LMFDB - Embedded newform 819.2.s.g.289.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,44,0,0,4,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	819.289
Dual form			819.2.s.g.802.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.85815 q^{2} +1.45273 q^{4} +(-1.41690 + 2.45414i) q^{5} +(-2.59533 - 0.514050i) q^{7} +1.01691 q^{8} +(2.63281 - 4.56016i) q^{10} +(-2.68094 + 4.64352i) q^{11} +(-1.80766 - 3.11967i) q^{13} +(4.82252 + 0.955184i) q^{14} -4.79504 q^{16} +0.835344 q^{17} +(1.94086 + 3.36167i) q^{19} +(-2.05837 + 3.56520i) q^{20} +(4.98159 - 8.62837i) q^{22} -4.10954 q^{23} +(-1.51520 - 2.62440i) q^{25} +(3.35892 + 5.79682i) q^{26} +(-3.77031 - 0.746775i) q^{28} +(-2.20885 - 3.82585i) q^{29} +(-0.678792 - 1.17570i) q^{31} +6.87608 q^{32} -1.55220 q^{34} +(4.93887 - 5.64095i) q^{35} +9.07618 q^{37} +(-3.60642 - 6.24650i) q^{38} +(-1.44086 + 2.49565i) q^{40} +(1.58802 + 2.75053i) q^{41} +(1.24815 - 2.16186i) q^{43} +(-3.89468 + 6.74578i) q^{44} +7.63615 q^{46} +(-0.0166628 + 0.0288608i) q^{47} +(6.47150 + 2.66826i) q^{49} +(2.81547 + 4.87653i) q^{50} +(-2.62604 - 4.53203i) q^{52} +(-5.18049 - 8.97288i) q^{53} +(-7.59723 - 13.1588i) q^{55} +(-2.63923 - 0.522745i) q^{56} +(4.10439 + 7.10901i) q^{58} -1.74373 q^{59} +(-3.04073 - 5.26670i) q^{61} +(1.26130 + 2.18463i) q^{62} -3.18672 q^{64} +(10.2174 - 0.0160046i) q^{65} +(-1.41231 + 2.44620i) q^{67} +1.21353 q^{68} +(-9.17717 + 10.4817i) q^{70} +(7.26976 - 12.5916i) q^{71} +(-2.16106 - 3.74307i) q^{73} -16.8649 q^{74} +(2.81955 + 4.88360i) q^{76} +(9.34494 - 10.6734i) q^{77} +(-2.96381 + 5.13347i) q^{79} +(6.79408 - 11.7677i) q^{80} +(-2.95078 - 5.11091i) q^{82} +3.75778 q^{83} +(-1.18360 + 2.05005i) q^{85} +(-2.31925 + 4.01706i) q^{86} +(-2.72629 + 4.72207i) q^{88} -12.3110 q^{89} +(3.08782 + 9.02582i) q^{91} -5.97004 q^{92} +(0.0309620 - 0.0536277i) q^{94} -11.0000 q^{95} +(8.56830 - 14.8407i) q^{97} +(-12.0250 - 4.95804i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) $ 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.85815			−1.31391			−0.656956	−	0.753929i	$-0.728156\pi$
$2$	−1.85815			−1.31391			−0.656956	+	0.753929i	$0.728156\pi$
$3$		0			0
$3$		0			0
$4$	1.45273			0.726364
$5$	−1.41690	+	2.45414i	−0.633656	+	1.09752i	0.353142	+	0.935570i	$0.385113\pi$
$5$	−1.41690	+	2.45414i	−0.633656	+	1.09752i	−0.986798	+	0.161954i	$0.948220\pi$
$6$		0			0
$7$	−2.59533	−	0.514050i	−0.980944	−	0.194293i
$7$	−2.59533	−	0.514050i	−0.980944	−	0.194293i
$8$	1.01691			0.359534
$9$		0			0
$10$	2.63281	−	4.56016i	0.832568	−	1.44205i
$11$	−2.68094	+	4.64352i	−0.808334	+	1.40008i	0.105683	+	0.994400i	$0.466297\pi$
$11$	−2.68094	+	4.64352i	−0.808334	+	1.40008i	−0.914017	+	0.405675i	$0.867036\pi$
$12$		0			0
$13$	−1.80766	−	3.11967i	−0.501356	−	0.865241i
$13$	−1.80766	−	3.11967i	−0.501356	−	0.865241i
$14$	4.82252	+	0.955184i	1.28887	+	0.255284i
$15$		0			0
$16$	−4.79504			−1.19876
$17$	0.835344			0.202601			0.101300	−	0.994856i	$-0.467700\pi$
$17$	0.835344			0.202601			0.101300	+	0.994856i	$0.467700\pi$
$18$		0			0
$19$	1.94086	+	3.36167i	0.445265	+	0.771221i	0.998071	−	0.0620890i	$-0.0197763\pi$
$19$	1.94086	+	3.36167i	0.445265	+	0.771221i	−0.552806	+	0.833310i	$0.686443\pi$
$20$	−2.05837	+	3.56520i	−0.460265	+	0.797202i
$21$		0			0
$22$	4.98159	−	8.62837i	1.06208	−	1.83958i
$23$	−4.10954			−0.856898			−0.428449	−	0.903566i	$-0.640940\pi$
$23$	−4.10954			−0.856898			−0.428449	+	0.903566i	$0.640940\pi$
$24$		0			0
$25$	−1.51520	−	2.62440i	−0.303039	−	0.524880i
$26$	3.35892	+	5.79682i	0.658737	+	1.13685i
$27$		0			0
$28$	−3.77031	−	0.746775i	−0.712522	−	0.141127i
$29$	−2.20885	−	3.82585i	−0.410174	−	0.710442i	0.584735	−	0.811225i	$-0.301199\pi$
$29$	−2.20885	−	3.82585i	−0.410174	−	0.710442i	−0.994908	+	0.100783i	$0.967865\pi$
$30$		0			0
$31$	−0.678792	−	1.17570i	−0.121915	−	0.211162i	0.798608	−	0.601852i	$-0.205570\pi$
$31$	−0.678792	−	1.17570i	−0.121915	−	0.211162i	−0.920523	+	0.390689i	$0.872237\pi$
$32$	6.87608			1.21553
$33$		0			0
$34$	−1.55220			−0.266199
$35$	4.93887	−	5.64095i	0.834822	−	0.953494i
$36$		0			0
$37$	9.07618			1.49212			0.746058	−	0.665881i	$-0.231944\pi$
$37$	9.07618			1.49212			0.746058	+	0.665881i	$0.231944\pi$
$38$	−3.60642	−	6.24650i	−0.585038	−	1.01332i
$39$		0			0
$40$	−1.44086	+	2.49565i	−0.227821	+	0.394597i
$41$	1.58802	+	2.75053i	0.248007	+	0.429561i	0.962973	−	0.269599i	$-0.0868910\pi$
$41$	1.58802	+	2.75053i	0.248007	+	0.429561i	−0.714966	+	0.699160i	$0.753558\pi$
$42$		0			0
$43$	1.24815	−	2.16186i	0.190341	−	0.329680i	−0.755022	−	0.655699i	$-0.772374\pi$
$43$	1.24815	−	2.16186i	0.190341	−	0.329680i	0.945363	+	0.326019i	$0.105707\pi$
$44$	−3.89468	+	6.74578i	−0.587145	+	1.01696i
$45$		0			0
$46$	7.63615			1.12589
$47$	−0.0166628	+	0.0288608i	−0.00243052	+	0.00420978i	−0.867238	−	0.497894i	$-0.834107\pi$
$47$	−0.0166628	+	0.0288608i	−0.00243052	+	0.00420978i	0.864808	+	0.502103i	$0.167440\pi$
$48$		0			0
$49$	6.47150	+	2.66826i	0.924501	+	0.381180i
$50$	2.81547	+	4.87653i	0.398167	+	0.689645i
$51$		0			0
$52$	−2.62604	−	4.53203i	−0.364167	−	0.628480i
$53$	−5.18049	−	8.97288i	−0.711595	−	1.23252i	−0.964258	−	0.264965i	$-0.914640\pi$
$53$	−5.18049	−	8.97288i	−0.711595	−	1.23252i	0.252663	−	0.967554i	$-0.418694\pi$
$54$		0			0
$55$	−7.59723	−	13.1588i	−1.02441	−	1.77433i
$56$	−2.63923	−	0.522745i	−0.352682	−	0.0698548i
$57$		0			0
$58$	4.10439	+	7.10901i	0.538932	+	0.933458i
$59$	−1.74373			−0.227014			−0.113507	−	0.993537i	$-0.536208\pi$
$59$	−1.74373			−0.227014			−0.113507	+	0.993537i	$0.536208\pi$
$60$		0			0
$61$	−3.04073	−	5.26670i	−0.389325	−	0.674332i	0.603033	−	0.797716i	$-0.293959\pi$
$61$	−3.04073	−	5.26670i	−0.389325	−	0.674332i	−0.992359	+	0.123384i	$0.960625\pi$
$62$	1.26130	+	2.18463i	0.160185	+	0.277449i
$63$		0			0
$64$	−3.18672			−0.398340
$65$	10.2174	−	0.0160046i	1.26731	−	0.00198513i
$66$		0			0
$67$	−1.41231	+	2.44620i	−0.172542	+	0.298851i	−0.939308	−	0.343076i	$-0.888531\pi$
$67$	−1.41231	+	2.44620i	−0.172542	+	0.298851i	0.766766	+	0.641927i	$0.221865\pi$
$68$	1.21353			0.147162
$69$		0			0
$70$	−9.17717	+	10.4817i	−1.09688	+	1.25281i
$71$	7.26976	−	12.5916i	0.862762	−	1.49435i	−0.00649110	−	0.999979i	$-0.502066\pi$
$71$	7.26976	−	12.5916i	0.862762	−	1.49435i	0.869253	−	0.494368i	$-0.164600\pi$
$72$		0			0
$73$	−2.16106	−	3.74307i	−0.252933	−	0.438093i	0.711399	−	0.702788i	$-0.248062\pi$
$73$	−2.16106	−	3.74307i	−0.252933	−	0.438093i	−0.964332	+	0.264695i	$0.914729\pi$
$74$	−16.8649			−1.96051
$75$		0			0
$76$	2.81955	+	4.88360i	0.323424	+	0.560187i
$77$	9.34494	−	10.6734i	1.06495	−	1.21634i
$78$		0			0
$79$	−2.96381	+	5.13347i	−0.333455	+	0.577561i	−0.983187	−	0.182603i	$-0.941548\pi$
$79$	−2.96381	+	5.13347i	−0.333455	+	0.577561i	0.649732	+	0.760163i	$0.274881\pi$
$80$	6.79408	−	11.7677i	0.759601	−	1.31567i
$81$		0			0
$82$	−2.95078	−	5.11091i	−0.325860	−	0.564405i
$83$	3.75778			0.412470			0.206235	−	0.978503i	$-0.433879\pi$
