LMFDB - Embedded newform 504.2.bm.c.107.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(107,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 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("504.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.15
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.576030 - 1.29158i) q^{2} +(-1.33638 - 1.48798i) q^{4} +(1.88256 - 3.26069i) q^{5} +(-2.23426 + 1.41706i) q^{7} +(-2.69165 + 0.868922i) q^{8} +(-3.12704 - 4.30974i) q^{10} +(1.47084 - 0.849192i) q^{11} -5.64222i q^{13} +(0.543254 + 3.70201i) q^{14} +(-0.428185 + 3.97702i) q^{16} +(-2.26012 + 1.30488i) q^{17} +(-1.18076 + 2.04513i) q^{19} +(-7.36767 + 1.55630i) q^{20} +(-0.249553 - 2.38888i) q^{22} +(-0.653873 + 1.13254i) q^{23} +(-4.58807 - 7.94677i) q^{25} +(-7.28740 - 3.25009i) q^{26} +(5.09439 + 1.43081i) q^{28} +6.80944 q^{29} +(4.75107 - 2.74303i) q^{31} +(4.89000 + 2.84392i) q^{32} +(0.383465 + 3.67078i) q^{34} +(0.414472 + 9.95295i) q^{35} +(-5.20109 - 3.00285i) q^{37} +(1.96131 + 2.70311i) q^{38} +(-2.23391 + 10.4124i) q^{40} +6.10456i q^{41} -6.49804 q^{43} +(-3.22919 - 1.05375i) q^{44} +(1.08612 + 1.49691i) q^{46} +(3.53360 - 6.12038i) q^{47} +(2.98386 - 6.33219i) q^{49} +(-12.9068 + 1.34830i) q^{50} +(-8.39552 + 7.54014i) q^{52} +(-0.488913 - 0.846821i) q^{53} -6.39462i q^{55} +(4.78253 - 5.75564i) q^{56} +(3.92244 - 8.79496i) q^{58} +(6.67395 - 3.85320i) q^{59} +(7.64484 + 4.41375i) q^{61} +(-0.806095 - 7.71647i) q^{62} +(6.48995 - 4.67767i) q^{64} +(-18.3975 - 10.6218i) q^{65} +(6.69828 + 11.6018i) q^{67} +(4.96201 + 1.61920i) q^{68} +(13.0938 + 5.19787i) q^{70} +9.40544 q^{71} +(-1.09003 - 1.88798i) q^{73} +(-6.87442 + 4.98791i) q^{74} +(4.62106 - 0.976124i) q^{76} +(-2.08289 + 3.98160i) q^{77} +(-15.0908 - 8.71267i) q^{79} +(12.1617 + 8.88315i) q^{80} +(7.88456 + 3.51641i) q^{82} -11.8864i q^{83} +9.82605i q^{85} +(-3.74307 + 8.39277i) q^{86} +(-3.22111 + 3.56378i) q^{88} +(9.58642 + 5.53472i) q^{89} +(7.99538 + 12.6062i) q^{91} +(2.55902 - 0.540552i) q^{92} +(-5.86952 - 8.08946i) q^{94} +(4.44570 + 7.70018i) q^{95} +15.0631 q^{97} +(-6.45976 - 7.50144i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82}+ \cdots + 240 q^{97}+O(q^{100}) $ 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.576030	−	1.29158i	0.407315	−	0.913288i
$2$	0.576030	−	1.29158i	0.407315	−	0.913288i
$3$		0			0
$3$		0			0
$4$	−1.33638	−	1.48798i	−0.668189	−	0.743991i
$5$	1.88256	−	3.26069i	0.841907	−	1.45823i	−0.0463738	−	0.998924i	$-0.514767\pi$
$5$	1.88256	−	3.26069i	0.841907	−	1.45823i	0.888281	−	0.459301i	$-0.151900\pi$
$6$		0			0
$7$	−2.23426	+	1.41706i	−0.844472	+	0.535600i
$7$	−2.23426	+	1.41706i	−0.844472	+	0.535600i
$8$	−2.69165	+	0.868922i	−0.951642	+	0.307210i
$9$		0			0
$10$	−3.12704	−	4.30974i	−0.988858	−	1.36286i
$11$	1.47084	−	0.849192i	0.443476	−	0.256041i	−0.261595	−	0.965178i	$-0.584248\pi$
$11$	1.47084	−	0.849192i	0.443476	−	0.256041i	0.705071	+	0.709137i	$0.250915\pi$
$12$		0			0
$13$		−	5.64222i		−	1.56487i	−0.622733	−	0.782435i	$-0.713978\pi$
