LMFDB - Embedded newform 177.3.g.a.10.2

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			10.2
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.2

$q$-expansion

$f(q)$	$=$	$q+(-3.48729 - 1.38946i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(7.32661 + 6.94014i) q^{4} +(0.951158 - 1.11979i) q^{5} +(5.74456 + 3.04557i) q^{6} +(1.10368 + 0.664063i) q^{7} +(-9.60207 - 20.7545i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(-3.48729 - 1.38946i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(7.32661 + 6.94014i) q^{4} +(0.951158 - 1.11979i) q^{5} +(5.74456 + 3.04557i) q^{6} +(1.10368 + 0.664063i) q^{7} +(-9.60207 - 20.7545i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-4.87287 + 2.58343i) q^{10} +(-13.0628 - 0.708243i) q^{11} +(-11.3160 - 13.3222i) q^{12} +(-1.53834 - 6.98874i) q^{13} +(-2.92617 - 3.84931i) q^{14} +(-1.84750 + 1.75004i) q^{15} +(2.46210 + 45.4108i) q^{16} +(-3.43897 + 2.06916i) q^{17} +(-9.32120 - 6.31993i) q^{18} +(-4.35868 + 15.6986i) q^{19} +(14.7403 - 1.60310i) q^{20} +(-1.77607 - 1.35013i) q^{21} +(44.5696 + 20.6201i) q^{22} +(14.2965 - 9.69329i) q^{23} +(12.6471 + 37.5353i) q^{24} +(3.69532 + 22.5405i) q^{25} +(-4.34597 + 26.5093i) q^{26} +(-4.92415 - 1.65914i) q^{27} +(3.47756 + 12.5250i) q^{28} +(18.4242 + 46.2413i) q^{29} +(8.87438 - 3.53588i) q^{30} +(-40.0881 + 11.1304i) q^{31} +(25.3033 - 75.0976i) q^{32} +(22.3601 + 3.66576i) q^{33} +(14.8677 - 2.43744i) q^{34} +(1.79339 - 0.604262i) q^{35} +(16.9902 + 25.0587i) q^{36} +(-2.59493 + 5.60885i) q^{37} +(37.0126 - 48.6892i) q^{38} +(1.34010 + 12.3220i) q^{39} +(-32.3738 - 8.98854i) q^{40} +(-23.7600 + 35.0433i) q^{41} +(4.31771 + 7.17609i) q^{42} +(14.3679 - 0.779003i) q^{43} +(-90.7906 - 95.8464i) q^{44} +(3.50893 - 2.66742i) q^{45} +(-63.3247 + 13.9388i) q^{46} +(-66.0098 + 56.0692i) q^{47} +(4.26449 - 78.6538i) q^{48} +(-22.1749 - 41.8263i) q^{49} +(18.4325 - 83.7397i) q^{50} +(6.30903 - 2.91887i) q^{51} +(37.2320 - 61.8801i) q^{52} +(-6.15817 + 11.6155i) q^{53} +(14.8666 + 12.6278i) q^{54} +(-13.2178 + 13.9539i) q^{55} +(3.18469 - 29.2828i) q^{56} +(10.4450 - 26.2151i) q^{57} -186.857i q^{58} +(-58.7342 + 5.59430i) q^{59} -25.6814 q^{60} +(88.5593 + 35.2853i) q^{61} +(155.264 + 16.8860i) q^{62} +(2.80537 + 2.65739i) q^{63} +(-74.8194 + 88.0842i) q^{64} +(-9.28912 - 4.92478i) q^{65} +(-72.8828 - 43.8521i) q^{66} +(11.0554 + 23.8957i) q^{67} +(-39.5562 - 8.70698i) q^{68} +(-26.4324 + 14.0136i) q^{69} +(-7.09366 - 0.384607i) q^{70} +(33.5178 + 39.4602i) q^{71} +(-14.7479 - 67.0004i) q^{72} +(-39.9812 - 52.5943i) q^{73} +(16.8426 - 15.9541i) q^{74} +(-2.14187 - 39.5044i) q^{75} +(-140.885 + 84.7674i) q^{76} +(-13.9468 - 9.45617i) q^{77} +(12.4476 - 44.8324i) q^{78} +(-70.0404 + 7.61735i) q^{79} +(53.1924 + 40.4358i) q^{80} +(8.16818 + 3.77900i) q^{81} +(131.549 - 89.1927i) q^{82} +(48.3924 + 143.624i) q^{83} +(-3.64246 - 22.2180i) q^{84} +(-0.953979 + 5.81901i) q^{85} +(-51.1873 - 17.2470i) q^{86} +(-23.0651 - 83.0731i) q^{87} +(110.730 + 277.912i) q^{88} +(11.2123 - 4.46740i) q^{89} +(-15.9429 + 4.42653i) q^{90} +(2.94313 - 8.73489i) q^{91} +(172.018 + 28.2009i) q^{92} +(71.1120 - 11.6582i) q^{93} +(308.102 - 103.812i) q^{94} +(13.4333 + 19.8126i) q^{95} +(-57.6331 + 124.572i) q^{96} +(43.5666 - 57.3109i) q^{97} +(19.2142 + 176.672i) q^{98} +(-37.8154 - 10.4994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) $	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−3.48729	−	1.38946i	−1.74365	−	0.694732i	−0.999647	−	0.0265509i	$-0.991548\pi$
$2$	−3.48729	−	1.38946i	−1.74365	−	0.694732i	−0.743999	−	0.668181i	$-0.767073\pi$
$3$	−1.72190	−	0.187268i	−0.573966	−	0.0624225i
$3$	−1.72190	−	0.187268i	−0.573966	−	0.0624225i
$4$	7.32661	+	6.94014i	1.83165	+	1.73503i
$5$	0.951158	−	1.11979i	0.190232	−	0.223958i	−0.658775	−	0.752340i	$-0.728925\pi$
$5$	0.951158	−	1.11979i	0.190232	−	0.223958i	0.849007	+	0.528382i	$0.177201\pi$
$6$	5.74456	+	3.04557i	0.957426	+	0.507595i
$7$	1.10368	+	0.664063i	0.157669	+	0.0948661i	0.592202	−	0.805790i	$-0.298259\pi$
$7$	1.10368	+	0.664063i	0.157669	+	0.0948661i	−0.434533	+	0.900656i	$0.643087\pi$
$8$	−9.60207	−	20.7545i	−1.20026	−	2.59432i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	−4.87287	+	2.58343i	−0.487287	+	0.258343i
$11$	−13.0628	−	0.708243i	−1.18752	−	0.0643857i	−0.550235	−	0.835010i	$-0.685462\pi$
$11$	−13.0628	−	0.708243i	−1.18752	−	0.0643857i	−0.637290	+	0.770624i	$0.719945\pi$
$12$	−11.3160	−	13.3222i	−0.943001	−	1.11019i
$13$	−1.53834	−	6.98874i	−0.118334	−	0.537596i	−0.998068	−	0.0621300i	$-0.980211\pi$
$13$	−1.53834	−	6.98874i	−0.118334	−	0.537596i	0.879734	−	0.475466i	$-0.157720\pi$
$14$	−2.92617	−	3.84931i	−0.209012	−	0.274950i
$15$	−1.84750	+	1.75004i	−0.123166	+	0.116669i
$16$	2.46210	+	45.4108i	0.153881	+	2.83817i
$17$	−3.43897	+	2.06916i	−0.202292	+	0.121715i	−0.613095	−	0.790009i	$-0.710076\pi$
$17$	−3.43897	+	2.06916i	−0.202292	+	0.121715i	0.410803	+	0.911724i	$0.365248\pi$
$18$	−9.32120	−	6.31993i	−0.517845	−	0.351107i
$19$	−4.35868	+	15.6986i	−0.229404	+	0.826240i	0.755792	+	0.654812i	$0.227252\pi$
$19$	−4.35868	+	15.6986i	−0.229404	+	0.826240i	−0.985197	+	0.171428i	$0.945162\pi$
$20$	14.7403	−	1.60310i	0.737013	−	0.0801550i
$21$	−1.77607	−	1.35013i	−0.0845747	−	0.0642920i
$22$	44.5696	+	20.6201i	2.02589	+	0.937277i
$23$	14.2965	−	9.69329i	0.621588	−	0.421447i	−0.209327	−	0.977846i	$-0.567127\pi$
$23$	14.2965	−	9.69329i	0.621588	−	0.421447i	0.830916	+	0.556398i	$0.187817\pi$
$24$	12.6471	+	37.5353i	0.526964	+	1.56397i
$25$	3.69532	+	22.5405i	0.147813	+	0.901619i
$26$	−4.34597	+	26.5093i	−0.167153	+	1.01959i
$27$	−4.92415	−	1.65914i	−0.182376	−	0.0614496i
$28$	3.47756	+	12.5250i	0.124198	+	0.447322i
$29$	18.4242	+	46.2413i	0.635318	+	1.59453i	0.794490	+	0.607277i	$0.207738\pi$
$29$	18.4242	+	46.2413i	0.635318	+	1.59453i	−0.159172	+	0.987251i	$0.550882\pi$
$30$	8.87438	−	3.53588i	0.295813	−	0.117863i
$31$	−40.0881	+	11.1304i	−1.29316	+	0.359045i	−0.844933	−	0.534872i	$-0.820360\pi$
$31$	−40.0881	+	11.1304i	−1.29316	+	0.359045i	−0.448232	+	0.893917i	$0.647946\pi$
$32$	25.3033	−	75.0976i	0.790729	−	2.34680i
$33$	22.3601	+	3.66576i	0.677579	+	0.111083i
$34$	14.8677	−	2.43744i	0.437285	−	0.0716893i
$35$	1.79339	−	0.604262i	0.0512396	−	0.0172646i
$36$	16.9902	+	25.0587i	0.471950	+	0.696074i
$37$	−2.59493	+	5.60885i	−0.0701332	+	0.151590i	−0.939472	−	0.342627i	$-0.888683\pi$
$37$	−2.59493	+	5.60885i	−0.0701332	+	0.151590i	0.869338	+	0.494218i	$0.164545\pi$
$38$	37.0126	−	48.6892i	0.974016	−	1.28130i
$39$	1.34010	+	12.3220i	0.0343614	+	0.315948i
$40$	−32.3738	−	8.98854i	−0.809345	−	0.224714i
$41$	−23.7600	+	35.0433i	−0.579512	+	0.854716i	−0.998582	−	0.0532381i	$-0.983046\pi$
$41$	−23.7600	+	35.0433i	−0.579512	+	0.854716i	0.419070	+	0.907954i	$0.362356\pi$
$42$	4.31771	+	7.17609i	0.102803	+	0.170859i
$43$	14.3679	−	0.779003i	0.334136	−	0.0181163i	0.113692	−	0.993516i	$-0.463732\pi$
$43$	14.3679	−	0.779003i	0.334136	−	0.0181163i	0.220444	+	0.975400i	$0.429249\pi$
$44$	−90.7906	−	95.8464i	−2.06342	−	2.17833i
$45$	3.50893	−	2.66742i	0.0779761	−	0.0592759i
$46$	−63.3247	+	13.9388i	−1.37662	+	0.303018i
$47$	−66.0098	+	56.0692i	−1.40446	+	1.19296i	−0.450599	+	0.892726i	$0.648790\pi$
$47$	−66.0098	+	56.0692i	−1.40446	+	1.19296i	−0.953865	+	0.300236i	$0.902934\pi$
$48$	4.26449	−	78.6538i	0.0888434	−	1.63862i
$49$	−22.1749	−	41.8263i	−0.452549	−	0.853597i
