LMFDB - Embedded newform 503.2.c.a.2.6

Newspace parameters

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.c (of order $251$, degree $250$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$10250$
Relative dimension:	$41$ over $\Q(\zeta_{251})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{251}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	503.2
Dual form			503.2.c.a.252.6

$q$-expansion

$f(q)$	$=$	$q+(-1.43081 - 1.76164i) q^{2} +(-1.19346 + 1.03295i) q^{3} +(-0.646042 + 3.08364i) q^{4} +(0.511937 + 1.61679i) q^{5} +(3.52731 + 0.624490i) q^{6} +(-1.13380 + 3.29205i) q^{7} +(2.32143 - 1.19567i) q^{8} +(-0.0729611 + 0.503389i) q^{9} +O(q^{10})$	\(q+(-1.43081 - 1.76164i) q^{2} +(-1.19346 + 1.03295i) q^{3} +(-0.646042 + 3.08364i) q^{4} +(0.511937 + 1.61679i) q^{5} +(3.52731 + 0.624490i) q^{6} +(-1.13380 + 3.29205i) q^{7} +(2.32143 - 1.19567i) q^{8} +(-0.0729611 + 0.503389i) q^{9} +(2.11572 - 3.21517i) q^{10} +(-4.01497 + 1.29899i) q^{11} +(-2.41424 - 4.34755i) q^{12} +(2.63886 - 0.890402i) q^{13} +(7.42166 - 2.71296i) q^{14} +(-2.28105 - 1.40078i) q^{15} +(0.343421 + 0.150504i) q^{16} +(-4.32246 - 2.15829i) q^{17} +(0.991183 - 0.591724i) q^{18} +(-2.53140 - 5.67925i) q^{19} +(-5.31635 + 0.534114i) q^{20} +(-2.04739 - 5.10011i) q^{21} +(8.03301 + 5.21431i) q^{22} +(0.991105 - 3.42581i) q^{23} +(-1.53548 + 3.82492i) q^{24} +(1.73683 - 1.22245i) q^{25} +(-5.34427 - 3.37471i) q^{26} +(-2.98614 - 4.66401i) q^{27} +(-9.41903 - 5.62304i) q^{28} +(-0.577953 + 4.83770i) q^{29} +(0.796090 + 6.02263i) q^{30} +(-0.390950 - 4.79481i) q^{31} +(-1.61472 - 5.85489i) q^{32} +(3.44992 - 5.69757i) q^{33} +(2.38250 + 10.7027i) q^{34} +(-5.90300 - 0.147798i) q^{35} +(-1.50514 - 0.550197i) q^{36} +(2.72917 + 3.44749i) q^{37} +(-6.38282 + 12.5853i) q^{38} +(-2.22963 + 3.78848i) q^{39} +(3.12157 + 3.14117i) q^{40} +(-2.36556 + 12.0401i) q^{41} +(-6.05512 + 10.9041i) q^{42} +(1.51231 - 8.24124i) q^{43} +(-1.41178 - 13.2199i) q^{44} +(-0.851227 + 0.139740i) q^{45} +(-7.45312 + 3.15571i) q^{46} +(-0.677057 + 0.0254347i) q^{47} +(-0.565324 + 0.175118i) q^{48} +(-4.03662 - 3.15466i) q^{49} +(-4.63859 - 1.31057i) q^{50} +(7.38811 - 1.88906i) q^{51} +(1.04087 + 8.71253i) q^{52} +(-0.739535 + 1.65916i) q^{53} +(-3.94370 + 11.9338i) q^{54} +(-4.15560 - 5.82637i) q^{55} +(1.30416 + 8.99793i) q^{56} +(8.88754 + 4.16315i) q^{57} +(9.34922 - 5.90369i) q^{58} +(3.36540 - 8.08897i) q^{59} +(5.79315 - 6.12899i) q^{60} +(3.38088 + 5.58355i) q^{61} +(-7.88735 + 7.54918i) q^{62} +(-1.57446 - 0.810935i) q^{63} +(-7.56839 + 10.6113i) q^{64} +(2.79052 + 3.81065i) q^{65} +(-14.9733 + 2.07463i) q^{66} +(-5.05245 + 3.10267i) q^{67} +(9.44788 - 11.9346i) q^{68} +(2.35585 + 5.11234i) q^{69} +(8.18571 + 10.6104i) q^{70} +(1.24570 + 7.89702i) q^{71} +(0.432512 + 1.25582i) q^{72} +(-2.58168 - 2.47099i) q^{73} +(2.16830 - 9.74051i) q^{74} +(-0.810107 + 3.25302i) q^{75} +(19.1482 - 4.13691i) q^{76} +(0.275834 - 14.6903i) q^{77} +(9.86412 - 1.49279i) q^{78} +(0.643384 + 11.4110i) q^{79} +(-0.0675233 + 0.632289i) q^{80} +(6.91841 + 2.04854i) q^{81} +(24.5950 - 13.0598i) q^{82} +(-8.03251 - 15.3585i) q^{83} +(17.0496 - 3.01853i) q^{84} +(1.27668 - 8.09342i) q^{85} +(-16.6819 + 9.12751i) q^{86} +(-4.30736 - 6.37062i) q^{87} +(-7.76732 + 7.81608i) q^{88} +(-3.25521 - 12.4071i) q^{89} +(1.46412 + 1.29961i) q^{90} +(-0.0606848 + 9.69679i) q^{91} +(9.92367 + 5.26943i) q^{92} +(5.41941 + 5.31860i) q^{93} +(1.01355 + 1.15634i) q^{94} +(7.88624 - 7.00017i) q^{95} +(7.97494 + 5.31967i) q^{96} +(0.373284 + 1.58318i) q^{97} +(0.218275 + 11.6248i) q^{98} +(-0.360960 - 2.11587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} + O(q^{10}) $	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} - 233q^{10} - 239q^{11} - 239q^{12} - 245q^{13} - 223q^{14} - 231q^{15} - 263q^{16} - 243q^{17} - 217q^{18} - 229q^{19} - 195q^{20} - 215q^{21} - 233q^{22} - 241q^{23} - 181q^{24} - 280q^{25} - 215q^{26} - 237q^{27} - 185q^{28} - 217q^{29} - 159q^{30} - 219q^{31} - 185q^{32} - 209q^{33} - 167q^{34} - 187q^{35} - 203q^{36} - 237q^{37} - 161q^{38} - 197q^{39} - 135q^{40} - 209q^{41} - 117q^{42} - 221q^{43} - 147q^{44} - 167q^{45} - 167q^{46} - 195q^{47} - 141q^{48} - 234q^{49} - 145q^{50} - 177q^{51} - 179q^{52} - 211q^{53} - 83q^{54} - 165q^{55} - 125q^{56} - 177q^{57} - 205q^{58} - 189q^{59} - 27q^{60} - 193q^{61} - 143q^{62} - 159q^{63} - 185q^{64} - 155q^{65} - 97q^{66} - 201q^{67} - 155q^{68} - 113q^{69} - 123q^{70} - 153q^{71} - 21q^{72} - 213q^{73} - 83q^{74} - 161q^{75} - 97q^{76} - 139q^{77} - 43q^{78} - 191q^{79} + 3q^{80} - 188q^{81} - 97q^{82} - 161q^{83} + 67q^{84} - 159q^{85} - 121q^{86} - 121q^{87} - 143q^{88} - 155q^{89} + 115q^{90} - 137q^{91} - 119q^{92} - 123q^{93} - 99q^{94} - 181q^{95} + 67q^{96} - 229q^{97} - 63q^{98} - 85q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/503\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{101}{251}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.43081	−	1.76164i	−1.01174	−	1.24567i	−0.969124	−	0.246575i	$-0.920695\pi$
$2$	−1.43081	−	1.76164i	−1.01174	−	1.24567i	−0.0426127	−	0.999092i	$-0.513568\pi$
$3$	−1.19346	+	1.03295i	−0.689047	+	0.596376i	−0.927072	−	0.374882i	$-0.877683\pi$
$3$	−1.19346	+	1.03295i	−0.689047	+	0.596376i	0.238026	+	0.971259i	$0.423500\pi$
$4$	−0.646042	+	3.08364i	−0.323021	+	1.54182i
$5$	0.511937	+	1.61679i	0.228945	+	0.723052i	0.996615	+	0.0822066i	$0.0261967\pi$
$5$	0.511937	+	1.61679i	0.228945	+	0.723052i	−0.767670	+	0.640845i	$0.778584\pi$
$6$	3.52731	+	0.624490i	1.44002	+	0.254947i
$7$	−1.13380	+	3.29205i	−0.428536	+	1.24428i	0.497705	+	0.867347i	$0.334176\pi$
$7$	−1.13380	+	3.29205i	−0.428536	+	1.24428i	−0.926241	+	0.376932i	$0.876979\pi$
$8$	2.32143	−	1.19567i	0.820751	−	0.422733i
$9$	−0.0729611	+	0.503389i	−0.0243204	+	0.167796i
$10$	2.11572	−	3.21517i	0.669049	−	1.01673i
$11$	−4.01497	+	1.29899i	−1.21056	+	0.391660i	−0.842782	−	0.538255i	$-0.819084\pi$
$11$	−4.01497	+	1.29899i	−1.21056	+	0.391660i	−0.367776	+	0.929915i	$0.619881\pi$
$12$	−2.41424	−	4.34755i	−0.696930	−	1.25503i
$13$	2.63886	−	0.890402i	0.731887	−	0.246953i	0.0710395	−	0.997474i	$-0.477368\pi$
$13$	2.63886	−	0.890402i	0.731887	−	0.246953i	0.660847	+	0.750520i	$0.270197\pi$
$14$	7.42166	−	2.71296i	1.98352	−	0.725068i
$15$	−2.28105	−	1.40078i	−0.588965	−	0.361679i
$16$	0.343421	+	0.150504i	0.0858553	+	0.0376259i
$17$	−4.32246	−	2.15829i	−1.04835	−	0.523462i	−0.162150	−	0.986766i	$-0.551843\pi$
$17$	−4.32246	−	2.15829i	−1.04835	−	0.523462i	−0.886199	+	0.463304i	$0.846664\pi$
$18$	0.991183	−	0.591724i	0.233624	−	0.139471i
$19$	−2.53140	−	5.67925i	−0.580744	−	1.30291i	−0.930577	−	0.366096i	$-0.880694\pi$
$19$	−2.53140	−	5.67925i	−0.580744	−	1.30291i	0.349833	−	0.936812i	$-0.386238\pi$
$20$	−5.31635	+	0.534114i	−1.18877	+	0.119432i
$21$	−2.04739	−	5.10011i	−0.446777	−	1.11294i
$22$	8.03301	+	5.21431i	1.71264	+	1.11170i
$23$	0.991105	−	3.42581i	0.206660	−	0.714330i	−0.788410	−	0.615150i	$-0.789095\pi$
$23$	0.991105	−	3.42581i	0.206660	−	0.714330i	0.995070	−	0.0991795i	$-0.0316218\pi$
$24$	−1.53548	+	3.82492i	−0.313428	+	0.780759i
$25$	1.73683	−	1.22245i	0.347366	−	0.244490i
$26$	−5.34427	−	3.37471i	−1.04810	−	0.661836i
$27$	−2.98614	−	4.66401i	−0.574684	−	0.897590i
$28$	−9.41903	−	5.62304i	−1.78003	−	1.06265i
$29$	−0.577953	+	4.83770i	−0.107323	+	0.898339i	0.831875	+	0.554963i	$0.187268\pi$
$29$	−0.577953	+	4.83770i	−0.107323	+	0.898339i	−0.939198	+	0.343376i	$0.888430\pi$
$30$	0.796090	+	6.02263i	0.145346	+	1.09958i
$31$	−0.390950	−	4.79481i	−0.0702166	−	0.861174i	−0.933991	−	0.357296i	$-0.883699\pi$
$31$	−0.390950	−	4.79481i	−0.0702166	−	0.861174i	0.863775	−	0.503878i	$-0.168094\pi$
$32$	−1.61472	−	5.85489i	−0.285445	−	1.03501i
$33$	3.44992	−	5.69757i	0.600554	−	0.991820i
$34$	2.38250	+	10.7027i	0.408595	+	1.83550i
