LMFDB - Embedded newform 93.3.n.b.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,3,Mod(13,93)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("93.13"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	93.n (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.53406645855$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	93.13
Dual form			93.3.n.b.43.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19842 + 1.59725i) q^{2} +(0.704489 + 1.58231i) q^{3} +(1.04579 - 3.21862i) q^{4} +(-4.22402 - 7.31621i) q^{5} +(-4.07610 - 2.35334i) q^{6} +(-1.04976 - 1.16587i) q^{7} +(-0.517049 - 1.59131i) q^{8} +(-2.00739 + 2.22943i) q^{9} +(20.9720 + 9.33732i) q^{10} +(-1.38936 - 6.53642i) q^{11} +(5.82960 - 0.612716i) q^{12} +(0.551480 + 0.0579629i) q^{13} +(4.16999 + 0.886359i) q^{14} +(8.60072 - 11.8379i) q^{15} +(14.6301 + 10.6294i) q^{16} +(1.76695 - 8.31285i) q^{17} +(0.852137 - 8.10754i) q^{18} +(-3.13904 - 29.8659i) q^{19} +(-27.9656 + 5.94427i) q^{20} +(1.10523 - 2.48238i) q^{21} +(13.4947 + 12.1507i) q^{22} +(-30.2032 + 9.81360i) q^{23} +(2.15369 - 1.93919i) q^{24} +(-23.1846 + 40.1569i) q^{25} +(-1.30497 + 0.753424i) q^{26} +(-4.94183 - 1.60570i) q^{27} +(-4.85033 + 2.15951i) q^{28} +(18.2235 + 25.0825i) q^{29} +39.7621i q^{30} +(-19.6253 - 23.9968i) q^{31} -42.4481 q^{32} +(9.36384 - 6.80322i) q^{33} +(9.39317 + 21.0974i) q^{34} +(-4.09558 + 12.6049i) q^{35} +(5.07639 + 8.79257i) q^{36} +(-29.5597 - 17.0663i) q^{37} +(54.6042 + 60.6441i) q^{38} +(0.296796 + 0.913446i) q^{39} +(-9.45836 + 10.5046i) q^{40} +(-4.90643 - 2.18448i) q^{41} +(1.53522 + 7.22264i) q^{42} +(23.8122 - 2.50276i) q^{43} +(-22.4913 - 2.36393i) q^{44} +(24.7903 + 5.26933i) q^{45} +(50.7245 - 69.8164i) q^{46} +(-52.0403 - 37.8095i) q^{47} +(-6.51223 + 30.6376i) q^{48} +(4.86462 - 46.2838i) q^{49} +(-13.1710 - 125.313i) q^{50} +(14.3983 - 3.06045i) q^{51} +(0.763296 - 1.71439i) q^{52} +(66.2966 + 59.6937i) q^{53} +(13.4289 - 4.36333i) q^{54} +(-41.9531 + 37.7748i) q^{55} +(-1.31249 + 2.27330i) q^{56} +(45.0457 - 26.0071i) q^{57} +(-80.1260 - 26.0345i) q^{58} +(40.1662 - 17.8832i) q^{59} +(-29.1071 - 40.0625i) q^{60} -8.62872i q^{61} +(81.4736 + 21.4088i) q^{62} +4.70650 q^{63} +(34.7985 - 25.2826i) q^{64} +(-1.90539 - 4.27958i) q^{65} +(-9.71923 + 29.9127i) q^{66} +(45.0227 + 77.9815i) q^{67} +(-24.9081 - 14.3807i) q^{68} +(-36.8059 - 40.8771i) q^{69} +(-11.1293 - 34.2525i) q^{70} +(64.8590 - 72.0332i) q^{71} +(4.58565 + 2.04166i) q^{72} +(17.7369 + 83.4454i) q^{73} +(92.2439 - 9.69523i) q^{74} +(-79.8739 - 8.39509i) q^{75} +(-99.4100 - 21.1302i) q^{76} +(-6.16214 + 8.48146i) q^{77} +(-2.11148 - 1.53408i) q^{78} +(-1.50486 + 7.07982i) q^{79} +(15.9691 - 151.936i) q^{80} +(-0.940756 - 8.95070i) q^{81} +(14.2756 - 3.03437i) q^{82} +(-65.7434 + 147.662i) q^{83} +(-6.83401 - 6.15337i) q^{84} +(-68.2822 + 22.1862i) q^{85} +(-48.3517 + 43.5361i) q^{86} +(-26.8500 + 46.5056i) q^{87} +(-9.68313 + 5.59056i) q^{88} +(69.7179 + 22.6527i) q^{89} +(-62.9159 + 28.0120i) q^{90} +(-0.511342 - 0.703802i) q^{91} +107.476i q^{92} +(24.1446 - 47.9587i) q^{93} +174.798 q^{94} +(-205.246 + 149.120i) q^{95} +(-29.9042 - 67.1660i) q^{96} +(38.9956 - 120.016i) q^{97} +(63.2322 + 109.521i) q^{98} +(17.3615 + 10.0237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} + 18 q^{3} - 30 q^{4} + 9 q^{6} + q^{7} + 30 q^{8} - 18 q^{9} + 6 q^{10} - 68 q^{11} + 45 q^{12} + 18 q^{13} - 5 q^{14} - 146 q^{16} + 31 q^{17} - 9 q^{18} + 55 q^{19} + 191 q^{20} - 108 q^{21}+ \cdots + 81 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 + 18 * q^3 - 30 * q^4 + 9 * q^6 + q^7 + 30 * q^8 - 18 * q^9 + 6 * q^10 - 68 * q^11 + 45 * q^12 + 18 * q^13 - 5 * q^14 - 146 * q^16 + 31 * q^17 - 9 * q^18 + 55 * q^19 + 191 * q^20 - 108 * q^21 + 106 * q^22 - 70 * q^23 - 75 * q^24 - 232 * q^25 - 30 * q^26 - 75 * q^28 - 35 * q^29 + 79 * q^31 + 164 * q^32 - 24 * q^33 + 8 * q^34 - 215 * q^35 + 195 * q^36 + 81 * q^37 - 75 * q^38 + 69 * q^39 - 34 * q^40 + 4 * q^41 + 15 * q^42 + 503 * q^43 + 253 * q^44 - 90 * q^45 + 245 * q^46 - 91 * q^47 + 9 * q^48 + 57 * q^49 - 131 * q^50 + 39 * q^51 - 963 * q^52 + 33 * q^53 + 45 * q^54 + 148 * q^55 - 765 * q^56 - 45 * q^57 - 190 * q^58 - 377 * q^59 + 225 * q^60 - 325 * q^62 - 54 * q^63 - 728 * q^64 + 262 * q^65 - 207 * q^66 + 870 * q^67 + 489 * q^68 - 39 * q^69 + 1041 * q^70 - 131 * q^71 - 180 * q^72 + 166 * q^73 + 1668 * q^74 - 114 * q^75 - 21 * q^76 + 75 * q^77 + 75 * q^78 + 71 * q^79 + 631 * q^80 + 54 * q^81 - 440 * q^82 + 84 * q^83 + 315 * q^84 + 30 * q^85 - 112 * q^86 - 123 * q^87 - 207 * q^88 + 285 * q^89 - 18 * q^90 - 605 * q^91 + 111 * q^93 - 380 * q^94 - 424 * q^95 - 126 * q^96 - 123 * q^97 + 681 * q^98 + 81 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

Coefficient data

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

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

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

$2$	−2.19842	+	1.59725i	−1.09921	+	0.798624i	−0.980931	−	0.194356i	$-0.937738\pi$
$2$	−2.19842	+	1.59725i	−1.09921	+	0.798624i	−0.118280	+	0.992980i	$0.537738\pi$
$3$	0.704489	+	1.58231i	0.234830	+	0.527436i
$3$	0.704489	+	1.58231i	0.234830	+	0.527436i
$4$	1.04579	−	3.21862i	0.261449	−	0.804656i
$5$	−4.22402	−	7.31621i	−0.844803	−	1.46324i	−0.885792	−	0.464082i	$-0.846384\pi$
$5$	−4.22402	−	7.31621i	−0.844803	−	1.46324i	0.0409889	−	0.999160i	$-0.486949\pi$
$6$	−4.07610	−	2.35334i	−0.679350	−	0.392223i
$7$	−1.04976	−	1.16587i	−0.149965	−	0.166553i	0.663482	−	0.748193i	$-0.269078\pi$
$7$	−1.04976	−	1.16587i	−0.149965	−	0.166553i	−0.813447	+	0.581640i	$0.802411\pi$
$8$	−0.517049	−	1.59131i	−0.0646311	−	0.198914i
$9$	−2.00739	+	2.22943i	−0.223044	+	0.247715i
$10$	20.9720	+	9.33732i	2.09720	+	0.933732i
$11$	−1.38936	−	6.53642i	−0.126305	−	0.594220i	−0.995085	−	0.0990216i	$-0.968429\pi$
$11$	−1.38936	−	6.53642i	−0.126305	−	0.594220i	0.868780	−	0.495198i	$-0.164905\pi$
$12$	5.82960	−	0.612716i	0.485800	−	0.0510597i
$13$	0.551480	+	0.0579629i	0.0424216	+	0.00445869i	0.125715	−	0.992066i	$-0.459877\pi$
$13$	0.551480	+	0.0579629i	0.0424216	+	0.00445869i	−0.0832939	+	0.996525i	$0.526544\pi$
$14$	4.16999	+	0.886359i	0.297857	+	0.0633114i
$15$	8.60072	−	11.8379i	0.573381	−	0.789192i
$16$	14.6301	+	10.6294i	0.914382	+	0.664338i
$17$	1.76695	−	8.31285i	0.103938	−	0.488991i	−0.895129	−	0.445807i	$-0.852917\pi$
$17$	1.76695	−	8.31285i	0.103938	−	0.488991i	0.999067	−	0.0431837i	$-0.0137501\pi$
$18$	0.852137	−	8.10754i	0.0473409	−	0.450419i
$19$	−3.13904	−	29.8659i	−0.165212	−	1.57189i	−0.692002	−	0.721895i	$-0.743271\pi$
$19$	−3.13904	−	29.8659i	−0.165212	−	1.57189i	0.526790	−	0.849996i	$-0.323395\pi$
$20$	−27.9656	+	5.94427i	−1.39828	+	0.297213i
$21$	1.10523	−	2.48238i	0.0526298	−	0.118209i
$22$	13.4947	+	12.1507i	0.613394	+	0.552303i
$23$	−30.2032	+	9.81360i	−1.31318	+	0.426678i	−0.880148	−	0.474700i	$-0.842557\pi$
$23$	−30.2032	+	9.81360i	−1.31318	+	0.426678i	−0.433033	+	0.901378i	$0.642557\pi$
$24$	2.15369	−	1.93919i	0.0897372	−	0.0807997i
$25$	−23.1846	+	40.1569i	−0.927385	+	1.60628i
$26$	−1.30497	+	0.753424i	−0.0501911	+	0.0289778i
$27$	−4.94183	−	1.60570i	−0.183031	−	0.0594703i
$28$	−4.85033	+	2.15951i	−0.173226	+	0.0771252i
$29$	18.2235	+	25.0825i	0.628397	+	0.864915i	0.997930	−	0.0643028i	$-0.0204823\pi$
$29$	18.2235	+	25.0825i	0.628397	+	0.864915i	−0.369533	+	0.929218i	$0.620482\pi$
$30$			39.7621i			1.32540i
$31$	−19.6253	−	23.9968i	−0.633073	−	0.774092i
$31$	−19.6253	−	23.9968i	−0.633073	−	0.774092i
$32$	−42.4481			−1.32650
$33$	9.36384	−	6.80322i	0.283753	−	0.206158i
$34$	9.39317	+	21.0974i	0.276270	+	0.620512i
$35$	−4.09558	+	12.6049i	−0.117017	+	0.360140i
$36$	5.07639	+	8.79257i	0.141011	+	0.244238i
$37$	−29.5597	−	17.0663i	−0.798912	−	0.461252i	0.0441786	−	0.999024i	$-0.485933\pi$
$37$	−29.5597	−	17.0663i	−0.798912	−	0.461252i	−0.843091	+	0.537772i	$0.819266\pi$
$38$	54.6042	+	60.6441i	1.43695	+	1.59590i
$39$	0.296796	+	0.913446i	0.00761017	+	0.0234217i
$40$	−9.45836	+	10.5046i	−0.236459	+	0.262614i
$41$	−4.90643	−	2.18448i	−0.119669	−	0.0532801i	0.346029	−	0.938224i	$-0.387530\pi$
$41$	−4.90643	−	2.18448i	−0.119669	−	0.0532801i	−0.465698	+	0.884944i	$0.654197\pi$
$42$	1.53522	+	7.22264i	0.0365528	+	0.171968i
$43$	23.8122	−	2.50276i	0.553772	−	0.0582037i	0.176490	−	0.984302i	$-0.443526\pi$
$43$	23.8122	−	2.50276i	0.553772	−	0.0582037i	0.377281	+	0.926099i	$0.376859\pi$
$44$	−22.4913	−	2.36393i	−0.511165	−	0.0537256i
$45$	24.7903	+	5.26933i	0.550895	+	0.117096i
$46$	50.7245	−	69.8164i	1.10271	−	1.51775i
$47$	−52.0403	−	37.8095i	−1.10724	−	0.804457i	−0.125013	−	0.992155i	$-0.539897\pi$
$47$	−52.0403	−	37.8095i	−1.10724	−	0.804457i	−0.982227	+	0.187698i	$0.939897\pi$
$48$	−6.51223	+	30.6376i	−0.135671	+	0.638284i
$49$	4.86462	−	46.2838i	0.0992781	−	0.944568i
$50$	−13.1710	−	125.313i	−0.263420	−	2.50627i
$51$	14.3983	−	3.06045i	0.282319	−	0.0600088i
$52$	0.763296	−	1.71439i	0.0146788	−	0.0329691i
$53$	66.2966	+	59.6937i	1.25088	+	1.12630i	0.986825	+	0.161789i	$0.0517264\pi$
$53$	66.2966	+	59.6937i	1.25088	+	1.12630i	0.264054	+	0.964508i	$0.414940\pi$
$54$	13.4289	−	4.36333i	0.248684	−	0.0808024i
$55$	−41.9531	+	37.7748i	−0.762784	+	0.686814i
$56$	−1.31249	+	2.27330i	−0.0234374	+	0.0405947i
$57$	45.0457	−	26.0071i	0.790275	−	0.456265i
$58$	−80.1260	−	26.0345i	−1.38148	−	0.448871i
$59$	40.1662	−	17.8832i	0.680783	−	0.303104i	−0.0370559	−	0.999313i	$-0.511798\pi$
$59$	40.1662	−	17.8832i	0.680783	−	0.303104i	0.717839	+	0.696209i	$0.245131\pi$
