LMFDB - Embedded newform 63.4.o.a.20.11

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.11
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.11

$q$-expansion

$f(q)$	$=$	$q+(-0.0847887 - 0.0489528i) q^{2} +(-5.17293 - 0.490712i) q^{3} +(-3.99521 - 6.91990i) q^{4} +(9.06347 + 15.6984i) q^{5} +(0.414584 + 0.294836i) q^{6} +(12.7516 + 13.4312i) q^{7} +1.56555i q^{8} +(26.5184 + 5.07683i) q^{9} +O(q^{10})$	\(q+(-0.0847887 - 0.0489528i) q^{2} +(-5.17293 - 0.490712i) q^{3} +(-3.99521 - 6.91990i) q^{4} +(9.06347 + 15.6984i) q^{5} +(0.414584 + 0.294836i) q^{6} +(12.7516 + 13.4312i) q^{7} +1.56555i q^{8} +(26.5184 + 5.07683i) q^{9} -1.77473i q^{10} +(32.0537 + 18.5062i) q^{11} +(17.2713 + 37.7567i) q^{12} +(-16.3673 + 9.44964i) q^{13} +(-0.423698 - 1.76304i) q^{14} +(-39.1813 - 85.6542i) q^{15} +(-31.8850 + 55.2265i) q^{16} -62.5187 q^{17} +(-1.99994 - 1.72861i) q^{18} +70.2680i q^{19} +(72.4209 - 125.437i) q^{20} +(-59.3723 - 75.7359i) q^{21} +(-1.81186 - 3.13823i) q^{22} +(140.692 - 81.2288i) q^{23} +(0.768234 - 8.09848i) q^{24} +(-101.793 + 176.311i) q^{25} +1.85034 q^{26} +(-134.687 - 39.2750i) q^{27} +(41.9972 - 141.900i) q^{28} +(82.5015 + 47.6323i) q^{29} +(-0.870879 + 9.18054i) q^{30} +(110.611 - 63.8612i) q^{31} +(16.2534 - 9.38392i) q^{32} +(-156.730 - 111.460i) q^{33} +(5.30088 + 3.06046i) q^{34} +(-95.2742 + 321.913i) q^{35} +(-70.8153 - 203.788i) q^{36} -378.832 q^{37} +(3.43981 - 5.95793i) q^{38} +(89.3037 - 40.8507i) q^{39} +(-24.5766 + 14.1893i) q^{40} +(99.1937 + 171.809i) q^{41} +(1.32662 + 9.32799i) q^{42} +(160.692 - 278.327i) q^{43} -295.744i q^{44} +(160.651 + 462.310i) q^{45} -15.9055 q^{46} +(79.3885 - 137.505i) q^{47} +(192.039 - 270.036i) q^{48} +(-17.7932 + 342.538i) q^{49} +(17.2618 - 9.96610i) q^{50} +(323.405 + 30.6786i) q^{51} +(130.781 + 75.5066i) q^{52} +191.780i q^{53} +(9.49728 + 9.92336i) q^{54} +670.922i q^{55} +(-21.0272 + 19.9633i) q^{56} +(34.4813 - 363.491i) q^{57} +(-4.66346 - 8.07736i) q^{58} +(-106.918 - 185.187i) q^{59} +(-436.181 + 613.337i) q^{60} +(-190.929 - 110.233i) q^{61} -12.5047 q^{62} +(269.964 + 420.911i) q^{63} +508.323 q^{64} +(-296.688 - 171.293i) q^{65} +(7.83266 + 17.1230i) q^{66} +(68.2947 + 118.290i) q^{67} +(249.775 + 432.623i) q^{68} +(-767.652 + 351.151i) q^{69} +(23.8367 - 22.6306i) q^{70} -458.924i q^{71} +(-7.94804 + 41.5159i) q^{72} -967.869i q^{73} +(32.1207 + 18.5449i) q^{74} +(613.086 - 862.091i) q^{75} +(486.248 - 280.735i) q^{76} +(160.176 + 666.503i) q^{77} +(-9.57170 - 0.907986i) q^{78} +(298.318 - 516.702i) q^{79} -1155.96 q^{80} +(677.452 + 269.259i) q^{81} -19.4232i q^{82} +(180.715 - 313.007i) q^{83} +(-286.880 + 713.431i) q^{84} +(-566.636 - 981.443i) q^{85} +(-27.2498 + 15.7327i) q^{86} +(-403.401 - 286.883i) q^{87} +(-28.9724 + 50.1817i) q^{88} +35.4987 q^{89} +(9.01000 - 47.0630i) q^{90} +(-335.629 - 99.3336i) q^{91} +(-1124.19 - 649.052i) q^{92} +(-603.519 + 276.071i) q^{93} +(-13.4625 + 7.77258i) q^{94} +(-1103.09 + 636.872i) q^{95} +(-88.6826 + 40.5666i) q^{96} +(-1151.63 - 664.894i) q^{97} +(18.2769 - 28.1723i) q^{98} +(756.060 + 653.486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 6q^{2} + 78q^{4} + 5q^{7} + O(q^{10}) $	$ 44q - 6q^{2} + 78q^{4} + 5q^{7} - 18q^{11} + 204q^{14} + 66q^{15} - 242q^{16} - 210q^{18} - 57q^{21} - 34q^{22} - 102q^{23} - 352q^{25} + 300q^{28} + 246q^{29} - 144q^{30} + 1068q^{32} - 1818q^{36} + 328q^{37} - 798q^{39} - 1158q^{42} - 170q^{43} + 968q^{46} - 79q^{49} + 288q^{50} - 204q^{51} + 1212q^{56} + 324q^{57} - 538q^{58} + 5316q^{60} + 783q^{63} - 808q^{64} + 4350q^{65} - 590q^{67} + 384q^{70} + 4284q^{72} - 5304q^{74} - 2787q^{77} + 612q^{78} - 302q^{79} - 3720q^{81} + 7050q^{84} - 612q^{85} - 13692q^{86} + 1294q^{88} + 210q^{91} - 10194q^{92} - 4266q^{93} + 6336q^{95} + 1014q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.0847887	−	0.0489528i	−0.0299773	−	0.0173074i	0.484936	−	0.874549i	$-0.338843\pi$
$2$	−0.0847887	−	0.0489528i	−0.0299773	−	0.0173074i	−0.514914	+	0.857242i	$0.672176\pi$
$3$	−5.17293	−	0.490712i	−0.995531	−	0.0944375i
$3$	−5.17293	−	0.490712i	−0.995531	−	0.0944375i
$4$	−3.99521	−	6.91990i	−0.499401	−	0.864988i
$5$	9.06347	+	15.6984i	0.810661	+	1.40411i	0.912402	+	0.409296i	$0.134226\pi$
$5$	9.06347	+	15.6984i	0.810661	+	1.40411i	−0.101740	+	0.994811i	$0.532441\pi$
$6$	0.414584	+	0.294836i	0.0282089	+	0.0200611i
$7$	12.7516	+	13.4312i	0.688522	+	0.725216i
$7$	12.7516	+	13.4312i	0.688522	+	0.725216i
$8$			1.56555i			0.0691882i
$9$	26.5184	+	5.07683i	0.982163	+	0.188031i
$10$		−	1.77473i		−	0.0561218i
$11$	32.0537	+	18.5062i	0.878595	+	0.507257i	0.870195	−	0.492707i	$-0.163993\pi$
$11$	32.0537	+	18.5062i	0.878595	+	0.507257i	0.00840042	+	0.999965i	$0.497326\pi$
$12$	17.2713	+	37.7567i	0.415482	+	0.908284i
$13$	−16.3673	+	9.44964i	−0.349189	+	0.201605i	−0.664328	−	0.747441i	$-0.731282\pi$
$13$	−16.3673	+	9.44964i	−0.349189	+	0.201605i	0.315139	+	0.949046i	$0.397949\pi$
$14$	−0.423698	−	1.76304i	−0.00808843	−	0.0336566i
$15$	−39.1813	−	85.6542i	−0.674438	−	1.47439i
$16$	−31.8850	+	55.2265i	−0.498203	+	0.862914i
$17$	−62.5187			−0.891941			−0.445971	−	0.895048i	$-0.647141\pi$
$17$	−62.5187			−0.891941			−0.445971	+	0.895048i	$0.647141\pi$
$18$	−1.99994	−	1.72861i	−0.0261883	−	0.0226354i
$19$			70.2680i			0.848452i	0.905556	+	0.424226i	$0.139454\pi$
$19$			70.2680i			0.848452i	−0.905556	+	0.424226i	$0.860546\pi$
$20$	72.4209	−	125.437i	0.809690	−	1.40242i
$21$	−59.3723	−	75.7359i	−0.616957	−	0.786997i
$22$	−1.81186	−	3.13823i	−0.0175586	−	0.0304124i
$23$	140.692	−	81.2288i	1.27550	−	0.736408i	0.299479	−	0.954103i	$-0.403187\pi$
$23$	140.692	−	81.2288i	1.27550	−	0.736408i	0.976017	+	0.217695i	$0.0698539\pi$
$24$	0.768234	−	8.09848i	0.00653396	−	0.0688790i
$25$	−101.793	+	176.311i	−0.814344	+	1.41048i
$26$	1.85034			0.0139570
$27$	−134.687	−	39.2750i	−0.960016	−	0.279944i
$28$	41.9972	−	141.900i	0.283454	−	0.957736i
$29$	82.5015	+	47.6323i	0.528281	+	0.305003i	0.740316	−	0.672259i	$-0.234676\pi$
$29$	82.5015	+	47.6323i	0.528281	+	0.305003i	−0.212035	+	0.977262i	$0.568009\pi$
$30$	−0.870879	+	9.18054i	−0.00530000	+	0.0558710i
$31$	110.611	−	63.8612i	0.640848	−	0.369994i	−0.144093	−	0.989564i	$-0.546027\pi$
$31$	110.611	−	63.8612i	0.640848	−	0.369994i	0.784941	+	0.619570i	$0.212693\pi$
$32$	16.2534	−	9.38392i	0.0897883	−	0.0518393i
$33$	−156.730	−	111.460i	−0.826765	−	0.587963i
$34$	5.30088	+	3.06046i	0.0267380	+	0.0154372i
$35$	−95.2742	+	321.913i	−0.460122	+	1.55466i
$36$	−70.8153	−	203.788i	−0.327849	−	0.943462i
$37$	−378.832			−1.68323			−0.841617	−	0.540075i	$-0.818396\pi$
$37$	−378.832			−1.68323			−0.841617	+	0.540075i	$0.818396\pi$
$38$	3.43981	−	5.95793i	0.0146845	−	0.0254343i
$39$	89.3037	−	40.8507i	0.366668	−	0.167727i
$40$	−24.5766	+	14.1893i	−0.0971476	+	0.0560882i
$41$	99.1937	+	171.809i	0.377840	+	0.654439i	0.990748	−	0.135716i	$-0.0433334\pi$
$41$	99.1937	+	171.809i	0.377840	+	0.654439i	−0.612907	+	0.790155i	$0.710000\pi$
$42$	1.32662	+	9.32799i	0.00487384	+	0.0342700i
$43$	160.692	−	278.327i	0.569892	−	0.987081i	−0.426685	−	0.904401i	$-0.640319\pi$
$43$	160.692	−	278.327i	0.569892	−	0.987081i	0.996576	−	0.0826806i	$-0.0263481\pi$
