LMFDB - Embedded newform 63.4.s.a.47.5

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			47.5
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.5

$q$-expansion

$f(q)$	$=$	$q+(-3.16085 + 1.82492i) q^{2} +(-3.78544 + 3.55956i) q^{3} +(2.66064 - 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 - 18.1593i) q^{6} +(4.78838 + 17.8905i) q^{7} -9.77690i q^{8} +(1.65907 - 26.9490i) q^{9} +O(q^{10})$	\(q+(-3.16085 + 1.82492i) q^{2} +(-3.78544 + 3.55956i) q^{3} +(2.66064 - 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 - 18.1593i) q^{6} +(4.78838 + 17.8905i) q^{7} -9.77690i q^{8} +(1.65907 - 26.9490i) q^{9} +(38.6615 - 22.3212i) q^{10} +10.0114i q^{11} +(6.33205 + 26.9153i) q^{12} +(57.0263 - 32.9241i) q^{13} +(-47.7841 - 47.8109i) q^{14} +(46.3010 - 43.5383i) q^{15} +(39.1271 + 67.7702i) q^{16} +(-38.6818 - 66.9989i) q^{17} +(43.9356 + 88.2093i) q^{18} +(-104.262 - 60.1959i) q^{19} +(-32.5432 + 56.3665i) q^{20} +(-81.8086 - 50.6790i) q^{21} +(-18.2699 - 31.6444i) q^{22} +122.606i q^{23} +(34.8015 + 37.0098i) q^{24} +24.6062 q^{25} +(-120.168 + 208.136i) q^{26} +(89.6462 + 107.919i) q^{27} +(95.1861 + 25.5337i) q^{28} +(-50.3417 - 29.0648i) q^{29} +(-66.8969 + 222.113i) q^{30} +(-174.476 - 100.734i) q^{31} +(-179.613 - 103.700i) q^{32} +(-35.6361 - 37.8974i) q^{33} +(244.535 + 141.182i) q^{34} +(-58.5684 - 218.826i) q^{35} +(-119.776 - 79.3470i) q^{36} +(82.9121 - 143.608i) q^{37} +439.410 q^{38} +(-98.6739 + 327.621i) q^{39} +119.585i q^{40} +(-112.422 - 194.721i) q^{41} +(351.069 + 10.8948i) q^{42} +(152.402 - 263.969i) q^{43} +(46.1360 + 26.6366i) q^{44} +(-20.2926 + 329.623i) q^{45} +(-223.746 - 387.539i) q^{46} +(11.2933 + 19.5606i) q^{47} +(-389.345 - 117.264i) q^{48} +(-297.143 + 171.333i) q^{49} +(-77.7763 + 44.9042i) q^{50} +(384.914 + 115.930i) q^{51} -350.397i q^{52} +(360.132 - 207.922i) q^{53} +(-480.301 - 177.519i) q^{54} -122.453i q^{55} +(174.914 - 46.8155i) q^{56} +(608.949 - 143.260i) q^{57} +212.163 q^{58} +(180.334 - 312.348i) q^{59} +(-77.4496 - 329.211i) q^{60} +(-635.689 + 367.015i) q^{61} +735.324 q^{62} +(490.076 - 99.3604i) q^{63} +130.940 q^{64} +(-697.509 + 402.707i) q^{65} +(181.800 + 54.7551i) q^{66} +(55.6457 - 96.3811i) q^{67} -411.673 q^{68} +(-436.423 - 464.117i) q^{69} +(584.464 + 584.792i) q^{70} +455.487i q^{71} +(-263.478 - 16.2205i) q^{72} +(-662.747 + 382.637i) q^{73} +605.230i q^{74} +(-93.1451 + 87.5871i) q^{75} +(-554.808 + 320.319i) q^{76} +(-179.109 + 47.9383i) q^{77} +(-285.987 - 1215.63i) q^{78} +(21.5683 + 37.3573i) q^{79} +(-478.578 - 828.921i) q^{80} +(-723.495 - 89.4203i) q^{81} +(710.697 + 410.321i) q^{82} +(-200.064 + 346.522i) q^{83} +(-451.210 + 242.165i) q^{84} +(473.131 + 819.488i) q^{85} +1112.49i q^{86} +(294.023 - 69.1714i) q^{87} +97.8802 q^{88} +(347.632 - 602.117i) q^{89} +(-537.392 - 1078.92i) q^{90} +(862.094 + 862.577i) q^{91} +(565.012 + 326.210i) q^{92} +(1019.04 - 239.737i) q^{93} +(-71.3928 - 41.2186i) q^{94} +(1275.27 + 736.277i) q^{95} +(1049.04 - 246.795i) q^{96} +(-955.178 - 551.472i) q^{97} +(626.554 - 1083.82i) q^{98} +(269.796 + 16.6095i) 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 $

$2$	−3.16085	+	1.82492i	−1.11753	+	0.645205i	−0.940769	−	0.339049i	$-0.889895\pi$
$2$	−3.16085	+	1.82492i	−1.11753	+	0.645205i	−0.176759	+	0.984254i	$0.556561\pi$
$3$	−3.78544	+	3.55956i	−0.728508	+	0.685038i
$3$	−3.78544	+	3.55956i	−0.728508	+	0.685038i
$4$	2.66064	−	4.60836i	0.332580	−	0.576045i
$5$	−12.2314			−1.09401			−0.547003	−	0.837131i	$-0.684231\pi$
$5$	−12.2314			−1.09401			−0.547003	+	0.837131i	$0.684231\pi$
$6$	5.46929	−	18.1593i	0.372138	−	1.23559i
$7$	4.78838	+	17.8905i	0.258548	+	0.965998i
$7$	4.78838	+	17.8905i	0.258548	+	0.965998i
$8$		−	9.77690i		−	0.432082i
$9$	1.65907	−	26.9490i	0.0614469	−	0.998110i
$10$	38.6615	−	22.3212i	1.22258	−	0.705858i
$11$			10.0114i			0.274413i	0.990542	+	0.137206i	$0.0438124\pi$
$11$			10.0114i			0.274413i	−0.990542	+	0.137206i	$0.956188\pi$
$12$	6.33205	+	26.9153i	0.152326	+	0.647483i
$13$	57.0263	−	32.9241i	1.21663	−	0.702424i	0.252437	−	0.967613i	$-0.418768\pi$
$13$	57.0263	−	32.9241i	1.21663	−	0.702424i	0.964196	+	0.265189i	$0.0854345\pi$
$14$	−47.7841	−	47.8109i	−0.912202	−	0.912714i
$15$	46.3010	−	43.5383i	0.796992	−	0.749435i
$16$	39.1271	+	67.7702i	0.611361	+	1.05891i
$17$	−38.6818	−	66.9989i	−0.551866	−	0.955860i	−0.998140	−	0.0609637i	$-0.980583\pi$
$17$	−38.6818	−	66.9989i	−0.551866	−	0.955860i	0.446274	−	0.894896i	$-0.352751\pi$
$18$	43.9356	+	88.2093i	0.575317	+	1.15506i
$19$	−104.262	−	60.1959i	−1.25892	−	0.726836i	−0.286053	−	0.958214i	$-0.592343\pi$
$19$	−104.262	−	60.1959i	−1.25892	−	0.726836i	−0.972864	+	0.231378i	$0.925677\pi$
$20$	−32.5432	+	56.3665i	−0.363844	+	0.630196i
$21$	−81.8086	−	50.6790i	−0.850100	−	0.526622i
$22$	−18.2699	−	31.6444i	−0.177053	−	0.306664i
$23$			122.606i			1.11153i	0.831341	+	0.555763i	$0.187574\pi$
$23$			122.606i			1.11153i	−0.831341	+	0.555763i	$0.812426\pi$
$24$	34.8015	+	37.0098i	0.295993	+	0.314775i
$25$	24.6062			0.196849
$26$	−120.168	+	208.136i	−0.906415	+	1.56996i
$27$	89.6462	+	107.919i	0.638979	+	0.769225i
$28$	95.1861	+	25.5337i	0.642446	+	0.172336i
$29$	−50.3417	−	29.0648i	−0.322352	−	0.186110i	0.330088	−	0.943950i	$-0.392922\pi$
$29$	−50.3417	−	29.0648i	−0.322352	−	0.186110i	−0.652441	+	0.757840i	$0.726255\pi$
$30$	−66.8969	+	222.113i	−0.407121	+	1.35174i
$31$	−174.476	−	100.734i	−1.01087	−	0.583624i	−0.0994218	−	0.995045i	$-0.531699\pi$
$31$	−174.476	−	100.734i	−1.01087	−	0.583624i	−0.911445	+	0.411421i	$0.865033\pi$
$32$	−179.613	−	103.700i	−0.992233	−	0.572866i
$33$	−35.6361	−	37.8974i	−0.187983	−	0.199912i
$34$	244.535	+	141.182i	1.23345	+	0.712134i
$35$	−58.5684	−	218.826i	−0.282853	−	1.05681i
$36$	−119.776	−	79.3470i	−0.554520	−	0.367347i
$37$	82.9121	−	143.608i	0.368396	−	0.638081i	−0.620919	−	0.783875i	$-0.713240\pi$
$37$	82.9121	−	143.608i	0.368396	−	0.638081i	0.989315	+	0.145794i	$0.0465737\pi$
$38$	439.410			1.87583
$39$	−98.6739	+	327.621i	−0.405140	+	1.34516i
$40$			119.585i			0.472700i
$41$	−112.422	−	194.721i	−0.428228	−	0.741713i	0.568487	−	0.822692i	$-0.307529\pi$
$41$	−112.422	−	194.721i	−0.428228	−	0.741713i	−0.996716	+	0.0809786i	$0.974195\pi$
$42$	351.069	+	10.8948i	1.28979	+	0.0400262i
$43$	152.402	−	263.969i	0.540492	−	0.936159i	−0.458384	−	0.888754i	$-0.651572\pi$
$43$	152.402	−	263.969i	0.540492	−	0.936159i	0.998876	−	0.0474048i	$-0.0150951\pi$
$44$	46.1360	+	26.6366i	0.158074	+	0.0912641i
$45$	−20.2926	+	329.623i	−0.0672233	+	1.09194i
$46$	−223.746	−	387.539i	−0.717163	−	1.24216i
$47$	11.2933	+	19.5606i	0.0350489	+	0.0607064i	0.883018	−	0.469340i	$-0.155508\pi$
$47$	11.2933	+	19.5606i	0.0350489	+	0.0607064i	−0.847969	+	0.530046i	$0.822175\pi$
$48$	−389.345	−	117.264i	−1.17077	−	0.352618i
$49$	−297.143	+	171.333i	−0.866306	+	0.499514i
$50$	−77.7763	+	44.9042i	−0.219985	+	0.127008i
$51$	384.914	+	115.930i	1.05684	+	0.318302i
