LMFDB - Embedded newform 177.3.h.a.5.8

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$1064$
Relative dimension:	$38$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	177.5
Dual form			177.3.h.a.71.8

$q$-expansion

$f(q)$	$=$	$q+(-0.892372 + 2.64847i) q^{2} +(0.713097 - 2.91402i) q^{3} +(-3.03367 - 2.30614i) q^{4} +(-2.87136 - 1.14405i) q^{5} +(7.08133 + 4.48900i) q^{6} +(2.33765 - 1.08151i) q^{7} +(-0.437890 + 0.296897i) q^{8} +(-7.98299 - 4.15595i) q^{9} +O(q^{10})$	\(q+(-0.892372 + 2.64847i) q^{2} +(0.713097 - 2.91402i) q^{3} +(-3.03367 - 2.30614i) q^{4} +(-2.87136 - 1.14405i) q^{5} +(7.08133 + 4.48900i) q^{6} +(2.33765 - 1.08151i) q^{7} +(-0.437890 + 0.296897i) q^{8} +(-7.98299 - 4.15595i) q^{9} +(5.59230 - 6.58377i) q^{10} +(-5.90871 - 1.64054i) q^{11} +(-8.88342 + 7.19567i) q^{12} +(11.2971 - 21.3085i) q^{13} +(0.778296 + 7.15631i) q^{14} +(-5.38134 + 7.55136i) q^{15} +(-4.47344 - 16.1119i) q^{16} +(8.75474 - 18.9231i) q^{17} +(18.1307 - 17.4340i) q^{18} +(1.82985 - 0.402779i) q^{19} +(6.07241 + 10.0924i) q^{20} +(-1.48458 - 7.58319i) q^{21} +(9.61769 - 14.1850i) q^{22} +(-21.5222 - 3.52838i) q^{23} +(0.552904 + 1.48773i) q^{24} +(-11.2141 - 10.6225i) q^{25} +(46.3538 + 48.9351i) q^{26} +(-17.8032 + 20.2990i) q^{27} +(-9.58579 - 2.10999i) q^{28} +(2.19392 + 6.51131i) q^{29} +(-15.1974 - 20.9909i) q^{30} +(44.5980 + 9.81675i) q^{31} +(44.5506 + 2.41546i) q^{32} +(-8.99405 + 16.0482i) q^{33} +(42.3046 + 40.0730i) q^{34} +(-7.94955 + 0.431012i) q^{35} +(14.6336 + 31.0177i) q^{36} +(-32.5155 + 47.9568i) q^{37} +(-0.566155 + 5.20571i) q^{38} +(-54.0376 - 48.1149i) q^{39} +(1.59700 - 0.351527i) q^{40} +(4.66989 - 0.765589i) q^{41} +(21.4086 + 2.83518i) q^{42} +(-12.9179 - 46.5262i) q^{43} +(14.1418 + 18.6032i) q^{44} +(18.1674 + 21.0662i) q^{45} +(28.5506 - 53.8521i) q^{46} +(22.9848 - 9.15799i) q^{47} +(-50.1403 + 1.54635i) q^{48} +(-27.4270 + 32.2895i) q^{49} +(38.1405 - 20.2208i) q^{50} +(-48.8991 - 39.0054i) q^{51} +(-83.4120 + 38.5905i) q^{52} +(-4.66273 + 3.96056i) q^{53} +(-37.8741 - 65.2653i) q^{54} +(15.0891 + 11.4705i) q^{55} +(-0.702537 + 1.16763i) q^{56} +(0.131151 - 5.61942i) q^{57} -19.2028 q^{58} +(-5.88414 - 58.7059i) q^{59} +(33.7397 - 10.4982i) q^{60} +(3.40546 + 1.14743i) q^{61} +(-65.7973 + 109.356i) q^{62} +(-23.1562 - 1.08147i) q^{63} +(-21.3961 + 53.7003i) q^{64} +(-56.8160 + 48.2600i) q^{65} +(-34.4771 - 38.1414i) q^{66} +(27.0774 + 39.9362i) q^{67} +(-70.1982 + 37.2167i) q^{68} +(-25.6292 + 60.1999i) q^{69} +(5.95243 - 21.4387i) q^{70} +(-32.5806 + 12.9813i) q^{71} +(4.72955 - 0.550272i) q^{72} +(20.7357 - 2.25515i) q^{73} +(-97.9960 - 128.912i) q^{74} +(-38.9509 + 25.1031i) q^{75} +(-6.48001 - 2.99797i) q^{76} +(-15.5868 + 2.55532i) q^{77} +(175.652 - 100.180i) q^{78} +(-82.7374 + 49.7814i) q^{79} +(-5.58800 + 51.3808i) q^{80} +(46.4561 + 66.3538i) q^{81} +(-2.13964 + 13.0512i) q^{82} +(104.552 - 5.66863i) q^{83} +(-12.9842 + 26.4285i) q^{84} +(-46.7870 + 44.3190i) q^{85} +(134.751 + 7.30597i) q^{86} +(20.5385 - 1.74991i) q^{87} +(3.07443 - 1.03590i) q^{88} +(6.55624 + 19.4582i) q^{89} +(-72.0051 + 29.3168i) q^{90} +(3.36317 - 62.0300i) q^{91} +(57.1543 + 60.3370i) q^{92} +(60.4089 - 122.959i) q^{93} +(3.74361 + 69.0468i) q^{94} +(-5.71494 - 0.936917i) q^{95} +(38.8076 - 128.099i) q^{96} +(-83.6208 - 9.09430i) q^{97} +(-61.0427 - 101.454i) q^{98} +(40.3511 + 37.6527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} + O(q^{10}) $	$ 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} - 94q^{10} - 29q^{12} - 54q^{13} - 12q^{15} - 158q^{16} - 27q^{18} - 30q^{19} - 18q^{21} - 142q^{22} - 23q^{24} + 108q^{25} - 32q^{27} - 70q^{28} - 131q^{30} - 18q^{31} + 17q^{33} + 90q^{34} + 67q^{36} - 170q^{37} - 91q^{39} - 2q^{40} - 43q^{42} - 222q^{43} - 461q^{45} - 54q^{46} - 1645q^{48} - 300q^{49} - 893q^{51} - 66q^{52} - 859q^{54} + 170q^{55} - 27q^{57} - 36q^{58} + 510q^{60} - 70q^{61} + 610q^{63} - 106q^{64} + 1619q^{66} - 182q^{67} + 1487q^{69} - 206q^{70} + 2241q^{72} + 134q^{73} + 542q^{75} + 246q^{76} - 273q^{78} - 122q^{79} + 127q^{81} + 122q^{82} - 329q^{84} - 6q^{85} + 54q^{87} + 38q^{88} + 347q^{90} + 274q^{91} - 483q^{93} - 826q^{94} + 693q^{96} - 474q^{97} - 523q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{3}{29}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.892372	+	2.64847i	−0.446186	+	1.32423i	0.454881	+	0.890552i	$0.349682\pi$
$2$	−0.892372	+	2.64847i	−0.446186	+	1.32423i	−0.901067	+	0.433681i	$0.857215\pi$
$3$	0.713097	−	2.91402i	0.237699	−	0.971339i
$3$	0.713097	−	2.91402i	0.237699	−	0.971339i
$4$	−3.03367	−	2.30614i	−0.758418	−	0.576534i
$5$	−2.87136	−	1.14405i	−0.574271	−	0.228811i	0.0648781	−	0.997893i	$-0.479334\pi$
$5$	−2.87136	−	1.14405i	−0.574271	−	0.228811i	−0.639149	+	0.769083i	$0.720713\pi$
$6$	7.08133	+	4.48900i	1.18022	+	0.748167i
$7$	2.33765	−	1.08151i	0.333951	−	0.154502i	−0.245746	−	0.969334i	$-0.579033\pi$
$7$	2.33765	−	1.08151i	0.333951	−	0.154502i	0.579697	+	0.814832i	$0.303171\pi$
$8$	−0.437890	+	0.296897i	−0.0547362	+	0.0371121i
$9$	−7.98299	−	4.15595i	−0.886998	−	0.461772i
$10$	5.59230	−	6.58377i	0.559230	−	0.658377i
$11$	−5.90871	−	1.64054i	−0.537155	−	0.149140i	−0.0116521	−	0.999932i	$-0.503709\pi$
$11$	−5.90871	−	1.64054i	−0.537155	−	0.149140i	−0.525503	+	0.850792i	$0.676123\pi$
$12$	−8.88342	+	7.19567i	−0.740285	+	0.599639i
$13$	11.2971	−	21.3085i	0.869006	−	1.63912i	0.104479	−	0.994527i	$-0.466682\pi$
$13$	11.2971	−	21.3085i	0.869006	−	1.63912i	0.764527	−	0.644592i	$-0.222973\pi$
$14$	0.778296	+	7.15631i	0.0555925	+	0.511165i
$15$	−5.38134	+	7.55136i	−0.358756	+	0.503424i
$16$	−4.47344	−	16.1119i	−0.279590	−	1.00699i
$17$	8.75474	−	18.9231i	0.514985	−	1.11312i	−0.459399	−	0.888230i	$-0.651935\pi$
$17$	8.75474	−	18.9231i	0.514985	−	1.11312i	0.974384	−	0.224891i	$-0.0722027\pi$
$18$	18.1307	−	17.4340i	1.00726	−	0.968556i
$19$	1.82985	−	0.402779i	0.0963076	−	0.0211989i	−0.166555	−	0.986032i	$-0.553264\pi$
$19$	1.82985	−	0.402779i	0.0963076	−	0.0211989i	0.262863	+	0.964833i	$0.415333\pi$
$20$	6.07241	+	10.0924i	0.303620	+	0.504621i
$21$	−1.48458	−	7.58319i	−0.0706941	−	0.361104i
$22$	9.61769	−	14.1850i	0.437168	−	0.644774i
$23$	−21.5222	−	3.52838i	−0.935747	−	0.153408i	−0.325431	−	0.945566i	$-0.605509\pi$
$23$	−21.5222	−	3.52838i	−0.935747	−	0.153408i	−0.610316	+	0.792158i	$0.708958\pi$
$24$	0.552904	+	1.48773i	0.0230377	+	0.0619889i
$25$	−11.2141	−	10.6225i	−0.448562	−	0.424901i
$26$	46.3538	+	48.9351i	1.78284	+	1.88212i
$27$	−17.8032	+	20.2990i	−0.659376	+	0.751813i
$28$	−9.58579	−	2.10999i	−0.342350	−	0.0753569i
$29$	2.19392	+	6.51131i	0.0756523	+	0.224528i	0.978806	−	0.204789i	$-0.0656508\pi$
$29$	2.19392	+	6.51131i	0.0756523	+	0.224528i	−0.903154	+	0.429317i	$0.858754\pi$
$30$	−15.1974	−	20.9909i	−0.506579	−	0.699698i
$31$	44.5980	+	9.81675i	1.43864	+	0.316669i	0.864726	−	0.502243i	$-0.167492\pi$
$31$	44.5980	+	9.81675i	1.43864	+	0.316669i	0.573918	+	0.818913i	$0.305423\pi$
$32$	44.5506	+	2.41546i	1.39221	+	0.0754833i
$33$	−8.99405	+	16.0482i	−0.272547	+	0.486309i
$34$	42.3046	+	40.0730i	1.24425	+	1.17862i
$35$	−7.94955	+	0.431012i	−0.227130	+	0.0123146i
$36$	14.6336	+	31.0177i	0.406488	+	0.861601i
$37$	−32.5155	+	47.9568i	−0.878798	+	1.29613i	0.0754617	+	0.997149i	$0.475957\pi$
$37$	−32.5155	+	47.9568i	−0.878798	+	1.29613i	−0.954259	+	0.298981i	$0.903353\pi$
$38$	−0.566155	+	5.20571i	−0.0148988	+	0.136992i
$39$	−54.0376	−	48.1149i	−1.38558	−	1.23372i
$40$	1.59700	−	0.351527i	0.0399251	−	0.00878817i
$41$	4.66989	−	0.765589i	0.113900	−	0.0186729i	−0.104563	−	0.994518i	$-0.533344\pi$
$41$	4.66989	−	0.765589i	0.113900	−	0.0186729i	0.218462	+	0.975845i	$0.429896\pi$
