LMFDB - Embedded newform 513.2.f.h.163.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(163,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.163"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,1,0,-3,5,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 8x^{10} - x^{9} + 41x^{8} - 7x^{7} + 91x^{6} + 9x^{5} + 135x^{4} - 12x^{3} + 45x^{2} + 9x + 9 $ x^12 - x^11 + 8x^10 - x^9 + 41x^8 - 7x^7 + 91x^6 + 9x^5 + 135x^4 - 12x^3 + 45x^2 + 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.5
Root			$0.792283 + 1.37227i$ of defining polynomial
Character	$\chi$	$=$	513.163
Dual form			513.2.f.h.406.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.792283 - 1.37227i) q^{2} +(-0.255424 - 0.442408i) q^{4} +(-0.780905 + 1.35257i) q^{5} -0.188849 q^{7} +2.35966 q^{8} +(1.23740 + 2.14323i) q^{10} +1.98564 q^{11} +(2.46073 + 4.26212i) q^{13} +(-0.149622 + 0.259153i) q^{14} +(2.38037 - 4.12291i) q^{16} +(3.67265 - 6.36121i) q^{17} +(-1.14266 + 4.20646i) q^{19} +0.797849 q^{20} +(1.57319 - 2.72484i) q^{22} +(-0.631283 - 1.09341i) q^{23} +(1.28038 + 2.21768i) q^{25} +7.79839 q^{26} +(0.0482366 + 0.0835483i) q^{28} +(-3.51165 - 6.08235i) q^{29} +3.84607 q^{31} +(-1.41219 - 2.44598i) q^{32} +(-5.81955 - 10.0798i) q^{34} +(0.147473 - 0.255431i) q^{35} -1.66426 q^{37} +(4.86711 + 4.90075i) q^{38} +(-1.84267 + 3.19160i) q^{40} +(-2.28090 + 3.95064i) q^{41} +(-0.776707 + 1.34530i) q^{43} +(-0.507181 - 0.878463i) q^{44} -2.00062 q^{46} +(2.88618 + 4.99901i) q^{47} -6.96434 q^{49} +4.05768 q^{50} +(1.25706 - 2.17730i) q^{52} +(-2.93892 - 5.09036i) q^{53} +(-1.55059 + 2.68571i) q^{55} -0.445619 q^{56} -11.1289 q^{58} +(-0.657293 + 1.13846i) q^{59} +(-5.56088 - 9.63172i) q^{61} +(3.04718 - 5.27787i) q^{62} +5.04605 q^{64} -7.68640 q^{65} +(-5.36574 - 9.29374i) q^{67} -3.75234 q^{68} +(-0.233681 - 0.404747i) q^{70} +(-2.93677 + 5.08664i) q^{71} +(-5.90339 + 10.2250i) q^{73} +(-1.31856 + 2.28382i) q^{74} +(2.15284 - 0.568911i) q^{76} -0.374986 q^{77} +(4.14124 - 7.17284i) q^{79} +(3.71768 + 6.43921i) q^{80} +(3.61424 + 6.26005i) q^{82} -11.5479 q^{83} +(5.73598 + 9.93500i) q^{85} +(1.23074 + 2.13171i) q^{86} +4.68543 q^{88} +(0.512993 + 0.888530i) q^{89} +(-0.464707 - 0.804896i) q^{91} +(-0.322490 + 0.558569i) q^{92} +9.14668 q^{94} +(-4.79721 - 4.83037i) q^{95} +(2.12169 - 3.67487i) q^{97} +(-5.51772 + 9.55698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} + q^{10} - 4 q^{11} - 5 q^{13} + 2 q^{14} + 3 q^{16} + 10 q^{17} - 9 q^{19} - 2 q^{20} - 4 q^{22} + 3 q^{23} - 5 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) $ 12 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 + q^10 - 4 * q^11 - 5 * q^13 + 2 * q^14 + 3 * q^16 + 10 * q^17 - 9 * q^19 - 2 * q^20 - 4 * q^22 + 3 * q^23 - 5 * q^25 - 2 * q^26 - 2 * q^28 - 6 * q^29 - 4 * q^31 + 8 * q^32 + 4 * q^34 + 3 * q^35 + 26 * q^37 - 10 * q^38 - 6 * q^40 - 13 * q^41 - 3 * q^43 - 20 * q^44 - 10 * q^46 + 18 * q^47 + 26 * q^49 + 6 * q^50 - 22 * q^52 - q^53 - 6 * q^55 + 48 * q^56 + 28 * q^58 + 11 * q^59 - 13 * q^61 + 22 * q^62 - 72 * q^65 + 9 * q^67 - 10 * q^68 - 30 * q^70 - 6 * q^71 - 15 * q^73 + 43 * q^74 - 33 * q^76 - 58 * q^77 - 13 * q^79 + q^80 + 4 * q^82 - 16 * q^83 - 3 * q^85 - 7 * q^86 - 30 * q^88 + 29 * q^89 + 22 * q^91 + 21 * q^92 + 36 * q^94 + 22 * q^95 + 20 * q^97 - 59 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.792283	−	1.37227i	0.560229	−	0.970344i	−0.437247	−	0.899341i	$-0.644047\pi$
$2$	0.792283	−	1.37227i	0.560229	−	0.970344i	0.997476	−	0.0710032i	$-0.0226201\pi$
$3$		0			0
$3$		0			0
$4$	−0.255424	−	0.442408i	−0.127712	−	0.221204i
$5$	−0.780905	+	1.35257i	−0.349231	+	0.604886i	−0.986113	−	0.166075i	$-0.946891\pi$
$5$	−0.780905	+	1.35257i	−0.349231	+	0.604886i	0.636882	+	0.770961i	$0.280224\pi$
$6$		0			0
$7$	−0.188849			−0.0713782			−0.0356891	−	0.999363i	$-0.511363\pi$
$7$	−0.188849			−0.0713782			−0.0356891	+	0.999363i	$0.511363\pi$
$8$	2.35966			0.834265
$9$		0			0
$10$	1.23740	+	2.14323i	0.391299	+	0.677749i
$11$	1.98564			0.598693			0.299346	−	0.954145i	$-0.403231\pi$
$11$	1.98564			0.598693			0.299346	+	0.954145i	$0.403231\pi$
$12$		0			0
$13$	2.46073	+	4.26212i	0.682485	+	1.18210i	0.974220	+	0.225599i	$0.0724340\pi$
$13$	2.46073	+	4.26212i	0.682485	+	1.18210i	−0.291735	+	0.956499i	$0.594233\pi$
$14$	−0.149622	+	0.259153i	−0.0399881	+	0.0692614i
$15$		0			0
$16$	2.38037	−	4.12291i	0.595091	−	1.03073i
$17$	3.67265	−	6.36121i	0.890748	−	1.54282i	0.0517678	−	0.998659i	$-0.483514\pi$
$17$	3.67265	−	6.36121i	0.890748	−	1.54282i	0.838980	−	0.544162i	$-0.183152\pi$
$18$		0			0
$19$	−1.14266	+	4.20646i	−0.262144	+	0.965029i
$19$	−1.14266	+	4.20646i	−0.262144	+	0.965029i
$20$	0.797849			0.178404
$21$		0			0
$22$	1.57319	−	2.72484i	0.335405	−	0.580938i
$23$	−0.631283	−	1.09341i	−0.131632	−	0.227993i	0.792674	−	0.609646i	$-0.208688\pi$
$23$	−0.631283	−	1.09341i	−0.131632	−	0.227993i	−0.924306	+	0.381653i	$0.875355\pi$
$24$		0			0
$25$	1.28038	+	2.21768i	0.256075	+	0.443535i
$26$	7.79839			1.52939
$27$		0			0
$28$	0.0482366	+	0.0835483i	0.00911587	+	0.0157891i
$29$	−3.51165	−	6.08235i	−0.652097	−	1.12946i	−0.982613	−	0.185664i	$-0.940556\pi$
$29$	−3.51165	−	6.08235i	−0.652097	−	1.12946i	0.330516	−	0.943800i	$-0.392777\pi$
$30$		0			0
$31$	3.84607			0.690775			0.345388	−	0.938460i	$-0.387747\pi$
$31$	3.84607			0.690775			0.345388	+	0.938460i	$0.387747\pi$
$32$	−1.41219	−	2.44598i	−0.249642	−	0.432392i
$33$		0			0
$34$	−5.81955	−	10.0798i	−0.998045	−	1.72866i
$35$	0.147473	−	0.255431i	0.0249275	−	0.0431757i
$36$		0			0
$37$	−1.66426			−0.273602			−0.136801	−	0.990599i	$-0.543682\pi$
$37$	−1.66426			−0.273602			−0.136801	+	0.990599i	$0.543682\pi$
$38$	4.86711	+	4.90075i	0.789549	+	0.795007i
$39$		0			0
$40$	−1.84267	+	3.19160i	−0.291351	+	0.504635i
$41$	−2.28090	+	3.95064i	−0.356217	+	0.616987i	−0.987326	−	0.158708i	$-0.949267\pi$
$41$	−2.28090	+	3.95064i	−0.356217	+	0.616987i	0.631108	+	0.775695i	$0.282600\pi$
$42$		0			0
$43$	−0.776707	+	1.34530i	−0.118447	+	0.205156i	−0.919152	−	0.393902i	$-0.871125\pi$
$43$	−0.776707	+	1.34530i	−0.118447	+	0.205156i	0.800706	+	0.599058i	$0.204458\pi$
$44$	−0.507181	−	0.878463i	−0.0764604	−	0.132433i
$45$		0			0
$46$	−2.00062			−0.294975
$47$	2.88618	+	4.99901i	0.420992	+	0.729180i	0.996037	−	0.0889420i	$-0.0283486\pi$
$47$	2.88618	+	4.99901i	0.420992	+	0.729180i	−0.575044	+	0.818122i	$0.695015\pi$
$48$		0			0
$49$	−6.96434			−0.994905
$50$	4.05768			0.573842
$51$		0			0
$52$	1.25706	−	2.17730i	0.174323	−	0.301937i
$53$	−2.93892	−	5.09036i	−0.403692	−	0.699215i	0.590476	−	0.807055i	$-0.298940\pi$
$53$	−2.93892	−	5.09036i	−0.403692	−	0.699215i	−0.994168	+	0.107840i	$0.965607\pi$
$54$		0			0
$55$	−1.55059	+	2.68571i	−0.209082	+	0.362141i
$56$	−0.445619			−0.0595483
$57$		0			0
$58$	−11.1289			−1.46129
$59$	−0.657293	+	1.13846i	−0.0855722	+	0.148215i	−0.905635	−	0.424058i	$-0.860605\pi$
$59$	−0.657293	+	1.13846i	−0.0855722	+	0.148215i	0.820063	+	0.572274i	$0.193939\pi$
$60$		0			0
$61$	−5.56088	−	9.63172i	−0.711997	−	1.23322i	−0.964106	−	0.265516i	$-0.914458\pi$
$61$	−5.56088	−	9.63172i	−0.711997	−	1.23322i	0.252109	−	0.967699i	$-0.418876\pi$
$62$	3.04718	−	5.27787i	0.386992	−	0.670290i