$13$		−	5.64222i		−	1.56487i	0.622733	−	0.782435i	$-0.286022\pi$
$14$	0.543254	+	3.70201i	0.145191	+	0.989404i
$15$		0			0
$16$	−0.428185	+	3.97702i	−0.107046	+	0.994254i
$17$	−2.26012	+	1.30488i	−0.548158	+	0.316479i	−0.748379	−	0.663271i	$-0.769167\pi$
$17$	−2.26012	+	1.30488i	−0.548158	+	0.316479i	0.200220	+	0.979751i	$0.435834\pi$
$18$		0			0
$19$	−1.18076	+	2.04513i	−0.270885	+	0.469186i	−0.969089	−	0.246713i	$-0.920649\pi$
$19$	−1.18076	+	2.04513i	−0.270885	+	0.469186i	0.698204	+	0.715899i	$0.253983\pi$
$20$	−7.36767	+	1.55630i	−1.64746	+	0.347999i
$21$		0			0
$22$	−0.249553	−	2.38888i	−0.0532048	−	0.509311i
$23$	−0.653873	+	1.13254i	−0.136342	+	0.236151i	−0.926109	−	0.377255i	$-0.876868\pi$
$23$	−0.653873	+	1.13254i	−0.136342	+	0.236151i	0.789767	+	0.613406i	$0.210201\pi$
$24$		0			0
$25$	−4.58807	−	7.94677i	−0.917614	−	1.58935i
$26$	−7.28740	−	3.25009i	−1.42918	−	0.637395i
$27$		0			0
$28$	5.09439	+	1.43081i	0.962749	+	0.270398i
$29$	6.80944			1.26448			0.632241	−	0.774772i	$-0.282135\pi$
$29$	6.80944			1.26448			0.632241	+	0.774772i	$0.282135\pi$
$30$		0			0
$31$	4.75107	−	2.74303i	0.853317	−	0.492663i	−0.00845183	−	0.999964i	$-0.502690\pi$
$31$	4.75107	−	2.74303i	0.853317	−	0.492663i	0.861769	+	0.507302i	$0.169357\pi$
$32$	4.89000	+	2.84392i	0.864439	+	0.502739i
$33$		0			0
$34$	0.383465	+	3.67078i	0.0657637	+	0.629533i
$35$	0.414472	+	9.95295i	0.0700586	+	1.68236i
$36$		0			0
$37$	−5.20109	−	3.00285i	−0.855054	−	0.493666i	0.00729899	−	0.999973i	$-0.497677\pi$
$37$	−5.20109	−	3.00285i	−0.855054	−	0.493666i	−0.862353	+	0.506308i	$0.831010\pi$
$38$	1.96131	+	2.70311i	0.318166	+	0.438502i
$39$		0			0
$40$	−2.23391	+	10.4124i	−0.353212	+	1.64635i
$41$			6.10456i			0.953373i	0.879073	+	0.476686i	$0.158162\pi$
$41$			6.10456i			0.953373i	−0.879073	+	0.476686i	$0.841838\pi$
$42$		0			0
$43$	−6.49804			−0.990943			−0.495471	−	0.868624i	$-0.665005\pi$
$43$	−6.49804			−0.990943			−0.495471	+	0.868624i	$0.665005\pi$
$44$	−3.22919	−	1.05375i	−0.486818	−	0.158859i
$45$		0			0
$46$	1.08612	+	1.49691i	0.160140	+	0.220707i
$47$	3.53360	−	6.12038i	0.515429	−	0.892749i	−0.484411	−	0.874841i	$-0.660966\pi$
$47$	3.53360	−	6.12038i	0.515429	−	0.892749i	0.999840	−	0.0179081i	$-0.00570062\pi$
$48$		0			0
$49$	2.98386	−	6.33219i	0.426266	−	0.904598i
$50$	−12.9068	+	1.34830i	−1.82530	+	0.190678i
$51$		0			0
$52$	−8.39552	+	7.54014i	−1.16425	+	1.04563i
$53$	−0.488913	−	0.846821i	−0.0671573	−	0.116320i	0.830492	−	0.557031i	$-0.188060\pi$
$53$	−0.488913	−	0.846821i	−0.0671573	−	0.116320i	−0.897649	+	0.440711i	$0.854726\pi$
$54$		0			0
$55$		−	6.39462i		−	0.862251i
$56$	4.78253	−	5.75564i	0.639093	−	0.769130i
$57$		0			0
$58$	3.92244	−	8.79496i	0.515042	−	1.15484i
$59$	6.67395	−	3.85320i	0.868874	−	0.501645i	0.00190001	−	0.999998i	$-0.499395\pi$
$59$	6.67395	−	3.85320i	0.868874	−	0.501645i	0.866974	+	0.498354i	$0.166062\pi$
$60$		0			0
$61$	7.64484	+	4.41375i	0.978822	+	0.565123i	0.901914	−	0.431915i	$-0.142162\pi$
$61$	7.64484	+	4.41375i	0.978822	+	0.565123i	0.0769075	+	0.997038i	$0.475495\pi$