$42$	21.4086	+	2.83518i	0.509729	+	0.0675042i
$43$	−12.9179	−	46.5262i	−0.300417	−	1.08201i	−0.947545	−	0.319623i	$-0.896444\pi$
$43$	−12.9179	−	46.5262i	−0.300417	−	1.08201i	0.647127	−	0.762382i	$-0.275970\pi$
$44$	14.1418	+	18.6032i	0.321403	+	0.422799i
$45$	18.1674	+	21.0662i	0.403719	+	0.468137i
$46$	28.5506	−	53.8521i	0.620665	−	1.17070i
$47$	22.9848	−	9.15799i	0.489039	−	0.194851i	−0.112567	−	0.993644i	$-0.535907\pi$
$47$	22.9848	−	9.15799i	0.489039	−	0.194851i	0.601606	+	0.798793i	$0.294528\pi$
$48$	−50.1403	+	1.54635i	−1.04459	+	0.0322156i
$49$	−27.4270	+	32.2895i	−0.559734	+	0.658970i
$50$	38.1405	−	20.2208i	0.762810	−	0.404416i
$51$	−48.8991	−	39.0054i	−0.958806	−	0.764812i
$52$	−83.4120	+	38.5905i	−1.60408	+	0.742125i
$53$	−4.66273	+	3.96056i	−0.0879761	+	0.0747276i	−0.690295	−	0.723528i	$-0.742519\pi$
$53$	−4.66273	+	3.96056i	−0.0879761	+	0.0747276i	0.602319	+	0.798255i	$0.294243\pi$
$54$	−37.8741	−	65.2653i	−0.701371	−	1.20862i
$55$	15.0891	+	11.4705i	0.274348	+	0.208554i
$56$	−0.702537	+	1.16763i	−0.0125453	+	0.0208504i
$57$	0.131151	−	5.61942i	0.00230090	−	0.0985863i
$58$	−19.2028			−0.331082
$59$	−5.88414	−	58.7059i	−0.0997312	−	0.995014i
$59$	−5.88414	−	58.7059i	−0.0997312	−	0.995014i
$60$	33.7397	−	10.4982i	0.562328	−	0.174970i
$61$	3.40546	+	1.14743i	0.0558273	+	0.0188104i	0.347077	−	0.937837i	$-0.387174\pi$
$61$	3.40546	+	1.14743i	0.0558273	+	0.0188104i	−0.291249	+	0.956647i	$0.594071\pi$
$62$	−65.7973	+	109.356i	−1.06125	+	1.76381i
$63$	−23.1562	−	1.08147i	−0.367558	−	0.0171662i
$64$	−21.3961	+	53.7003i	−0.334315	+	0.839067i
$65$	−56.8160	+	48.2600i	−0.874093	+	0.742461i
$66$	−34.4771	−	38.1414i	−0.522380	−	0.577900i
$67$	27.0774	+	39.9362i	0.404141	+	0.596063i	0.974240	−	0.225513i	$-0.0724057\pi$
$67$	27.0774	+	39.9362i	0.404141	+	0.596063i	−0.570100	+	0.821576i	$0.693095\pi$
$68$	−70.1982	+	37.2167i	−1.03233	+	0.547305i
$69$	−25.6292	+	60.1999i	−0.371437	+	0.872462i
$70$	5.95243	−	21.4387i	0.0850348	−	0.306268i
$71$	−32.5806	+	12.9813i	−0.458881	+	0.182835i	−0.588112	−	0.808779i	$-0.700129\pi$
$71$	−32.5806	+	12.9813i	−0.458881	+	0.182835i	0.129231	+	0.991615i	$0.458749\pi$
$72$	4.72955	−	0.550272i	0.0656883	−	0.00764267i
$73$	20.7357	−	2.25515i	0.284051	−	0.0308924i	0.0350157	−	0.999387i	$-0.488852\pi$
$73$	20.7357	−	2.25515i	0.284051	−	0.0308924i	0.249036	+	0.968494i	$0.419886\pi$
$74$	−97.9960	−	128.912i	−1.32427	−	1.74205i
$75$	−38.9509	+	25.1031i	−0.519345	+	0.334708i
$76$	−6.48001	−	2.99797i	−0.0852633	−	0.0394470i
$77$	−15.5868	+	2.55532i	−0.202426	+	0.0331860i
$78$	175.652	−	100.180i	2.25195	−	1.28436i
$79$	−82.7374	+	49.7814i	−1.04731	+	0.630144i	−0.931729	−	0.363154i	$-0.881700\pi$
$79$	−82.7374	+	49.7814i	−1.04731	+	0.630144i	−0.115579	+	0.993298i	$0.536872\pi$
$80$	−5.58800	+	51.3808i	−0.0698500	+	0.642260i
$81$	46.4561	+	66.3538i	0.573532	+	0.819183i
$82$	−2.13964	+	13.0512i	−0.0260932	+	0.159161i
$83$	104.552	−	5.66863i	1.25966	−	0.0682968i	0.587819	−	0.808992i	$-0.299987\pi$
$83$	104.552	−	5.66863i	1.25966	−	0.0682968i	0.671841	+	0.740695i	$0.265504\pi$
$84$	−12.9842	+	26.4285i	−0.154573	+	0.314625i
$85$	−46.7870	+	44.3190i	−0.550435	+	0.521399i
$86$	134.751	+	7.30597i	1.56687	+	0.0849532i
$87$	20.5385	−	1.74991i	0.236075	−	0.0201139i
$88$	3.07443	−	1.03590i	0.0349367	−	0.0117716i
$89$	6.55624	+	19.4582i	0.0736656	+	0.218632i	0.978160	−	0.207854i	$-0.0666479\pi$
$89$	6.55624	+	19.4582i	0.0736656	+	0.218632i	−0.904494	+	0.426486i	$0.859751\pi$
$90$	−72.0051	+	29.3168i	−0.800057	+	0.325742i
$91$	3.36317	−	62.0300i	0.0369579	−	0.681648i
$92$	57.1543	+	60.3370i	0.621242	+	0.655837i
$93$	60.4089	−	122.959i	0.649558	−	1.32214i
$94$	3.74361	+	69.0468i	0.0398256	+	0.734541i
$95$	−5.71494	−	0.936917i	−0.0601572	−	0.00986228i
$96$	38.8076	−	128.099i	0.404246	−	1.33436i
$97$	−83.6208	−	9.09430i	−0.862070	−	0.0937557i	−0.333607	−	0.942712i	$-0.608266\pi$
$97$	−83.6208	−	9.09430i	−0.862070	−	0.0937557i	−0.528463	+	0.848957i	$0.677231\pi$
$98$	−61.0427	−	101.454i	−0.622884	−	1.03524i
$99$	40.3511	+	37.6527i	0.407587	+	0.380331i
$100$	9.52278	+	58.0864i	0.0952278	+	0.580864i
$101$	73.0548	−	157.905i	0.723315	−	1.56342i	−0.0994537	−	0.995042i	$-0.531710\pi$
$101$	73.0548	−	157.905i	0.723315	−	1.56342i	0.822768	−	0.568377i	$-0.192428\pi$
$102$	146.941	−	94.7003i	1.44060	−	0.928434i
$103$	98.8081	−	75.1120i	0.959302	−	0.729242i	−0.00334714	−	0.999994i	$-0.501065\pi$
$103$	98.8081	−	75.1120i	0.959302	−	0.729242i	0.962649	+	0.270752i	$0.0872723\pi$
$104$	1.37956	+	12.6849i	0.0132650	+	0.121970i
$105$	−4.41282	+	23.4725i	−0.0420269	+	0.223547i
$106$	−6.32852	−	15.8834i	−0.0597030	−	0.149843i
$107$	159.735	+	44.3501i	1.49285	+	0.414487i	0.915603	−	0.402084i	$-0.131714\pi$
$107$	159.735	+	44.3501i	1.49285	+	0.414487i	0.577245	+	0.816571i	$0.304128\pi$
$108$	100.821	−	20.5238i	0.933529	−	0.190036i
$109$	14.4971	+	27.3444i	0.133001	+	0.250866i	0.941063	−	0.338231i	$-0.109828\pi$
$109$	14.4971	+	27.3444i	0.133001	+	0.250866i	−0.808062	+	0.589097i	$0.799484\pi$
$110$	−43.8442	+	29.7271i	−0.398584	+	0.270247i
$111$	116.560	+	128.949i	1.05009	+	1.16170i
$112$	−27.8826	−	32.8259i	−0.248952	−	0.293088i
$113$	38.4138	+	15.3055i	0.339945	+	0.135447i	0.533862	−	0.845571i	$-0.320740\pi$
$113$	38.4138	+	15.3055i	0.339945	+	0.135447i	−0.193917	+	0.981018i	$0.562119\pi$
$114$	14.7658	+	5.36196i	0.129525	+	0.0470348i
$115$	57.7612	+	34.7538i	0.502271	+	0.302207i
$116$	8.36035	−	24.8126i	0.0720720	−	0.213902i
$117$	−178.742	+	123.156i	−1.52771	+	1.05261i
$118$	160.731	+	36.8035i	1.36213	+	0.311894i
$119$		−	53.7039i		−	0.451294i
$120$	0.114462	−	4.90436i	0.000953854	−	0.0408697i
$121$	−71.4583	−	42.9950i	−0.590564	−	0.355331i
$122$	−6.07788	+	7.99531i	−0.0498187	+	0.0655354i
$123$	1.09914	−	14.1541i	0.00893611	−	0.115074i
$124$	−112.657	−	132.630i	−0.908522	−	1.06960i
$125$	52.4925	+	113.461i	0.419940	+	0.907686i
$126$	23.5282	−	60.3633i	0.186731	−	0.479074i
$127$	67.2804	+	126.904i	0.529767	+	0.999247i	0.993560	+	0.113303i	$0.0361432\pi$
$127$	67.2804	+	126.904i	0.529767	+	0.999247i	−0.463793	+	0.885943i	$0.653512\pi$
$128$	12.8887	+	10.9477i	0.100693	+	0.0855292i
$129$	−144.790	+	4.46539i	−1.12240	+	0.0346155i
$130$	−77.1139	−	193.541i	−0.593184	−	1.48878i
$131$	−131.894	−	69.9259i	−1.00683	−	0.533785i	−0.118478	−	0.992957i	$-0.537802\pi$
$131$	−131.894	−	69.9259i	−1.00683	−	0.533785i	−0.888348	+	0.459171i	$0.848146\pi$
$132$	64.2944	−	27.9434i	0.487078	−	0.211693i
$133$	3.84193	−	2.92056i	0.0288867	−	0.0219591i
$134$	−129.933	+	36.0757i	−0.969648	+	0.269221i
$135$	74.3423	−	37.9178i	0.550684	−	0.280872i
$136$	1.78458	+	10.8855i	0.0131219	+	0.0800402i
$137$	6.31632	+	28.6953i	0.0461045	+	0.209455i	0.994041	−	0.109003i	$-0.0347659\pi$
$137$	6.31632	+	28.6953i	0.0461045	+	0.209455i	−0.947937	+	0.318458i	$0.896835\pi$
$138$	−136.567	−	121.599i	−0.989613	−	0.881150i
$139$	155.999	+	16.9659i	1.12229	+	0.122057i	0.650396	−	0.759596i	$-0.274603\pi$
$139$	155.999	+	16.9659i	1.12229	+	0.122057i	0.471899	+	0.881653i	$0.343569\pi$
$140$	25.1103	+	17.0252i	0.179359	+	0.121609i
$141$	−10.2961	−	73.5087i	−0.0730222	−	0.521338i
$142$	−5.30650	−	97.8727i	−0.0373697	−	0.689244i
$143$	−101.709	+	107.373i	−0.711250	+	0.750857i
$144$	−31.2488	+	147.212i	−0.217005	+	1.02231i
$145$	1.14977	−	21.2063i	0.00792945	−	0.146250i
$146$	−12.5313	+	56.9303i	−0.0858309	+	0.389934i
$147$	74.5341	+	102.948i	0.507035	+	0.700328i
$148$	209.236	−	70.4999i	1.41376	−	0.476351i
$149$	44.5971	−	202.607i	0.299310	−	1.35978i	−0.551444	−	0.834212i	$-0.685923\pi$
$149$	44.5971	−	202.607i	0.299310	−	1.35978i	0.850753	−	0.525565i	$-0.176146\pi$
