LMFDB - Embedded newform 177.3.g.a.10.20

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			10.20
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.20

$q$-expansion

$f(q)$	$=$	$q+(3.40493 + 1.35665i) q^{2} +(1.72190 + 0.187268i) q^{3} +(6.84907 + 6.48778i) q^{4} +(1.18743 - 1.39795i) q^{5} +(5.60888 + 2.97364i) q^{6} +(-5.85901 - 3.52525i) q^{7} +(8.36297 + 18.0763i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(3.40493 + 1.35665i) q^{2} +(1.72190 + 0.187268i) q^{3} +(6.84907 + 6.48778i) q^{4} +(1.18743 - 1.39795i) q^{5} +(5.60888 + 2.97364i) q^{6} +(-5.85901 - 3.52525i) q^{7} +(8.36297 + 18.0763i) q^{8} +(2.92986 + 0.644911i) q^{9} +(5.93964 - 3.14900i) q^{10} +(-18.1191 - 0.982387i) q^{11} +(10.5784 + 12.4539i) q^{12} +(-2.12858 - 9.67024i) q^{13} +(-15.1670 - 19.9518i) q^{14} +(2.30642 - 2.18476i) q^{15} +(1.90921 + 35.2132i) q^{16} +(23.9564 - 14.4141i) q^{17} +(9.10106 + 6.17067i) q^{18} +(-3.55086 + 12.7890i) q^{19} +(17.2024 - 1.87087i) q^{20} +(-9.42845 - 7.16732i) q^{21} +(-60.3614 - 27.9261i) q^{22} +(-21.7336 + 14.7358i) q^{23} +(11.0151 + 32.6916i) q^{24} +(3.50027 + 21.3507i) q^{25} +(5.87144 - 35.8142i) q^{26} +(4.92415 + 1.65914i) q^{27} +(-17.2577 - 62.1567i) q^{28} +(6.39647 + 16.0539i) q^{29} +(10.8172 - 4.30995i) q^{30} +(-1.63201 + 0.453126i) q^{31} +(-15.8330 + 46.9907i) q^{32} +(-31.0152 - 5.08468i) q^{33} +(101.124 - 16.5785i) q^{34} +(-11.8853 + 4.00462i) q^{35} +(15.8828 + 23.4254i) q^{36} +(10.4600 - 22.6090i) q^{37} +(-29.4407 + 38.7285i) q^{38} +(-1.85427 - 17.0498i) q^{39} +(35.2002 + 9.77328i) q^{40} +(29.2958 - 43.2081i) q^{41} +(-22.3797 - 37.1953i) q^{42} +(47.9681 - 2.60076i) q^{43} +(-117.725 - 124.281i) q^{44} +(4.38056 - 3.33001i) q^{45} +(-93.9928 + 20.6894i) q^{46} +(-50.0867 + 42.5440i) q^{47} +(-3.30684 + 60.9911i) q^{48} +(-1.05140 - 1.98316i) q^{49} +(-17.0472 + 77.4464i) q^{50} +(43.9497 - 20.3333i) q^{51} +(48.1596 - 80.0419i) q^{52} +(-22.8094 + 43.0232i) q^{53} +(14.5155 + 12.3296i) q^{54} +(-22.8884 + 24.1630i) q^{55} +(14.7246 - 135.391i) q^{56} +(-8.50919 + 21.3565i) q^{57} +63.3403i q^{58} +(52.6928 + 26.5419i) q^{59} +29.9711 q^{60} +(-6.80785 - 2.71249i) q^{61} +(-6.17162 - 0.671204i) q^{62} +(-14.8926 - 14.1070i) q^{63} +(-26.3399 + 31.0097i) q^{64} +(-16.0461 - 8.50708i) q^{65} +(-98.7064 - 59.3897i) q^{66} +(-47.9508 - 103.644i) q^{67} +(257.594 + 56.7007i) q^{68} +(-40.1826 + 21.3035i) q^{69} +(-45.9014 - 2.48870i) q^{70} +(39.6022 + 46.6234i) q^{71} +(12.8448 + 58.3543i) q^{72} +(-37.9046 - 49.8626i) q^{73} +(66.2880 - 62.7913i) q^{74} +(2.02881 + 37.4193i) q^{75} +(-107.293 + 64.5558i) q^{76} +(102.697 + 69.6300i) q^{77} +(16.8169 - 60.5689i) q^{78} +(43.6669 - 4.74906i) q^{79} +(51.4934 + 39.1443i) q^{80} +(8.16818 + 3.77900i) q^{81} +(158.368 - 107.376i) q^{82} +(17.6699 + 52.4424i) q^{83} +(-18.0761 - 110.259i) q^{84} +(8.29635 - 50.6055i) q^{85} +(166.856 + 56.2205i) q^{86} +(8.00768 + 28.8411i) q^{87} +(-133.771 - 335.741i) q^{88} +(-89.1508 + 35.5209i) q^{89} +(19.4332 - 5.39559i) q^{90} +(-21.6186 + 64.1618i) q^{91} +(-244.458 - 40.0768i) q^{92} +(-2.89501 + 0.474613i) q^{93} +(-228.259 + 76.9094i) q^{94} +(13.6620 + 20.1500i) q^{95} +(-36.0626 + 77.9481i) q^{96} +(-47.1811 + 62.0657i) q^{97} +(-0.889509 - 8.17890i) q^{98} +(-52.4528 - 14.5634i) 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 $

$2$	3.40493	+	1.35665i	1.70246	+	0.678324i	0.999460	−	0.0328610i	$-0.0104619\pi$
$2$	3.40493	+	1.35665i	1.70246	+	0.678324i	0.703005	+	0.711185i	$0.251841\pi$
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$4$	6.84907	+	6.48778i	1.71227	+	1.62195i
$5$	1.18743	−	1.39795i	0.237486	−	0.279590i	−0.630489	−	0.776198i	$-0.717146\pi$
$5$	1.18743	−	1.39795i	0.237486	−	0.279590i	0.867975	+	0.496608i	$0.165421\pi$
$6$	5.60888	+	2.97364i	0.934814	+	0.495607i
$7$	−5.85901	−	3.52525i	−0.837001	−	0.503607i	0.0313780	−	0.999508i	$-0.490010\pi$
$7$	−5.85901	−	3.52525i	−0.837001	−	0.503607i	−0.868379	+	0.495901i	$0.834838\pi$
$8$	8.36297	+	18.0763i	1.04537	+	2.25953i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	5.93964	−	3.14900i	0.593964	−	0.314900i
$11$	−18.1191	−	0.982387i	−1.64719	−	0.0893079i	−0.792982	−	0.609245i	$-0.791473\pi$
$11$	−18.1191	−	0.982387i	−1.64719	−	0.0893079i	−0.854205	+	0.519937i	$0.825955\pi$
$12$	10.5784	+	12.4539i	0.881537	+	1.03783i
$13$	−2.12858	−	9.67024i	−0.163737	−	0.743864i	−0.984893	−	0.173161i	$-0.944602\pi$
$13$	−2.12858	−	9.67024i	−0.163737	−	0.743864i	0.821157	−	0.570703i	$-0.193329\pi$
$14$	−15.1670	−	19.9518i	−1.08336	−	1.42513i
$15$	2.30642	−	2.18476i	0.153762	−	0.145651i
$16$	1.90921	+	35.2132i	0.119325	+	2.20083i
$17$	23.9564	−	14.4141i	1.40920	−	0.847886i	0.411225	−	0.911534i	$-0.365101\pi$
$17$	23.9564	−	14.4141i	1.40920	−	0.847886i	0.997972	+	0.0636483i	$0.0202736\pi$
$18$	9.10106	+	6.17067i	0.505614	+	0.342815i
$19$	−3.55086	+	12.7890i	−0.186887	+	0.673107i	0.809419	+	0.587232i	$0.199782\pi$
$19$	−3.55086	+	12.7890i	−0.186887	+	0.673107i	−0.996306	+	0.0858753i	$0.972631\pi$
$20$	17.2024	−	1.87087i	0.860119	−	0.0935436i
$21$	−9.42845	−	7.16732i	−0.448974	−	0.341301i
$22$	−60.3614	−	27.9261i	−2.74370	−	1.26937i
$23$	−21.7336	+	14.7358i	−0.944941	+	0.640686i	−0.933243	−	0.359245i	$-0.883034\pi$
$23$	−21.7336	+	14.7358i	−0.944941	+	0.640686i	−0.0116982	+	0.999932i	$0.503724\pi$
$24$	11.0151	+	32.6916i	0.458962	+	1.36215i
$25$	3.50027	+	21.3507i	0.140011	+	0.854029i
$26$	5.87144	−	35.8142i	0.225825	−	1.37747i
$27$	4.92415	+	1.65914i	0.182376	+	0.0614496i
$28$	−17.2577	−	62.1567i	−0.616347	−	2.21988i
$29$	6.39647	+	16.0539i	0.220568	+	0.553584i	0.997067	−	0.0765347i	$-0.0243856\pi$
$29$	6.39647	+	16.0539i	0.220568	+	0.553584i	−0.776499	+	0.630119i	$0.783006\pi$
$30$	10.8172	−	4.30995i	0.360572	−	0.143665i
$31$	−1.63201	+	0.453126i	−0.0526455	+	0.0146170i	−0.293751	−	0.955882i	$-0.594904\pi$
$31$	−1.63201	+	0.453126i	−0.0526455	+	0.0146170i	0.241106	+	0.970499i	$0.422490\pi$
$32$	−15.8330	+	46.9907i	−0.494781	+	1.46846i
$33$	−31.0152	−	5.08468i	−0.939854	−	0.154081i
$34$	101.124	−	16.5785i	2.97425	−	0.487603i
$35$	−11.8853	+	4.00462i	−0.339580	+	0.114418i
$36$	15.8828	+	23.4254i	0.441188	+	0.650704i
$37$	10.4600	−	22.6090i	0.282703	−	0.611053i	−0.713252	−	0.700908i	$-0.752778\pi$
$37$	10.4600	−	22.6090i	0.282703	−	0.611053i	0.995955	+	0.0898552i	$0.0286404\pi$
$38$	−29.4407	+	38.7285i	−0.774754	+	1.01917i
$39$	−1.85427	−	17.0498i	−0.0475455	−	0.437174i
$40$	35.2002	+	9.77328i	0.880004	+	0.244332i
$41$	29.2958	−	43.2081i	0.714533	−	1.05386i	−0.281025	−	0.959700i	$-0.590674\pi$
$41$	29.2958	−	43.2081i	0.714533	−	1.05386i	0.995557	−	0.0941562i	$-0.0300153\pi$
$42$	−22.3797	−	37.1953i	−0.532849	−	0.885602i
$43$	47.9681	−	2.60076i	1.11554	−	0.0604827i	0.512864	−	0.858470i	$-0.328585\pi$
$43$	47.9681	−	2.60076i	1.11554	−	0.0604827i	0.602674	+	0.797987i	$0.294102\pi$
$44$	−117.725	−	124.281i	−2.67557	−	2.82457i
$45$	4.38056	−	3.33001i	0.0973458	−	0.0740003i
$46$	−93.9928	+	20.6894i	−2.04332	+	0.449769i
$47$	−50.0867	+	42.5440i	−1.06567	+	0.905192i	−0.995726	−	0.0923584i	$-0.970559\pi$
$47$	−50.0867	+	42.5440i	−1.06567	+	0.905192i	−0.0699488	+	0.997551i	$0.522284\pi$
$48$	−3.30684	+	60.9911i	−0.0688925	+	1.27065i
$49$	−1.05140	−	1.98316i	−0.0214572	−	0.0404726i
$50$	−17.0472	+	77.4464i	−0.340945	+	1.54893i
$51$	43.9497	−	20.3333i	0.861758	−	0.398692i
