LMFDB - Embedded newform 63.4.s.a.47.9

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.s (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			47.9
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.9

$q$-expansion

$f(q)$	$=$	$q+(-1.54833 + 0.893930i) q^{2} +(5.18374 + 0.358957i) q^{3} +(-2.40178 + 4.16000i) q^{4} -16.9434 q^{5} +(-8.34703 + 4.07812i) q^{6} +(-9.83512 + 15.6930i) q^{7} -22.8910i q^{8} +(26.7423 + 3.72148i) q^{9} +O(q^{10})$	\(q+(-1.54833 + 0.893930i) q^{2} +(5.18374 + 0.358957i) q^{3} +(-2.40178 + 4.16000i) q^{4} -16.9434 q^{5} +(-8.34703 + 4.07812i) q^{6} +(-9.83512 + 15.6930i) q^{7} -22.8910i q^{8} +(26.7423 + 3.72148i) q^{9} +(26.2340 - 15.1462i) q^{10} +7.14600i q^{11} +(-13.9435 + 20.7022i) q^{12} +(-67.0144 + 38.6908i) q^{13} +(1.19958 - 33.0899i) q^{14} +(-87.8300 - 6.08194i) q^{15} +(1.24870 + 2.16282i) q^{16} +(1.06481 + 1.84430i) q^{17} +(-44.7327 + 18.1437i) q^{18} +(104.730 + 60.4661i) q^{19} +(40.6942 - 70.4844i) q^{20} +(-56.6158 + 77.8181i) q^{21} +(-6.38802 - 11.0644i) q^{22} +10.8686i q^{23} +(8.21688 - 118.661i) q^{24} +162.077 q^{25} +(69.1737 - 119.812i) q^{26} +(137.289 + 28.8905i) q^{27} +(-41.6612 - 78.6052i) q^{28} +(-110.704 - 63.9149i) q^{29} +(141.427 - 69.0970i) q^{30} +(184.393 + 106.459i) q^{31} +(154.726 + 89.3314i) q^{32} +(-2.56511 + 37.0430i) q^{33} +(-3.29735 - 1.90372i) q^{34} +(166.640 - 265.892i) q^{35} +(-79.7104 + 102.310i) q^{36} +(-12.2062 + 21.1417i) q^{37} -216.210 q^{38} +(-361.273 + 176.507i) q^{39} +387.850i q^{40} +(-64.8686 - 112.356i) q^{41} +(18.0962 - 171.099i) q^{42} +(86.4878 - 149.801i) q^{43} +(-29.7274 - 17.1631i) q^{44} +(-453.104 - 63.0544i) q^{45} +(-9.71576 - 16.8282i) q^{46} +(202.426 + 350.613i) q^{47} +(5.69660 + 11.6597i) q^{48} +(-149.541 - 308.685i) q^{49} +(-250.950 + 144.886i) q^{50} +(4.85765 + 9.94258i) q^{51} -371.706i q^{52} +(-291.479 + 168.286i) q^{53} +(-238.396 + 77.9949i) q^{54} -121.077i q^{55} +(359.228 + 225.135i) q^{56} +(521.190 + 351.034i) q^{57} +228.542 q^{58} +(-330.799 + 572.960i) q^{59} +(236.249 - 350.765i) q^{60} +(-300.606 + 173.555i) q^{61} -380.669 q^{62} +(-321.415 + 383.066i) q^{63} -339.403 q^{64} +(1135.45 - 655.551i) q^{65} +(-29.1422 - 59.6479i) q^{66} +(134.558 - 233.062i) q^{67} -10.2297 q^{68} +(-3.90136 + 56.3399i) q^{69} +(-20.3249 + 560.654i) q^{70} -637.224i q^{71} +(85.1883 - 612.157i) q^{72} +(-503.982 + 290.974i) q^{73} -43.6458i q^{74} +(840.167 + 58.1789i) q^{75} +(-503.078 + 290.452i) q^{76} +(-112.142 - 70.2817i) q^{77} +(401.586 - 596.245i) q^{78} +(85.9381 + 148.849i) q^{79} +(-21.1572 - 36.6454i) q^{80} +(701.301 + 199.042i) q^{81} +(200.876 + 115.976i) q^{82} +(-635.597 + 1100.89i) q^{83} +(-187.745 - 422.423i) q^{84} +(-18.0414 - 31.2486i) q^{85} +309.256i q^{86} +(-550.917 - 371.056i) q^{87} +163.579 q^{88} +(-175.384 + 303.774i) q^{89} +(757.923 - 307.415i) q^{90} +(51.9198 - 1432.18i) q^{91} +(-45.2133 - 26.1039i) q^{92} +(917.632 + 618.047i) q^{93} +(-626.847 - 361.910i) q^{94} +(-1774.49 - 1024.50i) q^{95} +(769.995 + 518.611i) q^{96} +(-73.3753 - 42.3633i) q^{97} +(507.482 + 344.268i) q^{98} +(-26.5937 + 191.100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} + O(q^{10}) $	\( 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} - 6q^{10} - 3q^{12} + 36q^{13} + 129q^{14} - 141q^{15} - 263q^{16} + 72q^{17} - 15q^{18} - 6q^{19} - 24q^{20} - 306q^{21} + 14q^{22} - 66q^{24} + 698q^{25} + 96q^{26} - 432q^{27} - 156q^{28} - 132q^{29} + 852q^{30} + 177q^{31} - 501q^{32} + 849q^{33} - 24q^{34} - 765q^{35} + 1122q^{36} + 82q^{37} - 1746q^{38} - 645q^{39} - 618q^{41} - 963q^{42} + 82q^{43} - 603q^{44} + 303q^{45} + 266q^{46} - 201q^{47} + 1569q^{48} + 515q^{49} - 1845q^{50} + 417q^{51} - 564q^{53} - 684q^{54} + 3600q^{56} + 1170q^{57} - 538q^{58} + 747q^{59} - 516q^{60} - 1209q^{61} + 2904q^{62} + 1557q^{63} - 1144q^{64} - 831q^{65} + 1029q^{66} + 295q^{67} + 7008q^{68} + 1005q^{69} - 390q^{70} - 1119q^{72} - 6q^{73} - 1788q^{75} + 144q^{76} - 1203q^{77} - 5985q^{78} - 551q^{79} + 4239q^{80} + 3741q^{81} + 18q^{82} - 1830q^{83} - 7725q^{84} - 237q^{85} - 2130q^{87} + 1246q^{88} - 4266q^{89} - 9993q^{90} - 1140q^{91} + 7896q^{92} - 1479q^{93} - 3q^{94} - 1053q^{95} + 5034q^{96} + 792q^{97} - 5667q^{98} + 4335q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.54833	+	0.893930i	−0.547418	+	0.316052i	−0.748080	−	0.663609i	$-0.769024\pi$
$2$	−1.54833	+	0.893930i	−0.547418	+	0.316052i	0.200662	+	0.979661i	$0.435691\pi$
$3$	5.18374	+	0.358957i	0.997611	+	0.0690814i
$3$	5.18374	+	0.358957i	0.997611	+	0.0690814i
$4$	−2.40178	+	4.16000i	−0.300222	+	0.520000i
$5$	−16.9434			−1.51546			−0.757730	−	0.652568i	$-0.773692\pi$
$5$	−16.9434			−1.51546			−0.757730	+	0.652568i	$0.773692\pi$
$6$	−8.34703	+	4.07812i	−0.567944	+	0.277481i
$7$	−9.83512	+	15.6930i	−0.531046	+	0.847343i
$7$	−9.83512	+	15.6930i	−0.531046	+	0.847343i
$8$		−	22.8910i		−	1.01165i
$9$	26.7423	+	3.72148i	0.990456	+	0.137833i
$10$	26.2340	−	15.1462i	0.829591	−	0.478964i
$11$			7.14600i			0.195873i	0.995193	+	0.0979364i	$0.0312242\pi$
$11$			7.14600i			0.195873i	−0.995193	+	0.0979364i	$0.968776\pi$
$12$	−13.9435	+	20.7022i	−0.335427	+	0.498018i
$13$	−67.0144	+	38.6908i	−1.42973	+	0.825453i	−0.997099	−	0.0761201i	$-0.975747\pi$
$13$	−67.0144	+	38.6908i	−1.42973	+	0.825453i	−0.432627	+	0.901573i	$0.642413\pi$
$14$	1.19958	−	33.0899i	0.0229001	−	0.631689i
$15$	−87.8300	−	6.08194i	−1.51184	−	0.104690i
$16$	1.24870	+	2.16282i	0.0195110	+	0.0337941i
$17$	1.06481	+	1.84430i	0.0151914	+	0.0263122i	0.873521	−	0.486786i	$-0.161831\pi$
$17$	1.06481	+	1.84430i	0.0151914	+	0.0263122i	−0.858330	+	0.513098i	$0.828498\pi$
$18$	−44.7327	+	18.1437i	−0.585756	+	0.237583i
$19$	104.730	+	60.4661i	1.26457	+	0.730099i	0.973955	−	0.226741i	$-0.0728072\pi$
$19$	104.730	+	60.4661i	1.26457	+	0.730099i	0.290614	+	0.956840i	$0.406141\pi$
$20$	40.6942	−	70.4844i	0.454975	−	0.788040i
$21$	−56.6158	+	77.8181i	−0.588313	+	0.808633i
$22$	−6.38802	−	11.0644i	−0.0619060	−	0.107224i
$23$			10.8686i			0.0985329i	0.998786	+	0.0492664i	$0.0156883\pi$
$23$			10.8686i			0.0985329i	−0.998786	+	0.0492664i	$0.984312\pi$
$24$	8.21688	−	118.661i	0.0698860	−	1.00923i
$25$	162.077			1.29662
$26$	69.1737	−	119.812i	0.521772	−	0.903736i
$27$	137.289	+	28.8905i	0.978568	+	0.205925i
$28$	−41.6612	−	78.6052i	−0.281186	−	0.530535i
$29$	−110.704	−	63.9149i	−0.708869	−	0.409266i	0.101773	−	0.994808i	$-0.467548\pi$
$29$	−110.704	−	63.9149i	−0.708869	−	0.409266i	−0.810642	+	0.585542i	$0.800882\pi$
$30$	141.427	−	69.0970i	0.860696	−	0.420511i
$31$	184.393	+	106.459i	1.06832	+	0.616796i	0.927723	−	0.373270i	$-0.121764\pi$
$31$	184.393	+	106.459i	1.06832	+	0.616796i	0.140600	+	0.990067i	$0.455097\pi$
$32$	154.726	+	89.3314i	0.854751	+	0.493491i
$33$	−2.56511	+	37.0430i	−0.0135312	+	0.195405i
$34$	−3.29735	−	1.90372i	−0.0166321	−	0.00960253i
$35$	166.640	−	265.892i	0.804780	−	1.28411i
$36$	−79.7104	+	102.310i	−0.369030	+	0.473657i
$37$	−12.2062	+	21.1417i	−0.0542346	+	0.0939371i	−0.891868	−	0.452296i	$-0.850605\pi$
$37$	−12.2062	+	21.1417i	−0.0542346	+	0.0939371i	0.837634	+	0.546233i	$0.183939\pi$
$38$	−216.210			−0.922997
$39$	−361.273	+	176.507i	−1.48333	+	0.724713i
$40$			387.850i			1.53311i
