LMFDB - Embedded newform 690.2.n.a.89.5

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.5

$q$-expansion

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-1.42695 - 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.584056 - 2.15844i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(-1.28454 + 0.825522i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.42695 - 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.584056 - 2.15844i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(-1.28454 + 0.825522i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +(-2.05335 + 0.885290i) q^{10} +(-0.219473 + 1.52646i) q^{11} +(1.64574 + 0.539952i) q^{12} +(-2.39248 + 3.72277i) q^{13} +(0.999928 + 1.15398i) q^{14} +(-1.28560 + 3.65338i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.0211748 - 0.0721148i) q^{17} +(2.62065 - 1.46020i) q^{18} +(0.126511 + 0.430858i) q^{19} +(1.16850 + 1.90646i) q^{20} +(2.64342 + 0.0830986i) q^{21} +1.54216 q^{22} +(4.78300 - 0.350566i) q^{23} +(0.300243 - 1.70583i) q^{24} +(-4.31776 + 2.52131i) q^{25} +(4.02536 + 1.83832i) q^{26} +(1.22038 - 5.05081i) q^{27} +(0.999928 - 1.15398i) q^{28} +(-1.07283 + 3.65371i) q^{29} +(3.79916 + 0.752589i) q^{30} +(-2.98547 - 6.53727i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.81176 - 1.96273i) q^{33} +(-0.0743943 - 0.0106963i) q^{34} +(2.53208 + 2.29045i) q^{35} +(-1.81830 - 2.38617i) q^{36} +(1.83669 + 2.11966i) q^{37} +(0.408468 - 0.186541i) q^{38} +(7.06874 - 2.96343i) q^{39} +(1.72076 - 1.42793i) q^{40} +(4.70508 + 4.07697i) q^{41} +(-0.293945 - 2.62834i) q^{42} +(-1.54435 + 3.38165i) q^{43} +(-0.219473 - 1.52646i) q^{44} +(5.42116 - 3.95108i) q^{45} +(-1.02769 - 4.68443i) q^{46} +7.94130 q^{47} +(-1.73120 - 0.0544219i) q^{48} +(-1.93936 + 4.24660i) q^{49} +(3.11012 + 3.91499i) q^{50} +(-0.101013 + 0.0821162i) q^{51} +(1.24674 - 4.24601i) q^{52} +(5.45190 + 8.48332i) q^{53} +(-5.17308 - 0.489153i) q^{54} +(3.42297 - 0.417823i) q^{55} +(-1.28454 - 0.825522i) q^{56} +(0.242464 - 0.739014i) q^{57} +(3.76920 + 0.541929i) q^{58} +(0.831298 - 1.29353i) q^{59} +(0.204252 - 3.86759i) q^{60} +(-3.72803 + 1.70254i) q^{61} +(-6.04585 + 3.88544i) q^{62} +(-3.69045 - 2.71372i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(9.43274 + 2.98972i) q^{65} +(-2.20059 - 1.51400i) q^{66} +(-1.56866 - 10.9103i) q^{67} +0.0751593i q^{68} +(-7.16928 - 4.19541i) q^{69} +(1.90678 - 2.83228i) q^{70} +(-6.98782 + 1.00470i) q^{71} +(-2.10311 + 2.13938i) q^{72} +(3.21126 + 10.9365i) q^{73} +(1.83669 - 2.11966i) q^{74} +(8.63649 + 0.641123i) q^{75} +(-0.242773 - 0.377763i) q^{76} +(-0.978209 - 2.14198i) q^{77} +(-3.93925 - 6.57505i) q^{78} +(-4.68933 + 7.29674i) q^{79} +(-1.65828 - 1.50003i) q^{80} +(-6.69999 + 6.00917i) q^{81} +(3.36587 - 5.23740i) q^{82} +(-3.99704 + 3.46346i) q^{83} +(-2.55975 + 0.665004i) q^{84} +(-0.168023 - 0.00358553i) q^{85} +(3.56702 + 1.04737i) q^{86} +(5.11785 - 4.16043i) q^{87} +(-1.47969 + 0.434477i) q^{88} +(3.53383 - 7.73801i) q^{89} +(-4.68237 - 4.80369i) q^{90} -6.75708i q^{91} +(-4.49049 + 1.68389i) q^{92} +(-2.15776 + 12.2593i) q^{93} +(-1.13017 - 7.86047i) q^{94} +(0.856092 - 0.524712i) q^{95} +(0.192507 + 1.72132i) q^{96} +(3.14175 - 3.62578i) q^{97} +(4.47937 + 1.31526i) q^{98} +(-4.51218 + 1.02204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} + O(q^{10}) $	$ 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} - 9q^{12} + 11q^{15} - 24q^{16} - 6q^{18} - 4q^{23} + 2q^{24} - 12q^{25} + 2q^{27} + 22q^{30} + 28q^{31} - 24q^{32} - 36q^{35} - 6q^{36} - 4q^{46} + 104q^{47} - 9q^{48} + 70q^{49} + 54q^{50} - 9q^{54} - 26q^{55} - 44q^{57} - 11q^{60} + 44q^{61} + 28q^{62} - 121q^{63} - 24q^{64} + 44q^{65} + 44q^{66} - 102q^{69} - 36q^{70} + 16q^{72} - 82q^{75} + 8q^{77} - 44q^{79} + 74q^{81} - 11q^{84} + 22q^{85} - 93q^{87} - 4q^{92} + 172q^{93} + 16q^{94} + 26q^{95} + 2q^{96} + 4q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

Coefficient data

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

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

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

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−1.42695	−	0.981738i	−0.823851	−	0.566807i
$3$	−1.42695	−	0.981738i	−0.823851	−	0.566807i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.584056	−	2.15844i	−0.261198	−	0.965285i
$5$	−0.584056	−	2.15844i	−0.261198	−	0.965285i
$6$	−0.768669	+	1.55214i	−0.313808	+	0.633660i
$7$	−1.28454	+	0.825522i	−0.485509	+	0.312018i	−0.760397	−	0.649458i	$-0.774996\pi$
$7$	−1.28454	+	0.825522i	−0.485509	+	0.312018i	0.274888	+	0.961476i	$0.411359\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	1.07238	+	2.80178i	0.357461	+	0.933928i
$10$	−2.05335	+	0.885290i	−0.649327	+	0.279953i
$11$	−0.219473	+	1.52646i	−0.0661735	+	0.460246i	0.929612	+	0.368538i	$0.120142\pi$
$11$	−0.219473	+	1.52646i	−0.0661735	+	0.460246i	−0.995786	+	0.0917080i	$0.970767\pi$
$12$	1.64574	+	0.539952i	0.475084	+	0.155871i
$13$	−2.39248	+	3.72277i	−0.663555	+	1.03251i	0.332442	+	0.943124i	$0.392127\pi$
$13$	−2.39248	+	3.72277i	−0.663555	+	1.03251i	−0.995997	+	0.0893875i	$0.971509\pi$
$14$	0.999928	+	1.15398i	0.267242	+	0.308414i
$15$	−1.28560	+	3.65338i	−0.331942	+	0.943300i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.0211748	−	0.0721148i	0.00513565	−	0.0174904i	−0.956885	−	0.290466i	$-0.906190\pi$
$17$	0.0211748	−	0.0721148i	0.00513565	−	0.0174904i	0.962021	+	0.272976i	$0.0880078\pi$
$18$	2.62065	−	1.46020i	0.617693	−	0.344173i
$19$	0.126511	+	0.430858i	0.0290237	+	0.0988455i	0.972731	−	0.231936i	$-0.0745059\pi$
$19$	0.126511	+	0.430858i	0.0290237	+	0.0988455i	−0.943707	+	0.330781i	$0.892688\pi$
$20$	1.16850	+	1.90646i	0.261285	+	0.426298i
$21$	2.64342	+	0.0830986i	0.576841	+	0.0181336i
$22$	1.54216			0.328790
$23$	4.78300	−	0.350566i	0.997325	−	0.0730981i
$23$	4.78300	−	0.350566i	0.997325	−	0.0730981i
$24$	0.300243	−	1.70583i	0.0612868	−	0.348201i
$25$	−4.31776	+	2.52131i	−0.863551	+	0.504261i
$26$	4.02536	+	1.83832i	0.789439	+	0.360525i
$27$	1.22038	−	5.05081i	0.234862	−	0.972029i
$28$	0.999928	−	1.15398i	0.188969	−	0.218081i
$29$	−1.07283	+	3.65371i	−0.199219	+	0.678477i	0.797912	+	0.602774i	$0.205938\pi$
$29$	−1.07283	+	3.65371i	−0.199219	+	0.678477i	−0.997130	+	0.0757023i	$0.975880\pi$
$30$	3.79916	+	0.752589i	0.693628	+	0.137403i
$31$	−2.98547	−	6.53727i	−0.536207	−	1.17413i	−0.962931	−	0.269747i	$-0.913060\pi$
$31$	−2.98547	−	6.53727i	−0.536207	−	1.17413i	0.426725	−	0.904382i	$-0.359667\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	1.81176	−	1.96273i	0.315388	−	0.341667i
$34$	−0.0743943	−	0.0106963i	−0.0127585	−	0.00183440i
$35$	2.53208	+	2.29045i	0.428000	+	0.387157i
$36$	−1.81830	−	2.38617i	−0.303050	−	0.397695i
$37$	1.83669	+	2.11966i	0.301951	+	0.348470i	0.886366	−	0.462985i	$-0.153222\pi$
$37$	1.83669	+	2.11966i	0.301951	+	0.348470i	−0.584415	+	0.811455i	$0.698676\pi$
$38$	0.408468	−	0.186541i	0.0662622	−	0.0302609i
$39$	7.06874	−	2.96343i	1.13190	−	0.474528i
$40$	1.72076	−	1.42793i	0.272077	−	0.225775i
$41$	4.70508	+	4.07697i	0.734810	+	0.636716i	0.939673	−	0.342074i	$-0.111129\pi$
$41$	4.70508	+	4.07697i	0.734810	+	0.636716i	−0.204863	+	0.978791i	$0.565675\pi$
$42$	−0.293945	−	2.62834i	−0.0453567	−	0.405561i
$43$	−1.54435	+	3.38165i	−0.235511	+	0.515697i	−0.990077	−	0.140527i	$-0.955120\pi$
$43$	−1.54435	+	3.38165i	−0.235511	+	0.515697i	0.754566	+	0.656224i	$0.227848\pi$
$44$	−0.219473	−	1.52646i	−0.0330867	−	0.230123i
$45$	5.42116	−	3.95108i	0.808139	−	0.588992i
$46$	−1.02769	−	4.68443i	−0.151525	−	0.690681i