$63$		0			0
$64$	5.04605			0.630757
$65$	−7.68640			−0.953380
$66$		0			0
$67$	−5.36574	−	9.29374i	−0.655530	−	1.13541i	−0.981761	−	0.190121i	$-0.939112\pi$
$67$	−5.36574	−	9.29374i	−0.655530	−	1.13541i	0.326231	−	0.945290i	$-0.394221\pi$
$68$	−3.75234			−0.455038
$69$		0			0
$70$	−0.233681	−	0.404747i	−0.0279302	−	0.0483765i
$71$	−2.93677	+	5.08664i	−0.348531	+	0.603673i	−0.985989	−	0.166812i	$-0.946653\pi$
$71$	−2.93677	+	5.08664i	−0.348531	+	0.603673i	0.637458	+	0.770485i	$0.279986\pi$
$72$		0			0
$73$	−5.90339	+	10.2250i	−0.690940	+	1.19674i	0.280591	+	0.959828i	$0.409470\pi$
$73$	−5.90339	+	10.2250i	−0.690940	+	1.19674i	−0.971530	+	0.236915i	$0.923864\pi$
$74$	−1.31856	+	2.28382i	−0.153280	+	0.265488i
$75$		0			0
$76$	2.15284	−	0.568911i	0.246947	−	0.0652585i
$77$	−0.374986			−0.0427336
$78$		0			0
$79$	4.14124	−	7.17284i	0.465926	−	0.807008i	−0.533317	−	0.845916i	$-0.679055\pi$
$79$	4.14124	−	7.17284i	0.465926	−	0.807008i	0.999243	+	0.0389078i	$0.0123878\pi$
$80$	3.71768	+	6.43921i	0.415649	+	0.719925i
$81$		0			0
$82$	3.61424	+	6.26005i	0.399126	+	0.691307i
$83$	−11.5479			−1.26754			−0.633772	−	0.773520i	$-0.718494\pi$
$83$	−11.5479			−1.26754			−0.633772	+	0.773520i	$0.718494\pi$
$84$		0			0
$85$	5.73598	+	9.93500i	0.622154	+	1.07760i
$86$	1.23074	+	2.13171i	0.132715	+	0.229868i
$87$		0			0
$88$	4.68543			0.499468
$89$	0.512993	+	0.888530i	0.0543772	+	0.0941840i	0.891933	−	0.452168i	$-0.149349\pi$
$89$	0.512993	+	0.888530i	0.0543772	+	0.0941840i	−0.837556	+	0.546352i	$0.816016\pi$
$90$		0			0
$91$	−0.464707	−	0.804896i	−0.0487145	−	0.0843760i
$92$	−0.322490	+	0.558569i	−0.0336219	+	0.0582349i
$93$		0			0
$94$	9.14668			0.943408
$95$	−4.79721	−	4.83037i	−0.492184	−	0.495586i
$96$		0			0
$97$	2.12169	−	3.67487i	0.215425	−	0.373127i	−0.737979	−	0.674824i	$-0.764220\pi$
$97$	2.12169	−	3.67487i	0.215425	−	0.373127i	0.953404	+	0.301697i	$0.0975531\pi$
$98$	−5.51772	+	9.55698i	−0.557374	+	0.965401i
$99$		0			0
$100$	0.654078	−	1.13290i	0.0654078	−	0.113290i
$101$	−1.52601	−	2.64313i	−0.151844	−	0.263001i	0.780062	−	0.625703i	$-0.215188\pi$
$101$	−1.52601	−	2.64313i	−0.151844	−	0.263001i	−0.931905	+	0.362702i	$0.881854\pi$
$102$		0			0
$103$	16.8767			1.66291			0.831455	−	0.555593i	$-0.187509\pi$
$103$	16.8767			1.66291			0.831455	+	0.555593i	$0.187509\pi$
$104$	5.80649	+	10.0571i	0.569373	+	0.986183i
$105$		0			0
$106$	−9.31383			−0.904639
$107$	−10.0432			−0.970915			−0.485457	−	0.874260i	$-0.661347\pi$
$107$	−10.0432			−0.970915			−0.485457	+	0.874260i	$0.661347\pi$
$108$		0			0
$109$	−2.05395	+	3.55755i	−0.196733	+	0.340752i	−0.947467	−	0.319853i	$-0.896367\pi$
$109$	−2.05395	+	3.55755i	−0.196733	+	0.340752i	0.750734	+	0.660604i	$0.229700\pi$
$110$	2.45702	+	4.25568i	0.234268	+	0.405763i
$111$		0			0
$112$	−0.449530	+	0.778608i	−0.0424765	+	0.0735715i
$113$	6.97901			0.656530			0.328265	−	0.944586i	$-0.393536\pi$
$113$	6.97901			0.656530			0.328265	+	0.944586i	$0.393536\pi$
$114$		0			0
$115$	1.97189			0.183879
$116$	−1.79392	+	3.10716i	−0.166561	+	0.288493i
$117$		0			0
$118$	1.04152	+	1.80397i	0.0958800	+	0.166069i
$119$	−0.693576	+	1.20131i	−0.0635800	+	0.110124i
$120$		0			0
$121$	−7.05724			−0.641567
$122$	−17.6231			−1.59552
$123$		0			0
$124$	−0.982381	−	1.70153i	−0.0882204	−	0.152802i
$125$	−11.8085			−1.05618
$126$		0			0
$127$	8.43862	+	14.6161i	0.748806	+	1.29697i	0.948395	+	0.317091i	$0.102706\pi$
$127$	8.43862	+	14.6161i	0.748806	+	1.29697i	−0.199589	+	0.979880i	$0.563961\pi$
$128$	6.82228	−	11.8165i	0.603010	−	1.04444i
$129$		0			0
$130$	−6.08980	+	10.5478i	−0.534111	+	0.925107i
$131$	5.45097	−	9.44136i	0.476254	−	0.824895i	−0.523376	−	0.852102i	$-0.675328\pi$
$131$	5.45097	−	9.44136i	0.476254	−	0.824895i	0.999630	+	0.0272064i	$0.00866112\pi$
$132$		0			0
$133$	0.215790	−	0.794386i	0.0187114	−	0.0688820i
$134$	−17.0047			−1.46899
$135$		0			0
$136$	8.66619	−	15.0103i	0.743120	−	1.28712i
$137$	−4.71932	−	8.17410i	−0.403198	−	0.698360i	0.590912	−	0.806736i	$-0.298768\pi$
$137$	−4.71932	−	8.17410i	−0.403198	−	0.698360i	−0.994110	+	0.108376i	$0.965435\pi$
$138$		0			0
$139$	−2.33972	−	4.05252i	−0.198453	−	0.343730i	0.749574	−	0.661920i	$-0.230258\pi$
$139$	−2.33972	−	4.05252i	−0.198453	−	0.343730i	−0.948027	+	0.318190i	$0.896925\pi$
$140$	−0.150673			−0.0127342
$141$		0			0
$142$	4.65351	+	8.06012i	0.390514	+	0.676390i
$143$	4.88613	+	8.46302i	0.408599	+	0.707714i
$144$		0			0
$145$	10.9691			0.910930
$146$	9.35431	+	16.2021i	0.774168	+	1.34090i
$147$		0			0
$148$	0.425092	+	0.736281i	0.0349424	+	0.0605219i
$149$	−0.161417	+	0.279583i	−0.0132238	+	0.0229043i	−0.872562	−	0.488504i	$-0.837543\pi$
$149$	−0.161417	+	0.279583i	−0.0132238	+	0.0229043i	0.859338	+	0.511408i	$0.170876\pi$
$150$		0			0
$151$	10.7069			0.871312			0.435656	−	0.900113i	$-0.356516\pi$
$151$	10.7069			0.871312			0.435656	+	0.900113i	$0.356516\pi$
$152$	−2.69629	+	9.92581i	−0.218698	+	0.805090i
$153$		0			0
$154$	−0.297095	+	0.514583i	−0.0239406	+	0.0414663i
$155$	−3.00342	+	5.20207i	−0.241240	+	0.417840i
$156$		0			0
$157$	7.04579	−	12.2037i	0.562315	−	0.973959i	−0.434979	−	0.900441i	$-0.643244\pi$
$157$	7.04579	−	12.2037i	0.562315	−	0.973959i	0.997294	−	0.0735178i	$-0.0234226\pi$
$158$	−6.56207	−	11.3658i	−0.522050	−	0.904218i
$159$		0			0
$160$	4.41114			0.348731
$161$	0.119217	+	0.206490i	0.00939563	+	0.0162737i
$162$		0			0
$163$	−24.6568			−1.93127			−0.965636	−	0.259898i	$-0.916311\pi$
$163$	−24.6568			−1.93127			−0.965636	+	0.259898i	$0.916311\pi$
$164$	2.33039			0.181973
$165$		0			0
$166$	−9.14918	+	15.8469i	−0.710114	+	1.22995i
$167$	11.3586	+	19.6736i	0.878952	+	1.52239i	0.852492	+	0.522740i	$0.175090\pi$
$167$	11.3586	+	19.6736i	0.878952	+	1.52239i	0.0264603	+	0.999650i	$0.491576\pi$
$168$		0			0
$169$	−5.61042	+	9.71754i	−0.431571	+	0.747503i
$170$	18.1781			1.39419
$171$		0			0
$172$	0.793560			0.0605084
$173$	7.61902	−	13.1965i	0.579263	−	1.00331i	−0.416301	−	0.909227i	$-0.636674\pi$
$173$	7.61902	−	13.1965i	0.579263	−	1.00331i	0.995564	−	0.0940867i	$-0.0299931\pi$
$174$		0			0
$175$	−0.241798	−	0.418806i	−0.0182782	−	0.0316587i
$176$	4.72655	−	8.18662i	0.356277	−	0.617090i
$177$		0			0
$178$	1.62574			0.121855
$179$	−16.4930			−1.23275			−0.616374	−	0.787453i	$-0.711399\pi$
$179$	−16.4930			−1.23275			−0.616374	+	0.787453i	$0.711399\pi$
$180$		0			0
$181$	−4.49171	−	7.77987i	−0.333866	−	0.578273i	0.649400	−	0.760447i	$-0.275020\pi$
$181$	−4.49171	−	7.77987i	−0.333866	−	0.578273i	−0.983266	+	0.182174i	$0.941687\pi$
$182$	−1.47272			−0.109165
$183$		0			0
$184$	−1.48961	−	2.58008i	−0.109816	−	0.190206i
$185$	1.29963	−	2.25102i	0.0955505	−	0.165498i
$186$		0			0
$187$	7.29255	−	12.6311i	0.533284	−	0.923676i
$188$	1.47440	−	2.55374i	0.107532	−	0.186250i
$189$		0			0
$190$	−10.4293	+	2.75607i	−0.756624	+	0.199946i
$191$	−7.72534			−0.558986			−0.279493	−	0.960148i	$-0.590166\pi$
$191$	−7.72534			−0.558986			−0.279493	+	0.960148i	$0.590166\pi$
$192$		0			0
$193$	5.89636	−	10.2128i	0.424429	−	0.735133i	−0.571938	−	0.820297i	$-0.693808\pi$
$193$	5.89636	−	10.2128i	0.424429	−	0.735133i	0.996367	+	0.0851641i	$0.0271415\pi$
$194$	−3.36195	−	5.82307i	−0.241374	−	0.418072i
$195$		0			0