$150$	−31.7259	−	125.561i	−0.211506	−	0.837076i
$151$	−14.7692	+	13.9901i	−0.0978090	+	0.0926496i	−0.735042	−	0.678022i	$-0.762838\pi$
$151$	−14.7692	+	13.9901i	−0.0978090	+	0.0926496i	0.637233	+	0.770671i	$0.280079\pi$
$152$	−0.681686	+	0.719648i	−0.00448478	+	0.00473452i
$153$	−148.532	+	114.678i	−0.970799	+	0.749531i
$154$	7.14152	−	43.5614i	0.0463735	−	0.282866i
$155$	−116.826	−	79.2098i	−0.753715	−	0.511031i
$156$	52.9726	+	270.583i	0.339568	+	1.73451i
$157$	207.974	−	125.134i	1.32467	−	0.797029i	0.335256	−	0.942127i	$-0.391177\pi$
$157$	207.974	−	125.134i	1.32467	−	0.797029i	0.989417	+	0.145098i	$0.0463497\pi$
$158$	−58.0119	−	263.551i	−0.367164	−	1.66804i
$159$	8.21616	+	16.4115i	0.0516740	+	0.103217i
$160$	−125.157	−	57.9039i	−0.782233	−	0.361900i
$161$	−54.1274	+	15.0284i	−0.336195	+	0.0933441i
$162$	−217.192	+	63.8252i	−1.34069	+	0.393982i
$163$	38.1996	−	4.15446i	0.234353	−	0.0254875i	0.00981135	−	0.999952i	$-0.496877\pi$
$163$	38.1996	−	4.15446i	0.234353	−	0.0254875i	0.224542	+	0.974464i	$0.427911\pi$
$164$	−15.9324	−	8.44685i	−0.0971491	−	0.0515052i
$165$	44.1851	−	35.7904i	0.267789	−	0.216912i
$166$	−78.2859	+	281.960i	−0.471602	+	1.69856i
$167$	−61.2162	−	51.9975i	−0.366564	−	0.311362i	0.445107	−	0.895478i	$-0.353166\pi$
$167$	−61.2162	−	51.9975i	−0.366564	−	0.311362i	−0.811671	+	0.584115i	$0.801442\pi$
$168$	2.90150	+	2.87983i	0.0172708	+	0.0171419i
$169$	−231.590	−	341.569i	−1.37035	−	2.02112i
$170$	−75.6259	−	163.463i	−0.444858	−	0.961545i
$171$	−16.2816	−	4.38937i	−0.0952138	−	0.0256688i
$172$	−68.1070	+	170.936i	−0.395971	+	0.993813i
$173$	−175.955	+	231.465i	−1.01708	+	1.33795i	−0.0769872	+	0.997032i	$0.524530\pi$
$173$	−175.955	+	231.465i	−1.01708	+	1.33795i	−0.940094	+	0.340915i	$0.889263\pi$
$174$	−13.6934	+	55.9572i	−0.0786979	+	0.321593i
$175$	−37.7030	−	12.7036i	−0.215446	−	0.0725921i
$176$			102.539i			0.582609i
$177$	−175.266	−	24.7165i	−0.990202	−	0.139641i
$178$	−57.3851			−0.322388
$179$	−5.74119	+	17.0392i	−0.0320737	+	0.0951913i	−0.962494	−	0.271303i	$-0.912545\pi$
$179$	−5.74119	+	17.0392i	−0.0320737	+	0.0951913i	0.930420	+	0.366494i	$0.119442\pi$
$180$	−6.53233	−	105.804i	−0.0362907	−	0.587802i
$181$	−27.0512	−	20.5638i	−0.149454	−	0.113612i	0.527775	−	0.849384i	$-0.323026\pi$
$181$	−27.0512	−	20.5638i	−0.149454	−	0.113612i	−0.677229	+	0.735772i	$0.736820\pi$
$182$	161.283	+	64.2610i	0.886170	+	0.353083i
$183$	5.77207	−	9.10534i	0.0315413	−	0.0497560i
$184$	10.4719	−	4.84482i	0.0569125	−	0.0263305i
$185$	148.229	−	100.502i	0.801236	−	0.543252i
$186$	271.745	+	269.716i	1.46100	+	1.45009i
$187$	−82.7733	+	97.4483i	−0.442638	+	0.521114i
$188$	−90.8479	−	25.2238i	−0.483234	−	0.134169i
$189$	−19.6640	+	66.7063i	−0.104042	+	0.352943i
$190$	7.58124	−	14.2997i	0.0399013	−	0.0752618i
$191$	−20.2374	−	186.080i	−0.105955	−	0.974240i	−0.919594	−	0.392870i	$-0.871482\pi$
$191$	−20.2374	−	186.080i	−0.105955	−	0.974240i	0.813639	−	0.581370i	$-0.197483\pi$
$192$	141.226	+	100.642i	0.735552	+	0.524178i
$193$	−9.90674	−	35.6809i	−0.0513303	−	0.184875i	0.933441	−	0.358732i	$-0.116791\pi$
$193$	−9.90674	−	35.6809i	−0.0513303	−	0.184875i	−0.984771	+	0.173857i	$0.944377\pi$
$194$	98.7068	−	213.351i	0.508798	−	1.09975i
$195$	100.115	+	199.977i	0.513410	+	1.02552i
$196$	157.668	−	34.7055i	0.804431	−	0.177069i
$197$	4.33209	+	7.19999i	0.0219903	+	0.0365482i	0.867657	−	0.497163i	$-0.165625\pi$
$197$	4.33209	+	7.19999i	0.0219903	+	0.0365482i	−0.845667	+	0.533711i	$0.820797\pi$
$198$	−135.730	+	73.2682i	−0.685506	+	0.370042i
$199$	172.066	−	253.778i	0.864651	−	1.27526i	−0.0953999	−	0.995439i	$-0.530413\pi$
$199$	172.066	−	253.778i	0.864651	−	1.27526i	0.960051	−	0.279826i	$-0.0902767\pi$
$200$	8.06431	+	1.32208i	0.0403215	+	0.00661038i
$201$	135.684	−	50.4257i	0.675043	−	0.250874i
$202$	353.015	+	334.393i	1.74760	+	1.65541i
$203$	12.1707	+	12.8484i	0.0599541	+	0.0632928i
$204$	58.3920	+	231.098i	0.286235	+	1.13283i
$205$	−14.2848	−	3.14432i	−0.0696818	−	0.0153381i
$206$	110.758	+	328.718i	0.537660	+	1.59572i
$207$	157.147	+	117.612i	0.759167	+	0.568175i
$208$	−393.857	−	86.6946i	−1.89355	−	0.416801i
$209$	−11.4728	−	0.622037i	−0.0548938	−	0.00297625i
$210$	−58.2281	−	32.6334i	−0.277277	−	0.155397i
$211$	179.990	+	170.496i	0.853035	+	0.808037i	0.983024	−	0.183478i	$-0.0587357\pi$
$211$	179.990	+	170.496i	0.853035	+	0.808037i	−0.129989	+	0.991515i	$0.541494\pi$
$212$	23.2788	−	1.26214i	0.109806	−	0.00595349i
$213$	14.5946	+	104.197i	0.0685192	+	0.489189i
$214$	−260.003	+	383.475i	−1.21497	+	1.79194i
$215$	−16.1364	+	148.372i	−0.0750532	+	0.690103i
$216$	1.76913	−	14.1744i	0.00819040	−	0.0656222i
$217$	114.872	−	25.2851i	0.529362	−	0.116521i
$218$	−85.3576	+	13.9937i	−0.391549	+	0.0641912i
$219$	8.21505	−	62.0324i	0.0375117	−	0.283253i
$220$	−19.3230	−	69.5952i	−0.0878319	−	0.316342i
$221$	−304.320	−	400.326i	−1.37701	−	1.81143i
$222$	−445.531	+	193.636i	−2.00690	+	0.872232i
$223$	53.8667	−	101.603i	0.241555	−	0.455621i	−0.732860	−	0.680380i	$-0.761815\pi$
$223$	53.8667	−	101.603i	0.241555	−	0.455621i	0.974414	+	0.224759i	$0.0721596\pi$
$224$	106.756	−	42.5356i	0.476591	−	0.189891i
$225$	45.3750	+	131.405i	0.201667	+	0.584020i
$226$	−74.8154	+	88.0795i	−0.331042	+	0.389732i
$227$	290.188	−	153.848i	1.27836	−	0.677745i	0.315806	−	0.948824i	$-0.397725\pi$
$227$	290.188	−	153.848i	1.27836	−	0.677745i	0.962557	+	0.271078i	$0.0873803\pi$
$228$	−13.3570	+	16.7450i	−0.0585834	+	0.0734431i
$229$	131.236	−	60.7164i	0.573084	−	0.265137i	−0.111870	−	0.993723i	$-0.535684\pi$
$229$	131.236	−	60.7164i	0.573084	−	0.265137i	0.684955	+	0.728586i	$0.259822\pi$
$230$	−143.589	+	121.965i	−0.624298	+	0.530284i
$231$	−3.66863	+	47.2423i	−0.0158815	+	0.204512i
$232$	−2.89388	−	2.19987i	−0.0124736	−	0.00948220i
$233$	80.8218	−	134.327i	0.346875	−	0.576510i	−0.633478	−	0.773760i	$-0.718373\pi$
$233$	80.8218	−	134.327i	0.346875	−	0.576510i	0.980353	+	0.197250i	$0.0632010\pi$
$234$	−166.670	−	583.292i	−0.712263	−	2.49270i
$235$	−76.4748			−0.325425
$236$	−117.533	+	191.664i	−0.498022	+	0.812135i
$237$	86.0641	+	276.597i	0.363140	+	1.16708i
$238$	142.233	+	47.9239i	0.597618	+	0.201361i
$239$	52.6710	−	87.5399i	0.220381	−	0.366276i	−0.726867	−	0.686778i	$-0.759024\pi$
$239$	52.6710	−	87.5399i	0.220381	−	0.366276i	0.947248	+	0.320503i	$0.103852\pi$
$240$	145.740	+	52.9230i	0.607249	+	0.220512i
$241$	−123.387	+	309.678i	−0.511979	+	1.28497i	0.414988	+	0.909827i	$0.363786\pi$
$241$	−123.387	+	309.678i	−0.511979	+	1.28497i	−0.926967	+	0.375143i	$0.877593\pi$
$242$	177.638	−	150.887i	0.734042	−	0.623501i
$243$	226.484	−	88.0572i	0.932032	−	0.362375i
$244$	−7.68491	−	11.3344i	−0.0314955	−	0.0464525i
$245$	115.694	−	61.3368i	0.472219	−	0.250354i
$246$	36.5057	+	15.5417i	0.148397	+	0.0631778i
$247$	12.0893	−	43.5416i	0.0489444	−	0.176282i
$248$	−22.4435	+	8.94233i	−0.0904982	+	0.0360578i
$249$	58.0371	−	308.708i	0.233081	−	1.23979i
$250$	−347.340	+	37.7755i	−1.38936	+	0.151102i
$251$	−37.7196	−	49.6193i	−0.150277	−	0.197687i	0.714794	−	0.699335i	$-0.246520\pi$
$251$	−37.7196	−	49.6193i	−0.150277	−	0.197687i	−0.865072	+	0.501648i	$0.832727\pi$
$252$	67.7542	+	56.6821i	0.268866	+	0.224929i
$253$	121.380	+	56.1563i	0.479762	+	0.221962i
$254$	−396.141	+	64.9440i	−1.55961	+	0.255685i
$255$	95.7825	+	167.942i	0.375618	+	0.658595i
$256$	−238.622	+	143.574i	−0.932115	+	0.560835i
$257$	−44.1134	+	405.616i	−0.171648	+	1.57827i	0.518803	+	0.854894i	$0.326378\pi$
$257$	−44.1134	+	405.616i	−0.171648	+	1.57827i	−0.690451	+	0.723379i	$0.742588\pi$
$258$	117.380	−	387.456i	0.454961	−	1.50177i
$259$	−24.1441	+	147.272i	−0.0932204	+	0.568619i
$260$	283.655	−	15.3793i	1.09098	−	0.0591513i