$47$	7.94130			1.15836			0.579179	−	0.815200i	$-0.303373\pi$
$47$	7.94130			1.15836			0.579179	+	0.815200i	$0.303373\pi$
$48$	−1.73120	−	0.0544219i	−0.249877	−	0.00785513i
$49$	−1.93936	+	4.24660i	−0.277051	+	0.606657i
$50$	3.11012	+	3.91499i	0.439838	+	0.553663i
$51$	−0.101013	+	0.0821162i	−0.0141447	+	0.0114986i
$52$	1.24674	−	4.24601i	0.172892	−	0.588816i
$53$	5.45190	+	8.48332i	0.748876	+	1.16527i	0.981267	+	0.192652i	$0.0617087\pi$
$53$	5.45190	+	8.48332i	0.748876	+	1.16527i	−0.232391	+	0.972622i	$0.574655\pi$
$54$	−5.17308	−	0.489153i	−0.703967	−	0.0665653i
$55$	3.42297	−	0.417823i	0.461554	−	0.0563392i
$56$	−1.28454	−	0.825522i	−0.171653	−	0.110315i
$57$	0.242464	−	0.739014i	0.0321151	−	0.0978848i
$58$	3.76920	+	0.541929i	0.494920	+	0.0711587i
$59$	0.831298	−	1.29353i	0.108226	−	0.168403i	−0.782916	−	0.622127i	$-0.786269\pi$
$59$	0.831298	−	1.29353i	0.108226	−	0.168403i	0.891142	+	0.453725i	$0.149905\pi$
$60$	0.204252	−	3.86759i	0.0263688	−	0.499304i
$61$	−3.72803	+	1.70254i	−0.477326	+	0.217987i	−0.639524	−	0.768771i	$-0.720869\pi$
$61$	−3.72803	+	1.70254i	−0.477326	+	0.217987i	0.162199	+	0.986758i	$0.448141\pi$
$62$	−6.04585	+	3.88544i	−0.767824	+	0.493451i
$63$	−3.69045	−	2.71372i	−0.464953	−	0.341897i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	9.43274	+	2.98972i	1.16999	+	0.370830i
$66$	−2.20059	−	1.51400i	−0.270874	−	0.186360i
$67$	−1.56866	−	10.9103i	−0.191643	−	1.33290i	−0.827660	−	0.561229i	$-0.810329\pi$
$67$	−1.56866	−	10.9103i	−0.191643	−	1.33290i	0.636018	−	0.771674i	$-0.280581\pi$
$68$			0.0751593i			0.00911440i
$69$	−7.16928	−	4.19541i	−0.863079	−	0.505068i
$70$	1.90678	−	2.83228i	0.227904	−	0.338522i
$71$	−6.98782	+	1.00470i	−0.829302	+	0.119236i	−0.543876	−	0.839165i	$-0.683044\pi$
$71$	−6.98782	+	1.00470i	−0.829302	+	0.119236i	−0.285425	+	0.958401i	$0.592135\pi$
$72$	−2.10311	+	2.13938i	−0.247854	+	0.252128i
$73$	3.21126	+	10.9365i	0.375849	+	1.28002i	0.902775	+	0.430113i	$0.141526\pi$
$73$	3.21126	+	10.9365i	0.375849	+	1.28002i	−0.526926	+	0.849911i	$0.676655\pi$
$74$	1.83669	−	2.11966i	0.213511	−	0.246405i
$75$	8.63649	+	0.641123i	0.997256	+	0.0740305i
$76$	−0.242773	−	0.377763i	−0.0278480	−	0.0433323i
$77$	−0.978209	−	2.14198i	−0.111477	−	0.244101i
$78$	−3.93925	−	6.57505i	−0.446032	−	0.744478i
$79$	−4.68933	+	7.29674i	−0.527591	+	0.820947i	−0.998111	−	0.0614421i	$-0.980430\pi$
$79$	−4.68933	+	7.29674i	−0.527591	+	0.820947i	0.470520	+	0.882389i	$0.344066\pi$
$80$	−1.65828	−	1.50003i	−0.185402	−	0.167709i
$81$	−6.69999	+	6.00917i	−0.744444	+	0.667685i
$82$	3.36587	−	5.23740i	0.371699	−	0.578374i
$83$	−3.99704	+	3.46346i	−0.438732	+	0.380164i	−0.846033	−	0.533130i	$-0.821016\pi$
$83$	−3.99704	+	3.46346i	−0.438732	+	0.380164i	0.407301	+	0.913294i	$0.366470\pi$
$84$	−2.55975	+	0.665004i	−0.279292	+	0.0725579i
$85$	−0.168023	−	0.00358553i	−0.0182247	−	0.000388906i
$86$	3.56702	+	1.04737i	0.384641	+	0.112941i
$87$	5.11785	−	4.16043i	0.548691	−	0.446045i
$88$	−1.47969	+	0.434477i	−0.157736	+	0.0463154i
$89$	3.53383	−	7.73801i	0.374585	−	0.820227i	−0.624642	−	0.780912i	$-0.714755\pi$
$89$	3.53383	−	7.73801i	0.374585	−	0.820227i	0.999227	−	0.0393158i	$-0.0125178\pi$
$90$	−4.68237	−	4.80369i	−0.493565	−	0.506353i
$91$		−	6.75708i		−	0.708335i
$92$	−4.49049	+	1.68389i	−0.468166	+	0.175558i
$93$	−2.15776	+	12.2593i	−0.223749	+	1.27123i
$94$	−1.13017	−	7.86047i	−0.116568	−	0.810746i
$95$	0.856092	−	0.524712i	0.0878332	−	0.0538344i
$96$	0.192507	+	1.72132i	0.0196476	+	0.175681i
$97$	3.14175	−	3.62578i	0.318997	−	0.368142i	−0.573492	−	0.819211i	$-0.694412\pi$
$97$	3.14175	−	3.62578i	0.318997	−	0.368142i	0.892489	+	0.451069i	$0.148957\pi$
$98$	4.47937	+	1.31526i	0.452485	+	0.132862i
$99$	−4.51218	+	1.02204i	−0.453492	+	0.102719i
$100$	3.43252	−	3.63563i	0.343252	−	0.363563i
$101$	2.20987	−	1.91486i	0.219890	−	0.190536i	−0.537949	−	0.842978i	$-0.680801\pi$
$101$	2.20987	−	1.91486i	0.219890	−	0.190536i	0.757839	+	0.652441i	$0.226255\pi$
$102$	0.0956561	+	0.0882987i	0.00947136	+	0.00874288i
$103$	−2.47829	+	17.2369i	−0.244193	+	1.69840i	0.386435	+	0.922317i	$0.373706\pi$
$103$	−2.47829	+	17.2369i	−0.244193	+	1.69840i	−0.630628	+	0.776085i	$0.717203\pi$
$104$	−4.38022	−	0.629781i	−0.429516	−	0.0617551i
$105$	−1.36454	−	5.75420i	−0.133166	−	0.561553i
$106$	7.62109	−	6.60371i	0.740226	−	0.641409i
$107$	−15.6615	+	7.15239i	−1.51406	+	0.691447i	−0.987344	−	0.158595i	$-0.949304\pi$
$107$	−15.6615	+	7.15239i	−1.51406	+	0.691447i	−0.526714	+	0.850042i	$0.676576\pi$
$108$	0.252032	+	5.19004i	0.0242518	+	0.499412i
$109$	−4.09077	+	13.9319i	−0.391824	+	1.33443i	0.493617	+	0.869679i	$0.335675\pi$
$109$	−4.09077	+	13.9319i	−0.391824	+	1.33443i	−0.885441	+	0.464752i	$0.846144\pi$
$110$	−0.900709	−	3.32867i	−0.0858793	−	0.317376i
$111$	−0.539926	−	4.82780i	−0.0512475	−	0.458235i
$112$	−0.634310	+	1.38895i	−0.0599367	+	0.131243i
$113$	−9.61164	+	1.38195i	−0.904187	+	0.130003i	−0.578697	−	0.815543i	$-0.696439\pi$
$113$	−9.61164	+	1.38195i	−0.904187	+	0.130003i	−0.325491	+	0.945545i	$0.605529\pi$
$114$	−0.765998	−	0.134823i	−0.0717423	−	0.0126273i
$115$	−3.55022	−	10.1191i	−0.331060	−	0.943610i
$116$		−	3.80796i		−	0.353560i
$117$	−12.9961	−	2.71098i	−1.20149	−	0.250630i
$118$	−1.39866	−	0.638749i	−0.128758	−	0.0588016i
$119$	0.0323325	+	0.110114i	0.00296391	+	0.0100942i
$120$	−3.85730	+	0.348243i	−0.352121	+	0.0317901i
$121$	8.27250	+	2.42902i	0.752045	+	0.220820i
$122$	2.21576	+	3.44779i	0.200605	+	0.312148i
$123$	−2.71140	−	10.4368i	−0.244479	−	0.941055i
$124$	4.70630	+	5.43136i	0.422638	+	0.487751i
$125$	7.96391	+	7.84705i	0.712314	+	0.701861i
$126$	−2.16089	+	4.03909i	−0.192508	+	0.359831i
$127$	9.56945	+	1.37588i	0.849151	+	0.122090i	0.553133	−	0.833093i	$-0.313432\pi$
$127$	9.56945	+	1.37588i	0.849151	+	0.122090i	0.296018	+	0.955182i	$0.404341\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	5.52361	−	3.30931i	0.486327	−	0.291369i
$130$	1.61688	−	9.76221i	0.141809	−	0.856202i
$131$	−8.43094	−	13.1188i	−0.736615	−	1.14620i	−0.984154	−	0.177317i	$-0.943258\pi$
$131$	−8.43094	−	13.1188i	−0.736615	−	1.14620i	0.247539	−	0.968878i	$-0.420378\pi$
$132$	−1.18541	+	2.39366i	−0.103177	+	0.208341i
$133$	−0.518191	−	0.449015i	−0.0449328	−	0.0389345i
$134$	−10.5760	+	3.10539i	−0.913627	+	0.268265i
$135$	−11.6147	+	0.315837i	−0.999630	+	0.0271829i
$136$	0.0743943	−	0.0106963i	0.00637925	−	0.000917198i
$137$		−	5.79820i		−	0.495373i	−0.968840	−	0.247687i	$-0.920330\pi$
$137$		−	5.79820i		−	0.495373i	0.968840	−	0.247687i	$-0.0796703\pi$
$138$	−3.13241	+	7.69337i	−0.266649	+	0.654903i
$139$	−7.74202			−0.656669			−0.328335	−	0.944561i	$-0.606487\pi$
$139$	−7.74202			−0.656669			−0.328335	+	0.944561i	$0.606487\pi$
$140$	−3.07481	−	1.48430i	−0.259869	−	0.125446i
$141$	−11.3319	−	7.79628i	−0.954315	−	0.656565i
$142$	1.98894	+	6.77371i	0.166908	+	0.568437i
$143$	−5.15760	−	4.46908i	−0.431300	−	0.373723i
$144$	2.41690	+	1.77724i	0.201409	+	0.148103i
$145$	8.51291	+	0.181662i	0.706959	+	0.0150862i
$146$	10.3682	−	4.73500i	0.858079	−	0.391872i
$147$	6.93641	−	4.15575i	0.572106	−	0.342761i
$148$	−2.35947	−	1.51634i	−0.193947	−	0.124642i
$149$	0.816379	−	5.67804i	0.0668804	−	0.465163i	−0.928668	−	0.370912i	$-0.879045\pi$
$149$	0.816379	−	5.67804i	0.0668804	−	0.465163i	0.995548	−	0.0942513i	$-0.0300457\pi$
$150$	−0.594503	−	8.63982i	−0.0485410	−	0.705439i
$151$	7.53875	+	4.84486i	0.613495	+	0.394269i	0.810166	−	0.586200i	$-0.199377\pi$
$151$	7.53875	+	4.84486i	0.613495	+	0.394269i	−0.196671	+	0.980469i	$0.563013\pi$
$152$	−0.339367	+	0.294063i	−0.0275263	+	0.0238517i
