LMFDB - Embedded newform 300.2.w.a.67.18

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			67.18
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.18

$q$-expansion

$f(q)$	$=$	$q+(0.300359 + 1.38195i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.81957 + 0.830163i) q^{4} +(2.22495 - 0.222669i) q^{5} +(-0.0804769 - 1.41192i) q^{6} +(3.70249 - 3.70249i) q^{7} +(-1.69377 - 2.26520i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(0.300359 + 1.38195i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.81957 + 0.830163i) q^{4} +(2.22495 - 0.222669i) q^{5} +(-0.0804769 - 1.41192i) q^{6} +(3.70249 - 3.70249i) q^{7} +(-1.69377 - 2.26520i) q^{8} +(0.951057 + 0.309017i) q^{9} +(0.976003 + 3.00789i) q^{10} +(-0.352091 + 0.114401i) q^{11} +(1.92703 - 0.535299i) q^{12} +(2.36428 + 4.64017i) q^{13} +(6.22874 + 4.00458i) q^{14} +(-2.23239 - 0.128132i) q^{15} +(2.62166 - 3.02108i) q^{16} +(-0.155364 - 0.980930i) q^{17} +(-0.141387 + 1.40713i) q^{18} +(-2.30977 - 1.67815i) q^{19} +(-3.86360 + 2.25224i) q^{20} +(-4.23611 + 3.07771i) q^{21} +(-0.263851 - 0.452211i) q^{22} +(-3.21049 + 6.30095i) q^{23} +(1.31856 + 2.50228i) q^{24} +(4.90084 - 0.990856i) q^{25} +(-5.70234 + 4.66104i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-3.66327 + 9.81061i) q^{28} +(0.959703 + 1.32092i) q^{29} +(-0.493449 - 3.12354i) q^{30} +(3.91704 - 5.39135i) q^{31} +(4.96242 + 2.71559i) q^{32} +(0.365653 - 0.0579137i) q^{33} +(1.30893 - 0.509337i) q^{34} +(7.41344 - 9.06230i) q^{35} +(-1.98705 + 0.227254i) q^{36} +(-3.78075 + 1.92639i) q^{37} +(1.62535 - 3.69603i) q^{38} +(-1.60929 - 4.95290i) q^{39} +(-4.27295 - 4.66283i) q^{40} +(0.959013 - 2.95154i) q^{41} +(-5.52560 - 4.92967i) q^{42} +(0.302937 + 0.302937i) q^{43} +(0.545682 - 0.500454i) q^{44} +(2.18487 + 0.475778i) q^{45} +(-9.67190 - 2.54419i) q^{46} +(-0.817946 + 5.16431i) q^{47} +(-3.06198 + 2.57376i) q^{48} -20.4169i q^{49} +(2.84133 + 6.47510i) q^{50} +0.993157i q^{51} +(-8.15407 - 6.48036i) q^{52} +(-0.685412 + 4.32752i) q^{53} +(0.359770 - 1.36769i) q^{54} +(-0.757913 + 0.332938i) q^{55} +(-14.6581 - 2.11574i) q^{56} +(2.01881 + 2.01881i) q^{57} +(-1.53719 + 1.72301i) q^{58} +(-1.32518 + 4.07849i) q^{59} +(4.16836 - 1.62011i) q^{60} +(-2.66600 - 8.20510i) q^{61} +(8.62709 + 3.79382i) q^{62} +(4.66541 - 2.37715i) q^{63} +(-2.26230 + 7.67346i) q^{64} +(6.29364 + 9.79771i) q^{65} +(0.189861 + 0.487919i) q^{66} +(-4.13082 + 0.654258i) q^{67} +(1.09703 + 1.65589i) q^{68} +(4.15665 - 5.72114i) q^{69} +(14.7503 + 7.52306i) q^{70} +(-3.73936 - 5.14679i) q^{71} +(-0.910882 - 2.67774i) q^{72} +(-12.0226 - 6.12582i) q^{73} +(-3.79776 - 4.64620i) q^{74} +(-4.99550 + 0.211997i) q^{75} +(5.59592 + 1.13602i) q^{76} +(-0.880045 + 1.72719i) q^{77} +(6.36129 - 3.71161i) q^{78} +(-7.17475 + 5.21276i) q^{79} +(5.16037 - 7.30552i) q^{80} +(0.809017 + 0.587785i) q^{81} +(4.36692 + 0.438785i) q^{82} +(1.07499 + 6.78724i) q^{83} +(5.15288 - 9.11676i) q^{84} +(-0.564100 - 2.14793i) q^{85} +(-0.327653 + 0.509633i) q^{86} +(-0.741250 - 1.45479i) q^{87} +(0.855503 + 0.603789i) q^{88} +(-12.1162 + 3.93680i) q^{89} +(-0.00125607 + 3.16228i) q^{90} +(25.9339 + 8.42645i) q^{91} +(0.610899 - 14.1302i) q^{92} +(-4.71221 + 4.71221i) q^{93} +(-7.38249 + 0.420788i) q^{94} +(-5.51280 - 3.21948i) q^{95} +(-4.47651 - 3.45845i) q^{96} +(10.9115 + 1.72821i) q^{97} +(28.2151 - 6.13241i) q^{98} -0.370211 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 $

$2$	0.300359	+	1.38195i	0.212386	+	0.977186i
$2$	0.300359	+	1.38195i	0.212386	+	0.977186i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$4$	−1.81957	+	0.830163i	−0.909784	+	0.415081i
$5$	2.22495	−	0.222669i	0.995030	−	0.0995806i
$5$	2.22495	−	0.222669i	0.995030	−	0.0995806i
$6$	−0.0804769	−	1.41192i	−0.0328546	−	0.576415i
$7$	3.70249	−	3.70249i	1.39941	−	1.39941i	0.597664	−	0.801747i	$-0.296096\pi$
$7$	3.70249	−	3.70249i	1.39941	−	1.39941i	0.801747	−	0.597664i	$-0.203904\pi$
$8$	−1.69377	−	2.26520i	−0.598837	−	0.800871i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	0.976003	+	3.00789i	0.308639	+	0.951179i
$11$	−0.352091	+	0.114401i	−0.106160	+	0.0344933i	−0.361615	−	0.932327i	$-0.617775\pi$
$11$	−0.352091	+	0.114401i	−0.106160	+	0.0344933i	0.255456	+	0.966821i	$0.417775\pi$
$12$	1.92703	−	0.535299i	0.556286	−	0.154528i
$13$	2.36428	+	4.64017i	0.655734	+	1.28695i	0.944172	+	0.329453i	$0.106864\pi$
$13$	2.36428	+	4.64017i	0.655734	+	1.28695i	−0.288438	+	0.957499i	$0.593136\pi$
$14$	6.22874	+	4.00458i	1.66470	+	1.07027i
$15$	−2.23239	−	0.128132i	−0.576402	−	0.0330835i
$16$	2.62166	−	3.02108i	0.655415	−	0.755269i
$17$	−0.155364	−	0.980930i	−0.0376813	−	0.237910i	0.961658	−	0.274251i	$-0.0884299\pi$
$17$	−0.155364	−	0.980930i	−0.0376813	−	0.237910i	−0.999339	+	0.0363406i	$0.988430\pi$
$18$	−0.141387	+	1.40713i	−0.0333253	+	0.331663i
$19$	−2.30977	−	1.67815i	−0.529897	−	0.384993i	0.290422	−	0.956899i	$-0.406204\pi$
$19$	−2.30977	−	1.67815i	−0.529897	−	0.384993i	−0.820319	+	0.571906i	$0.806204\pi$
$20$	−3.86360	+	2.25224i	−0.863928	+	0.503615i
$21$	−4.23611	+	3.07771i	−0.924394	+	0.671612i
$22$	−0.263851	−	0.452211i	−0.0562532	−	0.0964117i
$23$	−3.21049	+	6.30095i	−0.669434	+	1.31384i	0.267237	+	0.963631i	$0.413889\pi$
$23$	−3.21049	+	6.30095i	−0.669434	+	1.31384i	−0.936672	+	0.350208i	$0.886111\pi$
$24$	1.31856	+	2.50228i	0.269150	+	0.510776i
$25$	4.90084	−	0.990856i	0.980167	−	0.198171i
$26$	−5.70234	+	4.66104i	−1.11832	+	0.914105i
$27$	−0.891007	−	0.453990i	−0.171474	−	0.0873705i
$28$	−3.66327	+	9.81061i	−0.692292	+	1.85403i
$29$	0.959703	+	1.32092i	0.178212	+	0.245288i	0.888773	−	0.458348i	$-0.151559\pi$
$29$	0.959703	+	1.32092i	0.178212	+	0.245288i	−0.710561	+	0.703636i	$0.751559\pi$
$30$	−0.493449	−	3.12354i	−0.0900910	−	0.570278i
$31$	3.91704	−	5.39135i	0.703522	−	0.968315i	−0.296390	−	0.955067i	$-0.595783\pi$
$31$	3.91704	−	5.39135i	0.703522	−	0.968315i	0.999912	−	0.0132480i	$-0.00421711\pi$
$32$	4.96242	+	2.71559i	0.877239	+	0.480053i
$33$	0.365653	−	0.0579137i	0.0636520	−	0.0100815i
$34$	1.30893	−	0.509337i	0.224480	−	0.0873505i
$35$	7.41344	−	9.06230i	1.25310	−	1.53181i
$36$	−1.98705	+	0.227254i	−0.331174	+	0.0378757i
$37$	−3.78075	+	1.92639i	−0.621552	+	0.316697i	−0.736256	−	0.676703i	$-0.763408\pi$
$37$	−3.78075	+	1.92639i	−0.621552	+	0.316697i	0.114704	+	0.993400i	$0.463408\pi$
$38$	1.62535	−	3.69603i	0.263667	−	0.599575i
$39$	−1.60929	−	4.95290i	−0.257693	−	0.793098i
$40$	−4.27295	−	4.66283i	−0.675612	−	0.737257i
$41$	0.959013	−	2.95154i	0.149773	−	0.460953i	−0.847821	−	0.530282i	$-0.822086\pi$
$41$	0.959013	−	2.95154i	0.149773	−	0.460953i	0.997594	+	0.0693295i	$0.0220860\pi$
$42$	−5.52560	−	4.92967i	−0.852618	−	0.760664i
$43$	0.302937	+	0.302937i	0.0461974	+	0.0461974i	0.729828	−	0.683631i	$-0.239600\pi$
$43$	0.302937	+	0.302937i	0.0461974	+	0.0461974i	−0.683631	+	0.729828i	$0.739600\pi$
$44$	0.545682	−	0.500454i	0.0822647	−	0.0754463i
$45$	2.18487	+	0.475778i	0.325700	+	0.0709248i
$46$	−9.67190	−	2.54419i	−1.42604	−	0.375121i
$47$	−0.817946	+	5.16431i	−0.119310	+	0.753292i	0.853398	+	0.521259i	$0.174538\pi$
$47$	−0.817946	+	5.16431i	−0.119310	+	0.753292i	−0.972708	+	0.232032i	$0.925462\pi$
$48$	−3.06198	+	2.57376i	−0.441959	+	0.371491i
$49$		−	20.4169i		−	2.91670i
$50$	2.84133	+	6.47510i	0.401824	+	0.915717i
$51$			0.993157i			0.139070i
$52$	−8.15407	−	6.48036i	−1.13077	−	0.898665i
