LMFDB - Embedded newform 512.2.k.a.273.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			273.9
Character	$\chi$	$=$	512.273
Dual form			512.2.k.a.497.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.467037 + 0.249636i) q^{3} +(0.246231 - 0.300034i) q^{5} +(-1.89160 - 1.26393i) q^{7} +(-1.51091 - 2.26123i) q^{9} +(-5.42541 - 1.64578i) q^{11} +(5.51786 - 4.52839i) q^{13} +(0.189898 - 0.0786585i) q^{15} +(-3.03177 - 1.25580i) q^{17} +(0.249350 - 2.53169i) q^{19} +(-0.567925 - 1.06251i) q^{21} +(5.91175 + 1.17592i) q^{23} +(0.946061 + 4.75617i) q^{25} +(-0.296883 - 3.01431i) q^{27} +(-0.110196 - 0.363268i) q^{29} +(0.158513 - 0.158513i) q^{31} +(-2.12302 - 2.12302i) q^{33} +(-0.844991 + 0.256325i) q^{35} +(-4.28002 + 0.421545i) q^{37} +(3.70750 - 0.737467i) q^{39} +(-1.22722 + 6.16964i) q^{41} +(7.59540 - 4.05983i) q^{43} +(-1.05048 - 0.103463i) q^{45} +(-1.45718 + 3.51794i) q^{47} +(-0.698143 - 1.68547i) q^{49} +(-1.10246 - 1.34335i) q^{51} +(2.06447 - 6.80565i) q^{53} +(-1.82969 + 1.22256i) q^{55} +(0.748459 - 1.12015i) q^{57} +(-7.12505 - 5.84738i) q^{59} +(2.08843 - 3.90718i) q^{61} +6.18702i q^{63} -2.77058i q^{65} +(-1.02948 + 1.92602i) q^{67} +(2.46745 + 2.02499i) q^{69} +(2.79145 - 4.17771i) q^{71} +(-8.95387 + 5.98279i) q^{73} +(-0.745468 + 2.45748i) q^{75} +(8.18256 + 9.97047i) q^{77} +(3.96157 + 9.56408i) q^{79} +(-2.50836 + 6.05573i) q^{81} +(10.9186 + 1.07539i) q^{83} +(-1.12330 + 0.600415i) q^{85} +(0.0392192 - 0.197168i) q^{87} +(-2.99053 + 0.594853i) q^{89} +(-16.1612 + 1.59173i) q^{91} +(0.113602 - 0.0344609i) q^{93} +(-0.698195 - 0.698195i) q^{95} +(4.90076 - 4.90076i) q^{97} +(4.47579 + 14.7547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.467037	+	0.249636i	0.269644	+	0.144128i	0.600678	−	0.799491i	$-0.294897\pi$
$3$	0.467037	+	0.249636i	0.269644	+	0.144128i	−0.331034	+	0.943619i	$0.607397\pi$
$4$		0			0
$5$	0.246231	−	0.300034i	0.110118	−	0.134179i	−0.715035	−	0.699089i	$-0.753589\pi$
$5$	0.246231	−	0.300034i	0.110118	−	0.134179i	0.825153	+	0.564910i	$0.191089\pi$
$6$		0			0
$7$	−1.89160	−	1.26393i	−0.714958	−	0.477720i	0.144123	−	0.989560i	$-0.453964\pi$
$7$	−1.89160	−	1.26393i	−0.714958	−	0.477720i	−0.859081	+	0.511840i	$0.828964\pi$
$8$		0			0
$9$	−1.51091	−	2.26123i	−0.503635	−	0.753743i
$10$		0			0
$11$	−5.42541	−	1.64578i	−1.63582	−	0.496221i	−0.667224	−	0.744857i	$-0.732518\pi$
$11$	−5.42541	−	1.64578i	−1.63582	−	0.496221i	−0.968597	+	0.248636i	$0.920018\pi$
$12$		0			0
$13$	5.51786	−	4.52839i	1.53038	−	1.25595i	0.675178	−	0.737655i	$-0.264067\pi$
$13$	5.51786	−	4.52839i	1.53038	−	1.25595i	0.855202	−	0.518296i	$-0.173433\pi$
$14$		0			0
$15$	0.189898	−	0.0786585i	0.0490315	−	0.0203095i
$16$		0			0
$17$	−3.03177	−	1.25580i	−0.735312	−	0.304576i	−0.0165793	−	0.999863i	$-0.505278\pi$
$17$	−3.03177	−	1.25580i	−0.735312	−	0.304576i	−0.718733	+	0.695286i	$0.755278\pi$
$18$		0			0
$19$	0.249350	−	2.53169i	0.0572048	−	0.580810i	−0.923268	−	0.384156i	$-0.874492\pi$
$19$	0.249350	−	2.53169i	0.0572048	−	0.580810i	0.980473	−	0.196654i	$-0.0630076\pi$
$20$		0			0
$21$	−0.567925	−	1.06251i	−0.123931	−	0.231859i
$22$		0			0
$23$	5.91175	+	1.17592i	1.23268	+	0.245196i	0.768098	−	0.640332i	$-0.221203\pi$
$23$	5.91175	+	1.17592i	1.23268	+	0.245196i	0.464586	+	0.885528i	$0.346203\pi$
$24$		0			0
$25$	0.946061	+	4.75617i	0.189212	+	0.951234i
$26$		0			0
$27$	−0.296883	−	3.01431i	−0.0571352	−	0.580104i
$28$		0			0
$29$	−0.110196	−	0.363268i	−0.0204629	−	0.0674571i	0.946114	−	0.323833i	$-0.104972\pi$
$29$	−0.110196	−	0.363268i	−0.0204629	−	0.0674571i	−0.966577	+	0.256376i	$0.917472\pi$
$30$		0			0
$31$	0.158513	−	0.158513i	0.0284698	−	0.0284698i	−0.692729	−	0.721198i	$-0.743592\pi$
$31$	0.158513	−	0.158513i	0.0284698	−	0.0284698i	0.721198	+	0.692729i	$0.243592\pi$
$32$		0			0
$33$	−2.12302	−	2.12302i	−0.369570	−	0.369570i
$34$		0			0
$35$	−0.844991	+	0.256325i	−0.142830	+	0.0433269i
$36$		0			0
$37$	−4.28002	+	0.421545i	−0.703630	+	0.0693015i	−0.443503	−	0.896273i	$-0.646264\pi$
$37$	−4.28002	+	0.421545i	−0.703630	+	0.0693015i	−0.260127	+	0.965574i	$0.583764\pi$
$38$		0			0
$39$	3.70750	−	0.737467i	0.593675	−	0.118089i
$40$		0			0
$41$	−1.22722	+	6.16964i	−0.191659	+	0.963536i	0.758477	+	0.651700i	$0.225944\pi$
$41$	−1.22722	+	6.16964i	−0.191659	+	0.963536i	−0.950136	+	0.311836i	$0.899056\pi$
$42$		0			0
$43$	7.59540	−	4.05983i	1.15829	−	0.619118i	0.223633	−	0.974674i	$-0.428208\pi$
$43$	7.59540	−	4.05983i	1.15829	−	0.619118i	0.934655	+	0.355556i	$0.115708\pi$
$44$		0			0
$45$	−1.05048	−	0.103463i	−0.156596	−	0.0154233i
$46$		0			0
$47$	−1.45718	+	3.51794i	−0.212551	+	0.513144i	−0.993814	−	0.111059i	$-0.964576\pi$
$47$	−1.45718	+	3.51794i	−0.212551	+	0.513144i	0.781263	+	0.624202i	$0.214576\pi$
$48$		0			0
$49$	−0.698143	−	1.68547i	−0.0997347	−	0.240781i
$50$		0			0
$51$	−1.10246	−	1.34335i	−0.154375	−	0.188106i
$52$		0			0
$53$	2.06447	−	6.80565i	0.283577	−	0.934828i	−0.693232	−	0.720715i	$-0.743814\pi$
$53$	2.06447	−	6.80565i	0.283577	−	0.934828i	0.976809	−	0.214113i	$-0.0686861\pi$
$54$		0			0
$55$	−1.82969	+	1.22256i	−0.246716	+	0.164850i
$56$		0			0
$57$	0.748459	−	1.12015i	0.0991358	−	0.148367i
$58$		0			0
$59$	−7.12505	−	5.84738i	−0.927603	−	0.761264i	0.0437162	−	0.999044i	$-0.486080\pi$
$59$	−7.12505	−	5.84738i	−0.927603	−	0.761264i	−0.971319	+	0.237780i	$0.923580\pi$
$60$		0			0
$61$	2.08843	−	3.90718i	0.267397	−	0.500264i	−0.712008	−	0.702171i	$-0.752214\pi$
$61$	2.08843	−	3.90718i	0.267397	−	0.500264i	0.979405	+	0.201908i	$0.0647141\pi$
$62$		0			0
$63$			6.18702i			0.779491i
$64$		0			0
$65$		−	2.77058i		−	0.343648i
$66$		0			0
$67$	−1.02948	+	1.92602i	−0.125771	+	0.235300i	−0.936924	−	0.349533i	$-0.886340\pi$
$67$	−1.02948	+	1.92602i	−0.125771	+	0.235300i	0.811153	+	0.584833i	$0.198840\pi$
$68$		0			0
$69$	2.46745	+	2.02499i	0.297046	+	0.243780i
$70$		0			0
$71$	2.79145	−	4.17771i	0.331285	−	0.495803i	−0.628012	−	0.778204i	$-0.716131\pi$
$71$	2.79145	−	4.17771i	0.331285	−	0.495803i	0.959296	+	0.282401i	$0.0911310\pi$
$72$		0			0
$73$	−8.95387	+	5.98279i	−1.04797	+	0.700232i	−0.955352	−	0.295469i	$-0.904524\pi$
$73$	−8.95387	+	5.98279i	−1.04797	+	0.700232i	−0.0926195	+	0.995702i	$0.529524\pi$
$74$		0			0
$75$	−0.745468	+	2.45748i	−0.0860792	+	0.283765i
$76$		0			0
$77$	8.18256	+	9.97047i	0.932489	+	1.13624i
$78$		0			0
$79$	3.96157	+	9.56408i	0.445712	+	1.07604i	0.973912	+	0.226924i	$0.0728669\pi$
$79$	3.96157	+	9.56408i	0.445712	+	1.07604i	−0.528201	+	0.849120i	$0.677133\pi$
$80$		0			0
$81$	−2.50836	+	6.05573i	−0.278707	+	0.672858i
$82$		0			0
$83$	10.9186	+	1.07539i	1.19848	+	0.118040i	0.677494	−	0.735528i	$-0.263066\pi$
$83$	10.9186	+	1.07539i	1.19848	+	0.118040i	0.520982	+	0.853568i	$0.325566\pi$