$60$	−29.1071	−	40.0625i	−0.485118	−	0.667708i
$61$		−	8.62872i		−	0.141454i	−0.997496	−	0.0707272i	$-0.977468\pi$
$61$		−	8.62872i		−	0.141454i	0.997496	−	0.0707272i	$-0.0225320\pi$
$62$	81.4736	+	21.4088i	1.31409	+	0.345303i
$63$	4.70650			0.0747064
$64$	34.7985	−	25.2826i	0.543726	−	0.395040i
$65$	−1.90539	−	4.27958i	−0.0293137	−	0.0658397i
$66$	−9.71923	+	29.9127i	−0.147261	+	0.453223i
$67$	45.0227	+	77.9815i	0.671980	+	1.16390i	0.977342	+	0.211667i	$0.0678893\pi$
$67$	45.0227	+	77.9815i	0.671980	+	1.16390i	−0.305362	+	0.952236i	$0.598777\pi$
$68$	−24.9081	−	14.3807i	−0.366295	−	0.211481i
$69$	−36.8059	−	40.8771i	−0.533419	−	0.592422i
$70$	−11.1293	−	34.2525i	−0.158990	−	0.489322i
$71$	64.8590	−	72.0332i	0.913507	−	1.01455i	−0.0863259	−	0.996267i	$-0.527513\pi$
$71$	64.8590	−	72.0332i	0.913507	−	1.01455i	0.999833	−	0.0182852i	$-0.00582070\pi$
$72$	4.58565	+	2.04166i	0.0636896	+	0.0283564i
$73$	17.7369	+	83.4454i	0.242971	+	1.14309i	0.915280	+	0.402817i	$0.131969\pi$
$73$	17.7369	+	83.4454i	0.242971	+	1.14309i	−0.672310	+	0.740270i	$0.734698\pi$
$74$	92.2439	−	9.69523i	1.24654	−	0.131017i
$75$	−79.8739	−	8.39509i	−1.06499	−	0.111934i
$76$	−99.4100	−	21.1302i	−1.30803	−	0.278030i
$77$	−6.16214	+	8.48146i	−0.0800278	+	0.110149i
$78$	−2.11148	−	1.53408i	−0.0270703	−	0.0196677i
$79$	−1.50486	+	7.07982i	−0.0190489	+	0.0896180i	−0.986645	−	0.162884i	$-0.947920\pi$
$79$	−1.50486	+	7.07982i	−0.0190489	+	0.0896180i	0.967596	+	0.252502i	$0.0812536\pi$
$80$	15.9691	−	151.936i	0.199614	−	1.89920i
$81$	−0.940756	−	8.95070i	−0.0116143	−	0.110502i
$82$	14.2756	−	3.03437i	0.174092	−	0.0370045i
$83$	−65.7434	+	147.662i	−0.792089	+	1.77906i	−0.187958	+	0.982177i	$0.560187\pi$
$83$	−65.7434	+	147.662i	−0.792089	+	1.77906i	−0.604131	+	0.796885i	$0.706480\pi$
$84$	−6.83401	−	6.15337i	−0.0813572	−	0.0732544i
$85$	−68.2822	+	22.1862i	−0.803320	+	0.261014i
$86$	−48.3517	+	43.5361i	−0.562229	+	0.506233i
$87$	−26.8500	+	46.5056i	−0.308621	+	0.534547i
$88$	−9.68313	+	5.59056i	−0.110036	+	0.0635290i
$89$	69.7179	+	22.6527i	0.783347	+	0.254525i	0.673269	−	0.739398i	$-0.264890\pi$
$89$	69.7179	+	22.6527i	0.783347	+	0.254525i	0.110079	+	0.993923i	$0.464890\pi$
$90$	−62.9159	+	28.0120i	−0.699066	+	0.311244i
$91$	−0.511342	−	0.703802i	−0.00561915	−	0.00773409i
$92$			107.476i			1.16821i
$93$	24.1446	−	47.9587i	0.259619	−	0.515685i
$94$	174.798			1.85955
$95$	−205.246	+	149.120i	−2.16048	+	1.56968i
$96$	−29.9042	−	67.1660i	−0.311502	−	0.699646i
$97$	38.9956	−	120.016i	0.402017	−	1.23728i	−0.521344	−	0.853347i	$-0.674569\pi$
$97$	38.9956	−	120.016i	0.402017	−	1.23728i	0.923361	−	0.383934i	$-0.125431\pi$
$98$	63.2322	+	109.521i	0.645227	+	1.11757i
$99$	17.3615	+	10.0237i	0.175369	+	0.101249i
$100$	105.004	+	116.618i	1.05004	+	1.16618i
$101$	−59.6262	−	183.510i	−0.590358	−	1.81694i	−0.576595	−	0.817030i	$-0.695619\pi$
$101$	−59.6262	−	183.510i	−0.590358	−	1.81694i	−0.0137626	−	0.999905i	$-0.504381\pi$
$102$	−26.7652	+	29.7258i	−0.262404	+	0.291429i
$103$	7.78809	+	3.46748i	0.0756125	+	0.0336649i	0.444194	−	0.895930i	$-0.353490\pi$
$103$	7.78809	+	3.46748i	0.0756125	+	0.0336649i	−0.368582	+	0.929595i	$0.620157\pi$
$104$	−0.192905	−	0.907548i	−0.00185486	−	0.00872642i
$105$	−22.8301	+	2.39954i	−0.217430	+	0.0228528i
$106$	−241.094	−	25.3400i	−2.27447	−	0.239056i
$107$	14.2706	+	3.03331i	0.133370	+	0.0283487i	0.274113	−	0.961697i	$-0.411616\pi$
$107$	14.2706	+	3.03331i	0.133370	+	0.0283487i	−0.140743	+	0.990046i	$0.544949\pi$
$108$	−10.3363	+	14.2267i	−0.0957064	+	0.131729i
$109$	6.42027	+	4.66460i	0.0589016	+	0.0427945i	0.616846	−	0.787084i	$-0.288410\pi$
$109$	6.42027	+	4.66460i	0.0589016	+	0.0427945i	−0.557945	+	0.829878i	$0.688410\pi$
$110$	31.8951	−	150.054i	0.289955	−	1.36413i
$111$	6.17967	−	58.7956i	0.0556727	−	0.529690i
$112$	−2.96553	−	28.2151i	−0.0264779	−	0.251921i
$113$	67.0146	−	14.2444i	0.593050	−	0.126057i	0.0983969	−	0.995147i	$-0.468629\pi$
$113$	67.0146	−	14.2444i	0.593050	−	0.126057i	0.494653	+	0.869091i	$0.335295\pi$
$114$	−57.4896	+	129.124i	−0.504295	+	1.13266i
$115$	199.377	+	179.520i	1.73371	+	1.56104i
$116$	99.7893	−	32.4235i	0.860253	−	0.279513i
$117$	−1.23626	+	1.11314i	−0.0105663	+	0.00951398i
$118$	−59.7385	+	103.470i	−0.506258	+	0.876865i
$119$	−11.5466	+	6.66642i	−0.0970301	+	0.0560204i
$120$	−23.2848	−	7.56568i	−0.194040	−	0.0630473i
$121$	69.7445	−	31.0523i	0.576401	−	0.256630i
$122$	13.7822	+	18.9696i	0.112969	+	0.155488i
$123$		−	9.30243i		−	0.0756295i
$124$	−97.7608	+	38.0706i	−0.788394	+	0.307021i
$125$	180.528			1.44422
$126$	−10.3469	+	7.51745i	−0.0821182	+	0.0596623i
$127$	−70.2147	−	157.705i	−0.552872	−	1.24177i	−0.946560	−	0.322527i	$-0.895468\pi$
$127$	−70.2147	−	157.705i	−0.552872	−	1.24177i	0.393688	−	0.919244i	$-0.371199\pi$
$128$	16.3495	−	50.3187i	0.127731	−	0.393115i
$129$	20.7355	+	35.9150i	0.160741	+	0.278411i
$130$	11.0244	+	6.36495i	0.0848032	+	0.0489611i
$131$	37.0770	+	41.1781i	0.283030	+	0.314337i	0.867850	−	0.496826i	$-0.165501\pi$
$131$	37.0770	+	41.1781i	0.283030	+	0.314337i	−0.584820	+	0.811163i	$0.698835\pi$
$132$	−12.1044	−	37.2534i	−0.0916998	−	0.282223i
$133$	−31.5246	+	35.0116i	−0.237027	+	0.263245i
$134$	−223.535	−	99.5241i	−1.66817	−	0.742717i
$135$	9.12675	+	42.9380i	0.0676056	+	0.318059i
$136$	−14.1420	+	1.48638i	−0.103985	+	0.0109293i
$137$	141.140	+	14.8345i	1.03022	+	0.108281i	0.604526	−	0.796585i	$-0.293363\pi$
$137$	141.140	+	14.8345i	1.03022	+	0.108281i	0.425696	+	0.904866i	$0.360029\pi$
$138$	146.206	+	31.0770i	1.05946	+	0.225196i
$139$	44.7905	−	61.6488i	0.322234	−	0.443517i	−0.616914	−	0.787031i	$-0.711617\pi$
$139$	44.7905	−	61.6488i	0.322234	−	0.443517i	0.939148	+	0.343514i	$0.111617\pi$
$140$	36.2873	+	26.3643i	0.259195	+	0.188316i
$141$	23.1644	−	108.980i	0.164287	−	0.772908i
$142$	−27.5326	+	261.955i	−0.193892	+	1.84476i
$143$	−0.387334	−	3.68524i	−0.00270863	−	0.0257709i
$144$	−53.0659	+	11.2795i	−0.368513	+	0.0783299i
$145$	106.533	−	239.276i	0.734708	−	1.65018i
$146$	−172.276	−	155.118i	−1.17997	−	1.06245i
$147$	76.6623	−	24.9091i	0.521512	−	0.169450i
$148$	−85.8435	+	77.2938i	−0.580024	+	0.522256i
$149$	−90.1914	+	156.216i	−0.605311	+	1.04843i	0.386691	+	0.922209i	$0.373618\pi$
$149$	−90.1914	+	156.216i	−0.605311	+	1.04843i	−0.992002	+	0.126221i	$0.959715\pi$
$150$	189.006	−	109.122i	1.26004	−	0.727483i
$151$	−192.189	−	62.4461i	−1.27278	−	0.413550i	−0.406747	−	0.913541i	$-0.633337\pi$
$151$	−192.189	−	62.4461i	−1.27278	−	0.413550i	−0.866031	+	0.499991i	$0.833337\pi$
$152$	−45.9030	+	20.4373i	−0.301994	+	0.134456i
$153$	14.9860	+	20.6264i	0.0979477	+	0.134813i
$154$		−	28.4883i		−	0.184989i
$155$	−92.6685	+	244.946i	−0.597861	+	1.58029i
$156$	3.25043			0.0208361
$157$	−56.3888	+	40.9688i	−0.359164	+	0.260948i	−0.752703	−	0.658360i	$-0.771251\pi$
$157$	−56.3888	+	40.9688i	−0.359164	+	0.260948i	0.393539	+	0.919308i	$0.371251\pi$
$158$	−7.99990	−	17.9681i	−0.0506323	−	0.113722i
$159$	−47.7486	+	146.955i	−0.300306	+	0.924246i
$160$	179.302	+	310.560i	1.12064	+	1.94100i
$161$	43.1473	+	24.9111i	0.267996	+	0.154727i
$162$	16.3647	+	18.1748i	0.101016	+	0.112190i
$163$	−57.4374	−	176.774i	−0.352376	−	1.08450i	−0.957515	−	0.288383i	$-0.906882\pi$
$163$	−57.4374	−	176.774i	−0.352376	−	1.08450i	0.605139	−	0.796120i	$-0.293118\pi$
$164$	−12.1622	+	13.5074i	−0.0741595	+	0.0823625i
$165$	−89.3268	−	39.7709i	−0.541375	−	0.241036i
$166$	−91.3212	−	429.632i	−0.550127	−	2.58815i
$167$	−178.108	+	18.7199i	−1.06651	+	0.112095i	−0.621488	−	0.783423i	$-0.713472\pi$
$167$	−178.108	+	18.7199i	−1.06651	+	0.112095i	−0.445024	+	0.895518i	$0.646805\pi$
$168$	−4.52170	−	0.475250i	−0.0269149	−	0.00282887i
$169$	−165.006	−	35.0731i	−0.976368	−	0.207533i
$170$	114.676	−	157.838i	0.674566	−	0.928460i
$171$	72.8854	+	52.9543i	0.426230	+	0.309675i
$172$	16.8472	−	79.2598i	0.0979488	−	0.460813i
$173$	23.3910	−	222.551i	0.135208	−	1.28642i	−0.690918	−	0.722933i	$-0.742793\pi$
$173$	23.3910	−	222.551i	0.135208	−	1.28642i	0.826126	−	0.563486i	$-0.190540\pi$
$174$	−15.2533	−	145.125i	−0.0876624	−	0.834052i
$175$	71.1560	−	15.1247i	0.406606	−	0.0864267i
$176$	49.1517	−	110.397i	0.279271	−	0.627254i
$177$	56.5933	+	50.9568i	0.319736	+	0.287892i
$178$	−189.451	+	61.5565i	−1.06433	+	0.345823i
$179$	77.1841	−	69.4969i	0.431196	−	0.388251i	−0.424754	−	0.905309i	$-0.639639\pi$
$179$	77.1841	−	69.4969i	0.431196	−	0.388251i	0.855950	+	0.517058i	$0.172973\pi$
$180$	42.8855	−	74.2799i	0.238253	−	0.412666i
$181$	187.743	−	108.394i	1.03726	−	0.598860i	0.118201	−	0.992990i	$-0.462287\pi$
$181$	187.743	−	108.394i	1.03726	−	0.598860i	0.919055	+	0.394130i	$0.128954\pi$
$182$	2.24829	+	0.730515i	0.0123533	+	0.00401382i
$183$	13.6533	−	6.07883i	0.0746081	−	0.0332177i
$184$	31.2330	+	42.9886i	0.169745	+	0.233634i
$185$			288.354i			1.55867i
$186$	23.5219	+	143.998i	0.126462	+	0.774185i
$187$	−56.7912			−0.303696
$188$	−176.118	+	127.957i	−0.936798	+	0.680623i
$189$	3.31568	+	7.44714i	0.0175433	+	0.0394028i
$190$	213.036	−	655.657i	1.12124	−	3.45083i
$191$	−55.3588	−	95.8842i	−0.289837	−	0.502012i	0.683934	−	0.729544i	$-0.260268\pi$
$191$	−55.3588	−	95.8842i	−0.289837	−	0.502012i	−0.973771	+	0.227532i	$0.926934\pi$
$192$	64.5200	+	37.2506i	0.336041	+	0.194014i
$193$	56.4858	+	62.7339i	0.292673	+	0.325046i	0.871492	−	0.490410i	$-0.163153\pi$
$193$	56.4858	+	62.7339i	0.292673	+	0.325046i	−0.578819	+	0.815456i	$0.696486\pi$
$194$	105.967	+	326.132i	0.546220	+	1.68109i
$195$	5.42929	−	6.02983i	0.0278425	−	0.0309222i
$196$	−143.883	−	64.0608i	−0.734096	−	0.326841i