$50$	18.4325	−	83.7397i	0.368650	−	1.67479i
$51$	6.30903	−	2.91887i	0.123707	−	0.0572327i
$52$	37.2320	−	61.8801i	0.716000	−	1.19000i
$53$	−6.15817	+	11.6155i	−0.116192	+	0.219161i	−0.934786	−	0.355211i	$-0.884409\pi$
$53$	−6.15817	+	11.6155i	−0.116192	+	0.219161i	0.818594	+	0.574372i	$0.194754\pi$
$54$	14.8666	+	12.6278i	0.275308	+	0.233849i
$55$	−13.2178	+	13.9539i	−0.240324	+	0.253707i
$56$	3.18469	−	29.2828i	0.0568695	−	0.522906i
$57$	10.4450	−	26.2151i	0.183246	−	0.459914i
$58$		−	186.857i		−	3.22167i
$59$	−58.7342	+	5.59430i	−0.995495	+	0.0948186i
$59$	−58.7342	+	5.59430i	−0.995495	+	0.0948186i
$60$	−25.6814			−0.428024
$61$	88.5593	+	35.2853i	1.45179	+	0.578447i	0.956877	−	0.290494i	$-0.0938196\pi$
$61$	88.5593	+	35.2853i	1.45179	+	0.578447i	0.494916	+	0.868941i	$0.335199\pi$
$62$	155.264	+	16.8860i	2.50426	+	0.272355i
$63$	2.80537	+	2.65739i	0.0445297	+	0.0421808i
$64$	−74.8194	+	88.0842i	−1.16905	+	1.37632i
$65$	−9.28912	−	4.92478i	−0.142910	−	0.0757659i
$66$	−72.8828	−	43.8521i	−1.10429	−	0.664426i
$67$	11.0554	+	23.8957i	0.165005	+	0.356653i	0.972386	−	0.233377i	$-0.0749778\pi$
$67$	11.0554	+	23.8957i	0.165005	+	0.356653i	−0.807381	+	0.590030i	$0.799116\pi$
$68$	−39.5562	−	8.70698i	−0.581709	−	0.128044i
$69$	−26.4324	+	14.0136i	−0.383078	+	0.203095i
$70$	−7.09366	−	0.384607i	−0.101338	−	0.00549438i
$71$	33.5178	+	39.4602i	0.472082	+	0.555778i	0.945737	−	0.324932i	$-0.105342\pi$
$71$	33.5178	+	39.4602i	0.472082	+	0.555778i	−0.473655	+	0.880710i	$0.657066\pi$
$72$	−14.7479	−	67.0004i	−0.204832	−	0.930561i
$73$	−39.9812	−	52.5943i	−0.547687	−	0.720470i	0.436083	−	0.899907i	$-0.356366\pi$
$73$	−39.9812	−	52.5943i	−0.547687	−	0.720470i	−0.983770	+	0.179437i	$0.942572\pi$
$74$	16.8426	−	15.9541i	0.227602	−	0.215596i
$75$	−2.14187	−	39.5044i	−0.0285582	−	0.526725i
$76$	−140.885	+	84.7674i	−1.85374	+	1.11536i
$77$	−13.9468	−	9.45617i	−0.181127	−	0.122807i
$78$	12.4476	−	44.8324i	0.159585	−	0.574774i
$79$	−70.0404	+	7.61735i	−0.886587	+	0.0964222i	−0.540069	−	0.841621i	$-0.681602\pi$
$79$	−70.0404	+	7.61735i	−0.886587	+	0.0964222i	−0.346518	+	0.938043i	$0.612636\pi$
$80$	53.1924	+	40.4358i	0.664905	+	0.505447i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	131.549	−	89.1927i	1.60426	−	1.08772i
$83$	48.3924	+	143.624i	0.583042	+	1.73041i	0.678135	+	0.734937i	$0.262788\pi$
$83$	48.3924	+	143.624i	0.583042	+	1.73041i	−0.0950935	+	0.995468i	$0.530315\pi$
$84$	−3.64246	−	22.2180i	−0.0433627	−	0.264501i
$85$	−0.953979	+	5.81901i	−0.0112233	+	0.0684590i
$86$	−51.1873	−	17.2470i	−0.595201	−	0.200547i
$87$	−23.0651	−	83.0731i	−0.265116	−	0.954863i
$88$	110.730	+	277.912i	1.25830	+	3.15809i
$89$	11.2123	−	4.46740i	0.125981	−	0.0501955i	−0.306296	−	0.951936i	$-0.599090\pi$
$89$	11.2123	−	4.46740i	0.125981	−	0.0501955i	0.432277	+	0.901741i	$0.357710\pi$
$90$	−15.9429	+	4.42653i	−0.177144	+	0.0491837i
$91$	2.94313	−	8.73489i	0.0323421	−	0.0959878i
$92$	172.018	+	28.2009i	1.86976	+	0.306532i
$93$	71.1120	−	11.6582i	0.764645	−	0.125357i
$94$	308.102	−	103.812i	3.27768	−	1.10438i
$95$	13.4333	+	19.8126i	0.141403	+	0.208554i
$96$	−57.6331	+	124.572i	−0.600344	+	1.29762i
$97$	43.5666	−	57.3109i	0.449141	−	0.590834i	−0.514681	−	0.857382i	$-0.672090\pi$
$97$	43.5666	−	57.3109i	0.449141	−	0.590834i	0.963822	+	0.266547i	$0.0858828\pi$
$98$	19.2142	+	176.672i	0.196063	+	1.80277i
$99$	−37.8154	−	10.4994i	−0.381973	−	0.106054i
$100$	−129.360	+	190.791i	−1.29360	+	1.90791i
$101$	32.4771	+	53.9774i	0.321556	+	0.534430i	0.974903	−	0.222628i	$-0.0714636\pi$
$101$	32.4771	+	53.9774i	0.321556	+	0.534430i	−0.653348	+	0.757058i	$0.726636\pi$
$102$	−26.0571	+	1.41278i	−0.255462	+	0.0138507i
$103$	−65.5203	−	69.1689i	−0.636119	−	0.671543i	0.325623	−	0.945500i	$-0.394426\pi$
$103$	−65.5203	−	69.1689i	−0.636119	−	0.671543i	−0.961742	+	0.273957i	$0.911667\pi$
$104$	−130.277	+	99.0339i	−1.25266	+	0.952249i
$105$	−3.20118	+	0.704634i	−0.0304875	+	0.00671080i
$106$	37.6147	−	31.9502i	0.354856	−	0.301417i
$107$	11.1902	−	206.391i	0.104581	−	1.92889i	−0.206393	−	0.978469i	$-0.566173\pi$
$107$	11.1902	−	206.391i	0.104581	−	1.92889i	0.310974	−	0.950418i	$-0.399345\pi$
$108$	−24.5627	−	46.3301i	−0.227432	−	0.428983i
$109$	−17.7525	+	80.6503i	−0.162867	+	0.739911i	0.822403	+	0.568905i	$0.192633\pi$
$109$	−17.7525	+	80.6503i	−0.162867	+	0.739911i	−0.985270	+	0.171006i	$0.945298\pi$
$110$	65.4829	−	30.2956i	0.595299	−	0.275415i
$111$	5.51856	−	9.17191i	0.0497167	−	0.0826299i
$112$	−27.4382	+	51.7540i	−0.244984	+	0.462089i
$113$	−151.316	−	128.529i	−1.33908	−	1.13742i	−0.978855	−	0.204555i	$-0.934425\pi$
$113$	−151.316	−	128.529i	−1.33908	−	1.13742i	−0.360222	−	0.932867i	$-0.617299\pi$
$114$	−72.8498	+	76.9066i	−0.639033	+	0.674619i
$115$	2.74381	−	25.2290i	0.0238593	−	0.219382i
$116$	−185.934	+	466.659i	−1.60288	+	4.02292i
$117$		−	21.4681i		−	0.183488i
$118$	212.596	+	62.1001i	1.80166	+	0.526272i
$119$	−5.16957			−0.0434418
$120$	54.0611	+	21.5399i	0.450509	+	0.179499i
$121$	49.8436	+	5.42082i	0.411931	+	0.0448002i
$122$	−259.805	−	246.100i	−2.12955	−	2.01721i
$123$	47.4747	−	55.8916i	0.385973	−	0.454403i
$124$	−370.957	−	196.669i	−2.99159	−	1.58604i
$125$	60.2284	+	36.2382i	0.481827	+	0.289906i
$126$	−6.09080	−	13.1650i	−0.0483397	−	0.104485i
$127$	32.9589	+	7.25480i	0.259519	+	0.0571244i	0.342824	−	0.939400i	$-0.388617\pi$
$127$	32.9589	+	7.25480i	0.259519	+	0.0571244i	−0.0833050	+	0.996524i	$0.526548\pi$
$128$	103.248	−	54.7388i	0.806628	−	0.427647i
$129$	−24.8859	−	1.34927i	−0.192914	−	0.0104595i
$130$	25.5511	+	30.0811i	0.196547	+	0.231393i
$131$	1.45396	+	6.60540i	0.0110989	+	0.0504229i	0.981845	−	0.189687i	$-0.0607474\pi$
$131$	1.45396	+	6.60540i	0.0110989	+	0.0504229i	−0.970746	+	0.240110i	$0.922816\pi$
$132$	138.383	+	182.040i	1.04836	+	1.37909i
$133$	−15.2354	+	14.4318i	−0.114552	+	0.108509i
$134$	−5.35095	−	98.6925i	−0.0399325	−	0.736511i
$135$	−6.54153	+	3.93591i	−0.0484558	+	0.0291549i
$136$	75.9656	+	51.5059i	0.558570	+	0.378720i
$137$	−21.3307	+	76.8264i	−0.155699	+	0.560776i	0.844003	+	0.536339i	$0.180193\pi$
$137$	−21.3307	+	76.8264i	−0.155699	+	0.560776i	−0.999701	+	0.0244373i	$0.992221\pi$
$138$	111.649	−	12.1425i	0.809050	−	0.0879895i
$139$	−62.7749	−	47.7202i	−0.451618	−	0.343311i	0.354510	−	0.935052i	$-0.384648\pi$
$139$	−62.7749	−	47.7202i	−0.451618	−	0.343311i	−0.806128	+	0.591741i	$0.798441\pi$
$140$	17.3331	+	8.01915i	0.123808	+	0.0572796i
$141$	124.162	−	84.1840i	0.880582	−	0.597050i
$142$	−62.0579	−	184.181i	−0.437027	−	1.29705i
$143$	15.1452	+	92.3818i	0.105911	+	0.646027i
$144$	−22.0723	+	134.635i	−0.153280	+	0.934967i
$145$	69.3049	+	23.3515i	0.477965	+	0.161045i
$146$	66.3480	+	238.964i	0.454439	+	1.63674i
$147$	30.3502	+	76.1732i	0.206464	+	0.518185i
$148$	−57.9382	+	23.0847i	−0.391474	+	0.155978i
$149$	250.867	−	69.6528i	1.68367	−	0.467468i	0.711681	−	0.702502i	$-0.247934\pi$
$149$	250.867	−	69.6528i	1.68367	−	0.467468i	0.971987	+	0.235034i	$0.0755202\pi$
$150$	−47.4206	+	140.739i	−0.316137	+	0.938263i
$151$	−175.627	−	28.7926i	−1.16309	−	0.190680i	−0.450842	−	0.892604i	$-0.648876\pi$
$151$	−175.627	−	28.7926i	−1.16309	−	0.190680i	−0.712252	+	0.701924i	$0.752325\pi$
$152$	367.669	−	60.2762i	2.41887	−	0.396554i
$153$	−11.4101	+	3.84452i	−0.0745759	+	0.0251276i
$154$	35.4976	+	52.3550i	0.230504	+	0.339968i
$155$	−25.6664	+	55.4770i	−0.165590	+	0.357916i
$156$	−75.6979	+	99.5788i	−0.485243	+	0.638326i