$44$		−	295.744i		−	1.01330i
$45$	160.651	+	462.310i	0.532186	+	1.53149i
$46$	−15.9055			−0.0509813
$47$	79.3885	−	137.505i	0.246383	−	0.426748i	−0.716136	−	0.697960i	$-0.754091\pi$
$47$	79.3885	−	137.505i	0.246383	−	0.426748i	0.962520	+	0.271212i	$0.0874245\pi$
$48$	192.039	−	270.036i	0.577468	−	0.812008i
$49$	−17.7932	+	342.538i	−0.0518754	+	0.998654i
$50$	17.2618	−	9.96610i	0.0488237	−	0.0281884i
$51$	323.405	+	30.6786i	0.887955	+	0.0842327i
$52$	130.781	+	75.5066i	0.348771	+	0.201363i
$53$			191.780i			0.497039i	0.968627	+	0.248519i	$0.0799440\pi$
$53$			191.780i			0.497039i	−0.968627	+	0.248519i	$0.920056\pi$
$54$	9.49728	+	9.92336i	0.0239336	+	0.0250074i
$55$			670.922i			1.64486i
$56$	−21.0272	+	19.9633i	−0.0501764	+	0.0476376i
$57$	34.4813	−	363.491i	0.0801257	−	0.844660i
$58$	−4.66346	−	8.07736i	−0.0105576	−	0.0182864i
$59$	−106.918	−	185.187i	−0.235924	−	0.408632i	0.723617	−	0.690202i	$-0.242478\pi$
$59$	−106.918	−	185.187i	−0.235924	−	0.408632i	−0.959541	+	0.281570i	$0.909145\pi$
$60$	−436.181	+	613.337i	−0.938513	+	1.31969i
$61$	−190.929	−	110.233i	−0.400754	−	0.231375i	0.286055	−	0.958213i	$-0.407656\pi$
$61$	−190.929	−	110.233i	−0.400754	−	0.231375i	−0.686809	+	0.726838i	$0.740989\pi$
$62$	−12.5047			−0.0256145
$63$	269.964	+	420.911i	0.539878	+	0.841743i
$64$	508.323			0.992818
$65$	−296.688	−	171.293i	−0.566149	−	0.326866i
$66$	7.83266	+	17.1230i	0.0146081	+	0.0319347i
$67$	68.2947	+	118.290i	0.124530	+	0.215693i	0.921549	−	0.388262i	$-0.126924\pi$
$67$	68.2947	+	118.290i	0.124530	+	0.215693i	−0.797019	+	0.603954i	$0.793591\pi$
$68$	249.775	+	432.623i	0.445436	+	0.771518i
$69$	−767.652	+	351.151i	−1.33934	+	0.612662i
$70$	23.8367	−	22.6306i	0.0407004	−	0.0386411i
$71$		−	458.924i		−	0.767102i	−0.923520	−	0.383551i	$-0.874701\pi$
$71$		−	458.924i		−	0.767102i	0.923520	−	0.383551i	$-0.125299\pi$
$72$	−7.94804	+	41.5159i	−0.0130095	+	0.0679541i
$73$		−	967.869i		−	1.55179i	−0.630863	−	0.775894i	$-0.717299\pi$
$73$		−	967.869i		−	1.55179i	0.630863	−	0.775894i	$-0.282701\pi$
$74$	32.1207	+	18.5449i	0.0504588	+	0.0291324i
$75$	613.086	−	862.091i	0.943907	−	1.32728i
$76$	486.248	−	280.735i	0.733900	−	0.423718i
$77$	160.176	+	666.503i	0.237061	+	0.986429i
$78$	−9.57170	−	0.907986i	−0.0138946	−	0.00131807i
$79$	298.318	−	516.702i	0.424853	−	0.735868i	−0.571553	−	0.820565i	$-0.693659\pi$
$79$	298.318	−	516.702i	0.424853	−	0.735868i	0.996407	+	0.0846971i	$0.0269923\pi$
$80$	−1155.96			−1.61550
$81$	677.452	+	269.259i	0.929289	+	0.369354i
$82$		−	19.4232i		−	0.0261578i
$83$	180.715	−	313.007i	0.238988	−	0.413940i	−0.721436	−	0.692481i	$-0.756518\pi$
$83$	180.715	−	313.007i	0.238988	−	0.413940i	0.960424	+	0.278541i	$0.0898509\pi$
$84$	−286.880	+	713.431i	−0.372634	+	0.926687i
$85$	−566.636	−	981.443i	−0.723063	−	1.25238i
$86$	−27.2498	+	15.7327i	−0.0341676	+	0.0197267i
$87$	−403.401	−	286.883i	−0.497116	−	0.353530i
$88$	−28.9724	+	50.1817i	−0.0350962	+	0.0607884i
$89$	35.4987			0.0422792			0.0211396	−	0.999777i	$-0.493271\pi$
$89$	35.4987			0.0422792			0.0211396	+	0.999777i	$0.493271\pi$
$90$	9.01000	−	47.0630i	0.0105526	−	0.0551208i
$91$	−335.629	−	99.3336i	−0.386631	−	0.114428i
$92$	−1124.19	−	649.052i	−1.27397	−	0.735525i
$93$	−603.519	+	276.071i	−0.672925	+	0.307820i
$94$	−13.4625	+	7.77258i	−0.0147718	+	0.00852851i
$95$	−1103.09	+	636.872i	−1.19132	+	0.687807i
$96$	−88.6826	+	40.5666i	−0.0942826	+	0.0431283i
$97$	−1151.63	−	664.894i	−1.20547	−	0.695977i	−0.243701	−	0.969850i	$-0.578362\pi$
$97$	−1151.63	−	664.894i	−1.20547	−	0.695977i	−0.961766	+	0.273874i	$0.911695\pi$
$98$	18.2769	−	28.1723i	0.0188392	−	0.0290391i
$99$	756.060	+	653.486i	0.767544	+	0.663413i
$100$	1626.74			1.62674
$101$	457.491	−	792.398i	0.450714	−	0.780659i	−0.547717	−	0.836664i	$-0.684503\pi$
$101$	457.491	−	792.398i	0.450714	−	0.780659i	0.998430	+	0.0560049i	$0.0178362\pi$
$102$	−25.9193	−	18.4328i	−0.0251607	−	0.0178933i
$103$	−721.873	+	416.774i	−0.690566	+	0.398698i	−0.803824	−	0.594867i	$-0.797205\pi$
$103$	−721.873	+	416.774i	−0.690566	+	0.398698i	0.113258	+	0.993566i	$0.463871\pi$
$104$	−14.7939	−	25.6238i	−0.0139487	−	0.0241598i
$105$	650.813	−	1618.48i	0.604884	−	1.50426i
$106$	9.38818	−	16.2608i	0.00860246	−	0.0148999i
$107$			1686.33i			1.52358i	0.647822	+	0.761792i	$0.275680\pi$
$107$			1686.33i			1.52358i	−0.647822	+	0.761792i	$0.724320\pi$
$108$	266.322	+	1088.93i	0.237285	+	0.970207i
$109$	641.258			0.563499			0.281750	−	0.959488i	$-0.409085\pi$
$109$	641.258			0.563499			0.281750	+	0.959488i	$0.409085\pi$
$110$	32.8435	−	56.8866i	0.0284682	−	0.0493084i
$111$	1959.67	+	185.897i	1.67571	+	0.158960i
$112$	−1148.34	+	275.973i	−0.968822	+	0.232830i
$113$	1245.30	−	718.974i	1.03671	−	0.598543i	0.117809	−	0.993036i	$-0.462413\pi$
$113$	1245.30	−	718.974i	1.03671	−	0.598543i	0.918899	+	0.394493i	$0.129080\pi$
$114$	−20.7175	+	29.1320i	−0.0170208	+	0.0239339i
$115$	2550.32	+	1472.43i	2.06799	+	1.19395i
$116$		−	761.203i		−	0.609275i
$117$	−482.008	+	167.496i	−0.380869	+	0.132350i
$118$			20.9357i			0.0163329i
$119$	−797.213	−	839.700i	−0.614121	−	0.646850i
$120$	134.096	−	61.3403i	0.102010	−	0.0466632i
$121$	19.4592	+	33.7044i	0.0146200	+	0.0253226i
$122$	10.7924	+	18.6930i	0.00800902	+	0.0138720i
$123$	−428.814	−	937.429i	−0.314348	−	0.687196i
$124$	−883.826	−	510.277i	−0.640080	−	0.369550i
$125$	−1424.52			−1.01931
$126$	−2.28515	−	48.9040i	−0.00161569	−	0.0345771i
$127$	−1845.03			−1.28914			−0.644568	−	0.764547i	$-0.722963\pi$
$127$	−1845.03			−1.28914			−0.644568	+	0.764547i	$0.722963\pi$
$128$	−173.127	−	99.9552i	−0.119550	−	0.0690224i
$129$	−967.828	+	1360.91i	−0.660562	+	0.928850i
$130$	16.7705	+	29.0474i	0.0113144	+	0.0195971i
$131$	1099.22	+	1903.91i	0.733125	+	1.26981i	0.955541	+	0.294858i	$0.0952724\pi$
$131$	1099.22	+	1903.91i	0.733125	+	1.26981i	−0.222416	+	0.974952i	$0.571394\pi$
$132$	−145.125	+	1529.87i	−0.0956934	+	1.00877i
$133$	−943.782	+	896.030i	−0.615311	+	0.584178i
$134$		−	13.3729i		−	0.00862119i
$135$	−604.174	−	2470.33i	−0.385178	−	1.57491i
$136$		−	97.8761i		−	0.0617118i
$137$	1869.64	+	1079.44i	1.16594	+	0.673156i	0.952720	−	0.303848i	$-0.0982716\pi$
$137$	1869.64	+	1079.44i	1.16594	+	0.673156i	0.213220	+	0.977004i	$0.431605\pi$
$138$	82.2780	+	7.80501i	0.0507534	+	0.00481454i
$139$	2521.54	−	1455.81i	1.53866	−	0.888348i	0.539746	−	0.841828i	$-0.318520\pi$
$139$	2521.54	−	1455.81i	1.53866	−	0.888348i	0.998917	−	0.0465196i	$-0.0148130\pi$
$140$	2608.24	−	626.820i	1.57455	−	0.378400i
$141$	−478.147	+	672.347i	−0.285583	+	0.401573i
$142$	−22.4656	+	38.9115i	−0.0132766	+	0.0229957i
$143$	−699.508			−0.409062
$144$	−1125.92	+	1302.64i	−0.651571	+	0.753844i
$145$			1726.85i			0.989017i
$146$	−47.3799	+	82.0644i	−0.0268574	+	0.0465185i
$147$	260.131	−	1763.19i	0.145954	−	0.989291i
$148$	1513.51	+	2621.48i	0.840608	+	1.45598i
$149$	−230.641	+	133.161i	−0.126811	+	0.0732144i	−0.562064	−	0.827094i	$-0.689992\pi$
$149$	−230.641	+	133.161i	−0.126811	+	0.0732144i	0.435253	+	0.900308i	$0.356659\pi$
$150$	−94.1845	+	43.0834i	−0.0512675	+	0.0234516i
$151$	467.757	−	810.180i	0.252090	−	0.436632i	−0.712011	−	0.702168i	$-0.752215\pi$
