LMFDB - Embedded newform 300.2.w.a.67.14

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.14
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.14

$q$-expansion

$f(q)$	$=$	$q+(-0.253401 + 1.39133i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.87158 - 0.705127i) q^{4} +(-0.698282 - 2.12424i) q^{5} +(-0.467933 + 1.33456i) q^{6} +(1.04258 - 1.04258i) q^{7} +(1.45532 - 2.42529i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.253401 + 1.39133i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.87158 - 0.705127i) q^{4} +(-0.698282 - 2.12424i) q^{5} +(-0.467933 + 1.33456i) q^{6} +(1.04258 - 1.04258i) q^{7} +(1.45532 - 2.42529i) q^{8} +(0.951057 + 0.309017i) q^{9} +(3.13246 - 0.433253i) q^{10} +(4.52673 - 1.47082i) q^{11} +(-1.73823 - 0.989225i) q^{12} +(2.54390 + 4.99269i) q^{13} +(1.18638 + 1.71477i) q^{14} +(-0.357381 - 2.20732i) q^{15} +(3.00559 + 2.63940i) q^{16} +(0.262171 + 1.65528i) q^{17} +(-0.670942 + 1.24492i) q^{18} +(-2.76811 - 2.01115i) q^{19} +(-0.190971 + 4.46806i) q^{20} +(1.19285 - 0.866653i) q^{21} +(0.899317 + 6.67086i) q^{22} +(3.62217 - 7.10891i) q^{23} +(1.81680 - 2.16777i) q^{24} +(-4.02480 + 2.96664i) q^{25} +(-7.59109 + 2.27425i) q^{26} +(0.891007 + 0.453990i) q^{27} +(-2.68643 + 1.21612i) q^{28} +(-4.76887 - 6.56378i) q^{29} +(3.16167 + 0.0621050i) q^{30} +(-1.29321 + 1.77995i) q^{31} +(-4.43388 + 3.51293i) q^{32} +(4.70108 - 0.744578i) q^{33} +(-2.36947 - 0.0546849i) q^{34} +(-2.94272 - 1.48668i) q^{35} +(-1.56208 - 1.24896i) q^{36} +(1.10983 - 0.565484i) q^{37} +(3.49960 - 3.34171i) q^{38} +(1.73155 + 5.32918i) q^{39} +(-6.16813 - 1.39791i) q^{40} +(-1.73027 + 5.32522i) q^{41} +(0.903528 + 1.87925i) q^{42} +(2.44396 + 2.44396i) q^{43} +(-9.50923 - 0.439160i) q^{44} +(-0.00767928 - 2.23605i) q^{45} +(8.97295 + 6.84103i) q^{46} +(0.899254 - 5.67766i) q^{47} +(2.55570 + 3.07708i) q^{48} +4.82603i q^{49} +(-3.10767 - 6.35156i) q^{50} +1.67591i q^{51} +(-1.24063 - 11.1380i) q^{52} +(-0.680800 + 4.29840i) q^{53} +(-0.857431 + 1.12464i) q^{54} +(-6.28532 - 8.58881i) q^{55} +(-1.01128 - 4.04587i) q^{56} +(-2.41941 - 2.41941i) q^{57} +(10.3408 - 4.97178i) q^{58} +(-3.92044 + 12.0659i) q^{59} +(-0.887578 + 4.38317i) q^{60} +(2.15405 + 6.62949i) q^{61} +(-2.14879 - 2.25032i) q^{62} +(1.31373 - 0.669381i) q^{63} +(-3.76408 - 7.05915i) q^{64} +(8.82932 - 8.89017i) q^{65} +(-0.155308 + 6.72942i) q^{66} +(7.39906 - 1.17190i) q^{67} +(0.676511 - 3.28285i) q^{68} +(4.68966 - 6.45476i) q^{69} +(2.81415 - 3.71756i) q^{70} +(-7.39857 - 10.1833i) q^{71} +(2.13355 - 1.85687i) q^{72} +(-9.08821 - 4.63068i) q^{73} +(0.505542 + 1.68742i) q^{74} +(-4.43934 + 2.30050i) q^{75} +(3.76261 + 5.71588i) q^{76} +(3.18604 - 6.25296i) q^{77} +(-7.85340 + 1.05874i) q^{78} +(-7.49468 + 5.44520i) q^{79} +(3.50796 - 8.22765i) q^{80} +(0.809017 + 0.587785i) q^{81} +(-6.97066 - 3.75678i) q^{82} +(0.974493 + 6.15271i) q^{83} +(-2.84360 + 0.780899i) q^{84} +(3.33315 - 1.71277i) q^{85} +(-4.01965 + 2.78105i) q^{86} +(-3.68335 - 7.22899i) q^{87} +(3.02066 - 13.1192i) q^{88} +(1.92856 - 0.626628i) q^{89} +(3.11303 + 0.555934i) q^{90} +(7.85754 + 2.55307i) q^{91} +(-11.7919 + 10.7508i) q^{92} +(-1.55574 + 1.55574i) q^{93} +(7.67161 + 2.68988i) q^{94} +(-2.33924 + 7.28448i) q^{95} +(-4.92884 + 2.77607i) q^{96} +(-3.36367 - 0.532753i) q^{97} +(-6.71459 - 1.22292i) q^{98} +4.75968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240q + 12q^{8} + O(q^{10}) $	$ 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.253401	+	1.39133i	−0.179182	+	0.983816i
$2$	−0.253401	+	1.39133i	−0.179182	+	0.983816i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$4$	−1.87158	−	0.705127i	−0.935788	−	0.352563i
$5$	−0.698282	−	2.12424i	−0.312281	−	0.949990i
$5$	−0.698282	−	2.12424i	−0.312281	−	0.949990i
$6$	−0.467933	+	1.33456i	−0.191033	+	0.544830i
$7$	1.04258	−	1.04258i	0.394060	−	0.394060i	−0.482072	−	0.876132i	$-0.660116\pi$
$7$	1.04258	−	1.04258i	0.394060	−	0.394060i	0.876132	+	0.482072i	$0.160116\pi$
$8$	1.45532	−	2.42529i	0.514534	−	0.857470i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	3.13246	−	0.433253i	0.990570	−	0.137007i
$11$	4.52673	−	1.47082i	1.36486	−	0.443470i	0.467197	−	0.884153i	$-0.345264\pi$
$11$	4.52673	−	1.47082i	1.36486	−	0.443470i	0.897663	+	0.440683i	$0.145264\pi$
$12$	−1.73823	−	0.989225i	−0.501783	−	0.285565i
$13$	2.54390	+	4.99269i	0.705552	+	1.38472i	0.913604	+	0.406606i	$0.133288\pi$
$13$	2.54390	+	4.99269i	0.705552	+	1.38472i	−0.208052	+	0.978118i	$0.566712\pi$
$14$	1.18638	+	1.71477i	0.317074	+	0.458291i
$15$	−0.357381	−	2.20732i	−0.0922753	−	0.569929i
$16$	3.00559	+	2.63940i	0.751398	+	0.659849i
$17$	0.262171	+	1.65528i	0.0635858	+	0.401465i	0.998868	+	0.0475627i	$0.0151454\pi$
$17$	0.262171	+	1.65528i	0.0635858	+	0.401465i	−0.935282	+	0.353902i	$0.884855\pi$
$18$	−0.670942	+	1.24492i	−0.158143	+	0.293431i
$19$	−2.76811	−	2.01115i	−0.635047	−	0.461389i	0.223098	−	0.974796i	$-0.428383\pi$
$19$	−2.76811	−	2.01115i	−0.635047	−	0.461389i	−0.858145	+	0.513407i	$0.828383\pi$
$20$	−0.190971	+	4.46806i	−0.0427025	+	0.999088i
$21$	1.19285	−	0.866653i	0.260300	−	0.189119i
$22$	0.899317	+	6.67086i	0.191735	+	1.42223i
$23$	3.62217	−	7.10891i	0.755275	−	1.48231i	−0.116914	−	0.993142i	$-0.537300\pi$
$23$	3.62217	−	7.10891i	0.755275	−	1.48231i	0.872189	−	0.489169i	$-0.162700\pi$
$24$	1.81680	−	2.16777i	0.370853	−	0.442494i
$25$	−4.02480	+	2.96664i	−0.804961	+	0.593328i
$26$	−7.59109	+	2.27425i	−1.48874	+	0.446016i
$27$	0.891007	+	0.453990i	0.171474	+	0.0873705i
$28$	−2.68643	+	1.21612i	−0.507688	+	0.229825i
$29$	−4.76887	−	6.56378i	−0.885556	−	1.21886i	−0.974851	−	0.222858i	$-0.928461\pi$
$29$	−4.76887	−	6.56378i	−0.885556	−	1.21886i	0.0892946	−	0.996005i	$-0.471539\pi$
$30$	3.16167	+	0.0621050i	0.577239	+	0.0113388i
$31$	−1.29321	+	1.77995i	−0.232268	+	0.319689i	−0.909203	−	0.416354i	$-0.863308\pi$
$31$	−1.29321	+	1.77995i	−0.232268	+	0.319689i	0.676935	+	0.736043i	$0.263308\pi$
$32$	−4.43388	+	3.51293i	−0.783807	+	0.621005i
$33$	4.70108	−	0.744578i	0.818354	−	0.129614i
$34$	−2.36947	−	0.0546849i	−0.406361	−	0.00937839i
$35$	−2.94272	−	1.48668i	−0.497411	−	0.251295i
$36$	−1.56208	−	1.24896i	−0.260346	−	0.208161i
$37$	1.10983	−	0.565484i	0.182454	−	0.0929650i	−0.360378	−	0.932807i	$-0.617352\pi$
$37$	1.10983	−	0.565484i	0.182454	−	0.0929650i	0.542832	+	0.839842i	$0.317352\pi$
$38$	3.49960	−	3.34171i	0.567710	−	0.542097i
$39$	1.73155	+	5.32918i	0.277271	+	0.853351i
$40$	−6.16813	−	1.39791i	−0.975267	−	0.221030i
$41$	−1.73027	+	5.32522i	−0.270222	+	0.831659i	0.720222	+	0.693744i	$0.244040\pi$
$41$	−1.73027	+	5.32522i	−0.270222	+	0.831659i	−0.990444	+	0.137915i	$0.955960\pi$
$42$	0.903528	+	1.87925i	0.139417	+	0.289974i
$43$	2.44396	+	2.44396i	0.372701	+	0.372701i	0.868460	−	0.495759i	$-0.165110\pi$
$43$	2.44396	+	2.44396i	0.372701	+	0.372701i	−0.495759	+	0.868460i	$0.665110\pi$
$44$	−9.50923	−	0.439160i	−1.43357	−	0.0662059i
$45$	−0.00767928	−	2.23605i	−0.00114476	−	0.333331i
$46$	8.97295	+	6.84103i	1.32299	+	1.00865i
$47$	0.899254	−	5.67766i	0.131170	−	0.828172i	−0.831110	−	0.556109i	$-0.812294\pi$
$47$	0.899254	−	5.67766i	0.131170	−	0.828172i	0.962279	−	0.272064i	$-0.0877062\pi$
$48$	2.55570	+	3.07708i	0.368883	+	0.444138i
$49$			4.82603i			0.689433i
$50$	−3.10767	−	6.35156i	−0.439492	−	0.898247i
$51$			1.67591i			0.234675i
$52$	−1.24063	−	11.1380i	−0.172044	−	1.54456i
