LMFDB - Embedded newform 570.2.n.a.179.17

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.17
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.17

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.44440 - 0.955888i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.79086 + 1.33896i) q^{5} +(-1.72883 + 0.105626i) q^{6} -2.53373i q^{7} -1.00000i q^{8} +(1.17255 - 2.76136i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.44440 - 0.955888i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.79086 + 1.33896i) q^{5} +(-1.72883 + 0.105626i) q^{6} -2.53373i q^{7} -1.00000i q^{8} +(1.17255 - 2.76136i) q^{9} +(2.22041 - 0.264142i) q^{10} +0.736692i q^{11} +(1.55002 + 0.772939i) q^{12} +(-2.38601 - 4.13269i) q^{13} +(-1.26686 + 2.19427i) q^{14} +(-1.30682 + 3.64585i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.03960 - 1.80064i) q^{17} +(-2.39614 + 1.80513i) q^{18} +(0.713722 + 4.30007i) q^{19} +(-2.05500 - 0.881452i) q^{20} +(-2.42196 - 3.65970i) q^{21} +(0.368346 - 0.637994i) q^{22} +(-3.12477 - 5.41225i) q^{23} +(-0.955888 - 1.44440i) q^{24} +(1.41437 - 4.79578i) q^{25} +4.77202i q^{26} +(-0.945920 - 5.10933i) q^{27} +(2.19427 - 1.26686i) q^{28} +(-1.30852 - 2.26642i) q^{29} +(2.95466 - 2.50399i) q^{30} -5.26487i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.704195 + 1.06407i) q^{33} +(-1.80064 + 1.03960i) q^{34} +(3.39256 + 4.53756i) q^{35} +(2.97769 - 0.365218i) q^{36} +10.3010 q^{37} +(1.53193 - 4.08083i) q^{38} +(-7.39673 - 3.68848i) q^{39} +(1.33896 + 1.79086i) q^{40} +(-1.22616 + 2.12377i) q^{41} +(0.267628 + 4.38038i) q^{42} +(-7.46202 - 4.30820i) q^{43} +(-0.637994 + 0.368346i) q^{44} +(1.59747 + 6.51522i) q^{45} +6.24953i q^{46} +(-0.809291 - 1.40173i) q^{47} +(0.105626 + 1.72883i) q^{48} +0.580221 q^{49} +(-3.62278 + 3.44608i) q^{50} +(-0.219618 - 3.59458i) q^{51} +(2.38601 - 4.13269i) q^{52} +(-11.0525 + 6.38115i) q^{53} +(-1.73547 + 4.89777i) q^{54} +(-0.986400 - 1.31931i) q^{55} -2.53373 q^{56} +(5.14128 + 5.52876i) q^{57} +2.61704i q^{58} +(2.59700 - 4.49814i) q^{59} +(-3.81081 + 0.691189i) q^{60} +(5.07194 + 8.78486i) q^{61} +(-2.63243 + 4.55951i) q^{62} +(-6.99654 - 2.97094i) q^{63} -1.00000 q^{64} +(9.80651 + 4.20630i) q^{65} +(-0.0778138 - 1.27361i) q^{66} +(2.74400 + 4.75275i) q^{67} +2.07920 q^{68} +(-9.68690 - 4.83050i) q^{69} +(-0.669264 - 5.62592i) q^{70} +(-0.182067 + 0.315350i) q^{71} +(-2.76136 - 1.17255i) q^{72} +(2.05162 + 1.18451i) q^{73} +(-8.92092 - 5.15050i) q^{74} +(-2.54132 - 8.27899i) q^{75} +(-3.36711 + 2.76814i) q^{76} +1.86658 q^{77} +(4.56152 + 6.89268i) q^{78} +(-0.280369 - 0.161871i) q^{79} +(-0.264142 - 2.22041i) q^{80} +(-6.25023 - 6.47570i) q^{81} +(2.12377 - 1.22616i) q^{82} +12.6729 q^{83} +(1.95842 - 3.92733i) q^{84} +(0.549205 + 4.61669i) q^{85} +(4.30820 + 7.46202i) q^{86} +(-4.05646 - 2.02281i) q^{87} +0.736692 q^{88} +(-6.18913 - 10.7199i) q^{89} +(1.87416 - 6.44108i) q^{90} +(-10.4711 + 6.04550i) q^{91} +(3.12477 - 5.41225i) q^{92} +(-5.03263 - 7.60455i) q^{93} +1.61858i q^{94} +(-7.03580 - 6.74519i) q^{95} +(0.772939 - 1.55002i) q^{96} +(-5.90419 + 10.2264i) q^{97} +(-0.502487 - 0.290111i) q^{98} +(2.03427 + 0.863811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80q + 40q^{4} + O(q^{10}) $	$ 80q + 40q^{4} + 30q^{15} - 40q^{16} + 8q^{19} + 8q^{25} - 4q^{30} + 48q^{39} + 12q^{45} - 128q^{49} - 36q^{54} + 12q^{55} + 30q^{60} - 24q^{61} - 80q^{64} + 4q^{66} + 36q^{70} + 16q^{76} + 24q^{79} + 32q^{81} - 8q^{85} - 54q^{90} + 24q^{91} - 60q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.44440	−	0.955888i	0.833922	−	0.551882i
$3$	1.44440	−	0.955888i	0.833922	−	0.551882i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.79086	+	1.33896i	−0.800898	+	0.598801i
$5$	−1.79086	+	1.33896i	−0.800898	+	0.598801i
$6$	−1.72883	+	0.105626i	−0.705791	+	0.0431216i
$7$		−	2.53373i		−	0.957659i	−0.877908	−	0.478830i	$-0.841061\pi$
$7$		−	2.53373i		−	0.957659i	0.877908	−	0.478830i	$-0.158939\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.17255	−	2.76136i	0.390852	−	0.920454i
$10$	2.22041	−	0.264142i	0.702156	−	0.0835291i
$11$			0.736692i			0.222121i	0.993814	+	0.111060i	$0.0354247\pi$
$11$			0.736692i			0.222121i	−0.993814	+	0.111060i	$0.964575\pi$
$12$	1.55002	+	0.772939i	0.447453	+	0.223128i
$13$	−2.38601	−	4.13269i	−0.661760	−	1.14620i	−0.980153	−	0.198243i	$-0.936477\pi$
$13$	−2.38601	−	4.13269i	−0.661760	−	1.14620i	0.318393	−	0.947959i	$-0.396857\pi$
$14$	−1.26686	+	2.19427i	−0.338584	+	0.586444i
$15$	−1.30682	+	3.64585i	−0.337419	+	0.941355i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.03960	−	1.80064i	0.252141	−	0.436720i	−0.711974	−	0.702205i	$-0.752199\pi$
$17$	1.03960	−	1.80064i	0.252141	−	0.436720i	0.964115	+	0.265485i	$0.0855321\pi$
$18$	−2.39614	+	1.80513i	−0.564776	+	0.425474i
$19$	0.713722	+	4.30007i	0.163739	+	0.986504i
$19$	0.713722	+	4.30007i	0.163739	+	0.986504i
$20$	−2.05500	−	0.881452i	−0.459513	−	0.197099i
$21$	−2.42196	−	3.65970i	−0.528515	−	0.798613i
$22$	0.368346	−	0.637994i	0.0785316	−	0.136021i
$23$	−3.12477	−	5.41225i	−0.651559	−	1.12853i	−0.982745	−	0.184967i	$-0.940782\pi$
$23$	−3.12477	−	5.41225i	−0.651559	−	1.12853i	0.331186	−	0.943565i	$-0.392551\pi$
$24$	−0.955888	−	1.44440i	−0.195120	−	0.294836i
$25$	1.41437	−	4.79578i	0.282875	−	0.959157i
$26$			4.77202i			0.935870i
$27$	−0.945920	−	5.10933i	−0.182042	−	0.983291i
$28$	2.19427	−	1.26686i	0.414679	−	0.239415i
$29$	−1.30852	−	2.26642i	−0.242986	−	0.420863i	0.718578	−	0.695447i	$-0.244793\pi$
$29$	−1.30852	−	2.26642i	−0.242986	−	0.420863i	−0.961563	+	0.274583i	$0.911460\pi$
$30$	2.95466	−	2.50399i	0.539445	−	0.457164i
$31$		−	5.26487i		−	0.945598i	−0.881170	−	0.472799i	$-0.843244\pi$
$31$		−	5.26487i		−	0.945598i	0.881170	−	0.472799i	$-0.156756\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.704195	+	1.06407i	0.122585	+	0.185231i
$34$	−1.80064	+	1.03960i	−0.308808	+	0.178290i
$35$	3.39256	+	4.53756i	0.573447	+	0.766987i
$36$	2.97769	−	0.365218i	0.496281	−	0.0608697i
$37$	10.3010			1.69347			0.846737	−	0.532012i	$-0.178564\pi$
$37$	10.3010			1.69347			0.846737	+	0.532012i	$0.178564\pi$
$38$	1.53193	−	4.08083i	0.248512	−	0.661998i
$39$	−7.39673	−	3.68848i	−1.18442	−	0.590629i
$40$	1.33896	+	1.79086i	0.211708	+	0.283160i
$41$	−1.22616	+	2.12377i	−0.191494	+	0.331677i	−0.945746	−	0.324908i	$-0.894667\pi$
$41$	−1.22616	+	2.12377i	−0.191494	+	0.331677i	0.754252	+	0.656585i	$0.228000\pi$
$42$	0.267628	+	4.38038i	0.0412958	+	0.675907i
$43$	−7.46202	−	4.30820i	−1.13795	−	0.656995i	−0.192026	−	0.981390i	$-0.561506\pi$
$43$	−7.46202	−	4.30820i	−1.13795	−	0.656995i	−0.945922	+	0.324395i	$0.894839\pi$
$44$	−0.637994	+	0.368346i	−0.0961811	+	0.0555302i
$45$	1.59747	+	6.51522i	0.238136	+	0.971232i
$46$			6.24953i			0.921443i
$47$	−0.809291	−	1.40173i	−0.118047	−	0.204464i	0.800947	−	0.598736i	$-0.204330\pi$
$47$	−0.809291	−	1.40173i	−0.118047	−	0.204464i	−0.918994	+	0.394272i	$0.870997\pi$
$48$	0.105626	+	1.72883i	0.0152458	+	0.249535i
$49$	0.580221			0.0828888
$50$	−3.62278	+	3.44608i	−0.512338	+	0.487350i
$51$	−0.219618	−	3.59458i	−0.0307527	−	0.503342i