$261$	9.54670	−	61.0975i	0.0365774	−	0.234090i
$262$	302.895	−	286.917i	1.15609	−	1.09510i
$263$	−37.5384	−	2.03527i	−0.142732	−	0.00773869i	−0.0173654	−	0.999849i	$-0.505528\pi$
$263$	−37.5384	−	2.03527i	−0.142732	−	0.00773869i	−0.125366	+	0.992111i	$0.540011\pi$
$264$	−0.826253	−	9.69764i	−0.00312975	−	0.0367335i
$265$	17.9195	−	6.03777i	0.0676206	−	0.0227840i
$266$	4.30657	+	12.7815i	0.0161901	+	0.0480506i
$267$	61.3769	−	5.22939i	0.229876	−	0.0195857i
$268$	9.95437	−	183.598i	0.0371432	−	0.685066i
$269$	−271.047	−	286.141i	−1.00761	−	1.06372i	−0.997965	−	0.0637670i	$-0.979689\pi$
$269$	−271.047	−	286.141i	−1.00761	−	1.06372i	−0.00964472	−	0.999953i	$-0.503070\pi$
$270$	34.0830	+	230.730i	0.126233	+	0.854555i
$271$	−20.1884	−	372.354i	−0.0744961	−	1.37400i	−0.761886	−	0.647711i	$-0.775726\pi$
$271$	−20.1884	−	372.354i	−0.0744961	−	1.37400i	0.687390	−	0.726289i	$-0.258756\pi$
$272$	−344.050	−	56.4041i	−1.26489	−	0.207368i
$273$	−178.358	−	54.0337i	−0.653326	−	0.197926i
$274$	−81.6351	−	8.87835i	−0.297938	−	0.0324027i
$275$	48.8339	+	81.1625i	0.177578	+	0.295136i
$276$	216.580	−	123.522i	0.784709	−	0.447545i
$277$	44.9739	+	274.329i	0.162361	+	0.990357i	0.934776	+	0.355239i	$0.115600\pi$
$277$	44.9739	+	274.329i	0.162361	+	0.990357i	−0.772415	+	0.635118i	$0.780951\pi$
$278$	−184.143	+	398.018i	−0.662384	+	1.43172i
$279$	−315.227	−	263.714i	−1.12985	−	0.945212i
$280$	3.35306	−	2.54893i	0.0119752	−	0.00910332i
$281$	13.1942	+	121.318i	0.0469543	+	0.431738i	0.993895	+	0.110330i	$0.0351907\pi$
$281$	13.1942	+	121.318i	0.0469543	+	0.431738i	−0.946941	+	0.321408i	$0.895844\pi$
$282$	203.873	+	38.3281i	0.722955	+	0.135915i
$283$	77.6928	+	194.994i	0.274533	+	0.689025i	1.00000		0.000768288i	$0.000244554\pi$
$283$	77.6928	+	194.994i	0.274533	+	0.689025i	−0.725467	+	0.688257i	$0.758376\pi$
$284$	128.775	+	35.7543i	0.453435	+	0.125895i
$285$	−6.80550	+	15.9853i	−0.0238789	+	0.0560888i
$286$	−193.611	−	365.188i	−0.676960	−	1.27688i
$287$	10.0886	−	6.84023i	0.0351519	−	0.0238335i
$288$	−345.608	−	204.433i	−1.20003	−	0.709836i
$289$	−94.3420	−	111.068i	−0.326443	−	0.384318i
$290$	55.1380	+	21.9690i	0.190131	+	0.0757551i
$291$	−86.1306	+	237.187i	−0.295982	+	0.815076i
$292$	−68.1061	−	40.9781i	−0.233240	−	0.140336i
$293$	138.312	−	410.494i	0.472053	−	1.40100i	−0.402208	−	0.915548i	$-0.631757\pi$
$293$	138.312	−	410.494i	0.472053	−	1.40100i	0.874261	−	0.485455i	$-0.161346\pi$
$294$	−339.167	+	105.533i	−1.15363	+	0.358956i
$295$	−50.2671	+	175.297i	−0.170397	+	0.594228i
$296$		−	30.6535i		−	0.103559i
$297$	138.495	−	90.7337i	0.466313	−	0.305501i
$298$	496.800	+	298.915i	1.66711	+	1.00307i
$299$	−318.322	+	418.746i	−1.06462	+	1.40049i
$300$	176.055	+	13.6717i	0.586851	+	0.0455723i
$301$	−80.5164	−	94.7913i	−0.267496	−	0.314921i
$302$	−23.8727	−	51.6000i	−0.0790487	−	0.170861i
$303$	−408.044	−	325.485i	−1.34668	−	1.07421i
$304$	−14.6752	−	27.6804i	−0.0482738	−	0.0910540i
$305$	−8.46557	−	7.19072i	−0.0277560	−	0.0235761i
$306$	−171.175	−	495.718i	−0.559396	−	1.61999i
$307$	−57.4802	−	144.264i	−0.187232	−	0.469917i	0.805157	−	0.593062i	$-0.202081\pi$
$307$	−57.4802	−	144.264i	−0.187232	−	0.469917i	−0.992389	+	0.123145i	$0.960702\pi$
$308$	53.1781	+	28.1932i	0.172656	+	0.0915365i
$309$	−148.418	−	341.491i	−0.480316	−	1.10515i
$310$	314.037	−	238.724i	1.01302	−	0.770079i
$311$	456.752	−	126.817i	1.46866	−	0.407771i	0.561117	−	0.827736i	$-0.310372\pi$
$311$	456.752	−	126.817i	1.46866	−	0.407771i	0.907540	+	0.419966i	$0.137958\pi$
$312$	37.9476	+	5.02547i	0.121627	+	0.0161073i
$313$	−23.7265	−	144.725i	−0.0758034	−	0.462380i	−0.997265	−	0.0739106i	$-0.976452\pi$
$313$	−23.7265	−	144.725i	−0.0758034	−	0.462380i	0.921461	−	0.388470i	$-0.126996\pi$
$314$	145.822	+	662.477i	0.464402	+	2.10980i
$315$	65.2524	+	29.5972i	0.207150	+	0.0939593i
$316$	365.801	+	39.7832i	1.15760	+	0.125896i
$317$	291.929	+	197.933i	0.920911	+	0.624393i	0.926786	−	0.375590i	$-0.122560\pi$
$317$	291.929	+	197.933i	0.920911	+	0.624393i	−0.00587506	+	0.999983i	$0.501870\pi$
$318$	−50.7973	+	7.11501i	−0.159740	+	0.0223743i
$319$	−2.28111	−	42.0726i	−0.00715082	−	0.131889i
$320$	122.872	−	129.714i	0.383975	−	0.405357i
$321$	243.143	−	433.844i	0.757456	−	1.35154i
$322$	8.49958	−	156.766i	0.0263962	−	0.486849i
$323$	8.39800	−	38.1525i	0.0260000	−	0.118119i
$324$	12.0884	−	308.430i	0.0373098	−	0.951944i
$325$	−353.037	+	118.952i	−1.08627	+	0.366006i
$326$	−23.0853	+	104.878i	−0.0708139	+	0.321711i
$327$	90.0200	−	22.7456i	0.275290	−	0.0695583i
$328$	−1.81759	+	1.72172i	−0.00554144	+	0.00524913i
$329$	43.8261	−	46.2666i	0.133210	−	0.140628i
$330$	55.3602	+	148.961i	0.167758	+	0.451397i
$331$	−82.8893	+	505.603i	−0.250421	+	1.52750i	0.499699	+	0.866199i	$0.333444\pi$
$331$	−82.8893	+	505.603i	−0.250421	+	1.52750i	−0.750120	+	0.661301i	$0.770004\pi$
$332$	−330.248	−	223.914i	−0.994724	−	0.674440i
$333$	458.877	−	247.705i	1.37801	−	0.743860i
$334$	192.341	−	115.728i	0.575872	−	0.346491i
$335$	−32.0598	−	145.649i	−0.0957009	−	0.434773i
$336$	−115.538	+	57.8422i	−0.343864	+	0.172149i
$337$	−445.741	−	206.222i	−1.32267	−	0.611933i	−0.373775	−	0.927519i	$-0.621937\pi$
$337$	−445.741	−	206.222i	−1.32267	−	0.611933i	−0.948897	+	0.315586i	$0.897799\pi$
$338$	1111.30	−	308.550i	3.28786	−	0.912871i
$339$	71.9931	−	101.024i	0.212369	−	0.298007i
$340$	244.142	−	26.5520i	0.718064	−	0.0780942i
$341$	−247.411	−	131.169i	−0.725547	−	0.384661i
$342$	26.1543	−	39.2042i	0.0764746	−	0.114632i
$343$	−62.9579	+	226.754i	−0.183551	+	0.661090i
$344$	19.4701	+	16.5381i	0.0565991	+	0.0480757i
$345$	142.462	−	143.534i	0.412934	−	0.416041i
$346$	−456.010	−	672.564i	−1.31795	−	1.94383i
$347$	126.577	+	273.592i	0.364776	+	0.788451i	0.999872	+	0.0160170i	$0.00509860\pi$
$347$	126.577	+	273.592i	0.364776	+	0.788451i	−0.635096	+	0.772434i	$0.719039\pi$
$348$	−66.3427	−	42.0560i	−0.190640	−	0.120851i
$349$	−177.452	+	445.370i	−0.508458	+	1.27613i	0.420952	+	0.907083i	$0.361696\pi$
$349$	−177.452	+	445.370i	−0.508458	+	1.27613i	−0.929410	+	0.369049i	$0.879683\pi$
$350$	67.2902	−	88.5187i	0.192258	−	0.252911i
$351$	231.418	+	608.678i	0.659310	+	1.73413i
$352$	−259.274	−	87.3595i	−0.736573	−	0.248181i
$353$			695.446i			1.97010i	0.172262	+	0.985051i	$0.444892\pi$
$353$			695.446i			1.97010i	−0.172262	+	0.985051i	$0.555108\pi$
$354$	221.863	−	442.129i	0.626732	−	1.24895i
$355$	108.402			0.305357
$356$	24.9839	−	74.1495i	0.0701794	−	0.208285i
$357$	−156.494	−	38.2961i	−0.438359	−	0.107272i
$358$	−40.0046	−	30.4107i	−0.111745	−	0.0849461i
$359$	−140.697	−	56.0589i	−0.391914	−	0.156153i	0.165853	−	0.986151i	$-0.446962\pi$
$359$	−140.697	−	56.0589i	−0.391914	−	0.156153i	−0.557767	+	0.829998i	$0.688342\pi$
$360$	−14.2098	−	3.83083i	−0.0394716	−	0.0106412i
$361$	−324.449	+	150.106i	−0.898750	+	0.415806i
$362$	78.6023	−	53.2937i	0.217133	−	0.147220i
$363$	−176.245	+	177.571i	−0.485523	+	0.489176i
$364$	−153.252	+	180.423i	−0.421023	+	0.495666i
$365$	−62.1197	−	17.2475i	−0.170191	−	0.0472533i
$366$	18.9644	+	23.4125i	0.0518152	+	0.0639685i
$367$	29.3932	−	55.4415i	0.0800905	−	0.151067i	−0.840232	−	0.542227i	$-0.817581\pi$
$367$	29.3932	−	55.4415i	0.0800905	−	0.151067i	0.920323	+	0.391160i	$0.127926\pi$
$368$	39.4293	+	362.547i	0.107145	+	0.985181i
$369$	−40.4614	−	13.2961i	−0.109651	−	0.0360329i
$370$	133.900	+	482.263i	0.361891	+	1.30341i
$371$	−6.61645	+	14.3012i	−0.0178341	+	0.0385478i
$372$	−466.821	+	233.706i	−1.25489	+	0.628241i
$373$	455.087	−	100.172i	1.22007	−	0.268558i	0.442163	−	0.896935i	$-0.354211\pi$
$373$	455.087	−	100.172i	1.22007	−	0.268558i	0.777909	+	0.628377i	$0.216280\pi$
$374$	−184.224	−	306.182i	−0.492577	−	0.818669i