$157$	−11.4443	−	105.228i	−0.0728934	−	0.670244i	−0.972397	−	0.233331i	$-0.925037\pi$
$157$	−11.4443	−	105.228i	−0.0728934	−	0.670244i	0.899504	−	0.436913i	$-0.143928\pi$
$158$	254.835	+	70.7547i	1.61288	+	0.447814i
$159$	12.7789	−	18.8475i	0.0803707	−	0.118538i
$160$	−60.0260	−	99.7640i	−0.375163	−	0.623525i
$161$	22.2158	−	1.20450i	0.137986	−	0.00748139i
$162$	−23.2340	−	24.5279i	−0.143420	−	0.151407i
$163$	−157.876	+	120.014i	−0.968563	+	0.736283i	−0.964602	−	0.263710i	$-0.915054\pi$
$163$	−157.876	+	120.014i	−0.968563	+	0.736283i	−0.00396111	+	0.999992i	$0.501261\pi$
$164$	−417.286	+	91.8515i	−2.54443	+	0.560070i
$165$	25.3729	−	21.5519i	0.153775	−	0.130618i
$166$	30.8013	−	568.097i	0.185550	−	3.42227i
$167$	−23.5721	−	44.4617i	−0.141150	−	0.266238i	0.802851	−	0.596180i	$-0.203316\pi$
$167$	−23.5721	−	44.4617i	−0.141150	−	0.266238i	−0.944001	+	0.329942i	$0.892971\pi$
$168$	−10.9674	+	49.8255i	−0.0652823	+	0.296580i
$169$	106.904	−	49.4592i	0.632569	−	0.292658i
$170$	11.4121	−	18.9671i	0.0671301	−	0.111571i
$171$	−22.8945	+	43.1836i	−0.133886	+	0.252536i
$172$	110.674	+	94.0075i	0.643454	+	0.546555i
$173$	201.806	−	213.044i	1.16651	−	1.23147i	0.198626	−	0.980075i	$-0.436352\pi$
$173$	201.806	−	213.044i	1.16651	−	1.23147i	0.967885	−	0.251395i	$-0.0808892\pi$
$174$	−34.9922	+	321.748i	−0.201105	+	1.84913i
$175$	−10.8898	+	27.3314i	−0.0622276	+	0.156179i
$176$		−	594.935i		−	3.38031i
$177$	102.182	+	1.36621i	0.577299	+	0.00771868i
$178$	−45.3079			−0.254539
$179$	−239.047	−	95.2451i	−1.33546	−	0.532095i	−0.410395	−	0.911908i	$-0.634609\pi$
$179$	−239.047	−	95.2451i	−1.33546	−	0.532095i	−0.925064	+	0.379812i	$0.875989\pi$
$180$	44.2208	+	4.80930i	0.245671	+	0.0267183i
$181$	−119.269	−	112.977i	−0.658942	−	0.624183i	0.283333	−	0.959021i	$-0.408560\pi$
$181$	−119.269	−	112.977i	−0.658942	−	0.624183i	−0.942276	+	0.334838i	$0.891318\pi$
$182$	−22.4004	+	26.3718i	−0.123079	+	0.144900i
$183$	−145.882	−	77.3419i	−0.797171	−	0.422633i
$184$	−338.456	−	203.642i	−1.83943	−	1.10675i
$185$	3.81254	+	8.24067i	0.0206083	+	0.0445442i
$186$	−264.187	−	58.1519i	−1.42036	−	0.312645i
$187$	46.3879	−	24.5933i	0.248064	−	0.131515i
$188$	−872.757	−	47.3195i	−4.64232	−	0.251699i
$189$	−4.33292	−	5.10110i	−0.0229255	−	0.0269900i
$190$	−19.3169	−	87.7575i	−0.101668	−	0.461881i
$191$	−40.8753	−	53.7705i	−0.214007	−	0.281521i	0.676547	−	0.736400i	$-0.263476\pi$
$191$	−40.8753	−	53.7705i	−0.214007	−	0.281521i	−0.890553	+	0.454879i	$0.849683\pi$
$192$	145.327	−	137.661i	0.756910	−	0.716983i
$193$	15.2016	+	280.377i	0.0787649	+	1.45273i	0.724554	+	0.689218i	$0.242046\pi$
$193$	15.2016	+	280.377i	0.0787649	+	1.45273i	−0.645790	+	0.763515i	$0.723472\pi$
$194$	−231.561	+	139.326i	−1.19361	+	0.718174i
$195$	15.0727	+	10.2195i	0.0772957	+	0.0524078i
$196$	127.813	−	460.342i	0.652108	−	2.34868i
$197$	66.8192	−	7.26702i	0.339184	−	0.0368884i	0.0630576	−	0.998010i	$-0.479915\pi$
$197$	66.8192	−	7.26702i	0.339184	−	0.0368884i	0.276126	+	0.961121i	$0.410949\pi$
$198$	117.285	+	89.1575i	0.592347	+	0.450290i
$199$	253.202	+	117.144i	1.27237	+	0.588661i	0.935645	−	0.352942i	$-0.114819\pi$
$199$	253.202	+	117.144i	1.27237	+	0.588661i	0.336725	+	0.941603i	$0.390681\pi$
$200$	432.334	−	293.130i	2.16167	−	1.46565i
$201$	−14.5613	−	43.2163i	−0.0724442	−	0.215007i
$202$	−38.2576	−	233.361i	−0.189394	−	1.15525i
$203$	−10.3727	+	63.2705i	−0.0510969	+	0.311677i
$204$	66.4812	+	22.4001i	0.325888	+	0.109805i
$205$	16.6417	+	59.9379i	0.0811789	+	0.292380i
$206$	132.381	+	332.250i	0.642624	+	1.61287i
$207$	48.1382	−	19.1800i	0.232552	−	0.0926570i
$208$	313.577	−	87.0642i	1.50758	−	0.418578i
$209$	68.0549	−	201.980i	0.325621	−	0.966410i
$210$	12.1425	+	1.99067i	0.0578216	+	0.00947936i
$211$	402.012	−	65.9065i	1.90527	−	0.312353i	0.910416	−	0.413693i	$-0.135761\pi$
$211$	402.012	−	65.9065i	1.90527	−	0.312353i	0.994852	+	0.101340i	$0.0323131\pi$
$212$	−125.732	+	42.3640i	−0.593075	+	0.199830i
$213$	−50.3246	−	74.2233i	−0.236266	−	0.348466i
$214$	−325.796	+	704.197i	−1.52241	+	3.29064i
$215$	12.7938	−	16.8299i	0.0595060	−	0.0782788i
$216$	12.8474	+	118.130i	0.0594786	+	0.546896i
$217$	−51.6358	−	14.3366i	−0.237953	−	0.0660673i
$218$	173.969	−	256.585i	0.798022	−	1.17699i
$219$	58.9942	+	98.0492i	0.269380	+	0.447713i
$220$	−193.684	+	10.5012i	−0.880382	+	0.0477329i
$221$	19.7511	+	20.8510i	0.0893715	+	0.0943483i
$222$	−31.9889	+	24.3173i	−0.144094	+	0.109537i
$223$	−374.950	+	82.5328i	−1.68139	+	0.370102i	−0.950096	−	0.311959i	$-0.899015\pi$
$223$	−374.950	+	82.5328i	−1.68139	+	0.370102i	−0.731296	+	0.682061i	$0.761084\pi$
$224$	77.7963	−	66.0807i	0.347305	−	0.295003i
$225$	−3.70982	+	68.4236i	−0.0164881	+	0.304105i
$226$	349.096	+	658.465i	1.54467	+	2.91356i
$227$	−32.6458	+	148.312i	−0.143814	+	0.653355i	0.848457	+	0.529265i	$0.177532\pi$
$227$	−32.6458	+	148.312i	−0.143814	+	0.653355i	−0.992271	+	0.124090i	$0.960399\pi$
$228$	258.463	−	119.578i	1.13361	−	0.524464i
$229$	−99.8528	+	165.957i	−0.436038	+	0.724702i	−0.994490	−	0.104836i	$-0.966568\pi$
$229$	−99.8528	+	165.957i	−0.436038	+	0.724702i	0.558451	+	0.829537i	$0.311396\pi$
$230$	−44.6232	+	84.1683i	−0.194014	+	0.365949i
$231$	22.2441	+	18.8943i	0.0962950	+	0.0817937i
$232$	782.806	−	826.399i	3.37416	−	3.56206i
$233$	−15.3627	+	141.258i	−0.0659343	+	0.606256i	0.913829	+	0.406098i	$0.133111\pi$
$233$	−15.3627	+	141.258i	−0.0659343	+	0.606256i	−0.979764	+	0.200158i	$0.935855\pi$
$234$	−29.8292	+	74.8657i	−0.127475	+	0.319939i
$235$			127.248i			0.541480i
$236$	−469.148	−	366.636i	−1.98791	−	1.55354i
$237$	122.029			0.514890
$238$	18.0278	+	7.18293i	0.0757471	+	0.0301804i
$239$	−173.497	−	18.8689i	−0.725929	−	0.0789495i	−0.262309	−	0.964984i	$-0.584484\pi$
$239$	−173.497	−	18.8689i	−0.725929	−	0.0789495i	−0.463620	+	0.886034i	$0.653450\pi$
$240$	−84.0195	−	79.5875i	−0.350081	−	0.331615i
$241$	23.1969	−	27.3095i	0.0962527	−	0.113317i	−0.711927	−	0.702254i	$-0.752177\pi$
$241$	23.1969	−	27.3095i	0.0962527	−	0.113317i	0.808180	+	0.588936i	$0.200453\pi$
$242$	−166.287	−	88.1599i	−0.687137	−	0.364297i
$243$	−13.3571	−	8.03669i	−0.0549674	−	0.0330728i
$244$	403.955	+	873.135i	1.65556	+	3.57842i
$245$	−67.9284	−	14.9522i	−0.277259	−	0.0610293i
$246$	−243.218	+	128.946i	−0.988689	+	0.524170i
$247$	116.418	+	6.31202i	0.471329	+	0.0255547i
$248$	615.935	+	725.135i	2.48361	+	2.92393i
$249$	−56.4308	−	256.368i	−0.226630	−	1.02959i
$250$	−159.682	−	210.058i	−0.638729	−	0.840234i
$251$	79.4639	−	75.2722i	0.316589	−	0.299889i	−0.512859	−	0.858473i	$-0.671414\pi$
$251$	79.4639	−	75.2722i	0.316589	−	0.299889i	0.829448	+	0.558584i	$0.188655\pi$
$252$	2.11123	+	38.9393i	0.00837789	+	0.154521i
$253$	−193.617	+	116.496i	−0.765286	+	0.460458i
$254$	−104.857	−	71.0948i	−0.412823	−	0.279901i
$255$	2.73237	−	9.84109i	0.0107152	−	0.0385925i
$256$	23.4613	−	2.55157i	0.0916457	−	0.00996707i
$257$	202.865	+	154.214i	0.789358	+	0.600054i	0.920245	−	0.391343i	$-0.127989\pi$
$257$	202.865	+	154.214i	0.789358	+	0.600054i	−0.130887	+	0.991397i	$0.541782\pi$
$258$	84.9095	+	39.2833i	0.329107	+	0.152261i
$259$	−6.58860	+	4.46718i	−0.0254386	+	0.0172478i
$260$	−33.8792	−	100.550i	−0.130304	−	0.386730i
$261$	24.1589	+	147.363i	0.0925627	+	0.564608i
$262$	4.10759	−	25.0552i	0.0156778	−	0.0956305i
$263$	3.45340	+	1.16359i	0.0131308	+	0.00442428i	0.325859	−	0.945418i	$-0.394346\pi$
$263$	3.45340	+	1.16359i	0.0131308	+	0.00442428i	−0.312728	+	0.949843i	$0.601243\pi$