$197$	−2.58122	−	12.1437i	−0.0131027	−	0.0616431i	0.971111	−	0.238630i	$-0.0766983\pi$
$197$	−2.58122	−	12.1437i	−0.0131027	−	0.0616431i	−0.984213	+	0.176987i	$0.943365\pi$
$198$	−54.1782	+	5.69436i	−0.273627	+	0.0287594i
$199$	284.107	+	29.8608i	1.42767	+	0.150054i	0.786618	−	0.617441i	$-0.211830\pi$
$199$	284.107	+	29.8608i	1.42767	+	0.150054i	0.641055	+	0.767495i	$0.278497\pi$
$200$	75.8899	+	16.1309i	0.379449	+	0.0806544i
$201$	−91.6728	+	126.177i	−0.456084	+	0.627745i
$202$	424.195	+	308.196i	2.09998	+	1.52572i
$203$	10.1128	−	47.5768i	0.0498166	−	0.234369i
$204$	5.20721	−	49.5433i	0.0255255	−	0.242859i
$205$	4.74270	+	45.1238i	0.0231351	+	0.220116i
$206$	−22.6599	+	4.81652i	−0.110000	+	0.0233812i
$207$	38.7508	−	87.0357i	0.187202	−	0.420462i
$208$	7.45211	+	6.70991i	0.0358275	+	0.0322592i
$209$	−190.855	+	62.0125i	−0.913182	+	0.296711i
$210$	46.3575	−	41.7405i	0.220750	−	0.198764i
$211$	−74.1531	+	128.437i	−0.351437	+	0.608706i	−0.986501	−	0.163753i	$-0.947640\pi$
$211$	−74.1531	+	128.437i	−0.351437	+	0.608706i	0.635065	+	0.772459i	$0.280973\pi$
$212$	261.464	−	150.957i	1.23332	−	0.712059i
$213$	159.671	+	51.8803i	0.749629	+	0.243569i
$214$	−36.2177	+	16.1252i	−0.169242	+	0.0753513i
$215$	−118.894	−	163.643i	−0.552994	−	0.761131i
$216$			8.69423i			0.0402511i
$217$	−7.37550	+	48.0714i	−0.0339885	+	0.221527i
$218$	−21.5650			−0.0989220
$219$	−119.541	+	86.8515i	−0.545848	+	0.396582i
$220$	77.7085	+	174.536i	0.353220	+	0.793346i
$221$	1.45628	−	4.48196i	0.00658948	−	0.0202803i
$222$	80.3256	+	139.128i	0.361827	+	0.626703i
$223$	−29.4147	−	16.9826i	−0.131904	−	0.0761550i	0.432596	−	0.901588i	$-0.357598\pi$
$223$	−29.4147	−	16.9826i	−0.131904	−	0.0761550i	−0.564500	+	0.825433i	$0.690931\pi$
$224$	44.5602	+	49.4891i	0.198929	+	0.220933i
$225$	−42.9866	−	132.299i	−0.191052	−	0.587997i
$226$	−124.575	+	138.354i	−0.551215	+	0.612187i
$227$	−276.642	−	123.169i	−1.21869	−	0.542594i	−0.306304	−	0.951934i	$-0.599092\pi$
$227$	−276.642	−	123.169i	−1.21869	−	0.542594i	−0.912382	+	0.409340i	$0.865759\pi$
$228$	−36.5987	−	172.183i	−0.160520	−	0.755189i
$229$	106.883	−	11.2338i	0.466737	−	0.0490561i	0.131759	−	0.991282i	$-0.457938\pi$
$229$	106.883	−	11.2338i	0.466737	−	0.0490561i	0.334979	+	0.942226i	$0.391271\pi$
$230$	−725.052	−	76.2061i	−3.15240	−	0.331331i
$231$	−17.7614	−	3.77531i	−0.0768893	−	0.0163433i
$232$	30.4917	−	41.9682i	0.131430	−	0.180898i
$233$	284.035	+	206.364i	1.21903	+	0.885681i	0.996020	−	0.0891342i	$-0.0284100\pi$
$233$	284.035	+	206.364i	1.21903	+	0.885681i	0.223015	+	0.974815i	$0.428410\pi$
$234$	0.939874	−	4.42176i	0.00401655	−	0.0188964i
$235$	−56.8031	+	540.445i	−0.241715	+	2.29977i
$236$	−15.5535	−	147.982i	−0.0659048	−	0.627043i
$237$	−12.2626	+	2.60650i	−0.0517410	+	0.0109979i
$238$	14.7363	−	33.0984i	0.0619174	−	0.139069i
$239$	−49.3532	−	44.4378i	−0.206499	−	0.185932i	0.559392	−	0.828904i	$-0.311035\pi$
$239$	−49.3532	−	44.4378i	−0.206499	−	0.185932i	−0.765890	+	0.642971i	$0.777701\pi$
$240$	251.659	−	81.7690i	1.04858	−	0.340704i
$241$	−97.5641	+	87.8472i	−0.404830	+	0.364511i	−0.846247	−	0.532792i	$-0.821143\pi$
$241$	−97.5641	+	87.8472i	−0.404830	+	0.364511i	0.441416	+	0.897303i	$0.354476\pi$
$242$	−103.730	+	179.665i	−0.428636	+	0.742419i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	−27.7726	−	9.02387i	−0.113822	−	0.0369831i
$245$	−359.170	+	159.913i	−1.46600	+	0.652706i
$246$	14.8583	+	20.4507i	0.0603995	+	0.0831328i
$247$		−	16.6524i		−	0.0674187i
$248$	−28.0393	+	43.6375i	−0.113062	+	0.175958i
$249$	−279.962			−1.12435
$250$	−396.877	+	288.348i	−1.58751	+	1.15339i
$251$	−158.592	−	356.204i	−0.631842	−	1.41914i	−0.891313	−	0.453389i	$-0.850215\pi$
$251$	−158.592	−	356.204i	−0.631842	−	1.41914i	0.259471	−	0.965751i	$-0.416452\pi$
$252$	4.92204	−	15.1485i	0.0195319	−	0.0601130i
$253$	106.109	+	183.786i	0.419402	+	0.726426i
$254$	406.255	+	234.552i	1.59943	+	0.923432i
$255$	−83.2094	−	92.4134i	−0.326312	−	0.362406i
$256$	97.5956	+	300.368i	0.381233	+	1.17331i
$257$	144.640	−	160.639i	0.562801	−	0.625054i	−0.392833	−	0.919610i	$-0.628505\pi$
$257$	144.640	−	160.639i	0.562801	−	0.625054i	0.955634	+	0.294556i	$0.0951717\pi$
$258$	−102.951	−	45.8366i	−0.399034	−	0.177661i
$259$	11.1334	+	52.3783i	0.0429859	+	0.202233i
$260$	−15.7670	+	1.65718i	−0.0606424	+	0.00637377i
$261$	−92.5016	−	9.72231i	−0.354412	−	0.0372502i
$262$	−147.282	−	31.3059i	−0.562147	−	0.119488i
$263$	104.023	−	143.175i	0.395524	−	0.544392i	−0.564090	−	0.825713i	$-0.690773\pi$
$263$	104.023	−	143.175i	0.395524	−	0.544392i	0.959613	+	0.281322i	$0.0907729\pi$
$264$	−15.6676	−	11.3832i	−0.0593471	−	0.0431182i
$265$	156.694	−	737.187i	0.591298	−	2.78184i
$266$	13.3822	−	127.323i	0.0503090	−	0.478658i
$267$	13.2719	+	126.274i	0.0497075	+	0.472935i
$268$	298.078	−	63.3584i	1.11223	−	0.236412i
$269$	−43.4182	+	97.5188i	−0.161406	+	0.362523i	−0.976085	−	0.217388i	$-0.930246\pi$
$269$	−43.4182	+	97.5188i	−0.161406	+	0.362523i	0.814679	+	0.579912i	$0.196913\pi$
$270$	−88.6471	−	79.8182i	−0.328323	−	0.295623i
$271$	−22.8659	+	7.42958i	−0.0843760	+	0.0274154i	−0.350901	−	0.936413i	$-0.614125\pi$
$271$	−22.8659	+	7.42958i	−0.0843760	+	0.0274154i	0.266525	+	0.963828i	$0.414125\pi$
$272$	114.211	−	102.836i	0.419895	−	0.378075i
$273$	0.753397	−	1.30492i	0.00275969	−	0.00477993i
$274$	−333.981	+	192.824i	−1.21891	+	0.703737i
$275$	294.694	+	95.7520i	1.07162	+	0.348189i
$276$	−170.059	+	75.7153i	−0.616157	+	0.274331i
$277$	189.650	+	261.030i	0.684656	+	0.942347i	0.999978	−	0.00663712i	$-0.00211268\pi$
$277$	189.650	+	261.030i	0.684656	+	0.942347i	−0.315322	+	0.948985i	$0.602113\pi$
$278$			207.072i			0.744862i
$279$	92.8950	+	4.41781i	0.332957	+	0.0158345i
$280$	22.1760			0.0791998
$281$	184.595	−	134.116i	0.656921	−	0.477281i	−0.208701	−	0.977980i	$-0.566923\pi$
$281$	184.595	−	134.116i	0.656921	−	0.477281i	0.865622	+	0.500698i	$0.166923\pi$
$282$	123.143	+	276.584i	0.436677	+	0.980793i
$283$	−67.1174	+	206.566i	−0.237164	+	0.729916i	0.759663	+	0.650317i	$0.225364\pi$
$283$	−67.1174	+	206.566i	−0.237164	+	0.729916i	−0.996827	+	0.0795987i	$0.974636\pi$
$284$	−164.019	−	284.089i	−0.577531	−	1.00031i
$285$	−380.547	−	219.709i	−1.33525	−	0.770909i
$286$	6.73776	+	7.48304i	0.0235586	+	0.0261645i
$287$	2.60373	+	8.01344i	0.00907222	+	0.0279214i
$288$	85.2101	−	94.6354i	0.295868	−	0.328595i
$289$	198.033	+	88.1701i	0.685236	+	0.305087i
$290$	147.980	+	696.189i	0.510274	+	2.40065i
$291$	217.375	−	22.8470i	0.746991	−	0.0785120i
$292$	287.128	+	30.1784i	0.983316	+	0.103351i
$293$	−62.8181	−	13.3524i	−0.214396	−	0.0455713i	0.0994612	−	0.995041i	$-0.468288\pi$
$293$	−62.8181	−	13.3524i	−0.214396	−	0.0455713i	−0.313857	+	0.949470i	$0.601621\pi$
$294$	−128.750	+	177.209i	−0.437926	+	0.602753i
$295$	−300.500	−	218.326i	−1.01864	−	0.740087i
$296$	−11.8740	+	55.8629i	−0.0401150	+	0.188726i
$297$	−3.62954	+	34.5328i	−0.0122207	+	0.116272i
$298$	−51.2369	−	487.487i	−0.171936	−	1.63586i
$299$	−17.2253	+	3.66134i	−0.0576096	+	0.0122453i
$300$	−110.552	+	248.305i	−0.368508	+	0.827682i
$301$	−27.9149	−	25.1347i	−0.0927404	−	0.0835038i
$302$	522.255	−	169.691i	1.72932	−	0.561891i
$303$	248.364	−	223.628i	0.819683	−	0.738046i
$304$	271.532	−	470.308i	0.893199	−	1.54707i
$305$	−63.1295	+	36.4478i	−0.206982	+	0.119501i
$306$	−65.8911	−	21.4093i	−0.215330	−	0.0699651i
$307$	44.1602	−	19.6614i	0.143844	−	0.0640436i	−0.333552	−	0.942732i	$-0.608247\pi$
$307$	44.1602	−	19.6614i	0.143844	−	0.0640436i	0.477396	+	0.878688i	$0.341581\pi$
$308$	20.8543	+	28.7035i	0.0677087	+	0.0931931i
$309$			14.7660i			0.0477863i
$310$	−187.514	−	686.509i	−0.604885	−	2.21454i
$311$	332.928			1.07051			0.535255	−	0.844691i	$-0.320216\pi$
$311$	332.928			1.07051			0.535255	+	0.844691i	$0.320216\pi$
$312$	1.30012	−	0.944593i	0.00416705	−	0.00302754i
$313$	−207.553	−	466.173i	−0.663110	−	1.48937i	−0.860715	−	0.509087i	$-0.829983\pi$
$313$	−207.553	−	466.173i	−0.663110	−	1.48937i	0.197605	−	0.980282i	$-0.436684\pi$
$314$	58.5290	−	180.134i	0.186398	−	0.573674i
$315$	−19.8804	−	34.4338i	−0.0631122	−	0.109314i
$316$	21.2135	+	12.2476i	0.0671314	+	0.0387583i
$317$	−173.561	−	192.759i	−0.547510	−	0.608072i	0.404350	−	0.914604i	$-0.367498\pi$
$317$	−173.561	−	192.759i	−0.547510	−	0.608072i	−0.951860	+	0.306533i	$0.900831\pi$
$318$	−129.752	−	399.336i	−0.408025	−	1.25577i
$319$	138.631	−	153.965i	0.434580	−	0.482650i
$320$	−331.962	−	147.799i	−1.03738	−	0.461872i
$321$	5.25384	+	24.7174i	0.0163671	+	0.0770012i
$322$	−134.645	+	14.1518i	−0.418153	+	0.0439497i
$323$	−253.817	−	26.6773i	−0.785813	−	0.0825922i
$324$	−29.7928	−	6.33265i	−0.0919530	−	0.0195452i
$325$	−15.1135	+	20.8019i	−0.0465030	+	0.0640059i
$326$	408.623	+	296.882i	1.25345	+	0.910682i
$327$	−2.85782	+	13.4450i	−0.00873952	+	0.0411162i
$328$	−0.939333	+	8.93716i	−0.00286382	+	0.0272474i
$329$	10.5486	+	100.363i	0.0320625	+	0.305055i
$330$	259.902	−	55.2439i	0.787582	−	0.167406i
$331$	−36.9063	+	82.8929i	−0.111499	+	0.250432i	−0.960673	−	0.277682i	$-0.910434\pi$
$331$	−36.9063	+	82.8929i	−0.111499	+	0.250432i	0.849174	+	0.528114i	$0.177100\pi$
$332$	406.515	+	366.028i	1.22444	+	1.10249i
$333$	97.3862	−	31.6427i	0.292451	−	0.0950231i
$334$	361.656	−	325.636i	1.08280	−	0.974959i
$335$	380.353	−	658.791i	1.13538	−	1.96654i
$336$	42.5558	−	24.5696i	0.126654	−	0.0731238i
$337$	−320.247	−	104.055i	−0.950289	−	0.308768i	−0.207456	−	0.978244i	$-0.566518\pi$
$337$	−320.247	−	104.055i	−0.950289	−	0.308768i	−0.742833	+	0.669477i	$0.766518\pi$
$338$	418.774	−	186.450i	1.23898	−	0.551628i