$41$	−64.8686	−	112.356i	−0.247092	−	0.427976i	0.715626	−	0.698484i	$-0.246142\pi$
$41$	−64.8686	−	112.356i	−0.247092	−	0.427976i	−0.962718	+	0.270508i	$0.912808\pi$
$42$	18.0962	−	171.099i	0.0664833	−	0.628598i
$43$	86.4878	−	149.801i	0.306727	−	0.531267i	−0.670917	−	0.741532i	$-0.734099\pi$
$43$	86.4878	−	149.801i	0.306727	−	0.531267i	0.977644	+	0.210265i	$0.0674327\pi$
$44$	−29.7274	−	17.1631i	−0.101854	−	0.0588053i
$45$	−453.104	−	63.0544i	−1.50100	−	0.208880i
$46$	−9.71576	−	16.8282i	−0.0311415	−	0.0539387i
$47$	202.426	+	350.613i	0.628232	+	1.08813i	0.987906	+	0.155052i	$0.0495546\pi$
$47$	202.426	+	350.613i	0.628232	+	1.08813i	−0.359674	+	0.933078i	$0.617112\pi$
$48$	5.69660	+	11.6597i	0.0171299	+	0.0350612i
$49$	−149.541	−	308.685i	−0.435979	−	0.899957i
$50$	−250.950	+	144.886i	−0.709793	+	0.409799i
$51$	4.85765	+	9.94258i	0.0133374	+	0.0272988i
$52$		−	371.706i		−	0.991277i
$53$	−291.479	+	168.286i	−0.755429	+	0.436147i	−0.827652	−	0.561241i	$-0.810324\pi$
$53$	−291.479	+	168.286i	−0.755429	+	0.436147i	0.0722231	+	0.997388i	$0.476991\pi$
$54$	−238.396	+	77.9949i	−0.600769	+	0.196551i
$55$		−	121.077i		−	0.296837i
$56$	359.228	+	225.135i	0.857212	+	0.537232i
$57$	521.190	+	351.034i	1.21111	+	0.815713i
$58$	228.542			0.517397
$59$	−330.799	+	572.960i	−0.729938	+	1.26429i	0.226971	+	0.973901i	$0.427118\pi$
$59$	−330.799	+	572.960i	−0.729938	+	1.26429i	−0.956909	+	0.290388i	$0.906216\pi$
$60$	236.249	−	350.765i	0.508327	−	0.754727i
$61$	−300.606	+	173.555i	−0.630961	+	0.364286i	−0.781124	−	0.624376i	$-0.785353\pi$
$61$	−300.606	+	173.555i	−0.630961	+	0.364286i	0.150163	+	0.988661i	$0.452020\pi$
$62$	−380.669			−0.779759
$63$	−321.415	+	383.066i	−0.642769	+	0.766060i
$64$	−339.403			−0.662897
$65$	1135.45	−	655.551i	2.16669	−	1.25094i
$66$	−29.1422	−	59.6479i	−0.0543509	−	0.111245i
$67$	134.558	−	233.062i	0.245357	−	0.424971i	−0.716875	−	0.697202i	$-0.754428\pi$
$67$	134.558	−	233.062i	0.245357	−	0.424971i	0.962232	+	0.272231i	$0.0877615\pi$
$68$	−10.2297			−0.0182432
$69$	−3.90136	+	56.3399i	−0.00680679	+	0.0982975i
$70$	−20.3249	+	560.654i	−0.0347042	+	0.957300i
$71$		−	637.224i		−	1.06514i	−0.846387	−	0.532568i	$-0.821227\pi$
$71$		−	637.224i		−	1.06514i	0.846387	−	0.532568i	$-0.178773\pi$
$72$	85.1883	−	612.157i	0.139438	−	1.00199i
$73$	−503.982	+	290.974i	−0.808036	+	0.466520i	−0.846273	−	0.532749i	$-0.821159\pi$
$73$	−503.982	+	290.974i	−0.808036	+	0.466520i	0.0382377	+	0.999269i	$0.487826\pi$
$74$		−	43.6458i		−	0.0685638i
$75$	840.167	+	58.1789i	1.29352	+	0.0895723i
$76$	−503.078	+	290.452i	−0.759303	+	0.438384i
$77$	−112.142	−	70.2817i	−0.165971	−	0.104018i
$78$	401.586	−	596.245i	0.582957	−	0.865532i
$79$	85.9381	+	148.849i	0.122390	+	0.211985i	0.920710	−	0.390248i	$-0.127611\pi$
$79$	85.9381	+	148.849i	0.122390	+	0.211985i	−0.798320	+	0.602234i	$0.794278\pi$
$80$	−21.1572	−	36.6454i	−0.0295682	−	0.0512135i
$81$	701.301	+	199.042i	0.962004	+	0.273034i
$82$	200.876	+	115.976i	0.270525	+	0.156188i
$83$	−635.597	+	1100.89i	−0.840552	+	1.45588i	0.0488762	+	0.998805i	$0.484436\pi$
$83$	−635.597	+	1100.89i	−0.840552	+	1.45588i	−0.889428	+	0.457074i	$0.848897\pi$
$84$	−187.745	−	422.423i	−0.243865	−	0.548693i
$85$	−18.0414	−	31.2486i	−0.0230219	−	0.0398751i
$86$			309.256i			0.387767i
$87$	−550.917	−	371.056i	−0.678903	−	0.457257i
$88$	163.579			0.198154
$89$	−175.384	+	303.774i	−0.208884	+	0.361798i	−0.951363	−	0.308071i	$-0.900316\pi$
$89$	−175.384	+	303.774i	−0.208884	+	0.361798i	0.742479	+	0.669869i	$0.233650\pi$
$90$	757.923	−	307.415i	0.887689	−	0.360048i
$91$	51.9198	−	1432.18i	0.0598096	−	1.64982i
$92$	−45.2133	−	26.1039i	−0.0512371	−	0.0295818i
$93$	917.632	+	618.047i	1.02316	+	0.689124i
$94$	−626.847	−	361.910i	−0.687812	−	0.397108i
$95$	−1774.49	−	1024.50i	−1.91640	−	1.10644i
$96$	769.995	+	518.611i	0.818618	+	0.551359i
$97$	−73.3753	−	42.3633i	−0.0768055	−	0.0443437i	0.461105	−	0.887345i	$-0.347453\pi$
$97$	−73.3753	−	42.3633i	−0.0768055	−	0.0443437i	−0.537911	+	0.843002i	$0.680786\pi$
$98$	507.482	+	344.268i	0.523096	+	0.354860i
$99$	−26.5937	+	191.100i	−0.0269977	+	0.194003i
$100$	−389.274	+	674.243i	−0.389274	+	0.674243i
$101$	1647.26			1.62285			0.811427	−	0.584453i	$-0.198691\pi$
$101$	1647.26			1.62285			0.811427	+	0.584453i	$0.198691\pi$
$102$	−16.4092	−	11.0520i	−0.0159290	−	0.0107286i
$103$		−	1841.23i		−	1.76137i	−0.473698	−	0.880687i	$-0.657081\pi$
$103$		−	1841.23i		−	1.76137i	0.473698	−	0.880687i	$-0.342919\pi$
$104$	885.669	+	1534.02i	0.835067	+	1.44638i
$105$	959.262	−	1318.50i	0.891566	−	1.22545i
$106$	300.871	−	521.124i	0.275690	−	0.477510i
$107$	−377.689	−	218.059i	−0.341239	−	0.197014i	0.319581	−	0.947559i	$-0.396458\pi$
$107$	−377.689	−	218.059i	−0.341239	−	0.197014i	−0.660820	+	0.750545i	$0.729791\pi$
$108$	−449.923	+	501.735i	−0.400869	+	0.447032i
$109$	583.379	+	1010.44i	0.512638	+	0.887915i	0.999893	+	0.0146552i	$0.00466507\pi$
$109$	583.379	+	1010.44i	0.512638	+	0.887915i	−0.487255	+	0.873260i	$0.662002\pi$
$110$	108.235	+	187.468i	0.0938160	+	0.162494i
$111$	−70.8625	+	105.211i	−0.0605943	+	0.0899661i
$112$	−46.2223	−	1.67566i	−0.0389964	−	0.00141370i
$113$	127.611	−	73.6761i	0.106236	−	0.0613351i	−0.445941	−	0.895062i	$-0.647131\pi$
$113$	127.611	−	73.6761i	0.106236	−	0.0613351i	0.552176	+	0.833727i	$0.313798\pi$
$114$	−1120.78	−	77.6101i	−0.920792	−	0.0637619i
$115$		−	184.150i		−	0.149323i
$116$	531.772	−	307.019i	0.425636	−	0.245741i
$117$	−1936.10	+	785.287i	−1.52985	+	0.620511i
$118$		−	1182.84i		−	0.922793i
$119$	−39.4151	−	1.42888i	−0.0303628	−	0.00110072i
$120$	−139.222	+	2010.51i	−0.105909	+	1.52945i
$121$	1279.93			0.961634
$122$	310.292	−	537.441i	0.230266	−	0.398833i
$123$	−295.931	−	605.708i	−0.216937	−	0.444023i
$124$	−885.743	+	511.384i	−0.641468	+	0.370352i
$125$	−628.217			−0.449516
$126$	155.223	−	880.436i	0.109749	−	0.622504i
$127$	−29.4522			−0.0205784			−0.0102892	−	0.999947i	$-0.503275\pi$
$127$	−29.4522			−0.0205784			−0.0102892	+	0.999947i	$0.503275\pi$
$128$	−712.303	+	411.248i	−0.491869	+	0.283981i
$129$	502.103	−	745.486i	0.342695	−	0.508809i
$130$	−1172.03	+	2030.02i	−0.790725	+	1.36958i
$131$	−979.694			−0.653407			−0.326703	−	0.945127i	$-0.605938\pi$
$131$	−979.694			−0.653407			−0.326703	+	0.945127i	$0.605938\pi$
$132$	−147.938	−	99.6399i	−0.0975482	−	0.0657011i
$133$	−1978.93	+	1048.84i	−1.29019	+	0.683807i
$134$			481.143i			0.310182i
$135$	−2326.14	−	489.503i	−1.48298	−	0.312072i
$136$	42.2178	−	24.3744i	0.0266187	−	0.0153683i
$137$			1243.14i			0.775244i	0.921818	+	0.387622i	$0.126703\pi$
$137$			1243.14i			0.775244i	−0.921818	+	0.387622i	$0.873297\pi$
$138$	−44.3233	−	90.7204i	−0.0273410	−	0.0559611i
$139$	976.590	−	563.835i	0.595923	−	0.344056i	−0.171513	−	0.985182i	$-0.554866\pi$
$139$	976.590	−	563.835i	0.595923	−	0.344056i	0.767436	+	0.641126i	$0.221532\pi$
$140$	705.880	+	1331.84i	0.426127	+	0.804005i
$141$	923.470	+	1890.15i	0.551562	+	1.12893i
$142$	569.634	+	986.635i	0.336638	+	0.583074i
$143$	−276.484	−	478.885i	−0.161684	−	0.280044i
$144$	25.3443	+	62.4858i	0.0146669	+	0.0361608i
$145$	1875.70	+	1082.93i	1.07426	+	0.620226i
$146$	520.221	−	901.049i	0.294889	−	0.510763i
$147$	−664.376	−	1653.82i	−0.372768	−	0.927925i