$52$	2.38601	−	4.13269i	0.330880	−	0.573101i
$53$	−11.0525	+	6.38115i	−1.51818	+	0.876519i	−0.518404	+	0.855136i	$0.673474\pi$
$53$	−11.0525	+	6.38115i	−1.51818	+	0.876519i	−0.999771	+	0.0213828i	$0.993193\pi$
$54$	−1.73547	+	4.89777i	−0.236168	+	0.666502i
$55$	−0.986400	−	1.31931i	−0.133006	−	0.177896i
$56$	−2.53373			−0.338584
$57$	5.14128	+	5.52876i	0.680980	+	0.732302i
$58$			2.61704i			0.343634i
$59$	2.59700	−	4.49814i	0.338101	−	0.585609i	−0.645974	−	0.763359i	$-0.723549\pi$
$59$	2.59700	−	4.49814i	0.338101	−	0.585609i	0.984076	+	0.177751i	$0.0568820\pi$
$60$	−3.81081	+	0.691189i	−0.491973	+	0.0892322i
$61$	5.07194	+	8.78486i	0.649396	+	1.12479i	0.983267	+	0.182168i	$0.0583114\pi$
$61$	5.07194	+	8.78486i	0.649396	+	1.12479i	−0.333872	+	0.942619i	$0.608355\pi$
$62$	−2.63243	+	4.55951i	−0.334319	+	0.579058i
$63$	−6.99654	−	2.97094i	−0.881481	−	0.374303i
$64$	−1.00000			−0.125000
$65$	9.80651	+	4.20630i	1.21635	+	0.521728i
$66$	−0.0778138	−	1.27361i	−0.00957821	−	0.156771i
$67$	2.74400	+	4.75275i	0.335233	+	0.580641i	0.983530	−	0.180747i	$-0.0578516\pi$
$67$	2.74400	+	4.75275i	0.335233	+	0.580641i	−0.648296	+	0.761388i	$0.724518\pi$
$68$	2.07920			0.252141
$69$	−9.68690	−	4.83050i	−1.16617	−	0.581524i
$70$	−0.669264	−	5.62592i	−0.0799924	−	0.672426i
$71$	−0.182067	+	0.315350i	−0.0216074	+	0.0374251i	−0.876627	−	0.481171i	$-0.840212\pi$
$71$	−0.182067	+	0.315350i	−0.0216074	+	0.0374251i	0.855020	+	0.518596i	$0.173545\pi$
$72$	−2.76136	−	1.17255i	−0.325430	−	0.138187i
$73$	2.05162	+	1.18451i	0.240124	+	0.138636i	0.615234	−	0.788345i	$-0.289062\pi$
$73$	2.05162	+	1.18451i	0.240124	+	0.138636i	−0.375110	+	0.926981i	$0.622395\pi$
$74$	−8.92092	−	5.15050i	−1.03704	−	0.598733i
$75$	−2.54132	−	8.27899i	−0.293446	−	0.955976i
$76$	−3.36711	+	2.76814i	−0.386234	+	0.317527i
$77$	1.86658			0.212716
$78$	4.56152	+	6.89268i	0.516490	+	0.780442i
$79$	−0.280369	−	0.161871i	−0.0315440	−	0.0182119i	0.484145	−	0.874988i	$-0.339131\pi$
$79$	−0.280369	−	0.161871i	−0.0315440	−	0.0182119i	−0.515689	+	0.856776i	$0.672464\pi$
$80$	−0.264142	−	2.22041i	−0.0295320	−	0.248250i
$81$	−6.25023	−	6.47570i	−0.694470	−	0.719522i
$82$	2.12377	−	1.22616i	0.234531	−	0.135407i
$83$	12.6729			1.39103			0.695515	−	0.718512i	$-0.255176\pi$
$83$	12.6729			1.39103			0.695515	+	0.718512i	$0.255176\pi$
$84$	1.95842	−	3.92733i	0.213681	−	0.428507i
$85$	0.549205	+	4.61669i	0.0595697	+	0.500750i
$86$	4.30820	+	7.46202i	0.464565	+	0.804651i
$87$	−4.05646	−	2.02281i	−0.434898	−	0.216868i
$88$	0.736692			0.0785316
$89$	−6.18913	−	10.7199i	−0.656046	−	1.13631i	−0.981630	−	0.190792i	$-0.938894\pi$
$89$	−6.18913	−	10.7199i	−0.656046	−	1.13631i	0.325584	−	0.945513i	$-0.394439\pi$
$90$	1.87416	−	6.44108i	0.197554	−	0.678949i
$91$	−10.4711	+	6.04550i	−1.09767	+	0.633740i
$92$	3.12477	−	5.41225i	0.325779	−	0.564266i
$93$	−5.03263	−	7.60455i	−0.521859	−	0.788555i
$94$			1.61858i			0.166944i
$95$	−7.03580	−	6.74519i	−0.721858	−	0.692042i
$96$	0.772939	−	1.55002i	0.0788877	−	0.158198i
$97$	−5.90419	+	10.2264i	−0.599480	+	1.03833i	0.393418	+	0.919360i	$0.371293\pi$
$97$	−5.90419	+	10.2264i	−0.599480	+	1.03833i	−0.992898	+	0.118970i	$0.962041\pi$
$98$	−0.502487	−	0.290111i	−0.0507588	−	0.0293056i
$99$	2.03427	+	0.863811i	0.204452	+	0.0868163i
$100$	4.86046	−	1.17301i	0.486046	−	0.117301i
$101$	13.1130	−	7.57082i	1.30480	−	0.753325i	0.323574	−	0.946203i	$-0.395116\pi$
$101$	13.1130	−	7.57082i	1.30480	−	0.753325i	0.981223	+	0.192878i	$0.0617822\pi$
$102$	−1.60710	+	3.22281i	−0.159126	+	0.319106i
$103$	−6.38269			−0.628905			−0.314453	−	0.949273i	$-0.601821\pi$
$103$	−6.38269			−0.628905			−0.314453	+	0.949273i	$0.601821\pi$
$104$	−4.13269	+	2.38601i	−0.405243	+	0.233967i
$105$	9.23760	+	3.31112i	0.901497	+	0.323132i
$106$	12.7623			1.23958
$107$			3.06876i			0.296668i	0.988937	+	0.148334i	$0.0473911\pi$
$107$			3.06876i			0.296668i	−0.988937	+	0.148334i	$0.952609\pi$
$108$	3.95185	−	3.37385i	0.380267	−	0.324649i
$109$	4.74852	+	2.74156i	0.454826	+	0.262594i	0.709866	−	0.704337i	$-0.248755\pi$
$109$	4.74852	+	2.74156i	0.454826	+	0.262594i	−0.255040	+	0.966930i	$0.582089\pi$
$110$	0.194591	+	1.63576i	0.0185536	+	0.155963i
$111$	14.8787	−	9.84660i	1.41222	−	0.934598i
$112$	2.19427	+	1.26686i	0.207339	+	0.119707i
$113$			3.44589i			0.324162i	0.986777	+	0.162081i	$0.0518205\pi$
$113$			3.44589i			0.324162i	−0.986777	+	0.162081i	$0.948179\pi$
$114$	−1.68810	−	7.35869i	−0.158105	−	0.689204i
$115$	12.8428	+	5.50866i	1.19760	+	0.513685i
$116$	1.30852	−	2.26642i	0.121493	−	0.210432i
$117$	−14.2096	+	1.74283i	−1.31368	+	0.161124i
$118$	−4.49814	+	2.59700i	−0.414088	+	0.239074i
$119$	−4.56234	−	2.63407i	−0.418229	−	0.241465i
$120$	3.64585	+	1.30682i	0.332819	+	0.119295i
$121$	10.4573			0.950662
$122$		−	10.1439i		−	0.918384i
$123$	0.259029	+	4.23963i	0.0233558	+	0.382275i
$124$	4.55951	−	2.63243i	0.409456	−	0.236400i
$125$	3.88841	+	10.4824i	0.347790	+	0.937572i
$126$	4.57371	+	6.07117i	0.407459	+	0.540863i
$127$	5.90757	+	10.2322i	0.524212	+	0.907962i	0.999603	+	0.0281869i	$0.00897335\pi$
$127$	5.90757	+	10.2322i	0.524212	+	0.907962i	−0.475391	+	0.879775i	$0.657693\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−14.8963	+	0.910116i	−1.31154	+	0.0801313i
$130$	−6.38954	−	8.54602i	−0.560400	−	0.749536i
$131$	12.9619	+	7.48358i	1.13249	+	0.653844i	0.944560	−	0.328339i	$-0.106489\pi$
$131$	12.9619	+	7.48358i	1.13249	+	0.653844i	0.187930	+	0.982182i	$0.439822\pi$
$132$	−0.569417	+	1.14189i	−0.0495614	+	0.0993885i
$133$	10.8952	−	1.80838i	0.944734	−	0.156806i
$134$		−	5.48800i		−	0.474091i
$135$	8.53520	+	7.88355i	0.734593	+	0.678508i
$136$	−1.80064	−	1.03960i	−0.154404	−	0.0891451i
$137$	10.8434	+	18.7813i	0.926416	+	1.60460i	0.789269	+	0.614048i	$0.210460\pi$
$137$	10.8434	+	18.7813i	0.926416	+	1.60460i	0.137147	+	0.990551i	$0.456207\pi$
$138$	5.97385	+	9.02679i	0.508528	+	0.768412i
$139$	6.33726	+	10.9765i	0.537519	+	0.931011i	0.999037	+	0.0438798i	$0.0139719\pi$
$139$	6.33726	+	10.9765i	0.537519	+	0.931011i	−0.461517	+	0.887131i	$0.652695\pi$
$140$	−2.23336	+	5.20682i	−0.188753	+	0.440057i
$141$	−2.50884	−	1.25106i	−0.211282	−	0.105359i
$142$	0.315350	−	0.182067i	0.0264636	−	0.0152787i
$143$	3.04452	−	1.75775i	0.254595	−	0.146991i
$144$	1.80513	+	2.39614i	0.150428	+	0.199679i
$145$	5.37802	+	2.30679i	0.446620	+	0.191569i
$146$	−1.18451	−	2.05162i	−0.0980304	−	0.169794i
$147$	0.838069	−	0.554627i	0.0691228	−	0.0457449i
$148$	5.15050	+	8.92092i	0.423368	+	0.733295i
$149$	−7.04652	−	4.06831i	−0.577274	−	0.333289i	0.182775	−	0.983155i	$-0.441492\pi$
$149$	−7.04652	−	4.06831i	−0.577274	−	0.333289i	−0.760049	+	0.649866i	$0.774825\pi$
$150$	−1.93865	+	8.44048i	−0.158290	+	0.689162i
$151$		−	12.8411i		−	1.04499i	−0.852641	−	0.522496i	$-0.825001\pi$
$151$		−	12.8411i		−	1.04499i	0.852641	−	0.522496i	$-0.174999\pi$
$152$	4.30007	−	0.713722i	0.348782	−	0.0578905i
$153$	−3.75324	−	4.98207i	−0.303431	−	0.402776i
$154$	−1.61650	−	0.933288i	−0.130261	−	0.0752065i
$155$	7.04945	+	9.42865i	0.566225	+	0.757328i
$156$	−0.504049	−	8.24999i	−0.0403562	−	0.660528i