$339$	69.7500	+	96.0027i	0.205752	+	0.283194i
$340$			242.977i			0.714638i
$341$	−129.587	+	161.619i	−0.380020	+	0.473957i
$342$	−244.814			−0.715831
$343$	−121.259	+	88.0999i	−0.353525	+	0.256851i
$344$	−16.2947	−	36.5986i	−0.0473684	−	0.106391i
$345$	−143.597	+	441.945i	−0.416222	+	1.28100i
$346$	304.045	+	526.621i	0.878743	+	1.52203i
$347$	−5.74162	−	3.31493i	−0.0165465	−	0.00955310i	0.491704	−	0.870762i	$-0.336374\pi$
$347$	−5.74162	−	3.31493i	−0.0165465	−	0.00955310i	−0.508250	+	0.861209i	$0.669708\pi$
$348$	121.604	+	135.055i	0.349438	+	0.388090i
$349$	63.4007	+	195.127i	0.181664	+	0.559104i	0.999875	−	0.0158142i	$-0.00503402\pi$
$349$	63.4007	+	195.127i	0.181664	+	0.559104i	−0.818211	+	0.574918i	$0.805034\pi$
$350$	−132.273	+	146.904i	−0.377923	+	0.419726i
$351$	−2.63225	−	1.17196i	−0.00749930	−	0.00333890i
$352$	58.9757	+	277.459i	0.167545	+	0.788235i
$353$	493.237	−	51.8413i	1.39727	−	0.146859i	0.624243	−	0.781230i	$-0.285407\pi$
$353$	493.237	−	51.8413i	1.39727	−	0.146859i	0.773029	+	0.634371i	$0.218741\pi$
$354$	−205.807	−	21.6311i	−0.581375	−	0.0611049i
$355$	−800.975	−	170.253i	−2.25627	−	0.479585i
$356$	145.821	−	200.706i	0.409610	−	0.563780i
$357$	−18.6828	−	13.5738i	−0.0523327	−	0.0380219i
$358$	−58.6796	+	276.066i	−0.163909	+	0.771134i
$359$	1.36971	−	13.0319i	0.00381533	−	0.0363005i	−0.992449	−	0.122661i	$-0.960857\pi$
$359$	1.36971	−	13.0319i	0.00381533	−	0.0363005i	0.996264	+	0.0863608i	$0.0275238\pi$
$360$	−4.43262	−	42.1736i	−0.0123128	−	0.117149i
$361$	−529.009	+	112.444i	−1.46540	+	0.311480i
$362$	−239.608	+	538.167i	−0.661899	+	1.48665i
$363$	98.2685	+	88.4813i	0.270712	+	0.243750i
$364$	−2.80003	+	0.909786i	−0.00769240	+	0.00249941i
$365$	535.583	−	482.241i	1.46735	−	1.32121i
$366$	−20.3063	+	35.1715i	−0.0554816	+	0.0960970i
$367$	−194.619	+	112.363i	−0.530296	+	0.306167i	−0.741137	−	0.671354i	$-0.765713\pi$
$367$	−194.619	+	112.363i	−0.530296	+	0.306167i	0.210841	+	0.977520i	$0.432380\pi$
$368$	−546.188	−	177.467i	−1.48421	−	0.482248i
$369$	14.7193	−	6.55345i	0.0398897	−	0.0177600i
$370$	−460.572	−	633.923i	−1.24479	−	1.71331i
$371$		−	139.957i		−	0.377243i
$372$	−129.111	−	127.867i	−0.347072	−	0.343729i
$373$	−583.635			−1.56471			−0.782353	−	0.622836i	$-0.785981\pi$
$373$	−583.635			−1.56471			−0.782353	+	0.622836i	$0.785981\pi$
$374$	124.851	−	90.7096i	0.333826	−	0.242539i
$375$	127.180	+	285.651i	0.339146	+	0.761735i
$376$	−33.2594	+	102.362i	−0.0884557	+	0.272239i
$377$	8.59606	+	14.8888i	0.0228012	+	0.0394929i
$378$	−19.1842	−	11.0760i	−0.0507518	−	0.0293016i
$379$	153.847	+	170.864i	0.405927	+	0.450828i	0.911097	−	0.412192i	$-0.135237\pi$
$379$	153.847	+	170.864i	0.405927	+	0.450828i	−0.505170	+	0.863020i	$0.668570\pi$
$380$	265.316	+	816.559i	0.698200	+	2.14884i
$381$	200.072	−	222.203i	0.525124	−	0.583209i
$382$	274.853	+	122.372i	0.719510	+	0.320346i
$383$	56.1466	+	264.149i	0.146597	+	0.689684i	0.988644	+	0.150279i	$0.0480173\pi$
$383$	56.1466	+	264.149i	0.146597	+	0.689684i	−0.842047	+	0.539405i	$0.818649\pi$
$384$	91.1377	−	9.57896i	0.237338	−	0.0249452i
$385$	88.0811	+	9.25770i	0.228782	+	0.0240460i
$386$	−224.381	−	47.6937i	−0.581299	−	0.123559i
$387$	−42.2206	+	58.1117i	−0.109097	+	0.150159i
$388$	−345.506	−	251.025i	−0.890479	−	0.646971i
$389$	16.8099	−	79.0843i	0.0432131	−	0.203301i	−0.951245	−	0.308437i	$-0.900194\pi$
$389$	16.8099	−	79.0843i	0.0432131	−	0.203301i	0.994458	+	0.105135i	$0.0335275\pi$
$390$	−2.30473	+	21.9280i	−0.00590956	+	0.0562257i
$391$	28.2115	+	268.414i	0.0721522	+	0.686482i
$392$	−76.1673	+	16.1899i	−0.194304	+	0.0413007i
$393$	−39.0362	+	87.6766i	−0.0993286	+	0.223096i
$394$	25.0711	+	22.5741i	0.0636322	+	0.0572947i
$395$	58.1540	−	18.8954i	0.147225	−	0.0478364i
$396$	50.4190	−	45.3975i	0.127321	−	0.114640i
$397$	−103.163	+	178.683i	−0.259856	+	0.450083i	−0.966203	−	0.257782i	$-0.917008\pi$
$397$	−103.163	+	178.683i	−0.259856	+	0.450083i	0.706347	+	0.707865i	$0.250342\pi$
$398$	−672.282	+	388.142i	−1.68915	+	0.975232i
$399$	−77.6079	−	25.2163i	−0.194506	−	0.0631988i
$400$	−766.038	+	341.062i	−1.91509	+	0.852655i
$401$	−238.032	−	327.622i	−0.593595	−	0.817013i	0.401508	−	0.915855i	$-0.368486\pi$
$401$	−238.032	−	327.622i	−0.593595	−	0.817013i	−0.995103	+	0.0988422i	$0.968486\pi$
$402$		−	423.814i		−	1.05426i
$403$	−9.43203	−	14.3713i	−0.0234045	−	0.0356609i
$404$	−653.008			−1.61636
$405$	−61.5114	+	44.6907i	−0.151880	+	0.110347i
$406$	53.7598	+	120.747i	0.132413	+	0.297405i
$407$	−70.4836	+	216.926i	−0.173178	+	0.532988i
$408$	−12.3148	−	21.3298i	−0.0301832	−	0.0522789i
$409$	495.593	+	286.131i	1.21172	+	0.699586i	0.963133	−	0.269024i	$-0.0867012\pi$
$409$	495.593	+	286.131i	1.21172	+	0.699586i	0.248585	+	0.968610i	$0.420035\pi$
$410$	−82.5003	−	91.6259i	−0.201220	−	0.223478i
$411$	75.9592	+	233.778i	0.184815	+	0.568804i
$412$	19.3053	−	21.4407i	0.0468574	−	0.0520405i
$413$	−63.0142	−	28.0557i	−0.152577	−	0.0679315i
$414$	53.8269	+	253.236i	0.130017	+	0.611681i
$415$	1358.03	−	142.735i	3.27236	−	0.343939i
$416$	−23.4093	−	2.46042i	−0.0562724	−	0.00591447i
$417$	129.102	+	27.4414i	0.309597	+	0.0658068i
$418$	320.531	−	441.172i	0.766819	−	1.05544i
$419$	−215.915	−	156.871i	−0.515310	−	0.374395i	0.299524	−	0.954089i	$-0.403172\pi$
$419$	−215.915	−	156.871i	−0.515310	−	0.374395i	−0.814834	+	0.579694i	$0.803172\pi$
$420$	−16.1524	+	75.9909i	−0.0384580	+	0.180931i
$421$	−53.5905	+	509.879i	−0.127293	+	1.21111i	0.725260	+	0.688475i	$0.241719\pi$
$421$	−53.5905	+	509.879i	−0.127293	+	1.21111i	−0.852554	+	0.522640i	$0.824947\pi$
$422$	−42.1257	−	400.800i	−0.0998241	−	0.949762i
$423$	188.759	−	40.1220i	0.446239	−	0.0948510i
$424$	60.7128	−	136.363i	0.143191	−	0.321612i
$425$	292.853	+	263.686i	0.689065	+	0.620437i
$426$	−433.890	+	140.979i	−1.01852	+	0.330938i
$427$	−10.0600	+	9.05804i	−0.0235597	+	0.0212132i
$428$	24.6872	−	42.7595i	0.0576803	−	0.0999053i
$429$	5.55831	−	3.20909i	0.0129564	−	0.00748040i
$430$	522.757	+	169.854i	1.21571	+	0.395010i
$431$	26.0630	−	11.6040i	0.0604710	−	0.0269234i	−0.376278	−	0.926507i	$-0.622796\pi$
$431$	26.0630	−	11.6040i	0.0604710	−	0.0269234i	0.436749	+	0.899583i	$0.356130\pi$
$432$	−55.2320	−	76.0203i	−0.127852	−	0.175973i
$433$			94.1293i			0.217389i	0.994075	+	0.108694i	$0.0346670\pi$
$433$			94.1293i			0.217389i	−0.994075	+	0.108694i	$0.965333\pi$
$434$	−60.5674	−	117.462i	−0.139556	−	0.270649i
$435$	453.659			1.04290
$436$	21.7279	−	15.7862i	0.0498346	−	0.0362070i
$437$	387.901	+	871.240i	0.887645	+	1.99368i
$438$	124.078	−	381.872i	0.283283	−	0.871855i
$439$	−18.7756	−	32.5203i	−0.0427691	−	0.0740782i	0.843848	−	0.536582i	$-0.180285\pi$
$439$	−18.7756	−	32.5203i	−0.0427691	−	0.0740782i	−0.886618	+	0.462503i	$0.846951\pi$
$440$	81.8034	+	47.2292i	0.185917	+	0.107339i
$441$	93.4215	+	103.755i	0.211840	+	0.235272i
$442$	3.95728	+	12.1793i	0.00895313	+	0.0275549i
$443$	71.1063	−	78.9715i	0.160511	−	0.178265i	−0.657525	−	0.753433i	$-0.728397\pi$
$443$	71.1063	−	78.9715i	0.160511	−	0.178265i	0.818036	+	0.575168i	$0.195063\pi$
$444$	−182.778	−	81.3782i	−0.411663	−	0.183284i
$445$	−128.757	−	605.756i	−0.289343	−	1.36125i
$446$	91.7912	−	9.64764i	0.205810	−	0.0216315i
$447$	−310.721	−	32.6581i	−0.695124	−	0.0730605i
$448$	−66.0062	−	14.0300i	−0.147335	−	0.0313171i
$449$	−142.133	+	195.629i	−0.316554	+	0.435700i	−0.937411	−	0.348224i	$-0.886785\pi$
$449$	−142.133	+	195.629i	−0.316554	+	0.435700i	0.620857	+	0.783924i	$0.286785\pi$
$450$	305.818	+	222.189i	0.679595	+	0.493754i
$451$	−7.46191	+	35.1055i	−0.0165453	+	0.0778393i
$452$	24.2362	−	230.592i	0.0536198	−	0.510158i
$453$	−36.5863	−	348.095i	−0.0807644	−	0.768422i
$454$	804.907	−	171.088i	1.77292	−	0.376846i
$455$	−2.98925	+	6.71396i	−0.00656977	+	0.0147560i
$456$	−64.6763	−	58.2348i	−0.141834	−	0.127708i
$457$	−580.464	+	188.604i	−1.27016	+	0.412701i	−0.865105	−	0.501590i	$-0.832748\pi$
$457$	−580.464	+	188.604i	−1.27016	+	0.412701i	−0.405057	+	0.914291i	$0.632748\pi$
$458$	−217.030	+	195.415i	−0.473866	+	0.426670i
$459$	−22.0799	+	38.2435i	−0.0481044	+	0.0833193i
$460$	786.314	−	453.979i	1.70938	−	0.986910i
$461$	719.908	+	233.912i	1.56162	+	0.507402i	0.957241	−	0.289292i	$-0.0934200\pi$
$461$	719.908	+	233.912i	1.56162	+	0.507402i	0.604382	+	0.796695i	$0.293420\pi$
$462$	45.0772	−	20.0697i	0.0975697	−	0.0434408i
$463$	198.257	+	272.878i	0.428201	+	0.589368i	0.967539	−	0.252721i	$-0.0813255\pi$
$463$	198.257	+	272.878i	0.428201	+	0.589368i	−0.539338	+	0.842089i	$0.681325\pi$
$464$			560.665i			1.20833i
$465$	−452.863	+	25.9314i	−0.973899	+	0.0557664i
$466$	−954.043			−2.04730
$467$	590.943	−	429.345i	1.26540	−	0.919368i	0.266392	−	0.963865i	$-0.414168\pi$
$467$	590.943	−	429.345i	1.26540	−	0.919368i	0.999010	+	0.0444964i	$0.0141683\pi$
$468$	2.28989	+	5.14317i	0.00489292	+	0.0109897i
$469$	43.6537	−	134.352i	0.0930782	−	0.286465i
$470$	−738.348	−	1278.86i	−1.57095	−	2.72097i
$471$	−104.551	−	60.3623i	−0.221976	−	0.128158i
$472$	−49.2256	−	54.6706i	−0.104292	−	0.115827i
$473$	−49.4428	−	152.169i	−0.104530	−	0.321711i
$474$	22.7952	−	25.3166i	0.0480911	−	0.0534106i
$475$	1272.10	+	566.376i	2.67811	+	1.19237i
$476$	9.38136	+	44.1358i	0.0197087	+	0.0927223i
$477$	−266.167	+	27.9752i	−0.558001	+	0.0586483i
$478$	179.477	+	18.8638i	0.375476	+	0.0394641i
$479$	−514.306	−	109.319i	−1.07371	−	0.228224i	−0.363056	−	0.931767i	$-0.618267\pi$
$479$	−514.306	−	109.319i	−1.07371	−	0.228224i	−0.710652	+	0.703544i	$0.751600\pi$
$480$	−365.085	+	502.496i	−0.760593	+	1.04687i