$52$		−	350.397i		−	0.934447i
$53$	360.132	−	207.922i	0.933358	−	0.538875i	0.0454860	−	0.998965i	$-0.485516\pi$
$53$	360.132	−	207.922i	0.933358	−	0.538875i	0.887872	+	0.460090i	$0.152183\pi$
$54$	−480.301	−	177.519i	−1.21038	−	0.447358i
$55$		−	122.453i		−	0.300209i
$56$	174.914	−	46.8155i	0.417391	−	0.111714i
$57$	608.949	−	143.260i	1.41504	−	0.332900i
$58$	212.163			0.480317
$59$	180.334	−	312.348i	0.397924	−	0.689225i	−0.595545	−	0.803322i	$-0.703064\pi$
$59$	180.334	−	312.348i	0.397924	−	0.689225i	0.993470	+	0.114096i	$0.0363973\pi$
$60$	−77.4496	−	329.211i	−0.166645	−	0.708350i
$61$	−635.689	+	367.015i	−1.33429	+	0.770353i	−0.985954	−	0.167017i	$-0.946586\pi$
$61$	−635.689	+	367.015i	−1.33429	+	0.770353i	−0.348336	+	0.937370i	$0.613253\pi$
$62$	735.324			1.50623
$63$	490.076	−	99.3604i	0.980060	−	0.198702i
$64$	130.940			0.255742
$65$	−697.509	+	402.707i	−1.33100	+	0.768456i
$66$	181.800	+	54.7551i	0.339061	+	0.102120i
$67$	55.6457	−	96.3811i	0.101466	−	0.175744i	−0.810823	−	0.585291i	$-0.800980\pi$
$67$	55.6457	−	96.3811i	0.101466	−	0.175744i	0.912289	+	0.409548i	$0.134313\pi$
$68$	−411.673			−0.734158
$69$	−436.423	−	464.117i	−0.761437	−	0.809755i
$70$	584.464	+	584.792i	0.997955	+	0.998514i
$71$			455.487i			0.761358i	0.924707	+	0.380679i	$0.124310\pi$
$71$			455.487i			0.761358i	−0.924707	+	0.380679i	$0.875690\pi$
$72$	−263.478	−	16.2205i	−0.431266	−	0.0265501i
$73$	−662.747	+	382.637i	−1.06258	+	0.613483i	−0.926146	−	0.377166i	$-0.876899\pi$
$73$	−662.747	+	382.637i	−1.06258	+	0.613483i	−0.136438	+	0.990649i	$0.543565\pi$
$74$			605.230i			0.950765i
$75$	−93.1451	+	87.5871i	−0.143406	+	0.134849i
$76$	−554.808	+	320.319i	−0.837380	+	0.483462i
$77$	−179.109	+	47.9383i	−0.265082	+	0.0709490i
$78$	−285.987	−	1215.63i	−0.415149	−	1.76465i
$79$	21.5683	+	37.3573i	0.0307167	+	0.0532029i	0.880975	−	0.473163i	$-0.156888\pi$
$79$	21.5683	+	37.3573i	0.0307167	+	0.0532029i	−0.850258	+	0.526366i	$0.823554\pi$
$80$	−478.578	−	828.921i	−0.668833	−	1.15845i
$81$	−723.495	−	89.4203i	−0.992449	−	0.122662i
$82$	710.697	+	410.321i	0.957115	+	0.552590i
$83$	−200.064	+	346.522i	−0.264577	+	0.458262i	−0.967453	−	0.253051i	$-0.918566\pi$
$83$	−200.064	+	346.522i	−0.264577	+	0.458262i	0.702875	+	0.711313i	$0.251899\pi$
$84$	−451.210	+	242.165i	−0.586084	+	0.314552i
$85$	473.131	+	819.488i	0.603745	+	1.04572i
$86$			1112.49i			1.39491i
$87$	294.023	−	69.1714i	0.362329	−	0.0852408i
$88$	97.8802			0.118569
$89$	347.632	−	602.117i	0.414033	−	0.717127i	−0.581293	−	0.813694i	$-0.697453\pi$
$89$	347.632	−	602.117i	0.414033	−	0.717127i	0.995326	+	0.0965674i	$0.0307863\pi$
$90$	−537.392	−	1078.92i	−0.629401	−	1.26365i
$91$	862.094	+	862.577i	0.993099	+	0.993656i
$92$	565.012	+	326.210i	0.640289	+	0.369671i
$93$	1019.04	−	239.737i	1.13623	−	0.267307i
$94$	−71.3928	−	41.2186i	−0.0783362	−	0.0452274i
$95$	1275.27	+	736.277i	1.37726	+	0.795163i
$96$	1049.04	−	246.795i	1.11528	−	0.262380i
$97$	−955.178	−	551.472i	−0.999831	−	0.577253i	−0.0916328	−	0.995793i	$-0.529209\pi$
$97$	−955.178	−	551.472i	−0.999831	−	0.577253i	−0.908198	+	0.418540i	$0.862542\pi$
$98$	626.554	−	1083.82i	0.645832	−	1.11717i
$99$	269.796	+	16.6095i	0.273894	+	0.0168618i
$100$	65.4681	−	113.394i	0.0654681	−	0.113394i
$101$	−704.387			−0.693951			−0.346976	−	0.937874i	$-0.612791\pi$
$101$	−704.387			−0.693951			−0.346976	+	0.937874i	$0.612791\pi$
$102$	−1428.22	+	336.000i	−1.38642	+	0.326166i
$103$		−	1038.72i		−	0.993672i	−0.867845	−	0.496836i	$-0.834495\pi$
$103$		−	1038.72i		−	0.993672i	0.867845	−	0.496836i	$-0.165505\pi$
$104$	−321.896	−	557.540i	−0.303505	−	0.525686i
$105$	1000.63	+	619.873i	0.930014	+	0.576128i
$106$	−758.882	+	1314.42i	−0.695369	+	1.20442i
$107$	50.4942	+	29.1528i	0.0456211	+	0.0263394i	0.522637	−	0.852555i	$-0.324948\pi$
$107$	50.4942	+	29.1528i	0.0456211	+	0.0263394i	−0.477016	+	0.878895i	$0.658282\pi$
$108$	735.846	−	125.988i	0.655619	−	0.112252i
$109$	−444.694	−	770.232i	−0.390770	−	0.676834i	0.601781	−	0.798661i	$-0.294458\pi$
$109$	−444.694	−	770.232i	−0.390770	−	0.676834i	−0.992551	+	0.121827i	$0.961125\pi$
$110$	223.466	+	387.054i	0.193697	+	0.335493i
$111$	197.323	+	838.749i	0.168730	+	0.717212i
$112$	−1025.09	+	1024.51i	−0.864838	+	0.864353i
$113$	−2032.03	+	1173.20i	−1.69166	+	0.976681i	−0.738481	+	0.674274i	$0.764457\pi$
$113$	−2032.03	+	1173.20i	−1.69166	+	0.976681i	−0.953179	+	0.302407i	$0.902210\pi$
$114$	−1663.36	+	1564.11i	−1.36656	+	1.28502i
$115$		−	1499.64i		−	1.21602i
$116$	−267.882	+	154.662i	−0.214416	+	0.123793i
$117$	−792.661	−	1591.42i	−0.626338	−	1.25750i
$118$			1316.38i			1.02697i
$119$	1013.42	−	1012.86i	0.780675	−	0.780238i
$120$	−425.669	−	452.681i	−0.323818	−	0.344366i
$121$	1230.77			0.924698
$122$	1339.54	−	2320.16i	0.994071	−	1.72178i
$123$	1118.69	+	336.930i	0.820069	+	0.246991i
$124$	−928.437	+	536.033i	−0.672388	+	0.388203i
$125$	1227.95			0.878652
$126$	−1367.73	+	1208.41i	−0.967041	+	0.854395i
$127$	−1026.54			−0.717251			−0.358625	−	0.933482i	$-0.616754\pi$
$127$	−1026.54			−0.717251			−0.358625	+	0.933482i	$0.616754\pi$
$128$	1023.03	−	590.644i	0.706434	−	0.407860i
$129$	362.703	+	1541.72i	0.247552	+	1.05226i
$130$	1469.81	−	2545.79i	0.991624	−	1.71754i
$131$	−1431.15			−0.954506			−0.477253	−	0.878766i	$-0.658368\pi$
$131$	−1431.15			−0.954506			−0.477253	+	0.878766i	$0.658368\pi$
$132$	−269.460	+	63.3925i	−0.177678	+	0.0418001i
$133$	577.689	−	2153.55i	0.376632	−	1.40403i
$134$			406.195i			0.261865i
$135$	−1096.50	−	1320.00i	−0.699046	−	0.841536i
$136$	−655.042	+	378.189i	−0.413010	+	0.238451i
$137$			2527.45i			1.57616i	0.615571	+	0.788081i	$0.288925\pi$
$137$			2527.45i			1.57616i	−0.615571	+	0.788081i	$0.711075\pi$
$138$	2226.44	+	670.567i	1.37339	+	0.413641i
$139$	−247.028	+	142.622i	−0.150739	+	0.0870290i	−0.573472	−	0.819225i	$-0.694404\pi$
$139$	−247.028	+	142.622i	−0.150739	+	0.0870290i	0.422734	+	0.906254i	$0.361071\pi$
$140$	−1164.26	−	312.311i	−0.702840	−	0.188537i
$141$	−112.377	−	33.8461i	−0.0671195	−	0.0202153i
$142$	−831.226	−	1439.73i	−0.491232	−	0.850839i
$143$	329.616	+	570.911i	0.192754	+	0.333860i
$144$	1891.25	−	942.001i	1.09447	−	0.545139i
$145$	615.748	+	355.502i	0.352656	+	0.203606i
$146$	1396.56	−	2418.91i	0.791645	−	1.37117i
$147$	514.944	−	1706.27i	0.288924	−	0.957352i
$148$	−441.198	−	764.177i	−0.245042	−	0.424425i
$149$		−	1884.28i		−	1.03601i	−0.855376	−	0.518007i	$-0.826674\pi$
$149$		−	1884.28i		−	1.03601i	0.855376	−	0.518007i	$-0.173326\pi$
$150$	134.578	−	446.831i	0.0732551	−	0.243224i
$151$	−400.447			−0.215814			−0.107907	−	0.994161i	$-0.534415\pi$
$151$	−400.447			−0.215814			−0.107907	+	0.994161i	$0.534415\pi$
$152$	−588.529	+	1019.36i	−0.314053	+	0.543955i
$153$	−1869.73	+	931.280i	−0.987964	+	0.492089i
$154$	478.652	−	478.384i	0.250460	−	0.250320i
$155$	2134.08	+	1232.11i	1.10589	+	0.638489i
$156$	1247.26	+	1326.40i	0.640132	+	0.680752i