$153$	0.224758	−	0.0180074i	0.0181706	−	0.00145581i
$154$	−1.98096	+	1.27309i	−0.159631	+	0.102588i
$155$	−12.3666	+	10.2621i	−0.993313	+	0.824272i
$156$	−5.94751	+	4.83488i	−0.476182	+	0.387100i
$157$	−17.0227	+	4.99833i	−1.35856	+	0.398910i	−0.878256	−	0.478191i	$-0.841293\pi$
$157$	−17.0227	+	4.99833i	−1.35856	+	0.398910i	−0.480306	+	0.877101i	$0.659474\pi$
$158$	7.88983	+	3.60316i	0.627681	+	0.286652i
$159$	0.548799	−	17.4576i	0.0435226	−	1.38448i
$160$	−1.24877	+	1.85488i	−0.0987237	+	0.146641i
$161$	−5.85454	+	4.39879i	−0.461403	+	0.346673i
$162$	6.90151	+	5.77660i	0.542234	+	0.453853i
$163$	−8.41298	+	1.20960i	−0.658956	+	0.0947435i	−0.463677	−	0.886004i	$-0.653470\pi$
$163$	−8.41298	+	1.20960i	−0.658956	+	0.0947435i	−0.195279	+	0.980748i	$0.562561\pi$
$164$	−5.66311	−	2.58625i	−0.442214	−	0.201953i
$165$	−5.29461	−	2.76425i	−0.412185	−	0.215196i
$166$	3.99704	+	3.46346i	0.310231	+	0.268816i
$167$	11.7390	+	3.44687i	0.908387	+	0.266727i	0.702362	−	0.711820i	$-0.252129\pi$
$167$	11.7390	+	3.44687i	0.908387	+	0.266727i	0.206025	+	0.978547i	$0.433947\pi$
$168$	1.02253	+	2.43906i	0.0788896	+	0.188177i
$169$	−2.73467	−	5.98810i	−0.210359	−	0.460623i
$170$	0.0203631	+	0.166823i	0.00156178	+	0.0127947i
$171$	−1.07150	+	0.816501i	−0.0819398	+	0.0624394i
$172$	0.529070	−	3.67977i	0.0403412	−	0.280580i
$173$	−2.39213	+	16.6376i	−0.181870	+	1.26494i	0.670465	+	0.741941i	$0.266095\pi$
$173$	−2.39213	+	16.6376i	−0.181870	+	1.26494i	−0.852335	+	0.522995i	$0.824814\pi$
$174$	−4.84643	−	4.47367i	−0.367407	−	0.339148i
$175$	3.46492	−	6.80311i	0.261924	−	0.514267i
$176$	0.640637	+	1.40280i	0.0482898	+	0.105740i
$177$	−2.45612	+	1.02968i	−0.184614	+	0.0773956i
$178$	−8.16216	−	2.39663i	−0.611780	−	0.179635i
$179$	8.11150	+	7.02865i	0.606282	+	0.525346i	0.903012	−	0.429615i	$-0.141351\pi$
$179$	8.11150	+	7.02865i	0.606282	+	0.525346i	−0.296730	+	0.954961i	$0.595896\pi$
$180$	−4.08842	+	5.31835i	−0.304733	+	0.396406i
$181$	4.56732	+	2.08583i	0.339486	+	0.155038i	0.577861	−	0.816135i	$-0.303887\pi$
$181$	4.56732	+	2.08583i	0.339486	+	0.155038i	−0.238375	+	0.971173i	$0.576615\pi$
$182$	−6.68830	+	0.961633i	−0.495770	+	0.0712810i
$183$	6.99116	+	1.23051i	0.516802	+	0.0909622i
$184$	2.30582	+	4.20514i	0.169987	+	0.310007i
$185$	3.50243	−	5.20240i	0.257504	−	0.382488i
$186$	12.4416	+	0.391115i	0.912264	+	0.0286780i
$187$	0.105433	+	0.0481498i	0.00771005	+	0.00352106i
$188$	−7.61963	+	2.23732i	−0.555718	+	0.163174i
$189$	2.60193	+	7.49540i	0.189263	+	0.545210i
$190$	−0.641206	−	0.772704i	−0.0465180	−	0.0560578i
$191$	7.60228	−	4.88569i	0.550082	−	0.353516i	−0.235889	−	0.971780i	$-0.575800\pi$
$191$	7.60228	−	4.88569i	0.550082	−	0.353516i	0.785970	+	0.618264i	$0.212164\pi$
$192$	1.67640	−	0.435517i	0.120984	−	0.0314307i
$193$	−13.6079	+	11.7913i	−0.979515	+	0.848755i	−0.988502	−	0.151205i	$-0.951685\pi$
$193$	−13.6079	+	11.7913i	−0.979515	+	0.848755i	0.00898712	+	0.999960i	$0.497139\pi$
$194$	−4.03599	−	2.59377i	−0.289767	−	0.186222i
$195$	−10.5249	−	13.5267i	−0.753706	−	0.968665i
$196$	0.664394	−	4.62096i	0.0474567	−	0.330069i
$197$	−1.21200	−	0.778906i	−0.0863515	−	0.0554947i	0.496753	−	0.867892i	$-0.334526\pi$
$197$	−1.21200	−	0.778906i	−0.0863515	−	0.0554947i	−0.583104	+	0.812397i	$0.698162\pi$
$198$	1.65379	+	4.32081i	0.117530	+	0.307066i
$199$	−10.6391	+	4.85870i	−0.754183	+	0.344424i	−0.755130	−	0.655576i	$-0.772426\pi$
$199$	−10.6391	+	4.85870i	−0.754183	+	0.344424i	0.000946248		1.00000i	$0.499699\pi$
$200$	−4.08712	−	2.88018i	−0.289003	−	0.203660i
$201$	−8.47264	+	17.1085i	−0.597614	+	1.20674i
$202$	−2.20987	−	1.91486i	−0.155486	−	0.134729i
$203$	−1.63813	−	5.57896i	−0.114974	−	0.391566i
$204$	0.0737867	−	0.107249i	0.00516610	−	0.00750891i
$205$	6.05189	−	12.5368i	0.422682	−	0.875610i
$206$	17.4141			1.21330
$207$	6.11142	+	13.0250i	0.424773	+	0.905300i
$208$			4.42527i			0.306837i
$209$	−0.685455	+	0.0985535i	−0.0474139	+	0.00681709i
$210$	−5.50144	+	2.16956i	−0.379635	+	0.149714i
$211$	−24.0656	+	7.06631i	−1.65675	+	0.486465i	−0.970540	−	0.240941i	$-0.922544\pi$
$211$	−24.0656	+	7.06631i	−1.65675	+	0.486465i	−0.686207	+	0.727406i	$0.740726\pi$
$212$	−7.62109	−	6.60371i	−0.523419	−	0.453545i
$213$	10.9576	+	5.42655i	0.750804	+	0.371821i
$214$	9.30845	+	14.4842i	0.636313	+	0.990122i
$215$	8.20109	+	1.35831i	0.559310	+	0.0926363i
$216$	5.10134	−	0.988086i	0.347102	−	0.0672307i
$217$	9.23161	+	5.93279i	0.626682	+	0.402744i
$218$	14.3722	+	2.06642i	0.973411	+	0.139955i
$219$	6.15450	−	18.7585i	0.415883	−	1.26758i
$220$	−3.16660	+	1.36526i	−0.213492	+	0.0920458i
$221$	0.217807	+	0.251362i	0.0146513	+	0.0169084i
$222$	−4.70182	+	1.22150i	−0.315566	+	0.0819816i
$223$	0.982571	+	1.52891i	0.0657978	+	0.102383i	0.872593	−	0.488447i	$-0.162437\pi$
$223$	0.982571	+	1.52891i	0.0657978	+	0.102383i	−0.806796	+	0.590831i	$0.798800\pi$
$224$	1.46508	+	0.430186i	0.0978898	+	0.0287430i
$225$	−11.6944	−	9.39362i	−0.779629	−	0.626241i
$226$	2.73576	+	9.31714i	0.181980	+	0.619767i
$227$	−12.1334	−	5.54114i	−0.805323	−	0.367778i	−0.0301638	−	0.999545i	$-0.509603\pi$
$227$	−12.1334	−	5.54114i	−0.805323	−	0.367778i	−0.775159	+	0.631766i	$0.782330\pi$
$228$	−0.0244380	+	0.777389i	−0.00161845	+	0.0514838i
$229$		−	20.2203i		−	1.33619i	−0.744075	−	0.668096i	$-0.767110\pi$
$229$		−	20.2203i		−	1.33619i	0.744075	−	0.668096i	$-0.232890\pi$
$230$	−9.51084	+	4.95418i	−0.627126	+	0.326669i
$231$	−0.707005	+	4.01685i	−0.0465175	+	0.264289i
$232$	−3.76920	+	0.541929i	−0.247460	+	0.0355794i
$233$	−5.44463	+	11.9221i	−0.356690	+	0.781042i	0.643193	+	0.765704i	$0.277609\pi$
$233$	−5.44463	+	11.9221i	−0.356690	+	0.781042i	−0.999882	+	0.0153372i	$0.995118\pi$
$234$	−0.833853	+	13.2496i	−0.0545107	+	0.866153i
$235$	−4.63817	−	17.1409i	−0.302561	−	1.11815i
$236$	−0.433197	+	1.47533i	−0.0281987	+	0.0960359i
$237$	13.8549	−	5.80840i	0.899975	−	0.377296i
$238$	0.104392	−	0.0476743i	0.00676674	−	0.00309027i
$239$	6.31658	−	5.47335i	0.408585	−	0.354041i	−0.426188	−	0.904634i	$-0.640144\pi$
$239$	6.31658	−	5.47335i	0.408585	−	0.354041i	0.834774	+	0.550593i	$0.185598\pi$
$240$	0.893649	+	3.76847i	0.0576848	+	0.243254i
$241$	18.7450	+	2.69512i	1.20747	+	0.173608i	0.716512	−	0.697575i	$-0.245738\pi$
$241$	18.7450	+	2.69512i	1.20747	+	0.173608i	0.490958	+	0.871183i	$0.336647\pi$
$242$	1.22700	−	8.53398i	0.0788746	−	0.548585i
$243$	15.4600	−	1.99716i	0.991759	−	0.128118i
$244$	3.09736	−	2.68388i	0.198288	−	0.171818i
$245$	10.2987	+	1.70574i	0.657962	+	0.108976i
$246$	−9.94470	+	4.16912i	−0.634051	+	0.265813i
$247$	−1.90666	−	0.559846i	−0.121318	−	0.0356221i
$248$	4.70630	−	5.43136i	0.298850	−	0.344892i
$249$	9.10379	−	1.01814i	0.576929	−	0.0645219i
$250$	6.63379	−	8.99960i	0.419558	−	0.569185i
$251$	0.108126	+	0.752035i	0.00682487	+	0.0474680i	0.992949	−	0.118540i	$-0.0378214\pi$
$251$	0.108126	+	0.752035i	0.00682487	+	0.0474680i	−0.986124	+	0.166008i	$0.946912\pi$
$252$	4.30550	+	1.56408i	0.271221	+	0.0985275i
$253$	−0.514611	+	7.37802i	−0.0323533	+	0.463852i
$254$		−	9.66786i		−	0.606615i
$255$	0.236241	+	0.170071i	0.0147940	+	0.0106503i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	25.5672	−	7.50720i	1.59484	−	0.468286i	0.640733	−	0.767764i	$-0.278630\pi$
$257$	25.5672	−	7.50720i	1.59484	−	0.468286i	0.954103	+	0.299477i	$0.0968123\pi$
$258$	−4.06172	−	4.99642i	−0.252871	−	0.311064i
$259$	−4.10912	−	1.20655i	−0.255329	−	0.0749712i
$260$	−9.89295	−	0.211111i	−0.613534	−	0.0130925i
$261$	−11.3874	+	0.912346i	−0.704861	+	0.0564728i
$262$	−11.7854	+	10.2121i	−0.728106	+	0.630907i
