LMFDB - Embedded newform 966.2.s.a.97.15

Newspace parameters

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			97.15
Character	$\chi$	$=$	966.97
Dual form			966.2.s.a.727.15

$q$-expansion

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.341716 - 2.37669i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(1.93632 + 1.80296i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.341716 - 2.37669i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(1.93632 + 1.80296i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-0.997464 + 2.18414i) q^{10} +(0.692982 + 2.36008i) q^{11} +(0.281733 + 0.959493i) q^{12} +(3.28973 + 1.50237i) q^{13} +(-1.34993 - 2.27545i) q^{14} +(1.81465 - 1.57240i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-5.60723 + 3.60355i) q^{17} +(0.142315 - 0.989821i) q^{18} +(1.18505 + 0.761584i) q^{19} +(1.57240 - 1.81465i) q^{20} +(0.282685 + 2.63061i) q^{21} -2.45972i q^{22} +(-2.49619 + 4.09500i) q^{23} -1.00000i q^{24} +(-0.734408 - 0.215642i) q^{25} +(-2.73321 - 2.36834i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(0.654182 + 2.56360i) q^{28} +(4.18123 - 2.68711i) q^{29} +(-2.18414 + 0.997464i) q^{30} +(2.24033 - 1.94126i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-1.02180 + 2.23744i) q^{33} +(6.39533 - 1.87784i) q^{34} +(4.94674 - 3.98593i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(3.08660 - 0.443787i) q^{37} +(-0.922482 - 1.06460i) q^{38} +(1.50237 + 3.28973i) q^{39} +(-2.01996 + 1.29815i) q^{40} +(-8.12767 - 1.16858i) q^{41} +(0.469893 - 2.60369i) q^{42} +(4.24949 + 3.68220i) q^{43} +(-0.692982 + 2.36008i) q^{44} +2.40113 q^{45} +(3.54877 - 3.22586i) q^{46} -4.45289i q^{47} +(-0.281733 + 0.959493i) q^{48} +(0.498671 + 6.98222i) q^{49} +(0.643906 + 0.413814i) q^{50} +(-6.59748 - 0.948574i) q^{51} +(1.95526 + 3.04244i) q^{52} +(7.96008 - 3.63525i) q^{53} +(0.755750 - 0.654861i) q^{54} +(5.84598 - 0.840525i) q^{55} +(0.0945662 - 2.64406i) q^{56} +(0.396868 + 1.35161i) q^{57} +(-4.76891 + 1.40028i) q^{58} +(5.00403 + 2.28526i) q^{59} +(2.37669 - 0.341716i) q^{60} +(-8.37626 - 9.66672i) q^{61} +(-2.69650 + 1.23145i) q^{62} +(-1.50904 + 2.17320i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(4.69482 - 7.30528i) q^{65} +(1.61077 - 1.85893i) q^{66} +(0.857529 - 2.92048i) q^{67} -6.66532 q^{68} +(-4.56815 + 1.46014i) q^{69} +(-5.86933 + 2.43081i) q^{70} +(14.8816 + 4.36963i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-7.27883 + 11.3261i) q^{73} +(-3.08660 - 0.443787i) q^{74} +(-0.413814 - 0.643906i) q^{75} +(0.585182 + 1.28137i) q^{76} +(-2.91330 + 5.81929i) q^{77} +(-0.514689 - 3.57974i) q^{78} +(-0.459240 - 0.209728i) q^{79} +(2.30386 - 0.676476i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(7.46921 + 3.41107i) q^{82} +(-0.0423414 - 0.294491i) q^{83} +(-1.18440 + 2.36584i) q^{84} +(6.64842 + 14.5580i) q^{85} +(-3.03996 - 4.73027i) q^{86} +(4.91965 + 0.707339i) q^{87} +(1.32982 - 2.06925i) q^{88} +(-2.92830 + 3.37944i) q^{89} +(-2.30386 - 0.676476i) q^{90} +(3.66126 + 8.84032i) q^{91} +(-4.31385 + 2.09539i) q^{92} +2.96439 q^{93} +(-1.25452 + 4.27251i) q^{94} +(2.21500 - 2.55624i) q^{95} +(0.540641 - 0.841254i) q^{96} +(-1.66184 + 11.5584i) q^{97} +(1.48865 - 6.83988i) q^{98} +(-2.23744 + 1.02180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} + O(q^{10}) $	$ 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} - 22q^{14} - 16q^{16} + 16q^{18} - 36q^{23} + 96q^{25} + 22q^{28} - 20q^{29} - 16q^{32} - 50q^{35} + 16q^{36} + 22q^{37} + 4q^{39} - 110q^{43} + 8q^{46} - 36q^{50} + 22q^{51} - 88q^{53} + 22q^{57} + 24q^{58} - 16q^{64} - 72q^{70} + 48q^{71} + 16q^{72} - 22q^{74} + 24q^{77} + 4q^{78} + 88q^{79} - 16q^{81} + 22q^{84} + 76q^{85} + 44q^{86} - 44q^{88} + 8q^{92} - 14q^{95} + 22q^{98} - 22q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.341716	−	2.37669i	0.152820	−	1.06289i	−0.758643	−	0.651506i	$-0.774138\pi$
$5$	0.341716	−	2.37669i	0.152820	−	1.06289i	0.911464	−	0.411381i	$-0.134953\pi$
$6$	−0.540641	−	0.841254i	−0.220716	−	0.343440i
$7$	1.93632	+	1.80296i	0.731860	+	0.681455i
$7$	1.93632	+	1.80296i	0.731860	+	0.681455i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	−0.997464	+	2.18414i	−0.315426	+	0.690686i
$11$	0.692982	+	2.36008i	0.208942	+	0.711591i	0.995558	+	0.0941488i	$0.0300129\pi$
$11$	0.692982	+	2.36008i	0.208942	+	0.711591i	−0.786616	+	0.617442i	$0.788169\pi$
$12$	0.281733	+	0.959493i	0.0813292	+	0.276982i
$13$	3.28973	+	1.50237i	0.912407	+	0.416682i	0.815597	−	0.578620i	$-0.196409\pi$
$13$	3.28973	+	1.50237i	0.912407	+	0.416682i	0.0968103	+	0.995303i	$0.469136\pi$
$14$	−1.34993	−	2.27545i	−0.360785	−	0.608140i
$15$	1.81465	−	1.57240i	0.468541	−	0.405993i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−5.60723	+	3.60355i	−1.35995	+	0.873988i	−0.998298	−	0.0583239i	$-0.981424\pi$
$17$	−5.60723	+	3.60355i	−1.35995	+	0.873988i	−0.361655	+	0.932312i	$0.617788\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	1.18505	+	0.761584i	0.271869	+	0.174719i	0.669470	−	0.742839i	$-0.266521\pi$
$19$	1.18505	+	0.761584i	0.271869	+	0.174719i	−0.397602	+	0.917558i	$0.630157\pi$
$20$	1.57240	−	1.81465i	0.351600	−	0.405768i
$21$	0.282685	+	2.63061i	0.0616870	+	0.574045i
$22$		−	2.45972i		−	0.524413i
$23$	−2.49619	+	4.09500i	−0.520492	+	0.853866i
$23$	−2.49619	+	4.09500i	−0.520492	+	0.853866i
$24$		−	1.00000i		−	0.204124i
$25$	−0.734408	−	0.215642i	−0.146882	−	0.0431284i
$26$	−2.73321	−	2.36834i	−0.536026	−	0.464469i
$27$	−0.540641	+	0.841254i	−0.104046	+	0.161899i
$28$	0.654182	+	2.56360i	0.123629	+	0.484475i
$29$	4.18123	−	2.68711i	0.776435	−	0.498984i	−0.0914137	−	0.995813i	$-0.529139\pi$
$29$	4.18123	−	2.68711i	0.776435	−	0.498984i	0.867849	+	0.496829i	$0.165502\pi$
$30$	−2.18414	+	0.997464i	−0.398768	+	0.182111i
$31$	2.24033	−	1.94126i	0.402376	−	0.348661i	−0.430042	−	0.902809i	$-0.641501\pi$
$31$	2.24033	−	1.94126i	0.402376	−	0.348661i	0.832418	+	0.554148i	$0.186956\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	−1.02180	+	2.23744i	−0.177873	+	0.389488i
$34$	6.39533	−	1.87784i	1.09679	−	0.322047i
$35$	4.94674	−	3.98593i	0.836152	−	0.673745i
$36$	−0.415415	+	0.909632i	−0.0692358	+	0.151605i
$37$	3.08660	−	0.443787i	0.507435	−	0.0729581i	0.116157	−	0.993231i	$-0.462942\pi$
$37$	3.08660	−	0.443787i	0.507435	−	0.0729581i	0.391278	+	0.920273i	$0.372033\pi$
$38$	−0.922482	−	1.06460i	−0.149646	−	0.172701i
$39$	1.50237	+	3.28973i	0.240572	+	0.526779i
$40$	−2.01996	+	1.29815i	−0.319383	+	0.205255i
$41$	−8.12767	−	1.16858i	−1.26933	−	0.182502i	−0.525454	−	0.850822i	$-0.676105\pi$
$41$	−8.12767	−	1.16858i	−1.26933	−	0.182502i	−0.743874	+	0.668320i	$0.767014\pi$
$42$	0.469893	−	2.60369i	0.0725060	−	0.401758i
$43$	4.24949	+	3.68220i	0.648041	+	0.561531i	0.915640	−	0.402000i	$-0.131685\pi$
$43$	4.24949	+	3.68220i	0.648041	+	0.561531i	−0.267599	+	0.963530i	$0.586230\pi$
$44$	−0.692982	+	2.36008i	−0.104471	+	0.355796i
$45$	2.40113			0.357939
$46$	3.54877	−	3.22586i	0.523238	−	0.475628i
$47$		−	4.45289i		−	0.649520i	−0.945796	−	0.324760i	$-0.894716\pi$
$47$		−	4.45289i		−	0.649520i	0.945796	−	0.324760i	$-0.105284\pi$
$48$	−0.281733	+	0.959493i	−0.0406646	+	0.138491i
$49$	0.498671	+	6.98222i	0.0712387	+	0.997459i
$50$	0.643906	+	0.413814i	0.0910621	+	0.0585221i
$51$	−6.59748	−	0.948574i	−0.923832	−	0.132827i
$52$	1.95526	+	3.04244i	0.271145	+	0.421910i
$53$	7.96008	−	3.63525i	1.09340	−	0.499340i	0.214685	−	0.976683i	$-0.431128\pi$
