LMFDB - Embedded newform 177.3.g.a.10.9

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label			10.9
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.9

$q$-expansion

$f(q)$	$=$	$q+(-0.911464 - 0.363160i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(-2.20510 - 2.08878i) q^{4} +(0.969991 - 1.14196i) q^{5} +(1.50144 + 0.796012i) q^{6} +(-4.53786 - 2.73034i) q^{7} +(2.89920 + 6.26652i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(-0.911464 - 0.363160i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(-2.20510 - 2.08878i) q^{4} +(0.969991 - 1.14196i) q^{5} +(1.50144 + 0.796012i) q^{6} +(-4.53786 - 2.73034i) q^{7} +(2.89920 + 6.26652i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-1.29883 + 0.688594i) q^{10} +(-5.02274 - 0.272325i) q^{11} +(3.40580 + 4.00961i) q^{12} +(2.47994 + 11.2665i) q^{13} +(3.14454 + 4.13657i) q^{14} +(-1.88408 + 1.78469i) q^{15} +(0.290990 + 5.36700i) q^{16} +(3.36350 - 2.02375i) q^{17} +(-2.43626 - 1.65182i) q^{18} +(-7.84823 + 28.2668i) q^{19} +(-4.52424 + 0.492041i) q^{20} +(7.30242 + 5.55116i) q^{21} +(4.47914 + 2.07227i) q^{22} +(-13.7897 + 9.34968i) q^{23} +(-3.81861 - 11.3332i) q^{24} +(3.68136 + 22.4553i) q^{25} +(1.83116 - 11.1696i) q^{26} +(-4.92415 - 1.65914i) q^{27} +(4.30335 + 15.4993i) q^{28} +(-3.47220 - 8.71456i) q^{29} +(2.36540 - 0.942461i) q^{30} +(-14.0161 + 3.89155i) q^{31} +(10.5026 - 31.1705i) q^{32} +(8.59764 + 1.40951i) q^{33} +(-3.80066 + 0.623086i) q^{34} +(-7.51962 + 2.53366i) q^{35} +(-5.11356 - 7.54194i) q^{36} +(-12.8285 + 27.7284i) q^{37} +(17.4187 - 22.9140i) q^{38} +(-2.16036 - 19.8641i) q^{39} +(9.96832 + 2.76769i) q^{40} +(20.7356 - 30.5827i) q^{41} +(-4.63993 - 7.71162i) q^{42} +(-7.43227 + 0.402966i) q^{43} +(10.5068 + 11.0919i) q^{44} +(3.57840 - 2.72023i) q^{45} +(15.9643 - 3.51400i) q^{46} +(8.89224 - 7.55314i) q^{47} +(0.504010 - 9.29592i) q^{48} +(-9.81462 - 18.5123i) q^{49} +(4.79944 - 21.8041i) q^{50} +(-6.17059 + 2.85482i) q^{51} +(18.0647 - 30.0238i) q^{52} +(-2.06176 + 3.88889i) q^{53} +(3.88565 + 3.30050i) q^{54} +(-5.18300 + 5.47162i) q^{55} +(3.95356 - 36.3524i) q^{56} +(18.8073 - 47.2027i) q^{57} +9.20397i q^{58} +(-54.8533 + 21.7283i) q^{59} +7.88242 q^{60} +(-43.9651 - 17.5173i) q^{61} +(14.1884 + 1.54308i) q^{62} +(-11.5345 - 10.9260i) q^{63} +(-6.97407 + 8.21050i) q^{64} +(15.2714 + 8.09639i) q^{65} +(-7.32456 - 4.40704i) q^{66} +(6.01377 + 12.9985i) q^{67} +(-11.6440 - 2.56305i) q^{68} +(25.4954 - 13.5168i) q^{69} +(7.77398 + 0.421493i) q^{70} +(-12.3398 - 14.5276i) q^{71} +(4.45291 + 20.2298i) q^{72} +(39.0998 + 51.4349i) q^{73} +(21.7626 - 20.6146i) q^{74} +(-2.13377 - 39.3551i) q^{75} +(76.3493 - 45.9378i) q^{76} +(22.0489 + 14.9495i) q^{77} +(-5.24478 + 18.8900i) q^{78} +(-101.382 + 11.0260i) q^{79} +(6.41117 + 4.87364i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-30.0062 + 20.3447i) q^{82} +(-35.3254 - 104.842i) q^{83} +(-4.50742 - 27.4940i) q^{84} +(0.951520 - 5.80402i) q^{85} +(6.92059 + 2.33182i) q^{86} +(4.34681 + 15.6558i) q^{87} +(-12.8554 - 32.2646i) q^{88} +(-88.4760 + 35.2521i) q^{89} +(-4.24947 + 1.17986i) q^{90} +(19.5077 - 57.8968i) q^{91} +(49.9372 + 8.18679i) q^{92} +(24.8630 - 4.07608i) q^{93} +(-10.8480 + 3.65510i) q^{94} +(24.6669 + 36.3809i) q^{95} +(-23.9215 + 51.7056i) q^{96} +(-30.5163 + 40.1435i) q^{97} +(2.22272 + 20.4376i) q^{98} +(-14.5403 - 4.03709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) $	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.911464	−	0.363160i	−0.455732	−	0.181580i	0.130965	−	0.991387i	$-0.458193\pi$
$2$	−0.911464	−	0.363160i	−0.455732	−	0.181580i	−0.586697	+	0.809807i	$0.699572\pi$
$3$	−1.72190	−	0.187268i	−0.573966	−	0.0624225i
$3$	−1.72190	−	0.187268i	−0.573966	−	0.0624225i
$4$	−2.20510	−	2.08878i	−0.551275	−	0.522196i
$5$	0.969991	−	1.14196i	0.193998	−	0.228392i	−0.656559	−	0.754274i	$-0.727989\pi$
$5$	0.969991	−	1.14196i	0.193998	−	0.228392i	0.850557	+	0.525882i	$0.176265\pi$
$6$	1.50144	+	0.796012i	0.250240	+	0.132669i
$7$	−4.53786	−	2.73034i	−0.648265	−	0.390048i	0.153111	−	0.988209i	$-0.451071\pi$
$7$	−4.53786	−	2.73034i	−0.648265	−	0.390048i	−0.801376	+	0.598161i	$0.795898\pi$
$8$	2.89920	+	6.26652i	0.362400	+	0.783315i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	−1.29883	+	0.688594i	−0.129883	+	0.0688594i
$11$	−5.02274	−	0.272325i	−0.456613	−	0.0247568i	−0.175601	−	0.984461i	$-0.556187\pi$
$11$	−5.02274	−	0.272325i	−0.456613	−	0.0247568i	−0.281011	+	0.959705i	$0.590670\pi$
$12$	3.40580	+	4.00961i	0.283816	+	0.334135i
$13$	2.47994	+	11.2665i	0.190765	+	0.866652i	0.970606	+	0.240675i	$0.0773688\pi$
$13$	2.47994	+	11.2665i	0.190765	+	0.866652i	−0.779841	+	0.625977i	$0.784700\pi$
$14$	3.14454	+	4.13657i	0.224610	+	0.295469i
$15$	−1.88408	+	1.78469i	−0.125605	+	0.118980i
$16$	0.290990	+	5.36700i	0.0181869	+	0.335438i
$17$	3.36350	−	2.02375i	0.197853	−	0.119044i	−0.413180	−	0.910649i	$-0.635582\pi$
$17$	3.36350	−	2.02375i	0.197853	−	0.119044i	0.611033	+	0.791605i	$0.290754\pi$
$18$	−2.43626	−	1.65182i	−0.135348	−	0.0917679i
$19$	−7.84823	+	28.2668i	−0.413065	+	1.48772i	0.405920	+	0.913909i	$0.366951\pi$
$19$	−7.84823	+	28.2668i	−0.413065	+	1.48772i	−0.818985	+	0.573816i	$0.805463\pi$
$20$	−4.52424	+	0.492041i	−0.226212	+	0.0246020i
$21$	7.30242	+	5.55116i	0.347734	+	0.264341i
$22$	4.47914	+	2.07227i	0.203597	+	0.0941942i
$23$	−13.7897	+	9.34968i	−0.599554	+	0.406508i	−0.822863	−	0.568240i	$-0.807624\pi$
$23$	−13.7897	+	9.34968i	−0.599554	+	0.406508i	0.223309	+	0.974748i	$0.428314\pi$
$24$	−3.81861	−	11.3332i	−0.159109	−	0.472218i
$25$	3.68136	+	22.4553i	0.147254	+	0.898211i
$26$	1.83116	−	11.1696i	0.0704294	−	0.429600i
$27$	−4.92415	−	1.65914i	−0.182376	−	0.0614496i
$28$	4.30335	+	15.4993i	0.153691	+	0.553545i
$29$	−3.47220	−	8.71456i	−0.119731	−	0.300502i	0.856880	−	0.515516i	$-0.172400\pi$
$29$	−3.47220	−	8.71456i	−0.119731	−	0.300502i	−0.976611	+	0.215014i	$0.931020\pi$
$30$	2.36540	−	0.942461i	0.0788466	−	0.0314154i
$31$	−14.0161	+	3.89155i	−0.452132	+	0.125534i	−0.486127	−	0.873888i	$-0.661591\pi$
$31$	−14.0161	+	3.89155i	−0.452132	+	0.125534i	0.0339952	+	0.999422i	$0.489177\pi$
$32$	10.5026	−	31.1705i	0.328205	−	0.974077i
$33$	8.59764	+	1.40951i	0.260535	+	0.0427125i
$34$	−3.80066	+	0.623086i	−0.111784	+	0.0183261i
$35$	−7.51962	+	2.53366i	−0.214846	+	0.0723902i
$36$	−5.11356	−	7.54194i	−0.142043	−	0.209498i
$37$	−12.8285	+	27.7284i	−0.346717	+	0.749417i	−0.999970	−	0.00772289i	$-0.997542\pi$
$37$	−12.8285	+	27.7284i	−0.346717	+	0.749417i	0.653253	+	0.757140i	$0.273404\pi$
$38$	17.4187	−	22.9140i	0.458388	−	0.602999i
$39$	−2.16036	−	19.8641i	−0.0553937	−	0.509337i
$40$	9.96832	+	2.76769i	0.249208	+	0.0691923i
$41$	20.7356	−	30.5827i	0.505746	−	0.745920i	−0.486024	−	0.873945i	$-0.661553\pi$
$41$	20.7356	−	30.5827i	0.505746	−	0.745920i	0.991771	+	0.128025i	$0.0408638\pi$
$42$	−4.63993	−	7.71162i	−0.110475	−	0.183610i
$43$	−7.43227	+	0.402966i	−0.172844	+	0.00937131i	−0.140358	−	0.990101i	$-0.544825\pi$
$43$	−7.43227	+	0.402966i	−0.172844	+	0.00937131i	−0.0324860	+	0.999472i	$0.510342\pi$
$44$	10.5068	+	11.0919i	0.238791	+	0.252089i
$45$	3.57840	−	2.72023i	0.0795201	−	0.0604496i
$46$	15.9643	−	3.51400i	0.347049	−	0.0763914i
$47$	8.89224	−	7.55314i	0.189197	−	0.160705i	−0.547782	−	0.836621i	$-0.684528\pi$
$47$	8.89224	−	7.55314i	0.189197	−	0.160705i	0.736979	+	0.675916i	$0.236252\pi$
$48$	0.504010	−	9.29592i	0.0105002	−	0.193665i
$49$	−9.81462	−	18.5123i	−0.200298	−	0.377803i
