LMFDB - Embedded newform 503.2.c.a.2.15

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			2.15
Character	$\chi$	$=$	503.2
Dual form			503.2.c.a.252.15

$q$-expansion

$f(q)$	$=$	$q+(-0.604817 - 0.744661i) q^{2} +(1.49016 - 1.28975i) q^{3} +(0.221392 - 1.05673i) q^{4} +(-1.03109 - 3.25639i) q^{5} +(-1.86170 - 0.329604i) q^{6} +(-0.182067 + 0.528642i) q^{7} +(-2.62653 + 1.35281i) q^{8} +(0.126808 - 0.874904i) q^{9} +O(q^{10})$	\(q+(-0.604817 - 0.744661i) q^{2} +(1.49016 - 1.28975i) q^{3} +(0.221392 - 1.05673i) q^{4} +(-1.03109 - 3.25639i) q^{5} +(-1.86170 - 0.329604i) q^{6} +(-0.182067 + 0.528642i) q^{7} +(-2.62653 + 1.35281i) q^{8} +(0.126808 - 0.874904i) q^{9} +(-1.80128 + 2.73733i) q^{10} +(3.75292 - 1.21421i) q^{11} +(-1.03301 - 1.86025i) q^{12} +(3.71827 - 1.25462i) q^{13} +(0.503777 - 0.184154i) q^{14} +(-5.73642 - 3.52270i) q^{15} +(0.618189 + 0.270920i) q^{16} +(-6.48961 - 3.24039i) q^{17} +(-0.728203 + 0.434728i) q^{18} +(2.74376 + 6.15567i) q^{19} +(-3.66941 + 0.368652i) q^{20} +(0.410507 + 1.02259i) q^{21} +(-3.17400 - 2.06028i) q^{22} +(1.88530 - 6.51663i) q^{23} +(-2.16917 + 5.40347i) q^{24} +(-5.45213 + 3.83743i) q^{25} +(-3.18314 - 2.01003i) q^{26} +(2.24855 + 3.51197i) q^{27} +(0.518326 + 0.309434i) q^{28} +(-0.719777 + 6.02483i) q^{29} +(0.846273 + 6.40228i) q^{30} +(0.317364 + 3.89232i) q^{31} +(1.39881 + 5.07203i) q^{32} +(4.02644 - 6.64970i) q^{33} +(1.51203 + 6.79240i) q^{34} +(1.90919 + 0.0478020i) q^{35} +(-0.896466 - 0.327700i) q^{36} +(-4.87200 - 6.15431i) q^{37} +(2.92442 - 5.76623i) q^{38} +(3.92268 - 6.66522i) q^{39} +(7.11345 + 7.15811i) q^{40} +(-1.46958 + 7.47978i) q^{41} +(0.513198 - 0.924166i) q^{42} +(0.662269 - 3.60899i) q^{43} +(-0.452226 - 4.23465i) q^{44} +(-2.97978 + 0.489170i) q^{45} +(-5.99294 + 2.53746i) q^{46} +(6.47276 - 0.243160i) q^{47} +(1.27062 - 0.393594i) q^{48} +(5.26916 + 4.11790i) q^{49} +(6.15512 + 1.73904i) q^{50} +(-13.8499 + 3.54126i) q^{51} +(-0.502601 - 4.20698i) q^{52} +(-1.22737 + 2.75362i) q^{53} +(1.25527 - 3.79850i) q^{54} +(-7.82354 - 10.9690i) q^{55} +(-0.236947 - 1.63479i) q^{56} +(12.0279 + 5.63420i) q^{57} +(4.92179 - 3.10793i) q^{58} +(2.74319 - 6.59344i) q^{59} +(-4.99255 + 5.28197i) q^{60} +(-5.03231 - 8.31090i) q^{61} +(2.70651 - 2.59047i) q^{62} +(0.439424 + 0.226328i) q^{63} +(3.71476 - 5.20829i) q^{64} +(-7.91939 - 10.8145i) q^{65} +(-7.38704 + 1.02352i) q^{66} +(-6.22519 + 3.82285i) q^{67} +(-4.86097 + 6.14039i) q^{68} +(-5.59543 - 12.1424i) q^{69} +(-1.11912 - 1.45061i) q^{70} +(-1.06458 - 6.74883i) q^{71} +(0.850511 + 2.46951i) q^{72} +(8.35396 + 7.99578i) q^{73} +(-1.63621 + 7.35022i) q^{74} +(-3.17524 + 12.7503i) q^{75} +(7.11235 - 1.53661i) q^{76} +(-0.0414029 + 2.20502i) q^{77} +(-7.33584 + 1.11017i) q^{78} +(-0.0817102 - 1.44920i) q^{79} +(0.244810 - 2.29240i) q^{80} +(10.4233 + 3.08633i) q^{81} +(6.45873 - 3.42956i) q^{82} +(-2.41625 - 4.61998i) q^{83} +(1.17148 - 0.207404i) q^{84} +(-3.86057 + 24.4738i) q^{85} +(-3.08802 + 1.68961i) q^{86} +(6.69794 + 9.90632i) q^{87} +(-8.21456 + 8.26613i) q^{88} +(-3.52484 - 13.4347i) q^{89} +(2.16649 + 1.92307i) q^{90} +(-0.0137309 + 2.19406i) q^{91} +(-6.46895 - 3.43499i) q^{92} +(5.49305 + 5.39088i) q^{93} +(-4.09591 - 4.67295i) q^{94} +(17.2162 - 15.2818i) q^{95} +(8.62611 + 5.75403i) q^{96} +(-1.04799 - 4.44478i) q^{97} +(-0.120439 - 6.41432i) q^{98} +(-0.586412 - 3.43742i) 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 $

$2$	−0.604817	−	0.744661i	−0.427670	−	0.526555i	0.516379	−	0.856360i	$-0.327280\pi$
$2$	−0.604817	−	0.744661i	−0.427670	−	0.526555i	−0.944049	+	0.329806i	$0.893017\pi$
$3$	1.49016	−	1.28975i	0.860347	−	0.744638i	−0.108026	−	0.994148i	$-0.534453\pi$
$3$	1.49016	−	1.28975i	0.860347	−	0.744638i	0.968372	+	0.249510i	$0.0802696\pi$
$4$	0.221392	−	1.05673i	0.110696	−	0.528367i
$5$	−1.03109	−	3.25639i	−0.461119	−	1.45630i	−0.845925	−	0.533302i	$-0.820951\pi$
$5$	−1.03109	−	3.25639i	−0.461119	−	1.45630i	0.384806	−	0.922997i	$-0.374268\pi$
$6$	−1.86170	−	0.329604i	−0.760038	−	0.134560i
$7$	−0.182067	+	0.528642i	−0.0688150	+	0.199808i	−0.974611	−	0.223907i	$-0.928119\pi$
$7$	−0.182067	+	0.528642i	−0.0688150	+	0.199808i	0.905796	+	0.423715i	$0.139274\pi$
$8$	−2.62653	+	1.35281i	−0.928617	+	0.478290i
$9$	0.126808	−	0.874904i	0.0422695	−	0.291635i
$10$	−1.80128	+	2.73733i	−0.569615	+	0.865621i
$11$	3.75292	−	1.21421i	1.13155	−	0.366097i	0.318286	−	0.947995i	$-0.396893\pi$
$11$	3.75292	−	1.21421i	1.13155	−	0.366097i	0.813262	+	0.581897i	$0.197690\pi$
$12$	−1.03301	−	1.86025i	−0.298205	−	0.537007i
$13$	3.71827	−	1.25462i	1.03126	−	0.347968i	0.247406	−	0.968912i	$-0.420422\pi$
$13$	3.71827	−	1.25462i	1.03126	−	0.347968i	0.783855	+	0.620944i	$0.213250\pi$
$14$	0.503777	−	0.184154i	0.134640	−	0.0492171i
$15$	−5.73642	−	3.52270i	−1.48114	−	0.909556i
$16$	0.618189	+	0.270920i	0.154547	+	0.0677300i
$17$	−6.48961	−	3.24039i	−1.57396	−	0.785910i	−0.574492	−	0.818510i	$-0.694800\pi$
$17$	−6.48961	−	3.24039i	−1.57396	−	0.785910i	−0.999468	+	0.0326003i	$0.989621\pi$
$18$	−0.728203	+	0.434728i	−0.171639	+	0.102466i
$19$	2.74376	+	6.15567i	0.629462	+	1.41221i	0.894103	+	0.447861i	$0.147814\pi$
$19$	2.74376	+	6.15567i	0.629462	+	1.41221i	−0.264641	+	0.964347i	$0.585254\pi$
$20$	−3.66941	+	0.368652i	−0.820504	+	0.0824332i
$21$	0.410507	+	1.02259i	0.0895799	+	0.223146i
$22$	−3.17400	−	2.06028i	−0.676700	−	0.439253i
$23$	1.88530	−	6.51663i	0.393112	−	1.35881i	−0.482542	−	0.875873i	$-0.660286\pi$
$23$	1.88530	−	6.51663i	0.393112	−	1.35881i	0.875654	−	0.482939i	$-0.160431\pi$
$24$	−2.16917	+	5.40347i	−0.442780	+	1.10298i
$25$	−5.45213	+	3.83743i	−1.09043	+	0.767486i
$26$	−3.18314	−	2.01003i	−0.624264	−	0.394200i
$27$	2.24855	+	3.51197i	0.432733	+	0.675879i
$28$	0.518326	+	0.309434i	0.0979544	+	0.0584775i
$29$	−0.719777	+	6.02483i	−0.133659	+	1.11878i	0.753542	+	0.657400i	$0.228344\pi$
$29$	−0.719777	+	6.02483i	−0.133659	+	1.11878i	−0.887201	+	0.461383i	$0.847353\pi$
$30$	0.846273	+	6.40228i	0.154508	+	1.16889i
$31$	0.317364	+	3.89232i	0.0570003	+	0.699081i	0.961890	+	0.273436i	$0.0881601\pi$
$31$	0.317364	+	3.89232i	0.0570003	+	0.699081i	−0.904890	+	0.425646i	$0.860047\pi$
$32$	1.39881	+	5.07203i	0.247278	+	0.896616i
$33$	4.02644	−	6.64970i	0.700914	−	1.15756i
$34$	1.51203	+	6.79240i	0.259312	+	1.16489i
$35$	1.90919	+	0.0478020i	0.322712	+	0.00808002i
$36$	−0.896466	−	0.327700i	−0.149411	−	0.0546166i
$37$	−4.87200	−	6.15431i	−0.800952	−	1.01176i	−0.999498	−	0.0316714i	$-0.989917\pi$
$37$	−4.87200	−	6.15431i	−0.800952	−	1.01176i	0.198547	−	0.980091i	$-0.436378\pi$
$38$	2.92442	−	5.76623i	0.474403	−	0.935406i
$39$	3.92268	−	6.66522i	0.628132	−	1.06729i
$40$	7.11345	+	7.15811i	1.12474	+	1.13180i
$41$	−1.46958	+	7.47978i	−0.229510	+	1.16814i	0.673720	+	0.738987i	$0.264696\pi$
$41$	−1.46958	+	7.47978i	−0.229510	+	1.16814i	−0.903230	+	0.429158i	$0.858810\pi$
$42$	0.513198	−	0.924166i	0.0791882	−	0.142602i
$43$	0.662269	−	3.60899i	0.100995	−	0.550365i	−0.893800	−	0.448467i	$-0.851970\pi$
$43$	0.662269	−	3.60899i	0.100995	−	0.550365i	0.994795	−	0.101899i	$-0.0324918\pi$
$44$	−0.452226	−	4.23465i	−0.0681757	−	0.638398i
$45$	−2.97978	+	0.489170i	−0.444199	+	0.0729211i
$46$	−5.99294	+	2.53746i	−0.883611	+	0.374128i
$47$	6.47276	−	0.243160i	0.944149	−	0.0354685i	0.438988	−	0.898493i	$-0.355337\pi$
$47$	6.47276	−	0.243160i	0.944149	−	0.0354685i	0.505162	+	0.863025i	$0.331433\pi$
$48$	1.27062	−	0.393594i	0.183398	−	0.0568104i
$49$	5.26916	+	4.11790i	0.752737	+	0.588271i