$53$	−0.680800	+	4.29840i	−0.0935150	+	0.590431i	0.895780	+	0.444498i	$0.146618\pi$
$53$	−0.680800	+	4.29840i	−0.0935150	+	0.590431i	−0.989295	+	0.145932i	$0.953382\pi$
$54$	−0.857431	+	1.12464i	−0.116682	+	0.153044i
$55$	−6.28532	−	8.58881i	−0.847512	−	1.15812i
$56$	−1.01128	−	4.04587i	−0.135138	−	0.540652i
$57$	−2.41941	−	2.41941i	−0.320459	−	0.320459i
$58$	10.3408	−	4.97178i	1.35781	−	0.652826i
$59$	−3.92044	+	12.0659i	−0.510398	+	1.57084i	0.281104	+	0.959677i	$0.409299\pi$
$59$	−3.92044	+	12.0659i	−0.510398	+	1.57084i	−0.791502	+	0.611166i	$0.790701\pi$
$60$	−0.887578	+	4.38317i	−0.114586	+	0.565865i
$61$	2.15405	+	6.62949i	0.275798	+	0.848819i	0.989007	+	0.147867i	$0.0472409\pi$
$61$	2.15405	+	6.62949i	0.275798	+	0.848819i	−0.713209	+	0.700951i	$0.752759\pi$
$62$	−2.14879	−	2.25032i	−0.272897	−	0.285791i
$63$	1.31373	−	0.669381i	0.165515	−	0.0843340i
$64$	−3.76408	−	7.05915i	−0.470511	−	0.882394i
$65$	8.82932	−	8.89017i	1.09514	−	1.10269i
$66$	−0.155308	+	6.72942i	−0.0191171	+	0.828334i
$67$	7.39906	−	1.17190i	0.903939	−	0.143170i	0.312875	−	0.949794i	$-0.398708\pi$
$67$	7.39906	−	1.17190i	0.903939	−	0.143170i	0.591064	+	0.806625i	$0.298708\pi$
$68$	0.676511	−	3.28285i	0.0820390	−	0.398104i
$69$	4.68966	−	6.45476i	0.564568	−	0.777061i
$70$	2.81415	−	3.71756i	0.336355	−	0.444333i
$71$	−7.39857	−	10.1833i	−0.878049	−	1.20853i	−0.976958	−	0.213434i	$-0.931535\pi$
$71$	−7.39857	−	10.1833i	−0.878049	−	1.20853i	0.0989090	−	0.995096i	$-0.468465\pi$
$72$	2.13355	−	1.85687i	0.251441	−	0.218834i
$73$	−9.08821	−	4.63068i	−1.06369	−	0.541980i	−0.167606	−	0.985854i	$-0.553604\pi$
$73$	−9.08821	−	4.63068i	−1.06369	−	0.541980i	−0.896089	+	0.443874i	$0.853604\pi$
$74$	0.505542	+	1.68742i	0.0587681	+	0.196159i
$75$	−4.43934	+	2.30050i	−0.512610	+	0.265639i
$76$	3.76261	+	5.71588i	0.431601	+	0.655657i
$77$	3.18604	−	6.25296i	0.363083	−	0.712590i
$78$	−7.85340	+	1.05874i	−0.889223	+	0.119878i
$79$	−7.49468	+	5.44520i	−0.843218	+	0.612633i	−0.923268	−	0.384157i	$-0.874492\pi$
$79$	−7.49468	+	5.44520i	−0.843218	+	0.612633i	0.0800501	+	0.996791i	$0.474492\pi$
$80$	3.50796	−	8.22765i	0.392202	−	0.919879i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	−6.97066	−	3.75678i	−0.769780	−	0.414867i
$83$	0.974493	+	6.15271i	0.106965	+	0.675348i	0.981655	+	0.190666i	$0.0610646\pi$
$83$	0.974493	+	6.15271i	0.106965	+	0.675348i	−0.874690	+	0.484682i	$0.838935\pi$
$84$	−2.84360	+	0.780899i	−0.310262	+	0.0852031i
$85$	3.33315	−	1.71277i	0.361531	−	0.185776i
$86$	−4.01965	+	2.78105i	−0.433450	+	0.299888i
$87$	−3.68335	−	7.22899i	−0.394897	−	0.775029i
$88$	3.02066	−	13.1192i	0.322004	−	1.39851i
$89$	1.92856	−	0.626628i	0.204427	−	0.0664225i	−0.205013	−	0.978759i	$-0.565724\pi$
$89$	1.92856	−	0.626628i	0.204427	−	0.0664225i	0.409441	+	0.912337i	$0.365724\pi$
$90$	3.11303	+	0.555934i	0.328142	+	0.0586006i
$91$	7.85754	+	2.55307i	0.823694	+	0.267634i
$92$	−11.7919	+	10.7508i	−1.22939	+	1.12085i
$93$	−1.55574	+	1.55574i	−0.161322	+	0.161322i
$94$	7.67161	+	2.68988i	0.791266	+	0.277440i
$95$	−2.33924	+	7.28448i	−0.240001	+	0.747371i
$96$	−4.92884	+	2.77607i	−0.503047	+	0.283332i
$97$	−3.36367	−	0.532753i	−0.341529	−	0.0540929i	−0.0166860	−	0.999861i	$-0.505312\pi$
$97$	−3.36367	−	0.532753i	−0.341529	−	0.0540929i	−0.324843	+	0.945768i	$0.605312\pi$
$98$	−6.71459	−	1.22292i	−0.678276	−	0.123534i
$99$	4.75968			0.478366
$100$	9.62458	−	2.71430i	0.962458	−	0.271430i
$101$	−13.7603			−1.36920			−0.684602	−	0.728917i	$-0.740024\pi$
$101$	−13.7603			−1.36920			−0.684602	+	0.728917i	$0.740024\pi$
$102$	−2.33174	−	0.424679i	−0.230877	−	0.0420494i
$103$	6.04390	+	0.957260i	0.595524	+	0.0943217i	0.446918	−	0.894575i	$-0.352522\pi$
$103$	6.04390	+	0.957260i	0.595524	+	0.0943217i	0.148606	+	0.988897i	$0.452522\pi$
$104$	15.8109	+	1.09626i	1.55039	+	0.107497i
$105$	−2.67392	−	1.92872i	−0.260948	−	0.188224i
$106$	−5.80796	−	2.03643i	−0.564119	−	0.197796i
$107$	−8.72357	+	8.72357i	−0.843339	+	0.843339i	−0.989292	−	0.145953i	$-0.953375\pi$
$107$	−8.72357	+	8.72357i	−0.843339	+	0.843339i	0.145953	+	0.989292i	$0.453375\pi$
$108$	−1.34747	−	1.47795i	−0.129660	−	0.142216i
$109$	−13.2840	−	4.31622i	−1.27237	−	0.413419i	−0.406486	−	0.913657i	$-0.633246\pi$
$109$	−13.2840	−	4.31622i	−1.27237	−	0.413419i	−0.865888	+	0.500238i	$0.833246\pi$
$110$	13.5425	−	6.56851i	1.29123	−	0.626283i
$111$	1.18462	−	0.384907i	0.112439	−	0.0365338i
$112$	5.88538	−	0.381790i	0.556116	−	0.0360758i
$113$	1.97483	+	3.87583i	0.185777	+	0.364607i	0.965045	−	0.262083i	$-0.0844093\pi$
$113$	1.97483	+	3.87583i	0.185777	+	0.364607i	−0.779269	+	0.626690i	$0.784409\pi$
$114$	3.97928	−	2.75311i	0.372693	−	0.257853i
$115$	−17.6303	−	2.73034i	−1.64404	−	0.254605i
$116$	4.29700	+	15.6473i	0.398966	+	1.45281i
$117$	0.876569	+	5.53444i	0.0810389	+	0.511659i
$118$	−15.7941	−	8.51212i	−1.45397	−	0.783604i
$119$	1.99911	+	1.45244i	0.183258	+	0.133145i
$120$	−5.87351	−	2.34561i	−0.536176	−	0.214124i
$121$	9.42875	−	6.85039i	0.857159	−	0.622763i
$122$	−9.76961	+	1.31707i	−0.884499	+	0.119242i
$123$	−2.54201	+	4.98898i	−0.229206	+	0.449841i
$124$	3.67544	−	2.41944i	0.330064	−	0.217272i
$125$	9.11231	+	6.47810i	0.815030	+	0.579419i
$126$	0.598425	+	1.99745i	0.0533120	+	0.177947i
$127$	−3.05770	−	1.55798i	−0.271327	−	0.138248i	0.313034	−	0.949742i	$-0.398655\pi$
$127$	−3.05770	−	1.55798i	−0.271327	−	0.138248i	−0.584361	+	0.811494i	$0.698655\pi$
$128$	10.7754	−	3.44827i	0.952421	−	0.304787i
$129$	2.03155	+	2.79619i	0.178868	+	0.246191i
$130$	10.1318	+	14.5372i	0.888615	+	1.27500i
$131$	4.34615	−	5.98196i	0.379725	−	0.522646i	−0.575787	−	0.817600i	$-0.695304\pi$
$131$	4.34615	−	5.98196i	0.379725	−	0.522646i	0.955512	+	0.294954i	$0.0953042\pi$
$132$	−9.32346	−	1.92132i	−0.811503	−	0.167230i
$133$	−4.98278	+	0.789194i	−0.432062	+	0.0684318i
$134$	−0.244440	+	10.5915i	−0.0211164	+	0.914963i
$135$	0.342211	−	2.20973i	0.0294529	−	0.190183i
$136$	4.39608	+	1.77312i	0.376961	+	0.152044i
$137$	10.0977	−	5.14506i	0.862708	−	0.439572i	0.0341118	−	0.999418i	$-0.489140\pi$
$137$	10.0977	−	5.14506i	0.862708	−	0.439572i	0.828597	+	0.559846i	$0.189140\pi$
$138$	7.79231	+	8.16048i	0.663325	+	0.694666i
$139$	4.52482	+	13.9260i	0.383791	+	1.18119i	0.937354	+	0.348379i	$0.113268\pi$
$139$	4.52482	+	13.9260i	0.383791	+	1.18119i	−0.553563	+	0.832807i	$0.686732\pi$
$140$	4.45922	+	4.85743i	0.376873	+	0.410528i
$141$	1.77636	−	5.46709i	0.149597	−	0.460412i
$142$	16.0430	−	7.71337i	1.34630	−	0.647292i
$143$	18.8589	+	18.8589i	1.57706	+	1.57706i
$144$	2.04287	+	3.43899i	0.170239	+	0.286583i
$145$	−10.6130	+	14.7136i	−0.881365	+	1.22190i
$146$	8.74574	−	11.4712i	0.723803	−	0.949367i
$147$	−0.754958	+	4.76662i	−0.0622679	+	0.393144i
$148$	−2.47586	+	0.275779i	−0.203514	+	0.0226689i
$149$			7.25270i			0.594165i	0.954852	+	0.297082i	$0.0960136\pi$
$149$			7.25270i			0.594165i	−0.954852	+	0.297082i	$0.903986\pi$
$150$	−2.07581	−	6.75951i	−0.169489	−	0.551912i
$151$		−	8.89011i		−	0.723467i	−0.932282	−	0.361733i	$-0.882185\pi$
$151$		−	8.89011i		−	0.723467i	0.932282	−	0.361733i	$-0.117815\pi$
$152$	−8.90610	+	3.78660i	−0.722380	+	0.307134i
$153$	−0.262171	+	1.65528i	−0.0211953	+	0.133822i
$154$	7.89255	+	6.01733i	0.636000	+	0.484890i
$155$	4.68408	+	1.50418i	0.376234	+	0.120819i
$156$	0.517010	−	11.1949i	0.0413939	−	0.896311i
$157$	−3.13469	−	3.13469i	−0.250175	−	0.250175i	0.570867	−	0.821043i	$-0.306607\pi$
