LMFDB - Embedded newform 588.3.g.h.295.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,4,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.2
Character	$\chi$	$=$	588.295
Dual form			588.3.g.h.295.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96525 - 0.371196i) q^{2} +1.73205i q^{3} +(3.72443 + 1.45899i) q^{4} -4.44657 q^{5} +(0.642930 - 3.40392i) q^{6} +(-6.77787 - 4.24976i) q^{8} -3.00000 q^{9} +(8.73863 + 1.65055i) q^{10} +14.7729i q^{11} +(-2.52704 + 6.45090i) q^{12} +0.580073 q^{13} -7.70169i q^{15} +(11.7427 + 10.8678i) q^{16} +1.84226 q^{17} +(5.89575 + 1.11359i) q^{18} -27.1631i q^{19} +(-16.5609 - 6.48748i) q^{20} +(5.48363 - 29.0324i) q^{22} +32.0092i q^{23} +(7.36081 - 11.7396i) q^{24} -5.22800 q^{25} +(-1.13999 - 0.215321i) q^{26} -5.19615i q^{27} -52.0783 q^{29} +(-2.85883 + 15.1358i) q^{30} +5.90518i q^{31} +(-19.0433 - 25.7168i) q^{32} -25.5874 q^{33} +(-3.62051 - 0.683840i) q^{34} +(-11.1733 - 4.37696i) q^{36} +29.9086 q^{37} +(-10.0828 + 53.3824i) q^{38} +1.00472i q^{39} +(30.1383 + 18.8969i) q^{40} +34.8858 q^{41} -63.2821i q^{43} +(-21.5534 + 55.0205i) q^{44} +13.3397 q^{45} +(11.8817 - 62.9061i) q^{46} -58.0829i q^{47} +(-18.8235 + 20.3390i) q^{48} +(10.2743 + 1.94061i) q^{50} +3.19089i q^{51} +(2.16044 + 0.846319i) q^{52} -24.1811 q^{53} +(-1.92879 + 10.2117i) q^{54} -65.6886i q^{55} +47.0479 q^{57} +(102.347 + 19.3312i) q^{58} -64.9879i q^{59} +(11.2367 - 28.6844i) q^{60} +44.3593 q^{61} +(2.19198 - 11.6052i) q^{62} +(27.8790 + 57.6087i) q^{64} -2.57934 q^{65} +(50.2856 + 9.49792i) q^{66} +42.3973i q^{67} +(6.86138 + 2.68784i) q^{68} -55.4416 q^{69} -33.6089i q^{71} +(20.3336 + 12.7493i) q^{72} -130.569 q^{73} +(-58.7779 - 11.1019i) q^{74} -9.05516i q^{75} +(39.6306 - 101.167i) q^{76} +(0.372946 - 1.97452i) q^{78} -48.7790i q^{79} +(-52.2149 - 48.3243i) q^{80} +9.00000 q^{81} +(-68.5594 - 12.9495i) q^{82} -137.835i q^{83} -8.19176 q^{85} +(-23.4900 + 124.365i) q^{86} -90.2022i q^{87} +(62.7812 - 100.129i) q^{88} -116.851 q^{89} +(-26.2159 - 4.95164i) q^{90} +(-46.7010 + 119.216i) q^{92} -10.2281 q^{93} +(-21.5601 + 114.148i) q^{94} +120.783i q^{95} +(44.5427 - 32.9840i) q^{96} -133.593 q^{97} -44.3186i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) $ 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.96525	−	0.371196i	−0.982626	−	0.185598i
$2$	−1.96525	−	0.371196i	−0.982626	−	0.185598i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.72443	+	1.45899i	0.931107	+	0.364746i
$5$	−4.44657			−0.889314			−0.444657	−	0.895701i	$-0.646674\pi$
$5$	−4.44657			−0.889314			−0.444657	+	0.895701i	$0.646674\pi$
$6$	0.642930	−	3.40392i	0.107155	−	0.567319i
$7$		0			0
$7$		0			0
$8$	−6.77787	−	4.24976i	−0.847234	−	0.531221i
$9$	−3.00000			−0.333333
$10$	8.73863	+	1.65055i	0.873863	+	0.165055i
$11$			14.7729i			1.34299i	0.741010	+	0.671494i	$0.234347\pi$
$11$			14.7729i			1.34299i	−0.741010	+	0.671494i	$0.765653\pi$
$12$	−2.52704	+	6.45090i	−0.210586	+	0.537575i
$13$	0.580073			0.0446210			0.0223105	−	0.999751i	$-0.492898\pi$
$13$	0.580073			0.0446210			0.0223105	+	0.999751i	$0.492898\pi$
$14$		0			0
$15$		−	7.70169i		−	0.513446i
$16$	11.7427	+	10.8678i	0.733920	+	0.679236i
$17$	1.84226			0.108368			0.0541842	−	0.998531i	$-0.482744\pi$
$17$	1.84226			0.108368			0.0541842	+	0.998531i	$0.482744\pi$
$18$	5.89575	+	1.11359i	0.327542	+	0.0618659i
$19$		−	27.1631i		−	1.42964i	−0.699310	−	0.714819i	$-0.746509\pi$
$19$		−	27.1631i		−	1.42964i	0.699310	−	0.714819i	$-0.253491\pi$
$20$	−16.5609	−	6.48748i	−0.828047	−	0.324374i
$21$		0			0
$22$	5.48363	−	29.0324i	0.249256	−	1.31965i
$23$			32.0092i			1.39170i	0.718185	+	0.695852i	$0.244973\pi$
$23$			32.0092i			1.39170i	−0.718185	+	0.695852i	$0.755027\pi$
$24$	7.36081	−	11.7396i	0.306700	−	0.489151i
$25$	−5.22800			−0.209120
$26$	−1.13999	−	0.215321i	−0.0438458	−	0.00828157i
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−52.0783			−1.79580			−0.897901	−	0.440197i	$-0.854909\pi$
$29$	−52.0783			−1.79580			−0.897901	+	0.440197i	$0.854909\pi$
$30$	−2.85883	+	15.1358i	−0.0952944	+	0.504525i
$31$			5.90518i			0.190490i	0.995454	+	0.0952449i	$0.0303634\pi$
$31$			5.90518i			0.190490i	−0.995454	+	0.0952449i	$0.969637\pi$
$32$	−19.0433	−	25.7168i	−0.595104	−	0.803649i
$33$	−25.5874			−0.775375
$34$	−3.62051	−	0.683840i	−0.106486	−	0.0201129i
$35$		0			0
$36$	−11.1733	−	4.37696i	−0.310369	−	0.121582i
$37$	29.9086			0.808340			0.404170	−	0.914684i	$-0.367560\pi$
$37$	29.9086			0.808340			0.404170	+	0.914684i	$0.367560\pi$
$38$	−10.0828	+	53.3824i	−0.265338	+	1.40480i
$39$			1.00472i			0.0257620i
$40$	30.1383	+	18.8969i	0.753457	+	0.472422i
$41$	34.8858			0.850873			0.425436	−	0.904988i	$-0.360121\pi$
$41$	34.8858			0.850873			0.425436	+	0.904988i	$0.360121\pi$
$42$		0			0
$43$		−	63.2821i		−	1.47168i	−0.677158	−	0.735838i	$-0.736788\pi$
$43$		−	63.2821i		−	1.47168i	0.677158	−	0.735838i	$-0.263212\pi$
$44$	−21.5534	+	55.0205i	−0.489850	+	1.25047i
$45$	13.3397			0.296438
$46$	11.8817	−	62.9061i	0.258297	−	1.36752i
$47$		−	58.0829i		−	1.23581i	−0.786254	−	0.617903i	$-0.787982\pi$
$47$		−	58.0829i		−	1.23581i	0.786254	−	0.617903i	$-0.212018\pi$
$48$	−18.8235	+	20.3390i	−0.392157	+	0.423729i
$49$		0			0
$50$	10.2743	+	1.94061i	0.205487	+	0.0388122i
$51$			3.19089i			0.0625666i
$52$	2.16044	+	0.846319i	0.0415470	+	0.0162754i
$53$	−24.1811			−0.456247			−0.228124	−	0.973632i	$-0.573259\pi$
$53$	−24.1811			−0.456247			−0.228124	+	0.973632i	$0.573259\pi$
$54$	−1.92879	+	10.2117i	−0.0357183	+	0.189106i
$55$		−	65.6886i		−	1.19434i
$56$		0			0
$57$	47.0479			0.825402
$58$	102.347	+	19.3312i	1.76460	+	0.333297i
$59$		−	64.9879i		−	1.10149i	−0.834674	−	0.550745i	$-0.814344\pi$
$59$		−	64.9879i		−	1.10149i	0.834674	−	0.550745i	$-0.185656\pi$
$60$	11.2367	−	28.6844i	0.187278	−	0.478073i
$61$	44.3593			0.727202			0.363601	−	0.931555i	$-0.381547\pi$
$61$	44.3593			0.727202			0.363601	+	0.931555i	$0.381547\pi$
$62$	2.19198	−	11.6052i	0.0353545	−	0.187180i
$63$		0			0
$64$	27.8790	+	57.6087i	0.435609	+	0.900136i
$65$	−2.57934			−0.0396821
$66$	50.2856	+	9.49792i	0.761903	+	0.143908i
$67$			42.3973i			0.632795i	0.948627	+	0.316398i	$0.102473\pi$
$67$			42.3973i			0.632795i	−0.948627	+	0.316398i	$0.897527\pi$
$68$	6.86138	+	2.68784i	0.100903	+	0.0395270i
$69$	−55.4416			−0.803501
$70$		0			0
$71$		−	33.6089i		−	0.473364i	−0.971587	−	0.236682i	$-0.923940\pi$
$71$		−	33.6089i		−	0.473364i	0.971587	−	0.236682i	$-0.0760600\pi$
$72$	20.3336	+	12.7493i	0.282411	+	0.177074i
$73$	−130.569			−1.78862			−0.894308	−	0.447453i	$-0.852331\pi$
$73$	−130.569			−1.78862			−0.894308	+	0.447453i	$0.852331\pi$
$74$	−58.7779	−	11.1019i	−0.794296	−	0.150026i
$75$		−	9.05516i		−	0.120736i
$76$	39.6306	−	101.167i	0.521455	−	1.33115i
$77$		0			0
$78$	0.372946	−	1.97452i	0.00478136	−	0.0253144i
$79$		−	48.7790i		−	0.617456i	−0.951150	−	0.308728i	$-0.900097\pi$
$79$		−	48.7790i		−	0.617456i	0.951150	−	0.308728i	$-0.0999032\pi$
$80$	−52.2149	−	48.3243i	−0.652686	−	0.604054i
$81$	9.00000			0.111111
