LMFDB - Embedded newform 63.4.h.a.25.3

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.h (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	63.25
Dual form			63.4.h.a.58.3

$q$-expansion

$f(q)$	$=$	$q-4.87128 q^{2} +(-1.11598 - 5.07490i) q^{3} +15.7294 q^{4} +(3.10540 - 5.37871i) q^{5} +(5.43624 + 24.7213i) q^{6} +(17.8495 - 4.93906i) q^{7} -37.6522 q^{8} +(-24.5092 + 11.3269i) q^{9} +O(q^{10})$	\(q-4.87128 q^{2} +(-1.11598 - 5.07490i) q^{3} +15.7294 q^{4} +(3.10540 - 5.37871i) q^{5} +(5.43624 + 24.7213i) q^{6} +(17.8495 - 4.93906i) q^{7} -37.6522 q^{8} +(-24.5092 + 11.3269i) q^{9} +(-15.1273 + 26.2012i) q^{10} +(-27.7660 - 48.0921i) q^{11} +(-17.5536 - 79.8252i) q^{12} +(-6.74110 - 11.6759i) q^{13} +(-86.9501 + 24.0596i) q^{14} +(-30.7619 - 9.75707i) q^{15} +57.5792 q^{16} +(-43.1841 + 74.7970i) q^{17} +(119.391 - 55.1767i) q^{18} +(-42.1062 - 72.9300i) q^{19} +(48.8461 - 84.6039i) q^{20} +(-44.9849 - 85.0727i) q^{21} +(135.256 + 234.270i) q^{22} +(-5.26820 + 9.12479i) q^{23} +(42.0189 + 191.081i) q^{24} +(43.2130 + 74.8471i) q^{25} +(32.8378 + 56.8767i) q^{26} +(84.8347 + 111.741i) q^{27} +(280.763 - 77.6886i) q^{28} +(76.2157 - 132.009i) q^{29} +(149.850 + 47.5295i) q^{30} -254.065 q^{31} +20.7328 q^{32} +(-213.076 + 194.579i) q^{33} +(210.362 - 364.358i) q^{34} +(28.8641 - 111.345i) q^{35} +(-385.515 + 178.166i) q^{36} +(-172.072 - 298.038i) q^{37} +(205.111 + 355.263i) q^{38} +(-51.7312 + 47.2404i) q^{39} +(-116.925 + 202.520i) q^{40} +(-57.9241 - 100.328i) q^{41} +(219.134 + 414.413i) q^{42} +(46.7504 - 80.9741i) q^{43} +(-436.743 - 756.461i) q^{44} +(-15.1866 + 167.002i) q^{45} +(25.6629 - 44.4494i) q^{46} +319.841 q^{47} +(-64.2570 - 292.209i) q^{48} +(294.211 - 176.320i) q^{49} +(-210.503 - 364.602i) q^{50} +(427.780 + 135.683i) q^{51} +(-106.034 - 183.655i) q^{52} +(-136.535 + 236.486i) q^{53} +(-413.254 - 544.323i) q^{54} -344.898 q^{55} +(-672.074 + 185.967i) q^{56} +(-323.123 + 295.073i) q^{57} +(-371.268 + 643.055i) q^{58} +350.298 q^{59} +(-483.867 - 153.473i) q^{60} -291.131 q^{61} +1237.63 q^{62} +(-381.533 + 323.233i) q^{63} -561.629 q^{64} -83.7352 q^{65} +(1037.96 - 947.851i) q^{66} +833.381 q^{67} +(-679.260 + 1176.51i) q^{68} +(52.1865 + 16.5525i) q^{69} +(-140.605 + 542.394i) q^{70} +771.625 q^{71} +(922.825 - 426.484i) q^{72} +(-140.112 + 242.682i) q^{73} +(838.212 + 1451.83i) q^{74} +(331.617 - 302.829i) q^{75} +(-662.305 - 1147.15i) q^{76} +(-733.140 - 721.283i) q^{77} +(251.998 - 230.122i) q^{78} +345.885 q^{79} +(178.806 - 309.702i) q^{80} +(472.401 - 555.228i) q^{81} +(282.165 + 488.724i) q^{82} +(-62.9091 + 108.962i) q^{83} +(-707.586 - 1338.14i) q^{84} +(268.207 + 464.549i) q^{85} +(-227.735 + 394.448i) q^{86} +(-754.989 - 239.467i) q^{87} +(1045.45 + 1810.77i) q^{88} +(-163.146 - 282.578i) q^{89} +(73.9782 - 813.516i) q^{90} +(-177.994 - 175.115i) q^{91} +(-82.8657 + 143.528i) q^{92} +(283.531 + 1289.36i) q^{93} -1558.04 q^{94} -523.025 q^{95} +(-23.1373 - 105.217i) q^{96} +(124.352 - 215.384i) q^{97} +(-1433.19 + 858.904i) q^{98} +(1225.26 + 864.196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) $	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.87128			−1.72226			−0.861130	−	0.508385i	$-0.830243\pi$
$2$	−4.87128			−1.72226			−0.861130	+	0.508385i	$0.830243\pi$
$3$	−1.11598	−	5.07490i	−0.214770	−	0.976665i
$3$	−1.11598	−	5.07490i	−0.214770	−	0.976665i
$4$	15.7294			1.96618
$5$	3.10540	−	5.37871i	0.277755	−	0.481086i	−0.693071	−	0.720869i	$-0.743743\pi$
$5$	3.10540	−	5.37871i	0.277755	−	0.481086i	0.970827	+	0.239783i	$0.0770762\pi$
$6$	5.43624	+	24.7213i	0.369889	+	1.68207i
$7$	17.8495	−	4.93906i	0.963784	−	0.266684i
$7$	17.8495	−	4.93906i	0.963784	−	0.266684i
$8$	−37.6522			−1.66401
$9$	−24.5092	+	11.3269i	−0.907748	+	0.419516i
$10$	−15.1273	+	26.2012i	−0.478367	+	0.828555i
$11$	−27.7660	−	48.0921i	−0.761069	−	1.31821i	−0.942300	−	0.334770i	$-0.891341\pi$
$11$	−27.7660	−	48.0921i	−0.761069	−	1.31821i	0.181231	−	0.983441i	$-0.441992\pi$
$12$	−17.5536	−	79.8252i	−0.422275	−	1.92030i
$13$	−6.74110	−	11.6759i	−0.143819	−	0.249101i	0.785113	−	0.619353i	$-0.212605\pi$
$13$	−6.74110	−	11.6759i	−0.143819	−	0.249101i	−0.928932	+	0.370251i	$0.879272\pi$
$14$	−86.9501	+	24.0596i	−1.65989	+	0.459300i
$15$	−30.7619	−	9.75707i	−0.529513	−	0.167951i
$16$	57.5792			0.899675
$17$	−43.1841	+	74.7970i	−0.616099	+	1.06711i	0.374092	+	0.927392i	$0.377954\pi$
$17$	−43.1841	+	74.7970i	−0.616099	+	1.06711i	−0.990191	+	0.139723i	$0.955379\pi$
$18$	119.391	−	55.1767i	1.56338	−	0.722515i
$19$	−42.1062	−	72.9300i	−0.508411	−	0.880594i	−0.999953	−	0.00973986i	$-0.996900\pi$
$19$	−42.1062	−	72.9300i	−0.508411	−	0.880594i	0.491541	−	0.870854i	$-0.336434\pi$
$20$	48.8461	−	84.6039i	0.546116	−	0.945901i
$21$	−44.9849	−	85.0727i	−0.467453	−	0.884018i
$22$	135.256	+	234.270i	1.31076	+	2.27030i
$23$	−5.26820	+	9.12479i	−0.0477607	+	0.0827239i	−0.888917	−	0.458067i	$-0.848542\pi$
$23$	−5.26820	+	9.12479i	−0.0477607	+	0.0827239i	0.841157	+	0.540791i	$0.181875\pi$
$24$	42.0189	+	191.081i	0.357378	+	1.62518i
$25$	43.2130	+	74.8471i	0.345704	+	0.598777i
$26$	32.8378	+	56.8767i	0.247693	+	0.429017i
$27$	84.8347	+	111.741i	0.604683	+	0.796466i
$28$	280.763	−	77.6886i	1.89497	−	0.524349i
$29$	76.2157	−	132.009i	0.488031	−	0.845294i	−0.511874	−	0.859060i	$-0.671049\pi$
$29$	76.2157	−	132.009i	0.488031	−	0.845294i	0.999905	+	0.0137662i	$0.00438205\pi$
$30$	149.850	+	47.5295i	0.911959	+	0.289255i
$31$	−254.065			−1.47198			−0.735992	−	0.676990i	$-0.763284\pi$
$31$	−254.065			−1.47198			−0.735992	+	0.676990i	$0.763284\pi$
$32$	20.7328			0.114534
$33$	−213.076	+	194.579i	−1.12400	+	1.02642i
$34$	210.362	−	364.358i	1.06108	−	1.83785i
$35$	28.8641	−	111.345i	0.139398	−	0.537736i
$36$	−385.515	+	178.166i	−1.78479	+	0.824842i
$37$	−172.072	−	298.038i	−0.764554	−	1.32425i	−0.940482	−	0.339843i	$-0.889626\pi$
$37$	−172.072	−	298.038i	−0.764554	−	1.32425i	0.175928	−	0.984403i	$-0.443707\pi$
$38$	205.111	+	355.263i	0.875616	+	1.51661i
$39$	−51.7312	+	47.2404i	−0.212401	+	0.193962i
$40$	−116.925	+	202.520i	−0.462187	+	0.800531i
$41$	−57.9241	−	100.328i	−0.220640	−	0.382159i	0.734363	−	0.678757i	$-0.237481\pi$
$41$	−57.9241	−	100.328i	−0.220640	−	0.382159i	−0.955002	+	0.296598i	$0.904148\pi$
$42$	219.134	+	414.413i	0.805075	+	1.52251i
$43$	46.7504	−	80.9741i	0.165799	−	0.287173i	−0.771139	−	0.636666i	$-0.780313\pi$
$43$	46.7504	−	80.9741i	0.165799	−	0.287173i	0.936939	+	0.349493i	$0.113646\pi$
$44$	−436.743	−	756.461i	−1.49640	−	2.59184i
$45$	−15.1866	+	167.002i	−0.0503085	+	0.553228i
$46$	25.6629	−	44.4494i	0.0822562	−	0.142472i
$47$	319.841			0.992631			0.496316	−	0.868142i	$-0.334686\pi$
$47$	319.841			0.992631			0.496316	+	0.868142i	$0.334686\pi$
$48$	−64.2570	−	292.209i	−0.193223	−	0.878681i
$49$	294.211	−	176.320i	0.857759	−	0.514052i
$50$	−210.503	−	364.602i	−0.595392	−	1.03125i