$481$	−15.3124	−	11.1251i	−0.0318345	−	0.0231291i
$482$	74.1736	−	348.959i	0.153887	−	0.723982i
$483$	−9.02025	+	85.8219i	−0.0186755	+	0.177685i
$484$	−27.0071	−	256.956i	−0.0557999	−	0.530900i
$485$	−1042.78	+	221.650i	−2.15007	+	0.457011i
$486$	−17.2294	+	38.6979i	−0.0354514	+	0.0796252i
$487$	−487.603	−	439.040i	−1.00124	−	0.901519i	−0.00609715	−	0.999981i	$-0.501941\pi$
$487$	−487.603	−	439.040i	−1.00124	−	0.901519i	−0.995141	+	0.0984628i	$0.968607\pi$
$488$	−13.7310	+	4.46147i	−0.0281373	+	0.00914236i
$489$	239.247	−	215.419i	0.489257	−	0.440529i
$490$	534.188	−	925.240i	1.09018	−	1.88825i
$491$	−710.652	+	410.295i	−1.44736	+	0.835631i	−0.998323	−	0.0578842i	$-0.981565\pi$
$491$	−710.652	+	410.295i	−1.44736	+	0.835631i	−0.449032	+	0.893515i	$0.648231\pi$
$492$	−29.9410	−	9.72843i	−0.0608557	−	0.0197732i
$493$	240.707	−	107.170i	0.488250	−	0.217383i
$494$	26.5980	+	36.6091i	0.0538422	+	0.0741074i
$495$		−	169.361i		−	0.342143i
$496$	−32.0479	−	559.682i	−0.0646127	−	1.12839i
$497$	−152.068			−0.305971
$498$	615.476	−	447.169i	1.23589	−	0.897930i
$499$	−183.952	−	413.164i	−0.368642	−	0.827983i	−0.998677	−	0.0514168i	$-0.983626\pi$
$499$	−183.952	−	413.164i	−0.368642	−	0.827983i	0.630035	−	0.776566i	$-0.283040\pi$
$500$	188.795	−	581.052i	0.377590	−	1.16210i
$501$	−155.095	−	268.633i	−0.309572	−	0.536194i
$502$	917.599	+	529.776i	1.82789	+	1.05533i
$503$	−370.272	−	411.229i	−0.736127	−	0.817552i	0.252554	−	0.967583i	$-0.418729\pi$
$503$	−370.272	−	411.229i	−0.736127	−	0.817552i	−0.988681	+	0.150031i	$0.952063\pi$
$504$	−2.43349	−	7.48953i	−0.00482836	−	0.0148602i
$505$	−1090.74	+	1211.39i	−2.15988	+	2.39879i
$506$	−526.824	−	234.557i	−1.04115	−	0.463551i
$507$	−60.7485	−	285.799i	−0.119819	−	0.563706i
$508$	−581.023	+	61.0680i	−1.14375	+	0.120213i
$509$	869.919	+	91.4322i	1.70907	+	0.179631i	0.908011	−	0.418947i	$-0.137601\pi$
$509$	869.919	+	91.4322i	1.70907	+	0.179631i	0.801064	+	0.598578i	$0.204267\pi$
$510$	330.537	+	70.2577i	0.648111	+	0.137760i
$511$	78.6672	−	108.276i	0.153948	−	0.211891i
$512$	−523.104	−	380.058i	−1.02169	−	0.742300i
$513$	−32.4431	+	152.633i	−0.0632419	+	0.297530i
$514$	−61.3995	+	584.178i	−0.119454	+	1.13653i
$515$	−7.52820	−	71.6260i	−0.0146179	−	0.139080i
$516$	137.282	−	29.1802i	0.266051	−	0.0565508i
$517$	−174.836	+	392.688i	−0.338174	+	0.759551i
$518$	−108.137	−	97.3670i	−0.208759	−	0.187967i
$519$	368.622	−	119.773i	0.710254	−	0.230776i
$520$	−5.82498	+	5.24483i	−0.0112019	+	0.0100862i
$521$	−479.894	+	831.201i	−0.921102	+	1.59539i	−0.123388	+	0.992359i	$0.539376\pi$
$521$	−479.894	+	831.201i	−0.921102	+	1.59539i	−0.797714	+	0.603036i	$0.793957\pi$
$522$	218.887	−	126.374i	0.419323	−	0.242096i
$523$	602.085	+	195.629i	1.15121	+	0.374052i	0.821601	−	0.570064i	$-0.193081\pi$
$523$	602.085	+	195.629i	1.15121	+	0.374052i	0.329614	+	0.944116i	$0.393081\pi$
$524$	171.312	−	76.2729i	0.326931	−	0.145559i
$525$	74.0605	+	101.936i	0.141068	+	0.194163i
$526$			480.909i			0.914276i
$527$	−234.159	+	120.741i	−0.444325	+	0.229109i
$528$	209.308			0.396417
$529$	387.954	−	281.865i	0.733372	−	0.532826i
$530$	832.991	+	1870.93i	1.57168	+	3.53005i
$531$	−40.7600	+	125.446i	−0.0767609	+	0.236246i
$532$	79.7210	+	138.081i	0.149852	+	0.259551i
$533$	−2.57918	−	1.48909i	−0.00483899	−	0.00279379i
$534$	−230.868	−	256.404i	−0.432336	−	0.480158i
$535$	−38.0869	−	117.219i	−0.0711904	−	0.219102i
$536$	100.814	−	111.965i	0.188086	−	0.208891i
$537$	164.341	+	73.1692i	0.306035	+	0.136256i
$538$	−60.3102	−	283.737i	−0.112101	−	0.527392i
$539$	−309.289	+	32.5076i	−0.573820	+	0.0603109i
$540$	147.746	+	15.5287i	0.273604	+	0.0287569i
$541$	875.049	+	185.997i	1.61747	+	0.343803i	0.925682	−	0.378302i	$-0.123492\pi$
$541$	875.049	+	185.997i	1.61747	+	0.343803i	0.691784	+	0.722105i	$0.256825\pi$
$542$	38.4020	−	52.8558i	0.0708524	−	0.0975200i
$543$	303.775	+	220.705i	0.559438	+	0.406456i
$544$	−75.0038	+	352.865i	−0.137875	+	0.648649i
$545$	7.00787	−	66.6754i	0.0128585	−	0.122340i
$546$	0.427998	+	4.07213i	0.000783879	+	0.00745811i
$547$	141.560	−	30.0895i	0.258794	−	0.0550083i	−0.0766876	−	0.997055i	$-0.524434\pi$
$547$	141.560	−	30.0895i	0.258794	−	0.0550083i	0.335481	+	0.942047i	$0.391101\pi$
$548$	195.350	−	438.764i	0.356479	−	0.800665i
$549$	19.2372	+	17.3212i	0.0350404	+	0.0315505i
$550$	−800.802	+	260.196i	−1.45600	+	0.473084i
$551$	691.909	−	622.997i	1.25573	−	1.13067i
$552$	−46.0178	+	79.7052i	−0.0833656	+	0.144393i
$553$	9.83390	−	5.67760i	0.0177828	−	0.0102669i
$554$	−833.860	−	270.937i	−1.50516	−	0.489057i
$555$	−456.264	+	203.142i	−0.822097	+	0.366021i
$556$	−151.583	−	208.636i	−0.272631	−	0.375244i
$557$		−	281.688i		−	0.505724i	−0.967502	−	0.252862i	$-0.918628\pi$
$557$		−	281.688i		−	0.505724i	0.967502	−	0.252862i	$-0.0813719\pi$
$558$	−211.279	+	138.664i	−0.378636	+	0.248502i
$559$	13.2770			0.0237514
$560$	−193.901	+	140.877i	−0.346252	+	0.251567i
$561$	−40.0088	−	89.8611i	−0.0713168	−	0.160180i
$562$	−191.601	+	589.687i	−0.340927	+	1.04927i
$563$	274.064	+	474.692i	0.486791	+	0.843148i	0.999885	−	0.0151854i	$-0.00483384\pi$
$563$	274.064	+	474.692i	0.486791	+	0.843148i	−0.513093	+	0.858333i	$0.671501\pi$
$564$	−326.541	−	188.528i	−0.578973	−	0.334270i
$565$	−387.286	−	430.125i	−0.685462	−	0.761282i
$566$	−182.385	−	561.323i	−0.322235	−	0.991736i
$567$	−9.44780	+	10.4928i	−0.0166628	+	0.0185059i
$568$	−148.163	−	65.9663i	−0.260850	−	0.116138i
$569$	−124.874	−	587.485i	−0.219462	−	1.03249i	−0.940553	−	0.339647i	$-0.889692\pi$
$569$	−124.874	−	587.485i	−0.219462	−	1.03249i	0.721091	−	0.692840i	$-0.243641\pi$
$570$	1187.53	−	124.815i	2.08339	−	0.218973i
$571$	334.139	+	35.1194i	0.585183	+	0.0615052i	0.392494	−	0.919755i	$-0.371613\pi$
$571$	334.139	+	35.1194i	0.585183	+	0.0615052i	0.192689	+	0.981260i	$0.438279\pi$
$572$	−12.2665	−	2.60732i	−0.0214449	−	0.00455825i
$573$	112.719	−	155.144i	0.196717	−	0.270757i
$574$	−18.5235	−	13.4581i	−0.0322710	−	0.0234462i
$575$	306.164	−	1440.39i	0.532460	−	2.50503i
$576$	−13.4883	+	128.333i	−0.0234173	+	0.222800i
$577$	−79.1738	−	753.289i	−0.137216	−	1.30553i	−0.818924	−	0.573902i	$-0.805429\pi$
$577$	−79.1738	−	753.289i	−0.137216	−	1.30553i	0.681708	−	0.731625i	$-0.261238\pi$
$578$	−576.190	+	122.473i	−0.996869	+	0.211891i
$579$	−59.4706	+	133.573i	−0.102713	+	0.230696i
$580$	−658.729	−	593.122i	−1.13574	−	1.02262i
$581$	241.170	−	78.3608i	0.415094	−	0.134872i
$582$	−441.389	+	397.428i	−0.758400	+	0.682866i
$583$	298.074	−	516.278i	0.511275	−	0.885555i
$584$	123.617	−	71.3703i	0.211673	−	0.122209i
$585$	13.3659	+	4.34285i	0.0228477	+	0.00742368i
$586$	159.428	−	70.9819i	0.272061	−	0.121129i
$587$	220.792	+	303.894i	0.376136	+	0.517707i	0.954556	−	0.298033i	$-0.0963304\pi$
$587$	220.792	+	303.894i	0.376136	+	0.517707i	−0.578420	+	0.815739i	$0.696330\pi$
$588$		−	272.797i		−	0.463940i
$589$	−655.084	+	661.454i	−1.11220	+	1.12301i
$590$	1009.35			1.71076
$591$	17.3966	−	12.6394i	0.0294359	−	0.0213864i
$592$	−251.058	−	563.885i	−0.424084	−	0.952508i
$593$	−150.427	+	462.965i	−0.253670	+	0.780718i	0.740418	+	0.672146i	$0.234627\pi$
$593$	−150.427	+	462.965i	−0.253670	+	0.780718i	−0.994089	+	0.108571i	$0.965373\pi$
$594$	−47.1782	−	81.7150i	−0.0794245	−	0.137567i
$595$	97.5459	+	56.3181i	0.163943	+	0.0946523i
$596$	408.479	+	453.662i	0.685368	+	0.761178i
$597$	152.901	+	470.581i	0.256116	+	0.788243i
$598$	32.0204	−	35.5622i	0.0535457	−	0.0594686i
$599$	−145.127	−	64.6148i	−0.242283	−	0.107871i	0.282003	−	0.959413i	$-0.409001\pi$
$599$	−145.127	−	64.6148i	−0.242283	−	0.107871i	−0.524286	+	0.851542i	$0.675668\pi$
$600$	27.9395	+	131.445i	0.0465659	+	0.219075i
$601$	−85.2244	+	8.95745i	−0.141804	+	0.0149042i	−0.175165	−	0.984539i	$-0.556046\pi$
$601$	−85.2244	+	8.95745i	−0.141804	+	0.0149042i	0.0333603	+	0.999443i	$0.489379\pi$
$602$	101.515	+	10.6697i	0.168629	+	0.0177237i
$603$	−264.233	−	56.1644i	−0.438197	−	0.0931417i
$604$	−401.981	+	553.280i	−0.665532	+	0.916026i
$605$	−521.787	−	379.100i	−0.862458	−	0.626612i
$606$	−188.820	+	888.327i	−0.311584	+	1.46589i
$607$	100.869	−	959.700i	0.166176	−	1.58105i	−0.520353	−	0.853951i	$-0.674200\pi$
$607$	100.869	−	959.700i	0.166176	−	1.58105i	0.686528	−	0.727103i	$-0.259134\pi$
$608$	133.246	+	1267.75i	0.219155	+	2.08512i
$609$	82.4055	−	17.5158i	0.135313	−	0.0287616i
$610$	80.5691	−	180.961i	0.132081	−	0.296658i
$611$	−26.5077	−	23.8676i	−0.0433840	−	0.0390632i
$612$	82.0611	−	26.6633i	0.134087	−	0.0435674i
$613$	−133.406	+	120.120i	−0.217629	+	0.195954i	−0.770733	−	0.637158i	$-0.780110\pi$
$613$	−133.406	+	120.120i	−0.217629	+	0.195954i	0.553104	+	0.833112i	$0.313443\pi$
$614$	−65.6786	+	113.759i	−0.106968	+	0.185275i
$615$	−68.0585	+	39.2936i	−0.110664	+	0.0638920i
$616$	16.6828	+	5.42057i	0.0270824	+	0.00879962i
$617$	200.530	−	89.2818i	0.325008	−	0.144703i	−0.237746	−	0.971327i	$-0.576408\pi$
$617$	200.530	−	89.2818i	0.325008	−	0.144703i	0.562754	+	0.826624i	$0.309742\pi$
$618$	−23.5849	−	32.4618i	−0.0381632	−	0.0525272i
$619$		−	452.614i		−	0.731201i	−0.930772	−	0.365601i	$-0.880864\pi$
$619$		−	452.614i		−	0.731201i	0.930772	−	0.365601i	$-0.119136\pi$
$620$	691.476	+	554.428i	1.11528	+	0.894239i
$621$	165.017			0.265727
$622$	−731.917	+	531.769i	−1.17672	+	0.854934i
$623$	−46.7766	−	105.062i	−0.0750828	−	0.168639i
$624$	−5.36721	+	16.5186i	−0.00860130	+	0.0264721i
$625$	−182.938	−	316.857i	−0.292700	−	0.506972i
$626$	1200.88	+	693.330i	1.91834	+	1.10756i
$627$	−232.578	−	258.304i	−0.370938	−	0.411968i
$628$	72.8922	+	224.339i	0.116070	+	0.357228i