$157$	1698.99	+	980.915i	0.863659	+	0.498634i	0.865236	−	0.501365i	$-0.167169\pi$
$157$	1698.99	+	980.915i	0.863659	+	0.498634i	−0.00157672	+	0.999999i	$0.500502\pi$
$158$	−136.348	−	78.7205i	−0.0686536	−	0.0396372i
$159$	−623.146	+	2068.99i	−0.310809	+	1.03196i
$160$	2196.92	+	1268.39i	1.08551	+	0.626719i
$161$	−2193.49	+	587.084i	−1.07373	+	0.287383i
$162$	2450.04	−	1037.67i	1.18823	−	0.503255i
$163$	1092.64	−	1892.50i	0.525043	−	0.909400i	−0.474532	−	0.880238i	$-0.657383\pi$
$163$	1092.64	−	1892.50i	0.525043	−	0.909400i	0.999575	−	0.0291623i	$-0.00928395\pi$
$164$	−1196.46			−0.569680
$165$	435.878	+	463.537i	0.205655	+	0.218705i
$166$		−	1460.40i		−	0.682827i
$167$	724.771	+	1255.34i	0.335835	+	0.581683i	0.983645	−	0.180119i	$-0.0576482\pi$
$167$	724.771	+	1255.34i	0.335835	+	0.581683i	−0.647810	+	0.761802i	$0.724315\pi$
$168$	−495.483	+	799.834i	−0.227544	+	0.367313i
$169$	1069.50	−	1852.42i	0.486798	−	0.843160i
$170$	−2990.99	−	1726.85i	−1.34940	−	0.779079i
$171$	−1795.20	+	2709.89i	−0.802819	+	1.21188i
$172$	−810.975	−	1404.65i	−0.359513	−	0.622695i
$173$	−922.964	−	1598.62i	−0.405617	−	0.702549i	0.588776	−	0.808296i	$-0.299610\pi$
$173$	−922.964	−	1598.62i	−0.405617	−	0.702549i	−0.994393	+	0.105747i	$0.966277\pi$
$174$	−803.131	+	755.208i	−0.349915	+	0.329035i
$175$	117.824	+	440.218i	0.0508951	+	0.190156i
$176$	−678.472	+	391.716i	−0.290578	+	0.167765i
$177$	429.178	+	1824.29i	0.182254	+	0.774699i
$178$			2537.60i			1.06855i
$179$	389.538	−	224.900i	0.162656	−	0.0939096i	−0.416462	−	0.909153i	$-0.636730\pi$
$179$	389.538	−	224.900i	0.162656	−	0.0939096i	0.579118	+	0.815243i	$0.303397\pi$
$180$	1465.03	+	970.522i	0.606648	+	0.401880i
$181$			3067.12i			1.25954i	0.776781	+	0.629771i	$0.216851\pi$
$181$			3067.12i			1.25954i	−0.776781	+	0.629771i	$0.783149\pi$
$182$	−4299.08	−	1153.23i	−1.75093	−	0.469686i
$183$	1099.95	−	3652.09i	0.444320	−	1.47525i
$184$	1198.71			0.480271
$185$	−1014.13	+	1756.52i	−0.403028	+	0.698064i
$186$	−2783.52	+	2617.43i	−1.09730	+	1.03182i
$187$	670.751	−	387.258i	0.262300	−	0.151439i
$188$	120.189			0.0466261
$189$	−1501.47	+	2120.58i	−0.577863	+	0.816134i
$190$	−5374.58			−2.05217
$191$	−4503.79	+	2600.27i	−1.70619	+	0.985071i	−0.767023	+	0.641619i	$0.778263\pi$
$191$	−4503.79	+	2600.27i	−1.70619	+	0.985071i	−0.939170	+	0.343452i	$0.888404\pi$
$192$	−495.664	+	466.088i	−0.186310	+	0.175193i
$193$	−1188.11	+	2057.87i	−0.443119	+	0.767505i	−0.997919	−	0.0644786i	$-0.979462\pi$
$193$	−1188.11	+	2057.87i	−0.443119	+	0.767505i	0.554800	+	0.831984i	$0.312795\pi$
$194$	4025.56			1.48979
$195$	1206.92	−	4007.25i	0.443226	−	1.47161i
$196$	−1.02330	+	1825.20i	−0.000372923	+	0.665159i
$197$			148.115i			0.0535672i	0.999641	+	0.0267836i	$0.00852651\pi$
$197$			148.115i			0.0535672i	−0.999641	+	0.0267836i	$0.991473\pi$
$198$	−883.096	+	439.855i	−0.316964	+	0.157875i
$199$	−1479.37	+	854.117i	−0.526985	+	0.304255i	−0.739788	−	0.672840i	$-0.765074\pi$
$199$	−1479.37	+	854.117i	−0.526985	+	0.304255i	0.212803	+	0.977095i	$0.431741\pi$
$200$		−	240.572i		−	0.0850551i
$201$	132.431	+	562.919i	0.0464725	+	0.197538i
$202$	2226.46	−	1285.45i	0.775510	−	0.447741i
$203$	278.930	−	1039.81i	0.0964386	−	0.359510i
$204$	1558.36	−	1465.38i	0.534839	−	0.502926i
$205$	1375.07	+	2381.70i	0.468484	+	0.811439i
$206$	1895.58	+	3283.24i	0.641122	+	1.11046i
$207$	3304.10	+	203.411i	1.10943	+	0.0682999i
$208$	4462.55	+	2576.45i	1.48761	+	0.858869i
$209$	602.643	−	1043.81i	0.199453	−	0.345463i
$210$	−4294.05	−	133.258i	−1.41104	−	0.0437889i
$211$	545.976	+	945.659i	0.178135	+	0.308540i	0.941242	−	0.337733i	$-0.109660\pi$
$211$	545.976	+	945.659i	0.178135	+	0.308540i	−0.763106	+	0.646273i	$0.776327\pi$
$212$		−	2212.82i		−	0.716875i
$213$	−1621.33	−	1724.22i	−0.521559	−	0.554655i
$214$	−212.806			−0.0679772
$215$	−1864.09	+	3228.70i	−0.591301	+	1.02416i
$216$	1055.12	−	876.462i	0.332368	−	0.276091i
$217$	966.726	−	3603.83i	0.302422	−	1.12739i
$218$	2811.22	+	1623.06i	0.873393	+	0.504254i
$219$	1146.77	−	3807.53i	0.353841	−	1.17484i
$220$	−564.306	−	325.802i	−0.172934	−	0.0998435i
$221$	−4411.76	−	2547.13i	−1.34284	−	0.775288i
$222$	−2154.35	−	2291.06i	−0.651310	−	0.692639i
$223$	1063.36	+	613.931i	0.319317	+	0.184358i	0.651088	−	0.759002i	$-0.274313\pi$
$223$	1063.36	+	613.931i	0.319317	+	0.184358i	−0.331771	+	0.943360i	$0.607646\pi$
$224$	995.188	−	3709.93i	0.296847	−	1.10661i
$225$	40.8233	−	663.111i	0.0120958	−	0.196477i
$226$	4281.96	−	7416.58i	1.26032	−	2.18294i
$227$	−2263.45			−0.661809			−0.330905	−	0.943664i	$-0.607354\pi$
$227$	−2263.45			−0.661809			−0.330905	+	0.943664i	$0.607354\pi$
$228$	959.998	−	3187.42i	0.278848	−	0.925842i
$229$		−	5152.41i		−	1.48682i	−0.668839	−	0.743408i	$-0.733208\pi$
$229$		−	5152.41i		−	1.48682i	0.668839	−	0.743408i	$-0.266792\pi$
$230$	2736.71	+	4740.12i	0.784580	+	1.35893i
$231$	507.366	−	819.016i	0.144512	−	0.233278i
$232$	−284.164	+	492.186i	−0.0804149	+	0.139283i
$233$	−361.488	−	208.705i	−0.101639	−	0.0586812i	0.448319	−	0.893874i	$-0.352023\pi$
$233$	−361.488	−	208.705i	−0.101639	−	0.0586812i	−0.549958	+	0.835192i	$0.685356\pi$
$234$	5409.69	+	3583.70i	1.51129	+	1.00117i
$235$	−138.132	−	239.252i	−0.0383437	−	0.0664132i
$236$	−959.609	−	1662.09i	−0.264683	−	0.458445i
$237$	−214.621	−	64.6403i	−0.0588233	−	0.0177166i
$238$	−1354.90	+	5050.89i	−0.369013	+	1.37563i
$239$	4832.69	−	2790.15i	1.30795	−	0.755146i	0.326198	−	0.945302i	$-0.394233\pi$
$239$	4832.69	−	2790.15i	1.30795	−	0.755146i	0.981754	+	0.190155i	$0.0608992\pi$
$240$	4762.22	+	1434.30i	1.28083	+	0.385766i
$241$		−	2773.85i		−	0.741409i	−0.928751	−	0.370704i	$-0.879116\pi$
$241$		−	2773.85i		−	0.741409i	0.928751	−	0.370704i	$-0.120884\pi$
$242$	−3890.28	+	2246.06i	−1.03338	+	0.596620i
$243$	3057.04	−	2236.83i	0.807034	−	0.590505i
$244$			3905.98i			1.02481i
$245$	3634.46	−	2095.64i	0.947744	−	0.546472i
$246$	−4150.86	+	976.524i	−1.07581	+	0.253093i
$247$	−7927.59			−2.04219
$248$	−984.866	+	1705.84i	−0.252174	+	0.436778i
$249$	−476.134	−	2023.88i	−0.121180	−	0.515093i
$250$	−3881.37	+	2240.91i	−0.981918	+	0.566911i
$251$	3751.34			0.943357			0.471678	−	0.881771i	$-0.343648\pi$
$251$	3751.34			0.943357			0.471678	+	0.881771i	$0.343648\pi$
$252$	846.026	−	2522.81i	0.211487	−	0.630643i
$253$	−1227.45			−0.305017
$254$	3244.74	−	1873.35i	0.801548	−	0.462774i
$255$	−4708.03	−	1417.98i	−1.15619	−	0.348225i
$256$	−2679.51	+	4641.05i	−0.654178	+	1.13307i
$257$	7511.72			1.82322			0.911612	−	0.411052i	$-0.134839\pi$
$257$	7511.72			1.82322			0.911612	+	0.411052i	$0.134839\pi$
$258$	−3959.96	−	4211.25i	−0.955567	−	1.01620i
$259$	2966.24	+	795.692i	0.711633	+	0.190895i
$260$			4285.83i			1.02229i
$261$	−866.787	+	1308.44i	−0.205566	+	0.310307i
$262$	4523.65	−	2611.73i	1.06669	−	0.615852i
$263$		−	5534.91i		−	1.29771i	−0.760913	−	0.648854i	$-0.775248\pi$
$263$		−	5534.91i		−	1.29771i	0.760913	−	0.648854i	$-0.224752\pi$
$264$	−370.519	+	348.410i	−0.0863784	+	0.0812242i