$50$	4.79944	−	21.8041i	0.0959889	−	0.436082i
$51$	−6.17059	+	2.85482i	−0.120992	+	0.0559769i
$52$	18.0647	−	30.0238i	0.347398	−	0.577381i
$53$	−2.06176	+	3.88889i	−0.0389011	+	0.0733752i	−0.902201	−	0.431317i	$-0.858049\pi$
$53$	−2.06176	+	3.88889i	−0.0389011	+	0.0733752i	0.863299	+	0.504692i	$0.168394\pi$
$54$	3.88565	+	3.30050i	0.0719565	+	0.0611204i
$55$	−5.18300	+	5.47162i	−0.0942363	+	0.0994840i
$56$	3.95356	−	36.3524i	0.0705992	−	0.649149i
$57$	18.8073	−	47.2027i	0.329952	−	0.828118i
$58$			9.20397i			0.158689i
$59$	−54.8533	+	21.7283i	−0.929716	+	0.368276i
$59$	−54.8533	+	21.7283i	−0.929716	+	0.368276i
$60$	7.88242			0.131374
$61$	−43.9651	−	17.5173i	−0.720740	−	0.287169i	−0.0192162	−	0.999815i	$-0.506117\pi$
$61$	−43.9651	−	17.5173i	−0.720740	−	0.287169i	−0.701523	+	0.712646i	$0.747496\pi$
$62$	14.1884	+	1.54308i	0.228845	+	0.0248884i
$63$	−11.5345	−	10.9260i	−0.183087	−	0.173429i
$64$	−6.97407	+	8.21050i	−0.108970	+	0.128289i
$65$	15.2714	+	8.09639i	0.234945	+	0.124560i
$66$	−7.32456	−	4.40704i	−0.110978	−	0.0667733i
$67$	6.01377	+	12.9985i	0.0897577	+	0.194008i	0.947255	−	0.320480i	$-0.103844\pi$
$67$	6.01377	+	12.9985i	0.0897577	+	0.194008i	−0.857498	+	0.514488i	$0.827982\pi$
$68$	−11.6440	−	2.56305i	−0.171236	−	0.0376919i
$69$	25.4954	−	13.5168i	0.369499	−	0.195896i
$70$	7.77398	+	0.421493i	0.111057	+	0.00602133i
$71$	−12.3398	−	14.5276i	−0.173800	−	0.204614i	0.668364	−	0.743834i	$-0.266995\pi$
$71$	−12.3398	−	14.5276i	−0.173800	−	0.204614i	−0.842165	+	0.539221i	$0.818719\pi$
$72$	4.45291	+	20.2298i	0.0618459	+	0.280969i
$73$	39.0998	+	51.4349i	0.535614	+	0.704588i	0.981707	−	0.190399i	$-0.0609781\pi$
$73$	39.0998	+	51.4349i	0.535614	+	0.704588i	−0.446093	+	0.894986i	$0.647185\pi$
$74$	21.7626	−	20.6146i	0.294089	−	0.278576i
$75$	−2.13377	−	39.3551i	−0.0284503	−	0.524734i
$76$	76.3493	−	45.9378i	1.00460	−	0.604445i
$77$	22.0489	+	14.9495i	0.286350	+	0.194150i
$78$	−5.24478	+	18.8900i	−0.0672408	+	0.242179i
$79$	−101.382	+	11.0260i	−1.28332	+	0.139569i	−0.724242	−	0.689546i	$-0.757810\pi$
$79$	−101.382	+	11.0260i	−1.28332	+	0.139569i	−0.559078	+	0.829115i	$0.688845\pi$
$80$	6.41117	+	4.87364i	0.0801396	+	0.0609206i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	−30.0062	+	20.3447i	−0.365929	+	0.248106i
$83$	−35.3254	−	104.842i	−0.425607	−	1.26316i	−0.919313	−	0.393528i	$-0.871255\pi$
$83$	−35.3254	−	104.842i	−0.425607	−	1.26316i	0.493706	−	0.869629i	$-0.335642\pi$
$84$	−4.50742	−	27.4940i	−0.0536597	−	0.327310i
$85$	0.951520	−	5.80402i	0.0111944	−	0.0682825i
$86$	6.92059	+	2.33182i	0.0804720	+	0.0271142i
$87$	4.34681	+	15.6558i	0.0499634	+	0.179952i
$88$	−12.8554	−	32.2646i	−0.146084	−	0.366643i
$89$	−88.4760	+	35.2521i	−0.994113	+	0.396091i	−0.809755	−	0.586768i	$-0.800400\pi$
$89$	−88.4760	+	35.2521i	−0.994113	+	0.396091i	−0.184358	+	0.982859i	$0.559021\pi$
$90$	−4.24947	+	1.17986i	−0.0472163	+	0.0131095i
$91$	19.5077	−	57.8968i	0.214370	−	0.636228i
$92$	49.9372	+	8.18679i	0.542796	+	0.0889869i
$93$	24.8630	−	4.07608i	0.267344	−	0.0438289i
$94$	−10.8480	+	3.65510i	−0.115404	+	0.0388841i
$95$	24.6669	+	36.3809i	0.259651	+	0.382957i
$96$	−23.9215	+	51.7056i	−0.249183	+	0.538600i
$97$	−30.5163	+	40.1435i	−0.314601	+	0.413850i	−0.926031	−	0.377448i	$-0.876802\pi$
$97$	−30.5163	+	40.1435i	−0.314601	+	0.413850i	0.611430	+	0.791299i	$0.290595\pi$
$98$	2.22272	+	20.4376i	0.0226808	+	0.208547i
$99$	−14.5403	−	4.03709i	−0.146872	−	0.0407787i
$100$	38.7864	−	57.2057i	0.387864	−	0.572057i
$101$	17.0143	+	28.2780i	0.168458	+	0.279980i	0.929573	−	0.368637i	$-0.120175\pi$
$101$	17.0143	+	28.2780i	0.168458	+	0.279980i	−0.761115	+	0.648617i	$0.775348\pi$
$102$	6.66103	−	0.361150i	0.0653042	−	0.00354069i
$103$	46.2149	+	48.7885i	0.448688	+	0.473674i	0.910622	−	0.413240i	$-0.135603\pi$
$103$	46.2149	+	48.7885i	0.448688	+	0.473674i	−0.461934	+	0.886914i	$0.652844\pi$
$104$	−63.4118	+	48.2044i	−0.609729	+	0.463504i
$105$	13.4225	−	2.95451i	0.127833	−	0.0281382i
$106$	3.29151	−	2.79583i	0.0310519	−	0.0263758i
$107$	−6.97563	+	128.658i	−0.0651928	+	1.20241i	0.764662	+	0.644431i	$0.222906\pi$
$107$	−6.97563	+	128.658i	−0.0651928	+	1.20241i	−0.829855	+	0.557979i	$0.811577\pi$
$108$	7.39267	+	13.9441i	0.0684506	+	0.129112i
$109$	−27.0204	+	122.755i	−0.247894	+	1.12619i	0.673994	+	0.738736i	$0.264577\pi$
$109$	−27.0204	+	122.755i	−0.247894	+	1.12619i	−0.921888	+	0.387456i	$0.873354\pi$
$110$	6.71119	−	3.10493i	0.0610108	−	0.0282266i
$111$	27.2821	−	45.3431i	0.245784	−	0.408497i
$112$	13.3333	−	25.1492i	0.119047	−	0.224546i
$113$	141.321	+	120.039i	1.25063	+	1.06229i	0.995439	+	0.0953993i	$0.0304128\pi$
$113$	141.321	+	120.039i	1.25063	+	1.06229i	0.255187	+	0.966892i	$0.417863\pi$
$114$	−34.2843	+	36.1935i	−0.300740	+	0.317487i
$115$	−2.69895	+	24.8165i	−0.0234692	+	0.215795i
$116$	−10.5463	+	26.4692i	−0.0909162	+	0.228182i
$117$			34.6086i			0.295800i
$118$	57.8876	+	0.115987i	0.490573	+	0.000982944i
$119$	−20.7886			−0.174694
$120$	−16.6461	−	6.63242i	−0.138718	−	0.0552702i
$121$	−95.1370	−	10.3468i	−0.786256	−	0.0855105i
$122$	33.7110	+	31.9328i	0.276320	+	0.261744i
$123$	−41.4317	+	48.7772i	−0.336843	+	0.396563i
$124$	39.0355	+	20.6953i	0.314802	+	0.166898i
$125$	61.3101	+	36.8891i	0.490481	+	0.295112i
$126$	6.54535	+	14.1475i	0.0519472	+	0.112282i
$127$	−180.014	−	39.6241i	−1.41744	−	0.312001i	−0.560812	−	0.827943i	$-0.689511\pi$
$127$	−180.014	−	39.6241i	−1.41744	−	0.312001i	−0.856623	+	0.515942i	$0.827442\pi$
$128$	−106.905	+	56.6772i	−0.835192	+	0.442791i
$129$	12.8731	+	0.697958i	0.0997913	+	0.00541053i
$130$	−10.9790	−	12.9255i	−0.0844542	−	0.0994272i
$131$	23.6486	+	107.437i	0.180524	+	0.820127i	0.976623	+	0.214961i	$0.0689624\pi$
$131$	23.6486	+	107.437i	0.180524	+	0.820127i	−0.796099	+	0.605166i	$0.793107\pi$
$132$	−16.0145	−	21.0667i	−0.121322	−	0.159596i
$133$	112.792	−	106.842i	0.848060	−	0.803325i
$134$	−0.760775	−	14.0317i	−0.00567742	−	0.104714i
$135$	−6.67106	+	4.01384i	−0.0494152	+	0.0297322i
$136$	22.4334	+	15.2102i	0.164951	+	0.111840i
$137$	57.7806	−	208.107i	0.421757	−	1.51903i	−0.382052	−	0.924141i	$-0.624782\pi$
$137$	57.7806	−	208.107i	0.421757	−	1.51903i	0.803808	−	0.594889i	$-0.202804\pi$
$138$	−28.1469	+	3.06116i	−0.203963	+	0.0221823i
$139$	−63.4221	−	48.2122i	−0.456274	−	0.346850i	0.351656	−	0.936129i	$-0.385619\pi$
$139$	−63.4221	−	48.2122i	−0.456274	−	0.346850i	−0.807930	+	0.589279i	$0.799412\pi$
$140$	21.8738	+	10.1199i	0.156241	+	0.0722849i
$141$	−16.7260	+	11.3405i	−0.118624	+	0.0804291i
$142$	5.97147	+	17.7227i	0.0420526	+	0.124808i
$143$	−9.38795	−	57.2639i	−0.0656500	−	0.400447i
$144$	−2.60868	+	15.9122i	−0.0181158	+	0.110502i
$145$	−13.3197	−	4.48793i	−0.0918600	−	0.0309512i
$146$	−16.9589	−	61.0805i	−0.116157	−	0.418360i
$147$	13.4330	+	33.7143i	0.0913810	+	0.229349i
$148$	86.2069	−	34.3480i	0.582479	−	0.232081i
$149$	−211.770	+	58.7978i	−1.42128	+	0.394616i	−0.891307	−	0.453400i	$-0.850211\pi$
$149$	−211.770	+	58.7978i	−1.42128	+	0.394616i	−0.529971	+	0.848016i	$0.677797\pi$
$150$	−12.3473	+	36.6456i	−0.0823157	+	0.244304i
$151$	107.188	+	17.5725i	0.709852	+	0.116374i	0.505882	−	0.862603i	$-0.331167\pi$
$151$	107.188	+	17.5725i	0.709852	+	0.116374i	0.203970	+	0.978977i	$0.434615\pi$
$152$	−199.888	+	32.7699i	−1.31505	+	0.215592i
$153$	11.1597	−	3.76015i	0.0729395	−	0.0245762i
$154$	−14.6677	−	21.6333i	−0.0952449	−	0.140476i
$155$	−9.15148	+	19.7806i	−0.0590418	+	0.127617i
$156$	−36.7281	+	48.3150i	−0.235436	+	0.309711i