$51$	427.780	+	135.683i	1.17453	+	0.372538i
$52$	−106.034	−	183.655i	−0.282773	−	0.489777i
$53$	−136.535	+	236.486i	−0.353859	+	0.612902i	−0.986922	−	0.161199i	$-0.948464\pi$
$53$	−136.535	+	236.486i	−0.353859	+	0.612902i	0.633063	+	0.774100i	$0.281797\pi$
$54$	−413.254	−	544.323i	−1.04142	−	1.37172i
$55$	−344.898			−0.845564
$56$	−672.074	+	185.967i	−1.60374	+	0.443765i
$57$	−323.123	+	295.073i	−0.750854	+	0.685672i
$58$	−371.268	+	643.055i	−0.840515	+	1.45582i
$59$	350.298			0.772964			0.386482	−	0.922297i	$-0.373690\pi$
$59$	350.298			0.772964			0.386482	+	0.922297i	$0.373690\pi$
$60$	−483.867	−	153.473i	−1.04112	−	0.330221i
$61$	−291.131			−0.611073			−0.305536	−	0.952180i	$-0.598836\pi$
$61$	−291.131			−0.611073			−0.305536	+	0.952180i	$0.598836\pi$
$62$	1237.63			2.53514
$63$	−381.533	+	323.233i	−0.762995	+	0.646405i
$64$	−561.629			−1.09693
$65$	−83.7352			−0.159786
$66$	1037.96	−	947.851i	1.93581	−	1.76776i
$67$	833.381			1.51961			0.759804	−	0.650153i	$-0.225295\pi$
$67$	833.381			1.51961			0.759804	+	0.650153i	$0.225295\pi$
$68$	−679.260	+	1176.51i	−1.21136	+	2.09814i
$69$	52.1865	+	16.5525i	0.0910510	+	0.0288796i
$70$	−140.605	+	542.394i	−0.240079	+	0.926121i
$71$	771.625			1.28979			0.644895	−	0.764271i	$-0.276901\pi$
$71$	771.625			1.28979			0.644895	+	0.764271i	$0.276901\pi$
$72$	922.825	−	426.484i	1.51050	−	0.698077i
$73$	−140.112	+	242.682i	−0.224643	+	0.389093i	−0.956212	−	0.292674i	$-0.905455\pi$
$73$	−140.112	+	242.682i	−0.224643	+	0.389093i	0.731569	+	0.681767i	$0.238788\pi$
$74$	838.212	+	1451.83i	1.31676	+	2.28069i
$75$	331.617	−	302.829i	0.510558	−	0.466236i
$76$	−662.305	−	1147.15i	−0.999627	−	1.73140i
$77$	−733.140	−	721.283i	−1.08505	−	1.06750i
$78$	251.998	−	230.122i	0.365809	−	0.334053i
$79$	345.885			0.492596			0.246298	−	0.969194i	$-0.420786\pi$
$79$	345.885			0.492596			0.246298	+	0.969194i	$0.420786\pi$
$80$	178.806	−	309.702i	0.249889	−	0.432821i
$81$	472.401	−	555.228i	0.648013	−	0.761629i
$82$	282.165	+	488.724i	0.379999	+	0.658177i
$83$	−62.9091	+	108.962i	−0.0831948	+	0.144098i	−0.904621	−	0.426218i	$-0.859846\pi$
$83$	−62.9091	+	108.962i	−0.0831948	+	0.144098i	0.821426	+	0.570315i	$0.193179\pi$
$84$	−707.586	−	1338.14i	−0.919095	−	1.73814i
$85$	268.207	+	464.549i	0.342249	+	0.592793i
$86$	−227.735	+	394.448i	−0.285550	+	0.494586i
$87$	−754.989	−	239.467i	−0.930383	−	0.295099i
$88$	1045.45	+	1810.77i	1.26642	+	2.19351i
$89$	−163.146	−	282.578i	−0.194309	−	0.336552i	0.752365	−	0.658746i	$-0.228913\pi$
$89$	−163.146	−	282.578i	−0.194309	−	0.336552i	−0.946674	+	0.322194i	$0.895580\pi$
$90$	73.9782	−	813.516i	0.0866443	−	0.952802i
$91$	−177.994	−	175.115i	−0.205042	−	0.201726i
$92$	−82.8657	+	143.528i	−0.0939059	+	0.162650i
$93$	283.531	+	1289.36i	0.316138	+	1.43764i
$94$	−1558.04			−1.70957
$95$	−523.025			−0.564856
$96$	−23.1373	−	105.217i	−0.0245984	−	0.111861i
$97$	124.352	−	215.384i	0.130165	−	0.225453i	−0.793575	−	0.608472i	$-0.791783\pi$
$97$	124.352	−	215.384i	0.130165	−	0.225453i	0.923740	+	0.383020i	$0.125116\pi$
$98$	−1433.19	+	858.904i	−1.47728	+	0.885331i
$99$	1225.26	+	864.196i	1.24387	+	0.877322i
$100$	679.715	+	1177.30i	0.679715	+	1.17730i
$101$	−978.371	−	1694.59i	−0.963877	−	1.66948i	−0.712603	−	0.701567i	$-0.752484\pi$
$101$	−978.371	−	1694.59i	−0.963877	−	1.66948i	−0.251274	−	0.967916i	$-0.580849\pi$
$102$	−2083.84	−	660.951i	−2.02285	−	0.641607i
$103$	947.900	−	1641.81i	0.906790	−	1.57061i	0.0882937	−	0.996094i	$-0.471859\pi$
$103$	947.900	−	1641.81i	0.906790	−	1.57061i	0.818496	−	0.574512i	$-0.194808\pi$
$104$	253.817	+	439.624i	0.239315	+	0.414507i
$105$	−597.277	−	22.2240i	−0.555126	−	0.0206556i
$106$	665.101	−	1151.99i	0.609437	−	1.05558i
$107$	−518.000	−	897.202i	−0.468009	−	0.810615i	0.531323	−	0.847169i	$-0.321695\pi$
$107$	−518.000	−	897.202i	−0.468009	−	0.810615i	−0.999332	+	0.0365546i	$0.988362\pi$
$108$	1334.40	+	1757.62i	1.18891	+	1.56599i
$109$	−21.1870	+	36.6969i	−0.0186178	+	0.0322470i	−0.875184	−	0.483790i	$-0.839260\pi$
$109$	−21.1870	+	36.6969i	−0.0186178	+	0.0322470i	0.856566	+	0.516037i	$0.172593\pi$
$110$	1680.10			1.45628
$111$	−1320.48	+	1205.85i	−1.12914	+	1.03112i
$112$	1027.76	−	284.387i	0.867092	−	0.239929i
$113$	1063.25	+	1841.60i	0.885149	+	1.53312i	0.845543	+	0.533908i	$0.179277\pi$
$113$	1063.25	+	1841.60i	0.885149	+	1.53312i	0.0396063	+	0.999215i	$0.487390\pi$
$114$	1574.02	−	1437.38i	1.29317	−	1.18091i
$115$	32.7197	+	56.6722i	0.0265315	+	0.0459540i
$116$	1198.83	−	2076.43i	0.959555	−	1.66200i
$117$	297.471	+	209.812i	0.235053	+	0.165787i
$118$	−1706.40			−1.33124
$119$	−401.388	+	1548.38i	−0.309203	+	1.19277i
$120$	1158.25	+	367.375i	0.881114	+	0.279472i
$121$	−876.401	+	1517.97i	−0.658453	+	1.14047i
$122$	1418.18			1.05243
$123$	−444.510	+	405.922i	−0.325855	+	0.297567i
$124$	−3996.30			−2.89418
$125$	1313.12			0.939595
$126$	1858.56	−	1574.56i	1.31407	−	1.11328i
$127$	1147.33			0.801646			0.400823	−	0.916156i	$-0.368724\pi$
$127$	1147.33			0.801646			0.400823	+	0.916156i	$0.368724\pi$
$128$	2569.99			1.77467
$129$	−463.108	−	146.889i	−0.316080	−	0.100254i
$130$	407.898			0.275192
$131$	−71.4716	+	123.792i	−0.0476679	+	0.0825633i	−0.888875	−	0.458150i	$-0.848512\pi$
$131$	−71.4716	+	123.792i	−0.0476679	+	0.0825633i	0.841207	+	0.540713i	$0.181846\pi$
$132$	−3351.57	+	3060.62i	−2.20997	+	2.01813i
$133$	−1111.78	−	1093.80i	−0.724839	−	0.713117i
$134$	−4059.64			−2.61716
$135$	864.468	−	109.300i	0.551123	−	0.0696820i
$136$	1625.97	−	2816.27i	1.02519	−	1.77569i
$137$	−682.289	−	1181.76i	−0.425488	−	0.736967i	0.570978	−	0.820966i	$-0.306564\pi$
$137$	−682.289	−	1181.76i	−0.425488	−	0.736967i	−0.996466	+	0.0839984i	$0.973231\pi$
$138$	−254.216	−	80.6321i	−0.156814	−	0.0497381i
$139$	549.346	+	951.496i	0.335215	+	0.580610i	0.983526	−	0.180766i	$-0.0578576\pi$
$139$	549.346	+	951.496i	0.335215	+	0.580610i	−0.648311	+	0.761376i	$0.724524\pi$
$140$	454.016	−	1751.39i	0.274081	−	1.05728i
$141$	−356.935	−	1623.16i	−0.213187	−	0.969468i
$142$	−3758.81			−2.22135
$143$	−374.346	+	648.387i	−0.218912	+	0.379167i
$144$	−1411.22	+	652.195i	−0.816678	+	0.377428i
$145$	−473.360	−	819.883i	−0.271106	−	0.469570i
$146$	682.527	−	1182.17i	0.386893	−	0.670118i
$147$	−1223.14	−	1296.32i	−0.686277	−	0.727340i
$148$	−2706.59	−	4687.96i	−1.50325	−	2.60370i
$149$	298.978	−	517.845i	0.164384	−	0.284722i	−0.772052	−	0.635559i	$-0.780770\pi$
$149$	298.978	−	517.845i	0.164384	−	0.284722i	0.936436	+	0.350837i	$0.114103\pi$
$150$	−1615.40	+	1475.17i	−0.879313	+	0.802979i
$151$	634.850	+	1099.59i	0.342141	+	0.592606i	0.984830	−	0.173521i	$-0.0555144\pi$
$151$	634.850	+	1099.59i	0.342141	+	0.592606i	−0.642689	+	0.766127i	$0.722181\pi$
$152$	1585.39	+	2745.97i	0.846000	+	1.46532i
$153$	211.187	−	2322.36i	0.111591	−	1.22713i
$154$	3571.33	+	3513.58i	1.86874	+	1.83852i
$155$	−788.975	+	1366.54i	−0.408851	+	0.708151i
$156$	−813.702	+	743.064i	−0.417617	+	0.381364i