$151$	467.757	−	810.180i	0.252090	−	0.436632i	0.964101	+	0.265536i	$0.0855488\pi$
$152$	−110.008			−0.0587029
$153$	−1657.90	−	317.397i	−0.876032	−	0.167713i
$154$	19.0461	−	64.3529i	0.00996607	−	0.0336734i
$155$	2005.04	+	1157.61i	1.03902	+	0.599879i
$156$	−639.470	−	454.766i	−0.328196	−	0.233400i
$157$	872.747	−	503.881i	0.443648	−	0.256141i	−0.261496	−	0.965205i	$-0.584216\pi$
$157$	872.747	−	503.881i	0.443648	−	0.256141i	0.705144	+	0.709064i	$0.250882\pi$
$158$	−50.5880	+	29.2070i	−0.0254719	+	0.0147062i
$159$	94.1088	−	992.066i	0.0469391	−	0.494817i
$160$	294.625	+	170.102i	0.145576	+	0.0840483i
$161$	2885.05	+	853.868i	1.41226	+	0.417976i
$162$	−44.2592	−	55.9932i	−0.0214650	−	0.0271558i
$163$	−1801.27			−0.865561			−0.432780	−	0.901499i	$-0.642467\pi$
$163$	−1801.27			−0.865561			−0.432780	+	0.901499i	$0.642467\pi$
$164$	792.599	−	1372.82i	0.377388	−	0.653655i
$165$	329.229	−	3470.63i	0.155336	−	1.63750i
$166$	−30.6451	+	17.6930i	−0.0143285	+	0.00827254i
$167$	−817.899	−	1416.64i	−0.378987	−	0.656425i	0.611928	−	0.790914i	$-0.290394\pi$
$167$	−817.899	−	1416.64i	−0.378987	−	0.656425i	−0.990915	+	0.134488i	$0.957061\pi$
$168$	118.568	−	92.9503i	0.0544509	−	0.0426862i
$169$	−919.908	+	1593.33i	−0.418711	+	0.725229i
$170$			110.954i			0.0500574i
$171$	−356.739	+	1863.40i	−0.159535	+	0.833318i
$172$	−2568.00			−1.13842
$173$	−399.759	+	692.402i	−0.175683	+	0.304291i	−0.940397	−	0.340078i	$-0.889547\pi$
$173$	−399.759	+	692.402i	−0.175683	+	0.304291i	0.764715	+	0.644369i	$0.222880\pi$
$174$	20.1601	+	44.0720i	0.00878353	+	0.0192017i
$175$	−3666.08	+	881.043i	−1.58360	+	0.380575i
$176$	−2044.06	+	1180.14i	−0.875439	+	0.505435i
$177$	462.205	+	1010.42i	0.196279	+	0.429086i
$178$	−3.00989	−	1.73776i	−0.00126742	−	0.000731745i
$179$		−	2940.19i		−	1.22771i	−0.789418	−	0.613856i	$-0.789618\pi$
$179$		−	2940.19i		−	1.22771i	0.789418	−	0.613856i	$-0.210382\pi$
$180$	2557.31	−	2958.71i	1.05895	−	1.22516i
$181$		−	376.924i		−	0.154788i	−0.997001	−	0.0773938i	$-0.975340\pi$
$181$		−	376.924i		−	0.154788i	0.997001	−	0.0773938i	$-0.0246599\pi$
$182$	23.5949	+	24.8523i	0.00960971	+	0.0101218i
$183$	933.571	+	663.919i	0.377112	+	0.268188i
$184$	127.168	+	220.261i	0.0509507	+	0.0882492i
$185$	−3433.53	−	5947.06i	−1.36453	−	2.36344i
$186$	64.6861	+	6.13621i	0.0255001	+	0.00241897i
$187$	−2003.95	−	1156.98i	−0.783656	−	0.452444i
$188$	−1268.69			−0.492176
$189$	−1189.96	−	2309.82i	−0.457973	−	0.888966i
$190$	124.707			0.0476167
$191$	1586.09	+	915.732i	0.600868	+	0.346911i	0.769383	−	0.638788i	$-0.220564\pi$
$191$	1586.09	+	915.732i	0.600868	+	0.346911i	−0.168515	+	0.985699i	$0.553897\pi$
$192$	−2629.52	−	249.440i	−0.988381	−	0.0937592i
$193$	190.008	+	329.104i	0.0708657	+	0.122743i	0.899281	−	0.437371i	$-0.144090\pi$
$193$	190.008	+	329.104i	0.0708657	+	0.122743i	−0.828415	+	0.560114i	$0.810757\pi$
$194$	65.0968	+	112.751i	0.0240911	+	0.0417270i
$195$	1450.69	+	1031.68i	0.532750	+	0.378871i
$196$	2441.42	−	1245.38i	0.889730	−	0.453857i
$197$			3579.56i			1.29458i	0.762243	+	0.647291i	$0.224098\pi$
$197$			3579.56i			1.29458i	−0.762243	+	0.647291i	$0.775902\pi$
$198$	−32.1153	−	92.4195i	−0.0115270	−	0.0331715i
$199$		−	881.304i		−	0.313939i	−0.987603	−	0.156970i	$-0.949827\pi$
$199$		−	881.304i		−	0.313939i	0.987603	−	0.156970i	$-0.0501725\pi$
$200$	−276.023	−	159.362i	−0.0975889	−	0.0563430i
$201$	−295.237	−	645.418i	−0.103604	−	0.226489i
$202$	−77.5802	+	44.7909i	−0.0270224	+	0.0156014i
$203$	412.269	+	1715.48i	0.142540	+	0.593119i
$204$	−1079.78	−	2360.50i	−0.370585	−	0.810136i
$205$	−1798.08	+	3114.36i	−0.612601	+	1.06106i
$206$	81.6089			0.0276018
$207$	4143.32	−	1439.79i	1.39121	−	0.483440i
$208$		−	1205.21i		−	0.401760i
$209$	−1300.39	+	2252.35i	−0.430383	+	0.745446i
$210$	−134.411	+	105.370i	−0.0441677	+	0.0346248i
$211$	−418.581	−	725.004i	−0.136570	−	0.236547i	0.789626	−	0.613588i	$-0.210275\pi$
$211$	−418.581	−	725.004i	−0.136570	−	0.236547i	−0.926196	+	0.377042i	$0.876941\pi$
$212$	1327.10	−	766.202i	0.429932	−	0.248222i
$213$	−225.199	+	2373.98i	−0.0724432	+	0.763674i
$214$	82.5504	−	142.981i	0.0263693	−	0.0456730i
$215$	5825.72			1.84796
$216$	61.4870	−	210.859i	0.0193688	−	0.0664218i
$217$	2268.20	+	671.301i	0.709563	+	0.210004i
$218$	−54.3715	−	31.3914i	−0.0168922	−	0.00975272i
$219$	−474.945	+	5006.72i	−0.146547	+	1.54485i
$220$	4642.71	−	2680.47i	1.42278	−	0.821442i
$221$	1023.26	−	590.779i	0.311456	−	0.179819i
$222$	−157.058	−	111.693i	−0.0474821	−	0.0337674i
$223$	981.825	+	566.857i	0.294834	+	0.170222i	0.640120	−	0.768275i	$-0.278885\pi$
$223$	981.825	+	566.857i	0.294834	+	0.170222i	−0.345286	+	0.938497i	$0.612218\pi$
$224$	333.294	+	98.6427i	0.0994159	+	0.0294234i
$225$	−3594.49	+	4158.69i	−1.06503	+	1.23220i
$226$	−140.783			−0.0414370
$227$	−1752.96	+	3036.21i	−0.512545	+	0.887754i	0.487349	+	0.873207i	$0.337964\pi$
$227$	−1752.96	+	3036.21i	−0.512545	+	0.887754i	−0.999894	+	0.0145471i	$0.995369\pi$
$228$	−2653.09	+	1213.62i	−0.770635	+	0.352516i
$229$	−2721.44	+	1571.23i	−0.785319	+	0.453404i	−0.838312	−	0.545191i	$-0.816457\pi$
$229$	−2721.44	+	1571.23i	−0.785319	+	0.453404i	0.0529930	+	0.998595i	$0.483124\pi$
$230$	−144.159	−	249.691i	−0.0413285	−	0.0715831i
$231$	−501.517	−	3526.37i	−0.142846	−	1.00441i
$232$	−74.5707	+	129.160i	−0.0211026	+	0.0365508i
$233$		−	6882.00i		−	1.93500i	−0.252872	−	0.967500i	$-0.581375\pi$
$233$		−	6882.00i		−	1.93500i	0.252872	−	0.967500i	$-0.418625\pi$
$234$	49.0682	+	9.39389i	0.0137081	+	0.00262435i
$235$	2878.14			0.798933
$236$	−854.317	+	1479.72i	−0.235641	+	0.408142i
$237$	−1796.73	+	2526.48i	−0.492448	+	0.692457i
$238$	26.4890	+	110.223i	0.00721441	+	0.0300197i
$239$	−1036.14	+	598.217i	−0.280429	+	0.161906i	−0.633617	−	0.773646i	$-0.718431\pi$
$239$	−1036.14	+	598.217i	−0.280429	+	0.161906i	0.353189	+	0.935552i	$0.385097\pi$
$240$	5979.68	+	567.241i	1.60828	+	0.152563i
$241$	3790.59	+	2188.50i	1.01317	+	0.584953i	0.912118	−	0.409928i	$-0.134446\pi$
$241$	3790.59	+	2188.50i	1.01317	+	0.584953i	0.101051	+	0.994881i	$0.467780\pi$
$242$		−	3.81033i		−	0.00101214i
$243$	−3372.28	−	1725.29i	−0.890255	−	0.455463i
$244$			1761.62i			0.462196i
$245$	−5538.57	+	2825.26i	−1.44427	+	0.736731i
$246$	−9.53120	+	100.475i	−0.00247027	+	0.0260409i
$247$	−664.008	−	1150.09i	−0.171052	−	0.296270i
$248$	99.9779	+	173.167i	0.0255992	+	0.0443391i
$249$	−1088.42	+	1530.49i	−0.277012	+	0.389520i
$250$	120.783	+	69.7344i	0.0305561	+	0.0176416i
$251$	5787.19			1.45532			0.727658	−	0.685940i	$-0.240609\pi$
$251$	5787.19			1.45532			0.727658	+	0.685940i	$0.240609\pi$
$252$	1834.10	−	3549.75i	0.458482	−	0.887355i
$253$	6012.95			1.49419
$254$	156.438	+	90.3195i	0.0386448	+	0.0223116i
$255$	2449.56	+	5354.99i	0.601559	+	1.31507i
$256$	−2023.51	−	3504.81i	−0.494020	−	0.855667i
$257$	−1074.45	−	1861.00i	−0.260786	−	0.451695i	0.705665	−	0.708546i	$-0.250649\pi$
$257$	−1074.45	−	1861.00i	−0.260786	−	0.451695i	−0.966451	+	0.256851i	$0.917315\pi$
$258$	148.681	−	68.0122i	0.0358779	−	0.0164118i
$259$	−4830.72	−	5088.16i	−1.15894	−	1.22071i
$260$			2737.41i			0.652949i
$261$	1945.99	+	1681.98i	0.461508	+	0.398896i
$262$		−	215.240i		−	0.0507540i