$157$	−3.13469	−	3.13469i	−0.250175	−	0.250175i	−0.821043	+	0.570867i	$0.806607\pi$
$158$	−5.67689	−	11.8074i	−0.451629	−	0.939344i
$159$	−1.34484	+	4.13898i	−0.106652	+	0.328242i
$160$	10.5584	+	6.96562i	0.834716	+	0.550680i
$161$	−3.63522	−	11.1881i	−0.286496	−	0.881743i
$162$	−1.02281	+	0.976661i	−0.0803593	+	0.0767337i
$163$	3.54660	−	1.80708i	0.277791	−	0.141542i	−0.309545	−	0.950885i	$-0.600177\pi$
$163$	3.54660	−	1.80708i	0.277791	−	0.141542i	0.587336	+	0.809343i	$0.300177\pi$
$164$	6.99328	−	8.74649i	0.546083	−	0.682986i
$165$	−4.86435	−	9.46631i	−0.378689	−	0.736951i
$166$	−8.80736	−	0.203265i	−0.683584	−	0.0157764i
$167$	20.0096	−	3.16922i	1.54839	−	0.245241i	0.677058	−	0.735930i	$-0.263255\pi$
$167$	20.0096	−	3.16922i	1.54839	−	0.245241i	0.871335	+	0.490689i	$0.163255\pi$
$168$	−0.365914	−	4.15426i	−0.0282309	−	0.320508i
$169$	−10.8143	+	14.8846i	−0.831871	+	1.14497i
$170$	1.53840	+	5.07151i	0.117990	+	0.388967i
$171$	−2.01115	−	2.76811i	−0.153796	−	0.211682i
$172$	−2.85076	−	6.29737i	−0.217368	−	0.480170i
$173$	6.81344	+	3.47162i	0.518016	+	0.263943i	0.693394	−	0.720559i	$-0.256115\pi$
$173$	6.81344	+	3.47162i	0.518016	+	0.263943i	−0.175377	+	0.984501i	$0.556115\pi$
$174$	10.9912	−	3.29291i	0.833244	−	0.249635i
$175$	−1.10322	+	7.28917i	−0.0833959	+	0.551010i
$176$	17.4876	+	7.52714i	1.31818	+	0.567379i
$177$	−5.75969	+	11.3040i	−0.432925	+	0.849663i
$178$	0.383144	+	2.84205i	0.0287179	+	0.213021i
$179$	−13.4766	+	9.79134i	−1.00729	+	0.731839i	−0.963639	−	0.267208i	$-0.913899\pi$
$179$	−13.4766	+	9.79134i	−1.00729	+	0.731839i	−0.0436509	+	0.999047i	$0.513899\pi$
$180$	−1.56233	+	4.19036i	−0.116449	+	0.312331i
$181$	14.3280	+	10.4099i	1.06499	+	0.773762i	0.975005	−	0.222181i	$-0.0713176\pi$
$181$	14.3280	+	10.4099i	1.06499	+	0.773762i	0.0899867	+	0.995943i	$0.471318\pi$
$182$	−5.54326	+	10.2854i	−0.410894	+	0.762408i
$183$	1.09045	+	6.88483i	0.0806084	+	0.508942i
$184$	−11.9698	−	19.1306i	−0.882423	−	1.41032i
$185$	−1.97620	−	1.96267i	−0.145293	−	0.144298i
$186$	−1.77031	−	2.55876i	−0.129805	−	0.187617i
$187$	3.62140	+	7.10740i	0.264823	+	0.519745i
$188$	−5.68649	+	9.99209i	−0.414730	+	0.728748i
$189$	1.40227	−	0.455626i	0.102000	−	0.0331419i
$190$	−9.54231	−	5.10054i	−0.692272	−	0.370032i
$191$	−9.15141	−	2.97347i	−0.662173	−	0.215153i	−0.0413989	−	0.999143i	$-0.513181\pi$
$191$	−9.15141	−	2.97347i	−0.662173	−	0.215153i	−0.620774	+	0.783990i	$0.713181\pi$
$192$	−2.61345	−	7.56108i	−0.188609	−	0.545674i
$193$	−8.11384	+	8.11384i	−0.584047	+	0.584047i	−0.936013	−	0.351966i	$-0.885513\pi$
$193$	−8.11384	+	8.11384i	−0.584047	+	0.584047i	0.351966	+	0.936013i	$0.385513\pi$
$194$	1.59359	−	4.54497i	0.114413	−	0.326309i
$195$	10.1113	−	7.39951i	0.724089	−	0.529890i
$196$	3.40297	−	9.03229i	0.243069	−	0.645163i
$197$	2.15209	+	0.340857i	0.153330	+	0.0242851i	0.232628	−	0.972566i	$-0.425268\pi$
$197$	2.15209	+	0.340857i	0.153330	+	0.0242851i	−0.0792975	+	0.996851i	$0.525268\pi$
$198$	−1.20611	+	6.62227i	−0.0857144	+	0.470624i
$199$	9.69051			0.686942			0.343471	−	0.939163i	$-0.388397\pi$
$199$	9.69051			0.686942			0.343471	+	0.939163i	$0.388397\pi$
$200$	1.33759	+	14.0787i	0.0945820	+	0.995517i
$201$	7.49129			0.528395
$202$	3.48688	−	19.1451i	0.245336	−	1.34704i
$203$	−11.8152	−	1.87135i	−0.829268	−	0.131343i
$204$	1.18173	−	3.13660i	0.0827378	−	0.219606i
$205$	12.5203	−	0.0429983i	0.874453	−	0.00300313i
$206$	−2.86339	+	8.16647i	−0.199502	+	0.568985i
$207$	5.64166	−	5.64166i	0.392123	−	0.392123i
$208$	−5.53176	+	21.7204i	−0.383558	+	1.50604i
$209$	−15.4885	−	5.03252i	−1.07136	−	0.348107i
$210$	3.36106	−	3.23156i	0.231935	−	0.222999i
$211$	−23.4844	+	7.63053i	−1.61673	+	0.525308i	−0.971167	−	0.238399i	$-0.923377\pi$
$211$	−23.4844	+	7.63053i	−1.61673	+	0.525308i	−0.645563	+	0.763707i	$0.723377\pi$
$212$	4.30508	−	7.56473i	0.295674	−	0.519548i
$213$	−5.71447	−	11.2153i	−0.391549	−	0.768458i
$214$	−9.92676	−	14.3479i	−0.678580	−	0.980801i
$215$	3.48499	−	6.89815i	0.237674	−	0.470450i
$216$	2.39776	−	1.50025i	0.163147	−	0.102079i
$217$	0.507469	+	3.20403i	0.0344493	+	0.217504i
$218$	9.37144	−	17.3886i	0.634714	−	1.17770i
$219$	−8.25193	−	5.99537i	−0.557613	−	0.405130i
$220$	5.70725	+	20.5066i	0.384782	+	1.38255i
$221$	−7.59737	+	5.51981i	−0.511055	+	0.371303i
$222$	0.235347	+	1.74573i	0.0157954	+	0.117166i
$223$	8.96950	−	17.6036i	0.600642	−	1.17883i	−0.367874	−	0.929876i	$-0.619914\pi$
$223$	8.96950	−	17.6036i	0.600642	−	1.17883i	0.968516	−	0.248951i	$-0.0800857\pi$
$224$	−0.960167	+	8.28523i	−0.0641539	+	0.553580i
$225$	−4.74456	+	1.57771i	−0.316304	+	0.105181i
$226$	−5.89296	+	1.76550i	−0.391994	+	0.117439i
$227$	0.147478	+	0.0751436i	0.00978843	+	0.00498746i	0.458878	−	0.888499i	$-0.348252\pi$
$227$	0.147478	+	0.0751436i	0.00978843	+	0.00498746i	−0.449089	+	0.893487i	$0.648252\pi$
$228$	2.82212	+	6.23411i	0.186900	+	0.412864i
$229$	4.40665	+	6.06523i	0.291200	+	0.400802i	0.929403	−	0.369066i	$-0.120322\pi$
$229$	4.40665	+	6.06523i	0.291200	+	0.400802i	−0.638204	+	0.769867i	$0.720322\pi$
$230$	8.26634	−	23.8377i	0.545066	−	1.57181i
$231$	4.12499	−	5.67756i	0.271405	−	0.373556i
$232$	−22.8593	+	2.01349i	−1.50079	+	0.132192i
$233$	10.5449	−	1.67016i	0.690822	−	0.109415i	0.198855	−	0.980029i	$-0.436278\pi$
$233$	10.5449	−	1.67016i	0.690822	−	0.109415i	0.491968	+	0.870614i	$0.336278\pi$
$234$	−7.92234	−	0.182839i	−0.517899	−	0.0119526i
$235$	−12.6887	+	2.05438i	−0.827717	+	0.134013i
$236$	15.8454	−	19.8178i	1.03145	−	1.29003i
$237$	−8.25423	+	4.20574i	−0.536170	+	0.273192i
$238$	−2.52739	+	2.41336i	−0.163826	+	0.156435i
$239$	−6.87021	−	21.1443i	−0.444397	−	1.36771i	−0.883143	−	0.469103i	$-0.844577\pi$
$239$	−6.87021	−	21.1443i	−0.444397	−	1.36771i	0.438746	−	0.898611i	$-0.355423\pi$
$240$	4.75186	−	7.57759i	0.306731	−	0.489131i
$241$	6.30289	−	19.3983i	0.406005	−	1.24956i	−0.514048	−	0.857761i	$-0.671855\pi$
$241$	6.30289	−	19.3983i	0.406005	−	1.24956i	0.920053	−	0.391794i	$-0.128145\pi$
$242$	7.14187	+	14.8544i	0.459097	+	0.954875i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	0.643159	−	13.9265i	0.0411741	−	0.891550i
$245$	10.2517	−	3.36993i	0.654955	−	0.215297i
$246$	−6.29715	−	4.80098i	−0.401492	−	0.306099i
$247$	2.99924	−	18.9365i	0.190837	−	1.20490i
$248$	2.43487	+	5.72682i	0.154614	+	0.363653i
$249$			6.22940i			0.394772i
$250$	−11.3222	+	11.0366i	−0.716080	+	0.698018i
$251$		−	18.0233i		−	1.13762i	−0.822468	−	0.568811i	$-0.807403\pi$
$251$		−	18.0233i		−	1.13762i	0.822468	−	0.568811i	$-0.192597\pi$
$252$	−2.93075	+	0.326448i	−0.184620	+	0.0205643i
$253$	5.94063	−	37.5077i	0.373484	−	2.35809i
$254$	2.94248	−	3.85946i	0.184627	−	0.242164i
$255$	3.56005	−	1.17026i	0.222939	−	0.0732846i
$256$	2.06717	+	15.8659i	0.129198	+	0.991619i
$257$	−1.16576	−	1.16576i	−0.0727178	−	0.0727178i	0.669812	−	0.742530i	$-0.266374\pi$
$257$	−1.16576	−	1.16576i	−0.0727178	−	0.0727178i	−0.742530	+	0.669812i	$0.766374\pi$
$258$	−4.40522	+	2.11800i	−0.274257	+	0.131861i
$259$	0.567522	−	1.74665i	0.0352641	−	0.108532i
$260$	−22.7934	+	10.4128i	−1.41359	+	0.645777i
$261$	−2.50714	−	7.71619i	−0.155188	−	0.477620i
$262$	7.22154	+	7.56274i	0.446148	+	0.467228i
$263$	−22.7301	+	11.5815i	−1.40160	+	0.714149i	−0.981164	−	0.193176i	$-0.938121\pi$
$263$	−22.7301	+	11.5815i	−1.40160	+	0.714149i	−0.420431	+	0.907324i	$0.638121\pi$
$264$	5.03576	−	12.4851i	0.309930	−	0.768405i
$265$	9.60623	−	1.55531i	0.590106	−	0.0955422i