$82$	−68.5594	−	12.9495i	−0.836090	−	0.157920i
$83$		−	137.835i		−	1.66066i	−0.557271	−	0.830330i	$-0.688152\pi$
$83$		−	137.835i		−	1.66066i	0.557271	−	0.830330i	$-0.311848\pi$
$84$		0			0
$85$	−8.19176			−0.0963736
$86$	−23.4900	+	124.365i	−0.273140	+	1.44611i
$87$		−	90.2022i		−	1.03681i
$88$	62.7812	−	100.129i	0.713423	−	1.13782i
$89$	−116.851			−1.31294			−0.656468	−	0.754354i	$-0.727950\pi$
$89$	−116.851			−1.31294			−0.656468	+	0.754354i	$0.727950\pi$
$90$	−26.2159	−	4.95164i	−0.291288	−	0.0550183i
$91$		0			0
$92$	−46.7010	+	119.216i	−0.507619	+	1.29583i
$93$	−10.2281			−0.109979
$94$	−21.5601	+	114.148i	−0.229363	+	1.21434i
$95$			120.783i			1.27140i
$96$	44.5427	−	32.9840i	0.463987	−	0.343584i
$97$	−133.593			−1.37725			−0.688623	−	0.725120i	$-0.741784\pi$
$97$	−133.593			−1.37725			−0.688623	+	0.725120i	$0.741784\pi$
$98$		0			0
$99$		−	44.3186i		−	0.447663i
$100$	−19.4713	−	7.62758i	−0.194713	−	0.0762758i
$101$	44.7373			0.442944			0.221472	−	0.975167i	$-0.428914\pi$
$101$	44.7373			0.442944			0.221472	+	0.975167i	$0.428914\pi$
$102$	1.18445	−	6.27091i	0.0116122	−	0.0614795i
$103$		−	189.267i		−	1.83755i	−0.394785	−	0.918774i	$-0.629181\pi$
$103$		−	189.267i		−	1.83755i	0.394785	−	0.918774i	$-0.370819\pi$
$104$	−3.93166	−	2.46518i	−0.0378044	−	0.0237036i
$105$		0			0
$106$	47.5219	+	8.97592i	0.448320	+	0.0846785i
$107$		−	167.732i		−	1.56759i	−0.621018	−	0.783796i	$-0.713281\pi$
$107$		−	167.732i		−	1.56759i	0.621018	−	0.783796i	$-0.286719\pi$
$108$	7.58111	−	19.3527i	0.0701955	−	0.179192i
$109$	169.830			1.55807			0.779036	−	0.626979i	$-0.215709\pi$
$109$	169.830			1.55807			0.779036	+	0.626979i	$0.215709\pi$
$110$	−24.3833	+	129.095i	−0.221667	+	1.17359i
$111$			51.8032i			0.466695i
$112$		0			0
$113$	−15.2588			−0.135033			−0.0675167	−	0.997718i	$-0.521508\pi$
$113$	−15.2588			−0.135033			−0.0675167	+	0.997718i	$0.521508\pi$
$114$	−92.4610	−	17.4640i	−0.811061	−	0.153193i
$115$		−	142.331i		−	1.23766i
$116$	−193.962	−	75.9815i	−1.67208	−	0.655013i
$117$	−1.74022			−0.0148737
$118$	−24.1232	+	127.718i	−0.204434	+	1.08235i
$119$		0			0
$120$	−32.7304	+	52.2010i	−0.272753	+	0.435009i
$121$	−97.2377			−0.803618
$122$	−87.1772	−	16.4660i	−0.714567	−	0.134967i
$123$			60.4240i			0.491252i
$124$	−8.61557	+	21.9934i	−0.0694804	+	0.177366i
$125$	134.411			1.07529
$126$		0			0
$127$			79.0861i			0.622725i	0.950291	+	0.311363i	$0.100785\pi$
$127$			79.0861i			0.622725i	−0.950291	+	0.311363i	$0.899215\pi$
$128$	−33.4052	−	123.564i	−0.260978	−	0.965345i
$129$	109.608			0.849673
$130$	5.06905	+	0.957439i	0.0389927	+	0.00736492i
$131$		−	42.9470i		−	0.327840i	−0.986474	−	0.163920i	$-0.947586\pi$
$131$		−	42.9470i		−	0.327840i	0.986474	−	0.163920i	$-0.0524138\pi$
$132$	−95.2983	−	37.3316i	−0.721957	−	0.282815i
$133$		0			0
$134$	15.7377	−	83.3213i	0.117445	−	0.621801i
$135$			23.1051i			0.171149i
$136$	−12.4866	−	7.82919i	−0.0918134	−	0.0575676i
$137$	−120.018			−0.876043			−0.438021	−	0.898965i	$-0.644321\pi$
$137$	−120.018			−0.876043			−0.438021	+	0.898965i	$0.644321\pi$
$138$	108.957	+	20.5797i	0.789541	+	0.149128i
$139$			159.348i			1.14639i	0.819418	+	0.573196i	$0.194297\pi$
$139$			159.348i			1.14639i	−0.819418	+	0.573196i	$0.805703\pi$
$140$		0			0
$141$	100.603			0.713493
$142$	−12.4755	+	66.0499i	−0.0878554	+	0.465140i
$143$			8.56935i			0.0599255i
$144$	−35.2282	−	32.6033i	−0.244640	−	0.226412i
$145$	231.570			1.59703
$146$	256.601	+	48.4666i	1.75754	+	0.331963i
$147$		0			0
$148$	111.392	+	43.6362i	0.752651	+	0.294839i
$149$	−3.71015			−0.0249003			−0.0124502	−	0.999922i	$-0.503963\pi$
$149$	−3.71015			−0.0249003			−0.0124502	+	0.999922i	$0.503963\pi$
$150$	−3.36124	+	17.7957i	−0.0224082	+	0.118638i
$151$			55.4227i			0.367038i	0.983016	+	0.183519i	$0.0587488\pi$
$151$			55.4227i			0.367038i	−0.983016	+	0.183519i	$0.941251\pi$
$152$	−115.437	+	184.108i	−0.759453	+	1.21124i
$153$	−5.52679			−0.0361228
$154$		0			0
$155$		−	26.2578i		−	0.169405i
$156$	−1.46587	+	3.74199i	−0.00939658	+	0.0239871i
$157$	67.8733			0.432314			0.216157	−	0.976359i	$-0.430648\pi$
$157$	67.8733			0.432314			0.216157	+	0.976359i	$0.430648\pi$
$158$	−18.1065	+	95.8630i	−0.114598	+	0.606728i
$159$		−	41.8829i		−	0.263414i
$160$	84.6776	+	114.351i	0.529235	+	0.714696i
$161$		0			0
$162$	−17.6873	−	3.34076i	−0.109181	−	0.0206220i
$163$		−	99.9061i		−	0.612921i	−0.951883	−	0.306460i	$-0.900855\pi$
$163$		−	99.9061i		−	0.612921i	0.951883	−	0.306460i	$-0.0991447\pi$
$164$	129.930	+	50.8979i	0.792254	+	0.310353i
$165$	113.776			0.689552
$166$	−51.1637	+	270.880i	−0.308215	+	1.63181i
$167$			140.330i			0.840299i	0.907455	+	0.420149i	$0.138022\pi$
$167$			140.330i			0.840299i	−0.907455	+	0.420149i	$0.861978\pi$
$168$		0			0
$169$	−168.664			−0.998009
$170$	16.0989	+	3.04074i	0.0946992	+	0.0178867i
$171$			81.4894i			0.476546i
$172$	92.3276	−	235.690i	0.536789	−	1.37029i
$173$	−226.422			−1.30880			−0.654399	−	0.756149i	$-0.727078\pi$
$173$	−226.422			−1.30880			−0.654399	+	0.756149i	$0.727078\pi$
$174$	−33.4827	+	177.270i	−0.192429	+	1.01879i
$175$		0			0
$176$	−160.548	+	173.474i	−0.912206	+	0.985646i
$177$	112.562			0.635945
$178$	229.642	+	43.3747i	1.29012	+	0.243678i
$179$			227.065i			1.26852i	0.773121	+	0.634258i	$0.218694\pi$
$179$			227.065i			1.26852i	−0.773121	+	0.634258i	$0.781306\pi$
$180$	49.6828	+	19.4625i	0.276016	+	0.108125i
$181$	−203.981			−1.12696			−0.563482	−	0.826128i	$-0.690539\pi$
$181$	−203.981			−1.12696			−0.563482	+	0.826128i	$0.690539\pi$
$182$		0			0
$183$			76.8326i			0.419850i
$184$	136.032	−	216.954i	0.739302	−	1.17910i
$185$	−132.991			−0.718869
$186$	20.1007	+	3.79662i	0.108068	+	0.0204119i
$187$			27.2155i			0.145538i
$188$	84.7421	−	216.326i	0.450756	−	1.15067i
$189$		0			0
$190$	44.8340	−	237.369i	0.235969	−	1.24931i
$191$			49.7977i			0.260721i	0.991467	+	0.130360i	$0.0416135\pi$
$191$			49.7977i			0.260721i	−0.991467	+	0.130360i	$0.958387\pi$
$192$	−99.7812	+	48.2878i	−0.519694	+	0.251499i
$193$	−30.2425			−0.156697			−0.0783484	−	0.996926i	$-0.524965\pi$
$193$	−30.2425			−0.156697			−0.0783484	+	0.996926i	$0.524965\pi$
$194$	262.544	+	49.5891i	1.35332	+	0.255614i
$195$		−	4.46754i		−	0.0229105i
$196$		0			0
$197$	294.382			1.49432			0.747162	−	0.664642i	$-0.231416\pi$
$197$	294.382			1.49432			0.747162	+	0.664642i	$0.231416\pi$
$198$	−16.4509	+	87.0972i	−0.0830852	+	0.439885i
$199$			289.112i			1.45283i	0.687259	+	0.726413i	$0.258814\pi$
$199$			289.112i			1.45283i	−0.687259	+	0.726413i	$0.741186\pi$
$200$	35.4347	+	22.2178i	0.177174	+	0.111089i
$201$	−73.4342			−0.365345
$202$	−87.9201	−	16.6063i	−0.435248	−	0.0822094i
$203$		0			0
$204$	−4.65547	+	11.8843i	−0.0228209	+	0.0582562i
$205$	−155.122			−0.756693
$206$	−70.2552	+	371.958i	−0.341045	+	1.80562i
$207$		−	96.0276i		−	0.463902i
$208$	6.81164	+	6.30411i	0.0327483	+	0.0303082i
$209$	401.277			1.91999
$210$		0			0
$211$		−	94.7081i		−	0.448854i	−0.974491	−	0.224427i	$-0.927949\pi$
$211$		−	94.7081i		−	0.448854i	0.974491	−	0.224427i	$-0.0720510\pi$
$212$	−90.0608	−	35.2799i	−0.424815	−	0.166414i