$157$	2565.17			1.30397			0.651984	−	0.758233i	$-0.273937\pi$
$157$	2565.17			1.30397			0.651984	+	0.758233i	$0.273937\pi$
$158$	−1684.90			−0.848378
$159$	1352.51	+	428.989i	0.674598	+	0.213969i
$160$	64.3836	−	111.516i	0.0318123	−	0.0551006i
$161$	−48.9670	+	188.893i	−0.0239698	+	0.0924650i
$162$	−2301.20	+	2704.67i	−1.11605	+	1.31172i
$163$	1074.23	+	1860.62i	0.516196	+	0.894078i	0.999823	+	0.0188039i	$0.00598583\pi$
$163$	1074.23	+	1860.62i	0.516196	+	0.894078i	−0.483627	+	0.875274i	$0.660681\pi$
$164$	−911.113	−	1578.09i	−0.433817	−	0.751393i
$165$	384.898	+	1750.32i	0.181601	+	0.825832i
$166$	306.448	−	530.784i	0.143283	−	0.248174i
$167$	−700.461	−	1213.23i	−0.324570	−	0.562173i	0.656855	−	0.754017i	$-0.271886\pi$
$167$	−700.461	−	1213.23i	−0.324570	−	0.562173i	−0.981425	+	0.191845i	$0.938553\pi$
$168$	1693.78	+	3203.17i	0.777845	+	1.47101i
$169$	1007.62	−	1745.24i	0.458632	−	0.794374i
$170$	−1306.52	−	2262.95i	−0.589442	−	1.02094i
$171$	1858.06	+	1310.52i	0.830932	+	0.586071i
$172$	735.357	−	1273.68i	0.325991	−	0.564633i
$173$	−1337.28			−0.587698			−0.293849	−	0.955852i	$-0.594936\pi$
$173$	−1337.28			−0.587698			−0.293849	+	0.955852i	$0.594936\pi$
$174$	3677.77	+	1166.51i	1.60236	+	0.508237i
$175$	1141.01	+	1122.55i	0.492868	+	0.484898i
$176$	−1598.74	−	2769.11i	−0.684715	−	1.18596i
$177$	−390.924	−	1777.73i	−0.166009	−	0.754927i
$178$	794.732	+	1376.52i	0.334650	+	0.579630i
$179$	512.284	−	887.302i	0.213910	−	0.370503i	−0.739025	−	0.673678i	$-0.764713\pi$
$179$	512.284	−	887.302i	0.213910	−	0.370503i	0.952935	+	0.303175i	$0.0980467\pi$
$180$	−238.876	+	2626.85i	−0.0989154	+	1.08774i
$181$	−892.316			−0.366438			−0.183219	−	0.983072i	$-0.558652\pi$
$181$	−892.316			−0.366438			−0.183219	+	0.983072i	$0.558652\pi$
$182$	867.057	+	853.035i	0.353135	+	0.347424i
$183$	324.895	+	1477.46i	0.131240	+	0.596813i
$184$	198.359	−	343.568i	0.0794741	−	0.137653i
$185$	−2137.41			−0.849435
$186$	−1381.16	−	6280.82i	−0.544471	−	2.47598i
$187$	4796.19			1.87557
$188$	5030.92			1.95169
$189$	2066.16	+	1575.52i	0.795189	+	0.606362i
$190$	2547.81			0.972828
$191$	−798.792			−0.302610			−0.151305	−	0.988487i	$-0.548348\pi$
$191$	−798.792			−0.302610			−0.151305	+	0.988487i	$0.548348\pi$
$192$	626.764	+	2850.21i	0.235588	+	1.07133i
$193$	−697.628			−0.260188			−0.130094	−	0.991502i	$-0.541528\pi$
$193$	−697.628			−0.260188			−0.130094	+	0.991502i	$0.541528\pi$
$194$	−605.753	+	1049.20i	−0.224178	+	0.388288i
$195$	93.4464	+	424.947i	0.0343171	+	0.156057i
$196$	4627.77	−	2773.41i	1.68651	−	1.01072i
$197$	84.5351			0.0305730			0.0152865	−	0.999883i	$-0.495134\pi$
$197$	84.5351			0.0305730			0.0152865	+	0.999883i	$0.495134\pi$
$198$	−5968.58	−	4209.74i	−2.14227	−	1.51098i
$199$	−1291.09	+	2236.23i	−0.459914	+	0.796595i	−0.998956	−	0.0456844i	$-0.985453\pi$
$199$	−1291.09	+	2236.23i	−0.459914	+	0.796595i	0.539042	+	0.842279i	$0.318786\pi$
$200$	−1627.06	−	2818.16i	−0.575254	−	0.996369i
$201$	−930.033	−	4229.32i	−0.326365	−	1.48415i
$202$	4765.92	+	8254.82i	1.66005	+	2.87528i
$203$	708.411	−	2732.74i	0.244930	−	0.944831i
$204$	6728.72	+	2134.22i	2.30934	+	0.732476i
$205$	−719.510			−0.245135
$206$	−4617.49	+	7997.73i	−1.56173	+	2.70499i
$207$	25.7635	−	283.314i	0.00865066	−	0.0951288i
$208$	−388.147	−	672.290i	−0.129390	−	0.224110i
$209$	−2338.24	+	4049.95i	−0.773872	+	1.34039i
$210$	2909.51	+	108.259i	0.956072	+	0.0355744i
$211$	−456.706	−	791.037i	−0.149009	−	0.258091i	0.781852	−	0.623464i	$-0.214275\pi$
$211$	−456.706	−	791.037i	−0.149009	−	0.258091i	−0.930861	+	0.365372i	$0.880942\pi$
$212$	−2147.62	+	3719.78i	−0.695749	+	1.20507i
$213$	−861.115	−	3915.92i	−0.277008	−	1.25969i
$214$	2523.32	+	4370.53i	0.806032	+	1.39609i
$215$	−290.357	−	502.914i	−0.0921033	−	0.159528i
$216$	−3194.21	−	4207.30i	−1.00620	−	1.32533i
$217$	−4534.95	+	1254.85i	−1.41867	+	0.392555i
$218$	103.208	−	178.761i	0.0320647	−	0.0555378i
$219$	1387.95	+	440.229i	0.428259	+	0.135835i
$220$	−5425.04			−1.66253
$221$	1164.43			0.354426
$222$	6432.45	−	5874.05i	1.94467	−	1.77586i
$223$	484.137	−	838.550i	0.145382	−	0.251809i	−0.784133	−	0.620592i	$-0.786892\pi$
$223$	484.137	−	838.550i	0.145382	−	0.251809i	0.929515	+	0.368783i	$0.120226\pi$
$224$	370.071	−	102.401i	0.110386	−	0.0305443i
$225$	−1906.90	−	1344.97i	−0.565009	−	0.398510i
$226$	−5179.38	−	8970.95i	−1.52446	−	2.64044i
$227$	−1656.75	−	2869.57i	−0.484415	−	0.839031i	0.515425	−	0.856935i	$-0.327634\pi$
$227$	−1656.75	−	2869.57i	−0.484415	−	0.839031i	−0.999840	+	0.0179035i	$0.994301\pi$
$228$	−5082.53	+	4641.32i	−1.47631	+	1.34815i
$229$	−1794.95	+	3108.95i	−0.517964	+	0.897140i	0.481818	+	0.876271i	$0.339977\pi$
$229$	−1794.95	+	3108.95i	−0.517964	+	0.897140i	−0.999782	+	0.0208691i	$0.993357\pi$
$230$	−159.387	−	276.066i	−0.0456942	−	0.0791447i
$231$	−2842.27	+	4525.55i	−0.809558	+	1.28900i
$232$	−2869.69	+	4970.44i	−0.812087	+	1.40658i
$233$	2516.03	+	4357.90i	0.707428	+	1.22530i	0.965808	+	0.259259i	$0.0834782\pi$
$233$	2516.03	+	4357.90i	0.707428	+	1.22530i	−0.258379	+	0.966044i	$0.583188\pi$
$234$	−1449.07	−	1022.05i	−0.404823	−	0.285528i
$235$	993.235	−	1720.33i	0.275709	−	0.477541i
$236$	5509.98			1.51978
$237$	−385.999	−	1755.33i	−0.105795	−	0.481101i
$238$	1955.28	−	7542.60i	0.532528	−	2.05426i
$239$	−322.817	−	559.135i	−0.0873694	−	0.151328i	0.819029	−	0.573752i	$-0.194513\pi$
$239$	−322.817	−	559.135i	−0.0873694	−	0.151328i	−0.906398	+	0.422424i	$0.861179\pi$
$240$	−1771.25	−	561.805i	−0.476390	−	0.151101i
$241$	−1597.86	−	2767.58i	−0.427084	−	0.739731i	0.569529	−	0.821972i	$-0.307126\pi$
$241$	−1597.86	−	2767.58i	−0.427084	−	0.739731i	−0.996613	+	0.0822404i	$0.973792\pi$
$242$	4269.20	−	7394.47i	1.13403	−	1.96419i
$243$	−3344.91	−	1777.77i	−0.883030	−	0.469316i
$244$	−4579.31			−1.20148
$245$	−34.7297	−	2130.02i	−0.00905632	−	0.555437i
$246$	2165.34	−	1977.36i	0.561206	−	0.512488i
$247$	−567.683	+	983.256i	−0.146238	+	0.253292i
$248$	9566.12			2.44939
$249$	623.175	+	197.659i	0.158603	+	0.0503057i
$250$	−6396.60			−1.61823
$251$	−3686.56			−0.927066			−0.463533	−	0.886080i	$-0.653418\pi$
$251$	−3686.56			−0.927066			−0.463533	+	0.886080i	$0.653418\pi$
$252$	−6001.29	+	5084.26i	−1.50018	+	1.27095i
$253$	585.107			0.145397
$254$	−5588.97			−1.38064
$255$	2058.23	−	1879.55i	0.505455	−	0.461577i
$256$	−8026.13			−1.95951
$257$	−795.880	+	1378.50i	−0.193174	+	0.334586i	−0.946300	−	0.323289i	$-0.895211\pi$
$257$	−795.880	+	1378.50i	−0.193174	+	0.334586i	0.753127	+	0.657876i	$0.228545\pi$
$258$	2255.93	+	715.536i	0.544372	+	0.172664i
$259$	−4543.43	−	4469.96i	−1.09002	−	1.07239i
$260$	−1317.11			−0.314167
$261$	−372.724	+	4098.73i	−0.0883947	+	0.972051i
$262$	348.158	−	603.028i	0.0820966	−	0.142195i
$263$	1955.64	+	3387.26i	0.458516	+	0.794173i	0.998883	−	0.0472564i	$-0.0150478\pi$
$263$	1955.64	+	3387.26i	0.458516	+	0.794173i	−0.540367	+	0.841430i	$0.681714\pi$