$52$	48.1596	−	80.0419i	0.926147	−	1.53927i
$53$	−22.8094	+	43.0232i	−0.430367	+	0.811758i	−0.999948	−	0.0101769i	$-0.996761\pi$
$53$	−22.8094	+	43.0232i	−0.430367	+	0.811758i	0.569581	+	0.821935i	$0.307105\pi$
$54$	14.5155	+	12.3296i	0.268806	+	0.228326i
$55$	−22.8884	+	24.1630i	−0.416153	+	0.439328i
$56$	14.7246	−	135.391i	0.262940	−	2.41769i
$57$	−8.50919	+	21.3565i	−0.149284	+	0.374675i
$58$			63.3403i			1.09207i
$59$	52.6928	+	26.5419i	0.893098	+	0.449863i
$59$	52.6928	+	26.5419i	0.893098	+	0.449863i
$60$	29.9711			0.499518
$61$	−6.80785	−	2.71249i	−0.111604	−	0.0444671i	0.313668	−	0.949533i	$-0.398442\pi$
$61$	−6.80785	−	2.71249i	−0.111604	−	0.0444671i	−0.425272	+	0.905066i	$0.639822\pi$
$62$	−6.17162	−	0.671204i	−0.0995422	−	0.0108259i
$63$	−14.8926	−	14.1070i	−0.236391	−	0.223921i
$64$	−26.3399	+	31.0097i	−0.411560	+	0.484526i
$65$	−16.0461	−	8.50708i	−0.246862	−	0.130878i
$66$	−98.7064	−	59.3897i	−1.49555	−	0.899843i
$67$	−47.9508	−	103.644i	−0.715683	−	1.54692i	−0.832657	−	0.553788i	$-0.813182\pi$
$67$	−47.9508	−	103.644i	−0.715683	−	1.54692i	0.116974	−	0.993135i	$-0.462680\pi$
$68$	257.594	+	56.7007i	3.78815	+	0.833834i
$69$	−40.1826	+	21.3035i	−0.582357	+	0.308746i
$70$	−45.9014	−	2.48870i	−0.655735	−	0.0355529i
$71$	39.6022	+	46.6234i	0.557778	+	0.656667i	0.966703	−	0.255901i	$-0.0823721\pi$
$71$	39.6022	+	46.6234i	0.557778	+	0.656667i	−0.408925	+	0.912568i	$0.634096\pi$
$72$	12.8448	+	58.3543i	0.178399	+	0.810477i
$73$	−37.9046	−	49.8626i	−0.519240	−	0.683049i	0.459494	−	0.888181i	$-0.348031\pi$
$73$	−37.9046	−	49.8626i	−0.519240	−	0.683049i	−0.978734	+	0.205132i	$0.934238\pi$
$74$	66.2880	−	62.7913i	0.895784	−	0.848531i
$75$	2.02881	+	37.4193i	0.0270508	+	0.498923i
$76$	−107.293	+	64.5558i	−1.41175	+	0.849419i
$77$	102.697	+	69.6300i	1.33372	+	0.904286i
$78$	16.8169	−	60.5689i	0.215601	−	0.776524i
$79$	43.6669	−	4.74906i	0.552746	−	0.0601147i	0.172516	−	0.985007i	$-0.444810\pi$
$79$	43.6669	−	4.74906i	0.552746	−	0.0601147i	0.380230	+	0.924892i	$0.375845\pi$
$80$	51.4934	+	39.1443i	0.643667	+	0.489303i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	158.368	−	107.376i	1.93132	−	1.30947i
$83$	17.6699	+	52.4424i	0.212891	+	0.631837i	0.999889	+	0.0148819i	$0.00473724\pi$
$83$	17.6699	+	52.4424i	0.212891	+	0.631837i	−0.786999	+	0.616955i	$0.788366\pi$
$84$	−18.0761	−	110.259i	−0.215191	−	1.31261i
$85$	8.29635	−	50.6055i	0.0976041	−	0.595358i
$86$	166.856	+	56.2205i	1.94019	+	0.653726i
$87$	8.00768	+	28.8411i	0.0920423	+	0.331507i
$88$	−133.771	−	335.741i	−1.52013	−	3.81523i
$89$	−89.1508	+	35.5209i	−1.00169	+	0.399112i	−0.812584	−	0.582844i	$-0.801940\pi$
$89$	−89.1508	+	35.5209i	−1.00169	+	0.399112i	−0.189111	+	0.981956i	$0.560561\pi$
$90$	19.4332	−	5.39559i	0.215924	−	0.0599510i
$91$	−21.6186	+	64.1618i	−0.237567	+	0.705075i
$92$	−244.458	−	40.0768i	−2.65715	−	0.435618i
$93$	−2.89501	+	0.474613i	−0.0311292	+	0.00510337i
$94$	−228.259	+	76.9094i	−2.42829	+	0.818185i
$95$	13.6620	+	20.1500i	0.143811	+	0.212105i
$96$	−36.0626	+	77.9481i	−0.375652	+	0.811959i
$97$	−47.1811	+	62.0657i	−0.486404	+	0.639853i	−0.972181	−	0.234229i	$-0.924743\pi$
$97$	−47.1811	+	62.0657i	−0.486404	+	0.639853i	0.485778	+	0.874082i	$0.338536\pi$
$98$	−0.889509	−	8.17890i	−0.00907663	−	0.0834582i
$99$	−52.4528	−	14.5634i	−0.529826	−	0.147105i
$100$	−114.545	+	168.942i	−1.14545	+	1.68942i
$101$	97.3232	+	161.752i	0.963596	+	1.60151i	0.786752	+	0.617269i	$0.211761\pi$
$101$	97.3232	+	161.752i	0.963596	+	1.60151i	0.176844	+	0.984239i	$0.443411\pi$
$102$	177.231	−	9.60917i	1.73756	−	0.0942075i
$103$	−42.9208	−	45.3109i	−0.416707	−	0.439912i	0.483520	−	0.875333i	$-0.339358\pi$
$103$	−42.9208	−	45.3109i	−0.416707	−	0.439912i	−0.900227	+	0.435421i	$0.856599\pi$
$104$	157.001	−	119.349i	1.50962	−	1.14758i
$105$	−21.2152	+	4.66981i	−0.202049	+	0.0444744i
$106$	−136.032	+	115.547i	−1.28332	+	1.09006i
$107$	7.86747	−	145.107i	0.0735278	−	1.35614i	−0.696237	−	0.717812i	$-0.745144\pi$
$107$	7.86747	−	145.107i	0.0735278	−	1.35614i	0.769765	−	0.638328i	$-0.220373\pi$
$108$	22.9617	+	43.3104i	0.212608	+	0.401022i
$109$	−0.604529	+	2.74640i	−0.00554614	+	0.0251964i	−0.979312	−	0.202354i	$-0.935141\pi$
$109$	−0.604529	+	2.74640i	−0.00554614	+	0.0251964i	0.973766	+	0.227551i	$0.0730718\pi$
$110$	−110.714	+	51.2218i	−1.00649	+	0.465653i
$111$	22.2450	−	36.9715i	0.200405	−	0.333076i
$112$	112.949	−	213.045i	1.00848	−	1.90219i
$113$	−47.5724	−	40.4083i	−0.420995	−	0.357596i	0.411709	−	0.911316i	$-0.364932\pi$
$113$	−47.5724	−	40.4083i	−0.420995	−	0.357596i	−0.832703	+	0.553720i	$0.813208\pi$
$114$	−57.9464	+	61.1733i	−0.508302	+	0.536608i
$115$	−5.20729	+	47.8803i	−0.0452808	+	0.416350i
$116$	−60.3446	+	151.453i	−0.520212	+	1.30563i
$117$		−	29.7052i		−	0.253891i
$118$	143.407	+	161.859i	1.21531	+	1.37169i
$119$	−191.174			−1.60650
$120$	58.7809	+	23.4204i	0.489841	+	0.195170i
$121$	207.044	+	22.5174i	1.71111	+	0.186094i
$122$	−19.5003	−	18.4717i	−0.159839	−	0.151407i
$123$	58.5359	−	68.9138i	0.475902	−	0.560275i
$124$	−14.1175	−	7.48465i	−0.113851	−	0.0603601i
$125$	73.2946	+	44.0999i	0.586357	+	0.352799i
$126$	−31.5700	−	68.2375i	−0.250556	−	0.541567i
$127$	−122.883	−	27.0487i	−0.967586	−	0.212982i	−0.297053	−	0.954861i	$-0.596004\pi$
$127$	−122.883	−	27.0487i	−0.967586	−	0.212982i	−0.670534	+	0.741879i	$0.733935\pi$
$128$	43.4859	−	23.0548i	0.339734	−	0.180116i
$129$	83.0832	+	4.50464i	0.644056	+	0.0349197i
$130$	−43.0946	−	50.7348i	−0.331497	−	0.390268i
$131$	35.8328	+	162.790i	0.273533	+	1.24267i	0.890245	+	0.455482i	$0.150533\pi$
$131$	35.8328	+	162.790i	0.273533	+	1.24267i	−0.616712	+	0.787189i	$0.711536\pi$
$132$	−179.437	−	236.045i	−1.35937	−	1.78822i
$133$	65.8891	−	62.4134i	0.495407	−	0.469274i
$134$	−22.6607	−	417.952i	−0.169110	−	3.11905i
$135$	8.16648	−	4.91361i	0.0604924	−	0.0363971i
$136$	460.899	+	312.497i	3.38896	+	2.29777i
$137$	−44.8475	+	161.526i	−0.327354	+	1.17902i	0.598495	+	0.801127i	$0.295766\pi$
$137$	−44.8475	+	161.526i	−0.327354	+	1.17902i	−0.925849	+	0.377895i	$0.876648\pi$
$138$	−165.720	+	18.0232i	−1.20087	+	0.130603i
$139$	36.2281	+	27.5399i	0.260634	+	0.198129i	0.727328	−	0.686290i	$-0.240762\pi$
$139$	36.2281	+	27.5399i	0.260634	+	0.198129i	−0.466694	+	0.884419i	$0.654555\pi$
$140$	−107.384	−	49.6812i	−0.767030	−	0.354866i
$141$	−94.2113	+	63.8768i	−0.668165	+	0.453027i
$142$	71.5914	+	212.476i	0.504165	+	1.49631i
$143$	29.0680	+	177.307i	0.203272	+	1.23991i
$144$	−17.1157	+	104.401i	−0.118859	+	0.725008i
$145$	30.0380	+	10.1210i	0.207158	+	0.0697998i
$146$	−61.4164	−	221.202i	−0.420660	−	1.51508i
$147$	−1.43903	−	3.61169i	−0.00978932	−	0.0245693i
$148$	218.323	−	86.9880i	1.47516	−	0.587757i
$149$	−218.542	+	60.6778i	−1.46672	+	0.407233i	−0.906888	−	0.421371i	$-0.861549\pi$
$149$	−218.542	+	60.6778i	−1.46672	+	0.407233i	−0.559834	+	0.828605i	$0.689135\pi$
$150$	−43.8568	+	130.162i	−0.292379	+	0.867749i
$151$	117.086	+	19.1953i	0.775404	+	0.127121i	0.536475	−	0.843916i	$-0.319755\pi$
$151$	117.086	+	19.1953i	0.775404	+	0.127121i	0.238929	+	0.971037i	$0.423204\pi$
$152$	−260.874	+	42.7681i	−1.71628	+	0.281369i
$153$	79.4846	−	26.7815i	0.519507	−	0.175042i
$154$	255.211	+	376.408i	1.65722	+	2.44421i
$155$	−1.30445	+	2.81953i	−0.00841582	+	0.0181905i
$156$	97.9152	−	128.805i	0.627661	−	0.825674i
$157$	−20.6544	−	189.914i	−0.131557	−	1.20964i	−0.854766	−	0.519014i	$-0.826299\pi$