$265$	−4404.91	+	2543.17i	−1.02110	+	0.589532i
$266$	2104.06	+	7861.28i	0.484993	+	1.81205i
$267$	827.331	+	3516.70i	0.189632	+	0.806061i
$268$	−296.106	−	512.870i	−0.0674908	−	0.116898i
$269$	−411.958	−	713.532i	−0.0933737	−	0.161728i	0.815555	−	0.578680i	$-0.196432\pi$
$269$	−411.958	−	713.532i	−0.0933737	−	0.161728i	−0.908929	+	0.416952i	$0.863098\pi$
$270$	5874.74	+	2171.30i	1.32417	+	0.489412i
$271$	−3757.66	−	2169.49i	−0.842294	−	0.486299i	0.0157492	−	0.999876i	$-0.494987\pi$
$271$	−3757.66	−	2169.49i	−0.842294	−	0.486299i	−0.858043	+	0.513577i	$0.828320\pi$
$272$	3027.02	−	5242.95i	0.674779	−	1.16875i
$273$	−6333.80	−	196.557i	−1.40417	−	0.0435758i
$274$	−4612.38	−	7988.87i	−1.01695	−	1.76141i
$275$			246.341i			0.0540180i
$276$	−3299.98	+	776.347i	−0.719694	+	0.169314i
$277$	−2642.56			−0.573199			−0.286599	−	0.958051i	$-0.592525\pi$
$277$	−2642.56			−0.573199			−0.286599	+	0.958051i	$0.592525\pi$
$278$	520.546	−	901.612i	0.112303	−	0.194515i
$279$	−3004.15	+	4534.84i	−0.644636	+	0.973095i
$280$	−2139.44	+	572.618i	−0.456628	+	0.122216i
$281$	−3315.71	−	1914.33i	−0.703910	−	0.406403i	0.104892	−	0.994484i	$-0.466550\pi$
$281$	−3315.71	−	1914.33i	−0.703910	−	0.406403i	−0.808802	+	0.588081i	$0.799884\pi$
$282$	416.973	−	98.0963i	0.0880510	−	0.0207147i
$283$	6229.03	+	3596.33i	1.30840	+	0.755406i	0.981829	−	0.189766i	$-0.0607731\pi$
$283$	6229.03	+	3596.33i	1.30840	+	0.755406i	0.326572	+	0.945172i	$0.394106\pi$
$284$	2099.05	+	1211.89i	0.438576	+	0.253212i
$285$	−7448.28	+	1752.27i	−1.54806	+	0.364194i
$286$	−2083.73	−	1203.04i	−0.430816	−	0.248732i
$287$	2945.34	−	2943.69i	0.605776	−	0.605437i
$288$	−3092.59	+	4668.35i	−0.632753	+	0.955157i
$289$	−536.069	+	928.499i	−0.109112	+	0.188988i
$290$	−2595.05			−0.525470
$291$	5578.76	−	1312.45i	1.12382	−	0.264389i
$292$			4072.23i			0.816128i
$293$	−1871.73	−	3241.93i	−0.373199	−	0.646400i	0.616856	−	0.787076i	$-0.288406\pi$
$293$	−1871.73	−	3241.93i	−0.373199	−	0.646400i	−0.990056	+	0.140675i	$0.955073\pi$
$294$	1486.14	+	6332.99i	0.294808	+	1.25628i
$295$	−2205.74	+	3820.45i	−0.435332	+	0.754017i
$296$	−1404.04	−	810.623i	−0.275703	−	0.159177i
$297$	−1080.42	+	897.482i	−0.211085	+	0.175344i
$298$	3438.65	+	5955.92i	0.668442	+	1.15778i
$299$	4036.69	+	6991.76i	0.780763	+	1.35232i
$300$	155.808	+	662.283i	0.0299852	+	0.127457i
$301$	5452.30	+	1462.58i	1.04407	+	0.280072i
$302$	1265.75	−	730.781i	0.241178	−	0.139244i
$303$	2666.41	−	2507.31i	0.505549	−	0.475383i
$304$		−	9421.17i		−	1.77744i
$305$	7775.35	−	4489.10i	1.45972	−	0.842771i
$306$	4210.42	−	6355.73i	0.786580	−	1.18736i
$307$			4199.35i			0.780682i	0.920670	+	0.390341i	$0.127643\pi$
$307$			4199.35i			0.780682i	−0.920670	+	0.390341i	$0.872357\pi$
$308$	−255.627	+	952.944i	−0.0472912	+	0.176296i
$309$	3697.39	+	3932.01i	0.680703	+	0.723898i
$310$	−8994.02			−1.64783
$311$	1241.68	−	2150.64i	0.226395	−	0.392128i	−0.730342	−	0.683082i	$-0.760639\pi$
$311$	1241.68	−	2150.64i	0.226395	−	0.392128i	0.956737	+	0.290954i	$0.0939725\pi$
$312$	3203.11	+	964.725i	0.581220	+	0.175054i
$313$	−710.623	+	410.278i	−0.128328	+	0.0740904i	−0.562790	−	0.826600i	$-0.690272\pi$
$313$	−710.623	+	410.278i	−0.128328	+	0.0740904i	0.434462	+	0.900690i	$0.356939\pi$
$314$	−7160.35			−1.28688
$315$	−5994.30	+	1215.31i	−1.07219	+	0.217381i
$316$	229.541			0.0408630
$317$	−3579.71	+	2066.74i	−0.634247	+	0.366183i	−0.782395	−	0.622782i	$-0.786002\pi$
$317$	−3579.71	+	2066.74i	−0.634247	+	0.366183i	0.148148	+	0.988965i	$0.452669\pi$
$318$	−1806.06	−	7676.95i	−0.318488	−	1.35378i
$319$	290.979	−	503.990i	0.0510711	−	0.0884577i
$320$	−1601.57			−0.279783
$321$	−294.914	+	69.3809i	−0.0512788	+	0.0120638i
$322$	5861.90	−	5858.61i	1.01451	−	1.01394i
$323$			9313.95i			1.60446i
$324$	−2337.04	+	3096.21i	−0.400727	+	0.530900i
$325$	1403.20	−	810.137i	0.239494	−	0.138272i
$326$			7975.88i			1.35504i
$327$	4425.05	+	1332.75i	0.748336	+	0.225386i
$328$	−1903.76	+	1099.14i	−0.320481	+	0.185030i
$329$	−295.872	+	295.707i	−0.0495805	+	0.0495527i
$330$	−2223.66	−	669.729i	−0.370935	−	0.111719i
$331$	4444.19	+	7697.57i	0.737991	+	1.27824i	0.953399	+	0.301713i	$0.0975584\pi$
$331$	4444.19	+	7697.57i	0.737991	+	1.27824i	−0.215408	+	0.976524i	$0.569108\pi$
$332$	1064.60	+	1843.94i	0.175986	+	0.304817i
$333$	−3732.53	−	2472.65i	−0.614238	−	0.406908i
$334$	−4581.78	−	2645.29i	−0.750610	−	0.433365i
$335$	−680.622	+	1178.87i	−0.111004	+	0.192265i
$336$	233.589	−	7527.10i	0.0379266	−	1.22213i
$337$	1800.32	+	3118.24i	0.291007	+	0.504040i	0.974048	−	0.226341i	$-0.0726763\pi$
$337$	1800.32	+	3118.24i	0.291007	+	0.504040i	−0.683041	+	0.730380i	$0.739343\pi$
$338$			7806.96i			1.25634i
$339$	3516.08	−	11674.2i	0.563325	−	1.87037i
$340$	5035.32			0.803173
$341$	1008.49	−	1746.75i	0.160154	−	0.277395i
$342$	729.010	−	11841.6i	0.115264	−	1.87229i
$343$	−4488.08	−	4495.64i	−0.706512	−	0.707701i
$344$	−2580.80	−	1490.02i	−0.404498	−	0.233537i
$345$	5338.05	+	5676.78i	0.833017	+	0.885877i
$346$	5834.70	+	3368.66i	0.906576	+	0.523412i
$347$	−8104.74	−	4679.27i	−1.25385	−	0.723909i	−0.281976	−	0.959421i	$-0.590990\pi$
$347$	−8104.74	−	4679.27i	−1.25385	−	0.723909i	−0.971871	+	0.235512i	$0.924323\pi$
$348$	463.523	−	1539.00i	0.0714006	−	0.237067i
$349$	−3496.96	−	2018.97i	−0.536355	−	0.309665i	0.207245	−	0.978289i	$-0.433550\pi$
$349$	−3496.96	−	2018.97i	−0.536355	−	0.309665i	−0.743601	+	0.668624i	$0.766884\pi$
$350$	−1175.78	−	1176.44i	−0.179566	−	0.179667i
$351$	8665.33	+	3202.71i	1.31772	+	0.487031i
$352$	1038.18	−	1798.18i	0.157202	−	0.272282i
$353$	−4358.17			−0.657117			−0.328558	−	0.944484i	$-0.606563\pi$
$353$	−4358.17			−0.657117			−0.328558	+	0.944484i	$0.606563\pi$
$354$	−4685.74	−	4983.08i	−0.703514	−	0.748157i
$355$		−	5571.23i		−	0.832930i
$356$	−1849.85	−	3204.03i	−0.275398	−	0.477003i
$357$	−230.931	+	7441.44i	−0.0342358	+	1.10320i
$358$	−820.847	+	1421.75i	−0.121182	+	0.209893i
$359$	−3099.17	−	1789.31i	−0.455621	−	0.263053i	0.254580	−	0.967052i	$-0.418063\pi$
$359$	−3099.17	−	1789.31i	−0.455621	−	0.263053i	−0.710201	+	0.703999i	$0.751396\pi$
$360$	3222.69	+	198.399i	0.471807	+	0.0290460i
$361$	3817.59	+	6612.26i	0.556581	+	0.964026i
$362$	−5597.23	−	9694.68i	−0.812662	−	1.40757i
$363$	−4659.01	+	4381.01i	−0.673649	+	0.633453i
$364$	6268.78	−	1677.83i	0.902675	−	0.241600i
$365$	8106.29	−	4680.17i	1.16247	−	0.671154i
$366$	3187.98	+	13551.0i	0.455297	+	1.93531i
$367$			10258.5i			1.45910i	0.683926	+	0.729551i	$0.260271\pi$
$367$			10258.5i			1.45910i	−0.683926	+	0.729551i	$0.739729\pi$
$368$	−8309.02	+	4797.22i	−1.17700	+	0.679544i
$369$	−5434.04	+	2706.60i	−0.766625	+	0.381843i
$370$		−	7402.79i		−	1.04014i
$371$	5444.30	+	5447.35i	0.761870	+	0.762297i
$372$	1606.50	−	5333.94i	0.223906	−	0.743420i
$373$	9853.78			1.36785			0.683927	−	0.729551i	$-0.260271\pi$
$373$	9853.78			1.36785			0.683927	+	0.729551i	$0.260271\pi$
$374$	−1413.43	+	2448.13i	−0.195419	+	0.338475i