$213$	58.2123			0.273297
$214$	−62.2615	+	329.636i	−0.290942	+	1.54036i
$215$			281.388i			1.30878i
$216$	−22.0824	+	35.2188i	−0.102233	+	0.163050i
$217$		0			0
$218$	−333.758	−	63.0401i	−1.53100	−	0.289175i
$219$		−	226.152i		−	1.03266i
$220$	95.8388	−	244.653i	0.435631	−	1.11206i
$221$	1.06865			0.00483551
$222$	19.2291	−	101.806i	0.0866176	−	0.458587i
$223$			189.481i			0.849689i	0.905266	+	0.424845i	$0.139671\pi$
$223$			189.481i			0.849689i	−0.905266	+	0.424845i	$0.860329\pi$
$224$		0			0
$225$	15.6840			0.0697067
$226$	29.9873	+	5.66399i	0.132687	+	0.0250619i
$227$			41.4861i			0.182758i	0.995816	+	0.0913790i	$0.0291275\pi$
$227$			41.4861i			0.182758i	−0.995816	+	0.0913790i	$0.970873\pi$
$228$	175.227	+	68.6422i	0.768537	+	0.301062i
$229$	392.105			1.71225			0.856124	−	0.516771i	$-0.172866\pi$
$229$	392.105			1.71225			0.856124	+	0.516771i	$0.172866\pi$
$230$	−52.8327	+	279.717i	−0.229708	+	1.21616i
$231$		0			0
$232$	352.980	+	221.320i	1.52146	+	0.953967i
$233$	7.03829			0.0302073			0.0151036	−	0.999886i	$-0.495192\pi$
$233$	7.03829			0.0302073			0.0151036	+	0.999886i	$0.495192\pi$
$234$	3.41997	+	0.645962i	0.0146153	+	0.00276052i
$235$			258.270i			1.09902i
$236$	94.8164	−	242.043i	0.401764	−	1.02560i
$237$	84.4877			0.356488
$238$		0			0
$239$			118.480i			0.495732i	0.968794	+	0.247866i	$0.0797293\pi$
$239$			118.480i			0.495732i	−0.968794	+	0.247866i	$0.920271\pi$
$240$	83.7002	−	90.4388i	0.348751	−	0.376828i
$241$	110.239			0.457425			0.228712	−	0.973494i	$-0.426548\pi$
$241$	110.239			0.457425			0.228712	+	0.973494i	$0.426548\pi$
$242$	191.097	+	36.0942i	0.789655	+	0.149150i
$243$			15.5885i			0.0641500i
$244$	165.213	+	64.7196i	0.677102	+	0.265244i
$245$		0			0
$246$	22.4291	−	118.748i	0.0911752	−	0.482717i
$247$		−	15.7566i		−	0.0637919i
$248$	25.0956	−	40.0245i	0.101192	−	0.161389i
$249$	238.737			0.958783
$250$	−264.151	−	49.8928i	−1.05661	−	0.199571i
$251$		−	26.0919i		−	0.103952i	−0.998648	−	0.0519759i	$-0.983448\pi$
$251$		−	26.0919i		−	0.103952i	0.998648	−	0.0519759i	$-0.0165519\pi$
$252$		0			0
$253$	−472.868			−1.86904
$254$	29.3564	−	155.424i	0.115576	−	0.611906i
$255$		−	14.1885i		−	0.0556413i
$256$	19.7831	+	255.234i	0.0772776	+	0.997010i
$257$	−8.63546			−0.0336010			−0.0168005	−	0.999859i	$-0.505348\pi$
$257$	−8.63546			−0.0336010			−0.0168005	+	0.999859i	$0.505348\pi$
$258$	−215.407	−	40.6859i	−0.834910	−	0.157697i
$259$		0			0
$260$	−9.60656	−	3.76322i	−0.0369483	−	0.0144739i
$261$	156.235			0.598601
$262$	−15.9417	+	84.4016i	−0.0608463	+	0.322144i
$263$		−	138.275i		−	0.525760i	−0.964829	−	0.262880i	$-0.915328\pi$
$263$		−	138.275i		−	0.525760i	0.964829	−	0.262880i	$-0.0846723\pi$
$264$	173.428	+	108.740i	0.656923	+	0.411895i
$265$	107.523			0.405747
$266$		0			0
$267$		−	202.392i		−	0.758024i
$268$	−61.8570	+	157.906i	−0.230810	+	0.589200i
$269$	−361.224			−1.34284			−0.671419	−	0.741078i	$-0.734315\pi$
$269$	−361.224			−1.34284			−0.671419	+	0.741078i	$0.734315\pi$
$270$	8.57650	−	45.4073i	0.0317648	−	0.168175i
$271$			197.285i			0.727989i	0.931401	+	0.363995i	$0.118587\pi$
$271$			197.285i			0.727989i	−0.931401	+	0.363995i	$0.881413\pi$
$272$	21.6332	+	20.0213i	0.0795338	+	0.0736077i
$273$		0			0
$274$	235.865	+	44.5501i	0.860822	+	0.162592i
$275$		−	77.2326i		−	0.280846i
$276$	−206.488	−	80.8885i	−0.748145	−	0.293074i
$277$	−282.947			−1.02147			−0.510734	−	0.859739i	$-0.670626\pi$
$277$	−282.947			−1.02147			−0.510734	+	0.859739i	$0.670626\pi$
$278$	59.1494	−	313.160i	0.212768	−	1.12647i
$279$		−	17.7155i		−	0.0634966i
$280$		0			0
$281$	−232.341			−0.826836			−0.413418	−	0.910541i	$-0.635665\pi$
$281$	−232.341			−0.826836			−0.413418	+	0.910541i	$0.635665\pi$
$282$	−197.709	−	37.3432i	−0.701097	−	0.132423i
$283$		−	347.649i		−	1.22844i	−0.789134	−	0.614222i	$-0.789470\pi$
$283$		−	347.649i		−	1.22844i	0.789134	−	0.614222i	$-0.210530\pi$
$284$	49.0348	−	125.174i	0.172658	−	0.440753i
$285$	−209.202			−0.734042
$286$	3.18091	−	16.8409i	0.0111220	−	0.0588844i
$287$		0			0
$288$	57.1300	+	77.1503i	0.198368	+	0.267883i
$289$	−285.606			−0.988256
$290$	−455.093	−	85.9577i	−1.56929	−	0.296406i
$291$		−	231.390i		−	0.795153i
$292$	−486.294	−	190.498i	−1.66539	−	0.652391i
$293$	−207.320			−0.707576			−0.353788	−	0.935326i	$-0.615107\pi$
$293$	−207.320			−0.707576			−0.353788	+	0.935326i	$0.615107\pi$
$294$		0			0
$295$			288.973i			0.979570i
$296$	−202.716	−	127.104i	−0.684853	−	0.429407i
$297$	76.7621			0.258458
$298$	7.29138	+	1.37719i	0.0244677	+	0.00462145i
$299$			18.5677i			0.0620993i
$300$	13.2114	−	33.7253i	0.0440378	−	0.112418i
$301$		0			0
$302$	20.5727	−	108.920i	0.0681214	−	0.360661i
$303$			77.4873i			0.255734i
$304$	295.203	−	318.969i	0.971061	−	1.04924i
$305$	−197.247			−0.646711
$306$	10.8615	+	2.05152i	0.0354952	+	0.00670432i
$307$		−	249.900i		−	0.814006i	−0.913427	−	0.407003i	$-0.866574\pi$
$307$		−	249.900i		−	0.814006i	0.913427	−	0.407003i	$-0.133426\pi$
$308$		0			0
$309$	327.821			1.06091
$310$	−9.74679	+	51.6032i	−0.0314412	+	0.166462i
$311$			257.172i			0.826921i	0.910522	+	0.413460i	$0.135680\pi$
$311$			257.172i			0.826921i	−0.910522	+	0.413460i	$0.864320\pi$
$312$	4.26981	−	6.80984i	0.0136853	−	0.0218264i
$313$	−125.903			−0.402245			−0.201123	−	0.979566i	$-0.564459\pi$
$313$	−125.903			−0.402245			−0.201123	+	0.979566i	$0.564459\pi$
$314$	−133.388	−	25.1943i	−0.424803	−	0.0802366i
$315$		0			0
$316$	71.1678	−	181.674i	0.225215	−	0.574917i
$317$	127.002			0.400638			0.200319	−	0.979731i	$-0.435802\pi$
$317$	127.002			0.400638			0.200319	+	0.979731i	$0.435802\pi$
$318$	−15.5467	+	82.3104i	−0.0488891	+	0.258838i
$319$		−	769.346i		−	2.41174i
$320$	−123.966	−	256.161i	−0.387394	−	0.800504i
$321$	290.521			0.905050
$322$		0			0
$323$		−	50.0416i		−	0.154928i
$324$	33.5198	+	13.1309i	0.103456	+	0.0405274i
$325$	−3.03262			−0.00933115
$326$	−37.0847	+	196.341i	−0.113757	+	0.602272i
$327$			294.154i			0.899554i
$328$	−236.451	−	148.256i	−0.720888	−	0.452001i
$329$		0			0
$330$	−223.599	−	42.2332i	−0.677571	−	0.127979i
$331$			535.736i			1.61854i	0.587438	+	0.809269i	$0.300137\pi$
$331$			535.736i			1.61854i	−0.587438	+	0.809269i	$0.699863\pi$
$332$	201.099	−	513.356i	0.605720	−	1.54625i
$333$	−89.7258			−0.269447
$334$	52.0898	−	275.784i	0.155958	−	0.825699i
$335$		−	188.523i		−	0.562754i
$336$		0			0
$337$	123.246			0.365715			0.182858	−	0.983139i	$-0.441465\pi$
$337$	123.246			0.365715			0.182858	+	0.983139i	$0.441465\pi$
$338$	331.466	+	62.6072i	0.980669	+	0.185228i
$339$		−	26.4290i		−	0.0779615i
$340$	−30.5096	−	11.9517i	−0.0897341	−	0.0351519i
$341$	−87.2365			−0.255826
$342$	30.2485	−	160.147i	0.0884459	−	0.468266i
$343$		0			0
$344$	−268.934	+	428.918i	−0.781785	+	1.24685i
$345$	246.525			0.714565
$346$	444.976	+	84.0469i	1.28606	+	0.242910i
$347$		−	590.358i		−	1.70132i	−0.525717	−	0.850659i	$-0.676203\pi$
$347$		−	590.358i		−	1.70132i	0.525717	−	0.850659i	$-0.323797\pi$
$348$	131.604	−	335.952i	0.378172	−	0.965378i