$263$	−1057.21	−	610.380i	−0.247872	−	0.143109i	0.370917	−	0.928666i	$-0.379043\pi$
$263$	−1057.21	−	610.380i	−0.247872	−	0.143109i	−0.618789	+	0.785557i	$0.712377\pi$
$264$	174.497	−	245.369i	0.0406801	−	0.0572024i
$265$	−3010.64	+	1738.20i	−0.697895	+	0.402930i
$266$	123.885	−	29.7724i	0.0285560	−	0.00686265i
$267$	−183.632	−	17.4196i	−0.0420903	−	0.00399275i
$268$	545.703	−	945.185i	0.124381	−	0.215434i
$269$	−4430.56			−1.00422			−0.502112	−	0.864803i	$-0.667444\pi$
$269$	−4430.56			−1.00422			−0.502112	+	0.864803i	$0.667444\pi$
$270$	−69.7024	+	239.032i	−0.0157109	+	0.0538779i
$271$			111.259i			0.0249391i	0.999922	+	0.0124695i	$0.00396928\pi$
$271$			111.259i			0.0249391i	−0.999922	+	0.0124695i	$0.996031\pi$
$272$	1993.41	−	3452.69i	0.444368	−	0.769668i
$273$	1687.44	+	678.542i	0.374097	+	0.150430i
$274$	−105.683	−	183.048i	−0.0233012	−	0.0403588i
$275$	−6525.68	+	3767.60i	−1.43096	+	0.826164i
$276$	5496.86	+	3909.15i	1.19881	+	0.852548i
$277$	1529.33	−	2648.87i	0.331727	−	0.574567i	−0.651124	−	0.758971i	$-0.725702\pi$
$277$	1529.33	−	2648.87i	0.331727	−	0.574567i	0.982850	+	0.184404i	$0.0590356\pi$
$278$	−285.064			−0.0615000
$279$	3257.43	−	1131.94i	0.698987	−	0.242895i
$280$	−503.971	−	149.156i	−0.107564	−	0.0318350i
$281$	−4124.03	−	2381.01i	−0.875513	−	0.505478i	−0.00633670	−	0.999980i	$-0.502017\pi$
$281$	−4124.03	−	2381.01i	−0.875513	−	0.505478i	−0.869176	+	0.494502i	$0.835350\pi$
$282$	73.4547	−	33.6008i	0.0155112	−	0.00709538i
$283$	3567.54	−	2059.72i	0.749358	−	0.432642i	−0.0761041	−	0.997100i	$-0.524248\pi$
$283$	3567.54	−	2059.72i	0.749358	−	0.432642i	0.825462	+	0.564458i	$0.190915\pi$
$284$	−3175.71	+	1833.50i	−0.663534	+	0.383091i
$285$	6018.75	−	2753.19i	1.25095	−	0.572228i
$286$	59.3104	+	34.2429i	0.0122626	+	0.00707980i
$287$	−1042.71	+	3523.12i	−0.214458	+	0.724611i
$288$	478.656	−	166.331i	0.0979342	−	0.0340317i
$289$	−1004.42			−0.204440
$290$	84.5343	−	146.418i	0.0171173	−	0.0296481i
$291$	5631.03	+	4004.57i	1.13435	+	0.806707i
$292$	−6697.56	+	3866.84i	−1.34228	+	0.774964i
$293$	−1401.70	−	2427.81i	−0.279482	−	0.484076i	0.691774	−	0.722114i	$-0.256829\pi$
$293$	−1401.70	−	2427.81i	−0.279482	−	0.484076i	−0.971256	+	0.238037i	$0.923496\pi$
$294$	−108.369	+	136.765i	−0.0214974	+	0.0271302i
$295$	1938.09	−	3356.87i	0.382509	−	0.662524i
$296$		−	593.081i		−	0.116460i
$297$	−3590.37	−	3751.45i	−0.701463	−	0.732933i
$298$	26.0743			0.00506861
$299$	−1535.17	+	2658.99i	−0.296926	+	0.514291i
$300$	−8414.99	−	798.258i	−1.61947	−	0.153625i
$301$	5787.35	−	1390.83i	1.10823	−	0.266333i
$302$	−79.3211	+	45.7960i	−0.0151140	+	0.00872605i
$303$	−2755.41	+	3874.52i	−0.522423	+	0.734606i
$304$	−3880.65	−	2240.50i	−0.732141	−	0.422702i
$305$		−	3996.38i		−	0.750268i
$306$	125.033	+	108.070i	0.0233584	+	0.0201894i
$307$		−	3959.31i		−	0.736058i	−0.929814	−	0.368029i	$-0.880033\pi$
$307$		−	3959.31i		−	0.736058i	0.929814	−	0.368029i	$-0.119967\pi$
$308$	3972.20	−	3771.22i	0.734860	−	0.697679i
$309$	3938.71	−	1801.71i	0.725132	−	0.331701i
$310$	−113.336	−	196.304i	−0.0207647	−	0.0359656i
$311$	−2492.25	−	4316.71i	−0.454413	−	0.787067i	0.544241	−	0.838929i	$-0.316818\pi$
$311$	−2492.25	−	4316.71i	−0.454413	−	0.787067i	−0.998654	+	0.0518618i	$0.983484\pi$
$312$	63.9539	+	139.809i	0.0116047	+	0.0253691i
$313$	699.706	+	403.976i	0.126357	+	0.0729522i	0.561846	−	0.827242i	$-0.310091\pi$
$313$	699.706	+	403.976i	0.126357	+	0.0729522i	−0.435489	+	0.900194i	$0.643425\pi$
$314$	−98.6654			−0.0177325
$315$	−4160.82	+	8052.92i	−0.744239	+	1.44042i
$316$	−4767.37			−0.848689
$317$	2061.65	+	1190.29i	0.365280	+	0.210894i	0.671394	−	0.741100i	$-0.265696\pi$
$317$	2061.65	+	1190.29i	0.365280	+	0.210894i	−0.306115	+	0.951995i	$0.599029\pi$
$318$	−56.5437	+	79.5091i	−0.00997112	+	0.0140209i
$319$	1762.99	+	3053.58i	0.309430	+	0.535949i
$320$	4607.17	+	7979.85i	0.804839	+	1.39402i
$321$	827.500	−	8723.25i	0.143883	−	1.51677i
$322$	−202.821	−	213.630i	−0.0351017	−	0.0369724i
$323$		−	4393.06i		−	0.756769i
$324$	−843.313	−	5763.64i	−0.144601	−	0.988279i
$325$		−	3847.63i		−	0.656702i
$326$	152.727	+	88.1772i	0.0259472	+	0.0149806i
$327$	−3317.19	−	314.673i	−0.560981	−	0.0532155i
$328$	−268.975	+	155.293i	−0.0452794	+	0.0261421i
$329$	2859.19	−	687.127i	0.479125	−	0.115145i
$330$	−197.812	+	278.154i	−0.0329975	+	0.0463995i
$331$	3727.74	−	6456.64i	0.619019	−	1.07217i	−0.370646	−	0.928774i	$-0.620864\pi$
$331$	3727.74	−	6456.64i	0.619019	−	1.07217i	0.989665	−	0.143398i	$-0.0458029\pi$
$332$	−2887.97			−0.477404
$333$	−10046.0	−	1923.27i	−1.65321	−	0.316500i
$334$			160.154i			0.0262372i
$335$	−1237.97	+	2144.23i	−0.201904	+	0.349707i
$336$	6075.71	−	864.082i	0.986480	−	0.140296i
$337$	978.259	+	1694.39i	0.158128	+	0.273886i	0.934194	−	0.356766i	$-0.116121\pi$
$337$	978.259	+	1694.39i	0.158128	+	0.273886i	−0.776066	+	0.630652i	$0.782787\pi$
$338$	155.996	−	90.0641i	0.0251037	−	0.0144936i
$339$	−6794.66	+	3108.12i	−1.08860	+	0.497964i
$340$	−4527.66	+	7842.13i	−0.722196	+	1.25088i
$341$	4727.31			0.750728
$342$	121.466	−	140.531i	0.0192050	−	0.0222195i
$343$	−4827.58	+	4128.93i	−0.759956	+	0.649974i
$344$	435.735	+	251.572i	0.0682944	+	0.0394298i
$345$	−12470.1	−	8868.25i	−1.94599	−	1.38391i
$346$	67.7900	−	39.1386i	0.0105330	−	0.00608122i
$347$	−1191.69	+	688.024i	−0.184361	+	0.106441i	−0.589340	−	0.807885i	$-0.700612\pi$
$347$	−1191.69	+	688.024i	−0.184361	+	0.106441i	0.404979	+	0.914326i	$0.367279\pi$
$348$	−373.531	+	3937.65i	−0.0575384	+	0.606552i
$349$	8098.04	+	4675.41i	1.24206	+	0.717103i	0.969513	−	0.245040i	$-0.0788011\pi$
$349$	8098.04	+	4675.41i	1.24206	+	0.717103i	0.272546	+	0.962143i	$0.412134\pi$
$350$	353.972	+	104.762i	0.0540588	+	0.0159994i
$351$	2575.59	−	629.916i	0.391665	−	0.0957904i
$352$	694.643			0.105184
$353$	338.836	−	586.881i	0.0510890	−	0.0884887i	−0.839350	−	0.543591i	$-0.817064\pi$
$353$	338.836	−	586.881i	0.0510890	−	0.0884887i	0.890439	+	0.455103i	$0.150397\pi$
$354$	10.2734	−	108.299i	0.00154244	−	0.0162599i
$355$	7204.37	−	4159.44i	1.07709	−	0.621860i
$356$	−141.825	−	245.647i	−0.0211143	−	0.0365710i
$357$	3711.88	+	4734.91i	0.550290	+	0.701955i
$358$	−143.931	+	249.295i	−0.0212485	+	0.0368035i
$359$		−	1662.36i		−	0.244390i	−0.992506	−	0.122195i	$-0.961007\pi$
$359$		−	1662.36i		−	0.244390i	0.992506	−	0.122195i	$-0.0389933\pi$
$360$	−723.769	+	251.507i	−0.105961	+	0.0368210i
$361$	1921.41			0.280129
$362$	−18.4515	+	31.9589i	−0.00267897	+	0.00464012i
$363$	−84.1221	−	183.899i	−0.0121633	−	0.0265901i
$364$	653.528	+	2719.38i	0.0941048	+	0.391577i
$365$	15194.0	−	8772.25i	2.17888	−	1.25797i
$366$	−46.6556	−	101.994i	−0.00666319	−	0.0145664i
$367$	−2653.41	−	1531.94i	−0.377402	−	0.217893i	0.299285	−	0.954164i	$-0.403252\pi$
$367$	−2653.41	−	1531.94i	−0.377402	−	0.217893i	−0.676687	+	0.736270i	$0.736585\pi$
$368$			10359.9i			1.46752i
$369$	1758.22	+	5059.68i	0.248046	+	0.713811i
$370$			672.324i			0.0944661i
$371$	−2575.84	+	2445.51i	−0.360460	+	0.342222i
$372$	4321.57	+	3073.33i	0.602320	+	0.428346i
$373$	3900.06	+	6755.10i	0.541387	+	0.937711i	0.998825	+	0.0484687i	$0.0154341\pi$
$373$	3900.06	+	6755.10i	0.541387	+	0.937711i	−0.457437	+	0.889242i	$0.651233\pi$