$157$	6.50640	+	59.8254i	0.0414421	+	0.381053i	0.996431	+	0.0844118i	$0.0269011\pi$
$157$	6.50640	+	59.8254i	0.0414421	+	0.381053i	−0.954989	+	0.296642i	$0.904133\pi$
$158$	96.4105	+	26.7682i	0.610193	+	0.169419i
$159$	4.27840	−	6.31016i	0.0269082	−	0.0396866i
$160$	−25.4081	−	42.2286i	−0.158801	−	0.263929i
$161$	88.1036	−	4.77684i	0.547228	−	0.0296698i
$162$	−6.07261	−	6.41078i	−0.0374853	−	0.0395727i
$163$	112.514	−	85.5309i	0.690270	−	0.524729i	−0.200210	−	0.979753i	$-0.564162\pi$
$163$	112.514	−	85.5309i	0.690270	−	0.524729i	0.890479	+	0.455024i	$0.150369\pi$
$164$	−109.605	+	24.1258i	−0.668322	+	0.147109i
$165$	9.94925	−	8.45097i	0.0602985	−	0.0512180i
$166$	−5.87665	+	108.388i	−0.0354015	+	0.652942i
$167$	−41.2336	−	77.7748i	−0.246908	−	0.465717i	0.728820	−	0.684706i	$-0.240069\pi$
$167$	−41.2336	−	77.7748i	−0.246908	−	0.465717i	−0.975728	+	0.218988i	$0.929724\pi$
$168$	−13.6152	+	61.8546i	−0.0810431	+	0.368182i
$169$	32.5967	−	15.0809i	0.192880	−	0.0892358i
$170$	−2.97506	+	4.94459i	−0.0175004	+	0.0290858i
$171$	−41.2238	+	77.7563i	−0.241075	+	0.454715i
$172$	17.2306	+	14.6358i	0.100178	+	0.0850920i
$173$	224.340	−	236.833i	1.29676	−	1.36898i	0.406419	−	0.913687i	$-0.366777\pi$
$173$	224.340	−	236.833i	1.29676	−	1.36898i	0.890344	−	0.455289i	$-0.150464\pi$
$174$	1.72361	−	15.8483i	0.00990578	−	0.0910821i
$175$	44.6050	−	111.950i	0.254886	−	0.639715i
$176$		−	27.0363i		−	0.153615i
$177$	98.5207	−	27.1416i	0.556614	−	0.153343i
$178$	93.4448			0.524971
$179$	−112.838	−	44.9588i	−0.630380	−	0.251166i	0.0329925	−	0.999456i	$-0.489496\pi$
$179$	−112.838	−	44.9588i	−0.630380	−	0.251166i	−0.663373	+	0.748289i	$0.730876\pi$
$180$	−13.5727	−	1.47612i	−0.0754040	−	0.00820068i
$181$	13.8627	+	13.1314i	0.0765894	+	0.0725494i	0.725037	−	0.688710i	$-0.241823\pi$
$181$	13.8627	+	13.1314i	0.0765894	+	0.0725494i	−0.648447	+	0.761259i	$0.724581\pi$
$182$	−38.8063	+	45.6864i	−0.213222	+	0.251024i
$183$	72.4230	+	38.3962i	0.395754	+	0.209816i
$184$	−98.5691	−	59.3071i	−0.535702	−	0.322321i
$185$	19.2212	+	41.5460i	0.103899	+	0.224573i
$186$	−24.1420	−	5.31406i	−0.129796	−	0.0285702i
$187$	−17.4451	+	9.24881i	−0.0932894	+	0.0494589i
$188$	−35.3852	−	1.91853i	−0.188219	−	0.0102049i
$189$	17.8151	+	20.9735i	0.0942597	+	0.110971i
$190$	−9.27084	−	42.1179i	−0.0487939	−	0.221673i
$191$	−44.2857	−	58.2569i	−0.231863	−	0.305010i	0.665418	−	0.746471i	$-0.268253\pi$
$191$	−44.2857	−	58.2569i	−0.231863	−	0.305010i	−0.897280	+	0.441461i	$0.854460\pi$
$192$	13.5462	−	12.8316i	0.0705531	−	0.0668314i
$193$	−17.9562	−	331.182i	−0.0930372	−	1.71597i	−0.557333	−	0.830289i	$-0.688175\pi$
$193$	−17.9562	−	331.182i	−0.0930372	−	1.71597i	0.464296	−	0.885680i	$-0.346307\pi$
$194$	42.3930	−	25.5070i	0.218520	−	0.131479i
$195$	−24.7796	−	16.8010i	−0.127075	−	0.0861590i
$196$	−17.0260	+	61.3222i	−0.0868674	+	0.312868i
$197$	215.952	−	23.4862i	1.09620	−	0.119219i	0.457899	−	0.889004i	$-0.348602\pi$
$197$	215.952	−	23.4862i	1.09620	−	0.119219i	0.638303	+	0.769785i	$0.279637\pi$
$198$	11.7868	+	8.96012i	0.0595295	+	0.0452532i
$199$	−44.0318	−	20.3713i	−0.221265	−	0.102368i	0.306125	−	0.951991i	$-0.400967\pi$
$199$	−44.0318	−	20.3713i	−0.221265	−	0.102368i	−0.527390	+	0.849623i	$0.676829\pi$
$200$	−130.043	+	88.1716i	−0.650217	+	0.440858i
$201$	−7.92088	−	23.5083i	−0.0394074	−	0.116957i
$202$	−5.23847	−	31.9532i	−0.0259330	−	0.158184i
$203$	−8.03735	+	49.0257i	−0.0395929	+	0.241506i
$204$	19.5699	+	6.59386i	0.0959308	+	0.0323228i
$205$	−14.8110	−	53.3443i	−0.0722486	−	0.260216i
$206$	−24.4051	−	61.2523i	−0.118472	−	0.297341i
$207$	−46.4317	+	18.5001i	−0.224308	+	0.0893724i
$208$	−59.7456	+	16.5883i	−0.287238	+	0.0797513i
$209$	47.1173	−	139.839i	0.225442	−	0.669087i
$210$	−13.3071	−	2.18158i	−0.0633670	−	0.0103885i
$211$	185.108	−	30.3469i	0.877290	−	0.143824i	0.293724	−	0.955890i	$-0.405105\pi$
$211$	185.108	−	30.3469i	0.877290	−	0.143824i	0.583566	+	0.812066i	$0.301657\pi$
$212$	12.6694	−	4.26883i	0.0597614	−	0.0201360i
$213$	18.5274	+	27.3258i	0.0869830	+	0.128290i
$214$	53.0815	−	114.734i	0.248044	−	0.536139i
$215$	−6.74907	+	8.87825i	−0.0313910	+	0.0412942i
$216$	−3.87907	−	35.6675i	−0.0179587	−	0.165127i
$217$	74.2282	+	20.6094i	0.342065	+	0.0949740i
$218$	69.2079	−	102.074i	0.317467	−	0.468229i
$219$	−57.6937	−	95.8877i	−0.263442	−	0.437844i
$220$	22.8581	−	1.23933i	0.103900	−	0.00563331i
$221$	31.1419	+	32.8761i	0.140913	+	0.148760i
$222$	−41.3334	+	31.4208i	−0.186187	+	0.141535i
$223$	−24.3694	+	5.36412i	−0.109280	+	0.0240543i	−0.269274	−	0.963064i	$-0.586784\pi$
$223$	−24.3694	+	5.36412i	−0.109280	+	0.0240543i	0.159994	+	0.987118i	$0.448853\pi$
$224$	−132.765	+	112.772i	−0.592701	+	0.503445i
$225$	−3.69580	+	68.1650i	−0.0164258	+	0.302956i
$226$	−85.2153	−	160.733i	−0.377059	−	0.711209i
$227$	9.48997	−	43.1134i	0.0418060	−	0.189927i	−0.951090	−	0.308915i	$-0.900034\pi$
$227$	9.48997	−	43.1134i	0.0418060	−	0.189927i	0.992896	+	0.118988i	$0.0379651\pi$
$228$	−140.068	+	64.8025i	−0.614335	+	0.284221i
$229$	127.441	−	211.808i	0.556510	−	0.924927i	−0.443085	−	0.896479i	$-0.646116\pi$
$229$	127.441	−	211.808i	0.556510	−	0.924927i	0.999595	−	0.0284472i	$-0.00905624\pi$
$230$	11.4723	−	21.6391i	0.0498798	−	0.0940832i
$231$	−35.1664	−	29.8706i	−0.152236	−	0.129310i
$232$	44.5433	−	47.0238i	0.191997	−	0.202689i
$233$	−28.6557	+	263.485i	−0.122986	+	1.13084i	0.756194	+	0.654347i	$0.227056\pi$
$233$	−28.6557	+	263.485i	−0.122986	+	1.13084i	−0.879180	+	0.476489i	$0.841909\pi$
$234$	12.5685	−	31.5445i	0.0537114	−	0.134805i
$235$		−	17.4811i		−	0.0743876i
$236$	166.343	+	66.6635i	0.704842	+	0.282473i
$237$	176.635			0.745294
$238$	18.9481	+	7.54960i	0.0796137	+	0.0317210i
$239$	−109.139	−	11.8696i	−0.456648	−	0.0496634i	−0.123095	−	0.992395i	$-0.539282\pi$
$239$	−109.139	−	11.8696i	−0.456648	−	0.0496634i	−0.333553	+	0.942731i	$0.608248\pi$
$240$	−10.1267	−	9.59252i	−0.0421946	−	0.0399688i
$241$	−159.800	+	188.131i	−0.663069	+	0.780626i	−0.986170	−	0.165739i	$-0.946999\pi$
$241$	−159.800	+	188.131i	−0.663069	+	0.780626i	0.323100	+	0.946365i	$0.395275\pi$
$242$	82.9563	+	43.9807i	0.342795	+	0.181738i
$243$	−13.3571	−	8.03669i	−0.0549674	−	0.0330728i
$244$	60.3577	+	130.461i	0.247368	+	0.534676i
$245$	−30.6605	−	6.74888i	−0.125145	−	0.0275464i
$246$	55.4775	−	29.4123i	0.225518	−	0.119562i
$247$	−337.930	−	18.3220i	−1.36814	−	0.0741783i
$248$	−65.0219	−	76.5496i	−0.262185	−	0.308668i
$249$	41.1932	+	187.142i	0.165434	+	0.751576i
$250$	−42.4853	−	55.8884i	−0.169941	−	0.223554i
$251$	34.4008	−	32.5862i	0.137055	−	0.129825i	−0.616102	−	0.787667i	$-0.711289\pi$
$251$	34.4008	−	32.5862i	0.137055	−	0.129825i	0.753156	+	0.657841i	$0.228530\pi$
$252$	2.61257	+	48.1860i	0.0103673	+	0.191214i
$253$	71.8084	−	43.2057i	0.283828	−	0.170773i
$254$	149.687	+	101.490i	0.589317	+	0.399567i
$255$	−2.72532	+	9.81573i	−0.0106875	+	0.0384931i
$256$	160.861	−	17.4946i	0.628361	−	0.0683384i
$257$	−2.55756	−	1.94421i	−0.00995160	−	0.00756501i	0.600187	−	0.799860i	$-0.295093\pi$
$257$	−2.55756	−	1.94421i	−0.00995160	−	0.00756501i	−0.610138	+	0.792295i	$0.708886\pi$
$258$	−11.4799	−	5.31115i	−0.0444956	−	0.0205859i
$259$	133.922	−	90.8014i	0.517073	−	0.350584i
$260$	−16.7634	−	49.7520i	−0.0644747	−	0.191354i
$261$	−4.55294	−	27.7717i	−0.0174442	−	0.106405i
$262$	17.4619	−	106.513i	0.0666484	−	0.406537i
$263$	209.037	+	70.4329i	0.794819	+	0.267806i	0.687278	−	0.726395i	$-0.258806\pi$
$263$	209.037	+	70.4329i	0.794819	+	0.267806i	0.107541	+	0.994201i	$0.465702\pi$