$263$	9.89708	−	15.4002i	0.610280	−	0.949614i	−0.389314	−	0.921105i	$-0.627288\pi$
$263$	9.89708	−	15.4002i	0.610280	−	0.949614i	0.999594	−	0.0285088i	$-0.00907585\pi$
$264$	2.53799	+	0.832693i	0.156203	+	0.0512487i
$265$	15.1266	−	16.7224i	0.929217	−	1.02725i
$266$	−0.370698	+	0.576818i	−0.0227290	+	0.0353670i
$267$	−12.6393	+	7.57247i	−0.773513	+	0.463428i
$268$	4.57890	+	10.0264i	0.279701	+	0.612460i
$269$	−4.11521	−	6.40339i	−0.250909	−	0.390422i	0.692837	−	0.721095i	$-0.256361\pi$
$269$	−4.11521	−	6.40339i	−0.250909	−	0.390422i	−0.943745	+	0.330673i	$0.892724\pi$
$270$	1.96556	+	11.4515i	0.119620	+	0.696915i
$271$	−6.62768	+	7.64875i	−0.402603	+	0.464628i	−0.920459	−	0.390839i	$-0.872185\pi$
$271$	−6.62768	+	7.64875i	−0.402603	+	0.464628i	0.517856	+	0.855468i	$0.326730\pi$
$272$	−0.0211748	−	0.0721148i	−0.00128391	−	0.00437260i
$273$	−6.63368	+	9.64203i	−0.401489	+	0.583562i
$274$	−5.73918	+	0.825169i	−0.346716	+	0.0498503i
$275$	−2.90106	−	7.14426i	−0.174940	−	0.430815i
$276$	8.06085	+	2.00565i	0.485206	+	0.120726i
$277$		−	2.53450i		−	0.152283i	−0.997097	−	0.0761416i	$-0.975740\pi$
$277$		−	2.53450i		−	0.152283i	0.997097	−	0.0761416i	$-0.0242601\pi$
$278$	1.10180	+	7.66321i	0.0660818	+	0.459609i
$279$	15.1145	−	15.3751i	0.904879	−	0.920483i
$280$	−1.03160	+	3.25475i	−0.0616499	+	0.194509i
$281$	−11.1025	+	12.8130i	−0.662319	+	0.764357i	−0.983154	−	0.182778i	$-0.941491\pi$
$281$	−11.1025	+	12.8130i	−0.662319	+	0.764357i	0.320835	+	0.947135i	$0.396036\pi$
$282$	−6.10423	+	12.3260i	−0.363502	+	0.734005i
$283$	25.1660	−	16.1732i	1.49596	−	0.961397i	0.500552	−	0.865706i	$-0.333130\pi$
$283$	25.1660	−	16.1732i	1.49596	−	0.961397i	0.995411	−	0.0956910i	$-0.0305061\pi$
$284$	6.42171	−	2.93270i	0.381058	−	0.174023i
$285$	−1.73673	−	0.0917186i	−0.102875	−	0.00543294i
$286$	−3.68959	+	5.74112i	−0.218170	+	0.339479i
$287$	−9.40948	−	1.35288i	−0.555424	−	0.0798579i
$288$	1.41519	−	2.64523i	0.0833907	−	0.155872i
$289$	14.2966	+	9.18784i	0.840974	+	0.540461i
$290$	−1.03170	−	8.45212i	−0.0605836	−	0.496325i
$291$	−8.04269	+	2.08943i	−0.471471	+	0.122485i
$292$	−6.16236	−	9.58881i	−0.360625	−	0.561143i
$293$	6.18090	−	21.0502i	0.361092	−	1.22977i	−0.556031	−	0.831162i	$-0.687676\pi$
$293$	6.18090	−	21.0502i	0.361092	−	1.22977i	0.917123	−	0.398604i	$-0.130505\pi$
$294$	−5.10061	−	6.27439i	−0.297473	−	0.365930i
$295$	−3.27753	−	1.03882i	−0.190825	−	0.0604823i
$296$	−1.16512	+	2.55125i	−0.0677211	+	0.148289i
$297$	7.44204	+	2.97138i	0.431831	+	0.172417i
$298$	−5.73643			−0.332302
$299$	−10.1382	+	18.6447i	−0.586305	+	1.07825i
$300$	−8.46728	+	1.81803i	−0.488858	+	0.104964i
$301$	−0.807855	−	5.61875i	−0.0465640	−	0.323859i
$302$	3.72267	−	8.15151i	0.214216	−	0.469067i
$303$	−5.03327	+	0.562905i	−0.289154	+	0.0323380i
$304$	0.339367	+	0.294063i	0.0194640	+	0.0168657i
$305$	5.85221	+	7.05237i	0.335096	+	0.403817i
$306$	−0.0498104	−	0.219907i	−0.00284747	−	0.0125713i
$307$	22.8416	−	10.4314i	1.30364	−	0.595351i	0.362061	−	0.932154i	$-0.382073\pi$
$307$	22.8416	−	10.4314i	1.30364	−	0.595351i	0.941575	+	0.336803i	$0.109346\pi$
$308$	1.54205	+	1.77962i	0.0878665	+	0.101403i
$309$	20.4585	−	22.1632i	1.16384	−	1.26082i
$310$	11.9176	+	10.7803i	0.676875	+	0.612281i
$311$	−27.2890	−	3.92357i	−1.54742	−	0.222485i	−0.684948	−	0.728592i	$-0.740175\pi$
$311$	−27.2890	−	3.92357i	−1.54742	−	0.222485i	−0.862471	+	0.506106i	$0.831084\pi$
$312$	5.63209	+	5.19890i	0.318854	+	0.294330i
$313$	0.0716998	+	0.0827460i	0.00405271	+	0.00467708i	0.757772	−	0.652519i	$-0.226288\pi$
$313$	0.0716998	+	0.0827460i	0.00405271	+	0.00467708i	−0.753720	+	0.657196i	$0.771742\pi$
$314$	7.37004	+	16.1381i	0.415915	+	0.910727i
$315$	−3.70198	+	9.55059i	−0.208583	+	0.538115i
$316$	2.44365	−	8.32231i	0.137466	−	0.468166i
$317$	−12.0872	+	13.9494i	−0.678887	+	0.783478i	−0.985739	−	0.168280i	$-0.946179\pi$
$317$	−12.0872	+	13.9494i	−0.678887	+	0.783478i	0.306852	+	0.951757i	$0.400724\pi$
$318$	−17.3580	+	1.94127i	−0.973390	+	0.108861i
$319$	−5.34180	−	2.43952i	−0.299083	−	0.136587i
$320$	2.01372	+	0.972079i	0.112570	+	0.0543409i
$321$	29.3700	+	5.16941i	1.63927	+	0.288529i
$322$	5.18720	+	5.16894i	0.289071	+	0.288054i
$323$	0.0337501			0.00187790
$324$	4.73562	−	7.65336i	0.263090	−	0.425187i
$325$	0.943902	−	22.1062i	0.0523582	−	1.22623i
$326$	2.39458	+	8.15521i	0.132624	+	0.451675i
$327$	19.5148	−	15.8640i	1.07917	−	0.877284i
$328$	−1.75399	+	5.97353i	−0.0968477	+	0.329833i
$329$	−10.2009	+	6.55572i	−0.562394	+	0.361429i
$330$	−1.98261	+	5.63411i	−0.109139	+	0.310148i
$331$	−0.680280	−	0.785085i	−0.0373916	−	0.0431522i	0.736746	−	0.676170i	$-0.236361\pi$
$331$	−0.680280	−	0.785085i	−0.0373916	−	0.0431522i	−0.774137	+	0.633018i	$0.781816\pi$
$332$	2.85936	−	4.44926i	0.156928	−	0.244185i
$333$	−3.96919	+	7.41910i	−0.217510	+	0.406564i
$334$	1.74116	−	12.1100i	0.0952718	−	0.662630i
$335$	−22.6331	+	9.75809i	−1.23658	+	0.533142i
$336$	2.26871	−	1.35923i	0.123768	−	0.0741522i
$337$	−11.5204	−	25.2263i	−0.627559	−	1.37416i	−0.909892	−	0.414846i	$-0.863836\pi$
$337$	−11.5204	−	25.2263i	−0.627559	−	1.37416i	0.282333	−	0.959316i	$-0.408892\pi$
$338$	−5.53796	+	3.55903i	−0.301225	+	0.193586i
$339$	15.0721	+	7.46414i	0.818602	+	0.405397i
$340$	0.162227	−	0.0438972i	0.00879800	−	0.00238066i
$341$	10.6341	−	3.12247i	0.575871	−	0.169091i
$342$	0.960681	+	0.944395i	0.0519477	+	0.0510670i
$343$	−2.53562	−	17.6356i	−0.136911	−	0.952234i
$344$	−3.71761			−0.200440
$345$	−4.86830	+	17.9248i	−0.262100	+	0.965041i
$346$	16.8087			0.903643
$347$	−2.24184	−	15.5924i	−0.120348	−	0.837042i	−0.957162	−	0.289554i	$-0.906493\pi$
$347$	−2.24184	−	15.5924i	−0.120348	−	0.837042i	0.836813	−	0.547488i	$-0.184416\pi$
$348$	−3.73841	+	5.43377i	−0.200400	+	0.291281i
$349$	−12.5921	+	3.69737i	−0.674038	+	0.197916i	−0.600801	−	0.799399i	$-0.705151\pi$
$349$	−12.5921	+	3.69737i	−0.674038	+	0.197916i	−0.0732379	+	0.997315i	$0.523333\pi$
$350$	−7.22698	−	2.46147i	−0.386298	−	0.131571i
$351$	15.8833	+	16.6272i	0.847787	+	0.887492i
$352$	1.29735	−	0.833756i	0.0691489	−	0.0444393i
$353$	−12.3316	−	27.0025i	−0.656346	−	1.43720i	−0.885888	−	0.463899i	$-0.846450\pi$
$353$	−12.3316	−	27.0025i	−0.656346	−	1.43720i	0.229542	−	0.973299i	$-0.426277\pi$
$354$	1.36874	+	2.28459i	0.0727479	+	0.121424i
$355$	6.24986	+	14.4960i	0.331708	+	0.769369i
$356$	−1.21064	+	8.42016i	−0.0641636	+	0.446268i
$357$	0.0619665	−	0.188870i	0.00327962	−	0.00999606i
$358$	5.80273	−	9.02922i	0.306684	−	0.477209i
$359$	24.6651	+	28.4650i	1.30177	+	1.50233i	0.734015	+	0.679133i	$0.237644\pi$
$359$	24.6651	+	28.4650i	1.30177	+	1.50233i	0.567759	+	0.823195i	$0.307810\pi$
$360$	5.84606	+	3.28993i	0.308114	+	0.173394i
$361$	15.8142	−	10.1632i	0.832325	−	0.534903i
$362$	1.41460	−	4.81768i	0.0743496	−	0.253211i
$363$	−9.41979	−	11.5875i	−0.494411	−	0.608187i
$364$	1.90369	+	6.48337i	0.0997805	+	0.339821i
$365$	21.7303	−	13.3189i	1.13742	−	0.697142i
$366$	0.223043	−	7.09512i	0.0116586	−	0.370868i
$367$	−2.24178			−0.117020			−0.0585101	−	0.998287i	$-0.518635\pi$
$367$	−2.24178			−0.117020			−0.0585101	+	0.998287i	$0.518635\pi$
$368$	3.83419	−	2.88080i	0.199871	−	0.150172i
$369$	−6.37716	+	17.5547i	−0.331982	+	0.913861i
$370$	−5.64789	−	2.72640i	−0.293620	−	0.141739i
$371$	−14.0063	−	6.39648i	−0.727173	−	0.332089i
$372$	−1.38349	−	12.3706i	−0.0717308	−	0.641388i
$373$	−0.540194	+	0.623417i	−0.0279702	+	0.0322793i	−0.769562	−	0.638572i	$-0.779526\pi$
$373$	−0.540194	+	0.623417i	−0.0279702	+	0.0322793i	0.741592	+	0.670851i	$0.234071\pi$
$374$	0.0326550	−	0.111213i	0.00168855	−	0.00575067i