$50$	6.15512	+	1.73904i	0.870466	+	0.245938i
$51$	−13.8499	+	3.54126i	−1.93937	+	0.495876i
$52$	−0.502601	−	4.20698i	−0.0696982	−	0.583403i
$53$	−1.22737	+	2.75362i	−0.168592	+	0.378238i	−0.977878	−	0.209176i	$-0.932922\pi$
$53$	−1.22737	+	2.75362i	−0.168592	+	0.378238i	0.809286	+	0.587414i	$0.199854\pi$
$54$	1.25527	−	3.79850i	0.170820	−	0.516911i
$55$	−7.82354	−	10.9690i	−1.05493	−	1.47906i
$56$	−0.236947	−	1.63479i	−0.0316634	−	0.218459i
$57$	12.0279	+	5.63420i	1.59314	+	0.746267i
$58$	4.92179	−	3.10793i	0.646263	−	0.408091i
$59$	2.74319	−	6.59344i	0.357132	−	0.858393i	−0.638891	−	0.769298i	$-0.720606\pi$
$59$	2.74319	−	6.59344i	0.357132	−	0.858393i	0.996023	−	0.0890954i	$-0.0283976\pi$
$60$	−4.99255	+	5.28197i	−0.644535	+	0.681900i
$61$	−5.03231	−	8.31090i	−0.644321	−	1.06410i	−0.991970	−	0.126476i	$-0.959633\pi$
$61$	−5.03231	−	8.31090i	−0.644321	−	1.06410i	0.347648	−	0.937625i	$-0.386980\pi$
$62$	2.70651	−	2.59047i	0.343727	−	0.328990i
$63$	0.439424	+	0.226328i	0.0553622	+	0.0285146i
$64$	3.71476	−	5.20829i	0.464346	−	0.651036i
$65$	−7.91939	−	10.8145i	−0.982280	−	1.34137i
$66$	−7.38704	+	1.02352i	−0.909281	+	0.125986i
$67$	−6.22519	+	3.82285i	−0.760528	+	0.467035i	−0.848571	−	0.529082i	$-0.822537\pi$
$67$	−6.22519	+	3.82285i	−0.760528	+	0.467035i	0.0880424	+	0.996117i	$0.471939\pi$
$68$	−4.86097	+	6.14039i	−0.589480	+	0.744631i
$69$	−5.59543	−	12.1424i	−0.673610	−	1.46178i
$70$	−1.11912	−	1.45061i	−0.133760	−	0.173381i
$71$	−1.06458	−	6.74883i	−0.126343	−	0.800939i	−0.966136	−	0.258033i	$-0.916926\pi$
$71$	−1.06458	−	6.74883i	−0.126343	−	0.800939i	0.839794	−	0.542906i	$-0.182676\pi$
$72$	0.850511	+	2.46951i	0.100234	+	0.291034i
$73$	8.35396	+	7.99578i	0.977757	+	0.935836i	0.997952	−	0.0639603i	$-0.0203731\pi$
$73$	8.35396	+	7.99578i	0.977757	+	0.935836i	−0.0201955	+	0.999796i	$0.506429\pi$
$74$	−1.63621	+	7.35022i	−0.190205	+	0.854446i
$75$	−3.17524	+	12.7503i	−0.366645	+	1.47228i
$76$	7.11235	−	1.53661i	0.815843	−	0.176261i
$77$	−0.0414029	+	2.20502i	−0.00471830	+	0.251285i
$78$	−7.33584	+	1.11017i	−0.830620	+	0.125702i
$79$	−0.0817102	−	1.44920i	−0.00919311	−	0.163048i	−0.999677	−	0.0254182i	$-0.991908\pi$
$79$	−0.0817102	−	1.44920i	−0.00919311	−	0.163048i	0.990484	−	0.137629i	$-0.0439483\pi$
$80$	0.244810	−	2.29240i	0.0273706	−	0.256299i
$81$	10.4233	+	3.08633i	1.15814	+	0.342926i
$82$	6.45873	−	3.42956i	0.713247	−	0.378731i
$83$	−2.41625	−	4.61998i	−0.265218	−	0.507109i	0.716467	−	0.697621i	$-0.245758\pi$
$83$	−2.41625	−	4.61998i	−0.265218	−	0.507109i	−0.981685	+	0.190512i	$0.938985\pi$
$84$	1.17148	−	0.207404i	0.127819	−	0.0226296i
$85$	−3.86057	+	24.4738i	−0.418738	+	2.65456i
$86$	−3.08802	+	1.68961i	−0.332990	+	0.182195i
$87$	6.69794	+	9.90632i	0.718095	+	1.06207i
$88$	−8.21456	+	8.26613i	−0.875675	+	0.881172i
$89$	−3.52484	−	13.4347i	−0.373632	−	1.42408i	−0.841488	−	0.540275i	$-0.818320\pi$
$89$	−3.52484	−	13.4347i	−0.373632	−	1.42408i	0.467856	−	0.883805i	$-0.345027\pi$
$90$	2.16649	+	1.92307i	0.228368	+	0.202709i
$91$	−0.0137309	+	2.19406i	−0.00143939	+	0.230000i
$92$	−6.46895	−	3.43499i	−0.674435	−	0.358122i
$93$	5.49305	+	5.39088i	0.569603	+	0.559008i
$94$	−4.09591	−	4.67295i	−0.422461	−	0.481978i
$95$	17.2162	−	15.2818i	1.76634	−	1.56788i
$96$	8.62611	+	5.75403i	0.880399	+	0.587268i
$97$	−1.04799	−	4.44478i	−0.106408	−	0.451299i	−0.999997	−	0.00241396i	$-0.999232\pi$
$97$	−1.04799	−	4.44478i	−0.106408	−	0.451299i	0.893589	−	0.448885i	$-0.148179\pi$
$98$	−0.120439	−	6.41432i	−0.0121662	−	0.647944i
$99$	−0.586412	−	3.43742i	−0.0589367	−	0.345474i
$100$	2.84808	+	6.61102i	0.284808	+	0.661102i
$101$	10.7494	−	4.23731i	1.06960	−	0.421628i	0.234723	−	0.972062i	$-0.424582\pi$
$101$	10.7494	−	4.23731i	1.06960	−	0.421628i	0.834878	+	0.550435i	$0.185538\pi$
$102$	11.0137	+	8.17164i	1.09052	+	0.809113i
$103$	18.2741	−	3.70930i	1.80060	−	0.365488i	0.821713	−	0.569902i	$-0.193019\pi$
$103$	18.2741	−	3.70930i	1.80060	−	0.365488i	0.978885	+	0.204414i	$0.0655288\pi$
$104$	−8.06886	+	8.32538i	−0.791217	+	0.816371i
$105$	2.90666	−	2.39115i	0.283661	−	0.233352i
$106$	2.79284	−	0.751463i	0.271265	−	0.0729885i
$107$	9.65489	+	0.362701i	0.933373	+	0.0350636i	0.499881	−	0.866094i	$-0.333377\pi$
$107$	9.65489	+	0.362701i	0.933373	+	0.0350636i	0.433492	+	0.901158i	$0.357281\pi$
$108$	4.20903	−	1.59859i	0.405014	−	0.153825i
$109$	−5.51280	−	5.83238i	−0.528030	−	0.558641i	0.406900	−	0.913473i	$-0.366610\pi$
$109$	−5.51280	−	5.83238i	−0.528030	−	0.558641i	−0.934930	+	0.354832i	$0.884538\pi$
$110$	−3.43638	+	12.4601i	−0.327646	+	1.18803i
$111$	−15.1976	−	2.88727i	−1.44249	−	0.274048i
$112$	−0.255772	+	0.277475i	−0.0241681	+	0.0262189i
$113$	−4.98644	−	10.1448i	−0.469085	−	0.954345i	−0.994622	−	0.103574i	$-0.966972\pi$
$113$	−4.98644	−	10.1448i	−0.469085	−	0.954345i	0.525537	−	0.850771i	$-0.323865\pi$
$114$	−3.07914	−	12.3644i	−0.288388	−	1.15803i
$115$	−23.1646	+	0.579991i	−2.16011	+	0.0540845i
$116$	6.20729	+	2.09446i	0.576332	+	0.194466i
$117$	−0.626162	−	3.41222i	−0.0578887	−	0.315460i
$118$	−6.56901	+	1.94508i	−0.604726	+	0.179059i
$119$	2.89455	−	2.84071i	0.265343	−	0.260408i
$120$	19.8324	+	1.49218i	1.81044	+	0.136216i
$121$	3.69478	−	2.67031i	0.335889	−	0.242755i
$122$	−3.14517	+	8.77394i	−0.284751	+	0.794355i
$123$	7.45713	+	13.0415i	0.672387	+	1.17591i
$124$	4.18341	+	0.526360i	0.375681	+	0.0472685i
$125$	4.53053	+	3.45019i	0.405223	+	0.308595i
$126$	−0.0972336	−	0.464109i	−0.00866226	−	0.0413461i
$127$	−4.87533	+	2.74737i	−0.432615	+	0.243790i	−0.691874	−	0.722018i	$-0.743215\pi$
$127$	−4.87533	+	2.74737i	−0.432615	+	0.243790i	0.259259	+	0.965808i	$0.416522\pi$
$128$	4.37700	−	0.274278i	0.386876	−	0.0242429i
$129$	−3.66780	−	6.23215i	−0.322932	−	0.548710i
$130$	−3.26334	+	12.4380i	−0.286214	+	1.09089i
$131$	−12.6715	+	8.45250i	−1.10712	+	0.738499i	−0.967793	−	0.251749i	$-0.918994\pi$
$131$	−12.6715	+	8.45250i	−1.10712	+	0.738499i	−0.139322	+	0.990247i	$0.544492\pi$
$132$	−6.13554	−	5.72707i	−0.534030	−	0.498477i
$133$	−3.75370	+	0.329721i	−0.325487	+	0.0285905i
$134$	6.61183	+	2.32354i	0.571175	+	0.200723i
$135$	9.11787	−	10.9433i	0.784741	−	0.941849i
$136$	21.4287	−	0.268223i	1.83750	−	0.0229999i
$137$	−3.02646	−	7.82073i	−0.258568	−	0.668170i	0.741428	−	0.671032i	$-0.234149\pi$
$137$	−3.02646	−	7.82073i	−0.258568	−	0.668170i	−0.999996	+	0.00286193i	$0.999089\pi$
$138$	−5.65777	+	11.5106i	−0.481622	+	0.979851i
$139$	−3.10441	−	0.670699i	−0.263312	−	0.0568880i	0.0775947	−	0.996985i	$-0.475276\pi$
$139$	−3.10441	−	0.670699i	−0.263312	−	0.0568880i	−0.340907	+	0.940097i	$0.610734\pi$
$140$	0.473194	−	2.00692i	0.0399922	−	0.169616i
$141$	9.33186	−	8.71060i	0.785885	−	0.733565i
$142$	−4.38172	+	4.87456i	−0.367705	+	0.409064i
$143$	12.4310	−	9.22322i	1.03953	−	0.771285i
$144$	0.315420	−	0.506501i	0.0262850	−	0.0422084i
$145$	20.3613	−	3.86828i	1.69092	−	0.321244i
$146$	0.901531	−	11.0569i	0.0746113	−	0.915072i
$147$	13.1630	−	0.659559i	1.08566	−	0.0543995i
$148$	−7.58209	+	3.78589i	−0.623244	+	0.311198i
$149$	−3.86695	+	6.03973i	−0.316793	+	0.494794i	−0.963414	−	0.268017i	$-0.913632\pi$
$149$	−3.86695	+	6.03973i	−0.316793	+	0.494794i	0.646621	+	0.762811i	$0.276181\pi$
$150$	11.4151	−	5.34712i	0.932037	−	0.436590i
$151$	12.3811	+	18.8151i	1.00756	+	1.53115i	0.838028	+	0.545626i	$0.183708\pi$
$151$	12.3811	+	18.8151i	1.00756	+	1.53115i	0.169534	+	0.985524i	$0.445774\pi$
$152$	−15.5340	−	12.4563i	−1.25997	−	1.01034i
$153$	−3.65797	+	5.26687i	−0.295729	+	0.425802i
$154$	1.66703	−	1.30280i	0.134333	−	0.104983i