$349$	−553.502			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$349$	−553.502			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$350$		0			0
$351$		−	3.01415i		−	0.00858732i
$352$	379.910	−	281.325i	1.07929	−	0.799218i
$353$	271.205			0.768286			0.384143	−	0.923274i	$-0.374497\pi$
$353$	271.205			0.768286			0.384143	+	0.923274i	$0.374497\pi$
$354$	−221.213	−	41.7826i	−0.624896	−	0.118030i
$355$			149.444i			0.420970i
$356$	−435.204	−	170.484i	−1.22248	−	0.478889i
$357$		0			0
$358$	84.2854	−	446.239i	0.235434	−	1.24648i
$359$			405.543i			1.12965i	0.825212	+	0.564823i	$0.191055\pi$
$359$			405.543i			1.12965i	−0.825212	+	0.564823i	$0.808945\pi$
$360$	−90.4148	−	56.6906i	−0.251152	−	0.157474i
$361$	−376.835			−1.04386
$362$	400.873	+	75.7167i	1.10738	+	0.209162i
$363$		−	168.421i		−	0.463969i
$364$		0			0
$365$	580.584			1.59064
$366$	28.5199	−	150.995i	0.0779233	−	0.412556i
$367$			33.2577i			0.0906204i	0.998973	+	0.0453102i	$0.0144276\pi$
$367$			33.2577i			0.0906204i	−0.998973	+	0.0453102i	$0.985572\pi$
$368$	−347.869	+	375.875i	−0.945296	+	1.02140i
$369$	−104.657			−0.283624
$370$	261.360	+	49.3656i	0.706379	+	0.133420i
$371$		0			0
$372$	−38.0937	−	14.9226i	−0.102402	−	0.0401146i
$373$	−311.937			−0.836292			−0.418146	−	0.908380i	$-0.637320\pi$
$373$	−311.937			−0.836292			−0.418146	+	0.908380i	$0.637320\pi$
$374$	10.1023	−	53.4854i	0.0270115	−	0.143009i
$375$			232.807i			0.620818i
$376$	−246.839	+	393.678i	−0.656486	+	1.04702i
$377$	−30.2092			−0.0801306
$378$		0			0
$379$			339.175i			0.894921i	0.894304	+	0.447461i	$0.147672\pi$
$379$			339.175i			0.894921i	−0.894304	+	0.447461i	$0.852328\pi$
$380$	−176.220	+	449.847i	−0.463738	+	1.18381i
$381$	−136.981			−0.359531
$382$	18.4847	−	97.8650i	0.0483892	−	0.256191i
$383$			18.1397i			0.0473622i	0.999720	+	0.0236811i	$0.00753863\pi$
$383$			18.1397i			0.0473622i	−0.999720	+	0.0236811i	$0.992461\pi$
$384$	214.019	−	57.8594i	0.557342	−	0.150676i
$385$		0			0
$386$	59.4341	+	11.2259i	0.153974	+	0.0290826i
$387$			189.846i			0.490559i
$388$	−497.557	−	194.910i	−1.28236	−	0.502345i
$389$	6.54448			0.0168239			0.00841193	−	0.999965i	$-0.497322\pi$
$389$	6.54448			0.0168239			0.00841193	+	0.999965i	$0.497322\pi$
$390$	−1.65833	+	8.77985i	−0.00425214	+	0.0225124i
$391$			58.9694i			0.150817i
$392$		0			0
$393$	74.3863			0.189278
$394$	−578.535	−	109.273i	−1.46836	−	0.277343i
$395$			216.899i			0.549112i
$396$	64.6602	−	165.061i	0.163283	−	0.416822i
$397$	619.101			1.55945			0.779724	−	0.626124i	$-0.215360\pi$
$397$	619.101			1.55945			0.779724	+	0.626124i	$0.215360\pi$
$398$	107.317	−	568.178i	0.269641	−	1.42758i
$399$		0			0
$400$	−61.3910	−	56.8167i	−0.153477	−	0.142042i
$401$	342.787			0.854830			0.427415	−	0.904056i	$-0.359424\pi$
$401$	342.787			0.854830			0.427415	+	0.904056i	$0.359424\pi$
$402$	144.317	+	27.2585i	0.358997	+	0.0678071i
$403$			3.42544i			0.00849985i
$404$	166.621	+	65.2711i	0.412428	+	0.161562i
$405$	−40.0191			−0.0988127
$406$		0			0
$407$			441.836i			1.08559i
$408$	13.5606	−	21.6275i	0.0332366	−	0.0530085i
$409$	−497.138			−1.21550			−0.607749	−	0.794129i	$-0.707927\pi$
$409$	−497.138			−1.21550			−0.607749	+	0.794129i	$0.707927\pi$
$410$	304.854	+	57.5807i	0.743547	+	0.140441i
$411$		−	207.877i		−	0.505784i
$412$	276.138	−	704.913i	0.670239	−	1.71095i
$413$		0			0
$414$	−35.6450	+	188.718i	−0.0860991	+	0.455842i
$415$			612.892i			1.47685i
$416$	−11.0465	−	14.9176i	−0.0265542	−	0.0358596i
$417$	−276.000			−0.661870
$418$	−788.611	−	148.952i	−1.88663	−	0.356345i
$419$		−	20.5194i		−	0.0489723i	−0.999700	−	0.0244861i	$-0.992205\pi$
$419$		−	20.5194i		−	0.0489723i	0.999700	−	0.0244861i	$-0.00779496\pi$
$420$		0			0
$421$	−628.679			−1.49330			−0.746650	−	0.665217i	$-0.768339\pi$
$421$	−628.679			−1.49330			−0.746650	+	0.665217i	$0.768339\pi$
$422$	−35.1552	+	186.125i	−0.0833063	+	0.441055i
$423$			174.249i			0.411936i
$424$	163.896	+	102.764i	0.386548	+	0.242368i
$425$	−9.63136			−0.0226620
$426$	−114.402	−	21.6081i	−0.268549	−	0.0507233i
$427$		0			0
$428$	244.719	−	624.707i	0.571774	−	1.45960i
$429$	−14.8426			−0.0345980
$430$	104.450	−	552.999i	0.242907	−	1.28604i
$431$		−	843.895i		−	1.95799i	−0.203876	−	0.978997i	$-0.565354\pi$
$431$		−	843.895i		−	1.95799i	0.203876	−	0.978997i	$-0.434646\pi$
$432$	56.4706	−	61.0170i	0.130719	−	0.141243i
$433$	−478.239			−1.10448			−0.552239	−	0.833686i	$-0.686226\pi$
$433$	−478.239			−1.10448			−0.552239	+	0.833686i	$0.686226\pi$
$434$		0			0
$435$			401.091i			0.922047i
$436$	632.519	+	247.779i	1.45073	+	0.568301i
$437$	869.470			1.98963
$438$	−83.9466	+	444.446i	−0.191659	+	1.01472i
$439$			299.816i			0.682953i	0.939890	+	0.341477i	$0.110927\pi$
$439$			299.816i			0.682953i	−0.939890	+	0.341477i	$0.889073\pi$
$440$	−279.161	+	445.229i	−0.634457	+	1.01188i
$441$		0			0
$442$	−2.10016	−	0.396678i	−0.00475150	−	0.000897461i
$443$			141.174i			0.318678i	0.987224	+	0.159339i	$0.0509363\pi$
$443$			141.174i			0.318678i	−0.987224	+	0.159339i	$0.949064\pi$
$444$	−75.5801	+	192.937i	−0.170225	+	0.434543i
$445$	519.588			1.16761
$446$	70.3344	−	372.377i	0.157700	−	0.834927i
$447$		−	6.42617i		−	0.0143762i
$448$		0			0
$449$	−9.59195			−0.0213629			−0.0106815	−	0.999943i	$-0.503400\pi$
$449$	−9.59195			−0.0213629			−0.0106815	+	0.999943i	$0.503400\pi$
$450$	−30.8230	−	5.82183i	−0.0684956	−	0.0129374i
$451$			515.363i			1.14271i
$452$	−56.8302	−	22.2623i	−0.125730	−	0.0492529i
$453$	−95.9949			−0.211909
$454$	15.3994	−	81.5305i	0.0339195	−	0.179583i
$455$		0			0
$456$	−318.885	−	199.943i	−0.699308	−	0.438470i
$457$	140.950			0.308426			0.154213	−	0.988038i	$-0.450716\pi$
$457$	140.950			0.308426			0.154213	+	0.988038i	$0.450716\pi$
$458$	−770.584	−	145.548i	−1.68250	−	0.317789i
$459$		−	9.57268i		−	0.0208555i
$460$	207.659	−	530.102i	0.451433	−	1.15240i
$461$	77.7365			0.168626			0.0843129	−	0.996439i	$-0.473130\pi$
$461$	77.7365			0.168626			0.0843129	+	0.996439i	$0.473130\pi$
$462$		0			0
$463$		−	396.222i		−	0.855771i	−0.903833	−	0.427886i	$-0.859259\pi$
$463$		−	396.222i		−	0.855771i	0.903833	−	0.427886i	$-0.140741\pi$
$464$	−611.541	−	565.975i	−1.31798	−	1.21977i
$465$	45.4799			0.0978062
$466$	−13.8320	−	2.61258i	−0.0296824	−	0.00560640i
$467$		−	358.771i		−	0.768247i	−0.923282	−	0.384123i	$-0.874504\pi$
$467$		−	358.771i		−	0.768247i	0.923282	−	0.384123i	$-0.125496\pi$
$468$	−6.48132	−	2.53896i	−0.0138490	−	0.00542512i
$469$		0			0
$470$	95.8686	−	507.565i	0.203976	−	1.07993i
$471$			117.560i			0.249597i
$472$	−276.183	+	440.479i	−0.585134	+	0.933219i
$473$	934.858			1.97644
$474$	−166.040	−	31.3615i	−0.350294	−	0.0661634i
$475$			142.009i			0.298966i
$476$		0			0
$477$	72.5433			0.152082
$478$	43.9793	−	232.843i	0.0920068	−	0.487119i
$479$		−	175.970i		−	0.367369i	−0.982985	−	0.183684i	$-0.941198\pi$
$479$		−	175.970i		−	0.367369i	0.982985	−	0.183684i	$-0.0588024\pi$
$480$	−198.062	+	146.666i	−0.412630	+	0.305554i
$481$	17.3492			0.0360690
$482$	−216.648	−	40.9204i	−0.449478	−	0.0848971i
$483$		0			0
$484$	−362.155	−	141.868i	−0.748254	−	0.293117i