$62$	−0.806095	−	7.71647i	−0.102374	−	0.979993i
$63$		0			0
$64$	6.48995	−	4.67767i	0.811244	−	0.584708i
$65$	−18.3975	−	10.6218i	−2.28193	−	1.31747i
$66$		0			0
$67$	6.69828	+	11.6018i	0.818325	+	1.41738i	0.906916	+	0.421312i	$0.138430\pi$
$67$	6.69828	+	11.6018i	0.818325	+	1.41738i	−0.0885910	+	0.996068i	$0.528236\pi$
$68$	4.96201	+	1.61920i	0.601732	+	0.196357i
$69$		0			0
$70$	13.0938	+	5.19787i	1.56501	+	0.621265i
$71$	9.40544			1.11622			0.558110	−	0.829767i	$-0.311527\pi$
$71$	9.40544			1.11622			0.558110	+	0.829767i	$0.311527\pi$
$72$		0			0
$73$	−1.09003	−	1.88798i	−0.127578	−	0.220971i	0.795160	−	0.606400i	$-0.207387\pi$
$73$	−1.09003	−	1.88798i	−0.127578	−	0.220971i	−0.922738	+	0.385429i	$0.874054\pi$
$74$	−6.87442	+	4.98791i	−0.799135	+	0.579833i
$75$		0			0
$76$	4.62106	−	0.976124i	0.530072	−	0.111969i
$77$	−2.08289	+	3.98160i	−0.237368	+	0.453745i
$78$		0			0
$79$	−15.0908	−	8.71267i	−1.69785	−	0.980252i	−0.947800	−	0.318865i	$-0.896698\pi$
$79$	−15.0908	−	8.71267i	−1.69785	−	0.980252i	−0.750045	−	0.661386i	$-0.769968\pi$
$80$	12.1617	+	8.88315i	1.35972	+	0.993167i
$81$		0			0
$82$	7.88456	+	3.51641i	0.870704	+	0.388323i
$83$		−	11.8864i		−	1.30471i	−0.757915	−	0.652353i	$-0.773782\pi$
$83$		−	11.8864i		−	1.30471i	0.757915	−	0.652353i	$-0.226218\pi$
$84$		0			0
$85$			9.82605i			1.06578i
$86$	−3.74307	+	8.39277i	−0.403626	+	0.905016i
$87$		0			0
$88$	−3.22111	+	3.56378i	−0.343372	+	0.379900i
$89$	9.58642	+	5.53472i	1.01616	+	0.586679i	0.912989	−	0.407984i	$-0.133768\pi$
$89$	9.58642	+	5.53472i	1.01616	+	0.586679i	0.103170	+	0.994664i	$0.467102\pi$
$90$		0			0
$91$	7.99538	+	12.6062i	0.838144	+	1.32149i
$92$	2.55902	−	0.540552i	0.266797	−	0.0563564i
$93$		0			0
$94$	−5.86952	−	8.08946i	−0.605395	−	0.834364i
$95$	4.44570	+	7.70018i	0.456119	+	0.790021i
$96$		0			0
$97$	15.0631			1.52943			0.764715	−	0.644369i	$-0.222880\pi$
$97$	15.0631			1.52943			0.764715	+	0.644369i	$0.222880\pi$
$98$	−6.45976	−	7.50144i	−0.652534	−	0.757759i
$99$		0			0
$100$	−5.69326	+	17.4469i	−0.569326	+	1.74469i
$101$	0.777899	+	1.34736i	0.0774039	+	0.134067i	0.902129	−	0.431466i	$-0.142004\pi$
$101$	0.777899	+	1.34736i	0.0774039	+	0.134067i	−0.824725	+	0.565534i	$0.808670\pi$
$102$		0			0
$103$	6.94066	+	4.00719i	0.683883	+	0.394840i	0.801317	−	0.598240i	$-0.204133\pi$
$103$	6.94066	+	4.00719i	0.683883	+	0.394840i	−0.117433	+	0.993081i	$0.537467\pi$
$104$	4.90265	+	15.1869i	0.480744	+	1.48919i
$105$		0			0
$106$	−1.37537	+	0.143677i	−0.133588	+	0.0139551i
$107$	12.6257	+	7.28943i	1.22057	+	0.704696i	0.965039	−	0.262105i	$-0.0844167\pi$
$107$	12.6257	+	7.28943i	1.22057	+	0.704696i	0.255530	+	0.966801i	$0.417750\pi$
$108$		0			0
$109$	−0.655188	+	0.378273i	−0.0627556	+	0.0362320i	−0.531050	−	0.847341i	$-0.678202\pi$
$109$	−0.655188	+	0.378273i	−0.0627556	+	0.0362320i	0.468294	+	0.883573i	$0.344869\pi$
$110$	−8.25920	−	3.68350i	−0.787483	−	0.351208i
$111$		0			0
$112$	−4.67901	−	9.49246i	−0.442125	−	0.896954i