$148$	−58.6330	−	101.555i	−0.0325649	−	0.0564040i
$149$		−	2166.55i		−	1.19121i	−0.803276	−	0.595607i	$-0.796912\pi$
$149$		−	2166.55i		−	1.19121i	0.803276	−	0.595607i	$-0.203088\pi$
$150$	−1352.87	+	660.971i	−0.736407	+	0.359787i
$151$	2142.13			1.15447			0.577233	−	0.816580i	$-0.304133\pi$
$151$	2142.13			1.15447			0.577233	+	0.816580i	$0.304133\pi$
$152$	1384.13	−	2397.38i	0.738603	−	1.27930i
$153$	21.6118	+	53.2834i	0.0114197	+	0.0281550i
$154$	236.460	+	8.57220i	0.123731	+	0.00448550i
$155$	−3124.24	−	1803.78i	−1.61900	−	0.934730i
$156$	133.427	−	1926.83i	0.0684788	−	0.988909i
$157$	2593.06	+	1497.11i	1.31815	+	0.761032i	0.983430	−	0.181287i	$-0.0580264\pi$
$157$	2593.06	+	1497.11i	1.31815	+	0.761032i	0.334716	+	0.942319i	$0.391360\pi$
$158$	−266.121	−	153.645i	−0.133997	−	0.0773630i
$159$	−1571.36	+	767.720i	−0.783754	+	0.382919i
$160$	−2621.59	−	1513.57i	−1.29534	−	0.747866i
$161$	−170.561	−	106.894i	−0.0834911	−	0.0523255i
$162$	−1263.78	+	318.731i	−0.612912	+	0.154580i
$163$	−1154.51	+	1999.68i	−0.554776	+	0.960901i	0.443145	+	0.896450i	$0.353863\pi$
$163$	−1154.51	+	1999.68i	−0.554776	+	0.960901i	−0.997921	+	0.0644506i	$0.979471\pi$
$164$	623.200			0.296730
$165$	43.4616	−	627.633i	0.0205059	−	0.296128i
$166$		−	2272.72i		−	1.06263i
$167$	1145.13	+	1983.42i	0.530616	+	0.919053i	0.999362	+	0.0357205i	$0.0113726\pi$
$167$	1145.13	+	1983.42i	0.530616	+	0.919053i	−0.468746	+	0.883333i	$0.655294\pi$
$168$	1781.33	+	1295.99i	0.818052	+	0.595166i
$169$	1895.45	−	3283.01i	0.862744	−	1.49432i
$170$	55.8681	+	32.2555i	0.0252052	+	0.0145523i
$171$	2575.71	+	2006.76i	1.15187	+	0.897430i
$172$	415.449	+	719.579i	0.184173	+	0.318996i
$173$	−821.495	−	1422.87i	−0.361024	−	0.625312i	0.627106	−	0.778934i	$-0.284239\pi$
$173$	−821.495	−	1422.87i	−0.361024	−	0.625312i	−0.988130	+	0.153622i	$0.950906\pi$
$174$	1184.70	+	82.0368i	0.516161	+	0.0357425i
$175$	−1594.05	+	2543.48i	−0.688565	+	1.09868i
$176$	−15.4555	+	8.92324i	−0.00661933	+	0.00382167i
$177$	−1920.44	+	2851.33i	−0.815533	+	1.21084i
$178$		−	627.125i		−	0.264073i
$179$	2452.01	−	1415.67i	1.02386	−	0.591129i	0.108644	−	0.994081i	$-0.465349\pi$
$179$	2452.01	−	1415.67i	1.02386	−	0.591129i	0.915221	+	0.402952i	$0.132016\pi$
$180$	1350.56	−	1733.47i	0.559250	−	0.717808i
$181$		−	918.046i		−	0.377005i	−0.982073	−	0.188502i	$-0.939637\pi$
$181$		−	918.046i		−	0.377005i	0.982073	−	0.188502i	$-0.0603633\pi$
$182$	1199.88	+	2263.91i	0.488689	+	0.922045i
$183$	−1620.56	+	791.758i	−0.654619	+	0.319828i
$184$	248.792			0.0996805
$185$	206.813	−	358.211i	0.0821904	−	0.142358i
$186$	−1973.29	−	136.644i	−0.777896	−	0.0538668i
$187$	−13.1794	+	7.60910i	−0.00515385	+	0.00297558i
$188$	−1944.73			−0.754437
$189$	−1803.64	+	1870.34i	−0.694154	+	0.719826i
$190$	3663.32			1.39877
$191$	1671.69	−	965.153i	0.633296	−	0.365634i	−0.148731	−	0.988878i	$-0.547519\pi$
$191$	1671.69	−	965.153i	0.633296	−	0.365634i	0.782027	+	0.623244i	$0.214186\pi$
$192$	−1759.38	−	121.831i	−0.661313	−	0.0457938i
$193$	666.196	−	1153.89i	0.248466	−	0.430355i	−0.714635	−	0.699498i	$-0.753407\pi$
$193$	666.196	−	1153.89i	0.248466	−	0.430355i	0.963100	+	0.269143i	$0.0867404\pi$
$194$	151.479			0.0560596
$195$	6121.18	−	2990.63i	2.24793	−	1.09827i
$196$	1643.29	+	119.303i	0.598868	+	0.0434777i
$197$		−	1816.48i		−	0.656949i	−0.944513	−	0.328474i	$-0.893466\pi$
$197$		−	1816.48i		−	0.656949i	0.944513	−	0.328474i	$-0.106534\pi$
$198$	−129.655	−	319.660i	−0.0465361	−	0.114734i
$199$	58.8698	−	33.9885i	0.0209707	−	0.0121074i	−0.489478	−	0.872016i	$-0.662813\pi$
$199$	58.8698	−	33.9885i	0.0209707	−	0.0121074i	0.510449	+	0.859908i	$0.329479\pi$
$200$		−	3710.11i		−	1.31172i
$201$	781.174	−	1159.83i	0.274128	−	0.407006i
$202$	−2550.50	+	1472.53i	−0.888380	+	0.512907i
$203$	2091.80	−	1108.67i	0.723230	−	0.383316i
$204$	−53.0281	−	3.67203i	−0.0181996	−	0.00126026i
$205$	1099.09	+	1903.68i	0.374458	+	0.648581i
$206$	1645.93	+	2850.83i	0.556686	+	0.964209i
$207$	−40.4472	+	290.651i	−0.0135810	+	0.0975924i
$208$	−167.362	−	96.6266i	−0.0557908	−	0.0322108i
$209$	−432.091	+	748.404i	−0.143007	+	0.247695i
$210$	−306.610	+	2898.99i	−0.100753	+	0.952615i
$211$	856.959	+	1484.30i	0.279599	+	0.484280i	0.971285	−	0.237918i	$-0.0764650\pi$
$211$	856.959	+	1484.30i	0.279599	+	0.484280i	−0.691686	+	0.722199i	$0.743132\pi$
$212$		−	1616.74i		−	0.523764i
$213$	228.736	−	3303.20i	0.0735810	−	1.06259i
$214$	779.717			0.249067
$215$	−1465.39	+	2538.14i	−0.464833	+	0.805114i
$216$	661.332	−	3142.68i	0.208324	−	0.989966i
$217$	−3484.20	+	1846.64i	−1.08997	+	0.577688i
$218$	−1806.53	−	1043.00i	−0.561255	−	0.324041i
$219$	−2716.96	+	1327.43i	−0.838333	+	0.409585i
$220$	503.682	+	290.801i	0.154355	+	0.0891172i
$221$	−142.715	−	82.3963i	−0.0434390	−	0.0250795i
$222$	15.6670	−	226.248i	0.00473648	−	0.0684000i
$223$	−2434.38	−	1405.49i	−0.731023	−	0.422056i	0.0877734	−	0.996140i	$-0.472025\pi$
$223$	−2434.38	−	1405.49i	−0.731023	−	0.422056i	−0.818796	+	0.574084i	$0.805358\pi$
$224$	−2923.63	+	1549.54i	−0.872068	+	0.462201i
$225$	4334.32	+	603.168i	1.28424	+	0.178717i
$226$	−131.723	+	228.150i	−0.0387702	+	0.0671519i
$227$	−3911.92			−1.14380			−0.571901	−	0.820322i	$-0.693794\pi$
$227$	−3911.92			−1.14380			−0.571901	+	0.820322i	$0.693794\pi$
$228$	−2712.09	+	1325.05i	−0.787774	+	0.384883i
$229$			1284.55i			0.370680i	0.982674	+	0.185340i	$0.0593386\pi$
$229$			1284.55i			0.370680i	−0.982674	+	0.185340i	$0.940661\pi$
$230$	164.618	+	285.126i	0.0471937	+	0.0817420i
$231$	−556.088	−	404.577i	−0.158389	−	0.115235i
$232$	−1463.07	+	2534.12i	−0.414032	+	0.717125i
$233$	1309.89	+	756.266i	0.368300	+	0.212638i	0.672715	−	0.739901i	$-0.265128\pi$
$233$	1309.89	+	756.266i	0.368300	+	0.212638i	−0.304416	+	0.952539i	$0.598461\pi$
$234$	2295.74	−	2946.63i	0.641356	−	0.823193i
$235$	−3429.78	−	5940.56i	−0.952061	−	1.64902i
$236$	−1589.01	−	2752.25i	−0.438287	−	0.759135i
$237$	392.050	+	802.443i	0.107453	+	0.219934i
$238$	62.3049	−	33.0219i	0.0169690	−	0.00899367i
$239$	−2341.49	+	1351.86i	−0.633718	+	0.365877i	−0.782191	−	0.623039i	$-0.785898\pi$
$239$	−2341.49	+	1351.86i	−0.633718	+	0.365877i	0.148473	+	0.988917i	$0.452564\pi$
$240$	−96.5195	−	197.555i	−0.0259596	−	0.0531338i
$241$			4934.13i			1.31882i	0.751785	+	0.659409i	$0.229193\pi$
$241$			4934.13i			1.31882i	−0.751785	+	0.659409i	$0.770807\pi$
$242$	−1981.76	+	1144.17i	−0.526416	+	0.303926i
$243$	3563.91	+	1283.52i	0.940845	+	0.338838i
$244$		−	1667.36i		−	0.437467i
$245$	2533.73	+	5230.16i	0.660709	+	1.36385i
$246$	999.660	+	673.295i	0.259089	+	0.174503i
$247$	−9357.92			−2.41065
$248$	2436.96	−	4220.94i	0.623980	−	1.08077i
$249$	−3689.94	+	5478.56i	−0.939118	+	1.39433i
$250$	972.689	−	561.582i	0.246073	−	0.142070i
$251$	−633.966			−0.159425			−0.0797123	−	0.996818i	$-0.525400\pi$
$251$	−633.966			−0.159425			−0.0797123	+	0.996818i	$0.525400\pi$
$252$	−821.587	−	2257.13i	−0.205378	−	0.564228i
$253$	−77.6669			−0.0192999
$254$	45.6018	−	26.3282i	0.0112650	−	0.00650386i
$255$	−82.3049	−	168.461i	−0.0202123	−	0.0413703i
$256$	2092.87	−	3624.95i	0.510954	−	0.884998i
$257$	−532.495			−0.129246			−0.0646228	−	0.997910i	$-0.520584\pi$
$257$	−532.495			−0.129246			−0.0646228	+	0.997910i	$0.520584\pi$
$258$	−111.010	+	1603.10i	−0.0267875	+	0.386841i