$155$	12.3477	−	5.04680i	0.991788	−	0.405369i
$156$	−6.17491	−	5.62086i	−0.494389	−	0.450029i
$157$	−5.14410	+	10.8051i	−0.410544	+	0.862342i	0.588024	+	0.808843i	$0.299906\pi$
$157$	−5.14410	+	10.8051i	−0.410544	+	0.862342i	−0.998568	+	0.0534990i	$0.982963\pi$
$158$	−1.02974	+	0.937347i	−0.0819219	+	0.0745713i
$159$	1.72250	+	5.68633i	0.136603	+	0.450956i
$160$	15.0742	−	9.78481i	1.19172	−	0.773557i
$161$	3.10172	+	2.18311i	0.244450	+	0.172054i
$162$	−4.00590	−	9.62847i	−0.314733	−	0.756484i
$163$	13.4040	+	5.09084i	1.04988	+	0.398746i	0.818734	−	0.574173i	$-0.194676\pi$
$163$	13.4040	+	5.09084i	1.04988	+	0.398746i	0.231147	+	0.972919i	$0.425752\pi$
$164$	7.57878	+	3.20892i	0.591803	+	0.250574i
$165$	−25.8056	−	6.25520i	−2.00897	−	0.486966i
$166$	−1.97893	+	4.59353i	−0.153595	+	0.356527i
$167$	−0.137492	+	4.39258i	−0.0106395	+	0.339908i	0.979636	+	0.200784i	$0.0643490\pi$
$167$	−0.137492	+	4.39258i	−0.0106395	+	0.339908i	−0.990275	+	0.139124i	$0.955571\pi$
$168$	−2.46157	−	2.13051i	−0.189914	−	0.164372i
$169$	1.90902	−	1.45380i	0.146848	−	0.111831i
$170$	20.5596	−	11.9274i	1.57685	−	0.914787i
$171$	5.73356	−	1.61994i	0.438456	−	0.123880i
$172$	−3.66712	−	1.49884i	−0.279615	−	0.114286i
$173$	5.30947	+	11.1525i	0.403672	+	0.847908i	0.999012	+	0.0444344i	$0.0141486\pi$
$173$	5.30947	+	11.1525i	0.403672	+	0.847908i	−0.595341	+	0.803473i	$0.702983\pi$
$174$	3.32582	−	10.9792i	0.252130	−	0.832332i
$175$	−1.03597	−	3.58090i	−0.0783122	−	0.270690i
$176$	2.64897	+	0.266132i	0.199673	+	0.0200605i
$177$	−4.41610	−	13.3633i	−0.331934	−	1.00445i
$178$	−7.87245	+	10.7504i	−0.590065	+	0.805775i
$179$	−1.72073	+	3.19218i	−0.128613	+	0.238594i	−0.936442	−	0.350823i	$-0.885902\pi$
$179$	−1.72073	+	3.19218i	−0.128613	+	0.238594i	0.807828	+	0.589418i	$0.200643\pi$
$180$	−0.142777	+	3.25713i	−0.0106419	+	0.242772i
$181$	0.794388	+	11.5215i	0.0590464	+	0.856383i	0.930590	+	0.366064i	$0.119295\pi$
$181$	0.794388	+	11.5215i	0.0590464	+	0.856383i	−0.871543	+	0.490319i	$0.836880\pi$
$182$	1.64213	−	1.31678i	0.121723	−	0.0976061i
$183$	−18.2180	−	5.89417i	−1.34671	−	0.435710i
$184$	3.86396	+	19.6665i	0.284855	+	1.44984i
$185$	−15.0173	+	22.2108i	−1.10410	+	1.63297i
$186$	0.692085	−	7.35095i	0.0507461	−	0.538998i
$187$	−28.2895	−	4.28120i	−2.06873	−	0.313072i
$188$	1.17606	−	6.89382i	0.0857732	−	0.502783i
$189$	−2.26596	+	0.549262i	−0.164825	+	0.0399529i
$190$	−21.7924	−	3.57751i	−1.58099	−	0.259540i
$191$	−1.28613	+	22.8105i	−0.0930609	+	1.65051i	0.515415	+	0.856940i	$0.327638\pi$
$191$	−1.28613	+	22.8105i	−0.0930609	+	1.65051i	−0.608476	+	0.793572i	$0.708219\pi$
$192$	−1.18179	−	12.5523i	−0.0852883	−	0.905886i
$193$	9.80258	+	5.36348i	0.705605	+	0.386072i	0.792274	−	0.610165i	$-0.208897\pi$
$193$	9.80258	+	5.36348i	0.705605	+	0.386072i	−0.0866686	+	0.996237i	$0.527622\pi$
$194$	−2.67601	+	3.46868i	−0.192126	+	0.249037i
$195$	−25.7492	−	5.90131i	−1.84394	−	0.422601i
$196$	5.51807	−	4.65643i	0.394148	−	0.332602i
$197$	27.0587	−	2.03588i	1.92785	−	0.145050i	0.944710	−	0.327907i	$-0.106343\pi$
$197$	27.0587	−	2.03588i	1.92785	−	0.145050i	0.983140	+	0.182857i	$0.0585345\pi$
$198$	−2.20504	+	2.51569i	−0.156705	+	0.178782i
$199$	−0.0826216	−	13.2021i	−0.00585689	−	0.935869i	−0.886669	−	0.462404i	$-0.846987\pi$
$199$	−0.0826216	−	13.2021i	−0.00585689	−	0.935869i	0.880813	−	0.473465i	$-0.156997\pi$
$200$	9.12885	−	17.4548i	0.645507	−	1.23424i
$201$	−4.34604	+	13.7256i	−0.306546	+	0.968130i
$202$	−9.65675	−	5.44183i	−0.679447	−	0.382886i
$203$	−3.05393	−	1.47743i	−0.214344	−	0.103695i
$204$	0.675921	+	15.4196i	0.0473240	+	1.07959i
$205$	25.8723	−	2.92682i	1.80700	−	0.204418i
$206$	−13.8146	−	11.3645i	−0.962512	−	0.791805i
$207$	−5.46236	−	2.47582i	−0.379660	−	0.172081i
$208$	2.63849	+	0.231762i	0.182946	+	0.0160698i
$209$	17.7714	+	19.7703i	1.22927	+	1.36754i
$210$	−3.53859	−	0.718270i	−0.244186	−	0.0495653i
$211$	−19.1900	+	13.1506i	−1.32109	+	0.905326i	−0.999141	−	0.0414302i	$-0.986809\pi$
$211$	−19.1900	+	13.1506i	−1.32109	+	0.905326i	−0.321951	+	0.946756i	$0.604338\pi$
$212$	2.63811	+	1.90663i	0.181186	+	0.130948i
$213$	−10.2907	−	8.68382i	−0.705108	−	0.595006i
$214$	−5.56935	−	7.40899i	−0.380713	−	0.506468i
$215$	−12.4351	+	1.56460i	−0.848068	+	0.106705i
$216$	−10.6569	−	6.18243i	−0.725109	−	0.420661i
$217$	−2.11543	−	0.540892i	−0.143605	−	0.0367182i
$218$	−1.00891	+	7.63269i	−0.0683322	+	0.516951i
$219$	22.7613	+	1.14050i	1.53807	+	0.0770682i
$220$	−13.3234	+	5.83894i	−0.898262	+	0.393661i
$221$	−28.1955	−	3.90666i	−1.89664	−	0.262790i
$222$	7.04174	+	13.0633i	0.472610	+	0.876754i
$223$	−9.67015	+	4.67822i	−0.647561	+	0.313277i	−0.730129	−	0.683309i	$-0.760540\pi$
$223$	−9.67015	+	4.67822i	−0.647561	+	0.313277i	0.0825685	+	0.996585i	$0.473688\pi$
$224$	−2.93597	−	0.183978i	−0.196168	−	0.0122925i
$225$	2.66601	+	5.25671i	0.177734	+	0.350447i
$226$	−4.53857	+	9.84898i	−0.301901	+	0.655144i
$227$	−16.2454	+	3.72319i	−1.07824	+	0.247117i	−0.725234	−	0.688502i	$-0.758268\pi$
$227$	−16.2454	+	3.72319i	−1.07824	+	0.247117i	−0.353011	+	0.935619i	$0.614842\pi$
$228$	8.61673	−	11.4630i	0.570657	−	0.759153i
$229$	2.09901	−	3.67088i	0.138707	−	0.242579i	−0.790236	−	0.612803i	$-0.790042\pi$
$229$	2.09901	−	3.67088i	0.138707	−	0.242579i	0.928942	+	0.370224i	$0.120719\pi$
$230$	14.4422	+	16.8990i	0.952293	+	1.11429i
$231$	2.78223	+	3.33924i	0.183057	+	0.219706i
$232$	−6.25992	−	16.7981i	−0.410984	−	1.10285i
$233$	−8.00359	−	0.100181i	−0.524333	−	0.00656305i	−0.250088	−	0.968223i	$-0.580460\pi$
$233$	−8.00359	−	0.100181i	−0.524333	−	0.00656305i	−0.274244	+	0.961660i	$0.588428\pi$
$234$	−2.16224	+	2.53005i	−0.141350	+	0.165394i
$235$	−7.46584	−	20.8271i	−0.487018	−	1.35861i
$236$	−6.36019	−	4.35855i	−0.414013	−	0.283718i
$237$	−1.99087	−	2.05416i	−0.129321	−	0.133432i
$238$	−3.86604	−	0.437349i	−0.250598	−	0.0283491i
$239$	0.529669	−	7.68208i	0.0342614	−	0.496913i	−0.949067	−	0.315074i	$-0.897971\pi$
$239$	0.529669	−	7.68208i	0.0342614	−	0.496913i	0.983328	−	0.181838i	$-0.0582047\pi$
$240$	−2.59182	−	3.73180i	−0.167301	−	0.240887i
$241$	−4.61983	−	1.43106i	−0.297589	−	0.0921828i	0.143487	−	0.989652i	$-0.454168\pi$
$241$	−4.61983	−	1.43106i	−0.297589	−	0.0921828i	−0.441077	+	0.897469i	$0.645403\pi$
$242$	−4.22314	−	1.13631i	−0.271473	−	0.0730447i
$243$	8.11842	−	3.67968i	0.520797	−	0.236052i
$244$	−9.89652	+	3.47785i	−0.633560	+	0.222646i
$245$	7.97648	−	21.4044i	0.509598	−	1.36747i
$246$	5.20128	−	13.4408i	0.331622	−	0.856951i
$247$	17.9250	+	19.4461i	1.14054	+	1.23732i
$248$	−6.09912	−	9.79395i	−0.387295	−	0.621916i
$249$	−9.55923	−	3.76817i	−0.605792	−	0.238798i
$250$	−0.170917	−	5.46045i	−0.0108098	−	0.345349i
$251$	−13.3935	+	16.4903i	−0.845389	+	1.04086i	0.153223	+	0.988192i	$0.451035\pi$
$251$	−13.3935	+	16.4903i	−0.845389	+	1.04086i	−0.998612	+	0.0526653i	$0.983228\pi$
$252$	0.336453	−	0.414247i	0.0211946	−	0.0260951i
$253$	−0.837162	−	26.7456i	−0.0526319	−	1.68148i
$254$	4.99454	+	1.96881i	0.313386	+	0.123534i
$255$	25.8122	+	41.4492i	1.61642	+	2.59565i
$256$	−11.5233	−	12.5011i	−0.720207	−	0.781320i
$257$	−1.38141	+	3.56974i	−0.0861701	+	0.222674i	−0.969020	−	0.246980i	$-0.920562\pi$
$257$	−1.38141	+	3.56974i	−0.0861701	+	0.222674i	0.882850	+	0.469654i	$0.155621\pi$
$258$	−2.42248	+	6.50058i	−0.150817	+	0.404708i
$259$	4.14046	−	1.45505i	0.257276	−	0.0904121i
$260$	−13.1813	+	5.97445i	−0.817470	+	0.370519i
$261$	5.17987	+	1.39374i	0.320626	+	0.0862700i
$262$	13.9582	+	4.32376i	0.862340	+	0.267123i