$485$	594.030			1.22480
$486$	5.78637	−	30.6352i	0.0119061	−	0.0630355i
$487$		−	356.695i		−	0.732434i	−0.930529	−	0.366217i	$-0.880653\pi$
$487$		−	356.695i		−	0.732434i	0.930529	−	0.366217i	$-0.119347\pi$
$488$	−300.662	−	188.517i	−0.616110	−	0.386304i
$489$	173.042			0.353870
$490$		0			0
$491$		−	826.372i		−	1.68304i	−0.540227	−	0.841519i	$-0.681662\pi$
$491$		−	826.372i		−	1.68304i	0.540227	−	0.841519i	$-0.318338\pi$
$492$	−88.1577	+	225.045i	−0.179182	+	0.457408i
$493$	−95.9419			−0.194608
$494$	−5.84878	+	30.9657i	−0.0118396	+	0.0626836i
$495$			197.066i			0.398113i
$496$	−64.1762	+	69.3429i	−0.129387	+	0.139804i
$497$		0			0
$498$	−469.178	−	88.6181i	−0.942125	−	0.177948i
$499$		−	114.303i		−	0.229064i	−0.993420	−	0.114532i	$-0.963463\pi$
$499$		−	114.303i		−	0.229064i	0.993420	−	0.114532i	$-0.0365369\pi$
$500$	500.604	+	196.104i	1.00121	+	0.392207i
$501$	−243.058			−0.485147
$502$	−9.68520	+	51.2772i	−0.0192932	+	0.102146i
$503$		−	76.9798i		−	0.153041i	−0.997068	−	0.0765207i	$-0.975619\pi$
$503$		−	76.9798i		−	0.153041i	0.997068	−	0.0765207i	$-0.0243811\pi$
$504$		0			0
$505$	−198.928			−0.393916
$506$	929.304	+	175.526i	1.83657	+	0.346890i
$507$		−	292.134i		−	0.576201i
$508$	−115.385	+	294.551i	−0.227137	+	0.579824i
$509$	13.7617			0.0270367			0.0135183	−	0.999909i	$-0.495697\pi$
$509$	13.7617			0.0270367			0.0135183	+	0.999909i	$0.495697\pi$
$510$	−5.26672	+	27.8841i	−0.0103269	+	0.0546746i
$511$		0			0
$512$	55.8632	−	508.943i	0.109108	−	0.994030i
$513$	−141.144			−0.275134
$514$	16.9709	+	3.20545i	0.0330172	+	0.00623628i
$515$			841.591i			1.63416i
$516$	408.226	+	159.916i	0.791136	+	0.309915i
$517$	858.052			1.65967
$518$		0			0
$519$		−	392.174i		−	0.755635i
$520$	17.4824	+	10.9616i	0.0336200	+	0.0210800i
$521$	332.169			0.637561			0.318781	−	0.947829i	$-0.396727\pi$
$521$	332.169			0.637561			0.318781	+	0.947829i	$0.396727\pi$
$522$	−307.041	−	57.9937i	−0.588201	−	0.111099i
$523$		−	999.341i		−	1.91079i	−0.295337	−	0.955393i	$-0.595432\pi$
$523$		−	999.341i		−	1.91079i	0.295337	−	0.955393i	$-0.404568\pi$
$524$	62.6590	−	159.953i	0.119578	−	0.305254i
$525$		0			0
$526$	−51.3270	+	271.745i	−0.0975799	+	0.516625i
$527$			10.8789i			0.0206431i
$528$	−300.465	−	278.078i	−0.569063	−	0.526662i
$529$	−495.589			−0.936842
$530$	−211.310	−	39.9121i	−0.398698	−	0.0753058i
$531$			194.964i			0.367163i
$532$		0			0
$533$	20.2363			0.0379668
$534$	−75.1271	+	397.752i	−0.140688	+	0.744854i
$535$			745.834i			1.39408i
$536$	180.178	−	287.363i	0.336154	−	0.536125i
$537$	−393.287			−0.732379
$538$	709.895	+	134.085i	1.31951	+	0.249228i
$539$		0			0
$540$	−33.7100	+	86.0531i	−0.0624258	+	0.159358i
$541$	267.767			0.494948			0.247474	−	0.968895i	$-0.420399\pi$
$541$	267.767			0.494948			0.247474	+	0.968895i	$0.420399\pi$
$542$	73.2314	−	387.715i	0.135113	−	0.715341i
$543$		−	353.305i		−	0.650653i
$544$	−35.0828	−	47.3770i	−0.0644905	−	0.0870902i
$545$	−755.161			−1.38562
$546$		0			0
$547$			43.0970i			0.0787879i	0.999224	+	0.0393940i	$0.0125427\pi$
$547$			43.0970i			0.0787879i	−0.999224	+	0.0393940i	$0.987457\pi$
$548$	−446.998	−	175.104i	−0.815690	−	0.319533i
$549$	−133.078			−0.242401
$550$	−28.6684	+	151.781i	−0.0521244	+	0.275966i
$551$			1414.61i			2.56735i
$552$	375.776	+	235.614i	0.680753	+	0.426836i
$553$		0			0
$554$	556.061	+	105.029i	1.00372	+	0.189582i
$555$		−	230.347i		−	0.415039i
$556$	−232.487	+	593.482i	−0.418142	+	1.06741i
$557$	592.394			1.06354			0.531772	−	0.846887i	$-0.321526\pi$
$557$	592.394			1.06354			0.531772	+	0.846887i	$0.321526\pi$
$558$	−6.57593	+	34.8155i	−0.0117848	+	0.0623934i
$559$		−	36.7083i		−	0.0656677i
$560$		0			0
$561$	−47.1387			−0.0840262
$562$	456.608	+	86.2439i	0.812470	+	0.153459i
$563$		−	763.753i		−	1.35658i	−0.734796	−	0.678288i	$-0.762722\pi$
$563$		−	763.753i		−	1.35658i	0.734796	−	0.678288i	$-0.237278\pi$
$564$	374.687	+	146.778i	0.664339	+	0.260244i
$565$	67.8492			0.120087
$566$	−129.046	+	683.219i	−0.227996	+	1.20710i
$567$		0			0
$568$	−142.830	+	227.796i	−0.251461	+	0.401050i
$569$	−336.581			−0.591530			−0.295765	−	0.955261i	$-0.595575\pi$
$569$	−336.581			−0.591530			−0.295765	+	0.955261i	$0.595575\pi$
$570$	411.134	+	77.6548i	0.721288	+	0.136237i
$571$			599.028i			1.04909i	0.851384	+	0.524543i	$0.175764\pi$
$571$			599.028i			1.04909i	−0.851384	+	0.524543i	$0.824236\pi$
$572$	−12.5026	+	31.9159i	−0.0218576	+	0.0557971i
$573$	−86.2522			−0.150527
$574$		0			0
$575$		−	167.344i		−	0.291033i
$576$	−83.6370	−	172.826i	−0.145203	−	0.300045i
$577$	−1038.35			−1.79957			−0.899785	−	0.436333i	$-0.856277\pi$
$577$	−1038.35			−1.79957			−0.899785	+	0.436333i	$0.856277\pi$
$578$	561.288	+	106.016i	0.971086	+	0.183418i
$579$		−	52.3815i		−	0.0904689i
$580$	862.465	+	337.857i	1.48701	+	0.582512i
$581$		0			0
$582$	−85.8908	+	454.739i	−0.147579	+	0.781338i
$583$		−	357.224i		−	0.612735i
$584$	884.979	+	554.887i	1.51537	+	0.950149i
$585$	7.73801			0.0132274
$586$	407.435	+	76.9562i	0.695282	+	0.131325i
$587$			753.468i			1.28359i	0.766876	+	0.641796i	$0.221810\pi$
$587$			753.468i			1.28359i	−0.766876	+	0.641796i	$0.778190\pi$
$588$		0			0
$589$	160.403			0.272331
$590$	107.266	−	567.905i	0.181806	−	0.962551i
$591$			509.885i			0.862749i
$592$	351.208	+	325.040i	0.593257	+	0.549054i
$593$	323.430			0.545412			0.272706	−	0.962097i	$-0.412081\pi$
$593$	323.430			0.545412			0.272706	+	0.962097i	$0.412081\pi$
$594$	−150.857	−	28.4938i	−0.253968	−	0.0479693i
$595$		0			0
$596$	−13.8182	−	5.41306i	−0.0231849	−	0.00908231i
$597$	−500.757			−0.838789
$598$	6.89225	−	36.4902i	0.0115255	−	0.0610204i
$599$		−	519.116i		−	0.866638i	−0.901241	−	0.433319i	$-0.857342\pi$
$599$		−	519.116i		−	0.866638i	0.901241	−	0.433319i	$-0.142658\pi$
$600$	−38.4823	+	61.3747i	−0.0641372	+	0.102291i
$601$	70.0467			0.116550			0.0582752	−	0.998301i	$-0.481440\pi$
$601$	70.0467			0.116550			0.0582752	+	0.998301i	$0.481440\pi$
$602$		0			0
$603$		−	127.192i		−	0.210932i
$604$	−80.8609	+	206.418i	−0.133876	+	0.341751i
$605$	432.375			0.714669
$606$	28.7630	−	152.282i	0.0474636	−	0.251291i
$607$			930.701i			1.53328i	0.642077	+	0.766640i	$0.278073\pi$
$607$			930.701i			1.53328i	−0.642077	+	0.766640i	$0.721927\pi$
$608$	−698.547	+	517.276i	−1.14893	+	0.850784i
$609$		0			0
$610$	387.640	+	73.2171i	0.635475	+	0.120028i
$611$		−	33.6924i		−	0.0551430i
$612$	−20.5841	−	8.06351i	−0.0336342	−	0.0131757i
$613$	−353.932			−0.577377			−0.288688	−	0.957423i	$-0.593219\pi$
$613$	−353.932			−0.577377			−0.288688	+	0.957423i	$0.593219\pi$
$614$	−92.7618	+	491.116i	−0.151078	+	0.799864i
$615$		−	268.679i		−	0.436877i
$616$		0			0
$617$	302.934			0.490979			0.245490	−	0.969399i	$-0.421051\pi$
$617$	302.934			0.490979			0.245490	+	0.969399i	$0.421051\pi$
$618$	−644.250	−	121.686i	−1.04248	−	0.196902i
$619$		−	176.432i		−	0.285028i	−0.989793	−	0.142514i	$-0.954481\pi$
$619$		−	176.432i		−	0.285028i	0.989793	−	0.142514i	$-0.0455186\pi$
$620$	38.3098	−	97.7953i	0.0617900	−	0.157734i
$621$	166.325			0.267834
$622$	95.4613	−	505.409i	0.153475	−	0.812554i