$264$	8022.79	−	7326.33i	1.87034	−	1.70797i
$265$	847.991	+	1468.76i	0.196572	+	0.340473i
$266$	5415.80	+	5328.22i	1.24836	+	1.22817i
$267$	−1251.99	+	1143.30i	−0.286967	+	0.262056i
$268$	13108.6			2.98782
$269$	−191.371	+	331.465i	−0.0433759	+	0.0751292i	−0.886898	−	0.461965i	$-0.847145\pi$
$269$	−191.371	+	331.465i	−0.0433759	+	0.0751292i	0.843522	+	0.537094i	$0.180478\pi$
$270$	−4211.07	+	532.433i	−0.949176	+	0.120010i
$271$	403.244	+	698.439i	0.0903887	+	0.156558i	0.907675	−	0.419674i	$-0.137856\pi$
$271$	403.244	+	698.439i	0.0903887	+	0.156558i	−0.817286	+	0.576232i	$0.804522\pi$
$272$	−2486.50	+	4306.75i	−0.554289	+	0.960056i
$273$	−690.055	+	1098.72i	−0.152982	+	0.243582i
$274$	3323.62	+	5756.69i	0.732801	+	1.26925i
$275$	2399.70	−	4156.41i	0.526209	−	0.911421i
$276$	820.864	+	260.362i	0.179022	+	0.0567824i
$277$	666.775	+	1154.89i	0.144630	+	0.250507i	0.929235	−	0.369489i	$-0.120467\pi$
$277$	666.775	+	1154.89i	0.144630	+	0.250507i	−0.784605	+	0.619996i	$0.787134\pi$
$278$	−2676.02	−	4635.01i	−0.577328	−	0.999961i
$279$	6226.94	−	2877.78i	1.33619	−	0.617521i
$280$	−1086.80	+	4192.39i	−0.231959	+	0.894797i
$281$	1518.16	−	2629.53i	0.322299	−	0.558238i	−0.658663	−	0.752438i	$-0.728878\pi$
$281$	1518.16	−	2629.53i	0.322299	−	0.558238i	0.980962	+	0.194200i	$0.0622111\pi$
$282$	1738.73	+	7906.89i	0.367163	+	1.66967i
$283$	2538.14			0.533133			0.266566	−	0.963817i	$-0.414111\pi$
$283$	2538.14			0.533133			0.266566	+	0.963817i	$0.414111\pi$
$284$	12137.2			2.53595
$285$	583.684	+	2654.30i	0.121314	+	0.551675i
$286$	1823.55	−	3158.48i	0.377023	−	0.653024i
$287$	−1529.44	−	1504.71i	−0.314565	−	0.309478i
$288$	−508.144	+	234.839i	−0.103968	+	0.0480487i
$289$	−1273.23	−	2205.30i	−0.259155	−	0.448870i
$290$	2305.87	+	3993.89i	0.466915	+	0.808721i
$291$	−1231.82	−	390.710i	−0.248147	−	0.0787073i
$292$	−2203.89	+	3817.24i	−0.441687	+	0.765025i
$293$	1537.15	+	2662.43i	0.306489	+	0.530855i	0.977592	−	0.210510i	$-0.0675123\pi$
$293$	1537.15	+	2662.43i	0.306489	+	0.530855i	−0.671102	+	0.741365i	$0.734179\pi$
$294$	5958.25	+	6314.76i	1.18195	+	1.25267i
$295$	1087.81	−	1884.15i	0.214695	−	0.371862i
$296$	6478.89	+	11221.8i	1.27222	+	2.20355i
$297$	3018.35	−	7182.48i	0.589705	−	1.40327i
$298$	−1456.41	+	2522.57i	−0.283112	+	0.490365i
$299$	142.054			0.0274755
$300$	5216.14	−	4763.33i	1.00385	−	0.916703i
$301$	434.537	−	1676.25i	0.0832103	−	0.320989i
$302$	−3092.54	−	5356.43i	−0.589256	−	1.02062i
$303$	−7508.03	+	6856.25i	−1.42351	+	1.29994i
$304$	−2424.44	−	4199.25i	−0.457405	−	0.792249i
$305$	−904.076	+	1565.91i	−0.169729	+	0.293979i
$306$	−1028.75	+	11312.9i	−0.192189	+	2.11344i
$307$	−8776.30			−1.63156			−0.815781	−	0.578360i	$-0.803693\pi$
$307$	−8776.30			−1.63156			−0.815781	+	0.578360i	$0.803693\pi$
$308$	−11531.9	−	11345.4i	−2.13341	−	2.09890i
$309$	−9389.86	−	2978.28i	−1.72871	−	0.548311i
$310$	3843.32	−	6656.82i	0.704148	−	1.21962i
$311$	2424.94			0.442140			0.221070	−	0.975258i	$-0.429045\pi$
$311$	2424.94			0.442140			0.221070	+	0.975258i	$0.429045\pi$
$312$	1947.79	−	1778.71i	0.353436	−	0.322754i
$313$	−6509.24			−1.17548			−0.587738	−	0.809051i	$-0.699982\pi$
$313$	−6509.24			−1.17548			−0.587738	+	0.809051i	$0.699982\pi$
$314$	−12495.7			−2.24577
$315$	553.762	+	3055.92i	0.0990507	+	0.546609i
$316$	5440.56			0.968531
$317$	9739.86			1.72569			0.862847	−	0.505464i	$-0.168679\pi$
$317$	9739.86			1.72569			0.862847	+	0.505464i	$0.168679\pi$
$318$	−6588.46	−	2089.73i	−1.16183	−	0.368510i
$319$	−8464.81			−1.48570
$320$	−1744.08	+	3020.84i	−0.304679	+	0.527719i
$321$	−3975.13	+	3630.05i	−0.691185	+	0.631183i
$322$	238.532	−	920.152i	0.0412822	−	0.159249i
$323$	7273.26			1.25293
$324$	7430.60	−	8733.41i	1.27411	−	1.49750i
$325$	582.606	−	1009.10i	0.0994375	−	0.172231i
$326$	−5232.87	−	9063.59i	−0.889024	−	1.53983i
$327$	209.877	+	66.5689i	0.0354931	+	0.0112577i
$328$	2180.97	+	3777.55i	0.367146	+	0.635916i
$329$	5709.02	−	1579.72i	0.956682	−	0.264719i
$330$	−1874.95	−	8526.32i	−0.312765	−	1.42230i
$331$	7350.00			1.22052			0.610261	−	0.792201i	$-0.291065\pi$
$331$	7350.00			1.22052			0.610261	+	0.792201i	$0.291065\pi$
$332$	−989.524	+	1713.91i	−0.163576	+	0.283322i
$333$	7593.20	+	5355.62i	1.24956	+	0.881339i
$334$	3412.14	+	5910.00i	0.558994	+	0.968207i
$335$	2587.98	−	4482.51i	0.422079	−	0.731062i
$336$	−2590.19	−	4898.42i	−0.420556	−	0.795329i
$337$	−2340.00	−	4053.01i	−0.378244	−	0.655137i	0.612563	−	0.790422i	$-0.290139\pi$
$337$	−2340.00	−	4053.01i	−0.378244	−	0.655137i	−0.990807	+	0.135284i	$0.956805\pi$
$338$	−4908.38	+	8501.56i	−0.789884	+	1.36812i
$339$	8159.36	−	7451.05i	1.30724	−	1.19376i
$340$	4218.75	+	7307.08i	0.672923	+	1.16554i
$341$	7054.38	+	12218.5i	1.12028	+	1.94039i
$342$	−9051.14	−	6383.93i	−1.43108	−	1.00937i
$343$	4380.68	−	4600.35i	0.689605	−	0.724186i
$344$	−1760.26	+	3048.85i	−0.275891	+	0.477858i
$345$	251.091	−	229.294i	0.0391835	−	0.0357820i
$346$	6514.29			1.01217
$347$	−7602.37			−1.17613			−0.588064	−	0.808814i	$-0.700110\pi$
$347$	−7602.37			−1.17613			−0.588064	+	0.808814i	$0.700110\pi$
$348$	−11875.5	−	3766.68i	−1.82930	−	0.580217i
$349$	−5989.27	+	10373.7i	−0.918619	+	1.59109i	−0.117105	+	0.993120i	$0.537361\pi$
$349$	−5989.27	+	10373.7i	−0.918619	+	1.59109i	−0.801515	+	0.597975i	$0.795972\pi$
$350$	−5558.17	−	5468.28i	−0.848847	−	0.835120i
$351$	732.802	−	1743.78i	0.111436	−	0.265174i
$352$	−575.667	−	997.084i	−0.0871681	−	0.150979i
$353$	3279.66	+	5680.54i	0.494500	+	0.856500i	0.999980	−	0.00633882i	$-0.00201772\pi$
$353$	3279.66	+	5680.54i	0.494500	+	0.856500i	−0.505480	+	0.862839i	$0.668684\pi$
$354$	1904.30	+	8659.81i	0.285911	+	1.30018i
$355$	2396.20	−	4150.35i	0.358246	−	0.620500i
$356$	−2566.19	−	4444.78i	−0.382045	−	0.661721i
$357$	8305.81	+	309.050i	1.23135	+	0.0458170i
$358$	−2495.48	+	4322.30i	−0.368409	+	0.638103i
$359$	132.469	+	229.443i	0.0194747	+	0.0337313i	0.875599	−	0.483040i	$-0.160467\pi$
$359$	132.469	+	229.443i	0.0194747	+	0.0337313i	−0.856124	+	0.516771i	$0.827134\pi$
$360$	571.808	−	6288.01i	0.0837137	−	0.920575i
$361$	−116.356	+	201.535i	−0.0169640	+	0.0293825i
$362$	4346.72			0.631102
$363$	8681.59	+	2753.63i	1.25528	+	0.398149i
$364$	−2799.73	−	2754.46i	−0.403148	−	0.396628i
$365$	870.210	+	1507.25i	0.124791	+	0.216145i
$366$	−1582.65	−	7197.12i	−0.226029	−	1.02787i
$367$	3000.03	+	5196.21i	0.426704	+	0.739073i	0.996578	−	0.0826591i	$-0.0263413\pi$
$367$	3000.03	+	5196.21i	0.426704	+	0.739073i	−0.569874	+	0.821732i	$0.693008\pi$
$368$	−303.339	+	525.398i	−0.0429691	+	0.0744246i
$369$	2556.08	+	1802.85i	0.360607	+	0.254342i
$370$	10411.9			1.46295
$371$	−1269.07	+	4895.51i	−0.177592	+	0.685073i
$372$	4459.78	+	20280.8i	0.621582	+	2.82664i
$373$	−459.470	+	795.825i	−0.0637813	+	0.110473i	−0.896153	−	0.443746i	$-0.853649\pi$
$373$	−459.470	+	795.825i	−0.0637813	+	0.110473i	0.832371	+	0.554218i	$0.186983\pi$
$374$	−23363.6			−3.23023