$263$	−1.14594	−	1.64996i	−0.0706616	−	0.101741i	0.784432	−	0.620215i	$-0.212955\pi$
$263$	−1.14594	−	1.64996i	−0.0706616	−	0.101741i	−0.855094	+	0.518474i	$0.826500\pi$
$264$	−1.57979	+	22.9126i	−0.0972296	+	1.41017i
$265$	10.2324	+	1.15754i	0.628569	+	0.0711073i
$266$	2.51583	+	2.59581i	0.154256	+	0.159159i
$267$	−22.5801	−	15.4738i	−1.38188	−	0.946982i
$268$	2.66152	+	7.42472i	0.162578	+	0.453537i
$269$	−1.23075	+	1.44011i	−0.0750402	+	0.0878052i	−0.796454	−	0.604699i	$-0.793293\pi$
$269$	−1.23075	+	1.44011i	−0.0750402	+	0.0878052i	0.721414	+	0.692504i	$0.243493\pi$
$270$	−13.6637	−	0.171028i	−0.831546	−	0.0104084i
$271$	−11.0401	−	29.6253i	−0.670637	−	1.79961i	−0.596873	−	0.802336i	$-0.703590\pi$
$271$	−11.0401	−	29.6253i	−0.670637	−	1.79961i	−0.0737640	−	0.997276i	$-0.523501\pi$
$272$	−3.13391	−	3.76133i	−0.190021	−	0.228064i
$273$	2.80933	+	3.28722i	0.170028	+	0.198951i
$274$	−3.99334	+	6.98380i	−0.241247	+	0.421907i
$275$	−15.8020	+	21.0216i	−0.952894	+	1.26765i
$276$	−14.0701	+	3.22464i	−0.846919	+	0.194101i
$277$	−0.386137	+	0.837941i	−0.0232007	+	0.0503470i	−0.919460	−	0.393183i	$-0.871374\pi$
$277$	−0.386137	+	0.837941i	−0.0232007	+	0.0503470i	0.896259	+	0.443530i	$0.146274\pi$
$278$	1.37815	+	2.71738i	0.0826562	+	0.162978i
$279$	3.44565	+	0.215916i	0.206286	+	0.0129266i
$280$	−5.07921	+	2.45722i	−0.303541	+	0.146847i
$281$	2.66231	+	4.93893i	0.158820	+	0.294632i	0.947252	−	0.320490i	$-0.103848\pi$
$281$	2.66231	+	4.93893i	0.158820	+	0.294632i	−0.788432	+	0.615122i	$0.789107\pi$
$282$	−12.1305	−	1.68075i	−0.722362	−	0.100087i
$283$	−14.6036	+	6.40001i	−0.868095	+	0.380441i	−0.787506	−	0.616306i	$-0.788628\pi$
$283$	−14.6036	+	6.40001i	−0.868095	+	0.380441i	−0.0805888	+	0.996747i	$0.525680\pi$
$284$	−7.36741	−	0.369159i	−0.437175	−	0.0219056i
$285$	5.94520	−	44.9770i	0.352163	−	2.66421i
$286$	−14.3867	−	3.67851i	−0.850701	−	0.217515i
$287$	−3.68656	−	2.13871i	−0.217611	−	0.126244i
$288$	4.61492	−	0.580653i	0.271937	−	0.0342153i
$289$	21.4001	+	28.4688i	1.25883	+	1.67464i
$290$	−15.1954	−	12.8227i	−0.892307	−	0.752974i
$291$	−7.29434	−	5.27180i	−0.427602	−	0.309038i
$292$	10.2989	−	7.05771i	0.602698	−	0.413021i
$293$	27.1063	+	5.50208i	1.58357	+	0.321435i	0.909006	−	0.416784i	$-0.136843\pi$
$293$	27.1063	+	5.50208i	1.58357	+	0.321435i	0.674561	+	0.738219i	$0.264333\pi$
$294$	−8.45235	−	9.40305i	−0.492951	−	0.548397i
$295$	−24.2993	−	2.13442i	−1.41476	−	0.124271i
$296$	21.1220	+	9.57359i	1.22769	+	0.556453i
$297$	12.7029	+	10.4499i	0.737095	+	0.606367i
$298$	6.83635	−	0.773366i	0.396019	−	0.0447999i
$299$	−1.16583	−	26.5959i	−0.0674219	−	1.53808i
$300$	12.7707	+	6.17819i	0.737315	+	0.356698i
$301$	1.78729	+	1.00718i	0.103017	+	0.0580530i
$302$	6.52255	−	20.5994i	0.375330	−	1.18536i
$303$	10.5532	−	20.1783i	0.606267	−	1.15921i
$304$	0.0284669	+	4.54871i	0.00163269	+	0.260886i
$305$	−21.8747	+	24.9565i	−1.25254	+	1.42900i
$306$	6.13444	−	0.461551i	0.350682	−	0.0263851i
$307$	1.68183	−	1.41921i	0.0959871	−	0.0809987i	−0.595649	−	0.803245i	$-0.703105\pi$
$307$	1.68183	−	1.41921i	0.0959871	−	0.0809987i	0.691636	+	0.722246i	$0.256890\pi$
$308$	2.32095	+	0.531926i	0.132249	+	0.0303093i
$309$	22.4473	−	29.0965i	1.27698	−	1.65524i
$310$	−11.2262	−	6.14243i	−0.637607	−	0.348867i
$311$	−1.21878	−	12.9452i	−0.0691106	−	0.734055i	−0.960031	−	0.279895i	$-0.909700\pi$
$311$	−1.21878	−	12.9452i	−0.0691106	−	0.734055i	0.890920	−	0.454160i	$-0.150061\pi$
$312$	−1.28627	+	22.8130i	−0.0728205	+	1.29153i
$313$	5.76054	+	0.945670i	0.325605	+	0.0534524i	0.322578	−	0.946543i	$-0.395451\pi$
$313$	5.76054	+	0.945670i	0.325605	+	0.0534524i	0.00302750	+	0.999995i	$0.499036\pi$
$314$	11.1574	−	2.70451i	0.629648	−	0.152624i
$315$	0.283924	−	1.66430i	0.0159973	−	0.0937726i
$316$	−1.54951	−	0.234495i	−0.0871666	−	0.0131914i
$317$	−0.332316	+	3.52968i	−0.0186647	+	0.198247i	0.981318	+	0.192392i	$0.0616246\pi$
$317$	−0.332316	+	3.52968i	−0.0186647	+	0.198247i	−0.999983	+	0.00585463i	$0.998136\pi$
$318$	3.19259	−	4.72187i	0.179032	−	0.264790i
$319$	4.61412	+	23.4847i	0.258341	+	1.31489i
$320$	−20.7905	−	6.72647i	−1.16222	−	0.376021i
$321$	14.8552	−	11.9119i	0.829134	−	0.664858i
$322$	−0.250291	−	3.63011i	−0.0139482	−	0.202298i
$323$	2.14085	−	48.8387i	0.119120	−	2.71746i
$324$	5.56906	−	10.3313i	0.309392	−	0.573963i
$325$	−15.4579	+	21.1089i	−0.857453	+	1.17091i
$326$	−4.31601	−	13.0605i	−0.239042	−	0.723352i
$327$	−15.7373	−	1.58107i	−0.870275	−	0.0874334i
$328$	−6.25881	−	21.6339i	−0.345585	−	1.19453i
$329$	−1.04993	+	3.46605i	−0.0578847	+	0.191089i
$330$	10.9497	+	22.9997i	0.602760	+	1.26609i
$331$	27.5198	+	11.2480i	1.51263	+	0.618249i	0.974454	−	0.224586i	$-0.0721031\pi$
$331$	27.5198	+	11.2480i	1.51263	+	0.618249i	0.538172	+	0.842835i	$0.319115\pi$
$332$	−5.41703	+	1.53051i	−0.297298	+	0.0839974i
$333$	−6.00224	+	3.48211i	−0.328921	+	0.190819i
$334$	3.35414	−	2.55432i	0.183530	−	0.139766i
$335$	18.8674	+	16.3299i	1.03084	+	0.892199i
$336$	−0.0232681	+	0.743365i	−0.00126938	+	0.0405539i
$337$	−1.49904	+	3.47960i	−0.0816579	+	0.189546i	−0.954325	−	0.298769i	$-0.903424\pi$
$337$	−1.49904	+	3.47960i	−0.0816579	+	0.189546i	0.872668	+	0.488315i	$0.162388\pi$
$338$	−2.23720	−	0.542289i	−0.121687	−	0.0294966i
$339$	−20.5149	−	8.68619i	−1.11422	−	0.471769i
$340$	25.0076	+	9.49790i	1.35623	+	0.515096i
$341$	5.91712	+	14.2222i	0.320430	+	0.770177i
$342$	−4.67406	−	3.28979i	−0.252744	−	0.177892i
$343$	−6.41909	+	4.16670i	−0.346598	+	0.224981i
$344$	3.14280	+	10.3750i	0.169448	+	0.559384i
$345$	−33.7710	+	30.7408i	−1.81817	+	1.65503i
$346$	5.09356	−	10.6990i	0.273832	−	0.575180i
$347$	−3.57428	−	3.25357i	−0.191877	−	0.174661i	0.571524	−	0.820586i	$-0.306353\pi$
$347$	−3.57428	−	3.25357i	−0.191877	−	0.174661i	−0.763401	+	0.645925i	$0.776472\pi$
$348$	11.9512	−	4.88476i	0.640652	−	0.261851i
$349$	11.4740	−	8.96703i	0.614188	−	0.479994i	−0.259982	−	0.965613i	$-0.583717\pi$
$349$	11.4740	−	8.96703i	0.614188	−	0.479994i	0.874170	+	0.485619i	$0.161406\pi$
$350$	−2.03998	+	2.93724i	−0.109041	+	0.157002i
$351$	12.7669	+	10.2374i	0.681445	+	0.546431i
$352$	11.4081	+	17.3365i	0.608055	+	0.924037i
$353$	−14.5749	+	6.82728i	−0.775746	+	0.363379i	−0.771186	−	0.636610i	$-0.780336\pi$
$353$	−14.5749	+	6.82728i	−0.775746	+	0.363379i	−0.00456008	+	0.999990i	$0.501452\pi$
$354$	−7.28022	+	11.3709i	−0.386940	+	0.604355i
$355$	−20.8791	+	10.4254i	−1.10815	+	0.553321i
$356$	−14.9773	+	0.750470i	−0.793796	+	0.0397748i
$357$	0.649546	−	7.96638i	0.0343776	−	0.421625i
$358$	3.41781	−	0.649323i	0.180637	−	0.0343178i
$359$	3.47059	−	5.57306i	0.183171	−	0.294135i	−0.744435	−	0.667695i	$-0.767281\pi$
$359$	3.47059	−	5.57306i	0.183171	−	0.294135i	0.927606	+	0.373560i	$0.121863\pi$
$360$	7.16471	−	5.31588i	0.377613	−	0.280172i
$361$	−17.6624	+	19.6490i	−0.929600	+	1.03416i
$362$	8.09912	−	7.55992i	0.425680	−	0.397341i
$363$	2.06179	−	8.74453i	0.108216	−	0.458969i
$364$	2.31549	+	0.500257i	0.121365	+	0.0262206i
$365$	17.4237	−	35.4481i	0.911996	−	1.85544i
$366$	6.62937	+	17.1311i	0.346523	+	0.895457i
$367$	−7.24012	+	0.0906243i	−0.377931	+	0.00473055i	−0.201256	−	0.979539i	$-0.564502\pi$
$367$	−7.24012	+	0.0906243i	−0.377931	+	0.00473055i	−0.176675	+	0.984269i	$0.556534\pi$
$368$	2.93096	−	3.51774i	0.152787	−	0.183375i
$369$	6.35773	+	2.23424i	0.330970	+	0.116310i
$370$	25.6222	−	2.25063i	1.33204	−	0.117005i
$371$	−1.23221	−	1.15018i	−0.0639734	−	0.0597144i
$372$	6.91284	−	4.61119i	0.358414	−	0.239079i