$35$	−5.90300	−	0.147798i	−0.997789	−	0.0249825i
$36$	−1.50514	−	0.550197i	−0.250856	−	0.0916995i
$37$	2.72917	+	3.44749i	0.448673	+	0.566764i	0.955389	−	0.295349i	$-0.0954359\pi$
$37$	2.72917	+	3.44749i	0.448673	+	0.566764i	−0.506717	+	0.862112i	$0.669141\pi$
$38$	−6.38282	+	12.5853i	−1.03543	+	2.04161i
$39$	−2.22963	+	3.78848i	−0.357027	+	0.606642i
$40$	3.12157	+	3.14117i	0.493564	+	0.496663i
$41$	−2.36556	+	12.0401i	−0.369439	+	1.88035i	0.0961850	+	0.995363i	$0.469336\pi$
$41$	−2.36556	+	12.0401i	−0.369439	+	1.88035i	−0.465624	+	0.884983i	$0.654170\pi$
$42$	−6.05512	+	10.9041i	−0.934326	+	1.68253i
$43$	1.51231	−	8.24124i	0.230626	−	1.25678i	−0.641358	−	0.767242i	$-0.721629\pi$
$43$	1.51231	−	8.24124i	0.230626	−	1.25678i	0.871984	−	0.489535i	$-0.162834\pi$
$44$	−1.41178	−	13.2199i	−0.212834	−	1.99298i
$45$	−0.851227	+	0.139740i	−0.126893	+	0.0208312i
$46$	−7.45312	+	3.15571i	−1.09890	+	0.465284i
$47$	−0.677057	+	0.0254347i	−0.0987588	+	0.00371003i	−0.0868737	−	0.996219i	$-0.527688\pi$
$47$	−0.677057	+	0.0254347i	−0.0987588	+	0.00371003i	−0.0118852	+	0.999929i	$0.503783\pi$
$48$	−0.565324	+	0.175118i	−0.0815975	+	0.0252761i
$49$	−4.03662	−	3.15466i	−0.576661	−	0.450666i
$50$	−4.63859	−	1.31057i	−0.655996	−	0.185342i
$51$	7.38811	−	1.88906i	1.03454	−	0.264521i
$52$	1.04087	+	8.71253i	0.144343	+	1.20821i
$53$	−0.739535	+	1.65916i	−0.101583	+	0.227903i	−0.957031	−	0.289985i	$-0.906350\pi$
$53$	−0.739535	+	1.65916i	−0.101583	+	0.227903i	0.855448	+	0.517888i	$0.173282\pi$
$54$	−3.94370	+	11.9338i	−0.536669	+	1.62399i
$55$	−4.15560	−	5.82637i	−0.560341	−	0.785627i
$56$	1.30416	+	8.99793i	0.174276	+	1.20240i
$57$	8.88754	+	4.16315i	1.17718	+	0.551423i
$58$	9.34922	−	5.90369i	1.22761	−	0.775193i
$59$	3.36540	−	8.08897i	0.438137	−	1.05309i	−0.539347	−	0.842084i	$-0.681329\pi$
$59$	3.36540	−	8.08897i	0.438137	−	1.05309i	0.977484	−	0.211010i	$-0.0676753\pi$
$60$	5.79315	−	6.12899i	0.747893	−	0.791249i
$61$	3.38088	+	5.58355i	0.432878	+	0.714901i	0.993582	−	0.113115i	$-0.0360830\pi$
$61$	3.38088	+	5.58355i	0.432878	+	0.714901i	−0.560704	+	0.828016i	$0.689469\pi$
$62$	−7.88735	+	7.54918i	−1.00169	+	0.958747i
$63$	−1.57446	−	0.810935i	−0.198363	−	0.102168i
$64$	−7.56839	+	10.6113i	−0.946049	+	1.32641i
$65$	2.79052	+	3.81065i	0.346122	+	0.472653i
$66$	−14.9733	+	2.07463i	−1.84308	+	0.255370i
$67$	−5.05245	+	3.10267i	−0.617255	+	0.379052i	−0.796400	−	0.604771i	$-0.793265\pi$
$67$	−5.05245	+	3.10267i	−0.617255	+	0.379052i	0.179144	+	0.983823i	$0.442667\pi$
$68$	9.44788	−	11.9346i	1.14572	−	1.44728i
$69$	2.35585	+	5.11234i	0.283611	+	0.615454i
$70$	8.18571	+	10.6104i	0.978379	+	1.26819i
$71$	1.24570	+	7.89702i	0.147837	+	0.937204i	0.943478	+	0.331435i	$0.107533\pi$
$71$	1.24570	+	7.89702i	0.147837	+	0.937204i	−0.795641	+	0.605769i	$0.792866\pi$
$72$	0.432512	+	1.25582i	0.0509720	+	0.148000i
$73$	−2.58168	−	2.47099i	−0.302163	−	0.289207i	0.525079	−	0.851053i	$-0.324036\pi$
$73$	−2.58168	−	2.47099i	−0.302163	−	0.289207i	−0.827242	+	0.561846i	$0.810091\pi$
$74$	2.16830	−	9.74051i	0.252060	−	1.13231i
$75$	−0.810107	+	3.25302i	−0.0935431	+	0.375626i
$76$	19.1482	−	4.13691i	2.19645	−	0.474537i
$77$	0.275834	−	14.6903i	0.0314342	−	1.67411i
$78$	9.86412	−	1.49279i	1.11689	−	0.169025i
$79$	0.643384	+	11.4110i	0.0723863	+	1.28383i	0.800899	+	0.598800i	$0.204355\pi$
$79$	0.643384	+	11.4110i	0.0723863	+	1.28383i	−0.728512	+	0.685033i	$0.759788\pi$
$80$	−0.0675233	+	0.632289i	−0.00754933	+	0.0706920i
$81$	6.91841	+	2.04854i	0.768713	+	0.227616i
$82$	24.5950	−	13.0598i	2.71606	−	1.44222i
$83$	−8.03251	−	15.3585i	−0.881683	−	1.68582i	−0.714198	−	0.699944i	$-0.753208\pi$
$83$	−8.03251	−	15.3585i	−0.881683	−	1.68582i	−0.167485	−	0.985875i	$-0.553565\pi$
$84$	17.0496	−	3.01853i	1.86027	−	0.329349i
$85$	1.27668	−	8.09342i	0.138475	−	0.877855i
$86$	−16.6819	+	9.12751i	−1.79886	+	0.984244i
$87$	−4.30736	−	6.37062i	−0.461797	−	0.683002i
$88$	−7.76732	+	7.81608i	−0.827999	+	0.833197i
$89$	−3.25521	−	12.4071i	−0.345052	−	1.31515i	−0.881888	−	0.471460i	$-0.843727\pi$
$89$	−3.25521	−	12.4071i	−0.345052	−	1.31515i	0.536836	−	0.843687i	$-0.319619\pi$
$90$	1.46412	+	1.29961i	0.154332	+	0.136991i
$91$	−0.0606848	+	9.69679i	−0.00636149	+	1.01650i
$92$	9.92367	+	5.26943i	1.03461	+	0.549376i
$93$	5.41941	+	5.31860i	0.561966	+	0.551513i
$94$	1.01355	+	1.15634i	0.104539	+	0.119267i
$95$	7.88624	−	7.00017i	0.809112	−	0.718202i
$96$	7.97494	+	5.31967i	0.813939	+	0.542936i
$97$	0.373284	+	1.58318i	0.0379012	+	0.160748i	0.988938	−	0.148330i	$-0.0473899\pi$
$97$	0.373284	+	1.58318i	0.0379012	+	0.160748i	−0.951037	+	0.309078i	$0.899980\pi$
$98$	0.218275	+	11.6248i	0.0220491	+	1.17428i
$99$	−0.360960	−	2.11587i	−0.0362778	−	0.212653i
$100$	2.64754	+	6.14552i	0.264754	+	0.614552i
$101$	−13.2055	+	5.20549i	−1.31400	+	0.517966i	−0.916645	−	0.399701i	$-0.869114\pi$
$101$	−13.2055	+	5.20549i	−1.31400	+	0.517966i	−0.397350	+	0.917667i	$0.630070\pi$
$102$	−13.8988	−	10.3123i	−1.37619	−	1.02107i
$103$	−5.17221	+	1.04986i	−0.509633	+	0.103446i	−0.446900	−	0.894584i	$-0.647472\pi$
$103$	−5.17221	+	1.04986i	−0.509633	+	0.103446i	−0.0627335	+	0.998030i	$0.519982\pi$
$104$	5.06130	−	5.22221i	0.496302	−	0.512079i
$105$	7.19768	−	5.92113i	0.702422	−	0.577844i
$106$	3.98097	−	1.07115i	0.386666	−	0.104039i
$107$	−2.61187	−	0.0981189i	−0.252499	−	0.00948552i	−0.0890101	−	0.996031i	$-0.528370\pi$
$107$	−2.61187	−	0.0981189i	−0.252499	−	0.00948552i	−0.163489	+	0.986545i	$0.552275\pi$
$108$	16.3113	−	6.19506i	1.56956	−	0.596119i
$109$	−3.42106	−	3.61938i	−0.327678	−	0.346674i	0.541924	−	0.840428i	$-0.317696\pi$
$109$	−3.42106	−	3.61938i	−0.327678	−	0.346674i	−0.869602	+	0.493754i	$0.835624\pi$
$110$	−4.31807	+	15.6571i	−0.411712	+	1.49285i
$111$	−6.81826	−	1.29535i	−0.647161	−	0.122949i
$112$	−0.884836	+	0.959919i	−0.0836092	+	0.0907038i
$113$	−6.36167	−	12.9427i	−0.598456	−	1.21755i	−0.958628	−	0.284661i	$-0.908119\pi$
$113$	−6.36167	−	12.9427i	−0.598456	−	1.21755i	0.360173	−	0.932886i	$-0.382718\pi$
$114$	−5.38242	−	21.6133i	−0.504110	−	2.02427i
$115$	6.04620	−	0.151384i	0.563811	−	0.0141166i
$116$	−14.5444	−	4.90756i	−1.35041	−	0.455655i
$117$	0.255685	+	1.39334i	0.0236381	+	0.128814i
$118$	−19.0651	+	5.64517i	−1.75508	+	0.519680i
$119$	12.0060	−	11.7827i	1.10059	−	1.08012i
$120$	−6.97017	−	0.524431i	−0.636287	−	0.0478738i
$121$	5.51724	−	3.98744i	0.501567	−	0.362495i
$122$	4.99880	−	13.9449i	0.452570	−	1.26251i
$123$	−9.61365	−	16.8129i	−0.866834	−	1.51597i
$124$	15.0381	+	1.89210i	1.35046	+	0.169916i
$125$	9.61166	+	7.31969i	0.859693	+	0.654693i
$126$	0.824181	+	3.93392i	0.0734238	+	0.350462i
$127$	−13.1950	+	7.43573i	−1.17087	+	0.659815i	−0.949004	−	0.315263i	$-0.897907\pi$
$127$	−13.1950	+	7.43573i	−1.17087	+	0.659815i	−0.221864	+	0.975078i	$0.571214\pi$
$128$	17.3990	−	1.09028i	1.53787	−	0.0963680i
$129$	6.70793	+	11.3978i	0.590600	+	1.00352i
$130$	2.72028	−	10.3682i	0.238585	−	0.909353i
$131$	−7.09436	+	4.73228i	−0.619837	+	0.413461i	−0.824893	−	0.565289i	$-0.808764\pi$
$131$	−7.09436	+	4.73228i	−0.619837	+	0.413461i	0.205056	+	0.978750i	$0.434262\pi$
$132$	15.3405	+	14.3192i	1.33522	+	1.24633i
$133$	21.5665	−	1.89438i	1.87005	−	0.164263i
$134$	12.6949	+	4.46125i	1.09667	+	0.385394i
$135$	6.01203	−	7.21565i	0.517433	−	0.621025i
$136$	−12.6149	+	0.157900i	−1.08172	+	0.0135398i
$137$	−6.93381	−	17.9178i	−0.592395	−	1.53082i	−0.829019	−	0.559220i	$-0.811101\pi$
$137$	−6.93381	−	17.9178i	−0.592395	−	1.53082i	0.236624	−	0.971601i	$-0.423959\pi$
$138$	5.63532	−	11.4650i	0.479710	−	0.975962i
$139$	21.9855	+	4.74990i	1.86478	+	0.402882i	0.995768	−	0.0919044i	$-0.0292954\pi$
$139$	21.9855	+	4.74990i	1.86478	+	0.402882i	0.869015	+	0.494786i	$0.164754\pi$
$140$	4.26934	−	18.1073i	0.360825	−	1.53034i
$141$	0.781770	−	0.729724i	0.0658369	−	0.0614538i