$266$	0.164614	−	7.13265i	0.0100931	−	0.437331i
$267$	2.00285	−	0.317220i	0.122572	−	0.0194135i
$268$	−14.6742	−	3.02398i	−0.896371	−	0.184719i
$269$	14.4616	−	19.9047i	0.881740	−	1.21361i	−0.0941958	−	0.995554i	$-0.530028\pi$
$269$	14.4616	−	19.9047i	0.881740	−	1.21361i	0.975936	−	0.218057i	$-0.0699720\pi$
$270$	2.98773	+	1.03607i	0.181828	+	0.0630535i
$271$	0.554963	+	0.763841i	0.0337116	+	0.0464000i	0.825540	−	0.564344i	$-0.190871\pi$
$271$	0.554963	+	0.763841i	0.0337116	+	0.0464000i	−0.791828	+	0.610744i	$0.790871\pi$
$272$	−3.58097	+	5.66707i	−0.217128	+	0.343617i
$273$	7.36141	+	3.75083i	0.445533	+	0.227010i
$274$	4.59967	+	15.3530i	0.277876	+	0.927509i
$275$	−13.8558	+	19.3489i	−0.835535	+	1.16679i
$276$	−13.3285	+	8.77377i	−0.802280	+	0.528119i
$277$	−5.23893	+	10.2820i	−0.314777	+	0.617784i	−0.993139	−	0.116944i	$-0.962690\pi$
$277$	−5.23893	+	10.2820i	−0.314777	+	0.617784i	0.678362	+	0.734728i	$0.262690\pi$
$278$	−20.5222	+	2.76665i	−1.23084	+	0.165933i
$279$	−1.77995	+	1.29321i	−0.106563	+	0.0774225i
$280$	−7.88824	+	4.97336i	−0.471413	+	0.297215i
$281$	4.14505	+	3.01155i	0.247273	+	0.179654i	0.704517	−	0.709687i	$-0.251164\pi$
$281$	4.14505	+	3.01155i	0.247273	+	0.179654i	−0.457244	+	0.889341i	$0.651164\pi$
$282$	7.15637	+	3.85687i	0.426156	+	0.229673i
$283$	1.43610	+	9.06715i	0.0853670	+	0.538986i	0.992895	+	0.118994i	$0.0379670\pi$
$283$	1.43610	+	9.06715i	0.0853670	+	0.538986i	−0.907528	+	0.419992i	$0.862033\pi$
$284$	6.66650	+	24.2757i	0.395584	+	1.44050i
$285$	−3.44999	+	6.82885i	−0.204359	+	0.404506i
$286$	−31.0178	+	21.4600i	−1.83412	+	1.26896i
$287$	3.74804	+	7.35594i	0.221240	+	0.434207i
$288$	−5.30243	+	1.97085i	−0.312449	+	0.116134i
$289$	13.4967	−	4.38536i	0.793926	−	0.257962i
$290$	−17.7821	−	18.4946i	−1.04420	−	1.08604i
$291$	−3.23892	−	1.05239i	−0.189869	−	0.0616921i
$292$	13.7441	+	15.0750i	0.804311	+	0.882198i
$293$	−20.8580	+	20.8580i	−1.21854	+	1.21854i	−0.250392	+	0.968145i	$0.580559\pi$
$293$	−20.8580	+	20.8580i	−1.21854	+	1.21854i	−0.968145	+	0.250392i	$0.919441\pi$
$294$	−6.44061	−	2.25826i	−0.375624	−	0.131704i
$295$	28.3684	−	0.0974256i	1.65167	−	0.00567234i
$296$	0.243687	−	3.51461i	0.0141640	−	0.204283i
$297$	4.70108	+	0.744578i	0.272785	+	0.0432048i
$298$	−10.0909	−	1.83784i	−0.584549	−	0.106463i
$299$	44.7071			2.58548
$300$	9.93070	−	1.17526i	0.573349	−	0.0678538i
$301$	5.09608			0.293733
$302$	12.3690	+	2.25276i	0.711758	+	0.129632i
$303$	−13.5909	−	2.15259i	−0.780777	−	0.123663i
$304$	−3.01158	−	13.3508i	−0.172726	−	0.765722i
$305$	12.5785	−	9.20498i	0.720242	−	0.527075i
$306$	−2.23660	−	0.784215i	−0.127858	−	0.0448306i
$307$	1.07224	−	1.07224i	0.0611962	−	0.0611962i	−0.675846	−	0.737043i	$-0.736222\pi$
$307$	1.07224	−	1.07224i	0.0611962	−	0.0611962i	0.737043	+	0.675846i	$0.236222\pi$
$308$	−10.3720	+	9.45632i	−0.591002	+	0.538824i
$309$	5.81975	+	1.89095i	0.331074	+	0.107572i
$310$	−3.27976	+	6.13591i	−0.186278	+	0.348497i
$311$	−0.0825240	+	0.0268137i	−0.00467951	+	0.00152046i	−0.311356	−	0.950293i	$-0.600783\pi$
$311$	−0.0825240	+	0.0268137i	−0.00467951	+	0.00152046i	0.306676	+	0.951814i	$0.400783\pi$
$312$	15.4448	+	3.55614i	0.874388	+	0.201327i
$313$	−10.0594	−	19.7428i	−0.568593	−	1.11593i	−0.978969	−	0.204011i	$-0.934602\pi$
$313$	−10.0594	−	19.7428i	−0.568593	−	1.11593i	0.410375	−	0.911917i	$-0.365398\pi$
$314$	5.15571	−	3.56704i	0.290953	−	0.201300i
$315$	−2.33928	−	2.32327i	−0.131804	−	0.130901i
$316$	17.8664	−	4.90641i	1.00506	−	0.276007i
$317$	4.98965	+	31.5034i	0.280247	+	1.76941i	0.579244	+	0.815154i	$0.303348\pi$
$317$	4.98965	+	31.5034i	0.280247	+	1.76941i	−0.298998	+	0.954254i	$0.596652\pi$
$318$	−5.41789	−	2.91993i	−0.303820	−	0.163741i
$319$	−31.2415	−	22.6983i	−1.74919	−	1.27086i
$320$	−12.3670	+	12.9251i	−0.691334	+	0.722535i
$321$	−9.98083	+	7.25150i	−0.557076	+	0.404739i
$322$	16.4874	−	2.22271i	0.918808	−	0.123867i
$323$	2.60330	−	5.10926i	0.144851	−	0.284287i
$324$	−1.09967	−	1.67054i	−0.0610930	−	0.0928080i
$325$	−25.0502	−	12.5478i	−1.38954	−	0.696024i
$326$	1.61553	+	5.39239i	0.0894759	+	0.298657i
$327$	−12.4452	−	6.34115i	−0.688222	−	0.350667i
$328$	10.3971	+	11.9463i	0.574084	+	0.659624i
$329$	−4.98190	−	6.85700i	−0.274661	−	0.378038i
$330$	14.4034	−	4.36912i	0.792879	−	0.240512i
$331$	11.2987	−	15.5513i	0.621031	−	0.854776i	−0.376396	−	0.926459i	$-0.622837\pi$
$331$	11.2987	−	15.5513i	0.621031	−	0.854776i	0.997428	+	0.0716824i	$0.0228368\pi$
$332$	2.51460	−	12.2024i	0.138007	−	0.669694i
$333$	1.23025	−	0.194853i	0.0674173	−	0.0106779i
$334$	−0.661051	+	28.6430i	−0.0361711	+	1.56728i
$335$	−7.65602	−	14.8991i	−0.418293	−	0.814023i
$336$	5.87265	+	0.543587i	0.320379	+	0.0296551i
$337$	12.8547	−	6.54977i	0.700238	−	0.356789i	−0.0673530	−	0.997729i	$-0.521455\pi$
$337$	12.8547	−	6.54977i	0.700238	−	0.356789i	0.767591	+	0.640940i	$0.221455\pi$
$338$	−17.9690	−	18.8180i	−0.977386	−	1.02357i
$339$	1.34421	+	4.13704i	0.0730072	+	0.224693i
$340$	−7.44596	+	0.855283i	−0.403814	+	0.0463842i
$341$	−3.23602	+	9.95944i	−0.175240	+	0.539334i
$342$	4.36097	−	2.09672i	0.235814	−	0.113378i
$343$	12.3296	+	12.3296i	0.665738	+	0.665738i
$344$	9.48408	−	2.37058i	0.511347	−	0.127813i
$345$	−16.9862	−	5.45472i	−0.914504	−	0.293672i
$346$	−6.55669	+	8.60001i	−0.352490	+	0.462339i
$347$	0.544569	−	3.43827i	0.0292340	−	0.184576i	−0.968750	−	0.248038i	$-0.920214\pi$
$347$	0.544569	−	3.43827i	0.0292340	−	0.184576i	0.997984	+	0.0634620i	$0.0202142\pi$
$348$	1.79632	+	16.1268i	0.0962929	+	0.864489i
$349$			1.06294i			0.0568981i	0.999595	+	0.0284490i	$0.00905683\pi$
$349$			1.06294i			0.0568981i	−0.999595	+	0.0284490i	$0.990943\pi$
$350$	−9.86206	−	3.38203i	−0.527149	−	0.180777i
$351$			5.60343i			0.299089i
$352$	−14.9041	+	22.4235i	−0.794390	+	1.19518i
$353$	−3.21923	+	20.3254i	−0.171342	+	1.08181i	0.740736	+	0.671797i	$0.234477\pi$
$353$	−3.21923	+	20.3254i	−0.171342	+	1.08181i	−0.912078	+	0.410017i	$0.865523\pi$
$354$	−14.2681	−	10.8781i	−0.758340	−	0.578163i
$355$	−16.4654	+	22.8271i	−0.873893	+	1.21154i
$356$	−4.05131	−	0.187100i	−0.214719	−	0.00991626i
$357$	1.74728	+	1.74728i	0.0924760	+	0.0924760i
$358$	−10.2080	−	21.2315i	−0.539507	−	1.12212i
$359$	5.08507	−	15.6502i	0.268380	−	0.825988i	−0.722516	−	0.691354i	$-0.757014\pi$
$359$	5.08507	−	15.6502i	0.268380	−	0.825988i	0.990895	−	0.134633i	$-0.0429856\pi$
$360$	−5.43426	−	3.23555i	−0.286411	−	0.170529i
$361$	−2.25362	−	6.93593i	−0.118612	−	0.365049i
$362$	−18.1143	+	17.2970i	−0.952066	+	0.909112i
$363$	10.3843	−	5.29107i	0.545035	−	0.277709i
$364$	−12.9057	−	10.3188i	−0.676445	−	0.540853i
$365$	−3.49054	+	22.5391i	−0.182703	+	1.17975i
$366$	−9.85537	−	0.227452i	−0.515148	−	0.0118891i
$367$	18.7851	−	2.97526i	0.980573	−	0.155307i	0.354486	−	0.935061i	$-0.384656\pi$
$367$	18.7851	−	2.97526i	0.980573	−	0.155307i	0.626086	+	0.779754i	$0.284656\pi$
$368$	29.6500	−	11.8061i	1.54561	−	0.615438i
$369$	−3.29116	+	4.52990i	−0.171331	+	0.235817i
$370$	3.23148	−	2.25219i	0.167997	−	0.117086i
$371$	3.77165	+	5.19124i	0.195815	+	0.269516i
$372$	4.00867	−	1.81469i	0.207840	−	0.0940871i
$373$	0.521594	+	0.265765i	0.0270071	+	0.0137608i	0.467442	−	0.884024i	$-0.345176\pi$
$373$	0.521594	+	0.265765i	0.0270071	+	0.0137608i	−0.440435	+	0.897785i	$0.645176\pi$
$374$	−10.8064	+	3.23753i	−0.558785	+	0.167409i
$375$	7.98672	+	7.82382i	0.412433	+	0.404021i
$376$	−12.4613	−	10.4438i	−0.642642	−	0.538597i