$157$	−13.5004	−	7.79447i	−1.07745	−	0.622067i	−0.147243	−	0.989100i	$-0.547040\pi$
$157$	−13.5004	−	7.79447i	−1.07745	−	0.622067i	−0.930208	+	0.367034i	$0.880373\pi$
$158$	0.161871	+	0.280369i	0.0128778	+	0.0223049i
$159$	−9.86448	+	19.7818i	−0.782304	+	1.56880i
$160$	−0.881452	+	2.05500i	−0.0696849	+	0.162462i
$161$	−13.7132	+	7.91731i	−1.08075	+	0.623971i
$162$	2.17501	+	8.73323i	0.170885	+	0.686147i
$163$			15.4275i			1.20838i	0.796842	+	0.604188i	$0.206503\pi$
$163$			15.4275i			1.20838i	−0.796842	+	0.604188i	$0.793497\pi$
$164$	−2.45232			−0.191494
$165$	−2.68587	−	0.962721i	−0.209095	−	0.0749477i
$166$	−10.9750	−	6.33644i	−0.851828	−	0.491803i
$167$	14.1230	−	8.15391i	1.09287	−	0.630969i	0.158531	−	0.987354i	$-0.449324\pi$
$167$	14.1230	−	8.15391i	1.09287	−	0.630969i	0.934339	+	0.356385i	$0.115991\pi$
$168$	−3.65970	+	2.42196i	−0.282352	+	0.186858i
$169$	−4.88607	+	8.46293i	−0.375852	+	0.650994i
$170$	1.83272	−	4.27277i	0.140563	−	0.327707i
$171$	12.7109	+	3.07122i	0.972029	+	0.234862i
$172$		−	8.61640i		−	0.656995i
$173$	−3.13191	−	1.80821i	−0.238115	−	0.137476i	0.376195	−	0.926540i	$-0.377232\pi$
$173$	−3.13191	−	1.80821i	−0.238115	−	0.137476i	−0.614310	+	0.789065i	$0.710566\pi$
$174$	2.50159	+	3.78003i	0.189645	+	0.286564i
$175$	−12.1512	−	3.58364i	−0.918545	−	0.270898i
$176$	−0.637994	−	0.368346i	−0.0480906	−	0.0277651i
$177$	−0.548622	−	8.97954i	−0.0412370	−	0.674944i
$178$			12.3783i			0.927789i
$179$	3.21520			0.240315			0.120158	−	0.992755i	$-0.461660\pi$
$179$	3.21520			0.240315			0.120158	+	0.992755i	$0.461660\pi$
$180$	−4.84361	+	4.64106i	−0.361022	+	0.345924i
$181$	−8.85537	+	5.11265i	−0.658214	+	0.380020i	−0.791596	−	0.611044i	$-0.790750\pi$
$181$	−8.85537	+	5.11265i	−0.658214	+	0.380020i	0.133382	+	0.991065i	$0.457416\pi$
$182$	12.0910			0.896244
$183$	15.7232	+	7.84060i	1.16230	+	0.579594i
$184$	−5.41225	+	3.12477i	−0.398997	+	0.230361i
$185$	−18.4477	+	13.7926i	−1.35630	+	1.01405i
$186$	0.556107	+	9.10205i	0.0407757	+	0.667394i
$187$	1.32652	+	0.765866i	0.0970047	+	0.0560057i
$188$	0.809291	−	1.40173i	0.0590236	−	0.102232i
$189$	−12.9456	+	2.39670i	−0.941657	+	0.174335i
$190$	2.72059	+	9.35940i	0.197372	+	0.679002i
$191$		−	13.0698i		−	0.945701i	−0.881143	−	0.472850i	$-0.843225\pi$
$191$		−	13.0698i		−	0.945701i	0.881143	−	0.472850i	$-0.156775\pi$
$192$	−1.44440	+	0.955888i	−0.104240	+	0.0689853i
$193$	10.6073	−	18.3725i	0.763534	−	1.32248i	−0.177485	−	0.984124i	$-0.556796\pi$
$193$	10.6073	−	18.3725i	0.763534	−	1.32248i	0.941018	−	0.338355i	$-0.109871\pi$
$194$	10.2264	−	5.90419i	0.734210	−	0.423896i
$195$	18.1852	−	3.29837i	1.30227	−	0.236201i
$196$	0.290111	+	0.502487i	0.0207222	+	0.0358919i
$197$	26.7052			1.90267			0.951333	−	0.308166i	$-0.0997151\pi$
$197$	26.7052			1.90267			0.951333	+	0.308166i	$0.0997151\pi$
$198$	−1.32982	−	1.76522i	−0.0945065	−	0.125449i
$199$	−1.29996	−	2.25160i	−0.0921519	−	0.159612i	0.816264	−	0.577678i	$-0.196041\pi$
$199$	−1.29996	−	2.25160i	−0.0921519	−	0.159612i	−0.908416	+	0.418067i	$0.862708\pi$
$200$	−4.79578	−	1.41437i	−0.339113	−	0.100011i
$201$	8.50652	+	4.24189i	0.600004	+	0.299200i
$202$	−15.1416			−1.06536
$203$	−5.74249	+	3.31543i	−0.403044	+	0.232697i
$204$	3.00319	−	1.98749i	0.210266	−	0.139152i
$205$	−0.647761	−	5.44516i	−0.0452416	−	0.380306i
$206$	5.52757	+	3.19134i	0.385124	+	0.222352i
$207$	−18.6091	+	2.28244i	−1.29342	+	0.158641i
$208$	4.77202			0.330880
$209$	−3.16782	+	0.525793i	−0.219123	+	0.0363699i
$210$	−6.34443	−	7.48631i	−0.437808	−	0.516604i
$211$	4.99550	+	2.88415i	0.343904	+	0.198553i	0.661997	−	0.749506i	$-0.269709\pi$
$211$	4.99550	+	2.88415i	0.343904	+	0.198553i	−0.318093	+	0.948060i	$0.603042\pi$
$212$	−11.0525	−	6.38115i	−0.759088	−	0.438259i
$213$	0.0384621	+	0.629525i	0.00263538	+	0.0431344i
$214$	1.53438	−	2.65762i	0.104888	−	0.181671i
$215$	19.1320	−	2.27596i	1.30479	−	0.155219i
$216$	−5.10933	+	0.945920i	−0.347646	+	0.0643617i
$217$	−13.3397			−0.905561
$218$	−2.74156	−	4.74852i	−0.185682	−	0.321611i
$219$	4.09561	−	0.250229i	0.276756	−	0.0169089i
$220$	0.649358	−	1.51390i	0.0437797	−	0.102067i
$221$	−9.92200			−0.667426
$222$	−17.8086	+	1.08805i	−1.19524	+	0.0730253i
$223$	10.6834	−	18.5042i	0.715412	−	1.23913i	−0.247388	−	0.968917i	$-0.579572\pi$
$223$	10.6834	−	18.5042i	0.715412	−	1.23913i	0.962800	−	0.270214i	$-0.0870945\pi$
$224$	−1.26686	−	2.19427i	−0.0846459	−	0.146611i
$225$	−11.5845	−	9.52892i	−0.772297	−	0.635261i
$226$	1.72294	−	2.98423i	0.114608	−	0.198508i
$227$		−	15.4916i		−	1.02822i	−0.857725	−	0.514108i	$-0.828123\pi$
$227$		−	15.4916i		−	1.02822i	0.857725	−	0.514108i	$-0.171877\pi$
$228$	−2.21741	+	7.21686i	−0.146851	+	0.477948i
$229$	−11.7275			−0.774978			−0.387489	−	0.921874i	$-0.626658\pi$
$229$	−11.7275			−0.774978			−0.387489	+	0.921874i	$0.626658\pi$
$230$	−8.36787	−	11.1920i	−0.551761	−	0.737982i
$231$	2.69607	−	1.78424i	0.177389	−	0.117394i
$232$	−2.26642	+	1.30852i	−0.148798	+	0.0859084i
$233$	−11.1235	+	19.2664i	−0.728724	+	1.26219i	0.228699	+	0.973497i	$0.426553\pi$
$233$	−11.1235	+	19.2664i	−0.728724	+	1.26219i	−0.957423	+	0.288689i	$0.906781\pi$
$234$	13.1773	+	5.59545i	0.861425	+	0.365786i
$235$	3.32619	+	1.42670i	0.216977	+	0.0930678i
$236$	5.19401			0.338101
$237$	−0.559694	+	0.0341956i	−0.0363560	+	0.00222124i
$238$	2.63407	+	4.56234i	0.170741	+	0.295733i
$239$		−	2.85417i		−	0.184621i	−0.995730	−	0.0923105i	$-0.970575\pi$
$239$		−	2.85417i		−	0.184621i	0.995730	−	0.0923105i	$-0.0294252\pi$
$240$	−2.50399	−	2.95466i	−0.161632	−	0.190723i
$241$	−2.89433	+	1.67104i	−0.186440	+	0.107641i	−0.590315	−	0.807173i	$-0.700996\pi$
$241$	−2.89433	+	1.67104i	−0.186440	+	0.107641i	0.403875	+	0.914814i	$0.367663\pi$
$242$	−9.05627	−	5.22864i	−0.582159	−	0.336110i
$243$	−15.2178	−	3.37894i	−0.976225	−	0.216759i
$244$	−5.07194	+	8.78486i	−0.324698	+	0.562393i
$245$	−1.03910	+	0.776893i	−0.0663854	+	0.0496339i
$246$	1.89549	−	3.80115i	0.120852	−	0.242352i
$247$	16.0679	−	13.2096i	1.02238	−	0.840506i
$248$	−5.26487			−0.334319
$249$	18.3047	−	12.1139i	1.16001	−	0.767685i
$250$	1.87372	−	11.0222i	0.118505	−	0.697106i
$251$	−4.22850	+	2.44132i	−0.266900	+	0.154095i	−0.627478	−	0.778634i	$-0.715913\pi$
$251$	−4.22850	+	2.44132i	−0.266900	+	0.154095i	0.360578	+	0.932729i	$0.382580\pi$
$252$	−0.925364	−	7.54465i	−0.0582924	−	0.475268i
$253$	3.98716	−	2.30199i	0.250671	−	0.144725i
$254$		−	11.8151i		−	0.741348i
$255$	5.20631	+	6.14334i	0.326032	+	0.384711i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.07388	−	1.19736i	0.129365	−	0.0746890i	−0.433921	−	0.900951i	$-0.642870\pi$
$257$	2.07388	−	1.19736i	0.129365	−	0.0746890i	0.563286	+	0.826262i	$0.309537\pi$
$258$	13.3556	+	6.65995i	0.831484	+	0.414631i
$259$		−	26.0999i		−	1.62177i
$260$	1.26049	+	10.5958i	0.0781723	+	0.657126i
$261$	−7.79271	+	0.955789i	−0.482357	+	0.0591618i
$262$	−7.48358	−	12.9619i	−0.462337	−	0.800792i
$263$	−4.58909	+	7.94853i	−0.282975	+	0.490127i	−0.972116	−	0.234500i	$-0.924655\pi$
$263$	−4.58909	+	7.94853i	−0.282975	+	0.490127i	0.689141	+	0.724627i	$0.257988\pi$
$264$	1.06407	−	0.704195i	0.0654892	−	0.0433402i