$629$	−194.100	+	215.570i	−0.308586	+	0.342719i
$630$	98.7047	+	43.9462i	0.156674	+	0.0697558i
$631$	175.325	+	824.841i	0.277853	+	1.30720i	0.866650	+	0.498916i	$0.166268\pi$
$631$	175.325	+	824.841i	0.277853	+	1.30720i	−0.588797	+	0.808281i	$0.700398\pi$
$632$	12.0443	−	1.26591i	0.0190574	−	0.00200302i
$633$	−255.467	−	26.8506i	−0.403581	−	0.0424181i
$634$	689.444	+	146.546i	1.08745	+	0.231145i
$635$	−857.214	+	1179.85i	−1.34994	+	1.85804i
$636$	423.058	+	307.370i	0.665186	+	0.483286i
$637$	5.36549	−	25.2426i	0.00842306	−	0.0396274i
$638$	−58.8488	+	559.909i	−0.0922394	+	0.877600i
$639$	30.3959	+	289.198i	0.0475679	+	0.452579i
$640$	−437.203	+	92.9304i	−0.683130	+	0.145204i
$641$	313.490	−	704.110i	0.489064	−	1.09846i	−0.485477	−	0.874249i	$-0.661354\pi$
$641$	313.490	−	704.110i	0.489064	−	1.09846i	0.974542	−	0.224207i	$-0.0719791\pi$
$642$	−51.0300	−	45.9476i	−0.0794859	−	0.0715694i
$643$	789.091	−	256.391i	1.22720	−	0.398742i	0.377502	−	0.926009i	$-0.376783\pi$
$643$	789.091	−	256.391i	1.22720	−	0.398742i	0.849700	+	0.527267i	$0.176783\pi$
$644$	125.303	−	112.823i	0.194570	−	0.175191i
$645$	175.175	−	303.411i	0.271588	−	0.470405i
$646$	600.608	−	346.761i	0.929734	−	0.536782i
$647$	−362.563	−	117.804i	−0.560376	−	0.182077i	0.0151145	−	0.999886i	$-0.495189\pi$
$647$	−362.563	−	117.804i	−0.560376	−	0.182077i	−0.575490	+	0.817809i	$0.695189\pi$
$648$	−13.7569	+	6.12499i	−0.0212299	+	0.00945214i
$649$	−172.697	−	237.697i	−0.266097	−	0.366251i
$650$		−	69.8714i		−	0.107494i
$651$	−81.2596	+	22.1954i	−0.124823	+	0.0340943i
$652$	−629.037			−0.964780
$653$	−346.387	+	251.665i	−0.530455	+	0.385398i	−0.820528	−	0.571606i	$-0.806320\pi$
$653$	−346.387	+	251.665i	−0.530455	+	0.385398i	0.290073	+	0.957005i	$0.406320\pi$
$654$	−15.1923	−	34.1225i	−0.0232298	−	0.0521750i
$655$	144.654	−	445.200i	0.220846	−	0.679694i
$656$	−48.5619	−	84.1117i	−0.0740273	−	0.128219i
$657$	−221.641	−	127.964i	−0.337353	−	0.194771i
$658$	−183.495	−	203.792i	−0.278867	−	0.309714i
$659$	234.645	+	722.164i	0.356062	+	1.09585i	0.955391	+	0.295344i	$0.0954344\pi$
$659$	234.645	+	722.164i	0.356062	+	1.09585i	−0.599328	+	0.800503i	$0.704566\pi$
$660$	−221.425	+	245.917i	−0.335492	+	0.372602i
$661$	391.910	+	174.489i	0.592904	+	0.263978i	0.681177	−	0.732118i	$-0.261468\pi$
$661$	391.910	+	174.489i	0.592904	+	0.263978i	−0.0882732	+	0.996096i	$0.528135\pi$
$662$	−51.2648	−	241.182i	−0.0774393	−	0.364323i
$663$	8.11776	−	0.853211i	0.0122440	−	0.00128689i
$664$	268.969	+	28.2698i	0.405074	+	0.0425750i
$665$	389.313	+	82.7510i	0.585433	+	0.124438i
$666$	−163.555	+	225.114i	−0.245578	+	0.338009i
$667$	−796.558	−	578.733i	−1.19424	−	0.867666i
$668$	−126.012	+	592.839i	−0.188640	+	0.887483i
$669$	6.14934	−	58.5070i	0.00919183	−	0.0874545i
$670$	216.075	+	2055.82i	0.322500	+	3.06838i
$671$	−56.4009	+	11.9884i	−0.0840550	+	0.0178664i
$672$	−46.9148	+	105.372i	−0.0698137	+	0.156804i
$673$	−505.221	−	454.903i	−0.750700	−	0.675933i	0.202157	−	0.979353i	$-0.435205\pi$
$673$	−505.221	−	454.903i	−0.750700	−	0.675933i	−0.952857	+	0.303420i	$0.901872\pi$
$674$	870.240	−	282.758i	1.29116	−	0.419522i
$675$	179.055	−	161.221i	0.265266	−	0.238847i
$676$	−285.450	+	494.414i	−0.422263	+	0.731381i
$677$	−413.574	+	238.777i	−0.610892	+	0.352699i	−0.773315	−	0.634023i	$-0.781403\pi$
$677$	−413.574	+	238.777i	−0.610892	+	0.352699i	0.162422	+	0.986721i	$0.448069\pi$
$678$	−306.680	−	99.6464i	−0.452331	−	0.146971i
$679$	−180.859	+	80.5238i	−0.266361	+	0.118592i
$680$	70.6105	+	97.1870i	0.103839	+	0.142922i
$681$		−	524.503i		−	0.770196i
$682$	26.7408	−	562.290i	0.0392095	−	0.824472i
$683$	590.448			0.864493			0.432246	−	0.901756i	$-0.357721\pi$
$683$	590.448			0.864493			0.432246	+	0.901756i	$0.357721\pi$
$684$	246.663	−	179.211i	0.360619	−	0.262005i
$685$	−487.647	−	1095.27i	−0.711894	−	1.59894i
$686$	125.861	−	387.362i	0.183472	−	0.564667i
$687$	93.0731	+	161.207i	0.135478	+	0.234654i
$688$	374.978	+	216.494i	0.545026	+	0.314671i
$689$	33.1013	+	36.7627i	0.0480425	+	0.0533566i
$690$	−390.210	−	1200.94i	−0.565521	−	1.74050i
$691$	−172.699	+	191.802i	−0.249926	+	0.277571i	−0.855033	−	0.518573i	$-0.826464\pi$
$691$	−172.699	+	191.802i	−0.249926	+	0.277571i	0.605107	+	0.796144i	$0.293130\pi$
$692$	−691.844	−	308.029i	−0.999775	−	0.445129i
$693$	−6.53902	−	30.7637i	−0.00943582	−	0.0443921i
$694$	17.9173	−	1.88318i	0.0258174	−	0.00271352i
$695$	−640.231	−	67.2910i	−0.921196	−	0.0968216i
$696$	87.8877	+	18.6811i	0.126275	+	0.0268407i
$697$	−26.8287	+	36.9266i	−0.0384917	+	0.0529793i
$698$	−451.048	−	327.705i	−0.646200	−	0.469492i
$699$	−126.431	+	594.812i	−0.180874	+	0.850947i
$700$	25.7339	−	244.842i	0.0367627	−	0.349774i
$701$	48.9224	+	465.465i	0.0697894	+	0.664002i	0.972364	+	0.233469i	$0.0750077\pi$
$701$	48.9224	+	465.465i	0.0697894	+	0.664002i	−0.902575	+	0.430533i	$0.858326\pi$
$702$	7.65871	−	1.62791i	0.0109098	−	0.00231896i
$703$	−416.912	+	936.401i	−0.593048	+	1.33201i
$704$	−213.605	−	192.331i	−0.303416	−	0.273197i
$705$	−895.168	+	290.858i	−1.26974	+	0.412564i
$706$	−1001.54	+	901.791i	−1.41861	+	1.27732i
$707$	−151.357	+	262.158i	−0.214083	+	0.370803i
$708$	223.196	−	128.862i	0.315248	−	0.182009i
$709$	−1057.43	−	343.578i	−1.49143	−	0.484596i	−0.553926	−	0.832566i	$-0.686871\pi$
$709$	−1057.43	−	343.578i	−1.49143	−	0.484596i	−0.937506	+	0.347970i	$0.886871\pi$
$710$	2032.82	−	905.069i	2.86312	−	1.27474i
$711$	−12.7631	−	17.5670i	−0.0179510	−	0.0247074i
$712$		−	122.656i		−	0.172269i
$713$	828.241	+	532.186i	1.16163	+	0.746404i
$714$	62.7534			0.0878899
$715$	−25.3259	+	18.4003i	−0.0354208	+	0.0257347i
$716$	−142.966	−	321.106i	−0.199673	−	0.448472i
$717$	35.5455	−	109.398i	0.0495754	−	0.152577i
$718$	17.8039	+	30.8373i	0.0247966	+	0.0429489i
$719$	−526.599	−	304.032i	−0.732404	−	0.422854i	0.0868969	−	0.996217i	$-0.472305\pi$
$719$	−526.599	−	304.032i	−0.732404	−	0.422854i	−0.819301	+	0.573364i	$0.805638\pi$
$720$	306.675	+	340.597i	0.425937	+	0.473051i
$721$	−4.13295	−	12.7199i	−0.00573225	−	0.0176421i
$722$	983.383	−	1092.16i	1.36203	−	1.51268i
$723$	−207.734	−	92.4891i	−0.287322	−	0.127924i
$724$	−152.537	−	717.632i	−0.210687	−	0.991205i
$725$	−1429.74	+	150.272i	−1.97206	+	0.207272i
$726$	−357.362	−	37.5603i	−0.492234	−	0.0517359i
$727$	−889.782	−	189.129i	−1.22391	−	0.260150i	−0.449758	−	0.893151i	$-0.648490\pi$
$727$	−889.782	−	189.129i	−1.22391	−	0.260150i	−0.774151	+	0.633001i	$0.781823\pi$
$728$	−0.855581	+	1.17761i	−0.00117525	+	0.00161759i
$729$	21.8435	+	15.8702i	0.0299636	+	0.0217698i
$730$	−407.179	+	1915.63i	−0.557780	+	2.62415i
$731$	21.2699	−	202.369i	0.0290970	−	0.276839i
$732$	−5.28695	−	50.3020i	−0.00722261	−	0.0687186i
$733$	1145.03	−	243.384i	1.56211	−	0.332038i	0.655897	−	0.754850i	$-0.272290\pi$
$733$	1145.03	−	243.384i	1.56211	−	0.332038i	0.906217	+	0.422812i	$0.138957\pi$
$734$	248.382	−	557.876i	0.338396	−	0.760049i
$735$	−506.063	−	455.661i	−0.688521	−	0.619947i
$736$	1282.07	−	416.569i	1.74194	−	0.565991i
$737$	447.167	−	402.631i	0.606740	−	0.546311i
$738$	−21.8917	+	37.9176i	−0.0296636	+	0.0513789i
$739$	−145.701	+	84.1206i	−0.197160	+	0.113830i	−0.595330	−	0.803481i	$-0.702979\pi$
$739$	−145.701	+	84.1206i	−0.197160	+	0.113830i	0.398170	+	0.917312i	$0.369645\pi$
$740$	928.102	+	301.559i	1.25419	+	0.407512i
$741$	26.3492	−	11.7314i	0.0355590	−	0.0158319i
$742$	223.546	+	307.685i	0.301275	+	0.414670i
$743$		−	361.135i		−	0.486049i	−0.970020	−	0.243025i	$-0.921860\pi$
$743$		−	361.135i		−	0.486049i	0.970020	−	0.243025i	$-0.0781396\pi$
$744$	−88.8013	−	13.6246i	−0.119357	−	0.0183127i
$745$	1523.88			2.04548
$746$	1283.08	−	932.210i	1.71994	−	1.24961i
$747$	−197.230	−	442.986i	−0.264030	−	0.593021i
$748$	−59.3919	+	182.790i	−0.0794010	+	0.244371i
$749$	−11.4442	−	19.8219i	−0.0152793	−	0.0264645i
$750$	−735.850	−	424.843i	−0.981133	−	0.566458i
$751$	−6.44616	−	7.15918i	−0.00858343	−	0.00953287i	0.738838	−	0.673883i	$-0.235375\pi$
$751$	−6.44616	−	7.15918i	−0.00858343	−	0.00953287i	−0.747421	+	0.664350i	$0.768708\pi$
$752$	−359.463	−	1106.31i	−0.478010	−	1.47116i
$753$	451.898	−	501.884i	0.600130	−	0.666512i
$754$	−42.6789	−	19.0019i	−0.0566033	−	0.0252014i
$755$	354.942	+	1669.87i	0.470122	+	2.21175i
$756$	27.4371	−	2.88375i	0.0362924	−	0.00381448i
$757$	1100.39	+	115.656i	1.45363	+	0.152782i	0.798161	−	0.602444i	$-0.205806\pi$
$757$	1100.39	+	115.656i	1.45363	+	0.152782i	0.655464	+	0.755226i	$0.272473\pi$
$758$	−611.132	−	129.900i	−0.806242	−	0.171372i
$759$	−216.053	+	297.372i	−0.284655	+	0.391794i
$760$	343.419	+	249.508i	0.451867	+	0.328301i
$761$	139.387	−	655.766i	0.183163	−	0.861716i	−0.786561	−	0.617513i	$-0.788140\pi$
$761$	139.387	−	655.766i	0.183163	−	0.861716i	0.969724	−	0.244203i	$-0.0785264\pi$
$762$	−84.9305	+	808.060i	−0.111457	+	1.06045i
$763$	−1.30139	−	12.3819i	−0.00170562	−	0.0162279i
$764$	−366.509	+	77.9039i	−0.479724	+	0.101968i
$765$	87.6064	−	196.767i	0.114518	−	0.257212i
$766$	−545.345	−	491.031i	−0.711939	−	0.641033i
$767$	23.1874	−	7.53406i	0.0302313	−	0.00982276i
$768$	−406.520	+	366.032i	−0.529323	+	0.476605i
$769$	−281.975	+	488.395i	−0.366677	+	0.635104i	−0.989044	−	0.147622i	$-0.952838\pi$
$769$	−281.975	+	488.395i	−0.366677	+	0.635104i	0.622367	+	0.782726i	$0.286171\pi$
$770$	−208.426	+	120.335i	−0.270683	+	0.156279i
$771$	356.077	+	115.696i	0.461838	+	0.150060i
$772$	260.989	−	116.200i	0.338069	−	0.150518i
$773$	4.61886	+	6.35732i	0.00597524	+	0.00822422i	0.811994	−	0.583666i	$-0.198382\pi$
$773$	4.61886	+	6.35732i	0.00597524	+	0.00822422i	−0.806019	+	0.591890i	$0.798382\pi$
