LMFDB - Embedded newform 63.4.s.a.47.11

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			47.11
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.11

$q$-expansion

$f(q)$	$=$	$q+(-0.223110 + 0.128812i) q^{2} +(-3.39738 - 3.93164i) q^{3} +(-3.96681 + 6.87072i) q^{4} +6.38772 q^{5} +(1.26443 + 0.439563i) q^{6} +(-1.54394 + 18.4558i) q^{7} -4.10490i q^{8} +(-3.91563 + 26.7146i) q^{9} +O(q^{10})$	\(q+(-0.223110 + 0.128812i) q^{2} +(-3.39738 - 3.93164i) q^{3} +(-3.96681 + 6.87072i) q^{4} +6.38772 q^{5} +(1.26443 + 0.439563i) q^{6} +(-1.54394 + 18.4558i) q^{7} -4.10490i q^{8} +(-3.91563 + 26.7146i) q^{9} +(-1.42516 + 0.822818i) q^{10} +61.0818i q^{11} +(40.4900 - 7.74636i) q^{12} +(8.78677 - 5.07304i) q^{13} +(-2.03287 - 4.31654i) q^{14} +(-21.7015 - 25.1142i) q^{15} +(-31.2058 - 54.0500i) q^{16} +(22.5082 + 38.9853i) q^{17} +(-2.56755 - 6.46466i) q^{18} +(-69.6373 - 40.2051i) q^{19} +(-25.3389 + 43.8883i) q^{20} +(77.8069 - 56.6311i) q^{21} +(-7.86810 - 13.6279i) q^{22} -27.6800i q^{23} +(-16.1390 + 13.9459i) q^{24} -84.1970 q^{25} +(-1.30694 + 2.26369i) q^{26} +(118.335 - 75.3646i) q^{27} +(-120.680 - 83.8187i) q^{28} +(48.9383 + 28.2545i) q^{29} +(8.07685 + 2.80781i) q^{30} +(92.1526 + 53.2043i) q^{31} +(42.3642 + 24.4590i) q^{32} +(240.152 - 207.518i) q^{33} +(-10.0436 - 5.79867i) q^{34} +(-9.86226 + 117.890i) q^{35} +(-168.016 - 132.875i) q^{36} +(95.6403 - 165.654i) q^{37} +20.7157 q^{38} +(-49.7974 - 17.3114i) q^{39} -26.2210i q^{40} +(-15.0856 - 26.1289i) q^{41} +(-10.0647 + 22.6574i) q^{42} +(-185.062 + 320.536i) q^{43} +(-419.676 - 242.300i) q^{44} +(-25.0120 + 170.645i) q^{45} +(3.56553 + 6.17569i) q^{46} +(248.041 + 429.620i) q^{47} +(-106.487 + 306.318i) q^{48} +(-338.232 - 56.9893i) q^{49} +(18.7852 - 10.8456i) q^{50} +(76.8076 - 220.942i) q^{51} +80.4953i q^{52} +(601.424 - 347.232i) q^{53} +(-16.6938 + 32.0576i) q^{54} +390.174i q^{55} +(75.7592 + 6.33772i) q^{56} +(78.5122 + 410.381i) q^{57} -14.5581 q^{58} +(-317.670 + 550.221i) q^{59} +(258.639 - 49.4816i) q^{60} +(647.712 - 373.957i) q^{61} -27.4135 q^{62} +(-486.993 - 113.512i) q^{63} +486.690 q^{64} +(56.1274 - 32.4052i) q^{65} +(-26.8493 + 77.2338i) q^{66} +(-82.3930 + 142.709i) q^{67} -357.143 q^{68} +(-108.828 + 94.0396i) q^{69} +(-12.9854 - 27.5729i) q^{70} -278.490i q^{71} +(109.661 + 16.0733i) q^{72} +(-313.876 + 181.216i) q^{73} +49.2787i q^{74} +(286.049 + 331.033i) q^{75} +(552.477 - 318.973i) q^{76} +(-1127.31 - 94.3066i) q^{77} +(13.3402 - 2.55218i) q^{78} +(-278.740 - 482.792i) q^{79} +(-199.334 - 345.256i) q^{80} +(-698.336 - 209.209i) q^{81} +(6.73147 + 3.88641i) q^{82} +(514.684 - 891.459i) q^{83} +(80.4510 + 759.235i) q^{84} +(143.776 + 249.028i) q^{85} -95.3530i q^{86} +(-55.1752 - 288.399i) q^{87} +250.735 q^{88} +(730.130 - 1264.62i) q^{89} +(-16.4008 - 41.2945i) q^{90} +(80.0608 + 169.999i) q^{91} +(190.182 + 109.802i) q^{92} +(-103.897 - 543.066i) q^{93} +(-110.681 - 63.9015i) q^{94} +(-444.824 - 256.819i) q^{95} +(-47.7633 - 249.657i) q^{96} +(878.164 + 507.008i) q^{97} +(82.8039 - 30.8537i) q^{98} +(-1631.77 - 239.174i) 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 $

$2$	−0.223110	+	0.128812i	−0.0788812	+	0.0455421i	−0.538922	−	0.842356i	$-0.681168\pi$
$2$	−0.223110	+	0.128812i	−0.0788812	+	0.0455421i	0.460041	+	0.887898i	$0.347835\pi$
$3$	−3.39738	−	3.93164i	−0.653826	−	0.756645i
$3$	−3.39738	−	3.93164i	−0.653826	−	0.756645i
$4$	−3.96681	+	6.87072i	−0.495852	+	0.858841i
$5$	6.38772			0.571335			0.285668	−	0.958329i	$-0.407785\pi$
$5$	6.38772			0.571335			0.285668	+	0.958329i	$0.407785\pi$
$6$	1.26443	+	0.439563i	0.0860337	+	0.0299085i
$7$	−1.54394	+	18.4558i	−0.0833649	+	0.996519i
$7$	−1.54394	+	18.4558i	−0.0833649	+	0.996519i
$8$		−	4.10490i		−	0.181413i
$9$	−3.91563	+	26.7146i	−0.145023	+	0.989428i
$10$	−1.42516	+	0.822818i	−0.0450676	+	0.0260198i
$11$			61.0818i			1.67426i	0.547004	+	0.837130i	$0.315768\pi$
$11$			61.0818i			1.67426i	−0.547004	+	0.837130i	$0.684232\pi$
$12$	40.4900	−	7.74636i	0.974038	−	0.186348i
$13$	8.78677	−	5.07304i	0.187462	−	0.108231i	−0.403332	−	0.915054i	$-0.632148\pi$
$13$	8.78677	−	5.07304i	0.187462	−	0.108231i	0.590794	+	0.806822i	$0.298815\pi$
$14$	−2.03287	−	4.31654i	−0.0388076	−	0.0824032i
$15$	−21.7015	−	25.1142i	−0.373554	−	0.432298i
$16$	−31.2058	−	54.0500i	−0.487590	−	0.844531i
$17$	22.5082	+	38.9853i	0.321120	+	0.556196i	0.980719	−	0.195421i	$-0.0626074\pi$
$17$	22.5082	+	38.9853i	0.321120	+	0.556196i	−0.659599	+	0.751617i	$0.729274\pi$
$18$	−2.56755	−	6.46466i	−0.0336210	−	0.0846519i
$19$	−69.6373	−	40.2051i	−0.840837	−	0.485457i	0.0167118	−	0.999860i	$-0.494680\pi$
$19$	−69.6373	−	40.2051i	−0.840837	−	0.485457i	−0.857549	+	0.514403i	$0.828014\pi$
$20$	−25.3389	+	43.8883i	−0.283298	+	0.490686i
$21$	77.8069	−	56.6311i	0.808517	−	0.588472i
$22$	−7.86810	−	13.6279i	−0.0762493	−	0.132068i
$23$		−	27.6800i		−	0.250943i	−0.992097	−	0.125471i	$-0.959956\pi$
$23$		−	27.6800i		−	0.250943i	0.992097	−	0.125471i	$-0.0400444\pi$
$24$	−16.1390	+	13.9459i	−0.137265	+	0.118612i
$25$	−84.1970			−0.673576
$26$	−1.30694	+	2.26369i	−0.00985817	+	0.0170749i
$27$	118.335	−	75.3646i	0.843466	−	0.537183i
$28$	−120.680	−	83.8187i	−0.814514	−	0.565723i
$29$	48.9383	+	28.2545i	0.313366	+	0.180922i	0.648432	−	0.761273i	$-0.275425\pi$
$29$	48.9383	+	28.2545i	0.313366	+	0.180922i	−0.335066	+	0.942195i	$0.608759\pi$
$30$	8.07685	+	2.80781i	0.0491541	+	0.0170878i
$31$	92.1526	+	53.2043i	0.533906	+	0.308251i	0.742606	−	0.669729i	$-0.233590\pi$
$31$	92.1526	+	53.2043i	0.533906	+	0.308251i	−0.208699	+	0.977980i	$0.566923\pi$
$32$	42.3642	+	24.4590i	0.234031	+	0.135118i
$33$	240.152	−	207.518i	1.26682	−	1.09467i
$34$	−10.0436	−	5.79867i	−0.0506607	−	0.0292489i
$35$	−9.86226	+	117.890i	−0.0476293	+	0.569347i
$36$	−168.016	−	132.875i	−0.777851	−	0.615162i
$37$	95.6403	−	165.654i	0.424951	−	0.736036i	−0.571465	−	0.820626i	$-0.693625\pi$
$37$	95.6403	−	165.654i	0.424951	−	0.736036i	0.996416	+	0.0845902i	$0.0269581\pi$
$38$	20.7157			0.0884349
$39$	−49.7974	−	17.3114i	−0.204461	−	0.0710779i
$40$		−	26.2210i		−	0.103647i
$41$	−15.0856	−	26.1289i	−0.0574626	−	0.0995282i	0.835863	−	0.548938i	$-0.184968\pi$
$41$	−15.0856	−	26.1289i	−0.0574626	−	0.0995282i	−0.893326	+	0.449410i	$0.851634\pi$
$42$	−10.0647	+	22.6574i	−0.0369766	+	0.0832410i
$43$	−185.062	+	320.536i	−0.656317	+	1.13678i	0.325244	+	0.945630i	$0.394553\pi$
$43$	−185.062	+	320.536i	−0.656317	+	1.13678i	−0.981562	+	0.191145i	$0.938780\pi$
$44$	−419.676	−	242.300i	−1.43792	−	0.830185i
$45$	−25.0120	+	170.645i	−0.0828569	+	0.565295i
$46$	3.56553	+	6.17569i	0.0114285	+	0.0197947i
$47$	248.041	+	429.620i	0.769798	+	1.33333i	0.937672	+	0.347521i	$0.112976\pi$
$47$	248.041	+	429.620i	0.769798	+	1.33333i	−0.167874	+	0.985808i	$0.553690\pi$
$48$	−106.487	+	306.318i	−0.320211	+	0.921108i
$49$	−338.232	−	56.9893i	−0.986101	−	0.166149i
$50$	18.7852	−	10.8456i	0.0531325	−	0.0306760i
$51$	76.8076	−	220.942i	0.210886	−	0.606629i