$264$	16.0936	+	57.9637i	0.0609604	+	0.219560i
$265$	2.44107	+	6.12664i	0.00921160	+	0.0231194i
$266$	−141.607	+	56.4212i	−0.532355	+	0.212110i
$267$	158.948	−	44.1318i	0.595312	−	0.165287i
$268$	13.8902	−	41.2246i	0.0518290	−	0.153823i
$269$	−75.9700	−	12.4546i	−0.282416	−	0.0462998i	0.0189090	−	0.999821i	$-0.493981\pi$
$269$	−75.9700	−	12.4546i	−0.282416	−	0.0462998i	−0.301325	+	0.953521i	$0.597429\pi$
$270$	7.53809	−	1.23581i	0.0279189	−	0.00457706i
$271$	−368.573	+	124.187i	−1.36005	+	0.458254i	−0.902408	−	0.430883i	$-0.858202\pi$
$271$	−368.573	+	124.187i	−1.36005	+	0.458254i	−0.457642	+	0.889137i	$0.651306\pi$
$272$	11.8402	+	17.4630i	0.0435303	+	0.0642023i
$273$	−44.4324	+	96.0391i	−0.162756	+	0.351792i
$274$	−128.241	+	168.698i	−0.468033	+	0.615687i
$275$	−12.3754	−	113.789i	−0.0450013	−	0.413780i
$276$	−84.4537	−	23.4484i	−0.305992	−	0.0849581i
$277$	−40.1182	+	59.1699i	−0.144831	+	0.213610i	−0.893184	−	0.449690i	$-0.851534\pi$
$277$	−40.1182	+	59.1699i	−0.144831	+	0.213610i	0.748354	+	0.663300i	$0.230845\pi$
$278$	40.2981	+	66.9760i	0.144957	+	0.240921i
$279$	−43.5749	+	2.36256i	−0.156182	+	0.00846796i
$280$	−37.6781	−	39.7763i	−0.134565	−	0.142058i
$281$	331.493	−	251.994i	1.17969	−	0.896777i	0.183418	−	0.983035i	$-0.441284\pi$
$281$	331.493	−	251.994i	1.17969	−	0.896777i	0.996273	+	0.0862577i	$0.0274909\pi$
$282$	19.3635	−	4.26224i	0.0686650	−	0.0151143i
$283$	−165.030	+	140.178i	−0.583146	+	0.495329i	−0.889713	−	0.456520i	$-0.849096\pi$
$283$	−165.030	+	140.178i	−0.583146	+	0.495329i	0.306567	+	0.951849i	$0.400820\pi$
$284$	−3.13437	+	57.8100i	−0.0110365	+	0.203556i
$285$	−35.6608	−	67.2635i	−0.125126	−	0.236012i
$286$	−12.2392	+	55.6033i	−0.0427945	+	0.194417i
$287$	−177.596	+	82.1648i	−0.618803	+	0.286289i
$288$	50.8732	−	84.5519i	0.176643	−	0.293583i
$289$	−128.152	+	241.721i	−0.443434	+	0.836405i
$290$	10.5106	+	8.92777i	0.0362434	+	0.0307854i
$291$	60.0634	−	63.4082i	0.206404	−	0.217898i
$292$	21.2173	−	195.090i	0.0726621	−	0.668117i
$293$	−162.978	+	409.044i	−0.556239	+	1.39605i	0.334870	+	0.942264i	$0.391308\pi$
$293$	−162.978	+	409.044i	−0.556239	+	1.39605i	−0.891109	+	0.453790i	$0.850072\pi$
$294$		−	35.6077i		−	0.121115i
$295$	−28.3943	+	83.7166i	−0.0962519	+	0.283785i
$296$	−210.953			−0.712679
$297$	24.2809	+	9.67439i	0.0817538	+	0.0325737i
$298$	214.374	+	23.3146i	0.719376	+	0.0782368i
$299$	−139.536	−	132.175i	−0.466675	−	0.442058i
$300$	−77.4991	+	91.2389i	−0.258330	+	0.304130i
$301$	34.8268	+	18.4640i	0.115704	+	0.0613422i
$302$	−91.3160	−	54.9430i	−0.302371	−	0.181931i
$303$	−24.0013	−	51.8780i	−0.0792122	−	0.171214i
$304$	−153.991	−	33.8961i	−0.506551	−	0.111500i
$305$	−62.6499	+	33.2149i	−0.205409	+	0.108901i
$306$	−11.5372	−	0.625531i	−0.0377034	−	0.00204422i
$307$	240.557	+	283.206i	0.783575	+	0.922495i	0.998534	−	0.0541276i	$-0.0172378\pi$
$307$	240.557	+	283.206i	0.783575	+	0.922495i	−0.214959	+	0.976623i	$0.568962\pi$
$308$	−17.3938	−	79.0207i	−0.0564733	−	0.256561i
$309$	−70.4408	−	92.6633i	−0.227964	−	0.299881i
$310$	15.5248	−	14.7058i	0.0500799	−	0.0474382i
$311$	−12.7207	−	234.619i	−0.0409025	−	0.754403i	−0.944999	−	0.327074i	$-0.893937\pi$
$311$	−12.7207	−	234.619i	−0.0409025	−	0.754403i	0.904096	−	0.427329i	$-0.140545\pi$
$312$	118.216	−	71.1280i	0.378896	−	0.227974i
$313$	289.414	+	196.227i	0.924644	+	0.626924i	0.927803	−	0.373071i	$-0.121695\pi$
$313$	289.414	+	196.227i	0.924644	+	0.626924i	−0.00315862	+	0.999995i	$0.501005\pi$
$314$	15.7959	−	56.8915i	0.0503053	−	0.181183i
$315$	−23.6654	+	2.57377i	−0.0751284	+	0.00817070i
$316$	246.589	+	187.452i	0.780346	+	0.593203i
$317$	493.430	+	228.285i	1.55656	+	0.720142i	0.994280	−	0.106803i	$-0.0340615\pi$
$317$	493.430	+	228.285i	1.55656	+	0.720142i	0.562282	+	0.826946i	$0.309924\pi$
$318$	−6.19120	+	4.19774i	−0.0194692	+	0.0132004i
$319$	15.0667	+	44.7165i	0.0472312	+	0.140177i
$320$	2.61130	+	15.9282i	0.00816032	+	0.0497757i
$321$	36.1048	−	220.229i	0.112476	−	0.686073i
$322$	−82.0380	−	27.6418i	−0.254776	−	0.0858442i
$323$	30.8074	+	110.958i	0.0953789	+	0.343524i
$324$	−10.1181	−	25.3946i	−0.0312289	−	0.0783785i
$325$	−243.862	+	97.1637i	−0.750346	+	0.298965i
$326$	−133.614	+	37.0977i	−0.409858	+	0.113797i
$327$	69.5144	−	206.311i	0.212582	−	0.630922i
$328$	251.764	+	41.2746i	0.767573	+	0.125837i
$329$	−60.9743	+	9.99623i	−0.185332	+	0.0303837i
$330$	−12.1374	+	4.08958i	−0.0367801	+	0.0123927i
$331$	219.354	+	323.523i	0.662700	+	0.977410i	0.999360	+	0.0357833i	$0.0113926\pi$
$331$	219.354	+	323.523i	0.662700	+	0.977410i	−0.336659	+	0.941627i	$0.609297\pi$
$332$	−141.096	+	304.974i	−0.424988	+	0.918597i
$333$	−55.4682	+	72.9672i	−0.166571	+	0.219121i
$334$	9.33820	+	85.8633i	0.0279587	+	0.257076i
$335$	20.6771	+	5.74098i	0.0617228	+	0.0171373i
$336$	−27.6681	+	40.8074i	−0.0823456	+	0.121451i
$337$	66.0180	+	109.723i	0.195899	+	0.325587i	0.939200	−	0.343370i	$-0.111569\pi$
$337$	66.0180	+	109.723i	0.195899	+	0.325587i	−0.743301	+	0.668957i	$0.766741\pi$
$338$	−35.1875	+	1.90781i	−0.104105	+	0.00564441i
$339$	−220.860	−	233.159i	−0.651506	−	0.687786i
$340$	−14.2215	+	10.8109i	−0.0418280	+	0.0317968i
$341$	71.4589	−	15.7293i	0.209557	−	0.0461269i
$342$	65.8120	−	55.9012i	0.192433	−	0.163454i
$343$	−20.0567	+	369.924i	−0.0584743	+	1.07849i
$344$	−24.0728	−	45.4062i	−0.0699792	−	0.131995i
$345$	9.29464	−	42.2260i	0.0269410	−	0.122394i
$346$	−290.486	+	134.393i	−0.839555	+	0.388419i
$347$	182.273	−	302.940i	0.525283	−	0.873027i	−0.474692	−	0.880152i	$-0.657440\pi$
$347$	182.273	−	302.940i	0.525283	−	0.873027i	0.999975	+	0.00712528i	$0.00226807\pi$
$348$	23.1164	−	43.6022i	0.0664265	−	0.125294i
$349$	−315.800	−	268.243i	−0.904872	−	0.768606i	0.0685440	−	0.997648i	$-0.478165\pi$
$349$	−315.800	−	268.243i	−0.904872	−	0.768606i	−0.973416	+	0.229043i	$0.926441\pi$
$350$	−81.3117	+	85.8397i	−0.232319	+	0.245256i
$351$	6.48107	−	59.5924i	0.0184646	−	0.169779i
$352$	−61.2401	+	153.701i	−0.173977	+	0.436651i
$353$		−	512.108i		−	1.45073i	−0.688364	−	0.725366i	$-0.741671\pi$
$353$		−	512.108i		−	1.45073i	0.688364	−	0.725366i	$-0.258329\pi$
$354$	−99.6548	−	11.0402i	−0.281511	−	0.0311870i
$355$	−28.5595			−0.0804492
$356$	268.733	+	107.073i	0.754867	+	0.300766i
$357$	35.7959	+	3.89304i	0.100269	+	0.0109049i
$358$	86.5205	+	81.9566i	0.241677	+	0.228929i
$359$	−199.073	+	234.367i	−0.554520	+	0.652832i	−0.965986	−	0.258593i	$-0.916741\pi$
$359$	−199.073	+	234.367i	−0.554520	+	0.652832i	0.411466	+	0.911425i	$0.365017\pi$
$360$	27.4209	+	14.5376i	0.0761691	+	0.0403823i
$361$	−428.090	−	257.573i	−1.18584	−	0.713498i
$362$	−7.86652	−	17.0032i	−0.0217307	−	0.0469702i
$363$	161.878	+	35.6321i	0.445946	+	0.0981602i
$364$	−163.950	+	86.9209i	−0.450413	+	0.238794i
$365$	96.6631	+	5.24092i	0.264831	+	0.0143587i
$366$	−52.0669	−	61.2979i	−0.142259	−	0.167481i
$367$	−7.62496	−	34.6405i	−0.0207765	−	0.0943884i	0.965091	−	0.261913i	$-0.0843535\pi$
$367$	−7.62496	−	34.6405i	−0.0207765	−	0.0943884i	−0.985868	+	0.167525i	$0.946422\pi$
$368$	−54.1924	−	71.2889i	−0.147262	−	0.193720i
$369$	80.4756	−	76.2305i	0.218091	−	0.206587i
$370$	−2.43159	−	44.8481i	−0.00657187	−	0.121211i
$371$	19.9739	−	12.0179i	0.0538381	−	0.0323933i
$372$	−63.3395	−	42.9453i	−0.170268	−	0.115444i
$373$	−63.2597	+	227.841i	−0.169597	+	0.610834i	0.829066	+	0.559150i	$0.188872\pi$
$373$	−63.2597	+	227.841i	−0.169597	+	0.610834i	−0.998664	+	0.0516835i	$0.983541\pi$
$374$	19.2594	−	2.09458i	0.0514957	−	0.00560049i
