54227i) q^{7} +(-2.67451 - 5.78087i) q^{8} +(2.92986 + 0.644911i) q^{9} +(1.58922 - 0.842551i) q^{10} +(8.00405 + 0.433967i) q^{11} +(-3.61304 - 4.25360i) q^{12} +(-2.74300 - 12.4616i) q^{13} +(4.70243 + 6.18594i) q^{14} +(2.56462 - 2.42934i) q^{15} +(0.393646 + 7.26038i) q^{16} +(21.3238 - 12.8301i) q^{17} +(2.18993 + 1.48481i) q^{18} +(5.94855 - 21.4248i) q^{19} +(-6.53316 + 0.710524i) q^{20} +(12.1485 + 9.23507i) q^{21} +(6.41612 + 2.96841i) q^{22} +(-34.7776 + 23.5798i) q^{23} +(-3.52267 - 10.4549i) q^{24} +(3.37159 + 20.5658i) q^{25} +(1.82062 - 11.1053i) q^{26} +(4.92415 + 1.65914i) q^{27} +(-7.59481 - 27.3540i) q^{28} +(11.4284 + 28.6832i) q^{29} +(2.89426 - 1.15318i) q^{30} +(-39.5754 + 10.9880i) q^{31} +(-10.1828 + 30.2216i) q^{32} +(13.7009 + 2.24615i) q^{33} +(21.6591 - 3.55083i) q^{34} +(17.0285 - 5.73758i) q^{35} +(-5.42472 - 8.00086i) q^{36} +(-20.3901 + 44.0726i) q^{37} +(11.8677 - 15.6116i) q^{38} +(-2.38952 - 21.9712i) q^{39} +(-12.5174 - 3.47543i) q^{40} +(24.0953 - 35.5378i) q^{41} +(6.93867 + 11.5322i) q^{42} +(-78.3897 + 4.25017i) q^{43} +(-17.7621 - 18.7512i) q^{44} +(4.87095 - 3.70280i) q^{45} +(-36.1910 + 7.96624i) q^{46} +(42.9177 - 36.4546i) q^{47} +(-0.681816 + 12.5753i) q^{48} +(13.4079 + 25.2900i) q^{49} +(-3.95118 + 17.9504i) q^{50} +(39.1201 - 18.0989i) q^{51} +(-21.1968 + 35.2293i) q^{52} +(8.86078 - 16.7132i) q^{53} +(3.49279 + 2.96680i) q^{54} +(11.2428 - 11.8689i) q^{55} +(6.06752 - 55.7900i) q^{56} +(14.2550 - 35.7773i) q^{57} +27.2311i q^{58} +(-8.63189 + 58.3651i) q^{59} -11.3825 q^{60} +(-90.9224 - 36.2268i) q^{61} +(-36.0114 - 3.91648i) q^{62} +(19.1891 + 18.1769i) q^{63} +(0.620203 - 0.730159i) q^{64} +(-22.9926 - 12.1899i) q^{65} +(10.4920 + 6.31284i) q^{66} +(-6.38717 - 13.8056i) q^{67} +(-78.3125 - 17.2379i) q^{68} +(-64.2991 + 34.0893i) q^{69} +(15.8246 + 0.857985i) q^{70} +(66.1839 + 77.9177i) q^{71} +(-4.10781 - 18.6620i) q^{72} +(49.5119 + 65.1318i) q^{73} +(-31.0930 + 29.4528i) q^{74} +(1.95423 + 36.0436i) q^{75} +(-61.3901 + 36.9372i) q^{76} +(58.4539 + 39.6327i) q^{77} +(5.21460 - 18.7813i) q^{78} +(-91.2954 + 9.92898i) q^{79} +(11.8056 + 8.97441i) q^{80} +(8.16818 + 3.77900i) q^{81} +(31.3425 - 21.2507i) q^{82} +(-2.10729 - 6.25421i) q^{83} +(-7.95496 - 48.5231i) q^{84} +(8.21138 - 50.0872i) q^{85} +(-65.6128 - 22.1075i) q^{86} +(14.3071 + 51.5297i) q^{87} +(-18.8982 - 47.4310i) q^{88} +(7.81364 - 3.11324i) q^{89} +(5.19956 - 1.44365i) q^{90} +(35.8961 - 106.536i) q^{91} +(133.605 + 21.9034i) q^{92} +(-70.2024 + 11.5091i) q^{93} +(47.0632 - 15.8574i) q^{94} +(-25.4494 - 37.5351i) q^{95} +(-23.1933 + 50.1316i) q^{96} +(71.2408 - 93.7156i) q^{97} +(2.72948 + 25.0972i) q^{98} +(23.1709 + 6.43337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) \)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about