$373$	−1.66632	+	6.35110i	−0.0862788	+	0.328847i	−0.996324	−	0.0856610i	$-0.972700\pi$
$373$	−1.66632	+	6.35110i	−0.0862788	+	0.328847i	0.910046	+	0.414508i	$0.136046\pi$
$374$	13.9219	+	23.6554i	0.719886	+	1.22319i
$375$	11.2011	−	0.701900i	0.578424	−	0.0362460i
$376$	−16.6719	+	9.39507i	−0.859789	+	0.484514i
$377$	4.88253	+	23.3050i	0.251463	+	1.20027i
$378$	1.77951	+	1.35517i	0.0915280	+	0.0697025i
$379$	19.5898	+	2.46481i	1.00626	+	0.126609i	0.610726	−	0.791842i	$-0.290878\pi$
$379$	19.5898	+	2.46481i	1.00626	+	0.126609i	0.395536	+	0.918451i	$0.370559\pi$
$380$	−12.3373	−	21.5762i	−0.632889	−	1.10683i
$381$	−3.72161	+	10.3820i	−0.190664	+	0.531886i
$382$	17.7640	−	12.8385i	0.908885	−	0.656874i
$383$	24.5662	+	1.84834i	1.25527	+	0.0944459i	0.685938	−	0.727660i	$-0.259392\pi$
$383$	24.5662	+	1.84834i	1.25527	+	0.0944459i	0.569335	+	0.822106i	$0.307201\pi$
$384$	6.16870	−	6.05396i	0.314795	−	0.308940i
$385$	7.22309	−	2.13876i	0.368123	−	0.109001i
$386$	−1.93480	−	10.5435i	−0.0984785	−	0.536651i
$387$	−3.07354	−	1.03707i	−0.156237	−	0.0527173i
$388$	−4.92897	+	0.123411i	−0.250230	+	0.00626523i
$389$	2.35104	+	9.44068i	0.119202	+	0.478662i	0.999987	+	0.00514413i	$0.00163744\pi$
$389$	2.35104	+	9.44068i	0.119202	+	0.478662i	−0.880784	+	0.473517i	$0.842984\pi$
$390$	11.1791	+	22.7436i	0.566074	+	1.15167i
$391$	−33.3513	+	36.1813i	−1.68665	+	1.82977i
$392$	−19.4103	−	3.68761i	−0.980369	−	0.186252i
$393$	−7.98101	+	28.9387i	−0.402589	+	1.45976i
$394$	−17.8816	−	18.9182i	−0.900861	−	0.953085i
$395$	−4.63490	+	1.76034i	−0.233207	+	0.0885722i
$396$	−3.76226	−	0.141335i	−0.189061	−	0.00710237i
$397$	−3.05490	+	0.821973i	−0.153321	+	0.0412536i	−0.335667	−	0.941981i	$-0.608962\pi$
$397$	−3.05490	+	0.821973i	−0.153321	+	0.0412536i	0.182346	+	0.983234i	$0.441631\pi$
$398$	−9.78109	+	8.04636i	−0.490282	+	0.403327i
$399$	−5.16837	+	5.33268i	−0.258742	+	0.266968i
$400$	−4.41008	+	0.895165i	−0.220504	+	0.0447582i
$401$	18.2957	+	13.5746i	0.913644	+	0.677882i	0.946887	−	0.321565i	$-0.104209\pi$
$401$	18.2957	+	13.5746i	0.913644	+	0.677882i	−0.0332429	+	0.999447i	$0.510584\pi$
$402$	12.8495	−	5.06516i	0.640874	−	0.252627i
$403$	6.06341	+	14.0745i	0.302040	+	0.701101i
$404$	−2.09788	−	12.2973i	−0.104373	−	0.611814i
$405$	−0.697074	−	37.1245i	−0.0346379	−	1.84473i
$406$	0.746887	+	3.16772i	0.0370674	+	0.157211i
$407$	−25.7568	−	17.1810i	−1.27672	−	0.851632i
$408$	31.5864	−	28.0374i	1.56376	−	1.38806i
$409$	12.5754	+	14.3471i	0.621814	+	0.709416i	0.974009	−	0.226511i	$-0.0727318\pi$
$409$	12.5754	+	14.3471i	0.621814	+	0.709416i	−0.352195	+	0.935927i	$0.614565\pi$
$410$	−17.8275	−	17.4959i	−0.880438	−	0.864061i
$411$	−14.5967	−	7.75080i	−0.720003	−	0.382319i
$412$	0.125991	−	20.1320i	0.00620713	−	0.991834i
$413$	2.98613	+	2.65061i	0.146938	+	0.130428i
$414$	1.46008	+	5.56502i	0.0717590	+	0.273506i
$415$	−12.5531	+	12.6319i	−0.616206	+	0.620074i
$416$	11.5646	+	17.1042i	0.567002	+	0.838601i
$417$	−5.49111	+	3.00446i	−0.268901	+	0.147129i
$418$	3.97371	−	25.1911i	0.194361	−	1.23213i
$419$	−13.6037	+	2.40846i	−0.664585	+	0.117661i	−0.496399	−	0.868094i	$-0.665345\pi$
$419$	−13.6037	+	2.40846i	−0.664585	+	0.117661i	−0.168186	+	0.985755i	$0.553791\pi$
$420$	−1.88330	−	3.60095i	−0.0918954	−	0.175708i
$421$	8.28698	−	4.40035i	0.403883	−	0.214460i	−0.254616	−	0.967042i	$-0.581949\pi$
$421$	8.28698	−	4.40035i	0.403883	−	0.214460i	0.658498	+	0.752582i	$0.271192\pi$
$422$	21.3992	+	6.33630i	1.04170	+	0.308446i
$423$	0.608060	−	5.69388i	0.0295649	−	0.276846i
$424$	−0.501405	−	8.89283i	−0.0243504	−	0.431874i
$425$	47.8169	−	7.23639i	2.31946	−	0.351016i
$426$	−0.242505	+	12.9152i	−0.0117494	+	0.625744i
$427$	5.30971	−	1.14715i	0.256955	−	0.0555145i
$428$	2.52079	−	10.1223i	0.121847	−	0.489282i
$429$	6.62856	−	29.7770i	0.320030	−	1.43765i
$430$	8.68606	+	8.31365i	0.418879	+	0.400920i
$431$	−0.0642381	−	0.186519i	−0.00309424	−	0.00898430i	0.943938	−	0.330122i	$-0.107090\pi$
$431$	−0.0642381	−	0.186519i	−0.00309424	−	0.00898430i	−0.947032	+	0.321138i	$0.895935\pi$
$432$	0.438563	+	2.78023i	0.0211004	+	0.133764i
$433$	−11.7149	−	15.1850i	−0.562981	−	0.729743i	0.421189	−	0.906973i	$-0.361613\pi$
$433$	−11.7149	−	15.1850i	−0.562981	−	0.729743i	−0.984169	+	0.177230i	$0.943286\pi$
$434$	0.876665	+	1.90242i	0.0420813	+	0.0913189i
$435$	25.3526	−	32.0254i	1.21556	−	1.53550i
$436$	−7.38377	+	4.53432i	−0.353618	+	0.217154i
$437$	45.2871	−	6.27479i	2.16637	−	0.300164i
$438$	−12.9172	−	17.6393i	−0.617206	−	0.842837i
$439$	6.69024	−	9.38006i	0.319308	−	0.447686i	−0.623105	−	0.782138i	$-0.714129\pi$
$439$	6.69024	−	9.38006i	0.319308	−	0.447686i	0.942413	+	0.334452i	$0.108551\pi$
$440$	35.3877	+	18.2266i	1.68704	+	0.868920i
$441$	4.27094	−	4.08783i	0.203378	−	0.194658i
$442$	14.1440	+	23.3589i	0.672762	+	1.11107i
$443$	12.4542	−	13.1761i	0.591715	−	0.626018i	−0.360018	−	0.932945i	$-0.617229\pi$
$443$	12.4542	−	13.1761i	0.591715	−	0.626018i	0.951733	+	0.306928i	$0.0993011\pi$
$444$	−6.41571	+	15.4206i	−0.304476	+	0.731829i
$445$	−40.1143	+	25.3307i	−1.90160	+	1.20079i
$446$	9.33236	+	4.37152i	0.441900	+	0.206997i
$447$	2.02736	+	13.9876i	0.0958908	+	0.661590i
$448$	2.07699	+	2.91204i	0.0981284	+	0.137581i
$449$	−4.47572	+	13.5437i	−0.211222	+	0.639169i	0.788487	+	0.615051i	$0.210865\pi$
$449$	−4.47572	+	13.5437i	−0.211222	+	0.639169i	−0.999709	+	0.0241173i	$0.992322\pi$
$450$	2.30202	−	5.16462i	0.108518	−	0.243462i
$451$	3.56678	+	29.8554i	0.167953	+	1.40584i
$452$	−11.8243	+	3.02336i	−0.556170	+	0.142207i
$453$	42.7167	+	12.0690i	2.00701	+	0.567051i
$454$	12.5980	+	9.84547i	0.591254	+	0.462071i
$455$	7.15885	−	2.21756i	0.335612	−	0.103961i
$456$	−39.2137	+	1.47312i	−1.83635	+	0.0689853i
$457$	27.1320	−	11.4879i	1.26918	−	0.537382i	0.352055	−	0.935979i	$-0.385483\pi$
$457$	27.1320	−	11.4879i	1.26918	−	0.537382i	0.917126	+	0.398597i	$0.130503\pi$
$458$	−4.00308	+	0.657159i	−0.187052	+	0.0307070i
$459$	−3.21203	−	30.0775i	−0.149925	−	1.40390i
$460$	−4.51556	+	24.6072i	−0.210539	+	1.14732i
$461$	−12.1026	+	21.7944i	−0.563676	+	1.01507i	0.430005	+	0.902826i	$0.358512\pi$
$461$	−12.1026	+	21.7944i	−0.563676	+	1.01507i	−0.993681	+	0.112240i	$0.964197\pi$
$462$	0.803863	−	4.09145i	0.0373991	−	0.190351i
$463$	−9.86744	−	9.92938i	−0.458579	−	0.461458i	0.441452	−	0.897285i	$-0.354464\pi$
$463$	−9.86744	−	9.92938i	−0.458579	−	0.461458i	−0.900030	+	0.435828i	$0.856456\pi$
$464$	−2.07720	+	3.52948i	−0.0964318	+	0.163852i
$465$	11.8909	−	23.4460i	0.551428	−	1.08728i
$466$	4.76611	+	6.02055i	0.220786	+	0.278897i
$467$	−35.2824	−	12.8973i	−1.63268	−	0.596818i	−0.646558	−	0.762865i	$-0.723792\pi$
$467$	−35.2824	−	12.8973i	−1.63268	−	0.596818i	−0.986118	+	0.166047i	$0.946900\pi$
$468$	−3.74444	−	0.0937526i	−0.173087	−	0.00433372i
$469$	−0.887515	−	3.98692i	−0.0409816	−	0.184099i
$470$	−10.9937	+	18.1561i	−0.507100	+	0.837479i
$471$	6.27036	+	22.7360i	0.288923	+	1.04762i
$472$	1.71461	+	21.0288i	0.0789212	+	0.967931i
$473$	−1.89661	−	14.3484i	−0.0872063	−	0.659739i
$474$	−0.325541	+	2.72491i	−0.0149526	+	0.125159i
$475$	−38.5813	−	23.0325i	−1.77023	−	1.05680i
$476$	−2.36105	−	3.68768i	−0.108218	−	0.169025i
$477$	2.25351	+	1.42301i	0.103181	+	0.0651551i
$478$	−6.04090	+	4.25183i	−0.276304	+	0.194474i
$479$	−6.59934	+	16.4392i	−0.301531	+	0.751124i	0.697860	+	0.716234i	$0.254136\pi$
$479$	−6.59934	+	16.4392i	−0.301531	+	0.751124i	−0.999391	+	0.0348898i	$0.988892\pi$
$480$	9.84302	−	34.0229i	0.449270	−	1.55293i
$481$	−25.8367	−	16.7709i	−1.17805	−	0.764686i
$482$	1.72850	+	4.30574i	0.0787309	+	0.196121i