$157$	−20.6544	−	189.914i	−0.131557	−	1.20964i	0.723209	−	0.690629i	$-0.242666\pi$
$158$	155.126	+	43.0704i	0.981807	+	0.272597i
$159$	−47.3324	+	69.8100i	−0.297688	+	0.439057i
$160$	46.8900	+	77.9319i	0.293063	+	0.487074i
$161$	179.285	−	9.72055i	1.11357	−	0.0603761i
$162$	22.6853	+	23.9486i	0.140033	+	0.147831i
$163$	133.097	−	101.178i	0.816548	−	0.620724i	−0.111256	−	0.993792i	$-0.535487\pi$
$163$	133.097	−	101.178i	0.816548	−	0.620724i	0.927804	+	0.373068i	$0.121694\pi$
$164$	480.974	−	105.870i	2.93277	−	0.645551i
$165$	−43.9365	+	37.3200i	−0.266282	+	0.226182i
$166$	−10.9811	+	202.535i	−0.0661513	+	1.22009i
$167$	82.7824	+	156.144i	0.495703	+	0.934996i	0.997544	+	0.0700358i	$0.0223114\pi$
$167$	82.7824	+	156.144i	0.495703	+	0.934996i	−0.501841	+	0.864960i	$0.667344\pi$
$168$	50.7086	−	230.371i	0.301837	−	1.37126i
$169$	64.3976	−	29.7935i	0.381051	−	0.176293i
$170$	96.9023	−	161.053i	0.570013	−	0.947370i
$171$	−18.6513	+	35.1801i	−0.109072	+	0.205732i
$172$	345.410	+	293.394i	2.00820	+	1.70578i
$173$	56.0103	−	59.1293i	0.323759	−	0.341788i	−0.543716	−	0.839269i	$-0.682983\pi$
$173$	56.0103	−	59.1293i	0.323759	−	0.341788i	0.867475	+	0.497481i	$0.165742\pi$
$174$	−11.8616	+	109.065i	−0.0681700	+	0.626813i
$175$	54.7585	−	137.433i	0.312906	−	0.785334i
$176$		−	639.906i		−	3.63583i
$177$	85.7611	+	55.5701i	0.484526	+	0.313955i
$178$	−351.742			−1.97608
$179$	120.249	+	47.9118i	0.671785	+	0.267663i	0.680988	−	0.732294i	$-0.261550\pi$
$179$	120.249	+	47.9118i	0.671785	+	0.267663i	−0.00920378	+	0.999958i	$0.502930\pi$
$180$	51.6072	+	5.61262i	0.286706	+	0.0311812i
$181$	−57.7627	−	54.7157i	−0.319131	−	0.302297i	0.511318	−	0.859391i	$-0.329157\pi$
$181$	−57.7627	−	54.7157i	−0.319131	−	0.302297i	−0.830449	+	0.557095i	$0.811916\pi$
$182$	−160.655	+	189.138i	−0.882719	+	1.03922i
$183$	−11.2145	−	5.94553i	−0.0612812	−	0.0324892i
$184$	−448.126	−	269.628i	−2.43547	−	1.46537i
$185$	−19.1857	−	41.4691i	−0.103706	−	0.224157i
$186$	−10.5012	−	2.31149i	−0.0564580	−	0.0124274i
$187$	−448.227	+	237.635i	−2.39693	+	1.27077i
$188$	−619.064	−	33.5647i	−3.29289	−	0.178535i
$189$	−23.0018	−	27.0798i	−0.121702	−	0.143279i
$190$	19.1818	+	87.1440i	0.100957	+	0.458652i
$191$	−191.364	−	251.736i	−1.00191	−	1.31799i	−0.947599	−	0.319463i	$-0.896497\pi$
$191$	−191.364	−	251.736i	−1.00191	−	1.31799i	−0.0543094	−	0.998524i	$-0.517296\pi$
$192$	−51.1617	+	48.4629i	−0.266467	+	0.252411i
$193$	−19.3081	−	356.118i	−0.100042	−	1.84517i	−0.431999	−	0.901874i	$-0.642191\pi$
$193$	−19.3081	−	356.118i	−0.100042	−	1.84517i	0.331956	−	0.943295i	$-0.392291\pi$
$194$	−244.850	+	147.321i	−1.26211	+	0.759388i
$195$	−26.0366	−	17.6532i	−0.133521	−	0.0905293i
$196$	5.66517	−	20.4041i	0.0289039	−	0.104102i
$197$	−81.5148	+	8.86527i	−0.413781	+	0.0450014i	−0.312642	−	0.949871i	$-0.601214\pi$
$197$	−81.5148	+	8.86527i	−0.413781	+	0.0450014i	−0.101139	+	0.994872i	$0.532249\pi$
$198$	−158.841	−	120.747i	−0.802225	−	0.609836i
$199$	188.731	+	87.3165i	0.948399	+	0.438776i	0.832216	−	0.554451i	$-0.187072\pi$
$199$	188.731	+	87.3165i	0.948399	+	0.438776i	0.116183	+	0.993228i	$0.462934\pi$
$200$	−356.669	+	241.827i	−1.78334	+	1.20914i
$201$	−63.1571	−	187.444i	−0.314215	−	0.932556i
$202$	111.938	+	682.789i	0.554146	+	3.38014i
$203$	19.1171	−	116.609i	0.0941730	−	0.574430i
$204$	432.932	+	145.872i	2.12222	+	0.715058i
$205$	−25.6161	−	92.2607i	−0.124956	−	0.450052i
$206$	−84.6713	−	212.509i	−0.411026	−	1.03160i
$207$	−73.1799	+	29.1575i	−0.353526	+	0.140858i
$208$	336.456	−	93.4167i	1.61758	−	0.449119i
$209$	76.9020	−	228.237i	0.367952	−	1.09204i
$210$	−78.5715	−	12.8811i	−0.374150	−	0.0613388i
$211$	−332.588	+	54.5250i	−1.57624	+	0.258412i	−0.885483	−	0.464671i	$-0.846173\pi$
$211$	−332.588	+	54.5250i	−1.57624	+	0.258412i	−0.690761	+	0.723083i	$0.742724\pi$
$212$	−435.349	+	146.686i	−2.05353	+	0.691915i
$213$	59.4600	+	87.6969i	0.279155	+	0.411722i
$214$	223.647	−	483.406i	1.04508	−	2.25890i
$215$	53.3231	−	70.1453i	0.248014	−	0.326257i
$216$	11.1895	+	102.886i	0.0518032	+	0.476322i
$217$	11.1594	+	3.09838i	0.0514256	+	0.0142782i
$218$	−5.78428	+	8.53117i	−0.0265334	+	0.0391338i
$219$	−55.9301	−	92.9566i	−0.255389	−	0.424459i
$220$	−313.529	+	16.9990i	−1.42513	+	0.0772684i
$221$	−190.380	−	200.982i	−0.861450	−	0.909421i
$222$	125.900	−	95.7066i	0.567117	−	0.431111i
$223$	−105.673	+	23.2604i	−0.473871	+	0.104307i	−0.445483	−	0.895290i	$-0.646968\pi$
$223$	−105.673	+	23.2604i	−0.473871	+	0.104307i	−0.0283872	+	0.999597i	$0.509037\pi$
$224$	258.419	−	219.503i	1.15366	−	0.979926i
$225$	−3.51401	+	64.8120i	−0.0156178	+	0.288054i
$226$	−107.161	−	202.127i	−0.474162	−	0.894365i
$227$	82.8968	−	376.604i	0.365184	−	1.65905i	−0.332848	−	0.942981i	$-0.608009\pi$
$227$	82.8968	−	376.604i	0.365184	−	1.65905i	0.698032	−	0.716067i	$-0.254059\pi$
$228$	−196.836	+	91.0661i	−0.863316	+	0.399413i
$229$	177.927	−	295.716i	0.776972	−	1.29134i	−0.174822	−	0.984600i	$-0.555935\pi$
$229$	177.927	−	295.716i	0.776972	−	1.29134i	0.951794	−	0.306738i	$-0.0992375\pi$
$230$	−82.6871	+	155.964i	−0.359509	+	0.678106i
$231$	163.793	+	139.127i	0.709063	+	0.602283i
$232$	−236.702	+	249.883i	−1.02027	+	1.07708i
$233$	32.0456	−	294.654i	0.137535	−	1.26461i	−0.698370	−	0.715736i	$-0.746091\pi$
$233$	32.0456	−	294.654i	0.137535	−	1.26461i	0.835905	−	0.548874i	$-0.184943\pi$
$234$	40.2995	−	101.144i	0.172220	−	0.432240i
$235$			120.537i			0.512922i
$236$	188.698	+	523.647i	0.799569	+	2.21884i
$237$	76.0793			0.321010
$238$	−650.933	−	259.355i	−2.73501	−	1.08973i
$239$	−199.402	−	21.6863i	−0.834319	−	0.0907377i	−0.319020	−	0.947748i	$-0.603354\pi$
$239$	−199.402	−	21.6863i	−0.834319	−	0.0907377i	−0.515299	+	0.857010i	$0.672319\pi$
$240$	81.3359	+	77.0454i	0.338900	+	0.321023i
$241$	112.567	−	132.524i	0.467084	−	0.549894i	−0.477299	−	0.878741i	$-0.658384\pi$
$241$	112.567	−	132.524i	0.467084	−	0.549894i	0.944383	+	0.328847i	$0.106660\pi$
$242$	674.423	+	357.557i	2.78687	+	1.47751i
$243$	13.3571	+	8.03669i	0.0549674	+	0.0330728i
$244$	−29.0294	−	62.7459i	−0.118973	−	0.257155i
$245$	−4.02083	−	0.885051i	−0.0164115	−	0.00361245i
$246$	292.802	−	155.234i	1.19025	−	0.631033i
$247$	131.231	+	7.11516i	0.531301	+	0.0288063i
$248$	−21.8393	−	25.7112i	−0.0880617	−	0.103674i
$249$	20.6050	+	93.6095i	0.0827510	+	0.375942i
$250$	189.735	+	249.592i	0.758939	+	0.998368i
$251$	−173.714	+	164.551i	−0.692088	+	0.655581i	−0.950597	−	0.310428i	$-0.899528\pi$
$251$	−173.714	+	164.551i	−0.692088	+	0.655581i	0.258508	+	0.966009i	$0.416769\pi$
$252$	−10.4772	−	193.240i	−0.0415761	−	0.766826i
$253$	408.269	−	245.648i	1.61371	−	0.970939i
$254$	−381.714	−	258.808i	−1.50281	−	1.01893i
$255$	23.7622	−	85.5838i	0.0931852	−	0.335623i
$256$	341.136	−	37.1007i	1.33256	−	0.144925i
$257$	183.233	+	139.290i	0.712969	+	0.541985i	0.897594	−	0.440824i	$-0.145314\pi$
$257$	183.233	+	139.290i	0.712969	+	0.541985i	−0.184624	+	0.982809i	$0.559107\pi$
$258$	276.781	+	128.053i	1.07280	+	0.496328i
$259$	−140.987	+	95.5919i	−0.544353	+	0.369081i
$260$	−54.7085	−	162.369i	−0.210417	−	0.624496i
$261$	8.38741	+	51.1609i	0.0321357	+	0.196019i
$262$	−98.8405	+	602.901i	−0.377254	+	2.30115i
$263$	254.827	+	85.8612i	0.968924	+	0.326468i	0.758885	−	0.651225i	$-0.225744\pi$
$263$	254.827	+	85.8612i	0.968924	+	0.326468i	0.210039	+	0.977693i	$0.432641\pi$
$264$	−167.467	−	603.162i	−0.634345	−	2.28470i