$375$	368.059	−	72.0556i	0.981490	−	0.192148i
$376$	−7.34584	+	10.8343i	−0.0195368	+	0.0288146i
$377$	163.531	+	26.8096i	0.433770	+	0.0711130i
$378$	−159.122	−	111.606i	−0.420957	−	0.295255i
$379$	310.165	+	293.804i	0.818378	+	0.775209i	0.977250	−	0.212090i	$-0.0680271\pi$
$379$	310.165	+	293.804i	0.818378	+	0.775209i	−0.158872	+	0.987299i	$0.550786\pi$
$380$	15.1766	+	16.0217i	0.0399384	+	0.0421624i
$381$	417.779	−	105.561i	1.09653	−	0.277063i
$382$	510.885	+	112.454i	1.33740	+	0.294383i
$383$	101.587	+	301.500i	0.265241	+	0.787207i	0.994666	+	0.103147i	$0.0328911\pi$
$383$	101.587	+	301.500i	0.265241	+	0.787207i	−0.729425	+	0.684061i	$0.760212\pi$
$384$	41.0928	−	29.7510i	0.107012	−	0.0774766i
$385$	47.6786	+	10.4949i	0.123841	+	0.0272594i
$386$	103.340	+	5.60293i	0.267720	+	0.0145154i
$387$	−90.2370	+	425.104i	−0.233171	+	1.09846i
$388$	232.705	+	220.430i	0.599756	+	0.568119i
$389$	73.2051	−	3.96907i	0.188188	−	0.0102033i	0.0401960	−	0.999192i	$-0.487202\pi$
$389$	73.2051	−	3.96907i	0.188188	−	0.0102033i	0.147992	+	0.988989i	$0.452719\pi$
$390$	−618.972	+	86.6974i	−1.58711	+	0.222301i
$391$	−255.189	+	376.375i	−0.652657	+	0.962597i
$392$	2.42334	−	22.2822i	0.00618198	−	0.0568424i
$393$	−297.818	+	334.478i	−0.757808	+	0.851089i
$394$	−22.9348	+	5.04832i	−0.0582100	+	0.0128130i
$395$	294.521	−	48.2843i	0.745623	−	0.122239i
$396$	−35.5796	−	207.281i	−0.0898474	−	0.523437i
$397$	−174.640	−	628.996i	−0.439899	−	1.58437i	−0.768465	−	0.639892i	$-0.778979\pi$
$397$	−174.640	−	628.996i	−0.439899	−	1.58437i	0.328566	−	0.944481i	$-0.393435\pi$
$398$	518.575	+	682.174i	1.30295	+	1.71400i
$399$	−5.77090	−	13.2781i	−0.0144634	−	0.0332785i
$400$	−120.983	+	228.199i	−0.302458	+	0.570497i
$401$	−273.663	+	109.037i	−0.682451	+	0.271913i	−0.685490	−	0.728082i	$-0.740412\pi$
$401$	−273.663	+	109.037i	−0.682451	+	0.271913i	0.00303875	+	0.999995i	$0.499033\pi$
$402$	12.4704	+	404.352i	0.0310209	+	1.00585i
$403$	713.007	−	839.417i	1.76925	−	2.08292i
$404$	−585.775	+	310.558i	−1.44994	+	0.768709i
$405$	−57.4798	−	243.674i	−0.141925	−	0.601663i
$406$	−44.8894	+	20.7681i	−0.110565	+	0.0511529i
$407$	270.800	−	230.019i	0.665356	−	0.565158i
$408$	32.9930	+	2.56209i	0.0808652	+	0.00627963i
$409$	−29.4274	−	22.3701i	−0.0719496	−	0.0546947i	0.568581	−	0.822627i	$-0.307493\pi$
$409$	−29.4274	−	22.3701i	−0.0719496	−	0.0546947i	−0.640531	+	0.767932i	$0.721286\pi$
$410$	21.0750	−	35.0268i	0.0514023	−	0.0854313i
$411$	88.1228	+	2.05669i	0.214411	+	0.00500411i
$412$	−472.970			−1.14798
$413$	−77.2463	−	130.870i	−0.187037	−	0.316877i
$414$	−451.726	+	311.246i	−1.09113	+	0.751802i
$415$	−306.691	−	103.336i	−0.739014	−	0.249003i
$416$	554.762	−	922.021i	1.33356	−	2.21640i
$417$	160.681	−	442.485i	0.385327	−	1.06112i
$418$	11.8854	−	29.8302i	0.0284341	−	0.0713642i
$419$	271.283	−	230.430i	0.647453	−	0.549951i	−0.262360	−	0.964970i	$-0.584501\pi$
$419$	271.283	−	230.430i	0.647453	−	0.549951i	0.909813	+	0.415019i	$0.136225\pi$
$420$	67.5178	−	61.0312i	0.160757	−	0.145312i
$421$	−322.405	−	475.511i	−0.765807	−	1.12948i	−0.987996	−	0.154477i	$-0.950631\pi$
$421$	−322.405	−	475.511i	−0.765807	−	1.12948i	0.222189	−	0.975004i	$-0.428680\pi$
$422$	−612.171	+	324.552i	−1.45064	+	0.769081i
$423$	−221.548	−	22.4157i	−0.523753	−	0.0529922i
$424$	0.865885	−	3.11864i	0.00204218	−	0.00735528i
$425$	−299.187	+	119.207i	−0.703969	+	0.280487i
$426$	−288.987	−	54.3295i	−0.678373	−	0.127534i
$427$	9.20176	−	1.00075i	0.0215498	−	0.00234368i
$428$	−382.305	−	502.914i	−0.893236	−	1.17503i
$429$	240.357	+	372.948i	0.560274	+	0.869343i
$430$	−378.559	−	175.140i	−0.880369	−	0.407302i
$431$	241.577	−	39.6045i	0.560502	−	0.0918897i	0.125130	−	0.992140i	$-0.460065\pi$
$431$	241.577	−	39.6045i	0.560502	−	0.0918897i	0.435372	+	0.900251i	$0.356617\pi$
$432$	406.696	+	196.036i	0.941425	+	0.453787i
$433$	−727.554	+	437.755i	−1.68026	+	1.01098i	−0.738764	+	0.673964i	$0.764590\pi$
$433$	−727.554	+	437.755i	−1.68026	+	1.01098i	−0.941499	+	0.337017i	$0.890582\pi$
$434$	−35.5413	+	326.797i	−0.0818925	+	0.752989i
$435$	−60.9755	−	18.4726i	−0.140173	−	0.0424657i
$436$	19.0806	−	116.386i	0.0437628	−	0.266941i
$437$	−40.8034	+	2.21230i	−0.0933717	+	0.00506246i
$438$	156.960	+	77.1133i	0.358356	+	0.176058i
$439$	−375.190	+	355.399i	−0.854648	+	0.809566i	−0.983275	−	0.182127i	$-0.941702\pi$
$439$	−375.190	+	355.399i	−0.854648	+	0.809566i	0.128627	+	0.991693i	$0.458943\pi$
$440$	−10.0129	−	0.542884i	−0.0227566	−	0.00123383i
$441$	353.143	−	143.782i	0.800778	−	0.326036i
$442$	1331.82	−	448.741i	3.01316	−	1.01525i
$443$	221.998	+	658.867i	0.501125	+	1.48728i	0.837966	+	0.545723i	$0.183745\pi$
$443$	221.998	+	658.867i	0.501125	+	1.48728i	−0.336841	+	0.941562i	$0.609358\pi$
$444$	−56.2322	−	659.991i	−0.126649	−	1.48647i
$445$	3.43594	−	63.3722i	0.00772122	−	0.142409i
$446$	221.024	+	233.332i	0.495570	+	0.523166i
$447$	−558.597	−	274.435i	−1.24966	−	0.613949i
$448$	8.06081	+	148.673i	0.0179929	+	0.331859i
$449$	68.1535	+	11.1732i	0.151790	+	0.0248846i	0.237198	−	0.971461i	$-0.423771\pi$
$449$	68.1535	+	11.1732i	0.151790	+	0.0248846i	−0.0854080	+	0.996346i	$0.527219\pi$
$450$	−388.512	+	2.91237i	−0.863359	+	0.00647193i
$451$	−28.8490	−	3.13751i	−0.0639667	−	0.00695679i
$452$	−81.2384	−	135.019i	−0.179731	−	0.298715i
$453$	30.2355	+	53.0139i	0.0667451	+	0.117028i
$454$	148.506	+	905.844i	0.327105	+	1.99525i
$455$	−80.6224	+	174.262i	−0.177192	+	0.382994i
$456$	1.61096	+	2.49962i	0.00353280	+	0.00548163i
$457$	306.050	−	232.654i	0.669695	−	0.509089i	−0.214191	−	0.976792i	$-0.568711\pi$
$457$	306.050	−	232.654i	0.669695	−	0.509089i	0.883886	+	0.467703i	$0.154918\pi$
$458$	43.6936	+	401.756i	0.0954010	+	0.877197i
$459$	228.256	+	514.602i	0.497291	+	1.12114i
$460$	−95.0815	−	238.637i	−0.206699	−	0.518775i
$461$	−657.172	−	182.463i	−1.42554	−	0.395798i	−0.532748	−	0.846274i	$-0.678841\pi$
$461$	−657.172	−	182.463i	−1.42554	−	0.395798i	−0.892789	+	0.450476i	$0.851254\pi$
$462$	−121.846	−	51.8740i	−0.263736	−	0.112281i
$463$	−135.066	−	254.761i	−0.291718	−	0.550239i	0.693726	−	0.720239i	$-0.255968\pi$
$463$	−135.066	−	254.761i	−0.291718	−	0.550239i	−0.985444	+	0.170000i	$0.945623\pi$
$464$	95.0951	−	64.4761i	0.204946	−	0.138957i
$465$	−314.127	+	283.948i	−0.675542	+	0.610641i
$466$	283.637	+	333.923i	0.608663	+	0.716574i
$467$	−829.110	−	330.348i	−1.77540	−	0.707382i	−0.996807	−	0.0798484i	$-0.974556\pi$
$467$	−829.110	−	330.348i	−1.77540	−	0.707382i	−0.778589	−	0.627534i	$-0.784064\pi$
$468$	826.258	+	38.5889i	1.76551	+	0.0824549i
$469$	106.489	+	64.0724i	0.227056	+	0.136615i
$470$	68.2440	−	202.541i	0.145200	−	0.430938i
$471$	−216.336	−	695.271i	−0.459312	−	1.47616i
$472$	20.0062	+	23.9597i	0.0423859	+	0.0507621i
$473$			296.102i			0.626009i
$474$	−809.359	−	18.8895i	−1.70751	−	0.0398514i
$475$	−24.7985	−	14.9208i	−0.0522074	−	0.0314122i
$476$	−123.849	+	162.920i	−0.260186	+	0.342269i
$477$	53.6824	−	12.2390i	0.112542	−	0.0256583i
$478$	184.844	+	217.615i	0.386703	+	0.455262i
$479$	−369.356	−	798.351i	−0.771099	−	1.66670i	−0.745019	−	0.667044i	$-0.767559\pi$
$479$	−369.356	−	798.351i	−0.771099	−	1.66670i	−0.0260804	−	0.999660i	$-0.508303\pi$
$480$	−257.982	+	323.419i	−0.537463	+	0.673790i
$481$	654.559	+	1234.63i	1.36083	+	2.56680i
$482$	−710.064	−	603.134i	−1.47316	−	1.25132i
$483$	5.19492	+	168.445i	0.0107555	+	0.348747i
$484$	117.629	+	295.225i	0.243034	+	0.609970i
$485$	229.701	+	121.780i	0.473609	+	0.251092i
$486$	31.1087	+	678.414i	0.0640096	+	1.39591i
$487$	282.270	−	214.576i	0.579610	−	0.440608i	−0.273846	−	0.961774i	$-0.588296\pi$
$487$	282.270	−	214.576i	0.579610	−	0.440608i	0.853455	+	0.521166i	$0.174503\pi$