$53$	−0.685412	+	4.32752i	−0.0941485	+	0.594431i	0.894834	+	0.446399i	$0.147294\pi$
$53$	−0.685412	+	4.32752i	−0.0941485	+	0.594431i	−0.988983	+	0.148032i	$0.952706\pi$
$54$	0.359770	−	1.36769i	0.0489585	−	0.186119i
$55$	−0.757913	+	0.332938i	−0.102197	+	0.0448933i
$56$	−14.6581	−	2.11574i	−1.95877	−	0.282728i
$57$	2.01881	+	2.01881i	0.267398	+	0.267398i
$58$	−1.53719	+	1.72301i	−0.201842	+	0.226242i
$59$	−1.32518	+	4.07849i	−0.172524	+	0.530974i	−0.999512	−	0.0312458i	$-0.990053\pi$
$59$	−1.32518	+	4.07849i	−0.172524	+	0.530974i	0.826988	+	0.562220i	$0.190053\pi$
$60$	4.16836	−	1.62011i	0.538133	−	0.209155i
$61$	−2.66600	−	8.20510i	−0.341346	−	1.05056i	−0.963511	−	0.267669i	$-0.913747\pi$
$61$	−2.66600	−	8.20510i	−0.341346	−	1.05056i	0.622165	−	0.782886i	$-0.286253\pi$
$62$	8.62709	+	3.79382i	1.09564	+	0.481815i
$63$	4.66541	−	2.37715i	0.587787	−	0.299492i
$64$	−2.26230	+	7.67346i	−0.282788	+	0.959183i
$65$	6.29364	+	9.79771i	0.780630	+	1.21526i
$66$	0.189861	+	0.487919i	0.0233703	+	0.0600586i
$67$	−4.13082	+	0.654258i	−0.504660	+	0.0799304i	−0.403573	−	0.914947i	$-0.632232\pi$
$67$	−4.13082	+	0.654258i	−0.504660	+	0.0799304i	−0.101087	+	0.994878i	$0.532232\pi$
$68$	1.09703	+	1.65589i	0.133034	+	0.200806i
$69$	4.15665	−	5.72114i	0.500402	−	0.688745i
$70$	14.7503	+	7.52306i	1.76300	+	0.899177i
$71$	−3.73936	−	5.14679i	−0.443780	−	0.610811i	0.527267	−	0.849700i	$-0.323217\pi$
$71$	−3.73936	−	5.14679i	−0.443780	−	0.610811i	−0.971047	+	0.238889i	$0.923217\pi$
$72$	−0.910882	−	2.67774i	−0.107348	−	0.315575i
$73$	−12.0226	−	6.12582i	−1.40714	−	0.716973i	−0.425011	−	0.905188i	$-0.639730\pi$
$73$	−12.0226	−	6.12582i	−1.40714	−	0.716973i	−0.982128	+	0.188215i	$0.939730\pi$
$74$	−3.79776	−	4.64620i	−0.441481	−	0.540110i
$75$	−4.99550	+	0.211997i	−0.576831	+	0.0244793i
$76$	5.59592	+	1.13602i	0.641896	+	0.130310i
$77$	−0.880045	+	1.72719i	−0.100290	+	0.196831i
$78$	6.36129	−	3.71161i	0.720274	−	0.420257i
$79$	−7.17475	+	5.21276i	−0.807222	+	0.586481i	−0.913024	−	0.407906i	$-0.866259\pi$
$79$	−7.17475	+	5.21276i	−0.807222	+	0.586481i	0.105802	+	0.994387i	$0.466259\pi$
$80$	5.16037	−	7.30552i	0.576947	−	0.816782i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	4.36692	+	0.438785i	0.482246	+	0.0484557i
$83$	1.07499	+	6.78724i	0.117996	+	0.744997i	0.973751	+	0.227616i	$0.0730930\pi$
$83$	1.07499	+	6.78724i	0.117996	+	0.744997i	−0.855755	+	0.517381i	$0.826907\pi$
$84$	5.15288	−	9.11676i	0.562226	−	0.994721i
$85$	−0.564100	−	2.14793i	−0.0611853	−	0.232976i
$86$	−0.327653	+	0.509633i	−0.0353318	+	0.0549552i
$87$	−0.741250	−	1.45479i	−0.0794704	−	0.155969i
$88$	0.855503	+	0.603789i	0.0911970	+	0.0643642i
$89$	−12.1162	+	3.93680i	−1.28432	+	0.417300i	−0.870099	−	0.492877i	$-0.835945\pi$
$89$	−12.1162	+	3.93680i	−1.28432	+	0.417300i	−0.414219	+	0.910177i	$0.635945\pi$
$90$	−0.00125607	+	3.16228i	−0.000132401	+	0.333333i
$91$	25.9339	+	8.42645i	2.71862	+	0.883332i
$92$	0.610899	−	14.1302i	0.0636907	−	1.47318i
$93$	−4.71221	+	4.71221i	−0.488634	+	0.488634i
$94$	−7.38249	+	0.420788i	−0.761446	+	0.0434010i
$95$	−5.51280	−	3.21948i	−0.565601	−	0.330312i
$96$	−4.47651	−	3.45845i	−0.456882	−	0.352977i
$97$	10.9115	+	1.72821i	1.10789	+	0.175473i	0.683461	−	0.729987i	$-0.260474\pi$
$97$	10.9115	+	1.72821i	1.10789	+	0.175473i	0.424431	+	0.905460i	$0.360474\pi$
$98$	28.2151	−	6.13241i	2.85016	−	0.619467i
$99$	−0.370211			−0.0372076
$100$	−8.09484	+	5.87142i	−0.809484	+	0.587142i
$101$	−2.66285			−0.264964			−0.132482	−	0.991185i	$-0.542295\pi$
$101$	−2.66285			−0.264964			−0.132482	+	0.991185i	$0.542295\pi$
$102$	−1.37249	+	0.298304i	−0.135897	+	0.0295365i
$103$	−3.88658	−	0.615574i	−0.382956	−	0.0606543i	−0.0380114	−	0.999277i	$-0.512102\pi$
$103$	−3.88658	−	0.615574i	−0.382956	−	0.0606543i	−0.344945	+	0.938623i	$0.612102\pi$
$104$	6.50638	−	13.2150i	0.638003	−	1.29583i
$105$	−8.73983	+	7.79101i	−0.852920	+	0.760325i
$106$	−6.18628	+	0.352607i	−0.600865	+	0.0342482i
$107$	−0.239138	+	0.239138i	−0.0231184	+	0.0231184i	−0.718571	−	0.695453i	$-0.755204\pi$
$107$	−0.239138	+	0.239138i	−0.0231184	+	0.0231184i	0.695453	+	0.718571i	$0.255204\pi$
$108$	1.99813	+	0.0863862i	0.192270	+	0.00831252i
$109$	11.4281	+	3.71322i	1.09462	+	0.355662i	0.800028	−	0.599962i	$-0.204818\pi$
$109$	11.4281	+	3.71322i	1.09462	+	0.355662i	0.294588	+	0.955624i	$0.404818\pi$
$110$	−0.687749	−	0.947397i	−0.0655743	−	0.0903307i
$111$	4.03556	−	1.31123i	0.383038	−	0.124457i
$112$	−1.47884	−	20.8922i	−0.139737	−	1.97413i
$113$	−6.18517	−	12.1391i	−0.581851	−	1.14195i	−0.974944	−	0.222449i	$-0.928595\pi$
$113$	−6.18517	−	12.1391i	−0.581851	−	1.14195i	0.393093	−	0.919499i	$-0.371405\pi$
$114$	−2.18353	+	3.39627i	−0.204506	+	0.318089i
$115$	−5.74018	+	14.7342i	−0.535274	+	1.37397i
$116$	−2.84282	−	1.60679i	−0.263949	−	0.149187i
$117$	0.814677	+	5.14367i	0.0753169	+	0.475532i
$118$	−6.03430	−	0.606321i	−0.555502	−	0.0558164i
$119$	−4.20712	−	3.05665i	−0.385666	−	0.280203i
$120$	3.49091	+	5.27385i	0.318675	+	0.481435i
$121$	−8.78831	+	6.38508i	−0.798937	+	0.580462i
$122$	10.5383	−	6.14875i	0.954091	−	0.556682i
$123$	−1.40893	+	2.76518i	−0.127039	+	0.249328i
$124$	−2.65163	+	13.0617i	−0.238124	+	1.17298i
$125$	10.6835	−	3.29587i	0.955562	−	0.294792i
$126$	4.68640	+	5.73337i	0.417497	+	0.510769i
$127$	11.7063	+	5.96467i	1.03877	+	0.529279i	0.888266	−	0.459330i	$-0.151911\pi$
$127$	11.7063	+	5.96467i	1.03877	+	0.529279i	0.150503	+	0.988610i	$0.451911\pi$
$128$	−11.2838	−	0.821591i	−0.997360	−	0.0726191i
$129$	−0.251817	−	0.346597i	−0.0221713	−	0.0305161i
$130$	−11.6496	+	11.6403i	−1.02174	+	1.02092i
$131$	−9.63540	+	13.2620i	−0.841849	+	1.15871i	0.143751	+	0.989614i	$0.454083\pi$
$131$	−9.63540	+	13.2620i	−0.841849	+	1.15871i	−0.985600	+	0.169092i	$0.945917\pi$
$132$	−0.617252	+	0.408929i	−0.0537249	+	0.0355927i
$133$	−14.7652	+	2.33858i	−1.28031	+	0.202781i
$134$	−2.14488	−	5.51208i	−0.185290	−	0.476171i
$135$	−2.08354	−	0.811708i	−0.179322	−	0.0698607i
$136$	−1.95886	+	2.01340i	−0.167971	+	0.172647i
$137$	−9.20904	+	4.69224i	−0.786782	+	0.400885i	−0.800736	−	0.599017i	$-0.795558\pi$
$137$	−9.20904	+	4.69224i	−0.786782	+	0.400885i	0.0139543	+	0.999903i	$0.495558\pi$
$138$	9.15482	+	4.02589i	0.779310	+	0.342706i
$139$	0.0731045	+	0.224993i	0.00620065	+	0.0190836i	0.954109	−	0.299460i	$-0.0968064\pi$
$139$	0.0731045	+	0.224993i	0.00620065	+	0.0190836i	−0.947908	+	0.318543i	$0.896806\pi$
$140$	−5.96608	+	22.6438i	−0.504226	+	1.91375i
$141$	1.61575	−	4.97277i	0.136071	−	0.418783i
$142$	5.98945	−	6.71349i	0.502623	−	0.563384i
$143$	−1.36329	−	1.36329i	−0.114004	−	0.114004i
$144$	3.42691	−	2.06308i	0.285576	−	0.171923i
$145$	2.42942	+	2.72528i	0.201752	+	0.226323i
$146$	4.85447	−	18.4546i	0.401759	−	1.52731i
$147$	−3.19391	+	20.1655i	−0.263429	+	1.66323i
$148$	5.28012	−	6.64384i	0.434023	−	0.546120i
$149$		−	18.9045i		−	1.54871i	−0.632748	−	0.774357i	$-0.718073\pi$
$149$		−	18.9045i		−	1.54871i	0.632748	−	0.774357i	$-0.281927\pi$
$150$	−1.79342	−	6.83986i	−0.146432	−	0.558472i
$151$		−	7.54220i		−	0.613775i	−0.951746	−	0.306888i	$-0.900712\pi$
$151$		−	7.54220i		−	0.613775i	0.951746	−	0.306888i	$-0.0992876\pi$
$152$	0.110870	+	8.07449i	0.00899272	+	0.654928i
$153$	0.155364	−	0.980930i	0.0125604	−	0.0793035i
$154$	−2.65121	−	0.697401i	−0.213641	−	0.0561982i
$155$	7.51476	−	12.8677i	0.603600	−	1.03356i
$156$	7.03993	+	7.67616i	0.563646	+	0.614585i
$157$	5.54998	+	5.54998i	0.442936	+	0.442936i	0.892998	−	0.450061i	$-0.148598\pi$