$83$	3.75778			0.412470			0.206235	+	0.978503i	$0.433879\pi$
$84$		0			0
$85$	−1.18360	+	2.05005i	−0.128379	+	0.222359i
$86$	−2.31925	+	4.01706i	−0.250091	+	0.433170i
$87$		0			0
$88$	−2.72629	+	4.72207i	−0.290623	+	0.503374i
$89$	−12.3110			−1.30496			−0.652480	−	0.757806i	$-0.726271\pi$
$89$	−12.3110			−1.30496			−0.652480	+	0.757806i	$0.726271\pi$
$90$		0			0
$91$	3.08782	+	9.02582i	0.323692	+	0.946163i
$92$	−5.97004			−0.622420
$93$		0			0
$94$	0.0309620	−	0.0536277i	0.00319349	−	0.00553128i
$95$	−11.0000			−1.12858
$96$		0			0
$97$	8.56830	−	14.8407i	0.869979	−	1.50685i	0.00796140	−	0.999968i	$-0.497466\pi$
$97$	8.56830	−	14.8407i	0.869979	−	1.50685i	0.862017	−	0.506879i	$-0.169201\pi$
$98$	−12.0250	−	4.95804i	−1.21471	−	0.500837i
$99$		0			0
$100$	−2.20117	−	3.81254i	−0.220117	−	0.381254i
$101$	2.43524	−	4.21797i	0.242316	−	0.419703i	−0.719058	−	0.694950i	$-0.755426\pi$
$101$	2.43524	−	4.21797i	0.242316	−	0.419703i	0.961374	+	0.275247i	$0.0887596\pi$
$102$		0			0
$103$	8.77482	−	15.1984i	0.864609	−	1.49755i	−0.00282630	−	0.999996i	$-0.500900\pi$
$103$	8.77482	−	15.1984i	0.864609	−	1.49755i	0.867435	−	0.497550i	$-0.165767\pi$
$104$	−1.83824	−	3.17244i	−0.180254	−	0.311083i
$105$		0			0
$106$	9.62614	+	16.6730i	0.934973	+	1.61942i
$107$	4.88317			0.472074			0.236037	−	0.971744i	$-0.424151\pi$
$107$	4.88317			0.472074			0.236037	+	0.971744i	$0.424151\pi$
$108$		0			0
$109$	−6.88804	−	11.9304i	−0.659755	−	1.14273i	−0.980679	−	0.195624i	$-0.937327\pi$
$109$	−6.88804	−	11.9304i	−0.659755	−	1.14273i	0.320925	−	0.947105i	$-0.396006\pi$
$110$	14.1168	+	24.4510i	1.34599	+	2.33131i
$111$		0			0
$112$	12.4447	+	2.46489i	1.17592	+	0.232910i
$113$	1.17062	−	2.02758i	0.110123	−	0.190739i	−0.805697	−	0.592328i	$-0.798209\pi$
$113$	1.17062	−	2.02758i	0.110123	−	0.190739i	0.915820	+	0.401590i	$0.131542\pi$
$114$		0			0
$115$	5.82280	−	10.0854i	0.542979	−	0.940467i
$116$	−3.20886	−	5.55792i	−0.297936	−	0.516039i
$117$		0			0
$118$	3.24012			0.298277
$119$	−2.16800	−	0.429409i	−0.198740	−	0.0393639i
$120$		0			0
$121$	−8.87488	−	15.3717i	−0.806807	−	1.39743i
$122$	5.65014	+	9.78632i	0.511539	+	0.886012i
$123$		0			0
$124$	−0.986101	−	1.70798i	−0.0885545	−	0.153381i
$125$	−5.58146			−0.499221
$126$		0			0
$127$	7.91555	+	13.7101i	0.702392	+	1.21658i	0.967625	+	0.252394i	$0.0812178\pi$
$127$	7.91555	+	13.7101i	0.702392	+	1.21658i	−0.265233	+	0.964184i	$0.585449\pi$
$128$	−7.83074			−0.692147
$129$		0			0
$130$	−18.9854	+	0.0297390i	−1.66513	+	0.00260828i
$131$	10.7165	−	18.5616i	0.936309	−	1.62173i	0.164025	−	0.986456i	$-0.447552\pi$
$131$	10.7165	−	18.5616i	0.936309	−	1.62173i	0.772283	−	0.635278i	$-0.219115\pi$
$132$		0			0
$133$	−3.30912	−	9.72237i	−0.286937	−	0.843036i
$134$	2.62429	−	4.54541i	0.226704	−	0.392664i
$135$		0			0
$136$	0.849474			0.0728418
$137$	−21.2927			−1.81916			−0.909579	−	0.415530i	$-0.863596\pi$
$137$	−21.2927			−1.81916			−0.909579	+	0.415530i	$0.863596\pi$
$138$		0			0
$139$	−9.47654	+	16.4139i	−0.803790	+	1.39220i	0.113315	+	0.993559i	$0.463853\pi$
$139$	−9.47654	+	16.4139i	−0.803790	+	1.39220i	−0.917105	+	0.398646i	$0.869480\pi$
$140$	7.17484	−	8.19476i	0.606384	−	0.692584i
$141$		0			0
$142$	−13.5083	+	23.3971i	−1.13359	+	1.96344i
$143$	19.3325	−	0.0302826i	1.61667	−	0.00253236i
$144$		0			0
$145$	12.5189			1.03964
$146$	4.01558	+	6.95519i	0.332332	+	0.575615i
$147$		0			0
$148$	13.1852			1.08382
$149$	7.10716	+	12.3100i	0.582241	+	1.00847i	0.995213	+	0.0977279i	$0.0311575\pi$
$149$	7.10716	+	12.3100i	0.582241	+	1.00847i	−0.412972	+	0.910744i	$0.635509\pi$
$150$		0			0
$151$	2.81984	+	4.88411i	0.229476	+	0.397463i	0.957653	−	0.287925i	$-0.0929655\pi$
$151$	2.81984	+	4.88411i	0.229476	+	0.397463i	−0.728177	+	0.685389i	$0.759632\pi$
$152$	1.97369	+	3.41854i	0.160088	+	0.277280i
$153$		0			0
$154$	−17.3643	+	19.8327i	−1.39926	+	1.59817i
$155$	3.84712			0.309008
$156$		0			0
$157$	−2.47825	−	4.29245i	−0.197786	−	0.342575i	0.750024	−	0.661410i	$-0.230042\pi$
$157$	−2.47825	−	4.29245i	−0.197786	−	0.342575i	−0.947810	+	0.318835i	$0.896708\pi$
$158$	5.50721	−	9.53877i	0.438130	−	0.758864i
$159$		0			0
$160$	−9.74270	+	16.8748i	−0.770228	+	1.33407i
$161$	10.6656	+	2.11251i	0.840569	+	0.166489i
$162$		0			0
$163$	10.3317	+	17.8950i	0.809239	+	1.40164i	0.913392	+	0.407081i	$0.133453\pi$
$163$	10.3317	+	17.8950i	0.809239	+	1.40164i	−0.104154	+	0.994561i	$0.533213\pi$
$164$	2.30696	+	3.99578i	0.180143	+	0.312018i
$165$		0			0
$166$	−6.98252			−0.541949
$167$	−4.16321	−	7.21090i	−0.322159	−	0.557996i	0.658774	−	0.752341i	$-0.271075\pi$
$167$	−4.16321	−	7.21090i	−0.322159	−	0.557996i	−0.980933	+	0.194345i	$0.937742\pi$
$168$		0			0
$169$	−6.46470	+	11.2786i	−0.497284	+	0.867588i
$170$	2.19930	−	3.80930i	0.168679	−	0.292160i
$171$		0			0
$172$	1.81322	−	3.14059i	0.138257	−	0.239468i
$173$	3.72209	+	6.44684i	0.282985	+	0.490144i	0.972119	−	0.234490i	$-0.0753420\pi$
$173$	3.72209	+	6.44684i	0.282985	+	0.490144i	−0.689134	+	0.724634i	$0.742009\pi$
$174$		0			0
$175$	2.58337	+	7.59007i	0.195284	+	0.573756i
$176$	12.8552	−	22.2659i	0.968998	−	1.67835i
$177$		0			0
$178$	22.8757			1.71460
$179$	−2.08557	+	3.61231i	−0.155883	+	0.269997i	−0.933380	−	0.358889i	$-0.883156\pi$
$179$	−2.08557	+	3.61231i	−0.155883	+	0.269997i	0.777497	+	0.628886i	$0.216489\pi$
$180$		0			0
$181$	−9.67165			−0.718888			−0.359444	−	0.933167i	$-0.617034\pi$
$181$	−9.67165			−0.718888			−0.359444	+	0.933167i	$0.617034\pi$
$182$	−5.73764	−	16.7713i	−0.425302	−	1.24317i
$183$		0			0
$184$	−4.17905			−0.308084
$185$	−12.8600	+	22.2742i	−0.945488	+	1.63763i
$186$		0			0
$187$	−2.23951	+	3.87894i	−0.163769	+	0.283656i
$188$	−0.0242065	+	0.0419269i	−0.00176544	+	0.00305783i
$189$		0			0
$190$	20.4397			1.48285
$191$	5.75225	+	9.96319i	0.416218	+	0.720911i	0.995555	−	0.0941770i	$-0.0300220\pi$
$191$	5.75225	+	9.96319i	0.416218	+	0.720911i	−0.579337	+	0.815088i	$0.696689\pi$
$192$		0			0
$193$	−5.44302	+	9.42759i	−0.391797	+	0.678613i	−0.992687	−	0.120719i	$-0.961480\pi$
$193$	−5.44302	+	9.42759i	−0.391797	+	0.678613i	0.600889	+	0.799332i	$0.294813\pi$
$194$	−15.9212	+	27.5763i	−1.14308	+	1.97986i
$195$		0			0
$196$	9.40134	+	3.87626i	0.671524	+	0.276876i
$197$	3.89465	+	6.74574i	0.277483	+	0.480614i	0.970758	−	0.240058i	$-0.0771666\pi$
$197$	3.89465	+	6.74574i	0.277483	+	0.480614i	−0.693276	+	0.720672i	$0.743833\pi$
$198$		0			0
$199$	−23.0342			−1.63285			−0.816426	−	0.577449i	$-0.804048\pi$
$199$	−23.0342			−1.63285			−0.816426	+	0.577449i	$0.804048\pi$
$200$	−1.54083	−	2.66879i	−0.108953	−	0.188712i
$201$		0			0
$202$	−4.52505	+	7.83762i	−0.318382	+	0.551453i
$203$	3.76603	+	11.0648i	0.264324	+	0.776597i
$204$		0			0
$205$	−9.00025			−0.628605
$206$	−16.3049	+	28.2410i	−1.13602	+	1.96764i
$207$		0			0
$208$	8.66782	+	14.9589i	0.601005	+	1.03722i
$209$	−20.8134			−1.43969
$210$		0			0
$211$	3.44245	+	5.96249i	0.236988	+	0.410475i	0.959849	−	0.280519i	$-0.0905065\pi$
$211$	3.44245	+	5.96249i	0.236988	+	0.410475i	−0.722861	+	0.690994i	$0.757173\pi$