$84$		0			0
$85$	−1.12330	+	0.600415i	−0.121839	+	0.0651242i
$86$		0			0
$87$	0.0392192	−	0.197168i	0.00420474	−	0.0211387i
$88$		0			0
$89$	−2.99053	+	0.594853i	−0.316995	+	0.0630543i	−0.351024	−	0.936367i	$-0.614166\pi$
$89$	−2.99053	+	0.594853i	−0.316995	+	0.0630543i	0.0340283	+	0.999421i	$0.489166\pi$
$90$		0			0
$91$	−16.1612	+	1.59173i	−1.69415	+	0.166859i
$92$		0			0
$93$	0.113602	−	0.0344609i	0.0117800	−	0.00357343i
$94$		0			0
$95$	−0.698195	−	0.698195i	−0.0716333	−	0.0716333i
$96$		0			0
$97$	4.90076	−	4.90076i	0.497597	−	0.497597i	−0.413092	−	0.910689i	$-0.635551\pi$
$97$	4.90076	−	4.90076i	0.497597	−	0.497597i	0.910689	+	0.413092i	$0.135551\pi$
$98$		0			0
$99$	4.47579	+	14.7547i	0.449834	+	1.48290i
$100$		0			0
$101$	1.24276	+	12.6179i	0.123659	+	1.25553i	0.834036	+	0.551709i	$0.186024\pi$
$101$	1.24276	+	12.6179i	0.123659	+	1.25553i	−0.710377	+	0.703821i	$0.751476\pi$
$102$		0			0
$103$	−1.72333	−	8.66376i	−0.169805	−	0.853665i	−0.967939	−	0.251186i	$-0.919179\pi$
$103$	−1.72333	−	8.66376i	−0.169805	−	0.853665i	0.798134	−	0.602480i	$-0.205821\pi$
$104$		0			0
$105$	−0.458630	−	0.0912273i	−0.0447577	−	0.00890287i
$106$		0			0
$107$	−1.46922	−	2.74872i	−0.142035	−	0.265729i	0.800838	−	0.598881i	$-0.204388\pi$
$107$	−1.46922	−	2.74872i	−0.142035	−	0.265729i	−0.942873	+	0.333152i	$0.891888\pi$
$108$		0			0
$109$	1.16763	−	11.8551i	0.111838	−	1.13552i	−0.761420	−	0.648259i	$-0.775498\pi$
$109$	1.16763	−	11.8551i	0.111838	−	1.13552i	0.873259	−	0.487257i	$-0.162002\pi$
$110$		0			0
$111$	−2.10416	−	0.871571i	−0.199718	−	0.0827259i
$112$		0			0
$113$	−0.712697	+	0.295209i	−0.0670449	+	0.0277709i	−0.415954	−	0.909386i	$-0.636552\pi$
$113$	−0.712697	+	0.295209i	−0.0670449	+	0.0277709i	0.348909	+	0.937157i	$0.386552\pi$
$114$		0			0
$115$	1.80847	−	1.48417i	0.168641	−	0.138400i
$116$		0			0
$117$	−18.5767	−	5.63518i	−1.71742	−	0.520973i
$118$		0			0
$119$	4.14766	+	6.20741i	0.380215	+	0.569032i
$120$		0			0
$121$	17.5803	+	11.7468i	1.59821	+	1.06789i
$122$		0			0
$123$	−2.11332	+	2.57509i	−0.190552	+	0.232188i
$124$		0			0
$125$	3.37149	+	1.80210i	0.301555	+	0.161185i
$126$		0			0
$127$	10.9144			0.968500			0.484250	−	0.874930i	$-0.339092\pi$
$127$	10.9144			0.968500			0.484250	+	0.874930i	$0.339092\pi$
$128$		0			0
$129$	4.56081			0.401557
$130$		0			0
$131$	−2.49435	−	1.33326i	−0.217933	−	0.116487i	0.358818	−	0.933407i	$-0.383180\pi$
$131$	−2.49435	−	1.33326i	−0.217933	−	0.116487i	−0.576751	+	0.816920i	$0.695680\pi$
$132$		0			0
$133$	−3.67155	+	4.47379i	−0.318364	+	0.387927i
$134$		0			0
$135$	−0.977495	−	0.653142i	−0.0841294	−	0.0562135i
$136$		0			0
$137$	6.35365	+	9.50891i	0.542829	+	0.812401i	0.996909	−	0.0785598i	$-0.0250322\pi$
$137$	6.35365	+	9.50891i	0.542829	+	0.812401i	−0.454080	+	0.890961i	$0.650032\pi$
$138$		0			0
$139$	13.9374	+	4.22788i	1.18216	+	0.358604i	0.819368	−	0.573267i	$-0.194324\pi$
$139$	13.9374	+	4.22788i	1.18216	+	0.358604i	0.362790	+	0.931871i	$0.381824\pi$
$140$		0			0
$141$	−1.55876	+	1.27924i	−0.131271	+	0.107732i
$142$		0			0
$143$	−37.3894	+	15.4872i	−3.12666	+	1.29510i
$144$		0			0
$145$	−0.136126	−	0.0563853i	−0.0113047	−	0.00468254i
$146$		0			0
$147$	0.0946952	−	0.961457i	0.00781033	−	0.0792996i
$148$		0			0
$149$	2.73650	+	5.11964i	0.224183	+	0.419417i	0.968717	−	0.248167i	$-0.0798283\pi$
$149$	2.73650	+	5.11964i	0.224183	+	0.419417i	−0.744534	+	0.667585i	$0.767328\pi$
$150$		0			0
$151$	12.1718	+	2.42112i	0.990528	+	0.197028i	0.663654	−	0.748040i	$-0.269005\pi$
$151$	12.1718	+	2.42112i	0.990528	+	0.197028i	0.326874	+	0.945068i	$0.394005\pi$
$152$		0			0
$153$	1.74106	+	8.75292i	0.140757	+	0.707632i
$154$		0			0
$155$	−0.00852839	−	0.0865902i	−0.000685017	−	0.00695509i
$156$		0			0
$157$	3.37431	+	11.1236i	0.269299	+	0.887760i	0.982414	+	0.186713i	$0.0597835\pi$
$157$	3.37431	+	11.1236i	0.269299	+	0.887760i	−0.713116	+	0.701047i	$0.752717\pi$
$158$		0			0
$159$	2.66312	−	2.66312i	0.211199	−	0.211199i
$160$		0			0
$161$	−9.69639	−	9.69639i	−0.764182	−	0.764182i
$162$		0			0
$163$	−1.99169	+	0.604172i	−0.156001	+	0.0473224i	−0.367319	−	0.930095i	$-0.619724\pi$
$163$	−1.99169	+	0.604172i	−0.156001	+	0.0473224i	0.211318	+	0.977417i	$0.432224\pi$
$164$		0			0
$165$	−1.15973	+	0.114223i	−0.0902849	+	0.00889228i
$166$		0			0
$167$	−18.4367	+	3.66729i	−1.42667	+	0.283783i	−0.847229	−	0.531228i	$-0.821731\pi$
$167$	−18.4367	+	3.66729i	−1.42667	+	0.283783i	−0.579446	+	0.815011i	$0.696731\pi$
$168$		0			0
$169$	7.40429	−	37.2239i	0.569561	−	2.86338i
$170$		0			0
$171$	−6.10149	+	3.26131i	−0.466592	+	0.249399i
$172$		0			0
$173$	12.2684	+	1.20833i	0.932747	+	0.0918676i	0.552962	−	0.833207i	$-0.313498\pi$
$173$	12.2684	+	1.20833i	0.932747	+	0.0918676i	0.379786	+	0.925074i	$0.375998\pi$
$174$		0			0
$175$	4.22188	−	10.1925i	0.319144	−	0.770483i
$176$		0			0
$177$	−1.86794	−	4.50962i	−0.140403	−	0.338963i
$178$		0			0
$179$	−2.78355	−	3.39176i	−0.208052	−	0.253512i	0.658521	−	0.752562i	$-0.271182\pi$
$179$	−2.78355	−	3.39176i	−0.208052	−	0.253512i	−0.866573	+	0.499050i	$0.833682\pi$
$180$		0			0
$181$	2.25173	−	7.42296i	0.167370	−	0.551744i	−0.832628	−	0.553832i	$-0.813165\pi$
$181$	2.25173	−	7.42296i	0.167370	−	0.551744i	0.999998	+	0.00208855i	$0.000664807\pi$
$182$		0			0
$183$	1.95075	−	1.30345i	0.144204	−	0.0963538i
$184$		0			0
$185$	−0.927396	+	1.38795i	−0.0681835	+	0.102044i
$186$		0			0
$187$	14.3818	+	11.8028i	1.05170	+	0.863110i
$188$		0			0
$189$	−3.24828	+	6.07711i	−0.236278	+	0.442044i
$190$		0			0
$191$		−	5.21183i		−	0.377115i	−0.982062	−	0.188557i	$-0.939619\pi$
$191$		−	5.21183i		−	0.377115i	0.982062	−	0.188557i	$-0.0603811\pi$
$192$		0			0
$193$		−	3.59450i		−	0.258738i	−0.991597	−	0.129369i	$-0.958705\pi$
$193$		−	3.59450i		−	0.258738i	0.991597	−	0.129369i	$-0.0412952\pi$
$194$		0			0
$195$	0.691637	−	1.29396i	0.0495291	−	0.0926625i
$196$		0			0
$197$	−0.436406	−	0.358149i	−0.0310926	−	0.0255171i	0.618719	−	0.785613i	$-0.287652\pi$
$197$	−0.436406	−	0.358149i	−0.0310926	−	0.0255171i	−0.649811	+	0.760096i	$0.725152\pi$
$198$		0			0
$199$	12.1596	−	18.1981i	0.861969	−	1.29003i	−0.0937054	−	0.995600i	$-0.529871\pi$
$199$	12.1596	−	18.1981i	0.861969	−	1.29003i	0.955674	−	0.294427i	$-0.0951288\pi$
$200$		0			0
$201$	−0.961607	+	0.642525i	−0.0678265	+	0.0453202i
$202$		0			0
$203$	−0.250697	+	0.826437i	−0.0175955	+	0.0580045i
$204$		0			0
$205$	1.54892	+	1.88736i	0.108181	+	0.131819i
$206$		0			0
$207$	−6.27307	−	15.1445i	−0.436008	−	1.05262i
$208$		0			0
$209$	−5.51943	+	13.3251i	−0.381787	+	0.921716i
$210$		0			0
$211$	9.62589	+	0.948068i	0.662674	+	0.0652677i	0.423762	−	0.905774i	$-0.360709\pi$
$211$	9.62589	+	0.948068i	0.662674	+	0.0652677i	0.238912	+	0.971041i	$0.423209\pi$