$265$	33.0597	+	82.9735i	0.124753	+	0.313107i
$266$	309.021	−	123.125i	1.16173	−	0.462876i
$267$	−160.161	+	44.4683i	−0.599852	+	0.166548i
$268$	344.001	−	1020.96i	1.28359	−	3.80955i
$269$	−13.6568	−	2.23891i	−0.0507686	−	0.00832309i	0.136344	−	0.990662i	$-0.456465\pi$
$269$	−13.6568	−	2.23891i	−0.0507686	−	0.00832309i	−0.187113	+	0.982338i	$0.559913\pi$
$270$	34.4723	−	5.65145i	0.127675	−	0.0209313i
$271$	−384.954	+	129.706i	−1.42050	+	0.478621i	−0.921634	−	0.388061i	$-0.873145\pi$
$271$	−384.954	+	129.706i	−1.42050	+	0.478621i	−0.498862	+	0.866681i	$0.666249\pi$
$272$	553.303	+	816.061i	2.03420	+	3.00022i
$273$	−49.2405	+	106.432i	−0.180368	+	0.389859i
$274$	−371.836	+	489.142i	−1.35707	+	1.78519i
$275$	−42.4470	−	390.294i	−0.154353	−	1.41925i
$276$	−413.426	−	114.787i	−1.49792	−	0.415896i
$277$	−261.864	+	386.220i	−0.945357	+	1.39430i	−0.0265244	+	0.999648i	$0.508444\pi$
$277$	−261.864	+	386.220i	−0.945357	+	1.39430i	−0.918832	+	0.394648i	$0.870866\pi$
$278$	85.9921	+	142.920i	0.309324	+	0.514101i
$279$	−5.07379	+	0.275093i	−0.0181856	+	0.000985997i
$280$	−171.785	−	181.351i	−0.613517	−	0.647683i
$281$	3.69808	−	2.81120i	0.0131604	−	0.0100043i	−0.598573	−	0.801068i	$-0.704265\pi$
$281$	3.69808	−	2.81120i	0.0131604	−	0.0100043i	0.611734	+	0.791064i	$0.290472\pi$
$282$	−407.441	+	89.6846i	−1.44483	+	0.318030i
$283$	194.898	−	165.548i	0.688685	−	0.584974i	−0.233204	−	0.972428i	$-0.574921\pi$
$283$	194.898	−	165.548i	0.688685	−	0.584974i	0.921889	+	0.387453i	$0.126645\pi$
$284$	−31.2438	+	576.258i	−0.110013	+	2.02908i
$285$	19.7512	+	37.2547i	0.0693025	+	0.130718i
$286$	−141.568	+	643.152i	−0.494994	+	2.24878i
$287$	−323.964	+	149.882i	−1.12879	+	0.522236i
$288$	−76.6933	+	127.465i	−0.266296	+	0.442588i
$289$	230.772	−	435.281i	0.798518	−	1.50616i
$290$	88.5465	+	75.2121i	0.305333	+	0.259352i
$291$	−92.8640	+	98.0353i	−0.319120	+	0.336891i
$292$	63.8867	−	587.429i	0.218790	−	2.01174i
$293$	76.8379	−	192.849i	0.262245	−	0.658186i	−0.737609	−	0.675228i	$-0.764045\pi$
$293$	76.8379	−	192.849i	0.262245	−	0.658186i	0.999855	+	0.0170413i	$0.00542467\pi$
$294$		−	14.2498i		−	0.0484687i
$295$	99.6732	−	42.1452i	0.337875	−	0.142865i
$296$	496.162			1.67622
$297$	−87.5910	−	34.8995i	−0.294919	−	0.117507i
$298$	−826.437	−	89.8805i	−2.77328	−	0.301612i
$299$	188.760	+	178.803i	0.631305	+	0.598004i
$300$	−228.873	+	269.450i	−0.762908	+	0.898165i
$301$	−290.214	−	153.862i	−0.964166	−	0.511169i
$302$	372.628	+	224.203i	1.23387	+	0.742394i
$303$	137.290	+	296.746i	0.453101	+	0.979361i
$304$	−457.123	−	100.620i	−1.50369	−	0.330988i
$305$	−11.8758	+	6.29614i	−0.0389370	+	0.0206431i
$306$	306.972	+	16.6436i	1.00318	+	0.0543907i
$307$	151.874	+	178.800i	0.494704	+	0.582411i	0.951689	−	0.307064i	$-0.0993465\pi$
$307$	151.874	+	178.800i	0.494704	+	0.582411i	−0.456985	+	0.889475i	$0.651071\pi$
$308$	251.632	+	1143.17i	0.816986	+	3.71160i
$309$	−65.4199	−	86.0584i	−0.211715	−	0.278506i
$310$	−8.26667	+	7.83061i	−0.0266667	+	0.0252600i
$311$	−23.0570	−	425.261i	−0.0741383	−	1.36740i	−0.764822	−	0.644242i	$-0.777173\pi$
$311$	−23.0570	−	425.261i	−0.0741383	−	1.36740i	0.690683	−	0.723157i	$-0.257310\pi$
$312$	292.689	−	176.105i	0.938106	−	0.564440i
$313$	211.331	+	143.286i	0.675178	+	0.457782i	0.849976	−	0.526822i	$-0.176617\pi$
$313$	211.331	+	143.286i	0.675178	+	0.457782i	−0.174797	+	0.984604i	$0.555927\pi$
$314$	187.320	−	674.665i	0.596560	−	2.14861i
$315$	−37.4049	+	4.06802i	−0.118746	+	0.0129144i
$316$	329.889	+	250.775i	1.04395	+	0.793591i
$317$	−339.506	−	157.072i	−1.07100	−	0.495496i	−0.196489	−	0.980506i	$-0.562954\pi$
$317$	−339.506	−	157.072i	−1.07100	−	0.495496i	−0.874509	+	0.485010i	$0.838816\pi$
$318$	−255.871	+	173.485i	−0.804626	+	0.545550i
$319$	−100.127	−	297.166i	−0.313877	−	0.931554i
$320$	12.0733	+	73.6436i	0.0377289	+	0.230136i
$321$	40.7208	−	248.386i	0.126856	−	0.773788i
$322$	623.640	+	210.129i	1.93677	+	0.652574i
$323$	99.2763	+	357.561i	0.307357	+	1.10700i
$324$	31.4271	+	78.8760i	0.0969972	+	0.243445i
$325$	199.016	−	79.2952i	0.612357	−	0.243985i
$326$	590.450	−	163.938i	1.81120	−	0.502876i
$327$	−1.55525	+	4.61582i	−0.00475611	+	0.0141156i
$328$	1026.04	+	168.211i	3.12818	+	0.512839i
$329$	443.437	−	72.6978i	1.34783	−	0.220966i
$330$	−200.231	+	67.4656i	−0.606760	+	0.204441i
$331$	−162.709	−	239.978i	−0.491567	−	0.725008i	0.498300	−	0.867005i	$-0.333958\pi$
$331$	−162.709	−	239.978i	−0.491567	−	0.725008i	−0.989867	+	0.141997i	$0.954648\pi$
$332$	−219.213	+	473.820i	−0.660279	+	1.42717i
$333$	45.2272	−	59.4953i	0.135817	−	0.178665i
$334$	70.0356	+	643.967i	0.209687	+	1.92804i
$335$	−201.827	−	56.0370i	−0.602469	−	0.167275i
$336$	234.384	−	345.690i	0.697570	−	1.02884i
$337$	31.4466	+	52.2646i	0.0933133	+	0.155088i	0.899998	−	0.435894i	$-0.143568\pi$
$337$	31.4466	+	52.2646i	0.0933133	+	0.155088i	−0.806685	+	0.590982i	$0.798740\pi$
$338$	259.689	−	14.0799i	0.768309	−	0.0416565i
$339$	−74.3476	−	78.4878i	−0.219314	−	0.231527i
$340$	385.140	−	292.776i	1.13276	−	0.861104i
$341$	30.0157	−	6.60694i	0.0880224	−	0.0193752i
$342$	−111.234	+	94.4826i	−0.325244	+	0.276265i
$343$	−18.9703	+	349.886i	−0.0553069	+	1.02008i
$344$	448.168	+	845.335i	1.30281	+	2.45737i
$345$	−17.9328	+	81.4697i	−0.0519793	+	0.236144i
$346$	270.929	−	125.345i	0.783031	−	0.362269i
$347$	−179.653	+	298.585i	−0.517731	+	0.860476i	−0.999878	−	0.0156145i	$-0.995030\pi$
$347$	−179.653	+	298.585i	−0.517731	+	0.860476i	0.482147	+	0.876090i	$0.339857\pi$
$348$	−132.269	+	249.487i	−0.380085	+	0.716916i
$349$	−51.3009	−	43.5754i	−0.146994	−	0.124858i	0.570872	−	0.821039i	$-0.306605\pi$
$349$	−51.3009	−	43.5754i	−0.146994	−	0.124858i	−0.717866	+	0.696181i	$0.754881\pi$
$350$	372.898	−	393.663i	1.06542	−	1.12475i
$351$	5.56282	−	51.1493i	0.0158485	−	0.145725i
$352$	333.042	−	835.872i	0.946142	−	2.37464i
$353$			306.342i			0.867823i	0.900955	+	0.433912i	$0.142867\pi$
$353$			306.342i			0.867823i	−0.900955	+	0.433912i	$0.857133\pi$
$354$	216.621	+	305.560i	0.611925	+	0.863164i
$355$	112.202			0.316062
$356$	−841.052	−	335.106i	−2.36251	−	0.941309i
$357$	−329.181	−	35.8006i	−0.922077	−	0.100282i
$358$	344.442	+	326.272i	0.962127	+	0.911375i
$359$	−345.280	+	406.495i	−0.961783	+	1.13230i	0.0293688	+	0.999569i	$0.490650\pi$
$359$	−345.280	+	406.495i	−0.961783	+	1.13230i	−0.991152	+	0.132730i	$0.957626\pi$
$360$	96.8287	+	51.3353i	0.268969	+	0.142598i
$361$	158.374	+	95.2908i	0.438710	+	0.263963i
$362$	−122.448	−	264.667i	−0.338254	−	0.731124i
$363$	352.292	+	77.5454i	0.970502	+	0.213624i
$364$	−564.335	+	299.192i	−1.55037	+	0.821955i
$365$	−114.714	−	6.21963i	−0.314286	−	0.0170401i
$366$	−30.1184	−	35.4582i	−0.0822908	−	0.0968803i
$367$	−57.2983	−	260.309i	−0.156126	−	0.709288i	−0.988016	−	0.154348i	$-0.950672\pi$
$367$	−57.2983	−	260.309i	−0.156126	−	0.709288i	0.831890	−	0.554940i	$-0.187259\pi$
$368$	−560.388	−	737.178i	−1.52279	−	2.00320i
$369$	113.698	−	107.701i	0.308125	−	0.291872i
$370$	−9.06682	−	167.228i	−0.0245049	−	0.451967i
$371$	285.308	−	171.664i	0.769025	−	0.462707i
$372$	−22.9073	−	15.5316i	−0.0615789	−	0.0417515i
$373$	−120.434	+	433.765i	−0.322880	+	1.16291i	0.606895	+	0.794782i	$0.292415\pi$
$373$	−120.434	+	433.765i	−0.322880	+	1.16291i	−0.929775	+	0.368128i	$0.879999\pi$
$374$	−1848.57	+	201.044i	−4.94269	+	0.537550i
$375$	117.947	+	89.6612i	0.314526	+	0.239096i