$774$		−	195.191i		−	0.252185i
$775$	1418.64	−	231.733i	1.83051	−	0.299010i
$776$	−211.146			−0.272096
$777$	−75.0353	+	54.5163i	−0.0965705	+	0.0701626i
$778$	89.3619	+	200.710i	0.114861	+	0.257982i
$779$	−49.8402	+	153.392i	−0.0639797	+	0.196909i
$780$	−13.7299	−	23.7808i	−0.0176024	−	0.0304882i
$781$	−560.952	−	323.866i	−0.718248	−	0.414681i
$782$	−490.745	−	545.028i	−0.627551	−	0.696966i
$783$	−49.7826	−	153.215i	−0.0635794	−	0.195677i
$784$	563.139	−	625.430i	0.718290	−	0.797742i
$785$	537.924	+	239.499i	0.685253	+	0.305094i
$786$	−54.2233	−	255.101i	−0.0689864	−	0.324556i
$787$	212.054	−	22.2877i	0.269446	−	0.0283199i	0.0311579	−	0.999514i	$-0.490081\pi$
$787$	212.054	−	22.2877i	0.269446	−	0.0283199i	0.238288	+	0.971195i	$0.423414\pi$
$788$	−41.7854	−	4.39183i	−0.0530272	−	0.00557338i
$789$	299.830	+	63.7307i	0.380012	+	0.0807741i
$790$	−97.6665	+	134.426i	−0.123628	+	0.170160i
$791$	−86.9561	−	63.1773i	−0.109932	−	0.0798702i
$792$	6.97405	−	32.8103i	0.00880562	−	0.0414272i
$793$	0.500146	−	4.75857i	0.000630701	−	0.00600072i
$794$	−58.6058	−	557.597i	−0.0738109	−	0.702263i
$795$	1276.85	−	271.402i	1.60610	−	0.341386i
$796$	393.228	−	883.205i	0.494005	−	1.10955i
$797$	611.697	+	550.774i	0.767499	+	0.691059i	0.956763	−	0.290867i	$-0.0939437\pi$
$797$	611.697	+	550.774i	0.767499	+	0.691059i	−0.189265	+	0.981926i	$0.560610\pi$
$798$	210.892	−	68.5229i	0.264275	−	0.0858682i
$799$	−406.257	+	365.796i	−0.508457	+	0.457817i
$800$	984.144	−	1704.59i	1.23018	−	2.13073i
$801$	−190.454	+	109.959i	−0.237770	+	0.137277i
$802$	1046.59	+	340.057i	1.30497	+	0.424011i
$803$	520.791	−	231.871i	0.648557	−	0.288756i
$804$	310.245	+	427.015i	0.385877	+	0.531114i
$805$		−	420.900i		−	0.522857i
$806$	43.6902	+	16.5290i	0.0542061	+	0.0205074i
$807$	−184.892			−0.229111
$808$	−261.193	+	189.768i	−0.323259	+	0.234861i
$809$	−131.778	−	295.978i	−0.162890	−	0.365857i	0.813598	−	0.581428i	$-0.197506\pi$
$809$	−131.778	−	295.978i	−0.162890	−	0.365857i	−0.976488	+	0.215570i	$0.930839\pi$
$810$	63.8460	−	196.498i	0.0788223	−	0.242590i
$811$	70.2912	+	121.748i	0.0866722	+	0.150121i	0.906103	−	0.423058i	$-0.139043\pi$
$811$	70.2912	+	121.748i	0.0866722	+	0.150121i	−0.819430	+	0.573179i	$0.805710\pi$
$812$	−142.556	−	82.3048i	−0.175562	−	0.101361i
$813$	−27.8646	−	30.9468i	−0.0342738	−	0.0380649i
$814$	−191.532	−	589.475i	−0.235297	−	0.724171i
$815$	−1050.70	+	1166.92i	−1.28920	+	1.43180i
$816$	243.179	+	108.270i	0.298014	+	0.132684i
$817$	−149.495	−	703.317i	−0.182980	−	0.860853i
$818$	−1546.54	+	162.548i	−1.89064	+	0.198714i
$819$	2.59555	+	0.272803i	0.00316916	+	0.000333093i
$820$	150.196	+	31.9252i	0.183166	+	0.0389332i
$821$	653.469	−	899.423i	0.795943	−	1.09552i	−0.197400	−	0.980323i	$-0.563250\pi$
$821$	653.469	−	899.423i	0.795943	−	1.09552i	0.993343	−	0.115198i	$-0.0367504\pi$
$822$	−540.392	−	392.618i	−0.657411	−	0.477637i
$823$	206.523	−	971.616i	0.250940	−	1.18058i	−0.654486	−	0.756074i	$-0.727115\pi$
$823$	206.523	−	971.616i	0.250940	−	1.18058i	0.905426	−	0.424505i	$-0.139552\pi$
$824$	1.49102	−	14.1862i	0.00180950	−	0.0172162i
$825$	56.0997	+	533.753i	0.0679997	+	0.646974i
$826$	183.344	−	38.9709i	0.221966	−	0.0471803i
$827$	260.656	−	585.442i	0.315182	−	0.707911i	−0.684597	−	0.728922i	$-0.740022\pi$
$827$	260.656	−	585.442i	0.315182	−	0.707911i	0.999779	+	0.0210110i	$0.00668849\pi$
$828$	−239.610	−	215.746i	−0.289384	−	0.260562i
$829$	−316.189	+	102.736i	−0.381410	+	0.123928i	−0.493446	−	0.869776i	$-0.664263\pi$
$829$	−316.189	+	102.736i	−0.381410	+	0.123928i	0.112036	+	0.993704i	$0.464263\pi$
$830$	−2757.54	+	2482.90i	−3.32234	+	2.99144i
$831$	−279.424	+	483.977i	−0.336250	+	0.582403i
$832$	20.6561	−	11.9258i	0.0248271	−	0.0143339i
$833$	−376.155	−	122.220i	−0.451566	−	0.146723i
$834$	−327.651	+	145.880i	−0.392867	+	0.174916i
$835$	889.288	+	1224.00i	1.06502	+	1.46587i
$836$			679.143i			0.812372i
$837$	58.4531	+	150.101i	0.0698365	+	0.179332i
$838$	725.234			0.865435
$839$	−344.506	+	250.299i	−0.410616	+	0.298330i	−0.773851	−	0.633368i	$-0.781672\pi$
$839$	−344.506	+	250.299i	−0.410616	+	0.298330i	0.363235	+	0.931697i	$0.381672\pi$
$840$	15.6227	+	35.0892i	0.0185985	+	0.0417728i
$841$	−37.1532	+	114.346i	−0.0441774	+	0.135964i
$842$	−696.589	−	1206.53i	−0.827303	−	1.43293i
$843$	342.258	+	197.603i	0.406000	+	0.234404i
$844$	335.842	+	372.990i	0.397917	+	0.441931i
$845$	440.386	+	1355.37i	0.521167	+	1.60399i
$846$	−350.887	+	389.700i	−0.414760	+	0.460638i
$847$	−109.418	−	48.7159i	−0.129183	−	0.0575158i
$848$	335.418	+	1578.02i	0.395541	+	1.86087i
$849$	−374.135	+	39.3231i	−0.440677	+	0.0463170i
$850$	−1064.98	−	111.934i	−1.25292	−	0.131688i
$851$	1060.28	+	225.369i	1.24592	+	0.264829i
$852$	333.966	−	459.665i	0.391979	−	0.539513i
$853$	525.347	+	381.687i	0.615882	+	0.447464i	0.851481	−	0.524386i	$-0.175705\pi$
$853$	525.347	+	381.687i	0.615882	+	0.447464i	−0.235599	+	0.971850i	$0.575705\pi$
$854$	7.64814	−	35.9817i	0.00895567	−	0.0421331i
$855$	79.5560	−	756.925i	0.0930480	−	0.885292i
$856$	−2.55165	−	24.2774i	−0.00298090	−	0.0283614i
$857$	507.261	−	107.822i	0.591903	−	0.125813i	0.0977850	−	0.995208i	$-0.468824\pi$
$857$	507.261	−	107.822i	0.591903	−	0.125813i	0.494118	+	0.869395i	$0.335491\pi$
$858$	−7.09380	+	15.9329i	−0.00826783	+	0.0185698i
$859$	631.956	+	569.016i	0.735688	+	0.662417i	0.949254	−	0.314512i	$-0.101841\pi$
$859$	631.956	+	569.016i	0.735688	+	0.662417i	−0.213565	+	0.976929i	$0.568508\pi$
$860$	−651.044	+	211.537i	−0.757028	+	0.245973i
$861$	−10.8454	+	9.76527i	−0.0125963	+	0.0113418i
$862$	−38.7630	+	67.1396i	−0.0449687	+	0.0778881i
$863$	−248.961	+	143.738i	−0.288483	+	0.166556i	−0.637258	−	0.770651i	$-0.719931\pi$
$863$	−248.961	+	143.738i	−0.288483	+	0.166556i	0.348774	+	0.937207i	$0.386598\pi$
$864$	209.772	+	68.1590i	0.242791	+	0.0788877i
$865$	−1727.03	+	768.923i	−1.99657	+	0.888929i
$866$	−150.348	−	206.936i	−0.173612	−	0.238956i
$867$			375.464i			0.433061i
$868$	147.010	+	74.0118i	0.169367	+	0.0852670i
$869$	48.3675			0.0556588
$870$	−997.335	+	724.606i	−1.14636	+	0.832881i
$871$	20.3091	+	45.6149i	0.0233170	+	0.0523708i
$872$	4.10325	−	12.6285i	0.00470556	−	0.0144822i
$873$	189.289	+	327.858i	0.216826	+	0.375553i
$874$	−2244.36	−	1295.78i	−2.56791	−	1.48259i
$875$	−189.510	−	210.472i	−0.216583	−	0.240540i
$876$	154.527	+	475.586i	0.176401	+	0.542906i
$877$	150.682	−	167.349i	0.171815	−	0.190820i	−0.651087	−	0.759003i	$-0.725687\pi$
$877$	150.682	−	167.349i	0.171815	−	0.190820i	0.822902	+	0.568183i	$0.192353\pi$
$878$	93.2197	+	41.5041i	0.106173	+	0.0472712i
$879$	−23.1270	−	108.804i	−0.0263106	−	0.123782i
$880$	−1015.30	+	106.713i	−1.15375	+	0.121264i
$881$	241.146	+	25.3455i	0.273718	+	0.0287690i	0.240393	−	0.970676i	$-0.422724\pi$
$881$	241.146	+	25.3455i	0.273718	+	0.0287690i	0.0333252	+	0.999445i	$0.489390\pi$
$882$	−371.103	−	78.8803i	−0.420751	−	0.0894334i
$883$	−631.048	+	868.563i	−0.714663	+	0.983650i	0.285021	+	0.958521i	$0.408000\pi$
$883$	−631.048	+	868.563i	−0.714663	+	0.983650i	−0.999684	+	0.0251286i	$0.992000\pi$
$884$	−12.9028	−	9.37441i	−0.0145959	−	0.0106045i
$885$	133.760	−	629.291i	0.151141	−	0.711063i
$886$	−30.1846	+	287.187i	−0.0340684	+	0.324139i
$887$	42.1882	+	401.394i	0.0475628	+	0.452530i	0.992222	+	0.124478i	$0.0397255\pi$
$887$	42.1882	+	401.394i	0.0475628	+	0.452530i	−0.944660	+	0.328052i	$0.893608\pi$
$888$	−96.7575	+	20.5664i	−0.108961	+	0.0231604i
$889$	−110.155	+	247.413i	−0.123909	+	0.278305i
$890$	1250.61	+	1126.05i	1.40518	+	1.26523i
$891$	−57.1985	+	18.5849i	−0.0641958	+	0.0208585i
$892$	−85.4222	+	76.9145i	−0.0957648	+	0.0862270i
$893$	−965.859	+	1672.92i	−1.08159	+	1.87337i
$894$	735.258	−	424.502i	0.822437	−	0.474834i
$895$	−834.481	−	271.139i	−0.932381	−	0.302949i
$896$	−75.8282	+	33.7609i	−0.0846297	+	0.0376796i
$897$	−17.9284	−	24.6763i	−0.0199870	−	0.0275098i
$898$		−	657.097i		−	0.731734i
$899$	244.260	−	929.559i	0.271702	−	1.03399i
$900$	−470.777			−0.523086
$901$	613.368	−	445.638i	0.680763	−	0.494604i
$902$	−39.6678	−	89.0953i	−0.0439776	−	0.0987753i
$903$	20.1050	−	61.8770i	0.0222647	−	0.0685238i
$904$	−57.3172	−	99.2762i	−0.0634039	−	0.109819i
$905$	−1586.06	−	915.713i	−1.75255	−	1.01184i
$906$	636.426	+	706.823i	0.702457	+	0.780158i
$907$	−59.8398	−	184.168i	−0.0659755	−	0.203052i	0.912634	−	0.408777i	$-0.134045\pi$
$907$	−59.8398	−	184.168i	−0.0659755	−	0.203052i	−0.978610	+	0.205725i	$0.934045\pi$
$908$	−685.745	+	761.597i	−0.755225	+	0.838763i
$909$	528.818	+	235.445i	0.581758	+	0.259015i
$910$	−4.15223	−	19.5347i	−0.00456289	−	0.0214667i
$911$	−386.287	+	40.6004i	−0.424026	+	0.0445669i	−0.314138	−	0.949377i	$-0.601716\pi$
$911$	−386.287	+	40.6004i	−0.424026	+	0.0445669i	−0.109887	+	0.993944i	$0.535049\pi$
$912$	935.463	+	98.3212i	1.02573	+	0.107808i
$913$	1056.52	+	224.571i	1.15720	+	0.245970i
$914$	974.858	−	1341.78i	1.06658	−	1.46803i
$915$	−102.146	−	74.2132i	−0.111635	−	0.0811073i
$916$	75.6200	−	355.764i	0.0825546	−	0.388389i
$917$	9.08667	−	86.4539i	0.00990913	−	0.0942791i
$918$	−12.5434	−	119.343i	−0.0136638	−	0.130003i
$919$	−872.388	+	185.432i	−0.949280	+	0.201776i	−0.656433	−	0.754384i	$-0.727936\pi$
$919$	−872.388	+	185.432i	−0.949280	+	0.201776i	−0.292846	+	0.956160i	$0.594602\pi$
$920$	182.585	−	410.092i	0.198462	−	0.445752i
$921$	62.2207	+	56.0237i	0.0675577	+	0.0608293i
$922$	−1956.28	+	635.633i	−2.12178	+	0.689407i
$923$	39.9437	−	35.9655i	0.0432760	−	0.0389659i
$924$	−30.7261	+	53.2192i	−0.0332534	+	0.0575965i
$925$	1370.66	−	791.352i	1.48180	−	0.855516i