$488$	−1.83189	+	0.508621i	−0.00375386	+	0.00104226i
$489$	15.1339	−	114.277i	0.0309486	−	0.233695i
$490$	59.2068	+	361.146i	0.120830	+	0.737032i
$491$	118.050	+	536.304i	0.240427	+	1.09227i	0.929858	+	0.367918i	$0.119929\pi$
$491$	118.050	+	536.304i	0.240427	+	1.09227i	−0.689431	+	0.724351i	$0.742140\pi$
$492$	−35.9756	+	40.4040i	−0.0731212	+	0.0821219i
$493$	142.421	+	15.4892i	0.288887	+	0.0314183i
$494$	104.530	+	70.8733i	0.211600	+	0.143468i
$495$	−72.7856	−	154.278i	−0.147042	−	0.311673i
$496$	−41.3400	−	762.471i	−0.0833468	−	1.53724i
$497$	−62.1227	+	65.5821i	−0.124995	+	0.131956i
$498$	765.812	+	429.192i	1.53777	+	0.861830i
$499$	14.8153	−	273.252i	0.0296899	−	0.547599i	−0.945417	−	0.325863i	$-0.894345\pi$
$499$	14.8153	−	273.252i	0.0296899	−	0.547599i	0.975107	−	0.221736i	$-0.0711722\pi$
$500$	102.411	−	465.257i	0.204822	−	0.930515i
$501$	−195.175	+	141.306i	−0.389570	+	0.282047i
$502$	165.075	−	55.6203i	0.328835	−	0.110797i
$503$	−20.1606	+	91.5903i	−0.0400806	+	0.182088i	−0.992408	−	0.122990i	$-0.960752\pi$
$503$	−20.1606	+	91.5903i	−0.0400806	+	0.182088i	0.952327	+	0.305078i	$0.0986827\pi$
$504$	10.4609	−	6.40143i	0.0207558	−	0.0127012i
$505$	−390.418	+	369.824i	−0.773106	+	0.732325i
$506$	−257.044	+	271.358i	−0.507992	+	0.536280i
$507$	−1160.48	+	431.284i	−2.28892	+	0.850659i
$508$	88.5521	−	540.144i	0.174315	−	1.06328i
$509$	212.054	+	143.776i	0.416610	+	0.282468i	0.751429	−	0.659814i	$-0.229365\pi$
$509$	212.054	+	143.776i	0.416610	+	0.282468i	−0.334819	+	0.942282i	$0.608675\pi$
$510$	−530.261	+	103.810i	−1.03973	+	0.203550i
$511$	46.0340	−	27.6978i	0.0900861	−	0.0542030i
$512$	−152.770	−	694.041i	−0.298379	−	1.35555i
$513$	−24.4010	+	44.3147i	−0.0475653	+	0.0863834i
$514$	−1034.89	−	478.793i	−2.01341	−	0.931505i
$515$	−369.645	+	102.632i	−0.717758	+	0.199285i
$516$	449.543	+	320.359i	0.871207	+	0.620850i
$517$	−150.835	+	16.4043i	−0.291750	+	0.0317297i
$518$	−368.500	−	195.366i	−0.711391	−	0.377155i
$519$	549.020	+	677.793i	1.05784	+	1.30596i
$520$	10.5509	−	38.0010i	0.0202903	−	0.0730789i
$521$	−431.831	−	366.800i	−0.828849	−	0.704031i	0.128893	−	0.991659i	$-0.458858\pi$
$521$	−431.831	−	366.800i	−0.828849	−	0.704031i	−0.957742	+	0.287627i	$0.907134\pi$
$522$	153.295	+	79.8058i	0.293670	+	0.152885i
$523$	105.654	+	155.829i	0.202016	+	0.297951i	0.915180	−	0.403046i	$-0.132049\pi$
$523$	105.654	+	155.829i	0.202016	+	0.297951i	−0.713163	+	0.700998i	$0.752738\pi$
$524$	238.865	+	516.298i	0.455849	+	0.985302i
$525$	−63.9044	+	100.808i	−0.121723	+	0.192016i
$526$	38.8886	−	97.6030i	0.0739327	−	0.185557i
$527$	576.207	−	757.987i	1.09337	−	1.43830i
$528$	298.801	+	73.1204i	0.565911	+	0.138486i
$529$	−50.5538	−	17.0335i	−0.0955648	−	0.0321995i
$530$			52.8470i			0.0997113i
$531$	−197.006	+	493.102i	−0.371009	+	0.928629i
$532$	−18.3904			−0.0345684
$533$	36.4425	−	108.157i	0.0683724	−	0.202922i
$534$	−40.9211	+	167.221i	−0.0766313	+	0.313148i
$535$	−407.916	−	310.090i	−0.762461	−	0.579607i
$536$	−23.7138	−	9.44846i	−0.0442422	−	0.0176277i
$537$	45.5586	+	28.8806i	0.0848391	+	0.0537813i
$538$	999.709	−	462.515i	1.85819	−	0.859693i
$539$	215.030	−	145.794i	0.398943	−	0.270490i
$540$	−312.974	−	56.4134i	−0.579581	−	0.104469i
$541$	257.592	−	303.261i	0.476141	−	0.560557i	−0.470685	−	0.882301i	$-0.655993\pi$
$541$	257.592	−	303.261i	0.476141	−	0.560557i	0.946827	+	0.321744i	$0.104269\pi$
$542$	1004.18	+	278.810i	1.85273	+	0.514409i
$543$	−79.2134	+	64.1637i	−0.145881	+	0.118165i
$544$	435.737	−	821.887i	0.800987	−	1.51082i
$545$	−10.3429	−	95.1011i	−0.0189777	−	0.174497i
$546$	302.268	−	424.157i	0.553605	−	0.776844i
$547$	76.9415	+	277.118i	0.140661	+	0.506615i	0.999988	−	0.00481097i	$-0.00153139\pi$
$547$	76.9415	+	277.118i	0.140661	+	0.506615i	−0.859328	+	0.511426i	$0.829118\pi$
$548$	47.0137	−	101.618i	0.0857914	−	0.185435i
$549$	−22.4171	−	23.3129i	−0.0408326	−	0.0424643i
$550$	−258.534	+	56.9077i	−0.470062	+	0.103468i
$551$	6.63715	+	11.0310i	0.0120456	+	0.0200200i
$552$	−6.65040	−	33.9701i	−0.0120478	−	0.0615401i
$553$	−139.572	+	205.853i	−0.252391	+	0.372248i
$554$	−766.684	−	125.692i	−1.38391	−	0.226880i
$555$	−187.162	−	503.608i	−0.337228	−	0.907402i
$556$	−434.124	−	411.224i	−0.780798	−	0.739611i
$557$	82.4431	+	87.0342i	0.148013	+	0.156255i	0.795786	−	0.605578i	$-0.207058\pi$
$557$	82.4431	+	87.0342i	0.148013	+	0.156255i	−0.647773	+	0.761833i	$0.724299\pi$
$558$	979.737	−	599.537i	1.75580	−	1.07444i
$559$	−1137.34	−	250.348i	−2.03460	−	0.447849i
$560$	42.5062	+	126.154i	0.0759040	+	0.225275i
$561$	224.940	+	310.693i	0.400963	+	0.553820i
$562$	−333.082	−	73.3168i	−0.592672	−	0.130457i
$563$	1053.44	+	57.1158i	1.87112	+	0.101449i	0.954480	−	0.298274i	$-0.0964110\pi$
$563$	1053.44	+	57.1158i	1.87112	+	0.101449i	0.916636	+	0.399723i	$0.130894\pi$
$564$	−138.286	+	246.745i	−0.245188	+	0.437492i
$565$	−92.7895	−	87.8949i	−0.164229	−	0.155566i
$566$	−585.766	+	31.7593i	−1.03492	+	0.0561119i
$567$	180.361	+	104.869i	0.318097	+	0.184955i
$568$	10.4126	−	15.3574i	0.0183320	−	0.0270377i
$569$	−51.7403	+	475.744i	−0.0909319	+	0.836105i	0.856500	+	0.516147i	$0.172634\pi$
$569$	−51.7403	+	475.744i	−0.0909319	+	0.836105i	−0.947432	+	0.319958i	$0.896331\pi$
$570$	−36.2635	−	32.2890i	−0.0636202	−	0.0566473i
$571$	101.635	−	22.3715i	0.177995	−	0.0391796i	−0.125079	−	0.992147i	$-0.539918\pi$
$571$	101.635	−	22.3715i	0.177995	−	0.0391796i	0.303073	+	0.952967i	$0.401987\pi$
$572$	556.167	−	91.1789i	0.972319	−	0.159404i
$573$	−556.671	−	73.7208i	−0.971502	−	0.128658i
$574$	9.11334	+	32.8233i	0.0158769	+	0.0571834i
$575$	203.871	+	268.187i	0.354558	+	0.466413i
$576$	393.981	−	339.767i	0.683994	−	0.589873i
$577$	316.687	−	597.335i	0.548851	−	1.03524i	−0.441579	−	0.897223i	$-0.645581\pi$
$577$	316.687	−	597.335i	0.548851	−	1.03524i	0.990429	−	0.138020i	$-0.0440738\pi$
$578$	378.348	−	150.748i	0.654581	−	0.260809i
$579$	−111.039	+	3.42450i	−0.191777	+	0.00591451i
$580$	−52.3925	+	61.6813i	−0.0903320	+	0.106347i
$581$	238.275	−	126.326i	0.410112	−	0.217428i
$582$	−551.321	−	439.773i	−0.947288	−	0.755624i
$583$	34.0482	−	15.7524i	0.0584017	−	0.0270195i
$584$	−8.41042	+	7.14388i	−0.0144014	+	0.0122327i
$585$	654.128	−	149.134i	1.11817	−	0.254930i
$586$	963.754	+	732.627i	1.64463	+	1.25022i
$587$	369.067	−	613.394i	0.628734	−	1.04496i	−0.364763	−	0.931100i	$-0.618850\pi$
$587$	369.067	−	613.394i	0.628734	−	1.04496i	0.993496	−	0.113863i	$-0.0363225\pi$
$588$	11.3006	−	484.197i	0.0192187	−	0.823464i
$589$	85.5614			0.145265
$590$	−419.412	−	289.561i	−0.710867	−	0.490781i
$591$	24.0701	−	7.48949i	0.0407277	−	0.0126726i
$592$	918.130	+	309.354i	1.55090	+	0.522557i
$593$	−104.579	+	173.811i	−0.176355	+	0.293105i	−0.932409	−	0.361405i	$-0.882297\pi$
$593$	−104.579	+	173.811i	−0.176355	+	0.293105i	0.756054	+	0.654509i	$0.227125\pi$
$594$	116.716	+	447.767i	0.196492	+	0.753817i
$595$	−61.4401	+	154.203i	−0.103261	+	0.259165i
$596$	−602.532	+	511.795i	−1.01096	+	0.858717i
$597$	−616.813	−	682.370i	−1.03319	−	1.14300i
$598$	−824.972	−	1216.74i	−1.37955	−	2.03469i
$599$	−466.115	+	247.118i	−0.778155	+	0.412552i	−0.809621	−	0.586953i	$-0.800327\pi$
$599$	−466.115	+	247.118i	−0.778155	+	0.412552i	0.0314659	+	0.999505i	$0.489982\pi$
$600$	9.60319	−	22.5568i	0.0160053	−	0.0375946i
$601$	95.6952	−	344.663i	0.159227	−	0.573482i	−0.840282	−	0.542149i	$-0.817611\pi$
$601$	95.6952	−	344.663i	0.159227	−	0.573482i	0.999509	−	0.0313333i	$-0.00997533\pi$
$602$	322.902	−	128.656i	0.536382	−	0.213714i
$603$	−50.1857	−	431.343i	−0.0832267	−	0.715328i
$604$	77.0678	−	8.38163i	0.127596	−	0.0138769i
$605$	155.994	+	205.206i	0.257841	+	0.339184i
$606$	1226.16	−	790.236i	2.02337	−	1.30402i