$483$	7.43774	−	0.747243i	0.338429	−	0.0340007i
$484$	−2.00381	−	4.49558i	−0.0910822	−	0.204344i
$485$	−13.3933	+	7.99565i	−0.608160	+	0.363064i
$486$	−7.65028	−	3.81994i	−0.347024	−	0.173276i
$487$	9.80708	+	4.29793i	0.444401	+	0.194758i	0.611603	−	0.791165i	$-0.290525\pi$
$487$	9.80708	+	4.29793i	0.444401	+	0.194758i	−0.167202	+	0.985923i	$0.553473\pi$
$488$	24.4605	+	15.0210i	1.10728	+	0.679971i
$489$	26.5401	−	9.70161i	1.20018	−	0.438722i
$490$	−20.7633	+	7.00595i	−0.937990	+	0.316497i
$491$	8.69858	+	15.6644i	0.392562	+	0.706924i	0.995890	−	0.0905686i	$-0.0288685\pi$
$491$	8.69858	+	15.6644i	0.392562	+	0.706924i	−0.603329	+	0.797493i	$0.706159\pi$
$492$	15.4323	−	4.99292i	0.695743	−	0.225098i
$493$	24.1939	−	36.7664i	1.08964	−	1.65588i
$494$	3.63935	−	25.1094i	0.163742	−	1.12972i
$495$	−10.5889	+	5.45388i	−0.475936	+	0.245134i
$496$	−0.858316	+	2.49217i	−0.0385395	+	0.111902i
$497$	3.76154	+	0.665959i	0.168728	+	0.0298723i
$498$	2.97558	+	9.39744i	0.133339	+	0.421110i
$499$	−4.11993	+	19.6650i	−0.184433	+	0.880325i	0.781974	+	0.623311i	$0.214213\pi$
$499$	−4.11993	+	19.6650i	−0.184433	+	0.880325i	−0.966408	+	0.257014i	$0.917261\pi$
$500$	4.64896	−	4.02372i	0.207908	−	0.179946i
$501$	5.46045	+	6.72300i	0.243955	+	0.300361i
$502$	20.3803			0.909616
$503$	−22.2473	−	2.83854i	−0.991958	−	0.126564i
$503$	−22.2473	−	2.83854i	−0.991958	−	0.126564i
$504$	−1.46034			−0.0650485
$505$	−24.8819	−	30.6350i	−1.10723	−	1.36324i
$506$	−19.4100	+	16.7996i	−0.862882	+	0.746832i
$507$	0.969711	−	4.62856i	0.0430664	−	0.205562i
$508$	1.82388	+	5.76017i	0.0809217	+	0.255566i
$509$	−4.58316	−	0.811421i	−0.203145	−	0.0359656i	0.0718304	−	0.997417i	$-0.477116\pi$
$509$	−4.58316	−	0.811421i	−0.203145	−	0.0359656i	−0.274975	+	0.961451i	$0.588670\pi$
$510$	15.2539	−	44.2905i	0.675454	−	1.96122i
$511$	−5.74789	+	2.96049i	−0.254272	+	0.130964i
$512$	−1.08145	+	7.46138i	−0.0477939	+	0.329750i
$513$	−15.4491	+	23.4773i	−0.682093	+	1.03655i
$514$	3.49375	−	1.13035i	0.154103	−	0.0498578i
$515$	−30.9212	−	55.6828i	−1.36255	−	2.45368i
$516$	−7.39774	+	2.49614i	−0.325667	+	0.109887i
$517$	23.9965	−	8.77183i	1.05537	−	0.385785i
$518$	−3.58774	−	2.20320i	−0.157636	−	0.0968033i
$519$	22.2959	+	9.77114i	0.978682	+	0.428905i
$520$	35.4304	+	17.6911i	1.55373	+	0.775806i
$521$	−33.8388	+	20.2013i	−1.48250	+	0.885035i	−0.482546	+	0.875871i	$0.660288\pi$
$521$	−33.8388	+	20.2013i	−1.48250	+	0.885035i	−0.999958	+	0.00916472i	$0.997083\pi$
$522$	−2.09502	−	4.70021i	−0.0916964	−	0.205722i
$523$	5.69414	−	0.572070i	0.248987	−	0.0250149i	0.0253160	−	0.999679i	$-0.491941\pi$
$523$	5.69414	−	0.572070i	0.248987	−	0.0250149i	0.223671	+	0.974665i	$0.428196\pi$
$524$	6.12667	+	15.2617i	0.267645	+	0.666712i
$525$	−6.16223	−	3.99997i	−0.268942	−	0.174573i
$526$	−0.535581	+	1.85126i	−0.0233524	+	0.0807189i
$527$	10.5531	−	26.2880i	0.459699	−	1.14512i
$528$	4.29064	−	3.01993i	0.186726	−	0.131425i
$529$	−19.4649	−	12.2914i	−0.846300	−	0.534407i
$530$	−5.32673	−	8.31974i	−0.231378	−	0.361387i
$531$	−5.42077	−	3.23613i	−0.235241	−	0.140436i
$532$	−0.482612	+	4.03966i	−0.0209239	+	0.175141i
$533$	3.91996	+	29.6556i	0.169792	+	1.28452i
$534$	2.13407	+	26.1733i	0.0923501	+	1.13263i
$535$	−8.77399	−	31.8140i	−0.379333	−	1.37544i
$536$	11.1791	−	18.4623i	0.482862	−	0.797450i
$537$	1.55294	+	6.97617i	0.0670145	+	0.301044i
$538$	1.81677	+	0.0454881i	0.0783267	+	0.00196113i
$539$	24.7747	+	9.05630i	1.06712	+	0.390083i
$540$	−9.54552	−	12.0579i	−0.410774	−	0.518890i
$541$	10.9254	−	21.5422i	0.469719	−	0.926171i	−0.527349	−	0.849649i	$-0.676814\pi$
$541$	10.9254	−	21.5422i	0.469719	−	0.926171i	0.997068	−	0.0765216i	$-0.0243814\pi$
$542$	−15.3836	+	26.1390i	−0.660782	+	1.12277i
$543$	16.0436	+	16.1443i	0.688496	+	0.692818i
$544$	7.35758	−	37.4482i	0.315454	−	1.60558i
$545$	−13.3083	+	23.9655i	−0.570064	+	1.02657i
$546$	0.748732	−	4.08016i	0.0320428	−	0.174615i
$547$	−0.0431601	−	0.404152i	−0.00184539	−	0.0172803i	0.993386	−	0.114824i	$-0.0366305\pi$
$547$	−0.0431601	−	0.404152i	−0.00184539	−	0.0172803i	−0.995231	+	0.0975439i	$0.968901\pi$
$548$	−8.93446	+	1.46671i	−0.381661	+	0.0626548i
$549$	−7.90938	+	3.34890i	−0.337564	+	0.142927i
$550$	25.2113	−	0.947100i	1.07501	−	0.0403845i
$551$	−39.0618	+	12.1000i	−1.66409	+	0.515476i
$552$	31.1229	+	24.3228i	1.32468	+	1.03525i
$553$	0.780985	+	0.220656i	0.0332108	+	0.00938326i
$554$	0.857524	−	0.219260i	0.0364327	−	0.00931546i
$555$	6.26807	+	52.4663i	0.266065	+	2.22707i
$556$	−1.39604	+	3.13204i	−0.0592053	+	0.132828i
$557$	4.19609	−	12.6976i	0.177794	−	0.538014i	−0.821697	−	0.569925i	$-0.806972\pi$
$557$	4.19609	−	12.6976i	0.177794	−	0.538014i	0.999491	+	0.0319115i	$0.0101595\pi$
$558$	−1.92321	−	2.69643i	−0.0814158	−	0.114149i
$559$	−2.06540	−	14.2501i	−0.0873572	−	0.602714i
$560$	1.16729	+	0.546789i	0.0493270	+	0.0231060i
$561$	−47.6777	+	30.1067i	−2.01295	+	1.27111i
$562$	2.06762	−	4.96967i	0.0872172	−	0.209633i
$563$	−3.95154	+	4.18061i	−0.166537	+	0.176192i	−0.804647	−	0.593754i	$-0.797645\pi$
$563$	−3.95154	+	4.18061i	−0.166537	+	0.176192i	0.638109	+	0.769946i	$0.279717\pi$
$564$	−7.13878	−	11.7897i	−0.300597	−	0.496438i
$565$	−27.8940	+	26.6980i	−1.17351	+	1.12319i
$566$	13.5984	+	7.00391i	0.571582	+	0.294396i
$567$	−3.52930	+	4.94826i	−0.148217	+	0.207807i
$568$	11.9260	+	16.2858i	0.500405	+	0.683337i
$569$	34.7390	−	4.81329i	1.45633	−	0.201784i	0.635124	−	0.772410i	$-0.280949\pi$
$569$	34.7390	−	4.81329i	1.45633	−	0.201784i	0.821210	+	0.570626i	$0.193299\pi$
$570$	−37.0884	+	22.7757i	−1.55346	+	0.953969i
$571$	6.20507	−	7.83825i	0.259674	−	0.328021i	−0.636873	−	0.770969i	$-0.719773\pi$
$571$	6.20507	−	7.83825i	0.259674	−	0.328021i	0.896547	+	0.442948i	$0.146067\pi$
$572$	−6.99436	−	15.1782i	−0.292449	−	0.634632i
$573$	27.5034	+	35.6502i	1.14897	+	1.48931i
$574$	0.637087	+	4.03877i	0.0265915	+	0.168575i
$575$	14.7282	+	42.7642i	0.614209	+	1.78339i
$576$	−4.08569	−	3.91052i	−0.170237	−	0.162938i
$577$	−0.145912	+	0.655469i	−0.00607439	+	0.0272875i	−0.979049	−	0.203623i	$-0.934728\pi$
$577$	−0.145912	+	0.655469i	−0.00607439	+	0.0272875i	0.972975	+	0.230911i	$0.0741705\pi$
$578$	8.25648	−	33.1542i	0.343424	−	1.37903i
$579$	21.5250	−	4.65043i	0.894549	−	0.193265i
$580$	0.420088	−	22.3729i	0.0174432	−	0.928984i
$581$	2.88224	−	0.436185i	0.119575	−	0.0180960i
$582$	0.486038	+	8.62029i	0.0201469	+	0.357322i
$583$	−1.26275	+	11.8244i	−0.0522976	+	0.489716i
$584$	−32.7586	−	9.69984i	−1.35556	−	0.401382i
$585$	−10.4659	+	5.55734i	−0.432711	+	0.229768i
$586$	−12.2972	−	23.5128i	−0.507991	−	0.971303i
$587$	−24.7725	+	4.38582i	−1.02247	+	0.181022i	−0.660231	−	0.751063i	$-0.729541\pi$
$587$	−24.7725	+	4.38582i	−1.02247	+	0.181022i	−0.362239	+	0.932085i	$0.617988\pi$
$588$	2.21720	−	14.0558i	0.0914358	−	0.579651i
$589$	−23.0891	+	12.6332i	−0.951369	+	0.520541i
$590$	13.1072	+	19.3857i	0.539615	+	0.798095i
$591$	37.6961	−	37.9327i	1.55061	−	1.56034i
$592$	−1.34449	−	5.12445i	−0.0552581	−	0.210613i
$593$	−22.4521	−	19.9294i	−0.921996	−	0.818403i	0.0617269	−	0.998093i	$-0.480339\pi$
$593$	−22.4521	−	19.9294i	−0.921996	−	0.818403i	−0.983723	+	0.179690i	$0.942491\pi$
$594$	0.0987527	−	15.7796i	0.00405187	−	0.647447i
$595$	−12.2350	−	6.49674i	−0.501586	−	0.266340i
$596$	5.52627	+	5.42348i	0.226365	+	0.222154i
$597$	−17.1505	−	19.5667i	−0.701923	−	0.800810i
$598$	−19.0998	+	16.9538i	−0.781049	+	0.693293i
$599$	19.7322	+	13.1623i	0.806236	+	0.537798i	0.888535	−	0.458810i	$-0.151724\pi$