$113$		−	9.87390i		−	0.928859i	−0.885610	−	0.464429i	$-0.846259\pi$
$113$		−	9.87390i		−	0.928859i	0.885610	−	0.464429i	$-0.153741\pi$
$114$		0			0
$115$	2.46191	+	4.26416i	0.229574	+	0.397635i
$116$	−9.09999	−	10.1323i	−0.844913	−	0.940763i
$117$		0			0
$118$	−1.13234	−	10.8395i	−0.104241	−	0.997859i
$119$	3.20060	−	6.11817i	0.293398	−	0.560852i
$120$		0			0
$121$	−4.05774	+	7.02822i	−0.368886	+	0.638929i
$122$	10.1044	−	7.33150i	0.914809	−	0.663763i
$123$		0			0
$124$	−10.4308	−	3.40378i	−0.936714	−	0.305668i
$125$	−15.7237			−1.40637
$126$		0			0
$127$			4.50847i			0.400062i	0.979790	+	0.200031i	$0.0641043\pi$
$127$			4.50847i			0.400062i	−0.979790	+	0.200031i	$0.935896\pi$
$128$	−2.30319	−	11.0768i	−0.203575	−	0.979059i
$129$		0			0
$130$	−24.3165	+	17.6435i	−2.13270	+	1.54743i
$131$	14.0673	+	8.12176i	1.22907	+	0.709601i	0.966835	−	0.255404i	$-0.0822084\pi$
$131$	14.0673	+	8.12176i	1.22907	+	0.709601i	0.262231	+	0.965005i	$0.415542\pi$
$132$		0			0
$133$	−0.259961	−	6.24258i	−0.0225414	−	0.541300i
$134$	18.8431	−	1.96843i	1.62779	−	0.170046i
$135$		0			0
$136$	4.94960	−	5.47614i	0.424425	−	0.469575i
$137$	3.63470	−	2.09849i	0.310533	−	0.179286i	−0.336632	−	0.941636i	$-0.609288\pi$
$137$	3.63470	−	2.09849i	0.310533	−	0.179286i	0.647165	+	0.762350i	$0.275954\pi$
$138$		0			0
$139$	−5.70274			−0.483700			−0.241850	−	0.970314i	$-0.577754\pi$
$139$	−5.70274			−0.483700			−0.241850	+	0.970314i	$0.577754\pi$
$140$	14.2559	−	13.9176i	1.20485	−	1.17625i
$141$		0			0
$142$	5.41782	−	12.1479i	0.454653	−	1.01943i
$143$	−4.79133	−	8.29882i	−0.400671	−	0.693982i
$144$		0			0
$145$	12.8192	−	22.2035i	1.06458	−	1.84390i
$146$	−3.06637	+	0.320326i	−0.253775	+	0.0265104i
$147$		0			0
$148$	2.48243	+	11.7521i	0.204055	+	0.966015i
$149$	6.74195	−	11.6774i	0.552322	−	0.956650i	−0.445784	−	0.895140i	$-0.647075\pi$
$149$	6.74195	−	11.6774i	0.552322	−	0.956650i	0.998106	−	0.0615095i	$-0.0195915\pi$
$150$		0			0
$151$	−18.4727	+	10.6652i	−1.50329	+	0.867924i	−0.503295	+	0.864115i	$0.667879\pi$
$151$	−18.4727	+	10.6652i	−1.50329	+	0.867924i	−0.999993	+	0.00380878i	$0.998788\pi$
$152$	1.40113	−	6.53077i	0.113646	−	0.529715i
$153$		0			0
$154$	3.94276	+	4.98375i	0.317717	+	0.401602i
$155$		−	20.6557i		−	1.65910i
$156$		0			0
$157$	−7.97251	+	4.60293i	−0.636276	+	0.367354i	−0.783179	−	0.621797i	$-0.786403\pi$
$157$	−7.97251	+	4.60293i	−0.636276	+	0.367354i	0.146903	+	0.989151i	$0.453070\pi$
$158$	−19.9459	+	14.4723i	−1.58681	+	1.15135i
$159$		0			0
$160$	18.4789	−	10.5909i	1.46088	−	0.837287i
$161$	−0.143959	−	3.45697i	−0.0113456	−	0.272448i
$162$		0			0
$163$	0.0600325	−	0.103979i	0.00470211	−	0.00814429i	−0.863665	−	0.504067i	$-0.831837\pi$
$163$	0.0600325	−	0.103979i	0.00470211	−	0.00814429i	0.868367	+	0.495922i	$0.165170\pi$
$164$	9.08349	−	8.15801i	0.709301	−	0.637033i
$165$		0			0
$166$	−15.3523	−	6.84695i	−1.19157	−	0.531426i
$167$	−12.9810			−1.00450			−0.502251	−	0.864722i	$-0.667495\pi$
$167$	−12.9810			−1.00450			−0.502251	+	0.864722i	$0.667495\pi$
$168$		0			0
$169$	−18.8346			−1.44882