$375$	−4648.34	+	4370.97i	−0.640105	+	0.601909i
$376$	191.242	−	110.413i	0.0262302	−	0.0151440i
$377$	−3827.73			−0.522913
$378$	876.050	−	9442.88i	0.119204	−	1.28489i
$379$	−11181.0			−1.51538			−0.757688	−	0.652617i	$-0.773671\pi$
$379$	−11181.0			−1.51538			−0.757688	+	0.652617i	$0.773671\pi$
$380$	6786.06	−	3917.93i	0.916099	−	0.528910i
$381$	3885.91	−	3654.04i	0.522523	−	0.491344i
$382$	9490.53	−	16438.1i	1.27115	−	2.20169i
$383$	−8990.60			−1.19947			−0.599737	−	0.800198i	$-0.704728\pi$
$383$	−8990.60			−1.19947			−0.599737	+	0.800198i	$0.704728\pi$
$384$	−1770.17	+	5877.37i	−0.235243	+	0.781063i
$385$	2190.74	−	586.350i	0.290002	−	0.0776186i
$386$		−	8672.81i		−	1.14361i
$387$	−6860.84	−	4545.03i	−0.901178	−	0.596994i
$388$	−5082.76	+	2934.53i	−0.665047	+	0.383965i
$389$		−	1888.31i		−	0.246121i	−0.992399	−	0.123061i	$-0.960729\pi$
$389$		−	1888.31i		−	0.246121i	0.992399	−	0.123061i	$-0.0392709\pi$
$390$	3498.01	+	14868.8i	0.454176	+	1.93054i
$391$	8214.46	−	4742.62i	1.06246	−	0.613414i
$392$	1675.11	+	2905.14i	0.215831	+	0.374315i
$393$	5417.54	−	5094.27i	0.695365	−	0.653873i
$394$	−270.297	−	468.168i	−0.0345618	−	0.0598629i
$395$	−263.809	−	456.931i	−0.0336043	−	0.0582043i
$396$	794.373	−	1199.13i	0.100805	−	0.152168i
$397$	9137.13	+	5275.32i	1.15511	+	0.666904i	0.950128	−	0.311861i	$-0.100952\pi$
$397$	9137.13	+	5275.32i	1.15511	+	0.666904i	0.204984	+	0.978765i	$0.434286\pi$
$398$	3117.38	−	5399.47i	0.392614	−	0.680027i
$399$	5478.88	+	10208.4i	0.687437	+	1.28086i
$400$	962.768	+	1667.56i	0.120346	+	0.208445i
$401$			2064.71i			0.257124i	0.991701	+	0.128562i	$0.0410361\pi$
$401$			2064.71i			0.257124i	−0.991701	+	0.128562i	$0.958964\pi$
$402$	−1445.87	−	1537.62i	−0.179387	−	0.190770i
$403$	−13266.3			−1.63981
$404$	−1874.12	+	3246.07i	−0.230794	+	0.399747i
$405$	8849.33	+	1093.73i	1.08574	+	0.134193i
$406$	1015.92	+	3795.72i	0.124185	+	0.463986i
$407$	1437.71	+	830.064i	0.175098	+	0.101093i
$408$	1133.43	−	3763.27i	0.137533	−	0.456641i
$409$	−124.596	−	71.9353i	−0.0150632	−	0.00869676i	0.492449	−	0.870341i	$-0.336102\pi$
$409$	−124.596	−	71.9353i	−0.0150632	−	0.00869676i	−0.507513	+	0.861644i	$0.669435\pi$
$410$	−8692.80	−	5018.79i	−1.04709	−	0.604537i
$411$	−8996.59	−	9567.49i	−1.07973	−	1.14825i
$412$	−4786.80	−	2763.66i	−0.572399	−	0.330475i
$413$	6451.59	+	1730.64i	0.768673	+	0.206196i
$414$	−10815.0	+	5386.76i	−1.28388	+	0.639480i
$415$	2447.06	−	4238.43i	0.289449	−	0.501341i
$416$	−13656.9			−1.60958
$417$	427.439	−	1419.20i	0.0501961	−	0.166663i
$418$			4399.09i			0.514753i
$419$	1974.15	+	3419.34i	0.230176	+	0.398677i	0.957860	−	0.287236i	$-0.0927365\pi$
$419$	1974.15	+	3419.34i	0.230176	+	0.398677i	−0.727684	+	0.685913i	$0.759403\pi$
$420$	5518.91	−	2962.00i	0.641179	−	0.344121i
$421$	5518.29	−	9557.95i	0.638824	−	1.10648i	−0.346868	−	0.937914i	$-0.612755\pi$
$421$	5518.29	−	9557.95i	0.638824	−	1.10648i	0.985691	−	0.168561i	$-0.0539120\pi$
$422$	−3451.50	−	1992.72i	−0.398143	−	0.229868i
$423$	545.874	−	271.891i	0.0627453	−	0.0312524i
$424$	−2032.84	−	3520.98i	−0.232838	−	0.403287i
$425$	−951.812	−	1648.59i	−0.108634	−	0.188160i
$426$	8271.34	+	2491.19i	0.940723	+	0.283330i
$427$	−9610.03	−	9615.42i	−1.08914	−	1.08975i
$428$	268.694	−	155.130i	0.0303453	−	0.0175199i
$429$	−3279.93	−	987.861i	−0.369130	−	0.111176i
$430$		−	13607.2i		−	1.52604i
$431$	1481.18	−	855.162i	0.165536	−	0.0955724i	−0.414943	−	0.909847i	$-0.636199\pi$
$431$	1481.18	−	855.162i	0.165536	−	0.0955724i	0.580479	+	0.814275i	$0.302865\pi$
$432$	−3806.10	+	10297.9i	−0.423892	+	1.14689i
$433$			11599.1i			1.28734i	0.765303	+	0.643670i	$0.222589\pi$
$433$			11599.1i			1.28734i	−0.765303	+	0.643670i	$0.777411\pi$
$434$	3521.01	+	13155.3i	0.389433	+	1.45502i
$435$	−3596.30	+	846.060i	−0.396390	+	0.0932539i
$436$	−4732.67			−0.519849
$437$	7380.37	−	12783.2i	0.807897	−	1.39932i
$438$	3323.68	+	14127.8i	0.362583	+	1.54121i
$439$	−3706.44	+	2139.92i	−0.402959	+	0.232648i	−0.687760	−	0.725938i	$-0.741406\pi$
$439$	−3706.44	+	2139.92i	−0.402959	+	0.232648i	0.284801	+	0.958587i	$0.408072\pi$
$440$	−1197.21			−0.129715
$441$	4124.28	+	8291.95i	0.445339	+	0.895362i
$442$	18593.2			2.00088
$443$	8038.03	−	4640.76i	0.862073	−	0.497718i	−0.00263274	−	0.999997i	$-0.500838\pi$
$443$	8038.03	−	4640.76i	0.862073	−	0.497718i	0.864706	+	0.502278i	$0.167505\pi$
$444$	4390.26	+	1322.27i	0.469262	+	0.141334i
$445$	−4252.02	+	7364.71i	−0.452955	+	0.784541i
$446$	−4481.49			−0.475795
$447$	6707.20	+	7132.82i	0.709709	+	0.754744i
$448$	626.989	+	2342.58i	0.0661216	+	0.247046i
$449$		−	6876.47i		−	0.722763i	−0.932418	−	0.361382i	$-0.882305\pi$
$449$		−	6876.47i		−	0.722763i	0.932418	−	0.361382i	$-0.117695\pi$
$450$	1081.09	+	2170.49i	0.113251	+	0.227373i
$451$	1949.42	−	1125.50i	0.203536	−	0.117511i
$452$			12485.8i			1.29930i
$453$	1515.87	−	1425.41i	0.157222	−	0.147841i
$454$	7154.43	−	4130.61i	0.739590	−	0.427003i
$455$	−10544.6	−	10550.5i	−1.08646	−	1.08707i
$456$	−1400.64	−	5953.64i	−0.143840	−	0.611414i
$457$	5580.75	+	9666.14i	0.571239	+	0.989416i	0.996439	+	0.0843160i	$0.0268705\pi$
$457$	5580.75	+	9666.14i	0.571239	+	0.989416i	−0.425200	+	0.905100i	$0.639796\pi$
$458$	9402.71	+	16286.0i	0.959301	+	1.66156i
$459$	3762.79	−	10180.7i	0.382640	−	1.03528i
$460$	−6910.87	−	3989.99i	−0.700480	−	0.404422i
$461$	193.554	−	335.245i	0.0195547	−	0.0338697i	−0.856082	−	0.516839i	$-0.827108\pi$
$461$	193.554	−	335.245i	0.0195547	−	0.0338697i	0.875637	+	0.482970i	$0.160442\pi$
$462$	−109.072	+	3514.68i	−0.0109837	+	0.353935i
$463$	−2485.01	−	4304.16i	−0.249435	−	0.432033i	0.713934	−	0.700213i	$-0.246911\pi$
$463$	−2485.01	−	4304.16i	−0.249435	−	0.432033i	−0.963369	+	0.268179i	$0.913578\pi$
$464$		−	4548.89i		−	0.455122i
$465$	−12464.2	+	2932.31i	−1.24304	+	0.292436i
$466$	1523.48			0.151446
$467$	−4548.20	+	7877.72i	−0.450676	+	0.780594i	−0.998428	−	0.0560470i	$-0.982150\pi$
$467$	−4548.20	+	7877.72i	−0.450676	+	0.780594i	0.547752	+	0.836641i	$0.315484\pi$
$468$	−9442.83	−	581.331i	−0.932681	−	0.0574189i
$469$	1990.76	+	534.021i	0.196002	+	0.0525774i
$470$	873.231	+	504.160i	0.0857003	+	0.0494791i
$471$	−9923.06	+	2334.48i	−0.970765	+	0.228380i
$472$	−3053.80	−	1763.11i	−0.297802	−	0.171936i
$473$	2642.69	+	1525.76i	0.256894	+	0.148318i
$474$	796.347	−	187.347i	0.0771676	−	0.0181543i
$475$	−2565.50	−	1481.19i	−0.247817	−	0.143077i
$476$	−1971.25	−	7365.06i	−0.189815	−	0.709195i
$477$	−5005.82	−	10050.2i	−0.480504	−	0.964707i
$478$	−10183.6	+	17638.5i	−0.974449	+	1.68779i
$479$	13858.1			1.32191			0.660953	−	0.750427i	$-0.270152\pi$
$479$	13858.1			1.32191			0.660953	+	0.750427i	$0.270152\pi$
$480$	−12831.2	+	3018.64i	−1.22013	+	0.287045i
$481$		−	10919.2i		−	1.03508i
$482$	5062.05	+	8767.72i	0.478361	+	0.828545i
$483$	6213.54	−	10030.2i	0.585354	−	0.944908i
$484$	3274.64	−	5671.84i	0.307536	−	0.532667i
$485$	11683.1	+	6745.26i	1.09382	+	0.631518i