$374$	113.275	+	196.198i	0.0156613	+	0.0271261i
$375$	7368.96	+	699.030i	1.01475	+	0.0962607i
$376$	215.271	+	124.287i	0.0295259	+	0.0170468i
$377$	−1800.43			−0.245960
$378$	−12.1769	+	254.098i	−0.00165691	+	0.0345752i
$379$	−6855.89			−0.929191			−0.464595	−	0.885523i	$-0.653800\pi$
$379$	−6855.89			−0.929191			−0.464595	+	0.885523i	$0.653800\pi$
$380$	8814.18	+	5088.87i	1.18989	+	0.686983i
$381$	9544.22	+	905.379i	1.28337	+	0.121743i
$382$	−89.6552	−	155.287i	−0.0120083	−	0.0207989i
$383$	−5511.46	−	9546.14i	−0.735307	−	1.27359i	−0.954588	−	0.297928i	$-0.903705\pi$
$383$	−5511.46	−	9546.14i	−0.735307	−	1.27359i	0.219281	−	0.975662i	$-0.429629\pi$
$384$	846.527	+	602.017i	0.112498	+	0.0800040i
$385$	−9011.27	+	8555.33i	−1.19288	+	1.13252i
$386$		−	37.2057i		−	0.00490601i
$387$	5674.32	−	6564.98i	0.745328	−	0.862317i
$388$			10625.6i			1.39029i
$389$	9460.70	+	5462.14i	1.23310	+	0.711931i	0.967675	−	0.252200i	$-0.0811541\pi$
$389$	9460.70	+	5462.14i	1.23310	+	0.711931i	0.265426	+	0.964131i	$0.414487\pi$
$390$	−72.4989	−	158.490i	−0.00941314	−	0.0205781i
$391$	−8795.90	+	5078.32i	−1.13767	+	0.656833i
$392$	−536.261	−	27.8562i	−0.0690950	−	0.00358916i
$393$	−4751.93	−	10388.2i	−0.609931	−	1.33337i
$394$	175.229	−	303.506i	0.0224059	−	0.0388081i
$395$	10815.2			1.37765
$396$	1501.45	−	7842.67i	0.190531	−	0.995225i
$397$			7203.22i			0.910627i	0.890331	+	0.455314i	$0.150473\pi$
$397$			7203.22i			0.910627i	−0.890331	+	0.455314i	$0.849527\pi$
$398$	−43.1423	+	74.7246i	−0.00543348	+	0.00941107i
$399$	5321.81	−	4171.97i	0.667729	−	0.523458i
$400$	−6491.34	−	11243.3i	−0.811418	−	1.40542i
$401$	−10633.1	+	6139.03i	−1.32417	+	0.764510i	−0.984391	−	0.175996i	$-0.943685\pi$
$401$	−10633.1	+	6139.03i	−1.32417	+	0.764510i	−0.339778	+	0.940506i	$0.610352\pi$
$402$	−6.56222	+	69.1768i	−0.000814163	+	0.00858266i
$403$	−1206.93	+	2090.46i	−0.149185	+	0.258396i
$404$	−7311.09			−0.900347
$405$	1913.13	+	13075.3i	0.234726	+	1.60424i
$406$	49.0218	−	165.635i	0.00599239	−	0.0202471i
$407$	−12143.0	−	7010.75i	−1.47888	−	0.853832i
$408$	−48.0289	+	506.306i	−0.00582791	+	0.0614360i
$409$	−735.497	+	424.639i	−0.0889193	+	0.0513376i	−0.543800	−	0.839215i	$-0.683015\pi$
$409$	−735.497	+	424.639i	−0.0889193	+	0.0513376i	0.454881	+	0.890552i	$0.349682\pi$
$410$	304.913	−	176.042i	0.0367283	−	0.0212051i
$411$	−9141.81	−	6501.29i	−1.09716	−	0.780256i
$412$	5768.07	+	3330.19i	0.689738	+	0.398221i
$413$	1123.91	−	3797.46i	0.133908	−	0.452448i
$414$	−421.788	−	80.7496i	−0.0500719	−	0.00958605i
$415$	6551.61			0.774954
$416$	−177.349	+	307.178i	−0.0209021	+	0.0362035i
$417$	−13758.1	+	6293.46i	−1.61568	+	0.739070i
$418$	220.517	−	127.316i	0.0258035	−	0.0148977i
$419$	3109.74	+	5386.23i	0.362579	+	0.628006i	0.988385	−	0.151973i	$-0.0485628\pi$
$419$	3109.74	+	5386.23i	0.362579	+	0.628006i	−0.625805	+	0.779979i	$0.715229\pi$
$420$	−13799.9	+	1962.60i	−1.60325	+	0.228012i
$421$	−1012.07	+	1752.95i	−0.117162	+	0.202930i	−0.918642	−	0.395091i	$-0.870713\pi$
$421$	−1012.07	+	1752.95i	−0.117162	+	0.202930i	0.801480	+	0.598021i	$0.204046\pi$
$422$			81.9628i			0.00945471i
$423$	2803.35	−	3243.37i	0.322230	−	0.372809i
$424$	−300.242			−0.0343892
$425$	6363.96	−	11022.7i	0.726347	−	1.25807i
$426$	135.307	−	190.263i	0.0153889	−	0.0216391i
$427$	−954.094	−	3970.05i	−0.108131	−	0.449940i
$428$	11669.2	−	6737.23i	1.31788	−	0.760879i
$429$	3618.51	+	343.257i	0.407233	+	0.0386307i
$430$	−493.955	−	285.185i	−0.0553968	−	0.0319834i
$431$			6519.65i			0.728633i	0.931275	+	0.364316i	$0.118697\pi$
$431$			6519.65i			0.728633i	−0.931275	+	0.364316i	$0.881303\pi$
$432$	6463.50	−	6185.98i	0.719851	−	0.688943i
$433$		−	17767.9i		−	1.97199i	−0.166772	−	0.985996i	$-0.553334\pi$
$433$		−	17767.9i		−	1.97199i	0.166772	−	0.985996i	$-0.446666\pi$
$434$	−159.455	−	167.953i	−0.0176362	−	0.0185761i
$435$	847.388	−	8932.90i	0.0934003	−	0.984597i
$436$	−2561.96	−	4437.45i	−0.281412	−	0.487420i
$437$	5707.79	+	9886.17i	0.624806	+	1.08220i
$438$	285.363	−	401.263i	0.0311305	−	0.0437742i
$439$	1280.80	+	739.472i	0.139247	+	0.0803942i	0.568005	−	0.823025i	$-0.307715\pi$
$439$	1280.80	+	739.472i	0.139247	+	0.0803942i	−0.428758	+	0.903419i	$0.641049\pi$
$440$	−1050.36			−0.113805
$441$	−2210.86	+	8993.23i	−0.238728	+	0.971087i
$442$	−115.681			−0.0124488
$443$	13484.2	+	7785.09i	1.44617	+	0.834945i	0.998250	−	0.0591295i	$-0.0188325\pi$
$443$	13484.2	+	7785.09i	1.44617	+	0.834945i	0.447918	+	0.894075i	$0.352166\pi$
$444$	−6542.91	−	14303.4i	−0.699353	−	1.52885i
$445$	321.741	+	557.272i	0.0342742	+	0.0593646i
$446$	−55.4985	−	96.1262i	−0.00589222	−	0.0102056i
$447$	1258.43	−	575.652i	0.133158	−	0.0609114i
$448$	6481.93	+	6827.38i	0.683577	+	0.720007i
$449$			6120.30i			0.643284i	0.946861	+	0.321642i	$0.104235\pi$
$449$			6120.30i			0.643284i	−0.946861	+	0.321642i	$0.895765\pi$
$450$	508.351	−	176.650i	0.0532531	−	0.0185052i
$451$			7342.80i			0.766649i
$452$	−9950.46	−	5744.90i	−1.03547	−	0.597826i
$453$	−2817.24	+	3961.47i	−0.292198	+	0.410874i
$454$	297.262	−	171.624i	0.0307295	−	0.0177417i
$455$	−1482.58	−	6169.14i	−0.152757	−	0.635634i
$456$	569.064	+	53.9822i	0.0584405	+	0.00554375i
$457$	−3498.22	+	6059.10i	−0.358074	+	0.620203i	−0.987639	−	0.156745i	$-0.949900\pi$
$457$	−3498.22	+	6059.10i	−0.358074	+	0.620203i	0.629565	+	0.776948i	$0.283233\pi$
$458$	307.663			0.0313890
$459$	8420.43	+	2455.42i	0.856278	+	0.249693i
$460$		−	23530.6i		−	2.38505i
$461$	−1833.17	+	3175.15i	−0.185205	+	0.320784i	−0.943646	−	0.330958i	$-0.892628\pi$
$461$	−1833.17	+	3175.15i	−0.185205	+	0.320784i	0.758441	+	0.651742i	$0.225962\pi$
$462$	−130.103	+	323.547i	−0.0131016	+	0.0325818i
$463$	3513.71	+	6085.92i	0.352691	+	0.610878i	0.986720	−	0.162431i	$-0.0519335\pi$
$463$	3513.71	+	6085.92i	0.352691	+	0.610878i	−0.634029	+	0.773309i	$0.718600\pi$
$464$	−5261.13	+	3037.51i	−0.526383	+	0.303907i
$465$	−9803.85	−	6972.12i	−0.977727	−	0.695321i
$466$	−336.893	+	583.516i	−0.0334898	+	0.0580061i
$467$	−13367.8			−1.32460			−0.662301	−	0.749238i	$-0.730420\pi$
$467$	−13367.8			−1.32460			−0.662301	+	0.749238i	$0.730420\pi$
$468$	3084.77	+	2666.27i	0.304688	+	0.263351i
$469$	−717.906	+	2425.66i	−0.0706819	+	0.238820i
$470$	−244.034	−	140.893i	−0.0239499	−	0.0138275i
$471$	−4761.92	+	2178.27i	−0.465855	+	0.213099i
$472$	289.919	−	167.385i	0.0282725	−	0.0163231i
$473$	10301.6	−	5947.61i	1.00141	−	0.578163i
$474$	276.021	−	126.262i	0.0267469	−	0.0122350i
$475$	−12389.0	−	7152.79i	−1.19673	−	0.690932i
$476$	−2625.61	+	8871.41i	−0.252825	+	0.854245i
$477$	−973.637	+	5085.71i	−0.0934586	+	0.488173i
$478$	117.138			0.0112087
$479$	3497.20	−	6057.33i	0.333593	−	0.577800i	−0.649620	−	0.760259i	$-0.725072\pi$
$479$	3497.20	−	6057.33i	0.333593	−	0.577800i	0.983214	+	0.182458i	$0.0584055\pi$
$480$	−1440.60	−	1024.50i	−0.136988	−	0.0974205i
$481$	6200.45	−	3579.83i	0.587767	−	0.339348i
$482$	−214.266	−	371.120i	−0.0202481	−	0.0350707i
$483$	−14505.2	−	5832.73i	−1.36648	−	0.549479i
$484$	155.487	−	269.312i	0.0146025	−	0.0252923i
$485$		−	24105.0i		−	2.25681i
$486$	201.473	+	311.368i	0.0188046	+	0.0290616i
$487$	−8233.24			−0.766086			−0.383043	−	0.923731i	$-0.625124\pi$