$170$	12.6912	+	5.66010i	0.973368	+	0.434110i
$171$		0			0
$172$	8.68385	+	9.66898i	0.662137	+	0.737253i
$173$	−3.44458	+	5.96618i	−0.261886	+	0.453600i	−0.966743	−	0.255749i	$-0.917678\pi$
$173$	−3.44458	+	5.96618i	−0.261886	+	0.453600i	0.704857	+	0.709350i	$0.251011\pi$
$174$		0			0
$175$	21.5120	+	11.2536i	1.62616	+	0.850691i
$176$	2.74746	+	6.21318i	0.207097	+	0.468336i
$177$		0			0
$178$	12.6706	−	9.19350i	0.949704	−	0.689082i
$179$	−13.6043	+	7.85445i	−1.01683	+	0.587070i	−0.913185	−	0.407544i	$-0.866385\pi$
$179$	−13.6043	+	7.85445i	−1.01683	+	0.587070i	−0.103649	+	0.994614i	$0.533052\pi$
$180$		0			0
$181$		−	15.6714i		−	1.16485i	−0.812886	−	0.582423i	$-0.802105\pi$
$181$		−	15.6714i		−	1.16485i	0.812886	−	0.582423i	$-0.197895\pi$
$182$	20.8875	−	3.06516i	1.54829	−	0.227205i
$183$		0			0
$184$	0.775906	−	3.61657i	0.0572006	−	0.266617i
$185$	−19.5827	+	11.3061i	−1.43975	+	0.831241i
$186$		0			0
$187$	−2.21618	+	3.83854i	−0.162063	+	0.280702i
$188$	−13.8292	+	2.92120i	−1.00860	+	0.213051i
$189$		0			0
$190$	12.5063	−	1.30646i	0.907301	−	0.0947805i
$191$	−12.0633	+	20.8943i	−0.872873	+	1.51186i	−0.0138617	+	0.999904i	$0.504412\pi$
$191$	−12.0633	+	20.8943i	−0.872873	+	1.51186i	−0.859011	+	0.511957i	$0.828921\pi$
$192$		0			0
$193$	−4.80306	−	8.31914i	−0.345732	−	0.598825i	0.639755	−	0.768579i	$-0.279036\pi$
$193$	−4.80306	−	8.31914i	−0.345732	−	0.598825i	−0.985486	+	0.169754i	$0.945703\pi$
$194$	8.67682	−	19.4553i	0.622959	−	1.39681i
$195$		0			0
$196$	−13.4097	+	4.02227i	−0.957839	+	0.287305i
$197$	2.05305			0.146274			0.0731371	−	0.997322i	$-0.476699\pi$
$197$	2.05305			0.146274			0.0731371	+	0.997322i	$0.476699\pi$
$198$		0			0
$199$	8.62103	−	4.97735i	0.611128	−	0.352835i	−0.162279	−	0.986745i	$-0.551884\pi$
$199$	8.62103	−	4.97735i	0.611128	−	0.352835i	0.773407	+	0.633910i	$0.218551\pi$
$200$	19.2546	+	17.4032i	1.36151	+	1.23060i
$201$		0			0
$202$	2.18832	−	0.228602i	0.153970	−	0.0160844i
$203$	−15.2141	+	9.64941i	−1.06782	+	0.677256i
$204$		0			0
$205$	19.9051	+	11.4922i	1.39023	+	0.802651i
$206$	9.17365	−	6.65618i	0.639159	−	0.463758i
$207$		0			0
$208$	22.4392	+	2.41591i	1.55588	+	0.167514i
$209$			4.01076i			0.277430i
$210$		0			0
$211$	−13.9757			−0.962128			−0.481064	−	0.876685i	$-0.659750\pi$
$211$	−13.9757			−0.962128			−0.481064	+	0.876685i	$0.659750\pi$
$212$	−0.606683	+	1.85917i	−0.0416672	+	0.127688i
$213$		0			0
$214$	16.6877	−	12.1082i	1.14075	−	0.827698i
$215$	−12.2330	+	21.1881i	−0.834281	+	1.44502i
$216$		0			0
$217$	−6.72808	+	12.8612i	−0.456732	+	0.873076i
$218$	0.111163	+	1.06413i	0.00752893	+	0.0720718i
$219$		0			0
$220$	−9.51509	+	8.54564i	−0.641507	+	0.576147i
$221$	7.36241	+	12.7521i	0.495249	+	0.857796i
$222$		0			0
$223$			15.8817i			1.06352i	0.846896	+	0.531759i	$0.178469\pi$
$223$			15.8817i			1.06352i	−0.846896	+	0.531759i	$0.821531\pi$
$224$	−14.9556	+	0.575385i	−0.999261	+	0.0384446i
$225$		0			0
$226$	−12.7530	−	5.68767i	−0.848315	−	0.378338i
$227$	−0.620059	+	0.357991i	−0.0411548	+	0.0237607i	−0.520436	−	0.853901i	$-0.674231\pi$