$607$	−92.9607	−	43.0082i	−0.153148	−	0.0708537i	0.341818	−	0.939766i	$-0.388957\pi$
$607$	−92.9607	−	43.0082i	−0.153148	−	0.0708537i	−0.494966	+	0.868912i	$0.664819\pi$
$608$	82.4936	−	13.5241i	0.135680	−	0.0222437i
$609$	46.1195	−	26.3034i	0.0757298	−	0.0431912i
$610$	26.5988	−	16.0040i	0.0436046	−	0.0262360i
$611$	64.5178	−	593.232i	0.105594	−	0.970919i
$612$	715.062	−	5.36026i	1.16840	−	0.00875859i
$613$	−114.317	+	697.301i	−0.186487	+	1.13752i	0.713191	+	0.700970i	$0.247249\pi$
$613$	−114.317	+	697.301i	−0.186487	+	1.13752i	−0.899679	+	0.436553i	$0.856199\pi$
$614$	433.373	−	23.4968i	0.705819	−	0.0382684i
$615$	−19.3490	+	39.3839i	−0.0314618	+	0.0640388i
$616$	6.06662	−	5.74661i	0.00984841	−	0.00932891i
$617$	−774.324	−	41.9826i	−1.25498	−	0.0680432i	−0.585378	−	0.810761i	$-0.699054\pi$
$617$	−774.324	−	41.9826i	−1.25498	−	0.0680432i	−0.669605	+	0.742718i	$0.733536\pi$
$618$	1036.87	−	88.3428i	1.67778	−	0.142949i
$619$	791.810	−	266.792i	1.27918	−	0.431005i	0.403978	−	0.914769i	$-0.367627\pi$
$619$	791.810	−	266.792i	1.27918	−	0.431005i	0.875198	+	0.483764i	$0.160731\pi$
$620$	171.742	+	509.713i	0.277004	+	0.822117i
$621$	454.785	−	374.061i	0.732343	−	0.602353i
$622$	−71.7234	+	1322.86i	−0.115311	+	2.12679i
$623$	36.3706	+	38.3960i	0.0583797	+	0.0616307i
$624$	−533.488	+	1085.89i	−0.854949	+	1.74020i
$625$	−0.0132959	−	0.245228i	−2.12734e−5	−	0.000392364i
$626$	404.472	+	66.3099i	0.646122	+	0.105926i
$627$	−9.99384	+	32.9883i	−0.0159391	+	0.0526130i
$628$	−919.499	−	100.002i	−1.46417	−	0.159238i
$629$	622.824	+	1035.14i	0.990182	+	1.64569i
$630$	−136.617	+	146.407i	−0.216852	+	0.232392i
$631$	−98.1898	−	598.931i	−0.155610	−	0.949178i	−0.943017	−	0.332744i	$-0.892025\pi$
$631$	−98.1898	−	598.931i	−0.155610	−	0.949178i	0.787407	−	0.616433i	$-0.211423\pi$
$632$	21.4499	−	46.3632i	0.0339397	−	0.0733595i
$633$	625.178	−	402.915i	0.987643	−	0.636516i
$634$	−784.727	+	596.534i	−1.23774	+	0.940905i
$635$	−48.0008	−	441.360i	−0.0755918	−	0.695055i
$636$	12.9221	−	68.7348i	0.0203178	−	0.108074i
$637$	378.198	+	949.206i	0.593718	+	1.49012i
$638$	113.464	+	31.5030i	0.177843	+	0.0493777i
$639$	314.040	+	31.7739i	0.491455	+	0.0497244i
$640$	−24.4832	−	46.1802i	−0.0382550	−	0.0721565i
$641$	−146.120	+	99.0721i	−0.227957	+	0.154559i	−0.669819	−	0.742524i	$-0.733628\pi$
$641$	−146.120	+	99.0721i	−0.227957	+	0.154559i	0.441862	+	0.897083i	$0.354318\pi$
$642$	932.046	+	1031.11i	1.45178	+	1.60609i
$643$	95.8311	+	112.821i	0.149037	+	0.175460i	0.831615	−	0.555353i	$-0.187417\pi$
$643$	95.8311	+	112.821i	0.149037	+	0.175460i	−0.682577	+	0.730813i	$0.739141\pi$
$644$	198.862	+	79.2340i	0.308792	+	0.123034i
$645$	420.852	+	152.826i	0.652484	+	0.236939i
$646$	93.5514	+	56.2880i	0.144816	+	0.0871332i
$647$	−12.9927	+	38.5609i	−0.0200814	+	0.0595995i	−0.957225	−	0.289344i	$-0.906563\pi$
$647$	−12.9927	+	38.5609i	−0.0200814	+	0.0595995i	0.937144	+	0.348943i	$0.113459\pi$
$648$	−40.0429	−	15.2630i	−0.0617946	−	0.0235540i
$649$	−61.5419	+	356.529i	−0.0948257	+	0.549351i
$650$		−	1041.15i		−	1.60178i
$651$	8.23322	−	352.768i	0.0126470	−	0.541887i
$652$	−125.466	−	75.4903i	−0.192432	−	0.115783i
$653$	200.187	−	263.341i	0.306565	−	0.403279i	−0.616851	−	0.787080i	$-0.711592\pi$
$653$	200.187	−	263.341i	0.306565	−	0.403279i	0.923416	+	0.383801i	$0.125385\pi$
$654$	−20.0905	+	258.712i	−0.0307194	+	0.395585i
$655$	298.716	+	351.676i	0.456055	+	0.536910i
$656$	−33.2255	−	71.8158i	−0.0506487	−	0.109475i
$657$	−174.905	−	68.1739i	−0.266218	−	0.103766i
$658$	83.4264	+	157.359i	0.126788	+	0.239147i
$659$	−598.816	−	508.639i	−0.908674	−	0.771835i	0.0654481	−	0.997856i	$-0.479152\pi$
$659$	−598.816	−	508.639i	−0.908674	−	0.771835i	−0.974122	+	0.226021i	$0.927428\pi$
$660$	−216.581	+	6.67946i	−0.328153	+	0.0101204i
$661$	−435.943	−	1094.13i	−0.659520	−	1.65527i	−0.751681	−	0.659527i	$-0.770757\pi$
$661$	−435.943	−	1094.13i	−0.659520	−	1.65527i	0.0921609	−	0.995744i	$-0.470623\pi$
$662$	−1265.10	−	670.715i	−1.91103	−	1.01316i
$663$	−1383.57	+	601.322i	−2.08683	+	0.906971i
$664$	−44.0992	+	33.5233i	−0.0664144	+	0.0504869i
$665$	−14.3728	+	3.99060i	−0.0216133	+	0.00600090i
$666$	246.550	+	1436.37i	0.370196	+	2.15670i
$667$	−24.2435	−	147.879i	−0.0363470	−	0.221707i
$668$	65.7965	+	298.916i	0.0984977	+	0.447480i
$669$	−257.662	−	229.422i	−0.385145	−	0.342932i
$670$	414.356	+	45.0639i	0.618442	+	0.0672596i
$671$	−18.2395	−	12.3667i	−0.0271825	−	0.0184302i
$672$	−47.8219	−	341.422i	−0.0711635	−	0.508068i
$673$	4.39956	+	81.1451i	0.00653724	+	0.120572i	0.999980	+	0.00624596i	$0.00198816\pi$
$673$	4.39956	+	81.1451i	0.00653724	+	0.120572i	−0.993443	+	0.114326i	$0.963529\pi$
$674$	943.937	−	996.502i	1.40050	−	1.47849i
$675$	415.272	−	38.5193i	0.615217	−	0.0570656i
$676$	−85.1384	+	1570.29i	−0.125944	+	2.32291i
$677$	−268.075	+	1217.88i	−0.395975	+	1.79893i	0.182470	+	0.983211i	$0.441591\pi$
$677$	−268.075	+	1217.88i	−0.395975	+	1.79893i	−0.578445	+	0.815721i	$0.696340\pi$
$678$	203.315	+	280.823i	0.299874	+	0.414193i
$679$	−205.312	+	69.1777i	−0.302374	+	0.101882i
$680$	7.32938	−	33.2977i	0.0107785	−	0.0489672i
$681$	−241.384	−	955.323i	−0.354455	−	1.40282i
$682$	568.180	−	538.209i	0.833109	−	0.789163i
$683$	−503.588	+	531.632i	−0.737318	+	0.778378i	−0.981523	−	0.191346i	$-0.938715\pi$
$683$	−503.588	+	531.632i	−0.737318	+	0.778378i	0.244204	+	0.969724i	$0.421473\pi$
$684$	39.2704	+	50.8634i	0.0574129	+	0.0743617i
$685$	14.6926	−	89.6207i	0.0214490	−	0.130833i
$686$	−544.368	−	369.091i	−0.793540	−	0.538033i
$687$	−83.3443	−	425.721i	−0.121316	−	0.619682i
$688$	−691.837	+	416.264i	−1.00558	+	0.605036i
$689$	31.7185	+	144.099i	0.0460356	+	0.209142i
$690$	253.016	+	505.393i	0.366690	+	0.732453i
$691$	424.718	+	196.496i	0.614643	+	0.284364i	0.702405	−	0.711777i	$-0.252109\pi$
$691$	424.718	+	196.496i	0.614643	+	0.284364i	−0.0877621	+	0.996141i	$0.527972\pi$
$692$	1067.58	−	296.412i	1.54274	−	0.428341i
$693$	135.049	+	44.3788i	0.194876	+	0.0640387i
$694$	−837.554	+	91.0895i	−1.20685	+	0.131253i
$695$	−428.519	−	227.186i	−0.616574	−	0.326887i
$696$	−8.47407	+	6.86409i	−0.0121754	+	0.00986220i
$697$	26.3963	−	95.0710i	0.0378714	−	0.136400i
$698$	−1021.19	−	867.411i	−1.46303	−	1.24271i
$699$	−333.797	−	331.304i	−0.477535	−	0.473969i
$700$	85.0822	+	125.487i	0.121546	+	0.179267i
$701$	309.916	+	669.871i	0.442105	+	0.955594i	0.992676	+	0.120806i	$0.0385479\pi$
$701$	309.916	+	669.871i	0.442105	+	0.955594i	−0.550571	+	0.834788i	$0.685590\pi$
$702$	−1818.57	+	69.7343i	−2.59056	+	0.0993366i
$703$	−40.1823	+	100.850i	−0.0571584	+	0.143457i
$704$	214.521	−	282.198i	0.304718	−	0.400849i
$705$	−54.5340	+	222.849i	−0.0773531	+	0.316098i
$706$	−1841.87	−	620.597i	−2.60887	−	0.879032i
$707$		−	448.138i		−	0.633858i
$708$	474.699	+	479.169i	0.670479	+	0.676792i
$709$	1140.45			1.60854			0.804268	−	0.594267i	$-0.202558\pi$
$709$	1140.45			1.60854			0.804268	+	0.594267i	$0.202558\pi$
$710$	−96.7347	+	287.098i	−0.136246	+	0.404364i
$711$	867.380	−	53.5518i	1.21994	−	0.0753190i
$712$	−8.64799	−	6.57403i	−0.0121461	−	0.00923319i
$713$	−925.208	−	368.637i	−1.29763	−	0.517022i
$714$	241.077	−	380.295i	0.337643	−	0.532626i
$715$	414.882	−	191.945i	0.580254	−	0.268454i
$716$	56.7117	−	38.4515i	0.0792063	−	0.0537032i
$717$	−217.533	−	215.909i	−0.303393	−	0.301128i
$718$	274.024	−	322.606i	0.381649	−	0.449312i
$719$	6.69354	+	1.85845i	0.00930951	+	0.00258477i	0.272180	−	0.962246i	$-0.412255\pi$
$719$	6.69354	+	1.85845i	0.00930951	+	0.00258477i	−0.262870	+	0.964831i	$0.584669\pi$
$720$	258.145	−	386.949i	0.358535	−	0.537429i
$721$	149.745	−	282.448i	0.207690	−	0.391745i
$722$	−108.022	−	993.241i	−0.149614	−	1.37568i