$212$	−7.52585	−	13.0351i	−0.516877	−	0.895257i
$213$		0			0
$214$	−9.07367			−0.620263
$215$	3.53700	+	6.12626i	0.241221	+	0.417807i
$216$		0			0
$217$	1.15732	+	3.40027i	0.0785641	+	0.230826i
$218$	12.7990	+	22.1686i	0.866859	+	1.50144i
$219$		0			0
$220$	−11.0367	−	19.1161i	−0.744095	−	1.28881i
$221$	−1.51002	−	2.60600i	−0.101575	−	0.175298i
$222$		0			0
$223$	7.93461	+	13.7432i	0.531341	+	0.920309i	0.999331	+	0.0365756i	$0.0116450\pi$
$223$	7.93461	+	13.7432i	0.531341	+	0.920309i	−0.467990	+	0.883734i	$0.655022\pi$
$224$	−17.8457	−	3.53465i	−1.19237	−	0.236169i
$225$		0			0
$226$	−2.17520	+	3.76755i	−0.144692	+	0.250614i
$227$	7.43520			0.493491			0.246746	−	0.969080i	$-0.420639\pi$
$227$	7.43520			0.493491			0.246746	+	0.969080i	$0.420639\pi$
$228$		0			0
$229$	11.2759	−	19.5304i	0.745130	−	1.29060i	−0.205005	−	0.978761i	$-0.565721\pi$
$229$	11.2759	−	19.5304i	0.745130	−	1.29060i	0.950134	−	0.311841i	$-0.100946\pi$
$230$	−10.8196	+	18.7402i	−0.713426	+	1.23569i
$231$		0			0
$232$	−2.24622	−	3.89056i	−0.147471	−	0.255428i
$233$	4.96401	−	8.59792i	0.325203	−	0.563269i	−0.656350	−	0.754456i	$-0.727901\pi$
$233$	4.96401	−	8.59792i	0.325203	−	0.563269i	0.981553	+	0.191188i	$0.0612339\pi$
$234$		0			0
$235$	−0.0472189	−	0.0817856i	−0.00308022	−	0.00533510i
$236$	−2.53317			−0.164895
$237$		0			0
$238$	4.02847	+	0.797907i	0.261127	+	0.0517206i
$239$	−17.2944			−1.11868			−0.559340	−	0.828938i	$-0.688946\pi$
$239$	−17.2944			−1.11868			−0.559340	+	0.828938i	$0.688946\pi$
$240$		0			0
$241$	−22.2104			−1.43070			−0.715350	−	0.698766i	$-0.753733\pi$
$241$	−22.2104			−1.43070			−0.715350	+	0.698766i	$0.753733\pi$
$242$	16.4909	+	28.5630i	1.06007	+	1.83610i
$243$		0			0
$244$	−4.41735	−	7.65108i	−0.282792	−	0.489810i
$245$	−15.7177	+	12.1013i	−1.00417	+	0.773124i
$246$		0			0
$247$	6.97889	−	12.1316i	0.444056	−	0.771918i
$248$	−0.690274	−	1.19559i	−0.0438324	−	0.0759200i
$249$		0			0
$250$	10.3712			0.655932
$251$	6.49243	−	11.2452i	0.409799	−	0.709792i	−0.585068	−	0.810984i	$-0.698932\pi$
$251$	6.49243	−	11.2452i	0.409799	−	0.709792i	0.994867	+	0.101192i	$0.0322656\pi$
$252$		0			0
$253$	11.0174	−	19.0827i	0.692660	−	1.19972i
$254$	−14.7083	−	25.4755i	−0.922881	−	1.59848i
$255$		0			0
$256$	20.9242			1.30776
$257$	−29.1115			−1.81593			−0.907963	−	0.419050i	$-0.862363\pi$
$257$	−29.1115			−1.81593			−0.907963	+	0.419050i	$0.862363\pi$
$258$		0			0
$259$	−23.5557	−	4.66562i	−1.46368	−	0.289907i
$260$	14.8431	−	0.0232503i	0.920528	−	0.00144193i
$261$		0			0
$262$	−19.9130	+	34.4903i	−1.23023	+	2.13082i
$263$	−7.36122	+	12.7500i	−0.453912	+	0.786199i	−0.998625	−	0.0524239i	$-0.983305\pi$
$263$	−7.36122	+	12.7500i	−0.453912	+	0.786199i	0.544713	+	0.838623i	$0.316639\pi$
$264$		0			0
$265$	29.3609			1.80363
$266$	6.14884	+	18.0656i	0.377010	+	1.10767i
$267$		0			0
$268$	−2.05171	+	3.55366i	−0.125328	+	0.217074i
$269$	30.8241			1.87938			0.939689	−	0.342031i	$-0.111115\pi$
$269$	30.8241			1.87938			0.939689	+	0.342031i	$0.111115\pi$
$270$		0			0
$271$	−14.7499			−0.895990			−0.447995	−	0.894036i	$-0.647862\pi$
$271$	−14.7499			−0.895990			−0.447995	+	0.894036i	$0.647862\pi$
$272$	−4.00551			−0.242870
$273$		0			0
$274$	39.5651			2.39021
$275$	16.2486			0.979828
$276$		0			0
$277$	29.9594			1.80008			0.900042	−	0.435804i	$-0.143536\pi$
$277$	29.9594			1.80008			0.900042	+	0.435804i	$0.143536\pi$
$278$	17.6089	−	30.4994i	1.05611	−	1.82923i
$279$		0			0
$280$	5.02241	−	5.73636i	0.300146	−	0.342813i
$281$	−11.9170			−0.710909			−0.355455	−	0.934694i	$-0.615674\pi$
$281$	−11.9170			−0.710909			−0.355455	+	0.934694i	$0.615674\pi$
$282$		0			0
$283$	11.2509	−	19.4871i	0.668795	−	1.15839i	−0.309446	−	0.950917i	$-0.600144\pi$
$283$	11.2509	−	19.4871i	0.668795	−	1.15839i	0.978241	−	0.207470i	$-0.0665231\pi$
$284$	10.5610	−	18.2922i	0.626679	−	1.08544i
$285$		0			0
$286$	−35.9227	+	0.0562697i	−2.12416	+	0.00332730i
$287$	−2.70753	−	7.95487i	−0.159820	−	0.469561i
$288$		0			0
$289$	−16.3022			−0.958953
$290$	−23.2620			−1.36599
$291$		0			0
$292$	−3.13943	−	5.43766i	−0.183721	−	0.318215i
$293$	−5.53051	+	9.57913i	−0.323096	+	0.559619i	−0.981125	−	0.193374i	$-0.938057\pi$
$293$	−5.53051	+	9.57913i	−0.323096	+	0.559619i	0.658029	+	0.752992i	$0.271390\pi$
$294$		0			0
$295$	2.47069	−	4.27936i	0.143849	−	0.249154i
$296$	9.22970			0.536466
$297$		0			0
$298$	−13.2062	−	22.8738i	−0.765014	−	1.32504i
$299$	7.42867	+	12.8204i	0.429611	+	0.741424i
$300$		0			0
$301$	−4.35066	+	4.96912i	−0.250768	+	0.286416i
$302$	−5.23970	−	9.07542i	−0.301511	−	0.522232i
$303$		0			0
$304$	−9.30651	−	16.1194i	−0.533765	−	0.924508i
$305$	17.2336			0.986793
$306$		0			0
$307$	−2.41729			−0.137962			−0.0689809	−	0.997618i	$-0.521975\pi$
$307$	−2.41729			−0.137962			−0.0689809	+	0.997618i	$0.521975\pi$
$308$	13.5756	−	15.5055i	0.773544	−	0.883507i
$309$		0			0
$310$	−7.14853			−0.406009
$311$	−2.04788	−	3.54704i	−0.116125	−	0.201134i	0.802104	−	0.597184i	$-0.203714\pi$
$311$	−2.04788	−	3.54704i	−0.116125	−	0.201134i	−0.918229	+	0.396050i	$0.870381\pi$
$312$		0			0
$313$	5.12773	−	8.88148i	0.289836	−	0.502011i	−0.683934	−	0.729544i	$-0.739732\pi$
$313$	5.12773	−	8.88148i	0.289836	−	0.502011i	0.973770	+	0.227533i	$0.0730658\pi$
$314$	4.60496	+	7.97603i	0.259873	+	0.450113i
$315$		0			0
$316$	−4.30561	+	7.45754i	−0.242210	+	0.419519i
$317$	1.79798	−	3.11420i	0.100985	−	0.174911i	−0.811106	−	0.584899i	$-0.801134\pi$
$317$	1.79798	−	3.11420i	0.100985	−	0.174911i	0.912091	+	0.409989i	$0.134467\pi$
$318$		0			0
$319$	23.6872			1.32623
$320$	4.51526	−	7.82066i	0.252411	−	0.437188i
$321$		0			0
$322$	−19.8183	−	3.92536i	−1.10443	−	0.218752i
$323$	1.62129	+	2.80816i	0.0902110	+	0.156250i
$324$		0			0
$325$	−5.44829	+	9.47095i	−0.302217	+	0.525354i
$326$	−19.1978	−	33.2516i	−1.06327	−	1.84163i
$327$		0			0
$328$	1.61488	+	2.79706i	0.0891669	+	0.154442i
$329$	0.0580814	−	0.0663379i	0.00320213	−	0.00365732i
$330$		0			0
$331$	−5.10390	−	8.84022i	−0.280536	−	0.485902i	0.690981	−	0.722873i	$-0.257179\pi$
$331$	−5.10390	−	8.84022i	−0.280536	−	0.485902i	−0.971517	+	0.236971i	$0.923846\pi$
$332$	5.45903			0.299603
$333$		0			0
$334$	7.73588	+	13.3989i	0.423289	+	0.733158i
$335$	−4.00221	−	6.93203i	−0.218664	−	0.378737i
$336$		0			0
$337$	6.30217			0.343301			0.171650	−	0.985158i	$-0.445090\pi$
$337$	6.30217			0.343301			0.171650	+	0.985158i	$0.445090\pi$
$338$	12.0124	−	20.9574i	0.653388	−	1.13993i
$339$		0			0
$340$	−1.71944	+	2.97817i	−0.0932500	+	0.161514i
$341$	7.27921			0.394191
$342$		0			0
$343$	−15.4241	−	10.2517i	−0.832822	−	0.553540i
$344$	1.26926	−	2.19842i	0.0684339	−	0.118531i
$345$		0			0
$346$	−6.91620	−	11.9792i	−0.371817	−	0.644006i
$347$	−10.4379			−0.560338			−0.280169	−	0.959951i	$-0.590390\pi$
$347$	−10.4379			−0.560338			−0.280169	+	0.959951i	$0.590390\pi$
$348$		0			0
$349$	−3.99640	−	6.92197i	−0.213923	−	0.370525i	0.739016	−	0.673688i	$-0.235291\pi$
$349$	−3.99640	−	6.92197i	−0.213923	−	0.370525i	−0.952939	+	0.303163i	$0.901957\pi$