$142$	12.1293	−	13.4936i	1.01787	−	1.13236i
$143$	−9.43829	+	7.00278i	−0.789270	+	0.585602i
$144$	−0.100818	+	0.161894i	−0.00840152	+	0.0134911i
$145$	−8.11744	+	1.54217i	−0.674116	+	0.128070i
$146$	−0.659096	+	8.08350i	−0.0545472	+	0.668996i
$147$	8.07619	−	0.404674i	0.666113	−	0.0333770i
$148$	−12.3940	+	6.18856i	−1.01878	+	0.508697i
$149$	0.307972	−	0.481016i	0.0252300	−	0.0394064i	−0.829330	−	0.558760i	$-0.811277\pi$
$149$	0.307972	−	0.481016i	0.0252300	−	0.0394064i	0.854560	+	0.519353i	$0.173827\pi$
$150$	6.88975	−	3.22734i	0.562546	−	0.263511i
$151$	−6.67463	−	10.1432i	−0.543174	−	0.825439i	0.454698	−	0.890646i	$-0.349747\pi$
$151$	−6.67463	−	10.1432i	−0.543174	−	0.825439i	−0.997872	+	0.0652069i	$0.979229\pi$
$152$	−12.6670	−	10.1573i	−1.02743	−	0.823864i
$153$	1.40183	−	2.01841i	0.113331	−	0.163178i
$154$	−26.2736	+	20.5331i	−2.11719	+	1.65460i
$155$	7.55208	−	3.08672i	0.606597	−	0.247932i
$156$	−10.2419	−	9.32292i	−0.820007	−	0.746431i
$157$	−6.78984	+	14.2620i	−0.541888	+	1.13823i	0.430009	+	0.902824i	$0.358510\pi$
$157$	−6.78984	+	14.2620i	−0.541888	+	1.13823i	−0.971897	+	0.235405i	$0.924358\pi$
$158$	19.1814	−	17.4603i	1.52599	−	1.38907i
$159$	−0.831227	−	2.74405i	−0.0659206	−	0.217617i
$160$	8.63951	−	5.60800i	0.683013	−	0.443351i
$161$	10.1542	+	7.14695i	0.800264	+	0.563258i
$162$	−6.29015	−	15.1188i	−0.494201	−	1.18785i
$163$	−2.40656	−	0.914015i	−0.188497	−	0.0715911i	0.258998	−	0.965878i	$-0.416608\pi$
$163$	−2.40656	−	0.914015i	−0.188497	−	0.0715911i	−0.447494	+	0.894287i	$0.647684\pi$
$164$	−35.5991	−	15.0730i	−2.77982	−	1.17700i
$165$	10.9779	+	2.66101i	0.854631	+	0.207160i
$166$	−15.5632	+	36.1256i	−1.20794	+	2.80389i
$167$	−0.326039	+	10.4162i	−0.0252296	+	0.806033i	0.902043	+	0.431646i	$0.142067\pi$
$167$	−0.326039	+	10.4162i	−0.0252296	+	0.806033i	−0.927273	+	0.374387i	$0.877853\pi$
$168$	−10.8509	−	9.39157i	−0.837166	−	0.724575i
$169$	−4.17167	+	3.17691i	−0.320898	+	0.244378i
$170$	−16.0844	+	9.33111i	−1.23362	+	0.715663i
$171$	3.04356	−	0.859916i	0.232747	−	0.0657594i
$172$	24.4360	+	9.98762i	1.86323	+	0.761549i
$173$	0.755955	+	1.58787i	0.0574742	+	0.120724i	0.929616	−	0.368528i	$-0.120138\pi$
$173$	0.755955	+	1.58787i	0.0574742	+	0.120724i	−0.872142	+	0.489252i	$0.837270\pi$
$174$	−5.05972	+	16.7032i	−0.383576	+	1.26626i
$175$	2.05515	+	7.10375i	0.155355	+	0.536993i
$176$	−1.57433	−	0.158167i	−0.118669	−	0.0119223i
$177$	4.33905	+	13.1302i	0.326143	+	0.986926i
$178$	−17.1992	+	23.4867i	−1.28913	+	1.76040i
$179$	−0.848603	+	1.57427i	−0.0634275	+	0.117666i	−0.910002	−	0.414604i	$-0.863920\pi$
$179$	−0.848603	+	1.57427i	−0.0634275	+	0.117666i	0.846574	+	0.532271i	$0.178661\pi$
$180$	0.119019	−	2.71516i	0.00887118	−	0.202376i
$181$	−0.396740	−	5.75414i	−0.0294894	−	0.427702i	−0.989186	−	0.146664i	$-0.953146\pi$
$181$	−0.396740	−	5.75414i	−0.0294894	−	0.427702i	0.959697	−	0.281037i	$-0.0906785\pi$
$182$	17.1691	−	13.7674i	1.27266	−	1.02051i
$183$	−9.80252	−	3.17147i	−0.724623	−	0.234442i
$184$	−1.79534	−	9.13781i	−0.132354	−	0.673649i
$185$	−4.17671	+	6.17739i	−0.307078	+	0.454171i
$186$	1.61531	−	17.1570i	0.118440	−	1.25801i
$187$	20.1581	+	3.05063i	1.47411	+	0.223084i
$188$	0.358975	−	2.10423i	0.0261810	−	0.153467i
$189$	18.7399	−	4.54248i	1.36312	−	0.330417i
$190$	−23.6155	−	3.87680i	−1.71325	−	0.281252i
$191$	−1.42085	+	25.2000i	−0.102809	+	1.82341i	0.355570	+	0.934650i	$0.384287\pi$
$191$	−1.42085	+	25.2000i	−0.102809	+	1.82341i	−0.458379	+	0.888757i	$0.651570\pi$
$192$	−1.92836	−	20.4820i	−0.139167	−	1.47816i
$193$	−7.51407	−	4.11132i	−0.540875	−	0.295940i	0.186184	−	0.982515i	$-0.440388\pi$
$193$	−7.51407	−	4.11132i	−0.540875	−	0.295940i	−0.727059	+	0.686575i	$0.759113\pi$
$194$	2.25490	−	2.92283i	0.161892	−	0.209847i
$195$	−7.26662	−	1.66539i	−0.520373	−	0.119261i
$196$	12.3357	−	10.4095i	0.881120	−	0.743534i
$197$	15.6380	−	1.17659i	1.11416	−	0.0838285i	0.494851	−	0.868978i	$-0.335222\pi$
$197$	15.6380	−	1.17659i	1.11416	−	0.0838285i	0.619307	+	0.785149i	$0.287414\pi$
$198$	−3.21093	+	3.66329i	−0.228191	+	0.260338i
$199$	0.00228033	+	0.364372i	0.000161648	+	0.0258297i	0.999978	+	0.00665724i	$0.00211908\pi$
$199$	0.00228033	+	0.364372i	0.000161648	+	0.0258297i	−0.999816	+	0.0191724i	$0.993897\pi$
$200$	2.57029	−	4.91451i	0.181747	−	0.347508i
$201$	2.82500	−	8.92188i	0.199260	−	0.629301i
$202$	28.0648	+	15.8152i	1.97463	+	1.11276i
$203$	−15.2707	−	7.38764i	−1.07179	−	0.518511i
$204$	1.05216	+	24.0027i	0.0736660	+	1.68053i
$205$	−20.6773	+	2.33914i	−1.44417	+	0.163372i
$206$	9.24994	+	7.60941i	0.644474	+	0.530173i
$207$	1.65220	+	0.748862i	0.114836	+	0.0520495i
$208$	1.04025	+	0.0913743i	0.0721282	+	0.00633567i
$209$	17.5408	+	19.5137i	1.21332	+	1.34979i
$210$	−20.7294	−	4.20769i	−1.43047	−	0.290358i
$211$	−19.1382	+	13.1152i	−1.31753	+	0.902885i	−0.998986	−	0.0450227i	$-0.985664\pi$
$211$	−19.1382	+	13.1152i	−1.31753	+	0.902885i	−0.318544	+	0.947908i	$0.603194\pi$
$212$	−4.63848	−	3.35235i	−0.318572	−	0.230240i
$213$	−9.64396	−	8.13806i	−0.660793	−	0.557611i
$214$	3.56424	+	4.74156i	0.243646	+	0.324126i
$215$	14.0986	−	1.77389i	0.961515	−	0.120979i
$216$	−12.5087	−	7.25676i	−0.851112	−	0.493760i
$217$	16.2280	+	4.14933i	1.10163	+	0.281675i
$218$	−1.48115	+	11.2053i	−0.100316	+	0.758920i
$219$	5.63356	+	0.282281i	0.380681	+	0.0190748i
$220$	20.6511	−	9.05032i	1.39230	−	0.610172i
$221$	−13.3281	−	1.84668i	−0.896544	−	0.124221i
$222$	7.47371	+	13.8647i	0.501603	+	0.930539i
$223$	2.87630	−	1.39149i	0.192611	−	0.0931813i	−0.336689	−	0.941616i	$-0.609307\pi$
$223$	2.87630	−	1.39149i	0.192611	−	0.0931813i	0.529300	+	0.848435i	$0.322455\pi$
$224$	21.1054	+	1.32253i	1.41016	+	0.0883655i
$225$	0.488648	+	0.963492i	0.0325765	+	0.0642328i
$226$	−13.6980	+	29.7255i	−0.911179	+	1.97731i
$227$	−10.7419	+	2.46188i	−0.712967	+	0.163401i	−0.564400	−	0.825501i	$-0.690892\pi$
$227$	−10.7419	+	2.46188i	−0.712967	+	0.163401i	−0.148567	+	0.988902i	$0.547466\pi$
$228$	−18.5794	+	24.7164i	−1.23045	+	1.63689i
$229$	5.08440	−	8.89191i	0.335987	−	0.587594i	−0.648883	−	0.760888i	$-0.724764\pi$
$229$	5.08440	−	8.89191i	0.335987	−	0.587594i	0.984870	+	0.173294i	$0.0554410\pi$
$230$	−8.91765	−	10.4346i	−0.588013	−	0.688038i
$231$	14.8452	+	17.8172i	0.976741	+	1.17229i
$232$	4.44261	+	11.9214i	0.291671	+	0.782681i
$233$	−20.2584	−	0.253574i	−1.32717	−	0.0166122i	−0.654223	−	0.756301i	$-0.727004\pi$
$233$	−20.2584	−	0.253574i	−1.32717	−	0.0166122i	−0.672949	+	0.739689i	$0.734972\pi$
$234$	2.08872	−	2.44403i	0.136544	−	0.159771i
$235$	−0.387733	−	1.08164i	−0.0252929	−	0.0705584i
$236$	22.7693	+	15.6035i	1.48216	+	1.01570i
$237$	−12.5548	−	12.9540i	−0.815525	−	0.841451i
$238$	−37.9351	−	4.29144i	−2.45897	−	0.278173i
$239$	−1.24578	+	18.0682i	−0.0805826	+	1.16873i	0.768278	+	0.640117i	$0.221114\pi$
$239$	−1.24578	+	18.0682i	−0.0805826	+	1.16873i	−0.848860	+	0.528617i	$0.822711\pi$
$240$	−0.572539	−	0.824363i	−0.0369572	−	0.0532124i
$241$	−19.1465	−	5.93091i	−1.23333	−	0.382044i	−0.390694	−	0.920521i	$-0.627765\pi$
$241$	−19.1465	−	5.93091i	−1.23333	−	0.382044i	−0.842640	+	0.538477i	$0.819000\pi$
$242$	−14.9186	−	4.01410i	−0.959002	−	0.258036i
$243$	4.75942	−	2.15721i	0.305317	−	0.138385i
$244$	−19.4019	+	6.81823i	−1.24208	+	0.436493i
$245$	3.03394	−	8.14137i	0.193831	−	0.520133i
$246$	−15.8630	+	40.9919i	−1.01139	+	2.61355i
$247$	−11.7368	−	12.7327i	−0.746796	−	0.810165i
$248$	−6.64057	−	10.6634i	−0.421676	−	0.677126i
$249$	25.4512	+	10.0326i	1.61290	+	0.635793i
$250$	−0.857815	−	27.4054i	−0.0542530	−	1.73327i
$251$	16.4941	−	20.3078i	1.04110	−	1.28181i	0.0826377	−	0.996580i	$-0.473666\pi$
$251$	16.4941	−	20.3078i	1.04110	−	1.28181i	0.958458	−	0.285234i	$-0.0920715\pi$
$252$	3.51780	−	4.33118i	0.221601	−	0.272838i
$253$	0.470827	+	15.0419i	0.0296006	+	0.945678i
$254$	31.9787	+	12.6057i	2.00652	+	0.790953i
$255$	6.83646	+	10.9780i	0.428116	+	0.687466i