$196$	1.77886	+	3.08108i	0.127062	+	0.220077i
$197$	−16.1567			−1.15112			−0.575558	−	0.817761i	$-0.695215\pi$
$197$	−16.1567			−1.15112			−0.575558	+	0.817761i	$0.695215\pi$
$198$		0			0
$199$	−3.15688	−	5.46787i	−0.223785	−	0.387607i	0.732169	−	0.681123i	$-0.238508\pi$
$199$	−3.15688	−	5.46787i	−0.223785	−	0.387607i	−0.955954	+	0.293516i	$0.905175\pi$
$200$	3.02125	+	5.23296i	0.213635	+	0.370026i
$201$		0			0
$202$	−4.83613			−0.340269
$203$	0.663171	+	1.14865i	0.0465455	+	0.0806192i
$204$		0			0
$205$	−3.56234	−	6.17015i	−0.248805	−	0.430942i
$206$	13.3711	−	23.1594i	0.931609	−	1.61359i
$207$		0			0
$208$	23.4298			1.62456
$209$	−2.26891	+	8.35251i	−0.156944	+	0.577756i
$210$		0			0
$211$	3.32994	−	5.76763i	0.229243	−	0.397060i	−0.728341	−	0.685215i	$-0.759708\pi$
$211$	3.32994	−	5.76763i	0.229243	−	0.397060i	0.957584	+	0.288155i	$0.0930418\pi$
$212$	−1.50134	+	2.60041i	−0.103113	+	0.178597i
$213$		0			0
$214$	−7.95707	+	13.7820i	−0.543934	+	0.942122i
$215$	−1.21307	−	2.10110i	−0.0827306	−	0.143294i
$216$		0			0
$217$	−0.726327			−0.0493063
$218$	3.25462	+	5.63718i	0.220431	+	0.381798i
$219$		0			0
$220$	1.58424			0.106809
$221$	36.1496			2.43169
$222$		0			0
$223$	−13.6703	+	23.6776i	−0.915431	+	1.58557i	−0.109161	+	0.994024i	$0.534817\pi$
$223$	−13.6703	+	23.6776i	−0.915431	+	1.58557i	−0.806269	+	0.591549i	$0.798517\pi$
$224$	0.266690	+	0.461921i	0.0178190	+	0.0308634i
$225$		0			0
$226$	5.52935	−	9.57712i	0.367807	−	0.637061i
$227$	0.489669			0.0325005			0.0162502	−	0.999868i	$-0.494827\pi$
$227$	0.489669			0.0325005			0.0162502	+	0.999868i	$0.494827\pi$
$228$		0			0
$229$	17.7207			1.17102			0.585508	−	0.810666i	$-0.300895\pi$
$229$	17.7207			1.17102			0.585508	+	0.810666i	$0.300895\pi$
$230$	1.56229	−	2.70597i	0.103015	−	0.178426i
$231$		0			0
$232$	−8.28629	−	14.3523i	−0.544022	−	0.942273i
$233$	6.72955	−	11.6559i	0.440867	−	0.763604i	−0.556887	−	0.830588i	$-0.688004\pi$
$233$	6.72955	−	11.6559i	0.440867	−	0.763604i	0.997754	+	0.0669840i	$0.0213376\pi$
$234$		0			0
$235$	−9.01532			−0.588095
$236$	0.671554			0.0437145
$237$		0			0
$238$	1.09902	+	1.90355i	0.0712387	+	0.123389i
$239$	−0.766796			−0.0495999			−0.0248000	−	0.999692i	$-0.507895\pi$
$239$	−0.766796			−0.0495999			−0.0248000	+	0.999692i	$0.507895\pi$
$240$		0			0
$241$	−6.05505	−	10.4877i	−0.390040	−	0.675570i	0.602414	−	0.798184i	$-0.294206\pi$
$241$	−6.05505	−	10.4877i	−0.390040	−	0.675570i	−0.992454	+	0.122614i	$0.960872\pi$
$242$	−5.59133	+	9.68447i	−0.359424	+	0.622541i
$243$		0			0
$244$	−2.84077	+	4.92035i	−0.181861	+	0.314993i
$245$	5.43848	−	9.41973i	0.347452	−	0.601804i
$246$		0			0
$247$	−20.7402	+	5.48083i	−1.31967	+	0.348737i
$248$	9.07542			0.576290
$249$		0			0
$250$	−9.35564	+	16.2044i	−0.591702	+	1.02486i
$251$	14.0093	+	24.2648i	0.884259	+	1.53158i	0.846560	+	0.532293i	$0.178670\pi$
$251$	14.0093	+	24.2648i	0.884259	+	1.53158i	0.0376993	+	0.999289i	$0.487997\pi$
$252$		0			0
$253$	−1.25350	−	2.17113i	−0.0788069	−	0.136498i
$254$	26.7431			1.67801
$255$		0			0
$256$	−5.76429	−	9.98405i	−0.360268	−	0.624003i
$257$	−14.0221	−	24.2870i	−0.874675	−	1.51498i	−0.857109	−	0.515135i	$-0.827742\pi$
$257$	−14.0221	−	24.2870i	−0.874675	−	1.51498i	−0.0175655	−	0.999846i	$-0.505592\pi$
$258$		0			0
$259$	0.314293			0.0195292
$260$	1.96329	+	3.40052i	0.121758	+	0.210891i
$261$		0			0
$262$	−8.63742	−	14.9605i	−0.533622	−	0.924260i
$263$	0.961003	−	1.66451i	0.0592580	−	0.102638i	−0.834875	−	0.550440i	$-0.814460\pi$
$263$	0.961003	−	1.66451i	0.0592580	−	0.102638i	0.894133	+	0.447802i	$0.147793\pi$
$264$		0			0
$265$	9.18007			0.563927
$266$	−0.919148	−	0.925502i	−0.0563566	−	0.0567462i
$267$		0			0
$268$	−2.74108	+	4.74769i	−0.167438	+	0.290012i
$269$	7.45127	−	12.9060i	0.454312	−	0.786892i	−0.544336	−	0.838867i	$-0.683218\pi$
$269$	7.45127	−	12.9060i	0.454312	−	0.786892i	0.998648	+	0.0519753i	$0.0165517\pi$
$270$		0			0
$271$	5.80402	−	10.0529i	0.352569	−	0.610667i	−0.634130	−	0.773227i	$-0.718642\pi$
$271$	5.80402	−	10.0529i	0.352569	−	0.610667i	0.986699	+	0.162559i	$0.0519749\pi$
$272$	−17.4845	−	30.2840i	−1.06015	−	1.83624i
$273$		0			0
$274$	−14.9561			−0.903533
$275$	2.54236	+	4.40350i	0.153310	+	0.265541i
$276$		0			0
$277$	−18.0840			−1.08656			−0.543281	−	0.839551i	$-0.682818\pi$
$277$	−18.0840			−1.08656			−0.543281	+	0.839551i	$0.682818\pi$
$278$	−7.41489			−0.444716
$279$		0			0
$280$	0.347986	−	0.602729i	0.0207961	−	0.0360200i
$281$	−3.07901	−	5.33300i	−0.183678	−	0.318140i	0.759452	−	0.650563i	$-0.225467\pi$
$281$	−3.07901	−	5.33300i	−0.183678	−	0.318140i	−0.943130	+	0.332423i	$0.892134\pi$
$282$		0			0
$283$	−4.73497	+	8.20121i	−0.281465	+	0.487511i	−0.971746	−	0.236030i	$-0.924154\pi$
$283$	−4.73497	+	8.20121i	−0.281465	+	0.487511i	0.690281	+	0.723541i	$0.257487\pi$
$284$	3.00049			0.178047
$285$		0			0
$286$	15.4848			0.915635
$287$	0.430746	−	0.746075i	0.0254262	−	0.0440394i
$288$		0			0
$289$	−18.4767	−	32.0026i	−1.08686	−	1.88250i
$290$	8.69059	−	15.0525i	0.510329	−	0.883916i
$291$		0			0
$292$	6.03148			0.352966
$293$	−16.7675			−0.979570			−0.489785	−	0.871843i	$-0.662925\pi$
$293$	−16.7675			−0.979570			−0.489785	+	0.871843i	$0.662925\pi$
$294$		0			0
$295$	−1.02657	−	1.77806i	−0.0597690	−	0.103523i
$296$	−3.92708			−0.228257
$297$		0			0
$298$	0.255776	+	0.443017i	0.0148167	+	0.0256633i
$299$	3.10684	−	5.38120i	0.179673	−	0.311203i
$300$		0			0
$301$	0.146680	−	0.254058i	0.00845451	−	0.0146436i
$302$	8.48286	−	14.6927i	0.488134	−	0.845472i
$303$		0			0
$304$	14.6229	+	14.7240i	0.838683	+	0.844480i
$305$	17.3701			0.994607
$306$		0			0
$307$	2.23267	−	3.86710i	0.127425	−	0.220707i	−0.795253	−	0.606278i	$-0.792662\pi$
$307$	2.23267	−	3.86710i	0.127425	−	0.220707i	0.922678	+	0.385570i	$0.125995\pi$
$308$	0.0957805	+	0.165897i	0.00545760	+	0.00945284i
$309$		0			0
$310$	4.75911	+	8.24302i	0.270299	+	0.468172i
$311$	25.0358			1.41965			0.709826	−	0.704377i	$-0.248774\pi$
$311$	25.0358			1.41965			0.709826	+	0.704377i	$0.248774\pi$
$312$		0			0
$313$	17.3728	+	30.0906i	0.981971	+	1.70082i	0.654693	+	0.755895i	$0.272798\pi$
$313$	17.3728	+	30.0906i	0.981971	+	1.70082i	0.327277	+	0.944928i	$0.393869\pi$
$314$	−11.1645	−	19.3375i	−0.630050	−	1.09128i
$315$		0			0
$316$	−4.23110			−0.238018
$317$	5.20174	+	9.00968i	0.292159	+	0.506034i	0.974320	−	0.225168i	$-0.0722931\pi$
$317$	5.20174	+	9.00968i	0.292159	+	0.506034i	−0.682161	+	0.731202i	$0.738960\pi$
$318$		0			0
$319$	−6.97287	−	12.0774i	−0.390406	−	0.676202i
$320$	−3.94049	+	6.82512i	−0.220280	+	0.381536i
$321$		0			0
$322$	0.377815			0.0210548
$323$	22.5616	+	22.7176i	1.25536	+	1.26404i
$324$		0			0
$325$	−6.30133	+	10.9142i	−0.349535	+	0.605412i
$326$	−19.5352	+	33.8359i	−1.08195	+	1.87400i
$327$		0			0
$328$	−5.38216	+	9.32217i	−0.297180	+	0.514731i
$329$	−0.545052	−	0.944057i	−0.0300497	−	0.0520476i
$330$		0			0
$331$	7.28326			0.400324			0.200162	−	0.979763i	$-0.435853\pi$
$331$	7.28326			0.400324			0.200162	+	0.979763i	$0.435853\pi$
$332$	2.94961	+	5.10887i	0.161881	+	0.280386i
$333$		0			0
$334$	35.9968			1.96966
$335$	16.7605			0.915726
$336$		0			0
$337$	10.6604	−	18.4644i	0.580711	−	1.00582i	−0.414684	−	0.909965i	$-0.636108\pi$