$212$		0			0
$213$	2.34662	−	1.25429i	0.160788	−	0.0859429i
$214$		0			0
$215$	0.652140	−	3.27853i	0.0444756	−	0.223594i
$216$		0			0
$217$	−0.500193	+	0.0994946i	−0.0339553	+	0.00675413i
$218$		0			0
$219$	−5.67531	+	0.558969i	−0.383502	+	0.0377717i
$220$		0			0
$221$	−22.4156	+	6.79971i	−1.50784	+	0.457398i
$222$		0			0
$223$	−6.73761	−	6.73761i	−0.451184	−	0.451184i	0.444564	−	0.895747i	$-0.353359\pi$
$223$	−6.73761	−	6.73761i	−0.451184	−	0.451184i	−0.895747	+	0.444564i	$0.853359\pi$
$224$		0			0
$225$	9.32539	−	9.32539i	0.621693	−	0.621693i
$226$		0			0
$227$	4.18669	+	13.8017i	0.277880	+	0.916048i	0.979148	+	0.203150i	$0.0651179\pi$
$227$	4.18669	+	13.8017i	0.277880	+	0.916048i	−0.701267	+	0.712898i	$0.747382\pi$
$228$		0			0
$229$	−0.318172	−	3.23045i	−0.0210254	−	0.213474i	−0.999957	−	0.00928538i	$-0.997044\pi$
$229$	−0.318172	−	3.23045i	−0.0210254	−	0.213474i	0.978932	−	0.204189i	$-0.0654557\pi$
$230$		0			0
$231$	1.33256	+	6.69924i	0.0876762	+	0.440778i
$232$		0			0
$233$	−23.1801	−	4.61082i	−1.51858	−	0.302065i	−0.635802	−	0.771852i	$-0.719331\pi$
$233$	−23.1801	−	4.61082i	−1.51858	−	0.302065i	−0.882780	+	0.469788i	$0.844331\pi$
$234$		0			0
$235$	0.696696	+	1.30343i	0.0454475	+	0.0850262i
$236$		0			0
$237$	−0.537343	+	5.45573i	−0.0349042	+	0.354388i
$238$		0			0
$239$	14.5949	+	6.04542i	0.944068	+	0.391046i	0.800998	−	0.598667i	$-0.204303\pi$
$239$	14.5949	+	6.04542i	0.944068	+	0.391046i	0.143070	+	0.989713i	$0.454303\pi$
$240$		0			0
$241$	12.1611	−	5.03731i	0.783368	−	0.324482i	0.0450943	−	0.998983i	$-0.485641\pi$
$241$	12.1611	−	5.03731i	0.783368	−	0.324482i	0.738274	+	0.674501i	$0.235641\pi$
$242$		0			0
$243$	−9.70733	+	7.96660i	−0.622725	+	0.511057i
$244$		0			0
$245$	−0.677601	−	0.205548i	−0.0432903	−	0.0131320i
$246$		0			0
$247$	−10.0886	−	15.0987i	−0.641924	−	0.960707i
$248$		0			0
$249$	4.83095	+	3.22794i	0.306149	+	0.204562i
$250$		0			0
$251$	4.31409	−	5.25673i	0.272303	−	0.331802i	−0.618847	−	0.785512i	$-0.712400\pi$
$251$	4.31409	−	5.25673i	0.272303	−	0.331802i	0.891149	+	0.453710i	$0.149900\pi$
$252$		0			0
$253$	−30.1383	−	16.1093i	−1.89478	−	1.01278i
$254$		0			0
$255$	−0.674507			−0.0422393
$256$		0			0
$257$	20.5954			1.28471			0.642354	−	0.766408i	$-0.277958\pi$
$257$	20.5954			1.28471			0.642354	+	0.766408i	$0.277958\pi$
$258$		0			0
$259$	8.62888	+	4.61223i	0.536173	+	0.286590i
$260$		0			0
$261$	−0.654936	+	0.798042i	−0.0405395	+	0.0493975i
$262$		0			0
$263$	−12.4436	−	8.31457i	−0.767307	−	0.512698i	0.109240	−	0.994015i	$-0.465158\pi$
$263$	−12.4436	−	8.31457i	−0.767307	−	0.512698i	−0.876546	+	0.481317i	$0.840158\pi$
$264$		0			0
$265$	−1.53359	−	2.29517i	−0.0942074	−	0.140991i
$266$		0			0
$267$	−1.54518	−	0.468727i	−0.0945638	−	0.0286856i
$268$		0			0
$269$	10.6274	−	8.72169i	0.647964	−	0.531771i	−0.252004	−	0.967726i	$-0.581090\pi$
$269$	10.6274	−	8.72169i	0.647964	−	0.531771i	0.899968	+	0.435956i	$0.143590\pi$
$270$		0			0
$271$	15.6133	−	6.46724i	0.948440	−	0.392857i	0.145796	−	0.989315i	$-0.453426\pi$
$271$	15.6133	−	6.46724i	0.948440	−	0.392857i	0.802644	+	0.596458i	$0.203426\pi$
$272$		0			0
$273$	−7.94521	−	3.29101i	−0.480866	−	0.199181i
$274$		0			0
$275$	2.69484	−	27.3612i	0.162505	−	1.64994i
$276$		0			0
$277$	−0.185232	−	0.346545i	−0.0111295	−	0.0208219i	0.876295	−	0.481775i	$-0.160008\pi$
$277$	−0.185232	−	0.346545i	−0.0111295	−	0.0208219i	−0.887425	+	0.460953i	$0.847508\pi$
$278$		0			0
$279$	−0.597934	−	0.118936i	−0.0357973	−	0.00712054i
$280$		0			0
$281$	−3.00413	−	15.1028i	−0.179211	−	0.900955i	−0.960817	−	0.277183i	$-0.910599\pi$
$281$	−3.00413	−	15.1028i	−0.179211	−	0.900955i	0.781606	−	0.623772i	$-0.214401\pi$
$282$		0			0
$283$	−2.32268	−	23.5825i	−0.138069	−	1.40184i	−0.775509	−	0.631337i	$-0.782507\pi$
$283$	−2.32268	−	23.5825i	−0.138069	−	1.40184i	0.637440	−	0.770500i	$-0.279993\pi$
$284$		0			0
$285$	−0.151788	−	0.500378i	−0.00899114	−	0.0296398i
$286$		0			0
$287$	10.1194	−	10.1194i	0.597328	−	0.597328i
$288$		0			0
$289$	−4.40622	−	4.40622i	−0.259189	−	0.259189i
$290$		0			0
$291$	3.51224	−	1.06543i	0.205891	−	0.0624565i
$292$		0			0
$293$	−25.0935	+	2.47150i	−1.46598	+	0.144386i	−0.799288	−	0.600948i	$-0.794790\pi$
$293$	−25.0935	+	2.47150i	−1.46598	+	0.144386i	−0.666691	+	0.745334i	$0.732290\pi$
$294$		0			0
$295$	−3.50882	+	0.697948i	−0.204291	+	0.0406361i
$296$		0			0
$297$	−3.35017	+	16.8424i	−0.194397	+	0.977298i
$298$		0			0
$299$	37.9452	−	20.2822i	2.19443	−	1.17295i
$300$		0			0
$301$	−19.4988	−	1.92046i	−1.12389	−	0.110694i
$302$		0			0
$303$	−2.56948	+	6.20327i	−0.147613	+	0.356369i
$304$		0			0
$305$	−0.658049	−	1.58867i	−0.0376798	−	0.0909670i
$306$		0			0
$307$	−7.65429	−	9.32678i	−0.436854	−	0.532308i	0.507319	−	0.861758i	$-0.330636\pi$
$307$	−7.65429	−	9.32678i	−0.436854	−	0.532308i	−0.944173	+	0.329451i	$0.893136\pi$
$308$		0			0
$309$	1.35793	−	4.47650i	0.0772500	−	0.254659i
$310$		0			0
$311$	−19.7640	+	13.2059i	−1.12072	+	0.748839i	−0.970807	−	0.239861i	$-0.922898\pi$
$311$	−19.7640	+	13.2059i	−1.12072	+	0.748839i	−0.149909	+	0.988700i	$0.547898\pi$
$312$		0			0
$313$	15.0340	−	22.5000i	0.849773	−	1.27178i	−0.110826	−	0.993840i	$-0.535350\pi$
$313$	15.0340	−	22.5000i	0.849773	−	1.27178i	0.960600	−	0.277936i	$-0.0896503\pi$
$314$		0			0
$315$	1.85631	+	1.52344i	0.104591	+	0.0858359i
$316$		0			0
$317$	10.9180	−	20.4262i	0.613217	−	1.14725i	−0.363272	−	0.931683i	$-0.618340\pi$
$317$	10.9180	−	20.4262i	0.613217	−	1.14725i	0.976489	−	0.215566i	$-0.0691596\pi$
$318$		0			0
$319$			2.15223i			0.120502i
$320$		0			0
$321$		−	1.65052i		−	0.0921232i
$322$		0			0
$323$	−3.93527	+	7.36238i	−0.218964	+	0.409654i
$324$		0			0
$325$	26.7580	+	21.9598i	1.48427	+	1.21811i
$326$		0			0
$327$	3.50480	−	5.24530i	0.193816	−	0.290066i
$328$		0			0
$329$	7.20281	−	4.81276i	0.397104	−	0.265336i
$330$		0			0
$331$	−8.97323	+	29.5808i	−0.493213	+	1.62591i	0.258213	+	0.966088i	$0.416867\pi$
$331$	−8.97323	+	29.5808i	−0.493213	+	1.62591i	−0.751426	+	0.659818i	$0.770633\pi$
$332$		0			0
$333$	7.41991	+	9.04119i	0.406609	+	0.495454i
$334$		0			0
$335$	0.324380	+	0.783122i	0.0177228	+	0.0427865i
$336$		0			0
$337$	−11.5412	+	27.8630i	−0.628692	+	1.51780i	0.212557	+	0.977149i	$0.431821\pi$
$337$	−11.5412	+	27.8630i	−0.628692	+	1.51780i	−0.841249	+	0.540648i	$0.818179\pi$
$338$		0			0
$339$	−0.406551	−	0.0400418i	−0.0220808	−	0.00217477i
$340$		0			0
$341$	−1.12088	+	0.599121i	−0.0606989	+	0.0324442i
$342$		0			0
$343$	−3.91652	+	19.6897i	−0.211472	+	1.06314i
$344$		0			0
$345$	1.21513	−	0.241704i	0.0654202	−	0.0130129i
$346$		0			0
$347$	−12.1774	+	1.19937i	−0.653716	+	0.0643854i	−0.419438	−	0.907784i	$-0.637773\pi$