$259$	−211.728	−	399.482i	−0.0507958	−	0.0958402i
$260$			6297.96i			1.50224i
$261$	−2722.62	−	2121.21i	−0.645693	−	0.503065i
$262$	1516.89	−	875.778i	0.357687	−	0.206511i
$263$			5230.97i			1.22645i	0.789910	+	0.613223i	$0.210127\pi$
$263$			5230.97i			1.22645i	−0.789910	+	0.613223i	$0.789873\pi$
$264$	847.950	+	58.7178i	0.197681	+	0.0136888i
$265$	4938.64	−	2851.32i	1.14482	−	0.660964i
$266$	2126.45	−	3392.99i	0.490154	−	0.782095i
$267$	−1018.19	+	1511.73i	−0.233379	+	0.346504i
$268$	646.358	+	1119.53i	0.147323	+	0.255171i
$269$	3581.36	+	6203.09i	0.811744	+	1.40598i	0.911642	+	0.410985i	$0.134815\pi$
$269$	3581.36	+	6203.09i	0.811744	+	1.40598i	−0.0998978	+	0.994998i	$0.531852\pi$
$270$	4039.22	−	1321.49i	0.910441	−	0.297865i
$271$	669.831	+	386.727i	0.150145	+	0.0866863i	0.573190	−	0.819422i	$-0.305706\pi$
$271$	669.831	+	386.727i	0.150145	+	0.0866863i	−0.423045	+	0.906109i	$0.639039\pi$
$272$	−2.65926	+	4.60597i	−0.000592798	+	0.00102676i
$273$	783.232	−	7405.44i	0.173639	−	1.64175i
$274$	−1111.28	−	1924.79i	−0.245017	−	0.424382i
$275$			1158.21i			0.253972i
$276$	−225.004	−	151.546i	−0.0490712	−	0.0330506i
$277$	−985.162			−0.213692			−0.106846	−	0.994276i	$-0.534075\pi$
$277$	−985.162			−0.213692			−0.106846	+	0.994276i	$0.534075\pi$
$278$	−1008.06	+	1746.01i	−0.217479	+	0.376685i
$279$	4534.91	+	3533.19i	0.973111	+	0.758159i
$280$	−6086.53	−	3814.55i	−1.29907	−	0.814153i
$281$	−68.0344	−	39.2797i	−0.0144434	−	0.00833890i	0.492761	−	0.870165i	$-0.335988\pi$
$281$	−68.0344	−	39.2797i	−0.0144434	−	0.00833890i	−0.507204	+	0.861826i	$0.669321\pi$
$282$	−3119.50	−	2101.06i	−0.658736	−	0.443674i
$283$	−2059.84	−	1189.25i	−0.432668	−	0.249801i	0.267815	−	0.963470i	$-0.413698\pi$
$283$	−2059.84	−	1189.25i	−0.432668	−	0.249801i	−0.700482	+	0.713670i	$0.747032\pi$
$284$	2650.85	+	1530.47i	0.553871	+	0.319777i
$285$	−8830.72	−	5947.70i	−1.83539	−	1.23618i
$286$	856.179	+	494.315i	0.177017	+	0.102201i
$287$	2401.19	+	87.0483i	0.493860	+	0.0179035i
$288$	3805.30	+	2964.74i	0.778574	+	0.606593i
$289$	2454.23	−	4250.86i	0.499538	−	0.865226i
$290$	−3872.27			−0.784094
$291$	−365.152	−	245.939i	−0.0735587	−	0.0495436i
$292$		−	2795.42i		−	0.560238i
$293$	1799.84	+	3117.41i	0.358866	+	0.621573i	0.987772	−	0.155908i	$-0.0498303\pi$
$293$	1799.84	+	3117.41i	0.358866	+	0.621573i	−0.628906	+	0.777481i	$0.716497\pi$
$294$	2507.08	+	1966.76i	0.497332	+	0.390149i
$295$	5604.84	−	9707.87i	1.10619	−	1.91598i
$296$	483.954	+	279.411i	0.0950312	+	0.0548663i
$297$	−206.452	+	981.069i	−0.0403352	+	0.191675i
$298$	1936.75	+	3354.54i	0.376485	+	0.652092i
$299$	−420.514	−	728.351i	−0.0813342	−	0.140875i
$300$	−2259.92	+	3355.36i	−0.434922	+	0.645740i
$301$	1500.22	+	2830.57i	0.287279	+	0.542031i
$302$	−3316.73	+	1914.92i	−0.631975	+	0.364871i
$303$	8538.96	+	591.295i	1.61898	+	0.112109i
$304$			302.017i			0.0569799i
$305$	5093.27	−	2940.60i	0.956197	−	0.552060i
$306$	−81.0940	−	63.1810i	−0.0151498	−	0.0118033i
$307$			2829.86i			0.526086i	0.964784	+	0.263043i	$0.0847262\pi$
$307$			2829.86i			0.526086i	−0.964784	+	0.263043i	$0.915274\pi$
$308$	561.713	−	297.711i	0.103917	−	0.0550767i
$309$	660.922	−	9544.45i	0.121678	−	1.75717i
$310$	6449.82			1.18169
$311$	3570.62	−	6184.49i	0.651033	−	1.12762i	−0.331840	−	0.943336i	$-0.607669\pi$
$311$	3570.62	−	6184.49i	0.651033	−	1.12762i	0.982873	−	0.184286i	$-0.0589974\pi$
$312$	4040.43	+	8269.89i	0.733154	+	1.50061i
$313$	−3058.15	+	1765.62i	−0.552259	+	0.318847i	−0.750032	−	0.661401i	$-0.769962\pi$
$313$	−3058.15	+	1765.62i	−0.552259	+	0.318847i	0.197774	+	0.980248i	$0.436629\pi$
$314$	−5353.23			−0.962103
$315$	5445.85	−	6490.42i	0.974091	−	1.16093i
$316$	−825.616			−0.146976
$317$	1844.54	−	1064.95i	0.326814	−	0.188686i	−0.327612	−	0.944812i	$-0.606244\pi$
$317$	1844.54	−	1064.95i	0.326814	−	0.188686i	0.654426	+	0.756126i	$0.272911\pi$
$318$	1746.70	−	2593.37i	0.308019	−	0.457324i
$319$	456.736	−	791.090i	0.0801640	−	0.138848i
$320$	5750.63			1.00459
$321$	−1879.57	−	1265.93i	−0.326813	−	0.220117i
$322$	359.640	+	13.0377i	0.0622422	+	0.00225641i
$323$			257.539i			0.0443648i
$324$	−2512.38	+	2439.36i	−0.430793	+	0.418271i
$325$	−10861.5	+	6270.90i	−1.85381	+	1.07030i
$326$		−	4128.22i		−	0.701353i
$327$	2661.38	+	5447.27i	0.450075	+	0.921208i
$328$	−2571.93	+	1484.91i	−0.432961	+	0.249970i
$329$	−7493.05	−	271.639i	−1.25564	−	0.0455196i
$330$	493.767	+	1010.64i	0.0823666	+	0.168587i
$331$	2449.86	+	4243.28i	0.406817	+	0.704628i	0.994531	−	0.104441i	$-0.0333054\pi$
$331$	2449.86	+	4243.28i	0.406817	+	0.704628i	−0.587714	+	0.809069i	$0.699972\pi$
$332$	−3053.13	−	5288.17i	−0.504705	−	0.874175i
$333$	−405.099	+	519.952i	−0.0666646	+	0.0855652i
$334$	−3546.08	−	2047.33i	−0.580937	−	0.335404i
$335$	−2279.87	+	3948.85i	−0.371829	+	0.644026i
$336$	−239.003	−	25.2780i	−0.0388056	−	0.00410425i
$337$	−1234.19	−	2137.68i	−0.199497	−	0.345539i	0.748868	−	0.662719i	$-0.230598\pi$
$337$	−1234.19	−	2137.68i	−0.199497	−	0.345539i	−0.948365	+	0.317180i	$0.897264\pi$
$338$			6777.60i			1.09069i
$339$	687.948	−	336.111i	0.110219	−	0.0538497i
$340$	173.326			0.0276468
$341$	−760.759	+	1317.67i	−0.120814	+	0.209255i
$342$	−5781.95	−	804.622i	−0.914188	−	0.127219i
$343$	6314.95	+	689.208i	0.994097	+	0.108495i
$344$	−3429.10	−	1979.79i	−0.537455	−	0.310300i
$345$	66.1021	−	954.587i	0.0103154	−	0.148966i
$346$	2543.90	+	1468.72i	0.395262	+	0.228205i
$347$	−8699.48	−	5022.64i	−1.34586	−	0.777031i	−0.358197	−	0.933646i	$-0.616608\pi$
$347$	−8699.48	−	5022.64i	−1.34586	−	0.777031i	−0.987660	+	0.156615i	$0.949942\pi$
$348$	2866.78	−	1400.62i	0.441596	−	0.215751i
$349$	−9911.49	−	5722.40i	−1.52020	−	0.877688i	−0.999716	−	0.0238161i	$-0.992418\pi$
$349$	−9911.49	−	5722.40i	−1.52020	−	0.877688i	−0.520484	−	0.853872i	$-0.674248\pi$
$350$	194.425	−	5363.13i	0.0296927	−	0.819061i
$351$	−10318.1	+	3375.74i	−1.56907	+	0.513345i
$352$	−638.362	+	1105.68i	−0.0966614	+	0.167422i
$353$	1456.87			0.219664			0.109832	−	0.993950i	$-0.464969\pi$
$353$	1456.87			0.219664			0.109832	+	0.993950i	$0.464969\pi$
$354$	424.590	−	6131.55i	0.0637478	−	0.920589i
$355$			10796.7i			1.61417i
$356$	−842.468	−	1459.20i	−0.125423	−	0.217240i
$357$	−203.805	−	21.5553i	−0.0302142	−	0.00319559i
$358$	−2531.02	+	4383.85i	−0.373655	+	0.647189i
$359$	282.828	+	163.291i	0.0415797	+	0.0240060i	0.520646	−	0.853773i	$-0.325691\pi$
$359$	282.828	+	163.291i	0.0415797	+	0.0240060i	−0.479066	+	0.877779i	$0.659025\pi$
$360$	−1443.38	+	10372.0i	−0.211313	+	1.51848i
$361$	3882.81	+	6725.22i	0.566089	+	0.980496i
$362$	820.669	+	1421.44i	0.119153	+	0.206379i
$363$	6634.85	+	459.442i	0.959337	+	0.0664310i
$364$	5833.19	+	3655.78i	0.839951	+	0.526414i
$365$	8539.14	−	4930.08i	1.22455	−	0.706992i
$366$	1801.39	−	2674.57i	0.257268	−	0.381973i
$367$		−	6367.01i		−	0.905599i	−0.891612	−	0.452800i	$-0.850425\pi$
$367$		−	6367.01i		−	0.905599i	0.891612	−	0.452800i	$-0.149575\pi$
$368$	−23.5068	+	13.5716i	−0.00332983	+	0.00192248i
$369$	−1316.61	−	3246.06i	−0.185745	−	0.457949i
$370$			739.507i			0.103906i
$371$	225.825	−	6229.29i	0.0316018	−	0.871722i
$372$	−4775.03	+	2332.94i	−0.665520	+	0.325154i
$373$	−1937.38			−0.268938			−0.134469	−	0.990918i	$-0.542933\pi$
$373$	−1937.38			−0.268938			−0.134469	+	0.990918i	$0.542933\pi$