$264$	−138.622	−	499.273i	−0.525085	−	1.89118i
$265$	7.14957	+	17.9441i	0.0269795	+	0.0677134i
$266$	73.1828	−	29.1587i	0.275123	−	0.109619i
$267$	−20.1431	+	5.59269i	−0.0754422	+	0.0209464i
$268$	−84.8415	+	251.801i	−0.316573	+	0.939554i
$269$	47.6089	+	7.80508i	0.176985	+	0.0290152i	0.249623	−	0.968343i	$-0.419693\pi$
$269$	47.6089	+	7.80508i	0.176985	+	0.0290152i	−0.0726379	+	0.997358i	$0.523142\pi$
$270$	28.2810	−	4.63644i	0.104745	−	0.0171720i
$271$	198.556	−	66.9014i	0.732680	−	0.246869i	0.0718618	−	0.997415i	$-0.477106\pi$
$271$	198.556	−	66.9014i	0.732680	−	0.246869i	0.660818	+	0.750546i	$0.270209\pi$
$272$	−102.429	−	151.072i	−0.376578	−	0.555411i
$273$	−6.70353	+	14.4894i	−0.0245550	+	0.0530749i
$274$	181.134	−	238.278i	0.661073	−	0.869627i
$275$	−32.3070	−	297.058i	−0.117480	−	1.08021i
$276$	−290.916	−	80.7724i	−1.05404	−	0.292654i
$277$	−25.0894	+	37.0040i	−0.0905753	+	0.133589i	−0.870277	−	0.492562i	$-0.836060\pi$
$277$	−25.0894	+	37.0040i	−0.0905753	+	0.133589i	0.779702	+	0.626151i	$0.215371\pi$
$278$	152.609	+	253.638i	0.548952	+	0.912366i
$279$	−124.631	+	6.75728i	−0.446705	+	0.0242197i
$280$	−29.7614	−	31.4187i	−0.106291	−	0.112210i
$281$	170.954	−	129.956i	0.608379	−	0.462478i	−0.255064	−	0.966924i	$-0.582097\pi$
$281$	170.954	−	129.956i	0.608379	−	0.462478i	0.863443	+	0.504447i	$0.168303\pi$
$282$	−549.960	+	121.055i	−1.95021	+	0.429274i
$283$	−270.773	+	229.996i	−0.956794	+	0.812708i	−0.982367	−	0.186965i	$-0.940135\pi$
$283$	−270.773	+	229.996i	−0.956794	+	0.812708i	0.0255726	+	0.999673i	$0.491859\pi$
$284$	−28.2873	+	521.728i	−0.0996031	+	1.83707i
$285$	−19.4205	−	36.6309i	−0.0681420	−	0.128530i
$286$	75.5454	−	343.206i	0.264145	−	1.20002i
$287$	−49.4944	+	22.8986i	−0.172454	+	0.0797859i
$288$	122.566	−	203.707i	0.425578	−	0.707316i
$289$	−127.825	+	241.103i	−0.442301	+	0.834268i
$290$	−209.240	−	177.730i	−0.721518	−	0.612863i
$291$	−85.7498	+	90.5249i	−0.294673	+	0.311082i
$292$	72.0852	−	662.813i	0.246867	−	2.26991i
$293$	−20.2722	+	50.8793i	−0.0691883	+	0.173649i	−0.959505	−	0.281693i	$-0.909104\pi$
$293$	−20.2722	+	50.8793i	−0.0691883	+	0.173649i	0.890316	+	0.455343i	$0.150483\pi$
$294$		−	307.809i		−	1.04697i
$295$	−49.6010	+	71.0910i	−0.168139	+	0.240986i
$296$	141.326			0.477452
$297$	63.1480	+	25.1604i	0.212619	+	0.0847153i
$298$	−971.625	−	105.671i	−3.26049	−	0.354599i
$299$	−89.7368	−	85.0032i	−0.300123	−	0.284292i
$300$	258.473	−	304.298i	0.861578	−	1.01433i
$301$	16.3748	+	8.68139i	0.0544014	+	0.0288418i
$302$	572.457	+	344.436i	1.89555	+	1.14052i
$303$	−45.8141	−	99.0255i	−0.151202	−	0.326817i
$304$	−723.616	−	159.280i	−2.38031	−	0.523947i
$305$	123.746	−	65.6060i	0.405725	−	0.215102i
$306$	45.1322	+	2.44700i	0.147491	+	0.00799673i
$307$	113.258	+	133.337i	0.368917	+	0.434323i	0.915028	−	0.403390i	$-0.132168\pi$
$307$	113.258	+	133.337i	0.368917	+	0.434323i	−0.546111	+	0.837713i	$0.683892\pi$
$308$	−36.5558	−	166.074i	−0.118688	−	0.539203i
$309$	99.8661	+	131.372i	0.323191	+	0.425151i
$310$	166.590	−	157.802i	0.537386	−	0.509039i
$311$	14.7631	+	272.289i	0.0474697	+	0.875526i	0.921194	+	0.389104i	$0.127215\pi$
$311$	14.7631	+	272.289i	0.0474697	+	0.875526i	−0.873724	+	0.486422i	$0.838302\pi$
$312$	242.869	−	146.130i	0.778427	−	0.468364i
$313$	−283.771	−	192.401i	−0.906615	−	0.614701i	0.0162312	−	0.999868i	$-0.494833\pi$
$313$	−283.771	−	192.401i	−0.906615	−	0.614701i	−0.922847	+	0.385168i	$0.874144\pi$
$314$	−106.301	+	382.863i	−0.338539	+	1.21931i
$315$	5.64407	−	0.613829i	0.0179177	−	0.00194866i
$316$	−566.024	−	430.280i	−1.79122	−	1.36165i
$317$	−70.9025	−	32.8030i	−0.223667	−	0.103479i	0.304856	−	0.952399i	$-0.401392\pi$
$317$	−70.9025	−	32.8030i	−0.223667	−	0.103479i	−0.528523	+	0.848919i	$0.677254\pi$
$318$	−70.7519	+	47.9710i	−0.222490	+	0.150852i
$319$	−207.921	−	617.088i	−0.651791	−	1.93445i
$320$	27.4707	+	167.564i	0.0858460	+	0.523637i
$321$	−57.9187	+	353.289i	−0.180432	+	1.10059i
$322$	−79.1464	−	26.6675i	−0.245796	−	0.0828185i
$323$	−17.4934	−	63.0056i	−0.0541592	−	0.195064i
$324$	33.6183	+	84.3756i	0.103760	+	0.260418i
$325$	151.845	−	60.5005i	0.467215	−	0.186155i
$326$	717.314	−	199.161i	2.20035	−	0.610924i
$327$	45.6711	−	135.547i	0.139667	−	0.414517i
$328$	955.453	+	156.639i	2.91297	+	0.477557i
$329$	−110.087	+	18.0479i	−0.334612	+	0.0548568i
$330$	−118.428	+	39.9031i	−0.358873	+	0.120919i
$331$	−18.6661	−	27.5305i	−0.0563932	−	0.0831737i	0.798447	−	0.602065i	$-0.205655\pi$
$331$	−18.6661	−	27.5305i	−0.0563932	−	0.0831737i	−0.854840	+	0.518891i	$0.826345\pi$
$332$	−642.215	+	1388.13i	−1.93438	+	4.18110i
$333$	−11.2200	+	14.7596i	−0.0336937	+	0.0443233i
$334$	20.4249	+	187.804i	0.0611523	+	0.562286i
$335$	37.2736	+	10.3490i	0.111264	+	0.0308924i
$336$	56.9377	−	83.9768i	0.169457	−	0.249931i
$337$	−211.245	−	351.091i	−0.626839	−	1.04181i	−0.993758	−	0.111561i	$-0.964415\pi$
$337$	−211.245	−	351.091i	−0.626839	−	1.04181i	0.366919	−	0.930253i	$-0.380413\pi$
$338$	−441.528	+	23.9389i	−1.30630	+	0.0708253i
$339$	236.481	+	249.650i	0.697583	+	0.736430i
$340$	−47.3742	+	36.0129i	−0.139336	+	0.105920i
$341$	531.545	−	117.002i	1.55878	−	0.343114i
$342$	139.842	−	118.783i	0.408895	−	0.347318i
$343$	6.71824	−	123.911i	0.0195867	−	0.361255i
$344$	−154.129	−	290.718i	−0.448050	−	0.845111i
$345$	−9.44913	+	42.9278i	−0.0273888	+	0.124429i
$346$	−999.775	+	462.545i	−2.88952	+	1.33684i
$347$	−57.3641	+	95.3399i	−0.165314	+	0.274755i	−0.928430	−	0.371507i	$-0.878841\pi$
$347$	−57.3641	+	95.3399i	−0.165314	+	0.274755i	0.763116	+	0.646262i	$0.223669\pi$
$348$	407.549	−	768.719i	1.17112	−	2.20896i
$349$	339.523	+	288.393i	0.972844	+	0.826341i	0.984819	−	0.173587i	$-0.0555358\pi$
$349$	339.523	+	288.393i	0.972844	+	0.826341i	−0.0119744	+	0.999928i	$0.503812\pi$
$350$	75.9520	−	80.1816i	0.217006	−	0.229090i
$351$	−4.02029	+	36.9659i	−0.0114538	+	0.105316i
$352$	−383.719	+	963.061i	−1.09011	+	2.73597i
$353$		−	418.077i		−	1.18435i	−0.805808	−	0.592177i	$-0.798269\pi$
$353$		−	418.077i		−	1.18435i	0.805808	−	0.592177i	$-0.201731\pi$
$354$	−354.440	−	146.742i	−1.00124	−	0.414527i
$355$	76.0679			0.214276
$356$	113.153	+	45.0841i	0.317845	+	0.126641i
$357$	8.90147	+	0.968093i	0.0249341	+	0.00271175i
$358$	701.287	+	664.295i	1.95890	+	1.85557i
$359$	308.714	−	363.447i	0.859929	−	1.01239i	−0.139825	−	0.990176i	$-0.544654\pi$
$359$	308.714	−	363.447i	0.859929	−	1.01239i	0.999753	−	0.0222101i	$-0.00707029\pi$
$360$	−89.0539	−	47.2134i	−0.247372	−	0.131148i
$361$	81.8788	+	49.2648i	0.226811	+	0.136468i
$362$	258.946	+	559.704i	0.715322	+	1.54614i
$363$	−84.8105	−	18.6682i	−0.233638	−	0.0514275i
$364$	82.1845	−	43.5715i	0.225782	−	0.119702i
$365$	−96.9229	−	5.25501i	−0.265542	−	0.0143973i
$366$	401.270	+	472.412i	1.09637	+	1.29074i
$367$	137.171	+	623.174i	0.373763	+	1.69802i	0.669549	+	0.742768i	$0.266488\pi$
$367$	137.171	+	623.174i	0.373763	+	1.69802i	−0.295786	+	0.955254i	$0.595581\pi$
$368$	475.379	+	625.351i	1.29179	+	1.69932i
$369$	−92.2133	+	87.3491i	−0.249901	+	0.236718i
$370$	−1.84533	−	34.0350i	−0.00498737	−	0.0919866i
$371$	−14.5101	+	8.73043i	−0.0391108	+	0.0235322i
$372$	601.920	+	408.112i	1.61806	+	1.09707i
$373$	117.034	−	421.518i	0.313764	−	1.13008i	−0.623606	−	0.781739i	$-0.714333\pi$
$373$	117.034	−	421.518i	0.313764	−	1.13008i	0.937370	−	0.348336i	$-0.113253\pi$
$374$	−195.940	+	21.3097i	−0.523903	+	0.0569778i