$377$	20.6394	−	40.5071i	1.06298	−	2.08622i
$378$	0.278587	+	2.06648i	0.0143290	+	0.106288i
$379$	4.02282	−	2.92275i	0.206639	−	0.150132i	−0.479653	−	0.877458i	$-0.659237\pi$
$379$	4.02282	−	2.92275i	0.206639	−	0.150132i	0.686292	+	0.727327i	$0.259237\pi$
$380$	9.51455	−	11.9840i	0.488086	−	0.614766i
$381$	−2.77633	−	2.01712i	−0.142236	−	0.103340i
$382$	6.45605	−	11.9791i	0.330320	−	0.612905i
$383$	−2.89726	−	18.2926i	−0.148043	−	0.934708i	−0.944141	−	0.329540i	$-0.893106\pi$
$383$	−2.89726	−	18.2926i	−0.148043	−	0.934708i	0.796098	−	0.605167i	$-0.206894\pi$
$384$	11.1822	−	1.72017i	0.570638	−	0.0877822i
$385$	−15.5075	−	2.40159i	−0.790338	−	0.122396i
$386$	−9.23294	−	13.3451i	−0.469944	−	0.679245i
$387$	1.56912	+	3.07957i	0.0797629	+	0.156544i
$388$	5.91971	+	3.36890i	0.300528	+	0.171030i
$389$	−14.1818	+	4.60795i	−0.719046	+	0.233632i	−0.645609	−	0.763668i	$-0.723397\pi$
$389$	−14.1818	+	4.60795i	−0.719046	+	0.233632i	−0.0734363	+	0.997300i	$0.523397\pi$
$390$	7.73291	+	15.9432i	0.391571	+	0.807316i
$391$	12.7169	+	4.13196i	0.643120	+	0.208962i
$392$	11.7045	+	7.02343i	0.591169	+	0.354737i
$393$	5.22842	−	5.22842i	0.263739	−	0.263739i
$394$	−1.01959	+	2.90788i	−0.0513660	+	0.146497i
$395$	16.8003	+	12.1182i	0.845317	+	0.609734i
$396$	−8.90811	−	3.35618i	−0.447649	−	0.168654i
$397$	17.2952	+	2.73929i	0.868021	+	0.137481i	0.574533	−	0.818482i	$-0.305184\pi$
$397$	17.2952	+	2.73929i	0.868021	+	0.137481i	0.293488	+	0.955963i	$0.405184\pi$
$398$	−2.45558	+	13.4827i	−0.123087	+	0.675825i
$399$	−5.04489			−0.252560
$400$	−19.9271	−	1.70654i	−0.996353	−	0.0853270i
$401$	−23.4783			−1.17245			−0.586226	−	0.810147i	$-0.699387\pi$
$401$	−23.4783			−1.17245			−0.586226	+	0.810147i	$0.699387\pi$
$402$	−1.89830	+	10.4228i	−0.0946786	+	0.519843i
$403$	−12.1766	−	1.92858i	−0.606558	−	0.0960693i
$404$	25.7535	+	9.70277i	1.28128	+	0.482731i
$405$	0.683675	−	2.12899i	0.0339721	−	0.105790i
$406$	5.59766	−	15.9647i	0.277807	−	0.792313i
$407$	4.19215	−	4.19215i	0.207797	−	0.207797i
$408$	4.06458	+	2.43899i	0.201227	+	0.120748i
$409$	36.3503	+	11.8109i	1.79741	+	0.584014i	0.999816	−	0.0191827i	$-0.00610643\pi$
$409$	36.3503	+	11.8109i	1.79741	+	0.584014i	0.797593	+	0.603196i	$0.206106\pi$
$410$	−3.11282	+	17.4307i	−0.153731	+	0.860839i
$411$	10.7783	−	3.50208i	0.531654	−	0.172745i
$412$	−10.6366	−	6.05331i	−0.524029	−	0.298225i
$413$	8.49231	+	16.6671i	0.417879	+	0.820134i
$414$	6.41979	+	9.27900i	0.315516	+	0.456038i
$415$	12.3894	−	6.36639i	0.608170	−	0.312514i
$416$	−28.8184	−	13.2004i	−1.41294	−	0.647205i
$417$	2.29061	+	14.4624i	0.112172	+	0.708225i
$418$	10.9267	−	20.2743i	0.534441	−	0.991649i
$419$	−8.44580	−	6.13623i	−0.412604	−	0.299775i	0.362051	−	0.932158i	$-0.382077\pi$
$419$	−8.44580	−	6.13623i	−0.412604	−	0.299775i	−0.774655	+	0.632384i	$0.782077\pi$
$420$	3.64445	+	5.49521i	0.177831	+	0.268139i
$421$	3.57920	−	2.60044i	0.174439	−	0.126738i	−0.497140	−	0.867671i	$-0.665616\pi$
$421$	3.57920	−	2.60044i	0.174439	−	0.126738i	0.671579	+	0.740933i	$0.265616\pi$
$422$	−4.66560	−	34.6080i	−0.227118	−	1.68469i
$423$	2.60974	−	5.12189i	0.126890	−	0.249035i
$424$	9.43409	+	7.90669i	0.458160	+	0.383983i
$425$	−5.96581	−	5.88442i	−0.289384	−	0.285436i
$426$	17.0522	−	5.10873i	0.826180	−	0.247519i
$427$	9.15758	+	4.66602i	0.443166	+	0.225805i
$428$	22.4780	−	10.1756i	1.08652	−	0.491856i
$429$	15.6766	+	21.5769i	0.756871	+	1.04174i
$430$	8.71447	+	6.59676i	0.420249	+	0.318124i
$431$	−14.7423	+	20.2911i	−0.710114	+	0.977388i	0.289681	+	0.957123i	$0.406451\pi$
$431$	−14.7423	+	20.2911i	−0.710114	+	0.977388i	−0.999795	+	0.0202643i	$0.993549\pi$
$432$	1.47974	+	3.71623i	0.0711941	+	0.178797i
$433$	11.9800	−	1.89745i	0.575723	−	0.0911856i	0.138219	−	0.990402i	$-0.455862\pi$
$433$	11.9800	−	1.89745i	0.575723	−	0.0911856i	0.437505	+	0.899216i	$0.355862\pi$
$434$	−4.58645	−	0.105851i	−0.220157	−	0.00508099i
$435$	−12.7841	+	12.8722i	−0.612950	+	0.617175i
$436$	21.8185	+	17.4450i	1.04492	+	0.835465i
$437$	−24.3236	+	12.3935i	−1.16356	+	0.592862i
$438$	10.4326	−	9.96188i	0.498487	−	0.475997i
$439$	−6.68775	−	20.5828i	−0.319189	−	0.982363i	−0.973996	−	0.226567i	$-0.927250\pi$
$439$	−6.68775	−	20.5828i	−0.319189	−	0.982363i	0.654807	−	0.755796i	$-0.272750\pi$
$440$	−29.9775	+	2.74426i	−1.42912	+	0.130827i
$441$	−1.49133	+	4.58983i	−0.0710155	+	0.218563i
$442$	−5.75468	−	11.9691i	−0.273722	−	0.569314i
$443$	−8.27711	−	8.27711i	−0.393257	−	0.393257i	0.482589	−	0.875847i	$-0.339696\pi$
$443$	−8.27711	−	8.27711i	−0.393257	−	0.393257i	−0.875847	+	0.482589i	$0.839696\pi$
$444$	−2.48852	−	0.114926i	−0.118100	−	0.00545415i
$445$	−2.67779	−	3.65917i	−0.126940	−	0.173461i
$446$	22.2195	+	16.9403i	1.05212	+	0.802145i
$447$	−1.13457	+	7.16341i	−0.0536635	+	0.338818i
$448$	−11.2841	−	3.43539i	−0.533126	−	0.162307i
$449$		−	15.5833i		−	0.735422i	−0.929940	−	0.367711i	$-0.880142\pi$
$449$		−	15.5833i		−	0.735422i	0.929940	−	0.367711i	$-0.119858\pi$
$450$	−0.992833	−	7.00102i	−0.0468026	−	0.330031i
$451$			26.6507i			1.25493i
$452$	−0.963099	−	8.64641i	−0.0453004	−	0.406693i
$453$	1.39072	−	8.78066i	0.0653417	−	0.412551i
$454$	−0.141920	+	0.186148i	−0.00666065	+	0.00873636i
$455$	−0.0634455	−	18.4741i	−0.00297437	−	0.866078i
$456$	−9.38881	+	2.34676i	−0.439671	+	0.109897i
$457$	−1.36886	−	1.36886i	−0.0640324	−	0.0640324i	0.674365	−	0.738398i	$-0.264417\pi$
$457$	−1.36886	−	1.36886i	−0.0640324	−	0.0640324i	−0.738398	+	0.674365i	$0.764417\pi$
$458$	−9.55536	+	4.59415i	−0.446493	+	0.214670i
$459$	−0.517886	+	1.59389i	−0.0241729	+	0.0743964i
$460$	31.0713	+	17.5417i	1.44871	+	0.817884i
$461$	1.20334	+	3.70349i	0.0560450	+	0.172489i	0.975161	−	0.221499i	$-0.0710951\pi$
$461$	1.20334	+	3.70349i	0.0560450	+	0.172489i	−0.919115	+	0.393988i	$0.871095\pi$
$462$	6.85407	+	7.17791i	0.318880	+	0.333947i
$463$	−30.4751	+	15.5278i	−1.41630	+	0.721639i	−0.983678	−	0.179938i	$-0.942410\pi$
$463$	−30.4751	+	15.5278i	−1.41630	+	0.721639i	−0.432618	+	0.901577i	$0.642410\pi$
$464$	2.99116	−	32.3150i	0.138861	−	1.50019i
$465$	4.39110	+	2.21842i	0.203632	+	0.102877i
$466$	−0.348370	+	15.0947i	−0.0161379	+	0.699247i
$467$	−1.58480	+	0.251008i	−0.0733359	+	0.0116153i	−0.192995	−	0.981200i	$-0.561820\pi$
$467$	−1.58480	+	0.251008i	−0.0733359	+	0.0116153i	0.119659	+	0.992815i	$0.461820\pi$
$468$	2.26192	−	10.9762i	0.104557	−	0.507376i
$469$	6.49234	−	8.93595i	0.299789	−	0.412624i
$470$	0.357007	−	18.1746i	0.0164675	−	0.838334i
$471$	−2.60572	−	3.58647i	−0.120065	−	0.165256i
$472$	23.5578	+	27.0679i	1.08433	+	1.24590i
$473$	14.6578	+	7.46852i	0.673966	+	0.343403i
$474$	−3.75992	−	12.5501i	−0.172699	−	0.576443i
$475$	17.1074	−	0.117506i	0.784943	−	0.00539152i
$476$	−2.71733	−	4.12797i	−0.124549	−	0.189205i
$477$	−1.97576	+	3.87764i	−0.0904637	+	0.177545i
$478$	31.1596	−	4.20071i	1.42521	−	0.192136i
$479$	5.24823	−	3.81306i	0.239798	−	0.174223i	−0.461395	−	0.887195i	$-0.652651\pi$
$479$	5.24823	−	3.81306i	0.239798	−	0.174223i	0.701193	+	0.712971i	$0.252651\pi$
$480$	9.33876	+	8.53156i	0.426254	+	0.389411i
$481$	5.64658	+	4.10248i	0.257462	+	0.187057i
$482$	25.3922	+	13.6849i	1.15658	+	0.623332i
$483$	−1.84027	−	11.6190i	−0.0837351	−	0.528683i
$484$	−22.4770	+	6.17256i	−1.02168	+	0.280571i
$485$	1.21710	+	7.51727i	0.0552655	+	0.341341i
$486$	−1.16300	+	0.804634i	−0.0527546	+	0.0364990i
$487$	1.10097	+	2.16077i	0.0498896	+	0.0979138i	0.914605	−	0.404348i	$-0.132501\pi$