$486$	−5580.82	+	12649.1i	−0.520887	+	1.18061i
$487$	−681.295	−	1180.04i	−0.0633931	−	0.109800i	0.832587	−	0.553894i	$-0.186859\pi$
$487$	−681.295	−	1180.04i	−0.0633931	−	0.109800i	−0.895980	+	0.444094i	$0.853526\pi$
$488$	3588.27	+	6215.07i	0.332856	+	0.576523i
$489$	2600.37	+	11053.3i	0.240476	+	1.02218i
$490$	−7663.61	+	13256.6i	−0.706544	+	1.22219i
$491$	−15324.0	+	8847.30i	−1.40847	+	0.813183i	−0.995241	−	0.0974422i	$-0.968934\pi$
$491$	−15324.0	+	8847.30i	−1.40847	+	0.813183i	−0.413233	+	0.910625i	$0.635601\pi$
$492$	4529.11	−	4258.86i	0.415016	−	0.390252i
$493$			4497.12i			0.410832i
$494$	25057.9	−	14467.2i	2.28220	−	1.31763i
$495$	−3299.98	−	203.157i	−0.299642	−	0.0184469i
$496$		−	15765.7i		−	1.42722i
$497$	−8148.91	+	2181.05i	−0.735470	+	0.196848i
$498$	5198.39	+	5528.26i	0.467762	+	0.497445i
$499$	−14157.8			−1.27012			−0.635059	−	0.772464i	$-0.719024\pi$
$499$	−14157.8			−1.27012			−0.635059	+	0.772464i	$0.719024\pi$
$500$	3267.14	−	5658.85i	0.292222	−	0.506143i
$501$	−7212.03	−	2172.15i	−0.643133	−	0.193701i
$502$	−11857.4	+	6845.88i	−1.05423	+	0.608659i
$503$	−5337.01			−0.473093			−0.236546	−	0.971620i	$-0.576015\pi$
$503$	−5337.01			−0.473093			−0.236546	+	0.971620i	$0.576015\pi$
$504$	−971.437	−	4791.43i	−0.0858556	−	0.423466i
$505$	8615.60			0.759187
$506$	3879.79	−	2240.00i	0.340865	−	0.196799i
$507$	2545.30	+	10819.2i	0.222960	+	0.947724i
$508$	−2731.25	+	4730.67i	−0.238543	+	0.413169i
$509$	−1521.38			−0.132483			−0.0662417	−	0.997804i	$-0.521101\pi$
$509$	−1521.38			−0.132483			−0.0662417	+	0.997804i	$0.521101\pi$
$510$	17469.0	−	4109.73i	1.51675	−	0.356828i
$511$	−10019.1	−	10024.7i	−0.867353	−	0.867839i
$512$		−	10109.2i		−	0.872595i
$513$	−2850.43	−	16648.2i	−0.245321	−	1.43282i
$514$	−23743.4	+	13708.3i	−2.03750	+	1.17635i
$515$			12705.0i			1.08708i
$516$	8069.83	+	2430.50i	0.688477	+	0.207358i
$517$	−195.828	+	113.061i	−0.0166586	+	0.00961786i
$518$	−10827.9	+	2898.07i	−0.918437	+	0.245819i
$519$	9184.21	+	2766.13i	0.776767	+	0.233949i
$520$	3937.23	+	6819.47i	0.332036	+	0.575103i
$521$	−8290.88	−	14360.2i	−0.697178	−	1.20755i	−0.969441	−	0.245325i	$-0.921105\pi$
$521$	−8290.88	−	14360.2i	−0.697178	−	1.20755i	0.272262	−	0.962223i	$-0.412228\pi$
$522$	351.993	−	5717.58i	0.0295140	−	0.479410i
$523$	8034.14	+	4638.51i	0.671718	+	0.387816i	0.796727	−	0.604339i	$-0.206563\pi$
$523$	8034.14	+	4638.51i	0.671718	+	0.387816i	−0.125009	+	0.992156i	$0.539896\pi$
$524$	−3807.78	+	6595.26i	−0.317449	+	0.549838i
$525$	−2013.00	−	1247.02i	−0.167342	−	0.103665i
$526$	10100.8	+	17495.0i	0.837288	+	1.45023i
$527$			15586.3i			1.28833i
$528$	1173.98	−	3897.88i	0.0967629	−	0.321275i
$529$	−2865.21			−0.235491
$530$	9282.16	−	16077.2i	0.760738	−	1.31764i
$531$	−8118.28	−	5378.04i	−0.663472	−	0.439523i
$532$	−8387.31	−	8392.01i	−0.683526	−	0.683910i
$533$	−12822.0	−	7402.79i	−1.04199	−	0.601596i
$534$	−9032.74	−	9605.93i	−0.731994	−	0.778444i
$535$	−617.613	−	356.579i	−0.0499098	−	0.0288154i
$536$	−942.309	−	544.042i	−0.0759357	−	0.0438415i
$537$	−674.028	+	2237.93i	−0.0541647	+	0.179839i
$538$	2604.27	+	1503.58i	0.208695	+	0.120490i
$539$	−1715.28	−	2974.81i	−0.137073	−	0.237725i
$540$	−9000.40	+	1541.00i	−0.717251	+	0.122804i
$541$	6256.31	−	10836.2i	0.497190	−	0.861158i	−0.502805	−	0.864400i	$-0.667699\pi$
$541$	6256.31	−	10836.2i	0.497190	−	0.861158i	0.999995	+	0.00324160i	$0.00103183\pi$
$542$	15836.5			1.25505
$543$	−10917.6	−	11610.4i	−0.862833	−	0.917585i
$544$			16045.2i			1.26458i
$545$	5439.21	+	9420.99i	0.427505	+	0.740460i
$546$	20378.9	−	10937.4i	1.59732	−	0.857282i
$547$	4213.76	−	7298.44i	0.329373	−	0.570491i	−0.653014	−	0.757346i	$-0.726496\pi$
$547$	4213.76	−	7298.44i	0.329373	−	0.570491i	0.982388	+	0.186854i	$0.0598292\pi$
$548$	11647.4	+	6724.61i	0.907940	+	0.524199i
$549$	8836.04	+	17740.1i	0.686909	+	1.37910i
$550$	−449.553	−	778.648i	−0.0348527	−	0.0603666i
$551$	3499.16	+	6060.73i	0.270543	+	0.468595i
$552$	−4537.63	+	4266.87i	−0.349881	+	0.329003i
$553$	−565.066	+	564.749i	−0.0434522	+	0.0434278i
$554$	8352.73	−	4822.45i	0.640566	−	0.369831i
$555$	−2413.52	−	10259.0i	−0.184592	−	0.784634i
$556$			1517.86i			0.115776i
$557$	17760.6	−	10254.1i	1.35106	−	0.780035i	0.362662	−	0.931921i	$-0.381868\pi$
$557$	17760.6	−	10254.1i	1.35106	−	0.780035i	0.988398	+	0.151886i	$0.0485347\pi$
$558$	1219.95	−	19816.2i	0.0925532	−	1.50338i
$559$		−	20070.9i		−	1.51862i
$560$	12538.2	−	12531.2i	0.946138	−	0.945607i
$561$	−1160.62	+	3853.52i	−0.0873463	+	0.290010i
$562$	13973.9			1.04885
$563$	2255.95	−	3907.43i	0.168876	−	0.292502i	−0.769149	−	0.639069i	$-0.779320\pi$
$563$	2255.95	−	3907.43i	0.168876	−	0.292502i	0.938025	+	0.346568i	$0.112653\pi$
$564$	−454.970	+	427.821i	−0.0339675	+	0.0319407i
$565$	24854.5	−	14349.8i	1.85069	−	1.06849i
$566$	−26252.0			−1.94957
$567$	−1864.59	−	13371.9i	−0.138105	−	0.990418i
$568$	4453.25			0.328969
$569$	−11133.3	+	6427.82i	−0.820268	+	0.473582i	−0.850509	−	0.525960i	$-0.823706\pi$
$569$	−11133.3	+	6427.82i	−0.820268	+	0.473582i	0.0302406	+	0.999543i	$0.490373\pi$
$570$	20345.1	−	19131.1i	1.49502	−	1.40582i
$571$	−3099.39	+	5368.30i	−0.227155	+	0.393444i	−0.956964	−	0.290208i	$-0.906276\pi$
$571$	−3099.39	+	5368.30i	−0.227155	+	0.393444i	0.729809	+	0.683651i	$0.239609\pi$
$572$	3507.95			0.256424
$573$	7793.02	−	25874.7i	0.568164	−	1.88644i
$574$	−3937.78	+	14679.5i	−0.286341	+	1.06744i
$575$			3016.86i			0.218803i
$576$	217.238	−	3528.69i	0.0157145	−	0.255258i
$577$	15660.3	−	9041.50i	1.12989	−	0.652344i	0.185985	−	0.982553i	$-0.440452\pi$
$577$	15660.3	−	9041.50i	1.12989	−	0.652344i	0.943908	+	0.330209i	$0.107119\pi$
$578$		−	3913.12i		−	0.281599i
$579$	−2827.59	−	12019.1i	−0.202954	−	0.862687i
$580$	3276.56	−	1891.72i	0.234572	−	0.135430i
$581$	−7157.45	−	1919.98i	−0.511086	−	0.137099i
$582$	−15238.5	+	14329.2i	−1.08532	+	1.02056i
$583$	2081.59	+	3605.42i	0.147874	+	0.256126i
$584$	3741.00	+	6479.61i	0.265075	+	0.459123i
$585$	9695.32	+	19465.3i	0.685218	+	1.37571i
$586$	11832.5	+	6831.49i	0.834122	+	0.481580i
$587$	−2442.51	+	4230.56i	−0.171743	+	0.297468i	−0.939029	−	0.343837i	$-0.888273\pi$
$587$	−2442.51	+	4230.56i	−0.171743	+	0.297468i	0.767286	+	0.641305i	$0.221607\pi$
$588$	−6493.02	−	6912.81i	−0.455387	−	0.484829i
$589$	12127.5	+	21005.5i	0.848398	+	1.46947i
$590$		−	16101.1i		−	1.12351i
$591$	−527.223	−	560.679i	−0.0366956	−	0.0390241i
$592$	12976.4			0.900893
$593$	−1304.78	+	2259.95i	−0.0903557	+	0.156501i	−0.907661	−	0.419704i	$-0.862134\pi$
$593$	−1304.78	+	2259.95i	−0.0903557	+	0.156501i	0.817305	+	0.576205i	$0.195467\pi$
$594$	1777.21	−	4808.48i	0.122761	−	0.332145i
$595$	−12395.5	+	12388.6i	−0.854063	+	0.853585i
$596$	−8683.43	−	5013.38i	−0.596791	−	0.344557i
$597$	2559.80	−	8499.13i	0.175487	−	0.582657i
$598$	−25518.7	−	14733.3i	−1.74505	−	1.00750i
$599$	13896.7	+	8023.27i	0.947920	+	0.547282i	0.892434	−	0.451177i	$-0.148996\pi$