$375$	−96.9208	−	73.6773i	−0.258456	−	0.196473i
$376$	1797.52	+	831.622i	4.78064	+	2.21176i
$377$	294.826	−	199.897i	0.782032	−	0.530231i
$378$	8.02235	+	23.8095i	0.0212231	+	0.0629880i
$379$	−67.9683	−	414.588i	−0.179336	−	1.09390i	−0.911052	−	0.412291i	$-0.864729\pi$
$379$	−67.9683	−	414.588i	−0.179336	−	1.09390i	0.731716	−	0.681609i	$-0.238720\pi$
$380$	−39.0818	+	238.388i	−0.102847	+	0.627337i
$381$	−55.3933	−	18.6642i	−0.145389	−	0.0489873i
$382$	67.8319	+	244.308i	0.177570	+	0.639550i
$383$	−54.0623	−	135.686i	−0.141155	−	0.354272i	0.841355	−	0.540483i	$-0.181758\pi$
$383$	−54.0623	−	135.686i	−0.141155	−	0.354272i	−0.982510	+	0.186211i	$0.940379\pi$
$384$	−188.034	+	74.9195i	−0.489671	+	0.195103i
$385$	−23.8545	+	6.62318i	−0.0619598	+	0.0172031i
$386$	336.562	−	998.880i	0.871922	−	2.58777i
$387$	42.5982	+	6.98362i	0.110073	+	0.0180455i
$388$	716.942	−	117.537i	1.84779	−	0.302929i
$389$	−448.155	+	151.001i	−1.15207	+	0.388177i	−0.829575	−	0.558395i	$-0.811418\pi$
$389$	−448.155	+	151.001i	−1.15207	+	0.388177i	−0.322493	+	0.946572i	$0.604521\pi$
$390$	−38.3631	−	56.5814i	−0.0983670	−	0.145080i
$391$	−29.1083	+	62.9167i	−0.0744459	+	0.160912i
$392$	−655.160	+	861.848i	−1.67133	+	2.19859i
$393$	−1.26659	−	11.6461i	−0.00322287	−	0.0296338i
$394$	−243.115	−	67.5006i	−0.617044	−	0.171321i
$395$	−58.0896	+	85.6758i	−0.147062	+	0.216901i
$396$	−204.191	−	339.369i	−0.515635	−	0.856991i
$397$	−510.936	+	27.7021i	−1.28699	+	0.0697786i	−0.684893	−	0.728643i	$-0.740151\pi$
$397$	−510.936	+	27.7021i	−1.28699	+	0.0697786i	−0.602098	+	0.798422i	$0.705668\pi$
$398$	−720.221	−	760.328i	−1.80960	−	1.91037i
$399$	28.9364	−	21.9969i	0.0725224	−	0.0551301i
$400$	−1014.48	+	223.304i	−2.53621	+	0.558261i
$401$	512.552	−	435.366i	1.27818	−	1.08570i	0.286355	−	0.958123i	$-0.407556\pi$
$401$	512.552	−	435.366i	1.27818	−	1.08570i	0.991829	−	0.127576i	$-0.0407197\pi$
$402$	−9.26812	+	170.940i	−0.0230550	+	0.425225i
$403$	139.457	+	263.043i	0.346046	+	0.652713i
$404$	−136.663	+	620.867i	−0.338275	+	1.53680i
$405$	12.0009	−	5.55221i	0.0296319	−	0.0137092i
$406$	124.085	−	206.230i	0.305627	−	0.507956i
$407$	37.8694	−	71.4292i	0.0930452	−	0.175502i
$408$	−121.160	−	102.914i	−0.296960	−	0.252240i
$409$	3.61325	−	3.81446i	0.00883434	−	0.00932630i	−0.721563	−	0.692348i	$-0.756576\pi$
$409$	3.61325	−	3.81446i	0.00883434	−	0.00932630i	0.730398	+	0.683022i	$0.239335\pi$
$410$	25.2472	−	232.144i	0.0615785	−	0.566205i
$411$	51.1164	−	128.293i	0.124371	−	0.312147i
$412$		−	961.493i		−	2.33372i
$413$	−68.5387	−	32.8289i	−0.165953	−	0.0794888i
$414$	−194.522			−0.469859
$415$	206.857	+	82.4194i	0.498451	+	0.198601i
$416$	−563.763	−	61.3129i	−1.35520	−	0.147387i
$417$	99.1554	+	93.9250i	0.237783	+	0.225240i
$418$	−517.971	+	609.802i	−1.23916	+	1.45886i
$419$	−151.297	−	80.2127i	−0.361091	−	0.191438i	0.277978	−	0.960587i	$-0.410336\pi$
$419$	−151.297	−	80.2127i	−0.361091	−	0.191438i	−0.639070	+	0.769149i	$0.720680\pi$
$420$	−28.3441	−	17.0541i	−0.0674859	−	0.0406049i
$421$	20.4038	+	44.1020i	0.0484650	+	0.104755i	0.930295	−	0.366812i	$-0.119551\pi$
$421$	20.4038	+	44.1020i	0.0484650	+	0.104755i	−0.881830	+	0.471567i	$0.843689\pi$
$422$	−1493.51	−	328.746i	−3.53911	−	0.779018i
$423$	−229.559	+	121.705i	−0.542693	+	0.287718i
$424$	300.206	+	16.2767i	0.708033	+	0.0383885i
$425$	−59.3479	−	69.8697i	−0.139642	−	0.164399i
$426$	72.3661	+	328.763i	0.169874	+	0.771743i
$427$	74.3096	+	97.7526i	0.174027	+	0.228929i
$428$	1514.37	−	1434.49i	3.53824	−	3.35160i
$429$	−8.77841	−	161.908i	−0.0204625	−	0.377409i
$430$	−68.0002	+	40.9144i	−0.158140	+	0.0951497i
$431$	−625.239	−	423.922i	−1.45067	−	0.983578i	−0.995657	−	0.0930932i	$-0.970325\pi$
$431$	−625.239	−	423.922i	−1.45067	−	0.983578i	−0.455012	−	0.890485i	$-0.650365\pi$
$432$	63.2191	−	227.695i	0.146340	−	0.527071i
$433$	−576.360	+	62.6829i	−1.33109	+	0.144764i	−0.745858	−	0.666105i	$-0.767960\pi$
$433$	−576.360	+	62.6829i	−1.33109	+	0.144764i	−0.585227	+	0.810869i	$0.698995\pi$
$434$	160.149	+	121.742i	0.369006	+	0.280511i
$435$	−114.963	−	53.1875i	−0.264283	−	0.122270i
$436$	−689.790	+	467.689i	−1.58209	+	1.07268i
$437$	89.8566	+	266.685i	0.205622	+	0.610263i
$438$	−69.4943	−	423.896i	−0.158663	−	0.967800i
$439$	−54.1607	+	330.366i	−0.123373	+	0.752542i	0.850589	+	0.525831i	$0.176245\pi$
$439$	−54.1607	+	330.366i	−0.123373	+	0.752542i	−0.973962	+	0.226711i	$0.927203\pi$
$440$	416.525	+	140.344i	0.946649	+	0.318963i
$441$	−37.9951	−	136.846i	−0.0861567	−	0.310308i
$442$	−39.9062	−	100.157i	−0.0902854	−	0.226599i
$443$	519.525	−	206.998i	1.17274	−	0.467263i	0.299285	−	0.954164i	$-0.403252\pi$
$443$	519.525	−	206.998i	1.17274	−	0.467263i	0.873457	+	0.486901i	$0.161873\pi$
$444$	104.087	−	28.8995i	0.234429	−	0.0650890i
$445$	5.66214	−	16.8046i	0.0127239	−	0.0377632i
$446$	1422.24	+	233.164i	3.18887	+	0.522789i
$447$	−445.010	+	72.9557i	−0.995549	+	0.163212i
$448$	−141.070	+	47.5321i	−0.314889	+	0.106098i
$449$	308.562	+	455.095i	0.687221	+	1.01357i	0.998008	+	0.0630949i	$0.0200971\pi$
$449$	308.562	+	455.095i	0.687221	+	1.01357i	−0.310787	+	0.950480i	$0.600593\pi$
$450$	108.009	−	233.458i	0.240021	−	0.518797i
$451$	335.190	−	440.935i	0.743216	−	0.977684i
$452$	−216.625	−	1991.83i	−0.479258	−	4.40671i
$453$	297.020	+	82.4672i	0.655673	+	0.182047i
$454$	319.919	−	471.845i	0.704668	−	1.03931i
$455$	−6.98186	−	11.6039i	−0.0153448	−	0.0255032i
$456$	−644.376	+	34.9370i	−1.41310	+	0.0766163i
$457$	391.254	+	413.041i	0.856135	+	0.903811i	0.996267	−	0.0863221i	$-0.0275114\pi$
$457$	391.254	+	413.041i	0.856135	+	0.903811i	−0.140132	+	0.990133i	$0.544753\pi$
$458$	578.807	−	439.997i	1.26377	−	0.960693i
$459$	20.3670	−	4.48312i	0.0443726	−	0.00976714i
$460$	195.195	−	165.800i	0.424337	−	0.360436i
$461$	−8.20215	+	151.280i	−0.0177921	+	0.328156i	0.976065	+	0.217481i	$0.0697840\pi$
$461$	−8.20215	+	151.280i	−0.0177921	+	0.328156i	−0.993857	+	0.110675i	$0.964699\pi$
$462$	−51.3188	−	96.7975i	−0.111080	−	0.209518i
$463$	109.275	−	496.442i	0.236015	−	1.07223i	−0.698307	−	0.715799i	$-0.746063\pi$
$463$	109.275	−	496.442i	0.236015	−	1.07223i	0.934322	−	0.356430i	$-0.116006\pi$
$464$	−2054.49	+	950.509i	−4.42779	+	2.04851i
$465$	54.5840	−	90.7193i	0.117385	−	0.195095i
$466$	249.847	−	471.261i	0.536152	−	1.01129i
$467$	−143.631	−	122.001i	−0.307561	−	0.261245i	0.480291	−	0.877109i	$-0.340531\pi$
$467$	−143.631	−	122.001i	−0.307561	−	0.261245i	−0.787852	+	0.615864i	$0.788807\pi$
$468$	148.992	−	157.289i	0.318359	−	0.336087i
$469$	−3.66670	+	33.7147i	−0.00781812	+	0.0718864i
$470$	176.806	−	443.750i	0.376184	−	0.944149i
$471$			183.335i			0.389247i
$472$	680.077	+	1165.28i	1.44084	+	2.46882i
$473$	−188.236			−0.397961
$474$	−425.550	−	169.555i	−0.897785	−	0.357710i
$475$	−369.960	−	40.2355i	−0.778862	−	0.0847064i
$476$	−37.8754	−	35.8775i	−0.0795703	−	0.0753730i
$477$	−25.5336	+	30.0604i	−0.0535295	+	0.0630198i
$478$	578.817	+	306.869i	1.21091	+	0.641986i
$479$	−135.692	−	81.6434i	−0.283283	−	0.170445i	0.366820	−	0.930292i	$-0.380446\pi$
$479$	−135.692	−	81.6434i	−0.283283	−	0.170445i	−0.650103	+	0.759846i	$0.725274\pi$
$480$	84.6761	+	183.024i	0.176408	+	0.381301i
$481$	43.1907	+	9.50699i	0.0897935	+	0.0197650i
$482$	−118.840	+	63.0050i	−0.246556	+	0.130716i
$483$	−38.4788	−	2.08626i	−0.0796663	−	0.00431938i
$484$	327.564	+	385.638i	0.676785	+	0.796773i
$485$	−22.7374	−	103.297i	−0.0468813	−	0.212984i
$486$	35.4134	+	46.5855i	0.0728670	+	0.0958549i