$227$	−0.620059	+	0.357991i	−0.0411548	+	0.0237607i	0.479281	+	0.877661i	$0.340897\pi$
$228$		0			0
$229$	3.89913	+	2.25117i	0.257662	+	0.148761i	0.623268	−	0.782009i	$-0.285805\pi$
$229$	3.89913	+	2.25117i	0.257662	+	0.148761i	−0.365606	+	0.930770i	$0.619138\pi$
$230$	6.92565	−	0.723483i	0.456664	−	0.0477051i
$231$		0			0
$232$	−18.3286	+	5.91687i	−1.20333	+	0.388462i
$233$	−6.69604	−	3.86596i	−0.438672	−	0.253267i	0.264362	−	0.964423i	$-0.414839\pi$
$233$	−6.69604	−	3.86596i	−0.438672	−	0.253267i	−0.703034	+	0.711156i	$0.748172\pi$
$234$		0			0
$235$	−13.3044	−	23.0440i	−0.867886	−	1.50322i
$236$	−14.6524	−	4.78138i	−0.953791	−	0.311241i
$237$		0			0
$238$	−6.05849	−	7.65809i	−0.392713	−	0.496400i
$239$	−21.3788			−1.38288			−0.691440	−	0.722433i	$-0.743024\pi$
$239$	−21.3788			−1.38288			−0.691440	+	0.722433i	$0.743024\pi$
$240$		0			0
$241$	4.25688	+	7.37313i	0.274210	+	0.474945i	0.969935	−	0.243362i	$-0.0782504\pi$
$241$	4.25688	+	7.37313i	0.274210	+	0.474945i	−0.695726	+	0.718308i	$0.744917\pi$
$242$	6.74015	+	9.28939i	0.433273	+	0.597144i
$243$		0			0
$244$	−3.64882	−	17.2738i	−0.233592	−	1.10584i
$245$	−15.0300	−	21.6502i	−0.960232	−	1.38318i
$246$		0			0
$247$	11.5391	+	6.66209i	0.734215	+	0.423899i
$248$	−10.4047	+	11.5116i	−0.660701	+	0.730986i
$249$		0			0
$250$	−9.05731	+	20.3084i	−0.572835	+	1.28442i
$251$		−	0.778871i		−	0.0491619i	−0.999698	−	0.0245810i	$-0.992175\pi$
$251$		−	0.778871i		−	0.0491619i	0.999698	−	0.0245810i	$-0.00782515\pi$
$252$		0			0
$253$			2.22106i			0.139637i
$254$	5.82307	+	2.59702i	0.365372	+	0.162951i
$255$		0			0
$256$	−15.6333	−	3.40580i	−0.977082	−	0.212862i
$257$	10.6901	+	6.17195i	0.666832	+	0.384996i	0.794875	−	0.606773i	$-0.207536\pi$
$257$	10.6901	+	6.17195i	0.666832	+	0.384996i	−0.128043	+	0.991769i	$0.540870\pi$
$258$		0			0
$259$	15.8758	−	0.661120i	0.986476	−	0.0410800i
$260$	8.78098	+	41.5700i	0.544573	+	2.57806i
$261$		0			0
$262$	18.5931	−	13.4907i	1.14869	−	0.833460i
$263$	−1.01432	−	1.75686i	−0.0625458	−	0.108333i	0.833057	−	0.553187i	$-0.186589\pi$
$263$	−1.01432	−	1.75686i	−0.0625458	−	0.108333i	−0.895603	+	0.444855i	$0.853255\pi$
$264$		0			0
$265$	−3.68163			−0.226161
$266$	−8.21256	−	3.26015i	−0.503544	−	0.199893i
$267$		0			0
$268$	8.31178	−	25.4713i	0.507723	−	1.55590i
$269$	13.1346	+	22.7498i	0.800833	+	1.38708i	0.919069	+	0.394097i	$0.128943\pi$
$269$	13.1346	+	22.7498i	0.800833	+	1.38708i	−0.118236	+	0.992986i	$0.537724\pi$
$270$		0			0
$271$	−7.01591	−	4.05064i	−0.426186	−	0.246059i	0.271535	−	0.962429i	$-0.412469\pi$
$271$	−7.01591	−	4.05064i	−0.426186	−	0.246059i	−0.697720	+	0.716370i	$0.745802\pi$
$272$	−4.22177	−	9.54724i	−0.255983	−	0.578887i
$273$		0			0
$274$	−0.616685	−	5.90331i	−0.0372553	−	0.356632i
$275$	−13.4967	−	7.79231i	−0.813880	−	0.469894i
$276$		0			0
$277$	−8.45693	+	4.88261i	−0.508127	+	0.293368i	−0.732064	−	0.681236i	$-0.761443\pi$
$277$	−8.45693	+	4.88261i	−0.508127	+	0.293368i	0.223936	+	0.974604i	$0.428109\pi$
$278$	−3.28495	+	7.36557i	−0.197018	+	0.441758i