$487$	−8233.24			−0.766086			−0.383043	+	0.923731i	$0.625124\pi$
$488$	172.575	−	298.909i	0.0160084	−	0.0277274i
$489$	9317.84	+	883.904i	0.861692	+	0.0817414i
$490$	607.912	+	31.5782i	0.0560463	+	0.00291134i
$491$	−12925.9	+	7462.77i	−1.18806	+	0.685927i	−0.957865	−	0.287218i	$-0.907270\pi$
$491$	−12925.9	+	7462.77i	−1.18806	+	0.685927i	−0.230195	+	0.973145i	$0.573936\pi$
$492$	−4773.72	+	6712.57i	−0.437431	+	0.615094i
$493$	−5157.89	−	2977.91i	−0.471196	−	0.272045i
$494$			130.020i			0.0118419i
$495$	−3406.16	+	17791.8i	−0.309284	+	1.61552i
$496$			8144.86i			0.737329i
$497$	6163.89	−	5852.01i	0.556314	−	0.528166i
$498$	167.207	−	76.4866i	0.0150457	−	0.00688242i
$499$	−4165.46	−	7214.80i	−0.373691	−	0.647252i	0.616439	−	0.787402i	$-0.288575\pi$
$499$	−4165.46	−	7214.80i	−0.373691	−	0.647252i	−0.990130	+	0.140151i	$0.955241\pi$
$500$	5691.27	+	9857.56i	0.509042	+	0.881687i
$501$	3535.77	+	7729.54i	0.315302	+	0.689282i
$502$	−490.688	−	283.299i	−0.0436265	−	0.0251878i
$503$	−15511.0			−1.37495			−0.687475	−	0.726208i	$-0.741281\pi$
$503$	−15511.0			−1.37495			−0.687475	+	0.726208i	$0.741281\pi$
$504$	−658.958	+	422.643i	−0.0582387	+	0.0373532i
$505$	16585.8			1.46150
$506$	−509.830	−	294.350i	−0.0447919	−	0.0258606i
$507$	5540.49	−	7790.77i	0.485329	−	0.682446i
$508$	7371.29	+	12767.4i	0.643795	+	1.11509i
$509$	1816.15	+	3145.66i	0.158152	+	0.273927i	0.934202	−	0.356744i	$-0.116113\pi$
$509$	1816.15	+	3145.66i	0.158152	+	0.273927i	−0.776050	+	0.630671i	$0.782780\pi$
$510$	54.4462	−	573.955i	0.00472729	−	0.0498337i
$511$	12999.6	−	12341.9i	1.12538	−	1.06844i
$512$			1995.51i			0.172246i
$513$	2759.77	−	9464.16i	0.237519	−	0.814528i
$514$			210.388i			0.0180542i
$515$	−13085.4	−	7554.83i	−1.11963	−	0.646419i
$516$	13284.1	+	1260.14i	1.13333	+	0.107509i
$517$	5089.39	−	2938.36i	0.432942	−	0.249959i
$518$	160.510	+	667.896i	0.0136147	+	0.0566518i
$519$	2407.69	−	3385.58i	0.203634	−	0.286340i
$520$	268.168	−	464.481i	0.0226153	−	0.0391708i
$521$	531.760			0.0447156			0.0223578	−	0.999750i	$-0.492883\pi$
$521$	531.760			0.0447156			0.0223578	+	0.999750i	$0.492883\pi$
$522$	−82.6602	−	237.874i	−0.00693092	−	0.0199453i
$523$			14041.2i			1.17395i	0.809604	+	0.586977i	$0.199682\pi$
$523$			14041.2i			1.17395i	−0.809604	+	0.586977i	$0.800318\pi$
$524$	8783.23	−	15213.0i	0.732247	−	1.26829i
$525$	19396.7	−	2758.58i	1.61246	−	0.229323i
$526$	59.7596	+	103.507i	0.00495369	+	0.00858005i
$527$	−6915.24	+	3992.52i	−0.571599	+	0.330013i
$528$	11152.9	−	5101.74i	0.919258	−	0.420502i
$529$	7112.74	−	12319.6i	0.584592	−	1.01254i
$530$	340.358			0.0278947
$531$	−1895.12	−	5453.67i	−0.154880	−	0.445704i
$532$	9971.04	+	2951.06i	0.812593	+	0.240497i
$533$	−3247.06	−	1874.69i	−0.263876	−	0.152349i
$534$	14.7172	+	10.4663i	0.00119265	+	0.000848166i
$535$	−26472.6	+	15284.0i	−2.13927	+	1.23511i
$536$	−185.189	+	106.919i	−0.0149234	+	0.00861602i
$537$	−1442.79	+	15209.4i	−0.115942	+	1.22222i
$538$	375.662	+	216.888i	0.0301040	+	0.0173805i
$539$	−6909.42	+	10650.3i	−0.552152	+	0.851098i
$540$	−14680.6	+	14050.3i	−1.16992	+	1.11968i
$541$	−11065.4			−0.879372			−0.439686	−	0.898151i	$-0.644910\pi$
$541$	−11065.4			−0.879372			−0.439686	+	0.898151i	$0.644910\pi$
$542$	5.44642	−	9.43348i	0.000431631	−	0.000747606i
$543$	−184.961	+	1949.80i	−0.0146177	+	0.154096i
$544$	−1016.14	+	586.670i	−0.0800860	+	0.0462376i
$545$	5812.03	+	10066.7i	0.456807	+	0.791213i
$546$	−109.859	−	140.138i	−0.00861088	−	0.0109841i
$547$	6024.28	−	10434.4i	0.470895	−	0.815614i	−0.528551	−	0.848902i	$-0.677264\pi$
$547$	6024.28	−	10434.4i	0.470895	−	0.815614i	0.999446	+	0.0332874i	$0.0105977\pi$
$548$		−	17250.3i		−	1.34470i
$549$	−4503.50	−	3892.52i	−0.350100	−	0.302602i
$550$	737.739			0.0571950
$551$	−3347.02	+	5797.22i	−0.258780	+	0.448221i
$552$	−549.745	−	1201.80i	−0.0423890	−	0.0926665i
$553$	10744.0	−	2582.02i	0.826184	−	0.198551i
$554$	−259.339	+	149.729i	−0.0198885	+	0.0114827i
$555$	14843.1	+	32448.6i	1.13524	+	2.48174i
$556$	−20148.1	−	11632.5i	−1.53682	−	0.887283i
$557$		−	2546.80i		−	0.193737i	−0.995297	−	0.0968684i	$-0.969117\pi$
$557$		−	2546.80i		−	0.193737i	0.995297	−	0.0968684i	$-0.0308826\pi$
$558$	−331.605	−	63.4844i	−0.0251577	−	0.00481632i
$559$			6073.94i			0.459571i
$560$	−14740.3	−	15525.9i	−1.11231	−	1.17158i
$561$	9798.57	+	6968.36i	0.737426	+	0.524428i
$562$	233.114	+	403.766i	0.0174970	+	0.0303057i
$563$	11536.2	+	19981.3i	0.863578	+	1.49576i	0.868452	+	0.495772i	$0.165115\pi$
$563$	11536.2	+	19981.3i	0.863578	+	1.49576i	−0.00487467	+	0.999988i	$0.501552\pi$
$564$	6562.87	+	622.563i	0.489976	+	0.0464799i
$565$	22573.5	+	13032.8i	1.68084	+	0.970432i
$566$	−403.316			−0.0299517
$567$	5022.13	+	12532.5i	0.371974	+	0.928243i
$568$	718.468			0.0530744
$569$	−5471.39	−	3158.91i	−0.403115	−	0.232739i	0.284712	−	0.958613i	$-0.408102\pi$
$569$	−5471.39	−	3158.91i	−0.403115	−	0.232739i	−0.687827	+	0.725874i	$0.741435\pi$
$570$	−645.098	−	61.1950i	−0.0474039	−	0.00449680i
$571$	−9276.07	−	16066.6i	−0.679845	−	1.17753i	−0.975027	−	0.222085i	$-0.928714\pi$
$571$	−9276.07	−	16066.6i	−0.679845	−	1.17753i	0.295182	−	0.955441i	$-0.404620\pi$
$572$	2794.68	+	4840.53i	0.204286	+	0.353833i
$573$	−7755.39	−	5515.33i	−0.565421	−	0.402105i
$574$	260.877	−	247.677i	0.0189700	−	0.0180102i
$575$			33074.1i			2.39876i
$576$	13479.9	+	2580.67i	0.975109	+	0.186680i
$577$		−	2684.61i		−	0.193695i	−0.995299	−	0.0968473i	$-0.969124\pi$
$577$		−	2684.61i		−	0.193695i	0.995299	−	0.0968473i	$-0.0308758\pi$
$578$	85.1631	+	49.1689i	0.00612858	+	0.00353834i
$579$	−821.404	−	1795.67i	−0.0589575	−	0.128887i
$580$	11949.7	−	6899.14i	0.855488	−	0.493916i
$581$	6508.46	−	1564.13i	0.464744	−	0.111689i
$582$	−281.413	−	615.196i	−0.0200429	−	0.0438157i
$583$	−3549.13	+	6147.27i	−0.252127	+	0.436696i
$584$	1515.25			0.107365
$585$	−6998.08	−	6048.66i	−0.494589	−	0.427489i
$586$			274.468i			0.0193484i
$587$	−9124.16	+	15803.5i	−0.641558	+	1.11121i	0.343527	+	0.939143i	$0.388378\pi$
$587$	−9124.16	+	15803.5i	−0.641558	+	1.11121i	−0.985085	+	0.172068i	$0.944955\pi$
$588$	−13240.4	+	5244.25i	−0.928614	+	0.367805i
$589$	4487.40	+	7772.40i	0.313922	+	0.543729i
$590$	−328.656	+	189.750i	−0.0229332	+	0.0132405i
$591$	1756.53	−	18516.8i	0.122257	−	1.28880i
$592$	12079.1	−	20921.6i	0.838593	−	1.45249i
$593$	−10331.8			−0.715473			−0.357736	−	0.933823i	$-0.616451\pi$
$593$	−10331.8			−0.715473			−0.357736	+	0.933823i	$0.616451\pi$
$594$	120.779	+	493.839i	0.00834281	+	0.0341119i
$595$	5956.41	−	20125.6i	0.410402	−	1.38667i
$596$	1842.92	+	1064.01i	0.126659	+	0.0731266i
$597$	−432.466	+	4558.92i	−0.0296477	+	0.312536i
$598$	260.329	−	150.301i	0.0178021	−	0.0102781i
$599$	−3453.17	+	1993.69i	−0.235547	+	0.135993i	−0.613129	−	0.789983i	$-0.710089\pi$
$599$	−3453.17	+	1993.69i	−0.235547	+	0.135993i	0.377581	+	0.925976i	$0.376756\pi$
$600$	1349.65	+	959.816i	0.0918319	+	0.0653072i
$601$	−15935.6	−	9200.43i	−1.08158	−	0.624448i	−0.150255	−	0.988647i	$-0.548010\pi$
$601$	−15935.6	−	9200.43i	−1.08158	−	0.624448i	−0.931321	+	0.364199i	$0.881343\pi$
$602$	−558.786	−	165.380i	−0.0378313	−	0.0111966i
$603$	1210.53	+	3483.58i	0.0817521	+	0.235261i
$604$	−7475.15			−0.503576