$347$	−12.1774	+	1.19937i	−0.653716	+	0.0643854i	−0.234278	+	0.972170i	$0.575273\pi$
$348$		0			0
$349$	−4.75992	+	1.44391i	−0.254793	+	0.0772906i	−0.415097	−	0.909777i	$-0.636252\pi$
$349$	−4.75992	+	1.44391i	−0.254793	+	0.0772906i	0.160304	+	0.987068i	$0.448752\pi$
$350$		0			0
$351$	−15.2881	−	15.2881i	−0.816020	−	0.816020i
$352$		0			0
$353$	−3.17306	+	3.17306i	−0.168885	+	0.168885i	−0.786489	−	0.617604i	$-0.788103\pi$
$353$	−3.17306	+	3.17306i	−0.168885	+	0.168885i	0.617604	+	0.786489i	$0.288103\pi$
$354$		0			0
$355$	−0.566109	−	1.86621i	−0.0300460	−	0.0990482i
$356$		0			0
$357$	0.387514	+	3.93450i	0.0205094	+	0.208236i
$358$		0			0
$359$	4.74923	+	23.8760i	0.250655	+	1.26013i	0.876966	+	0.480553i	$0.159564\pi$
$359$	4.74923	+	23.8760i	0.250655	+	1.26013i	−0.626311	+	0.779573i	$0.715436\pi$
$360$		0			0
$361$	12.2876	+	2.44416i	0.646717	+	0.128640i
$362$		0			0
$363$	5.27822	+	9.87485i	0.277035	+	0.518295i
$364$		0			0
$365$	−0.409686	+	4.15961i	−0.0214439	+	0.217724i
$366$		0			0
$367$	−12.5817	−	5.21152i	−0.656761	−	0.272039i	0.0293140	−	0.999570i	$-0.490668\pi$
$367$	−12.5817	−	5.21152i	−0.656761	−	0.272039i	−0.686075	+	0.727531i	$0.740668\pi$
$368$		0			0
$369$	15.8052	−	6.54672i	0.822785	−	0.340809i
$370$		0			0
$371$	−12.5070	+	10.2642i	−0.649331	+	0.532892i
$372$		0			0
$373$	8.62878	+	2.61751i	0.446781	+	0.135530i	0.505655	−	0.862736i	$-0.331251\pi$
$373$	8.62878	+	2.61751i	0.446781	+	0.135530i	−0.0588737	+	0.998265i	$0.518751\pi$
$374$		0			0
$375$	1.12474	+	1.68329i	0.0580814	+	0.0869249i
$376$		0			0
$377$	−2.25307	−	1.50545i	−0.116039	−	0.0775346i
$378$		0			0
$379$	−9.97217	+	12.1511i	−0.512236	+	0.624161i	−0.963331	−	0.268315i	$-0.913533\pi$
$379$	−9.97217	+	12.1511i	−0.512236	+	0.624161i	0.451096	+	0.892476i	$0.351033\pi$
$380$		0			0
$381$	5.09745	+	2.72464i	0.261150	+	0.139588i
$382$		0			0
$383$	21.2134			1.08395			0.541977	−	0.840393i	$-0.317676\pi$
$383$	21.2134			1.08395			0.541977	+	0.840393i	$0.317676\pi$
$384$		0			0
$385$	5.00628			0.255143
$386$		0			0
$387$	−20.6561	−	11.0409i	−1.05001	−	0.561242i
$388$		0			0
$389$	22.7612	−	27.7346i	1.15404	−	1.40620i	0.255780	−	0.966735i	$-0.417668\pi$
$389$	22.7612	−	27.7346i	1.15404	−	1.40620i	0.898259	−	0.439466i	$-0.144832\pi$
$390$		0			0
$391$	−16.4463	−	10.9891i	−0.831727	−	0.555742i
$392$		0			0
$393$	−0.832125	−	1.24536i	−0.0419752	−	0.0628203i
$394$		0			0
$395$	3.84501	+	1.16637i	0.193463	+	0.0586865i
$396$		0			0
$397$	6.49181	−	5.32769i	0.325814	−	0.267389i	−0.457238	−	0.889344i	$-0.651161\pi$
$397$	6.49181	−	5.32769i	0.325814	−	0.267389i	0.783053	+	0.621955i	$0.213661\pi$
$398$		0			0
$399$	−2.83157	+	1.17287i	−0.141756	+	0.0587172i
$400$		0			0
$401$	−10.6393	−	4.40694i	−0.531301	−	0.220072i	0.100872	−	0.994899i	$-0.467837\pi$
$401$	−10.6393	−	4.40694i	−0.531301	−	0.220072i	−0.632173	+	0.774827i	$0.717837\pi$
$402$		0			0
$403$	0.156844	−	1.59247i	0.00781296	−	0.0793263i
$404$		0			0
$405$	1.19928	+	2.24370i	0.0595929	+	0.111490i
$406$		0			0
$407$	23.9146	+	4.75691i	1.18540	+	0.235791i
$408$		0			0
$409$	−0.655109	−	3.29346i	−0.0323931	−	0.162851i	0.961203	−	0.275842i	$-0.0889567\pi$
$409$	−0.655109	−	3.29346i	−0.0323931	−	0.162851i	−0.993596	+	0.112991i	$0.963957\pi$
$410$		0			0
$411$	0.593619	+	6.02711i	0.0292811	+	0.297296i
$412$		0			0
$413$	6.08709	+	20.0665i	0.299526	+	0.987406i
$414$		0			0
$415$	3.01116	−	3.01116i	0.147812	−	0.147812i
$416$		0			0
$417$	5.45387	+	5.45387i	0.267077	+	0.267077i
$418$		0			0
$419$	−15.6047	+	4.73363i	−0.762339	+	0.231253i	−0.647432	−	0.762123i	$-0.724157\pi$
$419$	−15.6047	+	4.73363i	−0.762339	+	0.231253i	−0.114907	+	0.993376i	$0.536657\pi$
$420$		0			0
$421$	12.1998	−	1.20158i	0.594584	−	0.0585614i	0.203750	−	0.979023i	$-0.434687\pi$
$421$	12.1998	−	1.20158i	0.594584	−	0.0585614i	0.390833	+	0.920461i	$0.372187\pi$
$422$		0			0
$423$	10.1565	−	2.02026i	0.493827	−	0.0982283i
$424$		0			0
$425$	3.10456	−	15.6077i	0.150593	−	0.757084i
$426$		0			0
$427$	−8.88888	+	4.75120i	−0.430163	+	0.229927i
$428$		0			0
$429$	−21.3284	−	2.10066i	−1.02974	−	0.101421i
$430$		0			0
$431$	−1.39018	+	3.35620i	−0.0669627	+	0.161662i	−0.953818	−	0.300385i	$-0.902885\pi$
$431$	−1.39018	+	3.35620i	−0.0669627	+	0.161662i	0.886855	+	0.462047i	$0.152885\pi$
$432$		0			0
$433$	9.47246	+	22.8685i	0.455217	+	1.09899i	0.970312	+	0.241858i	$0.0777569\pi$
$433$	9.47246	+	22.8685i	0.455217	+	1.09899i	−0.515094	+	0.857133i	$0.672243\pi$
$434$		0			0
$435$	−0.0495001	−	0.0603161i	−0.00237335	−	0.00289193i
$436$		0			0
$437$	4.45116	−	14.6735i	0.212928	−	0.701930i
$438$		0			0
$439$	−11.6310	+	7.77162i	−0.555120	+	0.370919i	−0.801261	−	0.598315i	$-0.795837\pi$
$439$	−11.6310	+	7.77162i	−0.555120	+	0.370919i	0.246141	+	0.969234i	$0.420837\pi$
$440$		0			0
$441$	−2.75640	+	4.12524i	−0.131257	+	0.196440i
$442$		0			0
$443$	4.71942	+	3.87312i	0.224226	+	0.184018i	0.739799	−	0.672828i	$-0.234921\pi$
$443$	4.71942	+	3.87312i	0.224226	+	0.184018i	−0.515572	+	0.856846i	$0.672421\pi$
$444$		0			0
$445$	−0.557886	+	1.04373i	−0.0264463	+	0.0494776i
$446$		0			0
$447$			3.07419i			0.145404i
$448$		0			0
$449$			34.0770i			1.60819i	0.594499	+	0.804097i	$0.297351\pi$
$449$			34.0770i			1.60819i	−0.594499	+	0.804097i	$0.702649\pi$
$450$		0			0
$451$	16.8120	−	31.4531i	0.791647	−	1.48107i
$452$		0			0
$453$	5.08029	+	4.16928i	0.238693	+	0.195890i
$454$		0			0
$455$	−3.50181	+	5.24082i	−0.164167	+	0.245694i
$456$		0			0
$457$	−14.0905	+	9.41498i	−0.659126	+	0.440414i	−0.839629	−	0.543160i	$-0.817228\pi$
$457$	−14.0905	+	9.41498i	−0.659126	+	0.440414i	0.180503	+	0.983574i	$0.442228\pi$
$458$		0			0
$459$	−2.88529	+	9.51151i	−0.134674	+	0.443959i
$460$		0			0
$461$	0.00243575	+	0.00296797i	0.000113444	+	0.000138232i	0.773067	−	0.634324i	$-0.218722\pi$
$461$	0.00243575	+	0.00296797i	0.000113444	+	0.000138232i	−0.772954	+	0.634462i	$0.781222\pi$
$462$		0			0
$463$	8.66646	+	20.9227i	0.402765	+	0.972360i	0.986992	+	0.160770i	$0.0513977\pi$
$463$	8.66646	+	20.9227i	0.402765	+	0.972360i	−0.584227	+	0.811590i	$0.698602\pi$
$464$		0			0
$465$	0.0176330	−	0.0425698i	0.000817711	−	0.00197413i
$466$		0			0
$467$	1.09183	+	0.107536i	0.0505238	+	0.00497616i	0.123247	−	0.992376i	$-0.460669\pi$
$467$	1.09183	+	0.107536i	0.0505238	+	0.00497616i	−0.0727237	+	0.997352i	$0.523169\pi$
$468$		0			0
$469$	4.38170	−	2.34207i	0.202328	−	0.108147i
$470$		0			0
$471$	−1.20093	+	6.03748i	−0.0553359	+	0.278192i
$472$		0			0
$473$	−47.8897	+	9.52585i	−2.20197	+	0.437999i
$474$		0			0
$475$	12.2771	−	1.20919i	0.563311	−	0.0554812i
$476$		0			0
$477$	−18.5084	+	5.61445i	−0.847439	+	0.257068i
$478$		0			0
$479$	4.48915	+	4.48915i	0.205115	+	0.205115i	0.802187	−	0.597073i	$-0.203670\pi$