$265$	11.2494	−	26.2266i	0.691043	−	1.61109i
$266$	−10.3397	−	3.88150i	−0.633969	−	0.237990i
$267$	−19.1866	−	9.56763i	−1.17420	−	0.585530i
$268$	−2.74400	+	4.75275i	−0.167617	+	0.290320i
$269$	3.52258	−	6.10129i	0.214775	−	0.372002i	−0.738428	−	0.674333i	$-0.764431\pi$
$269$	3.52258	−	6.10129i	0.214775	−	0.372002i	0.953203	+	0.302331i	$0.0977647\pi$
$270$	−3.44992	−	11.0950i	−0.209956	−	0.675218i
$271$	−5.46433	+	9.46449i	−0.331934	+	0.574927i	−0.982891	−	0.184188i	$-0.941035\pi$
$271$	−5.46433	+	9.46449i	−0.331934	+	0.574927i	0.650957	+	0.759115i	$0.274368\pi$
$272$	1.03960	+	1.80064i	0.0630351	+	0.109180i
$273$	−9.34560	+	18.7413i	−0.565621	+	1.13427i
$274$		−	21.6868i		−	1.31015i
$275$	3.53301	+	1.04196i	0.213049	+	0.0628324i
$276$	−0.660113	−	10.8044i	−0.0397341	−	0.650346i
$277$		−	0.531383i		−	0.0319277i	−0.999873	−	0.0159638i	$-0.994918\pi$
$277$		−	0.531383i		−	0.0319277i	0.999873	−	0.0159638i	$-0.00508166\pi$
$278$		−	12.6745i		−	0.760167i
$279$	−14.5382	−	6.17335i	−0.870379	−	0.369589i
$280$	4.53756	−	3.39256i	0.271171	−	0.202744i
$281$	1.83424	+	3.17700i	0.109422	+	0.189524i	0.915536	−	0.402236i	$-0.131767\pi$
$281$	1.83424	+	3.17700i	0.109422	+	0.189524i	−0.806114	+	0.591760i	$0.798433\pi$
$282$	1.54718	+	2.33787i	0.0921335	+	0.139218i
$283$	−17.1468	−	9.89972i	−1.01927	−	0.588477i	−0.105379	−	0.994432i	$-0.533606\pi$
$283$	−17.1468	−	9.89972i	−1.01927	−	0.588477i	−0.913893	+	0.405955i	$0.866939\pi$
$284$	−0.364134			−0.0216074
$285$	−16.6101	−	3.01728i	−0.983899	−	0.178728i
$286$	−3.51550			−0.207876
$287$	5.38106	+	3.10675i	0.317634	+	0.183386i
$288$	−0.365218	−	2.97769i	−0.0215207	−	0.175462i
$289$	6.33846	+	10.9785i	0.372850	+	0.645796i
$290$	−3.50410	−	4.68675i	−0.205768	−	0.275215i
$291$	1.24727	+	20.4147i	0.0731164	+	1.19673i
$292$			2.36901i			0.138636i
$293$			5.12906i			0.299643i	0.988713	+	0.149821i	$0.0478699\pi$
$293$			5.12906i			0.299643i	−0.988713	+	0.149821i	$0.952130\pi$
$294$	−1.00310	+	0.0612865i	−0.0585021	+	0.00357430i
$295$	1.37196	+	11.5328i	0.0798784	+	0.671468i
$296$		−	10.3010i		−	0.598733i
$297$	3.76400	−	0.696851i	0.218409	−	0.0404354i
$298$	4.06831	+	7.04652i	0.235671	+	0.408194i
$299$	−14.9114	+	25.8274i	−0.862350	+	1.49363i
$300$	5.89916	−	6.34034i	0.340588	−	0.366060i
$301$	−10.9158	+	18.9067i	−0.629177	+	1.08977i
$302$	−6.42054	+	11.1207i	−0.369461	+	0.639925i
$303$	11.7036	−	23.4699i	0.672352	−	1.34831i
$304$	−4.08083	−	1.53193i	−0.234052	−	0.0878624i
$305$	−20.8457	−	8.94135i	−1.19362	−	0.511980i
$306$	0.759363	+	6.19122i	0.0434099	+	0.353928i
$307$	10.6455	−	18.4385i	0.607571	−	1.05234i	−0.384069	−	0.923304i	$-0.625477\pi$
$307$	10.6455	−	18.4385i	0.607571	−	1.05234i	0.991640	−	0.129039i	$-0.0411892\pi$
$308$	0.933288	+	1.61650i	0.0531790	+	0.0921088i
$309$	−9.21913	+	6.10114i	−0.524458	+	0.347082i
$310$	−1.39067	−	11.6902i	−0.0789850	−	0.663957i
$311$		−	18.5155i		−	1.04992i	−0.851128	−	0.524959i	$-0.824081\pi$
$311$		−	18.5155i		−	1.04992i	0.851128	−	0.524959i	$-0.175919\pi$
$312$	−3.68848	+	7.39673i	−0.208819	+	0.418757i
$313$	6.00769	−	3.46854i	0.339575	−	0.196054i	−0.320509	−	0.947245i	$-0.603854\pi$
$313$	6.00769	−	3.46854i	0.339575	−	0.196054i	0.660084	+	0.751192i	$0.270521\pi$
$314$	7.79447	+	13.5004i	0.439868	+	0.761873i
$315$	16.5078	−	4.04755i	0.930109	−	0.228053i
$316$		−	0.323742i		−	0.0182119i
$317$	−23.7623	+	13.7191i	−1.33462	+	0.770544i	−0.986004	−	0.166722i	$-0.946682\pi$
$317$	−23.7623	+	13.7191i	−1.33462	+	0.770544i	−0.348617	+	0.937265i	$0.613349\pi$
$318$	18.4338	−	12.1993i	1.03372	−	0.684105i
$319$	1.66965	−	0.963974i	0.0934825	−	0.0539722i
$320$	1.79086	−	1.33896i	0.100112	−	0.0748501i
$321$	2.93339	+	4.43250i	0.163726	+	0.247398i
$322$	15.8346			0.882428
$323$	8.48488	+	3.18520i	0.472111	+	0.177229i
$324$	2.48300	−	8.65071i	0.137945	−	0.480595i
$325$	−23.1942	+	5.59762i	−1.28658	+	0.310500i
$326$	7.71376	−	13.3606i	0.427226	−	0.739977i
$327$	9.47937	−	0.579160i	0.524210	−	0.0320276i
$328$	2.12377	+	1.22616i	0.117266	+	0.0677033i
$329$	−3.55161	+	2.05052i	−0.195807	+	0.113049i
$330$	1.84467	+	2.17667i	0.101546	+	0.119822i
$331$		−	21.6261i		−	1.18868i	−0.804214	−	0.594340i	$-0.797413\pi$
$331$		−	21.6261i		−	1.18868i	0.804214	−	0.594340i	$-0.202587\pi$
$332$	6.33644	+	10.9750i	0.347757	+	0.602334i
$333$	12.0785	−	28.4448i	0.661897	−	1.55876i
$334$	−16.3078			−0.892324
$335$	−11.2779	−	4.83741i	−0.616176	−	0.264296i
$336$	4.38038	−	0.267628i	0.238969	−	0.0146003i
$337$	−17.8583	+	30.9316i	−0.972806	+	1.68495i	−0.285812	+	0.958286i	$0.592263\pi$
$337$	−17.8583	+	30.9316i	−0.972806	+	1.68495i	−0.686994	+	0.726663i	$0.741070\pi$
$338$	8.46293	−	4.88607i	0.460323	−	0.265767i
$339$	3.29388	+	4.97722i	0.178899	+	0.270326i
$340$	−3.72357	+	2.78397i	−0.201939	+	0.150982i
$341$	3.87858			0.210037
$342$	−9.47237	−	9.01522i	−0.512207	−	0.487487i
$343$		−	19.2062i		−	1.03704i
$344$	−4.30820	+	7.46202i	−0.232283	+	0.402325i
$345$	23.8158	−	4.31961i	1.28220	−	0.232560i
$346$	1.80821	+	3.13191i	0.0972100	+	0.168373i
$347$	11.6976	−	20.2609i	0.627961	−	1.08766i	−0.359999	−	0.932953i	$-0.617223\pi$
$347$	11.6976	−	20.2609i	0.627961	−	1.08766i	0.987960	−	0.154708i	$-0.0494436\pi$
$348$	−0.276427	−	4.52440i	−0.0148180	−	0.242533i
$349$	19.1429			1.02469			0.512347	−	0.858778i	$-0.328776\pi$
$349$	19.1429			1.02469			0.512347	+	0.858778i	$0.328776\pi$
$350$	8.73144	+	9.17913i	0.466715	+	0.490645i
$351$	−18.8583	+	16.1001i	−1.00658	+	0.859359i
$352$	0.368346	+	0.637994i	0.0196329	+	0.0340052i
$353$	−26.2810			−1.39880			−0.699399	−	0.714732i	$-0.746549\pi$
$353$	−26.2810			−1.39880			−0.699399	+	0.714732i	$0.746549\pi$
$354$	−4.01465	+	8.05083i	−0.213376	+	0.427897i
$355$	−0.0961833	−	0.808528i	−0.00510488	−	0.0429122i
$356$	6.18913	−	10.7199i	0.328023	−	0.568153i
$357$	−9.10770	+	0.556452i	−0.482031	+	0.0294506i
$358$	−2.78444	−	1.60760i	−0.147162	−	0.0849642i
$359$	18.7474	+	10.8238i	0.989450	+	0.571259i	0.905110	−	0.425178i	$-0.139789\pi$
$359$	18.7474	+	10.8238i	0.989450	+	0.571259i	0.0843398	+	0.996437i	$0.473122\pi$
$360$	6.51522	−	1.59747i	0.343382	−	0.0841939i
$361$	−17.9812	+	6.13811i	−0.946379	+	0.323058i
$362$	10.2253			0.537430
$363$	15.1045	−	9.99600i	0.792778	−	0.524654i
$364$	−10.4711	−	6.04550i	−0.548835	−	0.316870i
$365$	−5.26018	+	0.625756i	−0.275330	+	0.0327536i
$366$	−9.69642	−	14.6518i	−0.506840	−	0.765861i
$367$	−31.0887	+	17.9491i	−1.62282	+	0.936935i	−0.636658	+	0.771146i	$0.719684\pi$
$367$	−31.0887	+	17.9491i	−1.62282	+	0.936935i	−0.986161	+	0.165789i	$0.946983\pi$
$368$	6.24953			0.325779
$369$	4.42676	+	5.87610i	0.230448	+	0.305898i
$370$	22.8724	−	2.72093i	1.18908	−	0.141454i
$371$	16.1681	+	28.0040i	0.839406	+	1.45389i
$372$	4.06942	−	8.16066i	0.210990	−	0.423110i
$373$	−6.39286			−0.331010			−0.165505	−	0.986209i	$-0.552925\pi$
$373$	−6.39286			−0.331010			−0.165505	+	0.986209i	$0.552925\pi$
$374$	−0.765866	−	1.32652i	−0.0396020	−	0.0685927i
$375$	15.6364	+	11.4238i	0.807460	+	0.589923i
$376$	−1.40173	+	0.809291i	−0.0722889	+	0.0417360i
$377$	−6.24427	+	10.8154i	−0.321596	+	0.557021i
$378$	12.4096	+	4.39722i	0.638282	+	0.226168i