$375$	−1465.41	−	6663.97i	−0.201796	−	0.917669i
$376$	−12042.7			−1.65175
$377$	−2055.11			−0.280752
$378$	−10064.8	−	7674.82i	−1.36952	−	1.04431i
$379$	6188.59			0.838751			0.419375	−	0.907813i	$-0.362249\pi$
$379$	6188.59			0.838751			0.419375	+	0.907813i	$0.362249\pi$
$380$	−8226.89			−1.11061
$381$	−1280.39	−	5822.58i	−0.172169	−	0.782939i
$382$	3891.14			0.521173
$383$	2070.97	−	3587.03i	0.276297	−	0.478560i	−0.694165	−	0.719816i	$-0.744226\pi$
$383$	2070.97	−	3587.03i	0.276297	−	0.478560i	0.970462	+	0.241256i	$0.0775594\pi$
$384$	−2868.05	−	13042.5i	−0.381145	−	1.73325i
$385$	−6156.26	+	1703.47i	−0.814941	+	0.225499i
$386$	3398.34			0.448112
$387$	−228.627	+	2514.15i	−0.0300305	+	0.330236i
$388$	1955.98	−	3387.86i	0.255928	−	0.443280i
$389$	−497.767	−	862.158i	−0.0648786	−	0.112373i	0.831762	−	0.555133i	$-0.187333\pi$
$389$	−497.767	−	862.158i	−0.0648786	−	0.112373i	−0.896640	+	0.442760i	$0.853999\pi$
$390$	−455.204	−	2070.04i	−0.0591030	−	0.268771i
$391$	−455.005	−	788.091i	−0.0588506	−	0.101932i
$392$	−11077.7	+	6638.83i	−1.42732	+	0.855386i
$393$	707.995	+	224.562i	0.0908743	+	0.0288235i
$394$	−411.795			−0.0526546
$395$	1074.11	−	1860.41i	0.136821	−	0.236981i
$396$	19272.6	+	13593.3i	2.44567	+	1.72497i
$397$	4285.78	+	7423.18i	0.541806	+	0.938435i	0.998800	+	0.0489659i	$0.0155926\pi$
$397$	4285.78	+	7423.18i	0.541806	+	0.938435i	−0.456994	+	0.889470i	$0.651074\pi$
$398$	6289.26	−	10893.3i	0.792091	−	1.37194i
$399$	−4310.21	+	6862.83i	−0.540803	+	0.861081i
$400$	2488.17	+	4309.64i	0.311021	+	0.538705i
$401$	7048.55	−	12208.4i	0.877775	−	1.52035i	0.0239977	−	0.999712i	$-0.492361\pi$
$401$	7048.55	−	12208.4i	0.877775	−	1.52035i	0.853777	−	0.520639i	$-0.174306\pi$
$402$	4530.45	+	20602.2i	0.562086	+	2.55609i
$403$	1712.68	+	2966.45i	0.211699	+	0.366673i
$404$	−15389.2	−	26654.9i	−1.89515	−	3.28250i
$405$	−1519.41	−	4265.11i	−0.186420	−	0.523297i
$406$	−3450.87	+	13312.0i	−0.421832	+	1.62724i
$407$	−9555.51	+	16550.6i	−1.16376	+	2.01569i
$408$	−16106.8	−	5108.77i	−1.95443	−	0.619906i
$409$	4858.23			0.587345			0.293673	−	0.955906i	$-0.405122\pi$
$409$	4858.23			0.587345			0.293673	+	0.955906i	$0.405122\pi$
$410$	3504.94			0.422187
$411$	−5235.89	+	4781.36i	−0.628388	+	0.573837i
$412$	14909.9	−	25824.7i	1.78291	−	3.08809i
$413$	6252.65	−	1730.14i	0.744970	−	0.206137i
$414$	−125.501	+	1380.10i	−0.0148987	+	0.163836i
$415$	390.716	+	676.739i	0.0462156	+	0.0800478i
$416$	−139.762	−	242.075i	−0.0164721	−	0.0285305i
$417$	4215.69	−	3849.72i	0.495067	−	0.452091i
$418$	11390.2	−	19728.4i	1.33281	−	2.30849i
$419$	−3476.72	−	6021.85i	−0.405367	−	0.702116i	0.588997	−	0.808135i	$-0.299523\pi$
$419$	−3476.72	−	6021.85i	−0.405367	−	0.702116i	−0.994364	+	0.106019i	$0.966190\pi$
$420$	−9394.82	−	349.571i	−1.09148	−	0.0406126i
$421$	4777.73	−	8275.27i	0.553094	−	0.957986i	−0.444956	−	0.895553i	$-0.646781\pi$
$421$	4777.73	−	8275.27i	0.553094	−	0.957986i	0.998049	−	0.0624335i	$-0.0198861\pi$
$422$	2224.74	+	3853.37i	0.256632	+	0.444500i
$423$	−7839.06	+	3622.82i	−0.901059	+	0.416425i
$424$	5140.84	−	8904.20i	0.588824	−	1.01987i
$425$	−7464.45			−0.851951
$426$	4194.74	+	19075.6i	0.477079	+	2.16952i
$427$	−5196.54	+	1437.91i	−0.588942	+	0.162964i
$428$	−8147.83	−	14112.5i	−0.920188	−	1.59381i
$429$	3708.26	+	1176.19i	0.417335	+	0.132370i
$430$	1414.41	+	2449.84i	0.158626	+	0.274748i
$431$	−1817.99	+	3148.84i	−0.203177	+	0.351913i	−0.949550	−	0.313615i	$-0.898460\pi$
$431$	−1817.99	+	3148.84i	−0.203177	+	0.351913i	0.746373	+	0.665527i	$0.231793\pi$
$432$	4884.71	+	6433.96i	0.544018	+	0.716561i
$433$	2102.96			0.233399			0.116700	−	0.993167i	$-0.462768\pi$
$433$	2102.96			0.233399			0.116700	+	0.993167i	$0.462768\pi$
$434$	22091.0	−	6112.71i	2.44333	−	0.676082i
$435$	−3632.57	+	3317.22i	−0.400387	+	0.365629i
$436$	−333.259	+	577.221i	−0.0366060	+	0.0634034i
$437$	887.294			0.0971282
$438$	−6761.09	−	2144.48i	−0.737574	−	0.233944i
$439$	−4046.29			−0.439907			−0.219953	−	0.975510i	$-0.570591\pi$
$439$	−4046.29			−0.439907			−0.219953	+	0.975510i	$0.570591\pi$
$440$	12986.2			1.40702
$441$	−5213.72	+	7653.97i	−0.562976	+	0.826473i
$442$	−5672.28			−0.610414
$443$	−3813.53			−0.408999			−0.204499	−	0.978867i	$-0.565557\pi$
$443$	−3813.53			−0.408999			−0.204499	+	0.978867i	$0.565557\pi$
$444$	−20770.4	+	18967.3i	−2.22009	+	2.02737i
$445$	−2026.54			−0.215881
$446$	−2358.37	+	4084.82i	−0.250386	+	0.433681i
$447$	−2961.66	−	939.381i	−0.313382	−	0.0993986i
$448$	−10024.8	+	2773.92i	−1.05721	+	0.292534i
$449$	2025.85			0.212931			0.106465	−	0.994316i	$-0.466047\pi$
$449$	2025.85			0.212931			0.106465	+	0.994316i	$0.466047\pi$
$450$	9289.07	+	6551.74i	0.973091	+	0.686338i
$451$	−3216.64	+	5571.39i	−0.335844	+	0.581699i
$452$	16724.3	+	28967.3i	1.74036	+	3.01439i
$453$	4871.84	−	4448.92i	0.505296	−	0.461431i
$454$	8070.49	+	13978.5i	0.834288	+	1.44503i
$455$	−1494.63	+	413.573i	−0.153999	+	0.0426123i
$456$	12166.3	−	11110.1i	1.24943	−	1.14096i
$457$	−18786.7			−1.92299			−0.961495	−	0.274822i	$-0.911381\pi$
$457$	−18786.7			−1.92299			−0.961495	+	0.274822i	$0.911381\pi$
$458$	8743.73	−	15144.6i	0.892069	−	1.54511i
$459$	−12021.4	+	1519.94i	−1.22246	+	0.154564i
$460$	514.662	+	891.420i	0.0521657	+	0.0903537i
$461$	2012.59	−	3485.90i	0.203331	−	0.352179i	−0.746269	−	0.665645i	$-0.768157\pi$
$461$	2012.59	−	3485.90i	0.203331	−	0.352179i	0.949600	+	0.313466i	$0.101490\pi$
$462$	13845.5	−	22045.2i	1.39427	−	2.21999i
$463$	−6347.17	−	10993.6i	−0.637101	−	1.10349i	−0.986066	−	0.166356i	$-0.946800\pi$
$463$	−6347.17	−	10993.6i	−0.637101	−	1.10349i	0.348965	−	0.937136i	$-0.386533\pi$
$464$	4388.44	−	7601.00i	0.439069	−	0.760490i
$465$	7815.55	+	2478.94i	0.779435	+	0.247221i
$466$	−12256.3	−	21228.6i	−1.21838	−	2.11029i
$467$	−1929.44	−	3341.89i	−0.191186	−	0.331144i	0.754457	−	0.656349i	$-0.227900\pi$
$467$	−1929.44	−	3341.89i	−0.191186	−	0.331144i	−0.945644	+	0.325205i	$0.894567\pi$
$468$	4679.05	+	3300.21i	0.462156	+	0.325967i
$469$	14875.5	−	4116.12i	1.46457	−	0.405255i
$470$	−4838.33	+	8380.23i	−0.474842	+	0.822450i
$471$	−2862.67	−	13018.0i	−0.280053	−	1.27354i
$472$	−13189.5			−1.28622
$473$	−5192.29			−0.504739
$474$	1880.31	+	8550.71i	0.182206	+	0.828581i
$475$	3639.07	−	6303.05i	0.351520	−	0.608850i
$476$	−6313.60	+	24355.1i	−0.607949	+	2.34520i
$477$	667.708	−	7342.59i	0.0640928	−	0.704810i
$478$	1572.53	+	2723.71i	0.150473	+	0.260627i
$479$	−4745.91	−	8220.15i	−0.452706	−	0.784109i	0.545848	−	0.837885i	$-0.316208\pi$
$479$	−4745.91	−	8220.15i	−0.452706	−	0.784109i	−0.998553	+	0.0537755i	$0.982874\pi$
$480$	−637.782	−	202.292i	−0.0606471	−	0.0192360i
$481$	−2319.91	+	4018.20i	−0.219914	+	0.380903i
$482$	7783.63	+	13481.6i	0.735549	+	1.27401i
$483$	1013.26	+	37.7022i	0.0954553	+	0.00355178i
$484$	−13785.3	+	23876.8i	−1.29463	+	2.24237i
$485$	−772.324	−	1337.70i	−0.0723081	−	0.125241i