$479$	4.48915	+	4.48915i	0.205115	+	0.205115i	−0.597073	+	0.802187i	$0.703670\pi$
$480$		0			0
$481$	−21.7076	+	21.7076i	−0.989782	+	0.989782i
$482$		0			0
$483$	−2.10800	−	6.94914i	−0.0959173	−	0.316197i
$484$		0			0
$485$	−0.263672	−	2.67711i	−0.0119727	−	0.121561i
$486$		0			0
$487$	4.29734	+	21.6042i	0.194731	+	0.978980i	0.947271	+	0.320433i	$0.103828\pi$
$487$	4.29734	+	21.6042i	0.194731	+	0.978980i	−0.752540	+	0.658547i	$0.771172\pi$
$488$		0			0
$489$	−1.08102	−	0.215027i	−0.0488852	−	0.00972387i
$490$		0			0
$491$	−7.21763	−	13.5032i	−0.325727	−	0.609393i	0.664751	−	0.747065i	$-0.268538\pi$
$491$	−7.21763	−	13.5032i	−0.325727	−	0.609393i	−0.990478	+	0.137673i	$0.956038\pi$
$492$		0			0
$493$	−0.122103	+	1.23973i	−0.00549922	+	0.0558345i
$494$		0			0
$495$	5.52899	+	2.29018i	0.248509	+	0.102936i
$496$		0			0
$497$	−10.5606	+	4.37436i	−0.473709	+	0.196217i
$498$		0			0
$499$	6.06328	−	4.97601i	0.271430	−	0.222757i	−0.488825	−	0.872382i	$-0.662574\pi$
$499$	6.06328	−	4.97601i	0.271430	−	0.222757i	0.760255	+	0.649625i	$0.225074\pi$
$500$		0			0
$501$	−9.52611	−	2.88971i	−0.425595	−	0.129103i
$502$		0			0
$503$	7.51362	+	11.2449i	0.335016	+	0.501386i	0.960284	−	0.279023i	$-0.0900107\pi$
$503$	7.51362	+	11.2449i	0.335016	+	0.501386i	−0.625269	+	0.780409i	$0.715011\pi$
$504$		0			0
$505$	4.09181	+	2.73406i	0.182083	+	0.121664i
$506$		0			0
$507$	12.7505	−	15.5366i	0.566270	−	0.690002i
$508$		0			0
$509$	27.5573	+	14.7297i	1.22145	+	0.652881i	0.950803	−	0.309797i	$-0.100261\pi$
$509$	27.5573	+	14.7297i	1.22145	+	0.652881i	0.270651	+	0.962678i	$0.412761\pi$
$510$		0			0
$511$	24.4990			1.08377
$512$		0			0
$513$	−7.70533			−0.340199
$514$		0			0
$515$	−3.02375	−	1.61623i	−0.133243	−	0.0712196i
$516$		0			0
$517$	13.6955	−	16.6880i	0.602328	−	0.733939i
$518$		0			0
$519$	5.42814	+	3.62697i	0.238269	+	0.159206i
$520$		0			0
$521$	−6.45817	−	9.66534i	−0.282938	−	0.423446i	0.662593	−	0.748980i	$-0.269456\pi$
$521$	−6.45817	−	9.66534i	−0.282938	−	0.423446i	−0.945530	+	0.325534i	$0.894456\pi$
$522$		0			0
$523$	−15.2569	−	4.62813i	−0.667137	−	0.202374i	−0.0614906	−	0.998108i	$-0.519585\pi$
$523$	−15.2569	−	4.62813i	−0.667137	−	0.202374i	−0.605646	+	0.795734i	$0.707085\pi$
$524$		0			0
$525$	4.51620	−	3.70635i	0.197103	−	0.161758i
$526$		0			0
$527$	−0.679637	+	0.281515i	−0.0296054	+	0.0122630i
$528$		0			0
$529$	12.3167	+	5.10176i	0.535510	+	0.221816i
$530$		0			0
$531$	−2.45699	+	24.9462i	−0.106624	+	1.08257i
$532$		0			0
$533$	21.1669	+	39.6006i	0.916842	+	1.71529i
$534$		0			0
$535$	−1.18647	−	0.236005i	−0.0512958	−	0.0102034i
$536$		0			0
$537$	−0.453312	−	2.27895i	−0.0195618	−	0.0983440i
$538$		0			0
$539$	1.01380	+	10.2933i	0.0436676	+	0.443365i
$540$		0			0
$541$	−3.82908	−	12.6228i	−0.164625	−	0.542695i	0.835350	−	0.549718i	$-0.185265\pi$
$541$	−3.82908	−	12.6228i	−0.164625	−	0.542695i	−0.999975	+	0.00702231i	$0.997765\pi$
$542$		0			0
$543$	2.90468	−	2.90468i	0.124652	−	0.124652i
$544$		0			0
$545$	−3.26943	−	3.26943i	−0.140047	−	0.140047i
$546$		0			0
$547$	−18.8627	+	5.72192i	−0.806509	+	0.244652i	−0.666506	−	0.745499i	$-0.732211\pi$
$547$	−18.8627	+	5.72192i	−0.806509	+	0.244652i	−0.140003	+	0.990151i	$0.544711\pi$
$548$		0			0
$549$	−11.9905	+	1.18096i	−0.511741	+	0.0504021i
$550$		0			0
$551$	−0.947160	+	0.188402i	−0.0403504	+	0.00802619i
$552$		0			0
$553$	4.59459	−	23.0986i	0.195382	−	0.982251i
$554$		0			0
$555$	−0.779610	+	0.416710i	−0.0330926	+	0.0176884i
$556$		0			0
$557$	−19.3845	−	1.90920i	−0.821347	−	0.0808956i	−0.321391	−	0.946947i	$-0.604150\pi$
$557$	−19.3845	−	1.90920i	−0.821347	−	0.0808956i	−0.499956	+	0.866051i	$0.666650\pi$
$558$		0			0
$559$	23.5259	−	56.7965i	0.995039	−	2.40224i
$560$		0			0
$561$	3.77042	+	9.10259i	0.159187	+	0.384312i
$562$		0			0
$563$	−13.7154	−	16.7123i	−0.578036	−	0.704339i	0.399111	−	0.916903i	$-0.369319\pi$
$563$	−13.7154	−	16.7123i	−0.578036	−	0.704339i	−0.977147	+	0.212563i	$0.931819\pi$
$564$		0			0
$565$	−0.0869157	+	0.286523i	−0.00365657	+	0.0120541i
$566$		0			0
$567$	12.3988	−	8.28463i	0.520701	−	0.347922i
$568$		0			0
$569$	−8.83996	+	13.2299i	−0.370590	+	0.554628i	−0.969157	−	0.246446i	$-0.920737\pi$
$569$	−8.83996	+	13.2299i	−0.370590	+	0.554628i	0.598566	+	0.801073i	$0.295737\pi$
$570$		0			0
$571$	26.6945	+	21.9076i	1.11713	+	0.916806i	0.997110	−	0.0759654i	$-0.0242039\pi$
$571$	26.6945	+	21.9076i	1.11713	+	0.916806i	0.120021	+	0.992771i	$0.461704\pi$
$572$		0			0
$573$	1.30106	−	2.43412i	0.0543527	−	0.101687i
$574$		0			0
$575$			29.2298i			1.21897i
$576$		0			0
$577$			17.8567i			0.743382i	0.928356	+	0.371691i	$0.121222\pi$
$577$			17.8567i			0.743382i	−0.928356	+	0.371691i	$0.878778\pi$
$578$		0			0
$579$	0.897319	−	1.67877i	0.0372913	−	0.0697671i
$580$		0			0
$581$	−19.2945	−	15.8346i	−0.800470	−	0.656929i
$582$		0			0
$583$	−22.4012	+	33.5257i	−0.927762	+	1.38849i
$584$		0			0
$585$	−6.26491	+	4.18608i	−0.259022	+	0.173073i
$586$		0			0
$587$	6.89478	−	22.7290i	0.284578	−	0.938128i	−0.691806	−	0.722084i	$-0.743184\pi$
$587$	6.89478	−	22.7290i	0.284578	−	0.938128i	0.976384	−	0.216044i	$-0.0693155\pi$
$588$		0			0
$589$	−0.361782	−	0.440832i	−0.0149070	−	0.0181642i
$590$		0			0
$591$	−0.114411	−	0.276212i	−0.00470622	−	0.0113618i
$592$		0			0
$593$	14.0716	−	33.9719i	0.577852	−	1.39506i	−0.316884	−	0.948464i	$-0.602637\pi$
$593$	14.0716	−	33.9719i	0.577852	−	1.39506i	0.894736	−	0.446595i	$-0.147363\pi$
$594$		0			0
$595$	2.88371	+	0.284021i	0.118221	+	0.0116437i
$596$		0			0
$597$	10.2219	−	5.46370i	0.418353	−	0.223614i
$598$		0			0
$599$	0.609490	−	3.06411i	0.0249031	−	0.125196i	−0.966334	−	0.257291i	$-0.917170\pi$
$599$	0.609490	−	3.06411i	0.0249031	−	0.125196i	0.991237	+	0.132094i	$0.0421702\pi$
$600$		0			0
$601$	10.1942	−	2.02775i	0.415830	−	0.0827138i	0.0172589	−	0.999851i	$-0.494506\pi$
$601$	10.1942	−	2.02775i	0.415830	−	0.0827138i	0.398572	+	0.917137i	$0.369506\pi$
$602$		0			0
$603$	5.91060	−	0.582144i	0.240698	−	0.0237067i
$604$		0			0
$605$	7.85323	−	2.38225i	0.319279	−	0.0968523i
$606$		0			0
$607$	−4.54706	−	4.54706i	−0.184559	−	0.184559i	0.608780	−	0.793339i	$-0.291659\pi$
$607$	−4.54706	−	4.54706i	−0.184559	−	0.184559i	−0.793339	+	0.608780i	$0.791659\pi$
$608$		0			0
$609$	−0.323394	+	0.323394i	−0.0131046	+	0.0131046i
$610$		0			0
$611$	7.89010	+	26.0102i	0.319199	+	1.05226i
$612$		0			0
$613$	2.81240	+	28.5547i	0.113592	+	1.15331i	0.867881	+	0.496772i	$0.165482\pi$
$613$	2.81240	+	28.5547i	0.113592	+	1.15331i	−0.754289	+	0.656542i	$0.772018\pi$
$614$		0			0
$615$	0.252248	+	1.26814i	0.0101716	+	0.0511362i
$616$		0			0
$617$	−1.85067	−	0.368121i	−0.0745051	−	0.0148200i	0.157697	−	0.987488i	$-0.449593\pi$