$379$		−	4.61075i		−	0.236838i	−0.992964	−	0.118419i	$-0.962217\pi$
$379$		−	4.61075i		−	0.236838i	0.992964	−	0.118419i	$-0.0377826\pi$
$380$	2.32360	−	9.46577i	0.119198	−	0.485584i
$381$	18.3137	+	9.13238i	0.938240	+	0.467866i
$382$	−6.53492	+	11.3188i	−0.334356	+	0.579121i
$383$	−6.52926	−	3.76967i	−0.333630	−	0.192621i	0.323822	−	0.946118i	$-0.395032\pi$
$383$	−6.52926	−	3.76967i	−0.333630	−	0.192621i	−0.657451	+	0.753497i	$0.728366\pi$
$384$	1.72883	−	0.105626i	0.0882238	−	0.00539020i
$385$	−3.34278	+	2.49927i	−0.170364	+	0.127375i
$386$	−18.3725	+	10.6073i	−0.935134	+	0.539900i
$387$	−20.6461	+	15.5537i	−1.04950	+	0.790641i
$388$	−11.8084			−0.599480
$389$	−10.1328	+	5.85016i	−0.513752	+	0.296615i	−0.734375	−	0.678744i	$-0.762524\pi$
$389$	−10.1328	+	5.85016i	−0.513752	+	0.296615i	0.220623	+	0.975359i	$0.429191\pi$
$390$	−17.3981	−	6.23615i	−0.880985	−	0.315780i
$391$	−12.9940			−0.657137
$392$		−	0.580221i		−	0.0293056i
$393$	25.8756	−	1.58092i	1.30525	−	0.0797470i
$394$	−23.1274	−	13.3526i	−1.16514	−	0.672694i
$395$	0.718841	−	0.0855139i	0.0361688	−	0.00430267i
$396$	0.269053	+	2.19364i	0.0135204	+	0.110234i
$397$	−18.2960	−	10.5632i	−0.918249	−	0.530152i	−0.0351733	−	0.999381i	$-0.511198\pi$
$397$	−18.2960	−	10.5632i	−0.918249	−	0.530152i	−0.883076	+	0.469230i	$0.844532\pi$
$398$			2.59993i			0.130322i
$399$	14.0084	−	13.0266i	0.701296	−	0.652146i
$400$	3.44608	+	3.62278i	0.172304	+	0.181139i
$401$	−12.1204	+	20.9931i	−0.605262	+	1.04835i	0.386748	+	0.922186i	$0.373598\pi$
$401$	−12.1204	+	20.9931i	−0.605262	+	1.04835i	−0.992010	+	0.126160i	$0.959735\pi$
$402$	−5.24592	−	7.92685i	−0.261643	−	0.395355i
$403$	−21.7581	+	12.5620i	−1.08385	+	0.625759i
$404$	13.1130	+	7.57082i	0.652398	+	0.376662i
$405$	19.8640	+	3.22827i	0.987050	+	0.160414i
$406$	6.63086			0.329084
$407$			7.58866i			0.376156i
$408$	−3.59458	+	0.219618i	−0.177958	+	0.0108727i
$409$	28.4205	−	16.4086i	1.40530	−	0.811352i	0.410372	−	0.911918i	$-0.365399\pi$
$409$	28.4205	−	16.4086i	1.40530	−	0.811352i	0.994930	+	0.100566i	$0.0320655\pi$
$410$	−2.16160	+	5.03952i	−0.106754	+	0.248884i
$411$	33.6150	+	16.7626i	1.65811	+	0.826838i
$412$	−3.19134	−	5.52757i	−0.157226	−	0.272324i
$413$	−11.3971	−	6.58010i	−0.560813	−	0.323786i
$414$	17.2572	+	7.32792i	0.848146	+	0.360148i
$415$	−22.6954	+	16.9685i	−1.11407	+	0.832950i
$416$	−4.13269	−	2.38601i	−0.202622	−	0.116984i
$417$	19.6458	+	9.79663i	0.962058	+	0.479743i
$418$	3.00631	+	1.12856i	0.147044	+	0.0551998i
$419$			14.0621i			0.686977i	0.939157	+	0.343489i	$0.111609\pi$
$419$			14.0621i			0.686977i	−0.939157	+	0.343489i	$0.888391\pi$
$420$	1.75129	+	9.65555i	0.0854540	+	0.471143i
$421$	−3.61816	−	2.08894i	−0.176338	−	0.101809i	0.409233	−	0.912430i	$-0.365796\pi$
$421$	−3.61816	−	2.08894i	−0.176338	−	0.101809i	−0.585571	+	0.810621i	$0.699130\pi$
$422$	−2.88415	−	4.99550i	−0.140398	−	0.243177i
$423$	−4.81963	+	0.591136i	−0.234338	+	0.0287420i
$424$	6.38115	+	11.0525i	0.309896	+	0.536756i
$425$	−7.16511	−	7.53249i	−0.347559	−	0.365379i
$426$	0.281454	−	0.564416i	0.0136365	−	0.0273460i
$427$	22.2585	−	12.8509i	1.07716	−	0.621900i
$428$	−2.65762	+	1.53438i	−0.128461	+	0.0741670i
$429$	2.71727	−	5.44911i	0.131191	−	0.263085i
$430$	−17.7067	−	7.59495i	−0.853895	−	0.366261i
$431$	−14.0803	−	24.3877i	−0.678222	−	1.17472i	−0.975516	−	0.219929i	$-0.929417\pi$
$431$	−14.0803	−	24.3877i	−0.678222	−	1.17472i	0.297294	−	0.954786i	$-0.403916\pi$
$432$	4.89777	+	1.73547i	0.235644	+	0.0834980i
$433$	−0.681161	−	1.17981i	−0.0327345	−	0.0566978i	0.849194	−	0.528081i	$-0.177088\pi$
$433$	−0.681161	−	1.17981i	−0.0327345	−	0.0566978i	−0.881929	+	0.471383i	$0.843755\pi$
$434$	11.5526	+	6.66987i	0.554541	+	0.320164i
$435$	9.97302	−	1.80887i	0.478170	−	0.0867285i
$436$			5.48312i			0.262594i
$437$	21.0428	−	17.2996i	1.00662	−	0.827550i
$438$	−3.67202	−	1.83110i	−0.175456	−	0.0874934i
$439$	−23.6014	−	13.6262i	−1.12643	−	0.650345i	−0.183396	−	0.983039i	$-0.558709\pi$
$439$	−23.6014	−	13.6262i	−1.12643	−	0.650345i	−0.943035	+	0.332694i	$0.892042\pi$
$440$	−1.31931	+	0.986400i	−0.0628958	+	0.0470248i
$441$	0.680342	−	1.60220i	0.0323972	−	0.0762953i
$442$	8.59270	+	4.96100i	0.408713	+	0.235971i
$443$	−1.06718	−	1.84841i	−0.0507032	−	0.0878205i	0.839560	−	0.543267i	$-0.182813\pi$
$443$	−1.06718	−	1.84841i	−0.0507032	−	0.0878205i	−0.890263	+	0.455447i	$0.849480\pi$
$444$	15.9668	+	7.96204i	0.757749	+	0.377862i
$445$	25.4374	+	10.9108i	1.20585	+	0.517223i
$446$	−18.5042	+	10.6834i	−0.876198	+	0.505873i
$447$	−14.0668	+	0.859439i	−0.665338	+	0.0406501i
$448$			2.53373i			0.119707i
$449$	26.4135			1.24653			0.623266	−	0.782010i	$-0.285805\pi$
$449$	26.4135			1.24653			0.623266	+	0.782010i	$0.285805\pi$
$450$	5.26798	+	14.0445i	0.248335	+	0.662065i
$451$	−1.56456	−	0.903301i	−0.0736724	−	0.0425348i
$452$	−2.98423	+	1.72294i	−0.140366	+	0.0810404i
$453$	−12.2746	−	18.5476i	−0.576713	−	0.871443i
$454$	−7.74582	+	13.4162i	−0.363529	+	0.629652i
$455$	10.6576	−	24.8470i	0.499637	−	1.16485i
$456$	5.52876	−	5.14128i	0.258908	−	0.240763i
$457$			9.71282i			0.454347i	0.973854	+	0.227173i	$0.0729484\pi$
$457$			9.71282i			0.454347i	−0.973854	+	0.227173i	$0.927052\pi$
$458$	10.1564	+	5.86377i	0.474575	+	0.273996i
$459$	−10.1835	−	3.60840i	−0.475323	−	0.168426i
$460$	1.65076	+	13.8765i	0.0769673	+	0.646997i
$461$	14.1536	+	8.17157i	0.659197	+	0.380588i	0.791971	−	0.610559i	$-0.209055\pi$
$461$	14.1536	+	8.17157i	0.659197	+	0.380588i	−0.132774	+	0.991146i	$0.542388\pi$
$462$	−3.22699	+	0.197159i	−0.150133	+	0.00917266i
$463$			31.7195i			1.47413i	0.675821	+	0.737066i	$0.263789\pi$
$463$			31.7195i			1.47413i	−0.675821	+	0.737066i	$0.736211\pi$
$464$	2.61704			0.121493
$465$	19.1949	+	6.88022i	0.890143	+	0.319062i
$466$	19.2664	−	11.1235i	0.892501	−	0.515285i
$467$	28.7636			1.33102			0.665510	−	0.746389i	$-0.268214\pi$
$467$	28.7636			1.33102			0.665510	+	0.746389i	$0.268214\pi$
$468$	−8.61412	−	11.4344i	−0.398188	−	0.528557i
$469$	12.0422	−	6.95255i	0.556056	−	0.321039i
$470$	−2.16722	−	2.89866i	−0.0999662	−	0.133705i
$471$	−26.9506	+	1.64660i	−1.24182	+	0.0758712i
$472$	−4.49814	−	2.59700i	−0.207044	−	0.119537i
$473$	3.17382	−	5.49721i	0.145932	−	0.252762i
$474$	0.501807	+	0.250233i	0.0230488	+	0.0114936i
$475$	21.6317	+	2.65905i	0.992529	+	0.122005i
$476$		−	5.26814i		−	0.241465i
$477$	4.66103	+	38.0021i	0.213414	+	1.74000i
$478$	−1.42709	+	2.47178i	−0.0652734	+	0.113057i
$479$	7.51093	−	4.33644i	0.343183	−	0.198137i	−0.318496	−	0.947924i	$-0.603178\pi$
$479$	7.51093	−	4.33644i	0.343183	−	0.198137i	0.661679	+	0.749787i	$0.269844\pi$
$480$	0.691189	+	3.81081i	0.0315483	+	0.173939i
$481$	−24.5783	−	42.5708i	−1.12067	−	1.94106i
$482$	3.34208			0.152228
$483$	−12.2392	+	24.5440i	−0.556902	+	1.11679i
$484$	5.22864	+	9.05627i	0.237666	+	0.411649i
$485$	−3.11909	−	26.2195i	−0.141631	−	1.19057i
$486$	11.4896	+	10.5352i	0.521177	+	0.477885i
$487$	28.7235			1.30159			0.650793	−	0.759255i	$-0.274437\pi$
$487$	28.7235			1.30159			0.650793	+	0.759255i	$0.274437\pi$
$488$	8.78486	−	5.07194i	0.397672	−	0.229596i