$375$	−3.66037	−	19.0158i	−0.189021	−	0.981973i
$376$	3.29894	+	7.22366i	0.170130	+	0.372532i
$377$	−11.0352	−	12.7353i	−0.568342	−	0.655902i
$378$	7.04881	−	3.64215i	0.362552	−	0.187332i
$379$	−4.45047	−	0.639881i	−0.228605	−	0.0328685i	0.0270602	−	0.999634i	$-0.491385\pi$
$379$	−4.45047	−	0.639881i	−0.228605	−	0.0328685i	−0.255665	+	0.966765i	$0.582295\pi$
$380$	−0.673586	+	0.744647i	−0.0345542	+	0.0381996i
$381$	−12.3044	−	11.3580i	−0.630373	−	0.581888i
$382$	−5.91788	−	6.82959i	−0.302785	−	0.349432i
$383$	27.1518	−	12.3998i	1.38739	−	0.633601i	0.424982	−	0.905202i	$-0.360280\pi$
$383$	27.1518	−	12.3998i	1.38739	−	0.633601i	0.962410	+	0.271601i	$0.0875532\pi$
$384$	−0.669661	−	1.59736i	−0.0341735	−	0.0815149i
$385$	−4.05201	+	3.36245i	−0.206510	+	0.171366i
$386$	13.6079	+	11.7913i	0.692622	+	0.600160i
$387$	−11.1308	−	0.700509i	−0.565810	−	0.0356089i
$388$	−1.99299	+	4.36404i	−0.101179	+	0.221551i
$389$	3.02213	+	21.0194i	0.153228	+	1.06572i	0.910763	+	0.412929i	$0.135494\pi$
$389$	3.02213	+	21.0194i	0.153228	+	1.06572i	−0.757535	+	0.652795i	$0.773597\pi$
$390$	−11.8911	+	12.3428i	−0.602131	+	0.625004i
$391$	0.0759982	−	0.352348i	0.00384339	−	0.0178190i
$392$	−4.66848			−0.235794
$393$	−0.848675	+	26.9969i	−0.0428100	+	1.36181i
$394$	−0.598492	+	1.31051i	−0.0301516	+	0.0660228i
$395$	18.4884	+	5.85995i	0.930254	+	0.294846i
$396$	4.04147	−	2.25187i	0.203091	−	0.113161i
$397$	−10.0165	+	34.1130i	−0.502712	+	1.71208i	0.182028	+	0.983293i	$0.441734\pi$
$397$	−10.0165	+	34.1130i	−0.502712	+	1.71208i	−0.684740	+	0.728787i	$0.740084\pi$
$398$	6.32334	+	9.83931i	0.316960	+	0.493200i
$399$	0.298618	+	1.14945i	0.0149496	+	0.0575445i
$400$	−2.26921	+	4.45541i	−0.113460	+	0.222771i
$401$	−11.4322	−	7.34702i	−0.570896	−	0.366893i	0.223118	−	0.974791i	$-0.428376\pi$
$401$	−11.4322	−	7.34702i	−0.570896	−	0.366893i	−0.794015	+	0.607898i	$0.792013\pi$
$402$	18.1401	+	5.95161i	0.904747	+	0.296839i
$403$	31.4795	+	4.52606i	1.56810	+	0.225459i
$404$	−1.58088	+	2.45989i	−0.0786515	+	0.122384i
$405$	16.8836	+	10.9519i	0.838954	+	0.544202i
$406$	−5.28905	+	2.41543i	−0.262491	+	0.119876i
$407$	−3.63869	+	2.33844i	−0.180363	+	0.115912i
$408$	−0.116658	−	0.0577726i	−0.00577543	−	0.00286017i
$409$	−22.8084	+	26.3222i	−1.12780	+	1.30155i	−0.179650	+	0.983731i	$0.557496\pi$
$409$	−22.8084	+	26.3222i	−1.12780	+	1.30155i	−0.948151	+	0.317821i	$0.897049\pi$
$410$	−13.2705	−	4.20611i	−0.655383	−	0.207725i
$411$	−5.69231	+	8.27374i	−0.280781	+	0.408114i
$412$	−2.47829	−	17.2369i	−0.122097	−	0.849201i
$413$			2.34784i			0.115529i
$414$	12.0227	−	7.90286i	0.590882	−	0.388404i
$415$	9.81017	+	6.60453i	0.481562	+	0.324204i
$416$	4.38022	−	0.629781i	0.214758	−	0.0308776i
$417$	11.0475	+	7.60063i	0.540998	+	0.372204i
$418$	0.195101	+	0.664452i	0.00954269	+	0.0324994i
$419$	20.7734	−	23.9738i	1.01485	−	1.17119i	0.0296855	−	0.999559i	$-0.490549\pi$
$419$	20.7734	−	23.9738i	1.01485	−	1.17119i	0.985161	−	0.171635i	$-0.0549051\pi$
$420$	2.93041	+	5.13668i	0.142990	+	0.250644i
$421$	−2.78229	−	4.32932i	−0.135600	−	0.210998i	0.766812	−	0.641872i	$-0.221842\pi$
$421$	−2.78229	−	4.32932i	−0.135600	−	0.210998i	−0.902412	+	0.430874i	$0.858206\pi$
$422$	10.4193	+	22.8150i	0.507203	+	1.11062i
$423$	8.51611	+	22.2498i	0.414068	+	1.08182i
$424$	−5.45190	+	8.48332i	−0.264768	+	0.411987i
$425$	0.0903957	+	0.364762i	0.00438484	+	0.0176936i
$426$	3.81188	−	11.6184i	0.184686	−	0.562912i
$427$	3.38331	−	5.26454i	0.163730	−	0.254769i
$428$	13.0121	−	11.2750i	0.628962	−	0.544999i
$429$	2.97217	+	11.4406i	0.143498	+	0.552356i
$430$	0.177351	−	8.31093i	0.00855264	−	0.400789i
$431$	1.19289	+	0.350265i	0.0574597	+	0.0168717i	0.310336	−	0.950627i	$-0.399558\pi$
$431$	1.19289	+	0.350265i	0.0574597	+	0.0168717i	−0.252876	+	0.967499i	$0.581377\pi$
$432$	−1.70403	−	4.90880i	−0.0819849	−	0.236175i
$433$	10.5570	−	3.09981i	0.507337	−	0.148968i	−0.0180399	−	0.999837i	$-0.505743\pi$
$433$	10.5570	−	3.09981i	0.507337	−	0.148968i	0.525377	+	0.850870i	$0.323924\pi$
$434$	4.55861	−	9.98197i	0.218820	−	0.479150i
$435$	−11.9692	−	8.61667i	−0.573878	−	0.413138i
$436$		−	14.5200i		−	0.695383i
$437$	0.756147	+	2.01644i	0.0361714	+	0.0964595i
$438$	−19.4435	−	3.42224i	−0.929045	−	0.163521i
$439$	2.39759	+	16.6756i	0.114431	+	0.795884i	0.963520	+	0.267635i	$0.0862421\pi$
$439$	2.39759	+	16.6756i	0.114431	+	0.795884i	−0.849090	+	0.528249i	$0.822849\pi$
$440$	1.80202	+	2.94008i	0.0859079	+	0.140163i
$441$	−13.9778	−	0.879682i	−0.665609	−	0.0418896i
$442$	0.217807	−	0.251362i	0.0103600	−	0.0119561i
$443$	4.83376	+	1.41932i	0.229659	+	0.0674339i	0.394537	−	0.918880i	$-0.370905\pi$
$443$	4.83376	+	1.41932i	0.229659	+	0.0674339i	−0.164878	+	0.986314i	$0.552723\pi$
$444$	1.87820	+	4.48013i	0.0891356	+	0.212617i
$445$	−18.7660	−	3.10814i	−0.889594	−	0.147340i
$446$	1.37351	−	1.19016i	0.0650377	−	0.0563555i
$447$	−6.73928	+	7.30082i	−0.318757	+	0.345317i
$448$	0.217305	−	1.51139i	0.0102667	−	0.0714065i
$449$	5.24080	+	0.753513i	0.247328	+	0.0355605i	0.264864	−	0.964286i	$-0.414673\pi$
$449$	5.24080	+	0.753513i	0.247328	+	0.0355605i	−0.0175355	+	0.999846i	$0.505582\pi$
$450$	−7.63371	+	12.9123i	−0.359857	+	0.608690i
$451$	−7.25599	+	6.28735i	−0.341671	+	0.296060i
$452$	8.83297	−	4.03388i	0.415468	−	0.189738i
$453$	−6.00105	−	14.3145i	−0.281954	−	0.672552i
$454$	−3.75798	+	12.7985i	−0.176371	+	0.600663i
$455$	−14.5848	+	3.94652i	−0.683745	+	0.185016i
$456$	0.772954	−	0.0864446i	0.0361969	−	0.00404814i
$457$	−0.00287378	+	0.00629269i	−0.000134430	+	0.000294360i	−0.909699	−	0.415268i	$-0.863688\pi$
$457$	−0.00287378	+	0.00629269i	−0.000134430	+	0.000294360i	0.909565	+	0.415562i	$0.136415\pi$
$458$	−20.0144	+	2.87764i	−0.935213	+	0.134463i
$459$	−0.338397	−	0.194957i	−0.0157950	−	0.00909983i
$460$	6.25729	+	8.70898i	0.291748	+	0.406058i
$461$			16.6775i			0.776748i	0.921502	+	0.388374i	$0.126963\pi$
$461$			16.6775i			0.776748i	−0.921502	+	0.388374i	$0.873037\pi$
$462$	4.07658	+	0.128151i	0.189660	+	0.00596215i
$463$	10.4491	+	4.77196i	0.485613	+	0.221772i	0.643149	−	0.765741i	$-0.277628\pi$
$463$	10.4491	+	4.77196i	0.485613	+	0.221772i	−0.157536	+	0.987513i	$0.550355\pi$
$464$	1.07283	+	3.65371i	0.0498047	+	0.169619i
$465$	27.7213	−	2.50273i	1.28554	−	0.116061i
$466$	12.5756	+	3.69252i	0.582553	+	0.171053i
$467$	−10.7050	−	16.6573i	−0.495368	−	0.770807i	0.500094	−	0.865971i	$-0.333299\pi$
$467$	−10.7050	−	16.6573i	−0.495368	−	0.770807i	−0.995462	+	0.0951638i	$0.969663\pi$
$468$	13.2334	−	1.06025i	0.611714	−	0.0490099i
$469$	11.0217	+	12.7197i	0.508934	+	0.587341i
$470$	−16.3063	+	7.03036i	−0.752154	+	0.324286i
$471$	29.1977	+	9.57949i	1.34536	+	0.441400i
$472$	1.52197	+	0.218826i	0.0700541	+	0.0100723i
$473$	−4.82303	−	3.09957i	−0.221763	−	0.142519i
$474$	−7.72104	−	12.8873i	−0.354639	−	0.591933i
$475$	−1.63257	−	1.54136i	−0.0749074	−	0.0707227i
$476$	−0.0620456	−	0.0965448i	−0.00284386	−	0.00442513i
$477$	−17.9219	+	24.3724i	−0.820588	+	1.11594i
$478$	−6.31658	−	5.47335i	−0.288914	−	0.250345i
$479$	28.4605	−	8.35677i	1.30039	−	0.381830i	0.443015	−	0.896514i	$-0.353909\pi$
$479$	28.4605	−	8.35677i	1.30039	−	0.381830i	0.857380	+	0.514684i	$0.172091\pi$
$480$	3.60294	−	1.42086i	0.164451	−	0.0648532i
$481$	−12.2853	+	1.76635i	−0.560159	+	0.0805388i
$482$		−	18.9377i		−	0.862590i
$483$	12.6726	−	0.529231i	0.576623	−	0.0240809i
$484$	−8.62174			−0.391897
$485$	−9.66099	−	4.66364i	−0.438683	−	0.211765i
$486$	−4.17702	−	15.0184i	−0.189473	−	0.681249i
$487$	−1.79475	−	6.11234i	−0.0813277	−	0.276977i	0.908782	−	0.417271i	$-0.137013\pi$
$487$	−1.79475	−	6.11234i	−0.0813277	−	0.276977i	−0.990110	+	0.140294i	$0.955195\pi$