$374$	13.6040	−	23.5628i	0.00188087	−	0.00325777i
$375$	−3256.52	−	225.503i	−0.448442	−	0.0310532i
$376$	8025.86	−	4633.73i	1.10080	−	0.635550i
$377$	9891.67			1.35132
$378$	1120.67	−	4508.23i	0.152490	−	0.613435i
$379$	9315.44			1.26254			0.631269	−	0.775564i	$-0.282534\pi$
$379$	9315.44			1.26254			0.631269	+	0.775564i	$0.282534\pi$
$380$	8523.84	−	4921.24i	1.15069	−	0.664354i
$381$	−152.673	−	10.5721i	−0.0205293	−	0.00142159i
$382$	−1725.56	+	2988.76i	−0.231119	+	0.400309i
$383$	2954.91			0.394227			0.197114	−	0.980381i	$-0.436843\pi$
$383$	2954.91			0.394227			0.197114	+	0.980381i	$0.436843\pi$
$384$	−3840.01	+	1876.12i	−0.510312	+	0.249323i
$385$	1900.07	+	1190.81i	0.251523	+	0.157634i
$386$			2382.13i			0.314112i
$387$	2870.37	−	3684.17i	0.377026	−	0.483919i
$388$	352.462	−	203.494i	0.0461174	−	0.0266259i
$389$			4739.61i			0.617757i	0.951101	+	0.308879i	$0.0999537\pi$
$389$			4739.61i			0.617757i	−0.951101	+	0.308879i	$0.900046\pi$
$390$	−6804.21	+	10102.4i	−0.883448	+	1.31168i
$391$	−20.0449	+	11.5729i	−0.00259262	+	0.00149685i
$392$	−7066.10	+	3423.14i	−0.910439	+	0.441057i
$393$	−5078.48	−	351.668i	−0.651846	−	0.0451382i
$394$	1623.81	+	2812.52i	0.207630	+	0.359626i
$395$	−1456.08	−	2522.00i	−0.185477	−	0.321255i
$396$	−731.106	−	569.611i	−0.0927764	−	0.0722829i
$397$	6808.08	+	3930.65i	0.860674	+	0.496911i	0.864238	−	0.503083i	$-0.167801\pi$
$397$	6808.08	+	3930.65i	0.860674	+	0.496911i	−0.00356368	+	0.999994i	$0.501134\pi$
$398$	−60.7667	+	105.251i	−0.00765316	+	0.0132557i
$399$	−10634.8	+	4726.58i	−1.33434	+	0.593045i
$400$	202.387	+	350.544i	0.0252984	+	0.0438180i
$401$		−	4166.67i		−	0.518886i	−0.965758	−	0.259443i	$-0.916461\pi$
$401$		−	4166.67i		−	0.518886i	0.965758	−	0.259443i	$-0.0835390\pi$
$402$	−172.710	+	2494.12i	−0.0214278	+	0.309441i
$403$	−16476.0			−2.03654
$404$	−3956.35	+	6852.60i	−0.487217	+	0.843885i
$405$	−11882.4	−	3372.44i	−1.45788	−	0.413772i
$406$	−2247.74	+	3586.51i	−0.274762	+	0.438412i
$407$	−151.078	−	87.2252i	−0.0183997	−	0.0106231i
$408$	227.595	−	111.196i	0.0276168	−	0.0134927i
$409$	−11636.0	−	6718.04i	−1.40675	−	0.812190i	−0.411681	−	0.911328i	$-0.635058\pi$
$409$	−11636.0	−	6718.04i	−1.40675	−	0.812190i	−0.995074	+	0.0991379i	$0.968392\pi$
$410$	−3403.52	−	1965.02i	−0.409971	−	0.236697i
$411$	−446.233	+	6444.10i	−0.0535549	+	0.773392i
$412$	7659.51	+	4422.22i	0.915915	+	0.528804i
$413$	−5738.02	−	10826.4i	−0.683655	−	1.28990i
$414$	−197.196	−	486.181i	−0.0234098	−	0.0577162i
$415$	10769.2	−	18652.7i	1.27382	−	2.20633i
$416$	−13825.2			−1.62941
$417$	5264.78	−	2572.22i	0.618267	−	0.302067i
$418$		−	1545.04i		−	0.180790i
$419$	5509.22	+	9542.24i	0.642346	+	1.11258i	0.984908	+	0.173080i	$0.0553719\pi$
$419$	5509.22	+	9542.24i	0.642346	+	1.11258i	−0.342562	+	0.939495i	$0.611295\pi$
$420$	3181.03	+	7157.27i	0.369567	+	0.831522i
$421$	−3981.69	+	6896.49i	−0.460940	+	0.798372i	−0.999008	−	0.0445296i	$-0.985821\pi$
$421$	−3981.69	+	6896.49i	−0.460940	+	0.798372i	0.538068	+	0.842902i	$0.319154\pi$
$422$	−2653.71	−	1532.12i	−0.306116	−	0.176736i
$423$	4108.55	+	10129.5i	0.472256	+	1.16434i
$424$	3852.22	+	6672.24i	0.441227	+	0.764228i
$425$	172.581	+	298.919i	0.0196974	+	0.0341170i
$426$	2598.67	+	5318.93i	0.295554	+	0.604937i
$427$	232.896	−	6424.34i	0.0263949	−	0.728093i
$428$	1814.25	−	1047.46i	0.204895	−	0.118296i
$429$	−1261.32	−	2581.66i	−0.141952	−	0.290545i
$430$		−	5239.84i		−	0.587646i
$431$	5455.54	−	3149.75i	0.609707	−	0.352015i	−0.163144	−	0.986602i	$-0.552163\pi$
$431$	5455.54	−	3149.75i	0.609707	−	0.352015i	0.772851	+	0.634588i	$0.218830\pi$
$432$	108.949	+	333.008i	0.0121338	+	0.0370876i
$433$			1195.77i			0.132714i	0.997796	+	0.0663571i	$0.0211377\pi$
$433$			1195.77i			0.132714i	−0.997796	+	0.0663571i	$0.978862\pi$
$434$	3743.93	−	5973.85i	0.414088	−	0.660723i
$435$	9334.39	+	6286.94i	1.02885	+	0.692956i
$436$	−5604.58			−0.615621
$437$	−657.181	+	1138.27i	−0.0719388	+	0.124602i
$438$	3020.13	−	4484.06i	0.329469	−	0.489171i
$439$	−4954.45	+	2860.45i	−0.538640	+	0.310984i	−0.744527	−	0.667592i	$-0.767325\pi$
$439$	−4954.45	+	2860.45i	−0.538640	+	0.310984i	0.205888	+	0.978576i	$0.433992\pi$
$440$	−2771.58			−0.300295
$441$	−2850.30	−	8811.46i	−0.307775	−	0.951459i
$442$	294.626			0.0317057
$443$	−7609.01	+	4393.06i	−0.816061	+	0.471153i	−0.849056	−	0.528302i	$-0.822829\pi$
$443$	−7609.01	+	4393.06i	−0.816061	+	0.471153i	0.0329952	+	0.999456i	$0.489495\pi$
$444$	−267.484	−	547.483i	−0.0285906	−	0.0585189i
$445$	2971.60	−	5146.96i	0.316556	−	0.548290i
$446$	5025.64			0.533567
$447$	777.699	−	11230.8i	0.0822906	−	1.18837i
$448$	3338.07	−	5326.26i	0.352029	−	0.561701i
$449$		−	14022.9i		−	1.47390i	−0.675945	−	0.736952i	$-0.736264\pi$
$449$		−	14022.9i		−	1.47390i	0.675945	−	0.736952i	$-0.263736\pi$
$450$	−7250.17	+	2940.68i	−0.759502	+	0.308055i
$451$	802.894	−	463.551i	0.0838288	−	0.0483986i
$452$			707.815i			0.0736566i
$453$	11104.3	+	768.934i	1.15171	+	0.0797520i
$454$	6056.95	−	3496.98i	0.626138	−	0.361501i
$455$	−879.695	+	24266.0i	−0.0906390	+	2.50024i
$456$	8035.52	−	11930.6i	0.825214	−	1.22522i
$457$	6061.20	+	10498.3i	0.620418	+	1.07459i	0.989408	+	0.145162i	$0.0463702\pi$
$457$	6061.20	+	10498.3i	0.620418	+	1.07459i	−0.368990	+	0.929433i	$0.620296\pi$
$458$	−1148.30	−	1988.92i	−0.117154	−	0.202917i
$459$	92.9036	+	283.965i	0.00944743	+	0.0288766i
$460$	766.066	+	442.288i	0.0776478	+	0.0448300i
$461$	7878.24	−	13645.5i	0.795935	−	1.37860i	−0.126309	−	0.991991i	$-0.540313\pi$
$461$	7878.24	−	13645.5i	0.795935	−	1.37860i	0.922244	−	0.386609i	$-0.126354\pi$
$462$	1222.67	+	129.315i	0.123125	+	0.0130223i
$463$	2355.94	+	4080.61i	0.236480	+	0.409595i	0.959702	−	0.281021i	$-0.0906731\pi$
$463$	2355.94	+	4080.61i	0.236480	+	0.409595i	−0.723222	+	0.690615i	$0.757340\pi$
$464$		−	319.243i		−	0.0319407i
$465$	−15547.8	−	10471.8i	−1.55056	−	1.04434i
$466$	−2704.20			−0.268819
$467$	4389.02	−	7602.00i	0.434903	−	0.753274i	−0.562385	−	0.826876i	$-0.690116\pi$
$467$	4389.02	−	7602.00i	0.434903	−	0.753274i	0.997288	+	0.0736019i	$0.0234494\pi$
$468$	1383.30	−	9940.28i	0.136630	−	0.981816i
$469$	2334.04	+	4403.82i	0.229800	+	0.433581i
$470$	10620.9	+	6131.97i	1.04235	+	0.601802i
$471$	12904.4	+	8691.40i	1.26242	+	0.850273i
$472$	13115.6	+	7572.30i	1.27902	+	0.738440i
$473$	1070.48	+	618.042i	0.104061	+	0.0600795i
$474$	−1324.35	−	891.983i	−0.128332	−	0.0864349i
$475$	16974.4	+	9800.20i	1.63967	+	0.946661i
$476$	100.610	−	160.535i	0.00968796	−	0.0154582i
$477$	−8421.09	+	3415.61i	−0.808334	+	0.327862i
$478$	2416.94	−	4186.26i	0.231272	−	0.400576i
$479$	9448.00			0.901232			0.450616	−	0.892718i	$-0.351204\pi$
$479$	9448.00			0.901232			0.450616	+	0.892718i	$0.351204\pi$
$480$	−13046.3	−	8787.01i	−1.24058	−	0.835563i
$481$		−	1889.06i		−	0.179072i
$482$	−4410.76	−	7639.67i	−0.416815	−	0.721945i
$483$	−845.772	−	615.334i	−0.0796770	−	0.0579682i
$484$	−3074.12	+	5324.53i	−0.288704	+	0.500050i
$485$	1243.22	+	717.776i	0.116396	+	0.0672011i
$486$	−6665.50	+	1198.58i	−0.622126	+	0.111869i
$487$	−3150.98	−	5457.65i	−0.293192	−	0.507823i	0.681371	−	0.731938i	$-0.261384\pi$
$487$	−3150.98	−	5457.65i	−0.293192	−	0.507823i	−0.974563	+	0.224115i	$0.928051\pi$
$488$	3972.84	+	6881.16i	0.368529	+	0.638310i