$489$	14.7470	+	22.2834i	0.666882	+	1.00769i
$490$	1.28833	−	0.153261i	0.0582008	−	0.00692362i
$491$	13.2797	+	7.66703i	0.599304	+	0.346008i	0.768768	−	0.639528i	$-0.220870\pi$
$491$	13.2797	+	7.66703i	0.599304	+	0.346008i	−0.169464	+	0.985536i	$0.554204\pi$
$492$	−3.54212	+	2.34414i	−0.159691	+	0.105682i
$493$	−5.44135			−0.245066
$494$	−20.5200	+	3.40589i	−0.923239	+	0.153238i
$495$	−4.79971	+	1.17684i	−0.215731	+	0.0528951i
$496$	4.55951	+	2.63243i	0.204728	+	0.118200i
$497$	0.799010	+	0.461309i	0.0358405	+	0.0206925i
$498$	−21.9092	+	1.33859i	−0.981776	+	0.0599835i
$499$	14.2737	−	24.7228i	0.638978	−	1.10674i	−0.346679	−	0.937984i	$-0.612691\pi$
$499$	14.2737	−	24.7228i	0.638978	−	1.10674i	0.985657	−	0.168759i	$-0.0539759\pi$
$500$	−7.13380	+	8.60865i	−0.319033	+	0.384991i
$501$	12.6049	−	25.2775i	0.563148	−	1.12931i
$502$	4.88265			0.217923
$503$	−7.40272	−	12.8219i	−0.330071	−	0.571700i	0.652454	−	0.757828i	$-0.273739\pi$
$503$	−7.40272	−	12.8219i	−0.330071	−	0.571700i	−0.982525	+	0.186128i	$0.940406\pi$
$504$	−2.97094	+	6.99654i	−0.132336	+	0.311651i
$505$	−13.3466	+	31.1161i	−0.593917	+	1.38465i
$506$	−4.60398			−0.204672
$507$	1.03219	+	16.8944i	0.0458413	+	0.750304i
$508$	−5.90757	+	10.2322i	−0.262106	+	0.453981i
$509$	−8.13316	−	14.0870i	−0.360496	−	0.624397i	0.627546	−	0.778579i	$-0.284059\pi$
$509$	−8.13316	−	14.0870i	−0.360496	−	0.624397i	−0.988043	+	0.154182i	$0.950726\pi$
$510$	−1.43712	−	7.92345i	−0.0636369	−	0.350856i
$511$	3.00122	−	5.19826i	0.132766	−	0.229957i
$512$			1.00000i			0.0441942i
$513$	21.2953	−	7.71416i	0.940212	−	0.340589i
$514$	−2.39471			−0.105626
$515$	11.4305	−	8.54616i	0.503689	−	0.376589i
$516$	−8.23632	−	12.4455i	−0.362584	−	0.547882i
$517$	1.03265	−	0.596198i	0.0454157	−	0.0262208i
$518$	−13.0500	+	22.6032i	−0.573382	+	0.993127i
$519$	−6.25217	+	0.381988i	−0.274440	+	0.0167674i
$520$	4.20630	−	9.80651i	0.184459	−	0.430044i
$521$	−28.1371			−1.23271			−0.616355	−	0.787469i	$-0.711391\pi$
$521$	−28.1371			−1.23271			−0.616355	+	0.787469i	$0.711391\pi$
$522$	7.22658	+	3.06862i	0.316299	+	0.134310i
$523$	2.56924	+	4.45006i	0.112345	+	0.194588i	0.916715	−	0.399541i	$-0.130830\pi$
$523$	2.56924	+	4.45006i	0.112345	+	0.194588i	−0.804370	+	0.594128i	$0.797497\pi$
$524$			14.9672i			0.653844i
$525$	−20.9767	+	6.43901i	−0.915499	+	0.281022i
$526$	7.94853	−	4.58909i	0.346572	−	0.200094i
$527$	−9.48015	−	5.47337i	−0.412962	−	0.238424i
$528$	−1.27361	+	0.0778138i	−0.0554269	+	0.00338641i
$529$	−8.02832	+	13.9055i	−0.349057	+	0.604585i
$530$	−22.8555	+	17.0882i	−0.992781	+	0.742265i
$531$	−9.37587	−	12.4456i	−0.406878	−	0.540093i
$532$	7.01371	+	8.53134i	0.304083	+	0.369880i
$533$	11.7025			0.506892
$534$	11.8322	+	17.8791i	0.512031	+	0.773704i
$535$	−4.10894	−	5.49572i	−0.177645	−	0.237601i
$536$	4.75275	−	2.74400i	0.205288	−	0.118523i
$537$	4.64402	−	3.07337i	0.200404	−	0.132626i
$538$	−6.10129	+	3.52258i	−0.263045	+	0.151869i
$539$			0.427444i			0.0184113i
$540$	−2.55976	+	11.3335i	−0.110154	+	0.487715i
$541$	12.9388	+	22.4107i	0.556282	+	0.963510i	0.997803	+	0.0662582i	$0.0211061\pi$
$541$	12.9388	+	22.4107i	0.556282	+	0.963510i	−0.441520	+	0.897251i	$0.645561\pi$
$542$	9.46449	−	5.46433i	0.406535	−	0.234713i
$543$	−7.90353	+	15.8494i	−0.339173	+	0.680164i
$544$		−	2.07920i		−	0.0891451i
$545$	−12.1748	+	1.44832i	−0.521511	+	0.0620394i
$546$	17.4642	−	11.5576i	0.747398	−	0.494621i
$547$	−20.6948	−	35.8445i	−0.884848	−	1.53260i	−0.845888	−	0.533360i	$-0.820929\pi$
$547$	−20.6948	−	35.8445i	−0.884848	−	1.53260i	−0.0389597	−	0.999241i	$-0.512404\pi$
$548$	−10.8434	+	18.7813i	−0.463208	+	0.802299i
$549$	30.2053	−	3.70473i	1.28913	−	0.158114i
$550$	−2.53870	−	2.66887i	−0.108251	−	0.113801i
$551$	8.81184	−	7.24431i	0.375397	−	0.308618i
$552$	−4.83050	+	9.68690i	−0.205600	+	0.412302i
$553$	−0.410137	+	0.710378i	−0.0174408	+	0.0302084i
$554$	−0.265691	+	0.460191i	−0.0112881	+	0.0195516i
$555$	−13.4615	+	37.5559i	−0.571409	+	1.59416i
$556$	−6.33726	+	10.9765i	−0.268760	+	0.465506i
$557$	1.45549	+	2.52098i	0.0616710	+	0.106817i	0.895212	−	0.445640i	$-0.147024\pi$
$557$	1.45549	+	2.52098i	0.0616710	+	0.106817i	−0.833541	+	0.552457i	$0.813690\pi$
$558$	9.50378	+	12.6154i	0.402327	+	0.534051i
$559$			41.1176i			1.73909i
$560$	−5.62592	+	0.669264i	−0.237739	+	0.0282816i
$561$	2.64810	−	0.161791i	0.111803	−	0.00683081i
$562$		−	3.66849i		−	0.154746i
$563$		−	11.7302i		−	0.494369i	−0.968968	−	0.247184i	$-0.920495\pi$
$563$		−	11.7302i		−	0.494369i	0.968968	−	0.247184i	$-0.0795053\pi$
$564$	−0.170964	−	2.79825i	−0.00719890	−	0.117828i
$565$	−4.61390	−	6.17111i	−0.194108	−	0.259620i
$566$	9.89972	+	17.1468i	0.416116	+	0.720734i
$567$	−16.4077	+	15.8364i	−0.689057	+	0.665066i
$568$	0.315350	+	0.182067i	0.0132318	+	0.00763937i
$569$	19.9566			0.836626			0.418313	−	0.908303i	$-0.362622\pi$
$569$	19.9566			0.836626			0.418313	+	0.908303i	$0.362622\pi$
$570$	12.8761	+	10.9181i	0.539322	+	0.457309i
$571$	−0.624912			−0.0261518			−0.0130759	−	0.999915i	$-0.504162\pi$
$571$	−0.624912			−0.0261518			−0.0130759	+	0.999915i	$0.504162\pi$
$572$	3.04452	+	1.75775i	0.127298	+	0.0734953i
$573$	−12.4933	−	18.8780i	−0.521916	−	0.788640i
$574$	−3.10675	−	5.38106i	−0.129673	−	0.224601i
$575$	−30.3756	+	7.33075i	−1.26675	+	0.305714i
$576$	−1.17255	+	2.76136i	−0.0488565	+	0.115057i
$577$			31.2690i			1.30174i	0.759187	+	0.650872i	$0.225597\pi$
$577$			31.2690i			1.30174i	−0.759187	+	0.650872i	$0.774403\pi$
$578$		−	12.6769i		−	0.527290i
$579$	−2.24082	−	36.6765i	−0.0931254	−	1.52422i
$580$	0.691269	+	5.81090i	0.0287034	+	0.241284i
$581$		−	32.1096i		−	1.33213i
$582$	9.12716	−	18.3032i	0.378333	−	0.758694i
$583$	−4.70094	−	8.14227i	−0.194693	−	0.337218i
$584$	1.18451	−	2.05162i	0.0490152	−	0.0848968i
$585$	23.1138	−	22.1472i	0.955638	−	0.915674i
$586$	2.56453	−	4.44190i	0.105940	−	0.183493i
$587$	8.33621	−	14.4387i	0.344072	−	0.595951i	−0.641113	−	0.767447i	$-0.721527\pi$
$587$	8.33621	−	14.4387i	0.344072	−	0.595951i	0.985185	+	0.171496i	$0.0548602\pi$
$588$	0.899356	+	0.448476i	0.0370888	+	0.0184948i
$589$	22.6393	−	3.75765i	0.932836	−	0.154831i
$590$	4.57827	−	10.6737i	0.188484	−	0.439430i
$591$	38.5728	−	25.5272i	1.58667	−	1.05005i
$592$	−5.15050	+	8.92092i	−0.211684	+	0.366648i
$593$	−8.39521	−	14.5409i	−0.344750	−	0.597125i	0.640558	−	0.767910i	$-0.278703\pi$
$593$	−8.39521	−	14.5409i	−0.344750	−	0.597125i	−0.985308	+	0.170785i	$0.945370\pi$
$594$	−3.60814	−	1.27851i	−0.148044	−	0.0524578i
$595$	11.6974	−	1.39154i	0.479548	−	0.0570475i
$596$		−	8.13662i		−	0.333289i
$597$	−4.02994	−	2.00958i	−0.164934	−	0.0822468i
$598$	25.8274	−	14.9114i	1.05616	−	0.609774i
$599$	−18.1333	−	31.4079i	−0.740908	−	1.28329i	−0.952082	−	0.305842i	$-0.901062\pi$
$599$	−18.1333	−	31.4079i	−0.740908	−	1.28329i	0.211174	−	0.977448i	$-0.432271\pi$
$600$	−8.27899	+	2.54132i	−0.337988	+	0.103749i
$601$		−	15.2278i		−	0.621153i	−0.950548	−	0.310577i	$-0.899478\pi$
$601$		−	15.2278i		−	0.621153i	0.950548	−	0.310577i	$-0.100522\pi$
$602$	18.9067	−	10.9158i	0.770581	−	0.444895i
$603$	16.3416	−	2.00432i	0.665479	−	0.0816222i
$604$	11.1207	−	6.42054i	0.452495	−	0.261248i