$337$	10.6604	−	18.4644i	0.580711	−	1.00582i	0.995395	−	0.0958555i	$-0.0305587\pi$
$338$	8.89008	+	15.3981i	0.483557	+	0.837545i
$339$		0			0
$340$	2.93022	−	5.07528i	0.158913	−	0.275246i
$341$	7.63691			0.413562
$342$		0			0
$343$	2.63715			0.142393
$344$	−1.83276	+	3.17444i	−0.0988160	+	0.171154i
$345$		0			0
$346$	−12.0728	−	20.9108i	−0.649040	−	1.12417i
$347$	−12.8833	+	22.3146i	−0.691613	+	1.19791i	0.279697	+	0.960088i	$0.409766\pi$
$347$	−12.8833	+	22.3146i	−0.691613	+	1.19791i	−0.971309	+	0.237820i	$0.923567\pi$
$348$		0			0
$349$	27.7113			1.48335			0.741677	−	0.670758i	$-0.234031\pi$
$349$	27.7113			1.48335			0.741677	+	0.670758i	$0.234031\pi$
$350$	−0.766288			−0.0409598
$351$		0			0
$352$	−2.80409	−	4.85683i	−0.149459	−	0.258870i
$353$	−27.0547			−1.43998			−0.719988	−	0.693986i	$-0.755853\pi$
$353$	−27.0547			−1.43998			−0.719988	+	0.693986i	$0.755853\pi$
$354$		0			0
$355$	−4.58668	−	7.94436i	−0.243436	−	0.421643i
$356$	0.262062	−	0.453905i	0.0138893	−	0.0240569i
$357$		0			0
$358$	−13.0672	+	22.6330i	−0.690621	+	1.19619i
$359$	18.0023	−	31.1809i	0.950126	−	1.64567i	0.204980	−	0.978766i	$-0.434287\pi$
$359$	18.0023	−	31.1809i	0.950126	−	1.64567i	0.745146	−	0.666901i	$-0.232380\pi$
$360$		0			0
$361$	−16.3887	−	9.61312i	−0.862561	−	0.505954i
$362$	−14.2348			−0.748166
$363$		0			0
$364$	−0.237395	+	0.411180i	−0.0124429	+	0.0215517i
$365$	−9.21997	−	15.9695i	−0.482596	−	0.835880i
$366$		0			0
$367$	8.02937	+	13.9073i	0.419130	+	0.725954i	0.995852	−	0.0909864i	$-0.0290020\pi$
$367$	8.02937	+	13.9073i	0.419130	+	0.725954i	−0.576723	+	0.816940i	$0.695669\pi$
$368$	−6.01074			−0.313331
$369$		0			0
$370$	−2.05934	−	3.56689i	−0.107060	−	0.185434i
$371$	0.555012	+	0.961309i	0.0288148	+	0.0499087i
$372$		0			0
$373$	27.2757			1.41228			0.706142	−	0.708071i	$-0.250434\pi$
$373$	27.2757			1.41228			0.706142	+	0.708071i	$0.250434\pi$
$374$	−11.5555	−	20.0148i	−0.597522	−	1.03494i
$375$		0			0
$376$	6.81039	+	11.7959i	0.351219	+	0.608330i
$377$	17.2825	−	29.9341i	0.890092	−	1.54168i
$378$		0			0
$379$	20.6347			1.05993			0.529967	−	0.848018i	$-0.322204\pi$
$379$	20.6347			1.05993			0.529967	+	0.848018i	$0.322204\pi$
$380$	−0.911670	+	3.35612i	−0.0467677	+	0.172165i
$381$		0			0
$382$	−6.12065	+	10.6013i	−0.313160	+	0.542409i
$383$	−13.6896	+	23.7112i	−0.699508	+	1.21158i	0.269129	+	0.963104i	$0.413264\pi$
$383$	−13.6896	+	23.7112i	−0.699508	+	1.21158i	−0.968637	+	0.248480i	$0.920069\pi$
$384$		0			0
$385$	0.292828	−	0.507193i	0.0149239	−	0.0258490i
$386$	−9.34317	−	16.1828i	−0.475555	−	0.823685i
$387$		0			0
$388$	−2.16772			−0.110049
$389$	11.9769	+	20.7447i	0.607255	+	1.05180i	0.991691	+	0.128645i	$0.0410626\pi$
$389$	11.9769	+	20.7447i	0.607255	+	1.05180i	−0.384436	+	0.923152i	$0.625604\pi$
$390$		0			0
$391$	−9.27392			−0.469002
$392$	−16.4335			−0.830015
$393$		0			0
$394$	−12.8007	+	22.1714i	−0.644888	+	1.11698i
$395$	6.46783	+	11.2026i	0.325432	+	0.563665i
$396$		0			0
$397$	−14.6385	+	25.3547i	−0.734687	+	1.27252i	0.220173	+	0.975461i	$0.429338\pi$
$397$	−14.6385	+	25.3547i	−0.734687	+	1.27252i	−0.954860	+	0.297055i	$0.903996\pi$
$398$	−10.0046			−0.501483
$399$		0			0
$400$	12.1910			0.609552
$401$	−11.3551	+	19.6675i	−0.567045	+	0.982151i	0.429811	+	0.902919i	$0.358580\pi$
$401$	−11.3551	+	19.6675i	−0.567045	+	0.982151i	−0.996856	+	0.0792318i	$0.974753\pi$
$402$		0			0
$403$	9.46416	+	16.3924i	0.471443	+	0.816564i
$404$	−0.779560	+	1.35024i	−0.0387846	+	0.0671768i
$405$		0			0
$406$	2.10168			0.104304
$407$	−3.30461			−0.163804
$408$		0			0
$409$	12.4691	+	21.5972i	0.616559	+	1.06791i	0.990109	+	0.140302i	$0.0448073\pi$
$409$	12.4691	+	21.5972i	0.616559	+	1.06791i	−0.373549	+	0.927610i	$0.621859\pi$
$410$	−11.2895			−0.557550
$411$		0			0
$412$	−4.31072	−	7.46638i	−0.212374	−	0.367842i
$413$	0.124129	−	0.214998i	0.00610799	−	0.0105794i
$414$		0			0
$415$	9.01779	−	15.6193i	0.442666	−	0.766720i
$416$	6.95004	−	12.0378i	0.340754	−	0.590202i
$417$		0			0
$418$	9.66432	+	9.73112i	0.472697	+	0.475965i
$419$	−20.7909			−1.01570			−0.507852	−	0.861444i	$-0.669560\pi$
$419$	−20.7909			−1.01570			−0.507852	+	0.861444i	$0.669560\pi$
$420$		0			0
$421$	5.74359	−	9.94819i	0.279926	−	0.484845i	−0.691440	−	0.722433i	$-0.743024\pi$
$421$	5.74359	−	9.94819i	0.279926	−	0.484845i	0.971366	+	0.237588i	$0.0763569\pi$
$422$	−5.27651	−	9.13918i	−0.256857	−	0.444889i
$423$		0			0
$424$	−6.93485	−	12.0115i	−0.336786	−	0.583331i
$425$	18.8095			0.912394
$426$		0			0
$427$	1.05017	+	1.81894i	0.0508211	+	0.0880247i
$428$	2.56528	+	4.44320i	0.123998	+	0.214770i
$429$		0			0
$430$	−3.84437			−0.185392
$431$	18.6968	+	32.3838i	0.900593	+	1.55987i	0.826726	+	0.562605i	$0.190201\pi$
$431$	18.6968	+	32.3838i	0.900593	+	1.55987i	0.0738670	+	0.997268i	$0.476466\pi$
$432$		0			0
$433$	19.0405	+	32.9791i	0.915027	+	1.58487i	0.806862	+	0.590740i	$0.201164\pi$
$433$	19.0405	+	32.9791i	0.915027	+	1.58487i	0.108165	+	0.994133i	$0.465503\pi$
$434$	−0.575456	+	0.996720i	−0.0276228	+	0.0478441i
$435$		0			0
$436$	2.09852			0.100501
$437$	5.32075	−	1.40607i	0.254526	−	0.0672613i
$438$		0			0
$439$	6.51854	−	11.2904i	0.311113	−	0.538863i	−0.667491	−	0.744618i	$-0.732632\pi$
$439$	6.51854	−	11.2904i	0.311113	−	0.538863i	0.978604	+	0.205755i	$0.0659650\pi$
$440$	−3.65887	+	6.33736i	−0.174430	+	0.302122i
$441$		0			0
$442$	28.6407	−	49.6072i	1.36230	−	2.35957i
$443$	1.47355	+	2.55226i	0.0700103	+	0.121261i	0.898906	−	0.438142i	$-0.144363\pi$
$443$	1.47355	+	2.55226i	0.0700103	+	0.121261i	−0.828895	+	0.559404i	$0.811030\pi$
$444$		0			0
$445$	−1.60240			−0.0759608
$446$	21.6615	+	37.5188i	1.02570	+	1.77657i
$447$		0			0
$448$	−0.952942			−0.0450223
$449$	−41.0478			−1.93717			−0.968584	−	0.248687i	$-0.920001\pi$
$449$	−41.0478			−1.93717			−0.968584	+	0.248687i	$0.920001\pi$
$450$		0			0
$451$	−4.52905	+	7.84455i	−0.213265	+	0.369385i
$452$	−1.78261	−	3.08757i	−0.0838469	−	0.145227i
$453$		0			0
$454$	0.387956	−	0.671960i	0.0182077	−	0.0315367i
$455$	1.45157			0.0680505
$456$		0			0
$457$	−12.2116			−0.571235			−0.285617	−	0.958344i	$-0.592199\pi$
$457$	−12.2116			−0.571235			−0.285617	+	0.958344i	$0.592199\pi$
$458$	14.0398	−	24.3177i	0.656037	−	1.13629i
$459$		0			0
$460$	−0.503668	−	0.872379i	−0.0234837	−	0.0406749i
$461$	−0.592471	+	1.02619i	−0.0275941	+	0.0477944i	−0.879493	−	0.475912i	$-0.842118\pi$
$461$	−0.592471	+	1.02619i	−0.0275941	+	0.0477944i	0.851899	+	0.523707i	$0.175451\pi$
$462$		0			0
$463$	−7.16475			−0.332974			−0.166487	−	0.986044i	$-0.553242\pi$
$463$	−7.16475			−0.332974			−0.166487	+	0.986044i	$0.553242\pi$
$464$	−33.4360			−1.55223
$465$		0			0
$466$	−10.6634	−	18.4696i	−0.493973	−	0.855586i
$467$	−17.6967			−0.818905			−0.409452	−	0.912332i	$-0.634280\pi$
$467$	−17.6967			−0.818905			−0.409452	+	0.912332i	$0.634280\pi$
$468$		0			0
$469$	1.01331	+	1.75511i	0.0467905	+	0.0810436i
$470$	−7.14268	+	12.3715i	−0.329467	+	0.570654i
$471$		0			0
$472$	−1.55099	+	2.68639i	−0.0713899	+	0.123651i
$473$	−1.54226	+	2.67127i	−0.0709132	+	0.122825i
$474$		0			0
$475$	−10.7916	+	2.85180i	−0.495153	+	0.130850i
$476$	0.708625			0.0324798
$477$		0			0
$478$	−0.607519	+	1.05225i	−0.0277873	+	0.0481290i