$599$	13896.7	+	8023.27i	0.947920	+	0.547282i	0.0554860	+	0.998459i	$0.482329\pi$
$600$	856.331	+	910.670i	0.0582659	+	0.0619633i
$601$	6848.07	+	3953.74i	0.464790	+	0.268347i	0.714056	−	0.700088i	$-0.246856\pi$
$601$	6848.07	+	3953.74i	0.464790	+	0.268347i	−0.249266	+	0.968435i	$0.580189\pi$
$602$	−19903.0	+	5327.01i	−1.34748	+	0.360652i
$603$	−2505.05	−	1659.50i	−0.169177	−	0.112073i
$604$	−1065.44	+	1845.40i	−0.0717753	+	0.124318i
$605$	−15054.0			−1.01162
$606$	−3852.49	+	12791.2i	−0.258246	+	0.857436i
$607$			3703.30i			0.247632i	0.992305	+	0.123816i	$0.0395132\pi$
$607$			3703.30i			0.247632i	−0.992305	+	0.123816i	$0.960487\pi$
$608$	12484.6	+	21624.0i	0.832759	+	1.44238i
$609$	2645.41	+	4929.02i	0.176022	+	0.327970i
$610$	−16384.5	+	28378.7i	−1.08752	+	1.88364i
$611$	1288.03	+	743.644i	0.0852833	+	0.0492383i
$612$	−682.993	+	11094.2i	−0.0451117	+	0.732770i
$613$	−4872.57	−	8439.53i	−0.321046	−	0.556068i	0.659658	−	0.751566i	$-0.270701\pi$
$613$	−4872.57	−	8439.53i	−0.321046	−	0.556068i	−0.980704	+	0.195498i	$0.937368\pi$
$614$	−7663.46	−	13273.5i	−0.503700	−	0.872435i
$615$	−13683.0	−	4121.11i	−0.897161	−	0.270210i
$616$	468.688	+	1751.13i	0.0306558	+	0.114537i
$617$	−22722.4	+	13118.8i	−1.48261	+	0.855985i	−0.999805	−	0.0197440i	$-0.993715\pi$
$617$	−22722.4	+	13118.8i	−1.48261	+	0.855985i	−0.482804	+	0.875729i	$0.660382\pi$
$618$	−18862.5	−	5681.06i	−1.22777	−	0.369783i
$619$			5165.08i			0.335383i	0.985839	+	0.167692i	$0.0536313\pi$
$619$			5165.08i			0.335383i	−0.985839	+	0.167692i	$0.946369\pi$
$620$	11356.0	−	6556.41i	0.735596	−	0.424697i
$621$	−13231.5	+	10991.2i	−0.855013	+	0.710241i
$622$			9063.81i			0.584286i
$623$	12436.8	+	3336.17i	0.799791	+	0.214544i
$624$	−26063.7	+	6131.70i	−1.67209	+	0.393373i
$625$	−18095.3			−1.15810
$626$	1497.45	−	2593.65i	0.0956070	−	0.165596i
$627$	1434.23	+	6096.42i	0.0913520	+	0.388305i
$628$	9040.81	−	5219.72i	0.574471	−	0.331671i
$629$	−12828.8			−0.813221
$630$	16729.2	−	14780.5i	1.05795	−	0.934713i
$631$	1350.06			0.0851743			0.0425871	−	0.999093i	$-0.486440\pi$
$631$	1350.06			0.0851743			0.0425871	+	0.999093i	$0.486440\pi$
$632$	365.239	−	210.871i	0.0229880	−	0.0132721i
$633$	−5432.89	−	1636.30i	−0.341134	−	0.102744i
$634$	7543.27	−	13065.3i	0.472526	−	0.818439i
$635$	12556.0			0.784677
$636$	7876.68	+	8376.51i	0.491086	+	0.522249i
$637$	−11303.9	+	19553.7i	−0.703106	+	1.21624i
$638$			2124.05i			0.131805i
$639$	12274.9	+	755.684i	0.759919	+	0.0467831i
$640$	−12513.0	+	7224.38i	−0.772843	+	0.446201i
$641$			18082.9i			1.11424i	0.830431	+	0.557122i	$0.188094\pi$
$641$			18082.9i			1.11424i	−0.830431	+	0.557122i	$0.811906\pi$
$642$	805.564	−	757.496i	0.0495219	−	0.0465669i
$643$	−16884.0	+	9748.00i	−1.03552	+	0.597859i	−0.918562	−	0.395277i	$-0.870649\pi$
$643$	−16884.0	+	9748.00i	−1.03552	+	0.597859i	−0.116961	+	0.993137i	$0.537315\pi$
$644$	−3130.58	+	11670.4i	−0.191556	+	0.714096i
$645$	−4436.35	−	18857.4i	−0.270823	−	1.15117i
$646$	−16997.2	−	29440.0i	−1.03521	−	1.79303i
$647$	8503.93	+	14729.2i	0.516730	+	0.895002i	0.999811	+	0.0194267i	$0.00618409\pi$
$647$	8503.93	+	14729.2i	0.516730	+	0.895002i	−0.483082	+	0.875575i	$0.660483\pi$
$648$	−874.254	+	7073.54i	−0.0529999	+	0.428819i
$649$	3127.04	+	1805.40i	0.189132	+	0.109196i
$650$	−2956.86	+	5121.44i	−0.178427	+	0.309045i
$651$	9168.57	+	17083.2i	0.551988	+	1.02848i
$652$	−5814.22	−	10070.5i	−0.349237	−	0.604896i
$653$		−	4331.50i		−	0.259578i	−0.991542	−	0.129789i	$-0.958570\pi$
$653$		−	4331.50i		−	0.259578i	0.991542	−	0.129789i	$-0.0414301\pi$
$654$	−16419.1	+	3862.72i	−0.981707	+	0.230954i
$655$	17504.9			1.04424
$656$	8797.50	−	15237.7i	0.523604	−	0.906909i
$657$	9212.13	+	18495.2i	0.547031	+	1.09827i
$658$	395.568	−	1474.63i	0.0234359	−	0.0873661i
$659$	2674.86	+	1544.33i	0.158115	+	0.0912875i	0.576970	−	0.816766i	$-0.304235\pi$
$659$	2674.86	+	1544.33i	0.158115	+	0.0912875i	−0.418855	+	0.908053i	$0.637568\pi$
$660$	3295.86	−	775.377i	0.194380	−	0.0457296i
$661$	−19561.4	−	11293.8i	−1.15106	−	0.664564i	−0.201914	−	0.979403i	$-0.564716\pi$
$661$	−19561.4	−	11293.8i	−1.15106	−	0.664564i	−0.949145	+	0.314839i	$0.898050\pi$
$662$	−28094.8	−	16220.6i	−1.64945	−	0.952311i
$663$	25767.1	−	6061.92i	1.50937	−	0.355091i
$664$	3387.91	+	1956.01i	0.198007	+	0.114319i
$665$	−7065.92	+	26340.8i	−0.412037	+	1.53602i
$666$	16310.3	+	1004.12i	0.948968	+	0.0584216i
$667$	3563.52	−	6172.19i	0.206866	−	0.358303i
$668$	7713.41			0.446768
$669$	−6210.60	+	1461.09i	−0.358917	+	0.0844382i
$670$		−	4968.31i		−	0.286482i
$671$	−3674.33	−	6364.12i	−0.211395	−	0.366146i
$672$	9438.51	+	17586.2i	0.541813	+	1.00952i
$673$	3978.45	−	6890.88i	0.227872	−	0.394686i	−0.729305	−	0.684189i	$-0.760156\pi$
$673$	3978.45	−	6890.88i	0.227872	−	0.394686i	0.957177	+	0.289502i	$0.0934898\pi$
$674$	−11381.0	−	6570.85i	−0.650418	−	0.375519i
$675$	2205.85	+	2655.48i	0.125783	+	0.151421i
$676$	−5691.08	−	9857.24i	−0.323798	−	0.560835i
$677$	−5552.77	−	9617.67i	−0.315229	−	0.545993i	0.664257	−	0.747504i	$-0.268748\pi$
$677$	−5552.77	−	9617.67i	−0.315229	−	0.545993i	−0.979486	+	0.201511i	$0.935415\pi$
$678$	10190.7	+	43316.9i	0.577241	+	2.45365i
$679$	5292.38	−	19729.3i	0.299121	−	1.11508i
$680$	8012.05	−	4625.76i	0.451836	−	0.260867i
$681$	8568.16	−	8056.90i	0.482133	−	0.453364i
$682$			7361.60i			0.413329i
$683$	16295.7	−	9408.31i	0.912938	−	0.527085i	0.0315626	−	0.999502i	$-0.489952\pi$
$683$	16295.7	−	9408.31i	0.912938	−	0.527085i	0.881375	+	0.472417i	$0.156618\pi$
$684$	7711.80	+	15482.9i	0.431094	+	0.865505i
$685$		−	30914.1i		−	1.72433i
$686$	22390.3	+	6019.65i	1.24616	+	0.335031i
$687$	18340.3	+	19504.1i	1.01852	+	1.08316i
$688$	23852.3			1.32174
$689$	13691.3	−	23714.1i	0.757037	−	1.31123i
$690$	−27232.4	−	8201.95i	−1.50249	−	0.452526i
$691$	−12726.4	+	7347.58i	−0.700629	+	0.404508i	−0.807582	−	0.589756i	$-0.799224\pi$
$691$	−12726.4	+	7347.58i	−0.700629	+	0.404508i	0.106953	+	0.994264i	$0.465891\pi$
$692$	−9822.69			−0.539599
$693$	994.734	+	4906.33i	0.0545264	+	0.268941i
$694$	34157.1			1.86828
$695$	3021.49	−	1744.46i	0.164909	−	0.0952103i
$696$	−676.282	−	2874.64i	−0.0368310	−	0.156556i
$697$	−8697.38	+	15064.3i	−0.472649	+	0.818653i
$698$	14737.8			0.799190
$699$	2111.29	−	496.697i	0.114243	−	0.0268767i
$700$	2342.17	+	628.285i	0.126465	+	0.0339242i
$701$			2167.47i			0.116782i	0.998294	+	0.0583910i	$0.0185970\pi$
$701$			2167.47i			0.116782i	−0.998294	+	0.0583910i	$0.981403\pi$
$702$	−33234.5	+	5690.24i	−1.78683	+	0.305932i
$703$	−17289.2	+	9981.93i	−0.927560	+	0.535527i
$704$			1310.89i			0.0701788i
$705$	1374.52	+	413.984i	0.0734292	+	0.0221157i
$706$	13775.5	−	7953.30i	0.734346	−	0.423975i
$707$	−3372.87	−	12601.9i	−0.179420	−	0.670356i
$708$	9548.85	+	2875.96i	0.506875	+	0.152663i
$709$	−17149.1	−	29703.1i	−0.908388	−	1.57337i	−0.816303	−	0.577623i	$-0.803980\pi$
$709$	−17149.1	−	29703.1i	−0.908388	−	1.57337i	−0.0920850	−	0.995751i	$-0.529353\pi$