$53$	7.96008	−	3.63525i	1.09340	−	0.499340i	0.878717	+	0.477344i	$0.158400\pi$
$54$	0.755750	−	0.654861i	0.102844	−	0.0891153i
$55$	5.84598	−	0.840525i	0.788272	−	0.113336i
$56$	0.0945662	−	2.64406i	0.0126369	−	0.353327i
$57$	0.396868	+	1.35161i	0.0525664	+	0.179025i
$58$	−4.76891	+	1.40028i	−0.626188	+	0.183866i
$59$	5.00403	+	2.28526i	0.651469	+	0.297516i	0.713602	−	0.700552i	$-0.247063\pi$
$59$	5.00403	+	2.28526i	0.651469	+	0.297516i	−0.0621321	+	0.998068i	$0.519790\pi$
$60$	2.37669	−	0.341716i	0.306829	−	0.0441154i
$61$	−8.37626	−	9.66672i	−1.07247	−	1.23770i	−0.970037	−	0.242957i	$-0.921883\pi$
$61$	−8.37626	−	9.66672i	−1.07247	−	1.23770i	−0.102433	−	0.994740i	$-0.532663\pi$
$62$	−2.69650	+	1.23145i	−0.342456	+	0.156394i
$63$	−1.50904	+	2.17320i	−0.190121	+	0.273797i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	4.69482	−	7.30528i	0.582320	−	0.906108i
$66$	1.61077	−	1.85893i	0.198272	−	0.228818i
$67$	0.857529	−	2.92048i	0.104764	−	0.356793i	−0.890381	−	0.455217i	$-0.849562\pi$
$67$	0.857529	−	2.92048i	0.104764	−	0.356793i	0.995145	+	0.0984236i	$0.0313800\pi$
$68$	−6.66532			−0.808289
$69$	−4.56815	+	1.46014i	−0.549941	+	0.175780i
$70$	−5.86933	+	2.43081i	−0.701519	+	0.290537i
$71$	14.8816	+	4.36963i	1.76612	+	0.518580i	0.993251	−	0.115986i	$-0.0370027\pi$
$71$	14.8816	+	4.36963i	1.76612	+	0.518580i	0.772869	+	0.634566i	$0.218821\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−7.27883	+	11.3261i	−0.851923	+	1.32562i	0.0921041	+	0.995749i	$0.470641\pi$
$73$	−7.27883	+	11.3261i	−0.851923	+	1.32562i	−0.944027	+	0.329868i	$0.892996\pi$
$74$	−3.08660	−	0.443787i	−0.358811	−	0.0515892i
$75$	−0.413814	−	0.643906i	−0.0477831	−	0.0743519i
$76$	0.585182	+	1.28137i	0.0671250	+	0.146983i
$77$	−2.91330	+	5.81929i	−0.332001	+	0.663170i
$78$	−0.514689	−	3.57974i	−0.0582770	−	0.405326i
$79$	−0.459240	−	0.209728i	−0.0516685	−	0.0235962i	0.389413	−	0.921063i	$-0.372678\pi$
$79$	−0.459240	−	0.209728i	−0.0516685	−	0.0235962i	−0.441082	+	0.897467i	$0.645405\pi$
$80$	2.30386	−	0.676476i	0.257580	−	0.0756323i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	7.46921	+	3.41107i	0.824836	+	0.376690i
$83$	−0.0423414	−	0.294491i	−0.00464757	−	0.0323246i	0.987366	−	0.158458i	$-0.0506523\pi$
$83$	−0.0423414	−	0.294491i	−0.00464757	−	0.0323246i	−0.992013	+	0.126134i	$0.959743\pi$
$84$	−1.18440	+	2.36584i	−0.129229	+	0.258134i
$85$	6.64842	+	14.5580i	0.721123	+	1.57904i
$86$	−3.03996	−	4.73027i	−0.327807	−	0.510078i
$87$	4.91965	+	0.707339i	0.527442	+	0.0758347i
$88$	1.32982	−	2.06925i	0.141760	−	0.220582i
$89$	−2.92830	+	3.37944i	−0.310399	+	0.358220i	−0.889418	−	0.457094i	$-0.848890\pi$
$89$	−2.92830	+	3.37944i	−0.310399	+	0.358220i	0.579019	+	0.815314i	$0.303436\pi$
$90$	−2.30386	−	0.676476i	−0.242849	−	0.0713068i
$91$	3.66126	+	8.84032i	0.383804	+	0.926718i
$92$	−4.31385	+	2.09539i	−0.449750	+	0.218459i
$93$	2.96439			0.307393
$94$	−1.25452	+	4.27251i	−0.129394	+	0.440676i
$95$	2.21500	−	2.55624i	0.227254	−	0.262265i
$96$	0.540641	−	0.841254i	0.0551789	−	0.0858601i
$97$	−1.66184	+	11.5584i	−0.168735	+	1.17357i	0.712770	+	0.701398i	$0.247440\pi$
$97$	−1.66184	+	11.5584i	−0.168735	+	1.17357i	−0.881504	+	0.472176i	$0.843469\pi$
$98$	1.48865	−	6.83988i	0.150376	−	0.690932i
$99$	−2.23744	+	1.02180i	−0.224871	+	0.102695i
$100$	−0.501239	−	0.578461i	−0.0501239	−	0.0578461i
$101$	−2.26081	+	0.325056i	−0.224959	+	0.0323443i	−0.253873	−	0.967238i	$-0.581704\pi$
$101$	−2.26081	+	0.325056i	−0.224959	+	0.0323443i	0.0289133	+	0.999582i	$0.490795\pi$
$102$	6.06299	+	2.76888i	0.600326	+	0.274160i
$103$	−6.13142	+	1.80035i	−0.604146	+	0.177393i	−0.569479	−	0.822006i	$-0.692855\pi$
$103$	−6.13142	+	1.80035i	−0.604146	+	0.177393i	−0.0346668	+	0.999399i	$0.511037\pi$
$104$	−1.01890	−	3.47006i	−0.0999114	−	0.340267i
$105$	6.34873	+	0.227065i	0.619572	+	0.0221593i
$106$	−8.66181	+	1.24538i	−0.841309	+	0.120962i
$107$	8.63552	−	7.48272i	0.834827	−	0.723382i	−0.128501	−	0.991709i	$-0.541016\pi$
$107$	8.63552	−	7.48272i	0.834827	−	0.723382i	0.963328	+	0.268328i	$0.0864710\pi$
$108$	−0.909632	+	0.415415i	−0.0875294	+	0.0399733i
$109$	−2.29125	−	3.56525i	−0.219462	−	0.341489i	0.714013	−	0.700133i	$-0.246876\pi$
$109$	−2.29125	−	3.56525i	−0.219462	−	0.341489i	−0.933475	+	0.358643i	$0.883239\pi$
$110$	−5.84598	−	0.840525i	−0.557392	−	0.0801409i
$111$	2.62332	+	1.68590i	0.248994	+	0.160019i
$112$	−0.835654	+	2.51032i	−0.0789618	+	0.237203i
$113$	0.0553548	−	0.188521i	0.00520735	−	0.0177346i	−0.956848	−	0.290588i	$-0.906149\pi$
$113$	0.0553548	−	0.188521i	0.00520735	−	0.0177346i	0.962056	+	0.272853i	$0.0879673\pi$
$114$		−	1.40867i		−	0.131934i
$115$	8.87955	+	7.33200i	0.828022	+	0.683712i
$116$	4.97024			0.461475
$117$	−1.01890	+	3.47006i	−0.0941974	+	0.320807i
$118$	−4.15750	−	3.60249i	−0.382729	−	0.331636i
$119$	−17.3544	−	3.13199i	−1.59088	−	0.287109i
$120$	−2.37669	−	0.341716i	−0.216961	−	0.0311943i
$121$	4.16403	−	2.67606i	0.378548	−	0.243278i
$122$	5.31353	+	11.6350i	0.481065	+	1.05338i
$123$	−5.37722	−	6.20564i	−0.484848	−	0.559544i
$124$	2.93421	−	0.421876i	0.263500	−	0.0378856i
$125$	4.22385	−	9.24894i	0.377793	−	0.827250i
$126$	2.06018	−	1.66002i	0.183535	−	0.147887i
$127$	10.3171	−	3.02939i	0.915499	−	0.268815i	0.210145	−	0.977670i	$-0.432606\pi$
$127$	10.3171	−	3.02939i	0.915499	−	0.268815i	0.705354	+	0.708855i	$0.250788\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.800219	+	5.56565i	0.0704554	+	0.490028i
$130$	−6.56278	+	5.68668i	−0.575594	+	0.498755i
$131$	13.7001	−	6.25662i	1.19698	−	0.546644i	0.285658	−	0.958332i	$-0.407788\pi$
$131$	13.7001	−	6.25662i	1.19698	−	0.546644i	0.911325	+	0.411688i	$0.135061\pi$
$132$	−2.06925	+	1.32982i	−0.180105	+	0.115746i
$133$	0.921526	+	3.61126i	0.0799065	+	0.313136i
$134$	−1.64559	+	2.56058i	−0.142157	+	0.221201i
$135$	1.81465	+	1.57240i	0.156180	+	0.135331i
$136$	6.39533	+	1.87784i	0.548395	+	0.161023i
$137$		−	3.81617i		−	0.326038i	−0.986623	−	0.163019i	$-0.947877\pi$
$137$		−	3.81617i		−	0.326038i	0.986623	−	0.163019i	$-0.0521231\pi$
$138$	4.79448	−	0.113993i	0.408133	−	0.00970376i
$139$		−	17.9397i		−	1.52162i	−0.648972	−	0.760812i	$-0.724801\pi$
$139$		−	17.9397i		−	1.52162i	0.648972	−	0.760812i	$-0.275199\pi$
$140$	6.31642	−	0.678764i	0.533835	−	0.0573660i
$141$	2.91602	−	3.36527i	0.245573	−	0.283407i
$142$	−13.0477	−	8.38526i	−1.09494	−	0.703675i
$143$	−1.26599	+	8.80515i	−0.105867	+	0.736323i
$144$	−0.841254	+	0.540641i	−0.0701045	+	0.0450534i
$145$	−4.95764	−	10.8557i	−0.411709	−	0.901517i
$146$	10.1749	−	8.81661i	0.842082	−	0.729668i
$147$	−4.19551	+	5.60337i	−0.346040	+	0.462158i
$148$	2.83655	+	1.29541i	0.233163	+	0.106482i
$149$	3.48036	+	11.8530i	0.285123	+	0.971038i	0.970147	+	0.242518i	$0.0779733\pi$
$149$	3.48036	+	11.8530i	0.285123	+	0.971038i	−0.685024	+	0.728520i	$0.740208\pi$
$150$	0.215642	+	0.734408i	0.0176071	+	0.0599642i
$151$	2.96277	−	6.48756i	0.241107	−	0.527950i	−0.749934	−	0.661513i	$-0.769915\pi$
$151$	2.96277	−	6.48756i	0.241107	−	0.527950i	0.991040	+	0.133563i	$0.0426419\pi$
$152$	−0.200474	−	1.39433i	−0.0162606	−	0.113095i
$153$	−4.36486	−	5.03732i	−0.352878	−	0.407243i
$154$	4.43477	−	4.76280i	0.357364	−	0.383797i
$155$	−3.84821	−	5.98793i	−0.309096	−	0.480962i
$156$	−0.514689	+	3.57974i	−0.0412081	+	0.286609i
$157$	3.91836	+	2.51818i	0.312719	+	0.200973i	0.687580	−	0.726109i	$-0.258673\pi$