$486$	16294.0	+	8660.02i	1.52081	+	0.808285i
$487$	7850.24	−	13597.0i	0.730448	−	1.26517i	−0.226244	−	0.974071i	$-0.572645\pi$
$487$	7850.24	−	13597.0i	0.730448	−	1.26517i	0.956692	−	0.291102i	$-0.0940220\pi$
$488$	10961.7			1.01683
$489$	8243.63	−	7528.00i	0.762351	−	0.696172i
$490$	169.178	+	10375.9i	0.0155973	+	0.956606i
$491$	5964.99	+	10331.7i	0.548261	+	0.949616i	0.998394	+	0.0566544i	$0.0180433\pi$
$491$	5964.99	+	10331.7i	0.548261	+	0.949616i	−0.450133	+	0.892962i	$0.648623\pi$
$492$	−6991.89	+	6384.92i	−0.640688	+	0.585070i
$493$	6582.61	+	11401.4i	0.601350	+	1.04157i
$494$	2765.35	−	4789.72i	0.251860	−	0.436234i
$495$	8453.17	−	3906.63i	0.767559	−	0.354727i
$496$	−14628.9			−1.32431
$497$	13773.1	−	3811.10i	1.24308	−	0.343967i
$498$	−3035.66	−	962.852i	−0.273155	−	0.0866394i
$499$	−9098.13	+	15758.4i	−0.816209	+	1.41372i	0.0922478	+	0.995736i	$0.470595\pi$
$499$	−9098.13	+	15758.4i	−0.816209	+	1.41372i	−0.908457	+	0.417979i	$0.862739\pi$
$500$	20654.7			1.84741
$501$	−5375.34	+	4908.71i	−0.479346	+	0.437734i
$502$	17958.3			1.59665
$503$	1851.20			0.164097			0.0820487	−	0.996628i	$-0.473854\pi$
$503$	1851.20			0.164097			0.0820487	+	0.996628i	$0.473854\pi$
$504$	14365.6	−	12170.4i	1.26963	−	1.07562i
$505$	−12152.9			−1.07089
$506$	−2850.22			−0.250411
$507$	−9981.39	−	3165.90i	−0.874338	−	0.277323i
$508$	18046.8			1.57618
$509$	−10796.3	+	18699.7i	−0.940151	+	1.62839i	−0.174971	+	0.984574i	$0.555983\pi$
$509$	−10796.3	+	18699.7i	−0.940151	+	1.62839i	−0.765180	+	0.643816i	$0.777350\pi$
$510$	−10026.2	+	9155.83i	−0.870525	+	0.794955i
$511$	−1302.32	+	5023.78i	−0.112742	+	0.434910i
$512$	18537.6			1.60011
$513$	4577.22	−	10892.0i	0.393936	−	0.937413i
$514$	3876.96	−	6715.09i	0.332695	−	0.576245i
$515$	−5887.21	−	10197.0i	−0.503731	−	0.872488i
$516$	−7284.42	−	2310.47i	−0.621470	−	0.197118i
$517$	−8880.71	−	15381.8i	−0.755461	−	1.30850i
$518$	22132.4	+	21774.4i	1.87730	+	1.84694i
$519$	1492.38	+	6786.58i	0.126220	+	0.573984i
$520$	3152.81			0.265885
$521$	−647.296	+	1121.15i	−0.0544310	+	0.0942772i	−0.891957	−	0.452120i	$-0.850668\pi$
$521$	−647.296	+	1121.15i	−0.0544310	+	0.0942772i	0.837526	+	0.546397i	$0.184001\pi$
$522$	1815.64	−	19966.1i	0.152239	−	1.67412i
$523$	5051.51	+	8749.48i	0.422347	+	0.731526i	0.996169	−	0.0874543i	$-0.0278732\pi$
$523$	5051.51	+	8749.48i	0.422347	+	0.731526i	−0.573822	+	0.818980i	$0.694540\pi$
$524$	−1124.21	+	1947.18i	−0.0937236	+	0.162334i
$525$	4423.51	−	7043.23i	0.367729	−	0.585509i
$526$	−9526.47	−	16500.3i	−0.789684	−	1.36777i
$527$	10971.6	−	19003.3i	0.906887	−	1.57078i
$528$	−12268.8	+	11203.7i	−1.01123	+	0.923445i
$529$	6027.99	+	10440.8i	0.495438	+	0.858124i
$530$	−4130.81	−	7154.77i	−0.338549	−	0.586383i
$531$	−8585.51	+	3967.80i	−0.701656	+	0.324271i
$532$	−17487.7	−	17204.9i	−1.42516	−	1.40211i
$533$	−780.945	+	1352.64i	−0.0634643	+	0.109923i
$534$	6098.78	−	5569.34i	0.494232	−	0.451328i
$535$	−6434.38			−0.519967
$536$	−31378.6			−2.52864
$537$	−5074.66	−	1609.58i	−0.407799	−	0.129346i
$538$	932.224	−	1614.66i	0.0747045	−	0.129392i
$539$	−16648.7	−	9253.55i	−1.33044	−	0.739478i
$540$	13597.6	−	1719.23i	1.08360	−	0.137007i
$541$	284.987	+	493.612i	0.0226480	+	0.0392275i	0.877127	−	0.480258i	$-0.159457\pi$
$541$	284.987	+	493.612i	0.0226480	+	0.0392275i	−0.854479	+	0.519485i	$0.826124\pi$
$542$	−1964.32	−	3402.30i	−0.155673	−	0.269633i
$543$	995.803	+	4528.41i	0.0786998	+	0.357887i
$544$	−895.327	+	1550.75i	−0.0705640	+	0.122220i
$545$	131.588	+	227.917i	0.0103424	+	0.0179136i
$546$	3361.45	−	5352.19i	0.263474	−	0.419511i
$547$	7263.43	−	12580.6i	0.567755	−	0.983380i	−0.429033	−	0.903289i	$-0.641145\pi$
$547$	7263.43	−	12580.6i	0.567755	−	0.983380i	0.996788	−	0.0800915i	$-0.0255212\pi$
$548$	−10732.0	−	18588.4i	−0.836585	−	1.44901i
$549$	7135.37	−	3297.61i	0.554700	−	0.256355i
$550$	−11689.6	+	20247.1i	−0.906269	+	1.56970i
$551$	−12836.6			−0.992481
$552$	−1964.94	−	623.239i	−0.151510	−	0.0480558i
$553$	6173.88	−	1708.35i	0.474756	−	0.131368i
$554$	−3248.05	−	5625.79i	−0.249091	−	0.431438i
$555$	2385.30	+	10847.1i	0.182433	+	0.829613i
$556$	8640.90	+	14966.5i	0.659093	+	1.14158i
$557$	−8262.96	+	14311.9i	−0.628569	+	1.08871i	0.359270	+	0.933234i	$0.383026\pi$
$557$	−8262.96	+	14311.9i	−0.628569	+	1.08871i	−0.987839	+	0.155480i	$0.950308\pi$
$558$	−30333.2	+	14018.5i	−2.30127	+	1.06353i
$559$	−1260.60			−0.0953803
$560$	1661.97	−	6411.16i	0.125413	−	0.483788i
$561$	−5352.44	−	24340.2i	−0.402817	−	1.83181i
$562$	−7395.40	+	12809.2i	−0.555082	+	0.961431i
$563$	−20739.3			−1.55250			−0.776249	−	0.630427i	$-0.782880\pi$
$563$	−20739.3			−1.55250			−0.776249	+	0.630427i	$0.782880\pi$
$564$	−5614.38	−	25531.4i	−0.419163	−	1.90615i
$565$	13207.2			0.983419
$566$	−12364.0			−0.918193
$567$	5689.84	−	12243.8i	0.421430	−	0.906861i
$568$	−29053.4			−2.14622
$569$	−14758.4			−1.08735			−0.543675	−	0.839296i	$-0.682968\pi$
$569$	−14758.4			−1.08735			−0.543675	+	0.839296i	$0.682968\pi$
$570$	−2843.29	−	12929.9i	−0.208934	−	0.950127i
$571$	9524.35			0.698041			0.349021	−	0.937115i	$-0.386514\pi$
$571$	9524.35			0.698041			0.349021	+	0.937115i	$0.386514\pi$
$572$	−5888.25	+	10198.8i	−0.430420	+	0.745509i
$573$	891.432	+	4053.79i	0.0649915	+	0.295549i
$574$	7450.35	+	7329.86i	0.541762	+	0.533001i
$575$	−910.619			−0.0660442
$576$	13765.1	−	6361.53i	0.995738	−	0.460180i
$577$	−3301.32	+	5718.06i	−0.238190	+	0.412558i	−0.960195	−	0.279330i	$-0.909888\pi$
$577$	−3301.32	+	5718.06i	−0.238190	+	0.412558i	0.722005	+	0.691888i	$0.243221\pi$
$578$	6202.26	+	10742.6i	0.446332	+	0.773070i
$579$	778.536	+	3540.39i	0.0558805	+	0.254117i
$580$	−7445.67	−	12896.3i	−0.533043	−	0.923257i
$581$	−584.729	+	2255.63i	−0.0417533	+	0.161066i
$582$	6000.57	+	1903.26i	0.427374	+	0.135554i
$583$	15164.1			1.07724
$584$	5275.54	−	9137.50i	0.373807	−	0.647453i
$585$	2052.28	−	948.462i	0.145045	−	0.0670326i
$586$	−7487.90	−	12969.4i	−0.527854	−	0.914270i
$587$	−9789.93	+	16956.7i	−0.688371	+	1.19229i	0.283994	+	0.958826i	$0.408341\pi$
$587$	−9789.93	+	16956.7i	−0.688371	+	1.19229i	−0.972365	+	0.233467i	$0.924993\pi$
$588$	−19239.2	−	20390.4i	−1.34934	−	1.43008i
$589$	10697.7	+	18529.0i	0.748373	+	1.29622i
$590$	−5299.05	+	9178.22i	−0.369760	+	0.640443i
$591$	−94.3391	−	429.007i	−0.00656615	−	0.0298596i
$592$	−9907.78	−	17160.8i	−0.687850	−	1.19139i
$593$	−207.262	−	358.988i	−0.0143528	−	0.0248598i	0.858760	−	0.512378i	$-0.171235\pi$
$593$	−207.262	−	358.988i	−0.0143528	−	0.0248598i	−0.873113	+	0.487519i	$0.837902\pi$
$594$	−14703.2	+	34987.9i	−1.01562	+	2.41679i
$595$	7081.81	+	6967.29i	0.487943	+	0.480052i
$596$	4702.75	−	8145.40i	0.323208	−	0.559813i
$597$	12789.5	+	4056.57i	0.876781	+	0.278098i
$598$	−691.984			−0.0473200
$599$	3780.11			0.257849			0.128924	−	0.991654i	$-0.458848\pi$
$599$	3780.11			0.257849			0.128924	+	0.991654i	$0.458848\pi$
$600$	−12486.1	+	11402.2i	−0.849572	+	0.775820i