$599$	19.7322	+	13.1623i	0.806236	+	0.537798i	−0.0822984	+	0.996608i	$0.526226\pi$
$600$	−8.90884	−	37.7844i	−0.363702	−	1.54254i
$601$	−0.544880	−	29.0190i	−0.0222261	−	1.18371i	−0.816939	−	0.576725i	$-0.804331\pi$
$601$	−0.544880	−	29.0190i	−0.0222261	−	1.18371i	0.794712	−	0.606986i	$-0.207622\pi$
$602$	−0.330972	−	1.94008i	−0.0134894	−	0.0790719i
$603$	2.55522	+	5.93122i	0.104056	+	0.241538i
$604$	22.6236	−	8.91804i	0.920542	−	0.362870i
$605$	−12.5052	−	9.27828i	−0.508409	−	0.377216i
$606$	−21.4087	+	4.34558i	−0.869671	+	0.176527i
$607$	−8.65105	+	8.92607i	−0.351135	+	0.362298i	−0.870426	−	0.492300i	$-0.836156\pi$
$607$	−8.65105	+	8.92607i	−0.351135	+	0.362298i	0.519290	+	0.854598i	$0.326196\pi$
$608$	−27.3837	+	22.5271i	−1.11056	+	0.913593i
$609$	−6.45638	+	1.73720i	−0.261626	+	0.0703949i
$610$	31.8143	+	1.19515i	1.28812	+	0.0483904i
$611$	23.7624	−	9.02497i	0.961323	−	0.365111i
$612$	4.75584	+	5.03154i	0.192243	+	0.203388i
$613$	11.8698	−	43.0393i	0.479418	−	1.73834i	−0.177253	−	0.984165i	$-0.556721\pi$
$613$	11.8698	−	43.0393i	0.479418	−	1.73834i	0.656671	−	0.754177i	$-0.271964\pi$
$614$	−2.07403	−	0.394029i	−0.0837011	−	0.0159017i
$615$	34.7791	−	37.7303i	1.40243	−	1.52143i
$616$	−2.87422	−	5.84755i	−0.115806	−	0.235605i
$617$	10.6616	+	42.8122i	0.429221	+	1.72356i	0.660642	+	0.750701i	$0.270284\pi$
$617$	10.6616	+	42.8122i	0.429221	+	1.72356i	−0.231420	+	0.972854i	$0.574337\pi$
$618$	−35.2435	+	0.882421i	−1.41770	+	0.0354962i
$619$	−27.1010	−	9.14441i	−1.08928	−	0.367545i	−0.283025	−	0.959112i	$-0.591338\pi$
$619$	−27.1010	−	9.14441i	−1.08928	−	0.367545i	−0.806255	+	0.591567i	$0.798509\pi$
$620$	−2.59945	−	14.1655i	−0.104396	−	0.568901i
$621$	27.1254	−	8.03183i	1.08850	−	0.322306i
$622$	−8.90265	+	8.73706i	−0.356964	+	0.350324i
$623$	7.74393	+	0.582648i	0.310254	+	0.0233433i
$624$	4.23070	−	3.05763i	0.169363	−	0.122403i
$625$	−4.68520	+	13.0701i	−0.187408	+	0.522803i
$626$	−2.77987	−	4.86161i	−0.111106	−	0.194309i
$627$	51.9810	+	6.54029i	2.07592	+	0.261194i
$628$	10.2793	+	7.82811i	0.410187	+	0.312375i
$629$	11.6750	+	55.7262i	0.465512	+	2.22195i
$630$	−1.41106	+	0.795169i	−0.0562180	+	0.0316803i
$631$	−13.3587	+	0.837099i	−0.531800	+	0.0333244i	−0.326180	−	0.945308i	$-0.605762\pi$
$631$	−13.3587	+	0.837099i	−0.531800	+	0.0333244i	−0.205620	+	0.978632i	$0.565921\pi$
$632$	2.17510	+	3.69582i	0.0865209	+	0.147012i
$633$	−11.6352	+	44.3469i	−0.462457	+	1.76263i
$634$	2.82941	−	1.88735i	0.112370	−	0.0749563i
$635$	13.9734	+	13.0431i	0.554518	+	0.517602i
$636$	6.39029	−	0.561317i	0.253391	−	0.0222577i
$637$	24.7585	+	8.70067i	0.980969	+	0.344733i
$638$	14.6974	−	17.6399i	0.581876	−	0.698370i
$639$	−6.03958	+	0.0755972i	−0.238922	+	0.00299058i
$640$	−5.40625	−	13.9704i	−0.213701	−	0.552228i
$641$	−18.1930	+	37.0134i	−0.718581	+	1.46194i	0.161379	+	0.986893i	$0.448406\pi$
$641$	−18.1930	+	37.0134i	−0.718581	+	1.46194i	−0.879960	+	0.475048i	$0.842431\pi$
$642$	−17.8550	−	3.85753i	−0.704681	−	0.152244i
$643$	0.976555	−	4.14179i	0.0385116	−	0.163336i	−0.950623	−	0.310347i	$-0.899555\pi$
$643$	0.976555	−	4.14179i	0.0385116	−	0.163336i	0.989135	+	0.147011i	$0.0469651\pi$
$644$	2.99367	−	2.79436i	0.117967	−	0.110113i
$645$	−16.5124	+	18.3697i	−0.650176	+	0.723306i
$646$	−37.6631	+	27.9443i	−1.48184	+	1.09945i
$647$	12.3578	−	19.8442i	0.485837	−	0.780154i	−0.511004	−	0.859578i	$-0.670726\pi$
$647$	12.3578	−	19.8442i	0.485837	−	0.780154i	0.996841	+	0.0794239i	$0.0253081\pi$
$648$	−31.5522	+	5.99435i	−1.23949	+	0.235480i
$649$	2.28916	−	28.0755i	0.0898574	−	1.10206i
$650$	25.0682	−	1.25610i	0.983256	−	0.0492681i
$651$	−3.84995	+	1.92236i	−0.150891	+	0.0753431i
$652$	8.34720	−	13.0374i	0.326902	−	0.510583i
$653$	−12.2168	+	5.72266i	−0.478080	+	0.223945i	−0.648188	−	0.761481i	$-0.724473\pi$
$653$	−12.2168	+	5.72266i	−0.478080	+	0.223945i	0.170108	+	0.985425i	$0.445588\pi$
$654$	8.34083	+	12.6752i	0.326152	+	0.495640i
$655$	40.5901	+	32.5480i	1.58599	+	1.27176i
$656$	−2.93490	+	4.22577i	−0.114588	+	0.164989i
$657$	8.05490	−	6.29498i	0.314251	−	0.245591i
$658$	3.21605	−	1.31448i	0.125375	−	0.0512438i
$659$	14.8941	+	13.5577i	0.580193	+	0.528134i	0.909291	−	0.416162i	$-0.136625\pi$
$659$	14.8941	+	13.5577i	0.580193	+	0.528134i	−0.329097	+	0.944296i	$0.606744\pi$
$660$	−12.3232	+	25.8848i	−0.479681	+	1.00757i
$661$	30.3550	−	27.6314i	1.18067	−	1.07474i	0.184913	−	0.982755i	$-0.440800\pi$
$661$	30.3550	−	27.6314i	1.18067	−	1.07474i	0.995761	−	0.0919803i	$-0.0293197\pi$
$662$	−8.26848	−	27.2960i	−0.321364	−	1.06089i
$663$	−47.0546	+	30.5436i	−1.82745	+	1.18622i
$664$	12.5963	+	8.86578i	0.488831	+	0.344059i
$665$	4.94411	+	11.8835i	0.191724	+	0.460823i
$666$	6.22325	+	2.36360i	0.241146	+	0.0915875i
$667$	37.9046	+	16.0491i	1.46767	+	0.621425i
$668$	4.61135	+	1.11778i	0.178418	+	0.0432480i
$669$	−8.37637	+	19.4434i	−0.323849	+	0.751725i
$670$	0.748921	−	23.9264i	0.0289334	−	0.924359i
$671$	−28.9770	−	25.0799i	−1.11865	−	0.968198i
$672$	−4.61236	+	3.51251i	−0.177926	+	0.135498i
$673$	−25.2768	+	14.6640i	−0.974349	+	0.565254i	−0.901820	−	0.432112i	$-0.857768\pi$
$673$	−25.2768	+	14.6640i	−0.974349	+	0.565254i	−0.0725293	+	0.997366i	$0.523107\pi$
$674$	3.49777	−	0.988244i	0.134729	−	0.0380657i
$675$	−25.7363	−	10.5191i	−0.990590	−	0.404879i
$676$	−1.11364	−	2.33918i	−0.0428322	−	0.0899686i
$677$	−10.6088	+	35.0217i	−0.407728	+	1.34600i	0.476596	+	0.879122i	$0.341870\pi$
$677$	−10.6088	+	35.0217i	−0.407728	+	1.34600i	−0.884325	+	0.466873i	$0.845381\pi$
$678$	5.93951	+	20.5302i	0.228106	+	0.788458i
$679$	2.54050	+	0.255235i	0.0974956	+	0.00979504i
$680$	−22.9685	−	69.5037i	−0.880800	−	2.66534i
$681$	−19.4063	+	26.5007i	−0.743652	+	1.01551i
$682$	7.01196	−	13.0081i	0.268502	−	0.498106i
$683$	−0.496531	+	11.3272i	−0.0189992	+	0.433425i	0.965753	+	0.259463i	$0.0835455\pi$
$683$	−0.496531	+	11.3272i	−0.0189992	+	0.433425i	−0.984752	+	0.173962i	$0.944343\pi$
$684$	−0.442477	−	6.41748i	−0.0169185	−	0.245379i
$685$	−22.3468	+	17.9192i	−0.853826	+	0.684658i
$686$	6.98515	+	2.25995i	0.266694	+	0.0862854i
$687$	−1.60665	−	8.17741i	−0.0612974	−	0.311988i
$688$	1.38715	−	2.05161i	0.0528847	−	0.0782170i
$689$	−1.10894	+	11.7785i	−0.0422472	+	0.448727i
$690$	43.3168	+	6.55536i	1.64904	+	0.249558i
$691$	5.23669	−	30.6963i	0.199213	−	1.16774i	−0.694632	−	0.719365i	$-0.744433\pi$
$691$	5.23669	−	30.6963i	0.199213	−	1.16774i	0.893845	−	0.448376i	$-0.147998\pi$
$692$	12.9607	−	3.14162i	0.492691	−	0.119427i
$693$	1.92393	+	0.315839i	0.0730841	+	0.0119977i
$694$	−0.261022	+	4.62945i	−0.00990826	+	0.175731i
$695$	1.01687	+	10.8007i	0.0385723	+	0.409694i
$696$	−30.9937	−	16.9582i	−1.17481	−	0.642798i
$697$	33.7744	−	43.7788i	1.27930	−	1.65824i
$698$	−13.6171	−	3.12082i	−0.515413	−	0.118125i
$699$	−12.0559	+	10.1734i	−0.455995	+	0.384792i
$700$	−4.01341	+	0.301966i	−0.151693	+	0.0114132i
$701$	−18.4829	+	21.0868i	−0.698091	+	0.796439i	−0.986966	−	0.160928i	$-0.948551\pi$
$701$	−18.4829	+	21.0868i	−0.698091	+	0.796439i	0.288875	+	0.957367i	$0.406719\pi$
$702$	−0.0982463	−	15.6987i	−0.00370807	−	0.592510i
$703$	24.5163	−	46.8764i	0.924652	−	1.76798i
$704$	7.61728	−	24.0568i	0.287087	−	0.906675i
$705$	−37.9871	−	21.4067i	−1.43068	−	0.806223i
$706$	13.8992	+	6.72414i	0.523103	+	0.253066i
$707$	0.282914	+	6.45404i	0.0106401	+	0.242729i
$708$	−15.0992	+	1.70810i	−0.567462	+	0.0641945i
$709$	11.4775	+	9.44192i	0.431048	+	0.354599i	0.825582	−	0.564282i	$-0.190847\pi$
$709$	11.4775	+	9.44192i	0.431048	+	0.354599i	−0.394534	+	0.918881i	$0.629094\pi$