$157$	5.54998	+	5.54998i	0.442936	+	0.442936i	−0.450061	+	0.892998i	$0.648598\pi$
$158$	−9.35877	−	8.34944i	−0.744544	−	0.664246i
$159$	1.35395	−	4.16702i	0.107375	−	0.330466i
$160$	11.6458	+	4.93709i	0.920683	+	0.390311i
$161$	11.4424	+	35.2161i	0.901787	+	2.77541i
$162$	−0.569294	+	1.29457i	−0.0447279	+	0.101711i
$163$	−8.50184	+	4.33190i	−0.665915	+	0.339301i	−0.754059	−	0.656807i	$-0.771907\pi$
$163$	−8.50184	+	4.33190i	−0.665915	+	0.339301i	0.0881433	+	0.996108i	$0.471907\pi$
$164$	0.705268	+	6.16666i	0.0550722	+	0.481535i
$165$	0.800665	−	0.210275i	0.0623317	−	0.0163699i
$166$	−9.05674	+	3.52420i	−0.702939	+	0.273531i
$167$	13.2086	−	2.09204i	1.02211	−	0.161887i	0.377191	−	0.926136i	$-0.376890\pi$
$167$	13.2086	−	2.09204i	1.02211	−	0.161887i	0.644921	+	0.764249i	$0.276890\pi$
$168$	14.1466	+	4.38272i	1.09144	+	0.338134i
$169$	−8.30012	+	11.4241i	−0.638471	+	0.878780i
$170$	2.79890	−	1.42471i	0.214665	−	0.109270i
$171$	−1.67815	−	2.30977i	−0.128331	−	0.176632i
$172$	−0.802701	−	0.299727i	−0.0612054	−	0.0228540i
$173$	2.31220	+	1.17813i	0.175794	+	0.0895713i	0.539673	−	0.841875i	$-0.318548\pi$
$173$	2.31220	+	1.17813i	0.175794	+	0.0895713i	−0.363879	+	0.931446i	$0.618548\pi$
$174$	1.78780	−	1.46133i	0.135533	−	0.110783i
$175$	14.4767	−	21.8139i	1.09433	−	1.64898i
$176$	−0.577448	+	1.36362i	−0.0435268	+	0.102786i
$177$	1.94688	−	3.82097i	0.146337	−	0.287202i
$178$	−9.07969	−	15.5616i	−0.680551	−	1.16639i
$179$	−2.40147	+	1.74477i	−0.179494	+	0.130410i	−0.673904	−	0.738819i	$-0.735384\pi$
$179$	−2.40147	+	1.74477i	−0.179494	+	0.130410i	0.494410	+	0.869229i	$0.335384\pi$
$180$	−4.37048	+	0.948084i	−0.325757	+	0.0706660i
$181$	10.4496	+	7.59211i	0.776716	+	0.564317i	0.903992	−	0.427550i	$-0.140623\pi$
$181$	10.4496	+	7.59211i	0.776716	+	0.564317i	−0.127276	+	0.991867i	$0.540623\pi$
$182$	−3.85542	+	38.3704i	−0.285783	+	2.84420i
$183$	1.34962	+	8.52114i	0.0997664	+	0.629900i
$184$	19.7108	−	3.39992i	1.45310	−	0.250645i
$185$	−7.98305	+	5.12799i	−0.586926	+	0.377017i
$186$	−7.92740	−	5.09668i	−0.581265	−	0.373707i
$187$	0.166922	+	0.327603i	0.0122065	+	0.0239567i
$188$	−2.79891	−	10.0758i	−0.204131	−	0.734856i
$189$	−4.97984	+	1.61805i	−0.362230	+	0.117696i
$190$	2.79334	−	8.58541i	0.202650	−	0.622851i
$191$	−15.1573	−	4.92491i	−1.09675	−	0.356354i	−0.295896	−	0.955220i	$-0.595618\pi$
$191$	−15.1573	−	4.92491i	−1.09675	−	0.356354i	−0.800849	+	0.598866i	$0.795618\pi$
$192$	3.43484	−	7.22508i	0.247888	−	0.521426i
$193$	6.71231	−	6.71231i	0.483163	−	0.483163i	−0.422977	−	0.906140i	$-0.639015\pi$
$193$	6.71231	−	6.71231i	0.483163	−	0.483163i	0.906140	+	0.422977i	$0.139015\pi$
$194$	0.889067	+	15.5982i	0.0638313	+	1.11988i
$195$	−4.68346	−	10.6616i	−0.335390	−	0.763495i
$196$	16.9494	+	37.1500i	1.21067	+	2.65357i
$197$	−20.1134	−	3.18565i	−1.43302	−	0.226968i	−0.608840	−	0.793293i	$-0.708365\pi$
$197$	−20.1134	−	3.18565i	−1.43302	−	0.226968i	−0.824182	+	0.566325i	$0.808365\pi$
$198$	−0.111196	−	0.511612i	−0.00790237	−	0.0363587i
$199$	−4.63909			−0.328856			−0.164428	−	0.986389i	$-0.552578\pi$
$199$	−4.63909			−0.328856			−0.164428	+	0.986389i	$0.552578\pi$
$200$	−10.5454	−	9.42312i	−0.745670	−	0.666315i
$201$	4.18231			0.294998
$202$	−0.799813	−	3.67993i	−0.0562747	−	0.258919i
$203$	8.44398	+	1.33739i	0.592651	+	0.0938667i
$204$	−0.824482	−	1.80712i	−0.0577253	−	0.126524i
$205$	1.47654	−	6.78058i	0.103126	−	0.473576i
$206$	−0.316679	−	5.55595i	−0.0220641	−	0.387101i
$207$	−5.00046	+	5.00046i	−0.347556	+	0.347556i
$208$	20.2167	+	5.02226i	1.40177	+	0.348231i
$209$	1.00523	+	0.326620i	0.0695333	+	0.0225928i
$210$	−13.3919	−	9.73790i	−0.924127	−	0.671979i
$211$	0.267929	−	0.0870554i	0.0184450	−	0.00599314i	−0.299780	−	0.954008i	$-0.596913\pi$
$211$	0.267929	−	0.0870554i	0.0184450	−	0.00599314i	0.318225	+	0.948015i	$0.396913\pi$
$212$	−2.34539	−	8.44322i	−0.161082	−	0.579883i
$213$	2.88819	+	5.66838i	0.197895	+	0.388391i
$214$	−0.402304	−	0.258650i	−0.0275010	−	0.0176809i
$215$	0.741475	+	0.606566i	0.0505682	+	0.0413674i
$216$	0.480777	+	2.78727i	0.0327127	+	0.189649i
$217$	−5.45860	−	34.4643i	−0.370554	−	2.33959i
$218$	−1.69894	+	16.9084i	−0.115067	+	1.14518i
$219$	10.9163	+	7.93115i	0.737654	+	0.535937i
$220$	1.10268	−	1.23499i	0.0743428	−	0.0832633i
$221$	4.18436	−	3.04011i	0.281470	−	0.204500i
$222$	3.02418	+	5.18310i	0.202969	+	0.347867i
$223$	−3.69002	+	7.24207i	−0.247102	+	0.484965i	−0.980928	−	0.194373i	$-0.937733\pi$
$223$	−3.69002	+	7.24207i	−0.247102	+	0.484965i	0.733826	+	0.679338i	$0.237733\pi$
$224$	28.4278	−	8.31885i	1.89941	−	0.555826i
$225$	4.96716	+	0.572082i	0.331144	+	0.0381388i
$226$	14.9178	−	12.1937i	0.992318	−	0.811111i
$227$	21.3646	+	10.8858i	1.41802	+	0.722517i	0.983964	−	0.178369i	$-0.0570822\pi$
$227$	21.3646	+	10.8858i	1.41802	+	0.722517i	0.434055	+	0.900886i	$0.357082\pi$
$228$	−5.34931	−	1.99742i	−0.354267	−	0.132283i
$229$	−0.207489	−	0.285584i	−0.0137113	−	0.0188719i	0.802106	−	0.597181i	$-0.203713\pi$
$229$	−0.207489	−	0.285584i	−0.0137113	−	0.0188719i	−0.815818	+	0.578309i	$0.803713\pi$
$230$	−22.0860	−	3.50708i	−1.45631	−	0.231250i
$231$	1.13940	−	1.56825i	0.0749671	−	0.103183i
$232$	1.36663	−	4.41125i	0.0897240	−	0.289613i
$233$	22.1577	−	3.50943i	1.45160	−	0.229911i	0.619700	−	0.784839i	$-0.287254\pi$
$233$	22.1577	−	3.50943i	1.45160	−	0.229911i	0.831898	+	0.554928i	$0.187254\pi$
$234$	−6.86359	+	2.67079i	−0.448687	+	0.174595i
$235$	−0.669961	+	11.6725i	−0.0437034	+	0.761428i
$236$	−0.974552	−	8.52121i	−0.0634379	−	0.554683i
$237$	7.90187	−	4.02620i	0.513282	−	0.261530i
$238$	2.96049	−	6.73212i	0.191900	−	0.436378i
$239$	−8.84046	−	27.2081i	−0.571842	−	1.75995i	−0.646689	−	0.762754i	$-0.723847\pi$
$239$	−8.84046	−	27.2081i	−0.571842	−	1.75995i	0.0748471	−	0.997195i	$-0.476153\pi$
$240$	−6.23967	+	6.40831i	−0.402769	+	0.413655i
$241$	0.347825	−	1.07050i	0.0224054	−	0.0689567i	−0.939229	−	0.343292i	$-0.888458\pi$
$241$	0.347825	−	1.07050i	0.0224054	−	0.0689567i	0.961634	+	0.274335i	$0.0884579\pi$
$242$	−11.4635	−	10.2272i	−0.736902	−	0.657428i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	11.6625	+	12.7165i	0.746617	+	0.814092i
$245$	−4.54621	−	45.4267i	−0.290447	−	2.90220i
$246$	−4.24452	−	1.11652i	−0.270621	−	0.0711867i
$247$	2.32593	−	14.6853i	0.147995	−	0.934405i
$248$	−18.8471	+	0.258787i	−1.19679	+	0.0164330i
$249$		−	6.87185i		−	0.435486i
$250$	7.76362	+	13.7741i	0.491014	+	0.871151i
$251$			2.00079i			0.126289i	0.998004	+	0.0631445i	$0.0201129\pi$
$251$			2.00079i			0.126289i	−0.998004	+	0.0631445i	$0.979887\pi$
$252$	−6.51562	+	8.19843i	−0.410445	+	0.516453i
$253$	0.409550	−	2.58580i	0.0257482	−	0.162568i
$254$	−4.72677	+	17.9691i	−0.296584	+	1.12748i
$255$	0.221145	+	2.20973i	0.0138487	+	0.138379i
$256$	−2.25381	−	15.8405i	−0.140863	−	0.990029i
$257$	6.57806	+	6.57806i	0.410328	+	0.410328i	0.881853	−	0.471525i	$-0.156296\pi$
$257$	6.57806	+	6.57806i	0.410328	+	0.410328i	−0.471525	+	0.881853i	$0.656296\pi$
$258$	0.403344	−	0.452102i	0.0251111	−	0.0281467i
$259$	−6.86577	+	21.1307i	−0.426618	+	1.31300i
$260$	−19.5854	−	12.6029i	−1.21464	−	0.781596i
$261$	0.504546	+	1.55283i	0.0312306	+	0.0961179i
$262$	−21.2215	−	9.33227i	−1.31107	−	0.576550i
$263$	3.97089	−	2.02327i	0.244856	−	0.124760i	−0.327257	−	0.944936i	$-0.606124\pi$
$263$	3.97089	−	2.02327i	0.244856	−	0.124760i	0.572112	+	0.820175i	$0.306124\pi$
$264$	−0.750517	−	0.730186i	−0.0461911	−	0.0449398i