$487$	−255.226	+	241.763i	−0.524079	+	0.496434i	−0.903381	−	0.428839i	$-0.858923\pi$
$487$	−255.226	+	241.763i	−0.524079	+	0.496434i	0.379302	+	0.925273i	$0.376164\pi$
$488$	−118.024	−	2176.82i	−0.241852	−	4.46070i
$489$	294.321	−	177.087i	0.601883	−	0.362141i
$490$	216.111	+	146.527i	0.441042	+	0.299034i
$491$	−45.8797	+	165.244i	−0.0934413	+	0.336545i	−0.995463	−	0.0951446i	$-0.969669\pi$
$491$	−45.8797	+	165.244i	−0.0934413	+	0.336545i	0.902022	+	0.431690i	$0.142082\pi$
$492$	735.724	−	80.0148i	1.49537	−	0.162632i
$493$	−159.041	−	120.900i	−0.322598	−	0.245233i
$494$	−397.214	−	183.771i	−0.804078	−	0.372006i
$495$	−47.7255	+	32.3587i	−0.0964151	+	0.0653710i
$496$	−604.142	−	1793.03i	−1.21803	−	3.61498i
$497$	10.7889	+	65.8095i	0.0217081	+	0.132413i
$498$	−159.423	+	972.437i	−0.320126	+	1.95268i
$499$	490.900	+	165.403i	0.983767	+	0.331470i	0.764804	−	0.644263i	$-0.222836\pi$
$499$	490.900	+	165.403i	0.983767	+	0.331470i	0.218963	+	0.975733i	$0.429732\pi$
$500$	189.772	+	683.496i	0.379544	+	1.36699i
$501$	32.2625	+	80.9728i	0.0643963	+	0.161622i
$502$	−381.702	+	152.084i	−0.760362	+	0.302956i
$503$	−528.160	+	146.643i	−1.05002	+	0.291537i	−0.749338	−	0.662188i	$-0.769628\pi$
$503$	−528.160	+	146.643i	−1.05002	+	0.291537i	−0.300682	+	0.953724i	$0.597214\pi$
$504$	28.2155	−	83.7406i	0.0559831	−	0.166152i
$505$	91.3342	+	14.9735i	0.180860	+	0.0296505i
$506$	837.067	−	137.230i	1.65428	−	0.271206i
$507$	−193.340	+	65.1439i	−0.381342	+	0.128489i
$508$	191.128	+	281.892i	0.376236	+	0.554906i
$509$	−100.368	+	216.942i	−0.197187	+	0.426213i	−0.980795	−	0.195043i	$-0.937515\pi$
$509$	−100.368	+	216.942i	−0.197187	+	0.426213i	0.783608	+	0.621256i	$0.213377\pi$
$510$	−23.2024	+	30.5222i	−0.0454949	+	0.0598475i
$511$	−9.20051	−	84.5973i	−0.0180049	−	0.165552i
$512$	−535.768	−	148.755i	−1.04642	−	0.290538i
$513$	47.5089	−	70.0704i	0.0926100	−	0.136589i
$514$	−493.175	−	819.663i	−0.959484	−	1.59467i
$515$	−139.775	+	7.57837i	−0.271407	+	0.0147153i
$516$	−172.965	−	182.597i	−0.335203	−	0.353870i
$517$	901.982	−	685.669i	1.74465	−	1.32624i
$518$	29.1834	−	6.42374i	0.0563385	−	0.0124010i
$519$	−387.386	+	329.049i	−0.746409	+	0.634005i
$520$	−13.0167	+	240.080i	−0.0250322	+	0.461691i
$521$	−221.253	−	417.328i	−0.424671	−	0.801014i	0.575185	−	0.818024i	$-0.304930\pi$
$521$	−221.253	−	417.328i	−0.424671	−	0.801014i	−0.999855	+	0.0170097i	$0.994585\pi$
$522$	120.506	−	547.464i	0.230854	−	1.04878i
$523$	−179.665	+	83.1220i	−0.343528	+	0.158933i	−0.584065	−	0.811707i	$-0.698539\pi$
$523$	−179.665	+	83.1220i	−0.343528	+	0.158933i	0.240537	+	0.970640i	$0.422677\pi$
$524$	−35.1898	+	58.4859i	−0.0671561	+	0.111614i
$525$	23.8695	−	45.0226i	0.0454656	−	0.0857573i
$526$	−10.4263	−	8.85614i	−0.0198218	−	0.0168368i
$527$	114.831	−	121.226i	0.217896	−	0.230030i
$528$	−111.412	+	1024.42i	−0.211008	+	1.94018i
$529$	−85.3721	+	214.268i	−0.161384	+	0.405043i
$530$		−	72.5102i		−	0.136812i
$531$	−175.691	−	21.4878i	−0.330868	−	0.0404667i
$532$	−211.782			−0.398087
$533$	281.460	+	112.144i	0.528067	+	0.210401i
$534$	78.0156	+	8.48471i	0.146097	+	0.0158890i
$535$	−220.471	−	208.841i	−0.412095	−	0.390357i
$536$	389.791	−	458.897i	0.727222	−	0.856152i
$537$	393.778	+	208.768i	0.733293	+	0.388767i
$538$	−155.181	−	93.3694i	−0.288441	−	0.173549i
$539$	260.042	+	562.072i	0.482453	+	1.04281i
$540$	−75.2430	−	16.5622i	−0.139339	−	0.0306708i
$541$	−438.866	+	232.672i	−0.811213	+	0.430078i	−0.821737	−	0.569867i	$-0.806995\pi$
$541$	−438.866	+	232.672i	−0.811213	+	0.430078i	0.0105243	+	0.999945i	$0.496650\pi$
$542$	−785.381	−	42.5821i	−1.44904	−	0.0785648i
$543$	184.211	+	216.870i	0.339247	+	0.399393i
$544$	68.3714	+	310.614i	0.125683	+	0.570982i
$545$	73.4260	+	96.5902i	0.134727	+	0.177230i
$546$	43.5097	−	41.2146i	0.0796881	−	0.0754846i
$547$	29.3782	+	541.849i	0.0537079	+	0.990584i	0.893892	+	0.448282i	$0.147964\pi$
$547$	29.3782	+	541.849i	0.0537079	+	0.990584i	−0.840184	+	0.542301i	$0.817553\pi$
$548$	−689.468	+	414.839i	−1.25815	+	0.757005i
$549$	236.711	+	160.494i	0.431167	+	0.292339i
$550$	−300.088	+	1080.82i	−0.545614	+	1.96512i
$551$	−806.227	+	87.6825i	−1.46321	+	0.159133i
$552$	544.651	+	414.033i	0.986686	+	0.750060i
$553$	−82.3606	−	38.1041i	−0.148934	−	0.0689043i
$554$	138.910	−	94.1831i	0.250740	−	0.170006i
$555$	−5.02159	−	14.9036i	−0.00904792	−	0.0268533i
$556$	−128.742	−	785.294i	−0.231551	−	1.41240i
$557$	−25.2505	+	154.021i	−0.0453330	+	0.276519i	−0.999760	−	0.0219269i	$-0.993020\pi$
$557$	−25.2505	+	154.021i	−0.0453330	+	0.276519i	0.954427	+	0.298446i	$0.0964682\pi$
$558$	444.013	+	149.605i	0.795722	+	0.268110i
$559$	−27.5469	−	99.2149i	−0.0492789	−	0.177486i
$560$	31.8555	+	79.9513i	0.0568848	+	0.142770i
$561$	−84.4807	+	33.6602i	−0.150589	+	0.0600003i
$562$	−776.738	+	215.660i	−1.38210	+	0.383737i
$563$	−126.554	+	375.600i	−0.224786	+	0.667141i	0.774612	+	0.632437i	$0.217945\pi$
$563$	−126.554	+	375.600i	−0.224786	+	0.667141i	−0.999398	+	0.0347038i	$0.988951\pi$
$564$	1493.94	+	244.918i	2.64882	+	0.434252i
$565$	−287.850	+	47.1906i	−0.509469	+	0.0835233i
$566$	1263.84	−	425.836i	2.23292	−	0.752360i
$567$	6.50557	+	9.59499i	0.0114737	+	0.0169224i
$568$	497.138	−	1074.55i	0.875244	−	1.89181i
$569$	−535.559	+	704.516i	−0.941229	+	1.23817i	0.0298859	+	0.999553i	$0.490486\pi$
$569$	−535.559	+	704.516i	−0.941229	+	1.23817i	−0.971115	+	0.238612i	$0.923307\pi$
$570$	16.8275	+	154.727i	0.0295220	+	0.271450i
$571$	681.848	+	189.314i	1.19413	+	0.331548i	0.807042	−	0.590495i	$-0.201067\pi$
$571$	681.848	+	189.314i	1.19413	+	0.331548i	0.387088	+	0.922043i	$0.373481\pi$
$572$	−530.179	+	781.956i	−0.926887	+	1.36706i
$573$	60.3136	+	100.242i	0.105259	+	0.174942i
$574$	204.418	−	11.0832i	0.356129	−	0.0193088i
$575$	271.322	+	286.431i	0.471864	+	0.498140i
$576$	−276.017	+	209.823i	−0.479196	+	0.364275i
$577$	284.655	−	62.6574i	0.493337	−	0.108592i	0.0386678	−	0.999252i	$-0.487689\pi$
$577$	284.655	−	62.6574i	0.493337	−	0.108592i	0.454669	+	0.890660i	$0.349758\pi$
$578$	780.768	−	663.190i	1.35081	−	1.14739i
$579$	26.3300	−	485.628i	0.0454749	−	0.838736i
$580$	345.707	+	652.073i	0.596047	+	1.12426i
$581$	−41.9653	+	190.650i	−0.0722294	+	0.328142i
$582$	424.816	−	196.541i	0.729924	−	0.337699i
$583$	88.6693	−	147.370i	0.152091	−	0.252778i
$584$	−707.669	+	1334.80i	−1.21176	+	2.28562i
$585$	−24.0398	−	20.4196i	−0.0410937	−	0.0349053i
$586$	141.390	−	149.263i	0.241280	−	0.254716i
$587$	−82.8640	+	761.922i	−0.141165	+	1.29799i	0.682487	+	0.730898i	$0.260898\pi$
$587$	−82.8640	+	761.922i	−0.141165	+	1.29799i	−0.823652	+	0.567095i	$0.808067\pi$
$588$	−306.288	+	768.726i	−0.520898	+	1.30736i
$589$		−	677.840i		−	1.15083i
$590$	271.752	−	178.996i	0.460596	−	0.303383i
$591$	−116.417			−0.196982
$592$	−261.091	−	104.028i	−0.441032	−	0.175723i
$593$	−680.799	−	74.0414i	−1.14806	−	0.124859i	−0.485756	−	0.874095i	$-0.661456\pi$
$593$	−680.799	−	74.0414i	−1.14806	−	0.124859i	−0.662304	+	0.749236i	$0.730421\pi$
$594$	−185.256	−	175.484i	−0.311879	−	0.295427i
$595$	−4.91708	+	5.78883i	−0.00826400	+	0.00972913i
$596$	2321.40	+	1230.73i	3.89497	+	2.06498i
$597$	−414.050	−	249.126i	−0.693551	−	0.417296i
$598$	194.830	+	421.117i	0.325802	+	0.704209i
$599$	787.615	+	173.367i	1.31488	+	0.289428i	0.816408	−	0.577476i	$-0.195962\pi$
$599$	787.615	+	173.367i	1.31488	+	0.289428i	0.498476	+	0.866904i	$0.333893\pi$
$600$	−799.329	+	423.777i	−1.33221	+	0.706296i