$489$	−6702.50	+	9951.38i	−0.619831	+	0.920280i
$490$	−8598.45	−	5833.06i	−0.792731	−	0.537777i
$491$	−11356.2	+	6556.53i	−1.04379	+	0.602632i	−0.920904	−	0.389789i	$-0.872548\pi$
$491$	−11356.2	+	6556.53i	−1.04379	+	0.602632i	−0.122884	+	0.992421i	$0.539214\pi$
$492$	3230.51	+	223.702i	0.296021	+	0.0204985i
$493$		−	272.228i		−	0.0248692i
$494$	14489.2	−	8365.33i	1.31963	−	0.761891i
$495$	450.587	−	3237.88i	0.0409139	−	0.294004i
$496$			531.746i			0.0481373i
$497$	9999.97	+	6267.18i	0.902535	+	0.565636i
$498$	815.808	−	11781.2i	0.0734081	−	1.06009i
$499$	1276.72			0.114537			0.0572684	−	0.998359i	$-0.481761\pi$
$499$	1276.72			0.114537			0.0572684	+	0.998359i	$0.481761\pi$
$500$	1508.84	−	2613.39i	0.134955	−	0.233748i
$501$	5224.09	+	10692.6i	0.465859	+	0.953513i
$502$	981.590	−	566.721i	0.0872720	−	0.0503865i
$503$	−17740.2			−1.57256			−0.786279	−	0.617872i	$-0.787995\pi$
$503$	−17740.2			−1.57256			−0.786279	+	0.617872i	$0.787995\pi$
$504$	8768.75	+	7357.50i	0.774982	+	0.650256i
$505$	−27910.1			−2.45937
$506$	120.254	−	69.4288i	0.0105651	−	0.00609977i
$507$	11004.0	−	16337.9i	0.963913	−	1.43115i
$508$	70.7377	−	122.521i	0.00617810	−	0.0107008i
$509$	−11516.0			−1.00282			−0.501411	−	0.865209i	$-0.667186\pi$
$509$	−11516.0			−1.00282			−0.501411	+	0.865209i	$0.667186\pi$
$510$	278.027	+	187.258i	0.0241397	+	0.0162587i
$511$	390.463	−	10770.8i	0.0338025	−	0.932427i
$512$			903.539i			0.0779905i
$513$	12631.5	+	11327.1i	1.08712	+	0.974858i
$514$	824.479	−	476.013i	0.0707514	−	0.0408483i
$515$			31196.6i			2.66929i
$516$	1895.28	+	3879.24i	0.161696	+	0.330957i
$517$	−2505.48	+	1446.54i	−0.213135	+	0.123054i
$518$	684.934	+	429.262i	0.0580971	+	0.0364106i
$519$	−3747.67	−	7670.68i	−0.316964	−	0.648758i
$520$	−15006.2	−	25991.5i	−1.26551	−	2.19193i
$521$	10167.1	+	17609.9i	0.854947	+	1.48081i	0.876694	+	0.481048i	$0.159744\pi$
$521$	10167.1	+	17609.9i	0.854947	+	1.48081i	−0.0217470	+	0.999764i	$0.506923\pi$
$522$	6111.74	+	850.514i	0.512459	+	0.0713142i
$523$	−8533.45	−	4926.79i	−0.713464	−	0.411919i	0.0988783	−	0.995100i	$-0.468475\pi$
$523$	−8533.45	−	4926.79i	−0.713464	−	0.411919i	−0.812342	+	0.583181i	$0.801808\pi$
$524$	2353.01	−	4075.53i	0.196167	−	0.339772i
$525$	−9176.15	+	12612.6i	−0.762819	+	1.04849i
$526$	−4676.12	−	8099.28i	−0.387621	−	0.671379i
$527$			453.435i			0.0374799i
$528$	−83.3204	+	40.7079i	−0.00686753	+	0.00335527i
$529$	12048.9			0.990291
$530$	−5097.77	+	8829.59i	−0.417798	+	0.723647i
$531$	−10978.6	+	14091.2i	−0.897231	+	1.15161i
$532$	389.763	−	10751.4i	0.0317638	−	0.876192i
$533$	8694.26	+	5019.63i	0.706548	+	0.407926i
$534$	225.111	−	3250.85i	0.0182425	−	0.263442i
$535$	6399.31	+	3694.65i	0.517134	+	0.298567i
$536$	−5335.01	−	3080.17i	−0.429921	−	0.248215i
$537$	13218.7	−	6458.29i	1.06225	−	0.518986i
$538$	−11090.3	−	6402.97i	−0.888727	−	0.513107i
$539$	2205.86	−	1068.62i	0.176277	−	0.0853965i
$540$	7623.21	−	8501.07i	0.607501	−	0.677459i
$541$	−9862.19	+	17081.8i	−0.783750	+	1.35749i	0.145993	+	0.989286i	$0.453362\pi$
$541$	−9862.19	+	17081.8i	−0.783750	+	1.35749i	−0.929743	+	0.368209i	$0.879971\pi$
$542$	−1382.83			−0.109590
$543$	329.539	−	4758.91i	0.0260440	−	0.376104i
$544$			380.482i			0.0299872i
$545$	−9884.40	−	17120.3i	−0.776883	−	1.34560i
$546$	5407.24	+	12166.2i	0.423825	+	0.953602i
$547$	−1833.52	+	3175.75i	−0.143319	+	0.248236i	−0.928745	−	0.370720i	$-0.879111\pi$
$547$	−1833.52	+	3175.75i	−0.143319	+	0.248236i	0.785425	+	0.618956i	$0.212444\pi$
$548$	−5171.45	−	2985.74i	−0.403127	−	0.232745i
$549$	−8684.77	+	3522.56i	−0.675149	+	0.273842i
$550$	−1035.36	−	1793.29i	−0.0802685	−	0.139029i
$551$	−7729.38	−	13387.7i	−0.597609	−	1.03509i
$552$	1289.67	+	89.3058i	0.0994424	+	0.00688607i
$553$	−3181.10	−	115.322i	−0.244619	−	0.00886795i
$554$	1525.36	−	880.666i	0.116979	−	0.0675377i
$555$	1200.65	−	1782.64i	0.0918283	−	0.136340i
$556$			5416.82i			0.413173i
$557$	−18967.2	+	10950.7i	−1.44285	+	0.833028i	−0.998039	−	0.0625971i	$-0.980062\pi$
$557$	−18967.2	+	10950.7i	−1.44285	+	0.833028i	−0.444809	+	0.895626i	$0.646728\pi$
$558$	−10180.0	−	1416.65i	−0.772316	−	0.107476i
$559$			13385.1i			1.01276i
$560$	783.161	+	28.3913i	0.0590975	+	0.00214241i
$561$	−71.0497	+	34.7128i	−0.00534709	+	0.00261243i
$562$	140.453			0.0105421
$563$	−6893.85	+	11940.5i	−0.516059	+	0.893840i	0.483767	+	0.875197i	$0.339268\pi$
$563$	−6893.85	+	11940.5i	−0.516059	+	0.893840i	−0.999826	+	0.0186434i	$0.994065\pi$
$564$	−10081.0	−	698.076i	−0.752635	−	0.0521175i
$565$	−2162.16	+	1248.32i	−0.160996	+	0.0929509i
$566$	4252.43			0.315800
$567$	−10020.9	+	9047.92i	−0.742223	+	0.670154i
$568$	−14586.7			−1.07754
$569$	−10087.0	+	5823.75i	−0.743181	+	0.429076i	−0.823225	−	0.567715i	$-0.807827\pi$
$569$	−10087.0	+	5823.75i	−0.743181	+	0.429076i	0.0800436	+	0.996791i	$0.474494\pi$
$570$	18989.7	+	1314.98i	1.39542	+	0.0966286i
$571$	−1244.70	+	2155.88i	−0.0912243	+	0.158005i	−0.908027	−	0.418913i	$-0.862411\pi$
$571$	−1244.70	+	2155.88i	−0.0912243	+	0.158005i	0.816802	+	0.576918i	$0.195745\pi$
$572$	2656.21			0.194164
$573$	9012.07	−	4403.03i	0.657042	−	0.321011i
$574$	−3795.66	+	2011.72i	−0.276006	+	0.146285i
$575$			1761.55i			0.127760i
$576$	−9076.42	−	1263.08i	−0.656570	−	0.0913688i
$577$	18275.1	−	10551.1i	1.31855	−	0.761265i	0.335055	−	0.942199i	$-0.391245\pi$
$577$	18275.1	−	10551.1i	1.31855	−	0.761265i	0.983495	+	0.180934i	$0.0579119\pi$
$578$			8775.65i			0.631521i
$579$	3867.58	−	5742.30i	0.277601	−	0.412162i
$580$	−9010.01	+	5201.93i	−0.645035	+	0.372411i
$581$	−11025.0	−	20801.8i	−0.787256	−	1.48538i
$582$	785.229	+	54.3745i	0.0559257	+	0.00387268i
$583$	−1202.57	−	2082.91i	−0.0854293	−	0.147968i
$584$	6660.68	+	11536.6i	0.471953	+	0.817447i
$585$	32804.1	−	13305.4i	2.31843	−	0.940360i
$586$	−5573.49	−	3217.86i	−0.392899	−	0.226840i
$587$	12811.9	−	22190.8i	0.900856	−	1.56033i	0.0744697	−	0.997223i	$-0.476274\pi$
$587$	12811.9	−	22190.8i	0.900856	−	1.56033i	0.826386	−	0.563104i	$-0.190393\pi$
$588$	8475.59	+	1208.31i	0.594434	+	0.0847444i
$589$	12874.4	+	22299.1i	0.900645	+	1.55996i
$590$			20041.4i			1.39846i
$591$	652.039	−	9416.17i	0.0453829	−	0.655380i
$592$	−60.9675			−0.00423269
$593$	−413.666	+	716.491i	−0.0286463	+	0.0496168i	−0.879993	−	0.474986i	$-0.842453\pi$
$593$	−413.666	+	716.491i	−0.0286463	+	0.0496168i	0.851347	+	0.524603i	$0.175786\pi$
$594$	−557.351	−	1703.57i	−0.0384990	−	0.117674i
$595$	667.824	+	24.2100i	0.0460136	+	0.00166809i
$596$	9012.86	+	5203.57i	0.619431	+	0.357629i
$597$	317.366	−	155.056i	0.0217570	−	0.0106298i
$598$	1302.19	+	751.820i	0.0890477	+	0.0514117i
$599$	−17.0623	−	9.85092i	−0.00116385	−	0.000671950i	0.499418	−	0.866361i	$-0.333547\pi$
$599$	−17.0623	−	9.85092i	−0.00116385	−	0.000671950i	−0.500582	+	0.865689i	$0.666881\pi$
$600$	1331.77	−	19232.2i	0.0906155	−	1.30859i
$601$	8877.74	+	5125.57i	0.602547	+	0.347881i	0.770043	−	0.637992i	$-0.220235\pi$
$601$	8877.74	+	5125.57i	0.602547	+	0.347881i	−0.167496	+	0.985873i	$0.553568\pi$
$602$	−4853.16	−	3041.57i	−0.328572	−	0.205922i
$603$	4465.73	−	5731.85i	0.301590	−	0.387096i
$604$	−5144.93	+	8911.27i	−0.346596	+	0.600322i
$605$	−21686.4			−1.45732
$606$	−13749.7	+	6717.71i	−0.921690	+	0.450311i