$487$	1.10097	+	2.16077i	0.0498896	+	0.0979138i	−0.864716	+	0.502262i	$0.832501\pi$
$488$	19.2133	+	4.42382i	0.869744	+	0.200257i
$489$	3.78563	−	1.23002i	0.171192	−	0.0556236i
$490$	2.09090	+	15.1173i	0.0944570	+	0.682932i
$491$	−12.7330	−	4.13721i	−0.574634	−	0.186710i	0.00726141	−	0.999974i	$-0.497689\pi$
$491$	−12.7330	−	4.13721i	−0.574634	−	0.186710i	−0.581895	+	0.813264i	$0.697689\pi$
$492$	8.27543	−	7.54481i	0.373085	−	0.340146i
$493$	9.61465	−	9.61465i	0.433022	−	0.433022i
$494$	25.5868	+	8.97144i	1.15120	+	0.403644i
$495$	−3.32360	−	10.1107i	−0.149385	−	0.454443i
$496$	−8.58487	+	1.93651i	−0.385472	+	0.0869521i
$497$	−18.3305	−	2.90327i	−0.822237	−	0.130230i
$498$	−8.66713	−	1.57854i	−0.388383	−	0.0707359i
$499$	33.0488			1.47947			0.739734	−	0.672900i	$-0.234951\pi$
$499$	33.0488			1.47947			0.739734	+	0.672900i	$0.234951\pi$
$500$	−12.4865	−	18.5496i	−0.558413	−	0.829563i
$501$	20.2591			0.905108
$502$	25.0763	+	4.56713i	1.11921	+	0.203841i
$503$	−14.8800	−	2.35677i	−0.663468	−	0.105083i	−0.184387	−	0.982854i	$-0.559030\pi$
$503$	−14.8800	−	2.35677i	−0.663468	−	0.105083i	−0.479081	+	0.877771i	$0.659030\pi$
$504$	0.288460	−	4.16035i	0.0128490	−	0.185317i
$505$	9.60859	+	29.2303i	0.427577	+	1.30073i
$506$	50.6800	+	17.7698i	2.25300	+	0.789966i
$507$	−13.0096	+	13.0096i	−0.577779	+	0.577779i
$508$	4.62415	+	5.07194i	0.205163	+	0.225031i
$509$	−15.1212	−	4.91317i	−0.670234	−	0.217772i	−0.0459196	−	0.998945i	$-0.514622\pi$
$509$	−15.1212	−	4.91317i	−0.670234	−	0.217772i	−0.624315	+	0.781173i	$0.714622\pi$
$510$	0.726096	+	5.24973i	0.0321521	+	0.232462i
$511$	−14.3031	+	4.64736i	−0.632732	+	0.205587i
$512$	−22.5985	−	1.14433i	−0.998720	−	0.0505727i
$513$	−1.55336	−	3.04864i	−0.0685825	−	0.134601i
$514$	1.91735	−	1.32654i	0.0845706	−	0.0585113i
$515$	−2.18690	−	13.5072i	−0.0963663	−	0.595196i
$516$	−1.83054	−	6.66579i	−0.0805849	−	0.293445i
$517$	−4.28016	−	27.0239i	−0.188241	−	1.18851i
$518$	2.28635	+	1.23221i	0.100457	+	0.0541402i
$519$	6.18648	+	4.49474i	0.271556	+	0.197297i
$520$	−8.71178	−	34.3517i	−0.382037	−	1.50642i
$521$	−18.9526	+	13.7698i	−0.830327	+	0.603268i	−0.919652	−	0.392735i	$-0.871529\pi$
$521$	−18.9526	+	13.7698i	−0.830327	+	0.603268i	0.0893252	+	0.996003i	$0.471529\pi$
$522$	11.3710	−	1.53296i	0.497697	−	0.0670959i
$523$	18.9802	−	37.2508i	0.829947	−	1.62886i	0.0535947	−	0.998563i	$-0.482932\pi$
$523$	18.9802	−	37.2508i	0.829947	−	1.62886i	0.776352	−	0.630300i	$-0.217068\pi$
$524$	−12.3522	+	8.13110i	−0.539608	+	0.355209i
$525$	−2.22992	+	7.02685i	−0.0973217	+	0.306677i
$526$	−10.3539	−	34.5597i	−0.451451	−	1.50687i
$527$	−3.28536	−	1.67398i	−0.143113	−	0.0729196i
$528$	16.0948	+	10.1701i	0.700435	+	0.442598i
$529$	−23.8974	−	32.8920i	−1.03902	−	1.43009i
$530$	−0.270280	+	13.7595i	−0.0117402	+	0.597675i
$531$	−7.45712	+	10.2638i	−0.323612	+	0.445413i
$532$	9.88213	+	2.03645i	0.428445	+	0.0882914i
$533$	−30.9888	+	4.90814i	−1.34227	+	0.212595i
$534$	−0.0661673	+	2.86700i	−0.00286334	+	0.124067i
$535$	24.6225	+	12.4394i	1.06452	+	0.537804i
$536$	7.92581	−	19.6504i	0.342343	−	0.848766i
$537$	−14.8424	+	7.56258i	−0.640497	+	0.326349i
$538$	24.0293	+	25.1647i	1.03598	+	1.08493i
$539$	7.09824	+	21.8461i	0.305743	+	0.940980i
$540$	−2.19861	+	3.89437i	−0.0946132	+	0.167587i
$541$	7.36951	−	22.6810i	0.316840	−	0.975133i	−0.658150	−	0.752886i	$-0.728661\pi$
$541$	7.36951	−	22.6810i	0.316840	−	0.975133i	0.974990	−	0.222247i	$-0.0713391\pi$
$542$	−1.20338	+	0.578576i	−0.0516896	+	0.0248520i
$543$	12.5231	+	12.5231i	0.537419	+	0.537419i
$544$	−6.97733	−	6.41833i	−0.299150	−	0.275184i
$545$	0.107261	+	31.2323i	0.00459456	+	1.33784i
$546$	−7.08401	+	9.29166i	−0.303168	+	0.397646i
$547$	−4.47666	+	28.2645i	−0.191408	+	1.20850i	0.685582	+	0.727996i	$0.259548\pi$
$547$	−4.47666	+	28.2645i	−0.191408	+	1.20850i	−0.876990	+	0.480509i	$0.840452\pi$
$548$	−22.5266	+	2.50917i	−0.962289	+	0.107187i
$549$			6.97065i			0.297500i
$550$	−23.4096	−	24.1810i	−0.998190	−	1.03108i
$551$			27.7601i			1.18262i
$552$	−8.82972	−	20.7675i	−0.375818	−	0.883925i
$553$	−2.13675	+	13.4909i	−0.0908640	+	0.573693i
$554$	−12.9780	−	9.89452i	−0.551384	−	0.420378i
$555$	−1.64484	−	2.24765i	−0.0698194	−	0.0954074i
$556$	1.35103	−	29.2541i	0.0572964	−	1.24065i
$557$	−19.6252	−	19.6252i	−0.831547	−	0.831547i	0.156181	−	0.987728i	$-0.450082\pi$
$557$	−19.6252	−	19.6252i	−0.831547	−	0.831547i	−0.987728	+	0.156181i	$0.950082\pi$
$558$	−1.34824	−	2.80420i	−0.0570754	−	0.118711i
$559$	−5.98475	+	18.4192i	−0.253128	+	0.779048i
$560$	−4.92067	−	12.2354i	−0.207936	−	0.517039i
$561$	2.46497	+	7.58641i	0.104071	+	0.320298i
$562$	−5.24041	+	5.00398i	−0.221053	+	0.211080i
$563$	−24.2640	+	12.3631i	−1.02261	+	0.521044i	−0.883104	−	0.469177i	$-0.844551\pi$
$563$	−24.2640	+	12.3631i	−1.02261	+	0.521044i	−0.139503	+	0.990222i	$0.544551\pi$
$564$	−7.17959	+	8.97951i	−0.302315	+	0.378105i
$565$	6.85420	−	6.90144i	0.288358	−	0.290346i
$566$	−12.9793	−	0.299548i	−0.545559	−	0.0125909i
$567$	1.45628	−	0.230653i	0.0611582	−	0.00968651i
$568$	−35.4647	+	3.12379i	−1.48806	+	0.131071i
$569$	20.7368	−	28.5418i	0.869333	−	1.19653i	−0.109930	−	0.993939i	$-0.535063\pi$
$569$	20.7368	−	28.5418i	0.869333	−	1.19653i	0.979263	−	0.202594i	$-0.0649373\pi$
$570$	−8.62693	−	6.53049i	−0.361342	−	0.273532i
$571$	2.29350	+	3.15674i	0.0959802	+	0.132105i	0.854306	−	0.519770i	$-0.173982\pi$
$571$	2.29350	+	3.15674i	0.0959802	+	0.132105i	−0.758326	+	0.651876i	$0.773982\pi$
$572$	−21.9980	−	48.5938i	−0.919781	−	2.03181i
$573$	−8.57359	−	4.36846i	−0.358167	−	0.182495i
$574$	−11.1843	+	3.35074i	−0.466822	+	0.139857i
$575$	6.51106	+	39.3577i	0.271530	+	1.64133i
$576$	−1.39846	−	7.87682i	−0.0582691	−	0.328201i
$577$	−11.1988	+	21.9789i	−0.466213	+	0.914994i	0.531478	+	0.847072i	$0.321637\pi$
$577$	−11.1988	+	21.9789i	−0.466213	+	0.914994i	−0.997691	+	0.0679219i	$0.978363\pi$
$578$	2.68137	+	19.8896i	0.111530	+	0.827299i
$579$	−9.28323	+	6.74466i	−0.385798	+	0.280299i
$580$	30.2381	−	20.0541i	1.25557	−	0.832700i
$581$	7.43071	+	5.39873i	0.308278	+	0.223977i
$582$	2.28496	−	4.23972i	0.0947147	−	0.175742i
$583$	3.24039	+	20.4590i	0.134203	+	0.847326i
$584$	−24.4570	+	15.3025i	−1.01204	+	0.633220i
$585$	11.1444	−	5.72665i	0.460764	−	0.236768i
$586$	−23.7348	−	34.3057i	−0.980476	−	1.41715i
$587$	1.15344	+	2.26375i	0.0476076	+	0.0934351i	0.913585	−	0.406648i	$-0.133303\pi$
$587$	1.15344	+	2.26375i	0.0476076	+	0.0934351i	−0.865977	+	0.500084i	$0.833303\pi$
$588$	4.77403	−	8.38874i	0.196878	−	0.345946i
$589$	7.15949	−	2.32626i	0.295002	−	0.0958519i
$590$	−7.05303	+	39.4944i	−0.290369	+	1.62596i
$591$	2.07227	+	0.673322i	0.0852419	+	0.0276968i
$592$	4.82822	+	1.22965i	0.198439	+	0.0505385i
$593$	24.4019	−	24.4019i	1.00206	−	1.00206i	0.00206677	−	0.999998i	$-0.499342\pi$
$593$	24.4019	−	24.4019i	1.00206	−	1.00206i	0.999998	−	0.00206677i	$-0.000657873\pi$
$594$	−2.22721	+	6.35206i	−0.0913836	+	0.260628i
$595$	1.68938	−	5.26080i	0.0692580	−	0.215672i
$596$	5.11408	−	13.5740i	0.209481	−	0.556012i
$597$	9.57120	+	1.51593i	0.391723	+	0.0620429i
$598$	−11.3288	+	62.2021i	−0.463270	+	2.54363i
$599$	−10.8060			−0.441521			−0.220761	−	0.975328i	$-0.570854\pi$
$599$	−10.8060			−0.441521			−0.220761	+	0.975328i	$0.570854\pi$
$600$	−0.881276	+	14.1147i	−0.0359780	+	0.576228i
$601$	−18.5184			−0.755379			−0.377690	−	0.925932i	$-0.623281\pi$