$52$			80.4953i			0.214667i
$53$	601.424	−	347.232i	1.55871	−	0.899924i	0.561335	−	0.827589i	$-0.310288\pi$
$53$	601.424	−	347.232i	1.55871	−	0.899924i	0.997380	−	0.0723355i	$-0.0230452\pi$
$54$	−16.6938	+	32.0576i	−0.0420692	+	0.0807868i
$55$			390.174i			0.956564i
$56$	75.7592	+	6.33772i	0.180781	+	0.0151235i
$57$	78.5122	+	410.381i	0.182442	+	0.953620i
$58$	−14.5581			−0.0329582
$59$	−317.670	+	550.221i	−0.700968	+	1.21411i	0.267159	+	0.963653i	$0.413915\pi$
$59$	−317.670	+	550.221i	−0.700968	+	1.21411i	−0.968127	+	0.250460i	$0.919418\pi$
$60$	258.639	−	49.4816i	0.556502	−	0.106467i
$61$	647.712	−	373.957i	1.35952	−	0.784922i	0.369965	−	0.929046i	$-0.379370\pi$
$61$	647.712	−	373.957i	1.35952	−	0.784922i	0.989560	+	0.144124i	$0.0460363\pi$
$62$	−27.4135			−0.0561536
$63$	−486.993	−	113.512i	−0.973894	−	0.227002i
$64$	486.690			0.950566
$65$	56.1274	−	32.4052i	0.107104	−	0.0618365i
$66$	−26.8493	+	77.2338i	−0.0500745	+	0.144043i
$67$	−82.3930	+	142.709i	−0.150237	+	0.260219i	−0.931315	−	0.364216i	$-0.881337\pi$
$67$	−82.3930	+	142.709i	−0.150237	+	0.260219i	0.781077	+	0.624434i	$0.214670\pi$
$68$	−357.143			−0.636912
$69$	−108.828	+	94.0396i	−0.189875	+	0.164073i
$70$	−12.9854	−	27.5729i	−0.0221722	−	0.0470799i
$71$		−	278.490i		−	0.465502i	−0.972536	−	0.232751i	$-0.925227\pi$
$71$		−	278.490i		−	0.465502i	0.972536	−	0.232751i	$-0.0747728\pi$
$72$	109.661	+	16.0733i	0.179495	+	0.0263091i
$73$	−313.876	+	181.216i	−0.503238	+	0.290545i	−0.730050	−	0.683394i	$-0.760503\pi$
$73$	−313.876	+	181.216i	−0.503238	+	0.290545i	0.226812	+	0.973939i	$0.427170\pi$
$74$			49.2787i			0.0774125i
$75$	286.049	+	331.033i	0.440401	+	0.509658i
$76$	552.477	−	318.973i	0.833861	−	0.481430i
$77$	−1127.31	−	94.3066i	−1.66843	−	0.139575i
$78$	13.3402	−	2.55218i	0.0193651	−	0.00370485i
$79$	−278.740	−	482.792i	−0.396971	−	0.687574i	0.596380	−	0.802702i	$-0.296605\pi$
$79$	−278.740	−	482.792i	−0.396971	−	0.687574i	−0.993351	+	0.115129i	$0.963272\pi$
$80$	−199.334	−	345.256i	−0.278577	−	0.482510i
$81$	−698.336	−	209.209i	−0.957936	−	0.286980i
$82$	6.73147	+	3.88641i	0.00906544	+	0.00523393i
$83$	514.684	−	891.459i	0.680650	−	1.17892i	−0.294133	−	0.955765i	$-0.595031\pi$
$83$	514.684	−	891.459i	0.680650	−	1.17892i	0.974783	−	0.223156i	$-0.0716358\pi$
$84$	80.4510	+	759.235i	0.104499	+	0.986183i
$85$	143.776	+	249.028i	0.183467	+	0.317775i
$86$		−	95.3530i		−	0.119560i
$87$	−55.1752	−	288.399i	−0.0679931	−	0.355398i
$88$	250.735			0.303732
$89$	730.130	−	1264.62i	0.869591	−	1.50618i	0.00717569	−	0.999974i	$-0.497716\pi$
$89$	730.130	−	1264.62i	0.869591	−	1.50618i	0.862415	−	0.506201i	$-0.168951\pi$
$90$	−16.4008	−	41.2945i	−0.0192089	−	0.0483646i
$91$	80.0608	+	169.999i	0.0922269	+	0.195833i
$92$	190.182	+	109.802i	0.215520	+	0.124431i
$93$	−103.897	−	543.066i	−0.115845	−	0.605520i
$94$	−110.681	−	63.9015i	−0.121445	−	0.0701164i
$95$	−444.824	−	256.819i	−0.480400	−	0.277359i
$96$	−47.7633	−	249.657i	−0.0507793	−	0.265422i
$97$	878.164	+	507.008i	0.919217	+	0.530710i	0.883385	−	0.468647i	$-0.155259\pi$
$97$	878.164	+	507.008i	0.919217	+	0.530710i	0.0358320	+	0.999358i	$0.488592\pi$
$98$	82.8039	−	30.8537i	0.0853516	−	0.0318030i
$99$	−1631.77	−	239.174i	−1.65656	−	0.242807i
$100$	333.994	−	578.494i	0.333994	−	0.578494i
$101$	143.704			0.141575			0.0707875	−	0.997491i	$-0.477449\pi$
$101$	143.704			0.141575			0.0707875	+	0.997491i	$0.477449\pi$
$102$	11.3236	+	59.1881i	0.0109922	+	0.0574559i
$103$			546.960i			0.523239i	0.965171	+	0.261619i	$0.0842565\pi$
$103$			546.960i			0.523239i	−0.965171	+	0.261619i	$0.915744\pi$
$104$	−20.8243	−	36.0688i	−0.0196346	−	0.0340080i
$105$	497.009	−	361.744i	0.461934	−	0.336215i
$106$	−89.4556	+	154.942i	−0.0819689	+	0.141974i
$107$	1153.06	+	665.722i	1.04178	+	0.601475i	0.920338	−	0.391123i	$-0.127913\pi$
$107$	1153.06	+	665.722i	1.04178	+	0.601475i	0.121447	+	0.992598i	$0.461247\pi$
$108$	48.3967	+	1112.00i	0.0431201	+	0.990766i
$109$	527.013	+	912.813i	0.463107	+	0.802125i	0.999114	−	0.0420888i	$-0.0134013\pi$
$109$	527.013	+	912.813i	0.463107	+	0.802125i	−0.536007	+	0.844214i	$0.680068\pi$
$110$	−50.2592	−	87.0515i	−0.0435639	−	0.0754549i
$111$	−976.219	+	186.766i	−0.834762	+	0.159703i
$112$	1045.71	−	492.477i	0.882239	−	0.415488i
$113$	804.987	−	464.760i	0.670149	−	0.386911i	−0.125984	−	0.992032i	$-0.540209\pi$
$113$	804.987	−	464.760i	0.670149	−	0.386911i	0.796133	+	0.605122i	$0.206875\pi$
$114$	−70.3790	−	81.4467i	−0.0578211	−	0.0669139i
$115$		−	176.812i		−	0.143373i
$116$	−388.258	+	224.161i	−0.310766	+	0.179421i
$117$	101.118	+	254.599i	0.0799008	+	0.201177i
$118$		−	163.679i		−	0.127694i
$119$	−754.257	+	355.216i	−0.581030	+	0.273635i
$120$	−103.091	+	89.0825i	−0.0784243	+	0.0677674i
$121$	−2399.99			−1.80315
$122$	−96.3405	+	166.867i	−0.0714940	+	0.123831i
$123$	−51.4783	+	148.081i	−0.0377369	+	0.108553i
$124$	−731.105	+	422.103i	−0.529477	+	0.305694i
$125$	−1336.29			−0.956173
$126$	123.275	−	37.4052i	0.0871601	−	0.0264470i
$127$	−1387.22			−0.969259			−0.484629	−	0.874720i	$-0.661046\pi$
$127$	−1387.22			−0.969259			−0.484629	+	0.874720i	$0.661046\pi$
$128$	−447.499	+	258.363i	−0.309013	+	0.178409i
$129$	1888.96	−	361.387i	1.28925	−	0.246654i
$130$	−8.34838	+	14.4598i	−0.00563232	+	0.00975547i
$131$	392.756			0.261949			0.130974	−	0.991386i	$-0.458189\pi$
$131$	392.756			0.261949			0.130974	+	0.991386i	$0.458189\pi$
$132$	473.162	+	2473.20i	0.311996	+	1.63079i
$133$	849.533	−	1223.14i	0.553864	−	0.797440i
$134$		−	42.4530i		−	0.0273685i
$135$	755.891	−	481.408i	0.481902	−	0.306911i
$136$	160.031	−	92.3939i	0.100901	−	0.0582552i
$137$			2081.76i			1.29822i	0.760693	+	0.649112i	$0.224859\pi$
$137$			2081.76i			1.29822i	−0.760693	+	0.649112i	$0.775141\pi$
$138$	12.1671	−	34.9995i	0.00750532	−	0.0215896i
$139$	1088.49	−	628.441i	0.664206	−	0.383479i	−0.129672	−	0.991557i	$-0.541392\pi$
$139$	1088.49	−	628.441i	0.664206	−	0.383479i	0.793878	+	0.608078i	$0.208059\pi$
$140$	−770.871	−	535.411i	−0.465361	−	0.323218i
$141$	846.422	−	2434.79i	0.505543	−	1.45423i
$142$	35.8730	+	62.1338i	0.0211999	+	0.0367194i
$143$	309.871	+	536.712i	0.181208	+	0.313861i
$144$	1566.11	−	622.008i	0.906314	−	0.359959i
$145$	312.604	+	180.482i	0.179037	+	0.103367i
$146$	46.6858	−	80.8622i	0.0264640	−	0.0458370i
$147$	925.043	+	1523.42i	0.519022	+	0.854761i
$148$	758.775	+	1314.24i	0.421425	+	0.729930i
$149$			3007.64i			1.65366i	0.562453	+	0.826830i	$0.309858\pi$
$149$			3007.64i			1.65366i	−0.562453	+	0.826830i	$0.690142\pi$
$150$	−106.461	−	37.0099i	−0.0579503	−	0.0201456i
$151$	−2870.22			−1.54686			−0.773428	−	0.633884i	$-0.781460\pi$
$151$	−2870.22			−1.54686			−0.773428	+	0.633884i	$0.781460\pi$
$152$	−165.038	+	285.854i	−0.0880681	+	0.152538i
$153$	−1129.61	+	448.645i	−0.596886	+	0.237064i
$154$	263.662	−	124.171i	0.137964	−	0.0649740i
$155$	588.645	+	339.855i	0.305040	+	0.176115i
$156$	316.479	−	273.473i	0.162427	−	0.140355i
$157$	−794.753	−	458.851i	−0.404001	−	0.233250i	0.284208	−	0.958763i	$-0.408269\pi$