$350$	−4.80029	−	14.1035i	−0.256586	−	0.753864i
$351$		0			0
$352$	−18.4344	+	31.9292i	−0.982554	+	1.70183i
$353$	8.07999	−	13.9950i	0.430055	−	0.744877i	−0.566823	−	0.823840i	$-0.691828\pi$
$353$	8.07999	−	13.9950i	0.430055	−	0.744877i	0.996878	+	0.0789632i	$0.0251609\pi$
$354$		0			0
$355$	20.6010	+	35.6820i	1.09339	+	1.89380i
$356$	−17.8845			−0.947876
$357$		0			0
$358$	3.87530	−	6.71222i	0.204816	−	0.354752i
$359$	−15.1209	+	26.1901i	−0.798048	+	1.38226i	0.122837	+	0.992427i	$0.460801\pi$
$359$	−15.1209	+	26.1901i	−0.798048	+	1.38226i	−0.920885	+	0.389833i	$0.872533\pi$
$360$		0			0
$361$	1.96610	−	3.40538i	0.103479	−	0.179230i
$362$	17.9714			0.944556
$363$		0			0
$364$	4.48577	+	13.1121i	0.235118	+	0.687258i
$365$	12.2480			0.641090
$366$		0			0
$367$	16.9861	−	29.4208i	0.886667	−	1.53575i	0.0428762	−	0.999080i	$-0.486348\pi$
$367$	16.9861	−	29.4208i	0.886667	−	1.53575i	0.843791	−	0.536672i	$-0.180319\pi$
$368$	19.7054			1.02721
$369$		0			0
$370$	23.8959	−	41.3889i	1.24229	−	2.15170i
$371$	8.83259	+	25.9506i	0.458565	+	1.34729i
$372$		0			0
$373$	−9.00874	−	15.6036i	−0.466455	−	0.807923i	0.532811	−	0.846234i	$-0.321136\pi$
$373$	−9.00874	−	15.6036i	−0.466455	−	0.807923i	−0.999266	+	0.0383108i	$0.987802\pi$
$374$	4.16135	−	7.20766i	0.215178	−	0.372699i
$375$		0			0
$376$	−0.0169446	+	0.0293490i	−0.000873853	+	0.00151356i
$377$	−7.94252	+	13.8067i	−0.409061	+	0.711084i
$378$		0			0
$379$	4.46667	+	7.73650i	0.229437	+	0.397397i	0.957642	−	0.287963i	$-0.0929780\pi$
$379$	4.46667	+	7.73650i	0.229437	+	0.397397i	−0.728204	+	0.685360i	$0.759645\pi$
$380$	−15.9800			−0.819759
$381$		0			0
$382$	−10.6885	−	18.5131i	−0.546874	−	0.947213i
$383$	−2.78825	−	4.82938i	−0.142473	−	0.246770i	0.785954	−	0.618284i	$-0.212172\pi$
$383$	−2.78825	−	4.82938i	−0.142473	−	0.246770i	−0.928427	+	0.371514i	$0.878839\pi$
$384$		0			0
$385$	12.9531	+	38.0568i	0.660149	+	1.93955i
$386$	10.1140	−	17.5179i	0.514787	−	0.891638i
$387$		0			0
$388$	12.4474	−	21.5595i	0.631921	−	1.09452i
$389$	−10.2140	−	17.6912i	−0.517871	−	0.896979i	−0.999784	−	0.0207599i	$-0.993391\pi$
$389$	−10.2140	−	17.6912i	−0.517871	−	0.896979i	0.481914	−	0.876219i	$-0.339942\pi$
$390$		0			0
$391$	−3.43288			−0.173608
$392$	6.58097	+	2.71340i	0.332389	+	0.137047i
$393$		0			0
$394$	−7.23686	−	12.5346i	−0.364588	−	0.631484i
$395$	−8.39884	−	14.5472i	−0.422591	−	0.731950i
$396$		0			0
$397$	−14.7254	−	25.5052i	−0.739047	−	1.28007i	−0.952925	−	0.303207i	$-0.901943\pi$
$397$	−14.7254	−	25.5052i	−0.739047	−	1.28007i	0.213878	−	0.976860i	$-0.431391\pi$
$398$	42.8011			2.14542
$399$		0			0
$400$	7.26543	+	12.5841i	0.363271	+	0.629204i
$401$	3.00650			0.150137			0.0750687	−	0.997178i	$-0.476082\pi$
$401$	3.00650			0.150137			0.0750687	+	0.997178i	$0.476082\pi$
$402$		0			0
$403$	−2.44078	+	4.24289i	−0.121584	+	0.211353i
$404$	3.53775	−	6.12756i	0.176010	−	0.304857i
$405$		0			0
$406$	−6.99786	−	20.5601i	−0.347298	−	1.02038i
$407$	−24.3327	+	42.1455i	−1.20613	+	2.08907i
$408$		0			0
$409$	33.1353			1.63843			0.819217	−	0.573484i	$-0.194409\pi$
$409$	33.1353			1.63843			0.819217	+	0.573484i	$0.194409\pi$
$410$	16.7238			0.825931
$411$		0			0
$412$	12.7474	−	22.0792i	0.628021	−	1.08776i
$413$	4.52556	+	0.896365i	0.222688	+	0.0441072i
$414$		0			0
$415$	−5.32439	+	9.22211i	−0.261364	+	0.452695i
$416$	−12.4296	−	21.4511i	−0.609413	−	1.05173i
$417$		0			0
$418$	38.6744			1.89163
$419$	−15.7760	−	27.3249i	−0.770709	−	1.33491i	−0.937175	−	0.348860i	$-0.886569\pi$
$419$	−15.7760	−	27.3249i	−0.770709	−	1.33491i	0.166465	−	0.986047i	$-0.446765\pi$
$420$		0			0
$421$	−4.20950			−0.205158			−0.102579	−	0.994725i	$-0.532709\pi$
$421$	−4.20950			−0.205158			−0.102579	+	0.994725i	$0.532709\pi$
$422$	−6.39659	−	11.0792i	−0.311381	−	0.539328i
$423$		0			0
$424$	−5.26812	−	9.12465i	−0.255842	−	0.443132i
$425$	−1.26571	−	2.19228i	−0.0613960	−	0.106341i
$426$		0			0
$427$	5.18436	+	15.2319i	0.250889	+	0.737124i
$428$	7.09392			0.342897
$429$		0			0
$430$	−6.57227	−	11.3835i	−0.316943	−	0.548962i
$431$	−5.92949	+	10.2702i	−0.285614	+	0.494697i	−0.972758	−	0.231824i	$-0.925531\pi$
$431$	−5.92949	+	10.2702i	−0.285614	+	0.494697i	0.687144	+	0.726521i	$0.258864\pi$
$432$		0			0
$433$	−14.0219	+	24.2867i	−0.673851	+	1.16714i	0.302953	+	0.953006i	$0.402028\pi$
$433$	−14.0219	+	24.2867i	−0.673851	+	1.16714i	−0.976803	+	0.214138i	$0.931306\pi$
$434$	−2.15048	−	6.31822i	−0.103226	−	0.303285i
$435$		0			0
$436$	−10.0064	−	17.3317i	−0.479222	−	0.830037i
$437$	−7.97606	−	13.8149i	−0.381547	−	0.660858i
$438$		0			0
$439$	−15.7994			−0.754065			−0.377033	−	0.926200i	$-0.623056\pi$
$439$	−15.7994			−0.754065			−0.377033	+	0.926200i	$0.623056\pi$
$440$	−7.72574	−	13.3814i	−0.368310	−	0.637932i
$441$		0			0
$442$	2.80585	+	4.84234i	0.133461	+	0.230327i
$443$	16.5707	−	28.7013i	0.787299	−	1.36364i	−0.140317	−	0.990107i	$-0.544812\pi$
$443$	16.5707	−	28.7013i	0.787299	−	1.36364i	0.927616	−	0.373535i	$-0.121855\pi$
$444$		0			0
$445$	17.4434	−	30.2128i	0.826896	−	1.43223i
$446$	−14.7437	−	25.5369i	−0.698135	−	1.20921i
$447$		0			0
$448$	8.27060	+	1.63814i	0.390749	+	0.0773946i
$449$	−4.75675	+	8.23894i	−0.224485	+	0.388819i	−0.956165	−	0.292829i	$-0.905403\pi$
$449$	−4.75675	+	8.23894i	−0.224485	+	0.388819i	0.731680	+	0.681648i	$0.238737\pi$
$450$		0			0
$451$	−17.0296			−0.801890
$452$	1.70060	−	2.94552i	0.0799893	−	0.138546i
$453$		0			0
$454$	−13.8157			−0.648404
$455$	−26.5257	−	5.21071i	−1.24355	−	0.244282i
$456$		0			0
$457$	−17.2764			−0.808157			−0.404078	−	0.914724i	$-0.632408\pi$
$457$	−17.2764			−0.808157			−0.404078	+	0.914724i	$0.632408\pi$
$458$	−20.9523	+	36.2904i	−0.979034	+	1.69574i
$459$		0			0
$460$	8.45894	−	14.6513i	0.394400	−	0.683121i
$461$	17.2623	−	29.8992i	0.803986	−	1.39254i	−0.112988	−	0.993596i	$-0.536042\pi$
$461$	17.2623	−	29.8992i	0.803986	−	1.39254i	0.916974	−	0.398948i	$-0.130625\pi$
$462$		0			0
$463$	−36.7039			−1.70578			−0.852888	−	0.522094i	$-0.825151\pi$
$463$	−36.7039			−1.70578			−0.852888	+	0.522094i	$0.825151\pi$
$464$	10.5915	+	18.3451i	0.491700	+	0.851649i
$465$		0			0
$466$	−9.22389	+	15.9762i	−0.427288	+	0.740085i
$467$	13.3190	−	23.0692i	0.616330	−	1.06751i	−0.373820	−	0.927501i	$-0.621952\pi$
$467$	13.3190	−	23.0692i	0.616330	−	1.06751i	0.990150	−	0.140013i	$-0.0447145\pi$
$468$		0			0
$469$	4.92289	−	5.62270i	0.227318	−	0.259632i
$470$	0.0877399	+	0.151970i	0.00404714	+	0.00700985i
$471$		0			0
$472$	−1.77322			−0.0816193
$473$	6.69242	+	11.5916i	0.307718	+	0.532983i
$474$		0			0
$475$	5.88158	−	10.1872i	0.269865	−	0.467421i
$476$	−3.14951	−	0.623814i	−0.144357	−	0.0285925i
$477$		0			0
$478$	32.1356			1.46985
$479$	0.626483	−	1.08510i	0.0286247	−	0.0495795i	−0.851358	−	0.524585i	$-0.824221\pi$
$479$	0.626483	−	1.08510i	0.0286247	−	0.0495795i	0.879983	+	0.475005i	$0.157554\pi$
$480$		0			0
$481$	−16.4067	−	28.3147i	−0.748081	−	1.29104i
$482$	41.2704			1.87981
$483$		0			0