$710$	10167.0	+	17609.8i	0.537411	+	0.930823i
$711$	1042.53	−	519.264i	0.0549898	−	0.0273895i
$712$	−5886.84	−	3398.77i	−0.309858	−	0.178896i
$713$	12350.6	−	21391.8i	0.648714	−	1.12361i
$714$	−12850.1	−	23942.7i	−0.673532	−	1.25495i
$715$	−4031.65	−	6983.02i	−0.210874	−	0.365245i
$716$		−	2393.51i		−	0.124930i
$717$	−8362.11	+	27764.2i	−0.435549	+	1.44613i
$718$	13061.3			0.678893
$719$	−7330.37	+	12696.6i	−0.380218	+	0.658557i	−0.991093	−	0.133170i	$-0.957484\pi$
$719$	−7330.37	+	12696.6i	−0.380218	+	0.658557i	0.610875	+	0.791727i	$0.290818\pi$
$720$	−23132.6	+	11521.9i	−1.19736	+	0.596386i
$721$	18583.3	−	4973.79i	0.959885	−	0.256912i
$722$	−24133.6	−	13933.6i	−1.24399	−	0.718218i
$723$	9873.69	+	10500.2i	0.507893	+	0.540122i
$724$	14134.4	+	8160.48i	0.725552	+	0.418898i
$725$	−1238.72	−	715.173i	−0.0634549	−	0.0366357i
$726$	6731.45	−	22350.0i	0.344115	−	1.14254i
$727$	−9274.34	−	5354.55i	−0.473131	−	0.273162i	0.244418	−	0.969670i	$-0.421403\pi$
$727$	−9274.34	−	5354.55i	−0.473131	−	0.273162i	−0.717550	+	0.696507i	$0.754736\pi$
$728$	8433.33	−	8428.61i	0.429341	−	0.429100i
$729$	−3610.11	+	19349.1i	−0.183413	+	0.983036i
$730$	−17081.8	+	29586.6i	−0.866064	+	1.50007i
$731$	−23580.8			−1.19312
$732$	−13903.6	−	14785.8i	−0.702036	−	0.746585i
$733$		−	15214.2i		−	0.766644i	−0.923615	−	0.383322i	$-0.874780\pi$
$733$		−	15214.2i		−	0.766644i	0.923615	−	0.383322i	$-0.125220\pi$
$734$	−18720.9	−	32425.6i	−0.941421	−	1.63059i
$735$	−6298.46	+	20870.0i	−0.316085	+	1.04735i
$736$	12714.2	−	22021.7i	0.636755	−	1.10289i
$737$	964.907	+	557.089i	0.0482263	+	0.0278435i
$738$	12236.8	−	18471.8i	0.610358	−	0.921351i
$739$	4828.54	+	8363.28i	0.240353	+	0.416304i	0.960815	−	0.277191i	$-0.0894035\pi$
$739$	4828.54	+	8363.28i	0.240353	+	0.416304i	−0.720462	+	0.693495i	$0.756070\pi$
$740$	5396.45	+	9346.92i	0.268078	+	0.464324i
$741$	30009.4	−	28218.7i	1.48775	−	1.39898i
$742$	−27149.5	−	7282.86i	−1.34325	−	0.360326i
$743$	−4935.72	+	2849.64i	−0.243706	+	0.140704i	−0.616879	−	0.787058i	$-0.711603\pi$
$743$	−4935.72	+	2849.64i	−0.243706	+	0.140704i	0.373173	+	0.927762i	$0.378270\pi$
$744$	−2343.89	−	9963.04i	−0.115499	−	0.490944i
$745$			23047.3i			1.13341i
$746$	−31146.3	+	17982.3i	−1.52861	+	0.882546i
$747$	9006.49	+	5966.44i	0.441138	+	0.292236i
$748$		−	4121.41i		−	0.201462i
$749$	−279.775	+	1042.96i	−0.0136485	+	0.0508799i
$750$	6716.03	−	22298.8i	0.326980	−	1.08565i
$751$	34815.7			1.69167			0.845833	−	0.533448i	$-0.179104\pi$
$751$	34815.7			1.69167			0.845833	+	0.533448i	$0.179104\pi$
$752$	−883.748	+	1530.70i	−0.0428550	+	0.0742271i
$753$	−14200.5	+	13353.1i	−0.687243	+	0.646235i
$754$	12098.9	−	6985.29i	0.584370	−	0.337386i
$755$	4898.01			0.236102
$756$	5777.51	+	12561.4i	0.277944	+	0.604304i
$757$	−12225.4			−0.586976			−0.293488	−	0.955963i	$-0.594816\pi$
$757$	−12225.4			−0.586976			−0.293488	+	0.955963i	$0.594816\pi$
$758$	35341.3	−	20404.3i	1.69348	−	0.977728i
$759$	4646.45	−	4369.19i	0.222207	−	0.208948i
$760$	7198.51	−	12468.2i	0.343576	−	0.595091i
$761$	11388.4			0.542482			0.271241	−	0.962512i	$-0.412566\pi$
$761$	11388.4			0.542482			0.271241	+	0.962512i	$0.412566\pi$
$762$	−5614.45	+	18641.3i	−0.266916	+	0.886225i
$763$	11650.5	−	11644.0i	0.552787	−	0.552477i
$764$			27673.4i			1.31046i
$765$	22869.3	−	11390.8i	1.08084	−	0.538348i
$766$	28417.9	−	16407.1i	1.34045	−	0.773906i
$767$		−	23749.4i		−	1.11805i
$768$	−6376.97	−	27106.3i	−0.299621	−	1.27359i
$769$	5063.88	−	2923.63i	0.237462	−	0.137099i	−0.376548	−	0.926397i	$-0.622889\pi$
$769$	5063.88	−	2923.63i	0.237462	−	0.137099i	0.614010	+	0.789299i	$0.289556\pi$
$770$	−5854.57	+	5851.29i	−0.274005	+	0.273852i
$771$	−28435.2	+	26738.4i	−1.32823	+	1.24898i
$772$	6322.26	+	10950.5i	0.294745	+	0.510513i
$773$	−2151.82	−	3727.06i	−0.100124	−	0.173419i	0.811612	−	0.584197i

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)

\(f(q)\)	\(=\)	\(q+(-3.16085 + 1.82492i) q^{2} +(-3.78544 + 3.55956i) q^{3} +(2.66064 - 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 - 18.1593i) q^{6} +(4.78838 + 17.8905i) q^{7} -9.77690i q^{8} +(1.65907 - 26.9490i) q^{9} +O(q^{10})\)	\(q+(-3.16085 + 1.82492i) q^{2} +(-3.78544 + 3.55956i) q^{3} +(2.66064 - 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 - 18.1593i) q^{6} +(4.78838 + 17.8905i) q^{7} -9.77690i q^{8} +(1.65907 - 26.9490i) q^{9} +(38.6615 - 22.3212i) q^{10} +10.0114i q^{11} +(6.33205 + 26.9153i) q^{12} +(57.0263 - 32.9241i) q^{13} +(-47.7841 - 47.8109i) q^{14} +(46.3010 - 43.5383i) q^{15} +(39.1271 + 67.7702i) q^{16} +(-38.6818 - 66.9989i) q^{17} +(43.9356 + 88.2093i) q^{18} +(-104.262 - 60.1959i) q^{19} +(-32.5432 + 56.3665i) q^{20} +(-81.8086 - 50.6790i) q^{21} +(-18.2699 - 31.6444i) q^{22} +122.606i q^{23} +(34.8015 + 37.0098i) q^{24} +24.6062 q^{25} +(-120.168 + 208.136i) q^{26} +(89.6462 + 107.919i) q^{27} +(95.1861 + 25.5337i) q^{28} +(-50.3417 - 29.0648i) q^{29} +(-66.8969 + 222.113i) q^{30} +(-174.476 - 100.734i) q^{31} +(-179.613 - 103.700i) q^{32} +(-35.6361 - 37.8974i) q^{33} +(244.535 + 141.182i) q^{34} +(-58.5684 - 218.826i) q^{35} +(-119.776 - 79.3470i) q^{36} +(82.9121 - 143.608i) q^{37} +439.410 q^{38} +(-98.6739 + 327.621i) q^{39} +119.585i q^{40} +(-112.422 - 194.721i) q^{41} +(351.069 + 10.8948i) q^{42} +(152.402 - 263.969i) q^{43} +(46.1360 + 26.6366i) q^{44} +(-20.2926 + 329.623i) q^{45} +(-223.746 - 387.539i) q^{46} +(11.2933 + 19.5606i) q^{47} +(-389.345 - 117.264i) q^{48} +(-297.143 + 171.333i) q^{49} +(-77.7763 + 44.9042i) q^{50} +(384.914 + 115.930i) q^{51} -350.397i q^{52} +(360.132 - 207.922i) q^{53} +(-480.301 - 177.519i) q^{54} -122.453i q^{55} +(174.914 - 46.8155i) q^{56} +(608.949 - 143.260i) q^{57} +212.163 q^{58} +(180.334 - 312.348i) q^{59} +(-77.4496 - 329.211i) q^{60} +(-635.689 + 367.015i) q^{61} +735.324 q^{62} +(490.076 - 99.3604i) q^{63} +130.940 q^{64} +(-697.509 + 402.707i) q^{65} +(181.800 + 54.7551i) q^{66} +(55.6457 - 96.3811i) q^{67} -411.673 q^{68} +(-436.423 - 464.117i) q^{69} +(584.464 + 584.792i) q^{70} +455.487i q^{71} +(-263.478 - 16.2205i) q^{72} +(-662.747 + 382.637i) q^{73} +605.230i q^{74} +(-93.1451 + 87.5871i) q^{75} +(-554.808 + 320.319i) q^{76} +(-179.109 + 47.9383i) q^{77} +(-285.987 - 1215.63i) q^{78} +(21.5683 + 37.3573i) q^{79} +(-478.578 - 828.921i) q^{80} +(-723.495 - 89.4203i) q^{81} +(710.697 + 410.321i) q^{82} +(-200.064 + 346.522i) q^{83} +(-451.210 + 242.165i) q^{84} +(473.131 + 819.488i) q^{85} +1112.49i q^{86} +(294.023 - 69.1714i) q^{87} +97.8802 q^{88} +(347.632 - 602.117i) q^{89} +(-537.392 - 1078.92i) q^{90} +(862.094 + 862.577i) q^{91} +(565.012 + 326.210i) q^{92} +(1019.04 - 239.737i) q^{93} +(-71.3928 - 41.2186i) q^{94} +(1275.27 + 736.277i) q^{95} +(1049.04 - 246.795i) q^{96} +(-955.178 - 551.472i) q^{97} +(626.554 - 1083.82i) q^{98} +(269.796 + 16.6095i) 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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