$265$	−0.561405	+	9.78115i	−0.0344869	+	0.600851i
$266$	−7.66668	−	19.7024i	−0.470074	−	1.20803i
$267$	12.5829	−	1.99294i	0.770062	−	0.121966i
$268$	6.97318	−	4.61972i	0.425955	−	0.282195i
$269$	−15.7496	+	21.6775i	−0.960272	+	1.32170i	−0.0134615	+	0.999909i	$0.504285\pi$
$269$	−15.7496	+	21.6775i	−0.960272	+	1.32170i	−0.946811	+	0.321792i	$0.895715\pi$
$270$	0.495930	−	3.12315i	0.0301813	−	0.190069i
$271$	−5.19079	−	7.14452i	−0.315318	−	0.433998i	0.621712	−	0.783246i	$-0.286437\pi$
$271$	−5.19079	−	7.14452i	−0.315318	−	0.433998i	−0.937031	+	0.349247i	$0.886437\pi$
$272$	−3.37078	−	2.10230i	−0.204383	−	0.127470i
$273$	−24.2965	−	12.3797i	−1.47049	−	0.749251i
$274$	−9.25047	−	11.3171i	−0.558841	−	0.683690i
$275$	−1.61219	+	0.909534i	−0.0972185	+	0.0548470i
$276$	−2.81384	+	13.8607i	−0.169373	+	0.834317i
$277$	−13.1831	+	25.8732i	−0.792093	+	1.55457i	0.0395222	+	0.999219i	$0.487416\pi$
$277$	−13.1831	+	25.8732i	−0.792093	+	1.55457i	−0.831615	+	0.555352i	$0.812584\pi$
$278$	−0.288971	+	0.168605i	−0.0173313	+	0.0101123i
$279$	5.39135	−	3.91704i	0.322772	−	0.234507i
$280$	−33.0846	−	1.44353i	−1.97718	−	0.0862673i
$281$	3.57706	+	2.59889i	0.213389	+	0.155036i	0.689346	−	0.724432i	$-0.257898\pi$
$281$	3.57706	+	2.59889i	0.213389	+	0.155036i	−0.475956	+	0.879469i	$0.657898\pi$
$282$	7.35742	+	0.739268i	0.438128	+	0.0440228i
$283$	−0.148343	−	0.936598i	−0.00881805	−	0.0556750i	0.982887	−	0.184210i	$-0.0589726\pi$
$283$	−0.148343	−	0.936598i	−0.00881805	−	0.0556750i	−0.991705	+	0.128535i	$0.958973\pi$
$284$	11.0767	+	6.26065i	0.657281	+	0.371501i
$285$	4.94129	+	4.04224i	0.292697	+	0.239441i
$286$	1.47452	−	2.29347i	0.0871900	−	0.135616i
$287$	−7.37731	−	14.4788i	−0.435469	−	0.854655i
$288$	3.88037	+	4.11615i	0.228653	+	0.242547i
$289$	15.2299	−	4.94849i	0.895875	−	0.291087i
$290$	−3.03651	+	4.17590i	−0.178310	+	0.245217i
$291$	−10.5068	−	3.41386i	−0.615918	−	0.200124i
$292$	26.9614	+	1.16563i	1.57779	+	0.0682135i
$293$	13.0996	−	13.0996i	0.765289	−	0.765289i	−0.211984	−	0.977273i	$-0.567992\pi$
$293$	13.0996	−	13.0996i	0.765289	−	0.765289i	0.977273	+	0.211984i	$0.0679924\pi$
$294$	−28.8271	+	1.64309i	−1.68123	+	0.0958269i
$295$	−2.04031	+	9.36953i	−0.118792	+	0.545515i
$296$	10.7674	+	5.30132i	0.625842	+	0.308133i
$297$	0.365653	+	0.0579137i	0.0212173	+	0.00336049i
$298$	26.1250	−	5.67814i	1.51338	−	0.328926i
$299$	−36.8280			−2.12982
$300$	8.91367	−	4.53283i	0.514631	−	0.261703i
$301$	2.24324			0.129298
$302$	10.4229	−	2.26537i	0.599773	−	0.130357i
$303$	2.63007	+	0.416562i	0.151094	+	0.0239309i
$304$	−11.1252	+	2.57846i	−0.638076	+	0.147885i
$305$	−7.75874	−	17.6623i	−0.444264	−	1.01134i
$306$	1.40226	−	0.0799262i	0.0801619	−	0.00456908i
$307$	−13.1612	+	13.1612i	−0.751147	+	0.751147i	−0.974693	−	0.223546i	$-0.928237\pi$
$307$	−13.1612	+	13.1612i	−0.751147	+	0.751147i	0.223546	+	0.974693i	$0.428237\pi$
$308$	0.167457	−	3.87331i	0.00954173	−	0.220703i
$309$	3.74243	+	1.21599i	0.212900	+	0.0691752i
$310$	20.0396	+	6.52008i	1.13818	+	0.370316i
$311$	19.9297	−	6.47555i	1.13011	−	0.367195i	0.316492	−	0.948595i	$-0.397495\pi$
$311$	19.9297	−	6.47555i	1.13011	−	0.367195i	0.813618	+	0.581400i	$0.197495\pi$
$312$	−8.49355	+	12.0344i	−0.480853	+	0.681316i
$313$	6.80071	+	13.3471i	0.384399	+	0.754425i	0.999419	−	0.0340866i	$-0.0108522\pi$
$313$	6.80071	+	13.3471i	0.384399	+	0.754425i	−0.615020	+	0.788511i	$0.710852\pi$
$314$	−6.00280	+	9.33678i	−0.338758	+	0.526905i
$315$	9.85101	−	6.32788i	0.555042	−	0.356536i
$316$	8.72751	−	15.4412i	0.490961	−	0.868634i
$317$	0.104878	+	0.662172i	0.00589052	+	0.0371913i	0.990459	−	0.137811i	$-0.0440067\pi$
$317$	0.104878	+	0.662172i	0.00589052	+	0.0371913i	−0.984568	+	0.175002i	$0.944007\pi$
$318$	6.16528	+	0.619482i	0.345732	+	0.0347388i
$319$	−0.489018	−	0.355292i	−0.0273797	−	0.0198925i
$320$	−3.32488	+	17.5768i	−0.185866	+	0.982575i
$321$	0.273604	−	0.198785i	0.0152711	−	0.0110951i
$322$	−45.2300	+	26.3903i	−2.52057	+	1.47067i
$323$	−1.28729	+	2.52644i	−0.0716266	+	0.140575i
$324$	−1.96002	−	0.397900i	−0.108890	−	0.0221055i
$325$	16.1847	+	20.3980i	0.897766	+	1.13148i
$326$	−8.54008	−	10.4480i	−0.472991	−	0.578660i
$327$	−10.7066	−	5.45526i	−0.592074	−	0.301677i
$328$	−8.31018	+	2.82686i	−0.458853	+	0.156087i
$329$	16.0924	+	22.1492i	0.887201	+	1.22113i
$330$	0.531076	+	1.04332i	0.0292348	+	0.0574329i
$331$	17.4371	−	24.0002i	0.958432	−	1.31917i	0.0107532	−	0.999942i	$-0.496577\pi$
$331$	17.4371	−	24.0002i	0.958432	−	1.31917i	0.947679	−	0.319226i	$-0.103423\pi$
$332$	−7.59054	−	11.4574i	−0.416585	−	0.628808i
$333$	−4.19100	+	0.663789i	−0.229665	+	0.0363754i
$334$	6.85842	+	17.6253i	0.375276	+	0.964411i
$335$	−9.04521	+	2.37550i	−0.494193	+	0.129787i
$336$	−1.80762	+	20.8663i	−0.0986140	+	1.13835i
$337$	−15.3221	+	7.80699i	−0.834647	+	0.425274i	−0.818438	−	0.574595i	$-0.805160\pi$
$337$	−15.3221	+	7.80699i	−0.834647	+	0.425274i	−0.0162086	+	0.999869i	$0.505160\pi$
$338$	−18.2806	−	8.03900i	−0.994333	−	0.437264i
$339$	4.21005	+	12.9572i	0.228658	+	0.703738i
$340$	2.80955	+	3.44001i	0.152369	+	0.186561i
$341$	−0.762379	+	2.34636i	−0.0412852	+	0.127063i
$342$	2.68794	−	3.01287i	0.145347	−	0.162918i
$343$	−49.6760	−	49.6760i	−2.68225	−	2.68225i
$344$	0.173109	−	1.19932i	0.00933342	−	0.0646629i
$345$	7.97444	−	13.6548i	0.429330	−	0.735152i
$346$	−0.933619	+	3.54921i	−0.0501917	+	0.190807i
$347$	2.33324	−	14.7315i	0.125255	−	0.790830i	−0.842456	−	0.538766i	$-0.818891\pi$
$347$	2.33324	−	14.7315i	0.125255	−	0.790830i	0.967711	−	0.252064i	$-0.0811093\pi$
$348$	2.55646	+	2.03172i	0.137041	+	0.108912i
$349$			8.09332i			0.433226i	0.976258	+	0.216613i	$0.0695009\pi$
$349$			8.09332i			0.433226i	−0.976258	+	0.216613i	$0.930499\pi$
$350$	34.4940	+	13.4540i	1.84378	+	0.719147i
$351$		−	5.20778i		−	0.277971i
$352$	−2.05789	−	0.388429i	−0.109686	−	0.0207033i
$353$	1.12096	−	7.07744i	0.0596625	−	0.376694i	−0.939732	−	0.341911i	$-0.888926\pi$
$353$	1.12096	−	7.07744i	0.0596625	−	0.376694i	0.999395	−	0.0347832i	$-0.0110741\pi$
$354$	5.86516	+	1.54283i	0.311729	+	0.0820004i
$355$	−9.46593	−	10.6187i	−0.502399	−	0.563583i
$356$	18.7781	−	17.2217i	0.995239	−	0.912750i
$357$	3.67716	+	3.67716i	0.194616	+	0.194616i
$358$	−3.13248	−	2.79465i	−0.165557	−	0.147702i
$359$	6.08656	−	18.7325i	0.321237	−	0.988665i	−0.651874	−	0.758327i	$-0.726017\pi$
$359$	6.08656	−	18.7325i	0.321237	−	0.988665i	0.973111	−	0.230337i	$-0.0739830\pi$
$360$	−2.62292	−	5.75502i	−0.138240	−	0.303316i
$361$	−3.35246	−	10.3178i	−0.176445	−	0.543043i
$362$	−7.35326	+	16.7212i	−0.386479	+	0.878849i
$363$	9.67895	−	4.93167i	0.508013	−	0.258846i
$364$	−54.1839	+	6.19690i	−2.84001	+	0.324806i
$365$	−28.1138	−	10.9526i	−1.47154	−	0.573286i
$366$	−11.3704	+	4.42450i	−0.594341	+	0.231272i
$367$	1.14434	−	0.181246i	0.0597341	−	0.00946095i	−0.126496	−	0.991967i	$-0.540373\pi$
$367$	1.14434	−	0.181246i	0.0597341	−	0.00946095i	0.186230	+	0.982506i	$0.440373\pi$
$368$	10.6188	+	26.2181i	0.553545	+	1.36671i
$369$	1.82415	−	2.51073i	0.0949615	−	0.130703i
$370$	−9.48440	−	9.49194i	−0.493071	−	0.493462i
$371$	13.4849	+	18.5603i	0.700100	+	0.963605i
$372$	4.66229	−	12.4861i	0.241728	−	0.647374i
$373$	−5.06396	−	2.58022i	−0.262202	−	0.133599i	0.317948	−	0.948108i	$-0.397006\pi$
$373$	−5.06396	−	2.58022i	−0.262202	−	0.133599i	−0.580150	+	0.814509i	$0.697006\pi$
$374$	−0.402594	+	0.329076i	−0.0208176	+	0.0170161i
$375$	−11.0676	+	1.58403i	−0.571526	+	0.0817988i