$484$	−12.8928	−	22.3310i	−0.586036	−	1.01504i
$485$	24.2808	+	42.0556i	1.10253	+	1.90965i
$486$		0			0
$487$	7.63257			0.345865			0.172932	−	0.984934i	$-0.444676\pi$
$487$	7.63257			0.345865			0.172932	+	0.984934i	$0.444676\pi$
$488$	−3.09216	−	5.35578i	−0.139976	−	0.242445i
$489$		0			0
$490$	29.2060	−	22.4861i	1.31939	−	1.01582i
$491$	−1.12442	−	1.94755i	−0.0507442	−	0.0878915i	0.839538	−	0.543302i	$-0.182826\pi$
$491$	−1.12442	−	1.94755i	−0.0507442	−	0.0878915i	−0.890282	+	0.455410i	$0.849493\pi$
$492$		0			0
$493$	−1.84515	−	3.19590i	−0.0831015	−	0.143936i
$494$	−12.9678	+	22.5424i	−0.583450	+	1.01423i
$495$		0			0
$496$	3.25484	+	5.63754i	0.146146	+	0.253133i
$497$	−25.3402	+	28.9423i	−1.13666	+	1.29824i
$498$		0			0
$499$	−17.2321	+	29.8469i	−0.771417	+	1.33613i	0.165370	+	0.986232i	$0.447118\pi$
$499$	−17.2321	+	29.8469i	−0.771417	+	1.33613i	−0.936787	+	0.349901i	$0.886215\pi$
$500$	−8.10834			−0.362616
$501$		0			0
$502$	−12.0639	+	20.8953i	−0.538439	+	0.932604i
$503$	−2.65078	+	4.59128i	−0.118192	+	0.204715i	−0.919051	−	0.394138i	$-0.871043\pi$
$503$	−2.65078	+	4.59128i	−0.118192	+	0.204715i	0.800859	+	0.598853i	$0.204377\pi$
$504$		0			0
$505$	6.90098	+	11.9529i	0.307090	+	0.531895i
$506$	−20.4721	+	35.4586i	−0.910094	+	1.57633i
$507$		0			0
$508$	11.4991	+	19.9171i	0.510192	+	0.883679i
$509$	−17.1384			−0.759646			−0.379823	−	0.925059i	$-0.624015\pi$
$509$	−17.1384			−0.759646			−0.379823	+	0.925059i	$0.624015\pi$
$510$		0			0
$511$	3.68455	+	10.8254i	0.162995	+	0.478887i
$512$	−23.2188			−1.02613
$513$		0			0
$514$	54.0936			2.38597
$515$	24.8660	+	43.0692i	1.09573	+	1.89786i
$516$		0			0
$517$	−0.0893439	−	0.154748i	−0.00392934	−	0.00680581i
$518$	43.7701	+	8.66942i	1.92315	+	0.380913i
$519$		0			0
$520$	10.3902	−	0.0162753i	0.455641	−	0.000713720i
$521$	−9.32232	−	16.1467i	−0.408418	−	0.707401i	0.586295	−	0.810098i	$-0.300586\pi$
$521$	−9.32232	−	16.1467i	−0.408418	−	0.707401i	−0.994713	+	0.102697i	$0.967253\pi$
$522$		0			0
$523$	−31.4131			−1.37360			−0.686800	−	0.726847i	$-0.740985\pi$
$523$	−31.4131			−1.37360			−0.686800	+	0.726847i	$0.740985\pi$
$524$	15.5682	−	26.9649i	0.680101	−	1.17797i
$525$		0			0
$526$	13.6783	−	23.6914i	0.596400	−	1.03300i
$527$	−0.567025	−	0.982117i	−0.0247000	−	0.0427817i
$528$		0			0
$529$	−6.11168			−0.265725
$530$	−54.5570			−2.36981
$531$		0			0
$532$	−4.80725	−	14.1240i	−0.208421	−	0.612351i
$533$	5.71015	−	9.92614i	0.247334	−	0.429949i
$534$		0			0
$535$	−6.91895	+	11.9840i	−0.299132	+	0.518112i
$536$	−1.43620	+	2.48758i	−0.0620345	+	0.107447i
$537$		0			0
$538$	−57.2758			−2.46934
$539$	−29.7399	+	22.8971i	−1.28099	+	0.986249i
$540$		0			0
$541$	−13.1855	+	22.8379i	−0.566887	+	0.981878i	0.429984	+	0.902836i	$0.358519\pi$
$541$	−13.1855	+	22.8379i	−0.566887	+	0.981878i	−0.996871	+	0.0790411i	$0.974814\pi$
$542$	27.4075			1.17725
$543$		0			0
$544$	5.74389			0.246267
$545$	39.0386			1.67223
$546$		0			0
$547$	10.0353			0.429077			0.214539	−	0.976715i	$-0.431175\pi$
$547$	10.0353			0.429077			0.214539	+	0.976715i	$0.431175\pi$
$548$	−30.9325			−1.32137
$549$		0			0
$550$	−30.1924			−1.28741
$551$	8.57417	−	14.8509i	0.365272	−	0.632669i
$552$		0			0
$553$	10.3309	−	11.7995i	0.439316	−	0.501767i
$554$	−55.6690			−2.36515
$555$		0			0
$556$	−13.7668	+	23.8449i	−0.583844	+	1.01125i
$557$	18.6341	−	32.2753i	0.789553	−	1.36755i	−0.136687	−	0.990614i	$-0.543646\pi$
$557$	18.6341	−	32.2753i	0.789553	−	1.36755i	0.926241	−	0.376932i	$-0.123021\pi$
$558$		0			0
$559$	−9.00051	+	0.0140985i	−0.380681	+	0.000596303i
$560$	−23.6821	+	27.0486i	−1.00075	+	1.14301i
$561$		0			0
$562$	22.1436			0.934072
$563$	−29.5262			−1.24438			−0.622191	−	0.782866i	$-0.713757\pi$
$563$	−29.5262			−1.24438			−0.622191	+	0.782866i	$0.713757\pi$
$564$		0			0
$565$	3.31731	+	5.74574i	0.139560	+	0.241725i
$566$	−20.9058	+	36.2100i	−0.878738	+	1.52202i
$567$		0			0
$568$	7.39272	−	12.8046i	0.310192	−	0.537268i
$569$	−35.0103			−1.46771			−0.733854	−	0.679307i	$-0.762280\pi$
$569$	−35.0103			−1.46771			−0.733854	+	0.679307i	$0.762280\pi$
$570$		0			0
$571$	−13.5415	−	23.4546i	−0.566696	−	0.981546i	−0.996890	−	0.0788096i	$-0.974888\pi$
$571$	−13.5415	−	23.4546i	−0.566696	−	0.981546i	0.430194	−	0.902737i	$-0.358445\pi$
$572$	28.0849	−	0.0439924i	1.17429	−	0.00183942i
$573$		0			0
$574$	5.03100	+	14.7814i	0.209990	+	0.616962i
$575$	6.22676	+	10.7851i	0.259674	+	0.449768i
$576$		0			0
$577$	2.11708	+	3.66689i	0.0881353	+	0.152655i	0.906723	−	0.421727i	$-0.138576\pi$
$577$	2.11708	+	3.66689i	0.0881353	+	0.152655i	−0.818588	+	0.574382i	$0.805243\pi$
$578$	30.2920			1.25998
$579$		0			0
$580$	18.1865			0.755154
$581$	−9.75269	−	1.93169i	−0.404610	−	0.0801399i
$582$		0			0
$583$	55.5543			2.30083
$584$	−2.19761	−	3.80638i	−0.0909379	−	0.157509i
$585$		0			0
$586$	10.2765	−	17.7995i	0.424520	−	0.735289i
$587$	−10.7462	−	18.6130i	−0.443544	−	0.768241i	0.554405	−	0.832247i	$-0.312946\pi$
$587$	−10.7462	−	18.6130i	−0.443544	−	0.768241i	−0.997950	+	0.0640058i	$0.979612\pi$
$588$		0			0
$589$	2.63489	−	4.56376i	0.108569	−	0.188046i
$590$	−4.59091	+	7.95169i	−0.189005	+	0.327366i
$591$		0			0
$592$	−43.5206			−1.78869
$593$	2.36578	−	4.09766i	0.0971511	−	0.168271i	−0.813353	−	0.581770i	$-0.802360\pi$
$593$	2.36578	−	4.09766i	0.0971511	−	0.168271i	0.910504	+	0.413500i	$0.135694\pi$
$594$		0			0
$595$	4.12566	−	4.71213i	0.169135	−	0.193179i
$596$	10.3248	+	17.8830i	0.422919	+	0.732518i
$597$		0			0
$598$	−13.8036	−	23.8223i	−0.564471	−	0.974165i
$599$	21.1050	+	36.5549i	0.862326	+	1.49359i	0.869678	+	0.493619i	$0.164326\pi$
$599$	21.1050	+	36.5549i	0.862326	+	1.49359i	−0.00735218	+	0.999973i	$0.502340\pi$
$600$		0			0
$601$	19.6243	+	33.9903i	0.800493	+	1.38649i	0.919292	+	0.393576i	$0.128762\pi$
$601$	19.6243	+	33.9903i	0.800493	+	1.38649i	−0.118800	+	0.992918i	$0.537905\pi$
$602$	8.08419	−	9.23339i	0.329487	−	0.376325i
$603$		0			0
$604$	4.09647	+	7.09529i	0.166683	+	0.288703i
$605$	50.2992			2.04495
$606$		0			0
$607$	−8.70003	−	15.0689i	−0.353123	−	0.611628i	0.633672	−	0.773602i	$-0.281547\pi$
$607$	−8.70003	−	15.0689i	−0.353123	−	0.611628i	−0.986795	+	0.161975i	$0.948214\pi$
$608$	13.3455	+	23.1151i	0.541233	+	0.937443i
$609$		0			0
$610$	−32.0227			−1.29656
$611$	0.120157		0.000188215i	0.00486103		7.61437e-6i
$612$		0			0
$613$	0.595546	−	1.03152i	0.0240539	−	0.0416625i	−0.853748	−	0.520687i	$-0.825676\pi$
$613$	0.595546	−	1.03152i	0.0240539	−	0.0416625i	0.877802	+	0.479024i	$0.159009\pi$
$614$	4.49168			0.181270
$615$		0			0
$616$	9.50300	−	10.8539i	0.382887	−	0.437316i
$617$	5.79049	−	10.0294i	0.233116	−	0.403769i	−0.725607	−	0.688109i	$-0.758441\pi$
$617$	5.79049	−	10.0294i	0.233116	−	0.403769i	0.958724	+	0.284340i	$0.0917744\pi$
$618$		0			0
$619$	17.5041	+	30.3179i	0.703547	+	1.21858i	0.967213	+	0.253966i	$0.0817350\pi$
$619$	17.5041	+	30.3179i	0.703547	+	1.21858i	−0.263666	+	0.964614i	$0.584932\pi$
$620$	5.58881			0.224452
$621$		0			0
$622$	3.80528	+	6.59094i	0.152578	+	0.264272i