$157$	−794.753	−	458.851i	−0.404001	−	0.233250i	−0.688209	+	0.725512i	$0.741603\pi$
$158$	124.379	+	71.8103i	0.0626271	+	0.0361577i
$159$	−3408.46	−	1184.90i	−1.70005	−	0.591000i
$160$	270.611	+	156.237i	0.133710	+	0.0771977i
$161$	510.857	+	42.7363i	0.250069	+	0.0209198i
$162$	182.754	−	43.2778i	0.0886328	−	0.0209891i
$163$	−806.536	+	1396.96i	−0.387563	+	0.671279i	−0.992121	−	0.125282i	$-0.960016\pi$
$163$	−806.536	+	1396.96i	−0.387563	+	0.671279i	0.604558	+	0.796561i	$0.293350\pi$
$164$	239.366			0.113972
$165$	1534.02	−	1325.57i	0.723779	−	0.625426i
$166$			265.191i			0.123993i
$167$	−922.384	−	1597.62i	−0.427402	−	0.740282i	0.569239	−	0.822172i	$-0.307238\pi$
$167$	−922.384	−	1597.62i	−0.427402	−	0.740282i	−0.996641	+	0.0818896i	$0.973905\pi$
$168$	−232.465	−	319.390i	−0.106756	−	0.146675i
$169$	−1047.03	+	1813.51i	−0.476572	+	0.825447i
$170$	−64.1557	−	37.0403i	−0.0289442	−	0.0167110i
$171$	1346.74	−	1702.90i	0.602266	−	0.761545i
$172$	−1468.21	−	2543.02i	−0.650872	−	1.12734i
$173$	1002.90	+	1737.08i	0.440747	+	0.763396i	0.997745	−	0.0671176i	$-0.0213803\pi$
$173$	1002.90	+	1737.08i	0.440747	+	0.763396i	−0.556998	+	0.830514i	$0.688047\pi$
$174$	49.4595	+	57.2374i	0.0215489	+	0.0249377i
$175$	129.995	−	1553.92i	0.0561526	−	0.671231i
$176$	3301.47	−	1906.10i	1.41396	−	0.816352i
$177$	3242.52	−	620.343i	1.37696	−	0.263434i
$178$			376.199i			0.158412i
$179$	1424.92	−	822.678i	0.594992	−	0.343519i	−0.172077	−	0.985083i	$-0.555048\pi$
$179$	1424.92	−	822.678i	0.594992	−	0.343519i	0.767069	+	0.641565i	$0.221714\pi$
$180$	−1073.24	−	848.768i	−0.444414	−	0.351464i
$181$		−	3394.40i		−	1.39394i	−0.717099	−	0.696971i	$-0.754531\pi$
$181$		−	3394.40i		−	1.39394i	0.717099	−	0.696971i	$-0.245469\pi$
$182$	−39.7604	−	27.6157i	−0.0161936	−	0.0112473i
$183$	−3670.79	−	1276.10i	−1.48280	−	0.515475i
$184$	−113.624			−0.0455242
$185$	610.924	−	1058.15i	0.242789	−	0.420523i
$186$	93.1341	+	107.780i	0.0367146	+	0.0424883i
$187$	−2381.30	+	1374.84i	−0.931217	+	0.537638i
$188$	−3935.73			−1.52682
$189$	1208.21	+	2300.32i	0.464997	+	0.885312i
$190$	132.326			0.0505260
$191$	98.1081	−	56.6427i	0.0371668	−	0.0214582i	−0.481301	−	0.876555i	$-0.659836\pi$
$191$	98.1081	−	56.6427i	0.0371668	−	0.0214582i	0.518468	+	0.855097i	$0.326502\pi$
$192$	−1653.47	−	1913.49i	−0.621504	−	0.719241i
$193$	437.900	−	758.465i	0.163320	−	0.282878i	−0.772737	−	0.634726i	$-0.781113\pi$
$193$	437.900	−	758.465i	0.163320	−	0.282878i	0.936057	+	0.351847i	$0.114446\pi$
$194$	−261.236			−0.0966786
$195$	−318.092	−	110.580i	−0.116816	−	0.0406093i
$196$	1733.26	−	2097.84i	0.631656	−	0.764518i
$197$			1004.09i			0.363140i	0.983378	+	0.181570i	$0.0581179\pi$
$197$			1004.09i			0.363140i	−0.983378	+	0.181570i	$0.941882\pi$
$198$	394.873	−	156.831i	0.141729	−	0.0562903i
$199$	1451.86	−	838.230i	0.517183	−	0.298596i	−0.218598	−	0.975815i	$-0.570148\pi$
$199$	1451.86	−	838.230i	0.517183	−	0.298596i	0.735781	+	0.677219i	$0.236815\pi$
$200$			345.620i			0.122195i
$201$	841.000	−	160.896i	0.295122	−	0.0564614i
$202$	−32.0618	+	18.5109i	−0.0111676	+	0.00644762i
$203$	−597.017	+	859.571i	−0.206416	+	0.297192i
$204$	1213.35	+	1404.16i	0.416429	+	0.481916i
$205$	−96.3623	−	166.904i	−0.0328304	−	0.0568640i
$206$	−70.4553	−	122.032i	−0.0238294	−	0.0412737i
$207$	739.460	+	108.385i	0.248290	+	0.0363926i
$208$	−548.396	−	316.616i	−0.182810	−	0.105545i
$209$	2455.80	−	4253.57i	0.812782	−	1.40778i
$210$	−64.2904	+	144.729i	−0.0211260	+	0.0475585i
$211$	1528.10	+	2646.75i	0.498572	+	0.863552i	0.999999	−	0.00164804i	$-0.000524587\pi$
$211$	1528.10	+	2646.75i	0.498572	+	0.863552i	−0.501427	+	0.865200i	$0.667191\pi$
$212$			5509.62i			1.78492i
$213$	−1094.92	+	946.136i	−0.352220	+	0.304358i
$214$	−343.013			−0.109570
$215$	−1182.12	+	2047.50i	−0.374977	+	0.649480i
$216$	−309.364	−	485.753i	−0.0974517	−	0.153015i
$217$	−1124.21	+	1618.60i	−0.351687	+	0.506351i
$218$	−235.163	−	135.772i	−0.0730608	−	0.0421817i
$219$	1778.83	+	618.387i	0.548869	+	0.190807i
$220$	−2680.78	−	1547.75i	−0.821536	−	0.474314i
$221$	395.549	+	228.370i	0.120396	+	0.0695106i
$222$	193.746	−	167.418i	0.0585738	−	0.0506143i
$223$	3580.72	+	2067.33i	1.07526	+	0.620801i	0.929613	−	0.368536i	$-0.120141\pi$
$223$	3580.72	+	2067.33i	1.07526	+	0.620801i	0.145645	+	0.989337i	$0.453474\pi$
$224$	−516.818	+	744.101i	−0.154158	+	0.221953i
$225$	329.684	−	2249.29i	0.0976842	−	0.666455i
$226$	−119.734	+	207.385i	−0.0352414	+	0.0610400i
$227$	−4441.16			−1.29855			−0.649274	−	0.760555i	$-0.724927\pi$
$227$	−4441.16			−1.29855			−0.649274	+	0.760555i	$0.724927\pi$
$228$	−3131.06	−	1088.47i	−0.909471	−	0.316165i
$229$			1299.87i			0.375099i	0.982255	+	0.187549i	$0.0600545\pi$
$229$			1299.87i			0.375099i	−0.982255	+	0.187549i	$0.939946\pi$
$230$	22.7756	+	39.4486i	0.00652948	+	0.0113094i
$231$	3459.13	+	4752.59i	0.985256	+	1.35367i
$232$	115.982	−	200.887i	0.0328215	−	0.0568485i
$233$	1741.16	+	1005.26i	0.489559	+	0.282647i	0.724392	−	0.689389i	$-0.242121\pi$
$233$	1741.16	+	1005.26i	0.489559	+	0.282647i	−0.234832	+	0.972036i	$0.575454\pi$
$234$	−55.3560	−	43.7782i	−0.0154647	−	0.0122302i
$235$	1584.42	+	2744.29i	0.439813	+	0.761778i
$236$	−2520.28	−	4365.25i	−0.695153	−	1.20404i
$237$	−951.179	+	2736.13i	−0.260699	+	0.749919i
$238$	122.526	−	176.410i	0.0333705	−	0.0480460i
$239$	4499.21	−	2597.62i	1.21770	−	0.703038i	0.253273	−	0.967395i	$-0.418493\pi$
$239$	4499.21	−	2597.62i	1.21770	−	0.703038i	0.964425	+	0.264356i	$0.0851595\pi$
$240$	−680.212	+	1956.67i	−0.182948	+	0.526262i
$241$		−	6739.77i		−	1.80144i	−0.434402	−	0.900719i	$-0.643040\pi$
$241$		−	6739.77i		−	1.80144i	0.434402	−	0.900719i	$-0.356960\pi$
$242$	535.460	−	309.148i	0.142234	−	0.0821190i
$243$	1549.98	+	3456.37i	0.409181	+	0.912453i
$244$			5933.67i			1.55682i
$245$	−2160.54	−	364.032i	−0.563394	−	0.0949271i
$246$	−7.58935	−	39.6693i	−0.00196699	−	0.0102814i
$247$	−815.849			−0.210167
$248$	218.398	−	378.277i	0.0559206	−	0.0968574i
$249$	−5253.48	+	1005.07i	−1.33705	+	0.255798i
$250$	298.140	−	172.131i	0.0754241	−	0.0435461i
$251$	−1818.28			−0.457246			−0.228623	−	0.973515i	$-0.573422\pi$
$251$	−1818.28			−0.457246			−0.228623	+	0.973515i	$0.573422\pi$
$252$	2711.72	−	2895.71i	0.677866	−	0.723860i
$253$	1690.75			0.420144
$254$	309.502	−	178.691i	0.0764563	−	0.0441421i
$255$	490.625	−	1411.32i	0.120487	−	0.346589i
$256$	−1880.20	+	3256.60i	−0.459033	+	0.795068i
$257$	−464.053			−0.112634			−0.0563168	−	0.998413i	$-0.517936\pi$
$257$	−464.053			−0.112634			−0.0563168	+	0.998413i	$0.517936\pi$
$258$	−374.894	+	323.950i	−0.0904647	+	0.0781716i
$259$	2909.61	+	2020.88i	0.698048	+	0.484831i
$260$			514.182i			0.122647i
$261$	−946.431	+	1196.73i	−0.224454	+	0.283815i
$262$	−87.6278	+	50.5919i	−0.0206628	+	0.0119297i
$263$		−	376.510i		−	0.0882759i	−0.999025	−	0.0441380i	$-0.985946\pi$
$263$		−	376.510i		−	0.0882759i	0.999025	−	0.0441380i	$-0.0140541\pi$
$264$	−851.841	−	985.799i	−0.198588	−	0.229817i