$376$	13.0836	−	6.89432i	0.674736	−	0.355547i
$377$	−3.86027	+	7.57621i	−0.198814	+	0.390195i
$378$	−3.73180	−	6.39589i	−0.191943	−	0.328969i
$379$	21.0848	−	15.3190i	1.08305	−	0.786883i	0.104840	−	0.994489i	$-0.466567\pi$
$379$	21.0848	−	15.3190i	1.08305	−	0.786883i	0.978213	+	0.207606i	$0.0665671\pi$
$380$	12.7036	+	1.28155i	0.651682	+	0.0657419i
$381$	−10.6291	−	7.72251i	−0.544547	−	0.395636i
$382$	2.25334	−	22.4259i	0.115291	−	1.14741i
$383$	2.36387	+	14.9249i	0.120788	+	0.762627i	0.971508	+	0.237007i	$0.0761665\pi$
$383$	2.36387	+	14.9249i	0.120788	+	0.762627i	−0.850720	+	0.525620i	$0.823834\pi$
$384$	11.0164	+	2.57666i	0.562178	+	0.131489i
$385$	−1.57347	+	4.03887i	−0.0801914	+	0.205840i
$386$	11.2922	+	7.25997i	0.574757	+	0.369523i
$387$	0.194497	+	0.381723i	0.00988686	+	0.0194040i
$388$	−21.2889	+	5.91371i	−1.08078	+	0.300223i
$389$	14.4497	−	4.69499i	0.732628	−	0.238045i	0.0811383	−	0.996703i	$-0.474144\pi$
$389$	14.4497	−	4.69499i	0.732628	−	0.238045i	0.651489	+	0.758658i	$0.274144\pi$
$390$	13.3271	−	9.67462i	0.674844	−	0.489894i
$391$	6.67959	+	2.17033i	0.337801	+	0.109758i
$392$	−46.2485	+	34.5815i	−2.33590	+	1.74663i
$393$	11.5914	−	11.5914i	0.584709	−	0.584709i
$394$	−1.63884	−	28.7526i	−0.0825638	−	1.44853i
$395$	−14.8028	+	13.1957i	−0.744808	+	0.663950i
$396$	0.673624	−	0.307335i	0.0338509	−	0.0154442i
$397$	−7.85952	−	1.24483i	−0.394458	−	0.0624760i	−0.0439452	−	0.999034i	$-0.513993\pi$
$397$	−7.85952	−	1.24483i	−0.394458	−	0.0624760i	−0.350513	+	0.936558i	$0.613993\pi$
$398$	−1.39339	−	6.41098i	−0.0698445	−	0.321354i
$399$	14.9493			0.748400
$400$	9.85487	−	17.4035i	0.492744	−	0.870175i
$401$	17.5609			0.876951			0.438476	−	0.898743i	$-0.355519\pi$
$401$	17.5609			0.876951			0.438476	+	0.898743i	$0.355519\pi$
$402$	1.25620	+	5.77975i	0.0626534	+	0.288268i
$403$	34.2778	+	5.42907i	1.70750	+	0.270441i
$404$	4.84525	−	2.21060i	0.241060	−	0.109982i
$405$	1.93091	+	1.12765i	0.0959475	+	0.0560335i
$406$	0.688016	+	12.0709i	0.0341457	+	0.599066i
$407$	1.11079	−	1.11079i	0.0550598	−	0.0550598i
$408$	2.24970	−	1.68218i	0.111377	−	0.0832802i
$409$	19.3261	+	6.27944i	0.955615	+	0.310498i	0.744995	−	0.667070i	$-0.232452\pi$
$409$	19.3261	+	6.27944i	0.955615	+	0.310498i	0.210620	+	0.977568i	$0.432452\pi$
$410$	9.81391	+	0.00389813i	0.484674	+	0.000192515i
$411$	9.82969	−	3.19386i	0.484863	−	0.157542i
$412$	7.58292	−	2.10642i	0.373584	−	0.103776i
$413$	10.1941	+	20.0071i	0.501619	+	0.984483i
$414$	−8.41232	−	5.40845i	−0.413443	−	0.265811i
$415$	3.90312	+	14.8619i	0.191597	+	0.729543i
$416$	−0.868244	+	29.4469i	−0.0425691	+	1.44375i
$417$	−0.0370079	−	0.233659i	−0.00181228	−	0.0114423i
$418$	−0.149441	+	1.48728i	−0.00730940	+	0.0727454i
$419$	28.1350	+	20.4413i	1.37449	+	0.998623i	0.997372	+	0.0724564i	$0.0230838\pi$
$419$	28.1350	+	20.4413i	1.37449	+	0.998623i	0.377115	+	0.926166i	$0.376916\pi$
$420$	9.43491	−	21.4318i	0.460376	−	1.04576i
$421$	18.7080	−	13.5921i	0.911770	−	0.662440i	−0.0296918	−	0.999559i	$-0.509453\pi$
$421$	18.7080	−	13.5921i	0.911770	−	0.662440i	0.941462	+	0.337119i	$0.109453\pi$
$422$	0.200781	+	0.344116i	0.00977387	+	0.0167513i
$423$	−2.37377	+	4.65879i	−0.115417	+	0.226518i
$424$	10.9636	−	5.77721i	0.532442	−	0.280566i
$425$	−1.73337	−	4.65343i	−0.0840810	−	0.225725i
$426$	−6.96593	+	5.69388i	−0.337500	+	0.275869i
$427$	−40.2502	−	20.5085i	−1.94784	−	0.992475i
$428$	0.236605	−	0.633652i	0.0114367	−	0.0306287i
$429$	1.13324	+	1.55977i	0.0547132	+	0.0753062i
$430$	−0.615534	+	1.20687i	−0.0296837	+	0.0582004i
$431$	−11.8267	+	16.2780i	−0.569670	+	0.784083i	−0.992516	−	0.122118i	$-0.961031\pi$
$431$	−11.8267	+	16.2780i	−0.569670	+	0.784083i	0.422846	+	0.906202i	$0.361031\pi$
$432$	−3.70746	+	1.50159i	−0.178375	+	0.0722453i
$433$	5.40084	−	0.855409i	0.259548	−	0.0411083i	−0.0253044	−	0.999680i	$-0.508056\pi$
$433$	5.40084	−	0.855409i	0.259548	−	0.0411083i	0.284852	+	0.958571i	$0.408056\pi$
$434$	45.9883	−	17.8952i	2.20751	−	0.858996i
$435$	−1.97318	−	3.07178i	−0.0946069	−	0.147280i
$436$	−23.8768	+	2.73074i	−1.14349	+	0.130779i
$437$	17.9894	−	9.16607i	0.860551	−	0.438472i
$438$	−7.68164	+	17.4680i	−0.367043	+	0.834651i
$439$	8.72231	+	26.8445i	0.416293	+	1.28122i	0.911089	+	0.412209i	$0.135243\pi$
$439$	8.72231	+	26.8445i	0.416293	+	1.28122i	−0.494796	+	0.869009i	$0.664757\pi$
$440$	2.03790	+	1.15291i	0.0971531	+	0.0549628i
$441$	6.30917	−	19.4176i	0.300437	−	0.924649i
$442$	5.45809	+	4.86944i	0.259615	+	0.231616i
$443$	9.60281	+	9.60281i	0.456243	+	0.456243i	0.897420	−	0.441177i	$-0.145439\pi$
$443$	9.60281	+	9.60281i	0.456243	+	0.456243i	−0.441177	+	0.897420i	$0.645439\pi$
$444$	−6.25444	+	5.73605i	−0.296823	+	0.272221i
$445$	−26.0815	+	11.4571i	−1.23638	+	0.543119i
$446$	−11.1165	−	2.92420i	−0.526382	−	0.138465i
$447$	−2.95731	+	18.6717i	−0.139876	+	0.883142i
$448$	20.0348	+	36.7871i	0.946554	+	1.73803i
$449$			6.32437i			0.298465i	0.988802	+	0.149233i	$0.0476803\pi$
$449$			6.32437i			0.298465i	−0.988802	+	0.149233i	$0.952320\pi$
$450$	0.701346	+	7.03620i	0.0330618	+	0.331690i
$451$			1.14892i			0.0541007i
$452$	21.3317	+	16.9532i	1.00336	+	0.797410i
$453$	−1.17986	+	7.44934i	−0.0554346	+	0.350001i
$454$	−8.62658	+	32.7945i	−0.404866	+	1.53912i
$455$	59.5781	+	12.9738i	2.79306	+	0.608220i
$456$	1.15362	−	7.99242i	0.0540234	−	0.374279i
$457$	23.2984	+	23.2984i	1.08985	+	1.08985i	0.995543	+	0.0943089i	$0.0300641\pi$
$457$	23.2984	+	23.2984i	1.08985	+	1.08985i	0.0943089	+	0.995543i	$0.469936\pi$
$458$	0.332342	−	0.372517i	0.0155293	−	0.0174066i
$459$	−0.306902	+	0.944549i	−0.0143250	+	0.0440878i
$460$	−1.78714	−	31.5752i	−0.0833260	−	1.47220i
$461$	−6.71640	−	20.6710i	−0.312814	−	0.962743i	−0.976645	−	0.214860i	$-0.931071\pi$
$461$	−6.71640	−	20.6710i	−0.312814	−	0.962743i	0.663831	−	0.747883i	$-0.268929\pi$
$462$	2.50947	+	1.10356i	0.116751	+	0.0513421i
$463$	−4.31937	+	2.20083i	−0.200738	+	0.102281i	−0.551470	−	0.834195i	$-0.685933\pi$
$463$	−4.31937	+	2.20083i	−0.200738	+	0.102281i	0.350732	+	0.936476i	$0.385933\pi$
$464$	6.50661	+	0.563660i	0.302062	+	0.0261672i
$465$	−9.43519	+	11.5337i	−0.437546	+	0.534863i
$466$	11.5051	+	29.5667i	0.532965	+	1.36965i
$467$	−32.7718	+	5.19055i	−1.51650	+	0.240190i	−0.858495	−	0.512823i	$-0.828600\pi$
$467$	−32.7718	+	5.19055i	−1.51650	+	0.240190i	−0.658006	+	0.753013i	$0.728600\pi$
$468$	−5.75244	−	8.68294i	−0.265907	−	0.401369i
$469$	−12.8720	+	17.7167i	−0.594372	+	0.818083i
$470$	−16.3320	+	2.58008i	−0.753339	+	0.119010i
$471$	−4.61344	−	6.34986i	−0.212576	−	0.292586i
$472$	11.4832	−	3.90621i	0.528555	−	0.179798i
$473$	−0.141318	−	0.0720050i	−0.00649780	−	0.00331079i
$474$	7.93741	+	9.71068i	0.364577	+	0.446026i
$475$	−12.9826	−	5.93567i	−0.595683	−	0.272347i
$476$	10.1927	+	2.06919i	0.467180	+	0.0948412i
$477$	−1.98914	+	3.90391i	−0.0910766	+	0.178748i
$478$	34.9450	−	20.3893i	1.59835	−	0.932585i
$479$	24.0616	−	17.4817i	1.09940	−	0.798761i	0.118439	−	0.992961i	$-0.462211\pi$
$479$	24.0616	−	17.4817i	1.09940	−	0.798761i	0.980962	+	0.194200i	$0.0622111\pi$
$480$	−10.7301	−	6.69811i	−0.489760	−	0.305726i
$481$	−17.8776	−	12.9888i	−0.815146	−	0.592238i
$482$	1.58384	+	0.159143i	0.0721421	+	0.00724879i
$483$	−5.79251	−	36.5725i	−0.263568	−	1.66411i
$484$	10.6903	−	18.9138i	0.485921	−	0.859719i
$485$	24.6623	+	1.41553i	1.11986	+	0.0642761i
$486$	0.764800	−	1.18957i	0.0346920	−	0.0539601i
$487$	17.4506	+	34.2488i	0.790764	+	1.55196i	0.833270	+	0.552866i	$0.186466\pi$