$376$	−1187.91	−	549.586i	−3.15934	−	1.46167i
$377$	141.630	−	96.0275i	0.375676	−	0.254715i
$378$	−41.5817	−	123.410i	−0.110004	−	0.326481i
$379$	−27.2537	−	166.240i	−0.0719096	−	0.438629i	−0.998102	−	0.0615784i	$-0.980387\pi$
$379$	−27.2537	−	166.240i	−0.0719096	−	0.438629i	0.926193	−	0.377051i	$-0.123062\pi$
$380$	−37.1566	+	226.645i	−0.0977805	+	0.596435i
$381$	−206.527	−	69.5872i	−0.542067	−	0.182643i
$382$	−310.066	−	1116.76i	−0.811691	−	2.92345i
$383$	−178.706	−	448.519i	−0.466597	−	1.17107i	−0.954510	−	0.298177i	$-0.903621\pi$
$383$	−178.706	−	448.519i	−0.466597	−	1.17107i	0.487914	−	0.872892i	$-0.337758\pi$
$384$	79.1957	−	31.5545i	0.206239	−	0.0821731i
$385$	219.284	−	60.8840i	0.569569	−	0.158140i
$386$	417.383	−	1238.75i	1.08130	−	3.20920i
$387$	142.217	+	23.3153i	0.367486	+	0.0602463i
$388$	−725.816	+	118.992i	−1.87066	+	0.306679i
$389$	493.376	−	166.238i	1.26832	−	0.427346i	0.396889	−	0.917867i	$-0.370090\pi$
$389$	493.376	−	166.238i	1.26832	−	0.427346i	0.871430	+	0.490521i	$0.163193\pi$
$390$	−64.7034	−	95.4304i	−0.165906	−	0.244693i
$391$	−308.257	+	666.286i	−0.788380	+	1.70406i
$392$	27.0553	−	35.5906i	0.0690185	−	0.0907923i
$393$	31.2151	+	287.018i	0.0794277	+	0.730325i
$394$	−289.579	−	80.4013i	−0.734972	−	0.204064i
$395$	45.2124	−	66.6834i	0.114462	−	0.168819i
$396$	−264.768	−	440.048i	−0.668607	−	1.11123i
$397$	−41.3762	+	2.24335i	−0.104222	+	0.00565076i	−0.106176	−	0.994347i	$-0.533861\pi$
$397$	−41.3762	+	2.24335i	−0.104222	+	0.00565076i	0.00195406	+	0.999998i	$0.499378\pi$
$398$	524.160	+	553.349i	1.31698	+	1.39032i
$399$	125.142	−	95.1307i	0.313640	−	0.238423i
$400$	−745.145	+	164.019i	−1.86286	+	0.410047i
$401$	42.7037	−	36.2729i	0.106493	−	0.0904561i	−0.592558	−	0.805528i	$-0.701882\pi$
$401$	42.7037	−	36.2729i	0.106493	−	0.0904561i	0.699051	+	0.715072i	$0.253606\pi$
$402$	39.2495	−	723.915i	0.0976356	−	1.80078i
$403$	7.85570	+	14.8174i	0.0194931	+	0.0367678i
$404$	−382.841	+	1739.26i	−0.947627	+	4.30511i
$405$	14.9820	−	6.93141i	0.0369926	−	0.0171146i
$406$	223.290	−	371.111i	0.549976	−	0.914067i
$407$	−211.736	+	399.377i	−0.520237	+	0.981270i
$408$	735.100	+	624.399i	1.80172	+	1.53039i
$409$	−111.496	+	117.705i	−0.272607	+	0.287788i	−0.847896	−	0.530162i	$-0.822131\pi$
$409$	−111.496	+	117.705i	−0.272607	+	0.287788i	0.575289	+	0.817950i	$0.304890\pi$
$410$	37.9444	−	348.893i	0.0925474	−	0.850959i
$411$	−107.471	+	269.733i	−0.261487	+	0.656284i
$412$		−	588.798i		−	1.42912i
$413$	−215.161	−	341.264i	−0.520970	−	0.826306i
$414$	−288.729			−0.697412
$415$	94.2937	+	37.5700i	0.227214	+	0.0905302i
$416$	488.113	+	53.0855i	1.17335	+	0.127609i
$417$	57.2237	+	54.2052i	0.137227	+	0.129988i
$418$	571.483	−	672.802i	1.36718	−	1.60957i
$419$	443.571	+	235.167i	1.05864	+	0.561257i	0.904360	−	0.426770i	$-0.140349\pi$
$419$	443.571	+	235.167i	1.05864	+	0.561257i	0.154283	+	0.988027i	$0.450693\pi$
$420$	−175.601	−	105.656i	−0.418098	−	0.251561i
$421$	117.237	+	253.403i	0.278472	+	0.601907i	0.995460	−	0.0951778i	$-0.0303420\pi$
$421$	117.237	+	253.403i	0.278472	+	0.601907i	−0.716988	+	0.697085i	$0.754480\pi$
$422$	−1206.41	−	265.551i	−2.85879	−	0.629267i
$423$	−174.184	+	92.3466i	−0.411783	+	0.218314i
$424$	−968.453	−	52.5080i	−2.28409	−	0.123840i
$425$	391.604	+	461.032i	0.921422	+	1.08478i
$426$	83.4832	+	379.268i	0.195970	+	0.890300i
$427$	30.3250	+	39.8919i	0.0710188	+	0.0934236i
$428$	995.307	−	942.805i	2.32548	−	2.20282i
$429$	16.8482	+	310.747i	0.0392733	+	0.724353i
$430$	276.724	−	166.499i	0.643544	−	0.387207i
$431$	−378.160	−	256.399i	−0.877401	−	0.594892i	0.0371743	−	0.999309i	$-0.488164\pi$
$431$	−378.160	−	256.399i	−0.877401	−	0.594892i	−0.914575	+	0.404416i	$0.867475\pi$
$432$	−49.0224	+	176.563i	−0.113478	+	0.408710i
$433$	−140.283	+	15.2567i	−0.323979	+	0.0352349i	−0.268664	−	0.963234i	$-0.586582\pi$
$433$	−140.283	+	15.2567i	−0.323979	+	0.0352349i	−0.0553157	+	0.998469i	$0.517617\pi$
$434$	33.7934	+	25.6891i	0.0778650	+	0.0591914i
$435$	49.8269	+	23.0524i	0.114545	+	0.0529940i
$436$	−21.9585	+	14.8883i	−0.0503636	+	0.0341474i
$437$	−111.283	−	330.277i	−0.254653	−	0.755783i
$438$	−64.3287	−	392.388i	−0.146869	−	0.895863i
$439$	−29.4005	+	179.335i	−0.0669715	+	0.408508i	0.931971	+	0.362533i	$0.118088\pi$
$439$	−29.4005	+	179.335i	−0.0669715	+	0.408508i	−0.998943	+	0.0459754i	$0.985360\pi$
$440$	−628.193	−	211.663i	−1.42771	−	0.481052i
$441$	−1.80151	−	6.48845i	−0.00408505	−	0.0147130i
$442$	−375.570	−	942.609i	−0.849705	−	2.13260i
$443$	171.165	−	68.1984i	0.386377	−	0.153947i	−0.168857	−	0.985640i	$-0.554008\pi$
$443$	171.165	−	68.1984i	0.386377	−	0.153947i	0.555235	+	0.831694i	$0.312628\pi$
$444$	392.220	−	108.899i	0.883379	−	0.245269i
$445$	−56.2038	+	166.807i	−0.126301	+	0.374847i
$446$	−391.366	−	64.1612i	−0.877502	−	0.143859i
$447$	−387.669	+	63.5551i	−0.867269	+	0.142182i
$448$	263.642	−	88.8315i	0.588487	−	0.198284i
$449$	62.7755	+	92.5869i	0.139812	+	0.206207i	0.891148	−	0.453713i	$-0.149901\pi$
$449$	62.7755	+	92.5869i	0.139812	+	0.206207i	−0.751336	+	0.659919i	$0.770590\pi$
$450$	−99.8921	+	215.913i	−0.221982	+	0.479807i
$451$	−573.260	+	754.110i	−1.27109	+	1.67209i
$452$	−63.6660	−	585.399i	−0.140854	−	1.29513i
$453$	198.015	+	54.9787i	0.437120	+	0.121366i
$454$	793.176	−	1169.85i	1.74708	−	2.57676i
$455$	64.0244	+	106.409i	0.140713	+	0.233867i
$456$	−457.207	+	24.7891i	−1.00265	+	0.0543620i
$457$	450.047	+	475.109i	0.984786	+	1.03963i	0.999210	+	0.0397298i	$0.0126497\pi$
$457$	450.047	+	475.109i	0.984786	+	1.03963i	−0.0144246	+	0.999896i	$0.504592\pi$
$458$	1007.01	−	765.510i	2.19871	−	1.67142i
$459$	141.880	−	31.2301i	0.309106	−	0.0680394i
$460$	−346.302	+	294.152i	−0.752830	+	0.639460i
$461$	−26.3217	+	485.475i	−0.0570970	+	1.05309i	0.819873	+	0.572546i	$0.194044\pi$
$461$	−26.3217	+	485.475i	−0.0570970	+	1.05309i	−0.876970	+	0.480546i	$0.840439\pi$
$462$	368.958	+	695.929i	0.798611	+	1.50634i
$463$	28.6850	−	130.317i	0.0619547	−	0.281463i	−0.935450	−	0.353458i	$-0.885006\pi$
$463$	28.6850	−	130.317i	0.0619547	−	0.281463i	0.997405	+	0.0719953i	$0.0229367\pi$
$464$	−553.098	+	255.891i	−1.19202	+	0.551488i
$465$	−2.77414	+	4.61065i	−0.00596589	+	0.00991538i
$466$	508.855	−	959.802i	1.09196	−	2.05966i
$467$	678.077	+	575.964i	1.45199	+	1.23333i	0.923058	+	0.384660i	$0.125681\pi$
$467$	678.077	+	575.964i	1.45199	+	1.23333i	0.528927	+	0.848667i	$0.322595\pi$
$468$	192.721	−	203.453i	0.411797	−	0.434729i
$469$	−84.4265	+	776.289i	−0.180014	+	1.65520i
$470$	−163.526	+	410.419i	−0.347928	+	0.873232i
$471$		−	330.880i		−	0.702506i
$472$	−39.1107	+	1174.46i	−0.0828616	+	2.48826i
$473$	−871.692			−1.84290
$474$	259.045	+	103.213i	0.546508	+	0.217749i
$475$	−285.484	−	31.0483i	−0.601020	−	0.0653648i
$476$	−1309.36	−	1240.29i	−2.75076	−	2.60566i
$477$	−94.5747	+	111.342i	−0.198270	+	0.233421i
$478$	−649.530	−	344.359i	−1.35885	−	0.720416i
$479$	−117.674	−	70.8023i	−0.245667	−	0.147813i	0.387396	−	0.921914i	$-0.373375\pi$
$479$	−117.674	−	70.8023i	−0.245667	−	0.147813i	−0.633062	+	0.774101i	$0.718202\pi$
$480$	66.1457	+	142.972i	0.137804	+	0.297858i
$481$	−240.899	−	53.0259i	−0.500829	−	0.110241i
$482$	563.073	−	298.522i	1.16820	−	0.619341i
$483$	310.531	+	16.8365i	0.642921	+	0.0348581i
$484$	1271.97	+	1497.48i	2.62804	+	3.09397i
$485$	30.7405	+	139.656i	0.0633825	+	0.287950i
$486$	34.5770	+	45.4852i	0.0711460	+	0.0935910i