$723$	814.420	+	580.382i	1.12644	+	0.802741i
$724$	34.6416	+	124.768i	0.0478475	+	0.172331i
$725$	44.5638	−	96.3231i	0.0614674	−	0.132860i
$726$	−313.015	−	625.238i	−0.431150	−	0.861209i
$727$	785.416	−	172.883i	1.08035	−	0.237803i	0.361082	−	0.932534i	$-0.382408\pi$
$727$	785.416	−	172.883i	1.08035	−	0.237803i	0.719270	+	0.694731i	$0.244476\pi$
$728$	16.9438	+	28.1608i	0.0232744	+	0.0386824i
$729$	−95.0953	−	722.771i	−0.130446	−	0.991455i
$730$	101.113	−	149.131i	0.138511	−	0.204289i
$731$	−993.512	−	162.878i	−1.35911	−	0.222815i
$732$	−38.5087	+	14.3114i	−0.0526075	+	0.0195511i
$733$	312.835	+	296.333i	0.426787	+	0.404274i	0.870715	−	0.491789i	$-0.163657\pi$
$733$	312.835	+	296.333i	0.426787	+	0.404274i	−0.443928	+	0.896063i	$0.646415\pi$
$734$	120.605	+	127.321i	0.164312	+	0.173462i
$735$	−96.2359	−	380.872i	−0.130933	−	0.518193i
$736$	−950.304	−	209.178i	−1.29117	−	0.284209i
$737$	−94.4754	−	280.393i	−0.128189	−	0.380452i
$738$	71.3210	−	95.2955i	0.0966409	−	0.129127i
$739$	−860.862	−	189.490i	−1.16490	−	0.256414i	−0.409896	−	0.912132i	$-0.634435\pi$
$739$	−860.862	−	189.490i	−1.16490	−	0.256414i	−0.755006	+	0.655718i	$0.772366\pi$
$740$	−681.448	−	36.9470i	−0.920875	−	0.0499284i
$741$	−118.260	−	66.2777i	−0.159595	−	0.0894435i
$742$	−31.9720	−	30.2855i	−0.0430889	−	0.0408160i
$743$	745.662	−	40.4286i	1.00358	−	0.0544127i	0.454985	−	0.890499i	$-0.349645\pi$
$743$	745.662	−	40.4286i	1.00358	−	0.0544127i	0.548598	+	0.836086i	$0.315162\pi$
$744$	10.0537	+	71.7776i	0.0135130	+	0.0964753i
$745$	−359.847	+	530.735i	−0.483016	+	0.712396i
$746$	−140.804	+	1294.67i	−0.188745	+	1.73549i
$747$	−858.194	−	389.260i	−1.14885	−	0.521097i
$748$	475.836	−	104.739i	0.636144	−	0.140026i
$749$	421.370	−	69.0801i	0.562577	−	0.0922297i
$750$	−137.608	+	1039.09i	−0.183478	+	1.38545i
$751$	251.710	+	906.576i	0.335166	+	1.20716i	0.918663	+	0.395043i	$0.129270\pi$
$751$	251.710	+	906.576i	0.335166	+	1.20716i	−0.583497	+	0.812116i	$0.698316\pi$
$752$	−250.374	−	329.361i	−0.332944	−	0.437980i
$753$	−171.489	+	74.5323i	−0.227741	+	0.0989804i
$754$	−216.935	+	409.183i	−0.287713	+	0.542683i
$755$	58.4129	−	23.2738i	0.0773681	−	0.0308263i
$756$	213.488	−	157.017i	0.282392	−	0.207695i
$757$	−130.817	+	154.009i	−0.172809	+	0.203447i	−0.841748	−	0.539871i	$-0.818473\pi$
$757$	−130.817	+	154.009i	−0.172809	+	0.203447i	0.668938	+	0.743318i	$0.266749\pi$
$758$	−1054.91	+	559.280i	−1.39171	+	0.737836i
$759$	250.196	−	313.658i	0.329639	−	0.413251i
$760$	2.78068	−	1.28648i	0.00365879	−	0.00169274i
$761$	−187.680	+	159.417i	−0.246622	+	0.209483i	−0.762168	−	0.647379i	$-0.775865\pi$
$761$	−187.680	+	159.417i	−0.246622	+	0.209483i	0.515546	+	0.856862i	$0.327589\pi$
$762$	−93.2389	+	1200.67i	−0.122361	+	1.57569i
$763$	63.4626	+	48.2430i	0.0831751	+	0.0632281i
$764$	−367.732	+	611.175i	−0.481324	+	0.799967i
$765$	557.687	−	159.353i	0.729003	−	0.208305i
$766$	−889.167			−1.16079
$767$	−1317.41	−	537.822i	−1.71761	−	0.701202i
$768$	248.216	+	797.729i	0.323198	+	1.03871i
$769$	875.543	+	295.005i	1.13855	+	0.383621i	0.824543	−	0.565800i	$-0.191433\pi$
$769$	875.543	+	295.005i	1.13855	+	0.383621i	0.314005	+	0.949421i	$0.398329\pi$
$770$	−70.3424	+	116.910i	−0.0913537	+	0.151831i
$771$	1150.52	+	417.791i	1.49224	+	0.541882i
$772$	−52.2312	+	131.090i	−0.0676569	+	0.169806i
$773$	−673.866	+	572.387i	−0.871754	+	0.740474i	−0.966945	−	0.254985i	$-0.917930\pi$
$773$	−673.866	+	572.387i	−0.871754	+	0.740474i	0.0951914

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.h (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.892372 + 2.64847i) q^{2} +(0.713097 - 2.91402i) q^{3} +(-3.03367 - 2.30614i) q^{4} +(-2.87136 - 1.14405i) q^{5} +(7.08133 + 4.48900i) q^{6} +(2.33765 - 1.08151i) q^{7} +(-0.437890 + 0.296897i) q^{8} +(-7.98299 - 4.15595i) q^{9} +O(q^{10})\)	\(q+(-0.892372 + 2.64847i) q^{2} +(0.713097 - 2.91402i) q^{3} +(-3.03367 - 2.30614i) q^{4} +(-2.87136 - 1.14405i) q^{5} +(7.08133 + 4.48900i) q^{6} +(2.33765 - 1.08151i) q^{7} +(-0.437890 + 0.296897i) q^{8} +(-7.98299 - 4.15595i) q^{9} +(5.59230 - 6.58377i) q^{10} +(-5.90871 - 1.64054i) q^{11} +(-8.88342 + 7.19567i) q^{12} +(11.2971 - 21.3085i) q^{13} +(0.778296 + 7.15631i) q^{14} +(-5.38134 + 7.55136i) q^{15} +(-4.47344 - 16.1119i) q^{16} +(8.75474 - 18.9231i) q^{17} +(18.1307 - 17.4340i) q^{18} +(1.82985 - 0.402779i) q^{19} +(6.07241 + 10.0924i) q^{20} +(-1.48458 - 7.58319i) q^{21} +(9.61769 - 14.1850i) q^{22} +(-21.5222 - 3.52838i) q^{23} +(0.552904 + 1.48773i) q^{24} +(-11.2141 - 10.6225i) q^{25} +(46.3538 + 48.9351i) q^{26} +(-17.8032 + 20.2990i) q^{27} +(-9.58579 - 2.10999i) q^{28} +(2.19392 + 6.51131i) q^{29} +(-15.1974 - 20.9909i) q^{30} +(44.5980 + 9.81675i) q^{31} +(44.5506 + 2.41546i) q^{32} +(-8.99405 + 16.0482i) q^{33} +(42.3046 + 40.0730i) q^{34} +(-7.94955 + 0.431012i) q^{35} +(14.6336 + 31.0177i) q^{36} +(-32.5155 + 47.9568i) q^{37} +(-0.566155 + 5.20571i) q^{38} +(-54.0376 - 48.1149i) q^{39} +(1.59700 - 0.351527i) q^{40} +(4.66989 - 0.765589i) q^{41} +(21.4086 + 2.83518i) q^{42} +(-12.9179 - 46.5262i) q^{43} +(14.1418 + 18.6032i) q^{44} +(18.1674 + 21.0662i) q^{45} +(28.5506 - 53.8521i) q^{46} +(22.9848 - 9.15799i) q^{47} +(-50.1403 + 1.54635i) q^{48} +(-27.4270 + 32.2895i) q^{49} +(38.1405 - 20.2208i) q^{50} +(-48.8991 - 39.0054i) q^{51} +(-83.4120 + 38.5905i) q^{52} +(-4.66273 + 3.96056i) q^{53} +(-37.8741 - 65.2653i) q^{54} +(15.0891 + 11.4705i) q^{55} +(-0.702537 + 1.16763i) q^{56} +(0.131151 - 5.61942i) q^{57} -19.2028 q^{58} +(-5.88414 - 58.7059i) q^{59} +(33.7397 - 10.4982i) q^{60} +(3.40546 + 1.14743i) q^{61} +(-65.7973 + 109.356i) q^{62} +(-23.1562 - 1.08147i) q^{63} +(-21.3961 + 53.7003i) q^{64} +(-56.8160 + 48.2600i) q^{65} +(-34.4771 - 38.1414i) q^{66} +(27.0774 + 39.9362i) q^{67} +(-70.1982 + 37.2167i) q^{68} +(-25.6292 + 60.1999i) q^{69} +(5.95243 - 21.4387i) q^{70} +(-32.5806 + 12.9813i) q^{71} +(4.72955 - 0.550272i) q^{72} +(20.7357 - 2.25515i) q^{73} +(-97.9960 - 128.912i) q^{74} +(-38.9509 + 25.1031i) q^{75} +(-6.48001 - 2.99797i) q^{76} +(-15.5868 + 2.55532i) q^{77} +(175.652 - 100.180i) q^{78} +(-82.7374 + 49.7814i) q^{79} +(-5.58800 + 51.3808i) q^{80} +(46.4561 + 66.3538i) q^{81} +(-2.13964 + 13.0512i) q^{82} +(104.552 - 5.66863i) q^{83} +(-12.9842 + 26.4285i) q^{84} +(-46.7870 + 44.3190i) q^{85} +(134.751 + 7.30597i) q^{86} +(20.5385 - 1.74991i) q^{87} +(3.07443 - 1.03590i) q^{88} +(6.55624 + 19.4582i) q^{89} +(-72.0051 + 29.3168i) q^{90} +(3.36317 - 62.0300i) q^{91} +(57.1543 + 60.3370i) q^{92} +(60.4089 - 122.959i) q^{93} +(3.74361 + 69.0468i) q^{94} +(-5.71494 - 0.936917i) q^{95} +(38.8076 - 128.099i) q^{96} +(-83.6208 - 9.09430i) q^{97} +(-61.0427 - 101.454i) q^{98} +(40.3511 + 37.6527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} + O(q^{10}) \)	\( 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} - 94q^{10} - 29q^{12} - 54q^{13} - 12q^{15} - 158q^{16} - 27q^{18} - 30q^{19} - 18q^{21} - 142q^{22} - 23q^{24} + 108q^{25} - 32q^{27} - 70q^{28} - 131q^{30} - 18q^{31} + 17q^{33} + 90q^{34} + 67q^{36} - 170q^{37} - 91q^{39} - 2q^{40} - 43q^{42} - 222q^{43} - 461q^{45} - 54q^{46} - 1645q^{48} - 300q^{49} - 893q^{51} - 66q^{52} - 859q^{54} + 170q^{55} - 27q^{57} - 36q^{58} + 510q^{60} - 70q^{61} + 610q^{63} - 106q^{64} + 1619q^{66} - 182q^{67} + 1487q^{69} - 206q^{70} + 2241q^{72} + 134q^{73} + 542q^{75} + 246q^{76} - 273q^{78} - 122q^{79} + 127q^{81} + 122q^{82} - 329q^{84} - 6q^{85} + 54q^{87} + 38q^{88} + 347q^{90} + 274q^{91} - 483q^{93} - 826q^{94} + 693q^{96} - 474q^{97} - 523q^{99} + O(q^{100}) \)

Introduction

L-functions

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