$256$	−9.14765	−	9.92387i	−0.571728	−	0.620242i
$257$	−1.01913	+	2.63355i	−0.0635715	+	0.164276i	−0.960767	−	0.277358i	$-0.910541\pi$
$257$	−1.01913	+	2.63355i	−0.0635715	+	0.164276i	0.897195	+	0.441634i	$0.145601\pi$
$258$	10.4810	−	28.1250i	0.652517	−	1.75099i
$259$	−14.4436	+	5.07580i	−0.897484	+	0.315395i
$260$	−13.5535	+	6.14314i	−0.840552	+	0.380981i
$261$	−2.39308	−	0.643899i	−0.148128	−	0.0398564i
$262$	18.4873	+	5.72671i	1.14215	+	0.353797i
$263$	5.79635	+	8.34580i	0.357418	+	0.514624i	0.958702	−	0.284411i	$-0.0917981\pi$
$263$	5.79635	+	8.34580i	0.357418	+	0.514624i	−0.601284	+	0.799035i	$0.705344\pi$
$264$	1.19636	−	17.3515i	0.0736310	−	1.06791i
$265$	−3.06111	−	0.346290i	−0.188043	−	0.0212724i
$266$	−34.1948	−	35.2818i	−2.09662	−	2.16327i
$267$	16.7009	+	11.4449i	1.02208	+	0.700417i
$268$	−6.30345	−	17.5844i	−0.385044	−	1.07414i
$269$	−13.2648	+	15.5212i	−0.808767	+	0.946345i	−0.999376	−	0.0353212i	$-0.988755\pi$
$269$	−13.2648	+	15.5212i	−0.808767	+	0.946345i	0.190609	+	0.981666i	$0.438954\pi$
$270$	−21.3134	−	0.266780i	−1.29710	−	0.0162357i
$271$	−4.55086	−	12.2119i	−0.276445	−	0.741823i	−0.998737	−	0.0502349i	$-0.984003\pi$
$271$	−4.55086	−	12.2119i	−0.276445	−	0.741823i	0.722292	−	0.691588i	$-0.243089\pi$
$272$	−1.15959	−	1.39175i	−0.0703106	−	0.0843870i
$273$	−9.94391	−	11.6355i	−0.601833	−	0.704210i
$274$	−21.6437	+	37.8519i	−1.30755	+	2.28671i
$275$	−5.38536	+	7.16422i	−0.324750	+	0.432019i
$276$	−17.2866	+	3.96182i	−1.04053	+	0.238474i
$277$	3.49719	−	7.58912i	0.210126	−	0.455986i	−0.774063	−	0.633109i	$-0.781779\pi$
$277$	3.49719	−	7.58912i	0.210126	−	0.455986i	0.984189	+	0.177123i	$0.0566790\pi$
$278$	−23.0894	−	45.5267i	−1.38481	−	2.73051i
$279$	2.44218	+	0.153035i	0.146210	+	0.00916198i
$280$	−13.8801	+	6.71492i	−0.829497	+	0.401293i
$281$	−1.23001	−	2.28183i	−0.0733761	−	0.136122i	0.840933	−	0.541139i	$-0.182007\pi$
$281$	−1.23001	−	2.28183i	−0.0733761	−	0.136122i	−0.914309	+	0.405017i	$0.867266\pi$
$282$	−2.40407	−	0.333099i	−0.143161	−	0.0198357i
$283$	−19.9049	+	8.72328i	−1.18322	+	0.518545i	−0.898034	−	0.439926i	$-0.855005\pi$
$283$	−19.9049	+	8.72328i	−1.18322	+	0.518545i	−0.285189	+	0.958471i	$0.592056\pi$
$284$	−25.1564	−	1.26051i	−1.49276	−	0.0747977i
$285$	−2.18110	+	16.5006i	−0.129197	+	0.977410i
$286$	25.8408	+	6.60721i	1.52800	+	0.390693i
$287$	−36.9545	−	21.4386i	−2.18136	−	1.26548i
$288$	3.06510	−	0.385653i	0.180613	−	0.0227248i
$289$	3.81062	+	5.06932i	0.224154	+	0.298195i
$290$	14.3313	+	12.0934i	0.841561	+	0.710151i
$291$	−2.08086	−	1.50389i	−0.121982	−	0.0881594i
$292$	9.28752	−	6.36461i	0.543511	−	0.372461i
$293$	11.7196	+	2.37887i	0.684669	+	0.138975i	0.528728	−	0.848791i	$-0.322669\pi$
$293$	11.7196	+	2.37887i	0.684669	+	0.138975i	0.155941	+	0.987766i	$0.450159\pi$
$294$	−12.2684	−	13.6483i	−0.715507	−	0.795986i
$295$	14.8011	+	1.30011i	0.861751	+	0.0756953i
$296$	10.4576	+	4.73994i	0.607838	+	0.275503i
$297$	18.0478	+	14.8469i	1.04724	+	0.861504i
$298$	−1.28803	+	0.145709i	−0.0746133	+	0.00844068i
$299$	−0.434962	−	9.92269i	−0.0251545	−	0.573844i
$300$	−9.50778	−	4.59967i	−0.548932	−	0.265562i
$301$	25.4159	+	14.3225i	1.46495	+	0.825537i
$302$	−8.31845	+	26.2712i	−0.478673	+	1.51174i
$303$	10.3832	−	19.8532i	0.596502	−	1.14054i
$304$	−0.0145902	−	2.33136i	−0.000836804	−	0.133713i
$305$	−7.29665	+	8.32461i	−0.417805	+	0.476666i
$306$	−5.56146	+	0.418440i	−0.317927	+	0.0239206i
$307$	−4.68533	+	3.95372i	−0.267406	+	0.225651i	−0.768673	−	0.639642i	$-0.779083\pi$
$307$	−4.68533	+	3.95372i	−0.267406	+	0.225651i	0.501267	+	0.865293i	$0.332867\pi$
$308$	45.1214	+	10.3411i	2.57103	+	0.589239i
$309$	5.08839	−	6.59563i	0.289468	−	0.375212i
$310$	−16.2433	−	8.88751i	−0.922557	−	0.504777i
$311$	−1.23787	−	13.1480i	−0.0701933	−	0.745555i	−0.958271	−	0.285862i	$-0.907720\pi$
$311$	−1.23787	−	13.1480i	−0.0701933	−	0.745555i	0.888078	−	0.459694i	$-0.152041\pi$
$312$	−0.646184	+	11.4606i	−0.0365829	+	0.648829i
$313$	19.7825	+	3.24755i	1.11817	+	0.183563i	0.692572	−	0.721349i	$-0.256478\pi$
$313$	19.7825	+	3.24755i	1.11817	+	0.183563i	0.425599	+	0.904912i	$0.360063\pi$
$314$	34.8394	−	8.44496i	1.96610	−	0.476576i
$315$	0.505090	−	2.96072i	0.0284586	−	0.166818i
$316$	−35.6030	−	5.38799i	−2.00282	−	0.303098i
$317$	0.127266	−	1.35175i	0.00714798	−	0.0759220i	−0.991299	−	0.131627i	$-0.957980\pi$
$317$	0.127266	−	1.35175i	0.00714798	−	0.0759220i	0.998447	+	0.0557053i	$0.0177407\pi$
$318$	−3.64470	+	5.39054i	−0.204385	+	0.302287i
$319$	−3.96366	−	20.1740i	−0.221922	−	1.12953i
$320$	−21.0308	−	6.80422i	−1.17566	−	0.380367i
$321$	3.21852	−	2.58084i	0.179640	−	0.144048i
$322$	−1.93842	−	28.1140i	−0.108024	−	1.56673i
$323$	−1.31557	+	30.0118i	−0.0732003	+	1.66990i
$324$	−10.7866	+	20.0105i	−0.599253	+	1.11169i
$325$	3.49477	−	4.77235i	0.193855	−	0.264722i
$326$	1.83317	+	5.54728i	0.101530	+	0.307235i
$327$	7.82157	+	0.785805i	0.432534	+	0.0434551i
$328$	8.90445	+	30.7787i	0.491666	+	1.69947i
$329$	0.683915	−	2.25774i	0.0377054	−	0.124473i
$330$	−11.0196	−	23.1466i	−0.606609	−	1.27418i
$331$	−7.74855	−	3.16703i	−0.425899	−	0.174076i	0.155246	−	0.987876i	$-0.450383\pi$
$331$	−7.74855	−	3.16703i	−0.425899	−	0.174076i	−0.581145	+	0.813800i	$0.697395\pi$
$332$	52.5496	−	14.8472i	2.88403	−	0.814843i
$333$	−1.93455	+	1.12230i	−0.106013	+	0.0615017i
$334$	18.8162	−	14.3293i	1.02957	−	0.784065i
$335$	−7.60292	−	6.58039i	−0.415392	−	0.359525i
$336$	0.0644683	−	2.05962i	0.00351703	−	0.112362i
$337$	5.99507	−	13.9159i	0.326572	−	0.758045i	−0.673254	−	0.739411i	$-0.735104\pi$
$337$	5.99507	−	13.9159i	0.326572	−	0.758045i	0.999826	−	0.0186341i	$-0.00593176\pi$
$338$	11.5654	+	2.80342i	0.629077	+	0.152486i
$339$	20.9616	+	8.87534i	1.13848	+	0.482042i
$340$	24.1324	+	9.16552i	1.30877	+	0.497070i
$341$	7.79805	+	18.7432i	0.422288	+	1.01500i
$342$	−5.86963	−	4.13128i	−0.317393	−	0.223394i
$343$	−5.48147	+	3.55808i	−0.295971	+	0.192118i
$344$	−6.34305	−	20.9397i	−0.341994	−	1.12899i
$345$	−7.05955	+	6.42612i	−0.380073	+	0.345971i
$346$	1.71563	−	3.60367i	0.0922330	−	0.193734i
$347$	−17.7549	−	16.1618i	−0.953135	−	0.867613i	0.0381606	−	0.999272i	$-0.487850\pi$
$347$	−17.7549	−	16.1618i	−0.953135	−	0.867613i	−0.991295	+	0.131659i	$0.957970\pi$
$348$	22.4275	−	9.16667i	1.20224	−	0.491385i
$349$	21.3167	−	16.6592i	1.14106	−	0.891746i	0.145826	−	0.989310i	$-0.453416\pi$
$349$	21.3167	−	16.6592i	1.14106	−	0.891746i	0.995229	+	0.0975642i	$0.0311051\pi$
$350$	9.57370	−	13.7846i	0.511736	−	0.736816i
$351$	−12.0329	−	9.64879i	−0.642266	−	0.515014i
$352$	14.0885	+	21.4097i	0.750918	+	1.14114i
$353$	−8.82550	+	4.13409i	−0.469734	+	0.220036i	−0.644545	−	0.764566i	$-0.722953\pi$
$353$	−8.82550	+	4.13409i	−0.469734	+	0.220036i	0.174811	+	0.984602i	$0.444069\pi$
$354$	16.9223	−	26.4307i	0.899410	−	1.40477i
$355$	−12.1301	+	6.05681i	−0.643800	+	0.321462i
$356$	40.3620	−	2.02242i	2.13918	−	0.107188i
$357$	−2.15776	+	26.4638i	−0.114201	+	1.40062i
$358$	3.98748	−	0.757550i	0.210745	−	0.0400378i
$359$	−4.37002	+	7.01735i	−0.230641	+	0.370362i	−0.943733	−	0.330708i	$-0.892712\pi$
$359$	−4.37002	+	7.01735i	−0.230641	+	0.370362i	0.713092	+	0.701070i	$0.247294\pi$
$360$	−1.80898	+	1.34218i	−0.0953419	+	0.0707393i
$361$	−13.1441	+	14.6226i	−0.691797	+	0.769608i
$362$	−9.56905	+	8.93200i	−0.502938	+	0.469455i
$363$	−2.46578	+	10.4579i	−0.129420	+	0.548899i
$364$	−29.8622	−	6.45166i	−1.56521	−	0.338159i
$365$	2.67342	−	5.43903i	0.139933	−	0.284692i
$366$	8.43857	+	21.8063i	0.441091	+	1.13983i
$367$	19.3973	−	0.242795i	1.01253	−	0.0126738i	0.495472	−	0.868624i	$-0.334995\pi$
$367$	19.3973	−	0.242795i	1.01253	−	0.0126738i	0.517058	+	0.855950i	$0.327027\pi$
$368$	0.855962	−	1.02733i	0.0446201	−	0.0535532i
$369$	−5.88826	−	2.06926i	−0.306530	−	0.107721i
$370$	16.8584	−	1.48083i	0.876428	−	0.0769846i