$375$	−98.6616	−	75.0006i	−0.263098	−	0.200002i
$376$	73.1123	+	33.8253i	0.194447	+	0.0899610i
$377$	89.5716	−	60.7310i	0.237590	−	0.161090i
$378$	−8.62104	−	25.5863i	−0.0228070	−	0.0676887i
$379$	34.3997	+	209.829i	0.0907644	+	0.553638i	0.992587	+	0.121533i	$0.0387809\pi$
$379$	34.3997	+	209.829i	0.0907644	+	0.553638i	−0.901823	+	0.432106i	$0.857771\pi$
$380$	21.5989	−	131.747i	0.0568391	−	0.346703i
$381$	302.546	+	101.940i	0.794083	+	0.267558i
$382$	19.2082	+	69.1819i	0.0502834	+	0.181104i
$383$	−85.5999	−	214.840i	−0.223498	−	0.560939i	0.773878	−	0.633335i	$-0.218315\pi$
$383$	−85.5999	−	214.840i	−0.223498	−	0.560939i	−0.997376	+	0.0723966i	$0.976935\pi$
$384$	194.692	−	77.5726i	0.507012	−	0.202012i
$385$	38.4591	−	10.6781i	0.0998937	−	0.0277353i
$386$	−103.906	+	308.381i	−0.269186	+	0.798915i
$387$	−22.0354	−	3.61252i	−0.0569391	−	0.00933468i
$388$	151.142	−	24.7785i	0.389542	−	0.0638622i
$389$	−195.468	+	65.8607i	−0.502488	+	0.169308i	−0.559119	−	0.829087i	$-0.688861\pi$
$389$	−195.468	+	65.8607i	−0.502488	+	0.169308i	0.0566314	+	0.998395i	$0.481964\pi$
$390$	16.4843	+	24.3125i	0.0422673	+	0.0623397i
$391$	−27.4604	+	59.3547i	−0.0702312	+	0.151802i
$392$	87.5533	−	115.174i	0.223350	−	0.293812i
$393$	−20.6010	−	189.423i	−0.0524200	−	0.481994i
$394$	−205.362	−	57.0184i	−0.521222	−	0.144717i
$395$	−85.7487	+	126.470i	−0.217085	+	0.320177i
$396$	23.6302	+	39.2737i	0.0596723	+	0.0991761i
$397$	472.660	−	25.6269i	1.19058	−	0.0645514i	0.551824	−	0.833960i	$-0.313932\pi$
$397$	472.660	−	25.6269i	1.19058	−	0.0645514i	0.638756	+	0.769409i	$0.279449\pi$
$398$	32.7354	+	34.5583i	0.0822496	+	0.0868299i
$399$	−214.224	+	162.849i	−0.536903	+	0.408143i
$400$	−119.446	+	26.2921i	−0.298616	+	0.0657303i
$401$	−138.397	+	117.556i	−0.345131	+	0.293157i	−0.803139	−	0.595791i	$-0.796839\pi$
$401$	−138.397	+	117.556i	−0.345131	+	0.293157i	0.458009	+	0.888948i	$0.348563\pi$
$402$	−1.31770	+	24.3036i	−0.00327786	+	0.0604566i
$403$	−78.6031	−	148.261i	−0.195045	−	0.367894i
$404$	21.5483	−	97.8949i	0.0533374	−	0.242314i
$405$	12.2385	−	5.66215i	0.0302186	−	0.0139806i
$406$	25.1299	−	41.7663i	0.0618964	−	0.102873i
$407$	71.9855	−	135.779i	0.176869	−	0.333609i
$408$	−35.7796	−	30.3914i	−0.0876950	−	0.0744888i
$409$	−10.0727	+	10.6336i	−0.0246275	+	0.0259990i	−0.738193	−	0.674590i	$-0.764321\pi$
$409$	−10.0727	+	10.6336i	−0.0246275	+	0.0259990i	0.713565	+	0.700589i	$0.247079\pi$
$410$	−5.87286	+	54.0001i	−0.0143241	+	0.131708i
$411$	−138.464	+	347.519i	−0.336896	+	0.845544i
$412$		−	204.116i		−	0.495428i
$413$	308.242	+	51.1681i	0.746348	+	0.123894i
$414$	49.0393			0.118453
$415$	−153.991	−	61.3556i	−0.371062	−	0.147845i
$416$	377.227	+	41.0259i	0.906796	+	0.0986200i
$417$	100.178	+	94.8934i	0.240234	+	0.227562i
$418$	−93.7298	+	110.347i	−0.224234	+	0.263989i
$419$	−192.996	−	102.320i	−0.460612	−	0.244201i	0.221909	−	0.975067i	$-0.428771\pi$
$419$	−192.996	−	102.320i	−0.460612	−	0.244201i	−0.682520	+	0.730867i	$0.739116\pi$
$420$	−35.7693	−	21.5217i	−0.0851650	−	0.0512421i
$421$	133.281	+	288.083i	0.316583	+	0.684283i	0.998906	−	0.0467683i	$-0.0148922\pi$
$421$	133.281	+	288.083i	0.316583	+	0.684283i	−0.682323	+	0.731051i	$0.739030\pi$
$422$	−179.740	−	39.5638i	−0.425924	−	0.0937530i
$423$	30.9241	−	16.3949i	0.0731067	−	0.0387587i
$424$	−30.3472	−	1.64538i	−0.0715736	−	0.00388061i
$425$	57.8262	+	68.0782i	0.136062	+	0.160184i
$426$	−6.96337	−	31.6349i	−0.0163459	−	0.0742603i
$427$	151.679	+	199.531i	0.355221	+	0.467285i
$428$	284.121	−	269.133i	0.663833	−	0.628816i
$429$	5.44140	+	100.361i	0.0126839	+	0.233941i
$430$	9.37576	−	5.64121i	0.0218041	−	0.0131191i
$431$	601.615	+	407.905i	1.39586	+	0.946416i	0.999600	+	0.0282765i	$0.00900190\pi$
$431$	601.615	+	407.905i	1.39586	+	0.946416i	0.396258	+	0.918139i	$0.370308\pi$
$432$	7.47172	−	26.9107i	0.0172957	−	0.0622933i
$433$	−6.49928	+	0.706839i	−0.0150099	+	0.00163242i	−0.115621	−	0.993293i	$-0.536886\pi$
$433$	−6.49928	+	0.706839i	−0.0150099	+	0.00163242i	0.100611	+	0.994926i	$0.467920\pi$
$434$	−60.1718	−	45.7414i	−0.138645	−	0.105395i
$435$	22.0947	+	10.2221i	0.0507924	+	0.0234991i
$436$	315.991	−	214.247i	0.724751	−	0.491393i
$437$	−156.060	−	463.170i	−0.357117	−	1.05988i
$438$	17.7631	+	108.350i	0.0405551	+	0.247375i
$439$	39.8497	−	243.073i	0.0907739	−	0.553696i	−0.901810	−	0.432133i	$-0.857761\pi$
$439$	39.8497	−	243.073i	0.0907739	−	0.553696i	0.992584	−	0.121563i	$-0.0387907\pi$
$440$	−49.3146	−	16.6160i	−0.112079	−	0.0377637i
$441$	−16.8167	−	60.5681i	−0.0381330	−	0.137343i
$442$	−16.4454	−	41.2748i	−0.0372068	−	0.0933819i
$443$	−48.5649	+	19.3500i	−0.109627	+	0.0436795i	−0.424307	−	0.905518i	$-0.639482\pi$
$443$	−48.5649	+	19.3500i	−0.109627	+	0.0436795i	0.314680	+	0.949198i	$0.398103\pi$
$444$	−154.872	+	42.9999i	−0.348810	+	0.0968466i
$445$	−45.5645	+	135.230i	−0.102392	+	0.303889i
$446$	24.1599	+	3.96081i	0.0541701	+	0.00888074i
$447$	375.658	−	61.5860i	0.840398	−	0.137776i
$448$	54.0648	−	18.2165i	0.120680	−	0.0406619i
$449$	−32.0031	−	47.2011i	−0.0712764	−	0.105125i	0.790380	−	0.612617i	$-0.209883\pi$
$449$	−32.0031	−	47.2011i	−0.0712764	−	0.105125i	−0.861657	+	0.507492i	$0.830573\pi$
$450$	28.1234	−	60.7877i	0.0624965	−	0.135084i
$451$	−112.478	+	147.962i	−0.249397	+	0.328076i
$452$	−60.8913	−	559.886i	−0.134715	−	1.23869i
$453$	−181.275	−	50.3309i	−0.400166	−	0.111106i
$454$	−24.3068	+	35.8499i	−0.0535392	+	0.0789645i
$455$	−47.1936	−	78.4364i	−0.103722	−	0.172388i
$456$	350.323	−	18.9940i	0.768252	−	0.0416534i
$457$	−295.687	−	312.153i	−0.647018	−	0.683048i	0.317140	−	0.948379i	$-0.397278\pi$
$457$	−295.687	−	312.153i	−0.647018	−	0.683048i	−0.964158	+	0.265330i	$0.914519\pi$
$458$	−193.078	+	146.774i	−0.421568	+	0.320467i
$459$	−19.9201	+	4.38474i	−0.0433989	+	0.00955281i
$460$	57.7877	−	49.0853i	0.125625	−	0.106707i
$461$	32.3530	−	596.716i	0.0701801	−	1.29439i	−0.725308	−	0.688425i	$-0.758302\pi$
$461$	32.3530	−	596.716i	0.0701801	−	1.29439i	0.795488	−	0.605970i	$-0.207215\pi$
$462$	21.2051	+	39.9970i	0.0458985	+	0.0865737i
$463$	144.451	−	656.247i	0.311989	−	1.41738i	−0.515977	−	0.856602i	$-0.672571\pi$
$463$	144.451	−	656.247i	0.311989	−	1.41738i	0.827966	−	0.560778i	$-0.189498\pi$
$464$	45.7607	−	21.1711i	0.0986221	−	0.0456275i
$465$	19.4622	−	32.3464i	0.0418541	−	0.0695621i
$466$	121.806	−	229.750i	0.261386	−	0.493026i
$467$	−155.560	−	132.134i	−0.333106	−	0.282943i	0.465187	−	0.885213i	$-0.345987\pi$
$467$	−155.560	−	132.134i	−0.333106	−	0.282943i	−0.798292	+	0.602270i	$0.794263\pi$
$468$	72.2898	−	76.3154i	0.154465	−	0.163067i
$469$	8.20080	−	75.4052i	0.0174857	−	0.160779i
$470$	−6.34843	+	15.9334i	−0.0135073	+	0.0339008i
$471$		−	104.232i		−	0.221299i
$472$	−295.191	−	280.744i	−0.625405	−	0.594797i
$473$	37.4401			0.0791546
$474$	−160.996	−	64.1467i	−0.339654	−	0.135331i
$475$	−663.630	−	72.1741i	−1.39712	−	0.151946i
$476$	45.8410	+	43.4229i	0.0963047	+	0.0912246i
$477$	−8.54865	+	10.0643i	−0.0179217	+	0.0210991i
$478$	95.1655	+	50.4536i	0.199091	+	0.105551i
$479$	−763.470	−	459.365i	−1.59388	−	0.959008i	−0.986340	−	0.164722i	$-0.947327\pi$
$479$	−763.470	−	459.365i	−1.59388	−	0.959008i	−0.607544	−	0.794286i	$-0.707845\pi$
$480$	35.8421	+	77.4714i	0.0746710	+	0.161399i
$481$	−344.216	−	75.7676i	−0.715625	−	0.157521i
$482$	213.973	−	113.441i	0.443928	−	0.235356i
$483$	−152.600	−	8.27373i	−0.315942	−	0.0171299i
$484$	188.175	+	221.536i	0.388790	+	0.457719i
$485$	16.2418	+	73.7872i	0.0334882	+	0.152139i