$605$	−352.736	+	610.957i	−0.0237038	+	0.0410561i
$606$	423.296	−	193.631i	0.0283750	−	0.0129797i
$607$	12276.2	−	7087.68i	0.820883	−	0.473937i	−0.0298377	−	0.999555i	$-0.509499\pi$
$607$	12276.2	−	7087.68i	0.820883	−	0.473937i	0.850721	+	0.525618i	$0.176166\pi$
$608$	659.389	+	1142.10i	0.0439832	+	0.0761811i
$609$	−1290.83	−	9076.37i	−0.0858902	−	0.603929i
$610$	−195.634	+	338.848i	−0.0129852	+	0.0224910i
$611$			3000.77i			0.198688i
$612$	4427.28	+	12740.5i	0.292422	+	0.841513i
$613$	−2164.43			−0.142611			−0.0713054	−	0.997455i	$-0.522716\pi$
$613$	−2164.43			−0.142611			−0.0713054	+	0.997455i	$0.522716\pi$
$614$	−193.819	+	335.705i	−0.0127393	+	0.0220650i
$615$	10829.6	−	15228.0i	0.710067	−	0.998462i
$616$	−1043.44	+	250.763i	−0.0682492	+	0.0164018i
$617$	2799.72	−	1616.42i	0.182678	−	0.105469i	−0.405872	−	0.913930i	$-0.633032\pi$
$617$	2799.72	−	1616.42i	0.182678	−	0.105469i	0.588550	+	0.808460i	$0.299699\pi$
$618$	−422.157	−	40.0464i	−0.0274784	−	0.00260664i
$619$	18943.3	+	10936.9i	1.23004	+	0.710166i	0.967039	−	0.254629i	$-0.0819532\pi$
$619$	18943.3	+	10936.9i	1.23004	+	0.710166i	0.263005	+	0.964795i	$0.415287\pi$
$620$		−	18499.5i		−	1.19832i
$621$	−22139.6	+	5414.74i	−1.43065	+	0.349897i
$622$			488.010i			0.0314589i
$623$	452.665	+	476.789i	0.0291102	+	0.0306616i
$624$	−591.410	+	6234.46i	−0.0379412	+	0.399965i
$625$	−187.001	−	323.895i	−0.0119680	−	0.0207292i
$626$	−39.5514	−	68.5051i	−0.00252523	−	0.00437383i
$627$	7832.10	−	11013.1i	0.498858	−	0.701470i
$628$	−6973.61	−	4026.22i	−0.443117	−	0.255834i
$629$	23684.1			1.50135
$630$	747.003	−	479.113i	0.0472402	−	0.0302989i
$631$	−9979.57			−0.629604			−0.314802	−	0.949157i	$-0.601938\pi$
$631$	−9979.57			−0.629604			−0.314802	+	0.949157i	$0.601938\pi$
$632$	808.923	+	467.032i	0.0509134	+	0.0293948i
$633$	1809.52	+	3955.80i	0.113621	+	0.248387i
$634$	−116.536	−	201.847i	−0.00730007	−	0.0126441i
$635$	−16722.4	−	28964.0i	−1.04505	−	1.81008i
$636$	−7240.98	+	3312.29i	−0.451452	+	0.206511i
$637$	−2945.64	−	5774.55i	−0.183219	−	0.359178i
$638$		−	345.212i		−	0.0214217i
$639$	2329.88	−	12169.9i	0.144239	−	0.753419i
$640$		−	3623.76i		−	0.223815i
$641$	13685.3	+	7901.22i	0.843272	+	0.486864i	0.858375	−	0.513022i	$-0.171474\pi$
$641$	13685.3	+	7901.22i	0.843272	+	0.486864i	−0.0151029	+	0.999886i	$0.504808\pi$
$642$	−497.190	+	699.125i	−0.0305647	+	0.0429786i
$643$	−10980.9	+	6339.83i	−0.673476	+	0.388831i	−0.797392	−	0.603461i	$-0.793788\pi$
$643$	−10980.9	+	6339.83i	−0.673476	+	0.388831i	0.123917	+	0.992293i	$0.460454\pi$
$644$	−5617.70	−	23375.7i	−0.343740	−	1.43033i
$645$	−30136.0	−	2858.75i	−1.83970	−	0.174516i
$646$	−215.053	+	372.482i	−0.0130977	+	0.0226859i
$647$	20710.7			1.25846			0.629230	−	0.777219i	$-0.283370\pi$
$647$	20710.7			1.25846			0.629230	+	0.777219i	$0.283370\pi$
$648$	−421.538	+	1060.58i	−0.0255549	+	0.0642958i
$649$		−	7914.57i		−	0.478696i
$650$	−188.352	+	326.235i	−0.0113658	+	0.0196862i
$651$	−11403.8	−	4585.62i	−0.686560	−	0.276075i
$652$	7196.45	+	12464.6i	0.432262	+	0.748699i
$653$	−1355.80	+	782.771i	−0.0812505	+	0.0469100i	−0.540075	−	0.841617i	$-0.681604\pi$
$653$	−1355.80	+	782.771i	−0.0812505	+	0.0469100i	0.458824	+	0.888527i	$0.348271\pi$
$654$	265.856	+	189.066i	0.0158957	+	0.0113044i
$655$	−19925.5	+	34512.0i	−1.18863	+	2.05877i
$656$	−12651.2			−0.752966
$657$	4913.71	−	25666.3i	0.291784	−	1.52411i
$658$	−276.063	−	81.7044i	−0.0163557	−	0.00484069i
$659$	−15480.8	−	8937.83i	−0.915091	−	0.528328i	−0.0330256	−	0.999455i	$-0.510514\pi$
$659$	−15480.8	−	8937.83i	−0.915091	−	0.528328i	−0.882066	+	0.471126i	$0.843848\pi$
$660$	−25331.8	+	11587.7i	−1.49400	+	0.683408i
$661$	−21911.3	+	12650.5i	−1.28934	+	0.744399i	−0.978536	−	0.206076i	$-0.933930\pi$
$661$	−21911.3	+	12650.5i	−1.28934	+	0.744399i	−0.310801	+	0.950475i	$0.600597\pi$
$662$	−632.141	+	364.967i	−0.0371131	+	0.0214272i
$663$	−5583.15	+	2553.93i	−0.327046	+	0.149603i
$664$	490.028	+	282.918i	0.0286397	+	0.0165352i
$665$	−22620.2	−	6694.72i	−1.31906	−	0.390391i
$666$	757.640	+	654.852i	0.0440810	+	0.0381006i
$667$	15476.4			0.898427
$668$	−6535.35	+	11319.6i	−0.378533	+	0.655639i
$669$	−4800.75	−	3414.11i	−0.277441	−	0.197305i
$670$	209.932	−	121.204i	0.0121051	−	0.00698886i
$671$	−4079.99	−	7066.75i	−0.234734	−	0.406571i
$672$	−1675.70	−	673.823i	−0.0961929	−	0.0386805i
$673$	−16774.4	+	29054.1i	−0.960781	+	1.66412i	−0.240233	+	0.970715i	$0.577224\pi$
$673$	−16774.4	+	29054.1i	−0.960781	+	1.66412i	−0.720548	+	0.693405i	$0.756110\pi$
$674$		−	191.554i		−	0.0109472i
$675$	20634.7	−	19748.8i	1.17664	−	1.12612i
$676$	14700.9			0.836419
$677$	16134.2	−	27945.3i	0.915935	−	1.58645i	0.110408	−	0.993886i	$-0.464784\pi$
$677$	16134.2	−	27945.3i	0.915935	−	1.58645i	0.805527	−	0.592559i	$-0.201882\pi$
$678$	728.261	+	69.0839i	0.0412518	+	0.00391320i
$679$	−5754.82	−	23946.2i	−0.325257	−	1.35342i
$680$	1536.50	−	887.097i	0.0866500	−	0.0500274i
$681$	10557.8	−	14845.9i	0.594092	−	0.835383i
$682$	−400.823	−	231.415i	−0.0225048	−	0.0129932i
$683$		−	14942.5i		−	0.837126i	−0.908188	−	0.418563i	$-0.862534\pi$
$683$		−	14942.5i		−	0.837126i	0.908188	−	0.418563i	$-0.137466\pi$
$684$	14319.8	−	4976.05i	0.800482	−	0.278164i
$685$			39133.7i			2.18281i
$686$	611.447	−	113.763i	0.0340308	−	0.00633160i
$687$	14848.9	−	6792.40i	0.824628	−	0.377214i
$688$	10247.4	+	17748.9i	0.567844	+	0.983534i
$689$	−1812.26	−	3138.92i	−0.100205	−	0.173561i
$690$	623.198	+	1362.37i	0.0343837	+	0.0751662i
$691$	−9734.42	−	5620.17i	−0.535912	−	0.309409i	0.207509	−	0.978233i	$-0.433464\pi$
$691$	−9734.42	−	5620.17i	−0.535912	−	0.309409i	−0.743420	+	0.668824i	$0.766798\pi$
$692$	6388.47			0.350944
$693$	863.881	+	18487.8i	0.0473537	+	1.01341i
$694$	134.723			0.00736889
$695$	45707.8	+	26389.4i	2.49467	+	1.44030i
$696$	449.129	−	631.544i	0.0244601	−	0.0343946i
$697$	−6201.46	−	10741.2i	−0.337012	−	0.583721i
$698$	−457.748	−	792.843i	−0.0248224	−	0.0429936i
$699$	−3377.08	+	35600.1i	−0.182737	+	1.92635i
$700$	20743.5	+	21849.0i	1.12004	+	1.17973i
$701$			19409.2i			1.04576i	0.852407	+	0.522879i	$0.175142\pi$
$701$			19409.2i			1.04576i	−0.852407	+	0.522879i	$0.824858\pi$
$702$	−249.217	−	72.6723i	−0.0133990	−	0.00390718i
$703$		−	26619.8i		−	1.42814i
$704$	16293.6	+	9407.13i	0.872285	+	0.503614i
$705$	−14888.4	−	1412.34i	−0.795363	−	0.0754493i
$706$	−57.4589	+	33.1739i	−0.00306302	+	0.00176844i
$707$	16476.6	−	3959.70i	0.876472	−	0.210636i
$708$	5145.44	−	7235.27i	0.273132	−	0.384065i
$709$	866.108	−	1500.14i	0.0458778	−	0.0794627i	−0.842175	−	0.539205i	$-0.818725\pi$
$709$	866.108	−	1500.14i	0.0458778	−	0.0794627i	0.888052	+	0.459742i	$0.152058\pi$
$710$	−814.465			−0.0430512
$711$	10534.1	−	12187.6i	0.555641	−	0.642857i
$712$			55.5750i			0.00292522i
$713$	10374.7	−	17969.6i	0.544932	−	0.943851i
$714$	−82.9383	−	583.173i	−0.00434718	−	0.0305668i
$715$	−6339.97	−	10981.2i	−0.331610	−	0.574366i
$716$	−20345.8	+	11746.7i	−1.06196	+	0.613120i
$717$	5653.44	−	2586.09i	0.294465	−	0.134699i
$718$	−81.3772	+	140.949i	−0.00422976	+	0.00732616i
$719$	36946.9			1.91639			0.958197	−	0.286109i	$-0.0923620\pi$
$719$	36946.9			1.91639			0.958197	+	0.286109i	$0.0923620\pi$