$488$	−3.09736	−	2.68388i	−0.140211	−	0.121493i
$489$	13.1924	+	6.53329i	0.596582	+	0.295446i
$490$	0.222713	−	10.4367i	0.0100612	−	0.471480i
$491$	−16.0080	+	7.31060i	−0.722430	+	0.329923i	−0.742473	−	0.669876i	$-0.766347\pi$
$491$	−16.0080	+	7.31060i	−0.722430	+	0.329923i	0.0200427	+	0.999799i	$0.493620\pi$
$492$	5.54196	+	9.25015i	0.249851	+	0.417029i
$493$	0.240769	+	0.154733i	0.0108437	+	0.00696883i
$494$	−0.282801	+	1.96693i	−0.0127238	+	0.0884962i
$495$	4.84138	+	9.14237i	0.217604	+	0.410919i
$496$	−6.04585	−	3.88544i	−0.271467	−	0.174461i
$497$	8.14671	−	7.05917i	0.365430	−	0.316647i
$498$	−2.30338	−	8.86623i	−0.103217	−	0.397305i
$499$	−17.5745	+	11.2945i	−0.786744	+	0.505610i	−0.871266	−	0.490812i	$-0.836700\pi$
$499$	−17.5745	+	11.2945i	−0.786744	+	0.505610i	0.0845214	+	0.996422i	$0.473064\pi$
$500$	−9.85208	−	5.28550i	−0.440599	−	0.236375i
$501$	−13.3670	−	16.4431i	−0.597193	−	0.734623i
$502$	0.728992	−	0.214051i	0.0325365	−	0.00955358i
$503$	−18.9156	−	8.63845i	−0.843403	−	0.385169i	−0.0536243	−	0.998561i	$-0.517077\pi$
$503$	−18.9156	−	8.63845i	−0.843403	−	0.385169i	−0.789779	+	0.613392i	$0.789805\pi$
$504$	0.935419	−	4.48427i	0.0416669	−	0.199745i
$505$	−5.42381	−	3.65149i	−0.241357	−	0.162489i
$506$	7.37616	−	0.540629i	0.327910	−	0.0240339i
$507$	−1.97650	+	11.2295i	−0.0877792	+	0.498718i
$508$	−9.56945	+	1.37588i	−0.424576	+	0.0610448i
$509$	−32.2664	−	14.7356i	−1.43018	−	0.653142i	−0.458340	−	0.888777i	$-0.651556\pi$
$509$	−32.2664	−	14.7356i	−1.43018	−	0.653142i	−0.971842	+	0.235635i	$0.924283\pi$
$510$	0.134719	−	0.258040i	0.00596547	−	0.0114262i
$511$	−13.1533	−	11.3974i	−0.581869	−	0.504192i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	2.33057	−	0.113174i	0.102897	−	0.00499676i
$514$	−11.0694	−	24.2386i	−0.488249	−	1.06912i
$515$	38.6523	−	4.71807i	1.70322	−	0.207903i
$516$	−4.36752	+	4.73144i	−0.192269	+	0.208290i
$517$	−1.74290	+	12.1221i	−0.0766526	+	0.533130i
$518$	−0.609478	+	4.23901i	−0.0267789	+	0.186251i
$519$	19.7473	−	21.3927i	0.866808	−	0.939034i
$520$	1.19895	+	9.82229i	0.0525775	+	0.430736i
$521$	−14.1015	−	30.8780i	−0.617799	−	1.35279i	−0.917109	−	0.398636i	$-0.869484\pi$
$521$	−14.1015	−	30.8780i	−0.617799	−	1.35279i	0.299310	−	0.954156i	$-0.403243\pi$
$522$	2.52365	+	11.1416i	0.110457	+	0.487656i
$523$	−30.1696	−	8.85861i	−1.31923	−	0.387360i	−0.455013	−	0.890485i	$-0.650365\pi$
$523$	−30.1696	−	8.85861i	−1.31923	−	0.387360i	−0.864214	+	0.503125i	$0.832184\pi$
$524$	11.7854	+	10.2121i	0.514849	+	0.446119i
$525$	−11.6232	+	6.30606i	−0.507276	+	0.275219i
$526$	−16.6519	−	7.60467i	−0.726057	−	0.331579i
$527$	−0.534651	+	0.0768712i	−0.0232898	+	0.00334856i
$528$	0.463023	−	2.63067i	0.0201505	−	0.114485i
$529$	22.7542	−	3.35351i	0.989313	−	0.145805i
$530$	−18.7049	−	12.5927i	−0.812488	−	0.546994i
$531$	4.51565	+	0.941965i	0.195962	+	0.0408778i
$532$	0.623702	+	0.284835i	0.0270409	+	0.0123492i
$533$	−26.4345	+	7.76186i	−1.14500	+	0.336203i
$534$	9.29415	+	11.4330i	0.402197	+	0.494753i
$535$	24.5852	+	29.6272i	1.06291	+	1.28089i
$536$	9.27270	−	5.95920i	0.400520	−	0.257398i
$537$	−4.67442	−	17.9929i	−0.201716	−	0.776452i
$538$	−5.75256	+	4.98462i	−0.248010	+	0.214902i
$539$	−6.05665	−	3.89237i	−0.260878	−	0.167656i
$540$	11.0552	−	3.57527i	0.475740	−	0.153855i
$541$	1.63207	−	11.3513i	0.0701682	−	0.488030i	−0.924188	−	0.381938i	$-0.875257\pi$
$541$	1.63207	−	11.3513i	0.0701682	−	0.488030i	0.994356	−	0.106093i	$-0.0338340\pi$
$542$	8.51411	+	5.47169i	0.365713	+	0.235029i
$543$	−4.46961	−	7.46028i	−0.191809	−	0.320151i
$544$	−0.0683673	+	0.0312223i	−0.00293122	+	0.00133864i
$545$	32.4604	+	0.692690i	1.39045	+	0.0296716i
$546$	10.4880	+	5.19396i	0.448843	+	0.222281i
$547$	23.7002	+	20.5363i	1.01335	+	0.878070i	0.992565	−	0.121714i	$-0.0388392\pi$
$547$	23.7002	+	20.5363i	1.01335	+	0.878070i	0.0207813	+	0.999784i	$0.493385\pi$
$548$	1.63354	+	5.56333i	0.0697814	+	0.237654i
$549$	−8.76801	−	8.61937i	−0.374210	−	0.367866i
$550$	−6.65868	+	3.88826i	−0.283927	+	0.165796i
$551$	−1.70995			−0.0728464
$552$	0.838056	−	8.26424i	0.0356700	−	0.351749i
$553$		−	13.2441i		−	0.563195i
$554$	−2.50870	+	0.360697i	−0.106584	+	0.0153245i
$555$	−10.1052	+	3.98511i	−0.428941	+	0.169158i
$556$	7.42841	−	2.18118i	0.315035	−	0.0925026i
$557$	5.71257	+	4.94997i	0.242049	+	0.209737i	0.767434	−	0.641128i	$-0.221533\pi$
$557$	5.71257	+	4.94997i	0.242049	+	0.209737i	−0.525385	+	0.850865i	$0.676079\pi$
$558$	−17.3696	−	12.7725i	−0.735315	−	0.540703i
$559$	−8.89430	−	13.8398i	−0.376189	−	0.585361i
$560$	3.36843	+	0.557900i	0.142342	+	0.0235756i
$561$	−0.103178	−	0.172215i	−0.00435617	−	0.00727094i
$562$	14.2626	+	9.16601i	0.601631	+	0.386645i
$563$	27.3594	+	3.93368i	1.15306	+	0.165785i	0.692212	−	0.721694i	$-0.256636\pi$
$563$	27.3594	+	3.93368i	1.15306	+	0.165785i	0.460847	+	0.887479i	$0.347546\pi$
$564$	13.0693	+	4.28792i	0.550317	+	0.180554i
$565$	8.59659	+	19.9391i	0.361661	+	0.838842i
$566$	−19.5901	−	22.6082i	−0.823433	−	0.950292i
$567$	3.64569	−	13.2500i	0.153105	−	0.556447i
$568$	−3.81675	−	5.93898i	−0.160147	−	0.249194i
$569$	−15.1019	−	4.43431i	−0.633104	−	0.185896i	−0.0505935	−	0.998719i	$-0.516111\pi$
$569$	−15.1019	−	4.43431i	−0.633104	−	0.185896i	−0.582510	+	0.812823i	$0.697929\pi$
$570$	0.156378	+	1.73211i	0.00654994	+	0.0725500i
$571$	−7.62777	−	25.9778i	−0.319212	−	1.08714i	−0.950277	−	0.311406i	$-0.899200\pi$
$571$	−7.62777	−	25.9778i	−0.319212	−	1.08714i	0.631065	−	0.775730i	$-0.282618\pi$
$572$	6.20776	+	2.83499i	0.259560	+	0.118537i
$573$	−15.6445	−	0.491803i	−0.653560	−	0.0205454i
$574$			9.50624i			0.396783i
$575$	−19.7680	+	13.5731i	−0.824381	+	0.566036i
$576$	−2.81971	−	1.02433i	−0.117488	−	0.0426803i
$577$	−8.64026	+	1.24228i	−0.359699	+	0.0517169i	−0.319795	−	0.947487i	$-0.603614\pi$
$577$	−8.64026	+	1.24228i	−0.359699	+	0.0517169i	−0.0399034	+	0.999204i	$0.512705\pi$
$578$	7.05971	−	15.4586i	0.293645	−	0.642993i
$579$	30.9937	−	3.46624i	1.28805	−	0.144052i
$580$	−8.21926	+	2.22406i	−0.341286	+	0.0923491i
$581$	2.27519	−	7.74858i	0.0943907	−	0.321465i
$582$	3.21276	+	7.66347i	0.133173	+	0.317661i
$583$	−14.1460	+	6.46028i	−0.585869	+	0.267557i
$584$	−8.61422	+	7.46426i	−0.356459	+	0.308873i
$585$	1.73894	+	29.6346i	0.0718961	+	1.22524i
$586$	−21.7156	−	3.12223i	−0.897062	−	0.128978i
$587$	2.03095	−	14.1256i	0.0838264	−	0.583025i	−0.904008	−	0.427516i	$-0.859389\pi$
$587$	2.03095	−	14.1256i	0.0838264	−	0.583025i	0.987834	−	0.155510i	$-0.0497020\pi$
$588$	−5.48463	+	5.94163i	−0.226182	+	0.245029i
$589$	2.43894	−	2.11335i	0.100495	−	0.0870791i
$590$	−0.561804	+	3.39200i	−0.0231291	+	0.139647i
$591$	0.964786	+	2.30133i	0.0396860	+	0.0946640i
$592$	2.69110	+	0.790178i	0.110603	+	0.0324761i
$593$	−30.9210	+	35.6848i	−1.26977	+	1.46540i	−0.449658	+	0.893201i	$0.648454\pi$
$593$	−30.9210	+	35.6848i	−1.26977	+	1.46540i	−0.820117	+	0.572196i	$0.806091\pi$
$594$	1.88202	−	7.78917i	0.0772203	−	0.319593i
$595$	0.218792	−	0.134101i	0.00896958	−	0.00549760i
$596$	0.816379	+	5.67804i	0.0334402	+	0.232582i
$597$	19.9514	+	3.51164i	0.816556	+	0.143722i
$598$	19.8978	+	7.38154i	0.813681	+	0.301854i
$599$		−	10.1000i		−	0.412676i	−0.978481	−	0.206338i	$-0.933845\pi$
$599$		−	10.1000i		−	0.412676i	0.978481	−	0.206338i	$-0.0661546\pi$
$600$	3.00454	+	8.12236i	0.122660	+	0.331594i
$601$	−2.79191	+	6.11343i	−0.113884	+	0.249372i	−0.957988	−	0.286808i	$-0.907406\pi$
$601$	−2.79191	+	6.11343i	−0.113884	+	0.249372i	0.844104	+	0.536180i	$0.180133\pi$
$602$	−5.44659	+	1.59926i	−0.221987	+	0.0651811i