$623$		0			0
$624$	−10.9190	+	11.7981i	−0.0174984	+	0.0189072i
$625$	−466.968			−0.747149
$626$	247.431	+	46.7346i	0.395257	+	0.0746558i
$627$			695.033i			1.10851i
$628$	252.789	+	99.0262i	0.402531	+	0.157685i
$629$	55.0995			0.0875986
$630$		0			0
$631$			348.007i			0.551516i	0.961227	+	0.275758i	$0.0889288\pi$
$631$			348.007i			0.551516i	−0.961227	+	0.275758i	$0.911071\pi$
$632$	−207.299	+	330.618i	−0.328005	+	0.523129i
$633$	164.039			0.259146
$634$	−249.591	−	47.1426i	−0.393677	−	0.0743575i
$635$		−	351.662i		−	0.553799i
$636$	61.1065	−	155.990i	0.0960795	−	0.245267i
$637$		0			0
$638$	−285.578	+	1511.96i	−0.447614	+	2.36984i
$639$			100.827i			0.157788i
$640$	148.538	+	549.437i	0.232091	+	0.858495i
$641$	−526.352			−0.821141			−0.410571	−	0.911829i	$-0.634670\pi$
$641$	−526.352			−0.821141			−0.410571	+	0.911829i	$0.634670\pi$
$642$	−570.947	−	107.840i	−0.889325	−	0.167975i
$643$		−	801.421i		−	1.24638i	−0.782071	−	0.623189i	$-0.785837\pi$
$643$		−	801.421i		−	1.24638i	0.782071	−	0.623189i	$-0.214163\pi$
$644$		0			0
$645$	−487.379			−0.755626
$646$	−18.5752	+	98.3444i	−0.0287542	+	0.152236i
$647$		−	98.8731i		−	0.152818i	−0.997077	−	0.0764089i	$-0.975655\pi$
$647$		−	98.8731i		−	0.152818i	0.997077	−	0.0764089i	$-0.0243454\pi$
$648$	−61.0008	−	38.2479i	−0.0941371	−	0.0590245i
$649$	960.058			1.47929
$650$	5.95987	+	1.12570i	0.00916903	+	0.00173184i
$651$		0			0
$652$	145.762	−	372.093i	0.223561	−	0.570695i
$653$	−224.973			−0.344523			−0.172261	−	0.985051i	$-0.555107\pi$
$653$	−224.973			−0.344523			−0.172261	+	0.985051i	$0.555107\pi$
$654$	109.189	−	578.087i	0.166955	−	0.883925i
$655$			190.967i			0.291552i
$656$	409.654	+	379.131i	0.624473	+	0.577943i
$657$	391.707			0.596205
$658$		0			0
$659$			372.583i			0.565376i	0.959212	+	0.282688i	$0.0912260\pi$
$659$			372.583i			0.565376i	−0.959212	+	0.282688i	$0.908774\pi$
$660$	423.751	+	165.998i	0.642046	+	0.251512i
$661$	571.609			0.864764			0.432382	−	0.901691i	$-0.357673\pi$
$661$	571.609			0.864764			0.432382	+	0.901691i	$0.357673\pi$
$662$	198.863	−	1052.86i	0.300397	−	1.59042i
$663$			1.85095i			0.00279178i
$664$	−585.766	+	934.226i	−0.882177	+	1.40697i
$665$		0			0
$666$	176.334	+	33.3058i	0.264765	+	0.0500087i
$667$		−	1666.98i		−	2.49923i
$668$	−204.739	+	522.649i	−0.306496	+	0.782408i
$669$	−328.190			−0.490568
$670$	−69.9787	+	370.494i	−0.104446	+	0.552976i
$671$			655.314i			0.976623i
$672$		0			0
$673$	389.233			0.578355			0.289177	−	0.957276i	$-0.406618\pi$
$673$	389.233			0.578355			0.289177	+	0.957276i	$0.406618\pi$
$674$	−242.210	−	45.7484i	−0.359361	−	0.0678760i
$675$			27.1655i			0.0402452i
$676$	−628.175	−	246.078i	−0.929253	−	0.364020i
$677$	−831.064			−1.22757			−0.613784	−	0.789474i	$-0.710354\pi$
$677$	−831.064			−1.22757			−0.613784	+	0.789474i	$0.710354\pi$
$678$	−9.81031	+	51.9396i	−0.0144695	+	0.0766070i
$679$		0			0
$680$	55.5227	+	34.8130i	0.0816510	+	0.0511957i
$681$	−71.8559			−0.105515
$682$	171.442	+	32.3818i	0.251381	+	0.0474807i
$683$			1146.27i			1.67828i	0.543915	+	0.839141i	$0.316942\pi$
$683$			1146.27i			1.67828i	−0.543915	+	0.839141i	$0.683058\pi$
$684$	−118.892	+	303.501i	−0.173818	+	0.443715i
$685$	533.668			0.779077
$686$		0			0
$687$			679.145i			0.988567i
$688$	687.735	−	743.104i	0.999615	−	1.08009i
$689$	−14.0268			−0.0203582
$690$	−484.483	−	91.5090i	−0.702150	−	0.132622i
$691$		−	604.353i		−	0.874607i	−0.899314	−	0.437303i	$-0.855934\pi$
$691$		−	604.353i		−	0.874607i	0.899314	−	0.437303i	$-0.144066\pi$
$692$	−843.292	−	330.346i	−1.21863	−	0.477379i
$693$		0			0
$694$	−219.138	+	1160.20i	−0.315761	+	1.67176i
$695$		−	708.554i		−	1.01950i
$696$	−383.338	+	611.379i	−0.550773	+	0.878418i
$697$	64.2688			0.0922078
$698$	1087.77	+	205.457i	1.55841	+	0.294352i
$699$			12.1907i			0.0174402i
$700$		0			0
$701$	136.164			0.194243			0.0971214	−	0.995273i	$-0.469037\pi$
$701$	136.164			0.194243			0.0971214	+	0.995273i	$0.469037\pi$
$702$	−1.11884	+	5.92356i	−0.00159379	+	0.00843812i
$703$		−	812.411i		−	1.15563i
$704$	−851.046	+	411.853i	−1.20887	+	0.585018i
$705$	−447.337			−0.634520
$706$	−532.986	−	100.670i	−0.754938	−	0.142592i
$707$		0			0
$708$	419.230	+	164.227i	0.592133	+	0.231959i
$709$	660.285			0.931291			0.465645	−	0.884971i	$-0.345822\pi$
$709$	660.285			0.931291			0.465645	+	0.884971i	$0.345822\pi$
$710$	55.4730	−	293.696i	0.0781310	−	0.413656i
$711$			146.337i			0.205819i
$712$	792.003	+	496.590i	1.11236	+	0.697458i
$713$	−189.020			−0.265105
$714$		0			0
$715$		−	38.1042i		−	0.0532926i
$716$	−331.284	+	845.685i	−0.462687	+	1.18112i
$717$	−205.213			−0.286211
$718$	150.536	−	796.993i	0.209660	−	1.11002i
$719$		−	820.759i		−	1.14153i	−0.821114	−	0.570764i	$-0.806647\pi$
$719$		−	820.759i		−	1.14153i	0.821114	−	0.570764i	$-0.193353\pi$
$720$	156.645	+	144.973i	0.217562	+	0.201351i
$721$		0			0
$722$	740.576	+	139.880i	1.02573	+	0.193739i
$723$			190.940i			0.264094i
$724$	−759.711	−	297.605i	−1.04932	−	0.411056i
$725$	272.265			0.375538
$726$	−62.5170	+	330.989i	−0.0861116	+	0.455908i
$727$			242.765i			0.333928i	0.985963	+	0.166964i	$0.0533963\pi$
$727$			242.765i			0.333928i	−0.985963	+	0.166964i	$0.946604\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−1140.99	−	215.510i	−1.56300	−	0.295219i
$731$		−	116.582i		−	0.159483i
$732$	−112.098	+	286.157i	−0.153139	+	0.390925i
$733$	−1104.69			−1.50708			−0.753541	−	0.657400i	$-0.771656\pi$
$733$	−1104.69			−1.50708			−0.753541	+	0.657400i	$0.771656\pi$
$734$	12.3451	−	65.3597i	0.0168189	−	0.0890459i
$735$		0			0
$736$	823.173	−	609.562i	1.11844	−	0.828209i
$737$	−626.330			−0.849837
$738$	205.678	+	38.8484i	0.278697	+	0.0526400i
$739$			442.727i			0.599089i	0.954082	+	0.299545i	$0.0968347\pi$
$739$			442.727i			0.599089i	−0.954082	+	0.299545i	$0.903165\pi$
$740$	−495.314	−	194.031i	−0.669343	−	0.262205i
$741$	27.2912			0.0368303
$742$		0			0
$743$			235.734i			0.317274i	0.987337	+	0.158637i	$0.0507099\pi$
$743$			235.734i			0.317274i	−0.987337	+	0.158637i	$0.949290\pi$
$744$	69.3245	+	43.4669i	0.0931782	+	0.0584233i
$745$	16.4975			0.0221442
$746$	613.034	+	115.790i	0.821762	+	0.155214i
$747$			413.505i			0.553554i
$748$	−39.7071	+	101.362i	−0.0530843	+	0.135511i
$749$		0			0
$750$	86.4168	−	457.524i	0.115222	−	0.610031i
$751$			216.209i			0.287895i	0.989585	+	0.143948i	$0.0459797\pi$
$751$			216.209i			0.287895i	−0.989585	+	0.143948i	$0.954020\pi$
$752$	631.232	−	682.052i	0.839404	−	0.906984i
$753$	45.1925			0.0600166
$754$	59.3687	+	11.2135i	0.0787384	+	0.0148721i
$755$		−	246.441i		−	0.326412i
$756$		0			0
$757$	−750.692			−0.991667			−0.495834	−	0.868418i	$-0.665137\pi$
$757$	−750.692			−0.991667			−0.495834	+	0.868418i	$0.665137\pi$
$758$	125.900	−	666.565i	0.166095	−	0.879373i
$759$		−	819.031i		−	1.07909i
$760$	513.298	−	818.650i	0.675393	−	1.07717i
$761$	951.226			1.24997			0.624984	−	0.780637i	$-0.285105\pi$
$761$	951.226			1.24997			0.624984	+	0.780637i	$0.285105\pi$
$762$	269.202	+	50.8468i	0.353284	+	0.0667281i
$763$		0			0
$764$	−72.6541	+	185.468i	−0.0950970	+	0.242759i