$265$	3841.73	−	2218.02i	0.890549	−	0.514159i
$266$	−31.9838	+	382.324i	−0.00737237	+	0.0881271i
$267$	−7452.57	+	1425.79i	−1.70820	+	0.326805i
$268$	−653.675	−	1132.20i	−0.148991	−	0.258060i
$269$	1998.09	+	3460.80i	0.452885	+	0.784419i	0.998564	−	0.0535750i	$-0.0170616\pi$
$269$	1998.09	+	3460.80i	0.452885	+	0.784419i	−0.545679	+	0.837994i	$0.683728\pi$
$270$	−106.635	+	204.775i	−0.0240356	+	0.0461563i
$271$	−729.622	−	421.248i	−0.163548	−	0.0944242i	0.415992	−	0.909368i	$-0.363434\pi$
$271$	−729.622	−	421.248i	−0.163548	−	0.0944242i	−0.579540	+	0.814944i	$0.696768\pi$
$272$	1404.77	−	2433.13i	0.313150	−	0.542391i
$273$	396.379	−	892.322i	0.0878754	−	0.197823i
$274$	−268.157	−	464.461i	−0.0591238	−	0.102405i
$275$		−	5142.90i		−	1.12774i
$276$	−214.420	−	1120.77i	−0.0467628	−	0.244428i
$277$	4166.18			0.903687			0.451844	−	0.892097i	$-0.350766\pi$
$277$	4166.18			0.903687			0.451844	+	0.892097i	$0.350766\pi$
$278$	−161.902	+	280.422i	−0.0349289	+	0.0604986i
$279$	−1782.17	+	2253.49i	−0.382421	+	0.483558i
$280$	483.929	+	40.4836i	0.103287	+	0.00864056i
$281$	−4478.35	−	2585.58i	−0.950733	−	0.548906i	−0.0574244	−	0.998350i	$-0.518289\pi$
$281$	−4478.35	−	2585.58i	−0.950733	−	0.548906i	−0.893309	+	0.449444i	$0.851622\pi$
$282$	124.786	+	652.255i	0.0263508	+	0.137735i
$283$	5213.04	+	3009.75i	1.09499	+	0.632195i	0.934901	−	0.354907i	$-0.115488\pi$
$283$	5213.04	+	3009.75i	1.09499	+	0.632195i	0.160092	+	0.987102i	$0.448821\pi$
$284$	1913.43	+	1104.72i	0.399792	+	0.230820i
$285$	501.514	+	2621.40i	0.104236	+	0.544836i
$286$	−138.270	−	79.8304i	−0.0285877	−	0.0165051i
$287$	505.521	−	238.074i	0.103972	−	0.0489654i
$288$	−819.293	+	1035.97i	−0.167630	+	0.211962i
$289$	1443.26	−	2499.80i	0.293764	−	0.508814i
$290$	−92.9933			−0.0188302
$291$	−990.081	−	5175.13i	−0.199449	−	1.04251i
$292$		−	2875.40i		−	0.576268i
$293$	−2243.89	−	3886.53i	−0.447404	−	0.774926i	0.550812	−	0.834629i	$-0.314318\pi$
$293$	−2243.89	−	3886.53i	−0.447404	−	0.774926i	−0.998216	+	0.0597027i	$0.980985\pi$
$294$	−402.622	−	220.734i	−0.0798687	−	0.0437872i
$295$	−2029.19	+	3514.66i	−0.400488	+	0.693665i
$296$	−679.993	−	392.594i	−0.133526	−	0.0770914i
$297$	4603.41	+	7228.12i	0.899383	+	1.41218i
$298$	−387.421	−	671.033i	−0.0753111	−	0.130443i
$299$	−140.422	−	243.218i	−0.0271599	−	0.0470424i
$300$	−3409.14	+	652.220i	−0.656089	+	0.125520i
$301$	−5630.03	−	3910.35i	−1.07810	−	0.748800i
$302$	640.374	−	369.720i	0.122018	−	0.0704471i
$303$	−488.217	−	564.993i	−0.0925655	−	0.107122i
$304$			5018.53i			0.946816i
$305$	4137.40	−	2388.73i	0.776744	−	0.448454i
$306$	194.236	−	245.605i	0.0362867	−	0.0458833i
$307$		−	263.461i		−	0.0489789i	−0.999700	−	0.0244895i	$-0.992204\pi$
$307$		−	263.461i		−	0.0489789i	0.999700	−	0.0244895i	$-0.00779602\pi$
$308$	5119.80	−	7371.36i	0.947167	−	1.36371i
$309$	2150.45	−	1858.23i	0.395906	−	0.342107i
$310$	−175.110			−0.0320825
$311$	2426.23	−	4202.36i	0.442377	−	0.766219i	−0.555489	−	0.831524i	$-0.687469\pi$
$311$	2426.23	−	4202.36i	0.442377	−	0.766219i	0.997865	+	0.0653054i	$0.0208021\pi$
$312$	−71.0615	+	204.413i	−0.0128944	+	0.0370917i
$313$	2371.65	−	1369.27i	0.428286	−	0.247271i	−0.270330	−	0.962768i	$-0.587133\pi$
$313$	2371.65	−	1369.27i	0.428286	−	0.247271i	0.698616	+	0.715497i	$0.253800\pi$
$314$	236.423			0.0424908
$315$	−3110.78	−	725.081i	−0.556420	−	0.129694i
$316$	4422.84			0.787355
$317$	−6423.47	+	3708.59i	−1.13810	+	0.657083i	−0.945959	−	0.324285i	$-0.894876\pi$
$317$	−6423.47	+	3708.59i	−1.13810	+	0.657083i	−0.192141	+	0.981367i	$0.561543\pi$
$318$	913.090	−	174.688i	0.161017	−	0.0308051i
$319$	−1725.84	+	2989.24i	−0.302910	+	0.524656i
$320$	3108.84			0.543092
$321$	−1300.02	−	6795.15i	−0.226043	−	1.18152i
$322$	−119.482	+	56.2699i	−0.0206785	+	0.00973850i
$323$		−	3619.78i		−	0.623560i
$324$	4207.58	−	3968.18i	0.721465	−	0.680415i
$325$	−739.820	+	427.135i	−0.126270	+	0.0729021i
$326$		−	415.568i		−	0.0706017i
$327$	1798.39	−	5173.20i	0.304132	−	0.874857i
$328$	−107.257	+	61.9247i	−0.0180557	+	0.0104244i
$329$	−8311.93	+	3914.49i	−1.39286	+	0.655966i
$330$	−171.506	+	493.348i	−0.0286094	+	0.0822968i
$331$	−2086.06	−	3613.16i	−0.346406	−	0.599992i	0.639203	−	0.769038i	$-0.279265\pi$
$331$	−2086.06	−	3613.16i	−0.346406	−	0.599992i	−0.985608	+	0.169046i	$0.945931\pi$
$332$	4083.31	+	7072.51i	0.675003	+	1.16914i
$333$	4050.88	+	3203.63i	0.666627	+	0.527201i
$334$	411.585	+	237.629i	0.0674280	+	0.0389296i
$335$	−526.303	+	911.584i	−0.0858359	+	0.148672i
$336$	−5488.93	−	2438.24i	−0.891208	−	0.395884i
$337$	−528.671	−	915.685i	−0.0854556	−	0.148013i	0.820130	−	0.572178i	$-0.193901\pi$
$337$	−528.671	−	915.685i	−0.0854556	−	0.148013i	−0.905585	+	0.424164i	$0.860568\pi$
$338$		−	539.481i		−	0.0868163i
$339$	−4562.12	−	1585.96i	−0.730915	−	0.254093i
$340$	−2281.33			−0.363890
$341$	−3249.82	+	5628.85i	−0.516092	+	0.893898i
$342$	−81.1149	+	553.410i	−0.0128251	+	0.0875000i
$343$	1573.99	−	6154.36i	0.247777	−	0.968817i
$344$	1315.77	+	759.660i	0.206225	+	0.119064i
$345$	−695.163	+	600.699i	−0.108482	+	0.0937407i
$346$	−447.514	−	258.373i	−0.0695333	−	0.0401451i
$347$	−4140.17	−	2390.33i	−0.640507	−	0.369797i	0.144303	−	0.989534i	$-0.453906\pi$
$347$	−4140.17	−	2390.33i	−0.640507	−	0.369797i	−0.784810	+	0.619736i	$0.787239\pi$
$348$	2200.38	+	764.932i	0.338945	+	0.117830i
$349$	−2180.04	−	1258.65i	−0.334370	−	0.193048i	0.323410	−	0.946259i	$-0.395171\pi$
$349$	−2180.04	−	1258.65i	−0.334370	−	0.193048i	−0.657780	+	0.753211i	$0.728504\pi$
$350$	171.161	+	363.440i	0.0261399	+	0.0555048i
$351$	657.454	−	1262.53i	0.0999781	−	0.191991i
$352$	−1494.00	+	2587.68i	−0.226223	+	0.391829i
$353$	−6005.81			−0.905544			−0.452772	−	0.891626i	$-0.649565\pi$
$353$	−6005.81			−0.905544			−0.452772	+	0.891626i	$0.649565\pi$
$354$	−643.529	+	556.081i	−0.0966192	+	0.0834898i
$355$		−	1778.92i		−	0.265958i
$356$	5792.58	+	10033.0i	0.862377	+	1.49368i
$357$	3959.08	+	1758.67i	0.586937	+	0.260724i
$358$	−211.942	+	367.095i	−0.0312891	+	0.0541943i
$359$	−5772.63	−	3332.83i	−0.848656	−	0.489972i	0.0115408	−	0.999933i	$-0.496326\pi$
$359$	−5772.63	−	3332.83i	−0.848656	−	0.489972i	−0.860197	+	0.509961i	$0.829660\pi$
$360$	700.481	+	102.672i	0.102552	+	0.0150313i
$361$	−196.595	−	340.513i	−0.0286624	−	0.0496447i
$362$	437.241	+	757.323i	0.0634830	+	0.109956i
$363$	8153.67	+	9435.89i	1.17894	+	1.36434i
$364$	−1485.60	−	124.280i	−0.213920	−	0.0178957i
$365$	−2004.95	+	1157.56i	−0.287518	+	0.165998i
$366$	983.366	−	188.133i	0.140441	−	0.0268685i
$367$			1609.91i			0.228982i	0.993424	+	0.114491i	$0.0365237\pi$
$367$			1609.91i			0.228982i	−0.993424	+	0.114491i	$0.963476\pi$
$368$	−1496.10	+	863.777i	−0.211929	+	0.122357i
$369$	757.093	−	300.693i	0.106809	−	0.0424212i
$370$			314.778i			0.0442285i
$371$	5479.88	+	11635.9i	0.766850	+	1.62831i
$372$	4143.40	+	1440.40i	0.577487	+	0.200756i
$373$	5211.06			0.723373			0.361687	−	0.932300i	$-0.382201\pi$
$373$	5211.06			0.723373			0.361687	+	0.932300i	$0.382201\pi$