$623$	31.9511	+	6.32846i	1.28009	+	0.253544i
$624$		0			0
$625$	15.4843	−	26.8197i	0.619374	−	1.07279i
$626$	−9.52810	+	16.5031i	−0.380819	+	0.659598i
$627$		0			0
$628$	−3.60022	−	6.23577i	−0.143664	−	0.248834i
$629$	7.58174			0.302304
$630$		0			0
$631$	0.511253	−	0.885516i	0.0203527	−	0.0352518i	−0.855670	−	0.517522i	$-0.826854\pi$
$631$	0.511253	−	0.885516i	0.0203527	−	0.0352518i	0.876022	+	0.482271i	$0.160188\pi$
$632$	−3.01394	+	5.22030i	−0.119888	+	0.207653i
$633$		0			0
$634$	−3.34093	+	5.78666i	−0.132685	+	0.229818i
$635$	−44.8621			−1.78030
$636$		0			0
$637$	−3.37420	−	25.0123i	−0.133691	−	0.991023i
$638$	−44.0144			−1.74255
$639$		0			0
$640$	11.0954	−	19.2177i	0.438583	−	0.759647i
$641$	44.3676			1.75242			0.876208	−	0.481933i	$-0.160065\pi$
$641$	44.3676			1.75242			0.876208	+	0.481933i	$0.160065\pi$
$642$		0			0
$643$	4.17452	−	7.23048i	0.164627	−	0.285142i	−0.771896	−	0.635749i	$-0.780691\pi$
$643$	4.17452	−	7.23048i	0.164627	−	0.285142i	0.936523	+	0.350607i	$0.114025\pi$
$644$	15.4942	+	3.06890i	0.610559	+	0.120932i
$645$		0			0
$646$	−3.01260	−	5.21798i	−0.118529	−	0.205299i
$647$	13.2862	−	23.0124i	0.522334	−	0.904709i	−0.477328	−	0.878725i	$-0.658395\pi$
$647$	13.2862	−	23.0124i	0.522334	−	0.904709i	0.999662	−	0.0259840i	$-0.00827191\pi$
$648$		0			0
$649$	4.67484	−	8.09705i	0.183503	−	0.317837i
$650$	10.1238	−	17.5985i	0.397086	−	0.690268i
$651$		0			0
$652$	15.0091	+	25.9965i	0.587802	+	1.01810i
$653$	41.6970			1.63173			0.815864	−	0.578243i	$-0.196262\pi$
$653$	41.6970			1.63173			0.815864	+	0.578243i	$0.196262\pi$
$654$		0			0
$655$	30.3685	+	52.5998i	1.18659	+	2.05524i
$656$	−7.61462	−	13.1889i	−0.297301	−	0.514940i
$657$		0			0
$658$	−0.107924	+	0.123266i	−0.00420732	+	0.00480540i
$659$	−12.7312	+	22.0510i	−0.495936	+	0.858986i	−0.999989	−	0.00468666i	$-0.998508\pi$
$659$	−12.7312	+	22.0510i	−0.495936	+	0.858986i	0.504053	+	0.863673i	$0.331842\pi$
$660$		0			0
$661$	−13.2426	+	22.9368i	−0.515076	+	0.892137i	0.484771	+	0.874641i	$0.338903\pi$
$661$	−13.2426	+	22.9368i	−0.515076	+	0.892137i	−0.999847	+	0.0174961i	$0.994431\pi$
$662$	9.48383	+	16.4265i	0.368599	+	0.638433i
$663$		0			0
$664$	3.82134			0.148297
$665$	28.5487	+	5.65456i	1.10707	+	0.219275i
$666$		0			0
$667$	9.07737	+	15.7225i	0.351477	+	0.608777i
$668$	−6.04802	−	10.4755i	−0.234005	−	0.405308i
$669$		0			0
$670$	7.43671	+	12.8808i	0.287305	+	0.497627i
$671$	32.6080			1.25882
$672$		0			0
$673$	−6.25914	−	10.8411i	−0.241272	−	0.417895i	0.719805	−	0.694176i	$-0.244231\pi$
$673$	−6.25914	−	10.8411i	−0.241272	−	0.417895i	−0.961077	+	0.276281i	$0.910898\pi$
$674$	−11.7104			−0.451067
$675$		0			0
$676$	−9.39145	+	16.3848i	−0.361209	+	0.630184i
$677$	−0.555472	+	0.962106i	−0.0213485	+	0.0369767i	−0.876502	−	0.481398i	$-0.840129\pi$
$677$	−0.555472	+	0.962106i	−0.0213485	+	0.0369767i	0.855154	+	0.518374i	$0.173463\pi$
$678$		0			0
$679$	−29.8665	+	34.1121i	−1.14617	+	1.30910i
$680$	−1.20362	+	2.08473i	−0.0461566	+	0.0799456i
$681$		0			0
$682$	−13.5259			−0.517932
$683$	−14.3258			−0.548160			−0.274080	−	0.961707i	$-0.588373\pi$
$683$	−14.3258			−0.548160			−0.274080	+	0.961707i	$0.588373\pi$
$684$		0			0
$685$	30.1696	−	52.2552i	1.15272	−	1.99657i
$686$	28.6603	+	19.0492i	1.09426	+	0.727303i
$687$		0			0
$688$	−5.98492	+	10.3662i	−0.228173	+	0.395207i
$689$	−18.6278	+	32.3814i	−0.709664	+	1.23363i
$690$		0			0
$691$	−1.03759			−0.0394718			−0.0197359	−	0.999805i	$-0.506283\pi$
$691$	−1.03759			−0.0394718			−0.0197359	+	0.999805i	$0.506283\pi$
$692$	5.40718	+	9.36551i	0.205550	+	0.356023i
$693$		0			0
$694$	19.3953			0.736235
$695$	−26.8546	−	46.5135i	−1.01865	−	1.76436i
$696$		0			0
$697$	1.32654	+	2.29764i	0.0502464	+	0.0870294i
$698$	7.42592	+	12.8621i	0.281075	+	0.486837i
$699$		0			0
$700$	3.75293	+	11.0263i	0.141847	+	0.416755i
$701$	13.5992			0.513635			0.256818	−	0.966460i	$-0.417326\pi$
$701$	13.5992			0.513635			0.256818	+	0.966460i	$0.417326\pi$
$702$		0			0
$703$	17.6156	+	30.5112i	0.664386	+	1.15075i
$704$	8.54341	−	14.7976i	0.321992	−	0.557706i
$705$		0			0
$706$	−15.0139	+	26.0048i	−0.565054	+	0.978702i
$707$	−8.48852	+	9.69519i	−0.319244	+	0.364625i
$708$		0			0
$709$	−4.16384	−	7.21198i	−0.156376	−	0.270852i	0.777183	−	0.629275i	$-0.216648\pi$
$709$	−4.16384	−	7.21198i	−0.156376	−	0.270852i	−0.933559	+	0.358423i	$0.883315\pi$
$710$	−38.2798	−	66.3025i	−1.43662	−	2.48829i
$711$		0			0
$712$	−12.5192			−0.469177
$713$	2.78952	+	4.83160i	0.104469	+	0.180945i
$714$		0			0
$715$	−27.3179	+	47.4876i	−1.02163	+	1.77593i
$716$	−3.02976	+	5.24770i	−0.113228	+	0.196116i
$717$		0			0
$718$	28.0968	−	48.6652i	1.04856	−	1.81617i
$719$	0.808178	+	1.39981i	0.0301400	+	0.0522039i	0.880702	−	0.473671i	$-0.157071\pi$
$719$	0.808178	+	1.39981i	0.0301400	+	0.0522039i	−0.850562	+	0.525875i	$0.823738\pi$
$720$		0			0
$721$	−30.5863	+	34.9343i	−1.13909	+	1.30102i
$722$	−3.65330	+	6.32771i	−0.135962	+	0.235493i
$723$		0			0
$724$	−14.0503			−0.522175
$725$	−6.69370	+	11.5938i	−0.248598	+	0.430584i
$726$		0			0
$727$	−27.3732			−1.01522			−0.507609	−	0.861588i	$-0.669470\pi$
$727$	−27.3732			−1.01522			−0.507609	+	0.861588i	$0.669470\pi$
$728$	3.14005	+	9.17848i	0.116378	+	0.340177i
$729$		0			0
$730$	−22.7587			−0.842336
$731$	1.04263	−	1.80589i	0.0385632	−	0.0667934i
$732$		0			0
$733$	−7.61372	+	13.1874i	−0.281219	+	0.487086i	−0.971685	−	0.236279i	$-0.924072\pi$
$733$	−7.61372	+	13.1874i	−0.281219	+	0.487086i	0.690466	+	0.723365i	$0.257405\pi$
$734$	−31.5627	+	54.6683i	−1.16500	+	2.01784i
$735$		0			0
$736$	−28.2575			−1.04159
$737$	−7.57266	−	13.1162i	−0.278942	−	0.483142i
$738$		0			0
$739$	1.23392	−	2.13720i	0.0453903	−	0.0786183i	−0.842438	−	0.538794i	$-0.818880\pi$
$739$	1.23392	−	2.13720i	0.0453903	−	0.0786183i	0.887828	+	0.460176i	$0.152214\pi$
$740$	−18.6821	+	32.3584i	−0.686768	+	1.18952i
$741$		0			0
$742$	−16.4123	−	48.2202i	−0.602514	−	1.77022i
$743$	−17.7081	−	30.6713i	−0.649646	−	1.12522i	−0.983207	−	0.182491i	$-0.941584\pi$
$743$	−17.7081	−	30.6713i	−0.649646	−	1.12522i	0.333562	−	0.942728i	$-0.391749\pi$
$744$		0			0
$745$	−40.2805			−1.47576
$746$	16.7396	+	28.9938i	0.612880	+	1.06154i
$747$		0			0
$748$	−3.25340	+	5.63505i	−0.118956	+	0.206038i
$749$	−12.6735	−	2.51019i	−0.463078	−	0.0917205i
$750$		0			0
$751$	6.25786			0.228353			0.114176	−	0.993461i	$-0.463577\pi$
$751$	6.25786			0.228353			0.114176	+	0.993461i	$0.463577\pi$
$752$	0.0798987	−	0.138389i	0.00291361	−	0.00504651i
$753$		0			0
$754$	14.7584	−	25.6550i	0.537469	−	0.934301i
$755$	−15.9817			−0.581634
$756$		0			0
$757$	7.06876	+	12.2435i	0.256918	+	0.444996i	0.965415	−	0.260719i	$-0.0839595\pi$
$757$	7.06876	+	12.2435i	0.256918	+	0.444996i	−0.708496	+	0.705714i	$0.750626\pi$
$758$	−8.29975	−	14.3756i	−0.301461	−	0.522145i
$759$		0			0
$760$	−11.1861			−0.405762
$761$	−9.33281	−	16.1649i	−0.338314	−	0.585977i	0.645802	−	0.763505i	$-0.276523\pi$
$761$	−9.33281	−	16.1649i	−0.338314	−	0.585977i	−0.984116	+	0.177528i	$0.943190\pi$