$765$	24.5753			0.0321245
$766$	6.73338	−	35.6491i	0.00879031	−	0.0465393i
$767$		−	37.6977i		−	0.0491496i
$768$	−442.079	+	34.2653i	−0.575624	+	0.0446163i
$769$	860.996			1.11963			0.559816	−	0.828617i	$-0.310872\pi$
$769$	860.996			1.11963			0.559816	+	0.828617i	$0.310872\pi$
$770$		0			0
$771$		−	14.9571i		−	0.0193996i
$772$	−112.636	−	44.1233i	−0.145901	−	0.0571546i
$773$	−1310.03			−1.69474			−0.847368	−	0.531006i	$-0.821814\pi$
$773$	−1310.03			−1.69474			−0.847368	+	0.531006i	$0.821814\pi$
$774$	70.4701	−	373.096i	0.0910466	−	0.482036i
$775$		−	30.8723i		−	0.0398352i
$776$	905.475	+	567.738i	1.16685	+	0.731621i
$777$		0			0
$778$	−12.8615	−	2.42928i	−0.0165316	−	0.00312247i
$779$		−	947.607i		−	1.21644i
$780$	6.51808	−	16.6390i	0.00835652	−	0.0213321i
$781$	496.499			0.635723
$782$	21.8892	−	115.890i	0.0279913	−	0.148197i
$783$			270.607i			0.345602i
$784$		0			0
$785$	−301.804			−0.384463
$786$	−146.188	−	27.6119i	−0.185990	−	0.0351296i
$787$		−	545.873i		−	0.693612i	−0.937937	−	0.346806i	$-0.887266\pi$
$787$		−	545.873i		−	0.693612i	0.937937	−	0.346806i	$-0.112734\pi$
$788$	1096.40	+	429.499i	1.39138	+	0.545050i
$789$	239.499			0.303548
$790$	80.5121	−	426.262i	0.101914	−	0.539572i
$791$		0			0
$792$	−188.344	+	300.386i	−0.237808	+	0.379275i
$793$	25.7317			0.0324485
$794$	−1216.69	−	229.807i	−1.53235	−	0.289430i
$795$			186.235i			0.234258i
$796$	−421.810	+	1076.78i	−0.529913	+	1.35274i
$797$	−637.380			−0.799724			−0.399862	−	0.916575i	$-0.630942\pi$
$797$	−637.380			−0.799724			−0.399862	+	0.916575i	$0.630942\pi$
$798$		0			0
$799$		−	107.004i		−	0.133922i
$800$	99.5586	+	134.447i	0.124448	+	0.168059i
$801$	350.554			0.437645
$802$	−673.662	−	127.241i	−0.839978	−	0.158654i
$803$		−	1928.88i		−	2.40209i
$804$	−273.501	−	107.139i	−0.340175	−	0.133258i
$805$		0			0
$806$	1.27151	−	6.73185i	0.00157755	−	0.00835217i
$807$		−	625.658i		−	0.775288i
$808$	−303.224	−	190.123i	−0.375277	−	0.235301i
$809$	180.314			0.222885			0.111442	−	0.993771i	$-0.464453\pi$
$809$	180.314			0.222885			0.111442	+	0.993771i	$0.464453\pi$
$810$	78.6477	+	14.8549i	0.0970959	+	0.0183394i
$811$			1483.99i			1.82982i	0.403654	+	0.914912i	$0.367740\pi$
$811$			1483.99i			1.82982i	−0.403654	+	0.914912i	$0.632260\pi$
$812$		0			0
$813$	−341.708			−0.420305
$814$	164.007	−	868.318i	0.201483	−	1.06673i
$815$			444.240i			0.545079i
$816$	−34.6779	+	37.4698i	−0.0424974	+	0.0459189i
$817$	−1718.94			−2.10396
$818$	977.002	+	184.536i	1.19438	+	0.225594i
$819$		0			0
$820$	−577.741	−	226.321i	−0.704563	−	0.276001i
$821$	−1508.64			−1.83756			−0.918779	−	0.394772i	$-0.870824\pi$
$821$	−1508.64			−1.83756			−0.918779	+	0.394772i	$0.870824\pi$
$822$	−77.1630	+	408.531i	−0.0938723	+	0.496996i
$823$			924.774i			1.12366i	0.827252	+	0.561831i	$0.189903\pi$
$823$			924.774i			1.12366i	−0.827252	+	0.561831i	$0.810097\pi$
$824$	−804.342	+	1282.83i	−0.976143	+	1.55683i
$825$	133.771			0.162146
$826$		0			0
$827$			760.522i			0.919615i	0.888019	+	0.459808i	$0.152082\pi$
$827$			760.522i			0.919615i	−0.888019	+	0.459808i	$0.847918\pi$
$828$	140.103	−	357.648i	0.169206	−	0.431942i
$829$	−650.325			−0.784469			−0.392234	−	0.919865i	$-0.628298\pi$
$829$	−650.325			−0.784469			−0.392234	+	0.919865i	$0.628298\pi$
$830$	227.503	−	1204.49i	0.274100	−	1.45119i
$831$		−	490.078i		−	0.589745i
$832$	16.1719	+	33.4173i	0.0194373	+	0.0401650i
$833$		0			0
$834$	542.409	+	102.450i	0.650370	+	0.122842i
$835$		−	623.987i		−	0.747290i
$836$	1494.53	+	585.458i	1.78771	+	0.700308i
$837$	30.6842			0.0366598
$838$	−7.61670	+	40.3258i	−0.00908915	+	0.0481214i
$839$		−	836.751i		−	0.997319i	−0.866798	−	0.498660i	$-0.833826\pi$
$839$		−	836.751i		−	0.997319i	0.866798	−	0.498660i	$-0.166174\pi$
$840$		0			0
$841$	1871.15			2.22491
$842$	1235.51	+	233.363i	1.46736	+	0.277153i
$843$		−	402.426i		−	0.477374i
$844$	138.178	−	352.734i	0.163718	−	0.417931i
$845$	749.974			0.887544
$846$	64.6804	−	342.443i	0.0764543	−	0.404779i
$847$		0			0
$848$	−283.952	−	262.795i	−0.334849	−	0.309899i
$849$	602.146			0.709242
$850$	18.9280	+	3.57512i	0.0222683	+	0.00420602i
$851$			957.350i			1.12497i
$852$	216.807	+	84.9309i	0.254469	+	0.0996841i
$853$	24.8289			0.0291078			0.0145539	−	0.999894i	$-0.495367\pi$
$853$	24.8289			0.0291078			0.0145539	+	0.999894i	$0.495367\pi$
$854$		0			0
$855$		−	362.348i		−	0.423799i
$856$	−712.823	+	1136.87i	−0.832737	+	1.32812i
$857$	−623.609			−0.727665			−0.363832	−	0.931464i	$-0.618532\pi$
$857$	−623.609			−0.727665			−0.363832	+	0.931464i	$0.618532\pi$
$858$	29.1693	+	5.50949i	0.0339969	+	0.00642132i
$859$		−	1325.05i		−	1.54255i	−0.636501	−	0.771276i	$-0.719619\pi$
$859$		−	1325.05i		−	1.54255i	0.636501	−	0.771276i	$-0.280381\pi$
$860$	−410.541	+	1048.01i	−0.477374	+	1.21862i
$861$		0			0
$862$	−313.250	+	1658.47i	−0.363399	+	1.92397i
$863$		−	0.0467712i		−	5.41961e-5i	−1.00000		2.70980e-5i	$-0.999991\pi$
$863$		−	0.0467712i		−	5.41961e-5i	1.00000		2.70980e-5i	$-8.62558e-6\pi$
$864$	−133.628	+	98.9521i	−0.154662	+	0.114528i
$865$	1006.80			1.16393
$866$	939.860	+	177.520i	1.08529	+	0.204989i
$867$		−	494.684i		−	0.570570i
$868$		0			0
$869$	720.606			0.829236
$870$	148.883	−	788.244i	0.171130	−	0.906028i
$871$			24.5935i			0.0282360i
$872$	−1151.08	−	721.737i	−1.32005	−	0.827680i
$873$	400.779			0.459082
$874$	−1708.73	−	322.743i	−1.95507	−	0.369272i
$875$		0			0
$876$	329.952	−	842.287i	0.376658	−	0.961514i
$877$	162.979			0.185837			0.0929186	−	0.995674i	$-0.470380\pi$
$877$	162.979			0.185837			0.0929186	+	0.995674i	$0.470380\pi$
$878$	111.291	−	589.215i	0.126755	−	0.671087i
$879$		−	359.088i		−	0.408519i
$880$	713.889	−	771.363i	0.811238	−	0.876549i
$881$	−385.225			−0.437258			−0.218629	−	0.975808i	$-0.570159\pi$
$881$	−385.225			−0.437258			−0.218629	+	0.975808i	$0.570159\pi$
$882$		0			0
$883$		−	1319.84i		−	1.49472i	−0.664419	−	0.747360i	$-0.731321\pi$
$883$		−	1319.84i		−	1.49472i	0.664419	−	0.747360i	$-0.268679\pi$
$884$	3.98010	+	1.55914i	0.00450238	+	0.00176374i
$885$	−500.516			−0.565555
$886$	52.4033	−	277.443i	0.0591459	−	0.313141i
$887$		−	31.8112i		−	0.0358638i	−0.999839	−	0.0179319i	$-0.994292\pi$
$887$		−	31.8112i		−	0.0358638i	0.999839	−	0.0179319i	$-0.00570821\pi$
$888$	220.151	−	351.115i	0.247918	−	0.395400i
$889$		0			0
$890$	−1021.12	−	192.869i	−1.14733	−	0.216706i
$891$			132.956i			0.149221i
$892$	−276.450	+	705.707i	−0.309921	+	0.791152i
$893$	−1577.71			−1.76676
$894$	−2.38537	+	12.6290i	−0.00266819	+	0.0141264i
$895$		−	1009.66i		−	1.12811i
$896$		0			0
$897$	−32.1602			−0.0358530
$898$	18.8506	+	3.56049i	0.0209917	+	0.00396491i
$899$		−	307.532i		−	0.342082i
$900$	58.4139	+	22.8827i	0.0649044	+	0.0254253i
$901$	−44.5480			−0.0494428
$902$	191.301	−	1012.82i	0.212085	−	1.12286i
$903$		0			0
$904$	103.422	+	64.8462i	0.114405	+	0.0717325i
$905$	907.014			1.00223
$906$	188.654	+	35.6329i	0.208228	+	0.0393299i
$907$			551.111i			0.607619i	0.952733	+	0.303810i	$0.0982587\pi$
$907$			551.111i			0.607619i	−0.952733	+	0.303810i	$0.901741\pi$