$603$	28.8861	−	16.0951i	1.17633	−	0.655441i
$604$	−8.59833	−	2.52470i	−0.349861	−	0.102728i
$605$	0.411307	−	19.2744i	0.0167220	−	0.783616i
$606$	1.27348	+	4.90193i	0.0517318	+	0.199127i
$607$	−27.5224	+	23.8483i	−1.11710	+	0.967972i	−0.999685	−	0.0251109i	$-0.992006\pi$
$607$	−27.5224	+	23.8483i	−1.11710	+	0.967972i	−0.117415	+	0.993083i	$0.537461\pi$
$608$	0.242773	−	0.377763i	0.00984576	−	0.0153203i
$609$	−3.13954	+	9.56913i	−0.127221	+	0.387761i
$610$	6.14773	−	6.79630i	0.248914	−	0.275174i
$611$	−18.9994	+	29.5637i	−0.768634	+	1.19602i
$612$	−0.210580	+	0.0805995i	−0.00851219	+	0.00325804i
$613$	−20.2525	−	44.3468i	−0.817992	−	1.79115i	−0.568288	−	0.822829i	$-0.692394\pi$
$613$	−20.2525	−	44.3468i	−0.817992	−	1.79115i	−0.249703	−	0.968322i	$-0.580333\pi$
$614$	−13.5759	−	21.1245i	−0.547879	−	0.852516i
$615$	−20.9436	+	11.9481i	−0.844529	+	0.481793i
$616$	1.54205	−	1.77962i	0.0621310	−	0.0717030i
$617$	3.58628	+	12.2137i	0.144378	+	0.491707i	0.999650	−	0.0264735i	$-0.00842778\pi$
$617$	3.58628	+	12.2137i	0.144378	+	0.491707i	−0.855271	+	0.518180i	$0.826610\pi$
$618$	−24.8491	−	17.0961i	−0.999579	−	0.687707i
$619$	−20.2238	+	2.90775i	−0.812864	+	0.116872i	−0.536196	−	0.844093i	$-0.680139\pi$
$619$	−20.2238	+	2.90775i	−0.812864	+	0.116872i	−0.276668	+	0.960966i	$0.589230\pi$
$620$	8.97454	−	13.3305i	0.360426	−	0.535366i
$621$	4.06644	−	24.5859i	0.163180	−	0.986596i
$622$			27.5697i			1.10544i
$623$	1.84856	+	12.8570i	0.0740610	+	0.515105i
$624$	4.34445	−	6.31464i	0.173917	−	0.252788i
$625$	12.2860	−	21.7728i	0.491442	−	0.870911i
$626$	0.0716998	−	0.0827460i	0.00286570	−	0.00330719i
$627$	1.07486	+	0.532306i	0.0429260	+	0.0212582i
$628$	14.9250	−	9.59172i	0.595572	−	0.382751i
$629$	0.191750	−	0.0875694i	0.00764559	−	0.00349162i
$630$	9.98023	+	2.30511i	0.397622	+	0.0918378i
$631$	−17.6051	+	27.3940i	−0.700847	+	1.09054i	0.290193	+	0.956968i	$0.406281\pi$
$631$	−17.6051	+	27.3940i	−0.700847	+	1.09054i	−0.991039	+	0.133570i	$0.957356\pi$
$632$	−8.58537	−	1.23439i	−0.341508	−	0.0491014i
$633$	41.2778	+	13.5429i	1.64064	+	0.538280i
$634$	15.5276	+	9.97900i	0.616681	+	0.396317i
$635$	−2.61934	−	21.4587i	−0.103945	−	0.851563i
$636$	4.39181	+	16.9051i	0.174147	+	0.670330i
$637$	−11.1692	−	17.3797i	−0.442542	−	0.688608i
$638$	−1.65447	+	5.63461i	−0.0655011	+	0.223076i
$639$	−10.3086	−	18.5009i	−0.407800	−	0.731886i
$640$	0.675603	−	2.13156i	0.0267056	−	0.0842574i
$641$	9.15806	−	20.0534i	0.361722	−	0.792060i	−0.638035	−	0.770007i	$-0.720253\pi$
$641$	9.15806	−	20.0534i	0.361722	−	0.792060i	0.999757	−	0.0220528i	$-0.00702020\pi$
$642$	0.937007	−	29.8068i	0.0369807	−	1.17638i
$643$	−1.63341			−0.0644152			−0.0322076	−	0.999481i	$-0.510254\pi$
$643$	−1.63341			−0.0644152			−0.0322076	+	0.999481i	$0.510254\pi$
$644$	4.37811	−	5.87002i	0.172522	−	0.231311i
$645$	−10.3691	−	9.98957i	−0.408281	−	0.393339i
$646$	−0.00480313	−	0.0334065i	−0.000188977	−	0.00131436i
$647$	−7.93010	+	17.3645i	−0.311765	+	0.682669i	−0.999044	−	0.0437243i	$-0.986078\pi$
$647$	−7.93010	+	17.3645i	−0.311765	+	0.682669i	0.687279	+	0.726393i	$0.258805\pi$
$648$	−8.24941	−	3.59823i	−0.324067	−	0.141352i
$649$	1.79207	+	1.55284i	0.0703450	+	0.0609543i
$650$	−22.0155	+	2.21175i	−0.863520	+	0.0867518i
$651$	−7.34861	−	17.5288i	−0.288015	−	0.687009i
$652$	7.73141	−	3.53082i	0.302785	−	0.138277i
$653$	−13.9775	−	16.1309i	−0.546983	−	0.631252i	0.413195	−	0.910643i	$-0.364413\pi$
$653$	−13.9775	−	16.1309i	−0.546983	−	0.631252i	−0.960177	+	0.279391i	$0.909867\pi$
$654$	−18.4798	−	17.0584i	−0.722618	−	0.667038i
$655$	−23.3920	+	25.8598i	−0.914003	+	1.01043i
$656$	6.16234	+	0.886011i	0.240599	+	0.0345929i
$657$	−27.1981	+	20.7254i	−1.06110	+	0.808575i
$658$	7.94073	+	9.16409i	0.309562	+	0.357253i
$659$	8.73973	+	19.1373i	0.340452	+	0.745485i	0.999981	−	0.00619385i	$-0.00197158\pi$
$659$	8.73973	+	19.1373i	0.340452	+	0.745485i	−0.659529	+	0.751679i	$0.729244\pi$
$660$	5.85892	+	1.16061i	0.228058	+	0.0451768i
$661$	2.85263	−	9.71516i	0.110954	−	0.377876i	−0.885230	−	0.465154i	$-0.845999\pi$
$661$	2.85263	−	9.71516i	0.110954	−	0.377876i	0.996184	+	0.0872785i	$0.0278170\pi$
$662$	−0.680280	+	0.785085i	−0.0264398	+	0.0305132i
$663$	−0.0640277	−	0.572511i	−0.00248663	−	0.0222345i
$664$	−4.81090	−	2.19707i	−0.186699	−	0.0852627i
$665$	−0.666520	+	1.38074i	−0.0258466	+	0.0535426i
$666$	7.90846	+	2.87294i	0.306447	+	0.111324i
$667$	−3.85046	+	17.8518i	−0.149090	+	0.691224i
$668$	−12.2345			−0.473368
$669$	0.0989075	−	3.14631i	0.00382398	−	0.121643i
$670$	12.8798	+	21.0140i	0.497590	+	0.811840i
$671$	−1.78066	−	6.06437i	−0.0687416	−	0.234112i
$672$	−1.66827	−	2.05218i	−0.0643549	−	0.0791646i
$673$	−1.67119	+	5.69154i	−0.0644196	+	0.219393i	−0.985411	−	0.170189i	$-0.945562\pi$
$673$	−1.67119	+	5.69154i	−0.0644196	+	0.219393i	0.920992	+	0.389582i	$0.127380\pi$
$674$	−23.3300	+	14.9933i	−0.898637	+	0.577519i
$675$	7.46533	+	24.8851i	0.287341	+	0.957828i
$676$	4.31094	+	4.97509i	0.165805	+	0.191350i
$677$	−9.44586	+	14.6980i	−0.363034	+	0.564892i	−0.973938	−	0.226813i	$-0.927170\pi$
$677$	−9.44586	+	14.6980i	−0.363034	+	0.564892i	0.610905	+	0.791704i	$0.290806\pi$
$678$	5.24319	−	15.9809i	0.201364	−	0.613743i
$679$	−1.04254	+	7.25103i	−0.0400090	+	0.278269i
$680$	−0.0665378	−	0.154329i	−0.00255161	−	0.00591823i
$681$	11.8738	+	19.8188i	0.455006	+	0.759457i
$682$	−4.60408	−	10.0815i	−0.176299	−	0.386042i
$683$	−14.1226	+	9.07606i	−0.540387	+	0.347286i	−0.782190	−	0.623040i	$-0.785897\pi$
$683$	−14.1226	+	9.07606i	−0.540387	+	0.347286i	0.241803	+	0.970325i	$0.422261\pi$
$684$	0.798063	−	1.08530i	0.0305147	−	0.0414976i
$685$	−12.5151	+	3.38647i	−0.478177	+	0.129390i
$686$	−17.0953	+	5.01962i	−0.652700	+	0.191650i
$687$	−19.8510	+	28.8533i	−0.757362	+	1.10082i
$688$	0.529070	+	3.67977i	0.0201706	+	0.140290i
$689$	−44.6250			−1.70008
$690$	18.4352	+	2.26778i	0.701817	+	0.0863328i
$691$	48.2189			1.83433			0.917166	−	0.398505i	$-0.130471\pi$
$691$	48.2189			1.83433			0.917166	+	0.398505i	$0.130471\pi$
$692$	−2.39213	−	16.6376i	−0.0909352	−	0.632468i
$693$	4.95235	−	5.03775i	0.188124	−	0.191368i
$694$	−15.1146	+	4.43805i	−0.573743	+	0.168466i
$695$	4.52177	+	16.7107i	0.171521	+	0.633873i
$696$	5.91049	+	2.92706i	0.224037	+	0.110950i
$697$	0.393639	−	0.252977i	0.0149102	−	0.00958217i
$698$	5.45177	+	11.9377i	0.206353	+	0.451849i
$699$	19.4736	−	11.6670i	0.736559	−	0.441288i
$700$	−1.40791	+	7.50372i	−0.0532141	+	0.283614i
$701$	−2.27772	+	15.8419i	−0.0860282	+	0.598340i	0.900513	+	0.434829i	$0.143191\pi$
$701$	−2.27772	+	15.8419i	−0.0860282	+	0.598340i	−0.986542	+	0.163511i	$0.947718\pi$
$702$	14.1975	−	18.0879i	0.535850	−	0.682684i
$703$	−0.680908	+	1.05951i	−0.0256809	+	0.0399603i
$704$	−1.00990	−	1.16549i	−0.0380621	−	0.0439260i
$705$	−10.2094	+	29.0126i	−0.384508	+	1.09268i
$706$	−24.9727	+	16.0490i	−0.939859	+	0.604011i
$707$	−1.25790	+	4.28401i	−0.0473081	+	0.161117i
$708$	2.06654	−	1.67994i	0.0776653	−	0.0631361i
$709$	8.89931	+	30.3083i	0.334220	+	1.13825i	0.939589	+	0.342305i	$0.111208\pi$
$709$	8.89931	+	30.3083i	0.334220	+	1.13825i	−0.605368	+	0.795945i	$0.706974\pi$
$710$	13.4590	−	8.24925i	0.505108	−	0.309589i
$711$	−25.4726	−	5.31360i	−0.955299	−	0.199275i
$712$	8.50675			0.318804
$713$	−16.5713	−	30.2212i	−0.620599	−	1.13179i
$714$	−0.195766	−	0.0344568i	−0.00732637	−	0.00128951i
$715$	−6.63394	+	13.7426i	−0.248095	+	0.513943i
$716$	−9.76313	−	4.45867i	−0.364865	−	0.166628i
$717$	−14.3868	+	1.60898i	−0.537286	+	0.0600884i
$718$	24.6651	−	28.4650i	0.920494	−	1.06231i
$719$	1.32460	−	4.51118i	0.0493993	−	0.168239i	−0.931099	−	0.364767i	$-0.881149\pi$