$487$	17.4506	+	34.2488i	0.790764	+	1.55196i	−0.0425064	+	0.999096i	$0.513534\pi$
$488$	−14.0706	+	19.9366i	−0.636948	+	0.902486i
$489$	9.07483	−	2.94859i	0.410378	−	0.133340i
$490$	61.4118	−	19.9270i	2.77430	−	0.900208i
$491$	−5.04088	−	1.63788i	−0.227492	−	0.0739166i	0.193053	−	0.981188i	$-0.438161\pi$
$491$	−5.04088	−	1.63788i	−0.227492	−	0.0739166i	−0.420545	+	0.907272i	$0.638161\pi$
$492$	0.268094	−	6.20107i	0.0120866	−	0.279566i
$493$	1.14662	−	1.14662i	0.0516413	−	0.0516413i
$494$	20.9930	−	1.19656i	0.944520	−	0.0538359i
$495$	−0.823702	+	0.0824344i	−0.0370226	+	0.00370515i
$496$	−6.01852	−	25.9680i	−0.270240	−	1.16600i
$497$	−32.9009	−	5.21099i	−1.47581	−	0.233745i
$498$	9.49654	−	2.06402i	0.425550	−	0.0924911i
$499$	−24.3883			−1.09177			−0.545884	−	0.837861i	$-0.683806\pi$
$499$	−24.3883			−1.09177			−0.545884	+	0.837861i	$0.683806\pi$
$500$	−16.7033	+	14.8661i	−0.746992	+	0.664833i
$501$	−13.3732			−0.597473
$502$	−2.76500	+	0.600957i	−0.123408	+	0.0268220i
$503$	23.5109	+	3.72375i	1.04830	+	0.166034i	0.656738	−	0.754119i	$-0.271936\pi$
$503$	23.5109	+	3.72375i	1.04830	+	0.166034i	0.391559	+	0.920153i	$0.371936\pi$
$504$	−13.2868	−	6.54178i	−0.591843	−	0.291394i
$505$	−5.92473	+	0.592935i	−0.263647	+	0.0263853i
$506$	3.69645	−	0.210691i	0.164327	−	0.00936635i
$507$	9.98506	−	9.98506i	0.443452	−	0.443452i
$508$	−26.2521	−	1.13497i	−1.16475	−	0.0503561i
$509$	−23.6141	−	7.67268i	−1.04668	−	0.340086i	−0.265313	−	0.964162i	$-0.585475\pi$
$509$	−23.6141	−	7.67268i	−1.04668	−	0.340086i	−0.781363	+	0.624077i	$0.785475\pi$
$510$	−2.98731	+	0.969324i	−0.132280	+	0.0429224i
$511$	−67.1944	+	21.8328i	−2.97250	+	0.965825i
$512$	21.2138	−	7.87248i	0.937525	−	0.347918i
$513$	1.29616	+	2.54385i	0.0572267	+	0.112314i
$514$	−7.11476	+	11.0663i	−0.313819	+	0.488115i
$515$	−8.78453	−	0.504202i	−0.387093	−	0.0222178i
$516$	0.745931	+	0.421607i	0.0328378	+	0.0185602i
$517$	−0.302812	−	1.91188i	−0.0133177	−	0.0840845i
$518$	−31.2637	−	3.14135i	−1.37365	−	0.138023i
$519$	−2.09944	−	1.52533i	−0.0921551	−	0.0669546i
$520$	11.5338	−	30.8514i	0.505792	−	1.35292i
$521$	−15.1720	+	11.0231i	−0.664697	+	0.482930i	−0.868246	−	0.496134i	$-0.834752\pi$
$521$	−15.1720	+	11.0231i	−0.664697	+	0.482930i	0.203549	+	0.979065i	$0.434752\pi$
$522$	−1.99439	+	1.16366i	−0.0872921	+	0.0509322i
$523$	0.351650	−	0.690152i	0.0153766	−	0.0301782i	−0.883190	−	0.469015i	$-0.844609\pi$
$523$	0.351650	−	0.690152i	0.0153766	−	0.0301782i	0.898567	+	0.438836i	$0.144609\pi$
$524$	6.52266	−	32.1301i	0.284944	−	1.40361i
$525$	−17.7109	+	19.2807i	−0.772967	+	0.841480i
$526$	3.98875	+	4.87986i	0.173918	+	0.212772i
$527$	−5.89710	−	3.00472i	−0.256882	−	0.130888i
$528$	0.783655	−	1.25650i	0.0341042	−	0.0546819i
$529$	−15.8756	−	21.8510i	−0.690245	−	0.950041i
$530$	−13.6857	+	2.16203i	−0.594468	+	0.0939124i
$531$	−2.52065	+	3.46937i	−0.109387	+	0.150558i
$532$	24.9249	−	16.5128i	1.08063	−	0.715919i
$533$	15.9630	−	2.52829i	0.691435	−	0.109512i
$534$	6.53354	+	16.7904i	0.282734	+	0.726590i
$535$	−0.478823	+	0.585320i	−0.0207013	+	0.0253056i
$536$	8.47868	+	8.24900i	0.366223	+	0.356302i
$537$	2.64484	−	1.34761i	0.114133	−	0.0581538i
$538$	−34.6878	−	15.2542i	−1.49550	−	0.657653i
$539$	2.33572	+	7.18861i	0.100607	+	0.309636i
$540$	4.46499	−	0.252717i	0.192143	−	0.0108752i
$541$	−3.92130	+	12.0685i	−0.168590	+	0.518866i	−0.999283	−	0.0378646i	$-0.987944\pi$
$541$	−3.92130	+	12.0685i	−0.168590	+	0.518866i	0.830693	+	0.556731i	$0.187944\pi$
$542$	8.31426	−	9.31934i	0.357128	−	0.400300i
$543$	−9.13332	−	9.13332i	−0.391948	−	0.391948i
$544$	1.89282	−	5.28969i	0.0811541	−	0.226793i
$545$	26.2539	+	5.71706i	1.12459	+	0.244892i
$546$	9.81040	−	37.2948i	0.419846	−	1.59607i
$547$	2.48483	−	15.6886i	0.106244	−	0.670797i	−0.875876	−	0.482537i	$-0.839715\pi$
$547$	2.48483	−	15.6886i	0.106244	−	0.670797i	0.982119	−	0.188260i	$-0.0602846\pi$
$548$	12.8612	−	16.1829i	0.549402	−	0.691298i
$549$		−	8.62735i		−	0.368206i
$550$	−1.74117	−	1.95477i	−0.0742436	−	0.0833518i
$551$		−	4.66154i		−	0.198588i
$552$	−20.0000	+	0.274617i	−0.851255	+	0.0116885i
$553$	−7.26425	+	45.8647i	−0.308907	+	1.95036i
$554$	−39.7151	−	10.4471i	−1.68733	−	0.443853i
$555$	8.68696	−	3.81603i	0.368741	−	0.161981i
$556$	−0.319799	−	0.348701i	−0.0135625	−	0.0147882i
$557$	−27.0131	−	27.0131i	−1.14458	−	1.14458i	−0.987602	−	0.156979i	$-0.949824\pi$
$557$	−27.0131	−	27.0131i	−1.14458	−	1.14458i	−0.156979	−	0.987602i	$-0.550176\pi$
$558$	7.03250	+	6.27405i	0.297709	+	0.265602i
$559$	−0.689449	+	2.12191i	−0.0291606	+	0.0897471i
$560$	−7.94239	−	46.1549i	−0.335627	−	1.95040i
$561$	−0.113619	−	0.349682i	−0.00479698	−	0.0147636i
$562$	−2.51712	+	5.72391i	−0.106179	+	0.241449i
$563$	13.9788	−	7.12253i	0.589134	−	0.300179i	−0.133896	−	0.990995i	$-0.542749\pi$
$563$	13.9788	−	7.12253i	0.589134	−	0.300179i	0.723030	+	0.690817i	$0.242749\pi$
$564$	1.18824	+	10.3896i	0.0500339	+	0.437482i
$565$	−16.4647	−	25.6316i	−0.692675	−	1.07833i
$566$	1.24978	−	0.486318i	0.0525320	−	0.0204415i
$567$	5.17165	−	0.819109i	0.217189	−	0.0343993i
$568$	−5.32492	+	17.1879i	−0.223429	+	0.721187i
$569$	−14.3030	+	19.6864i	−0.599612	+	0.825296i	−0.995673	−	0.0929289i	$-0.970377\pi$
$569$	−14.3030	+	19.6864i	−0.599612	+	0.825296i	0.396060	+	0.918224i	$0.370377\pi$
$570$	−4.10200	+	8.04274i	−0.171814	+	0.336873i
$571$	10.6807	+	14.7008i	0.446975	+	0.615208i	0.971744	−	0.236036i	$-0.0758484\pi$
$571$	10.6807	+	14.7008i	0.446975	+	0.615208i	−0.524769	+	0.851244i	$0.675848\pi$
$572$	3.61234	+	1.34884i	0.151040	+	0.0563979i
$573$	14.2003	+	7.23541i	0.593225	+	0.302263i
$574$	17.7931	−	14.5439i	0.742670	−	0.607051i
$575$	−9.49078	+	34.0611i	−0.395793	+	1.42044i
$576$	−4.52281	+	6.59880i	−0.188450	+	0.274950i
$577$	−15.2366	+	29.9035i	−0.634308	+	1.24490i	0.320380	+	0.947289i	$0.396189\pi$
$577$	−15.2366	+	29.9035i	−0.634308	+	1.24490i	−0.954688	+	0.297610i	$0.903811\pi$
$578$	11.4130	+	19.5606i	0.474718	+	0.813613i
$579$	−7.67971	+	5.57963i	−0.319158	+	0.231882i
$580$	−6.68293	−	2.94203i	−0.277494	−	0.122161i
$581$	29.1099	+	21.1496i	1.20768	+	0.877431i
$582$	1.56197	−	15.5452i	0.0647458	−	0.644370i
$583$	−0.253747	−	1.60209i	−0.0105091	−	0.0663520i
$584$	6.48725	+	37.6094i	0.268444	+	1.55629i
$585$	2.95795	+	11.2630i	0.122296	+	0.465668i
$586$	22.0376	+	14.1684i	0.910367	+	0.585293i
$587$	−6.48594	−	12.7294i	−0.267703	−	0.525397i	0.717548	−	0.696509i	$-0.245264\pi$
$587$	−6.48594	−	12.7294i	−0.267703	−	0.525397i	−0.985252	+	0.171111i	$0.945264\pi$
$588$	−10.9291	−	39.3440i	−0.450710	−	1.62252i
$589$	−18.0949	+	5.87940i	−0.745589	+	0.242257i
$590$	−13.5610	−	0.00538651i	−0.558299	−	0.000221759i
$591$	19.3674	+	6.29287i	0.796670	+	0.258854i
$592$	−4.09207	+	16.4723i	−0.168183	+	0.677007i
$593$	−1.73642	+	1.73642i	−0.0713063	+	0.0713063i	−0.741861	−	0.670554i	$-0.766056\pi$
$593$	−1.73642	+	1.73642i	−0.0713063	+	0.0713063i	0.670554	+	0.741861i	$0.266056\pi$
$594$	0.0297934	+	0.522709i	0.00122244	+	0.0214470i
$595$	−10.0413	−	5.86411i	−0.411652	−	0.240405i
$596$	15.6938	+	34.3980i	0.642843	+	1.40900i
$597$	4.58197	+	0.725713i	0.187528	+	0.0297015i
$598$	−11.0616	−	50.8944i	−0.452344	−	2.08123i
$599$	4.92161			0.201092			0.100546	−	0.994932i	$-0.467941\pi$
$599$	4.92161			0.201092			0.100546	+	0.994932i	$0.467941\pi$
$600$	8.94144	+	10.9568i	0.365033	+	0.447308i
$601$	−21.9172			−0.894020			−0.447010	−	0.894529i	$-0.647511\pi$