$157$	3.91836	+	2.51818i	0.312719	+	0.200973i	−0.374861	+	0.927081i	$0.622309\pi$
$158$	0.381550	+	0.330615i	0.0303545	+	0.0263023i
$159$	8.39641	+	2.46541i	0.665879	+	0.195520i
$160$	−2.40113			−0.189826
$161$	−12.2165	+	3.42870i	−0.962799	+	0.270219i
$162$	1.00000			0.0785674
$163$	−13.6295	−	4.00198i	−1.06754	−	0.313459i	−0.299658	−	0.954047i	$-0.596873\pi$
$163$	−13.6295	−	4.00198i	−1.06754	−	0.313459i	−0.767885	+	0.640588i	$0.778691\pi$
$164$	−6.20564	−	5.37722i	−0.484579	−	0.419890i
$165$	4.96852	+	3.19308i	0.386799	+	0.248581i
$166$	−0.0423414	+	0.294491i	−0.00328633	+	0.0228569i
$167$	−6.68111	−	10.3960i	−0.517000	−	0.804468i	0.480361	−	0.877071i	$-0.340506\pi$
$167$	−6.68111	−	10.3960i	−0.517000	−	0.804468i	−0.997361	+	0.0726033i	$0.976869\pi$
$168$	1.80296	−	1.93632i	0.139101	−	0.149390i
$169$	0.0520260	+	0.0600412i	0.00400200	+	0.00461855i
$170$	−2.27765	−	15.8414i	−0.174688	−	1.21498i
$171$	−0.585182	+	1.28137i	−0.0447500	+	0.0979888i
$172$	1.58415	+	5.39511i	0.120790	+	0.411373i
$173$	−6.74082	−	22.9571i	−0.512495	−	1.74540i	−0.655025	−	0.755607i	$-0.727342\pi$
$173$	−6.74082	−	22.9571i	−0.512495	−	1.74540i	0.142531	−	0.989790i	$-0.454476\pi$
$174$	−4.52109	−	2.06471i	−0.342743	−	0.156525i
$175$	−1.03326	−	1.74166i	−0.0781068	−	0.131657i
$176$	−1.85893	+	1.61077i	−0.140122	+	0.121417i
$177$	2.28526	+	5.00403i	0.171771	+	0.376126i
$178$	3.76178	−	2.41755i	0.281958	−	0.181203i
$179$	−3.08460	+	21.4538i	−0.230554	+	1.60354i	0.465167	+	0.885223i	$0.345994\pi$
$179$	−3.08460	+	21.4538i	−0.230554	+	1.60354i	−0.695721	+	0.718312i	$0.744915\pi$
$180$	2.01996	+	1.29815i	0.150559	+	0.0967582i
$181$	−3.96422	+	4.57495i	−0.294658	+	0.340054i	−0.883704	−	0.468046i	$-0.844958\pi$
$181$	−3.96422	+	4.57495i	−0.294658	+	0.340054i	0.589046	+	0.808100i	$0.299504\pi$
$182$	−1.02235	−	9.51372i	−0.0757814	−	0.705204i
$183$		−	12.7909i		−	0.945531i
$184$	4.72945	−	0.795158i	0.348660	−	0.0586198i
$185$		−	7.48754i		−	0.550495i
$186$	−2.84431	−	0.835164i	−0.208555	−	0.0612372i
$187$	−12.3904	−	10.7363i	−0.906074	−	0.785117i
$188$	2.40741	−	3.74601i	0.175579	−	0.273206i
$189$	−2.56360	+	0.654182i	−0.186474	+	0.0475848i
$190$	−2.84545	+	1.82866i	−0.206431	+	0.132665i
$191$	−12.8357	+	5.86189i	−0.928762	+	0.424151i	−0.821583	−	0.570089i	$-0.806909\pi$
$191$	−12.8357	+	5.86189i	−0.928762	+	0.424151i	−0.107178	+	0.994240i	$0.534182\pi$
$192$	−0.755750	+	0.654861i	−0.0545415	+	0.0472605i
$193$	−2.11111	−	14.6831i	−0.151961	−	1.05691i	−0.912928	−	0.408121i	$-0.866184\pi$
$193$	−2.11111	−	14.6831i	−0.151961	−	1.05691i	0.760967	−	0.648791i	$-0.224725\pi$
$194$	4.85089	−	10.6220i	0.348274	−	0.762613i
$195$	8.33205	−	2.44651i	0.596670	−	0.175198i
$196$	−3.35536	+	6.14342i	−0.239669	+	0.438815i
$197$	−11.3539	+	24.8616i	−0.808932	+	1.77131i	−0.197001	+	0.980403i	$0.563120\pi$
$197$	−11.3539	+	24.8616i	−0.808932	+	1.77131i	−0.611931	+	0.790911i	$0.709607\pi$
$198$	2.43468	−	0.350054i	0.173025	−	0.0248773i
$199$	3.22577	+	3.72274i	0.228669	+	0.263898i	0.858476	−	0.512853i	$-0.171412\pi$
$199$	3.22577	+	3.72274i	0.228669	+	0.263898i	−0.629807	+	0.776752i	$0.716866\pi$
$200$	0.317964	+	0.696244i	0.0224835	+	0.0492319i
$201$	2.56058	−	1.64559i	0.180610	−	0.116071i
$202$	2.26081	+	0.325056i	0.159070	+	0.0228708i
$203$	12.9410	+	2.33548i	0.908277	+	0.163918i
$204$	−5.03732	−	4.36486i	−0.352683	−	0.305601i
$205$	−5.55471	+	18.9176i	−0.387958	+	1.32126i
$206$	6.39027			0.445231
$207$	−4.40856	−	1.88801i	−0.306416	−	0.131225i
$208$			3.61655i			0.250763i
$209$	−0.976183	+	3.32457i	−0.0675240	+	0.229965i
$210$	−6.02759	−	2.00651i	−0.415943	−	0.138462i
$211$	−19.2657	−	12.3813i	−1.32630	−	0.852364i	−0.330494	−	0.943808i	$-0.607215\pi$
$211$	−19.2657	−	12.3813i	−1.32630	−	0.852364i	−0.995810	+	0.0914441i	$0.970852\pi$
$212$	8.66181	+	1.24538i	0.594896	+	0.0855331i
$213$	8.38526	+	13.0477i	0.574548	+	0.894015i
$214$	−10.3938	+	4.74671i	−0.710509	+	0.324478i
$215$	10.2036	−	8.84144i	0.695877	−	0.602981i
$216$	0.989821	−	0.142315i	0.0673488	−	0.00968330i
$217$	7.83802	+	0.280331i	0.532079	+	0.0190301i
$218$	1.19399	+	4.06635i	0.0808671	+	0.275408i
$219$	−12.9180	+	3.79306i	−0.872916	+	0.256311i
$220$	5.37237	+	2.45348i	0.362205	+	0.165414i
$221$	−23.8601	+	3.43057i	−1.60501	+	0.230765i
$222$	−2.04208	−	2.35669i	−0.137056	−	0.158171i
$223$	7.09139	−	3.23853i	0.474875	−	0.216868i	−0.163576	−	0.986531i	$-0.552303\pi$
$223$	7.09139	−	3.23853i	0.474875	−	0.216868i	0.638451	+	0.769663i	$0.279576\pi$
$224$	1.50904	−	2.17320i	0.100827	−	0.145203i
$225$	0.108930	−	0.757622i	0.00726198	−	0.0505082i
$226$	−0.106225	+	0.165290i	−0.00706599	+	0.0109949i
$227$	−6.79740	+	7.84461i	−0.451159	+	0.520665i	−0.935075	−	0.354449i	$-0.884668\pi$
$227$	−6.79740	+	7.84461i	−0.451159	+	0.520665i	0.483916	+	0.875114i	$0.339214\pi$
$228$	−0.396868	+	1.35161i	−0.0262832	+	0.0895124i
$229$	−0.560336			−0.0370280			−0.0185140	−	0.999829i	$-0.505894\pi$
$229$	−0.560336			−0.0370280			−0.0185140	+	0.999829i	$0.505894\pi$
$230$	−6.45420	−	9.53666i	−0.425577	−	0.628828i
$231$	−6.01255	+	2.49012i	−0.395597	+	0.163838i
$232$	−4.76891	−	1.40028i	−0.313094	−	0.0919328i
$233$	0.955398	−	1.10259i	0.0625902	−	0.0722330i	−0.723591	−	0.690229i	$-0.757510\pi$
$233$	0.955398	−	1.10259i	0.0625902	−	0.0722330i	0.786181	+	0.617996i	$0.212055\pi$
$234$	1.95526	−	3.04244i	0.127819	−	0.198890i
$235$	−10.5831	−	1.52162i	−0.690367	−	0.0992597i
$236$	2.97415	+	4.62787i	0.193601	+	0.301249i
$237$	−0.209728	−	0.459240i	−0.0136233	−	0.0298308i
$238$	15.7691	+	7.89443i	1.02216	+	0.511720i
$239$	−3.99347	−	27.7752i	−0.258316	−	1.79663i	−0.544823	−	0.838551i	$-0.683403\pi$
$239$	−3.99347	−	27.7752i	−0.258316	−	1.79663i	0.286506	−	0.958078i	$-0.407506\pi$
$240$	2.18414	+	0.997464i	0.140986	+	0.0643860i
$241$	17.5219	−	5.14489i	1.12868	−	0.331412i	0.336494	−	0.941686i	$-0.390759\pi$
$241$	17.5219	−	5.14489i	1.12868	−	0.331412i	0.792191	+	0.610274i	$0.208941\pi$
$242$	−4.74929	+	1.39452i	−0.305296	+	0.0896430i
$243$	−0.909632	−	0.415415i	−0.0583529	−	0.0266489i
$244$	−1.82034	−	12.6607i	−0.116535	−	0.810519i
$245$	16.7649	+	1.20075i	1.07107	+	0.0767131i
$246$	3.41107	+	7.46921i	0.217482	+	0.476219i
$247$	2.75431	+	4.28579i	0.175252	+	0.272698i
$248$	−2.93421	−	0.421876i	−0.186323	−	0.0267892i
$249$	0.160851	−	0.250289i	0.0101935	−	0.0158614i
$250$	−6.65848	+	7.68430i	−0.421119	+	0.485998i
$251$	−24.7585	−	7.26974i	−1.56274	−	0.458862i	−0.617863	−	0.786286i	$-0.712001\pi$
$251$	−24.7585	−	7.26974i	−1.56274	−	0.458862i	−0.944878	+	0.327424i	$0.893820\pi$
$252$	−2.44441	+	1.01236i	−0.153983	+	0.0637728i
$253$	−11.3943	−	3.05345i	−0.716357	−	0.191969i
$254$	−10.7527			−0.674685
$255$	−4.50893	+	15.3560i	−0.282360	+	0.961630i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	0.161494	−	0.251289i	0.0100737	−	0.0156750i	−0.836180	−	0.548455i	$-0.815216\pi$
$257$	0.161494	−	0.251289i	0.0100737	−	0.0156750i	0.846254	+	0.532780i	$0.178853\pi$
$258$	0.800219	−	5.56565i	0.0498195	−	0.346502i
$259$	6.77679	+	4.70571i	0.421089	+	0.292399i
$260$	7.89906	−	3.60738i	0.489879	−	0.223720i
$261$	3.25481	+	3.75626i	0.201468	+	0.232506i
$262$	−14.9078	+	2.14342i	−0.921009	+	0.132421i
$263$	−23.6803	−	10.8144i	−1.46019	−	0.666847i	−0.482309	−	0.876001i	$-0.660202\pi$
$263$	−23.6803	−	10.8144i	−1.46019	−	0.666847i	−0.977883	+	0.209154i	$0.932929\pi$
$264$	2.36008	−	0.692982i	0.145253	−	0.0426501i
$265$	−5.91976	−	20.1608i	−0.363648	−	1.23847i