$601$	−936.860	−	50.7951i	−1.55883	−	0.0845176i	−0.745576	−	0.666420i	$-0.767826\pi$
$601$	−936.860	−	50.7951i	−1.55883	−	0.0845176i	−0.813258	+	0.581903i	$0.802308\pi$
$602$	−45.0414	−	53.0268i	−0.0748195	−	0.0880844i
$603$	16.9800	+	77.1410i	0.0281592	+	0.127929i
$604$	−1086.93	−	1429.83i	−1.79955	−	2.36727i
$605$	53.4793	−	50.6583i	0.0883956	−	0.0837328i
$606$	22.1747	+	408.988i	0.0365919	+	0.674897i
$607$	444.865	−	267.666i	0.732891	−	0.440966i	−0.0995835	−	0.995029i	$-0.531751\pi$
$607$	444.865	−	267.666i	0.732891	−	0.440966i	0.832475	+	0.554063i	$0.186923\pi$
$608$	1068.63	+	724.552i	1.75762	+	1.19170i
$609$	29.7092	−	107.003i	0.0487836	−	0.175702i
$610$	−522.696	+	56.8466i	−0.856878	+	0.0931911i
$611$	493.399	+	375.072i	0.807527	+	0.613866i
$612$	−110.279	−	51.0205i	−0.180194	−	0.0833668i
$613$	−395.706	+	268.295i	−0.645523	+	0.437676i	−0.839522	−	0.543326i	$-0.817165\pi$
$613$	−395.706	+	268.295i	−0.645523	+	0.437676i	0.193998	+	0.981002i	$0.437854\pi$
$614$	−209.695	−	622.353i	−0.341523	−	1.01360i
$615$	−17.4308	−	106.323i	−0.0283428	−	0.172884i
$616$	−62.3402	+	380.258i	−0.101202	+	0.617303i
$617$	−245.196	−	82.6160i	−0.397400	−	0.133900i	0.113504	−	0.993538i	$-0.463793\pi$
$617$	−245.196	−	82.6160i	−0.397400	−	0.133900i	−0.510904	+	0.859638i	$0.670689\pi$
$618$	−165.726	−	596.891i	−0.268165	−	0.965844i
$619$	−200.428	−	503.035i	−0.323792	−	0.812658i	−0.997297	−	0.0734747i	$-0.976591\pi$
$619$	−200.428	−	503.035i	−0.323792	−	0.812658i	0.673505	−	0.739183i	$-0.264788\pi$
$620$	−573.066	+	228.330i	−0.924300	+	0.368275i
$621$	−86.4808	+	24.0113i	−0.139261	+	0.0386655i
$622$	326.852	−	970.063i	0.525486	−	1.55959i
$623$	15.3415	+	2.51510i	0.0246251	+	0.00403708i
$624$	−556.251	+	91.1928i	−0.891429	+	0.146142i
$625$	−443.277	+	149.357i	−0.709243	+	0.238972i
$626$	722.256	+	1065.25i	1.15376	+	1.70167i
$627$	−155.008	+	335.044i	−0.247221	+	0.534360i
$628$	646.451	−	850.391i	1.02938	−	1.35413i
$629$	−2.68171	−	24.6580i	−0.00426346	−	0.0392018i
$630$	−20.5354	−	5.70163i	−0.0325959	−	0.00905020i
$631$	−75.9001	+	111.944i	−0.120285	+	0.177408i	−0.883065	−	0.469251i	$-0.844524\pi$
$631$	−75.9001	+	111.944i	−0.120285	+	0.177408i	0.762779	+	0.646659i	$0.223834\pi$
$632$	830.627	+	1380.51i	1.31428	+	2.18436i
$633$	−704.565	+	38.2004i	−1.11306	+	0.0603482i
$634$	201.679	+	212.910i	0.318106	+	0.335820i
$635$	39.4730	−	30.0066i	0.0621622	−	0.0472545i
$636$	224.431	−	49.4010i	0.352879	−	0.0776745i
$637$	−258.201	+	219.317i	−0.405338	+	0.344297i
$638$	−132.340	+	2440.87i	−0.207429	+	3.82581i
$639$	72.7543	+	137.229i	0.113856	+	0.214756i
$640$	36.9095	−	167.682i	0.0576711	−	0.262003i
$641$	323.707	−	149.763i	0.505002	−	0.233639i	−0.150810	−	0.988563i	$-0.548188\pi$
$641$	323.707	−	149.763i	0.505002	−	0.233639i	0.655813	+	0.754924i	$0.272326\pi$
$642$	692.861	−	1151.54i	1.07922	−	1.79368i
$643$	−61.6730	+	116.328i	−0.0959144	+	0.180914i	−0.926826	−	0.375490i	$-0.877474\pi$
$643$	−61.6730	+	116.328i	−0.0959144	+	0.180914i	0.830912	+	0.556404i	$0.187819\pi$
$644$	171.126	+	145.355i	0.265723	+	0.225707i
$645$	−25.1813	+	26.5836i	−0.0390407	+	0.0412148i
$646$	−26.5394	+	244.025i	−0.0410826	+	0.377748i
$647$	154.824	−	388.579i	0.239295	−	0.600585i	−0.759456	−	0.650559i	$-0.774535\pi$
$647$	154.824	−	388.579i	0.239295	−	0.600585i	0.998751	+	0.0499741i	$0.0159139\pi$
$648$		−	205.813i		−	0.317613i
$649$	771.193	−	31.4789i	1.18828	−	0.0485038i
$650$	−613.591			−0.943986
$651$	86.2267	+	34.3559i	0.132453	+	0.0527740i
$652$	−1989.61	−	216.383i	−3.05155	−	0.331876i
$653$	463.803	+	439.337i	0.710264	+	0.672798i	0.954937	−	0.296808i	$-0.0959220\pi$
$653$	463.803	+	439.337i	0.710264	+	0.672798i	−0.244673	+	0.969606i	$0.578681\pi$
$654$	−347.606	+	409.234i	−0.531508	+	0.625740i
$655$	8.77960	+	4.65465i	0.0134040	+	0.00710634i
$656$	−1649.85	−	992.679i	−2.51501	−	1.51323i
$657$	−83.2206	−	179.878i	−0.126668	−	0.273787i
$658$	408.983	+	90.0240i	0.621555	+	0.136815i
$659$	−353.692	+	187.516i	−0.536710	+	0.284546i	−0.714634	−	0.699499i	$-0.753407\pi$
$659$	−353.692	+	187.516i	−0.536710	+	0.284546i	0.177924	+	0.984044i	$0.443062\pi$
$660$	335.470	+	18.1887i	0.508289	+	0.0275586i
$661$	60.6529	+	71.4062i	0.0917594	+	0.108027i	0.806125	−	0.591745i	$-0.201561\pi$
$661$	60.6529	+	71.4062i	0.0917594	+	0.108027i	−0.714366	+	0.699772i	$0.753285\pi$
$662$	26.8416	+	121.943i	0.0405463	+	0.184204i
$663$	−30.1047	−	39.6020i	−0.0454067	−	0.0597315i
$664$	2516.17	−	2383.45i	3.78942	−	3.58953i
$665$	1.66924	+	30.7874i	0.00251014	+	0.0462968i
$666$	59.6354	−	35.8814i	0.0895426	−	0.0538760i
$667$	711.633	+	482.499i	1.06692	+	0.723387i
$668$	135.867	−	489.348i	0.203393	−	0.732556i
$669$	661.082	−	71.8970i	0.988164	−	0.107469i
$670$	−115.604	−	87.8802i	−0.172544	−	0.131164i
$671$	−1131.84	−	523.645i	−1.68680	−	0.780395i
$672$	−146.332	+	99.2155i	−0.217756	+	0.147642i
$673$	282.322	+	837.901i	0.419497	+	1.24502i	0.924259	+	0.381765i	$0.124684\pi$
$673$	282.322	+	837.901i	0.419497	+	1.24502i	−0.504762	+	0.863258i	$0.668420\pi$
$674$	248.843	+	1517.87i	0.369203	+	2.25204i
$675$	19.2015	−	117.124i	0.0284466	−	0.173517i
$676$	1126.50	+	379.562i	1.66642	+	0.561482i
$677$	132.893	+	478.638i	0.196297	+	0.706998i	0.994512	+	0.104625i	$0.0333642\pi$
$677$	132.893	+	478.638i	0.196297	+	0.706998i	−0.798215	+	0.602373i	$0.794222\pi$
$678$	−477.798	−	1199.18i	−0.704717	−	1.76871i
$679$	86.1417	−	34.3220i	0.126866	−	0.0505479i
$680$	129.931	−	36.0752i	0.191075	−	0.0530517i
$681$	83.9867	−	249.264i	0.123329	−	0.366026i
$682$	−2016.22	−	330.543i	−2.95634	−	0.484667i
$683$	1023.55	−	167.803i	1.49861	−	0.245685i	0.644028	−	0.765002i	$-0.277262\pi$
$683$	1023.55	−	167.803i	1.49861	−	0.245685i	0.854581	+	0.519317i	$0.173814\pi$
$684$	−467.440	+	157.499i	−0.683391	+	0.230261i
$685$	65.7405	+	96.9599i	0.0959715	+	0.141547i
$686$	−195.598	+	422.778i	−0.285128	+	0.616294i
$687$	203.015	−	267.061i	0.295509	−	0.388735i
$688$	70.7503	+	650.538i	0.102835	+	0.945549i
$689$	90.6513	+	25.1692i	0.131569	+	0.0365301i
$690$	92.5986	−	136.573i	0.134201	−	0.197931i
$691$	163.885	+	272.380i	0.237171	+	0.394182i	0.952468	−	0.304639i	$-0.0985359\pi$
$691$	163.885	+	272.380i	0.237171	+	0.394182i	−0.715296	+	0.698821i	$0.753708\pi$
$692$	2957.11	−	160.330i	4.27329	−	0.231691i
$693$	−34.7638	−	36.6997i	−0.0501643	−	0.0529578i
$694$	332.517	−	252.773i	0.479131	−	0.364226i
$695$	−113.145	+	24.9052i	−0.162799	+	0.0358348i
$696$	−1502.67	+	1276.38i	−2.15901	+	1.83388i
$697$	9.19957	−	169.676i	0.0131988	−	0.243438i
$698$	−783.303	−	1477.47i	−1.12221	−	2.11671i
$699$	52.9060	−	240.354i	0.0756881	−	0.343854i
$700$	−269.469	+	124.670i	−0.384956	+	0.178100i
$701$	290.321	−	482.517i	0.414153	−	0.688327i	−0.577625	−	0.816303i	$-0.696020\pi$
$701$	290.321	−	482.517i	0.414153	−	0.688327i	0.991777	+	0.127975i	$0.0408478\pi$
$702$	65.3828	−	123.325i	0.0931378	−	0.175677i
$703$	−76.7404	−	65.1838i	−0.109161	−	0.0927224i
$704$	1039.73	−	1097.63i	1.47689	−	1.55914i
$705$	23.8294	−	219.108i	0.0338006	−	0.310791i
$706$	−580.903	+	1457.96i	−0.822809	+	2.06510i
$707$			81.1407i			0.114768i
$708$	739.165	+	719.166i	1.04402	+	1.01577i
$709$	−388.144			−0.547452			−0.273726	−	0.961808i	$-0.588256\pi$
$709$	−388.144			−0.547452			−0.273726	+	0.961808i	$0.588256\pi$
$710$	−265.271	−	105.694i	−0.373621	−	0.148864i
$711$	−210.121	−	22.8521i	−0.295529	−	0.0321407i
$712$	−200.380	−	189.810i	−0.281433	−	0.266587i