$617$	−1.85067	−	0.368121i	−0.0745051	−	0.0148200i	−0.232202	+	0.972668i	$0.574593\pi$
$618$		0			0
$619$	−2.06273	−	3.85910i	−0.0829082	−	0.155110i	0.837051	−	0.547126i	$-0.184278\pi$
$619$	−2.06273	−	3.85910i	−0.0829082	−	0.155110i	−0.919959	+	0.392015i	$0.871778\pi$
$620$		0			0
$621$	1.78948	−	18.1689i	0.0718095	−	0.729094i
$622$		0			0
$623$	6.40874	+	2.65459i	0.256761	+	0.106354i
$624$		0			0
$625$	−21.0302	+	8.71100i	−0.841209	+	0.348440i
$626$		0			0
$627$	−5.90421	+	4.84546i	−0.235791	+	0.193509i
$628$		0			0
$629$	13.5054	+	4.09682i	0.538496	+	0.163351i
$630$		0			0
$631$	−16.0731	−	24.0551i	−0.639861	−	0.957619i	−0.999697	−	0.0246040i	$-0.992168\pi$
$631$	−16.0731	−	24.0551i	−0.639861	−	0.957619i	0.359836	−	0.933015i	$-0.382832\pi$
$632$		0			0
$633$	4.25898	+	2.84576i	0.169279	+	0.113109i
$634$		0			0
$635$	2.68748	−	3.27470i	0.106649	−	0.129952i
$636$		0			0
$637$	−11.4847	−	6.13871i	−0.455041	−	0.243224i
$638$		0			0
$639$	−13.6644			−0.540555
$640$		0			0
$641$	−21.9690			−0.867722			−0.433861	−	0.900980i	$-0.642849\pi$
$641$	−21.9690			−0.867722			−0.433861	+	0.900980i	$0.642849\pi$
$642$		0			0
$643$	−43.4598	−	23.2298i	−1.71389	−	0.916093i	−0.968338	−	0.249644i	$-0.919686\pi$
$643$	−43.4598	−	23.2298i	−1.71389	−	0.916093i	−0.745551	−	0.666448i	$-0.767814\pi$
$644$		0			0
$645$	1.12301	−	1.36840i	0.0442186	−	0.0538806i
$646$		0			0
$647$	37.6102	+	25.1303i	1.47861	+	0.987976i	0.993538	+	0.113501i	$0.0362066\pi$
$647$	37.6102	+	25.1303i	1.47861	+	0.987976i	0.485072	+	0.874474i	$0.338793\pi$
$648$		0			0
$649$	29.0328	+	43.4507i	1.13964	+	1.70559i
$650$		0			0
$651$	−0.258446	−	0.0783988i	−0.0101293	−	0.00307269i
$652$		0			0
$653$	−21.2645	+	17.4513i	−0.832144	+	0.682923i	−0.950730	−	0.310021i	$-0.899664\pi$
$653$	−21.2645	+	17.4513i	−0.832144	+	0.682923i	0.118586	+	0.992944i	$0.462164\pi$
$654$		0			0
$655$	−1.01421	+	0.420100i	−0.0396285	+	0.0164146i
$656$		0			0
$657$	27.0569	+	11.2073i	1.05559	+	0.437240i
$658$		0			0
$659$	0.147820	−	1.50084i	0.00575824	−	0.0584643i	−0.991876	−	0.127207i	$-0.959399\pi$
$659$	0.147820	−	1.50084i	0.00575824	−	0.0584643i	0.997634	+	0.0687427i	$0.0218987\pi$
$660$		0			0
$661$	−3.10228	−	5.80395i	−0.120665	−	0.225747i	0.814336	−	0.580394i	$-0.197101\pi$
$661$	−3.10228	−	5.80395i	−0.120665	−	0.225747i	−0.935001	+	0.354646i	$0.884601\pi$
$662$		0			0
$663$	−12.1664	−	2.42005i	−0.472503	−	0.0939868i
$664$		0			0
$665$	0.438239	+	2.20317i	0.0169942	+	0.0854354i
$666$		0			0
$667$	−0.224278	−	2.27713i	−0.00868406	−	0.0881708i
$668$		0			0
$669$	−1.46476	−	4.82866i	−0.0566309	−	0.186687i
$670$		0			0
$671$	−17.7610	+	17.7610i	−0.685654	+	0.685654i
$672$		0			0
$673$	−23.8409	−	23.8409i	−0.918998	−	0.918998i	0.0779582	−	0.996957i	$-0.475160\pi$
$673$	−23.8409	−	23.8409i	−0.918998	−	0.918998i	−0.996957	+	0.0779582i	$0.975160\pi$
$674$		0			0
$675$	14.0557	−	4.26375i	0.541004	−	0.164112i
$676$		0			0
$677$	17.0501	−	1.67928i	0.655287	−	0.0645401i	0.235091	−	0.971973i	$-0.424461\pi$
$677$	17.0501	−	1.67928i	0.655287	−	0.0645401i	0.420196	+	0.907433i	$0.361961\pi$
$678$		0			0
$679$	−15.4645	+	3.07608i	−0.593472	+	0.118049i
$680$		0			0
$681$	−1.49006	+	7.49103i	−0.0570992	+	0.287057i
$682$		0			0
$683$	13.0914	−	6.99752i	0.500930	−	0.267753i	−0.201522	−	0.979484i	$-0.564589\pi$
$683$	13.0914	−	6.99752i	0.500930	−	0.267753i	0.702452	+	0.711731i	$0.252089\pi$
$684$		0			0
$685$	4.41746	+	0.435082i	0.168782	+	0.0166236i
$686$		0			0
$687$	0.657841	−	1.58817i	0.0250982	−	0.0605924i
$688$		0			0
$689$	−19.4272	−	46.9014i	−0.740117	−	1.78680i
$690$		0			0
$691$	−13.3214	−	16.2322i	−0.506770	−	0.617501i	0.455289	−	0.890344i	$-0.349536\pi$
$691$	−13.3214	−	16.2322i	−0.506770	−	0.617501i	−0.962059	+	0.272843i	$0.912036\pi$
$692$		0			0
$693$	10.1825	−	33.5671i	0.386800	−	1.27511i
$694$		0			0
$695$	4.70034	−	3.14066i	0.178294	−	0.119132i
$696$		0			0
$697$	11.4685	−	17.1638i	0.434400	−	0.650125i
$698$		0			0
$699$	−9.67495	−	7.94003i	−0.365940	−	0.300320i
$700$		0			0
$701$	18.3551	−	34.3400i	0.693262	−	1.29700i	−0.251057	−	0.967972i	$-0.580778\pi$
$701$	18.3551	−	34.3400i	0.693262	−	1.29700i	0.944319	−	0.329030i	$-0.106722\pi$
$702$		0			0
$703$			10.9408i			0.412640i
$704$		0			0
$705$			0.782670i			0.0294770i
$706$		0			0
$707$	13.5973	−	25.4388i	0.511380	−	0.956725i
$708$		0			0
$709$	−21.6791	−	17.7916i	−0.814177	−	0.668178i	0.132207	−	0.991222i	$-0.457794\pi$
$709$	−21.6791	−	17.7916i	−0.814177	−	0.668178i	−0.946384	+	0.323045i	$0.895294\pi$
$710$		0			0
$711$	15.6410	−	23.4085i	0.586584	−	0.877886i
$712$		0			0
$713$	1.12349	−	0.750692i	0.0420750	−	0.0281136i
$714$		0			0
$715$	−4.55975	+	15.0315i	−0.170525	+	0.562146i
$716$		0			0
$717$	5.30722	+	6.46686i	0.198202	+	0.241509i
$718$		0			0
$719$	5.40009	+	13.0370i	0.201389	+	0.486197i	0.992018	−	0.126100i	$-0.0402459\pi$
$719$	5.40009	+	13.0370i	0.201389	+	0.486197i	−0.790628	+	0.612296i	$0.790246\pi$
$720$		0			0
$721$	−7.69051	+	18.5665i	−0.286409	+	0.691454i
$722$		0			0
$723$	6.93720	+	0.683255i	0.257997	+	0.0254105i
$724$		0			0
$725$	1.62351	−	0.867785i	0.0602957	−	0.0322287i
$726$		0			0
$727$	7.01362	−	35.2599i	0.260121	−	1.30772i	−0.600973	−	0.799269i	$-0.705220\pi$
$727$	7.01362	−	35.2599i	0.260121	−	1.30772i	0.861094	−	0.508446i	$-0.169780\pi$
$728$		0			0
$729$	12.7637	−	2.53887i	0.472731	−	0.0940321i
$730$		0			0
$731$	−28.1258	+	2.77015i	−1.04027	+	0.102458i
$732$		0			0
$733$	25.4206	−	7.71125i	0.938930	−	0.284821i	0.216514	−	0.976280i	$-0.430531\pi$
$733$	25.4206	−	7.71125i	0.938930	−	0.284821i	0.722417	+	0.691458i	$0.243031\pi$
$734$		0			0
$735$	−0.265152	−	0.265152i	−0.00978029	−	0.00978029i
$736$		0			0
$737$	8.75512	−	8.75512i	0.322499	−	0.322499i
$738$		0			0
$739$	−5.44233	−	17.9409i	−0.200199	−	0.659968i	−0.998345	−	0.0575043i	$-0.981686\pi$
$739$	−5.44233	−	17.9409i	−0.200199	−	0.659968i	0.798146	−	0.602464i	$-0.205814\pi$
$740$		0			0
$741$	−0.942576	−	9.57014i	−0.0346264	−	0.351568i
$742$		0			0
$743$	−4.06520	−	20.4371i	−0.149138	−	0.749766i	−0.980881	−	0.194606i	$-0.937657\pi$
$743$	−4.06520	−	20.4371i	−0.149138	−	0.749766i	0.831744	−	0.555160i	$-0.187343\pi$
$744$		0			0
$745$	2.20988	+	0.439572i	0.0809636	+	0.0161047i
$746$		0			0
$747$	−14.0653	−	26.3144i	−0.514623	−	0.962793i
$748$		0			0
$749$	−0.695001	+	7.05646i	−0.0253948	+	0.257837i
$750$		0			0
$751$	29.9648	+	12.4118i	1.09343	+	0.452913i	0.855201	−	0.518296i	$-0.173433\pi$
$751$	29.9648	+	12.4118i	1.09343	+	0.452913i	0.238228	+	0.971209i	$0.423433\pi$
$752$		0			0
$753$	3.32711	−	1.37813i	0.121247	−	0.0502220i
$754$		0			0
$755$	3.72350	−	3.05580i	0.135512	−	0.111212i
$756$		0			0
$757$	−2.71000	−	0.822069i	−0.0984965	−	0.0298786i	0.240652	−	0.970612i	$-0.422639\pi$