$762$		0			0
$763$	11.7439	+	34.5042i	0.425158	+	1.24914i
$764$	8.35645	+	14.4738i	0.302326	+	0.523644i
$765$		0			0
$766$	5.18098	+	8.97373i	0.187197	+	0.324234i
$767$	3.15208	+	5.43987i	0.113815	+	0.196422i
$768$		0			0
$769$	−4.51337	−	7.81739i	−0.162756	−	0.281902i	0.773100	−	0.634284i	$-0.218705\pi$
$769$	−4.51337	−	7.81739i	−0.162756	−	0.281902i	−0.935856	+	0.352382i	$0.885372\pi$
$770$	−24.0688	−	70.7153i	−0.867378	−	2.54840i
$771$		0			0
$772$	−7.90723	+	13.6957i	−0.284588	+	0.492920i
$773$	−2.66286			−0.0957765			−0.0478882	−	0.998853i	$-0.515249\pi$
$773$	−2.66286			−0.0957765			−0.0478882	+	0.998853i	$0.515249\pi$
$774$		0			0
$775$	−2.05701	+	3.56284i	−0.0738899	+	0.127981i
$776$	8.71323	−	15.0917i	0.312787	−	0.541762i
$777$		0			0
$778$	18.9792	+	32.8729i	0.680437	+	1.17855i
$779$	−6.16426	+	10.6768i	−0.220858	+	0.382537i
$780$		0			0
$781$	38.9796	+	67.5146i	1.39480	+	2.41586i
$782$	6.37881			0.228106
$783$		0			0
$784$	−31.0311	−	12.7944i	−1.10825	−	0.456944i
$785$	14.0457			0.501313
$786$		0			0
$787$	−15.7793			−0.562470			−0.281235	−	0.959639i	$-0.590744\pi$
$787$	−15.7793			−0.562470			−0.281235	+	0.959639i	$0.590744\pi$
$788$	5.65787	+	9.79972i	0.201553	+	0.349101i
$789$		0			0
$790$	15.6063	+	27.0309i	0.555248	+	0.961717i
$791$	−4.08043	+	4.66048i	−0.145084	+	0.165708i
$792$		0			0
$793$	−10.9337	+	19.0065i	−0.388269	+	0.674941i
$794$	27.3620	+	47.3924i	0.971043	+	1.68189i
$795$		0			0
$796$	−33.4625			−1.18605
$797$	10.5164	−	18.2150i	0.372510	−	0.645207i	−0.617441	−	0.786617i	$-0.711830\pi$
$797$	10.5164	−	18.2150i	0.372510	−	0.645207i	0.989951	+	0.141411i	$0.0451638\pi$
$798$		0			0
$799$	−0.0139192	+	0.0241087i	−0.000492425	+	0.000852905i
$800$	−10.4186	−	18.0456i	−0.368354	−	0.638007i
$801$		0			0
$802$	−5.58653			−0.197267
$803$	23.1747			0.817817
$804$		0			0
$805$	−20.2965	+	23.1817i	−0.715357	+	0.817048i
$806$	4.53534	−	7.88393i	0.159750	−	0.277699i
$807$		0			0
$808$	2.47644	−	4.28931i	0.0871207	−	0.150897i
$809$	15.3266	−	26.5465i	0.538855	−	0.933324i	−0.460111	−	0.887861i	$-0.652190\pi$
$809$	15.3266	−	26.5465i	0.538855	−	0.933324i	0.998966	−	0.0454626i	$-0.0144762\pi$
$810$		0			0
$811$	8.17525			0.287072			0.143536	−	0.989645i	$-0.454153\pi$
$811$	8.17525			0.287072			0.143536	+	0.989645i	$0.454153\pi$
$812$	5.47102	+	16.0742i	0.191995	+	0.564092i
$813$		0			0
$814$	45.2139	−	78.3127i	1.58474	−	2.74486i
$815$	−58.5556			−2.05111
$816$		0			0
$817$	9.68994			0.339008
$818$	−61.5704			−2.15276
$819$		0			0
$820$	−13.0749			−0.456596
$821$	11.9826			0.418195			0.209097	−	0.977895i	$-0.432947\pi$
$821$	11.9826			0.418195			0.209097	+	0.977895i	$0.432947\pi$
$822$		0			0
$823$	24.6941			0.860781			0.430390	−	0.902643i	$-0.358376\pi$
$823$	24.6941			0.860781			0.430390	+	0.902643i	$0.358376\pi$
$824$	8.92324	−	15.4555i	0.310856	−	0.538418i
$825$		0			0
$826$	−8.40918	−	1.66558i	−0.292593	−	0.0579530i
$827$	−18.5259			−0.644210			−0.322105	−	0.946704i	$-0.604390\pi$
$827$	−18.5259			−0.644210			−0.322105	+	0.946704i	$0.604390\pi$
$828$		0			0
$829$	26.0106	−	45.0516i	0.903384	−	1.56471i	0.0803132	−	0.996770i	$-0.474408\pi$
$829$	26.0106	−	45.0516i	0.903384	−	1.56471i	0.823071	−	0.567938i	$-0.192259\pi$
$830$	9.89352	−	17.1361i	0.343409	−	0.594802i
$831$		0			0
$832$	5.76052	+	9.94152i	0.199710	+	0.344660i
$833$	5.40593	+	2.22892i	0.187305	+	0.0772274i
$834$		0			0
$835$	23.5954			0.816552
$836$	−30.2361			−1.04574
$837$		0			0
$838$	29.3143	+	50.7738i	1.01264	+	1.75395i
$839$	17.5146	−	30.3361i	0.604670	−	1.04732i	−0.387433	−	0.921898i	$-0.626638\pi$
$839$	17.5146	−	30.3361i	0.604670	−	1.04732i	0.992104	−	0.125422i	$-0.0400284\pi$
$840$		0			0
$841$	4.74193	−	8.21326i	0.163515	−	0.283216i
$842$	7.82188			0.269560
$843$		0			0
$844$	5.00094	+	8.66188i	0.172139	+	0.298154i
$845$	−18.5195	−	31.8459i	−0.637091	−	1.09553i
$846$		0			0
$847$	15.1314	+	44.4569i	0.519921	+	1.52756i
$848$	24.8407	+	43.0253i	0.853031	+	1.47749i
$849$		0			0
$850$	2.35188	+	4.07358i	0.0806689	+	0.139723i
$851$	−37.2989			−1.27859
$852$		0			0
$853$	33.9514			1.16247			0.581237	−	0.813735i	$-0.302569\pi$
$853$	33.9514			1.16247			0.581237	+	0.813735i	$0.302569\pi$
$854$	−9.63332	−	28.3032i	−0.329645	−	0.968516i
$855$		0			0
$856$	4.96577			0.169726
$857$	−18.8655	−	32.6759i	−0.644432	−	1.11619i	−0.984432	−	0.175764i	$-0.943761\pi$
$857$	−18.8655	−	32.6759i	−0.644432	−	1.11619i	0.340000	−	0.940425i	$-0.389573\pi$
$858$		0			0
$859$	−2.63510	+	4.56413i	−0.0899086	+	0.155726i	−0.907472	−	0.420112i	$-0.861991\pi$
$859$	−2.63510	+	4.56413i	−0.0899086	+	0.155726i	0.817564	+	0.575838i	$0.195324\pi$
$860$	5.13829	+	8.89978i	0.175214	+	0.303480i
$861$		0			0
$862$	11.0179	−	19.0836i	0.375271	−	0.649989i
$863$	14.5016	−	25.1175i	0.493640	−	0.855010i	−0.506333	−	0.862338i	$-0.668999\pi$
$863$	14.5016	−	25.1175i	0.493640	−	0.855010i	0.999973	+	0.00732829i	$0.00233269\pi$
$864$		0			0
$865$	−21.0953			−0.717260
$866$	26.0549	−	45.1283i	0.885380	−	1.53352i
$867$		0			0
$868$	1.68127	+	4.93967i	0.0570661	+	0.167663i
$869$	−15.8916	−	27.5251i	−0.539086	−	0.933724i
$870$		0			0
$871$	10.1843	−	0.0159528i	0.345083	−	0.000540541i
$872$	−7.00455	−	12.1322i	−0.237204	−	0.410849i
$873$		0			0
$874$	14.8207	+	25.6702i	0.501318	+	0.868309i
$875$	14.4857	+	2.86915i	0.489708	+	0.0969950i
$876$		0			0
$877$	−8.68615	−	15.0449i	−0.293310	−	0.508029i	0.681280	−	0.732023i	$-0.261424\pi$
$877$	−8.68615	−	15.0449i	−0.293310	−	0.508029i	−0.974590	+	0.223994i	$0.928090\pi$
$878$	29.3577			0.990775
$879$		0			0
$880$	36.4290	+	63.0969i	1.22802	+	2.12700i
$881$	−9.75793	−	16.9012i	−0.328753	−	0.569417i	0.653512	−	0.756916i	$-0.273295\pi$
$881$	−9.75793	−	16.9012i	−0.328753	−	0.569417i	−0.982265	+	0.187500i	$0.939962\pi$
$882$		0			0
$883$	−27.9041			−0.939047			−0.469524	−	0.882920i	$-0.655574\pi$
$883$	−27.9041			−0.939047			−0.469524	+	0.882920i	$0.655574\pi$
$884$	−2.19365	−	3.78581i	−0.0737805	−	0.127331i
$885$		0			0
$886$	−30.7909	+	53.3315i	−1.03444	+	1.79171i
$887$	40.6053			1.36339			0.681696	−	0.731635i	$-0.261243\pi$
$887$	40.6053			1.36339			0.681696	+	0.731635i	$0.261243\pi$
$888$		0			0
$889$	−13.4958	−	39.6514i	−0.452634	−	1.32986i
$890$	−32.4125	+	56.1400i	−1.08647	+	1.88182i
$891$		0			0
$892$	11.5268	+	19.9651i	0.385947	+	0.668480i
$893$	−0.129361			−0.00432889
$894$		0			0
$895$	−5.91007	−	10.2365i	−0.197552	−	0.342170i
$896$	20.3234	+	4.02540i	0.678957	+	0.134479i
$897$		0			0
$898$	8.83877	−	15.3092i	0.294953	−	0.510874i
$899$	−2.99871	+	5.19391i	−0.100012	+	0.173227i
$900$		0			0
$901$	−4.32749	−	7.49544i	−0.144170	−	0.249709i
$902$	31.6435			1.05361
$903$		0			0
$904$	1.19042	−	2.06187i	0.0395929	−	0.0685769i
$905$	13.7037	−	23.7356i	0.455528	−	0.788997i
$906$		0			0
$907$	−14.6904	+	25.4446i	−0.487787	+	0.844872i	−0.999901	−	0.0140450i	$-0.995529\pi$
$907$	−14.6904	+	25.4446i	−0.487787	+	0.844872i	0.512114	+	0.858917i	$0.328863\pi$
$908$	10.8013			0.358454
$909$		0			0