$266$	0.133212	−	3.72461i	0.00816778	−	0.228370i
$267$	−4.42613	+	0.636381i	−0.270875	+	0.0389459i
$268$	2.30033	−	1.99325i	0.140515	−	0.121757i
$269$	10.5770	−	4.83034i	0.644889	−	0.294511i	−0.0659953	−	0.997820i	$-0.521022\pi$
$269$	10.5770	−	4.83034i	0.644889	−	0.294511i	0.710884	+	0.703309i	$0.248295\pi$
$270$	−1.29815	−	2.01996i	−0.0790027	−	0.122931i
$271$	−21.2607	−	3.05682i	−1.29149	−	0.185689i	−0.537888	−	0.843016i	$-0.680778\pi$
$271$	−21.2607	−	3.05682i	−1.29149	−	0.185689i	−0.753605	+	0.657328i	$0.771687\pi$
$272$	−5.60723	−	3.60355i	−0.339988	−	0.218497i
$273$	−3.02218	+	9.07869i	−0.182911	+	0.549467i
$274$	−1.07514	+	3.66159i	−0.0649516	+	0.221205i
$275$		−	1.88270i		−	0.113531i
$276$	−4.63238	−	1.24138i	−0.278837	−	0.0747226i
$277$	9.02419			0.542211			0.271106	−	0.962550i	$-0.412611\pi$
$277$	9.02419			0.542211			0.271106	+	0.962550i	$0.412611\pi$
$278$	−5.05419	+	17.2130i	−0.303130	+	1.03237i
$279$	2.24033	+	1.94126i	0.134125	+	0.116220i
$280$	−6.25179	−	1.12827i	−0.373616	−	0.0674272i
$281$	−20.9356	−	3.01009i	−1.24892	−	0.179567i	−0.514038	−	0.857767i	$-0.671851\pi$
$281$	−20.9356	−	3.01009i	−1.24892	−	0.179567i	−0.734877	+	0.678200i	$0.762760\pi$
$282$	−3.74601	+	2.40741i	−0.223071	+	0.143359i
$283$	−0.997361	−	2.18392i	−0.0592870	−	0.129820i	0.877670	−	0.479266i	$-0.159097\pi$
$283$	−0.997361	−	2.18392i	−0.0592870	−	0.129820i	−0.936957	+	0.349446i	$0.886370\pi$
$284$	10.1568	+	11.7216i	0.602695	+	0.695547i
$285$	3.34797	−	0.481365i	0.198316	−	0.0285136i
$286$	3.69540	−	8.09181i	0.218514	−	0.478479i
$287$	−13.6309	−	16.9166i	−0.804604	−	0.998556i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	11.3934	−	24.9481i	0.670200	−	1.46753i
$290$	1.69841	+	11.8127i	0.0997341	+	0.693666i
$291$	−8.82506	+	7.64696i	−0.517334	+	0.448272i
$292$	−12.2467	+	5.59287i	−0.716683	+	0.327298i
$293$	13.2389	−	8.50811i	0.773424	−	0.497049i	−0.0934214	−	0.995627i	$-0.529780\pi$
$293$	13.2389	−	8.50811i	0.773424	−	0.497049i	0.866845	+	0.498577i	$0.166144\pi$
$294$	5.60421	−	4.19438i	0.326844	−	0.244621i
$295$	7.14132	−	11.1121i	0.415784	−	0.646972i
$296$	−2.35669	−	2.04208i	−0.136980	−	0.118694i
$297$	−2.36008	−	0.692982i	−0.136946	−	0.0402109i
$298$		−	12.3534i		−	0.715615i
$299$	−14.3640	+	9.72124i	−0.830692	+	0.562194i
$300$		−	0.765413i		−	0.0441911i
$301$	1.58951	+	14.7916i	0.0916176	+	0.852572i
$302$	−4.67051	+	5.39006i	−0.268758	+	0.310163i
$303$	−1.92147	−	1.23486i	−0.110386	−	0.0709407i
$304$	−0.200474	+	1.39433i	−0.0114980	+	0.0799703i
$305$	−25.8371	+	16.6045i	−1.47943	+	0.950770i
$306$	2.76888	+	6.06299i	0.158286	+	0.346598i
$307$	−6.78321	+	5.87768i	−0.387138	+	0.335457i	−0.826585	−	0.562811i	$-0.809720\pi$
$307$	−6.78321	+	5.87768i	−0.387138	+	0.335457i	0.439447	+	0.898268i	$0.355174\pi$
$308$	−5.59697	+	3.32045i	−0.318917	+	0.189200i
$309$	−5.81279	−	2.65461i	−0.330678	−	0.151016i
$310$	2.00534	+	6.82955i	0.113895	+	0.387892i
$311$	3.10003	+	10.5577i	0.175786	+	0.598673i	0.999499	+	0.0316651i	$0.0100810\pi$
$311$	3.10003	+	10.5577i	0.175786	+	0.598673i	−0.823712	+	0.567008i	$0.808101\pi$
$312$	1.50237	−	3.28973i	0.0850549	−	0.186244i
$313$	−0.772281	−	5.37133i	−0.0436519	−	0.303606i	−0.999938	−	0.0111716i	$-0.996444\pi$
$313$	−0.772281	−	5.37133i	−0.0436519	−	0.303606i	0.956286	−	0.292434i	$-0.0944652\pi$
$314$	−3.05019	−	3.52011i	−0.172132	−	0.198651i
$315$	4.64935	+	4.32914i	0.261961	+	0.243919i
$316$	−0.272950	−	0.424718i	−0.0153546	−	0.0238923i
$317$	0.740816	−	5.15249i	0.0416084	−	0.289393i	−0.958384	−	0.285482i	$-0.907846\pi$
$317$	0.740816	−	5.15249i	0.0416084	−	0.289393i	0.999992	−	0.00391028i	$-0.00124468\pi$
$318$	−7.36171	−	4.73108i	−0.412824	−	0.265306i
$319$	9.23932	+	8.00592i	0.517303	+	0.448245i
$320$	2.30386	+	0.676476i	0.128790	+	0.0378161i
$321$	11.4264			0.637761
$322$	12.6877	+	0.151990i	0.707056	+	0.00847006i
$323$	−9.38923			−0.522431
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−2.09203	−	1.81276i	−0.116045	−	0.100554i
$326$	11.9499	+	7.67974i	0.661844	+	0.425341i
$327$	0.603134	−	4.19489i	0.0333534	−	0.231978i
$328$	4.43933	+	6.90774i	0.245121	+	0.381416i
$329$	8.02838	−	8.62221i	0.442619	−	0.475358i
$330$	−3.86767	−	4.46353i	−0.212908	−	0.245709i
$331$	−4.64984	−	32.3404i	−0.255579	−	1.77759i	−0.563440	−	0.826157i	$-0.690522\pi$
$331$	−4.64984	−	32.3404i	−0.255579	−	1.77759i	0.307861	−	0.951431i	$-0.400387\pi$
$332$	0.123594	−	0.270633i	0.00678310	−	0.0148529i
$333$	0.878539	+	2.99203i	0.0481437	+	0.163962i
$334$	3.48158	+	11.8572i	0.190504	+	0.648796i
$335$	−6.64803	−	3.03605i	−0.363221	−	0.165877i
$336$	−2.27545	+	1.34993i	−0.124136	+	0.0736449i
$337$	−16.9206	+	14.6618i	−0.921724	+	0.798678i	−0.979871	−	0.199630i	$-0.936026\pi$
$337$	−16.9206	+	14.6618i	−0.921724	+	0.798678i	0.0581474	+	0.998308i	$0.481481\pi$
$338$	−0.0330030	−	0.0722665i	−0.00179513	−	0.00393078i
$339$	0.165290	−	0.106225i	0.00897730	−	0.00576936i
$340$	−2.27765	+	15.8414i	−0.123523	+	0.859120i
$341$	6.13404	+	3.94211i	0.332177	+	0.213477i
$342$	0.922482	−	1.06460i	0.0498821	−	0.0575670i
$343$	−11.6231	+	14.4189i	−0.627587	+	0.778547i
$344$		−	5.62288i		−	0.303165i
$345$	1.90928	+	11.3560i	0.102792	+	0.611388i
$346$			23.9263i			1.28629i
$347$	22.1621	+	6.50738i	1.18972	+	0.349334i	0.815915	−	0.578171i	$-0.196233\pi$
$347$	22.1621	+	6.50738i	1.18972	+	0.349334i	0.373809	+	0.927506i	$0.378052\pi$
$348$	3.75626	+	3.25481i	0.201356	+	0.174476i
$349$	−10.6148	+	16.5170i	−0.568200	+	0.884136i	−0.999840	−	0.0179101i	$-0.994299\pi$
$349$	−10.6148	+	16.5170i	−0.568200	+	0.884136i	0.431640	+	0.902046i	$0.357935\pi$
$350$	0.500720	+	1.96221i	0.0267646	+	0.104885i
$351$	−3.04244	+	1.95526i	−0.162393	+	0.104364i
$352$	2.23744	−	1.02180i	0.119256	−	0.0544623i
$353$	1.20343	−	1.04278i	0.0640522	−	0.0555015i	−0.622246	−	0.782821i	$-0.713780\pi$
$353$	1.20343	−	1.04278i	0.0640522	−	0.0555015i	0.686299	+	0.727320i	$0.259234\pi$
$354$	−0.782897	−	5.44517i	−0.0416105	−	0.289407i
$355$	15.4705	−	33.8757i	0.821090	−	1.79794i
$356$	−4.29051	+	1.25981i	−0.227397	+	0.0667696i
$357$	−11.0646	−	13.7317i	−0.585600	−	0.726761i
$358$	9.00389	−	19.7158i	0.475871	−	1.04201i
$359$	4.29578	−	0.617639i	0.226722	−	0.0325978i	−0.0280172	−	0.999607i	$-0.508919\pi$
$359$	4.29578	−	0.617639i	0.226722	−	0.0325978i	0.254740	+	0.967010i	$0.418010\pi$
$360$	−1.57240	−	1.81465i	−0.0828730	−	0.0956405i
$361$	−7.06856	−	15.4780i	−0.372029	−	0.814631i
$362$	5.09256	−	3.27279i	0.267659	−	0.172014i
$363$	4.89941	+	0.704429i	0.257152	+	0.0369729i
$364$	−1.69939	+	9.41638i	−0.0890723	+	0.493552i
$365$	24.4313	+	21.1698i	1.27879	+	1.10808i
$366$	−3.60361	+	12.2728i	−0.188364	+	0.641509i
$367$	3.15505			0.164692			0.0823462	−	0.996604i	$-0.473759\pi$
$367$	3.15505			0.164692			0.0823462	+	0.996604i	$0.473759\pi$
$368$	−4.76190	−	0.569492i	−0.248231	−	0.0296868i
$369$		−	8.21124i		−	0.427460i
$370$	−2.10949	+	7.18425i	−0.109667	+	0.373491i
$371$	21.9675	+	7.31270i	1.14049	+	0.379657i
$372$	2.49380	+	1.60267i	0.129298	+	0.0830945i
$373$	22.1710	+	3.18771i	1.14797	+	0.165054i	0.689930	−	0.723876i	$-0.257641\pi$
$373$	22.1710	+	3.18771i	1.14797	+	0.165054i	0.458043	+	0.888930i	$0.348550\pi$
$374$	8.86370	+	13.7922i	0.458331	+	0.713177i
$375$	9.24894	−	4.22385i	0.477613	−	0.218119i
$376$	−3.36527	+	2.91602i	−0.173550	+	0.150382i
$377$	17.7922	−	2.55813i	0.916343	−	0.131750i
$378$	2.64406	+	0.0945662i	0.135996	+	0.00486396i