$487$	−87.9013	+	83.2645i	−0.180495	+	0.170974i	−0.772613	−	0.634877i	$-0.781051\pi$
$487$	−87.9013	+	83.2645i	−0.180495	+	0.170974i	0.592118	+	0.805852i	$0.298292\pi$
$488$	−7.90207	−	145.745i	−0.0161928	−	0.298658i
$489$	248.127	−	149.293i	0.507418	−	0.305303i
$490$	−12.4899	−	8.46838i	−0.0254897	−	0.0172824i
$491$	138.833	−	500.030i	0.282755	−	1.01839i	−0.676637	−	0.736317i	$-0.736563\pi$
$491$	138.833	−	500.030i	0.282755	−	1.01839i	0.959392	−	0.282075i	$-0.0910228\pi$
$492$	848.014	−	92.2271i	1.72361	−	0.187453i
$493$	384.638	+	292.394i	0.780199	+	0.593092i
$494$	437.181	+	202.261i	0.884981	+	0.409436i
$495$	−82.6429	+	56.0333i	−0.166955	+	0.113199i
$496$	−19.0719	−	56.6033i	−0.0384513	−	0.114120i
$497$	−67.6710	−	412.775i	−0.136159	−	0.830532i
$498$	−56.8365	+	346.687i	−0.114130	+	0.696160i
$499$	−271.939	−	91.6271i	−0.544969	−	0.183621i	0.0333329	−	0.999444i	$-0.489388\pi$
$499$	−271.939	−	91.6271i	−0.544969	−	0.183621i	−0.578302	+	0.815823i	$0.696284\pi$
$500$	215.889	+	777.562i	0.431778	+	1.55512i
$501$	113.302	+	284.367i	0.226152	+	0.567599i
$502$	−814.722	+	324.615i	−1.62295	+	0.646643i
$503$	37.4935	−	10.4100i	0.0745398	−	0.0206959i	−0.230058	−	0.973177i	$-0.573892\pi$
$503$	37.4935	−	10.4100i	0.0745398	−	0.0206959i	0.304598	+	0.952481i	$0.401478\pi$
$504$	130.456	−	387.180i	0.258841	−	0.768214i
$505$	341.686	+	56.0166i	0.676606	+	0.110924i
$506$	1723.39	−	282.535i	3.40590	−	0.558369i
$507$	116.465	−	39.2418i	0.229715	−	0.0773999i
$508$	−666.151	−	982.500i	−1.31132	−	1.93405i
$509$	−114.230	+	246.904i	−0.224420	+	0.485077i	−0.986778	−	0.162080i	$-0.948180\pi$
$509$	−114.230	+	246.904i	−0.224420	+	0.485077i	0.762357	+	0.647156i	$0.224042\pi$
$510$	197.016	−	259.170i	0.386305	−	0.508176i
$511$	46.3051	+	425.768i	0.0906166	+	0.833206i
$512$	1022.17	+	283.805i	1.99643	+	0.554307i
$513$	−38.7038	+	57.0838i	−0.0754459	+	0.111274i
$514$	434.928	+	722.856i	0.846164	+	1.40634i
$515$	−114.308	+	6.19759i	−0.221957	+	0.0120342i
$516$	539.818	+	569.879i	1.04616	+	1.10442i
$517$	949.318	−	721.653i	1.83621	−	1.39585i
$518$	−609.737	+	134.213i	−1.17710	+	0.259099i
$519$	107.517	−	91.3257i	0.207162	−	0.175965i
$520$	19.5835	−	361.197i	0.0376607	−	0.694610i
$521$	−253.381	−	477.927i	−0.486335	−	0.917326i	−0.998298	−	0.0583183i	$-0.981426\pi$
$521$	−253.381	−	477.927i	−0.486335	−	0.917326i	0.511963	−	0.859008i	$-0.328919\pi$
$522$	−40.8488	+	185.578i	−0.0782545	+	0.355514i
$523$	367.134	−	169.854i	0.701977	−	0.324769i	−0.0362299	−	0.999343i	$-0.511535\pi$
$523$	367.134	−	169.854i	0.701977	−	0.324769i	0.738207	+	0.674574i	$0.235673\pi$
$524$	−810.725	+	1347.43i	−1.54718	+	2.57144i
$525$	120.025	−	226.392i	0.228620	−	0.431222i
$526$	751.184	+	638.062i	1.42811	+	1.21305i
$527$	−32.5657	+	34.3792i	−0.0617944	+	0.0652356i
$528$	119.834	−	1101.85i	0.226958	−	2.08684i
$529$	59.4052	−	149.096i	0.112297	−	0.281845i
$530$			327.369i			0.617678i
$531$	137.265	+	111.746i	0.258503	+	0.210445i
$532$	856.204			1.60941
$533$	−480.191	−	191.326i	−0.900922	−	0.358960i
$534$	−605.663	−	65.8698i	−1.13420	−	0.123352i
$535$	−193.510	−	183.303i	−0.361701	−	0.342622i
$536$	1472.48	−	1733.54i	2.74717	−	3.23422i
$537$	198.085	+	105.018i	0.368873	+	0.195564i
$538$	−43.4629	−	26.1507i	−0.0807860	−	0.0486073i
$539$	17.1022	+	36.9659i	0.0317296	+	0.0685823i
$540$	87.8112	+	19.3287i	0.162613	+	0.0357939i
$541$	413.291	−	219.113i	0.763938	−	0.405014i	−0.0404020	−	0.999184i	$-0.512864\pi$
$541$	413.291	−	219.113i	0.763938	−	0.405014i	0.804340	+	0.594169i	$0.202519\pi$
$542$	−1486.71	−	80.6070i	−2.74300	−	0.148721i
$543$	−89.2149	−	105.032i	−0.164300	−	0.193429i
$544$	298.025	+	1353.94i	0.547841	+	2.48886i
$545$	3.12150	+	4.10626i	0.00572752	+	0.00753443i
$546$	−312.051	+	295.590i	−0.571521	+	0.541374i
$547$	15.5257	+	286.355i	0.0283834	+	0.523501i	0.977808	+	0.209505i	$0.0671852\pi$
$547$	15.5257	+	286.355i	0.0283834	+	0.523501i	−0.949424	+	0.313996i	$0.898332\pi$
$548$	−1355.11	+	815.342i	−2.47283	+	1.48785i
$549$	−18.1967	−	12.3377i	−0.0331452	−	0.0224730i
$550$	384.962	−	1386.51i	0.699931	−	2.52092i
$551$	−228.027	+	24.7995i	−0.413843	+	0.0450081i
$552$	−721.134	−	548.192i	−1.30640	−	0.993101i
$553$	−272.586	−	126.112i	−0.492923	−	0.228051i
$554$	−1415.59	+	959.796i	−2.55522	+	1.73248i
$555$	−25.2699	−	74.9984i	−0.0455314	−	0.135132i
$556$	69.4559	+	423.662i	0.124921	+	0.761983i
$557$	−34.6606	+	211.420i	−0.0622273	+	0.379570i	0.937291	+	0.348547i	$0.113325\pi$
$557$	−34.6606	+	211.420i	−0.0622273	+	0.379570i	−0.999519	+	0.0310231i	$0.990123\pi$
$558$	−17.6491	−	5.94668i	−0.0316292	−	0.0106571i
$559$	−127.254	−	458.327i	−0.227646	−	0.819906i
$560$	−163.707	−	410.874i	−0.292334	−	0.733703i
$561$	−816.302	+	325.244i	−1.45508	+	0.579758i
$562$	16.4055	−	4.55497i	0.0291913	−	0.00810492i
$563$	−183.994	+	546.075i	−0.326810	+	0.969938i	0.650752	+	0.759290i	$0.274454\pi$
$563$	−183.994	+	546.075i	−0.326810	+	0.969938i	−0.977562	+	0.210647i	$0.932443\pi$
$564$	−1059.68	−	173.726i	−1.87886	−	0.308024i
$565$	−112.978	+	18.5218i	−0.199961	+	0.0327819i
$566$	888.204	−	299.271i	1.56926	−	0.528747i
$567$	−34.5355	−	50.9361i	−0.0609092	−	0.0898343i
$568$	−511.584	+	1105.77i	−0.900676	+	1.94678i
$569$	−425.423	+	559.634i	−0.747667	+	0.983539i	0.252207	+	0.967673i	$0.418844\pi$
$569$	−425.423	+	559.634i	−0.747667	+	0.983539i	−0.999874	+	0.0158659i	$0.994950\pi$
$570$	16.7099	+	153.645i	0.0293156	+	0.269553i
$571$	668.914	+	185.723i	1.17148	+	0.325259i	0.798161	−	0.602445i	$-0.205807\pi$
$571$	668.914	+	185.723i	1.17148	+	0.325259i	0.373317	+	0.927704i	$0.378220\pi$
$572$	−951.239	+	1402.97i	−1.66300	+	2.45275i
$573$	−282.368	−	469.299i	−0.492789	−	0.819021i
$574$	−1306.41	+	70.8316i	−2.27598	+	0.123400i
$575$	−390.693	−	412.450i	−0.679467	−	0.717304i
$576$	−97.1707	+	73.8672i	−0.168699	+	0.128242i
$577$	−226.130	+	49.7750i	−0.391907	+	0.0862652i	−0.406552	−	0.913628i	$-0.633269\pi$
$577$	−226.130	+	49.7750i	−0.391907	+	0.0862652i	0.0146453	+	0.999893i	$0.495338\pi$
$578$	1376.28	−	1169.03i	2.38112	−	2.02254i
$579$	33.4427	−	616.814i	0.0577594	−	1.06531i
$580$	140.069	+	264.199i	0.241499	+	0.455515i
$581$	81.3444	−	369.552i	0.140008	−	0.636061i
$582$	−449.195	+	207.820i	−0.771812	+	0.357078i
$583$	455.551	−	757.132i	0.781391	−	1.29868i
$584$	584.335	−	1102.17i	1.00057	−	1.88728i
$585$	−41.5264	−	35.2728i	−0.0709853	−	0.0602955i
$586$	523.255	−	552.394i	0.892927	−	0.942652i
$587$	80.5592	−	740.730i	0.137239	−	1.26189i	−0.699637	−	0.714498i	$-0.746655\pi$
$587$	80.5592	−	740.730i	0.137239	−	1.26189i	0.836876	−	0.547392i	$-0.184379\pi$
$588$	13.5759	−	34.0728i	0.0230882	−	0.0579470i
$589$		−	22.4809i		−	0.0381678i
$590$	396.557	−	8.27997i	0.672130	−	0.0140339i
$591$	−142.020			−0.240305
$592$	816.104	+	325.166i	1.37855	+	0.549266i
$593$	89.8338	+	9.77001i	0.151490	+	0.0164756i	0.183550	−	0.983010i	$-0.441241\pi$
$593$	89.8338	+	9.77001i	0.151490	+	0.0164756i	−0.0320595	+	0.999486i	$0.510207\pi$
$594$	−250.895	−	237.660i	−0.422382	−	0.400102i
$595$	−227.005	+	267.251i	−0.381521	+	0.449162i
$596$	−1890.47	−	1002.26i	−3.17193	−	1.68165i
$597$	308.625	+	185.693i	0.516959	+	0.311044i
$598$	400.143	+	864.894i	0.669135	+	1.44631i
$599$	240.705	+	52.9831i	0.401844	+	0.0884525i	0.411294	−	0.911503i	$-0.365077\pi$
$599$	240.705	+	52.9831i	0.401844	+	0.0884525i	−0.00944992	+	0.999955i	$0.503008\pi$
$600$	−659.434	+	349.610i	−1.09906	+	0.582683i