$374$	354.193	−	613.481i	0.0489703	−	0.0848191i
$375$	4539.89	+	5253.82i	0.625171	+	0.723484i
$376$	1763.55	−	1018.18i	0.241883	−	0.139651i
$377$	573.346			0.0783257
$378$	−565.874	−	357.592i	−0.0769985	−	0.0486575i
$379$	−9946.69			−1.34809			−0.674046	−	0.738689i	$-0.735445\pi$
$379$	−9946.69			−1.34809			−0.674046	+	0.738689i	$0.735445\pi$
$380$	3529.07	−	2037.51i	0.476414	−	0.275058i
$381$	4712.91	+	5454.05i	0.633727	+	0.733385i
$382$	−14.5926	+	25.2751i	−0.00195451	+	0.00338530i
$383$	14449.0			1.92770			0.963848	−	0.266452i	$-0.0858513\pi$
$383$	14449.0			1.92770			0.963848	+	0.266452i	$0.0858513\pi$
$384$	2536.12	+	881.646i	0.337033	+	0.117165i
$385$	−7200.96	−	602.405i	−0.953234	−	0.0797439i
$386$			225.628i			0.0297517i
$387$	−7838.36	−	6198.95i	−1.02958	−	0.814238i
$388$	−6967.03	+	4022.42i	−0.911591	+	0.526307i
$389$			9079.32i			1.18339i	0.806161	+	0.591696i	$0.201542\pi$
$389$			9079.32i			1.18339i	−0.806161	+	0.591696i	$0.798458\pi$
$390$	85.2135	−	16.3026i	0.0110640	−	0.00211671i
$391$	1079.12	−	623.028i	0.139574	−	0.0805828i
$392$	−233.935	+	1388.41i	−0.0301416	+	0.178891i
$393$	−1334.34	−	1544.18i	−0.171269	−	0.198202i
$394$	−129.340	−	224.023i	−0.0165381	−	0.0286449i
$395$	−1780.51	−	3083.94i	−0.226803	−	0.392835i
$396$	8116.24	−	10262.7i	1.02994	−	1.30232i
$397$	1879.14	+	1084.92i	0.237559	+	0.137155i	0.614055	−	0.789264i	$-0.289537\pi$
$397$	1879.14	+	1084.92i	0.237559	+	0.137155i	−0.376495	+	0.926419i	$0.622871\pi$
$398$	−215.949	+	374.035i	−0.0271973	+	0.0471072i
$399$	−7695.13	+	815.401i	−0.965509	+	0.102309i
$400$	2627.43	+	4550.84i	0.328429	+	0.568855i
$401$			301.096i			0.0374963i	0.999824	+	0.0187482i	$0.00596808\pi$
$401$			301.096i			0.0374963i	−0.999824	+	0.0187482i	$0.994032\pi$
$402$	−166.910	+	144.229i	−0.0207082	+	0.0178942i
$403$	1079.63			0.133450
$404$	−570.047	+	987.351i	−0.0702003	+	0.121590i
$405$	−4460.77	−	1336.37i	−0.547303	−	0.163962i
$406$	22.4769	−	268.682i	0.00274756	−	0.0328435i
$407$	10118.4	+	5841.88i	1.23232	+	0.711478i
$408$	−906.946	−	315.287i	−0.110050	−	0.0382575i
$409$	−3938.78	−	2274.06i	−0.476186	−	0.274926i	0.242639	−	0.970117i	$-0.421987\pi$
$409$	−3938.78	−	2274.06i	−0.476186	−	0.274926i	−0.718826	+	0.695190i	$0.755320\pi$
$410$	42.9987	+	24.8253i	0.00517941	+	0.00299033i
$411$	8184.74	−	7072.53i	0.982295	−	0.848813i
$412$	−3758.01	−	2169.69i	−0.449379	−	0.259449i
$413$	−9664.29	−	6712.36i	−1.15145	−	0.799743i
$414$	−178.942	+	71.0700i	−0.0212428	+	0.00843695i
$415$	3287.66	−	5694.40i	0.388879	−	0.673559i
$416$	496.326			0.0584961
$417$	−6168.82	−	2144.51i	−0.724433	−	0.251839i
$418$			1265.35i			0.148063i
$419$	687.732	+	1191.19i	0.0801859	+	0.138886i	0.903330	−	0.428947i	$-0.141115\pi$
$419$	687.732	+	1191.19i	0.0801859	+	0.138886i	−0.823144	+	0.567833i	$0.807782\pi$
$420$	513.899	+	4849.78i	0.0597040	+	0.563441i
$421$	−1505.07	+	2606.85i	−0.174234	+	0.301782i	−0.939896	−	0.341461i	$-0.889078\pi$
$421$	−1505.07	+	2606.85i	−0.174234	+	0.301782i	0.765662	+	0.643243i	$0.222412\pi$
$422$	−681.868	−	393.676i	−0.0786559	−	0.0454120i
$423$	−12448.3	+	4944.08i	−1.43087	+	0.568296i
$424$	−1425.35	−	2468.78i	−0.163258	−	0.282771i
$425$	−1895.12	−	3282.45i	−0.216299	−	0.374640i
$426$	122.414	−	352.132i	0.0139225	−	0.0400489i
$427$	5901.64	+	12531.4i	0.668853	+	1.42023i
$428$	−9147.99	+	5281.59i	−1.03314	+	0.596485i
$429$	1057.41	−	3041.71i	0.119003	−	0.342320i
$430$		−	609.089i		−	0.0683090i
$431$	2888.94	−	1667.93i	0.322867	−	0.186407i	−0.329803	−	0.944050i	$-0.606982\pi$
$431$	2888.94	−	1667.93i	0.322867	−	0.186407i	0.652670	+	0.757643i	$0.273649\pi$
$432$	−7766.19	−	4044.19i	−0.864933	−	0.450408i
$433$		−	3574.98i		−	0.396772i	−0.980124	−	0.198386i	$-0.936430\pi$
$433$		−	3574.98i		−	0.396772i	0.980124	−	0.198386i	$-0.0635700\pi$
$434$	42.3248	−	505.938i	0.00468124	−	0.0559581i
$435$	−352.444	−	1842.21i	−0.0388468	−	0.203051i
$436$	−8362.25			−0.918530
$437$	−1112.88	+	1927.56i	−0.121822	+	0.211002i
$438$	−476.531	+	91.1676i	−0.0519852	+	0.00994556i
$439$	−5246.27	+	3028.94i	−0.570367	+	0.329301i	−0.757296	−	0.653072i	$-0.773480\pi$
$439$	−5246.27	+	3028.94i	−0.570367	+	0.329301i	0.186929	+	0.982373i	$0.440147\pi$
$440$	1601.62			0.173533
$441$	2846.84	−	8812.58i	0.307401	−	0.951580i
$442$	−117.668			−0.0126626
$443$	13774.2	−	7952.52i	1.47727	−	0.852902i	0.477599	−	0.878578i	$-0.341507\pi$
$443$	13774.2	−	7952.52i	1.47727	−	0.852902i	0.999670	+	0.0256763i	$0.00817391\pi$
$444$	2589.26	−	7448.19i	0.276759	−	0.796116i
$445$	4663.87	−	8078.05i	0.496828	−	0.860531i
$446$	−1065.19			−0.113090
$447$	11825.0	−	10218.1i	1.25123	−	1.08121i
$448$	−751.420	+	8982.24i	−0.0792438	+	0.947257i
$449$			3388.65i			0.356169i	0.984015	+	0.178085i	$0.0569901\pi$
$449$			3388.65i			0.356169i	−0.984015	+	0.178085i	$0.943010\pi$
$450$	216.180	+	544.305i	0.0226463	+	0.0570195i
$451$	1596.00	−	921.453i	0.166636	−	0.0962073i
$452$			7374.46i			0.767402i
$453$	9751.23	+	11284.7i	1.01137	+	1.17042i
$454$	990.867	−	572.077i	0.102431	−	0.0591386i
$455$	511.406	+	1085.91i	0.0526925	+	0.111886i
$456$	1684.57	−	322.285i	0.172999	−	0.0330973i
$457$	−1140.74	−	1975.82i	−0.116765	−	0.202243i	0.801719	−	0.597701i	$-0.203919\pi$
$457$	−1140.74	−	1975.82i	−0.116765	−	0.202243i	−0.918484	+	0.395458i	$0.870586\pi$
$458$	−167.439	−	290.013i	−0.0170828	−	0.0295882i
$459$	5601.62	+	2917.01i	0.569633	+	0.296632i
$460$	1214.83	+	701.382i	0.123134	+	0.0710915i
$461$	−2730.79	+	4729.87i	−0.275891	+	0.477856i	−0.970359	−	0.241666i	$-0.922306\pi$
$461$	−2730.79	+	4729.87i	−0.275891	+	0.477856i	0.694469	+	0.719523i	$0.255639\pi$
$462$	−1383.96	−	614.769i	−0.139367	−	0.0619084i
$463$	−5628.16	−	9748.26i	−0.564931	−	0.978488i	−0.997056	−	0.0766749i	$-0.975570\pi$
$463$	−5628.16	−	9748.26i	−0.564931	−	0.978488i	0.432126	−	0.901813i	$-0.357764\pi$
$464$		−	3526.81i		−	0.352863i
$465$	−663.665	−	3468.96i	−0.0661865	−	0.345955i
$466$	−517.960			−0.0514894
$467$	8118.96	−	14062.5i	0.804498	−	1.39343i	−0.112131	−	0.993693i	$-0.535768\pi$
$467$	8118.96	−	14062.5i	0.804498	−	1.39343i	0.916629	−	0.399738i	$-0.130899\pi$
$468$	−2150.40	−	315.190i	−0.212398	−	0.0311317i
$469$	−2506.59	−	1740.96i	−0.246788	−	0.171407i
$470$	−706.998	−	408.185i	−0.0693859	−	0.0400600i
$471$	896.040	+	4683.58i	0.0876589	+	0.458191i
$472$	2258.60	+	1304.00i	0.220255	+	0.127164i
$473$	−19578.9	−	11303.9i	−1.90326	−	1.09885i
$474$	−140.231	−	732.981i	−0.0135886	−	0.0710273i
$475$	5863.25	+	3385.15i	0.566367	+	0.326992i
$476$	551.408	−	6591.37i	0.0530961	−	0.634695i
$477$	6921.20	+	17426.4i	0.664361	+	1.67275i
$478$	−669.212	+	1159.11i	−0.0640356	+	0.110913i
$479$	−6266.51			−0.597754			−0.298877	−	0.954292i	$-0.596612\pi$
$479$	−6266.51			−0.597754			−0.298877	+	0.954292i	$0.596612\pi$
$480$	−305.098	−	1594.74i	−0.0290120	−	0.151645i
$481$		−	1940.75i		−	0.183972i
$482$	868.166	+	1503.71i	0.0820412	+	0.142100i
$483$	−1567.55	−	2153.70i	−0.147673	−	0.202892i
$484$	9520.30	−	16489.6i	0.894093	−	1.54861i