$719$	1.32460	−	4.51118i	0.0493993	−	0.168239i	0.980498	+	0.196528i	$0.0629668\pi$
$720$	2.42446	−	6.25476i	0.0903542	−	0.233101i
$721$	−11.0460	−	24.1873i	−0.411374	−	0.900782i
$722$	−12.3103	−	14.2069i	−0.458142	−	0.528724i
$723$	−24.1023	−	22.2484i	−0.896373	−	0.827429i
$724$	−4.96996	−	0.714572i	−0.184707	−	0.0265569i
$725$	−4.57991	−	18.4807i	−0.170094	−	0.686357i
$726$	−10.1290	+	10.9730i	−0.375922	+	0.407246i
$727$	23.5744	+	27.2063i	0.874325	+	1.00902i	0.999857	+	0.0169347i	$0.00539074\pi$
$727$	23.5744	+	27.2063i	0.874325	+	1.00902i	−0.125532	+	0.992090i	$0.540064\pi$
$728$	6.14646	−	2.80699i	0.227803	−	0.104034i
$729$	−24.0213	−	12.3278i	−0.889680	−	0.456586i
$730$	−16.2759	−	19.6137i	−0.602396	−	0.725935i
$731$	0.211166	+	0.182976i	0.00781025	+	0.00676762i
$732$	−7.05465	+	0.788969i	−0.260747	+	0.0291611i
$733$	−0.546364	+	1.19637i	−0.0201804	+	0.0441889i	−0.919454	−	0.393198i	$-0.871369\pi$
$733$	−0.546364	+	1.19637i	−0.0201804	+	0.0441889i	0.899273	+	0.437387i	$0.144096\pi$
$734$	0.319039	+	2.21897i	0.0117760	+	0.0819036i
$735$	−13.0212	−	12.5447i	−0.480295	−	0.462717i
$736$	−3.39714	−	3.38518i	−0.125220	−	0.124779i
$737$	16.9985			0.626146
$738$	18.2836	+	3.81396i	0.673028	+	0.140394i
$739$	−4.76050	+	10.4240i	−0.175118	+	0.383455i	−0.976756	−	0.214355i	$-0.931235\pi$
$739$	−4.76050	+	10.4240i	−0.175118	+	0.383455i	0.801638	+	0.597810i	$0.203962\pi$
$740$	−1.89487	+	5.97841i	−0.0696568	+	0.219771i
$741$	2.17109	+	2.67071i	0.0797570	+	0.0981111i
$742$	−4.33806	+	14.7741i	−0.159255	+	0.542374i
$743$	−22.8197	−	35.5081i	−0.837173	−	1.30267i	−0.951008	−	0.309167i	$-0.899950\pi$
$743$	−22.8197	−	35.5081i	−0.837173	−	1.30267i	0.113835	−	0.993500i	$-0.463687\pi$
$744$	−12.0478	+	3.12994i	−0.441695	+	0.114749i
$745$	−12.7325	+	1.55419i	−0.466484	+	0.0569410i
$746$	0.693949	+	0.445974i	0.0254073	+	0.0163283i
$747$	−13.9902	−	7.48470i	−0.511875	−	0.273851i
$748$	−0.114728	−	0.0164954i	−0.00419487	−	0.000603131i
$749$	14.2134	−	22.1164i	0.519345	−	0.808117i
$750$	−18.3013	+	6.32935i	−0.668271	+	0.231115i
$751$	15.7618	−	7.19819i	0.575158	−	0.262666i	−0.106529	−	0.994310i	$-0.533974\pi$
$751$	15.7618	−	7.19819i	0.575158	−	0.262666i	0.681687	+	0.731644i	$0.261247\pi$
$752$	6.68065	−	4.29339i	0.243618	−	0.156564i
$753$	0.584010	−	1.17927i	0.0212825	−	0.0429749i
$754$	−11.0352	+	12.7353i	−0.401879	+	0.463793i
$755$	6.05430	−	19.1016i	0.220339	−	0.695180i
$756$	−4.60823	−	6.45874i	−0.167600	−	0.234902i
$757$	−4.35875	−	30.3158i	−0.158422	−	1.10185i	−0.901543	−	0.432689i	$-0.857565\pi$
$757$	−4.35875	−	30.3158i	−0.158422	−	1.10185i	0.743122	−	0.669156i	$-0.233344\pi$
$758$			4.49623i			0.163311i
$759$	7.97761	−	10.0229i	0.289569	−	0.363807i
$760$	0.832929	+	0.560755i	0.0302135	+	0.0203407i
$761$	3.43249	−	0.493518i	0.124428	−	0.0178900i	−0.0798196	−	0.996809i	$-0.525434\pi$
$761$	3.43249	−	0.493518i	0.124428	−	0.0178900i	0.204247	+	0.978919i	$0.434525\pi$
$762$	−9.49130	+	13.7956i	−0.343833	+	0.499761i
$763$	−6.24632	−	21.2730i	−0.226132	−	0.770135i
$764$	−5.91788	+	6.82959i	−0.214101	+	0.247086i
$765$	−0.170139	−	0.474609i	−0.00615139	−	0.0171595i
$766$	−16.1377	−	25.1108i	−0.583079	−	0.907288i
$767$	2.82663	+	6.18947i	0.102064	+	0.223489i
$768$	−1.48580	+	0.890172i	−0.0536141	+	0.0321213i
$769$	9.85737	−	15.3384i	0.355466	−	0.553115i	−0.616763	−	0.787149i	$-0.711556\pi$
$769$	9.85737	−	15.3384i	0.355466	−	0.553115i	0.972228	+	0.234034i	$0.0751926\pi$
$770$	3.90488	+	3.53224i	0.140722	+	0.127293i
$771$	−43.8532	−	14.3878i	−1.57934	−	0.518166i
$772$	9.73466	−	15.1474i	0.350358	−	0.545168i
$773$	17.7827	−	15.4088i	0.639599	−	0.554216i	−0.273542	−

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.42695 - 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.584056 - 2.15844i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(-1.28454 + 0.825522i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.42695 - 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.584056 - 2.15844i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(-1.28454 + 0.825522i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +(-2.05335 + 0.885290i) q^{10} +(-0.219473 + 1.52646i) q^{11} +(1.64574 + 0.539952i) q^{12} +(-2.39248 + 3.72277i) q^{13} +(0.999928 + 1.15398i) q^{14} +(-1.28560 + 3.65338i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.0211748 - 0.0721148i) q^{17} +(2.62065 - 1.46020i) q^{18} +(0.126511 + 0.430858i) q^{19} +(1.16850 + 1.90646i) q^{20} +(2.64342 + 0.0830986i) q^{21} +1.54216 q^{22} +(4.78300 - 0.350566i) q^{23} +(0.300243 - 1.70583i) q^{24} +(-4.31776 + 2.52131i) q^{25} +(4.02536 + 1.83832i) q^{26} +(1.22038 - 5.05081i) q^{27} +(0.999928 - 1.15398i) q^{28} +(-1.07283 + 3.65371i) q^{29} +(3.79916 + 0.752589i) q^{30} +(-2.98547 - 6.53727i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.81176 - 1.96273i) q^{33} +(-0.0743943 - 0.0106963i) q^{34} +(2.53208 + 2.29045i) q^{35} +(-1.81830 - 2.38617i) q^{36} +(1.83669 + 2.11966i) q^{37} +(0.408468 - 0.186541i) q^{38} +(7.06874 - 2.96343i) q^{39} +(1.72076 - 1.42793i) q^{40} +(4.70508 + 4.07697i) q^{41} +(-0.293945 - 2.62834i) q^{42} +(-1.54435 + 3.38165i) q^{43} +(-0.219473 - 1.52646i) q^{44} +(5.42116 - 3.95108i) q^{45} +(-1.02769 - 4.68443i) q^{46} +7.94130 q^{47} +(-1.73120 - 0.0544219i) q^{48} +(-1.93936 + 4.24660i) q^{49} +(3.11012 + 3.91499i) q^{50} +(-0.101013 + 0.0821162i) q^{51} +(1.24674 - 4.24601i) q^{52} +(5.45190 + 8.48332i) q^{53} +(-5.17308 - 0.489153i) q^{54} +(3.42297 - 0.417823i) q^{55} +(-1.28454 - 0.825522i) q^{56} +(0.242464 - 0.739014i) q^{57} +(3.76920 + 0.541929i) q^{58} +(0.831298 - 1.29353i) q^{59} +(0.204252 - 3.86759i) q^{60} +(-3.72803 + 1.70254i) q^{61} +(-6.04585 + 3.88544i) q^{62} +(-3.69045 - 2.71372i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(9.43274 + 2.98972i) q^{65} +(-2.20059 - 1.51400i) q^{66} +(-1.56866 - 10.9103i) q^{67} +0.0751593i q^{68} +(-7.16928 - 4.19541i) q^{69} +(1.90678 - 2.83228i) q^{70} +(-6.98782 + 1.00470i) q^{71} +(-2.10311 + 2.13938i) q^{72} +(3.21126 + 10.9365i) q^{73} +(1.83669 - 2.11966i) q^{74} +(8.63649 + 0.641123i) q^{75} +(-0.242773 - 0.377763i) q^{76} +(-0.978209 - 2.14198i) q^{77} +(-3.93925 - 6.57505i) q^{78} +(-4.68933 + 7.29674i) q^{79} +(-1.65828 - 1.50003i) q^{80} +(-6.69999 + 6.00917i) q^{81} +(3.36587 - 5.23740i) q^{82} +(-3.99704 + 3.46346i) q^{83} +(-2.55975 + 0.665004i) q^{84} +(-0.168023 - 0.00358553i) q^{85} +(3.56702 + 1.04737i) q^{86} +(5.11785 - 4.16043i) q^{87} +(-1.47969 + 0.434477i) q^{88} +(3.53383 - 7.73801i) q^{89} +(-4.68237 - 4.80369i) q^{90} -6.75708i q^{91} +(-4.49049 + 1.68389i) q^{92} +(-2.15776 + 12.2593i) q^{93} +(-1.13017 - 7.86047i) q^{94} +(0.856092 - 0.524712i) q^{95} +(0.192507 + 1.72132i) q^{96} +(3.14175 - 3.62578i) q^{97} +(4.47937 + 1.31526i) q^{98} +(-4.51218 + 1.02204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} + O(q^{10}) \)	\( 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} - 9q^{12} + 11q^{15} - 24q^{16} - 6q^{18} - 4q^{23} + 2q^{24} - 12q^{25} + 2q^{27} + 22q^{30} + 28q^{31} - 24q^{32} - 36q^{35} - 6q^{36} - 4q^{46} + 104q^{47} - 9q^{48} + 70q^{49} + 54q^{50} - 9q^{54} - 26q^{55} - 44q^{57} - 11q^{60} + 44q^{61} + 28q^{62} - 121q^{63} - 24q^{64} + 44q^{65} + 44q^{66} - 102q^{69} - 36q^{70} + 16q^{72} - 82q^{75} + 8q^{77} - 44q^{79} + 74q^{81} - 11q^{84} + 22q^{85} - 93q^{87} - 4q^{92} + 172q^{93} + 16q^{94} + 26q^{95} + 2q^{96} + 4q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Fields

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