$607$		−	17590.0i		−	1.17620i	−0.808788	−	0.588101i	$-0.799876\pi$
$607$		−	17590.0i		−	1.17620i	0.808788	−	0.588101i	$-0.200124\pi$
$608$	10803.0	+	18711.4i	0.720594	+	1.24811i
$609$	11241.3	−	4996.17i	0.747983	−	0.332438i
$610$	−5257.39	+	9106.06i	−0.348960	+	0.604416i
$611$	−27130.9	−	15664.1i	−1.79640	−	1.03715i
$612$	−273.566	−	38.0697i	−0.0180690	−	0.00251450i
$613$	−13259.6	−	22966.2i	−0.873652	−	1.51321i	−0.858192	−	0.513330i	$-0.828412\pi$
$613$	−13259.6	−	22966.2i	−0.873652	−	1.51321i	−0.0154607	−	0.999880i	$-0.504921\pi$
$614$	−2529.69	−	4381.56i	−0.166271	−	0.287989i
$615$	5014.07	+	10262.7i	0.328759	+	0.672899i
$616$	−1608.82	+	2567.04i	−0.105229	+	0.167904i
$617$	20820.5	−	12020.7i	1.35851	−	0.784336i	0.369086	−	0.929395i	$-0.379671\pi$
$617$	20820.5	−	12020.7i	1.35851	−	0.784336i	0.989423	+	0.145060i	$0.0463374\pi$
$618$	7508.74	+	15368.8i	0.488747	+	1.00036i
$619$		−	16042.3i		−	1.04167i	−0.853656	−	0.520837i	$-0.825620\pi$
$619$		−	16042.3i		−	1.04167i	0.853656	−	0.520837i	$-0.174380\pi$
$620$	15007.5	−	8664.56i	0.972120	−	0.561254i
$621$	−313.999	+	1492.14i	−0.0202904	+	0.0964211i
$622$			12767.5i			0.823041i
$623$	−3042.21	−	5739.96i	−0.195640	−	0.369128i
$624$	−832.877	−	560.963i	−0.0534323	−	0.0359880i
$625$	−9615.57			−0.615397
$626$	3156.69	−	5467.55i	0.201544	−	0.349085i
$627$	−2508.49	+	3724.43i	−0.159776	+	0.237224i
$628$	−12455.9	+	7191.43i	−0.791473	+	0.456957i
$629$	−51.9888			−0.00329559
$630$	−2630.00	+	14917.5i	−0.166320	+	0.943380i
$631$	8270.89			0.521805			0.260902	−	0.965365i	$-0.415980\pi$
$631$	8270.89			0.521805			0.260902	+	0.965365i	$0.415980\pi$
$632$	3407.30	−	1967.21i	0.214454	−	0.123815i
$633$	3909.45	+	8001.82i	0.245477	+	0.502439i
$634$	−1903.98	+	3297.79i	−0.119269	+	0.206580i
$635$	499.020			0.0311858
$636$	580.340	−	8380.75i	0.0361823	−	0.522513i
$637$	21964.7	+	14900.5i	1.36620	+	0.926811i
$638$			1633.16i			0.101344i
$639$	2371.42	−	17040.8i	0.146810	−	1.05497i
$640$	12068.8	−	6967.93i	0.745408	−	0.430362i
$641$			7425.79i			0.457568i	0.973477	+	0.228784i	$0.0734750\pi$
$641$			7425.79i			0.457568i	−0.973477	+	0.228784i	$0.926525\pi$
$642$	4041.85	+	279.885i	0.248472	+	0.0172059i
$643$	5121.19	−	2956.72i	0.314090	−	0.181340i	−0.334665	−	0.942337i	$-0.608623\pi$
$643$	5121.19	−	2956.72i	0.314090	−	0.181340i	0.648755	+	0.760997i	$0.275290\pi$
$644$	854.327	−	452.798i	0.0522752	−	0.0277061i
$645$	−8507.31	+	12631.0i	−0.519341	+	0.771080i
$646$	−230.222	−	398.756i	−0.0140216	−	0.0242861i
$647$	9583.58	+	16599.2i	0.582333	+	1.00863i	0.995202	+	0.0978399i	$0.0311933\pi$
$647$	9583.58	+	16599.2i	0.582333	+	1.00863i	−0.412869	+	0.910790i	$0.635473\pi$
$648$	4556.26	−	16053.5i	0.276214	−	0.973209i
$649$	−4094.37	−	2363.89i	−0.247640	−	0.142975i
$650$	11211.5	−	19418.9i	0.676540	−	1.17180i
$651$	−18724.0	+	8321.83i	−1.12727	+	0.501011i
$652$	−5545.77	−	9605.56i	−0.333112	−	0.576967i
$653$			9070.14i			0.543556i	0.962360	+	0.271778i	$0.0876116\pi$
$653$			9070.14i			0.543556i	−0.962360	+	0.271778i	$0.912388\pi$
$654$	−8990.18	−	6055.10i	−0.537529	−	0.362039i
$655$	16599.3			0.990212
$656$	162.003	−	280.598i	0.00964203	−	0.0167005i
$657$	−14560.5	+	5905.75i	−0.864625	+	0.350693i
$658$	11844.6	−	6277.68i	0.701747	−	0.371929i
$659$	25154.3	+	14522.8i	1.48691	+	0.858465i	0.999889	−	0.0149269i	$-0.00475157\pi$
$659$	25154.3	+	14522.8i	1.48691	+	0.858465i	0.487017	+	0.873392i	$0.338085\pi$
$660$	2506.57	+	1688.23i	0.147830	+	0.0995674i
$661$	−7059.83	−	4075.99i	−0.415424	−	0.239845i	0.277693	−	0.960670i	$-0.410430\pi$
$661$	−7059.83	−	4075.99i	−0.415424	−	0.239845i	−0.693118	+	0.720824i	$0.743763\pi$
$662$	−7586.39	−	4380.00i	−0.445398	−	0.257151i
$663$	−710.218	−	478.349i	−0.0416027	−	0.0280204i
$664$	25200.4	+	14549.4i	1.47284	+	0.850343i
$665$	33529.8	−	17770.9i	1.95523	−	1.03628i
$666$	162.427	−	1167.19i	0.00945033	−	0.0679094i
$667$	694.665	−	1203.19i	0.0403261	−	0.0698469i
$668$	−11001.4			−0.637211
$669$	−12114.7	−	8159.53i	−0.700120	−	0.471548i
$670$		−	8152.18i		−	0.470069i
$671$	−1240.22	−	2148.13i	−0.0713536	−	0.123588i
$672$	−15711.6	+	6982.95i	−0.901914	+	0.400853i
$673$	376.383	−	651.914i	0.0215579	−	0.0373395i	−0.855045	−	0.518554i	$-0.826471\pi$
$673$	376.383	−	651.914i	0.0215579	−	0.0373395i	0.876603	+	0.481214i	$0.159804\pi$
$674$	3821.87	+	2206.56i	0.218417	+	0.126103i
$675$	22251.5	+	4682.50i	1.26883	+	0.267007i
$676$	9104.90	+	15770.1i	0.518030	+	0.897254i
$677$	−1991.13	−	3448.73i	−0.113036	−	0.195784i	0.803957	−	0.594687i	$-0.202724\pi$
$677$	−1991.13	−	3448.73i	−0.113036	−	0.195784i	−0.916993	+	0.398904i	$0.869391\pi$
$678$	−764.712	+	1135.39i	−0.0433165	+	0.0643132i
$679$	1386.46	−	734.832i	0.0783616	−	0.0415320i
$680$	−715.311	+	412.985i	−0.0403396	+	0.0232901i
$681$	−20278.4	−	1404.21i	−1.14107	−	0.0790154i
$682$		−	2720.26i		−	0.152733i
$683$	−4073.29	+	2351.72i	−0.228199	+	0.131751i	−0.609741	−	0.792601i	$-0.708727\pi$
$683$	−4073.29	+	2351.72i	−0.228199	+	0.131751i	0.381542	+	0.924352i	$0.375393\pi$
$684$	−14534.4	+	5895.17i	−0.812480	+	0.329543i
$685$		−	21062.9i		−	1.17485i
$686$	−10393.7	+	4578.00i	−0.578477	+	0.254794i
$687$	−461.100	+	6658.79i	−0.0256071	+	0.369794i
$688$	431.991			0.0239382
$689$	13022.2	−	22555.1i	0.720038	−	1.24714i
$690$	750.986	+	1537.11i	0.0414341	+	0.0848069i
$691$	2015.73	−	1163.78i	0.110972	−	0.0640700i	−0.443486	−	0.896281i	$-0.646259\pi$
$691$	2015.73	−	1163.78i	0.110972	−	0.0640700i	0.554459	+	0.832211i	$0.312925\pi$
$692$	7892.20			0.433550
$693$	−2737.39	−	2296.83i	−0.150050	−	0.125901i
$694$	17959.6			0.982329
$695$	−16546.7	+	9553.25i	−0.903098	+	0.521404i
$696$	−8493.84	+	12611.0i	−0.462583	+	0.686810i
$697$	138.145	−	239.274i	0.00750734	−	0.0130031i
$698$	20461.7			1.10958
$699$	6518.67	+	4390.48i	0.352731	+	0.237573i
$700$	−6752.34	−	12740.1i	−0.364592	−	0.687903i
$701$			1250.95i			0.0674005i	0.999432	+	0.0337003i	$0.0107292\pi$
$701$			1250.95i			0.0674005i	−0.999432	+	0.0337003i	$0.989271\pi$
$702$	12958.2	−	14450.5i	0.696691	−	0.776920i
$703$	−2556.71	+	1476.12i	−0.137167	+	0.0791933i
$704$		−	2425.38i		−	0.129843i
$705$	−15646.7	−	32025.4i	−0.835870	−	1.71085i
$706$	−2255.72	+	1302.34i	−0.120248	+	0.0694253i
$707$	−16201.0	+	25850.4i	−0.861811	+	1.37511i
$708$	−7249.08	−	14837.3i	−0.384798	−	0.787599i
$709$	−17364.5	−	30076.3i	−0.919801	−	1.59314i	−0.799716	−	0.600379i	$-0.795017\pi$
$709$	−17364.5	−	30076.3i	−0.919801	−	1.59314i	−0.120085	−	0.992764i	$-0.538317\pi$
$710$	−9651.52	−	16716.9i	−0.510162	−	0.883626i
$711$	1744.24	+	4300.38i	0.0920031	+	0.226831i
$712$	6953.69	+	4014.71i	0.366012	+	0.211317i
$713$	−1157.06	+	2004.09i	−0.0607747	+	0.105265i
$714$	334.826	−	148.812i	0.0175498	−	0.00779994i
$715$	4684.57	+	8113.91i	0.245025	+	0.424396i
$716$			13600.5i			0.709880i
$717$	−12622.9	+	6167.20i	−0.657479	+	0.321225i
$718$	−583.883			−0.0303486
$719$	14119.5	−	24455.6i	0.732361	−	1.26849i	−0.223511	−	0.974701i	$-0.571752\pi$
$719$	14119.5	−	24455.6i	0.732361	−	1.26849i	0.955872	−	0.293785i	$-0.0949149\pi$
$720$	−429.418	−	1058.72i	−0.0222270	−	0.0548002i
$721$	28894.4	+	18108.7i	1.49249	+	0.935372i
$722$	−12023.8	−	6941.92i	−0.619775	−	0.357827i
$723$	−1771.14	+	25577.2i	−0.0911057	+	1.31567i
$724$	3819.07	+	2204.94i	0.196042	+	0.113185i