$601$	−9461.13	+	16387.2i	−0.642143	+	1.11222i	0.342811	+	0.939404i	$0.388621\pi$
$601$	−9461.13	+	16387.2i	−0.642143	+	1.11222i	−0.984954	+	0.172819i	$0.944712\pi$
$602$	−2116.75	+	8165.51i	−0.143310	+	0.552826i
$603$	−20425.5	+	9439.65i	−1.37942	+	0.637499i
$604$	9985.82	+	17295.9i	0.672711	+	1.16517i
$605$	5443.15	+	9427.81i	0.365777	+	0.633545i
$606$	36573.7	−	33398.8i	2.45166	−	2.23883i
$607$	14088.3	−	24401.6i	0.942050	−	1.63168i	0.180498	−	0.983575i	$-0.442229\pi$
$607$	14088.3	−	24401.6i	0.942050	−	1.63168i	0.761552	−	0.648104i	$-0.224438\pi$
$608$	−872.979	−	1512.04i	−0.0582302	−	0.100858i
$609$	−14658.9	−	545.443i	−0.975387	−	0.0362930i
$610$	4404.01	−	7627.97i	0.292317	−	0.506308i
$611$	−2156.08	−	3734.44i	−0.142759	−	0.247266i
$612$	3321.84	−	36529.3i	0.219408	−	2.41276i
$613$	3008.42	−	5210.73i	0.198220	−	0.343327i	−0.749731	−	0.661742i	$-0.769817\pi$
$613$	3008.42	−	5210.73i	0.198220	−	0.343327i	0.947951	+	0.318415i	$0.103151\pi$
$614$	42751.9			2.80997
$615$	802.956	+	3651.44i	0.0526477	+	0.239415i
$616$	27604.3	+	27157.9i	1.80554	+	1.77634i
$617$	3597.75	+	6231.49i	0.234749	+	0.406597i	0.959200	−	0.282729i	$-0.0912399\pi$
$617$	3597.75	+	6231.49i	0.234749	+	0.406597i	−0.724451	+	0.689327i	$0.757907\pi$
$618$	45740.7	+	14508.0i	2.97728	+	0.944334i
$619$	−4582.96	−	7937.92i	−0.297584	−	0.515431i	0.677998	−	0.735063i	$-0.262848\pi$
$619$	−4582.96	−	7937.92i	−0.297584	−	0.515431i	−0.975583	+	0.219632i	$0.929514\pi$
$620$	−12410.1	+	21494.9i	−0.803874	+	1.39235i
$621$	−1466.54	+	185.424i	−0.0947668	+	0.0119820i
$622$	−11812.6			−0.761480
$623$	−4307.75	−	4238.09i	−0.277025	−	0.272545i
$624$	−2978.64	+	2720.07i	−0.191092	+	0.174503i
$625$	−1323.85	+	2292.98i	−0.0847266	+	0.146751i
$626$	31708.4			2.02448
$627$	23162.5	+	7346.68i	1.47531	+	0.467940i
$628$	40348.6			2.56383
$629$	29723.1			1.88416
$630$	−2697.53	−	14886.3i	−0.170591	−	0.941402i
$631$	19395.9			1.22368			0.611838	−	0.790983i	$-0.290431\pi$
$631$	19395.9			1.22368			0.611838	+	0.790983i	$0.290431\pi$
$632$	−13023.3			−0.819683
$633$	−3504.76	+	3200.51i	−0.220066	+	0.200962i
$634$	−47445.7			−2.97209
$635$	3562.91	−	6171.15i	0.222661	−	0.385661i
$636$	21274.2	+	6747.75i	1.32638	+	0.420701i
$637$	−4042.00	−	2246.60i	−0.251413	−	0.139739i
$638$	41234.5			2.55876
$639$	−18911.9	+	8740.14i	−1.17080	+	0.541087i
$640$	7980.85	−	13823.2i	0.492923	−	0.853768i
$641$	−3889.62	−	6737.03i	−0.239674	−	0.415127i	0.720947	−	0.692990i	$-0.243707\pi$
$641$	−3889.62	−	6737.03i	−0.239674	−	0.415127i	−0.960621	+	0.277863i	$0.910374\pi$
$642$	19364.0	−	17683.0i	1.19040	−	1.08706i
$643$	1786.80	+	3094.83i	0.109587	+	0.189810i	0.915603	−	0.402083i	$-0.131714\pi$
$643$	1786.80	+	3094.83i	0.109587	+	0.189810i	−0.806016	+	0.591894i	$0.798380\pi$
$644$	−770.222	+	2971.18i	−0.0471289	+	0.181803i
$645$	−2228.21	+	2034.77i	−0.136024	+	0.124216i
$646$	−35430.1			−2.15786
$647$	8518.34	−	14754.2i	0.517605	−	0.896518i	−0.482186	−	0.876069i	$-0.660157\pi$
$647$	8518.34	−	14754.2i	0.517605	−	0.896518i	0.999791	−	0.0204493i	$-0.00650967\pi$
$648$	−17786.9	+	20905.5i	−1.07830	+	1.26736i
$649$	−9726.36	−	16846.6i	−0.588279	−	1.01893i
$650$	−2838.04	+	4915.63i	−0.171257	+	0.296626i
$651$	11429.1	+	21614.0i	0.688083	+	1.30126i
$652$	16897.0	+	29266.4i	1.01493	+	1.75792i
$653$	−2113.89	+	3661.36i	−0.126681	+	0.219418i	−0.922389	−	0.386263i	$-0.873766\pi$
$653$	−2113.89	+	3661.36i	−0.126681	+	0.219418i	0.795708	+	0.605681i	$0.207099\pi$
$654$	−1022.37	−	324.276i	−0.0611283	−	0.0193887i
$655$	443.895	+	768.849i	0.0264800	+	0.0458648i
$656$	−3335.23	−	5776.78i	−0.198504	−	0.343819i
$657$	685.203	−	7534.98i	0.0406885	−	0.447439i
$658$	−27810.3	+	7695.25i	−1.64765	+	0.455915i
$659$	9443.52	−	16356.6i	0.558220	−	0.966866i	−0.439425	−	0.898279i	$-0.644818\pi$
$659$	9443.52	−	16356.6i	0.558220	−	0.966866i	0.997645	−	0.0685865i	$-0.0218489\pi$
$660$	6054.22	+	27531.5i	0.357061	+	1.62373i
$661$	−1558.01			−0.0916788			−0.0458394	−	0.998949i	$-0.514596\pi$
$661$	−1558.01			−0.0916788			−0.0458394	+	0.998949i	$0.514596\pi$
$662$	−35804.0			−2.10205
$663$	−1299.48	−	5909.38i	−0.0761200	−	0.346156i
$664$	2368.67	−	4102.65i	0.138437	−	0.239780i
$665$	−9335.76	+	2583.26i	−0.544399	+	0.150638i
$666$	−36988.6	−	26088.7i	−2.15207	−	1.51789i
$667$	803.038	+	1390.90i	0.0466173	+	0.0807436i
$668$	−11017.8	−	19083.5i	−0.638163	−	1.10533i
$669$	−4795.84	−	1521.15i	−0.277157	−	0.0879086i
$670$	−12606.8	+	21835.6i	−0.726929	+	1.25908i
$671$	8083.53	+	14001.1i	0.465069	+	0.805523i
$672$	−932.663	−	1763.80i	−0.0535391	−	0.101250i
$673$	−4809.90	+	8330.98i	−0.275495	+	0.477171i	−0.970260	−	0.242066i	$-0.922175\pi$
$673$	−4809.90	+	8330.98i	−0.275495	+	0.477171i	0.694765	+	0.719237i	$0.255508\pi$
$674$	11398.8	+	19743.3i	0.651434	+	1.12832i
$675$	−4697.54	+	11178.3i	−0.267864	+	0.637412i
$676$	15849.2	−	27451.6i	0.901752	−	1.56188i
$677$	13651.3			0.774981			0.387491	−	0.921874i	$-0.373342\pi$
$677$	13651.3			0.774981			0.387491	+	0.921874i	$0.373342\pi$
$678$	−39746.6	+	36296.2i	−2.25141	+	2.05597i
$679$	1155.83	−	4458.68i	0.0653264	−	0.252001i
$680$	−10098.6	−	17491.3i	−0.569505	−	0.986412i
$681$	−12713.9	+	11610.2i	−0.715415	+	0.653309i
$682$	−34363.9	−	59520.0i	−1.92942	−	3.34185i
$683$	1545.24	−	2676.43i	0.0865694	−	0.149943i	−0.819489	−	0.573094i	$-0.805743\pi$
$683$	1545.24	−	2676.43i	0.0865694	−	0.149943i	0.906059	+	0.423152i	$0.139076\pi$
$684$	29226.2	+	20613.7i	1.63376	+	1.15232i
$685$	−8475.12			−0.472726
$686$	−21339.5	+	22409.6i	−1.18768	+	1.24724i
$687$	17780.7	+	5639.69i	0.987448	+	0.313199i
$688$	2691.85	−	4662.43i	0.149166	−	0.258362i
$689$	3681.58			0.203566
$690$	−1223.14	+	1116.96i	−0.0674841	+	0.0616258i
$691$	1058.30			0.0582630			0.0291315	−	0.999576i	$-0.490726\pi$
$691$	1058.30			0.0582630			0.0291315	+	0.999576i	$0.490726\pi$
$692$	−21034.7			−1.15552
$693$	26138.6	+	9373.86i	1.43279	+	0.513829i
$694$	37033.3			2.02560
$695$	6823.76			0.372431
$696$	28427.0	+	9016.47i	1.54816	+	0.491047i
$697$	10005.6			0.543744
$698$	29175.4	−	50533.3i	1.58210	−	2.74028i
$699$	19308.1	−	17631.9i	1.04478	−	0.954078i
$700$	17947.4	+	17657.1i	0.969067	+	0.953395i
$701$	3542.05			0.190844			0.0954219	−	0.995437i	$-0.469580\pi$
$701$	3542.05			0.190844			0.0954219	+	0.995437i	$0.469580\pi$
$702$	−3569.69	+	8494.45i	−0.191922	+	0.456699i
$703$	−14490.6	+	25098.4i	−0.777415	+	1.34652i
$704$	15594.2	+	27009.9i	0.834841	+	1.44599i
$705$	−9838.94	−	3120.72i	−0.525611	−	0.166713i
$706$	−15976.2	−	27671.5i	−0.851658	−	1.47511i
$707$	−25833.1	−	25415.4i	−1.37419	−	1.35197i
$708$	−6149.00	−	27962.6i	−0.326403	−	1.48432i
$709$	20868.8			1.10542			0.552712	−	0.833372i	$-0.313593\pi$
$709$	20868.8			1.10542			0.552712	+	0.833372i	$0.313593\pi$
$710$	−11672.6	+	20217.5i	−0.616992	+	1.06866i
$711$	−8477.36	+	3917.81i	−0.447153	+	0.206652i
$712$	6142.81	+	10639.7i	0.323331	+	0.560026i