$601$	−18.5184			−0.755379			−0.377690	+	0.925932i	$0.623281\pi$
$602$	−1.29135	+	7.09031i	−0.0526316	+	0.288979i
$603$	7.39906	+	1.17190i	0.301313	+	0.0477233i
$604$	−6.26866	+	16.6385i	−0.255068	+	0.677012i
$605$	−21.1358	−	15.2454i	−0.859293	−	0.619815i
$606$	6.43890	−	18.3639i	0.261563	−	0.745983i
$607$	−31.2527	+	31.2527i	−1.26851	+	1.26851i	−0.321651	+	0.946858i	$0.604238\pi$
$607$	−31.2527	+	31.2527i	−1.26851	+	1.26851i	−0.946858	+	0.321651i	$0.895762\pi$
$608$	19.3385	−	0.806984i	0.784279	−	0.0327275i
$609$	−11.3770	−	3.69662i	−0.461021	−	0.149795i
$610$	9.61972	+	19.8333i	0.389491	+	0.803028i
$611$	30.6344	−	9.95373i	1.23934	−	0.402685i
$612$	1.65786	−	2.91312i	0.0670149	−	0.117756i
$613$	−3.45059	−	6.77216i	−0.139368	−	0.273525i	0.810764	−	0.585373i	$-0.199052\pi$
$613$	−3.45059	−	6.77216i	−0.139368	−	0.273525i	−0.950132	+	0.311848i	$0.899052\pi$
$614$	1.22013	+	1.76355i	0.0492406	+	0.0711711i
$615$	12.3728	+	1.91613i	0.498921	+	0.0772659i
$616$	−10.5285	−	16.8271i	−0.424207	−	0.677984i
$617$	−5.40602	−	34.1323i	−0.217638	−	1.37411i	−0.818384	−	0.574672i	$-0.805130\pi$
$617$	−5.40602	−	34.1323i	−0.217638	−	1.37411i	0.600746	−	0.799440i	$-0.294870\pi$
$618$	−4.10566	+	7.61799i	−0.165154	+	0.306441i
$619$	−11.1832	−	8.12509i	−0.449492	−	0.326575i	0.339903	−	0.940460i	$-0.389606\pi$
$619$	−11.1832	−	8.12509i	−0.449492	−	0.326575i	−0.789395	+	0.613885i	$0.789606\pi$
$620$	−7.70596	−	6.11806i	−0.309479	−	0.245707i
$621$	6.45476	−	4.68966i	0.259020	−	0.188189i
$622$	−0.0163949	−	0.121612i	−0.000657375	−	0.00487621i
$623$	1.35738	−	2.66400i	0.0543822	−	0.106731i
$624$	−8.86147	+	20.5876i	−0.354743	+	0.824163i
$625$	7.39809	−	23.8803i	0.295923	−	0.955212i
$626$	30.0177	−	8.99313i	1.19975	−	0.359438i
$627$	−14.5106	−	7.39350i	−0.579496	−	0.295268i
$628$	3.65646	+	8.07716i	0.145908	+	0.322314i
$629$	1.22700	+	1.68882i	0.0489237	+	0.0673376i
$630$	3.82520	−	2.66599i	0.152400	−	0.106215i
$631$	−15.1133	+	20.8017i	−0.601652	+	0.828103i	−0.995858	−	0.0909189i	$-0.971020\pi$
$631$	−15.1133	+	20.8017i	−0.601652	+	0.828103i	0.394206	+	0.919022i	$0.371020\pi$
$632$	2.29905	+	26.1013i	0.0914513	+	1.03825i
$633$	−24.3889	+	3.86282i	−0.969372	+	0.153533i
$634$	−45.0959	−	1.04077i	−1.79099	−	0.0413341i
$635$	−1.17438	+	7.58320i	−0.0466038	+	0.300930i
$636$	5.43547	−	6.79813i	0.215530	−	0.269563i
$637$	−24.0949	+	12.2770i	−0.954675	+	0.486431i
$638$	39.4974	−	37.7154i	1.56372	−	1.49317i
$639$	−3.88966	−	11.9711i	−0.153872	−	0.473571i
$640$	−14.8492	−	20.4817i	−0.586968	−	0.809610i
$641$	−3.11325	+	9.58161i	−0.122966	+	0.378451i	−0.993525	−	0.113613i	$-0.963757\pi$
$641$	−3.11325	+	9.58161i	−0.122966	+	0.378451i	0.870559	+	0.492064i	$0.163757\pi$
$642$	−7.56005	−	15.7241i	−0.298371	−	0.620582i
$643$	−17.4447	−	17.4447i	−0.687951	−	0.687951i	0.273828	−	0.961779i	$-0.411710\pi$
$643$	−17.4447	−	17.4447i	−0.687951	−	0.687951i	−0.961779	+	0.273828i	$0.911710\pi$
$644$	−1.08541	+	23.5026i	−0.0427711	+	0.926132i
$645$	4.52119	−	6.26805i	0.178022	−	0.246804i
$646$	6.44897	+	4.91673i	0.253731	+	0.193446i
$647$	4.48496	−	28.3169i	0.176322	−	1.11325i	−0.727741	−	0.685852i	$-0.759430\pi$
$647$	4.48496	−	28.3169i	0.176322	−	1.11325i	0.904063	−	0.427400i	$-0.140570\pi$
$648$	2.60293	−	1.10669i	0.102253	−	0.0434748i
$649$			60.3852i			2.37033i
$650$	23.8058	−	31.6734i	0.933739	−	1.24233i
$651$			3.24397i			0.127141i
$652$	−7.91195	+	0.881290i	−0.309856	+	0.0345140i
$653$	−0.257017	+	1.62274i	−0.0100578	+	0.0635027i	−0.992207	−	0.124602i	$-0.960235\pi$
$653$	−0.257017	+	1.62274i	−0.0100578	+	0.0635027i	0.982149	+	0.188105i	$0.0602345\pi$
$654$	11.9762	−	15.7085i	0.468308	−	0.614251i
$655$	−15.7420	−	5.05517i	−0.615089	−	0.197522i
$656$	−19.2558	+	11.4386i	−0.751814	+	0.446601i
$657$	−7.21245	−	7.21245i	−0.281384	−	0.281384i
$658$	10.8027	−	5.19388i	0.421134	−	0.202478i
$659$	6.95495	−	21.4051i	0.270926	−	0.833826i	−0.719342	−	0.694656i	$-0.755557\pi$
$659$	6.95495	−	21.4051i	0.270926	−	0.833826i	0.990269	−	0.139170i	$-0.0444434\pi$
$660$	2.42905	+	21.1469i	0.0945505	+	0.823142i
$661$	12.2871	+	37.8159i	0.477914	+	1.47087i	0.841986	+	0.539499i	$0.181386\pi$
$661$	12.2871	+	37.8159i	0.477914	+	1.47087i	−0.364072	+	0.931371i	$0.618614\pi$
$662$	18.7738	+	19.6609i	0.729665	+	0.764141i
$663$	−8.36733	+	4.26337i	−0.324960	+	0.165575i
$664$	16.3403	+	6.59073i	0.634127	+	0.255770i
$665$	5.15583	+	10.0335i	0.199934	+	0.389084i
$666$	−0.0406433	+	1.76106i	−0.00157490	+	0.0682395i
$667$	−63.9350	+	10.1263i	−2.47557	+	0.392092i
$668$	−39.6843	−	8.17791i	−1.53543	−	0.316413i
$669$	11.6129	−	15.9838i	0.448980	−	0.617968i
$670$	22.6695	−	6.87658i	0.875799	−	0.265665i
$671$	19.5016	+	26.8416i	0.752851	+	1.03621i
$672$	−2.24444	+	8.03302i	−0.0865812	+	0.309880i
$673$	9.74354	+	4.96458i	0.375586	+	0.191371i	0.631585	−	0.775306i	$-0.282405\pi$
$673$	9.74354	+	4.96458i	0.375586	+	0.191371i	−0.255999	+	0.966677i	$0.582405\pi$
$674$	5.85549	+	19.5447i	0.225545	+	0.752835i
$675$	−4.93295	+	0.816074i	−0.189869	+	0.0314107i
$676$	30.7354	−	20.2323i	1.18213	−	0.778164i
$677$	20.7348	−	40.6944i	0.796904	−	1.56401i	−0.0285840	−	0.999591i	$-0.509100\pi$
$677$	20.7348	−	40.6944i	0.796904	−	1.56401i	0.825488	−	0.564420i	$-0.190900\pi$
$678$	−6.09659	+	0.821898i	−0.234138	+	0.0315648i
$679$	−4.06236	+	2.95147i	−0.155899	+	0.113267i
$680$	0.696836	−	10.5765i	0.0267224	−	0.405590i
$681$	0.133907	+	0.0972891i	0.00513132	+	0.00372812i
$682$	−13.0368	−	7.02609i	−0.499206	−	0.269043i
$683$	−3.21000	−	20.2671i	−0.122827	−	0.775500i	−0.969807	−	0.243875i	$-0.921581\pi$
$683$	−3.21000	−	20.2671i	−0.122827	−	0.775500i	0.846980	−	0.531626i	$-0.178419\pi$
$684$	1.81215	+	6.59884i	0.0692892	+	0.252313i
$685$	−17.9804	−	17.8573i	−0.686996	−	0.682294i
$686$	−20.2789	+	14.0302i	−0.774252	+	0.535676i
$687$	3.40358	+	6.67991i	0.129855	+	0.254854i
$688$	0.894969	+	13.7961i	0.0341204	+	0.525973i
$689$	−23.1925	+	7.53569i	−0.883563	+	0.287087i
$690$	11.8936	−	22.2511i	0.452782	−	0.847084i
$691$	19.2612	+	6.25835i	0.732731	+	0.238079i	0.651534	−	0.758619i	$-0.274126\pi$
$691$	19.2612	+	6.25835i	0.732731	+	0.238079i	0.0811970	+	0.996698i	$0.474126\pi$
$692$	−10.3039	−	11.3017i	−0.391697	−	0.429628i
$693$	4.96237	−	4.96237i	0.188505	−	0.188505i
$694$	4.64576	+	1.62893i	0.176351	+	0.0618335i
$695$	26.4225	−	19.3361i	1.00226	−	0.733460i
$696$	−22.8929	−	1.58729i	−0.867752	−	0.0601659i
$697$	−9.26836	−	1.46796i	−0.351064	−	0.0556031i
$698$	−1.47890	−	0.269351i	−0.0559772	−	0.0101951i
$699$	10.6764			0.403818
$700$	7.20456	−	12.8643i	0.272307	−	0.486226i
$701$	13.8933			0.524741			0.262370	−	0.964967i	$-0.415496\pi$
$701$	13.8933			0.524741			0.262370	+	0.964967i	$0.415496\pi$
$702$	−7.79620	−	1.41991i	−0.294248	−	0.0535912i
$703$	−4.20939	−	0.666701i	−0.158760	−	0.0251451i
$704$	−27.4218	−	26.4186i	−1.03350	−	0.995687i
$705$	−12.8538	+	0.0441439i	−0.484103	+	0.00166255i
$706$	−27.4635	−	9.62948i	−1.03360	−	0.362410i
$707$	−14.3463	+	14.3463i	−0.539548	+	0.539548i
$708$	18.7505	−	17.0950i	0.704686	−	0.642471i
$709$	15.5492	+	5.05225i	0.583964	+	0.189741i	0.586076	−	0.810256i	$-0.300672\pi$
$709$	15.5492	+	5.05225i	0.583964	+	0.189741i	−0.00211169	+	0.999998i	$0.500672\pi$
$710$	−27.5876	−	28.6932i	−1.03535	−	1.07684i
$711$	−8.81053	+	2.86271i	−0.330421	+	0.107360i
$712$	1.28692	−	5.58928i	0.0482294	−	0.209467i
$713$	7.96929	+	15.6406i	0.298452	+	0.585746i