$371$	−4.62355	−	4.31574i	−0.240043	−	0.224062i
$372$	−19.9018	+	13.2755i	−1.03186	+	0.688302i
$373$	−1.25623	+	4.78806i	−0.0650451	+	0.247916i	−0.991809	−	0.127727i	$-0.959232\pi$
$373$	−1.25623	+	4.78806i	−0.0650451	+	0.247916i	0.926764	+	0.375644i	$0.122578\pi$
$374$	−23.4683	−	39.8762i	−1.21352	−	2.06195i
$375$	−19.0321	+	1.19261i	−0.982812	+	0.0615863i
$376$	−1.54133	+	0.868580i	−0.0794881	+	0.0447936i
$377$	2.78237	+	13.2806i	0.143299	+	0.683986i
$378$	−34.8154	−	26.5134i	−1.79071	−	1.36370i
$379$	−28.7124	−	3.61262i	−1.47486	−	0.185568i	−0.653911	−	0.756571i	$-0.726873\pi$
$379$	−28.7124	−	3.61262i	−1.47486	−	0.185568i	−0.820948	+	0.571003i	$0.806554\pi$
$380$	16.4912	+	28.8408i	0.845980	+	1.47950i
$381$	8.06700	−	22.5041i	0.413285	−	1.15292i
$382$	46.4262	−	33.5534i	2.37537	−	1.71674i
$383$	19.3712	+	1.45748i	0.989825	+	0.0744737i	0.560047	−	0.828461i	$-0.310783\pi$
$383$	19.3712	+	1.45748i	0.989825	+	0.0744737i	0.429778	+	0.902935i	$0.358592\pi$
$384$	−19.6389	+	19.2736i	−1.00219	+	0.983551i
$385$	23.8923	−	7.07452i	1.21767	−	0.360551i
$386$	3.50856	+	19.1196i	0.178581	+	0.973163i
$387$	4.03821	+	1.36257i	0.205274	+	0.0692634i
$388$	−5.12313	+	0.128272i	−0.260088	+	0.00651203i
$389$	−2.46869	−	9.91313i	−0.125168	−	0.502616i	−0.999840	−	0.0179006i	$-0.994302\pi$
$389$	−2.46869	−	9.91313i	−0.125168	−	0.502616i	0.874672	−	0.484715i	$-0.161077\pi$
$390$	7.46334	+	15.1840i	0.377921	+	0.768873i
$391$	−11.6779	+	12.6688i	−0.590576	+	0.640689i
$392$	−13.1427	−	2.49687i	−0.663806	−	0.126111i
$393$	3.57864	−	12.9760i	0.180518	−	0.654550i
$394$	−24.4477	−	25.8650i	−1.23166	−	1.30306i
$395$	−18.1198	+	6.88190i	−0.911705	+	0.346266i
$396$	6.75777	+	0.253866i	0.339591	+	0.0127573i
$397$	−0.516964	+	0.139098i	−0.0259457	+	0.00698114i	−0.272776	−	0.962078i	$-0.587942\pi$
$397$	−0.516964	+	0.139098i	−0.0259457	+	0.00698114i	0.246830	+	0.969059i	$0.420611\pi$
$398$	0.638629	−	0.525365i	0.0320116	−	0.0263342i
$399$	−23.7820	+	24.5381i	−1.19059	+	1.22844i
$400$	0.780447	−	0.158416i	0.0390224	−	0.00792082i
$401$	−3.45340	−	2.56227i	−0.172455	−	0.127953i	0.506184	−	0.862425i	$-0.331055\pi$
$401$	−3.45340	−	2.56227i	−0.172455	−	0.127953i	−0.678639	+	0.734472i	$0.737430\pi$
$402$	−19.7592	+	7.78890i	−0.985498	+	0.388475i
$403$	−5.30097	−	12.3047i	−0.264060	−	0.612942i
$404$	−7.52059	−	44.0840i	−0.374163	−	2.19326i
$405$	0.229721	+	12.2344i	0.0114149	+	0.607930i
$406$	8.83511	+	37.4717i	0.438479	+	1.85969i
$407$	−15.4358	−	10.2964i	−0.765122	−	0.510373i
$408$	14.8923	−	13.2191i	0.737279	−	0.654441i
$409$	−17.3271	−	19.7681i	−0.856768	−	0.977471i	0.143157	−	0.989700i	$-0.454275\pi$
$409$	−17.3271	−	19.7681i	−0.856768	−	0.977471i	−0.999925	+	0.0122288i	$0.996107\pi$
$410$	33.7061	+	33.0792i	1.66463	+	1.63366i
$411$	26.7835	+	14.2219i	1.32113	+	0.701517i
$412$	0.104059	−	16.6275i	0.00512661	−	0.819179i
$413$	22.8136	+	20.2503i	1.12258	+	0.996454i
$414$	−1.04476	−	3.98206i	−0.0513473	−	0.195708i
$415$	20.7194	−	20.8495i	1.01708	−	1.02346i
$416$	−9.47422	−	14.0125i	−0.464512	−	0.687017i
$417$	−31.1453	+	17.0411i	−1.52519	+	0.834508i
$418$	9.27859	−	58.8209i	0.453831	−	2.87703i
$419$	17.5575	−	3.10845i	0.857739	−	0.151858i	0.271941	−	0.962314i	$-0.412335\pi$
$419$	17.5575	−	3.10845i	0.857739	−	0.151858i	0.585799	+	0.810456i	$0.300781\pi$
$420$	13.6087	+	26.0204i	0.664035	+	1.26967i
$421$	23.8527	−	12.6657i	1.16251	−	0.617287i	0.228151	−	0.973626i	$-0.426732\pi$
$421$	23.8527	−	12.6657i	1.16251	−	0.617287i	0.934357	+	0.356338i	$0.115975\pi$
$422$	50.4874	+	14.9493i	2.45769	+	0.727721i
$423$	0.0365953	−	0.342679i	0.00177932	−	0.0166616i
$424$	0.267022	+	4.73587i	0.0129678	+	0.229994i
$425$	−10.1458	+	1.53541i	−0.492142	+	0.0744785i
$426$	−0.537636	+	28.6332i	−0.0260486	+	1.38728i
$427$	−22.2146	+	4.79941i	−1.07504	+	0.232260i
$428$	1.98994	−	7.99068i	0.0961874	−	0.386244i
$429$	4.03072	−	18.1069i	0.194605	−	0.874209i
$430$	−23.2974	−	22.2985i	−1.12350	−	1.07533i
$431$	6.69653	+	19.4438i	0.322561	+	0.936573i	0.982664	+	0.185398i	$0.0593573\pi$
$431$	6.69653	+	19.4438i	0.322561	+	0.936573i	−0.660103	+	0.751175i	$0.729487\pi$
$432$	−0.323554	−	2.05115i	−0.0155670	−	0.0986858i
$433$	17.8357	+	23.1189i	0.857130	+	1.11102i	0.992742	+	0.120261i	$0.0383732\pi$
$433$	17.8357	+	23.1189i	0.857130	+	1.11102i	−0.135612	+	0.990762i	$0.543300\pi$
$434$	−15.9096	−	34.5248i	−0.763686	−	1.65725i
$435$	8.09488	−	10.2255i	0.388120	−	0.490273i
$436$	13.3710	−	8.21106i	0.640356	−	0.393238i
$437$	−21.9649	+	3.04336i	−1.05072	+	0.145584i
$438$	−7.56328	−	10.3282i	−0.361388	−	0.493500i
$439$	−14.3554	+	20.1271i	−0.685148	+	0.960612i	0.314787	+	0.949162i	$0.398067\pi$
$439$	−14.3554	+	20.1271i	−0.685148	+	0.960612i	−0.999934	+	0.0114500i	$0.996355\pi$
$440$	−16.6134	−	8.55681i	−0.792011	−	0.407930i
$441$	1.88254	−	1.80182i	0.0896447	−	0.0858012i
$442$	15.8168	+	26.1215i	0.752327	+	1.24247i
$443$	22.1927	−	23.4792i	1.05441	−	1.11553i	0.0613234	−	0.998118i	$-0.480468\pi$
$443$	22.1927	−	23.4792i	1.05441	−	1.11553i	0.993083	−	0.117414i	$-0.0374604\pi$
$444$	8.39927	−	20.1882i	0.398612	−	0.958092i
$445$	18.3932	−	11.6146i	0.871921	−	0.550586i
$446$	−6.56675	−	3.07604i	−0.310945	−	0.145655i
$447$	0.129315	+	0.892196i	0.00611638	+	0.0421994i
$448$	−26.3518	−	36.9466i	−1.24501	−	1.74556i
$449$	0.449774	−	1.36104i	0.0212262	−	0.0642314i	−0.938341	−	0.345711i	$-0.887638\pi$
$449$	0.449774	−	1.36104i	0.0212262	−	0.0642314i	0.959567	+	0.281479i	$0.0908251\pi$
$450$	0.998163	−	2.23940i	0.0470539	−	0.105566i
$451$	−6.14228	−	51.4134i	−0.289229	−	2.42096i
$452$	44.0206	−	11.2556i	2.07055	−	0.529419i
$453$	18.4434	+	5.21091i	0.866544	+	0.244830i
$454$	19.7066	+	15.4009i	0.924878	+	0.722801i
$455$	−15.7088	+	4.86603i	−0.736438	+	0.228123i
$456$	25.6096	−	0.962064i	1.19928	−	0.0450528i
$457$	−10.0053	+	4.23633i	−0.468029	+	0.198167i	−0.611113	−	0.791543i	$-0.709278\pi$
$457$	−10.0053	+	4.23633i	−0.468029	+	0.198167i	0.143085	+	0.989710i	$0.454298\pi$
$458$	−22.9392	+	3.76577i	−1.07188	+	0.175963i
$459$	2.84119	+	26.6049i	0.132615	+	1.24181i
$460$	−3.43929	+	18.7421i	−0.160358	+	0.873856i
$461$	−3.40063	+	6.12385i	−0.158383	+	0.285216i	−0.941731	−	0.336368i	$-0.890801\pi$
$461$	−3.40063	+	6.12385i	−0.158383	+	0.285216i	0.783347	+	0.621584i	$0.213511\pi$
$462$	10.1469	−	51.6449i	0.472076	−	2.40274i
$463$	−1.74732	−	1.75829i	−0.0812049	−	0.0817147i	0.667536	−	0.744578i	$-0.267349\pi$
$463$	−1.74732	−	1.75829i	−0.0812049	−	0.0817147i	−0.748741	+	0.662863i	$0.769341\pi$
$464$	−0.926573	+	1.57438i	−0.0430151	+	0.0730890i
$465$	−5.82469	+	11.4848i	−0.270113	+	0.532597i
$466$	28.5392	+	36.0508i	1.32205	+	1.67002i
$467$	25.3127	+	9.25294i	1.17133	+	0.428175i	0.854067	−	0.520163i	$-0.174129\pi$
$467$	25.3127	+	9.25294i	1.17133	+	0.428175i	0.317263	+	0.948338i	$0.397236\pi$
$468$	−4.46174	−	0.111712i	−0.206244	−	0.00516390i
$469$	−4.48569	−	20.1507i	−0.207130	−	0.930475i
$470$	−1.35069	+	2.23067i	−0.0623025	+	0.102893i
$471$	−6.62854	−	24.0347i	−0.305427	−	1.10746i
$472$	−1.85917	−	22.8019i	−0.0855755	−	1.04954i
$473$	4.63338	+	35.0528i	0.213043	+	1.61173i
$474$	−4.85661	+	40.6518i	−0.223071	+	1.86720i
$475$	−11.3392	−	6.76936i	−0.520279	−	0.310600i
$476$	28.5772	+	44.6343i	1.30983	+	2.04581i
$477$	−0.781245	−	0.493328i	−0.0357708	−	0.0225879i
$478$	33.6121	−	23.6576i	1.53738	−	1.08207i
$479$	−14.1948	+	35.3598i	−0.648579	+	1.61563i	0.132489	+	0.991185i	$0.457703\pi$
$479$	−14.1948	+	35.3598i	−0.648579	+	1.61563i	−0.781068	+	0.624446i	$0.785325\pi$
$480$	−4.51813	+	15.6172i	−0.206224	+	0.712823i
$481$	10.2715	+	6.66737i	0.468342	+	0.304006i
$482$	16.9469	+	42.2152i	0.771909	+	1.92285i
$483$	−19.5012	+	1.95921i	−0.887333	+	0.0891472i
$484$	8.73149	+	19.5893i	0.396886	+	0.890421i
$485$	−2.36858	+	1.41401i	−0.107552	+	0.0642070i
$486$	−10.6101	−	5.29782i	−0.481283	−	0.240314i