$486$	9.25589	+	12.1759i	0.0190450	+	0.0250533i
$487$	547.896	−	518.995i	1.12504	−	1.06570i	0.127777	−	0.991803i	$-0.459216\pi$
$487$	547.896	−	518.995i	1.12504	−	1.06570i	0.997266	−	0.0738942i	$-0.0235427\pi$
$488$	−17.6912	−	326.294i	−0.0362524	−	0.668636i
$489$	−209.755	+	126.205i	−0.428946	+	0.258088i
$490$	25.4950	+	17.2860i	0.0520306	+	0.0352776i
$491$	163.543	−	589.027i	0.333081	−	1.19965i	−0.587542	−	0.809194i	$-0.699904\pi$
$491$	163.543	−	589.027i	0.333081	−	1.19965i	0.920622	−	0.390454i	$-0.127682\pi$
$492$	193.246	−	21.0168i	0.392777	−	0.0427171i
$493$	−29.3149	−	22.2846i	−0.0594622	−	0.0452020i
$494$	301.357	+	139.423i	0.610035	+	0.282232i
$495$	−18.7142	+	12.6885i	−0.0378064	+	0.0256334i
$496$	−24.9645	−	74.0919i	−0.0503316	−	0.149379i
$497$	16.3312	+	99.6159i	0.0328596	+	0.200434i
$498$	30.4166	−	185.533i	0.0610776	−	0.372557i
$499$	292.878	+	98.6820i	0.586929	+	0.197760i	0.597070	−	0.802189i	$-0.296331\pi$
$499$	292.878	+	98.6820i	0.586929	+	0.197760i	−0.0101407	+	0.999949i	$0.503228\pi$
$500$	−58.1417	−	209.408i	−0.116283	−	0.418815i
$501$	56.4353	+	141.642i	0.112645	+	0.282718i
$502$	−43.1891	+	17.2081i	−0.0860340	+	0.0342791i
$503$	−314.082	+	87.2044i	−0.624417	+	0.173369i	−0.565304	−	0.824883i	$-0.691241\pi$
$503$	−314.082	+	87.2044i	−0.624417	+	0.173369i	−0.0591132	+	0.998251i	$0.518827\pi$
$504$	35.0274	−	103.958i	0.0694988	−	0.206265i
$505$	48.7961	+	7.99971i	0.0966258	+	0.0158410i
$506$	−81.1413	+	13.3024i	−0.160358	+	0.0262894i
$507$	−58.9524	+	19.8634i	−0.116277	+	0.0391782i
$508$	314.184	+	463.386i	0.618471	+	0.912177i
$509$	−243.194	+	525.654i	−0.477787	+	1.03272i	0.507475	+	0.861667i	$0.330579\pi$
$509$	−243.194	+	525.654i	−0.477787	+	1.03272i	−0.985262	+	0.171053i	$0.945283\pi$
$510$	6.04872	−	7.95695i	0.0118602	−	0.0156019i
$511$	−36.9946	−	340.160i	−0.0723965	−	0.665675i
$512$	313.385	+	87.0108i	0.612079	+	0.169943i
$513$	85.5443	−	126.168i	0.166753	−	0.245942i
$514$	1.62506	+	2.70088i	0.00316160	+	0.00525463i
$515$	100.543	−	5.45126i	0.195228	−	0.0105850i
$516$	−26.9286	−	28.4281i	−0.0521871	−	0.0550933i
$517$	−46.7203	+	35.5158i	−0.0903681	+	0.0686960i
$518$	−155.040	+	34.1270i	−0.299306	+	0.0658822i
$519$	−430.642	+	365.790i	−0.829752	+	0.704798i
$520$	−6.46130	+	119.172i	−0.0124256	+	0.229176i
$521$	51.7805	+	97.6684i	0.0993868	+	0.187463i	0.928219	−	0.372033i	$-0.121339\pi$
$521$	51.7805	+	97.6684i	0.0993868	+	0.187463i	−0.828833	+	0.559497i	$0.810994\pi$
$522$	−5.93574	+	26.9664i	−0.0113712	+	0.0516597i
$523$	276.874	−	128.095i	0.529395	−	0.244924i	−0.136936	−	0.990580i	$-0.543726\pi$
$523$	276.874	−	128.095i	0.529395	−	0.244924i	0.666332	+	0.745656i	$0.267864\pi$
$524$	172.264	−	286.305i	0.328749	−	0.546385i
$525$	−97.7699	+	184.414i	−0.186228	+	0.351264i
$526$	−164.952	−	140.111i	−0.313596	−	0.266371i
$527$	−39.2676	+	41.4543i	−0.0745116	+	0.0786609i
$528$	−5.06302	+	46.5537i	−0.00958905	+	0.0881699i
$529$	−93.0626	+	233.569i	−0.175922	+	0.441530i
$530$		−	6.47071i		−	0.0122089i
$531$	−174.725	+	28.2854i	−0.329050	+	0.0532681i
$532$	−471.888			−0.887007
$533$	395.983	+	157.774i	0.742932	+	0.296011i
$534$	−160.902	−	17.4992i	−0.301315	−	0.0327700i
$535$	140.156	+	132.763i	0.261974	+	0.248155i
$536$	−64.0205	+	75.3708i	−0.119441	+	0.140617i
$537$	185.876	+	98.5453i	0.346138	+	0.183511i
$538$	64.7208	+	38.9412i	0.120299	+	0.0723815i
$539$	44.2549	+	95.6553i	0.0821055	+	0.177468i
$540$	23.0944	+	5.08346i	0.0427674	+	0.00941382i
$541$	−443.242	+	234.992i	−0.819301	+	0.434366i	−0.824666	−	0.565619i	$-0.808637\pi$
$541$	−443.242	+	234.992i	−0.819301	+	0.434366i	0.00536495	+	0.999986i	$0.498292\pi$
$542$	381.041	+	20.6594i	0.703028	+	0.0381170i
$543$	−21.4110	−	25.2070i	−0.0394310	−	0.0464218i
$544$	−27.7559	−	126.097i	−0.0510220	−	0.231795i
$545$	113.972	+	149.928i	0.209123	+	0.275096i
$546$	75.3761	−	71.4001i	0.138052	−	0.130769i
$547$	14.3666	+	264.976i	0.0262643	+	0.484417i	0.981845	+	0.189687i	$0.0607472\pi$
$547$	14.3666	+	264.976i	0.0262643	+	0.484417i	−0.955580	+	0.294731i	$0.904770\pi$
$548$	−562.103	+	338.206i	−1.02573	+	0.617164i
$549$	−117.515	−	79.6769i	−0.214052	−	0.145131i
$550$	−30.0441	+	108.209i	−0.0546257	+	0.196744i
$551$	273.583	−	29.7539i	0.496521	−	0.0539999i
$552$	158.620	+	120.579i	0.287354	+	0.218441i
$553$	490.163	+	226.774i	0.886371	+	0.410079i
$554$	58.0544	−	39.3618i	0.104791	−	0.0710503i
$555$	−25.3168	−	75.1375i	−0.0456158	−	0.135383i
$556$	39.1473	+	238.788i	0.0704087	+	0.429474i
$557$	−158.357	+	965.936i	−0.284304	+	1.73418i	0.329001	+	0.944330i	$0.393288\pi$
$557$	−158.357	+	965.936i	−0.284304	+	1.73418i	−0.613304	+	0.789847i	$0.710160\pi$
$558$	40.5749	+	13.6713i	0.0727149	+	0.0245005i
$559$	−22.9716	−	82.7363i	−0.0410941	−	0.148008i
$560$	−15.7863	−	39.6206i	−0.0281898	−	0.0707510i
$561$	31.7707	−	12.6586i	0.0566323	−	0.0225644i
$562$	−393.658	+	109.299i	−0.700459	+	0.194482i
$563$	−262.555	+	779.234i	−0.466349	+	1.38407i	0.414229	+	0.910173i	$0.364051\pi$
$563$	−262.555	+	779.234i	−0.466349	+	1.38407i	−0.880578	+	0.473902i	$0.842845\pi$
$564$	60.5703	+	9.93000i	0.107394	+	0.0176064i
$565$	274.160	−	44.9462i	0.485238	−	0.0795508i
$566$	201.326	−	67.8347i	0.355700	−	0.119849i
$567$	−26.7481	−	39.4505i	−0.0471747	−	0.0695775i
$568$	55.2616	−	119.446i	0.0972916	−	0.210292i
$569$	229.241	−	301.562i	0.402885	−	0.529986i	−0.549253	−	0.835656i	$-0.685088\pi$
$569$	229.241	−	301.562i	0.402885	−	0.529986i	0.952137	+	0.305671i	$0.0988806\pi$
$570$	8.07613	+	74.2588i	0.0141686	+	0.130279i
$571$	797.749	+	221.494i	1.39711	+	0.387905i	0.882820	−	0.469711i	$-0.155642\pi$
$571$	797.749	+	221.494i	1.39711	+	0.387905i	0.514289	+	0.857617i	$0.328056\pi$
$572$	−98.9106	+	145.882i	−0.172921	+	0.255039i
$573$	65.3459	+	108.606i	0.114042	+	0.189539i
$574$	191.712	−	10.3943i	0.333992	−	0.0181085i
$575$	−260.714	−	275.233i	−0.453417	−	0.478666i
$576$	−25.7281	+	19.5580i	−0.0446668	+	0.0339548i
$577$	−563.197	+	123.969i	−0.976078	+	0.214851i	−0.674243	−	0.738509i	$-0.735530\pi$
$577$	−563.197	+	123.969i	−0.976078	+	0.214851i	−0.301835	+	0.953360i	$0.597599\pi$
$578$	204.590	−	173.780i	0.353962	−	0.300658i
$579$	−31.1010	+	573.624i	−0.0537150	+	0.990715i
$580$	19.9970	+	37.7183i	0.0344775	+	0.0650315i
$581$	−125.953	+	572.208i	−0.216786	+	0.984868i
$582$	−77.7730	+	35.9816i	−0.133631	+	0.0618241i
$583$	11.4147	−	18.9714i	0.0195793	−	0.0325410i
$584$	−208.960	+	394.140i	−0.357807	+	0.674896i
$585$	39.5217	+	33.5700i	0.0675584	+	0.0573846i
$586$	297.097	−	313.641i	0.506991	−	0.535224i
$587$	−117.906	+	1084.12i	−0.200861	+	1.84689i	0.267756	+	0.963487i	$0.413718\pi$
$587$	−117.906	+	1084.12i	−0.200861	+	1.84689i	−0.468617	+	0.883402i	$0.655248\pi$
$588$	40.8007	−	102.402i	0.0693890	−	0.174153i
$589$		−	426.731i		−	0.724501i
$590$	56.2829	−	65.9929i	0.0953948	−	0.111852i
$591$	−376.245			−0.636625
$592$	−152.551	−	60.7820i	−0.257688	−	0.102672i
$593$	−1176.14	−	127.912i	−1.98336	−	0.215704i	−0.999277	−	0.0380228i	$-0.987894\pi$
$593$	−1176.14	−	127.912i	−1.98336	−	0.215704i	−0.984088	−	0.177681i	$-0.943140\pi$
$594$	−18.6178	−	17.6357i	−0.0313431	−	0.0296897i
$595$	−20.1648	+	23.7398i	−0.0338904	+	0.0398989i
$596$	589.791	+	312.687i	0.989582	+	0.524643i
$597$	72.0034	+	43.3230i	0.120609	+	0.0725678i
$598$	79.1809	+	171.147i	0.132410	+	0.286199i
$599$	−900.699	−	198.259i	−1.50367	−	0.330983i	−0.614632	−	0.788814i	$-0.710696\pi$
$599$	−900.699	−	198.259i	−1.50367	−	0.330983i	−0.889039	+	0.457831i	$0.848627\pi$
$600$	240.433	−	127.470i	0.400722	−	0.212449i