$279$		0			0
$280$	−9.76395	−	26.4297i	−0.583508	−	1.57948i
$281$			1.88752i			0.112600i	0.998414	+	0.0562999i	$0.0179303\pi$
$281$			1.88752i			0.112600i	−0.998414	+	0.0562999i	$0.982070\pi$
$282$		0			0
$283$	3.28892	+	5.69657i	0.195506	+	0.338626i	0.947066	−	0.321038i	$-0.104032\pi$
$283$	3.28892	+	5.69657i	0.195506	+	0.338626i	−0.751560	+	0.659664i	$0.770698\pi$
$284$	−12.5692	−	13.9951i	−0.745847	−	0.830458i
$285$		0			0
$286$	−13.4786	+	1.40803i	−0.797005	+	0.0832585i
$287$	−8.65056	−	13.6392i	−0.510626	−	0.805097i
$288$		0			0
$289$	−5.09459	+	8.82408i	−0.299682	+	0.519064i
$290$	−21.2934	−	29.3469i	−1.25039	−	1.72331i
$291$		0			0
$292$	−1.35259	+	4.14500i	−0.0791546	+	0.242567i
$293$	−14.1311			−0.825545			−0.412772	−	0.910834i	$-0.635440\pi$
$293$	−14.1311			−0.825545			−0.412772	+	0.910834i	$0.635440\pi$
$294$		0			0
$295$		−	29.0156i		−	1.68935i
$296$	16.6088	+	3.56328i	0.965364	+	0.207111i
$297$		0			0
$298$	−11.1988	−	15.4343i	−0.648728	−	0.894087i
$299$	6.39004	+	3.68929i	0.369546	+	0.213357i
$300$		0			0
$301$	14.5183	−	9.20814i	0.836823	−	0.530749i
$302$	3.13419	+	30.0025i	0.180353	+	1.72645i
$303$		0			0
$304$	−7.62795	−	5.57159i	−0.437493	−	0.319553i
$305$	28.7838	−	16.6183i	1.64815	−	0.951562i
$306$		0			0
$307$	−17.5973			−1.00433			−0.502167	−	0.864771i	$-0.667464\pi$
$307$	−17.5973			−1.00433			−0.502167	+	0.864771i	$0.667464\pi$
$308$	8.70808	−	2.22162i	0.496189	−	0.126588i
$309$		0			0
$310$	−26.6785	−	11.8983i	−1.51524	−	0.675778i
$311$	−5.44683	−	9.43418i	−0.308861	−	0.534963i	0.669252	−	0.743035i	$-0.266615\pi$
$311$	−5.44683	−	9.43418i	−0.308861	−	0.534963i	−0.978114	+	0.208072i	$0.933281\pi$
$312$		0			0
$313$	−1.76535	+	3.05768i	−0.0997835	+	0.172830i	−0.911595	−	0.411090i	$-0.865148\pi$
$313$	−1.76535	+	3.05768i	−0.0997835	+	0.172830i	0.811811	+	0.583920i	$0.198482\pi$
$314$	1.35267	+	12.9486i	0.0763354	+	0.730732i
$315$		0			0
$316$	7.20270	+	34.0982i	0.405183	+	1.91818i
$317$	−8.09426	+	14.0197i	−0.454619	+	0.787423i	−0.998666	−	0.0516316i	$-0.983558\pi$
$317$	−8.09426	+	14.0197i	−0.454619	+	0.787423i	0.544047	+	0.839055i	$0.316891\pi$
$318$		0			0
$319$	10.0156	−	5.78252i	0.560767	−	0.323759i
$320$	−3.03470	−	29.9677i	−0.169645	−	1.67525i
$321$		0			0
$322$	−4.54790	−	1.80539i	−0.253444	−	0.100610i
$323$		−	6.16298i		−	0.342918i
$324$		0			0
$325$	−44.8374	+	25.8869i	−2.48713	+	1.43595i
$326$	−0.0997175	−	0.137432i	−0.00552284	−	0.00761167i
$327$		0			0
$328$	−5.30439	−	16.4313i	−0.292886	−	0.907269i
$329$	0.777972	+	18.6819i	0.0428910	+	1.02996i
$330$		0			0
$331$	5.79835	−	10.0430i	0.318706	−	0.552016i	−0.661512	−	0.749935i	$-0.730085\pi$
$331$	5.79835	−	10.0430i	0.318706	−	0.552016i	0.980218	+	0.197919i	$0.0634183\pi$
$332$	−17.6868	+	15.8848i	−0.970690	+	0.871791i
$333$		0			0
$334$	−7.47747	+	16.7661i	−0.409149	+	0.917400i
$335$	50.4397			2.75581
$336$		0			0
$337$	2.81073			0.153110			0.0765550	−	0.997065i	$-0.475608\pi$
$337$	2.81073			0.153110			0.0765550	+	0.997065i	$0.475608\pi$
$338$	−10.8493	+	24.3265i	−0.590124	+	1.32319i