$479$	5.74972	+	9.95881i	0.262711	+	0.455030i	0.966962	−	0.254922i	$-0.0820499\pi$
$479$	5.74972	+	9.95881i	0.262711	+	0.455030i	−0.704250	+	0.709952i	$0.748717\pi$
$480$		0			0
$481$	−4.09530	−	7.09326i	−0.186729	−	0.323425i
$482$	−19.1893			−0.874047
$483$		0			0
$484$	1.80259	+	3.12218i	0.0819359	+	0.141917i
$485$	3.31367	+	5.73945i	0.150466	+	0.260615i
$486$		0			0
$487$	−22.9323			−1.03916			−0.519580	−	0.854422i	$-0.673912\pi$
$487$	−22.9323			−1.03916			−0.519580	+	0.854422i	$0.673912\pi$
$488$	−13.1218	−	22.7276i	−0.593994	−	1.02883i
$489$		0			0
$490$	−8.61763	−	14.9262i	−0.389305	−	0.674296i
$491$	−12.7364	+	22.0600i	−0.574784	+	0.995556i	0.421281	+	0.906930i	$0.361581\pi$
$491$	−12.7364	+	22.0600i	−0.574784	+	0.995556i	−0.996065	+	0.0886254i	$0.971753\pi$
$492$		0			0
$493$	−51.5882			−2.32342
$494$	−8.91092	+	32.8036i	−0.400921	+	1.47591i
$495$		0			0
$496$	9.15506	−	15.8570i	0.411074	−	0.712002i
$497$	0.554606	−	0.960607i	0.0248775	−	0.0430891i
$498$		0			0
$499$	−3.45927	+	5.99162i	−0.154858	+	0.268222i	−0.933007	−	0.359857i	$-0.882825\pi$
$499$	−3.45927	+	5.99162i	−0.154858	+	0.268222i	0.778149	+	0.628079i	$0.216159\pi$
$500$	3.01617	+	5.22415i	0.134887	+	0.233631i
$501$		0			0
$502$	44.3973			1.98155
$503$	−6.65543	−	11.5275i	−0.296751	−	0.513988i	0.678640	−	0.734471i	$-0.262570\pi$
$503$	−6.65543	−	11.5275i	−0.296751	−	0.513988i	−0.975391	+	0.220484i	$0.929236\pi$
$504$		0			0
$505$	4.76667			0.212114
$506$	−3.97251			−0.176599
$507$		0			0
$508$	4.31086	−	7.46663i	0.191263	−	0.331278i
$509$	−7.41563	−	12.8442i	−0.328692	−	0.569311i	0.653561	−	0.756874i	$-0.273274\pi$
$509$	−7.41563	−	12.8442i	−0.328692	−	0.569311i	−0.982253	+	0.187563i	$0.939941\pi$
$510$		0			0
$511$	1.11485	−	1.93098i	0.0493180	−	0.0854213i
$512$	9.02130			0.398689
$513$		0			0
$514$	−44.4379			−1.96007
$515$	−13.1791	+	22.8268i	−0.580740	+	1.00587i
$516$		0			0
$517$	5.73091	+	9.92622i	0.252045	+	0.436555i
$518$	0.249009	−	0.431297i	0.0109408	−	0.0189501i
$519$		0			0
$520$	−18.1373			−0.795372
$521$	22.4237			0.982399			0.491199	−	0.871047i	$-0.336559\pi$
$521$	22.4237			0.982399			0.491199	+	0.871047i	$0.336559\pi$
$522$		0			0
$523$	7.50603	+	13.0008i	0.328216	+	0.568486i	0.982158	−	0.188058i	$-0.0602194\pi$
$523$	7.50603	+	13.0008i	0.328216	+	0.568486i	−0.653942	+	0.756544i	$0.726886\pi$
$524$	−5.56924			−0.243294
$525$		0			0
$526$	−1.52277	−	2.63752i	−0.0663960	−	0.115001i
$527$	14.1253	−	24.4657i	0.615307	−	1.06574i
$528$		0			0
$529$	10.7030	−	18.5381i	0.465346	−	0.806003i
$530$	7.27321	−	12.5976i	0.315928	−	0.547204i
$531$		0			0
$532$	−0.406561	+	0.107438i	−0.0176266	+	0.00465804i
$533$	−22.4508			−0.972452
$534$		0			0
$535$	7.84280	−	13.5841i	0.339074	−	0.587293i
$536$	−12.6613	−	21.9300i	−0.546885	−	0.947233i
$537$		0			0
$538$	−11.8070	−	20.4504i	−0.509037	−	0.881679i
$539$	−13.8287			−0.595642
$540$		0			0
$541$	−5.20352	−	9.01276i	−0.223717	−	0.387489i	0.732217	−	0.681072i	$-0.238486\pi$
$541$	−5.20352	−	9.01276i	−0.223717	−	0.387489i	−0.955934	+	0.293583i	$0.905152\pi$
$542$	−9.19685	−	15.9294i	−0.395038	−	0.684227i
$543$		0			0
$544$	−20.7459			−0.889472
$545$	−3.20788	−	5.55622i	−0.137411	−	0.238002i
$546$		0			0
$547$	10.5544	+	18.2807i	0.451272	+	0.781625i	0.998465	−	0.0553807i	$-0.0176373\pi$
$547$	10.5544	+	18.2807i	0.451272	+	0.781625i	−0.547194	+	0.837006i	$0.684304\pi$
$548$	−2.41086	+	4.17573i	−0.102987	+	0.178378i
$549$		0			0
$550$	8.05708			0.343555
$551$	29.5978	−	7.82155i	1.26091	−	0.333209i
$552$		0			0
$553$	−0.782070	+	1.35458i	−0.0332570	+	0.0576028i
$554$	−14.3276	+	24.8162i	−0.608723	+	1.05434i
$555$		0			0
$556$	−1.19525	+	2.07023i	−0.0506897	+	0.0877971i
$557$	−7.32112	−	12.6806i	−0.310206	−	0.537292i	0.668201	−	0.743981i	$-0.267065\pi$
$557$	−7.32112	−	12.6806i	−0.310206	−	0.537292i	−0.978407	+	0.206688i	$0.933731\pi$
$558$		0			0
$559$	−7.64508			−0.323352
$560$	−0.702080	−	1.21604i	−0.0296683	−	0.0513870i
$561$		0			0
$562$	−9.75778			−0.411607
$563$	33.9139			1.42930			0.714651	−	0.699481i	$-0.246585\pi$
$563$	33.9139			1.42930			0.714651	+	0.699481i	$0.246585\pi$
$564$		0			0
$565$	−5.44994	+	9.43958i	−0.229281	+	0.397126i
$566$	7.50287	+	12.9954i	0.315369	+	0.546236i
$567$		0			0
$568$	−6.92978	+	12.0027i	−0.290767	+	0.503623i
$569$	44.9621			1.88491			0.942454	−	0.334337i	$-0.108512\pi$
$569$	44.9621			1.88491			0.942454	+	0.334337i	$0.108512\pi$
$570$		0			0
$571$	−11.8519			−0.495986			−0.247993	−	0.968762i	$-0.579771\pi$
$571$	−11.8519			−0.495986			−0.247993	+	0.968762i	$0.579771\pi$
$572$	2.49607	−	4.32333i	0.104366	−	0.180767i
$573$		0			0
$574$	−0.682546	−	1.18220i	−0.0284889	−	0.0493443i
$575$	1.61656	−	2.79996i	0.0674151	−	0.116766i
$576$		0			0
$577$	−26.8524			−1.11788			−0.558939	−	0.829209i	$-0.688792\pi$
$577$	−26.8524			−1.11788			−0.558939	+	0.829209i	$0.688792\pi$
$578$	−58.5551			−2.43557
$579$		0			0
$580$	−2.80176	−	4.85280i	−0.116337	−	0.201501i
$581$	2.18080			0.0904750
$582$		0			0
$583$	−5.83564	−	10.1076i	−0.241687	−	0.418615i
$584$	−13.9300	+	24.1274i	−0.576427	+	0.998401i
$585$		0			0
$586$	−13.2846	+	23.0097i	−0.548783	+	0.950520i
$587$	−14.9660	+	25.9218i	−0.617711	+	1.06991i	0.372191	+	0.928156i	$0.378607\pi$
$587$	−14.9660	+	25.9218i	−0.617711	+	1.06991i	−0.989902	+	0.141751i	$0.954727\pi$
$588$		0			0
$589$	−4.39476	+	16.1784i	−0.181083	+	0.666618i
$590$	−3.25332			−0.133937
$591$		0			0
$592$	−3.96154	+	6.86159i	−0.162818	+	0.282010i
$593$	8.23480	+	14.2631i	0.338163	+	0.585715i	0.984087	−	0.177686i	$-0.0568612\pi$
$593$	8.23480	+	14.2631i	0.338163	+	0.585715i	−0.645924	+	0.763401i	$0.723528\pi$
$594$		0			0
$595$	−1.08323	−	1.87622i	−0.0444082	−	0.0769173i
$596$	0.164920			0.00675537
$597$		0			0
$598$	−4.92299	−	8.52687i	−0.201316	−	0.348690i
$599$	−3.75683	−	6.50702i	−0.153500	−	0.265869i	0.779012	−	0.627009i	$-0.215721\pi$
$599$	−3.75683	−	6.50702i	−0.153500	−	0.265869i	−0.932512	+	0.361140i	$0.882388\pi$
$600$		0			0
$601$	−3.48062			−0.141978			−0.0709888	−	0.997477i	$-0.522615\pi$
$601$	−3.48062			−0.141978			−0.0709888	+	0.997477i	$0.522615\pi$
$602$	−0.232425	−	0.402571i	−0.00947292	−	0.0164076i
$603$		0			0
$604$	−2.73479	−	4.73680i	−0.111277	−	0.192738i
$605$	5.51103	−	9.54539i	0.224055	−	0.388075i
$606$		0			0
$607$	−8.49878			−0.344955			−0.172477	−	0.985013i	$-0.555177\pi$
$607$	−8.49878			−0.344955			−0.172477	+	0.985013i	$0.555177\pi$
$608$	11.9026	−	3.14539i	0.482713	−	0.127562i
$609$		0			0
$610$	13.7620	−	23.8365i	0.557207	−	0.965111i
$611$	−14.2042	+	24.6025i	−0.574642	+	0.995309i
$612$		0			0
$613$	−1.45063	+	2.51256i	−0.0585902	+	0.101481i	−0.893833	−	0.448400i	$-0.851994\pi$
$613$	−1.45063	+	2.51256i	−0.0585902	+	0.101481i	0.835243	+	0.549882i	$0.185327\pi$
$614$	−3.53782	−	6.12768i	−0.142775	−	0.247293i
$615$		0			0
$616$	−0.884838			−0.0356512
$617$	5.06258	+	8.76864i	0.203812	+	0.353012i	0.949753	−	0.312999i	$-0.101334\pi$
$617$	5.06258	+	8.76864i	0.203812	+	0.353012i	−0.745942	+	0.666011i	$0.768000\pi$
$618$		0			0
$619$	1.22046			0.0490543			0.0245272	−	0.999699i	$-0.492192\pi$
$619$	1.22046			0.0490543			0.0245272	+	0.999699i	$0.492192\pi$
$620$	3.06858			0.123237
$621$		0			0
$622$	19.8355	−	34.3560i	0.795329	−	1.37755i