$710$	20.3914	+	9.24243i	0.765276	+	0.346862i
$711$	−1.27827	−	0.112282i	−0.0479389	−	0.00421091i
$712$	27.4327	+	30.5183i	1.02808	+	1.14372i
$713$	25.9631	+	5.27004i	0.972327	+	0.197365i
$714$	−6.32511	+	4.33451i	−0.236711	+	0.162215i
$715$	−42.8519	−	30.9701i	−1.60257	−	1.15822i
$716$	2.99232	+	2.52507i	0.111828	+	0.0943664i
$717$	−9.11868	−	12.1307i	−0.340543	−	0.453029i
$718$	−6.24912	+	0.786269i	−0.233215	+	0.0293433i
$719$	−27.1938	−	15.7761i	−1.01416	−	0.588349i	−0.100545	−	0.994933i	$-0.532059\pi$
$719$	−27.1938	−	15.7761i	−1.01416	−	0.588349i	−0.913614	+	0.406583i	$0.866720\pi$
$720$	−1.97459	−	0.504881i	−0.0735886	−	0.0188158i
$721$	−1.36622	+	10.3358i	−0.0508806	+	0.384925i
$722$	25.3144	+	1.26843i	0.942104	+	0.0472061i
$723$	−8.73002	+	3.82591i	−0.324673	+	0.142287i
$724$	12.3510	+	1.71130i	0.459020	+	0.0636000i
$725$	−19.1955	−	35.6102i	−0.712904	−	1.32253i
$726$	−7.75872	+	3.75351i	−0.287953	+	0.139306i
$727$	30.2228	+	1.89386i	1.12090	+	0.0702394i	0.612199	−	0.790704i	$-0.290285\pi$
$727$	30.2228	+	1.89386i	1.12090	+	0.0702394i	0.508701	+	0.860943i	$0.330126\pi$
$728$	−2.93207	−	5.78132i	−0.108670	−	0.214270i
$729$	−6.29671	+	13.6642i	−0.233212	+	0.506083i
$730$	−36.9349	+	8.46491i	−1.36702	+	0.313300i
$731$	−15.9924	+	21.2749i	−0.591500	+	0.786880i
$732$	−10.2619	+	17.9466i	−0.379290	+	0.663326i
$733$	10.9862	+	12.8551i	0.405785	+	0.474812i	0.925074	−	0.379786i	$-0.124003\pi$
$733$	10.9862	+	12.8551i	0.405785	+	0.474812i	−0.519289	+	0.854598i	$0.673803\pi$
$734$	4.44644	+	5.33663i	0.164121	+	0.196978i
$735$	−15.7200	−	42.1837i	−0.579842	−	1.55597i
$736$	35.6897	+	0.446727i	1.31554	+	0.0164666i
$737$	−18.7209	+	21.9055i	−0.689595	+	0.806900i
$738$	−2.18151	−	6.08566i	−0.0803026	−	0.224016i
$739$	−42.8037	−	29.3328i	−1.57456	−	1.07902i	−0.956033	−	0.293259i	$-0.905260\pi$
$739$	−42.8037	−	29.3328i	−1.57456	−	1.07902i	−0.618525	−	0.785765i	$-0.712270\pi$
$740$	20.1461	+	20.7866i	0.740587	+	0.764131i
$741$	51.7918	+	5.85898i	1.90262	+	0.215235i
$742$	−0.111230	+	1.61323i	−0.00408339	+	0.0592236i
$743$	−13.7102	−	19.7404i	−0.502978	−	0.724206i	0.485722	−	0.874113i	$-0.338557\pi$
$743$	−13.7102	−	19.7404i	−0.502978	−	0.724206i	−0.988700	+	0.149907i	$0.952102\pi$
$744$	−21.7204	−	6.72824i	−0.796310	−	0.246669i
$745$	23.6549	+	6.36475i	0.866647	+	0.233187i
$746$	5.73723	−	2.60041i	0.210055	−	0.0952077i
$747$	−4.34844	+	1.52813i	−0.159101	+	0.0559115i
$748$	−10.7872	+	28.9466i	−0.394417	+	1.05839i
$749$	−1.94958	+	5.03795i	−0.0712360	+	0.184083i
$750$	−7.29731	−	7.91652i	−0.266460	−	0.289070i
$751$	−12.0080	−	19.2824i	−0.438178	−	0.703624i	0.553431	−	0.832895i	$-0.313318\pi$
$751$	−12.0080	−	19.2824i	−0.438178	−	0.703624i	−0.991609	+	0.129271i	$0.958736\pi$
$752$	4.06726	+	1.60328i	0.148318	+	0.0584657i
$753$	1.30987	+	41.8475i	0.0477342	+	1.52501i
$754$	14.4013	−	17.7311i	0.524463	−	0.645727i
$755$	48.5031	−	59.7178i	1.76521	−	2.17335i
$756$	0.0787571	+	2.51612i	0.00286437	+	0.0915104i
$757$	−9.42952	−	3.71704i	−0.342722	−	0.135098i	0.189092	−	0.981959i	$-0.439446\pi$
$757$	−9.42952	−	3.71704i	−0.342722	−	0.135098i	−0.531814	+	0.846861i	$0.678489\pi$
$758$	−10.0128	−	16.0785i	−0.363682	−	0.583999i
$759$	−35.7426	−	38.7755i	−1.29737	−	1.40746i
$760$	−24.5454	+	63.4282i	−0.890354	+	2.30078i
$761$	15.4484	−	41.4549i	0.560006	−	1.50274i	−0.279913	−	0.960025i	$-0.590306\pi$
$761$	15.4484	−	41.4549i	0.560006	−	1.50274i	0.839918	−	0.542713i	$-0.182603\pi$
$762$	9.98196	−	3.50787i	0.361608	−	0.127077i
$763$	4.08695	−	1.85241i	0.147957	−	0.0670619i
$764$	23.8199	+	6.40916i	0.861775	+	0.231875i
$765$	20.9227	+	6.48111i	0.756461	+	0.234325i
$766$	−13.4817	−	19.4114i	−0.487112	−	0.701362i
$767$	1.92765	−	27.9578i	0.0696035	−	1.00950i
$768$	−33.2949	−	3.76651i	−1.20143	−	0.135912i
$769$	−5.77633	−	5.95996i	−0.208300	−	0.214922i	0.605847	−	0.795582i	$-0.292835\pi$
$769$	−5.77633	−	5.95996i	−0.208300	−	0.214922i	−0.814146	+	0.580660i	$0.802795\pi$
$770$	−5.96130	−	4.08520i	−0.214830	−	0.147220i
$771$	2.54554	+	7.10117i	0.0916754	+	0.255742i
$772$	7.83798	−	9.17129i	0.282095	−	0.330082i
$773$	20.2302

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)

\(f(q)\)	\(=\)	\(q+(-0.604817 - 0.744661i) q^{2} +(1.49016 - 1.28975i) q^{3} +(0.221392 - 1.05673i) q^{4} +(-1.03109 - 3.25639i) q^{5} +(-1.86170 - 0.329604i) q^{6} +(-0.182067 + 0.528642i) q^{7} +(-2.62653 + 1.35281i) q^{8} +(0.126808 - 0.874904i) q^{9} +O(q^{10})\)	\(q+(-0.604817 - 0.744661i) q^{2} +(1.49016 - 1.28975i) q^{3} +(0.221392 - 1.05673i) q^{4} +(-1.03109 - 3.25639i) q^{5} +(-1.86170 - 0.329604i) q^{6} +(-0.182067 + 0.528642i) q^{7} +(-2.62653 + 1.35281i) q^{8} +(0.126808 - 0.874904i) q^{9} +(-1.80128 + 2.73733i) q^{10} +(3.75292 - 1.21421i) q^{11} +(-1.03301 - 1.86025i) q^{12} +(3.71827 - 1.25462i) q^{13} +(0.503777 - 0.184154i) q^{14} +(-5.73642 - 3.52270i) q^{15} +(0.618189 + 0.270920i) q^{16} +(-6.48961 - 3.24039i) q^{17} +(-0.728203 + 0.434728i) q^{18} +(2.74376 + 6.15567i) q^{19} +(-3.66941 + 0.368652i) q^{20} +(0.410507 + 1.02259i) q^{21} +(-3.17400 - 2.06028i) q^{22} +(1.88530 - 6.51663i) q^{23} +(-2.16917 + 5.40347i) q^{24} +(-5.45213 + 3.83743i) q^{25} +(-3.18314 - 2.01003i) q^{26} +(2.24855 + 3.51197i) q^{27} +(0.518326 + 0.309434i) q^{28} +(-0.719777 + 6.02483i) q^{29} +(0.846273 + 6.40228i) q^{30} +(0.317364 + 3.89232i) q^{31} +(1.39881 + 5.07203i) q^{32} +(4.02644 - 6.64970i) q^{33} +(1.51203 + 6.79240i) q^{34} +(1.90919 + 0.0478020i) q^{35} +(-0.896466 - 0.327700i) q^{36} +(-4.87200 - 6.15431i) q^{37} +(2.92442 - 5.76623i) q^{38} +(3.92268 - 6.66522i) q^{39} +(7.11345 + 7.15811i) q^{40} +(-1.46958 + 7.47978i) q^{41} +(0.513198 - 0.924166i) q^{42} +(0.662269 - 3.60899i) q^{43} +(-0.452226 - 4.23465i) q^{44} +(-2.97978 + 0.489170i) q^{45} +(-5.99294 + 2.53746i) q^{46} +(6.47276 - 0.243160i) q^{47} +(1.27062 - 0.393594i) q^{48} +(5.26916 + 4.11790i) q^{49} +(6.15512 + 1.73904i) q^{50} +(-13.8499 + 3.54126i) q^{51} +(-0.502601 - 4.20698i) q^{52} +(-1.22737 + 2.75362i) q^{53} +(1.25527 - 3.79850i) q^{54} +(-7.82354 - 10.9690i) q^{55} +(-0.236947 - 1.63479i) q^{56} +(12.0279 + 5.63420i) q^{57} +(4.92179 - 3.10793i) q^{58} +(2.74319 - 6.59344i) q^{59} +(-4.99255 + 5.28197i) q^{60} +(-5.03231 - 8.31090i) q^{61} +(2.70651 - 2.59047i) q^{62} +(0.439424 + 0.226328i) q^{63} +(3.71476 - 5.20829i) q^{64} +(-7.91939 - 10.8145i) q^{65} +(-7.38704 + 1.02352i) q^{66} +(-6.22519 + 3.82285i) q^{67} +(-4.86097 + 6.14039i) q^{68} +(-5.59543 - 12.1424i) q^{69} +(-1.11912 - 1.45061i) q^{70} +(-1.06458 - 6.74883i) q^{71} +(0.850511 + 2.46951i) q^{72} +(8.35396 + 7.99578i) q^{73} +(-1.63621 + 7.35022i) q^{74} +(-3.17524 + 12.7503i) q^{75} +(7.11235 - 1.53661i) q^{76} +(-0.0414029 + 2.20502i) q^{77} +(-7.33584 + 1.11017i) q^{78} +(-0.0817102 - 1.44920i) q^{79} +(0.244810 - 2.29240i) q^{80} +(10.4233 + 3.08633i) q^{81} +(6.45873 - 3.42956i) q^{82} +(-2.41625 - 4.61998i) q^{83} +(1.17148 - 0.207404i) q^{84} +(-3.86057 + 24.4738i) q^{85} +(-3.08802 + 1.68961i) q^{86} +(6.69794 + 9.90632i) q^{87} +(-8.21456 + 8.26613i) q^{88} +(-3.52484 - 13.4347i) q^{89} +(2.16649 + 1.92307i) q^{90} +(-0.0137309 + 2.19406i) q^{91} +(-6.46895 - 3.43499i) q^{92} +(5.49305 + 5.39088i) q^{93} +(-4.09591 - 4.67295i) q^{94} +(17.2162 - 15.2818i) q^{95} +(8.62611 + 5.75403i) q^{96} +(-1.04799 - 4.44478i) q^{97} +(-0.120439 - 6.41432i) q^{98} +(-0.586412 - 3.43742i) 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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