$601$	−21.9172			−0.894020			−0.447010	+	0.894529i	$0.647511\pi$
$602$	0.673779	+	3.10005i	0.0274612	+	0.126348i
$603$	−4.13082	−	0.654258i	−0.168220	−	0.0266435i
$604$	6.26125	+	13.7235i	0.254767	+	0.558403i
$605$	−18.1318	+	16.1634i	−0.737163	+	0.657135i
$606$	0.214298	+	3.75974i	0.00870528	+	0.152729i
$607$	24.0001	−	24.0001i	0.974133	−	0.974133i	−0.0255408	−	0.999674i	$-0.508131\pi$
$607$	24.0001	−	24.0001i	0.974133	−	0.974133i	0.999674	+	0.0255408i	$0.00813078\pi$
$608$	−6.90488	−	14.6000i	−0.280030	−	0.592110i
$609$	−8.13081	−	2.64186i	−0.329477	−	0.107054i
$610$	22.0780	−	16.0272i	0.893914	−	0.648924i
$611$	−25.8971	+	8.41448i	−1.04769	+	0.340414i
$612$	0.531636	+	1.91385i	0.0214901	+	0.0773626i
$613$	−8.12093	−	15.9382i	−0.328001	−	0.643738i	0.666838	−	0.745203i	$-0.267647\pi$
$613$	−8.12093	−	15.9382i	−0.328001	−	0.643738i	−0.994839	+	0.101464i	$0.967647\pi$
$614$	−22.1411	−	14.2350i	−0.893544	−	0.574477i
$615$	−2.51908	+	6.46611i	−0.101579	+	0.260739i
$616$	5.40302	−	0.931969i	0.217694	−	0.0375501i
$617$	−5.91551	−	37.3491i	−0.238150	−	1.50362i	−0.759631	−	0.650354i	$-0.774620\pi$
$617$	−5.91551	−	37.3491i	−0.238150	−	1.50362i	0.521482	−	0.853263i	$-0.325380\pi$
$618$	−0.556362	+	5.53709i	−0.0223802	+	0.222734i
$619$	17.2330	+	12.5205i	0.692654	+	0.503243i	0.877532	−	0.479519i	$-0.159189\pi$
$619$	17.2330	+	12.5205i	0.692654	+	0.503243i	−0.184877	+	0.982762i	$0.559189\pi$
$620$	−2.99132	+	29.6521i	−0.120134	+	1.19086i
$621$	5.72114	−	4.15665i	0.229582	−	0.166801i
$622$	14.9350	+	25.5968i	0.598837	+	1.02634i
$623$	−30.2843	+	59.4362i	−1.21331	+	2.38126i
$624$	−19.1821	−	8.12301i	−0.767899	−	0.325180i
$625$	23.0364	−	9.71205i	0.921456	−	0.388482i
$626$	−16.4024	+	13.4072i	−0.655572	+	0.535858i
$627$	−0.941761	−	0.479851i	−0.0376103	−	0.0191634i
$628$	−14.7060	−	5.49118i	−0.586831	−	0.219122i
$629$	2.47705	+	3.40936i	0.0987663	+	0.135940i
$630$	11.7037	+	11.7130i	0.466285	+	0.466655i
$631$	−4.06255	+	5.59161i	−0.161727	+	0.222599i	−0.882188	−	0.470897i	$-0.843930\pi$
$631$	−4.06255	+	5.59161i	−0.161727	+	0.222599i	0.720461	+	0.693496i	$0.243930\pi$
$632$	23.9603	+	7.42307i	0.953091	+	0.295274i
$633$	−0.278249	+	0.0440703i	−0.0110594	+	0.00175164i
$634$	−0.883587	+	0.343825i	−0.0350917	+	0.0136550i
$635$	27.3742	+	10.6645i	1.08631	+	0.423207i
$636$	0.995706	+	8.70617i	0.0394823	+	0.345222i
$637$	94.7379	−	48.2714i	3.75365	−	1.91258i
$638$	0.344115	−	0.782513i	0.0136236	−	0.0309800i
$639$	−1.96590	−	6.05041i	−0.0777697	−	0.239350i
$640$	−25.2890	+	0.684557i	−0.999634	+	0.0270595i
$641$	−0.733499	+	2.25748i	−0.0289715	+	0.0891650i	−0.964497	−	0.264095i	$-0.914927\pi$
$641$	−0.733499	+	2.25748i	−0.0289715	+	0.0891650i	0.935525	+	0.353260i	$0.114927\pi$
$642$	0.356890	+	0.318399i	0.0140853	+	0.0125662i
$643$	4.36401	+	4.36401i	0.172100	+	0.172100i	0.787901	−	0.615801i	$-0.211168\pi$
$643$	4.36401	+	4.36401i	0.172100	+	0.172100i	−0.615801	+	0.787901i	$0.711168\pi$
$644$	−50.0553	−	54.5790i	−1.97245	−	2.15071i
$645$	−0.637458	−	0.715090i	−0.0250999	−	0.0281566i
$646$	−3.87807	−	1.02013i	−0.152581	−	0.0401363i
$647$	6.93647	−	43.7951i	0.272701	−	1.72176i	−0.347809	−	0.937565i	$-0.613074\pi$
$647$	6.93647	−	43.7951i	0.272701	−	1.72176i	0.620510	−	0.784199i	$-0.286926\pi$
$648$	−0.0388331	−	2.82816i	−0.00152551	−	0.111101i
$649$		−	1.58760i		−	0.0623189i
$650$	−23.3278	+	28.4932i	−0.914993	+	1.11760i
$651$			34.8939i			1.36760i
$652$	11.8735	−	14.9401i	0.465002	−	0.585100i
$653$	3.85995	−	24.3708i	0.151052	−	0.953702i	−0.789426	−	0.613846i	$-0.789622\pi$
$653$	3.85995	−	24.3708i	0.151052	−	0.953702i	0.940477	−	0.339856i	$-0.110378\pi$
$654$	4.32308	−	16.4345i	0.169046	−	0.642638i
$655$	−18.4853	+	31.6528i	−0.722280	+	1.23678i
$656$	−6.40262	−	10.6352i	−0.249980	−	0.415234i
$657$	−9.54119	−	9.54119i	−0.372237	−	0.372237i
$658$	−25.7756	+	28.8916i	−1.00484	+	1.12631i
$659$	−2.24945	+	6.92309i	−0.0876260	+	0.269685i	−0.985262	−	0.171053i	$-0.945283\pi$
$659$	−2.24945	+	6.92309i	−0.0876260	+	0.269685i	0.897636	+	0.440738i	$0.145283\pi$
$660$	−1.28230	+	1.04729i	−0.0499135	+	0.0407658i
$661$	−4.69519	−	14.4503i	−0.182622	−	0.562052i	0.817277	−	0.576244i	$-0.195482\pi$
$661$	−4.69519	−	14.4503i	−0.182622	−	0.562052i	−0.999899	+	0.0141920i	$0.995482\pi$
$662$	38.4044	+	16.8886i	1.49263	+	0.656393i
$663$	−4.60842	+	2.34811i	−0.178976	+	0.0911929i
$664$	13.5537	−	13.9311i	0.525986	−	0.540631i
$665$	−32.3312	+	8.49099i	−1.25375	+	0.329267i
$666$	−2.17613	−	5.59237i	−0.0843233	−	0.216700i
$667$	−11.4042	+	1.80624i	−0.441571	+	0.0699379i
$668$	−22.2972	+	14.7719i	−0.862705	+	0.571542i
$669$	4.77750	−	6.57566i	0.184709	−	0.254230i
$670$	−5.99963	−	11.7865i	−0.231786	−	0.455353i
$671$	1.87735	+	2.58395i	0.0724743	+	0.0997523i
$672$	−29.3791	+	3.76935i	−1.13332	+	0.145406i
$673$	−2.83209	−	1.44302i	−0.109169	−	0.0556245i	0.398553	−	0.917145i	$-0.369512\pi$
$673$	−2.83209	−	1.44302i	−0.109169	−	0.0556245i	−0.507722	+	0.861521i	$0.669512\pi$
$674$	−15.3910	−	18.8294i	−0.592839	−	0.725283i
$675$	−4.81652	−	1.34207i	−0.185388	−	0.0516565i
$676$	5.61874	−	27.6775i	0.216106	−	1.06452i
$677$	18.1131	−	35.5491i	0.696145	−	1.36626i	−0.223964	−	0.974597i	$-0.571900\pi$
$677$	18.1131	−	35.5491i	0.696145	−	1.36626i	0.920108	−	0.391664i	$-0.128100\pi$
$678$	−16.6417	+	9.70989i	−0.639119	+	0.372906i
$679$	46.7983	−	34.0010i	1.79595	−	1.30484i
$680$	−3.91004	+	4.91589i	−0.149943	+	0.188516i
$681$	−19.3987	−	14.0940i	−0.743358	−	0.540081i
$682$	−3.47154	−	0.348818i	−0.132932	−	0.0133569i
$683$	−5.05528	−	31.9178i	−0.193435	−	1.22130i	−0.873013	−	0.487697i	$-0.837837\pi$
$683$	−5.05528	−	31.9178i	−0.193435	−	1.22130i	0.679578	−	0.733603i	$-0.262163\pi$
$684$	4.97099	+	2.80965i	0.190070	+	0.107430i
$685$	−19.4449	+	12.4906i	−0.742951	+	0.477241i
$686$	53.7290	−	83.5703i	2.05138	−	3.19073i
$687$	0.160259	+	0.314527i	0.00611427	+	0.0119999i
$688$	1.70939	−	0.120998i	0.0651700	−	0.00461302i
$689$	−21.7009	+	7.05106i	−0.826740	+	0.268624i
$690$	21.2655	+	6.91892i	0.809563	+	0.263399i
$691$	2.35753	+	0.766009i	0.0896848	+	0.0291404i	0.353516	−	0.935429i	$-0.384986\pi$
$691$	2.35753	+	0.766009i	0.0896848	+	0.0291404i	−0.263831	+	0.964569i	$0.584986\pi$
$692$	−5.18525	−	0.224176i	−0.197114	−	0.00852190i
$693$	−1.37070	+	1.37070i	−0.0520687	+	0.0520687i
$694$	21.0590	−	1.20033i	0.799390	−	0.0455637i
$695$	0.212753	+	0.484320i	0.00807018	+	0.0183713i
$696$	−2.03988	+	4.14315i	−0.0773215	+	0.157046i
$697$	−3.04425	−	0.482161i	−0.115309	−	0.0182632i
$698$	−11.1846	+	2.43091i	−0.423342	+	0.0920111i
$699$	−22.4339			−0.848527
$700$	−8.23217	+	51.7100i	−0.311147	+	1.95445i
$701$	−9.19901			−0.347442			−0.173721	−	0.984795i	$-0.555579\pi$
$701$	−9.19901			−0.347442			−0.173721	+	0.984795i	$0.555579\pi$
$702$	7.19689	−	1.56421i	0.271629	−	0.0590372i
$703$	11.9654	+	1.89514i	0.451285	+	0.0714765i
$704$	−0.0813177	−	2.96057i	−0.00306477	−	0.111581i
$705$	2.48769	−	11.4240i	0.0936918	−	0.430251i
$706$	10.1174	−	0.576670i	0.380772	−	0.0217033i
$707$	−9.85920	+	9.85920i	−0.370793	+	0.370793i
$708$	−0.370457	+	8.56875i	−0.0139226	+	0.322033i
$709$	−24.6840	−	8.02031i	−0.927027	−	0.301209i	−0.193681	−	0.981065i	$-0.562043\pi$
$709$	−24.6840	−	8.02031i	−0.927027	−	0.301209i	−0.733346	+	0.679855i	$0.762043\pi$
$710$	11.8314	−	16.2709i	0.444023	−	0.610635i
$711$	−8.43442	+	2.74051i	−0.316316	+	0.102777i
$712$	29.4397	+	20.7777i	1.10330	+	0.778678i
$713$	21.3950	+	41.9900i	0.801248	+	1.57254i