$757$	−2.71000	−	0.822069i	−0.0984965	−	0.0298786i	−0.339148	+	0.940733i	$0.610139\pi$
$758$		0			0
$759$	−10.0543	−	15.0472i	−0.364946	−	0.546181i
$760$		0			0
$761$	−11.4102	−	7.62405i	−0.413619	−	0.276372i	0.331301	−	0.943525i	$-0.392512\pi$
$761$	−11.4102	−	7.62405i	−0.413619	−	0.276372i	−0.744920	+	0.667154i	$0.767512\pi$
$762$		0			0
$763$	−17.1927	+	20.9494i	−0.622418	+	0.758418i
$764$		0			0
$765$	3.05488	+	1.63286i	0.110449	+	0.0590363i
$766$		0			0
$767$	−65.7943			−2.37569
$768$		0			0
$769$	30.0420			1.08334			0.541671	−	0.840591i	$-0.317792\pi$
$769$	30.0420			1.08334			0.541671	+	0.840591i	$0.317792\pi$
$770$		0			0
$771$	9.61883	+	5.14137i	0.346414	+	0.185162i
$772$		0			0
$773$	−0.818360	+	0.997175i	−0.0294344	+	0.0358659i	−0.787520	−	0.616290i	$-0.788635\pi$
$773$	−0.818360	+	0.997175i	−0.0294344	+	0.0358659i	0.758085	+	0.652155i	$0.226135\pi$
$774$		0			0
$775$	0.903880	+	0.603953i	0.0324683	+	0.0216946i
$776$		0			0
$777$	2.87863	+	4.30817i	0.103270	+	0.154555i
$778$		0			0
$779$	15.3136	+	4.64534i	0.548668	+	0.166437i
$780$		0			0
$781$	−22.0204	+	18.0716i	−0.787950	+	0.646654i
$782$		0			0
$783$	−1.06229	+	0.440013i	−0.0379630	+	0.0157248i
$784$		0			0
$785$	4.16831	+	1.72657i	0.148773	+	0.0616240i
$786$		0			0
$787$	−3.03274	+	30.7919i	−0.108106	+	1.09761i	0.776130	+	0.630573i	$0.217180\pi$
$787$	−3.03274	+	30.7919i	−0.108106	+	1.09761i	−0.884236	+	0.467041i	$0.845320\pi$
$788$		0			0
$789$	−3.73601	−	6.98959i	−0.133006	−	0.248836i
$790$		0			0
$791$	1.72126	+	0.342380i	0.0612010	+	0.0121736i
$792$		0			0
$793$	−6.16958	−	31.0166i	−0.219088	−	1.10143i
$794$		0			0
$795$	−0.143282	−	1.45477i	−0.00508170	−	0.0515954i
$796$		0			0
$797$	6.78387	+	22.3634i	0.240297	+	0.792153i	0.991273	+	0.131824i	$0.0420833\pi$
$797$	6.78387	+	22.3634i	0.240297	+	0.792153i	−0.750976	+	0.660329i	$0.770417\pi$
$798$		0			0
$799$	8.83565	−	8.83565i	0.312583	−	0.312583i
$800$		0			0
$801$	5.86351	+	5.86351i	0.207177	+	0.207177i
$802$		0			0
$803$	58.4247	−	17.7230i	2.06176	−	0.625429i
$804$		0			0
$805$	−5.29679	+	0.521689i	−0.186687	+	0.0183871i
$806$		0			0
$807$	7.14064	−	1.42036i	0.251362	−	0.0499991i
$808$		0			0
$809$	0.0208599	−	0.104870i	0.000733394	−	0.00368702i	−0.980417	−	0.196933i	$-0.936902\pi$
$809$	0.0208599	−	0.104870i	0.000733394	−	0.00368702i	0.981150	+	0.193246i	$0.0619017\pi$
$810$		0			0
$811$	−43.1512	+	23.0648i	−1.51525	+	0.809915i	−0.998919	−	0.0464769i	$-0.985201\pi$
$811$	−43.1512	+	23.0648i	−1.51525	+	0.809915i	−0.516326	+	0.856392i	$0.672701\pi$
$812$		0			0
$813$	8.90644	+	0.877208i	0.312363	+	0.0307650i
$814$		0			0
$815$	−0.309144	+	0.746339i	−0.0108288	+	0.0261431i
$816$		0			0
$817$	−8.38432	−	20.2415i	−0.293330	−	0.708162i
$818$		0			0
$819$	28.0173	+	34.1391i	0.979002	+	1.19292i
$820$		0			0
$821$	−9.55156	+	31.4873i	−0.333352	+	1.09891i	0.616798	+	0.787121i	$0.288429\pi$
$821$	−9.55156	+	31.4873i	−0.333352	+	1.09891i	−0.950150	+	0.311793i	$0.899071\pi$
$822$		0			0
$823$	−29.4917	+	19.7057i	−1.02802	+	0.686898i	−0.950701	−	0.310109i	$-0.899635\pi$
$823$	−29.4917	+	19.7057i	−1.02802	+	0.686898i	−0.0773144	+	0.997007i	$0.524635\pi$
$824$		0			0
$825$	8.08893	−	12.1059i	0.281621	−	0.421475i
$826$		0			0
$827$	13.1680	+	10.8067i	0.457895	+	0.375785i	0.834878	−	0.550435i	$-0.185538\pi$
$827$	13.1680	+	10.8067i	0.457895	+	0.375785i	−0.376982	+	0.926220i	$0.623038\pi$
$828$		0			0
$829$	−10.6839	+	19.9883i	−0.371069	+	0.694221i	−0.996274	−	0.0862393i	$-0.972515\pi$
$829$	−10.6839	+	19.9883i	−0.371069	+	0.694221i	0.625206	+	0.780460i	$0.285015\pi$
$830$		0			0
$831$		−	0.208090i		−	0.00721857i
$832$		0			0
$833$			5.98667i			0.207426i
$834$		0			0
$835$	−3.43938	+	6.43463i	−0.119025	+	0.222680i
$836$		0			0
$837$	−0.524868	−	0.430748i	−0.0181421	−	0.0148888i
$838$		0			0
$839$	24.1250	−	36.1056i	0.832887	−	1.24650i	−0.133919	−	0.990992i	$-0.542756\pi$
$839$	24.1250	−	36.1056i	0.832887	−	1.24650i	0.966806	−	0.255511i	$-0.0822438\pi$
$840$		0			0
$841$	23.9928	−	16.0315i	0.827338	−	0.552809i
$842$		0			0
$843$	2.36716	−	7.80349i	0.0815294	−	0.268766i
$844$		0			0
$845$	−9.34525	−	11.3872i	−0.321486	−	0.391732i
$846$		0			0
$847$	−18.4078	−	44.4404i	−0.632500	−	1.52699i
$848$		0			0
$849$	4.80229	−	11.5937i	0.164814	−	0.397896i
$850$		0			0
$851$	−25.7981	−	2.54089i	−0.884347	−	0.0871005i
$852$		0			0
$853$	−34.4823	+	18.4312i	−1.18065	+	0.631071i	−0.940543	−	0.339675i	$-0.889683\pi$
$853$	−34.4823	+	18.4312i	−1.18065	+	0.631071i	−0.240109	+	0.970746i	$0.577183\pi$
$854$		0			0
$855$	−0.523873	+	2.63369i	−0.0179161	+	0.0900702i
$856$		0			0
$857$	−9.96996	+	1.98315i	−0.340567	+	0.0677431i	−0.362411	−	0.932018i	$-0.618046\pi$
$857$	−9.96996	+	1.98315i	−0.340567	+	0.0677431i	0.0218437	+	0.999761i	$0.493046\pi$
$858$		0			0
$859$	52.5371	−	5.17446i	1.79254	−	0.176550i	0.853671	−	0.520813i	$-0.174371\pi$
$859$	52.5371	−	5.17446i	1.79254	−	0.176550i	0.938873	+	0.344263i	$0.111871\pi$
$860$		0			0
$861$	7.25229	−	2.19996i	0.247158	−	0.0749744i
$862$		0			0
$863$	−26.9090	−	26.9090i	−0.915993	−	0.915993i	0.0807419	−	0.996735i	$-0.474271\pi$
$863$	−26.9090	−	26.9090i	−0.915993	−	0.915993i	−0.996735	+	0.0807419i	$0.974271\pi$
$864$		0			0
$865$	3.38340	−	3.38340i	0.115039	−	0.115039i
$866$		0			0
$867$	−0.957915	−	3.15782i	−0.0325325	−	0.107245i
$868$		0			0
$869$	−5.75278	−	58.4089i	−0.195150	−	1.98139i
$870$		0			0
$871$	3.04124	+	15.2894i	0.103049	+	0.518060i
$872$		0			0
$873$	−18.4863	−	3.67716i	−0.625667	−	0.124453i
$874$		0			0
$875$	−4.09979	−	7.67017i	−0.138598	−	0.259299i
$876$		0			0
$877$	−0.904601	+	9.18457i	−0.0305462	+	0.310141i	0.967756	+	0.251890i	$0.0810522\pi$
$877$	−0.904601	+	9.18457i	−0.0305462	+	0.310141i	−0.998302	+	0.0582506i	$0.981448\pi$
$878$		0			0
$879$	−12.3366	−	5.10998i	−0.416102	−	0.172355i
$880$		0			0
$881$	50.7430	−	21.0184i	1.70957	−	0.708129i	0.709580	−	0.704625i	$-0.248885\pi$
$881$	50.7430	−	21.0184i	1.70957	−	0.708129i	0.999994	−	0.00350337i	$-0.00111516\pi$
$882$		0			0
$883$	−9.47285	+	7.77417i	−0.318787	+	0.261622i	−0.780154	−	0.625588i	$-0.784859\pi$
$883$	−9.47285	+	7.77417i	−0.318787	+	0.261622i	0.461367	+	0.887209i	$0.347359\pi$
$884$		0			0
$885$	−1.81298	−	0.549962i	−0.0609427	−	0.0184868i
$886$		0			0
$887$	−0.746354	−	1.11700i	−0.0250601	−	0.0375051i	0.818728	−	0.574181i	$-0.194680\pi$
$887$	−0.746354	−	1.11700i	−0.0250601	−	0.0375051i	−0.843788	+	0.536676i	$0.819680\pi$
$888$		0			0
$889$	−20.6458	−	13.7951i	−0.692437	−	0.462671i
$890$		0			0
$891$	23.5753	−	28.7266i	0.789802	−	0.962376i
$892$		0			0
$893$	8.54299	+	4.56632i	0.285880	+	0.152806i
$894$		0			0
$895$	−1.70304			−0.0569262
$896$		0			0
$897$	22.7850			0.760769
$898$		0			0