$725$	−17942.6	−	10359.2i	−0.919133	−	0.530662i
$726$	−10683.7	+	5219.72i	−0.546154	+	0.266835i
$727$	−4105.21	−	2370.14i	−0.209427	−	0.120913i	0.391618	−	0.920128i	$-0.371916\pi$
$727$	−4105.21	−	2370.14i	−0.209427	−	0.120913i	−0.601045	+	0.799215i	$0.705249\pi$
$728$	−32784.1	−	1188.49i	−1.66904	−	0.0605062i
$729$	18013.7	+	7932.72i	0.915189	+	0.403024i
$730$	−8814.29	+	15266.8i	−0.446892	+	0.774040i
$731$	368.371			0.0186384
$732$	598.511	−	8643.16i	0.0302208	−	0.436421i
$733$			20291.2i			1.02248i	0.859439	+	0.511238i	$0.170813\pi$
$733$			20291.2i			1.02248i	−0.859439	+	0.511238i	$0.829187\pi$
$734$	5691.66	+	9858.24i	0.286217	+	0.495742i
$735$	11256.8	+	28021.3i	0.564915	+	1.40623i
$736$	−970.905	+	1681.66i	−0.0486251	+	0.0842211i
$737$	1665.46	+	961.554i	0.0832402	+	0.0480587i
$738$	4940.29	+	3849.02i	0.246416	+	0.191984i
$739$	−14186.1	−	24571.1i	−0.706151	−	1.22309i	−0.966274	−	0.257515i	$-0.917096\pi$
$739$	−14186.1	−	24571.1i	−0.706151	−	1.22309i	0.260123	−	0.965575i	$-0.416237\pi$
$740$	993.439	+	1720.69i	0.0493508	+	0.0854780i
$741$	−48509.0	−	3359.09i	−2.40489	−	0.166531i
$742$	5218.90	+	9846.89i	0.258210	+	0.487184i
$743$	7268.83	−	4196.66i	0.358907	−	0.207215i	−0.309694	−	0.950836i	$-0.600227\pi$
$743$	7268.83	−	4196.66i	0.358907	−	0.207215i	0.668601	+	0.743621i	$0.266893\pi$
$744$	14147.7	−	21005.5i	0.697150	−	1.03508i
$745$			36708.7i			1.80524i
$746$	2999.71	−	1731.88i	0.147221	−	0.0849983i
$747$	−21094.3	+	27074.9i	−1.03320	+	1.32613i
$748$		−	73.1015i		−	0.00357334i
$749$	7136.61	−	3782.44i	0.348152	−	0.184522i
$750$	5243.75	−	2561.94i	0.255300	−	0.124732i
$751$	28345.3			1.37727			0.688637	−	0.725106i	$-0.258209\pi$
$751$	28345.3			1.37727			0.688637	+	0.725106i	$0.258209\pi$
$752$	−505.541	+	875.623i	−0.0245149	+	0.0424610i
$753$	−3286.31	−	227.567i	−0.159044	−	0.0110133i
$754$	−15315.6	+	8842.46i	−0.739736	+	0.427087i
$755$	−36294.9			−1.74955
$756$	−3448.68	−	11995.3i	−0.165909	−	0.577068i
$757$	−18383.7			−0.882651			−0.441326	−	0.897347i	$-0.645492\pi$
$757$	−18383.7			−0.882651			−0.441326	+	0.897347i	$0.645492\pi$
$758$	−14423.4	+	8327.35i	−0.691136	+	0.399028i
$759$	−402.605	−	27.8791i	−0.0192538	−	0.00133326i
$760$	−23451.8	+	40619.7i	−1.11932	+	1.93872i
$761$	29518.0			1.40608			0.703040	−	0.711150i	$-0.251825\pi$
$761$	29518.0			1.40608			0.703040	+	0.711150i	$0.251825\pi$
$762$	245.839	−	120.110i	0.0116874	−	0.00571012i
$763$	−21594.5	−	782.846i	−1.02460	−	0.0371441i
$764$			9272.33i			0.439085i
$765$	−366.177	−	902.800i	−0.0173061	−	0.0426677i
$766$	−4575.19	+	2641.49i	−0.215807	+	0.124596i
$767$		−	51195.4i		−	2.41012i
$768$	12150.1	−	18039.6i	0.570870	−	0.847587i
$769$	21532.4	−	12431.8i	1.00973	−	0.582965i	0.0986144	−	0.995126i	$-0.468559\pi$
$769$	21532.4	−	12431.8i	1.00973	−	0.582965i	0.911111	+	0.412160i	$0.135226\pi$
$770$	−4006.43	−	145.242i	−0.187509	−	0.00679760i
$771$	−2760.31	−	191.143i	−0.128937	−	0.00892846i
$772$	3200.11	+	5542.75i	0.149190	+	0.258404i
$773$	14395.5	+	24933.8i	0.669820	+	1.16016i

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

\(f(q)\)	\(=\)	\(q+(-1.54833 + 0.893930i) q^{2} +(5.18374 + 0.358957i) q^{3} +(-2.40178 + 4.16000i) q^{4} -16.9434 q^{5} +(-8.34703 + 4.07812i) q^{6} +(-9.83512 + 15.6930i) q^{7} -22.8910i q^{8} +(26.7423 + 3.72148i) q^{9} +O(q^{10})\)	\(q+(-1.54833 + 0.893930i) q^{2} +(5.18374 + 0.358957i) q^{3} +(-2.40178 + 4.16000i) q^{4} -16.9434 q^{5} +(-8.34703 + 4.07812i) q^{6} +(-9.83512 + 15.6930i) q^{7} -22.8910i q^{8} +(26.7423 + 3.72148i) q^{9} +(26.2340 - 15.1462i) q^{10} +7.14600i q^{11} +(-13.9435 + 20.7022i) q^{12} +(-67.0144 + 38.6908i) q^{13} +(1.19958 - 33.0899i) q^{14} +(-87.8300 - 6.08194i) q^{15} +(1.24870 + 2.16282i) q^{16} +(1.06481 + 1.84430i) q^{17} +(-44.7327 + 18.1437i) q^{18} +(104.730 + 60.4661i) q^{19} +(40.6942 - 70.4844i) q^{20} +(-56.6158 + 77.8181i) q^{21} +(-6.38802 - 11.0644i) q^{22} +10.8686i q^{23} +(8.21688 - 118.661i) q^{24} +162.077 q^{25} +(69.1737 - 119.812i) q^{26} +(137.289 + 28.8905i) q^{27} +(-41.6612 - 78.6052i) q^{28} +(-110.704 - 63.9149i) q^{29} +(141.427 - 69.0970i) q^{30} +(184.393 + 106.459i) q^{31} +(154.726 + 89.3314i) q^{32} +(-2.56511 + 37.0430i) q^{33} +(-3.29735 - 1.90372i) q^{34} +(166.640 - 265.892i) q^{35} +(-79.7104 + 102.310i) q^{36} +(-12.2062 + 21.1417i) q^{37} -216.210 q^{38} +(-361.273 + 176.507i) q^{39} +387.850i q^{40} +(-64.8686 - 112.356i) q^{41} +(18.0962 - 171.099i) q^{42} +(86.4878 - 149.801i) q^{43} +(-29.7274 - 17.1631i) q^{44} +(-453.104 - 63.0544i) q^{45} +(-9.71576 - 16.8282i) q^{46} +(202.426 + 350.613i) q^{47} +(5.69660 + 11.6597i) q^{48} +(-149.541 - 308.685i) q^{49} +(-250.950 + 144.886i) q^{50} +(4.85765 + 9.94258i) q^{51} -371.706i q^{52} +(-291.479 + 168.286i) q^{53} +(-238.396 + 77.9949i) q^{54} -121.077i q^{55} +(359.228 + 225.135i) q^{56} +(521.190 + 351.034i) q^{57} +228.542 q^{58} +(-330.799 + 572.960i) q^{59} +(236.249 - 350.765i) q^{60} +(-300.606 + 173.555i) q^{61} -380.669 q^{62} +(-321.415 + 383.066i) q^{63} -339.403 q^{64} +(1135.45 - 655.551i) q^{65} +(-29.1422 - 59.6479i) q^{66} +(134.558 - 233.062i) q^{67} -10.2297 q^{68} +(-3.90136 + 56.3399i) q^{69} +(-20.3249 + 560.654i) q^{70} -637.224i q^{71} +(85.1883 - 612.157i) q^{72} +(-503.982 + 290.974i) q^{73} -43.6458i q^{74} +(840.167 + 58.1789i) q^{75} +(-503.078 + 290.452i) q^{76} +(-112.142 - 70.2817i) q^{77} +(401.586 - 596.245i) q^{78} +(85.9381 + 148.849i) q^{79} +(-21.1572 - 36.6454i) q^{80} +(701.301 + 199.042i) q^{81} +(200.876 + 115.976i) q^{82} +(-635.597 + 1100.89i) q^{83} +(-187.745 - 422.423i) q^{84} +(-18.0414 - 31.2486i) q^{85} +309.256i q^{86} +(-550.917 - 371.056i) q^{87} +163.579 q^{88} +(-175.384 + 303.774i) q^{89} +(757.923 - 307.415i) q^{90} +(51.9198 - 1432.18i) q^{91} +(-45.2133 - 26.1039i) q^{92} +(917.632 + 618.047i) q^{93} +(-626.847 - 361.910i) q^{94} +(-1774.49 - 1024.50i) q^{95} +(769.995 + 518.611i) q^{96} +(-73.3753 - 42.3633i) q^{97} +(507.482 + 344.268i) q^{98} +(-26.5937 + 191.100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} + O(q^{10}) \)	\( 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} - 6q^{10} - 3q^{12} + 36q^{13} + 129q^{14} - 141q^{15} - 263q^{16} + 72q^{17} - 15q^{18} - 6q^{19} - 24q^{20} - 306q^{21} + 14q^{22} - 66q^{24} + 698q^{25} + 96q^{26} - 432q^{27} - 156q^{28} - 132q^{29} + 852q^{30} + 177q^{31} - 501q^{32} + 849q^{33} - 24q^{34} - 765q^{35} + 1122q^{36} + 82q^{37} - 1746q^{38} - 645q^{39} - 618q^{41} - 963q^{42} + 82q^{43} - 603q^{44} + 303q^{45} + 266q^{46} - 201q^{47} + 1569q^{48} + 515q^{49} - 1845q^{50} + 417q^{51} - 564q^{53} - 684q^{54} + 3600q^{56} + 1170q^{57} - 538q^{58} + 747q^{59} - 516q^{60} - 1209q^{61} + 2904q^{62} + 1557q^{63} - 1144q^{64} - 831q^{65} + 1029q^{66} + 295q^{67} + 7008q^{68} + 1005q^{69} - 390q^{70} - 1119q^{72} - 6q^{73} - 1788q^{75} + 144q^{76} - 1203q^{77} - 5985q^{78} - 551q^{79} + 4239q^{80} + 3741q^{81} + 18q^{82} - 1830q^{83} - 7725q^{84} - 237q^{85} - 2130q^{87} + 1246q^{88} - 4266q^{89} - 9993q^{90} - 1140q^{91} + 7896q^{92} - 1479q^{93} - 3q^{94} - 1053q^{95} + 5034q^{96} + 792q^{97} - 5667q^{98} + 4335q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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