$908$	−60.5275	+	154.512i	−0.0666603	+	0.170167i
$909$	−134.212			−0.147648
$910$		0			0
$911$		−	1357.71i		−	1.49035i	−0.666868	−	0.745176i	$-0.732365\pi$
$911$		−	1357.71i		−	1.49035i	0.666868	−	0.745176i	$-0.267635\pi$
$912$	552.470	+	511.306i	0.605779	+	0.560642i
$913$	2036.22			2.23025
$914$	−277.003	−	52.3202i	−0.303067	−	0.0572431i
$915$		−	341.641i		−	0.373379i
$916$	1460.37	+	572.075i	1.59429	+	0.624536i
$917$		0			0
$918$	−3.55334	+	18.8127i	−0.00387074	+	0.0204932i
$919$			1644.63i			1.78959i	0.446477	+	0.894795i	$0.352678\pi$
$919$			1644.63i			1.78959i	−0.446477	+	0.894795i	$0.647322\pi$
$920$	−604.874	+	964.702i	−0.657472	+	1.04859i
$921$	432.839			0.469967
$922$	−152.772	−	28.8554i	−0.165696	−	0.0312966i
$923$		−	19.4956i		−	0.0211220i
$924$		0			0
$925$	−156.362			−0.169040
$926$	−147.076	+	778.676i	−0.158829	+	0.840903i
$927$			567.802i			0.612516i
$928$	991.744	+	1339.28i	1.06869	+	1.44319i
$929$	27.3333			0.0294222			0.0147111	−	0.999892i	$-0.495317\pi$
$929$	27.3333			0.0294222			0.0147111	+	0.999892i	$0.495317\pi$
$930$	−89.3794	−	16.8819i	−0.0961069	−	0.0181526i
$931$		0			0
$932$	26.2136	+	10.2688i	0.0281262	+	0.0110180i
$933$	−445.436			−0.477423
$934$	−133.174	+	705.076i	−0.142585	+	0.754899i
$935$		−	121.016i		−	0.129429i
$936$	11.7950	+	7.39553i	0.0126015	+	0.00790120i
$937$	−703.111			−0.750385			−0.375193	−	0.926947i	$-0.622423\pi$
$937$	−703.111			−0.750385			−0.375193	+	0.926947i	$0.622423\pi$
$938$		0			0
$939$		−	218.070i		−	0.232236i
$940$	−376.812	+	961.907i	−0.400864	+	1.02331i
$941$	28.5002			0.0302871			0.0151436	−	0.999885i	$-0.495179\pi$
$941$	28.5002			0.0302871			0.0151436	+	0.999885i	$0.495179\pi$
$942$	43.6378	−	231.035i	0.0463246	−	0.245260i
$943$			1116.67i			1.18416i
$944$	706.273	−	763.135i	0.748171	−	0.808405i
$945$		0			0
$946$	−1837.23	−	347.015i	−1.94210	−	0.366824i
$947$			449.028i			0.474158i	0.971490	+	0.237079i	$0.0761901\pi$
$947$			449.028i			0.474158i	−0.971490	+	0.237079i	$0.923810\pi$
$948$	314.668	+	123.266i	0.331929	+	0.130028i
$949$	−75.7396			−0.0798099
$950$	52.7131	−	279.083i	0.0554874	−	0.293772i
$951$			219.974i			0.231308i
$952$		0			0
$953$	−1455.66			−1.52745			−0.763724	−	0.645543i	$-0.776631\pi$
$953$	−1455.66			−1.52745			−0.763724	+	0.645543i	$0.776631\pi$
$954$	−142.566	−	26.9278i	−0.149440	−	0.0282262i
$955$		−	221.429i		−	0.231863i
$956$	−172.861	+	441.270i	−0.180817	+	0.461580i
$957$	1332.55			1.39242
$958$	−65.3191	+	345.825i	−0.0681828	+	0.360986i
$959$		0			0
$960$	443.684	−	214.715i	0.462171	−	0.223662i
$961$	926.129			0.963714
$962$	−34.0955	−	6.43994i	−0.0354423	−	0.00669432i
$963$			503.197i			0.522531i
$964$	410.579	+	160.838i	0.425912	+	0.166844i
$965$	134.475			0.139353
$966$		0			0
$967$			1048.55i			1.08433i	0.840272	+	0.542165i	$0.182395\pi$
$967$			1048.55i			1.08433i	−0.840272	+	0.542165i	$0.817605\pi$
$968$	659.065	+	413.238i	0.680852	+	0.426898i
$969$	86.6747			0.0894475
$970$	−1167.42	−	220.501i	−1.20352	−	0.227321i
$971$			531.198i			0.547062i	0.961863	+	0.273531i	$0.0881917\pi$
$971$			531.198i			0.547062i	−0.961863	+	0.273531i	$0.911808\pi$
$972$	−22.7433	+	58.0581i	−0.0233985	+	0.0597305i
$973$		0			0
$974$	−132.404	+	700.996i	−0.135938	+	0.719708i
$975$		−	5.25266i		−	0.00538734i
$976$	520.899	+	482.087i	0.533708	+	0.493941i
$977$	863.471			0.883798			0.441899	−	0.897065i	$-0.354305\pi$
$977$	863.471			0.883798			0.441899	+	0.897065i	$0.354305\pi$
$978$	−340.072	−	64.2326i	−0.347722	−	0.0656775i
$979$		−	1726.23i		−	1.76326i
$980$		0			0
$981$	−509.490			−0.519357
$982$	−306.746	+	1624.03i	−0.312368	+	1.65380i
$983$			1127.79i			1.14730i	0.819102	+	0.573648i	$0.194472\pi$
$983$			1127.79i			1.14730i	−0.819102	+	0.573648i	$0.805528\pi$
$984$	256.788	−	409.546i	0.260963	−	0.416205i
$985$	−1308.99			−1.32892
$986$	188.550	+	35.6132i	0.191227	+	0.0361189i
$987$		0			0
$988$	22.9887	−	58.6843i	0.0232679	−	0.0593971i
$989$	2025.61			2.04814
$990$	73.1500	−	387.284i	0.0738889	−	0.391196i
$991$		−	1099.50i		−	1.10949i	−0.832021	−	0.554744i	$-0.812816\pi$
$991$		−	1099.50i		−	1.10949i	0.832021	−	0.554744i	$-0.187184\pi$
$992$	151.862	−	112.454i	0.153087	−	0.113361i
$993$	−927.922			−0.934463
$994$		0			0
$995$		−	1285.56i		−	1.29202i
$996$	889.159	+	348.314i	0.892729	+	0.349713i
$997$	567.785			0.569494			0.284747	−	0.958603i	$-0.408090\pi$
$997$	567.785			0.569494			0.284747	+	0.958603i	$0.408090\pi$
$998$	−42.4288	+	224.634i	−0.0425139	+	0.225085i
$999$		−	155.410i		−	0.155565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.h.295.2	yes	24
4.3	odd	2	inner	588.3.g.h.295.3	yes	24
7.6	odd	2	inner	588.3.g.h.295.1	✓	24
28.27	even	2	inner	588.3.g.h.295.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.3.g.h.295.1	✓	24	7.6	odd	2	inner
588.3.g.h.295.2	yes	24	1.1	even	1	trivial
588.3.g.h.295.3	yes	24	4.3	odd	2	inner
588.3.g.h.295.4	yes	24	28.27	even	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96525 - 0.371196i) q^{2} +1.73205i q^{3} +(3.72443 + 1.45899i) q^{4} -4.44657 q^{5} +(0.642930 - 3.40392i) q^{6} +(-6.77787 - 4.24976i) q^{8} -3.00000 q^{9} +(8.73863 + 1.65055i) q^{10} +14.7729i q^{11} +(-2.52704 + 6.45090i) q^{12} +0.580073 q^{13} -7.70169i q^{15} +(11.7427 + 10.8678i) q^{16} +1.84226 q^{17} +(5.89575 + 1.11359i) q^{18} -27.1631i q^{19} +(-16.5609 - 6.48748i) q^{20} +(5.48363 - 29.0324i) q^{22} +32.0092i q^{23} +(7.36081 - 11.7396i) q^{24} -5.22800 q^{25} +(-1.13999 - 0.215321i) q^{26} -5.19615i q^{27} -52.0783 q^{29} +(-2.85883 + 15.1358i) q^{30} +5.90518i q^{31} +(-19.0433 - 25.7168i) q^{32} -25.5874 q^{33} +(-3.62051 - 0.683840i) q^{34} +(-11.1733 - 4.37696i) q^{36} +29.9086 q^{37} +(-10.0828 + 53.3824i) q^{38} +1.00472i q^{39} +(30.1383 + 18.8969i) q^{40} +34.8858 q^{41} -63.2821i q^{43} +(-21.5534 + 55.0205i) q^{44} +13.3397 q^{45} +(11.8817 - 62.9061i) q^{46} -58.0829i q^{47} +(-18.8235 + 20.3390i) q^{48} +(10.2743 + 1.94061i) q^{50} +3.19089i q^{51} +(2.16044 + 0.846319i) q^{52} -24.1811 q^{53} +(-1.92879 + 10.2117i) q^{54} -65.6886i q^{55} +47.0479 q^{57} +(102.347 + 19.3312i) q^{58} -64.9879i q^{59} +(11.2367 - 28.6844i) q^{60} +44.3593 q^{61} +(2.19198 - 11.6052i) q^{62} +(27.8790 + 57.6087i) q^{64} -2.57934 q^{65} +(50.2856 + 9.49792i) q^{66} +42.3973i q^{67} +(6.86138 + 2.68784i) q^{68} -55.4416 q^{69} -33.6089i q^{71} +(20.3336 + 12.7493i) q^{72} -130.569 q^{73} +(-58.7779 - 11.1019i) q^{74} -9.05516i q^{75} +(39.6306 - 101.167i) q^{76} +(0.372946 - 1.97452i) q^{78} -48.7790i q^{79} +(-52.2149 - 48.3243i) q^{80} +9.00000 q^{81} +(-68.5594 - 12.9495i) q^{82} -137.835i q^{83} -8.19176 q^{85} +(-23.4900 + 124.365i) q^{86} -90.2022i q^{87} +(62.7812 - 100.129i) q^{88} -116.851 q^{89} +(-26.2159 - 4.95164i) q^{90} +(-46.7010 + 119.216i) q^{92} -10.2281 q^{93} +(-21.5601 + 114.148i) q^{94} +120.783i q^{95} +(44.5427 - 32.9840i) q^{96} -133.593 q^{97} -44.3186i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) \) 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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