$487$	3.43570	+	1.50569i	0.155686	+	0.0682293i	0.477785	−	0.878477i	$-0.341440\pi$
$487$	3.43570	+	1.50569i	0.155686	+	0.0682293i	−0.322098	+	0.946706i	$0.604388\pi$
$488$	14.5246	+	8.91944i	0.657497	+	0.403764i
$489$	3.81628	−	1.39503i	0.172578	−	0.0630853i
$490$	−18.6831	+	6.30406i	−0.844018	+	0.284789i
$491$	13.2278	+	23.8206i	0.596962	+	1.07501i	0.987974	+	0.154623i	$0.0494162\pi$
$491$	13.2278	+	23.8206i	0.596962	+	1.07501i	−0.391011	+	0.920386i	$0.627875\pi$
$492$	58.0559	−	18.7832i	2.61736	−	0.846813i
$493$	12.9393	−	19.6634i	0.582758	−	0.885593i
$494$	−5.63732	+	38.8942i	−0.253635	+	1.74993i
$495$	3.23613	−	1.66679i	0.145453	−	0.0749165i
$496$	0.587376	−	1.70548i	0.0263740	−	0.0765783i
$497$	−27.4098	−	4.85274i	−1.22950	−	0.217675i
$498$	−18.7419	−	59.1906i	−0.839847	−	2.65239i
$499$	−0.876323	+	4.18280i	−0.0392296	+	0.187248i	−0.993877	−	0.110490i	$-0.964758\pi$
$499$	−0.876323	+	4.18280i	−0.0392296	+	0.187248i	0.954648	+	0.297738i	$0.0962321\pi$
$500$	−28.7809	+	24.9101i	−1.28712	+	1.11401i
$501$	−10.3704	−	12.7682i	−0.463315	−	0.570441i
$502$	−59.3748			−2.65003
$503$	−19.9168	−	10.3113i	−0.888045	−	0.459757i
$503$	−19.9168	−	10.3113i	−0.888045	−	0.459757i
$504$	−4.62461			−0.205997
$505$	−15.1766	−	18.6857i	−0.675349	−	0.831501i
$506$	25.8248	−	22.3516i	1.14805	−	0.993649i
$507$	1.69714	−	8.10067i	0.0753726	−	0.359763i
$508$	−14.4046	−	45.4925i	−0.639102	−	2.01840i
$509$	−23.5637	−	4.17181i	−1.04444	−	0.184912i	−0.374424	−	0.927258i	$-0.622160\pi$
$509$	−23.5637	−	4.17181i	−1.04444	−	0.184912i	−0.670017	+	0.742345i	$0.733713\pi$
$510$	9.55751	−	27.7508i	0.423214	−	1.22882i
$511$	11.0617	−	5.69741i	0.489342	−	0.252039i
$512$	0.607539	−	4.19166i	0.0268497	−	0.185247i
$513$	−18.9289	+	28.7655i	−0.835733	+	1.27003i
$514$	6.09755	−	1.97278i	0.268951	−	0.0870155i
$515$	−4.34526	−	7.82493i	−0.191475	−	0.344808i
$516$	−39.4803	+	13.3214i	−1.73802	+	0.586443i
$517$	2.68532	−	0.981608i	0.118100	−	0.0431711i
$518$	29.6079	+	18.1820i	1.30089	+	0.798870i
$519$	−2.54241	−	1.11420i	−0.111599	−	0.0489082i
$520$	11.0343	+	5.50964i	0.483886	+	0.241614i
$521$	11.3910	−	6.80028i	0.499049	−	0.297926i	−0.240946	−	0.970539i	$-0.577458\pi$
$521$	11.3910	−	6.80028i	0.499049	−	0.297926i	0.739994	+	0.672613i	$0.234828\pi$
$522$	2.28973	+	5.13704i	0.100219	+	0.224842i
$523$	19.5524	−	1.96436i	0.854965	−	0.0858953i	0.337215	−	0.941428i	$-0.390515\pi$
$523$	19.5524	−	1.96436i	0.854965	−	0.0858953i	0.517749	+	0.855532i	$0.326770\pi$
$524$	−10.0094	−	24.9337i	−0.437263	−	1.08924i
$525$	−9.79060	−	6.35519i	−0.427297	−	0.277363i
$526$	6.40880	−	22.1523i	0.279437	−	0.965888i
$527$	−8.65872	+	21.5691i	−0.377180	+	0.939567i
$528$	2.04228	−	1.43744i	0.0888789	−	0.0625566i
$529$	8.69341	+	5.48957i	0.377974	+	0.238677i
$530$	3.76983	+	5.88805i	0.163751	+	0.255760i
$531$	3.82636	+	2.28428i	0.166050	+	0.0991295i
$532$	−8.09126	+	67.7272i	−0.350801	+	2.93635i
$533$	4.47815	+	33.8784i	0.193970	+	1.46743i
$534$	−3.73406	−	45.7965i	−0.161589	−	1.98181i
$535$	−1.17847	−	4.27308i	−0.0509498	−	0.184741i
$536$	−8.01916	+	13.2437i	−0.346375	+	0.572041i
$537$	−0.613371	−	2.75540i	−0.0264689	−	0.118904i
$538$	46.3221	+	1.15981i	1.99709	+	0.0500028i
$539$	20.3048	+	7.42233i	0.874589	+	0.319702i
$540$	18.3665	+	23.2006i	0.790368	+	0.998393i
$541$	−13.0973	+	25.8247i	−0.563098	+	1.11029i	0.416464	+	0.909152i	$0.363269\pi$
$541$	−13.0973	+	25.8247i	−0.563098	+	1.11029i	−0.979563	+	0.201139i	$0.935536\pi$
$542$	−15.0016	+	25.4900i	−0.644374	+	1.09489i
$543$	6.41726	+	6.45754i	0.275391	+	0.277120i
$544$	−5.65698	+	28.7925i	−0.242541	+	1.23447i
$545$	4.10042	−	7.38404i	0.175643	−	0.316297i
$546$	−6.26960	+	34.1657i	−0.268314	+	1.46216i
$547$	−1.56335	−	14.6392i	−0.0668440	−	0.625928i	−0.977232	−	0.212173i	$-0.931946\pi$
$547$	−1.56335	−	14.6392i	−0.0668440	−	0.625928i	0.910388	−	0.413755i	$-0.135783\pi$
$548$	59.7317	−	9.80575i	2.55161	−	0.418881i
$549$	−3.05737	+	1.29452i	−0.130486	+	0.0552487i
$550$	20.3262	−	0.763586i	0.866712	−	0.0325594i
$551$	28.9375	−	8.96384i	1.23278	−	0.381872i
$552$	11.5816	+	9.05115i	0.492946	+	0.385242i
$553$	−38.2949	−	10.8197i	−1.62847	−	0.460100i
$554$	−18.3731	+	4.69781i	−0.780598	+	0.199591i
$555$	−1.39621	−	11.6869i	−0.0592658	−	0.496079i
$556$	−28.8506	+	64.7267i	−1.22354	+	2.74502i
$557$	4.26534	−	12.9071i	0.180728	−	0.546893i	−0.818906	−	0.573927i	$-0.805419\pi$
$557$	4.26534	−	12.9071i	0.180728	−	0.546893i	0.999635	+	0.0270344i	$0.00860637\pi$
$558$	−3.22471	−	4.52120i	−0.136513	−	0.191398i
$559$	−3.34724	−	23.0940i	−0.141573	−	0.976772i
$560$	−2.00497	−	0.939179i	−0.0847254	−	0.0396876i
$561$	−27.2091	+	17.1816i	−1.14877	+	0.725407i
$562$	−2.25984	+	5.43169i	−0.0953257	+	0.229122i
$563$	14.9577	−	15.8248i	0.630392	−	0.666936i	−0.330518	−	0.943800i	$-0.607223\pi$
$563$	14.9577	−	15.8248i	0.630392	−	0.666936i	0.960909	+	0.276864i	$0.0892950\pi$
$564$	1.74515	+	2.88213i	0.0734842	+	0.121360i
$565$	17.6689	−	16.9113i	0.743336	−	0.711466i
$566$	43.8474	+	22.5839i	1.84304	+	0.949270i
$567$	−14.5880	+	20.4531i	−0.612639	+	0.858951i
$568$	12.3340	+	16.8430i	0.517524	+	0.706715i
$569$	9.22426	−	1.27808i	0.386701	−	0.0535797i	0.0587457	−	0.998273i	$-0.481290\pi$
$569$	9.22426	−	1.27808i	0.386701	−	0.0535797i	0.327955	+	0.944693i	$0.393640\pi$
$570$	32.1888	−	19.7669i	1.34824	−	0.827945i
$571$	−17.6322	+	22.2731i	−0.737886	+	0.932098i	−0.999452	−	0.0330871i	$-0.989466\pi$
$571$	−17.6322	+	22.2731i	−0.737886	+	0.932098i	0.261566	+	0.965185i	$0.415761\pi$
$572$	−15.4965	−	33.6284i	−0.647943	−	1.40608i
$573$	−24.3347	−	31.5429i	−1.01660	−	1.31773i
$574$	15.1079	+	95.7751i	0.630590	+	3.99758i
$575$	−2.46650	−	7.16162i	−0.102860	−	0.298660i
$576$	−4.78940	−	4.58406i	−0.199558	−	0.191002i
$577$	−7.86628	+	35.3371i	−0.327477	+	1.47110i	0.477939	+	0.878393i	$0.341384\pi$
$577$	−7.86628	+	35.3371i	−0.327477	+	1.47110i	−0.805416	+	0.592710i	$0.798058\pi$
$578$	3.47803	−	13.9662i	0.144667	−	0.580916i
$579$	13.2146	−	2.85498i	0.549179	−	0.118649i
$580$	0.488711	−	26.0276i	0.0202926	−	1.08074i
$581$	59.6684	−	9.02993i	2.47546	−	0.374625i
$582$	0.328008	+	5.81750i	0.0135964	+	0.241143i
$583$	0.813979	−	7.62211i	0.0337116	−	0.315676i
$584$	−8.94768	−	2.64941i	−0.370258	−	0.109633i
$585$	−2.12184	+	1.12669i	−0.0877273	+	0.0465829i
$586$	−12.5779	−	24.0495i	−0.519587	−	0.993475i
$587$	−9.35212	+	1.65574i	−0.386003	+	0.0683396i	−0.363953	−	0.931417i	$-0.618573\pi$
$587$	−9.35212	+	1.65574i	−0.386003	+	0.0683396i	−0.0220502	+	0.999757i	$0.507019\pi$
$588$	−3.96968	+	25.1655i	−0.163707	+	1.03781i
$589$	−26.2413	+	14.3579i	−1.08125	+	0.591607i
$590$	−18.8872	−	27.9343i	−0.777573	−	1.15004i
$591$	−17.4480	+	17.5575i	−0.717714	+	0.722219i
$592$	0.418395	+	1.59469i	0.0171959	+	0.0655413i
$593$	−28.5584	−	25.3497i	−1.17275	−	1.04099i	−0.998414	−	0.0563005i	$-0.982070\pi$
$593$	−28.5584	−	25.3497i	−1.17275	−	1.04099i	−0.174340	−	0.984686i	$-0.555779\pi$
$594$	0.331916	−	53.0367i	0.0136187	−	2.17612i
$595$	25.1965	+	13.3792i	1.03295	+	0.548495i
$596$	1.28432	+	1.26043i	0.0526078	+	0.0516293i
$597$	−0.379101	−	0.432510i	−0.0155156	−	0.0177014i
$598$	−16.8578	+	14.9637i	−0.689369	+	0.611913i
$599$	19.6026	+	13.0759i	0.800939	+	0.534265i	0.886861	−	0.462037i	$-0.152881\pi$
$599$	19.6026	+	13.0759i	0.800939	+	0.534265i	−0.0859212	+	0.996302i	$0.527383\pi$
$600$	2.00892	+	8.52028i	0.0820137	+	0.347839i
$601$	0.315564	+	16.8062i	0.0128721	+	0.685539i	0.945668	+	0.325134i	$0.105409\pi$
$601$	0.315564	+	16.8062i	0.0128721	+	0.685539i	−0.932796	+	0.360405i	$0.882638\pi$
$602$	−11.1343	−	65.2665i	−0.453798	−	2.66006i
$603$	−1.19322	−	2.76972i	−0.0485917	−	0.112792i
$604$	35.5900	−	14.0293i	1.44814	−	0.570843i
$605$	9.27135	+	6.87891i	0.376934	+	0.279667i
$606$	−49.8307	+	10.1147i	−2.02423	+	0.410882i
$607$	−10.9051	+	11.2518i	−0.442626	+	0.456697i	−0.902121	−	0.431483i	$-0.857990\pi$