$485$	5609.47	+	3238.63i	0.525181	+	0.303214i
$486$	−791.038	−	571.493i	−0.0738317	−	0.0533404i
$487$	262.826	+	455.227i	0.0244554	+	0.0423580i	0.877994	−	0.478671i	$-0.158882\pi$
$487$	262.826	+	455.227i	0.0244554	+	0.0423580i	−0.853539	+	0.521029i	$0.825548\pi$
$488$	−1535.05	−	2658.79i	−0.142395	−	0.246635i
$489$	8232.46	−	1575.00i	0.761319	−	0.145652i
$490$	528.928	−	197.085i	0.0487644	−	0.0181702i
$491$	−13426.5	+	7751.78i	−1.23407	+	0.712491i	−0.967876	−	0.251429i	$-0.919100\pi$
$491$	−13426.5	+	7751.78i	−1.23407	+	0.712491i	−0.266194	+	0.963919i	$0.585766\pi$
$492$	−813.218	−	941.103i	−0.0745177	−	0.0862362i
$493$			2543.83i			0.232390i
$494$	182.024	−	105.092i	0.0165782	−	0.00957144i
$495$	−10423.3	−	1527.78i	−0.946451	−	0.138724i
$496$		−	6641.13i		−	0.601200i
$497$	5139.75	+	429.972i	0.463882	+	0.0388066i
$498$	1042.64	−	900.954i	0.0938186	−	0.0810697i
$499$	9320.68			0.836175			0.418087	−	0.908407i	$-0.362701\pi$
$499$	9320.68			0.836175			0.418087	+	0.908407i	$0.362701\pi$
$500$	5300.82	−	9181.30i	0.474120	−	0.821200i
$501$	−3147.57	+	9054.19i	−0.280684	+	0.807408i
$502$	405.676	−	234.217i	0.0360681	−	0.0208239i
$503$	1065.29			0.0944311			0.0472155	−	0.998885i	$-0.484965\pi$
$503$	1065.29			0.0944311			0.0472155	+	0.998885i	$0.484965\pi$
$504$	−465.954	+	1999.06i	−0.0411811	+	0.176677i
$505$	917.941			0.0808868
$506$	−377.222	+	217.789i	−0.0331414	+	0.0191342i
$507$	10687.2	−	2044.63i	0.936165	−	0.179103i
$508$	5502.84	−	9531.21i	0.480609	−	0.832439i
$509$	−9387.36			−0.817460			−0.408730	−	0.912655i	$-0.634028\pi$
$509$	−9387.36			−0.817460			−0.408730	+	0.912655i	$0.634028\pi$
$510$	72.3320	+	378.077i	0.00628022	+	0.0328266i
$511$	−2859.88	−	6072.61i	−0.247581	−	0.525707i
$512$		−	5102.59i		−	0.440439i
$513$	−11270.6	+	490.518i	−0.969996	+	0.0422162i
$514$	103.535	−	59.7758i	0.00888467	−	0.00512957i
$515$			3493.83i			0.298945i
$516$	−5010.16	+	14412.1i	−0.427442	+	1.22957i
$517$	−26241.9	+	15150.8i	−2.23234	+	1.28884i
$518$	−909.477	−	76.0833i	−0.0771431	−	0.00645349i
$519$	3422.33	−	9844.56i	0.289448	−	0.832617i
$520$	−133.020	−	230.397i	−0.0112179	−	0.0194300i
$521$	10087.0	+	17471.2i	0.848216	+	1.46915i	0.882799	+	0.469751i	$0.155656\pi$
$521$	10087.0	+	17471.2i	0.848216	+	1.46915i	−0.0345837	+	0.999402i	$0.511011\pi$
$522$	57.0043	−	388.914i	0.00477971	−	0.0326098i
$523$	13914.0	+	8033.23i	1.16332	+	0.671642i	0.952097	−	0.305797i	$-0.0989227\pi$
$523$	13914.0	+	8033.23i	1.16332	+	0.671642i	0.211221	+	0.977438i	$0.432256\pi$
$524$	−1557.99	+	2698.52i	−0.129888	+	0.224972i
$525$	−6551.11	+	4768.17i	−0.544598	+	0.396381i
$526$	48.4991	+	84.0029i	0.00402027	+	0.00696331i
$527$			4790.14i			0.395942i
$528$	−18710.5	−	6504.44i	−1.54217	−	0.536116i
$529$	11400.8			0.937028
$530$	−571.418	+	989.725i	−0.0468317	+	0.0811149i
$531$	−13455.0	−	10640.9i	−1.09962	−	0.869632i
$532$	5033.90	+	10688.9i	0.410239	+	0.871093i
$533$	−265.106	−	153.059i	−0.0215442	−	0.0124385i
$534$	1479.08	−	1278.09i	0.119862	−	0.103574i
$535$	7365.46	+	4252.45i	0.595208	+	0.343644i
$536$	585.805	+	338.215i	0.0472070	+	0.0272550i
$537$	−8075.47	−	2807.33i	−0.648943	−	0.225596i
$538$	−891.588	−	514.759i	−0.0714482	−	0.0412506i
$539$	3481.01	−	20659.9i	0.278177	−	1.65099i
$540$	309.145	+	7103.18i	0.0246361	+	0.566059i
$541$	−12174.8	+	21087.4i	−0.967535	+	1.67582i	−0.264890	+	0.964279i	$0.585336\pi$
$541$	−12174.8	+	21087.4i	−0.967535	+	1.67582i	−0.702645	+	0.711541i	$0.747998\pi$
$542$	217.048			0.0172011
$543$	−13345.6	+	11532.1i	−1.05472	+	0.911396i
$544$			2202.11i			0.173556i
$545$	3366.41	+	5830.79i	0.264589	+	0.458282i
$546$	26.5061	+	250.144i	0.00207758	+	0.0196066i
$547$	5442.16	−	9426.10i	0.425393	−	0.736802i	−0.571064	−	0.820906i	$-0.693469\pi$
$547$	5442.16	−	9426.10i	0.425393	−	0.736802i	0.996457	+	0.0841031i	$0.0268025\pi$
$548$	−14303.2	−	8257.96i	−1.11497	−	0.643727i
$549$	7453.89	+	18767.6i	0.579461	+	1.45898i
$550$	662.470	+	1147.43i	0.0513597	+	0.0889576i
$551$	−2271.95	−	3935.14i	−0.175660	−	0.304251i
$552$	386.023	+	446.728i	0.0297649	+	0.0344457i
$553$	9340.66	−	4398.96i	0.718274	−	0.338269i
$554$	−929.515	+	536.656i	−0.0712839	+	0.0411558i
$555$	−6235.81	+	1193.01i	−0.476929	+	0.0912438i
$556$			9971.63i			0.760596i
$557$	21701.2	−	12529.2i	1.65082	−	0.953104i	0.674090	−	0.738649i	$-0.264536\pi$
$557$	21701.2	−	12529.2i	1.65082	−	0.953104i	0.976734	−	0.214455i	$-0.0687975\pi$
$558$	107.341	−	732.340i	0.00814357	−	0.0555599i
$559$			3755.31i			0.284137i
$560$	6679.73	−	3145.81i	0.504054	−	0.237383i
$561$	13495.5	+	4691.54i	1.01566	+	0.353079i
$562$	1332.22			0.0999933
$563$	8948.10	−	15498.6i	0.669836	−	1.16019i	−0.308114	−	0.951349i	$-0.599698\pi$
$563$	8948.10	−	15498.6i	0.669836	−	1.16019i	0.977950	−	0.208840i	$-0.0669688\pi$
$564$	13371.2	+	15473.9i	0.998277	+	1.15526i
$565$	5142.04	−	2968.76i	0.382880	−	0.221056i
$566$	−1550.77			−0.115166
$567$	4939.30	−	12565.3i	0.365840	−	0.930678i
$568$	−1143.17			−0.0844480
$569$	764.970	−	441.656i	0.0563607	−	0.0325399i	−0.471555	−	0.881837i	$-0.656307\pi$
$569$	764.970	−	441.656i	0.0563607	−	0.0325399i	0.527916	+	0.849297i	$0.322974\pi$
$570$	−449.562	−	520.259i	−0.0330352	−	0.0382302i
$571$	−5229.75	+	9058.20i	−0.383290	+	0.663877i	−0.991530	−	0.129876i	$-0.958542\pi$
$571$	−5229.75	+	9058.20i	−0.383290	+	0.663877i	0.608241	+	0.793753i	$0.291876\pi$
$572$	−4916.80			−0.359408
$573$	−556.009	−	193.289i	−0.0405369	−	0.0140921i
$574$	−82.1198	+	118.234i	−0.00597145	+	0.00859756i
$575$			2330.58i			0.169029i
$576$	−1905.70	+	13001.7i	−0.137854	+	0.940516i
$577$	17098.4	−	9871.79i	1.23365	−	0.712249i	0.265863	−	0.964011i	$-0.414343\pi$
$577$	17098.4	−	9871.79i	1.23365	−	0.712249i	0.967789	+	0.251762i	$0.0810099\pi$
$578$			743.640i			0.0535145i
$579$	−4469.73	+	855.127i	−0.320821	+	0.0613780i
$580$	−2480.08	+	1431.88i	−0.177552	+	0.102509i
$581$	15657.9	+	10875.3i	1.11807	+	0.776561i
$582$	887.518	+	1027.09i	0.0632110	+	0.0731514i
$583$	21209.6	+	36736.0i	1.50671	+	2.60969i
$584$	743.874	+	1288.43i	0.0527084	+	0.0912937i
$585$	645.916	+	1626.31i	0.0456502	+	0.114939i
$586$	1001.27	+	578.082i	0.0705835	+	0.0407514i
$587$	4130.99	−	7155.09i	0.290467	−	0.503104i	−0.683453	−	0.729995i	$-0.739523\pi$
$587$	4130.99	−	7155.09i	0.290467	−	0.503104i	0.973920	+	0.226890i	$0.0728559\pi$
$588$	−14136.5	+	312.574i	−0.991461	+	0.0219223i
$589$	−4278.17	−	7410.01i	−0.299285	−	0.518377i
$590$		−	1045.54i		−	0.0729562i
$591$	3947.73	−	3411.28i	0.274768	−	0.237430i
$592$	−11938.1			−0.828807
$593$	−13435.3	+	23270.7i	−0.930392	+	1.61149i	−0.147741	+	0.989026i	$0.547200\pi$
$593$	−13435.3	+	23270.7i	−0.930392	+	1.61149i	−0.782652	+	0.622460i	$0.786133\pi$
$594$	−1958.14	−	1019.69i	−0.135258	−	0.0704347i
$595$	−4817.98	+	2269.02i	−0.331963	+	0.156337i
$596$	−20664.6	−	11930.7i	−1.42023	−	0.819970i
$597$	−8228.13	−	2860.40i	−0.564079	−	0.196094i
$598$	62.6590	+	36.1762i	0.00428481	+	0.00247384i
$599$	−14454.8	−	8345.50i	−0.985991	−	0.569262i	−0.0819174	−	0.996639i	$-0.526104\pi$