$713$	1338.47	−	2318.29i	0.0703029	−	0.121768i
$714$	−40460.0	−	1505.47i	−2.12070	−	0.0789087i
$715$	2324.99	+	4027.00i	0.121608	+	0.210631i
$716$	8057.93	−	13956.7i	0.420585	−	0.728475i
$717$	−2477.30	+	2262.24i	−0.129033	+	0.117831i
$718$	−645.293	−	1117.68i	−0.0335406	−	0.0580940i
$719$	−4711.93	−	8161.31i	−0.244403	−	0.423318i	0.717561	−	0.696496i	$-0.245258\pi$
$719$	−4711.93	−	8161.31i	−0.244403	−	0.423318i	−0.961963	+	0.273178i	$0.911925\pi$
$720$	−874.431	+	9615.87i	−0.0452613	+	0.497725i
$721$	8810.56	−	33987.3i	0.455094	−	1.75555i
$722$	566.803	−	981.732i	0.0292164	−	0.0506043i
$723$	−12262.0	+	11197.5i	−0.630745	+	0.575990i
$724$	−14035.6			−0.720482
$725$	13174.0			0.674857
$726$	−42290.5	−	13413.7i	−2.16191	−	0.685715i
$727$	−5340.37	+	9249.79i	−0.272439	+	0.471879i	−0.969486	−	0.245147i	$-0.921164\pi$
$727$	−5340.37	+	9249.79i	−0.272439	+	0.471879i	0.697047	+	0.717026i	$0.254497\pi$
$728$	6701.85	+	6593.46i	0.341191	+	0.335673i
$729$	−5289.15	+	18959.0i	−0.268717	+	0.963219i
$730$	−4239.04	−	7342.23i	−0.214923	−	0.372258i
$731$	4037.75	+	6993.59i	0.204298	+	0.353854i
$732$	5110.40	+	23239.6i	0.258041	+	1.17344i
$733$	−13755.7	+	23825.6i	−0.693149	+	1.20057i	0.277651	+	0.960682i	$0.410444\pi$
$733$	−13755.7	+	23825.6i	−0.693149	+	1.20057i	−0.970801	+	0.239888i	$0.922889\pi$
$734$	−14614.0	−	25312.2i	−0.734895	−	1.27288i
$735$	−10770.9	+	2553.30i	−0.540530	+	0.128136i
$736$	−109.225	+	189.182i	−0.00547020	+	0.00947467i
$737$	−23139.6	−	40079.0i	−1.15653	−	2.00316i
$738$	−12451.4	−	8782.17i	−0.621059	−	0.438044i
$739$	10392.7	−	18000.7i	0.517322	−	0.896028i	−0.482476	−	0.875909i	$-0.660262\pi$
$739$	10392.7	−	18000.7i	0.517322	−	0.896028i	0.999798	−	0.0201186i	$-0.00640440\pi$
$740$	−33620.2			−1.67014
$741$	5623.45	+	1783.65i	0.278789	+	0.0884262i
$742$	6181.99	−	23847.4i	0.305860	−	1.17987i
$743$	2159.74	+	3740.79i	0.106640	+	0.184705i	0.914407	−	0.404796i	$-0.132658\pi$
$743$	2159.74	+	3740.79i	0.106640	+	0.184705i	−0.807767	+	0.589502i	$0.799324\pi$
$744$	−10675.6	−	48547.1i	−0.526055	−	2.39224i
$745$	−1856.89	−	3216.23i	−0.0913171	−	0.158166i
$746$	2238.21	−	3876.69i	0.109848	−	0.190262i
$747$	307.650	−	3383.13i	0.0150687	−	0.165706i
$748$	75441.3			3.68771
$749$	−13677.4	−	13456.2i	−0.667237	−	0.656447i
$750$	7138.45	+	32462.1i	0.347546	+	1.58046i
$751$	4532.84	−	7851.11i	0.220247	−	0.381480i	−0.734636	−	0.678462i	$-0.762647\pi$
$751$	4532.84	−	7851.11i	0.220247	−	0.381480i	0.954883	+	0.296982i	$0.0959802\pi$
$752$	18416.2			0.893045
$753$	4114.11	+	18708.9i	0.199106	+	0.905433i
$754$	10011.0			0.483528
$755$	7885.85			0.380126
$756$	32499.4	+	24782.0i	1.56348	+	1.19221i
$757$	−21632.0			−1.03861			−0.519305	−	0.854589i	$-0.673809\pi$
$757$	−21632.0			−1.03861			−0.519305	+	0.854589i	$0.673809\pi$
$758$	−30146.4			−1.44455
$759$	−652.965	−	2969.36i	−0.0312268	−	0.142004i
$760$	19693.1			0.939924
$761$	−9534.67	+	16514.5i	−0.454181	+	0.786664i	−0.998641	−	0.0521229i	$-0.983401\pi$
$761$	−9534.67	+	16514.5i	−0.454181	+	0.786664i	0.544460	+	0.838787i	$0.316735\pi$
$762$	6237.15	+	28363.4i	0.296520	+	1.34842i
$763$	−196.929	+	759.666i	−0.00934379	+	0.0360443i
$764$	−12564.5			−0.594985
$765$	−11835.5	−	8347.76i	−0.559362	−	0.394528i
$766$	−10088.3	+	17473.4i	−0.475855	+	0.824205i
$767$	−2361.39	−	4090.05i	−0.111167	−	0.192546i
$768$	8956.97	+	40731.8i	0.420842	+	1.91378i
$769$	−13418.5	−	23241.4i	−0.629235	−	1.08987i	−0.987706	−	0.156326i	$-0.950035\pi$
$769$	−13418.5	−	23241.4i	−0.629235	−	1.08987i	0.358471	−	0.933541i	$-0.383298\pi$
$770$	29988.9	−	8298.10i	1.40354	−	0.388367i
$771$	7883.95	+	2500.63i	0.368267	+	0.116807i
$772$	−10973.3			−0.511576
$773$	−12766.9	+	22113.0i	−0.594043	+	1.02891i	0.399639	+	0.916673i	$0.369136\pi$
$773$	−12766.9	+	22113.0i	−0.594043	+	1.02891i	−0.993681

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-4.87128 q^{2} +(-1.11598 - 5.07490i) q^{3} +15.7294 q^{4} +(3.10540 - 5.37871i) q^{5} +(5.43624 + 24.7213i) q^{6} +(17.8495 - 4.93906i) q^{7} -37.6522 q^{8} +(-24.5092 + 11.3269i) q^{9} +O(q^{10})\)	\(q-4.87128 q^{2} +(-1.11598 - 5.07490i) q^{3} +15.7294 q^{4} +(3.10540 - 5.37871i) q^{5} +(5.43624 + 24.7213i) q^{6} +(17.8495 - 4.93906i) q^{7} -37.6522 q^{8} +(-24.5092 + 11.3269i) q^{9} +(-15.1273 + 26.2012i) q^{10} +(-27.7660 - 48.0921i) q^{11} +(-17.5536 - 79.8252i) q^{12} +(-6.74110 - 11.6759i) q^{13} +(-86.9501 + 24.0596i) q^{14} +(-30.7619 - 9.75707i) q^{15} +57.5792 q^{16} +(-43.1841 + 74.7970i) q^{17} +(119.391 - 55.1767i) q^{18} +(-42.1062 - 72.9300i) q^{19} +(48.8461 - 84.6039i) q^{20} +(-44.9849 - 85.0727i) q^{21} +(135.256 + 234.270i) q^{22} +(-5.26820 + 9.12479i) q^{23} +(42.0189 + 191.081i) q^{24} +(43.2130 + 74.8471i) q^{25} +(32.8378 + 56.8767i) q^{26} +(84.8347 + 111.741i) q^{27} +(280.763 - 77.6886i) q^{28} +(76.2157 - 132.009i) q^{29} +(149.850 + 47.5295i) q^{30} -254.065 q^{31} +20.7328 q^{32} +(-213.076 + 194.579i) q^{33} +(210.362 - 364.358i) q^{34} +(28.8641 - 111.345i) q^{35} +(-385.515 + 178.166i) q^{36} +(-172.072 - 298.038i) q^{37} +(205.111 + 355.263i) q^{38} +(-51.7312 + 47.2404i) q^{39} +(-116.925 + 202.520i) q^{40} +(-57.9241 - 100.328i) q^{41} +(219.134 + 414.413i) q^{42} +(46.7504 - 80.9741i) q^{43} +(-436.743 - 756.461i) q^{44} +(-15.1866 + 167.002i) q^{45} +(25.6629 - 44.4494i) q^{46} +319.841 q^{47} +(-64.2570 - 292.209i) q^{48} +(294.211 - 176.320i) q^{49} +(-210.503 - 364.602i) q^{50} +(427.780 + 135.683i) q^{51} +(-106.034 - 183.655i) q^{52} +(-136.535 + 236.486i) q^{53} +(-413.254 - 544.323i) q^{54} -344.898 q^{55} +(-672.074 + 185.967i) q^{56} +(-323.123 + 295.073i) q^{57} +(-371.268 + 643.055i) q^{58} +350.298 q^{59} +(-483.867 - 153.473i) q^{60} -291.131 q^{61} +1237.63 q^{62} +(-381.533 + 323.233i) q^{63} -561.629 q^{64} -83.7352 q^{65} +(1037.96 - 947.851i) q^{66} +833.381 q^{67} +(-679.260 + 1176.51i) q^{68} +(52.1865 + 16.5525i) q^{69} +(-140.605 + 542.394i) q^{70} +771.625 q^{71} +(922.825 - 426.484i) q^{72} +(-140.112 + 242.682i) q^{73} +(838.212 + 1451.83i) q^{74} +(331.617 - 302.829i) q^{75} +(-662.305 - 1147.15i) q^{76} +(-733.140 - 721.283i) q^{77} +(251.998 - 230.122i) q^{78} +345.885 q^{79} +(178.806 - 309.702i) q^{80} +(472.401 - 555.228i) q^{81} +(282.165 + 488.724i) q^{82} +(-62.9091 + 108.962i) q^{83} +(-707.586 - 1338.14i) q^{84} +(268.207 + 464.549i) q^{85} +(-227.735 + 394.448i) q^{86} +(-754.989 - 239.467i) q^{87} +(1045.45 + 1810.77i) q^{88} +(-163.146 - 282.578i) q^{89} +(73.9782 - 813.516i) q^{90} +(-177.994 - 175.115i) q^{91} +(-82.8657 + 143.528i) q^{92} +(283.531 + 1289.36i) q^{93} -1558.04 q^{94} -523.025 q^{95} +(-23.1373 - 105.217i) q^{96} +(124.352 - 215.384i) q^{97} +(-1433.19 + 858.904i) q^{98} +(1225.26 + 864.196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) \)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

Properties

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