$379$	−0.880012	−	2.99705i	−0.0452032	−	0.153948i	0.933799	−	0.357798i	$-0.116473\pi$
$379$	−0.880012	−	2.99705i	−0.0452032	−	0.153948i	−0.979002	+	0.203851i	$0.934654\pi$
$380$	3.24538	−	0.952930i	0.166485	−	0.0488843i
$381$	9.78101	+	4.46684i	0.501096	+	0.228843i
$382$	13.9673	−	2.00819i	0.714629	−	0.102748i
$383$	10.6892	+	12.3359i	0.546191	+	0.630338i	0.959991	−	0.280030i	$-0.0903444\pi$
$383$	10.6892	+	12.3359i	0.546191	+	0.630338i	−0.413801	+	0.910368i	$0.635799\pi$
$384$	0.909632	−	0.415415i	0.0464195	−	0.0211991i
$385$	12.8351	+	8.91254i	0.654138	+	0.454225i
$386$	−2.11111	+	14.6831i	−0.107453	+	0.747349i
$387$	−3.03996	+	4.73027i	−0.154530	+	0.240453i
$388$	−7.64696	+	8.82506i	−0.388215	+	0.448024i
$389$	−6.19999	+	21.1152i	−0.314352	+	1.07058i	0.639121	+	0.769106i	$0.279298\pi$
$389$	−6.19999	+	21.1152i	−0.314352	+	1.07058i	−0.953473	+	0.301478i	$0.902520\pi$
$390$	−8.68380			−0.439721
$391$	−0.759803	−	31.9567i	−0.0384249	−	1.61612i
$392$	4.95025	−	4.94925i	0.250025	−	0.249975i
$393$	14.4511	+	4.24321i	0.728959	+	0.214042i
$394$	17.8983	−	20.6557i	0.901704	−	1.04062i
$395$	−0.655387	+	1.01980i	−0.0329761	+	0.0513118i
$396$	−2.43468	−	0.350054i	−0.122347	−	0.0175909i
$397$	−1.13341	−	1.76362i	−0.0568843	−	0.0885137i	0.811646	−	0.584149i	$-0.198572\pi$
$397$	−1.13341	−	1.76362i	−0.0568843	−	0.0885137i	−0.868531	+	0.495635i	$0.834935\pi$
$398$	−2.04629	−	4.48075i	−0.102571	−	0.224600i
$399$	−1.66843	+	3.33268i	−0.0835260	+	0.166843i
$400$	−0.108930	−	0.757622i	−0.00544648	−	0.0378811i
$401$	3.74378	+	1.70973i	0.186956	+	0.0853798i	0.506694	−	0.862126i	$-0.330868\pi$
$401$	3.74378	+	1.70973i	0.186956	+	0.0853798i	−0.319738	+	0.947506i	$0.603595\pi$
$402$	−2.92048	+	0.857529i	−0.145660	+	0.0427697i
$403$	10.2866	−	3.02041i	0.512411	−	0.150458i
$404$	−2.07766	−	0.948833i	−0.103367	−	0.0472062i
$405$	0.341716	+	2.37669i	0.0169800	+	0.118099i
$406$	−11.7588	−	5.88676i	−0.583578	−	0.292155i
$407$	3.18634	+	6.97710i	0.157941	+	0.345842i
$408$	3.60355	+	5.60723i	0.178402	+	0.277599i
$409$	−6.44905	−	0.927233i	−0.318885	−	0.0458487i	−0.0189861	−	0.999820i	$-0.506044\pi$
$409$	−6.44905	−	0.927233i	−0.318885	−	0.0458487i	−0.299899	+	0.953971i	$0.596953\pi$
$410$	10.6594	−	16.5864i	0.526431	−	0.819142i
$411$	2.49906	−	2.88407i	0.123270	−	0.142261i
$412$	−6.13142	−	1.80035i	−0.302073	−	0.0886967i
$413$	5.56917	+	13.4471i	0.274041	+	0.661687i
$414$	3.69807	+	3.05356i	0.181750	+	0.150074i
$415$	−0.714381			−0.0350676
$416$	1.01890	−	3.47006i	0.0499557	−	0.170133i
$417$	11.7480	−	13.5579i	0.575302	−	0.663934i
$418$	1.87328	−	2.91488i	0.0916251	−	0.142572i
$419$	3.13665	−	21.8159i	0.153236	−	1.06578i	−0.757514	−	0.652818i	$-0.773586\pi$
$419$	3.13665	−	21.8159i	0.153236	−	1.06578i	0.910750	−	0.412958i	$-0.135504\pi$
$420$	5.21813	+	3.62340i	0.254619	+	0.176804i
$421$	−0.222993	+	0.101837i	−0.0108680	+	0.00496325i	−0.420842	−	0.907134i	$-0.638265\pi$
$421$	−0.222993	+	0.101837i	−0.0108680	+	0.00496325i	0.409974	+	0.912097i	$0.365538\pi$
$422$	14.9971	+	17.3075i	0.730046	+	0.842518i
$423$	4.40756	−	0.633712i	0.214303	−	0.0308121i
$424$	−7.96008	−	3.63525i	−0.386576	−	0.176543i
$425$	4.89507	−	1.43732i	0.237446	−	0.0697204i
$426$	−4.36963	−	14.8816i	−0.211709	−	0.721015i
$427$	1.20959	−	33.8199i	0.0585360	−	1.63666i
$428$	11.3101	−	1.62615i	0.546695	−	0.0786029i
$429$	−6.72292	+	5.82544i	−0.324585	+	0.281255i
$430$	−12.2812	+	5.60862i	−0.592250	+	0.270472i
$431$	−11.5985	−	18.0476i	−0.558678	−	0.869321i	0.440923	−	0.897545i	$-0.354651\pi$
$431$	−11.5985	−	18.0476i	−0.558678	−	0.869321i	−0.999602	+	0.0282243i	$0.991015\pi$
$432$	−0.989821	−	0.142315i	−0.0476228	−	0.00684713i
$433$	−6.16783	−	3.96382i	−0.296407	−	0.190489i	0.383982	−	0.923341i	$-0.374553\pi$
$433$	−6.16783	−	3.96382i	−0.296407	−	0.190489i	−0.680389	+	0.732852i	$0.738189\pi$
$434$	−7.44154	−	2.47720i	−0.357206	−	0.118909i
$435$	3.36225	−	11.4508i	0.161207	−	0.549022i
$436$		−	4.23802i		−	0.202965i
$437$	−6.07679	+	2.95171i	−0.290692	+	0.141199i
$438$	13.4633			0.643303
$439$	8.17284	−	27.8341i	0.390068	−	1.32845i	−0.497376	−	0.867535i	$-0.665703\pi$
$439$	8.17284	−	27.8341i	0.390068	−	1.32845i	0.887444	−	0.460915i	$-0.152479\pi$
$440$	−4.46353	−	3.86767i	−0.212790	−	0.184384i
$441$	−6.84018	+	1.48727i	−0.325723	+	0.0708223i
$442$	23.8601	+	3.43057i	1.13491	+	0.163175i
$443$	20.7664	−	13.3458i	0.986641	−	0.634076i	0.0553945	−	0.998465i	$-0.482358\pi$
$443$	20.7664	−	13.3458i	0.986641	−	0.634076i	0.931247	+	0.364389i	$0.118722\pi$
$444$	1.29541	+	2.83655i	0.0614773	+	0.134617i
$445$	7.03123	+	8.11447i	0.333312	+	0.384663i
$446$	−7.71654	+	1.10947i	−0.365389	+	0.0525350i
$447$	−5.13180	+	11.2371i	−0.242726	+	0.531495i
$448$	−2.06018	+	1.66002i	−0.0973341	+	0.0784287i
$449$	22.3002	−	6.54792i	1.05241	−	0.309016i	0.290619	−	0.956839i	$-0.406139\pi$
$449$	22.3002	−	6.54792i	1.05241	−	0.309016i	0.761791	+	0.647823i	$0.224320\pi$
$450$	−0.317964	+	0.696244i	−0.0149890	+	0.0328213i
$451$	−2.87438	−	19.9918i	−0.135349	−	0.941375i
$452$	0.148490	−	0.128667i	0.00698437	−	0.00605199i
$453$	6.48756	−	2.96277i	0.304812	−	0.139203i
$454$	8.73214	−	5.61180i	0.409820	−	0.263375i
$455$	22.2618	−	5.68079i	1.04365	−	0.266320i
$456$	0.761584	−	1.18505i	0.0356644	−	0.0554949i
$457$	13.1550	+	11.3989i	0.615364	+	0.533216i	0.905815	−	0.423674i	$-0.139260\pi$
$457$	13.1550	+	11.3989i	0.615364	+	0.533216i	−0.290451	+	0.956890i	$0.593805\pi$
$458$	0.537638	+	0.157865i	0.0251222	+	0.00737654i
$459$		−	6.66532i		−	0.311111i
$460$	3.50597	+	10.9687i	0.163467	+	0.511419i
$461$			32.4450i			1.51111i	0.655084	+	0.755556i	$0.272633\pi$
$461$			32.4450i			1.51111i	−0.655084	+	0.755556i	$0.727367\pi$
$462$	6.47055	−	0.695326i	0.301037	−	0.0323495i
$463$	−16.4059	+	18.9334i	−0.762446	+	0.879910i	−0.995712	−	0.0925030i	$-0.970513\pi$
$463$	−16.4059	+	18.9334i	−0.762446	+	0.879910i	0.233266	+	0.972413i	$0.425059\pi$
$464$	4.18123	+	2.68711i	0.194109	+	0.124746i
$465$	1.01298	−	7.04542i	0.0469757	−	0.326724i
$466$	−1.22733	+	0.788759i	−0.0568551	+	0.0365386i
$467$	14.5759	+	31.9168i	0.674493	+	1.47693i	0.868375	+	0.495909i	$0.165165\pi$
$467$	14.5759	+	31.9168i	0.674493	+	1.47693i	−0.193881	+	0.981025i	$0.562108\pi$
$468$	−2.73321	+	2.36834i	−0.126343	+	0.109476i
$469$	6.92595	−	4.10889i	0.319811	−	0.189731i
$470$	9.72574	+	4.44160i	0.448615	+	0.204876i
$471$	1.31224	+	4.46909i	0.0604650	+	0.205925i
$472$	−1.54986	−	5.27832i	−0.0713379	−	0.242955i
$473$	−5.74548	+	12.5808i	−0.264177	+	0.578467i
$474$	0.0718495	+	0.499725i	0.00330016	+	0.0229531i
$475$	−0.706080	−	0.814859i	−0.0323972	−	0.0373883i
$476$	−12.9062	−	12.0173i	−0.591555	−	0.550813i
$477$	4.73108	+	7.36171i	0.216621	+	0.337070i
$478$	−3.99347	+	27.7752i	−0.182657	+	1.27041i
$479$	−1.47546	−	0.948219i	−0.0674154	−	0.0433252i	0.506499	−	0.862241i	$-0.330939\pi$
$479$	−1.47546	−	0.948219i	−0.0674154	−	0.0433252i	−0.573914	+	0.818915i	$0.694576\pi$
$480$	−1.81465	−	1.57240i	−0.0828271	−	0.0717701i
$481$	10.8208	+	3.17728i	0.493387	+	0.144872i
$482$	−18.2616			−0.831794
$483$	−11.4780	−	5.40890i	−0.522266	−	0.246114i
$484$	4.94979			0.224991
$485$	26.9027	+	7.89936i	1.22159	+	0.358691i
$486$	0.755750	+	0.654861i	0.0342815	+	0.0297051i
$487$	35.9674	+	23.1148i	1.62984	+	1.04743i	0.949134	+	0.314873i	$0.101962\pi$
$487$	35.9674	+	23.1148i	1.62984	+	1.04743i	0.680703	+	0.732560i	$0.261675\pi$
$488$	−1.82034	+	12.6607i	−0.0824027	+	0.573123i
$489$	−7.67974	−	11.9499i	−0.347290	−	0.540393i