$599$	−14454.8	−	8345.50i	−0.985991	−	0.569262i	−0.904074	+	0.427377i	$0.859438\pi$
$600$	1358.86	−	1174.20i	0.0924584	−	0.0798944i
$601$	−16426.9	−	9484.10i	−1.11492	−	0.643702i	−0.174824	−	0.984600i	$-0.555936\pi$
$601$	−16426.9	−	9484.10i	−1.11492	−	0.643702i	−0.940100	+	0.340898i	$0.889269\pi$
$602$	1759.82	+	147.219i	0.119144	+	0.00996713i
$603$	−3489.78	−	2759.89i	−0.235680	−	0.186387i
$604$	11385.6	−	19720.5i	0.767012	−	1.32850i
$605$	−15330.5			−1.03020
$606$	181.704	+	63.1670i	0.0121802	+	0.00423429i
$607$		−	5154.91i		−	0.344698i	−0.985036	−	0.172349i	$-0.944864\pi$
$607$		−	5154.91i		−	0.344698i	0.985036	−	0.172349i	$-0.0551356\pi$
$608$	−1966.75	−	3406.52i	−0.131188	−	0.227224i
$609$	5407.82	−	573.030i	0.359829	−	0.0381287i
$610$	−615.397	+	1065.90i	−0.0408470	+	0.0707491i
$611$	4358.96	+	2516.65i	0.288616	+	0.166633i
$612$	1398.44	−	9540.93i	0.0923671	−	0.630179i
$613$	4050.42	+	7015.53i	0.266876	+	0.462242i	0.968053	−	0.250744i	$-0.0806754\pi$
$613$	4050.42	+	7015.53i	0.266876	+	0.462242i	−0.701178	+	0.712987i	$0.747342\pi$
$614$	33.9371	+	58.7808i	0.00223060	+	0.00386352i
$615$	−328.829	+	945.900i	−0.0215604	+	0.0620201i
$616$	−387.119	+	4627.51i	−0.0253206	+	0.302675i
$617$	−6750.27	+	3897.27i	−0.440447	+	0.254292i	−0.703787	−	0.710411i	$-0.748509\pi$
$617$	−6750.27	+	3897.27i	−0.440447	+	0.254292i	0.263340	+	0.964703i	$0.415176\pi$
$618$	−240.423	+	691.594i	−0.0156493	+	0.0450162i
$619$		−	17518.1i		−	1.13750i	−0.822510	−	0.568750i	$-0.807427\pi$
$619$		−	17518.1i		−	1.13750i	0.822510	−	0.568750i	$-0.192573\pi$
$620$	−4670.09	+	2696.28i	−0.302509	+	0.174654i
$621$	−2086.10	−	3275.52i	−0.134802	−	0.211662i
$622$			1250.12i			0.0805870i
$623$	22212.3	+	15427.6i	1.42844	+	0.992126i
$624$	618.285	+	3231.76i	0.0396654	+	0.207330i
$625$	1988.76			0.127281
$626$	−352.758	+	610.995i	−0.0225225	+	0.0390100i
$627$	−25066.8	+	4795.67i	−1.59661	+	0.305455i
$628$	6305.28	−	3640.35i	0.400650	−	0.231315i
$629$	8610.77			0.545841
$630$	787.444	−	238.934i	0.0497976	−	0.0151101i
$631$	8636.00			0.544839			0.272420	−	0.962179i	$-0.412176\pi$
$631$	8636.00			0.544839			0.272420	+	0.962179i	$0.412176\pi$
$632$	−1981.81	+	1144.20i	−0.124735	+	0.0720155i
$633$	5214.53	−	14999.9i	0.327423	−	0.941855i
$634$	955.425	−	1654.84i	0.0598498	−	0.103663i
$635$	−8861.18			−0.553772
$636$	21661.9	−	18718.3i	1.35055	−	1.16702i
$637$	−3261.08	+	1215.12i	−0.202839	+	0.0755803i
$638$		−	889.237i		−	0.0551806i
$639$	7439.74	+	1090.46i	0.460581	+	0.0675087i
$640$	−2858.50	+	1650.35i	−0.176550	+	0.101931i
$641$		−	15365.3i		−	0.946791i	−0.880850	−	0.473396i	$-0.843028\pi$
$641$		−	15365.3i		−	0.946791i	0.880850	−	0.473396i	$-0.156972\pi$
$642$	1165.35	+	1348.61i	0.0716395	+	0.0829053i
$643$	6869.74	−	3966.25i	0.421332	−	0.243256i	−0.274315	−	0.961640i	$-0.588451\pi$
$643$	6869.74	−	3966.25i	0.421332	−	0.243256i	0.695647	+	0.718384i	$0.255118\pi$
$644$	−2320.10	+	3340.43i	−0.141964	+	0.204397i
$645$	12066.1	−	2308.44i	0.736596	−	0.140922i
$646$	466.273	+	807.608i	0.0283982	+	0.0491872i
$647$	−9673.35	−	16754.7i	−0.587788	−	1.01808i	−0.994522	−	0.104531i	$-0.966666\pi$
$647$	−9673.35	−	16754.7i	−0.587788	−	1.01808i	0.406734	−	0.913547i	$-0.366668\pi$
$648$	−858.781	+	2866.60i	−0.0520619	+	0.173782i
$649$	−33608.5	−	19403.9i	−2.03274	−	1.17360i
$650$	110.041	−	190.596i	0.00664023	−	0.0115012i
$651$	10183.1	−	1079.04i	0.613070	−	0.0649629i
$652$	−6398.76	−	11083.0i	−0.384348	−	0.665710i
$653$		−	19303.6i		−	1.15683i	−0.815743	−	0.578414i	$-0.803672\pi$
$653$		−	19303.6i		−	1.15683i	0.815743	−	0.578414i	$-0.196328\pi$
$654$	265.133	+	1385.85i	0.0158525	+	0.0828606i
$655$	2508.82			0.149661
$656$	−941.512	+	1630.75i	−0.0560364	+	0.0970579i
$657$	−3612.09	−	9094.63i	−0.214492	−	0.540054i
$658$	1350.24	−	1944.04i	0.0799966	−	0.115177i
$659$	6426.97	+	3710.61i	0.379908	+	0.219340i	0.677778	−	0.735266i	$-0.262943\pi$
$659$	6426.97	+	3710.61i	0.379908	+	0.219340i	−0.297870	+	0.954606i	$0.596276\pi$
$660$	3022.42	+	15798.1i	0.178254	+	0.931730i
$661$	−12251.0	−	7073.14i	−0.720893	−	0.416208i	0.0941886	−	0.995554i	$-0.469974\pi$
$661$	−12251.0	−	7073.14i	−0.720893	−	0.416208i	−0.815081	+	0.579347i	$0.803308\pi$
$662$	930.840	+	537.421i	0.0546498	+	0.0315521i
$663$	−445.959	−	2331.02i	−0.0261231	−	0.136545i
$664$	−3659.35	−	2112.73i	−0.213871	−	0.123478i
$665$	5426.58	−	7813.06i	0.316442	−	0.455605i
$666$	−1316.46	−	192.957i	−0.0765942	−	0.0112266i
$667$	782.086	−	1354.61i	0.0454011	−	0.0786369i
$668$	14635.7			0.847713
$669$	−4037.06	−	21101.6i	−0.233306	−	1.21948i
$670$		−	271.178i		−	0.0156366i
$671$	22841.9	+	39563.4i	1.31416	+	2.27620i
$672$	4681.37	−	496.053i	0.268732	−	0.0284757i
$673$	4164.46	−	7213.05i	0.238526	−	0.413139i	−0.721766	−	0.692138i	$-0.756669\pi$
$673$	4164.46	−	7213.05i	0.238526	−	0.413139i	0.960292	+	0.278998i	$0.0900024\pi$
$674$	235.903	+	136.199i	0.0134817	+	0.00778365i
$675$	−9963.45	+	6345.48i	−0.568138	+	0.361833i
$676$	−8306.74	−	14387.7i	−0.472618	−	0.818599i
$677$	−2239.79	−	3879.44i	−0.127153	−	0.220235i	0.795420	−	0.606059i	$-0.207250\pi$
$677$	−2239.79	−	3879.44i	−0.127153	−	0.220235i	−0.922572	+	0.385824i	$0.873917\pi$
$678$	1222.14	−	233.815i	0.0692273	−	0.0132442i
$679$	−10713.1	+	15424.4i	−0.605493	+	0.871775i
$680$	1022.23	−	590.187i	0.0576483	−	0.0332833i
$681$	15088.3	+	17461.1i	0.849024	+	0.982540i
$682$		−	1674.47i		−	0.0940156i
$683$	−2140.00	+	1235.53i	−0.119890	+	0.0692184i	−0.558746	−	0.829339i	$-0.688717\pi$
$683$	−2140.00	+	1235.53i	−0.119890	+	0.0692184i	0.438856	+	0.898557i	$0.355384\pi$
$684$	6357.92	+	16008.2i	0.355411	+	0.894864i
$685$			13297.7i			0.741721i
$686$	441.585	+	1575.85i	0.0245770	+	0.0877057i
$687$	5110.61	−	4416.14i	0.283817	−	0.245249i
$688$	23100.0			1.28006
$689$	3523.05	−	6102.10i	0.194800	−	0.337404i
$690$	77.7202	−	223.567i	0.00428805	−	0.0123349i
$691$	−20070.0	+	11587.4i	−1.10492	+	0.637926i	−0.937509	−	0.347961i	$-0.886874\pi$
$691$	−20070.0	+	11587.4i	−1.10492	+	0.637926i	−0.167412	+	0.985887i	$0.553541\pi$
$692$	−15913.3			−0.874181
$693$	6933.50	−	29746.4i	0.380061	−	1.63055i
$694$	1231.62			0.0673653
$695$	6952.98	−	4014.30i	0.379484	−	0.219095i
$696$	−1183.85	+	226.488i	−0.0644737	+	0.0123348i
$697$	679.097	−	1176.23i	0.0369048	−	0.0639210i
$698$	648.518			0.0351673
$699$	−1963.06	−	10260.9i	−0.106223	−	0.555225i
$700$	10160.9	+	7057.28i	0.548637	+	0.381057i
$701$			21807.9i			1.17500i	0.809225	+	0.587498i	$0.199887\pi$
$701$			21807.9i			1.17500i	−0.809225	+	0.587498i	$0.800113\pi$
$702$	15.9452	+	366.371i	0.000857283	+	0.0196977i
$703$	−13320.3	+	7690.46i	−0.714628	+	0.412591i
$704$			29727.9i			1.59149i
$705$	5406.71	−	15552.8i	0.288835	−	0.830852i
$706$	1339.95	−	773.623i	0.0714304	−	0.0412404i
$707$	−221.870	+	2652.17i	−0.0118024	+	0.141082i
$708$	−8600.26	+	24739.2i	−0.456522	+	1.31322i
$709$	−6487.34	−	11236.4i	−0.343635	−	0.595193i	0.641470	−	0.767148i	$-0.278325\pi$