$720$	−30654.1	−	5868.59i	−1.58668	−	0.303763i
$721$	−14802.8	−	4381.08i	−0.764612	−	0.226297i
$722$	−162.914	−	94.0582i	−0.00839753	−	0.00484832i
$723$	−18534.6	−	13181.0i	−0.953399	−	0.678020i
$724$	−2608.28	+	1505.89i	−0.133889	+	0.0773011i
$725$	−16796.2	+	9697.26i	−0.860405	+	0.496755i
$726$	−1.86977	+	19.7106i	−9.55838e−5	+	0.00100762i
$727$	−1776.00	−	1025.38i	−0.0906029	−	0.0523096i	0.454014	−	0.890995i	$-0.349992\pi$
$727$	−1776.00	−	1025.38i	−0.0906029	−	0.0523096i	−0.544617	+	0.838685i	$0.683325\pi$
$728$	155.512	−	525.444i	0.00791710	−	0.0267503i
$729$	16598.0	+	10579.6i	0.843263	+	0.537501i
$730$	−1717.70			−0.0870892
$731$	−10046.3	+	17400.6i	−0.508310	+	0.880419i
$732$	864.445	−	9112.71i	0.0436487	−	0.460131i
$733$	27156.6	−	15678.9i	1.36842	−	0.790058i	0.377694	−	0.925931i	$-0.376717\pi$
$733$	27156.6	−	15678.9i	1.36842	−	0.790058i	0.990726	+	0.135873i	$0.0433839\pi$
$734$	149.986	+	259.783i	0.00754234	+	0.0130637i
$735$	30037.0	−	11897.0i	1.50739	−	0.597046i
$736$	1524.49	−	2640.49i	0.0763498	−	0.132242i
$737$			5055.50i			0.252675i
$738$	98.6085	−	515.073i	0.00491847	−	0.0256912i
$739$	1233.93			0.0614219			0.0307109	−	0.999528i	$-0.490223\pi$
$739$	1233.93			0.0614219			0.0307109	+	0.999528i	$0.490223\pi$
$740$	−27435.4	+	47519.4i	−1.36290	+	2.36061i
$741$	2870.50	+	6275.20i	0.142308	+	0.311100i
$742$	338.116	−	81.2570i	0.0167286	−	0.00402027i
$743$	26190.4	−	15121.0i	1.29318	−	0.746618i	0.313963	−	0.949435i	$-0.398343\pi$
$743$	26190.4	−	15121.0i	1.29318	−	0.746618i	0.979217	+	0.202818i	$0.0650098\pi$
$744$	−432.204	−	944.840i	−0.0212975	−	0.0465585i
$745$	−4180.81	−	2413.79i	−0.205602	−	0.118704i
$746$		−	763.675i		−	0.0374801i
$747$	6381.35	−	7382.99i	0.312559	−	0.361619i
$748$			18489.6i			0.903803i
$749$	−22649.4	+	21503.4i	−1.10493	+	1.04902i
$750$	−590.585	−	420.001i	−0.0287535	−	0.0204483i
$751$	−2746.70	−	4757.42i	−0.133460	−	0.231159i	0.791548	−	0.611107i	$-0.209275\pi$
$751$	−2746.70	−	4757.42i	−0.133460	−	0.231159i	−0.925008	+	0.379947i	$0.875942\pi$
$752$	5062.61	+	8768.70i	0.245498	+	0.425215i
$753$	−29936.7	−	2839.84i	−1.44881	−	0.137436i
$754$	152.656	+	88.1361i	0.00737323	+	0.00425693i
$755$	16958.0			0.817438
$756$	−11229.6	+	17462.6i	−0.540233	+	0.840091i
$757$	−31971.7			−1.53505			−0.767523	−	0.641021i	$-0.778511\pi$
$757$	−31971.7			−1.53505			−0.767523	+	0.641021i	$0.778511\pi$
$758$	581.302	+	335.615i	0.0278547	+	0.0160819i
$759$	−31104.6	−	2950.62i	−1.48751	−	0.141108i
$760$	−997.055	−	1726.95i	−0.0475881	−	0.0824251i
$761$	−8220.51	−	14238.3i	−0.391581	−	0.678238i	0.601077	−	0.799191i	$-0.294738\pi$
$761$	−8220.51	−	14238.3i	−0.391581	−	0.678238i	−0.992658	+	0.120953i	$0.961405\pi$
$762$	−764.921	−	543.982i	−0.0363651	−	0.0258614i
$763$	8177.07	+	8612.86i	0.387982	+	0.408658i
$764$		−	14634.2i		−	0.692991i
$765$	−10043.7	−	28903.0i	−0.474679	−	1.36600i
$766$			1079.21i			0.0509051i
$767$	3499.90	+	2020.67i	0.164764	+	0.0951266i
$768$	8747.60	+	19123.1i	0.411005	+	0.898497i
$769$	1220.92	−	704.900i	0.0572531	−	0.0330551i	−0.471100	−	0.882080i	$-0.656143\pi$
$769$	1220.92	−	704.900i	0.0572531	−	0.0330551i	0.528353	+	0.849025i	$0.322810\pi$
$770$	1182.86	−	284.268i	0.0553602	−	0.0133043i
$771$	4644.82	+	10154.0i	0.216964	+	0.474305i
$772$	1518.24	−	2629.67i	0.0707808	−	0.122596i
$773$	−9575.08			−0.445526

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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0847887 - 0.0489528i) q^{2} +(-5.17293 - 0.490712i) q^{3} +(-3.99521 - 6.91990i) q^{4} +(9.06347 + 15.6984i) q^{5} +(0.414584 + 0.294836i) q^{6} +(12.7516 + 13.4312i) q^{7} +1.56555i q^{8} +(26.5184 + 5.07683i) q^{9} +O(q^{10})\)	\(q+(-0.0847887 - 0.0489528i) q^{2} +(-5.17293 - 0.490712i) q^{3} +(-3.99521 - 6.91990i) q^{4} +(9.06347 + 15.6984i) q^{5} +(0.414584 + 0.294836i) q^{6} +(12.7516 + 13.4312i) q^{7} +1.56555i q^{8} +(26.5184 + 5.07683i) q^{9} -1.77473i q^{10} +(32.0537 + 18.5062i) q^{11} +(17.2713 + 37.7567i) q^{12} +(-16.3673 + 9.44964i) q^{13} +(-0.423698 - 1.76304i) q^{14} +(-39.1813 - 85.6542i) q^{15} +(-31.8850 + 55.2265i) q^{16} -62.5187 q^{17} +(-1.99994 - 1.72861i) q^{18} +70.2680i q^{19} +(72.4209 - 125.437i) q^{20} +(-59.3723 - 75.7359i) q^{21} +(-1.81186 - 3.13823i) q^{22} +(140.692 - 81.2288i) q^{23} +(0.768234 - 8.09848i) q^{24} +(-101.793 + 176.311i) q^{25} +1.85034 q^{26} +(-134.687 - 39.2750i) q^{27} +(41.9972 - 141.900i) q^{28} +(82.5015 + 47.6323i) q^{29} +(-0.870879 + 9.18054i) q^{30} +(110.611 - 63.8612i) q^{31} +(16.2534 - 9.38392i) q^{32} +(-156.730 - 111.460i) q^{33} +(5.30088 + 3.06046i) q^{34} +(-95.2742 + 321.913i) q^{35} +(-70.8153 - 203.788i) q^{36} -378.832 q^{37} +(3.43981 - 5.95793i) q^{38} +(89.3037 - 40.8507i) q^{39} +(-24.5766 + 14.1893i) q^{40} +(99.1937 + 171.809i) q^{41} +(1.32662 + 9.32799i) q^{42} +(160.692 - 278.327i) q^{43} -295.744i q^{44} +(160.651 + 462.310i) q^{45} -15.9055 q^{46} +(79.3885 - 137.505i) q^{47} +(192.039 - 270.036i) q^{48} +(-17.7932 + 342.538i) q^{49} +(17.2618 - 9.96610i) q^{50} +(323.405 + 30.6786i) q^{51} +(130.781 + 75.5066i) q^{52} +191.780i q^{53} +(9.49728 + 9.92336i) q^{54} +670.922i q^{55} +(-21.0272 + 19.9633i) q^{56} +(34.4813 - 363.491i) q^{57} +(-4.66346 - 8.07736i) q^{58} +(-106.918 - 185.187i) q^{59} +(-436.181 + 613.337i) q^{60} +(-190.929 - 110.233i) q^{61} -12.5047 q^{62} +(269.964 + 420.911i) q^{63} +508.323 q^{64} +(-296.688 - 171.293i) q^{65} +(7.83266 + 17.1230i) q^{66} +(68.2947 + 118.290i) q^{67} +(249.775 + 432.623i) q^{68} +(-767.652 + 351.151i) q^{69} +(23.8367 - 22.6306i) q^{70} -458.924i q^{71} +(-7.94804 + 41.5159i) q^{72} -967.869i q^{73} +(32.1207 + 18.5449i) q^{74} +(613.086 - 862.091i) q^{75} +(486.248 - 280.735i) q^{76} +(160.176 + 666.503i) q^{77} +(-9.57170 - 0.907986i) q^{78} +(298.318 - 516.702i) q^{79} -1155.96 q^{80} +(677.452 + 269.259i) q^{81} -19.4232i q^{82} +(180.715 - 313.007i) q^{83} +(-286.880 + 713.431i) q^{84} +(-566.636 - 981.443i) q^{85} +(-27.2498 + 15.7327i) q^{86} +(-403.401 - 286.883i) q^{87} +(-28.9724 + 50.1817i) q^{88} +35.4987 q^{89} +(9.01000 - 47.0630i) q^{90} +(-335.629 - 99.3336i) q^{91} +(-1124.19 - 649.052i) q^{92} +(-603.519 + 276.071i) q^{93} +(-13.4625 + 7.77258i) q^{94} +(-1103.09 + 636.872i) q^{95} +(-88.6826 + 40.5666i) q^{96} +(-1151.63 - 664.894i) q^{97} +(18.2769 - 28.1723i) q^{98} +(756.060 + 653.486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 6q^{2} + 78q^{4} + 5q^{7} + O(q^{10}) \)	\( 44q - 6q^{2} + 78q^{4} + 5q^{7} - 18q^{11} + 204q^{14} + 66q^{15} - 242q^{16} - 210q^{18} - 57q^{21} - 34q^{22} - 102q^{23} - 352q^{25} + 300q^{28} + 246q^{29} - 144q^{30} + 1068q^{32} - 1818q^{36} + 328q^{37} - 798q^{39} - 1158q^{42} - 170q^{43} + 968q^{46} - 79q^{49} + 288q^{50} - 204q^{51} + 1212q^{56} + 324q^{57} - 538q^{58} + 5316q^{60} + 783q^{63} - 808q^{64} + 4350q^{65} - 590q^{67} + 384q^{70} + 4284q^{72} - 5304q^{74} - 2787q^{77} + 612q^{78} - 302q^{79} - 3720q^{81} + 7050q^{84} - 612q^{85} - 13692q^{86} + 1294q^{88} + 210q^{91} - 10194q^{92} - 4266q^{93} + 6336q^{95} + 1014q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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