$601$	−298.907	−	16.2063i	−0.497350	−	0.0269655i	−0.196242	−	0.980556i	$-0.562874\pi$
$601$	−298.907	−	16.2063i	−0.497350	−	0.0269655i	−0.301108	+	0.953590i	$0.597357\pi$
$602$	−25.0380	−	29.4770i	−0.0415913	−	0.0489651i
$603$	9.23660	+	41.9623i	0.0153177	+	0.0695892i
$604$	−199.654	−	262.641i	−0.330554	−	0.434836i
$605$	−104.098	+	98.6065i	−0.172062	+	0.162986i
$606$	3.03630	+	56.0012i	0.00501039	+	0.0924112i
$607$	182.361	−	109.723i	0.300430	−	0.180763i	−0.357355	−	0.933969i	$-0.616321\pi$
$607$	182.361	−	109.723i	0.300430	−	0.180763i	0.657785	+	0.753206i	$0.271494\pi$
$608$	798.662	+	541.506i	1.31359	+	0.890635i
$609$	23.0204	−	82.9121i	0.0378004	−	0.136145i
$610$	69.1654	−	7.52219i	0.113386	−	0.0123315i
$611$	107.150	+	81.4529i	0.175367	+	0.133311i
$612$	−32.4625	−	15.0188i	−0.0530433	−	0.0245405i
$613$	619.825	−	420.252i	1.01113	−	0.685565i	0.0612346	−	0.998123i	$-0.480496\pi$
$613$	619.825	−	420.252i	1.01113	−	0.685565i	0.949899	+	0.312558i	$0.101186\pi$
$614$	−116.410	−	345.493i	−0.189593	−	0.562692i
$615$	15.5133	+	94.6269i	0.0252249	+	0.153865i
$616$	−29.7573	+	181.512i	−0.0483074	+	0.294662i
$617$	287.352	+	96.8200i	0.465724	+	0.156921i	0.542374	−	0.840137i	$-0.317526\pi$
$617$	287.352	+	96.8200i	0.465724	+	0.156921i	−0.0766497	+	0.997058i	$0.524422\pi$
$618$	30.5526	+	110.040i	0.0494378	+	0.178059i
$619$	451.301	+	1132.68i	0.729080	+	1.82985i	0.525496	+	0.850796i	$0.323880\pi$
$619$	451.301	+	1132.68i	0.729080	+	1.82985i	0.203585	+	0.979057i	$0.434741\pi$
$620$	61.4973	−	24.5028i	0.0991892	−	0.0395206i
$621$	83.4152	−	23.1601i	0.134324	−	0.0372949i
$622$	−73.6100	+	218.467i	−0.118344	+	0.351232i
$623$	497.742	+	81.6006i	0.798943	+	0.130980i
$624$	105.982	−	17.3749i	0.169843	−	0.0278444i
$625$	−437.501	+	147.411i	−0.700002	+	0.235858i
$626$	−192.528	−	283.958i	−0.307553	−	0.453606i
$627$	−107.319	+	231.965i	−0.171162	+	0.369961i
$628$	110.615	−	145.512i	0.176138	−	0.231706i
$629$	12.9667	+	119.226i	0.0206147	+	0.189549i
$630$	22.5049	+	6.24845i	0.0357220	+	0.00991817i
$631$	516.539	−	761.838i	0.818604	−	1.20735i	−0.156953	−	0.987606i	$-0.550167\pi$
$631$	516.539	−	761.838i	0.818604	−	1.20735i	0.975557	−	0.219745i	$-0.0705225\pi$
$632$	−363.022	−	603.347i	−0.574402	−	0.954664i
$633$	−324.420	+	17.5896i	−0.512512	+	0.0277876i
$634$	−366.840	−	387.268i	−0.578611	−	0.610833i
$635$	−219.862	+	167.134i	−0.346239	+	0.263204i
$636$	−22.6149	+	4.97791i	−0.0355580	+	0.00782690i
$637$	184.229	−	156.486i	0.289214	−	0.245660i
$638$	2.50647	−	46.2291i	0.00392864	−	0.0724594i
$639$	−26.7850	−	50.5219i	−0.0419170	−	0.0790639i
$640$	−38.9733	+	177.057i	−0.0608957	+	0.276652i
$641$	−172.109	+	79.6261i	−0.268501	+	0.124222i	−0.549520	−	0.835480i	$-0.685190\pi$
$641$	−172.109	+	79.6261i	−0.268501	+	0.124222i	0.281019	+	0.959702i	$0.409327\pi$
$642$	−112.887	+	187.619i	−0.175836	+	0.292242i
$643$	41.7958	−	78.8353i	0.0650013	−	0.122605i	−0.848882	−	0.528582i	$-0.822724\pi$
$643$	41.7958	−	78.8353i	0.0650013	−	0.122605i	0.913883	+	0.405977i	$0.133069\pi$
$644$	−204.255	−	173.496i	−0.317167	−	0.269404i
$645$	13.2838	−	14.0236i	0.0205951	−	0.0217419i
$646$	12.2158	−	112.322i	0.0189099	−	0.173874i
$647$	−434.060	+	1089.41i	−0.670881	+	1.68379i	0.0572608	+	0.998359i	$0.481763\pi$
$647$	−434.060	+	1089.41i	−0.670881	+	1.68379i	−0.728142	+	0.685426i	$0.759616\pi$
$648$			62.1421i			0.0958983i
$649$	281.431	−	94.1976i	0.433638	−	0.145143i
$650$	257.558			0.396243
$651$	−123.954	−	49.3877i	−0.190405	−	0.0758644i
$652$	−426.760	−	46.4130i	−0.654540	−	0.0711855i
$653$	−21.9888	−	20.8289i	−0.0336734	−	0.0318972i	0.670678	−	0.741749i	$-0.266003\pi$
$653$	−21.9888	−	20.8289i	−0.0336734	−	0.0318972i	−0.704351	+	0.709852i	$0.748762\pi$
$654$	−138.284	+	162.800i	−0.211443	+	0.248930i
$655$	145.627	+	77.2068i	0.222332	+	0.117873i
$656$	170.171	+	102.389i	0.259408	+	0.156080i
$657$	81.3860	+	175.913i	0.123875	+	0.267752i
$658$	59.2061	+	13.0323i	0.0899789	+	0.0198059i
$659$	−183.637	+	97.3583i	−0.278661	+	0.147736i	−0.601877	−	0.798588i	$-0.705580\pi$
$659$	−183.637	+	97.3583i	−0.278661	+	0.147736i	0.323217	+	0.946325i	$0.395236\pi$
$660$	−39.5913	−	2.14658i	−0.0599869	−	0.00325239i
$661$	−414.629	−	488.139i	−0.627275	−	0.738485i	0.353109	−	0.935582i	$-0.385125\pi$
$661$	−414.629	−	488.139i	−0.627275	−	0.738485i	−0.980384	+	0.197097i	$0.936849\pi$
$662$	−82.4424	−	374.540i	−0.124535	−	0.565770i
$663$	−47.4665	−	62.4411i	−0.0715935	−	0.0941796i
$664$	554.579	−	525.325i	0.835209	−	0.791152i
$665$	−12.6025	−	232.440i	−0.0189512	−	0.349534i
$666$	77.0560	−	46.3631i	0.115700	−	0.0696142i
$667$	129.359	+	87.7076i	0.193942	+	0.131496i
$668$	−71.5305	+	257.629i	−0.107082	+	0.385673i
$669$	42.9662	−	4.67285i	0.0642245	−	0.00698483i
$670$	−16.7616	−	12.7418i	−0.0250173	−	0.0190176i
$671$	216.055	+	99.9576i	0.321989	+	0.148968i
$672$	249.726	−	169.319i	0.371616	−	0.251962i
$673$	−212.783	−	631.516i	−0.316170	−	0.938360i	−0.981442	−	0.191759i	$-0.938581\pi$
$673$	−212.783	−	631.516i	−0.316170	−	0.938360i	0.665272	−	0.746601i	$-0.268316\pi$
$674$	−20.3260	−	123.983i	−0.0301573	−	0.183952i
$675$	19.1289	−	116.681i	0.0283391	−	0.172861i
$676$	−103.380	−	34.8327i	−0.152929	−	0.0515276i
$677$	180.742	+	650.972i	0.266974	+	0.961554i	0.968521	+	0.248931i	$0.0800793\pi$
$677$	180.742	+	650.972i	0.266974	+	0.961554i	−0.701547	+	0.712623i	$0.747507\pi$
$678$	116.632	+	292.724i	0.172023	+	0.431746i
$679$	248.084	−	98.8455i	0.365366	−	0.145575i
$680$	39.1296	−	10.8643i	0.0575435	−	0.0159769i
$681$	−24.4145	+	72.4596i	−0.0358509	+	0.106402i
$682$	−70.8444	−	11.6143i	−0.103877	−	0.0170298i
$683$	145.550	−	23.8617i	0.213103	−	0.0349365i	−0.0542845	−	0.998526i	$-0.517288\pi$
$683$	145.550	−	23.8617i	0.213103	−	0.0349365i	0.267388	+	0.963589i	$0.413840\pi$
$684$	253.319	−	85.3530i	0.370349	−	0.124785i
$685$	−181.604	−	267.845i	−0.265115	−	0.391015i
$686$	152.622	−	329.888i	0.222482	−	0.480886i
$687$	−259.105	+	340.846i	−0.377154	+	0.496137i
$688$	−4.32544	−	39.7718i	−0.00628698	−	0.0578078i
$689$	−48.9271	−	13.5845i	−0.0710118	−	0.0197163i
$690$	−23.8065	+	35.1120i	−0.0345022	+	0.0508869i
$691$	−139.682	−	232.154i	−0.202145	−	0.335968i	0.739157	−	0.673533i	$-0.235224\pi$
$691$	−139.682	−	232.154i	−0.202145	−	0.335968i	−0.941302	+	0.337566i	$0.890397\pi$
$692$	−989.385	+	53.6429i	−1.42975	+	0.0775186i
$693$	54.9592	+	58.0197i	0.0793062	+	0.0837225i
$694$	−276.151	+	209.925i	−0.397912	+	0.302485i
$695$	−116.575	+	25.6602i	−0.167734	+	0.0369211i
$696$	−85.5051	+	72.6287i	−0.122852	+	0.104352i
$697$	7.85239	−	144.829i	0.0112660	−	0.207789i
$698$	190.425	+	359.180i	0.272816	+	0.514585i
$699$	98.6844	−	448.328i	0.141179	−	0.641384i
$700$	−332.198	+	153.691i	−0.474569	+	0.219559i
$701$	578.118	−	960.840i	0.824705	−	1.37067i	−0.101963	−	0.994788i	$-0.532512\pi$
$701$	578.118	−	960.840i	0.824705	−	1.37067i	0.926668	−	0.375882i	$-0.122660\pi$
$702$	−27.5489	+	51.9626i	−0.0392434	+	0.0740209i
$703$	−683.111	−	580.240i	−0.971709	−	0.825377i
$704$	37.2648	−	39.3400i	0.0529330	−	0.0558807i
$705$	−3.27364	+	30.1006i	−0.00464346	+	0.0426959i
$706$	−185.977	+	466.768i	−0.263424	+	0.661144i
$707$		−	174.776i		−	0.247208i
$708$	−273.941	−	145.938i	−0.386923	−	0.206128i
$709$	90.8312			0.128112			0.0640559	−	0.997946i	$-0.479596\pi$
$709$	90.8312			0.128112			0.0640559	+	0.997946i	$0.479596\pi$
$710$	26.0309	+	10.3717i	0.0366632	+	0.0146080i
$711$	−304.147	−	33.0780i	−0.427773	−	0.0465232i
$712$	−477.417	−	452.234i	−0.670530	−	0.635160i