$714$	−2.87380	+	1.98828i	−0.107549	+	0.0744094i
$715$	26.8921	−	53.2298i	1.00571	−	1.99068i
$716$	32.1266	−	8.82250i	1.20063	−	0.329712i
$717$	−3.47793	−	21.9588i	−0.129886	−	0.820065i
$718$	20.4860	+	11.0408i	0.764531	+	0.412038i
$719$	−6.10365	−	4.43456i	−0.227628	−	0.165381i	0.468126	−	0.883662i	$-0.344929\pi$
$719$	−6.10365	−	4.43456i	−0.227628	−	0.165381i	−0.695753	+	0.718281i	$0.744929\pi$
$720$	5.87875	−	6.74094i	0.219088	−	0.251220i
$721$	7.29931	−	5.30326i	0.271840	−	0.197504i
$722$	10.2212	−	1.37795i	0.380394	−	0.0512820i
$723$	9.25986	−	18.1735i	0.344378	−	0.675880i
$724$	−19.4756	−	29.5860i	−0.723807	−	1.09955i
$725$	38.6661	+	12.2704i	1.43602	+	0.455712i
$726$	4.73021	+	15.7887i	0.175554	+	0.585974i
$727$	−42.6795	−	21.7463i	−1.58289	−	0.806525i	−0.582913	−	0.812535i	$-0.698087\pi$
$727$	−42.6795	−	21.7463i	−1.58289	−	0.806525i	−0.999982	+	0.00600972i	$0.998087\pi$
$728$	17.6272	−	15.3413i	0.653307	−	0.568586i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	−30.4747	−	10.5679i	−1.12792	−	0.391135i
$731$	−3.40471	+	4.68618i	−0.125928	+	0.173325i
$732$	2.81382	−	13.6544i	0.104002	−	0.504681i
$733$	12.5781	−	1.99218i	0.464584	−	0.0735829i	0.0802457	−	0.996775i	$-0.474430\pi$
$733$	12.5781	−	1.99218i	0.464584	−	0.0735829i	0.384339	+	0.923192i	$0.374430\pi$
$734$	−0.620596	+	26.8901i	−0.0229066	+	0.992531i
$735$	10.6526	−	1.72473i	0.392928	−	0.0636177i
$736$	8.91285	+	44.2445i	0.328532	+	1.63087i
$737$	31.7699	−	16.1876i	1.17026	−	0.596276i
$738$	−5.46858	−	5.72696i	−0.201301	−	0.210812i
$739$	7.24911	+	22.3105i	0.266663	+	0.820704i	0.991306	+	0.131579i	$0.0420048\pi$
$739$	7.24911	+	22.3105i	0.266663	+	0.820704i	−0.724643	+	0.689125i	$0.757995\pi$
$740$	2.31467	+	5.06675i	0.0850890	+	0.186258i
$741$	5.92463	−	18.2341i	0.217647	−	0.669848i
$742$	−8.17844	+	3.93214i	−0.300240	+	0.144353i
$743$	31.2758	+	31.2758i	1.14740	+	1.14740i	0.987062	+	0.160337i	$0.0512581\pi$
$743$	31.2758	+	31.2758i	1.14740	+	1.14740i	0.160337	+	0.987062i	$0.448742\pi$
$744$	1.50902	+	6.03721i	0.0553233	+	0.221335i
$745$	15.4065	−	5.06444i	0.564450	−	0.185547i
$746$	−0.501939	+	0.658362i	−0.0183773	+	0.0241043i
$747$	−0.974493	+	6.15271i	−0.0356548	+	0.225116i
$748$	−1.76611	−	15.8556i	−0.0645753	−	0.579738i
$749$			18.1901i			0.664652i
$750$	−12.9093	+	9.12957i	−0.471382	+	0.333365i
$751$		−	25.1683i		−	0.918404i	−0.888332	−	0.459202i	$-0.848135\pi$
$751$		−	25.1683i		−	0.918404i	0.888332	−	0.459202i	$-0.151865\pi$
$752$	17.6884	−	14.6913i	0.645029	−	0.535735i
$753$	2.81947	−	17.8014i	0.102747	−	0.648721i
$754$	51.1285	+	38.9807i	1.86199	+	1.41959i
$755$	−18.8847	+	6.20781i	−0.687286	+	0.225925i
$756$	−2.94574	−	0.136042i	−0.107135	−	0.00494778i
$757$	19.3441	+	19.3441i	0.703072	+	0.703072i	0.965069	−	0.261997i	$-0.0843809\pi$
$757$	19.3441	+	19.3441i	0.703072	+	0.703072i	−0.261997	+	0.965069i	$0.584381\pi$
$758$	3.04711	+	6.33769i	0.110676	+	0.230195i
$759$	11.7350	−	36.1166i	0.425953	−	1.31095i
$760$	14.2626	+	16.2746i	0.517360	+	0.590342i
$761$	−8.59037	−	26.4384i	−0.311401	−	0.958392i	−0.977211	−	0.212271i	$-0.931914\pi$
$761$	−8.59037	−	26.4384i	−0.311401	−	0.958392i	0.665810	−	0.746121i	$-0.268086\pi$
$762$	3.51000	−	3.35164i	0.127154	−	0.121417i
$763$	−18.3497	+	9.34964i	−0.664304	+	0.338480i
$764$	15.0309	+	12.0180i	0.543798	+	0.434795i
$765$	3.69929	−	0.598940i	0.133748	−	0.0216547i
$766$	26.1851	+	0.604326i	0.946107	+	0.0218352i
$767$	−70.2144	+	11.1209i	−2.53530	+	0.401551i
$768$	−0.440254	+	15.9939i	−0.0158863	+	0.577132i
$769$	−13.5028	+	18.5850i	−0.486923	+	0.670192i	−0.979817	−	0.199897i	$-0.935939\pi$
$769$	−13.5028	+	18.5850i	−0.486923	+	0.670192i	0.492894	+	0.870090i	$0.335939\pi$
$770$	7.27102	−	20.9675i	0.262029	−	0.755616i
$771$	−0.969038	−	1.33377i	−0.0348991	−	0.0480344i
$772$	20.9070	−	9.46438i	0.752458	−	0.340631i
$773$	17.5103	+	8.92192i	0.629800	+	0.320899i	0.739592	−	0.673055i	$-0.235018\pi$
$773$	17.5103	+	8.92192i	0.629800	+	0.320899i	−0.109792

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.253401 + 1.39133i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.87158 - 0.705127i) q^{4} +(-0.698282 - 2.12424i) q^{5} +(-0.467933 + 1.33456i) q^{6} +(1.04258 - 1.04258i) q^{7} +(1.45532 - 2.42529i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.253401 + 1.39133i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.87158 - 0.705127i) q^{4} +(-0.698282 - 2.12424i) q^{5} +(-0.467933 + 1.33456i) q^{6} +(1.04258 - 1.04258i) q^{7} +(1.45532 - 2.42529i) q^{8} +(0.951057 + 0.309017i) q^{9} +(3.13246 - 0.433253i) q^{10} +(4.52673 - 1.47082i) q^{11} +(-1.73823 - 0.989225i) q^{12} +(2.54390 + 4.99269i) q^{13} +(1.18638 + 1.71477i) q^{14} +(-0.357381 - 2.20732i) q^{15} +(3.00559 + 2.63940i) q^{16} +(0.262171 + 1.65528i) q^{17} +(-0.670942 + 1.24492i) q^{18} +(-2.76811 - 2.01115i) q^{19} +(-0.190971 + 4.46806i) q^{20} +(1.19285 - 0.866653i) q^{21} +(0.899317 + 6.67086i) q^{22} +(3.62217 - 7.10891i) q^{23} +(1.81680 - 2.16777i) q^{24} +(-4.02480 + 2.96664i) q^{25} +(-7.59109 + 2.27425i) q^{26} +(0.891007 + 0.453990i) q^{27} +(-2.68643 + 1.21612i) q^{28} +(-4.76887 - 6.56378i) q^{29} +(3.16167 + 0.0621050i) q^{30} +(-1.29321 + 1.77995i) q^{31} +(-4.43388 + 3.51293i) q^{32} +(4.70108 - 0.744578i) q^{33} +(-2.36947 - 0.0546849i) q^{34} +(-2.94272 - 1.48668i) q^{35} +(-1.56208 - 1.24896i) q^{36} +(1.10983 - 0.565484i) q^{37} +(3.49960 - 3.34171i) q^{38} +(1.73155 + 5.32918i) q^{39} +(-6.16813 - 1.39791i) q^{40} +(-1.73027 + 5.32522i) q^{41} +(0.903528 + 1.87925i) q^{42} +(2.44396 + 2.44396i) q^{43} +(-9.50923 - 0.439160i) q^{44} +(-0.00767928 - 2.23605i) q^{45} +(8.97295 + 6.84103i) q^{46} +(0.899254 - 5.67766i) q^{47} +(2.55570 + 3.07708i) q^{48} +4.82603i q^{49} +(-3.10767 - 6.35156i) q^{50} +1.67591i q^{51} +(-1.24063 - 11.1380i) q^{52} +(-0.680800 + 4.29840i) q^{53} +(-0.857431 + 1.12464i) q^{54} +(-6.28532 - 8.58881i) q^{55} +(-1.01128 - 4.04587i) q^{56} +(-2.41941 - 2.41941i) q^{57} +(10.3408 - 4.97178i) q^{58} +(-3.92044 + 12.0659i) q^{59} +(-0.887578 + 4.38317i) q^{60} +(2.15405 + 6.62949i) q^{61} +(-2.14879 - 2.25032i) q^{62} +(1.31373 - 0.669381i) q^{63} +(-3.76408 - 7.05915i) q^{64} +(8.82932 - 8.89017i) q^{65} +(-0.155308 + 6.72942i) q^{66} +(7.39906 - 1.17190i) q^{67} +(0.676511 - 3.28285i) q^{68} +(4.68966 - 6.45476i) q^{69} +(2.81415 - 3.71756i) q^{70} +(-7.39857 - 10.1833i) q^{71} +(2.13355 - 1.85687i) q^{72} +(-9.08821 - 4.63068i) q^{73} +(0.505542 + 1.68742i) q^{74} +(-4.43934 + 2.30050i) q^{75} +(3.76261 + 5.71588i) q^{76} +(3.18604 - 6.25296i) q^{77} +(-7.85340 + 1.05874i) q^{78} +(-7.49468 + 5.44520i) q^{79} +(3.50796 - 8.22765i) q^{80} +(0.809017 + 0.587785i) q^{81} +(-6.97066 - 3.75678i) q^{82} +(0.974493 + 6.15271i) q^{83} +(-2.84360 + 0.780899i) q^{84} +(3.33315 - 1.71277i) q^{85} +(-4.01965 + 2.78105i) q^{86} +(-3.68335 - 7.22899i) q^{87} +(3.02066 - 13.1192i) q^{88} +(1.92856 - 0.626628i) q^{89} +(3.11303 + 0.555934i) q^{90} +(7.85754 + 2.55307i) q^{91} +(-11.7919 + 10.7508i) q^{92} +(-1.55574 + 1.55574i) q^{93} +(7.67161 + 2.68988i) q^{94} +(-2.33924 + 7.28448i) q^{95} +(-4.92884 + 2.77607i) q^{96} +(-3.36367 - 0.532753i) q^{97} +(-6.71459 - 1.22292i) q^{98} +4.75968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240q + 12q^{8} + O(q^{10}) \)	\( 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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