$601$	−1175.32	−	63.7240i	−1.95561	−	0.106030i	−0.966830	−	0.255423i	$-0.917785\pi$
$601$	−1175.32	−	63.7240i	−1.95561	−	0.106030i	−0.988778	+	0.149393i	$0.952268\pi$
$602$	−779.422	−	917.607i	−1.29472	−	1.52426i
$603$	−73.6480	−	334.586i	−0.122136	−	0.554869i
$604$	677.395	+	891.098i	1.12152	+	1.47533i
$605$	277.329	−	262.700i	0.458395	−	0.434215i
$606$	64.8807	+	1196.65i	0.107064	+	1.97468i
$607$	−676.806	+	407.221i	−1.11500	+	0.670874i	−0.949008	−	0.315253i	$-0.897911\pi$
$607$	−676.806	+	407.221i	−1.11500	+	0.670874i	−0.165994	+	0.986127i	$0.553083\pi$
$608$	−544.745	−	369.346i	−0.895962	−	0.607477i
$609$	54.7549	−	197.209i	0.0899095	−	0.323825i
$610$	−48.9778	+	5.32666i	−0.0802915	+	0.00873223i
$611$	518.024	+	393.792i	0.847831	+	0.644504i
$612$	718.148	+	332.251i	1.17344	+	0.542893i
$613$	323.230	−	219.155i	0.527292	−	0.357513i	−0.268310	−	0.963333i	$-0.586465\pi$
$613$	323.230	−	219.155i	0.527292	−	0.357513i	0.795602	+	0.605820i	$0.207155\pi$
$614$	274.552	+	814.842i	0.447153	+	1.32710i
$615$	−26.8308	−	163.661i	−0.0436273	−	0.266115i
$616$	−399.802	+	2438.68i	−0.649029	+	3.95890i
$617$	377.864	+	127.317i	0.612421	+	0.206349i	0.608384	−	0.793643i	$-0.291818\pi$
$617$	377.864	+	127.317i	0.612421	+	0.206349i	0.00403749	+	0.999992i	$0.498715\pi$
$618$	−105.999	−	381.775i	−0.171520	−	0.617758i
$619$	34.1095	+	85.6084i	0.0551042	+	0.138301i	0.953952	−	0.299961i	$-0.0969736\pi$
$619$	34.1095	+	85.6084i	0.0551042	+	0.138301i	−0.898847	+	0.438262i	$0.855594\pi$
$620$	−27.2268	+	10.8481i	−0.0439141	+	0.0174970i
$621$	−131.468	+	36.5020i	−0.211704	+	0.0587795i
$622$	498.422	−	1479.26i	0.801322	−	2.37824i
$623$	647.556	+	106.161i	1.03942	+	0.170403i
$624$	596.837	−	97.8465i	0.956470	−	0.156805i
$625$	−363.898	+	122.612i	−0.582237	+	0.196178i
$626$	525.178	+	774.580i	0.838943	+	1.23735i
$627$	175.159	−	378.599i	0.279360	−	0.603827i
$628$	1090.66	−	1434.74i	1.73672	−	2.28461i
$629$	−75.3030	−	692.399i	−0.119719	−	1.10079i
$630$	−132.880	−	36.8939i	−0.210920	−	0.0585617i
$631$	−1.71183	+	2.52476i	−0.00271288	+	0.00400120i	−0.829043	−	0.559185i	$-0.811114\pi$
$631$	−1.71183	+	2.52476i	−0.00271288	+	0.00400120i	0.826330	+	0.563186i	$0.190425\pi$
$632$	451.031	+	749.619i	0.713656	+	1.18611i
$633$	−582.892	+	31.6035i	−0.920841	+	0.0499265i
$634$	−942.903	−	995.411i	−1.48723	−	1.57005i
$635$	−183.728	+	139.667i	−0.289336	+	0.219947i
$636$	−777.095	+	171.052i	−1.22185	+	0.268949i
$637$	−16.9396	+	14.3886i	−0.0265928	+	0.0225881i
$638$	62.2246	−	1147.67i	0.0975308	−	1.79885i
$639$	85.9612	+	162.140i	0.134525	+	0.253740i
$640$	19.4071	−	88.1671i	0.0303235	−	0.137761i
$641$	−673.357	+	311.528i	−1.05048	+	0.486004i	−0.867668	−	0.497144i	$-0.834382\pi$
$641$	−673.357	+	311.528i	−1.05048	+	0.486004i	−0.182812	+	0.983148i	$0.558520\pi$
$642$	475.624	−	790.493i	0.740847	−	1.23130i
$643$	8.87064	−	16.7318i	0.0137957	−	0.0260215i	−0.876518	−	0.481368i	$-0.840140\pi$
$643$	8.87064	−	16.7318i	0.0137957	−	0.0260215i	0.890314	+	0.455347i	$0.150485\pi$
$644$	1291.00	+	1096.59i	2.00466	+	1.70277i
$645$	104.953	−	110.797i	0.162717	−	0.171779i
$646$	−147.056	+	1352.15i	−0.227640	+	2.09312i
$647$	−68.9431	+	173.034i	−0.106558	+	0.267441i	−0.972581	−	0.232563i	$-0.925289\pi$
$647$	−68.9431	+	173.034i	−0.106558	+	0.267441i	0.866023	+	0.500004i	$0.166668\pi$
$648$			179.254i			0.276626i
$649$	−928.669	−	532.679i	−1.43092	−	0.820769i
$650$	785.211			1.20802
$651$	18.6350	+	7.42488i	0.0286252	+	0.0114053i
$652$	1568.01	+	170.532i	2.40493	+	0.261552i
$653$	418.836	+	396.743i	0.641403	+	0.607569i	0.937666	−	0.347537i	$-0.112982\pi$
$653$	418.836	+	396.743i	0.641403	+	0.607569i	−0.296263	+	0.955106i	$0.595741\pi$
$654$	−11.5576	+	13.6066i	−0.0176721	+	0.0208052i
$655$	270.121	+	143.209i	0.412399	+	0.218640i
$656$	1577.43	+	949.108i	2.40462	+	1.44681i
$657$	−78.8981	−	170.536i	−0.120089	−	0.259567i
$658$	1608.50	+	354.057i	2.44452	+	0.538080i
$659$	304.664	−	161.523i	0.462313	−	0.245103i	−0.220936	−	0.975288i	$-0.570911\pi$
$659$	304.664	−	161.523i	0.462313	−	0.245103i	0.683249	+	0.730185i	$0.260566\pi$
$660$	−543.048	−	29.4432i	−0.822800	−	0.0446109i
$661$	194.723	+	229.246i	0.294589	+	0.346816i	0.889467	−	0.456999i	$-0.151076\pi$
$661$	194.723	+	229.246i	0.294589	+	0.346816i	−0.594879	+	0.803816i	$0.702800\pi$
$662$	−228.447	−	1037.85i	−0.345086	−	1.56774i
$663$	−290.178	−	381.723i	−0.437674	−	0.575751i
$664$	−800.191	+	757.981i	−1.20511	+	1.14154i
$665$	−9.01225	−	166.221i	−0.0135523	−	0.249957i
$666$	234.710	−	141.220i	0.352417	−	0.212042i
$667$	−375.586	−	254.653i	−0.563097	−	0.381789i
$668$	−446.047	+	1606.52i	−0.667736	+	2.40497i
$669$	−186.314	+	20.2629i	−0.278497	+	0.0302883i
$670$	−611.185	−	464.611i	−0.912216	−	0.693449i
$671$	120.687	+	55.8358i	0.179861	+	0.0832128i
$672$	486.078	−	329.569i	0.723330	−	0.490430i
$673$	−6.04066	−	17.9281i	−0.00897573	−	0.0266390i	0.943072	−	0.332589i	$-0.107922\pi$
$673$	−6.04066	−	17.9281i	−0.00897573	−	0.0266390i	−0.952047	+	0.305950i	$0.901026\pi$
$674$	36.1687	+	220.619i	0.0536628	+	0.327328i
$675$	−18.1880	+	110.942i	−0.0269451	+	0.164358i
$676$	634.357	+	213.740i	0.938399	+	0.316183i
$677$	87.2725	+	314.327i	0.128911	+	0.464294i	0.999622	−	0.0275007i	$-0.00875486\pi$
$677$	87.2725	+	314.327i	0.128911	+	0.464294i	−0.870711	+	0.491795i	$0.836341\pi$
$678$	−146.668	−	368.109i	−0.216324	−	0.542934i
$679$	495.232	−	197.318i	0.729355	−	0.290602i
$680$	984.140	−	273.245i	1.44727	−	0.401831i
$681$	213.265	−	632.949i	0.313165	−	0.929441i
$682$	111.164	+	18.2245i	0.162998	+	0.0267221i
$683$	565.278	−	92.6727i	0.827640	−	0.135685i	0.266950	−	0.963710i	$-0.413984\pi$
$683$	565.278	−	92.6727i	0.827640	−	0.135685i	0.560690	+	0.828026i	$0.310536\pi$
$684$	−355.985	+	119.945i	−0.520446	+	0.175359i
$685$	172.552	+	254.495i	0.251901	+	0.371526i
$686$	−539.265	+	1165.60i	−0.786100	+	1.69913i
$687$	361.750	−	475.873i	0.526564	−	0.692683i
$688$	183.162	+	1684.15i	0.266224	+	2.44789i
$689$	464.596	+	128.994i	0.674305	+	0.187220i
$690$	−171.586	+	253.070i	−0.248675	+	0.366768i
$691$	−338.227	−	562.138i	−0.489475	−	0.813514i	0.509420	−	0.860518i	$-0.329860\pi$
$691$	−338.227	−	562.138i	−0.489475	−	0.813514i	−0.998895	+	0.0470044i	$0.985033\pi$
$692$	767.236	−	41.5984i	1.10872	−	0.0601132i
$693$	255.982	+	270.236i	0.369382	+	0.389952i
$694$	−1016.78	+	772.936i	−1.46510	+	1.11374i
$695$	81.5176	−	17.9434i	0.117292	−	0.0258178i
$696$	−454.371	+	385.946i	−0.652832	+	0.554520i
$697$	79.0169	−	1457.38i	0.113367	−	2.09093i
$698$	−115.559	−	217.968i	−0.165558	−	0.312275i
$699$	110.358	−	501.363i	0.157880	−	0.717258i
$700$	1266.68	−	586.030i	1.80955	−	0.837186i
$701$	−443.105	+	736.446i	−0.632104	+	1.05056i	0.360914	+	0.932599i	$0.382465\pi$
$701$	−443.105	+	736.446i	−0.632104	+	1.05056i	−0.993018	+	0.117966i	$0.962363\pi$
$702$	88.3326	−	166.613i	0.125830	−	0.237341i
$703$	252.005	+	214.055i	0.358470	+	0.304488i
$704$	507.717	−	535.990i	0.721189	−	0.761350i
$705$	−22.5726	+	207.552i	−0.0320179	+	0.294400i
$706$	−415.598	+	1043.07i	−0.588665	+	1.47744i
$707$		−	1290.80i		−	1.82574i
$708$	226.857	+	937.003i	0.320419	+	1.32345i
$709$	−573.685			−0.809147			−0.404573	−	0.914506i	$-0.632580\pi$
$709$	−573.685			−0.809147			−0.404573	+	0.914506i	$0.632580\pi$
$710$	382.040	+	152.219i	0.538085	+	0.214393i
$711$	131.001	+	14.2472i	0.184249	+	0.0200382i
$712$	−1387.65	−	1314.45i	−1.94895	−	1.84614i