$607$	−10.9051	+	11.2518i	−0.442626	+	0.456697i	0.459495	+	0.888180i	$0.348030\pi$
$608$	−29.1638	+	23.9915i	−1.18275	+	0.972983i
$609$	25.8561	−	6.95703i	1.04774	−	0.281913i
$610$	25.1051	+	0.943112i	1.01648	+	0.0381855i
$611$	−1.76401	+	0.669971i	−0.0713641	+	0.0271041i
$612$	5.31840	+	5.62672i	0.214984	+	0.227447i
$613$	−6.70250	+	24.3029i	−0.270712	+	0.981586i	0.694366	+	0.719622i	$0.255685\pi$
$613$	−6.70250	+	24.3029i	−0.270712	+	0.981586i	−0.965078	+	0.261964i	$0.915630\pi$
$614$	13.6688	+	2.59683i	0.551630	+	0.104800i
$615$	22.2614	−	24.1504i	0.897668	−	0.973839i
$616$	−16.9244	−	34.4323i	−0.681902	−	1.38732i
$617$	−5.73655	−	23.0353i	−0.230945	−	0.927367i	−0.967882	−	0.251406i	$-0.919107\pi$
$617$	−5.73655	−	23.0353i	−0.230945	−	0.927367i	0.736937	−	0.675961i	$-0.236271\pi$
$618$	−18.8996	+	0.473206i	−0.760255	+	0.0190351i
$619$	13.3325	+	4.49865i	0.535878	+	0.180816i	0.574600	−	0.818434i	$-0.305158\pi$
$619$	13.3325	+	4.49865i	0.535878	+	0.180816i	−0.0387225	+	0.999250i	$0.512329\pi$
$620$	4.63940	+	25.2821i	0.186323	+	1.01535i
$621$	−18.9376	+	5.60742i	−0.759939	+	0.225018i
$622$	−21.3909	+	20.9930i	−0.857696	+	0.841743i
$623$	44.5355	+	3.35082i	1.78428	+	0.134248i
$624$	−1.33588	+	0.965476i	−0.0534781	+	0.0386500i
$625$	−3.33039	+	9.29064i	−0.133216	+	0.371625i
$626$	−22.5840	−	39.4962i	−0.902636	−	1.57859i
$627$	−41.0911	−	5.17011i	−1.64102	−	0.206474i
$628$	−39.5923	−	30.1513i	−1.57991	−	1.20317i
$629$	−4.35604	−	20.7919i	−0.173687	−	0.829029i
$630$	−5.93841	+	3.34645i	−0.236592	+	0.133326i
$631$	−42.7065	+	2.67613i	−1.70012	+	0.106535i	−0.882830	−	0.469692i	$-0.844365\pi$
$631$	−42.7065	+	2.67613i	−1.70012	+	0.106535i	−0.817289	+	0.576227i	$0.804524\pi$
$632$	15.1373	+	25.7205i	0.602129	+	1.02311i
$633$	9.29342	−	35.4214i	0.369380	−	1.40787i
$634$	−2.56339	+	1.70991i	−0.101805	+	0.0679090i
$635$	−18.7771	−	17.5270i	−0.745145	−	0.695537i
$636$	8.99869	−	0.790436i	0.356821	−	0.0313428i
$637$	−13.4610	−	4.73047i	−0.533344	−	0.187428i
$638$	−29.8680	+	35.8477i	−1.18249	+	1.41922i
$639$	−4.06616	+	0.0508960i	−0.160855	+	0.00201341i
$640$	10.6699	+	27.5724i	0.421766	+	1.08990i
$641$	−1.74530	+	3.55078i	−0.0689352	+	0.140247i	−0.929172	−	0.369647i	$-0.879479\pi$
$641$	−1.74530	+	3.55078i	−0.0689352	+	0.140247i	0.860237	+	0.509894i	$0.170315\pi$
$642$	−9.15161	−	1.97718i	−0.361185	−	0.0780331i
$643$	−0.600331	+	2.54614i	−0.0236748	+	0.100410i	−0.983853	−	0.178977i	$-0.942721\pi$
$643$	−0.600331	+	2.54614i	−0.0236748	+	0.100410i	0.960178	+	0.279388i	$0.0901314\pi$
$644$	−28.5987	+	26.6947i	−1.12695	+	1.05192i
$645$	−14.9938	+	16.6803i	−0.590380	+	0.656785i
$646$	54.7523	−	40.6236i	2.15420	−	1.59832i
$647$	−22.8973	+	36.7684i	−0.900187	+	1.44552i	−0.00491970	+	0.999988i	$0.501566\pi$
$647$	−22.8973	+	36.7684i	−0.900187	+	1.44552i	−0.895268	+	0.445529i	$0.853016\pi$
$648$	18.5100	−	3.51657i	0.727142	−	0.138144i
$649$	−3.00448	+	36.8485i	−0.117936	+	1.44643i
$650$	−13.4075	+	0.671811i	−0.525886	+	0.0263506i
$651$	−23.6536	+	11.8107i	−0.927059	+	0.462899i
$652$	4.37324	−	6.83049i	0.171269	−	0.267503i
$653$	30.2317	−	14.1613i	1.18306	−	0.554174i	0.270339	−	0.962765i	$-0.412864\pi$
$653$	30.2317	−	14.1613i	1.18306	−	0.554174i	0.912718	+	0.408591i	$0.133980\pi$
$654$	−9.80688	−	14.9031i	−0.383479	−	0.582758i
$655$	−11.2830	−	9.04748i	−0.440862	−	0.353514i
$656$	−2.62446	+	3.77880i	−0.102468	+	0.147537i
$657$	1.43223	−	1.11930i	0.0558767	−	0.0436681i
$658$	−4.95588	+	2.02559i	−0.193200	+	0.0789659i
$659$	21.7386	+	19.7881i	0.846817	+	0.770835i	0.975302	−	0.220877i	$-0.0708918\pi$
$659$	21.7386	+	19.7881i	0.846817	+	0.770835i	−0.128485	+	0.991711i	$0.541011\pi$
$660$	−15.2978	+	32.1329i	−0.595467	+	1.25077i
$661$	28.9992	−	26.3972i	1.12794	−	1.02673i	0.128553	−	0.991703i	$-0.458967\pi$
$661$	28.9992	−	26.3972i	1.12794	−	1.02673i	0.999386	−	0.0350303i	$-0.0111528\pi$
$662$	5.50755	+	18.1816i	0.214057	+	0.706647i
$663$	17.8141	−	11.5633i	0.691843	−	0.449083i
$664$	−37.0107	−	26.0496i	−1.43629	−	1.01092i
$665$	14.1035	+	33.8987i	0.546910	+	1.31454i
$666$	4.74507	+	1.80218i	0.183868	+	0.0698330i
$667$	16.0002	+	6.77462i	0.619531	+	0.262315i
$668$	−31.9094	−	7.73472i	−1.23461	−	0.299265i
$669$	−1.99541	+	4.63178i	−0.0771470	+	0.179075i
$670$	−0.713941	+	22.8089i	−0.0275819	+	0.881184i
$671$	−20.8271	−	18.0261i	−0.804021	−	0.695888i
$672$	−26.5546	+	20.2225i	−1.02437	+	0.780099i
$673$	−15.2192	+	8.82920i	−0.586657	+	0.340341i	−0.765400	−	0.643555i	$-0.777459\pi$
$673$	−15.2192	+	8.82920i	−0.586657	+	0.340341i	0.178742	+	0.983896i	$0.442797\pi$
$674$	−33.0925	+	9.34983i	−1.27468	+	0.360142i
$675$	−10.8880	−	4.45018i	−0.419077	−	0.171288i
$676$	−7.10138	−	14.9164i	−0.273130	−	0.573706i
$677$	8.28837	−	27.3616i	0.318548	−	1.05159i	−0.640408	−	0.768035i	$-0.721235\pi$
$677$	8.28837	−	27.3616i	0.318548	−	1.05159i	0.958955	−	0.283557i	$-0.0915145\pi$
$678$	−14.3570	−	49.6258i	−0.551378	−	1.90587i
$679$	−5.63515	−	0.566143i	−0.216257	−	0.0217266i
$680$	−6.71332	−	20.3148i	−0.257444	−	0.779038i
$681$	10.2771	−	14.0341i	0.393819	−	0.537788i
$682$	21.8612	−	40.5553i	0.837107	−	1.55294i
$683$	−0.957793	+	21.8499i	−0.0366489	+	0.836063i	0.889052	+	0.457807i	$0.151365\pi$
$683$	−0.957793	+	21.8499i	−0.0366489	+	0.836063i	−0.925701	+	0.378257i	$0.876524\pi$
$684$	0.685405	+	9.94081i	0.0262071	+	0.380096i
$685$	25.4197	−	20.3833i	0.971237	−	0.778806i
$686$	14.1110	+	4.56542i	0.538761	+	0.174309i
$687$	3.11689	+	15.8641i	0.118917	+	0.605254i
$688$	1.75970	−	2.60261i	0.0670878	−	0.0992234i
$689$	−0.474206	+	5.03676i	−0.0180658	+	0.191885i
$690$	21.4214	+	3.24181i	0.815498	+	0.123414i
$691$	2.61841	−	15.3485i	0.0996090	−	0.583886i	−0.891731	−	0.452566i	$-0.850509\pi$
$691$	2.61841	−	15.3485i	0.0996090	−	0.583886i	0.991340	−	0.131320i	$-0.0419215\pi$
$692$	−5.38482	+	1.30526i	−0.204700	+	0.0496186i
$693$	7.37480	+	1.21067i	0.280145	+	0.0459896i
$694$	−3.06737	+	54.4023i	−0.116436	+	2.06508i
$695$	3.57555	+	37.9776i	0.135628	+	1.44057i
$696$	−17.6164	−	9.63881i	−0.667748	−	0.365358i
$697$	36.2110	−	46.9372i	1.37159	−	1.77787i
$698$	−59.8476	−	13.7161i	−2.26527	−	0.519163i
$699$	24.4396	−	20.6234i	0.924391	−	0.780047i
$700$	−23.2331	+	1.74805i	−0.878130	+	0.0660699i
$701$	15.6285	−	17.8303i	0.590282	−	0.673442i	−0.377273	−	0.926102i	$-0.623138\pi$
$701$	15.6285	−	17.8303i	0.590282	−	0.673442i	0.967555	+	0.252660i	$0.0813055\pi$
$702$	0.219058	+	35.0031i	0.00826780	+	1.32111i
$703$	12.6705	−	24.2266i	0.477877	−	0.913723i
$704$	16.6029	−	52.4351i	0.625746	−	1.97622i
$705$	1.58003	+	0.890387i	0.0595073	+	0.0335339i
$706$	19.9104	+	9.63224i	0.749338	+	0.362514i
$707$	−2.16436	−	49.3751i	−0.0813993	−	1.85694i
$708$	−43.2921	+	4.89744i	−1.62702	+	0.184057i
$709$	−16.3237	−	13.4286i	−0.613049	−	0.504321i	0.276589	−	0.960988i	$-0.410796\pi$
$709$	−16.3237	−	13.4286i	−0.613049	−	0.504321i	−0.889638	+	0.456667i	$0.849043\pi$
$710$	28.0258	+	12.7027i	1.05179	+	0.476726i
$711$	−5.79109	−	0.508684i	−0.217183	−	0.0190771i
$712$	−22.3915	−	24.9100i	−0.839157	−	0.933543i
$713$	−16.8136	−	3.41285i	−0.629673	−	0.127812i
$714$	49.7071	−	34.0636i	1.86024	−	1.27480i
$715$	−16.1538	−	11.6748i	−0.604120	−	0.436612i
$716$	−4.30625	−	3.63383i	−0.160932	−	0.135803i
$717$	−17.1768	−	22.8506i	−0.641480	−	0.853370i
$718$	18.6147	−	2.34212i	0.694695	−	0.0874071i
$719$	−7.30524	−	4.23803i	−0.272440	−	0.158052i	0.359324	−	0.933213i	$-0.383007\pi$
$719$	−7.30524	−	4.23803i	−0.272440	−	0.158052i	−0.631764	+	0.775161i	$0.717669\pi$
$720$	−0.313361	−	0.0801230i	−0.0116783	−	0.00298601i
$721$	2.40805	−	18.2175i	0.0896804	−	0.678456i
$722$	44.5664	+	2.23309i	1.65859	+	0.0831072i
$723$	28.9770	−	12.6991i	1.07767	−	0.472285i
$724$	18.0000	+	2.49401i	0.668966	+	0.0926892i
$725$	4.91005	+	9.10878i	0.182355	+	0.338292i
$726$	21.9512	−	10.6195i	0.814684	−	0.394127i