$623$	−0.0968782	−	0.167798i	−0.00388134	−	0.00672268i
$624$		0			0
$625$	2.81940	−	4.88334i	0.112776	−	0.195334i
$626$	55.0568			2.20051
$627$		0			0
$628$	−7.19867			−0.287258
$629$	−6.11223	+	10.5867i	−0.243711	+	0.422119i
$630$		0			0
$631$	21.1876	+	36.6980i	0.843465	+	1.46092i	0.886948	+	0.461870i	$0.152821\pi$
$631$	21.1876	+	36.6980i	0.843465	+	1.46092i	−0.0434829	+	0.999054i	$0.513845\pi$
$632$	9.77192	−	16.9255i	0.388706	−	0.673259i
$633$		0			0
$634$	16.4850			0.654703
$635$	−26.3590			−1.04603
$636$		0			0
$637$	−17.1374	−	29.6828i	−0.679008	−	1.17608i
$638$	−22.0979			−0.874865
$639$		0			0
$640$	10.6551	+	18.4552i	0.421180	+	0.729505i
$641$	13.8600	−	24.0062i	0.547437	−	0.948188i	−0.451013	−	0.892518i	$-0.648937\pi$
$641$	13.8600	−	24.0062i	0.547437	−	0.948188i	0.998449	−	0.0556704i	$-0.0177296\pi$
$642$		0			0
$643$	8.67071	−	15.0181i	0.341939	−	0.592256i	−0.642854	−	0.765989i	$-0.722250\pi$
$643$	8.67071	−	15.0181i	0.341939	−	0.592256i	0.984793	+	0.173733i	$0.0555829\pi$
$644$	0.0609019	−	0.105485i	0.00239987	−	0.00415670i
$645$		0			0
$646$	49.0499	−	12.9620i	1.92984	−	0.509982i
$647$	−22.2177			−0.873468			−0.436734	−	0.899591i	$-0.643865\pi$
$647$	−22.2177			−0.873468			−0.436734	+	0.899591i	$0.643865\pi$
$648$		0			0
$649$	−1.30515	+	2.26058i	−0.0512315	+	0.0887355i
$650$	9.98487	+	17.2943i	0.391639	+	0.678338i
$651$		0			0
$652$	6.29796	+	10.9084i	0.246647	+	0.427205i
$653$	28.3472			1.10931			0.554656	−	0.832080i	$-0.312850\pi$
$653$	28.3472			1.10931			0.554656	+	0.832080i	$0.312850\pi$
$654$		0			0
$655$	8.51338	+	14.7456i	0.332645	+	0.576158i
$656$	10.8588	+	18.8079i	0.423964	+	0.734327i
$657$		0			0
$658$	−1.72734			−0.0673387
$659$	8.31334	+	14.3991i	0.323842	+	0.560910i	0.981277	−	0.192600i	$-0.0616921\pi$
$659$	8.31334	+	14.3991i	0.323842	+	0.560910i	−0.657435	+	0.753511i	$0.728359\pi$
$660$		0			0
$661$	5.96426	+	10.3304i	0.231983	+	0.401806i	0.958392	−	0.285457i	$-0.0921454\pi$
$661$	5.96426	+	10.3304i	0.231983	+	0.401806i	−0.726409	+	0.687263i	$0.758812\pi$
$662$	5.77040	−	9.99462i	0.224273	−	0.388452i
$663$		0			0
$664$	−27.2490			−1.05747
$665$	0.905948	+	0.912211i	0.0351312	+	0.0353740i
$666$		0			0
$667$	−4.43369	+	7.67937i	−0.171673	+	0.297347i
$668$	5.80251	−	10.0502i	0.224506	−	0.388856i
$669$		0			0
$670$	13.2791	−	23.0000i	0.513016	−	0.888569i
$671$	−11.0419	−	19.1251i	−0.426267	−	0.738317i
$672$		0			0
$673$	13.6535			0.526305			0.263152	−	0.964754i	$-0.415238\pi$
$673$	13.6535			0.526305			0.263152	+	0.964754i	$0.415238\pi$
$674$	−16.8922	−	29.2581i	−0.650662	−	1.12698i
$675$		0			0
$676$	5.73215			0.220467
$677$	16.9365			0.650922			0.325461	−	0.945555i	$-0.394481\pi$
$677$	16.9365			0.650922			0.325461	+	0.945555i	$0.394481\pi$
$678$		0			0
$679$	−0.400678	+	0.693996i	−0.0153766	+	0.0266331i
$680$	13.5349	+	23.4432i	0.519041	+	0.899006i
$681$		0			0
$682$	6.05059	−	10.4799i	0.231689	−	0.401298i
$683$	1.16439			0.0445542			0.0222771	−	0.999752i	$-0.492908\pi$
$683$	1.16439			0.0445542			0.0222771	+	0.999752i	$0.492908\pi$
$684$		0			0
$685$	14.7413			0.563238
$686$	2.08937	−	3.61889i	0.0797725	−	0.138170i
$687$		0			0
$688$	3.69769	+	6.40459i	0.140973	+	0.244173i
$689$	14.4638	−	25.0520i	0.551027	−	0.954407i
$690$		0			0
$691$	35.6996			1.35808			0.679038	−	0.734103i	$-0.262397\pi$
$691$	35.6996			1.35808			0.679038	+	0.734103i	$0.262397\pi$
$692$	−7.78434			−0.295916
$693$		0			0
$694$	20.4145	+	35.3589i	0.774922	+	1.34220i
$695$	7.30841			0.277224
$696$		0			0
$697$	16.7539	+	29.0186i	0.634600	+	1.09916i
$698$	21.9552	−	38.0275i	0.831017	−	1.43936i
$699$		0			0
$700$	−0.123522	+	0.213946i	−0.00466869	+	0.00808641i
$701$	1.70437	−	2.95205i	0.0643732	−	0.111498i	−0.832043	−	0.554712i	$-0.812829\pi$
$701$	1.70437	−	2.95205i	0.0643732	−	0.111498i	0.896416	+	0.443214i	$0.146162\pi$
$702$		0			0
$703$	1.90168	−	7.00064i	0.0717233	−	0.264034i
$704$	10.0196			0.377629
$705$		0			0
$706$	−21.4350	+	37.1265i	−0.806716	+	1.39727i
$707$	0.288185	+	0.499152i	0.0108383	+	0.0187725i
$708$		0			0
$709$	−12.1346	−	21.0178i	−0.455725	−	0.789338i	0.543005	−	0.839730i	$-0.317287\pi$
$709$	−12.1346	−	21.0178i	−0.455725	−	0.789338i	−0.998730	+	0.0503912i	$0.983953\pi$
$710$	−14.5358			−0.545519
$711$		0			0
$712$	1.21049	+	2.09663i	0.0453650	+	0.0785744i
$713$	−2.42796	−	4.20535i	−0.0909278	−	0.157492i
$714$		0			0
$715$	−15.2624			−0.570782
$716$	4.21273	+	7.29666i	0.157437	+	0.272689i
$717$		0			0
$718$	−28.5259	−	49.4083i	−1.06458	−	1.84390i
$719$	19.9862	−	34.6171i	0.745360	−	1.29100i	−0.204666	−	0.978832i	$-0.565611\pi$
$719$	19.9862	−	34.6171i	0.745360	−	1.29100i	0.950026	−	0.312170i	$-0.101056\pi$
$720$		0			0
$721$	−3.18714			−0.118695
$722$	−26.1763	+	14.8734i	−0.974181	+	0.553531i
$723$		0			0
$724$	−2.29459	+	3.97434i	−0.0852776	+	0.147705i
$725$	8.99246	−	15.5754i	0.333971	−	0.578456i
$726$		0			0
$727$	−17.8431	+	30.9051i	−0.661764	+	1.14621i	0.318388	+	0.947960i	$0.396858\pi$
$727$	−17.8431	+	30.9051i	−0.661764	+	1.14621i	−0.980152	+	0.198248i	$0.936475\pi$
$728$	−1.09655	−	1.89928i	−0.0406408	−	0.0703920i
$729$		0			0
$730$	−29.2193			−1.08146
$731$	5.70515	+	9.88160i	0.211012	+	0.365484i
$732$		0			0
$733$	49.0097			1.81021			0.905107	−	0.425183i	$-0.139790\pi$
$733$	49.0097			1.81021			0.905107	+	0.425183i	$0.139790\pi$
$734$	25.4461			0.939233
$735$		0			0
$736$	−1.78298	+	3.08821i	−0.0657215	+	0.113833i
$737$	−10.6544	−	18.4540i	−0.392461	−	0.679762i
$738$		0			0
$739$	2.82997	−	4.90164i	0.104102	−	0.180310i	−0.809269	−	0.587438i	$-0.800137\pi$
$739$	2.82997	−	4.90164i	0.104102	−	0.180310i	0.913371	+	0.407128i	$0.133470\pi$
$740$	−1.32783			−0.0488118
$741$		0			0
$742$	1.75891			0.0645715
$743$	9.61471	−	16.6532i	0.352729	−	0.610945i	−0.633997	−	0.773335i	$-0.718587\pi$
$743$	9.61471	−	16.6532i	0.352729	−	0.610945i	0.986727	+	0.162390i	$0.0519203\pi$
$744$		0			0
$745$	−0.252103	−	0.436655i	−0.00923634	−	0.0159978i
$746$	21.6101	−	37.4298i	0.791201	−	1.37040i
$747$		0			0
$748$	−7.45078			−0.272428
$749$	1.89665			0.0693021
$750$		0			0
$751$	5.22708	+	9.05357i	0.190739	+	0.330369i	0.945495	−	0.325636i	$-0.105578\pi$
$751$	5.22708	+	9.05357i	0.190739	+	0.330369i	−0.754756	+	0.656005i	$0.772245\pi$
$752$	27.4806			1.00212
$753$		0			0
$754$	−27.3852	−	47.4326i	−0.997310	−	1.72739i
$755$	−8.36104	+	14.4817i	−0.304289	+	0.527044i
$756$		0			0
$757$	−5.30205	+	9.18342i	−0.192706	+	0.333777i	−0.946146	−	0.323740i	$-0.895060\pi$
$757$	−5.30205	+	9.18342i	−0.192706	+	0.333777i	0.753440	+	0.657517i	$0.228393\pi$
$758$	16.3485	−	28.3165i	0.593805	−	1.02850i
$759$		0			0
$760$	−11.3198	−	11.3980i	−0.410612	−	0.413450i
$761$	−13.2950			−0.481944			−0.240972	−	0.970532i	$-0.577466\pi$
$761$	−13.2950			−0.481944			−0.240972	+	0.970532i	$0.577466\pi$
$762$		0			0
$763$	0.387887	−	0.671840i	0.0140425	−	0.0243222i
$764$	1.97324	+	3.41775i	0.0713893	+	0.123650i
$765$		0			0
$766$	21.6922	+	37.5719i	0.783769	+	1.35753i
$767$	−6.46969			−0.233607
$768$		0			0
$769$	−1.75226	−	3.03501i	−0.0631882	−	0.109445i	0.832701	−	0.553723i	$-0.186794\pi$
$769$	−1.75226	−	3.03501i	−0.0631882	−	0.109445i	−0.895889	+	0.444278i	$0.853460\pi$
$770$	−0.464006	−	0.803681i	−0.0167216	−	0.0289627i