$490$	−15.7476	−	5.87534i	−0.711402	−	0.265421i
$491$	2.57962	+	2.97704i	0.116417	+	0.134352i	0.810966	−	0.585093i	$-0.198942\pi$
$491$	2.57962	+	2.97704i	0.116417	+	0.134352i	−0.694550	+	0.719445i	$0.744396\pi$
$492$	−1.16858	−	8.12767i	−0.0526837	−	0.366423i
$493$	−13.7620	+	30.1345i	−0.619808	+	1.35719i
$494$	−1.43529	−	4.88816i	−0.0645769	−	0.219929i
$495$	1.66394	+	5.66686i	0.0747885	+	0.254706i
$496$	2.69650	+	1.23145i	0.121076	+	0.0552938i
$497$	20.9373	+	35.2919i	0.939164	+	1.58306i
$498$	−0.224850	+	0.194834i	−0.0100758	+	0.00873070i
$499$	−4.83554	−	10.5884i	−0.216469	−	0.474000i	0.769981	−	0.638067i	$-0.220266\pi$
$499$	−4.83554	−	10.5884i	−0.216469	−	0.474000i	−0.986449	+	0.164067i	$0.947539\pi$
$500$	8.55368	−	5.49712i	0.382532	−	0.245839i
$501$	1.75869	−	12.2320i	0.0785726	−	0.546485i
$502$	21.7075	+	13.9505i	0.968851	+	0.622643i
$503$	−3.36926	+	3.88834i	−0.150228	+	0.173372i	−0.825876	−	0.563852i	$-0.809319\pi$
$503$	−3.36926	+	3.88834i	−0.150228	+	0.173372i	0.675648	+	0.737225i	$0.263864\pi$
$504$	2.63061	−	0.282685i	0.117177	−	0.0125918i
$505$			5.48432i			0.244049i
$506$	10.0725	+	6.13993i	0.447779	+	0.272953i
$507$			0.0794458i			0.00352831i
$508$	10.3171	+	3.02939i	0.457749	+	0.134407i
$509$	−16.1130	−	13.9620i	−0.714196	−	0.618855i	0.220048	−	0.975489i	$-0.429379\pi$
$509$	−16.1130	−	13.9620i	−0.714196	−	0.618855i	−0.934244	+	0.356634i	$0.883924\pi$
$510$	8.65257	−	13.4637i	0.383142	−	0.596181i
$511$	−34.5146	+	8.80748i	−1.52684	+	0.389620i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−1.28137	+	0.585182i	−0.0565739	+	0.0258364i
$514$	−0.225748	+	0.195612i	−0.00995733	+	0.00862807i
$515$	2.18366	+	15.1877i	0.0962234	+	0.669248i
$516$	−2.33583	+	5.11475i	−0.102829	+	0.225164i
$517$	10.5092	−	3.08577i	0.462193	−	0.135712i
$518$	−5.17653	−	6.42434i	−0.227443	−	0.282269i
$519$	9.93934	−	21.7641i	0.436289	−	0.955339i
$520$	−8.59541	+	1.23583i	−0.376934	+	0.0541949i
$521$	−2.48517	−	2.86804i	−0.108877	−	0.125651i	0.698695	−	0.715420i	$-0.253764\pi$
$521$	−2.48517	−	2.86804i	−0.108877	−	0.125651i	−0.807572	+	0.589768i	$0.799219\pi$
$522$	−2.06471	−	4.52109i	−0.0903700	−	0.197883i
$523$	−8.77507	+	5.63939i	−0.383707	+	0.246594i	−0.718247	−	0.695788i	$-0.755055\pi$
$523$	−8.77507	+	5.63939i	−0.383707	+	0.246594i	0.334540	+	0.942381i	$0.391419\pi$
$524$	14.9078	+	2.14342i	0.651252	+	0.0936359i
$525$	0.359662	−	1.99290i	0.0156969	−	0.0869772i
$526$	19.6743	+	17.0479i	0.857842	+	0.743324i
$527$	−5.56664	+	18.9582i	−0.242487	+	0.825833i
$528$	−2.45972			−0.107045
$529$	−10.5380	−	20.4438i	−0.458176	−	0.888862i
$530$			21.0120i			0.912702i
$531$	−1.54986	+	5.27832i	−0.0672580	+	0.229060i
$532$	−1.17716	+	3.53620i	−0.0510363	+	0.153314i
$533$	−24.9822	−	16.0551i	−1.08210	−	0.695423i
$534$	4.42613	+	0.636381i	0.191537	+	0.0275389i
$535$	−14.8332	−	23.0809i	−0.641295	−	0.997874i
$536$	−2.76871	+	1.26443i	−0.119590	+	0.0546150i
$537$	−16.3805	+	14.1937i	−0.706869	+	0.612505i
$538$	−11.5094	+	1.65480i	−0.496205	+	0.0713435i
$539$	−16.1330	+	6.01546i	−0.694898	+	0.259104i
$540$	0.676476	+	2.30386i	0.0291109	+	0.0991426i
$541$	−24.4289	+	7.17298i	−1.05028	+	0.308391i	−0.760931	−	0.648833i	$-0.775257\pi$
$541$	−24.4289	+	7.17298i	−1.05028	+	0.308391i	−0.289351	+	0.957223i	$0.593439\pi$
$542$	19.5382	+	8.92282i	0.839240	+	0.383268i
$543$	−5.99192	+	0.861507i	−0.257138	+	0.0369708i
$544$	4.36486	+	5.03732i	0.187142	+	0.215973i
$545$	−9.25645	+	4.22728i	−0.396503	+	0.181077i
$546$	5.45753	−	7.85949i	0.233561	−	0.336355i
$547$	−3.77858	+	26.2806i	−0.161560	+	1.12368i	0.734133	+	0.679005i	$0.237589\pi$
$547$	−3.77858	+	26.2806i	−0.161560	+	1.12368i	−0.895694	+	0.444671i	$0.853320\pi$
$548$	2.06318	−	3.21037i	0.0881347	−	0.137140i
$549$	8.37626	−	9.66672i	0.357490	−	0.412566i
$550$	−0.530418	+	1.80644i	−0.0226171	+	0.0770267i
$551$	7.00142			0.298270
$552$	4.09500	+	2.49619i	0.174295	+	0.106245i
$553$	−0.511105	−	1.23409i	−0.0217344	−	0.0524789i
$554$	−8.65865	−	2.54241i	−0.367871	−	0.108017i
$555$	4.90330	−	5.65871i	0.208133	−	0.240199i
$556$	9.69893	−	15.0918i	0.411326	−	0.640036i
$557$	−22.9139	−	3.29453i	−0.970895	−	0.139594i	−0.361423	−	0.932402i	$-0.617709\pi$
$557$	−22.9139	−	3.29453i	−0.970895	−	0.139594i	−0.609471	+	0.792808i	$0.708618\pi$
$558$	−1.60267	−	2.49380i	−0.0678464	−	0.105571i
$559$	8.44764	+	18.4978i	0.357297	+	0.782372i
$560$	5.68068	+	2.84390i	0.240052	+	0.120177i
$561$	−2.33322	−	16.2279i	−0.0985088	−	0.685144i
$562$	19.2396	+	8.78641i	0.811571	+	0.370632i
$563$	4.06533	−	1.19369i	0.171333	−	0.0503080i	−0.194941	−	0.980815i	$-0.562451\pi$
$563$	4.06533	−	1.19369i	0.171333	−	0.0503080i	0.366274	+	0.930507i	$0.380633\pi$
$564$	4.27251	−	1.25452i	0.179905	−	0.0528250i
$565$	−0.429141	−	0.195982i	−0.0180541	−	0.00824502i
$566$	0.341681	+	2.37644i	0.0143619	+	0.0998893i
$567$	−2.36584	−	1.18440i	−0.0993559	−	0.0497402i
$568$	−6.44302	−	14.1083i	−0.270343	−	0.591969i
$569$	−6.11422	−	9.51392i	−0.256322	−	0.398844i	0.689114	−	0.724653i	$-0.258000\pi$
$569$	−6.11422	−	9.51392i	−0.256322	−	0.398844i	−0.945436	+	0.325809i	$0.894363\pi$
$570$	−3.34797	−	0.481365i	−0.140231	−	0.0201622i
$571$	12.0242	−	18.7101i	0.503199	−	0.782993i	−0.493006	−	0.870026i	$-0.664102\pi$
$571$	12.0242	−	18.7101i	0.503199	−	0.782993i	0.996205	+	0.0870327i	$0.0277385\pi$
$572$	−5.82544	+	6.72292i	−0.243574	+	0.281099i
$573$	−13.5393	−	3.97550i	−0.565613	−	0.166079i
$574$	8.31275	+	20.0716i	0.346968	+	0.837773i
$575$	2.71628	−	2.46912i	0.113277	−	0.102969i
$576$	−1.00000			−0.0416667
$577$	−7.52646	+	25.6328i	−0.313330	+	1.06711i	0.640798	+	0.767709i	$0.278603\pi$
$577$	−7.52646	+	25.6328i	−0.313330	+	1.06711i	−0.954129	+	0.299396i	$0.903215\pi$
$578$	−17.9606	+	20.7276i	−0.747061	+	0.862154i
$579$	8.01991	−	12.4792i	0.333296	−	0.518619i
$580$	1.69841	−	11.8127i	0.0705226	−	0.490496i
$581$	0.448969	−	0.646568i	0.0186264	−	0.0268242i
$582$	10.6220	−	4.85089i	0.440295	−	0.201076i
$583$	14.0957	+	16.2673i	0.583783	+	0.673722i
$584$	13.3263	−	1.91603i	0.551446	−	0.0792860i
$585$	7.89906	+	3.60738i	0.326586	+	0.149147i
$586$	−15.0996	+	4.43365i	−0.623760	+	0.183152i
$587$	4.97897	+	16.9568i	0.205504	+	0.699882i	0.996154	+	0.0876144i	$0.0279243\pi$
$587$	4.97897	+	16.9568i	0.205504	+	0.699882i	−0.790651	+	0.612268i	$0.790257\pi$
$588$	−6.55889	+	2.44559i	−0.270484	+	0.100854i
$589$	4.13333	−	0.594284i	0.170311	−	0.0244870i
$590$	−9.98269	+	8.65005i	−0.410981	+	0.356117i
$591$	−24.8616	+	11.3539i	−1.02267	+	0.467037i
$592$	1.68590	+	2.62332i	0.0692903	+	0.107818i
$593$	10.4697	+	1.50532i	0.429941	+	0.0618161i	0.353888	−	0.935288i	$-0.384859\pi$
$593$	10.4697	+	1.50532i	0.429941	+	0.0618161i	0.0760524	+	0.997104i	$0.475768\pi$
$594$	2.06925	+	1.32982i	0.0849022	+	0.0545633i
$595$	−13.3740	+	40.1758i	−0.548282	+	1.64705i
$596$	−3.48036	+	11.8530i	−0.142561	+	0.485519i
$597$			4.92589i			0.201603i
$598$	16.5210	−	5.28066i	0.675592	−	0.215942i
$599$	8.53087			0.348562			0.174281	−	0.984696i	$-0.444240\pi$
$599$	8.53087			0.348562			0.174281	+	0.984696i	$0.444240\pi$
$600$	−0.215642	+	0.734408i	−0.00880354	+	0.0299821i
$601$	−28.9879	−	25.1181i	−1.18244	−	1.02459i	−0.999137	−	0.0415336i	$-0.986776\pi$
$601$	−28.9879	−	25.1181i	−1.18244	−	1.02459i	−0.183303	−	0.983056i	$-0.558679\pi$
$602$	2.64215	−	14.6402i	0.107686	−	0.596691i
$603$	3.01279	+	0.433174i	0.122690	+	0.0176402i
$604$	5.99988	−	3.85589i	0.244132	−	0.156894i