$605$	−18.7276	+	14.0019i	−0.761383	+	0.569258i
$606$	−21.8705	+	14.4737i	−0.888429	+	0.587955i
$607$	38.5686			1.56545			0.782725	−	0.622368i	$-0.213829\pi$
$607$	38.5686			1.56545			0.782725	+	0.622368i	$0.213829\pi$
$608$	2.76814	+	3.36711i	0.112263	+	0.136554i
$609$	−5.12525	+	10.2780i	−0.207685	+	0.416484i
$610$	13.5823	+	18.1663i	0.549929	+	0.735532i
$611$	−3.86195	+	6.68910i	−0.156238	+	0.270612i
$612$	2.43798	−	5.74143i	0.0985495	−	0.232084i
$613$	4.15957	+	2.40153i	0.168004	+	0.0969969i	0.581644	−	0.813443i	$-0.302410\pi$
$613$	4.15957	+	2.40153i	0.168004	+	0.0969969i	−0.413641	+	0.910440i	$0.635743\pi$
$614$	−18.4385	+	10.6455i	−0.744119	+	0.429617i
$615$	−6.14058	−	7.24577i	−0.247612	−	0.292178i
$616$		−	1.86658i		−	0.0752065i
$617$	−9.14813	−	15.8450i	−0.368290	−	0.637897i	0.621008	−	0.783804i	$-0.286723\pi$
$617$	−9.14813	−	15.8450i	−0.368290	−	0.637897i	−0.989298	+	0.145907i	$0.953390\pi$
$618$	11.0346	−	0.674178i	0.443875	−	0.0271194i
$619$	13.3123			0.535066			0.267533	−	0.963549i	$-0.413792\pi$
$619$	13.3123			0.535066			0.267533	+	0.963549i	$0.413792\pi$
$620$	−4.64073	+	10.8193i	−0.186376	+	0.434515i
$621$	−24.6972	+	21.0850i	−0.991064	+	0.846112i
$622$	−9.25775	+	16.0349i	−0.371202	+	0.642941i
$623$	−27.1613	+	15.6816i	−1.08819	+	0.628269i
$624$	6.89268	−	4.56152i	0.275928	−	0.182607i
$625$	−20.9991	−	13.5661i	−0.839964	−	0.542642i
$626$	−6.93708			−0.277262
$627$	−4.07299	+	3.78754i	−0.162660	+	0.151260i
$628$		−	15.5889i		−	0.622067i
$629$	10.7089	−	18.5484i	0.426993	−	0.739574i
$630$	−16.3199	−	4.74862i	−0.650202	−	0.189190i
$631$	14.9958	+	25.9734i	0.596972	+	1.03399i	0.993265	+	0.115862i	$0.0369629\pi$
$631$	14.9958	+	25.9734i	0.596972	+	1.03399i	−0.396294	+	0.918124i	$0.629704\pi$
$632$	−0.161871	+	0.280369i	−0.00643888	+	0.0111525i
$633$	9.97240	−	0.609283i	0.396368	−	0.0242168i
$634$	27.4383			1.08971
$635$	−24.2802	−	10.4145i	−0.963529	−	0.413286i
$636$	−22.0638	+	1.34803i	−0.874887	+	0.0534529i
$637$	−1.38441	−	2.39787i	−0.0548525	−	0.0950072i
$638$	−1.92795			−0.0763282
$639$	0.657310	+	0.872518i	0.0260028	+	0.0345163i
$640$	−2.22041	+	0.264142i	−0.0877695	+	0.0104411i
$641$	21.3344	−	36.9523i	0.842659	−	1.45953i	−0.0449792	−	0.998988i	$-0.514322\pi$
$641$	21.3344	−	36.9523i	0.842659	−	1.45953i	0.887639	−	0.460541i	$-0.152345\pi$
$642$	−0.324141	−	5.30535i	−0.0127928	−	0.209385i
$643$	−22.4555	−	12.9647i	−0.885557	−	0.511277i	−0.0130704	−	0.999915i	$-0.504161\pi$
$643$	−22.4555	−	12.9647i	−0.885557	−	0.511277i	−0.872487	+	0.488638i	$0.837494\pi$
$644$	−13.7132	−	7.91731i	−0.540375	−	0.311986i
$645$	25.4586	−	21.5754i	1.00243	−	0.849531i
$646$	−5.75552	−	7.00091i	−0.226448	−	0.275447i
$647$	37.1804			1.46171			0.730856	−	0.682532i	$-0.239121\pi$
$647$	37.1804			1.46171			0.730856	+	0.682532i	$0.239121\pi$
$648$	−6.47570	+	6.25023i	−0.254389	+	0.245532i
$649$	3.31374	+	1.91319i	0.130076	+	0.0750993i
$650$	22.8856	+	6.74941i	0.897646	+	0.264734i
$651$	−19.2679	+	12.7513i	−0.755167	+	0.499763i
$652$	−13.3606	+	7.71376i	−0.523242	+	0.302094i
$653$	46.6082			1.82392			0.911960	−	0.410278i	$-0.134568\pi$
$653$	46.6082			1.82392			0.911960	+	0.410278i	$0.134568\pi$
$654$	−8.49896	−	4.23812i	−0.332335	−	0.165724i
$655$	−33.2333	+	3.95346i	−1.29853	+	0.154474i
$656$	−1.22616	−	2.12377i	−0.0478735	−	0.0829193i
$657$	5.67649	−	4.27638i	0.221461	−	0.166837i
$658$	4.10105			0.159875
$659$	21.4093	+	37.0820i	0.833988	+	1.44451i	0.894852	+	0.446363i	$0.147281\pi$
$659$	21.4093	+	37.0820i	0.833988	+	1.44451i	−0.0608646	+	0.998146i	$0.519386\pi$
$660$	−0.509193	−	2.80739i	−0.0198203	−	0.109278i
$661$	1.49321	−	0.862106i	0.0580792	−	0.0335320i	−0.470679	−	0.882304i	$-0.655991\pi$
$661$	1.49321	−	0.862106i	0.0580792	−	0.0335320i	0.528758	+	0.848772i	$0.322658\pi$
$662$	−10.8131	+	18.7288i	−0.420262	+	0.727915i
$663$	−14.3313	+	9.48432i	−0.556581	+	0.368341i
$664$		−	12.6729i		−	0.491803i
$665$	−17.0905	+	17.8268i	−0.662740	+	0.691294i
$666$	−24.6827	+	18.5946i	−0.956433	+	0.720528i
$667$	−8.17762	+	14.1641i	−0.316639	+	0.548434i
$668$	14.1230	+	8.15391i	0.546435	+	0.315484i
$669$	−2.25689	−	36.9395i	−0.0872563	−	1.42816i
$670$	7.34822	+	9.82826i	0.283886	+	0.379699i
$671$	−6.47173	+	3.73646i	−0.249839	+	0.144244i
$672$	−3.92733	−	1.95842i	−0.151500	−	0.0755476i
$673$	−25.0136			−0.964204			−0.482102	−	0.876115i	$-0.660126\pi$
$673$	−25.0136			−0.964204			−0.482102	+	0.876115i	$0.660126\pi$
$674$	30.9316	−	17.8583i	1.19144	−	0.687878i
$675$	−25.8411	−	2.69007i	−0.994625	−	0.103541i
$676$	−9.77215			−0.375852
$677$			10.0935i			0.387924i	0.981009	+	0.193962i	$0.0621339\pi$
$677$			10.0935i			0.387924i	−0.981009	+	0.193962i	$0.937866\pi$
$678$	−0.363975	−	5.95734i	−0.0139784	−	0.228790i
$679$	25.9108	+	14.9596i	0.994366	+	0.574098i
$680$	4.61669	−	0.549205i	0.177042	−	0.0210611i
$681$	−14.8083	−	22.3761i	−0.567455	−	0.857452i
$682$	−3.35895	−	1.93929i	−0.128621	−	0.0742593i
$683$		−	27.4795i		−	1.05148i	−0.850647	−	0.525738i	$-0.823789\pi$
$683$		−	27.4795i		−	1.05148i	0.850647	−	0.525738i	$-0.176211\pi$
$684$	3.69570	+	12.5436i	0.141309	+	0.479616i
$685$	−44.5665	−	19.1159i	−1.70280	−	0.730381i
$686$	−9.60311	+	16.6331i	−0.366648	+	0.635054i
$687$	−16.9392	+	11.2102i	−0.646271	+	0.427697i
$688$	7.46202	−	4.30820i	0.284487	−	0.164249i
$689$	52.7426	+	30.4510i	2.00933	+	1.16009i
$690$	−22.7849	−	8.16699i	−0.867405	−	0.310912i
$691$	3.74385			0.142423			0.0712114	−	0.997461i	$-0.477314\pi$
$691$	3.74385			0.142423			0.0712114	+	0.997461i	$0.477314\pi$
$692$		−	3.61642i		−	0.137476i
$693$	2.18866	−	5.15429i	0.0831404	−	0.195795i
$694$	−20.2609	+	11.6976i	−0.769092	+	0.444035i
$695$	−26.0462	−	11.1720i	−0.987989	−	0.423778i
$696$	−2.02281	+	4.05646i	−0.0766743	+	0.153760i
$697$	2.54943	+	4.41575i	0.0965667	+	0.167258i
$698$	−16.5782	−	9.57144i	−0.627495	−	0.362284i
$699$	2.34986	+	38.4612i	0.0888798	+	1.45473i
$700$	−2.97209	−	12.3151i	−0.112334	−	0.465466i
$701$	32.2898	+	18.6425i	1.21957	+	0.704118i	0.964826	−	0.262891i	$-0.0846759\pi$
$701$	32.2898	+	18.6425i	1.21957	+	0.704118i	0.254743	+	0.967009i	$0.418009\pi$
$702$	24.3818	−	4.51395i	0.920232	−	0.170368i
$703$	7.35205	+	44.2950i	0.277288	+	1.67062i
$704$		−	0.736692i		−	0.0277651i
$705$	6.16811	−	1.11875i	0.232304	−	0.0421344i
$706$	22.7600	+	13.1405i	0.856585	+	0.494550i
$707$	−19.1824	−	33.2249i	−0.721428	−	1.24955i
$708$	7.50220	−	4.96489i	0.281950	−	0.186592i
$709$	−22.4207	−	38.8338i	−0.842027	−	1.45843i	−0.888179	−	0.459499i	$-0.848029\pi$
$709$	−22.4207	−	38.8338i	−0.842027	−	1.45843i	0.0461519	−	0.998934i	$-0.485304\pi$
$710$	−0.320967	+	0.748298i	−0.0120457	+	0.0280831i
$711$	−0.775732	+	0.584397i	−0.0290922	+	0.0219166i
$712$	−10.7199	+	6.18913i	−0.401745	+	0.231947i
$713$	−28.4948	+	16.4515i	−1.06714	+	0.616113i
$714$	8.16573	+	4.07195i	0.305595	+	0.152389i
$715$	−3.09875	+	7.22438i	−0.115887	+	0.270176i
$716$	1.60760	+	2.78444i	0.0600788	+	0.104060i
$717$	−2.72827	−	4.12255i	−0.101889	−	0.153959i
$718$	−10.8238	−	18.7474i	−0.403941	−	0.699646i
$719$	−23.0640	−	13.3160i	−0.860141	−	0.496603i	0.00391864	−	0.999992i	$-0.498753\pi$