$727$	−22.8031	−	1.42892i	−0.845722	−	0.0529958i	−0.366211	−	0.930532i	$-0.619345\pi$
$727$	−22.8031	−	1.42892i	−0.845722	−	0.0529958i	−0.479511	+	0.877536i	$0.659186\pi$
$728$	11.4533	+	22.5830i	0.424486	+	0.836982i
$729$	−12.5111	+	27.1499i	−0.463375	+	1.00555i
$730$	−13.4068	+	3.07262i	−0.496207	+	0.113723i
$731$	−24.3239	+	32.3584i	−0.899651	+	1.19682i
$732$	16.1125	−	28.1786i	0.595536	−	1.04151i
$733$	3.14490	+	3.67987i	0.116159	+	0.135919i	0.815239	−	0.579125i	$-0.196606\pi$
$733$	3.14490	+	3.67987i	0.116159	+	0.135919i	−0.699079	+	0.715044i	$0.746407\pi$
$734$	−28.1816	−	33.8236i	−1.04020	−	1.24845i
$735$	4.78877	+	12.8503i	0.176636	+	0.473992i
$736$	−21.6581	−	0.271093i	−0.798327	−	0.00999263i
$737$	16.2551	−	19.0202i	0.598764	−	0.700618i
$738$	4.77970	+	13.3337i	0.175943	+	0.490820i
$739$	14.2772	+	9.78395i	0.525194	+	0.359908i	0.798477	−	0.602025i	$-0.205639\pi$
$739$	14.2772	+	9.78395i	0.525194	+	0.359908i	−0.273283	+	0.961934i	$0.588110\pi$
$740$	−16.3506	−	16.8704i	−0.601058	−	0.620166i
$741$	27.1598	+	3.07247i	0.997741	+	0.112870i
$742$	−0.987347	+	14.3200i	−0.0362466	+	0.525705i
$743$	2.30637	+	3.32079i	0.0846123	+	0.121828i	0.861384	−	0.507955i	$-0.169598\pi$
$743$	2.30637	+	3.32079i	0.0846123	+	0.121828i	−0.776772	+	0.629782i	$0.783144\pi$
$744$	18.9401	+	5.86697i	0.694377	+	0.215094i
$745$	0.935365	+	0.251676i	0.0342691	+	0.00922071i
$746$	10.2323	−	4.63778i	0.374629	−	0.169801i
$747$	8.31738	−	2.92290i	0.304317	−	0.106943i
$748$	−22.4301	+	60.1896i	−0.820124	+	2.20075i
$749$	3.28435	−	8.48716i	0.120008	−	0.310114i
$750$	29.3323	+	31.8212i	1.07106	+	1.16195i
$751$	−7.05323	−	11.3260i	−0.257376	−	0.413293i	0.694632	−	0.719365i	$-0.255567\pi$
$751$	−7.05323	−	11.3260i	−0.257376	−	0.413293i	−0.952009	+	0.306072i	$0.900985\pi$
$752$	−0.236343	−	0.0931646i	−0.00861856	−	0.00339736i
$753$	1.29192	+	41.2742i	0.0470803	+	1.50411i
$754$	19.4146	−	23.9036i	0.707038	−	0.870517i
$755$	12.9824	−	15.9841i	0.472478	−	0.581723i
$756$	1.90065	+	60.7217i	0.0691259	+	2.20843i
$757$	−46.5522	−	18.3505i	−1.69197	−	0.666959i	−0.693404	−	0.720549i	$-0.743890\pi$
$757$	−46.5522	−	18.3505i	−1.69197	−	0.666959i	−0.998563	+	0.0535901i	$0.982934\pi$
$758$	34.7180	+	55.7499i	1.26101	+	2.02493i
$759$	−16.0995	−	17.4657i	−0.584376	−	0.633963i
$760$	9.93752	−	25.6798i	0.360472	−	0.931503i
$761$	−7.46398	+	20.0291i	−0.270569	+	0.726054i	0.728586	+	0.684954i	$0.240178\pi$
$761$	−7.46398	+	20.0291i	−0.270569	+	0.726054i	−0.999155	+	0.0411000i	$0.986914\pi$
$762$	−51.1865	+	17.9880i	−1.85429	+	0.651637i
$763$	15.7940	−	7.15865i	0.571781	−	0.259160i
$764$	−76.7898	−	20.6616i	−2.77816	−	0.747512i
$765$	3.98099	+	1.23317i	0.143933	+	0.0445854i
$766$	−25.1490	−	36.2105i	−0.908672	−	1.30834i
$767$	1.67836	−	24.3422i	0.0606021	−	0.878945i
$768$	21.1683	+	2.39468i	0.763845	+	0.0864105i
$769$	−12.7871	−	13.1936i	−0.461114	−	0.475774i	0.446977	−	0.894545i	$-0.352501\pi$
$769$	−12.7871	−	13.1936i	−0.461114	−	0.475774i	−0.908091	+	0.418772i	$0.862461\pi$
$770$	−46.6482	−	31.9673i	−1.68108	−	1.15202i
$771$	−1.50404	−	4.19576i	−0.0541669	−	0.151107i
$772$	17.5323	−	20.5146i	0.631000	−	0.738338i
$773$

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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.c (of order \(251\), degree \(250\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43081 - 1.76164i) q^{2} +(-1.19346 + 1.03295i) q^{3} +(-0.646042 + 3.08364i) q^{4} +(0.511937 + 1.61679i) q^{5} +(3.52731 + 0.624490i) q^{6} +(-1.13380 + 3.29205i) q^{7} +(2.32143 - 1.19567i) q^{8} +(-0.0729611 + 0.503389i) q^{9} +O(q^{10})\)	\(q+(-1.43081 - 1.76164i) q^{2} +(-1.19346 + 1.03295i) q^{3} +(-0.646042 + 3.08364i) q^{4} +(0.511937 + 1.61679i) q^{5} +(3.52731 + 0.624490i) q^{6} +(-1.13380 + 3.29205i) q^{7} +(2.32143 - 1.19567i) q^{8} +(-0.0729611 + 0.503389i) q^{9} +(2.11572 - 3.21517i) q^{10} +(-4.01497 + 1.29899i) q^{11} +(-2.41424 - 4.34755i) q^{12} +(2.63886 - 0.890402i) q^{13} +(7.42166 - 2.71296i) q^{14} +(-2.28105 - 1.40078i) q^{15} +(0.343421 + 0.150504i) q^{16} +(-4.32246 - 2.15829i) q^{17} +(0.991183 - 0.591724i) q^{18} +(-2.53140 - 5.67925i) q^{19} +(-5.31635 + 0.534114i) q^{20} +(-2.04739 - 5.10011i) q^{21} +(8.03301 + 5.21431i) q^{22} +(0.991105 - 3.42581i) q^{23} +(-1.53548 + 3.82492i) q^{24} +(1.73683 - 1.22245i) q^{25} +(-5.34427 - 3.37471i) q^{26} +(-2.98614 - 4.66401i) q^{27} +(-9.41903 - 5.62304i) q^{28} +(-0.577953 + 4.83770i) q^{29} +(0.796090 + 6.02263i) q^{30} +(-0.390950 - 4.79481i) q^{31} +(-1.61472 - 5.85489i) q^{32} +(3.44992 - 5.69757i) q^{33} +(2.38250 + 10.7027i) q^{34} +(-5.90300 - 0.147798i) q^{35} +(-1.50514 - 0.550197i) q^{36} +(2.72917 + 3.44749i) q^{37} +(-6.38282 + 12.5853i) q^{38} +(-2.22963 + 3.78848i) q^{39} +(3.12157 + 3.14117i) q^{40} +(-2.36556 + 12.0401i) q^{41} +(-6.05512 + 10.9041i) q^{42} +(1.51231 - 8.24124i) q^{43} +(-1.41178 - 13.2199i) q^{44} +(-0.851227 + 0.139740i) q^{45} +(-7.45312 + 3.15571i) q^{46} +(-0.677057 + 0.0254347i) q^{47} +(-0.565324 + 0.175118i) q^{48} +(-4.03662 - 3.15466i) q^{49} +(-4.63859 - 1.31057i) q^{50} +(7.38811 - 1.88906i) q^{51} +(1.04087 + 8.71253i) q^{52} +(-0.739535 + 1.65916i) q^{53} +(-3.94370 + 11.9338i) q^{54} +(-4.15560 - 5.82637i) q^{55} +(1.30416 + 8.99793i) q^{56} +(8.88754 + 4.16315i) q^{57} +(9.34922 - 5.90369i) q^{58} +(3.36540 - 8.08897i) q^{59} +(5.79315 - 6.12899i) q^{60} +(3.38088 + 5.58355i) q^{61} +(-7.88735 + 7.54918i) q^{62} +(-1.57446 - 0.810935i) q^{63} +(-7.56839 + 10.6113i) q^{64} +(2.79052 + 3.81065i) q^{65} +(-14.9733 + 2.07463i) q^{66} +(-5.05245 + 3.10267i) q^{67} +(9.44788 - 11.9346i) q^{68} +(2.35585 + 5.11234i) q^{69} +(8.18571 + 10.6104i) q^{70} +(1.24570 + 7.89702i) q^{71} +(0.432512 + 1.25582i) q^{72} +(-2.58168 - 2.47099i) q^{73} +(2.16830 - 9.74051i) q^{74} +(-0.810107 + 3.25302i) q^{75} +(19.1482 - 4.13691i) q^{76} +(0.275834 - 14.6903i) q^{77} +(9.86412 - 1.49279i) q^{78} +(0.643384 + 11.4110i) q^{79} +(-0.0675233 + 0.632289i) q^{80} +(6.91841 + 2.04854i) q^{81} +(24.5950 - 13.0598i) q^{82} +(-8.03251 - 15.3585i) q^{83} +(17.0496 - 3.01853i) q^{84} +(1.27668 - 8.09342i) q^{85} +(-16.6819 + 9.12751i) q^{86} +(-4.30736 - 6.37062i) q^{87} +(-7.76732 + 7.81608i) q^{88} +(-3.25521 - 12.4071i) q^{89} +(1.46412 + 1.29961i) q^{90} +(-0.0606848 + 9.69679i) q^{91} +(9.92367 + 5.26943i) q^{92} +(5.41941 + 5.31860i) q^{93} +(1.01355 + 1.15634i) q^{94} +(7.88624 - 7.00017i) q^{95} +(7.97494 + 5.31967i) q^{96} +(0.373284 + 1.58318i) q^{97} +(0.218275 + 11.6248i) q^{98} +(-0.360960 - 2.11587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} + O(q^{10}) \)	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} - 233q^{10} - 239q^{11} - 239q^{12} - 245q^{13} - 223q^{14} - 231q^{15} - 263q^{16} - 243q^{17} - 217q^{18} - 229q^{19} - 195q^{20} - 215q^{21} - 233q^{22} - 241q^{23} - 181q^{24} - 280q^{25} - 215q^{26} - 237q^{27} - 185q^{28} - 217q^{29} - 159q^{30} - 219q^{31} - 185q^{32} - 209q^{33} - 167q^{34} - 187q^{35} - 203q^{36} - 237q^{37} - 161q^{38} - 197q^{39} - 135q^{40} - 209q^{41} - 117q^{42} - 221q^{43} - 147q^{44} - 167q^{45} - 167q^{46} - 195q^{47} - 141q^{48} - 234q^{49} - 145q^{50} - 177q^{51} - 179q^{52} - 211q^{53} - 83q^{54} - 165q^{55} - 125q^{56} - 177q^{57} - 205q^{58} - 189q^{59} - 27q^{60} - 193q^{61} - 143q^{62} - 159q^{63} - 185q^{64} - 155q^{65} - 97q^{66} - 201q^{67} - 155q^{68} - 113q^{69} - 123q^{70} - 153q^{71} - 21q^{72} - 213q^{73} - 83q^{74} - 161q^{75} - 97q^{76} - 139q^{77} - 43q^{78} - 191q^{79} + 3q^{80} - 188q^{81} - 97q^{82} - 161q^{83} + 67q^{84} - 159q^{85} - 121q^{86} - 121q^{87} - 143q^{88} - 155q^{89} + 115q^{90} - 137q^{91} - 119q^{92} - 123q^{93} - 99q^{94} - 181q^{95} + 67q^{96} - 229q^{97} - 63q^{98} - 85q^{99} + O(q^{100}) \)

Introduction

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