$899$	−0.0750503	−	0.0401152i	−0.00250307	−	0.00133792i
$900$		0			0
$901$	−14.8055	+	18.0406i	−0.493244	+	0.601019i
$902$		0			0
$903$	−8.62724	−	5.76453i	−0.287096	−	0.191832i
$904$		0			0
$905$	−1.67269	−	2.50336i	−0.0556021	−	0.0832144i
$906$		0			0
$907$	−49.7486	−	15.0911i	−1.65187	−	0.501090i	−0.679334	−	0.733829i	$-0.737731\pi$
$907$	−49.7486	−	15.0911i	−1.65187	−	0.501090i	−0.972539	+	0.232738i	$0.925231\pi$
$908$		0			0
$909$	26.6543	−	21.8746i	0.884069	−	0.725536i
$910$		0			0
$911$	40.2036	−	16.6529i	1.33200	−	0.551734i	0.400778	−	0.916175i	$-0.368740\pi$
$911$	40.2036	−	16.6529i	1.33200	−	0.551734i	0.931226	+	0.364441i	$0.118740\pi$
$912$		0			0
$913$	−57.4682	−	23.8041i	−1.90192	−	0.787801i
$914$		0			0
$915$	0.0892569	−	0.906241i	0.00295074	−	0.0299594i
$916$		0			0
$917$	3.03318	+	5.67468i	0.100164	+	0.187394i
$918$		0			0
$919$	−13.6851	−	2.72213i	−0.451428	−	0.0897946i	−0.0358603	−	0.999357i	$-0.511417\pi$
$919$	−13.6851	−	2.72213i	−0.451428	−	0.0897946i	−0.415568	+	0.909562i	$0.636417\pi$
$920$		0			0
$921$	−1.24653	−	6.26674i	−0.0410746	−	0.206496i
$922$		0			0
$923$	−3.51544	−	35.6928i	−0.115712	−	1.17484i
$924$		0			0
$925$	−6.05410	−	19.9577i	−0.199057	−	0.656205i
$926$		0			0
$927$	−16.9870	+	16.9870i	−0.557925	+	0.557925i
$928$		0			0
$929$	15.5130	+	15.5130i	0.508966	+	0.508966i	0.914209	−	0.405243i	$-0.132813\pi$
$929$	15.5130	+	15.5130i	0.508966	+	0.508966i	−0.405243	+	0.914209i	$0.632813\pi$
$930$		0			0
$931$	−4.44117	+	1.34721i	−0.145553	+	0.0441531i
$932$		0			0
$933$	−12.5272	+	1.23382i	−0.410123	+	0.0403936i
$934$		0			0
$935$	7.08250	−	1.40880i	0.231623	−	0.0460726i
$936$		0			0
$937$	−9.01979	+	45.3455i	−0.294664	+	1.48137i	0.495570	+	0.868568i	$0.334959\pi$
$937$	−9.01979	+	45.3455i	−0.294664	+	1.48137i	−0.790234	+	0.612806i	$0.790041\pi$
$938$		0			0
$939$	12.6383	−	6.75529i	0.412434	−	0.220451i
$940$		0			0
$941$	−33.1007	−	3.26014i	−1.07905	−	0.106277i	−0.457163	−	0.889383i	$-0.651135\pi$
$941$	−33.1007	−	3.26014i	−1.07905	−	0.106277i	−0.621889	+	0.783105i	$0.713635\pi$
$942$		0			0
$943$	−14.5100	+	35.0303i	−0.472511	+	1.14074i
$944$		0			0
$945$	1.02351	+	2.47097i	0.0332947	+	0.0803805i
$946$		0			0
$947$	35.6196	+	43.4026i	1.15748	+	1.41039i	0.895351	+	0.445361i	$0.146925\pi$
$947$	35.6196	+	43.4026i	1.15748	+	1.41039i	0.262129	+	0.965033i	$0.415575\pi$
$948$		0			0
$949$	−22.3138	+	73.5589i	−0.724338	+	2.38782i
$950$		0			0
$951$	10.1982	−	6.81425i	0.330701	−	0.220967i
$952$		0			0
$953$	−13.3647	+	20.0017i	−0.432925	+	0.647918i	−0.982225	−	0.187707i	$-0.939894\pi$
$953$	−13.3647	+	20.0017i	−0.432925	+	0.647918i	0.549300	+	0.835625i	$0.314894\pi$
$954$		0			0
$955$	−1.56372	−	1.28331i	−0.0506009	−	0.0415271i
$956$		0			0
$957$	−0.537276	+	1.00517i	−0.0173677	+	0.0324926i
$958$		0			0
$959$		−	26.0176i		−	0.840152i
$960$		0			0
$961$			30.9497i			0.998379i
$962$		0			0
$963$	−3.99563	+	7.47530i	−0.128757	+	0.240888i
$964$		0			0
$965$	−1.07847	−	0.885078i	−0.0347172	−	0.0284917i
$966$		0			0
$967$	−8.59907	+	12.8694i	−0.276527	+	0.413853i	−0.943573	−	0.331164i	$-0.892559\pi$
$967$	−8.59907	+	12.8694i	−0.276527	+	0.413853i	0.667046	+	0.745017i	$0.267559\pi$
$968$		0			0
$969$	−3.67584	+	2.45612i	−0.118085	+	0.0789018i
$970$		0			0
$971$	−4.13247	+	13.6229i	−0.132617	+	0.437181i	−0.997949	−	0.0640194i	$-0.979608\pi$
$971$	−4.13247	+	13.6229i	−0.132617	+	0.437181i	0.865331	+	0.501200i	$0.167108\pi$
$972$		0			0
$973$	−21.0203	−	25.6134i	−0.673881	−	0.821126i
$974$		0			0
$975$	7.01504	+	16.9358i	0.224661	+	0.542380i
$976$		0			0
$977$	14.4604	−	34.9105i	0.462629	−	1.11689i	−0.504685	−	0.863304i	$-0.668391\pi$
$977$	14.4604	−	34.9105i	0.462629	−	1.11689i	0.967314	−	0.253582i	$-0.0816087\pi$
$978$		0			0
$979$	17.2038	+	1.69443i	0.549837	+	0.0541542i
$980$		0			0
$981$	−28.5713	+	15.2717i	−0.912213	+	0.487588i
$982$		0			0
$983$	−5.42528	+	27.2747i	−0.173040	+	0.869928i	0.792540	+	0.609820i	$0.208758\pi$
$983$	−5.42528	+	27.2747i	−0.173040	+	0.869928i	−0.965579	+	0.260108i	$0.916242\pi$
$984$		0			0
$985$	−0.214913	+	0.0427489i	−0.00684771	+	0.00136209i
$986$		0			0
$987$	4.56542	−	0.449655i	0.145319	−	0.0143127i
$988$		0			0
$989$	49.6761	−	15.0691i	1.57961	−	0.479169i
$990$		0			0
$991$	34.7879	+	34.7879i	1.10507	+	1.10507i	0.993788	+	0.111286i	$0.0354968\pi$
$991$	34.7879	+	34.7879i	1.10507	+	1.10507i	0.111286	+	0.993788i	$0.464503\pi$
$992$		0			0
$993$	−11.5753	+	11.5753i	−0.367330	+	0.367330i
$994$		0			0
$995$	−2.46597	−	8.12921i	−0.0781765	−	0.257713i
$996$		0			0
$997$	0.0356299	+	0.361756i	0.00112841	+	0.0114569i	0.995732	−	0.0922871i	$-0.0294177\pi$
$997$	0.0356299	+	0.361756i	0.00112841	+	0.0114569i	−0.994604	+	0.103744i	$0.966918\pi$
$998$		0			0
$999$	2.54133	+	12.7761i	0.0804042	+	0.404219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.273.9		240
4.3	odd	2		128.2.k.a.109.2	yes	240
128.27	odd	32		128.2.k.a.101.2	✓	240
128.101	even	32	inner	512.2.k.a.497.9		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.2	✓	240	128.27	odd	32
128.2.k.a.109.2	yes	240	4.3	odd	2
512.2.k.a.273.9		240	1.1	even	1	trivial
512.2.k.a.497.9		240	128.101	even	32	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.467037 + 0.249636i) q^{3} +(0.246231 - 0.300034i) q^{5} +(-1.89160 - 1.26393i) q^{7} +(-1.51091 - 2.26123i) q^{9} +(-5.42541 - 1.64578i) q^{11} +(5.51786 - 4.52839i) q^{13} +(0.189898 - 0.0786585i) q^{15} +(-3.03177 - 1.25580i) q^{17} +(0.249350 - 2.53169i) q^{19} +(-0.567925 - 1.06251i) q^{21} +(5.91175 + 1.17592i) q^{23} +(0.946061 + 4.75617i) q^{25} +(-0.296883 - 3.01431i) q^{27} +(-0.110196 - 0.363268i) q^{29} +(0.158513 - 0.158513i) q^{31} +(-2.12302 - 2.12302i) q^{33} +(-0.844991 + 0.256325i) q^{35} +(-4.28002 + 0.421545i) q^{37} +(3.70750 - 0.737467i) q^{39} +(-1.22722 + 6.16964i) q^{41} +(7.59540 - 4.05983i) q^{43} +(-1.05048 - 0.103463i) q^{45} +(-1.45718 + 3.51794i) q^{47} +(-0.698143 - 1.68547i) q^{49} +(-1.10246 - 1.34335i) q^{51} +(2.06447 - 6.80565i) q^{53} +(-1.82969 + 1.22256i) q^{55} +(0.748459 - 1.12015i) q^{57} +(-7.12505 - 5.84738i) q^{59} +(2.08843 - 3.90718i) q^{61} +6.18702i q^{63} -2.77058i q^{65} +(-1.02948 + 1.92602i) q^{67} +(2.46745 + 2.02499i) q^{69} +(2.79145 - 4.17771i) q^{71} +(-8.95387 + 5.98279i) q^{73} +(-0.745468 + 2.45748i) q^{75} +(8.18256 + 9.97047i) q^{77} +(3.96157 + 9.56408i) q^{79} +(-2.50836 + 6.05573i) q^{81} +(10.9186 + 1.07539i) q^{83} +(-1.12330 + 0.600415i) q^{85} +(0.0392192 - 0.197168i) q^{87} +(-2.99053 + 0.594853i) q^{89} +(-16.1612 + 1.59173i) q^{91} +(0.113602 - 0.0344609i) q^{93} +(-0.698195 - 0.698195i) q^{95} +(4.90076 - 4.90076i) q^{97} +(4.47579 + 14.7547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more