$709$	−6487.34	−	11236.4i	−0.343635	−	0.595193i	−0.985105	+	0.171955i	$0.944992\pi$
$710$	229.147	+	396.893i	0.0121123	+	0.0209791i
$711$	13989.0	−	5555.98i	0.737875	−	0.293060i
$712$	−5191.14	−	2997.11i	−0.273239	−	0.157755i
$713$	1472.70	−	2550.79i	0.0773534	−	0.133980i
$714$	−1109.85	+	117.603i	−0.0581722	+	0.00616412i
$715$	1979.37	+	3428.37i	0.103530	+	0.179320i
$716$			13053.6i			0.681337i
$717$	−25498.4	−	8864.19i	−1.32811	−	0.461701i
$718$	1717.24			0.0892574
$719$	−8416.91	+	14578.5i	−0.436575	+	0.756171i	−0.997423	−	0.0717486i	$-0.977142\pi$
$719$	−8416.91	+	14578.5i	−0.436575	+	0.756171i	0.560847	+	0.827919i	$0.310475\pi$
$720$	10003.9	−	3973.22i	0.517809	−	0.205657i
$721$	−10094.6	−	844.474i	−0.521417	−	0.0436197i
$722$	87.7246	+	50.6478i	0.00452184	+	0.00261069i
$723$	−26498.4	+	22897.5i	−1.36305	+	1.17783i
$724$	23322.0	+	13464.9i	1.19717	+	0.691189i
$725$	−4120.45	−	2378.95i	−0.211076	−	0.121865i
$726$	−3034.62	−	1054.95i	−0.155131	−	0.0539293i
$727$	−28354.9	−	16370.7i	−1.44653	−	0.835152i	−0.448253	−	0.893907i	$-0.647954\pi$
$727$	−28354.9	−	16370.7i	−1.44653	−	0.835152i	−0.998272	+	0.0587547i	$0.981287\pi$
$728$	697.830	−	328.641i	0.0355265	−	0.0167311i
$729$	8323.34	−	17836.5i	0.422870	−	0.906191i
$730$	298.216	−	516.525i	0.0151198	−	0.0261883i
$731$	−16661.6			−0.843027
$732$	23329.1	−	20158.9i	1.17796	−	1.01789i
$733$			7405.70i			0.373173i	0.982439	+	0.186586i	$0.0597424\pi$
$733$			7405.70i			0.373173i	−0.982439	+	0.186586i	$0.940258\pi$
$734$	−207.376	−	359.186i	−0.0104283	−	0.0180624i
$735$	5908.92	+	9731.21i	0.296536	+	0.488355i
$736$	677.025	−	1172.64i	0.0339069	−	0.0587285i
$737$	−8716.91	−	5032.71i	−0.435674	−	0.251536i
$738$	−130.182	+	164.610i	−0.00649330	+	0.00821056i
$739$	6333.95	+	10970.7i	0.315288	+	0.546095i	0.979499	−	0.201450i	$-0.0645655\pi$
$739$	6333.95	+	10970.7i	0.315288	+	0.546095i	−0.664210	+	0.747546i	$0.731232\pi$
$740$	4846.84	+	8394.98i	0.240775	+	0.417035i
$741$	2771.75	+	3207.63i	0.137413	+	0.159022i
$742$	−2721.46	−	1890.20i	−0.134647	−	0.0935192i
$743$	16940.8	−	9780.78i	0.836471	−	0.482937i	−0.0195919	−	0.999808i	$-0.506237\pi$
$743$	16940.8	−	9780.78i	0.836471	−	0.482937i	0.856063	+	0.516871i	$0.172903\pi$
$744$	−2229.23	+	426.486i	−0.109849	+	0.0210158i
$745$			19211.9i			0.944794i
$746$	−1162.64	+	671.249i	−0.0570605	+	0.0329439i
$747$	21799.6	+	17240.2i	1.06775	+	0.844425i
$748$		−	21815.0i		−	1.06636i
$749$	−14066.7	+	20252.9i	−0.686229	+	0.988017i
$750$	−1689.65	−	587.385i	−0.0822631	−	0.0285977i
$751$	−2326.49			−0.113042			−0.0565211	−	0.998401i	$-0.518001\pi$
$751$	−2326.49			−0.113042			−0.0565211	+	0.998401i	$0.518001\pi$
$752$	15480.6	−	26813.2i	0.750692	−	1.30024i
$753$	6177.38	+	7148.82i	0.298959	+	0.345973i
$754$	−127.919	+	73.8540i	−0.00617843	+	0.00356712i
$755$	−18334.2			−0.883774
$756$	−20597.6	−	823.669i	−0.990912	−	0.0396251i
$757$	5811.77			0.279039			0.139519	−	0.990219i	$-0.455444\pi$
$757$	5811.77			0.279039			0.139519	+	0.990219i	$0.455444\pi$
$758$	2219.20	−	1281.26i	0.106339	−	0.0613950i
$759$	−5744.11	−	6647.41i	−0.274701	−	0.317900i
$760$	−1054.22	+	1825.96i	−0.0503164	+	0.0871506i
$761$	26599.4			1.26705			0.633526	−	0.773721i	$-0.281607\pi$
$761$	26599.4			1.26705			0.633526	+	0.773721i	$0.281607\pi$
$762$	−1754.05	−	609.770i	−0.0833890	−	0.0289890i
$763$	−17660.4	+	8317.11i	−0.837939	+	0.394626i
$764$			898.765i			0.0425604i
$765$	−7215.64	+	2865.82i	−0.341022	+	0.135443i
$766$	−3223.70	+	1861.21i	−0.152059	+	0.0877913i
$767$			6446.22i			0.303467i
$768$	19191.5	−	3671.63i	0.901712	−	0.172511i
$769$	−5505.13	+	3178.39i	−0.258153	+	0.149045i	−0.623492	−	0.781830i	$-0.714287\pi$
$769$	−5505.13	+	3178.39i	−0.258153	+	0.149045i	0.365339	+	0.930875i	$0.380953\pi$
$770$	1684.20	−	793.171i	0.0788239	−	0.0371220i
$771$	1576.56	+	1824.49i	0.0736428	+	0.0852236i
$772$	3474.14	+	6017.38i	0.161965	+	0.280531i
$773$	3466.39	+

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)

\(f(q)\)	\(=\)	\(q+(-0.223110 + 0.128812i) q^{2} +(-3.39738 - 3.93164i) q^{3} +(-3.96681 + 6.87072i) q^{4} +6.38772 q^{5} +(1.26443 + 0.439563i) q^{6} +(-1.54394 + 18.4558i) q^{7} -4.10490i q^{8} +(-3.91563 + 26.7146i) q^{9} +O(q^{10})\)	\(q+(-0.223110 + 0.128812i) q^{2} +(-3.39738 - 3.93164i) q^{3} +(-3.96681 + 6.87072i) q^{4} +6.38772 q^{5} +(1.26443 + 0.439563i) q^{6} +(-1.54394 + 18.4558i) q^{7} -4.10490i q^{8} +(-3.91563 + 26.7146i) q^{9} +(-1.42516 + 0.822818i) q^{10} +61.0818i q^{11} +(40.4900 - 7.74636i) q^{12} +(8.78677 - 5.07304i) q^{13} +(-2.03287 - 4.31654i) q^{14} +(-21.7015 - 25.1142i) q^{15} +(-31.2058 - 54.0500i) q^{16} +(22.5082 + 38.9853i) q^{17} +(-2.56755 - 6.46466i) q^{18} +(-69.6373 - 40.2051i) q^{19} +(-25.3389 + 43.8883i) q^{20} +(77.8069 - 56.6311i) q^{21} +(-7.86810 - 13.6279i) q^{22} -27.6800i q^{23} +(-16.1390 + 13.9459i) q^{24} -84.1970 q^{25} +(-1.30694 + 2.26369i) q^{26} +(118.335 - 75.3646i) q^{27} +(-120.680 - 83.8187i) q^{28} +(48.9383 + 28.2545i) q^{29} +(8.07685 + 2.80781i) q^{30} +(92.1526 + 53.2043i) q^{31} +(42.3642 + 24.4590i) q^{32} +(240.152 - 207.518i) q^{33} +(-10.0436 - 5.79867i) q^{34} +(-9.86226 + 117.890i) q^{35} +(-168.016 - 132.875i) q^{36} +(95.6403 - 165.654i) q^{37} +20.7157 q^{38} +(-49.7974 - 17.3114i) q^{39} -26.2210i q^{40} +(-15.0856 - 26.1289i) q^{41} +(-10.0647 + 22.6574i) q^{42} +(-185.062 + 320.536i) q^{43} +(-419.676 - 242.300i) q^{44} +(-25.0120 + 170.645i) q^{45} +(3.56553 + 6.17569i) q^{46} +(248.041 + 429.620i) q^{47} +(-106.487 + 306.318i) q^{48} +(-338.232 - 56.9893i) q^{49} +(18.7852 - 10.8456i) q^{50} +(76.8076 - 220.942i) q^{51} +80.4953i q^{52} +(601.424 - 347.232i) q^{53} +(-16.6938 + 32.0576i) q^{54} +390.174i q^{55} +(75.7592 + 6.33772i) q^{56} +(78.5122 + 410.381i) q^{57} -14.5581 q^{58} +(-317.670 + 550.221i) q^{59} +(258.639 - 49.4816i) q^{60} +(647.712 - 373.957i) q^{61} -27.4135 q^{62} +(-486.993 - 113.512i) q^{63} +486.690 q^{64} +(56.1274 - 32.4052i) q^{65} +(-26.8493 + 77.2338i) q^{66} +(-82.3930 + 142.709i) q^{67} -357.143 q^{68} +(-108.828 + 94.0396i) q^{69} +(-12.9854 - 27.5729i) q^{70} -278.490i q^{71} +(109.661 + 16.0733i) q^{72} +(-313.876 + 181.216i) q^{73} +49.2787i q^{74} +(286.049 + 331.033i) q^{75} +(552.477 - 318.973i) q^{76} +(-1127.31 - 94.3066i) q^{77} +(13.3402 - 2.55218i) q^{78} +(-278.740 - 482.792i) q^{79} +(-199.334 - 345.256i) q^{80} +(-698.336 - 209.209i) q^{81} +(6.73147 + 3.88641i) q^{82} +(514.684 - 891.459i) q^{83} +(80.4510 + 759.235i) q^{84} +(143.776 + 249.028i) q^{85} -95.3530i q^{86} +(-55.1752 - 288.399i) q^{87} +250.735 q^{88} +(730.130 - 1264.62i) q^{89} +(-16.4008 - 41.2945i) q^{90} +(80.0608 + 169.999i) q^{91} +(190.182 + 109.802i) q^{92} +(-103.897 - 543.066i) q^{93} +(-110.681 - 63.9015i) q^{94} +(-444.824 - 256.819i) q^{95} +(-47.7633 - 249.657i) q^{96} +(878.164 + 507.008i) q^{97} +(82.8039 - 30.8537i) q^{98} +(-1631.77 - 239.174i) 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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