$719$	−23.0640	−	13.3160i	−0.860141	−	0.496603i	−0.864059	+	0.503390i	$0.832086\pi$
$720$	−6.44108	−	1.87416i	−0.240045	−	0.0698459i
$721$			16.1720i			0.602277i
$722$	18.6412	+	3.67484i	0.693755	+	0.136763i
$723$	−2.58323	+	5.18030i	−0.0960712	+	0.192657i
$724$	−8.85537	−	5.11265i	−0.329107	−	0.190010i
$725$	−12.7200	+	3.06981i	−0.472409	+	0.114010i
$726$	−18.0788	+	1.10456i	−0.670969	+	0.0409941i
$727$	0.844783	+	0.487735i	0.0313313	+	0.0180891i	0.515584	−	0.856839i	$-0.327575\pi$
$727$	0.844783	+	0.487735i	0.0313313	+	0.0180891i	−0.484253	+	0.874928i	$0.660908\pi$
$728$	6.04550	+	10.4711i	0.224061	+	0.388085i
$729$	−25.2105	+	9.66603i	−0.933721	+	0.358001i
$730$	4.86833	+	2.08817i	0.180185	+	0.0772866i
$731$	−15.5151	+	8.95763i	−0.573846	+	0.331310i
$732$	1.07146	+	17.5370i	0.0396022	+	0.648187i
$733$			19.5654i			0.722665i	0.932437	+	0.361332i	$0.117678\pi$
$733$			19.5654i			0.722665i	−0.932437	+	0.361332i	$0.882322\pi$
$734$	35.8982			1.32503
$735$	−0.758243	+	2.11540i	−0.0279682	+	0.0780277i
$736$	−5.41225	−	3.12477i	−0.199498	−	0.115180i
$737$	−3.50131	+	2.02148i	−0.128972	+	0.0744623i
$738$	−0.895631	−	7.30223i	−0.0329686	−	0.268799i
$739$	−16.2565	+	28.1571i	−0.598006	+	1.03578i	0.395109	+	0.918634i	$0.370707\pi$
$739$	−16.2565	+	28.1571i	−0.598006	+	1.03578i	−0.993115	+	0.117143i	$0.962626\pi$
$740$	−21.1686	−	9.07983i	−0.778173	−	0.333781i
$741$	10.5815	−	34.4390i	0.388721	−	1.26515i
$742$		−	32.3362i		−	1.18710i
$743$	32.7180	+	18.8897i	1.20031	+	0.692998i	0.960623	−	0.277854i	$-0.0896230\pi$
$743$	32.7180	+	18.8897i	1.20031	+	0.692998i	0.239683	+	0.970851i	$0.422956\pi$
$744$	−7.60455	+	5.03263i	−0.278796	+	0.184505i
$745$	18.0667	−	2.14923i	0.661911	−	0.0787415i
$746$	5.53638	+	3.19643i	0.202701	+	0.117030i
$747$	14.8597	−	34.9944i	0.543686	−	1.28038i
$748$			1.53173i			0.0560057i
$749$	7.77540			0.284107
$750$	−7.82961	−	17.7115i	−0.285897	−	0.646733i
$751$	1.16537	−	0.672824i	0.0425248	−	0.0245517i	−0.478587	−	0.878040i	$-0.658851\pi$
$751$	1.16537	−	0.672824i	0.0425248	−	0.0245517i	0.521112	+	0.853488i	$0.325517\pi$
$752$	1.61858			0.0590236
$753$	−3.77399	+	7.56821i	−0.137532	+	0.275801i
$754$	10.8154	−	6.24427i	0.393873	−	0.227403i
$755$	17.1937	+	22.9966i	0.625743	+	0.836933i
$756$	−8.54843	−	10.0129i	−0.310903	−	0.364166i
$757$	14.6311	+	8.44728i	0.531777	+	0.307022i	0.741740	−	0.670688i	$-0.234001\pi$
$757$	14.6311	+	8.44728i	0.531777	+	0.307022i	−0.209963	+	0.977709i	$0.567334\pi$
$758$	−2.30537	+	3.99303i	−0.0837350	+	0.145033i
$759$	3.55859	−	7.13626i	0.129169	−	0.259030i
$760$	−6.74519	+	7.03580i	−0.244674	+	0.255215i
$761$			38.1541i			1.38309i	0.722336	+	0.691543i	$0.243069\pi$
$761$			38.1541i			1.38309i	−0.722336	+	0.691543i	$0.756931\pi$
$762$	−11.2940	−	17.0657i	−0.409137	−	0.618226i
$763$	6.94637	−	12.0315i	0.251476	−	0.435568i
$764$	11.3188	−	6.53492i	0.409500	−	0.236425i
$765$	13.3923	+	3.89677i	0.484200	+	0.140888i
$766$	3.76967	+	6.52926i	0.136204	+	0.235912i
$767$	−24.7859			−0.894967
$768$	−1.55002	−	0.772939i	−0.0559316	−	0.0278910i
$769$	2.27302	+	3.93699i	0.0819673	+	0.141971i	0.904095	−	0.427332i	$-0.140546\pi$
$769$	2.27302	+	3.93699i	0.0819673	+	0.141971i	−0.822128	+	0.569303i	$0.807213\pi$
$770$	4.14457	−	0.493041i	0.149360	−	0.0177680i
$771$	1.85096	−	3.71185i	0.0666609	−	0.133679i
$772$	21.2147			0.763534
$773$	−12.6054	+	7.27776i	−0.453387	+	0.261763i	−0.709259	−	0.704948i	$-0.750970\pi$
$773$	−12.6054	+	7.27776i	−0.453387	+	0.261763i	0.255873	+	0.966710i	$0.417637\pi$
$774$	25.6569	−	3.14687i	0.922220	−	0.113112i
$775$	−25.2492	−	7.44649i	−0.906977	−	0.267486i

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.44440 - 0.955888i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.79086 + 1.33896i) q^{5} +(-1.72883 + 0.105626i) q^{6} -2.53373i q^{7} -1.00000i q^{8} +(1.17255 - 2.76136i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.44440 - 0.955888i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.79086 + 1.33896i) q^{5} +(-1.72883 + 0.105626i) q^{6} -2.53373i q^{7} -1.00000i q^{8} +(1.17255 - 2.76136i) q^{9} +(2.22041 - 0.264142i) q^{10} +0.736692i q^{11} +(1.55002 + 0.772939i) q^{12} +(-2.38601 - 4.13269i) q^{13} +(-1.26686 + 2.19427i) q^{14} +(-1.30682 + 3.64585i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.03960 - 1.80064i) q^{17} +(-2.39614 + 1.80513i) q^{18} +(0.713722 + 4.30007i) q^{19} +(-2.05500 - 0.881452i) q^{20} +(-2.42196 - 3.65970i) q^{21} +(0.368346 - 0.637994i) q^{22} +(-3.12477 - 5.41225i) q^{23} +(-0.955888 - 1.44440i) q^{24} +(1.41437 - 4.79578i) q^{25} +4.77202i q^{26} +(-0.945920 - 5.10933i) q^{27} +(2.19427 - 1.26686i) q^{28} +(-1.30852 - 2.26642i) q^{29} +(2.95466 - 2.50399i) q^{30} -5.26487i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.704195 + 1.06407i) q^{33} +(-1.80064 + 1.03960i) q^{34} +(3.39256 + 4.53756i) q^{35} +(2.97769 - 0.365218i) q^{36} +10.3010 q^{37} +(1.53193 - 4.08083i) q^{38} +(-7.39673 - 3.68848i) q^{39} +(1.33896 + 1.79086i) q^{40} +(-1.22616 + 2.12377i) q^{41} +(0.267628 + 4.38038i) q^{42} +(-7.46202 - 4.30820i) q^{43} +(-0.637994 + 0.368346i) q^{44} +(1.59747 + 6.51522i) q^{45} +6.24953i q^{46} +(-0.809291 - 1.40173i) q^{47} +(0.105626 + 1.72883i) q^{48} +0.580221 q^{49} +(-3.62278 + 3.44608i) q^{50} +(-0.219618 - 3.59458i) q^{51} +(2.38601 - 4.13269i) q^{52} +(-11.0525 + 6.38115i) q^{53} +(-1.73547 + 4.89777i) q^{54} +(-0.986400 - 1.31931i) q^{55} -2.53373 q^{56} +(5.14128 + 5.52876i) q^{57} +2.61704i q^{58} +(2.59700 - 4.49814i) q^{59} +(-3.81081 + 0.691189i) q^{60} +(5.07194 + 8.78486i) q^{61} +(-2.63243 + 4.55951i) q^{62} +(-6.99654 - 2.97094i) q^{63} -1.00000 q^{64} +(9.80651 + 4.20630i) q^{65} +(-0.0778138 - 1.27361i) q^{66} +(2.74400 + 4.75275i) q^{67} +2.07920 q^{68} +(-9.68690 - 4.83050i) q^{69} +(-0.669264 - 5.62592i) q^{70} +(-0.182067 + 0.315350i) q^{71} +(-2.76136 - 1.17255i) q^{72} +(2.05162 + 1.18451i) q^{73} +(-8.92092 - 5.15050i) q^{74} +(-2.54132 - 8.27899i) q^{75} +(-3.36711 + 2.76814i) q^{76} +1.86658 q^{77} +(4.56152 + 6.89268i) q^{78} +(-0.280369 - 0.161871i) q^{79} +(-0.264142 - 2.22041i) q^{80} +(-6.25023 - 6.47570i) q^{81} +(2.12377 - 1.22616i) q^{82} +12.6729 q^{83} +(1.95842 - 3.92733i) q^{84} +(0.549205 + 4.61669i) q^{85} +(4.30820 + 7.46202i) q^{86} +(-4.05646 - 2.02281i) q^{87} +0.736692 q^{88} +(-6.18913 - 10.7199i) q^{89} +(1.87416 - 6.44108i) q^{90} +(-10.4711 + 6.04550i) q^{91} +(3.12477 - 5.41225i) q^{92} +(-5.03263 - 7.60455i) q^{93} +1.61858i q^{94} +(-7.03580 - 6.74519i) q^{95} +(0.772939 - 1.55002i) q^{96} +(-5.90419 + 10.2264i) q^{97} +(-0.502487 - 0.290111i) q^{98} +(2.03427 + 0.863811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q + 40q^{4} + O(q^{10}) \)	\( 80q + 40q^{4} + 30q^{15} - 40q^{16} + 8q^{19} + 8q^{25} - 4q^{30} + 48q^{39} + 12q^{45} - 128q^{49} - 36q^{54} + 12q^{55} + 30q^{60} - 24q^{61} - 80q^{64} + 4q^{66} + 36q^{70} + 16q^{76} + 24q^{79} + 32q^{81} - 8q^{85} - 54q^{90} + 24q^{91} - 60q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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