$605$	−4.93724	−	10.8111i	−0.200727	−	0.439532i
$606$	1.49574	+	1.72618i	0.0607604	+	0.0701212i
$607$	45.4487	−	6.53454i	1.84471	−	0.265229i	0.870710	−	0.491796i	$-0.163660\pi$
$607$	45.4487	−	6.53454i	1.84471	−	0.265229i	0.973995	+	0.226568i	$0.0727505\pi$
$608$	0.585182	−	1.28137i	0.0237323	−	0.0519664i
$609$	8.25071	+	10.2396i	0.334336	+	0.414928i
$610$	29.4685	−	8.65274i	1.19315	−	0.350339i
$611$	6.68988	−	14.6488i	0.270644	−	0.592627i
$612$	−0.948574	−	6.59748i	−0.0383438	−	0.266687i
$613$	3.45400	−	2.99291i	0.139506	−	0.120882i	−0.582313	−	0.812965i	$-0.697852\pi$
$613$	3.45400	−	2.99291i	0.139506	−	0.120882i	0.721818	+	0.692082i	$0.243307\pi$
$614$	8.16437	−	3.72854i	0.329487	−	0.150472i
$615$	−16.5864	+	10.6594i	−0.668827	+	0.429829i
$616$	6.30573	−	1.60910i	0.254065	−	0.0648326i
$617$	20.9525	−	32.6028i	0.843517	−	1.31254i	−0.104567	−	0.994518i	$-0.533346\pi$
$617$	20.9525	−	32.6028i	0.843517	−	1.31254i	0.948084	−	0.318020i	$-0.103018\pi$
$618$	4.82944	+	4.18473i	0.194269	+	0.168335i
$619$	−13.8717	−	4.07309i	−0.557549	−	0.163711i	−0.00919539	−	0.999958i	$-0.502927\pi$
$619$	−13.8717	−	4.07309i	−0.557549	−	0.163711i	−0.548354	+	0.836247i	$0.684745\pi$
$620$		−	7.11787i		−	0.285861i
$621$	−2.09539	−	4.31385i	−0.0840851	−	0.173109i
$622$		−	11.0034i		−	0.441197i
$623$	−11.7631	+	1.26407i	−0.471280	+	0.0506438i
$624$	−2.36834	+	2.73321i	−0.0948094	+	0.109416i
$625$	−23.7580	−	15.2683i	−0.950321	−	0.610734i
$626$	−0.772281	+	5.37133i	−0.0308666	+	0.214682i
$627$	−2.91488	+	1.87328i	−0.116409	+	0.0748116i
$628$	1.93491	+	4.23685i	0.0772112	+	0.169069i
$629$	−15.7081	+	13.6111i	−0.626322	+	0.542712i
$630$	−3.24136	−	5.46365i	−0.129139	−	0.217677i
$631$	−37.4023	−	17.0810i	−1.48896	−	0.679986i	−0.505787	−	0.862658i	$-0.668798\pi$
$631$	−37.4023	−	17.0810i	−1.48896	−	0.679986i	−0.983174	+	0.182673i	$0.941525\pi$
$632$	0.142236	+	0.484413i	0.00565786	+	0.0192689i
$633$	−6.45200	−	21.9735i	−0.256444	−	0.873368i
$634$	−2.16243	+	4.73506i	−0.0858811	+	0.188053i
$635$	−3.67437	−	25.5558i	−0.145813	−	1.01415i
$636$	5.73061	+	6.61347i	0.227233	+	0.262241i
$637$	−8.84938	+	23.7188i	−0.350625	+	0.939773i
$638$	−6.60954	−	10.2846i	−0.261674	−	0.407173i
$639$	−2.20728	+	15.3520i	−0.0873187	+	0.607315i
$640$	−2.01996	−	1.29815i	−0.0798458	−	0.0513138i
$641$	24.4216	+	21.1615i	0.964596	+	0.835827i	0.986471	−	0.163933i	$-0.0524182\pi$
$641$	24.4216	+	21.1615i	0.964596	+	0.835827i	−0.0218753	+	0.999761i	$0.506964\pi$
$642$	−10.9636	−	3.21920i	−0.432698	−	0.127052i
$643$	40.2738			1.58825			0.794123	−	0.607758i	$-0.207931\pi$
$643$	40.2738			1.58825			0.794123	+	0.607758i	$0.207931\pi$
$644$	−12.1309	−	3.72036i	−0.478025	−	0.146603i
$645$	13.5012			0.531611
$646$	9.00890	+	2.64525i	0.354451	+	0.104076i
$647$	23.5367	+	20.3946i	0.925322	+	0.801796i	0.980467	−	0.196682i	$-0.0630168\pi$
$647$	23.5367	+	20.3946i	0.925322	+	0.801796i	−0.0551454	+	0.998478i	$0.517562\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	−1.92570	+	13.3936i	−0.0755905	+	0.525743i
$650$	1.49658	+	2.32872i	0.0587006	+	0.0913399i
$651$	5.74000	+	5.34467i	0.224968	+	0.209474i
$652$	−9.30221	−	10.7353i	−0.364303	−	0.420428i
$653$	−2.80403	−	19.5025i	−0.109730	−	0.763190i	−0.968173	−	0.250281i	$-0.919477\pi$
$653$	−2.80403	−	19.5025i	−0.109730	−	0.763190i	0.858443	−	0.512909i	$-0.171432\pi$
$654$	−1.76054	+	3.85504i	−0.0688425	+	0.150744i
$655$	−10.1885	−	34.6988i	−0.398097	−	1.35580i
$656$	−2.31337	−	7.87863i	−0.0903221	−	0.307609i
$657$	−12.2467	−	5.59287i	−0.477789	−	0.218199i
$658$	−10.1323	+	6.01110i	−0.394999	+	0.234337i
$659$	−30.6043	+	26.5188i	−1.19217	+	1.03303i	−0.193524	+	0.981096i	$0.561992\pi$
$659$	−30.6043	+	26.5188i	−1.19217	+	1.03303i	−0.998651	+	0.0519294i	$0.983463\pi$
$660$	2.45348	+	5.37237i	0.0955016	+	0.209119i
$661$	−14.9433	+	9.60346i	−0.581226	+	0.373531i	−0.797970	−	0.602697i	$-0.794093\pi$
$661$	−14.9433	+	9.60346i	−0.581226	+	0.373531i	0.216744	+	0.976229i	$0.430456\pi$
$662$	−4.64984	+	32.3404i	−0.180721	+	1.25694i
$663$	−20.2788	−	13.0324i	−0.787564	−	0.506137i
$664$	−0.194834	+	0.224850i	−0.00756101	+	0.00872587i
$665$	8.89774	−	0.956153i	0.345040	−	0.0370780i
$666$		−	3.11835i		−	0.120833i
$667$	0.566574	+	23.8297i	0.0219378	+	0.922689i
$668$		−	12.3578i		−	0.478136i
$669$	7.48011	+	2.19636i	0.289198	+	0.0849161i
$670$	5.52338	+	4.78604i	0.213387	+	0.184901i
$671$	17.0096	−	26.4675i	0.656650	−	1.02177i
$672$	2.56360	−	0.654182i	0.0988930	−	0.0252356i
$673$	10.9866	−	7.06065i	0.423501	−	0.272168i	−0.311483	−	0.950252i	$-0.600826\pi$
$673$	10.9866	−	7.06065i	0.423501	−	0.272168i	0.734985	+	0.678084i	$0.237189\pi$
$674$	20.3659	−	9.30080i	0.784465	−	0.358253i
$675$	0.578461	−	0.501239i	0.0222650	−	0.0192927i
$676$	0.0113063	+	0.0786372i	0.000434859	+	0.00302451i
$677$	−14.3865	+	31.5020i	−0.552917	+	1.21072i	0.402489	+	0.915425i	$0.368145\pi$
$677$	−14.3865	+	31.5020i	−0.552917	+	1.21072i	−0.955406	+	0.295295i	$0.904582\pi$
$678$	−0.188521	+	0.0553548i	−0.00724012	+	0.00212589i
$679$	−24.0571	+	19.3845i	−0.923228	+	0.743907i
$680$	6.64842	−	14.5580i	0.254955	−	0.558274i
$681$	−10.2743	+	1.47722i	−0.393710	+	0.0566070i
$682$	−4.77495	−	5.51059i	−0.182842	−	0.211011i
$683$	7.59330	+	16.6270i	0.290550	+	0.636215i	0.997471	−	0.0710774i	$-0.0226437\pi$
$683$	7.59330	+	16.6270i	0.290550	+	0.636215i	−0.706921	+	0.707292i	$0.749916\pi$
$684$	−1.18505	+	0.761584i	−0.0453114	+	0.0291199i
$685$	−9.06985	−	1.30405i	−0.346541	−	0.0498251i
$686$	15.2145	−	10.5602i	0.580893	−	0.403191i
$687$	−0.423473	−	0.366942i	−0.0161565	−	0.0139997i
$688$	−1.58415	+	5.39511i	−0.0603951	+	0.205687i
$689$	31.6480			1.20569
$690$	1.36742	−	11.4339i	0.0520569	−	0.435282i
$691$			4.11954i			0.156715i	0.996925	+	0.0783574i	$0.0249675\pi$
$691$			4.11954i			0.156715i	−0.996925	+	0.0783574i	$0.975032\pi$
$692$	6.74082	−	22.9571i	0.256247	−	0.872699i
$693$	−6.17466	−	2.05547i	−0.234556	−	0.0780809i
$694$	−19.4310	−	12.4876i	−0.737592	−	0.474022i
$695$	−42.6370	−	6.13028i	−1.61731	−	0.232535i
$696$	−2.68711	−	4.18123i	−0.101855	−	0.158489i
$697$	49.7847	−	22.7359i	1.88573	−	0.861184i
$698$	14.8383	−	12.8574i	0.561636	−	0.486660i
$699$	1.44408	−	0.207628i	0.0546203	−	0.00785321i
$700$	0.0723822	−	2.02380i	0.00273579	−	0.0764924i
$701$	2.86883	+	9.77032i	0.108354	+	0.369020i	0.995762	−	0.0919644i	$-0.0293146\pi$
$701$	2.86883	+	9.77032i	0.108354	+	0.369020i	−0.887408	+	0.460984i	$0.847496\pi$
$702$	3.47006	−	1.01890i	0.130969	−	0.0384559i
$703$	3.99575	+	1.82480i	0.150703	+	0.0688236i
$704$	−2.43468	+	0.350054i	−0.0917605	+	0.0131932i
$705$	−7.00174	−	8.08044i	−0.263701	−	0.304327i
$706$	−1.44847	+	0.661493i	−0.0545138	+	0.0248956i
$707$	−4.96372	−	3.44674i	−0.186680	−	0.129628i
$708$	−0.782897	+	5.44517i	−0.0294231	+	0.204642i
$709$	−17.9631	+	27.9511i	−0.674618	+	1.04973i	0.320130	+	0.947373i	$0.396273\pi$
$709$	−17.9631	+	27.9511i	−0.674618	+	1.04973i	−0.994748	+	0.102352i	$0.967363\pi$
$710$	−24.3877	+	28.1450i	−0.915256	+	1.05626i
$711$	0.142236	−	0.484413i	0.00533428	−	0.0181669i
$712$	4.47164			0.167582
$713$	2.35716	+	14.0199i	0.0882762	+	0.525050i
$714$	6.74772	+	16.2928i	0.252527	+	0.609741i
$715$	20.4945	+	6.01772i	0.766450	+	0.225050i
$716$	−14.1937	+	16.3805i	−0.530445	+	0.612167i
$717$	15.1708	−	23.6063i	0.566565	−	0.881593i
$718$	−4.29578	−	0.617639i	−0.160317	−	0.0230501i
$719$	10.6523	+	16.5752i	0.397262	+	0.618152i	0.981050	−	0.193754i	$-0.0620665\pi$