$771$		0			0
$772$	−6.02430			−0.216819
$773$	24.0034	+	41.5750i	0.863341	+	1.49535i	0.868685	+	0.495365i	$0.164966\pi$
$773$	24.0034	+	41.5750i	0.863341	+	1.49535i	−0.00534399	+	0.999986i	$0.501701\pi$
$774$		0			0
$775$	4.92442	+	8.52934i	0.176890	+	0.306383i
$776$	5.00646	−	8.67144i	0.179721	−	0.311287i
$777$		0			0
$778$	37.9565			1.36081
$779$	−14.0119	−	14.1088i	−0.502029	−	0.505500i
$780$		0			0
$781$	−5.83137	+	10.1002i	−0.208663	+	0.361415i
$782$	−7.34757	+	12.7264i	−0.262749	+	0.455094i
$783$		0			0
$784$	−16.5777	+	28.7134i	−0.592059	+	1.02548i
$785$	11.0042	+	19.0598i	0.392756	+	0.680274i
$786$		0			0
$787$	−44.9965			−1.60395			−0.801976	−	0.597356i	$-0.796218\pi$
$787$	−44.9965			−1.60395			−0.801976	+	0.597356i	$0.796218\pi$
$788$	4.12681	+	7.14784i	0.147011	+	0.254631i
$789$		0			0
$790$	20.4974			0.729265
$791$	−1.31798			−0.0468620
$792$		0			0
$793$	27.3677	−	47.4022i	0.971854	−	1.68330i
$794$	23.1957	+	40.1762i	0.823186	+	1.42580i
$795$		0			0
$796$	−1.61269	+	2.79325i	−0.0571601	+	0.0990043i
$797$	−42.0439			−1.48927			−0.744636	−	0.667471i	$-0.767377\pi$
$797$	−42.0439			−1.48927			−0.744636	+	0.667471i	$0.767377\pi$
$798$		0			0
$799$	42.3997			1.49999
$800$	3.61626	−	6.26355i	0.127854	−	0.221450i
$801$		0			0
$802$	17.9928	+	31.1645i	0.635350	+	1.10046i
$803$	−11.7220	+	20.3031i	−0.413661	+	0.716481i
$804$		0			0
$805$	−0.372389			−0.0131250
$806$	29.9932			1.05646
$807$		0			0
$808$	−3.60086	−	6.23687i	−0.126678	−	0.219412i
$809$	−37.6699			−1.32440			−0.662202	−	0.749325i	$-0.730378\pi$
$809$	−37.6699			−1.32440			−0.662202	+	0.749325i	$0.730378\pi$
$810$		0			0
$811$	16.0198	+	27.7471i	0.562532	+	0.974334i	0.997275	+	0.0737793i	$0.0235060\pi$
$811$	16.0198	+	27.7471i	0.562532	+	0.974334i	−0.434743	+	0.900555i	$0.643161\pi$
$812$	0.338780	−	0.586784i	0.0118889	−	0.0205921i
$813$		0			0
$814$	−2.61819	+	4.53484i	−0.0917675	+	0.158946i
$815$	19.2546	−	33.3500i	0.674461	−	1.16820i
$816$		0			0
$817$	−4.77143	−	4.80441i	−0.166931	−	0.168085i
$818$	39.5163			1.38166
$819$		0			0
$820$	−1.81982	+	3.15201i	−0.0635507	+	0.110073i
$821$	−12.9111	−	22.3626i	−0.450600	−	0.780461i	0.547824	−	0.836594i	$-0.315456\pi$
$821$	−12.9111	−	22.3626i	−0.450600	−	0.780461i	−0.998423	+	0.0561324i	$0.982123\pi$
$822$		0			0
$823$	−17.5559	−	30.4077i	−0.611961	−	1.05995i	−0.990910	−	0.134530i	$-0.957048\pi$
$823$	−17.5559	−	30.4077i	−0.611961	−	1.05995i	0.378949	−	0.925418i	$-0.376286\pi$
$824$	39.8232			1.38731
$825$		0			0
$826$	−0.196691	−	0.340678i	−0.00684374	−	0.0118537i
$827$	8.57009	+	14.8438i	0.298011	+	0.516170i	0.975681	−	0.219196i	$-0.0703434\pi$
$827$	8.57009	+	14.8438i	0.298011	+	0.516170i	−0.677670	+	0.735366i	$0.737010\pi$
$828$		0			0
$829$	41.3825			1.43727			0.718636	−	0.695386i	$-0.244767\pi$
$829$	41.3825			1.43727			0.718636	+	0.695386i	$0.244767\pi$
$830$	−14.2893	−	24.7498i	−0.495988	−	0.859077i
$831$		0			0
$832$	12.4170	+	21.5069i	0.430482	+	0.745616i
$833$	−25.5776	+	44.3016i	−0.886210	+	1.53496i
$834$		0			0
$835$	−35.4798			−1.22783
$836$	4.27476	−	1.12965i	0.147846	−	0.0390698i
$837$		0			0
$838$	−16.4723	+	28.5309i	−0.569027	+	0.985583i
$839$	21.5126	−	37.2609i	0.742698	−	1.28639i	−0.208565	−	0.978009i	$-0.566879\pi$
$839$	21.5126	−	37.2609i	0.742698	−	1.28639i	0.951263	−	0.308382i	$-0.0997875\pi$
$840$		0			0
$841$	−10.1634	+	17.6034i	−0.350460	+	0.607015i
$842$	−9.10110	−	15.7636i	−0.313645	−	0.543248i
$843$		0			0
$844$	−3.40219			−0.117108
$845$	−8.76241	−	15.1769i	−0.301436	−	0.522103i
$846$		0			0
$847$	1.33275			0.0457939
$848$	−27.9828			−0.960934
$849$		0			0
$850$	14.9024	−	25.8118i	0.511149	−	0.885336i
$851$	1.05062	+	1.81972i	0.0360147	+	0.0623793i
$852$		0			0
$853$	16.8625	−	29.2067i	0.577361	−	1.00002i	−0.418420	−	0.908254i	$-0.637416\pi$
$853$	16.8625	−	29.2067i	0.577361	−	1.00002i	0.995781	−	0.0917646i	$-0.0292507\pi$
$854$	3.32811			0.113886
$855$		0			0
$856$	−23.6986			−0.810000
$857$	8.14798	−	14.1127i	0.278330	−	0.482081i	−0.692640	−	0.721283i	$-0.743553\pi$
$857$	8.14798	−	14.1127i	0.278330	−	0.482081i	0.970970	+	0.239202i	$0.0768859\pi$
$858$		0			0
$859$	2.49290	+	4.31783i	0.0850567	+	0.147322i	0.905415	−	0.424527i	$-0.139560\pi$
$859$	2.49290	+	4.31783i	0.0850567	+	0.147322i	−0.820359	+	0.571849i	$0.806226\pi$
$860$	−0.619695	+	1.07334i	−0.0211314	+	0.0366007i
$861$		0			0
$862$	59.2526			2.01815
$863$	14.0770			0.479187			0.239593	−	0.970873i	$-0.422986\pi$
$863$	14.0770			0.479187			0.239593	+	0.970873i	$0.422986\pi$
$864$		0			0
$865$	11.8995	+	20.6105i	0.404594	+	0.700777i
$866$	60.3418			2.05050
$867$		0			0
$868$	0.185522	+	0.321333i	0.00629701	+	0.0109067i
$869$	8.22301	−	14.2427i	0.278947	−	0.483150i
$870$		0			0
$871$	26.4073	−	45.7388i	0.894778	−	1.54980i
$872$	−4.84663	+	8.39461i	−0.164128	+	0.284277i
$873$		0			0
$874$	2.28603	−	8.41553i	0.0773261	−	0.284659i
$875$	2.23001			0.0753882
$876$		0			0
$877$	−10.3417	+	17.9123i	−0.349214	+	0.604857i	−0.986110	−	0.166093i	$-0.946885\pi$
$877$	−10.3417	+	17.9123i	−0.349214	+	0.604857i	0.636896	+	0.770950i	$0.280218\pi$
$878$	−10.3290	−	17.8904i	−0.348589	−	0.603773i
$879$		0			0
$880$	7.38197	+	12.7859i	0.248846	+	0.431014i
$881$	−13.0479			−0.439594			−0.219797	−	0.975546i	$-0.570539\pi$
$881$	−13.0479			−0.439594			−0.219797	+	0.975546i	$0.570539\pi$
$882$		0			0
$883$	−28.1464	−	48.7510i	−0.947201	−	1.64060i	−0.751283	−	0.659980i	$-0.770565\pi$
$883$	−28.1464	−	48.7510i	−0.947201	−	1.64060i	−0.195918	−	0.980620i	$-0.562769\pi$
$884$	−9.23350	−	15.9929i	−0.310556	−	0.537899i
$885$		0			0
$886$	4.66986			0.156887
$887$	15.8246	+	27.4090i	0.531338	+	0.920304i	0.999331	+	0.0365721i	$0.0116439\pi$
$887$	15.8246	+	27.4090i	0.531338	+	0.920304i	−0.467993	+	0.883732i	$0.655023\pi$
$888$		0			0
$889$	−1.59362	−	2.76024i	−0.0534484	−	0.0925754i
$890$	−1.26955	+	2.19893i	−0.0425554	+	0.0737081i
$891$		0			0
$892$	13.9669			0.467647
$893$	−24.3261	+	6.42843i	−0.814041	+	0.215119i
$894$		0			0
$895$	12.8795	−	22.3079i	0.430514	−	0.745672i
$896$	−1.28838	+	2.23154i	−0.0430418	+	0.0745505i
$897$		0			0
$898$	−32.5215	+	56.3289i	−1.08526	+	1.87972i
$899$	−13.5061	−	23.3932i	−0.450452	−	0.780206i
$900$		0			0
$901$	−43.1745			−1.43835
$902$	7.17658	+	12.4302i	0.238954	+	0.413881i
$903$		0			0
$904$	16.4681			0.547720
$905$	14.0304			0.466386
$906$		0			0
$907$	18.4800	−	32.0084i	0.613620	−	1.06282i	−0.377005	−	0.926211i	$-0.623046\pi$
$907$	18.4800	−	32.0084i	0.613620	−	1.06282i	0.990625	−	0.136610i	$-0.0436206\pi$
$908$	−0.125073	−	0.216634i	−0.00415071	−	0.00718924i
$909$		0			0
$910$	1.15005	−	1.99195i	0.0381239	−	0.0660325i
$911$	3.15788			0.104625			0.0523126	−	0.998631i	$-0.483341\pi$
$911$	3.15788			0.104625			0.0523126	+	0.998631i	$0.483341\pi$
$912$		0			0
$913$	−22.9299			−0.758869
$914$	−9.67505	+	16.7577i	−0.320022	+	0.554295i
$915$		0			0
$916$	−4.52630	−	7.83978i	−0.149553	−	0.259034i
$917$	−1.02941	+	1.78299i	−0.0339941	+	0.0588795i
$918$		0			0
$919$	−20.6780			−0.682104			−0.341052	−	0.940044i	$-0.610783\pi$
$919$	−20.6780			−0.682104			−0.341052	+	0.940044i	$0.610783\pi$
$920$	4.65298			0.153404
$921$		0			0
$922$	0.938809	+	1.62606i	0.0309180	+	0.0535516i