$926$	−871.706	−	283.234i	−0.941367	−	0.305869i
$927$	−23.3643	+	10.4024i	−0.0252042	+	0.0112216i
$928$	−773.555	−	1064.71i	−0.833572	−	1.14731i
$929$			763.244i			0.821576i	0.911731	+	0.410788i	$0.134746\pi$
$929$			763.244i			0.821576i	−0.911731	+	0.410788i	$0.865254\pi$
$930$	954.166	−	780.343i	1.02598	−	0.839078i
$931$	−1397.58			−1.50116
$932$	961.249	−	698.389i	1.03138	−	0.749344i
$933$	234.544	+	526.795i	0.251387	+	0.564625i
$934$	−613.372	+	1887.76i	−0.656715	+	2.02116i
$935$	239.887	+	415.496i	0.256564	+	0.444381i
$936$	2.41056	+	1.39173i	0.00257538	+	0.00148690i
$937$	971.535	+	1079.00i	1.03686	+	1.15155i	0.988268	+	0.152727i	$0.0488055\pi$
$937$	971.535	+	1079.00i	1.03686	+	1.15155i	0.0485880	+	0.998819i	$0.484528\pi$
$938$	118.624	+	365.089i	0.126465	+	0.389220i
$939$	591.409	−	656.826i	0.629829	−	0.699496i
$940$	1680.09	+	748.023i	1.78733	+	0.795769i
$941$	−259.385	−	1220.31i	−0.275648	−	1.29682i	−0.870173	−	0.492746i	$-0.835993\pi$
$941$	−259.385	−	1220.31i	−0.275648	−	1.29682i	0.594525	−	0.804077i	$-0.297340\pi$
$942$	326.260	−	34.2913i	0.346348	−	0.0364026i
$943$	169.627	+	17.8286i	0.179881	+	0.0189062i
$944$	777.724	+	165.310i	0.823860	+	0.175117i
$945$	40.4793	−	55.7150i	0.0428353	−	0.0589577i
$946$	351.748	+	255.560i	0.371827	+	0.270148i
$947$	−340.809	+	1603.38i	−0.359882	+	1.69311i	0.310074	+	0.950712i	$0.399646\pi$
$947$	−340.809	+	1603.38i	−0.359882	+	1.69311i	−0.669956	+	0.742401i	$0.733687\pi$
$948$	−4.43483	+	42.1946i	−0.00467809	+	0.0445091i
$949$	4.94479	+	47.0466i	0.00521053	+	0.0495749i
$950$	−3701.26	+	786.727i	−3.89606	+	0.828134i
$951$	182.732	−	410.423i	0.192147	−	0.431570i
$952$	16.5785	+	14.9274i	0.0174144	+	0.0156800i
$953$	975.012	−	316.801i	1.02310	−	0.332425i	0.251040	−	0.967977i	$-0.419228\pi$
$953$	975.012	−	316.801i	1.02310	−	0.332425i	0.772058	+	0.635552i	$0.219228\pi$
$954$	540.463	−	486.635i	0.566523	−	0.510100i
$955$	−467.673	+	810.033i	−0.489710	+	0.848202i
$956$	−194.642	+	112.377i	−0.203600	+	0.117549i
$957$	341.284	+	110.890i	0.356619	+	0.115872i
$958$	1305.27	−	581.145i	1.36250	−	0.606623i
$959$	−130.868	−	180.124i	−0.136463	−	0.187825i
$960$		−	629.389i		−	0.655613i
$961$	−190.697	+	941.889i	−0.198436	+	0.980114i
$962$	51.4327			0.0534643
$963$	−35.4092	+	25.7263i	−0.0367697	+	0.0267148i
$964$	180.715	+	405.892i	0.187464	+	0.421050i
$965$	220.377	−	678.251i	0.228370	−	0.702851i
$966$	−117.249	−	203.080i	−0.121375	−	0.210228i
$967$	−1296.04	−	748.267i	−1.34026	−	0.773802i	−0.353419	−	0.935465i	$-0.614981\pi$
$967$	−1296.04	−	748.267i	−1.34026	−	0.773802i	−0.986846	+	0.161663i	$0.948314\pi$
$968$	−85.4753	−	94.9299i	−0.0883009	−	0.0980681i
$969$	−136.600	−	420.411i	−0.140970	−	0.433861i
$970$	1938.45	−	2152.86i	1.99840	−	2.21945i
$971$	367.844	+	163.775i	0.378830	+	0.168666i	0.587313	−	0.809360i	$-0.300186\pi$
$971$	367.844	+	163.775i	0.378830	+	0.168666i	−0.208483	+	0.978026i	$0.566852\pi$
$972$	−10.9685	−	51.6026i	−0.0112844	−	0.0530891i
$973$	−118.894	+	12.4962i	−0.122193	+	0.0128430i
$974$	1773.21	+	186.372i	1.82055	+	0.191347i
$975$	−43.5623	−	9.25945i	−0.0446793	−	0.00949687i
$976$	91.7181	−	126.239i	0.0939735	−	0.129343i
$977$	577.886	+	419.859i	0.591490	+	0.429743i	0.842848	−	0.538152i	$-0.180877\pi$
$977$	577.886	+	419.859i	0.591490	+	0.429743i	−0.251358	+	0.967894i	$0.580877\pi$
$978$	−181.888	+	855.718i	−0.185980	+	0.874967i
$979$	51.2045	−	487.178i	0.0523028	−	0.497628i
$980$	139.081	+	1323.27i	0.141920	+	1.35028i
$981$	−23.2874	+	4.94990i	−0.0237385	+	0.00504577i
$982$	906.970	−	2037.09i	0.923595	−	2.07443i
$983$	−557.127	−	501.639i	−0.566762	−	0.510314i	0.335191	−	0.942150i	$-0.391199\pi$
$983$	−557.127	−	501.639i	−0.566762	−	0.510314i	−0.901952	+	0.431836i	$0.857866\pi$
$984$	−14.8031	+	4.80981i	−0.0150438	+	0.00488802i
$985$	−77.9427	+	70.1799i	−0.0791296	+	0.0712487i
$986$	−358.000	+	620.074i	−0.363083	+	0.628878i
$987$	−151.374	+	87.3957i	−0.153368	+	0.0885468i
$988$	−53.5979	−	17.4150i	−0.0542489	−	0.0176265i
$989$	−694.642	+	309.274i	−0.702368	+	0.312714i
$990$	270.511	+	372.326i	0.273243	+	0.376087i
$991$		−	928.137i		−	0.936566i	−0.883579	−	0.468283i	$-0.844873\pi$
$991$		−	928.137i		−	0.936566i	0.883579	−	0.468283i	$-0.155127\pi$
$992$	833.056	+	1018.62i	0.839775	+	1.02684i
$993$	−157.162			−0.158270
$994$	334.309	−	242.890i	0.336327	−	0.244356i
$995$	−981.604	−	2204.72i	−0.986536	−	2.21580i
$996$	−292.783	+	901.094i	−0.293959	+	0.904712i
$997$	−373.749	−	647.352i	−0.374873	−	0.649300i	0.615435	−	0.788188i	$-0.288980\pi$
$997$	−373.749	−	647.352i	−0.374873	−	0.649300i	−0.990308	+	0.138888i	$0.955647\pi$
$998$	1064.33	+	614.491i	1.06646	+	0.615722i
$999$	118.676	+	131.803i	0.118795	+	0.131935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.3.n.b.13.2	✓	48
3.2	odd	2		279.3.bc.d.199.5		48
31.12	odd	30	inner	93.3.n.b.43.2	yes	48
93.74	even	30		279.3.bc.d.136.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.3.n.b.13.2	✓	48	1.1	even	1	trivial
93.3.n.b.43.2	yes	48	31.12	odd	30	inner
279.3.bc.d.136.5		48	93.74	even	30
279.3.bc.d.199.5		48	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	93.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19842 + 1.59725i) q^{2} +(0.704489 + 1.58231i) q^{3} +(1.04579 - 3.21862i) q^{4} +(-4.22402 - 7.31621i) q^{5} +(-4.07610 - 2.35334i) q^{6} +(-1.04976 - 1.16587i) q^{7} +(-0.517049 - 1.59131i) q^{8} +(-2.00739 + 2.22943i) q^{9} +(20.9720 + 9.33732i) q^{10} +(-1.38936 - 6.53642i) q^{11} +(5.82960 - 0.612716i) q^{12} +(0.551480 + 0.0579629i) q^{13} +(4.16999 + 0.886359i) q^{14} +(8.60072 - 11.8379i) q^{15} +(14.6301 + 10.6294i) q^{16} +(1.76695 - 8.31285i) q^{17} +(0.852137 - 8.10754i) q^{18} +(-3.13904 - 29.8659i) q^{19} +(-27.9656 + 5.94427i) q^{20} +(1.10523 - 2.48238i) q^{21} +(13.4947 + 12.1507i) q^{22} +(-30.2032 + 9.81360i) q^{23} +(2.15369 - 1.93919i) q^{24} +(-23.1846 + 40.1569i) q^{25} +(-1.30497 + 0.753424i) q^{26} +(-4.94183 - 1.60570i) q^{27} +(-4.85033 + 2.15951i) q^{28} +(18.2235 + 25.0825i) q^{29} +39.7621i q^{30} +(-19.6253 - 23.9968i) q^{31} -42.4481 q^{32} +(9.36384 - 6.80322i) q^{33} +(9.39317 + 21.0974i) q^{34} +(-4.09558 + 12.6049i) q^{35} +(5.07639 + 8.79257i) q^{36} +(-29.5597 - 17.0663i) q^{37} +(54.6042 + 60.6441i) q^{38} +(0.296796 + 0.913446i) q^{39} +(-9.45836 + 10.5046i) q^{40} +(-4.90643 - 2.18448i) q^{41} +(1.53522 + 7.22264i) q^{42} +(23.8122 - 2.50276i) q^{43} +(-22.4913 - 2.36393i) q^{44} +(24.7903 + 5.26933i) q^{45} +(50.7245 - 69.8164i) q^{46} +(-52.0403 - 37.8095i) q^{47} +(-6.51223 + 30.6376i) q^{48} +(4.86462 - 46.2838i) q^{49} +(-13.1710 - 125.313i) q^{50} +(14.3983 - 3.06045i) q^{51} +(0.763296 - 1.71439i) q^{52} +(66.2966 + 59.6937i) q^{53} +(13.4289 - 4.36333i) q^{54} +(-41.9531 + 37.7748i) q^{55} +(-1.31249 + 2.27330i) q^{56} +(45.0457 - 26.0071i) q^{57} +(-80.1260 - 26.0345i) q^{58} +(40.1662 - 17.8832i) q^{59} +(-29.1071 - 40.0625i) q^{60} -8.62872i q^{61} +(81.4736 + 21.4088i) q^{62} +4.70650 q^{63} +(34.7985 - 25.2826i) q^{64} +(-1.90539 - 4.27958i) q^{65} +(-9.71923 + 29.9127i) q^{66} +(45.0227 + 77.9815i) q^{67} +(-24.9081 - 14.3807i) q^{68} +(-36.8059 - 40.8771i) q^{69} +(-11.1293 - 34.2525i) q^{70} +(64.8590 - 72.0332i) q^{71} +(4.58565 + 2.04166i) q^{72} +(17.7369 + 83.4454i) q^{73} +(92.2439 - 9.69523i) q^{74} +(-79.8739 - 8.39509i) q^{75} +(-99.4100 - 21.1302i) q^{76} +(-6.16214 + 8.48146i) q^{77} +(-2.11148 - 1.53408i) q^{78} +(-1.50486 + 7.07982i) q^{79} +(15.9691 - 151.936i) q^{80} +(-0.940756 - 8.95070i) q^{81} +(14.2756 - 3.03437i) q^{82} +(-65.7434 + 147.662i) q^{83} +(-6.83401 - 6.15337i) q^{84} +(-68.2822 + 22.1862i) q^{85} +(-48.3517 + 43.5361i) q^{86} +(-26.8500 + 46.5056i) q^{87} +(-9.68313 + 5.59056i) q^{88} +(69.7179 + 22.6527i) q^{89} +(-62.9159 + 28.0120i) q^{90} +(-0.511342 - 0.703802i) q^{91} +107.476i q^{92} +(24.1446 - 47.9587i) q^{93} +174.798 q^{94} +(-205.246 + 149.120i) q^{95} +(-29.9042 - 67.1660i) q^{96} +(38.9956 - 120.016i) q^{97} +(63.2322 + 109.521i) q^{98} +(17.3615 + 10.0237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} + 18 q^{3} - 30 q^{4} + 9 q^{6} + q^{7} + 30 q^{8} - 18 q^{9} + 6 q^{10} - 68 q^{11} + 45 q^{12} + 18 q^{13} - 5 q^{14} - 146 q^{16} + 31 q^{17} - 9 q^{18} + 55 q^{19} + 191 q^{20} - 108 q^{21}+ \cdots + 81 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 + 18 * q^3 - 30 * q^4 + 9 * q^6 + q^7 + 30 * q^8 - 18 * q^9 + 6 * q^10 - 68 * q^11 + 45 * q^12 + 18 * q^13 - 5 * q^14 - 146 * q^16 + 31 * q^17 - 9 * q^18 + 55 * q^19 + 191 * q^20 - 108 * q^21 + 106 * q^22 - 70 * q^23 - 75 * q^24 - 232 * q^25 - 30 * q^26 - 75 * q^28 - 35 * q^29 + 79 * q^31 + 164 * q^32 - 24 * q^33 + 8 * q^34 - 215 * q^35 + 195 * q^36 + 81 * q^37 - 75 * q^38 + 69 * q^39 - 34 * q^40 + 4 * q^41 + 15 * q^42 + 503 * q^43 + 253 * q^44 - 90 * q^45 + 245 * q^46 - 91 * q^47 + 9 * q^48 + 57 * q^49 - 131 * q^50 + 39 * q^51 - 963 * q^52 + 33 * q^53 + 45 * q^54 + 148 * q^55 - 765 * q^56 - 45 * q^57 - 190 * q^58 - 377 * q^59 + 225 * q^60 - 325 * q^62 - 54 * q^63 - 728 * q^64 + 262 * q^65 - 207 * q^66 + 870 * q^67 + 489 * q^68 - 39 * q^69 + 1041 * q^70 - 131 * q^71 - 180 * q^72 + 166 * q^73 + 1668 * q^74 - 114 * q^75 - 21 * q^76 + 75 * q^77 + 75 * q^78 + 71 * q^79 + 631 * q^80 + 54 * q^81 - 440 * q^82 + 84 * q^83 + 315 * q^84 + 30 * q^85 - 112 * q^86 - 123 * q^87 - 207 * q^88 + 285 * q^89 - 18 * q^90 - 605 * q^91 + 111 * q^93 - 380 * q^94 - 424 * q^95 - 126 * q^96 - 123 * q^97 + 681 * q^98 + 81 * q^99

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