$910$	49.2888	+	9.68229i	1.63391	+	0.320965i
$911$	24.7686			0.820622			0.410311	−	0.911946i	$-0.365420\pi$
$911$	24.7686			0.820622			0.410311	+	0.911946i	$0.365420\pi$
$912$		0			0
$913$	−10.0744	+	17.4493i	−0.333413	+	0.577489i
$914$	32.1022			1.06185
$915$		0			0
$916$	16.3808	−	28.3723i	0.541235	−	0.937447i
$917$	−37.3546	+	42.6647i	−1.23356	+	1.40891i
$918$		0			0
$919$	6.38891	+	11.0659i	0.210751	+	0.365031i	0.951950	−	0.306254i	$-0.0990758\pi$
$919$	6.38891	+	11.0659i	0.210751	+	0.365031i	−0.741199	+	0.671285i	$0.765743\pi$
$920$	5.92129	−	10.2560i	0.195219	−	0.338129i
$921$		0			0
$922$	−32.0760	+	55.5572i	−1.05637	+	1.82968i
$923$	−52.4229	+	0.0821158i	−1.72552	+	0.00270287i
$924$		0			0
$925$	−13.7522	−	23.8195i	−0.452170	−	0.783181i
$926$	68.2014			2.24124
$927$		0			0
$928$	−15.1883	−	26.3068i	−0.498579	−	0.863564i
$929$	−14.9490	−	25.8925i	−0.490461	−	0.849504i	0.509478	−	0.860484i	$-0.329838\pi$
$929$	−14.9490	−	25.8925i	−0.490461	−	0.849504i	−0.999940	+	0.0109793i	$0.996505\pi$
$930$		0			0
$931$	3.59048	+	26.9338i	0.117673	+	0.882721i
$932$	7.21136	−	12.4904i	0.236216	−	0.409138i
$933$		0			0
$934$	−24.7487	+	42.8660i	−0.809803	+	1.40262i
$935$	−6.34631	−	10.9921i	−0.207546	−	0.359481i
$936$		0			0
$937$	−30.8277			−1.00710			−0.503549	−	0.863967i	$-0.667972\pi$
$937$	−30.8277			−1.00710			−0.503549	+	0.863967i	$0.667972\pi$
$938$	−9.14748	+	10.4478i	−0.298676	+	0.341134i
$939$		0			0
$940$	−0.0685963	−	0.118812i	−0.00223736	−	0.00387523i
$941$	3.03988	+	5.26522i	0.0990972	+	0.171641i	0.911311	−	0.411718i	$-0.135071\pi$
$941$	3.03988	+	5.26522i	0.0990972	+	0.171641i	−0.812214	+	0.583360i	$0.801738\pi$
$942$		0			0
$943$	−6.52604	−	11.3034i	−0.212517	−	0.368090i
$944$	8.36125			0.272136
$945$		0			0
$946$	−12.4355	−	21.5390i	−0.404314	−	0.700292i
$947$	33.6489			1.09344			0.546722	−	0.837314i	$-0.315876\pi$
$947$	33.6489			1.09344			0.546722	+	0.837314i	$0.315876\pi$
$948$		0			0
$949$	−7.77067	+	13.5080i	−0.252247	+	0.438489i
$950$	−10.9289	+	18.9294i	−0.354579	+	0.614149i
$951$		0			0
$952$	−2.20467	−	0.436672i	−0.0714537	−	0.0141526i
$953$	−5.48006	+	9.49174i	−0.177516	+	0.307468i	−0.941029	−	0.338325i	$-0.890140\pi$
$953$	−5.48006	+	9.49174i	−0.177516	+	0.307468i	0.763513	+	0.645793i	$0.223473\pi$
$954$		0			0
$955$	−32.6014			−1.05496
$956$	−25.1240			−0.812569
$957$		0			0
$958$	−1.16410	+	2.01628i	−0.0376104	+	0.0651431i
$959$	55.2617	+	10.9455i	1.78449	+	0.353449i
$960$		0			0
$961$	14.5785	−	25.2507i	0.470274	−	0.814538i
$962$	30.4861	+	52.6130i	0.982912	+	1.69631i
$963$		0			0
$964$	−32.2657			−1.03921
$965$	−15.4244	−	26.7159i	−0.496529	−	0.860014i
$966$		0			0
$967$	−34.7715			−1.11818			−0.559088	−	0.829108i	$-0.688849\pi$
$967$	−34.7715			−1.11818			−0.559088	+	0.829108i	$0.688849\pi$
$968$	−9.02499	−	15.6317i	−0.290074	−	0.502423i
$969$		0			0
$970$	−45.1174	−	78.1456i	−1.44863	−	2.50910i
$971$	19.6214	+	33.9852i	0.629680	+	1.09064i	0.987616	+	0.156892i	$0.0501475\pi$
$971$	19.6214	+	33.9852i	0.629680	+	1.09064i	−0.357935	+	0.933746i	$0.616519\pi$
$972$		0			0
$973$	33.0323	−	37.7280i	1.05897	−	1.20950i
$974$	−14.1825			−0.454436
$975$		0			0
$976$	14.5804	+	25.2540i	0.466708	+	0.808361i
$977$	−1.28435	+	2.22455i	−0.0410898	+	0.0711697i	−0.885839	−	0.463993i	$-0.846416\pi$
$977$	−1.28435	+	2.22455i	−0.0410898	+	0.0711697i	0.844749	+	0.535163i	$0.179750\pi$
$978$		0			0
$979$	33.0050	−	57.1663i	1.05484	−	1.82704i
$980$	−22.8336	+	17.5799i	−0.729393	+	0.561570i
$981$		0			0
$982$	2.08934	+	3.61884i	0.0666734	+	0.115482i
$983$	−17.0691	−	29.5646i	−0.544421	−	0.942965i	−0.998643	−	0.0520764i	$-0.983416\pi$
$983$	−17.0691	−	29.5646i	−0.544421	−	0.942965i	0.454222	−	0.890888i	$-0.349917\pi$
$984$		0			0
$985$	−22.0733			−0.703314
$986$	3.42858	+	5.93847i	0.109188	+	0.189119i
$987$		0			0
$988$	10.1384	−	17.6240i	0.322546	−	0.560693i
$989$	−5.12931	+	8.88423i	−0.163103	+	0.282502i
$990$		0			0
$991$	−13.1761	+	22.8217i	−0.418553	+	0.724955i	−0.995794	−	0.0916188i	$-0.970796\pi$
$991$	−13.1761	+	22.8217i	−0.418553	+	0.724955i	0.577241	+	0.816574i	$0.304129\pi$
$992$	−4.66743	−	8.08423i	−0.148191	−	0.256674i
$993$		0			0
$994$	47.0859	−	53.7793i	1.49347	−	1.70577i
$995$	32.6371	−	56.5292i	1.03467	−	1.79210i
$996$		0			0
$997$	−28.0208			−0.887427			−0.443713	−	0.896169i	$-0.646339\pi$
$997$	−28.0208			−0.887427			−0.443713	+	0.896169i	$0.646339\pi$
$998$	32.0199	−	55.4602i	1.01357	−	1.75556i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.g.289.5	yes	36
3.2	odd	2	inner	819.2.s.g.289.14	yes	36
7.4	even	3		819.2.n.g.172.14	yes	36
13.9	even	3		819.2.n.g.100.14	yes	36
21.11	odd	6		819.2.n.g.172.5	yes	36
39.35	odd	6		819.2.n.g.100.5	✓	36
91.74	even	3	inner	819.2.s.g.802.5	yes	36
273.74	odd	6	inner	819.2.s.g.802.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.5	✓	36	39.35	odd	6
819.2.n.g.100.14	yes	36	13.9	even	3
819.2.n.g.172.5	yes	36	21.11	odd	6
819.2.n.g.172.14	yes	36	7.4	even	3
819.2.s.g.289.5	yes	36	1.1	even	1	trivial
819.2.s.g.289.14	yes	36	3.2	odd	2	inner
819.2.s.g.802.5	yes	36	91.74	even	3	inner
819.2.s.g.802.14	yes	36	273.74	odd	6	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.85815 q^{2} +1.45273 q^{4} +(-1.41690 + 2.45414i) q^{5} +(-2.59533 - 0.514050i) q^{7} +1.01691 q^{8} +(2.63281 - 4.56016i) q^{10} +(-2.68094 + 4.64352i) q^{11} +(-1.80766 - 3.11967i) q^{13} +(4.82252 + 0.955184i) q^{14} -4.79504 q^{16} +0.835344 q^{17} +(1.94086 + 3.36167i) q^{19} +(-2.05837 + 3.56520i) q^{20} +(4.98159 - 8.62837i) q^{22} -4.10954 q^{23} +(-1.51520 - 2.62440i) q^{25} +(3.35892 + 5.79682i) q^{26} +(-3.77031 - 0.746775i) q^{28} +(-2.20885 - 3.82585i) q^{29} +(-0.678792 - 1.17570i) q^{31} +6.87608 q^{32} -1.55220 q^{34} +(4.93887 - 5.64095i) q^{35} +9.07618 q^{37} +(-3.60642 - 6.24650i) q^{38} +(-1.44086 + 2.49565i) q^{40} +(1.58802 + 2.75053i) q^{41} +(1.24815 - 2.16186i) q^{43} +(-3.89468 + 6.74578i) q^{44} +7.63615 q^{46} +(-0.0166628 + 0.0288608i) q^{47} +(6.47150 + 2.66826i) q^{49} +(2.81547 + 4.87653i) q^{50} +(-2.62604 - 4.53203i) q^{52} +(-5.18049 - 8.97288i) q^{53} +(-7.59723 - 13.1588i) q^{55} +(-2.63923 - 0.522745i) q^{56} +(4.10439 + 7.10901i) q^{58} -1.74373 q^{59} +(-3.04073 - 5.26670i) q^{61} +(1.26130 + 2.18463i) q^{62} -3.18672 q^{64} +(10.2174 - 0.0160046i) q^{65} +(-1.41231 + 2.44620i) q^{67} +1.21353 q^{68} +(-9.17717 + 10.4817i) q^{70} +(7.26976 - 12.5916i) q^{71} +(-2.16106 - 3.74307i) q^{73} -16.8649 q^{74} +(2.81955 + 4.88360i) q^{76} +(9.34494 - 10.6734i) q^{77} +(-2.96381 + 5.13347i) q^{79} +(6.79408 - 11.7677i) q^{80} +(-2.95078 - 5.11091i) q^{82} +3.75778 q^{83} +(-1.18360 + 2.05005i) q^{85} +(-2.31925 + 4.01706i) q^{86} +(-2.72629 + 4.72207i) q^{88} -12.3110 q^{89} +(3.08782 + 9.02582i) q^{91} -5.97004 q^{92} +(0.0309620 - 0.0536277i) q^{94} -11.0000 q^{95} +(8.56830 - 14.8407i) q^{97} +(-12.0250 - 4.95804i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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