$713$	156.893	−	184.709i	0.220047	−	0.259059i
$714$	−31.2128	−	16.5480i	−0.0437155	−	0.0231765i
$715$	−74.4995	−	44.8248i	−0.104195	−	0.0626921i
$716$	154.910	+	334.833i	0.216355	+	0.467644i
$717$	185.703	+	40.8763i	0.259000	+	0.0570102i
$718$	266.560	−	141.321i	0.371254	−	0.196826i
$719$	261.342	+	14.1695i	0.363479	+	0.0197073i	0.234974	−	0.972002i	$-0.424499\pi$
$719$	261.342	+	14.1695i	0.363479	+	0.0197073i	0.128505	+	0.991709i	$0.458982\pi$
$720$	15.6408	+	18.4137i	0.0217233	+	0.0255746i
$721$	−76.5075	−	347.577i	−0.106113	−	0.482077i
$722$	296.648	+	390.233i	0.410869	+	0.540490i
$723$	310.390	−	294.017i	0.429308	−	0.406662i
$724$	−3.13991	−	57.9123i	−0.00433690	−	0.0799894i
$725$	182.905	−	110.051i	0.252283	−	0.151794i
$726$	−134.606	−	91.2652i	−0.185408	−	0.125710i
$727$	2.95416	−	10.6399i	0.00406349	−	0.0146354i	−0.961490	−	0.274838i	$-0.911376\pi$
$727$	2.95416	−	10.6399i	0.00406349	−	0.0146354i	0.965554	+	0.260203i	$0.0837895\pi$
$728$	419.368	−	45.6090i	0.576055	−	0.0626497i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	−86.2016	−	39.8811i	−0.118084	−	0.0546317i
$731$	−24.1830	+	16.3965i	−0.0330820	+	0.0224302i
$732$	−79.4986	−	235.944i	−0.108605	−	0.322327i
$733$	−116.252	−	709.108i	−0.158598	−	0.967405i	−0.939449	−	0.342688i	$-0.888663\pi$
$733$	−116.252	−	709.108i	−0.158598	−	0.967405i	0.780851	−	0.624717i	$-0.214786\pi$
$734$	−5.63020	+	34.3427i	−0.00767057	+	0.0467884i
$735$	51.5303	+	17.3626i	0.0701093	+	0.0236226i
$736$	146.606	+	528.028i	0.199193	+	0.717430i
$737$	−26.6658	−	66.9260i	−0.0361815	−	0.0908087i
$738$	−101.034	+	40.2558i	−0.136903	+	0.0545472i
$739$	1135.34	−	315.225i	1.53632	−	0.426557i	0.606655	−	0.794965i	$-0.292511\pi$
$739$	1135.34	−	315.225i	1.53632	−	0.426557i	0.929664	+	0.368409i	$0.120097\pi$
$740$	44.3959	−	131.762i	0.0599944	−	0.178057i
$741$	578.450	+	94.8320i	0.780634	+	0.127978i
$742$	−22.5699	+	3.70015i	−0.0304177	+	0.00498673i
$743$	194.669	−	65.5916i	0.262004	−	0.0882794i	−0.185234	−	0.982694i	$-0.559304\pi$
$743$	194.669	−	65.5916i	0.262004	−	0.0882794i	0.447238	+	0.894415i	$0.352408\pi$
$744$	97.6257	+	143.987i	0.131217	+	0.193531i
$745$	−138.271	+	298.867i	−0.185598	+	0.401164i
$746$	140.402	−	184.695i	0.188206	−	0.247581i
$747$	−35.8847	−	329.954i	−0.0480384	−	0.441706i
$748$	57.7870	+	16.0445i	0.0772554	+	0.0214498i
$749$	382.934	−	564.785i	0.511260	−	0.754053i
$750$	62.6892	+	104.190i	0.0835856	+	0.138920i
$751$	635.613	−	34.4619i	0.846355	−	0.0458880i	0.374141	−	0.927372i	$-0.377938\pi$
$751$	635.613	−	34.4619i	0.846355	−	0.0458880i	0.472214	+	0.881484i	$0.343455\pi$
$752$	43.1253	+	45.5268i	0.0573474	+	0.0605409i
$753$	−65.3370	+	49.6679i	−0.0867689	+	0.0659600i
$754$	−103.696	+	22.8253i	−0.137528	+	0.0302723i
$755$	124.038	−	105.359i	0.164289	−	0.139548i
$756$	4.52510	−	83.4606i	0.00598558	−	0.110398i
$757$	−411.578	−	776.319i	−0.543696	−	1.02552i	−0.991342	−	0.131309i	$-0.958082\pi$
$757$	−411.578	−	776.319i	−0.543696	−	1.02552i	0.447645	−	0.894211i	$-0.352263\pi$
$758$	44.8475	−	203.744i	0.0591655	−	0.268792i
$759$	−131.738	+	60.9484i	−0.173567	+	0.0803009i
$760$	−156.467	+	260.051i	−0.205878	+	0.342172i
$761$	−488.824	+	922.020i	−0.642345	+	1.21159i	0.321950	+	0.946757i	$0.395662\pi$
$761$	−488.824	+	922.020i	−0.642345	+	1.21159i	−0.964294	+	0.264834i	$0.914683\pi$
$762$	−238.739	−	202.787i	−0.313306	−	0.266124i
$763$	457.777	−	483.270i	0.599970	−	0.633381i
$764$	−24.0315	+	220.966i	−0.0314548	+	0.289222i
$765$	6.53090	−	16.3913i	0.00853712	−	0.0214266i
$766$			226.905i			0.296220i
$767$	−380.834	−	564.119i	−0.496524	−	0.735487i
$768$	−280.261			−0.364924
$769$	936.533	+	373.149i	1.21786	+	0.485239i	0.888461	−	0.458952i	$-0.151775\pi$
$769$	936.533	+	373.149i	1.21786	+	0.485239i	0.329397	+	0.944191i	$0.393154\pi$
$770$	−38.9319	−	4.23410i	−0.0505609	−	0.00549883i
$771$	4.03977	+	3.82667i	0.00523965	+	0.00496326i
$772$	−652.172	+	767.797i	−0.844783	+	0.994555i
$773$	166.583	+	88.3165i	0.215501	+	0.114252i	0.572663	−	0.819791i	\(-0.305911\p

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.911464 - 0.363160i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(-2.20510 - 2.08878i) q^{4} +(0.969991 - 1.14196i) q^{5} +(1.50144 + 0.796012i) q^{6} +(-4.53786 - 2.73034i) q^{7} +(2.89920 + 6.26652i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(-0.911464 - 0.363160i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(-2.20510 - 2.08878i) q^{4} +(0.969991 - 1.14196i) q^{5} +(1.50144 + 0.796012i) q^{6} +(-4.53786 - 2.73034i) q^{7} +(2.89920 + 6.26652i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-1.29883 + 0.688594i) q^{10} +(-5.02274 - 0.272325i) q^{11} +(3.40580 + 4.00961i) q^{12} +(2.47994 + 11.2665i) q^{13} +(3.14454 + 4.13657i) q^{14} +(-1.88408 + 1.78469i) q^{15} +(0.290990 + 5.36700i) q^{16} +(3.36350 - 2.02375i) q^{17} +(-2.43626 - 1.65182i) q^{18} +(-7.84823 + 28.2668i) q^{19} +(-4.52424 + 0.492041i) q^{20} +(7.30242 + 5.55116i) q^{21} +(4.47914 + 2.07227i) q^{22} +(-13.7897 + 9.34968i) q^{23} +(-3.81861 - 11.3332i) q^{24} +(3.68136 + 22.4553i) q^{25} +(1.83116 - 11.1696i) q^{26} +(-4.92415 - 1.65914i) q^{27} +(4.30335 + 15.4993i) q^{28} +(-3.47220 - 8.71456i) q^{29} +(2.36540 - 0.942461i) q^{30} +(-14.0161 + 3.89155i) q^{31} +(10.5026 - 31.1705i) q^{32} +(8.59764 + 1.40951i) q^{33} +(-3.80066 + 0.623086i) q^{34} +(-7.51962 + 2.53366i) q^{35} +(-5.11356 - 7.54194i) q^{36} +(-12.8285 + 27.7284i) q^{37} +(17.4187 - 22.9140i) q^{38} +(-2.16036 - 19.8641i) q^{39} +(9.96832 + 2.76769i) q^{40} +(20.7356 - 30.5827i) q^{41} +(-4.63993 - 7.71162i) q^{42} +(-7.43227 + 0.402966i) q^{43} +(10.5068 + 11.0919i) q^{44} +(3.57840 - 2.72023i) q^{45} +(15.9643 - 3.51400i) q^{46} +(8.89224 - 7.55314i) q^{47} +(0.504010 - 9.29592i) q^{48} +(-9.81462 - 18.5123i) q^{49} +(4.79944 - 21.8041i) q^{50} +(-6.17059 + 2.85482i) q^{51} +(18.0647 - 30.0238i) q^{52} +(-2.06176 + 3.88889i) q^{53} +(3.88565 + 3.30050i) q^{54} +(-5.18300 + 5.47162i) q^{55} +(3.95356 - 36.3524i) q^{56} +(18.8073 - 47.2027i) q^{57} +9.20397i q^{58} +(-54.8533 + 21.7283i) q^{59} +7.88242 q^{60} +(-43.9651 - 17.5173i) q^{61} +(14.1884 + 1.54308i) q^{62} +(-11.5345 - 10.9260i) q^{63} +(-6.97407 + 8.21050i) q^{64} +(15.2714 + 8.09639i) q^{65} +(-7.32456 - 4.40704i) q^{66} +(6.01377 + 12.9985i) q^{67} +(-11.6440 - 2.56305i) q^{68} +(25.4954 - 13.5168i) q^{69} +(7.77398 + 0.421493i) q^{70} +(-12.3398 - 14.5276i) q^{71} +(4.45291 + 20.2298i) q^{72} +(39.0998 + 51.4349i) q^{73} +(21.7626 - 20.6146i) q^{74} +(-2.13377 - 39.3551i) q^{75} +(76.3493 - 45.9378i) q^{76} +(22.0489 + 14.9495i) q^{77} +(-5.24478 + 18.8900i) q^{78} +(-101.382 + 11.0260i) q^{79} +(6.41117 + 4.87364i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-30.0062 + 20.3447i) q^{82} +(-35.3254 - 104.842i) q^{83} +(-4.50742 - 27.4940i) q^{84} +(0.951520 - 5.80402i) q^{85} +(6.92059 + 2.33182i) q^{86} +(4.34681 + 15.6558i) q^{87} +(-12.8554 - 32.2646i) q^{88} +(-88.4760 + 35.2521i) q^{89} +(-4.24947 + 1.17986i) q^{90} +(19.5077 - 57.8968i) q^{91} +(49.9372 + 8.18679i) q^{92} +(24.8630 - 4.07608i) q^{93} +(-10.8480 + 3.65510i) q^{94} +(24.6669 + 36.3809i) q^{95} +(-23.9215 + 51.7056i) q^{96} +(-30.5163 + 40.1435i) q^{97} +(2.22272 + 20.4376i) q^{98} +(-14.5403 - 4.03709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) \)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) \)

Introduction

L-functions

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