$719$	10.6523	+	16.5752i	0.397262	+	0.618152i	−0.583788	+	0.811906i	$0.698430\pi$
$720$	0.997464	+	2.18414i	0.0371733	+	0.0813982i
$721$	−15.1183	−	7.56865i	−0.563036	−	0.281871i
$722$	2.42158	+	16.8425i	0.0901219	+	0.626811i
$723$	16.6114	+	7.58615i	0.617783	+	0.282132i
$724$	−5.80832	+	1.70548i	−0.215865	+	0.0633836i
$725$	−3.65019	+	1.07179i	−0.135564	+	0.0398053i
$726$	−4.50249	−	2.05622i	−0.167103	−	0.0763134i
$727$	−6.30408	−	43.8459i	−0.233806	−	1.62615i	−0.681396	−	0.731915i	$-0.738627\pi$
$727$	−6.30408	−	43.8459i	−0.233806	−	1.62615i	0.447591	−	0.894239i	$-0.352282\pi$
$728$	4.28345	−	8.55618i	0.158755	−	0.317113i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	−17.4774	−	27.1954i	−0.646868	−	1.00655i
$731$	−37.0968	−	5.33372i	−1.37208	−	0.197275i
$732$	6.91528	−	10.7604i	0.255596	−	0.397716i
$733$	5.38369	−	6.21311i	0.198851	−	0.229486i	−0.647563	−	0.762012i	$-0.724212\pi$
$733$	5.38369	−	6.21311i	0.198851	−	0.229486i	0.846414	+	0.532526i	$0.178757\pi$
$734$	−3.02725	−	0.888881i	−0.111738	−	0.0328092i
$735$	11.8838	+	11.8862i	0.438340	+	0.438428i
$736$	4.40856	+	1.88801i	0.162502	+	0.0695928i
$737$	7.48681			0.275780
$738$	−2.31337	+	7.87863i	−0.0851565	+	0.290016i
$739$	30.7215	−	35.4546i	1.13011	−	1.30422i	0.183071	−	0.983100i	$-0.441396\pi$
$739$	30.7215	−	35.4546i	1.13011	−	1.30422i	0.947039	−	0.321117i	$-0.104058\pi$
$740$	4.04807	−	6.29892i	0.148810	−	0.231553i
$741$	−0.725026	+	5.04267i	−0.0266345	+	0.185247i
$742$	−19.0174	−	13.2054i	−0.698151	−	0.484787i
$743$	−40.3843	+	18.4429i	−1.48156	+	0.676604i	−0.981862	−	0.189598i	$-0.939281\pi$
$743$	−40.3843	+	18.4429i	−1.48156	+	0.676604i	−0.499694	+	0.866202i	$0.666554\pi$
$744$	−1.94126	−	2.24033i	−0.0711701	−	0.0821346i
$745$	29.3602	−	4.22137i	1.07568	−	0.154659i
$746$	−20.3749	−	9.30489i	−0.745977	−	0.340676i
$747$	0.285467	−	0.0838208i	0.0104447	−	0.00306684i
$748$	−4.61895	−	15.7307i	−0.168886	−	0.575171i
$749$	30.2122	+	1.08055i	1.10393	+	0.0394826i
$750$	−10.0643	+	1.44703i	−0.367496	+	0.0528379i
$751$	15.9106	−	13.7866i	0.580587	−	0.503081i	−0.314330	−	0.949314i	$-0.601780\pi$
$751$	15.9106	−	13.7866i	0.580587	−	0.503081i	0.894917	+	0.446232i	$0.147235\pi$
$752$	4.05049	−	1.84980i	0.147706	−	0.0674551i
$753$	−13.9505	−	21.7075i	−0.508386	−	0.791064i
$754$	−17.7922	−	2.55813i	−0.647952	−	0.0931615i
$755$	−14.4065	−	9.25848i	−0.524305	−	0.336951i
$756$	−2.51032	−	0.835654i	−0.0912993	−	0.0303924i
$757$	−13.6941	+	46.6379i	−0.497721	+	1.69508i	0.200918	+	0.979608i	$0.435607\pi$
$757$	−13.6941	+	46.6379i	−0.497721	+	1.69508i	−0.698639	+	0.715474i	$0.746211\pi$
$758$			3.12357i			0.113453i
$759$	−6.61169	−	9.76936i	−0.239989	−	0.354605i
$760$	−3.38239			−0.122692
$761$	12.5617	−	42.7812i	0.455361	−	1.55082i	−0.337445	−	0.941345i	$-0.609563\pi$
$761$	12.5617	−	42.7812i	0.455361	−	1.55082i	0.792807	−	0.609473i	$-0.208619\pi$
$762$	−8.12635	−	7.04153i	−0.294387	−	0.255088i
$763$	1.99142	−	11.0345i	0.0720941	−	0.399476i
$764$	−13.9673	−	2.00819i	−0.505319	−	0.0726539i
$765$	−13.4637	+	8.65257i	−0.486780	+	0.312834i
$766$	−6.78074	−	14.8477i	−0.244998	−	0.536471i
$767$	13.0286	+	15.0358i	0.470436	+	0.542912i
$768$	−0.989821	+	0.142315i	−0.0357171	+	0.00513534i
$769$	−10.1720	+	22.2736i	−0.366811	+	0.803205i	0.632772	+	0.774338i	$0.281917\pi$
$769$	−10.1720	+	22.2736i	−0.366811	+	0.803205i	−0.999583	+	0.0288666i	$0.990810\pi$
$770$	−9.80425	−	12.1676i	−0.353321	−	0.438489i
$771$	0.286608	−	0.0841557i	0.0103219	−	0.00303079i
$772$	6.16230	−	13.4936i	0.221786	−	0.485643i
$773$	−5.94387	−	41.3405i	−0.213786	−	1.48691i	−0.760359	−	0.649503i	$-0.774977\pi$
$773$	−5.94387	−	41.3405i	−0.213786	−	1.48691i	0.546573	−	0.837411i	$-0.315932\pi$
$774$

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.341716 - 2.37669i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(1.93632 + 1.80296i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.341716 - 2.37669i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(1.93632 + 1.80296i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-0.997464 + 2.18414i) q^{10} +(0.692982 + 2.36008i) q^{11} +(0.281733 + 0.959493i) q^{12} +(3.28973 + 1.50237i) q^{13} +(-1.34993 - 2.27545i) q^{14} +(1.81465 - 1.57240i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-5.60723 + 3.60355i) q^{17} +(0.142315 - 0.989821i) q^{18} +(1.18505 + 0.761584i) q^{19} +(1.57240 - 1.81465i) q^{20} +(0.282685 + 2.63061i) q^{21} -2.45972i q^{22} +(-2.49619 + 4.09500i) q^{23} -1.00000i q^{24} +(-0.734408 - 0.215642i) q^{25} +(-2.73321 - 2.36834i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(0.654182 + 2.56360i) q^{28} +(4.18123 - 2.68711i) q^{29} +(-2.18414 + 0.997464i) q^{30} +(2.24033 - 1.94126i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-1.02180 + 2.23744i) q^{33} +(6.39533 - 1.87784i) q^{34} +(4.94674 - 3.98593i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(3.08660 - 0.443787i) q^{37} +(-0.922482 - 1.06460i) q^{38} +(1.50237 + 3.28973i) q^{39} +(-2.01996 + 1.29815i) q^{40} +(-8.12767 - 1.16858i) q^{41} +(0.469893 - 2.60369i) q^{42} +(4.24949 + 3.68220i) q^{43} +(-0.692982 + 2.36008i) q^{44} +2.40113 q^{45} +(3.54877 - 3.22586i) q^{46} -4.45289i q^{47} +(-0.281733 + 0.959493i) q^{48} +(0.498671 + 6.98222i) q^{49} +(0.643906 + 0.413814i) q^{50} +(-6.59748 - 0.948574i) q^{51} +(1.95526 + 3.04244i) q^{52} +(7.96008 - 3.63525i) q^{53} +(0.755750 - 0.654861i) q^{54} +(5.84598 - 0.840525i) q^{55} +(0.0945662 - 2.64406i) q^{56} +(0.396868 + 1.35161i) q^{57} +(-4.76891 + 1.40028i) q^{58} +(5.00403 + 2.28526i) q^{59} +(2.37669 - 0.341716i) q^{60} +(-8.37626 - 9.66672i) q^{61} +(-2.69650 + 1.23145i) q^{62} +(-1.50904 + 2.17320i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(4.69482 - 7.30528i) q^{65} +(1.61077 - 1.85893i) q^{66} +(0.857529 - 2.92048i) q^{67} -6.66532 q^{68} +(-4.56815 + 1.46014i) q^{69} +(-5.86933 + 2.43081i) q^{70} +(14.8816 + 4.36963i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-7.27883 + 11.3261i) q^{73} +(-3.08660 - 0.443787i) q^{74} +(-0.413814 - 0.643906i) q^{75} +(0.585182 + 1.28137i) q^{76} +(-2.91330 + 5.81929i) q^{77} +(-0.514689 - 3.57974i) q^{78} +(-0.459240 - 0.209728i) q^{79} +(2.30386 - 0.676476i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(7.46921 + 3.41107i) q^{82} +(-0.0423414 - 0.294491i) q^{83} +(-1.18440 + 2.36584i) q^{84} +(6.64842 + 14.5580i) q^{85} +(-3.03996 - 4.73027i) q^{86} +(4.91965 + 0.707339i) q^{87} +(1.32982 - 2.06925i) q^{88} +(-2.92830 + 3.37944i) q^{89} +(-2.30386 - 0.676476i) q^{90} +(3.66126 + 8.84032i) q^{91} +(-4.31385 + 2.09539i) q^{92} +2.96439 q^{93} +(-1.25452 + 4.27251i) q^{94} +(2.21500 - 2.55624i) q^{95} +(0.540641 - 0.841254i) q^{96} +(-1.66184 + 11.5584i) q^{97} +(1.48865 - 6.83988i) q^{98} +(-2.23744 + 1.02180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} + O(q^{10}) \)	\( 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} - 22q^{14} - 16q^{16} + 16q^{18} - 36q^{23} + 96q^{25} + 22q^{28} - 20q^{29} - 16q^{32} - 50q^{35} + 16q^{36} + 22q^{37} + 4q^{39} - 110q^{43} + 8q^{46} - 36q^{50} + 22q^{51} - 88q^{53} + 22q^{57} + 24q^{58} - 16q^{64} - 72q^{70} + 48q^{71} + 16q^{72} - 22q^{74} + 24q^{77} + 4q^{78} + 88q^{79} - 16q^{81} + 22q^{84} + 76q^{85} + 44q^{86} - 44q^{88} + 8q^{92} - 14q^{95} + 22q^{98} - 22q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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