$714$	−3.97718	+	6.18611i	−0.148842	+	0.231509i
$715$	−3.33681	−	2.72969i	−0.124790	−	0.102084i
$716$	2.92119	−	5.16833i	0.109170	−	0.193150i
$717$	4.47533	+	28.2561i	0.167134	+	1.05524i
$718$	27.7156	+	2.78484i	1.03434	+	0.103929i
$719$	−8.69185	−	6.31500i	−0.324151	−	0.235510i	0.413793	−	0.910371i	$-0.364204\pi$
$719$	−8.69185	−	6.31500i	−0.324151	−	0.235510i	−0.737945	+	0.674861i	$0.764204\pi$
$720$	7.16533	−	5.35332i	0.267036	−	0.199506i
$721$	−16.6692	+	12.1109i	−0.620793	+	0.451033i
$722$	13.2518	−	7.73198i	0.493179	−	0.287755i
$723$	−0.511006	+	1.00291i	−0.0190045	+	0.0372984i
$724$	−25.3165	−	5.13946i	−0.940881	−	0.191006i
$725$	6.01219	+	5.52267i	0.223287	+	0.205107i
$726$	9.72249	+	11.8946i	0.360835	+	0.441448i
$727$	20.3289	+	10.3581i	0.753958	+	0.384161i	0.788333	−	0.615248i	$-0.210944\pi$
$727$	20.3289	+	10.3581i	0.753958	+	0.384161i	−0.0343757	+	0.999409i	$0.510944\pi$
$728$	−24.8384	−	73.0181i	−0.920574	−	2.70623i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	6.69172	−	42.1415i	0.247672	−	1.55973i
$731$	0.250094	−	0.344225i	0.00925007	−	0.0127316i
$732$	−9.52965	−	14.3844i	−0.352226	−	0.531662i
$733$	3.59155	−	0.568846i	0.132657	−	0.0210108i	−0.0897528	−	0.995964i	$-0.528608\pi$
$733$	3.59155	−	0.568846i	0.132657	−	0.0210108i	0.222410	+	0.974953i	$0.428608\pi$
$734$	0.594186	+	1.52698i	0.0219318	+	0.0563620i
$735$	−2.61606	+	45.5786i	−0.0964947	+	1.68119i
$736$	−33.0426	+	22.5495i	−1.21797	+	0.831187i
$737$	1.37958	−	0.702931i	0.0508174	−	0.0258928i
$738$	4.01760	+	1.76676i	0.147890	+	0.0650354i
$739$	−7.22761	−	22.2443i	−0.265872	−	0.818269i	−0.991491	−	0.130173i	$-0.958447\pi$
$739$	−7.22761	−	22.2443i	−0.265872	−	0.818269i	0.725620	−	0.688096i	$-0.241553\pi$
$740$	10.2687	−	15.9580i	0.377483	−	0.586626i
$741$	−4.59458	+	14.1407i	−0.168786	+	0.519471i
$742$	−21.5991	+	24.2102i	−0.792929	+	0.888784i
$743$	0.983008	+	0.983008i	0.0360631	+	0.0360631i	0.724908	−	0.688845i	$-0.241882\pi$
$743$	0.983008	+	0.983008i	0.0360631	+	0.0360631i	−0.688845	+	0.724908i	$0.741882\pi$
$744$	18.6555	+	2.69273i	0.683944	+	0.0987203i
$745$	−4.20944	−	42.0616i	−0.154222	−	1.54102i
$746$	2.04472	−	7.77313i	0.0748626	−	0.284595i
$747$	−1.07499	+	6.78724i	−0.0393320	+	0.248332i
$748$	−0.575690	−	0.457524i	−0.0210493	−	0.0167287i
$749$			1.77082i			0.0647042i
$750$	−5.51329	−	14.8190i	−0.201317	−	0.541114i
$751$			4.90529i			0.178997i	0.995987	+	0.0894983i	$0.0285264\pi$
$751$			4.90529i			0.178997i	−0.995987	+	0.0894983i	$0.971474\pi$
$752$	13.4574	+	16.0101i	0.490741	+	0.583829i
$753$	0.312993	−	1.97616i	0.0114061	−	0.0720153i
$754$	−11.6294	−	3.05911i	−0.423518	−	0.111406i
$755$	−1.67941	−	16.7810i	−0.0611201	−	0.610725i
$756$	7.71792	−	7.07823i	0.280698	−	0.257433i
$757$	7.38605	+	7.38605i	0.268451	+	0.268451i	0.828476	−	0.560025i	$-0.189208\pi$
$757$	7.38605	+	7.38605i	0.268451	+	0.268451i	−0.560025	+	0.828476i	$0.689208\pi$
$758$	27.5031	+	24.5369i	0.998957	+	0.891220i
$759$	−0.809015	+	2.48989i	−0.0293654	+	0.0903774i
$760$	2.04462	+	17.9407i	0.0741661	+	0.650777i
$761$	−8.40625	−	25.8718i	−0.304726	−	0.937851i	−0.979779	−	0.200082i	$-0.935879\pi$
$761$	−8.40625	−	25.8718i	−0.304726	−	0.937851i	0.675053	−	0.737769i	$-0.264121\pi$
$762$	7.47956	−	17.0084i	0.270956	−	0.616151i
$763$	56.0607	−	28.5644i	2.02953	−	1.03410i
$764$	31.6683	−	3.62183i	1.14572	−	0.131033i
$765$	0.127255	−	2.21712i	0.00460092	−	0.0801601i
$766$	−19.9154	+	7.74958i	−0.719574	+	0.280004i
$767$	−22.0580	+	3.49364i	−0.796468	+	0.126148i
$768$	−0.251934	+	15.9980i	−0.00909090	+	0.577279i
$769$	4.36004	−	6.00107i	0.157227	−	0.216404i	−0.723135	−	0.690707i	$-0.757300\pi$
$769$	4.36004	−	6.00107i	0.157227	−	0.216404i	0.880362	+	0.474302i	$0.157300\pi$
$770$	−6.05412	−	0.961343i	−0.218175	−	0.0346444i
$771$	−5.46804	−	7.52611i	−0.196926	−	0.271046i
$772$	−6.64120	+	17.7858i	−0.239022	+	0.640126i
$773$	−42.1935	−	21.4986i	−1.51759	−	0.773252i	−0.520831	−	0.853660i	$-0.674378\pi$
$773$	−42.1935	−	21.4986i	−1.51759	−	0.773252i	−0.996762

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)

\(f(q)\)	\(=\)	\(q+(0.300359 + 1.38195i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.81957 + 0.830163i) q^{4} +(2.22495 - 0.222669i) q^{5} +(-0.0804769 - 1.41192i) q^{6} +(3.70249 - 3.70249i) q^{7} +(-1.69377 - 2.26520i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(0.300359 + 1.38195i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.81957 + 0.830163i) q^{4} +(2.22495 - 0.222669i) q^{5} +(-0.0804769 - 1.41192i) q^{6} +(3.70249 - 3.70249i) q^{7} +(-1.69377 - 2.26520i) q^{8} +(0.951057 + 0.309017i) q^{9} +(0.976003 + 3.00789i) q^{10} +(-0.352091 + 0.114401i) q^{11} +(1.92703 - 0.535299i) q^{12} +(2.36428 + 4.64017i) q^{13} +(6.22874 + 4.00458i) q^{14} +(-2.23239 - 0.128132i) q^{15} +(2.62166 - 3.02108i) q^{16} +(-0.155364 - 0.980930i) q^{17} +(-0.141387 + 1.40713i) q^{18} +(-2.30977 - 1.67815i) q^{19} +(-3.86360 + 2.25224i) q^{20} +(-4.23611 + 3.07771i) q^{21} +(-0.263851 - 0.452211i) q^{22} +(-3.21049 + 6.30095i) q^{23} +(1.31856 + 2.50228i) q^{24} +(4.90084 - 0.990856i) q^{25} +(-5.70234 + 4.66104i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-3.66327 + 9.81061i) q^{28} +(0.959703 + 1.32092i) q^{29} +(-0.493449 - 3.12354i) q^{30} +(3.91704 - 5.39135i) q^{31} +(4.96242 + 2.71559i) q^{32} +(0.365653 - 0.0579137i) q^{33} +(1.30893 - 0.509337i) q^{34} +(7.41344 - 9.06230i) q^{35} +(-1.98705 + 0.227254i) q^{36} +(-3.78075 + 1.92639i) q^{37} +(1.62535 - 3.69603i) q^{38} +(-1.60929 - 4.95290i) q^{39} +(-4.27295 - 4.66283i) q^{40} +(0.959013 - 2.95154i) q^{41} +(-5.52560 - 4.92967i) q^{42} +(0.302937 + 0.302937i) q^{43} +(0.545682 - 0.500454i) q^{44} +(2.18487 + 0.475778i) q^{45} +(-9.67190 - 2.54419i) q^{46} +(-0.817946 + 5.16431i) q^{47} +(-3.06198 + 2.57376i) q^{48} -20.4169i q^{49} +(2.84133 + 6.47510i) q^{50} +0.993157i q^{51} +(-8.15407 - 6.48036i) q^{52} +(-0.685412 + 4.32752i) q^{53} +(0.359770 - 1.36769i) q^{54} +(-0.757913 + 0.332938i) q^{55} +(-14.6581 - 2.11574i) q^{56} +(2.01881 + 2.01881i) q^{57} +(-1.53719 + 1.72301i) q^{58} +(-1.32518 + 4.07849i) q^{59} +(4.16836 - 1.62011i) q^{60} +(-2.66600 - 8.20510i) q^{61} +(8.62709 + 3.79382i) q^{62} +(4.66541 - 2.37715i) q^{63} +(-2.26230 + 7.67346i) q^{64} +(6.29364 + 9.79771i) q^{65} +(0.189861 + 0.487919i) q^{66} +(-4.13082 + 0.654258i) q^{67} +(1.09703 + 1.65589i) q^{68} +(4.15665 - 5.72114i) q^{69} +(14.7503 + 7.52306i) q^{70} +(-3.73936 - 5.14679i) q^{71} +(-0.910882 - 2.67774i) q^{72} +(-12.0226 - 6.12582i) q^{73} +(-3.79776 - 4.64620i) q^{74} +(-4.99550 + 0.211997i) q^{75} +(5.59592 + 1.13602i) q^{76} +(-0.880045 + 1.72719i) q^{77} +(6.36129 - 3.71161i) q^{78} +(-7.17475 + 5.21276i) q^{79} +(5.16037 - 7.30552i) q^{80} +(0.809017 + 0.587785i) q^{81} +(4.36692 + 0.438785i) q^{82} +(1.07499 + 6.78724i) q^{83} +(5.15288 - 9.11676i) q^{84} +(-0.564100 - 2.14793i) q^{85} +(-0.327653 + 0.509633i) q^{86} +(-0.741250 - 1.45479i) q^{87} +(0.855503 + 0.603789i) q^{88} +(-12.1162 + 3.93680i) q^{89} +(-0.00125607 + 3.16228i) q^{90} +(25.9339 + 8.42645i) q^{91} +(0.610899 - 14.1302i) q^{92} +(-4.71221 + 4.71221i) q^{93} +(-7.38249 + 0.420788i) q^{94} +(-5.51280 - 3.21948i) q^{95} +(-4.47651 - 3.45845i) q^{96} +(10.9115 + 1.72821i) q^{97} +(28.2151 - 6.13241i) q^{98} -0.370211 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

Related objects

Downloads

Learn more about