$713$	28.7924	−	33.8970i	0.0403821	−	0.0475414i
$714$	−1072.27	−	568.482i	−1.50178	−	0.796193i
$715$	282.382	+	169.904i	0.394940	+	0.237627i
$716$	512.756	+	1108.30i	0.716139	+	1.54791i
$717$	−339.289	−	74.6832i	−0.473207	−	0.104161i
$718$	−1727.13	+	915.664i	−2.40547	+	1.27530i
$719$	−813.069	−	44.0833i	−1.13083	−	0.0613120i	−0.520793	−	0.853683i	$-0.674364\pi$
$719$	−813.069	−	44.0833i	−1.13083	−	0.0613120i	−0.610040	+	0.792371i	$0.708847\pi$
$720$	125.624	+	147.896i	0.174478	+	0.205411i
$721$	91.7410	+	416.783i	0.127241	+	0.578063i
$722$	409.978	+	539.317i	0.567836	+	0.746976i
$723$	218.647	−	207.113i	0.302416	−	0.286464i
$724$	−40.6369	−	749.503i	−0.0561283	−	1.03523i
$725$	−320.374	+	192.762i	−0.441895	+	0.265879i
$726$	1094.33	+	741.973i	1.50734	+	1.02200i
$727$	−73.6192	+	265.153i	−0.101264	+	0.364721i	−0.996768	−	0.0803326i	$-0.974402\pi$
$727$	−73.6192	+	265.153i	−0.101264	+	0.364721i	0.895504	+	0.445054i	$0.146816\pi$
$728$	−1340.60	+	145.799i	−1.84149	+	0.200274i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	−382.157	−	176.804i	−0.523502	−	0.242198i
$731$	1111.65	−	753.720i	1.52073	−	1.03108i
$732$	−38.2353	−	113.478i	−0.0522340	−	0.155025i
$733$	−99.4965	−	606.902i	−0.135739	−	0.827970i	−0.963661	−	0.267127i	$-0.913926\pi$
$733$	−99.4965	−	606.902i	−0.135739	−	0.827970i	0.827923	−	0.560842i	$-0.189523\pi$
$734$	158.051	−	964.067i	0.215328	−	1.31344i
$735$	−6.75771	−	2.27694i	−0.00919417	−	0.00309787i
$736$	−348.335	−	1254.59i	−0.473282	−	1.70461i
$737$	767.004	+	1925.03i	1.04071	+	2.61199i
$738$	533.246	−	212.465i	0.722556	−	0.287892i
$739$	−133.324	+	37.0173i	−0.180412	+	0.0500911i	−0.356559	−	0.934273i	$-0.616050\pi$
$739$	−133.324	+	37.0173i	−0.180412	+	0.0500911i	0.176147	+	0.984364i	$0.443636\pi$
$740$	137.639	−	408.497i	0.185998	−	0.552023i
$741$	224.635	+	36.8270i	0.303150	+	0.0496990i
$742$	1204.34	−	197.442i	1.62310	−	0.266094i
$743$	607.321	−	204.630i	0.817390	−	0.275411i	0.120614	−	0.992699i	$-0.461514\pi$
$743$	607.321	−	204.630i	0.817390	−	0.275411i	0.696776	+	0.717289i	$0.254617\pi$
$744$	−32.7901	−	48.3619i	−0.0440728	−	0.0650025i
$745$	−174.678	+	377.561i	−0.234467	+	0.506793i
$746$	−998.537	+	1313.55i	−1.33852	+	1.76080i
$747$	17.9497	+	165.045i	0.0240290	+	0.220943i
$748$	−4611.66	−	1280.42i	−6.16532	−	1.71179i
$749$	−557.634	+	822.448i	−0.744504	+	1.09806i
$750$	279.963	+	465.303i	0.373285	+	0.620404i
$751$	−1267.30	+	68.7108i	−1.68748	+	0.0914925i	−0.872693	−	0.488269i	$-0.837628\pi$
$751$	−1267.30	+	68.7108i	−1.68748	+	0.0914925i	−0.814786	+	0.579762i	$0.803146\pi$
$752$	−1593.74	−	1682.49i	−2.11933	−	2.23735i
$753$	−329.933	+	250.809i	−0.438158	+	0.333079i
$754$	612.515	−	134.825i	0.812355	−	0.178813i
$755$	165.865	−	140.887i	0.219689	−	0.186606i
$756$	18.1470	−	334.702i	0.0240040	−	0.442727i
$757$	−128.405	−	242.197i	−0.169623	−	0.319944i	0.784097	−	0.620638i	$-0.213126\pi$
$757$	−128.405	−	242.197i	−0.169623	−	0.319944i	−0.953721	+	0.300694i	$0.902782\pi$
$758$	132.733	−	603.010i	0.175109	−	0.795528i
$759$	749.000	−	346.524i	0.986825	−	0.456554i
$760$	−249.982	+	415.473i	−0.328923	+	0.546675i
$761$	−357.315	+	673.967i	−0.469533	+	0.885633i	0.529764	+	0.848145i	$0.322281\pi$
$761$	−357.315	+	673.967i	−0.469533	+	0.885633i	−0.999297	+	0.0374883i	$0.988064\pi$
$762$	−608.806	−	517.124i	−0.798958	−	0.678641i
$763$	13.2237	−	13.9601i	0.0173312	−	0.0182963i
$764$	322.538	−	2965.69i	0.422170	−	3.88179i
$765$	56.9432	−	142.917i	0.0744355	−	0.186819i
$766$		−	1769.62i		−	2.31021i
$767$	144.506	−	566.048i	0.188404	−	0.738003i
$768$	594.348			0.773891
$769$	786.170	+	313.239i	1.02233	+	0.407333i	0.820231	−	0.572033i	$-0.193845\pi$
$769$	786.170	+	313.239i	1.02233	+	0.407333i	0.202097	+	0.979365i	$0.435224\pi$
$770$	829.245	+	90.1859i	1.07694	+	0.117125i
$771$	289.424	+	274.157i	0.375388	+	0.355586i
$772$	2178.17	−	2564.34i	2.82147	−	3.32169i
$773$	−830.082	−	440.082i	−1.07384	−	0.569316i	−0.164933	−	0.986305i	$-0.552741\pi$
$773$	−830.082	−	440.082i	−1.07384	−	0.569316i	−0.908912	+	0.416988i	$0.863086\pi$

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)

\(f(q)\)	\(=\)	\(q+(3.40493 + 1.35665i) q^{2} +(1.72190 + 0.187268i) q^{3} +(6.84907 + 6.48778i) q^{4} +(1.18743 - 1.39795i) q^{5} +(5.60888 + 2.97364i) q^{6} +(-5.85901 - 3.52525i) q^{7} +(8.36297 + 18.0763i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(3.40493 + 1.35665i) q^{2} +(1.72190 + 0.187268i) q^{3} +(6.84907 + 6.48778i) q^{4} +(1.18743 - 1.39795i) q^{5} +(5.60888 + 2.97364i) q^{6} +(-5.85901 - 3.52525i) q^{7} +(8.36297 + 18.0763i) q^{8} +(2.92986 + 0.644911i) q^{9} +(5.93964 - 3.14900i) q^{10} +(-18.1191 - 0.982387i) q^{11} +(10.5784 + 12.4539i) q^{12} +(-2.12858 - 9.67024i) q^{13} +(-15.1670 - 19.9518i) q^{14} +(2.30642 - 2.18476i) q^{15} +(1.90921 + 35.2132i) q^{16} +(23.9564 - 14.4141i) q^{17} +(9.10106 + 6.17067i) q^{18} +(-3.55086 + 12.7890i) q^{19} +(17.2024 - 1.87087i) q^{20} +(-9.42845 - 7.16732i) q^{21} +(-60.3614 - 27.9261i) q^{22} +(-21.7336 + 14.7358i) q^{23} +(11.0151 + 32.6916i) q^{24} +(3.50027 + 21.3507i) q^{25} +(5.87144 - 35.8142i) q^{26} +(4.92415 + 1.65914i) q^{27} +(-17.2577 - 62.1567i) q^{28} +(6.39647 + 16.0539i) q^{29} +(10.8172 - 4.30995i) q^{30} +(-1.63201 + 0.453126i) q^{31} +(-15.8330 + 46.9907i) q^{32} +(-31.0152 - 5.08468i) q^{33} +(101.124 - 16.5785i) q^{34} +(-11.8853 + 4.00462i) q^{35} +(15.8828 + 23.4254i) q^{36} +(10.4600 - 22.6090i) q^{37} +(-29.4407 + 38.7285i) q^{38} +(-1.85427 - 17.0498i) q^{39} +(35.2002 + 9.77328i) q^{40} +(29.2958 - 43.2081i) q^{41} +(-22.3797 - 37.1953i) q^{42} +(47.9681 - 2.60076i) q^{43} +(-117.725 - 124.281i) q^{44} +(4.38056 - 3.33001i) q^{45} +(-93.9928 + 20.6894i) q^{46} +(-50.0867 + 42.5440i) q^{47} +(-3.30684 + 60.9911i) q^{48} +(-1.05140 - 1.98316i) q^{49} +(-17.0472 + 77.4464i) q^{50} +(43.9497 - 20.3333i) q^{51} +(48.1596 - 80.0419i) q^{52} +(-22.8094 + 43.0232i) q^{53} +(14.5155 + 12.3296i) q^{54} +(-22.8884 + 24.1630i) q^{55} +(14.7246 - 135.391i) q^{56} +(-8.50919 + 21.3565i) q^{57} +63.3403i q^{58} +(52.6928 + 26.5419i) q^{59} +29.9711 q^{60} +(-6.80785 - 2.71249i) q^{61} +(-6.17162 - 0.671204i) q^{62} +(-14.8926 - 14.1070i) q^{63} +(-26.3399 + 31.0097i) q^{64} +(-16.0461 - 8.50708i) q^{65} +(-98.7064 - 59.3897i) q^{66} +(-47.9508 - 103.644i) q^{67} +(257.594 + 56.7007i) q^{68} +(-40.1826 + 21.3035i) q^{69} +(-45.9014 - 2.48870i) q^{70} +(39.6022 + 46.6234i) q^{71} +(12.8448 + 58.3543i) q^{72} +(-37.9046 - 49.8626i) q^{73} +(66.2880 - 62.7913i) q^{74} +(2.02881 + 37.4193i) q^{75} +(-107.293 + 64.5558i) q^{76} +(102.697 + 69.6300i) q^{77} +(16.8169 - 60.5689i) q^{78} +(43.6669 - 4.74906i) q^{79} +(51.4934 + 39.1443i) q^{80} +(8.16818 + 3.77900i) q^{81} +(158.368 - 107.376i) q^{82} +(17.6699 + 52.4424i) q^{83} +(-18.0761 - 110.259i) q^{84} +(8.29635 - 50.6055i) q^{85} +(166.856 + 56.2205i) q^{86} +(8.00768 + 28.8411i) q^{87} +(-133.771 - 335.741i) q^{88} +(-89.1508 + 35.5209i) q^{89} +(19.4332 - 5.39559i) q^{90} +(-21.6186 + 64.1618i) q^{91} +(-244.458 - 40.0768i) q^{92} +(-2.89501 + 0.474613i) q^{93} +(-228.259 + 76.9094i) q^{94} +(13.6620 + 20.1500i) q^{95} +(-36.0626 + 77.9481i) q^{96} +(-47.1811 + 62.0657i) q^{97} +(-0.889509 - 8.17890i) q^{98} +(-52.4528 - 14.5634i) 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

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