$713$	−465.231	+	547.712i	−0.652497	+	0.768179i
$714$	−29.6969	−	15.7443i	−0.0415923	−	0.0220508i
$715$	117.854	+	70.9102i	0.164830	+	0.0991752i
$716$	−1090.39	−	2356.84i	−1.52289	−	3.29168i
$717$	295.211	+	64.9807i	0.411730	+	0.0906287i
$718$	−1581.57	+	838.497i	−2.20275	+	1.16782i
$719$	−295.084	−	15.9990i	−0.410408	−	0.0222517i	−0.152221	−	0.988347i	$-0.548642\pi$
$719$	−295.084	−	15.9990i	−0.410408	−	0.0222517i	−0.258188	+	0.966095i	$0.583125\pi$
$720$	129.769	+	152.776i	0.180234	+	0.212188i
$721$	−26.3810	−	119.850i	−0.0365894	−	0.166227i
$722$	−217.083	−	285.568i	−0.300670	−	0.395524i
$723$	−45.0569	+	42.6801i	−0.0623193	+	0.0590320i
$724$	−89.7575	−	1655.48i	−0.123974	−	2.28657i
$725$	−974.217	+	586.167i	−1.34375	+	0.808506i
$726$	269.820	+	182.943i	0.371653	+	0.251987i
$727$	329.107	−	1185.34i	0.452691	−	1.63045i	−0.287307	−	0.957839i	$-0.592760\pi$
$727$	329.107	−	1185.34i	0.452691	−	1.63045i	0.739998	−	0.672609i	$-0.234826\pi$
$728$	−209.549	+	22.7898i	−0.287842	+	0.0313047i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	330.697	+	152.997i	0.453010	+	0.209585i
$731$	−47.7987	+	32.4083i	−0.0653881	+	0.0443342i
$732$	−532.060	−	1579.10i	−0.726858	−	2.15724i
$733$	−31.5629	−	192.525i	−0.0430598	−	0.262653i	0.956519	−	0.291670i	$-0.0942108\pi$
$733$	−31.5629	−	192.525i	−0.0430598	−	0.262653i	−0.999579	+	0.0290163i	$0.990763\pi$
$734$	387.523	−	2363.78i	0.527960	−	3.22042i
$735$	114.166	+	38.4669i	0.155328	+	0.0523359i
$736$	−366.193	−	1318.91i	−0.497544	−	1.79199i
$737$	−127.490	−	319.975i	−0.172984	−	0.434158i
$738$	442.943	−	176.485i	0.600194	−	0.239139i
$739$	880.596	−	244.496i	1.19160	−	0.330847i	0.385549	−	0.922687i	$-0.374012\pi$
$739$	880.596	−	244.496i	1.19160	−	0.330847i	0.806056	+	0.591840i	$0.201598\pi$
$740$	−29.2584	+	86.8358i	−0.0395384	+	0.117346i
$741$	−199.278	−	32.6700i	−0.268932	−	0.0440891i
$742$	62.7316	−	10.2843i	0.0845439	−	0.0138603i
$743$	−1225.93	+	413.063i	−1.64997	+	0.555940i	−0.982104	−	0.188341i	$-0.939689\pi$
$743$	−1225.93	+	413.063i	−1.64997	+	0.555940i	−0.667867	+	0.744280i	$0.732793\pi$
$744$	−924.783	−	1363.95i	−1.24299	−	1.83327i
$745$	160.617	−	347.169i	0.215594	−	0.465998i
$746$	−993.816	+	1307.34i	−1.33219	+	1.75247i
$747$	49.1586	+	452.006i	0.0658081	+	0.605095i
$748$	510.547	+	141.753i	0.682549	+	0.189509i
$749$	149.407	−	220.359i	0.199475	−	0.294204i
$750$	235.619	+	391.602i	0.314159	+	0.522136i
$751$	1300.11	−	70.4898i	1.73117	−	0.0938613i	0.838593	−	0.544758i	$-0.183378\pi$
$751$	1300.11	−	70.4898i	1.73117	−	0.0938613i	0.892576	+	0.450897i	$0.148896\pi$
$752$	−2708.67	−	2859.51i	−3.60196	−	3.80254i
$753$	−150.925	+	114.730i	−0.200431	+	0.152364i
$754$	−1305.89	+	287.449i	−1.73195	+	0.381232i
$755$	−199.291	+	169.279i	−0.263961	+	0.224211i
$756$	3.65675	−	67.4449i	0.00483698	−	0.0892128i
$757$	−281.268	−	530.527i	−0.371556	−	0.700828i	0.625273	−	0.780406i	$-0.284988\pi$
$757$	−281.268	−	530.527i	−0.371556	−	0.700828i	−0.996829	+	0.0795779i	$0.974643\pi$
$758$	−339.030	+	1540.23i	−0.447270	+	2.03197i
$759$	355.205	−	164.335i	0.467991	−	0.216516i
$760$	282.214	−	469.044i	0.371335	−	0.617163i
$761$	85.3465	−	160.981i	0.112151	−	0.211538i	−0.821083	−	0.570809i	$-0.806630\pi$
$761$	85.3465	−	160.981i	0.112151	−	0.211538i	0.933233	+	0.359271i	$0.116975\pi$
$762$	167.239	+	142.054i	0.219474	+	0.186423i
$763$	−73.1499	+	77.2234i	−0.0958715	+	0.101210i
$764$	73.6974	−	677.636i	0.0964625	−	0.886958i
$765$	−6.54777	+	16.4337i	−0.00855918	+	0.0214819i
$766$			548.294i			0.715789i
$767$	129.450	+	401.872i	0.168775	+	0.523953i
$768$	−40.8758			−0.0532237
$769$	−45.0351	−	17.9436i	−0.0585632	−	0.0233337i	0.340673	−	0.940182i	$-0.389345\pi$
$769$	−45.0351	−	17.9436i	−0.0585632	−	0.0233337i	−0.399236	+	0.916848i	$0.630725\pi$
$770$	92.3904	+	10.0481i	0.119988	+	0.0130494i
$771$	−320.433	−	303.531i	−0.415608	−	0.393684i
$772$	−1834.48	+	2159.72i	−2.37627	+	2.79756i
$773$	−376.014	−	199.350i	−0.486434	−	0.257891i	0.207093	−	0.978321i	$-0.433600\pi$
$773$	−376.014	−	199.350i	−0.486434	−	0.257891i	−0.693527	+	0.720430i	$0.743944\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.48729 - 1.38946i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(7.32661 + 6.94014i) q^{4} +(0.951158 - 1.11979i) q^{5} +(5.74456 + 3.04557i) q^{6} +(1.10368 + 0.664063i) q^{7} +(-9.60207 - 20.7545i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(-3.48729 - 1.38946i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(7.32661 + 6.94014i) q^{4} +(0.951158 - 1.11979i) q^{5} +(5.74456 + 3.04557i) q^{6} +(1.10368 + 0.664063i) q^{7} +(-9.60207 - 20.7545i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-4.87287 + 2.58343i) q^{10} +(-13.0628 - 0.708243i) q^{11} +(-11.3160 - 13.3222i) q^{12} +(-1.53834 - 6.98874i) q^{13} +(-2.92617 - 3.84931i) q^{14} +(-1.84750 + 1.75004i) q^{15} +(2.46210 + 45.4108i) q^{16} +(-3.43897 + 2.06916i) q^{17} +(-9.32120 - 6.31993i) q^{18} +(-4.35868 + 15.6986i) q^{19} +(14.7403 - 1.60310i) q^{20} +(-1.77607 - 1.35013i) q^{21} +(44.5696 + 20.6201i) q^{22} +(14.2965 - 9.69329i) q^{23} +(12.6471 + 37.5353i) q^{24} +(3.69532 + 22.5405i) q^{25} +(-4.34597 + 26.5093i) q^{26} +(-4.92415 - 1.65914i) q^{27} +(3.47756 + 12.5250i) q^{28} +(18.4242 + 46.2413i) q^{29} +(8.87438 - 3.53588i) q^{30} +(-40.0881 + 11.1304i) q^{31} +(25.3033 - 75.0976i) q^{32} +(22.3601 + 3.66576i) q^{33} +(14.8677 - 2.43744i) q^{34} +(1.79339 - 0.604262i) q^{35} +(16.9902 + 25.0587i) q^{36} +(-2.59493 + 5.60885i) q^{37} +(37.0126 - 48.6892i) q^{38} +(1.34010 + 12.3220i) q^{39} +(-32.3738 - 8.98854i) q^{40} +(-23.7600 + 35.0433i) q^{41} +(4.31771 + 7.17609i) q^{42} +(14.3679 - 0.779003i) q^{43} +(-90.7906 - 95.8464i) q^{44} +(3.50893 - 2.66742i) q^{45} +(-63.3247 + 13.9388i) q^{46} +(-66.0098 + 56.0692i) q^{47} +(4.26449 - 78.6538i) q^{48} +(-22.1749 - 41.8263i) q^{49} +(18.4325 - 83.7397i) q^{50} +(6.30903 - 2.91887i) q^{51} +(37.2320 - 61.8801i) q^{52} +(-6.15817 + 11.6155i) q^{53} +(14.8666 + 12.6278i) q^{54} +(-13.2178 + 13.9539i) q^{55} +(3.18469 - 29.2828i) q^{56} +(10.4450 - 26.2151i) q^{57} -186.857i q^{58} +(-58.7342 + 5.59430i) q^{59} -25.6814 q^{60} +(88.5593 + 35.2853i) q^{61} +(155.264 + 16.8860i) q^{62} +(2.80537 + 2.65739i) q^{63} +(-74.8194 + 88.0842i) q^{64} +(-9.28912 - 4.92478i) q^{65} +(-72.8828 - 43.8521i) q^{66} +(11.0554 + 23.8957i) q^{67} +(-39.5562 - 8.70698i) q^{68} +(-26.4324 + 14.0136i) q^{69} +(-7.09366 - 0.384607i) q^{70} +(33.5178 + 39.4602i) q^{71} +(-14.7479 - 67.0004i) q^{72} +(-39.9812 - 52.5943i) q^{73} +(16.8426 - 15.9541i) q^{74} +(-2.14187 - 39.5044i) q^{75} +(-140.885 + 84.7674i) q^{76} +(-13.9468 - 9.45617i) q^{77} +(12.4476 - 44.8324i) q^{78} +(-70.0404 + 7.61735i) q^{79} +(53.1924 + 40.4358i) q^{80} +(8.16818 + 3.77900i) q^{81} +(131.549 - 89.1927i) q^{82} +(48.3924 + 143.624i) q^{83} +(-3.64246 - 22.2180i) q^{84} +(-0.953979 + 5.81901i) q^{85} +(-51.1873 - 17.2470i) q^{86} +(-23.0651 - 83.0731i) q^{87} +(110.730 + 277.912i) q^{88} +(11.2123 - 4.46740i) q^{89} +(-15.9429 + 4.42653i) q^{90} +(2.94313 - 8.73489i) q^{91} +(172.018 + 28.2009i) q^{92} +(71.1120 - 11.6582i) q^{93} +(308.102 - 103.812i) q^{94} +(13.4333 + 19.8126i) q^{95} +(-57.6331 + 124.572i) q^{96} +(43.5666 - 57.3109i) q^{97} +(19.2142 + 176.672i) q^{98} +(-37.8154 - 10.4994i) 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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