$923$	−28.9065			−0.951468
$924$		0			0
$925$	−2.13087	−	3.69078i	−0.0700627	−	0.121352i
$926$	−5.67651	+	9.83200i	−0.186542	+	0.323100i
$927$		0			0
$928$	−9.91821	+	17.1789i	−0.325581	+	0.563923i
$929$	22.6072	−	39.1568i	0.741717	−	1.28469i	−0.209996	−	0.977702i	$-0.567345\pi$
$929$	22.6072	−	39.1568i	0.741717	−	1.28469i	0.951713	−	0.306989i	$-0.0993215\pi$
$930$		0			0
$931$	7.95788	−	29.2952i	0.260809	−	0.960112i
$932$	−6.87556			−0.225216
$933$		0			0
$934$	−14.0208	+	24.2847i	−0.458774	+	0.794620i
$935$	11.3896	+	19.7273i	0.372479	+	0.645153i
$936$		0			0
$937$	0.855365	+	1.48154i	0.0279435	+	0.0483996i	0.879659	−	0.475605i	$-0.157771\pi$
$937$	0.855365	+	1.48154i	0.0279435	+	0.0483996i	−0.851715	+	0.524005i	$0.824437\pi$
$938$	3.21133			0.104854
$939$		0			0
$940$	2.30273	+	3.98845i	0.0751069	+	0.130089i
$941$	−17.6978	−	30.6536i	−0.576933	−	0.999278i	−0.995829	−	0.0912431i	$-0.970916\pi$
$941$	−17.6978	−	30.6536i	−0.576933	−	0.999278i	0.418895	−	0.908034i	$-0.362417\pi$
$942$		0			0
$943$	5.75959			0.187558
$944$	3.12919	+	5.41992i	0.101847	+	0.176403i
$945$		0			0
$946$	2.44381	+	4.23281i	0.0794552	+	0.137620i
$947$	3.27579	−	5.67384i	0.106449	−	0.184375i	−0.807880	−	0.589347i	$-0.799385\pi$
$947$	3.27579	−	5.67384i	0.106449	−	0.184375i	0.914329	+	0.404972i	$0.132719\pi$
$948$		0			0
$949$	−58.1067			−1.88622
$950$	−4.63655	+	17.0685i	−0.150430	+	0.553774i
$951$		0			0
$952$	−1.63660	+	2.83468i	−0.0530426	+	0.0918724i
$953$	−6.93938	+	12.0194i	−0.224789	+	0.389345i	−0.956256	−	0.292531i	$-0.905503\pi$
$953$	−6.93938	+	12.0194i	−0.224789	+	0.389345i	0.731467	+	0.681877i	$0.238836\pi$
$954$		0			0
$955$	6.03275	−	10.4490i	0.195215	−	0.338123i
$956$	0.195858	+	0.339237i	0.00633451	+	0.0109717i
$957$		0			0
$958$	18.2216			0.588714
$959$	0.891238	+	1.54367i	0.0287796	+	0.0498477i
$960$		0			0
$961$	−16.2077			−0.522830
$962$	−12.9785			−0.418445
$963$		0			0
$964$	−3.09322	+	5.35761i	−0.0996258	+	0.172557i
$965$	9.20899	+	15.9504i	0.296448	+	0.513463i
$966$		0			0
$967$	−7.92561	+	13.7276i	−0.254870	+	0.441448i	−0.964860	−	0.262763i	$-0.915366\pi$
$967$	−7.92561	+	13.7276i	−0.254870	+	0.441448i	0.709990	+	0.704212i	$0.248699\pi$
$968$	−16.6527			−0.535237
$969$		0			0
$970$	10.5015			0.337182
$971$	4.22725	−	7.32181i	0.135659	−	0.234968i	−0.790190	−	0.612862i	$-0.790018\pi$
$971$	4.22725	−	7.32181i	0.135659	−	0.234968i	0.925849	+	0.377894i	$0.123352\pi$
$972$		0			0
$973$	0.441854	+	0.765314i	0.0141652	+	0.0245349i
$974$	−18.1688	+	31.4694i	−0.582167	+	1.00834i
$975$		0			0
$976$	−52.9477			−1.69481
$977$	−29.4345			−0.941693			−0.470847	−	0.882215i	$-0.656051\pi$
$977$	−29.4345			−0.941693			−0.470847	+	0.882215i	$0.656051\pi$
$978$		0			0
$979$	1.01862	+	1.76430i	0.0325552	+	0.0563873i
$980$	−5.55649			−0.177495
$981$		0			0
$982$	20.1816	+	34.9556i	0.644021	+	1.11548i
$983$	−3.89757	+	6.75078i	−0.124313	+	0.215317i	−0.921464	−	0.388463i	$-0.873006\pi$
$983$	−3.89757	+	6.75078i	−0.124313	+	0.215317i	0.797151	+	0.603780i	$0.206339\pi$
$984$		0			0
$985$	12.6168	−	21.8530i	0.402005	−	0.696294i
$986$	−40.8725	+	70.7932i	−1.30164	+	2.25451i
$987$		0			0
$988$	7.72232	+	7.77570i	0.245680	+	0.247378i
$989$	1.96129			0.0623653
$990$		0			0
$991$	4.41893	−	7.65382i	0.140372	−	0.243132i	−0.787265	−	0.616615i	$-0.788503\pi$
$991$	4.41893	−	7.65382i	0.140372	−	0.243132i	0.927637	+	0.373484i	$0.121837\pi$
$992$	−5.43138	−	9.40742i	−0.172446	−	0.298686i
$993$		0			0
$994$	−0.878810	−	1.52214i	−0.0278742	−	0.0482795i
$995$	9.86088			0.312611
$996$		0			0
$997$	−25.5217	−	44.2049i	−0.808280	−	1.39998i	−0.914054	−	0.405592i	$-0.867065\pi$
$997$	−25.5217	−	44.2049i	−0.808280	−	1.39998i	0.105774	−	0.994390i	$-0.466268\pi$
$998$	5.48143	+	9.49412i	0.173512	+	0.300531i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.f.h.163.5	yes	12
3.2	odd	2		513.2.f.f.163.2	✓	12
19.7	even	3	inner	513.2.f.h.406.5	yes	12
19.8	odd	6		9747.2.a.br.1.5		6
19.11	even	3		9747.2.a.bl.1.2		6
57.8	even	6		9747.2.a.bm.1.2		6
57.11	odd	6		9747.2.a.bs.1.5		6
57.26	odd	6		513.2.f.f.406.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.f.f.163.2	✓	12	3.2	odd	2
513.2.f.f.406.2	yes	12	57.26	odd	6
513.2.f.h.163.5	yes	12	1.1	even	1	trivial
513.2.f.h.406.5	yes	12	19.7	even	3	inner
9747.2.a.bl.1.2		6	19.11	even	3
9747.2.a.bm.1.2		6	57.8	even	6
9747.2.a.br.1.5		6	19.8	odd	6
9747.2.a.bs.1.5		6	57.11	odd	6

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.792283 - 1.37227i) q^{2} +(-0.255424 - 0.442408i) q^{4} +(-0.780905 + 1.35257i) q^{5} -0.188849 q^{7} +2.35966 q^{8} +(1.23740 + 2.14323i) q^{10} +1.98564 q^{11} +(2.46073 + 4.26212i) q^{13} +(-0.149622 + 0.259153i) q^{14} +(2.38037 - 4.12291i) q^{16} +(3.67265 - 6.36121i) q^{17} +(-1.14266 + 4.20646i) q^{19} +0.797849 q^{20} +(1.57319 - 2.72484i) q^{22} +(-0.631283 - 1.09341i) q^{23} +(1.28038 + 2.21768i) q^{25} +7.79839 q^{26} +(0.0482366 + 0.0835483i) q^{28} +(-3.51165 - 6.08235i) q^{29} +3.84607 q^{31} +(-1.41219 - 2.44598i) q^{32} +(-5.81955 - 10.0798i) q^{34} +(0.147473 - 0.255431i) q^{35} -1.66426 q^{37} +(4.86711 + 4.90075i) q^{38} +(-1.84267 + 3.19160i) q^{40} +(-2.28090 + 3.95064i) q^{41} +(-0.776707 + 1.34530i) q^{43} +(-0.507181 - 0.878463i) q^{44} -2.00062 q^{46} +(2.88618 + 4.99901i) q^{47} -6.96434 q^{49} +4.05768 q^{50} +(1.25706 - 2.17730i) q^{52} +(-2.93892 - 5.09036i) q^{53} +(-1.55059 + 2.68571i) q^{55} -0.445619 q^{56} -11.1289 q^{58} +(-0.657293 + 1.13846i) q^{59} +(-5.56088 - 9.63172i) q^{61} +(3.04718 - 5.27787i) q^{62} +5.04605 q^{64} -7.68640 q^{65} +(-5.36574 - 9.29374i) q^{67} -3.75234 q^{68} +(-0.233681 - 0.404747i) q^{70} +(-2.93677 + 5.08664i) q^{71} +(-5.90339 + 10.2250i) q^{73} +(-1.31856 + 2.28382i) q^{74} +(2.15284 - 0.568911i) q^{76} -0.374986 q^{77} +(4.14124 - 7.17284i) q^{79} +(3.71768 + 6.43921i) q^{80} +(3.61424 + 6.26005i) q^{82} -11.5479 q^{83} +(5.73598 + 9.93500i) q^{85} +(1.23074 + 2.13171i) q^{86} +4.68543 q^{88} +(0.512993 + 0.888530i) q^{89} +(-0.464707 - 0.804896i) q^{91} +(-0.322490 + 0.558569i) q^{92} +9.14668 q^{94} +(-4.79721 - 4.83037i) q^{95} +(2.12169 - 3.67487i) q^{97} +(-5.51772 + 9.55698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} + q^{10} - 4 q^{11} - 5 q^{13} + 2 q^{14} + 3 q^{16} + 10 q^{17} - 9 q^{19} - 2 q^{20} - 4 q^{22} + 3 q^{23} - 5 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) \) 12 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 + q^10 - 4 * q^11 - 5 * q^13 + 2 * q^14 + 3 * q^16 + 10 * q^17 - 9 * q^19 - 2 * q^20 - 4 * q^22 + 3 * q^23 - 5 * q^25 - 2 * q^26 - 2 * q^28 - 6 * q^29 - 4 * q^31 + 8 * q^32 + 4 * q^34 + 3 * q^35 + 26 * q^37 - 10 * q^38 - 6 * q^40 - 13 * q^41 - 3 * q^43 - 20 * q^44 - 10 * q^46 + 18 * q^47 + 26 * q^49 + 6 * q^50 - 22 * q^52 - q^53 - 6 * q^55 + 48 * q^56 + 28 * q^58 + 11 * q^59 - 13 * q^61 + 22 * q^62 - 72 * q^65 + 9 * q^67 - 10 * q^68 - 30 * q^70 - 6 * q^71 - 15 * q^73 + 43 * q^74 - 33 * q^76 - 58 * q^77 - 13 * q^79 + q^80 + 4 * q^82 - 16 * q^83 - 3 * q^85 - 7 * q^86 - 30 * q^88 + 29 * q^89 + 22 * q^91 + 21 * q^92 + 36 * q^94 + 22 * q^95 + 20 * q^97 - 59 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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