$339$		0			0
$340$	14.6210	−	13.1313i	0.792935	−	0.712146i
$341$	4.65872	−	8.06914i	0.252284	−	0.436968i
$342$		0			0
$343$	2.30639	+	18.3761i	0.124533	+	0.992215i
$344$	17.4905	−	5.64629i	0.943022	−	0.304428i
$345$		0			0
$346$	5.72164	+	7.88566i	0.307597	+	0.423936i
$347$	18.7883	−	10.8474i	1.00861	−	0.582320i	0.0978242	−	0.995204i	$-0.468812\pi$
$347$	18.7883	−	10.8474i	1.00861	−	0.582320i	0.910784	+	0.412884i	$0.135478\pi$
$348$		0			0
$349$		−	7.44465i		−	0.398503i	−0.979948	−	0.199251i	$-0.936149\pi$
$349$		−	7.44465i		−	0.398503i	0.979948	−	0.199251i	$-0.0638511\pi$
$350$	26.9265	−	21.3022i	1.43928	−	1.13865i
$351$		0			0
$352$	9.60747	+	0.0304086i	0.512080	+	0.00162078i
$353$	−13.0365	+	7.52665i	−0.693865	+	0.400603i	−0.805058	−	0.593196i	$-0.797866\pi$
$353$	−13.0365	+	7.52665i	−0.693865	+	0.400603i	0.111193	+	0.993799i	$0.464533\pi$
$354$		0			0
$355$	17.7063	−	30.6682i	0.939754	−	1.62770i
$356$	−4.57551	−	21.6609i	−0.242502	−	1.14803i
$357$		0			0
$358$	2.30819	+	22.0955i	0.121992	+	1.16778i
$359$	9.01876	−	15.6210i	0.475992	−	0.824442i	−0.523630	−	0.851946i	$-0.675422\pi$
$359$	9.01876	−	15.6210i	0.475992	−	0.824442i	0.999622	+	0.0275035i	$0.00875575\pi$
$360$		0			0
$361$	6.71162	+	11.6249i	0.353243	+	0.611835i
$362$	−20.2409	−	9.02720i	−1.06384	−	0.474459i
$363$		0			0
$364$	8.07294	−	28.7436i	0.423137	−	1.50658i
$365$	−8.20816			−0.429635
$366$		0			0
$367$	−3.38897	+	1.95662i	−0.176903	+	0.102135i	−0.585837	−	0.810429i	$-0.699234\pi$
$367$	−3.38897	+	1.95662i	−0.176903	+	0.102135i	0.408934	+	0.912564i	$0.365901\pi$
$368$	−4.22416	−	3.08540i	−0.220199	−	0.160838i
$369$		0			0
$370$	3.32253	+	31.8054i	0.172730	+	1.65348i
$371$	2.29236	+	1.19920i	0.119013	+	0.0622594i
$372$		0			0
$373$	15.8513	+	9.15178i	0.820752	+	0.473861i	0.850676	−	0.525691i	$-0.176193\pi$
$373$	15.8513	+	9.15178i	0.820752	+	0.473861i	−0.0299239	+	0.999552i	$0.509527\pi$
$374$	3.68121	+	5.07351i	0.190351	+	0.262345i
$375$		0			0
$376$	−4.19308	+	19.5443i	−0.216242	+	1.00792i
$377$		−	38.4203i		−	1.97875i
$378$		0			0
$379$	25.8073			1.32563			0.662816	−	0.748783i	$-0.269361\pi$
$379$	25.8073			1.32563			0.662816	+	0.748783i	$0.269361\pi$
$380$	5.51659	−	16.9055i	0.282995	−	0.867232i
$381$		0			0
$382$	20.0379	+	27.6166i	1.02523	+	1.41299i
$383$	7.37665	−	12.7767i	0.376929	−	0.652860i	−0.613685	−	0.789551i	$-0.710313\pi$
$383$	7.37665	−	12.7767i	0.376929	−	0.652860i	0.990614	+	0.136691i	$0.0436467\pi$
$384$		0			0
$385$	9.06159	+	14.2873i	0.461822	+	0.728147i
$386$	−13.5116	+	1.41148i	−0.687721	+	0.0718423i
$387$		0			0
$388$	−20.1300	−	22.4137i	−1.02195	−	1.13788i
$389$	−8.70264	−	15.0734i	−0.441242	−	0.764253i	0.556540	−	0.830821i	$-0.312128\pi$
$389$	−8.70264	−	15.0734i	−0.441242	−	0.764253i	−0.997782	+	0.0665677i	$0.978795\pi$
$390$		0			0
$391$		−	3.41290i		−	0.172598i
$392$	−2.52933	+	19.6368i	−0.127750	+	0.991806i
$393$		0			0
$394$	1.18262	−	2.65169i	0.0595796	−	0.133590i
$395$	−56.8186	+	32.8042i	−2.85886	+	1.65056i
$396$		0			0
$397$	10.0273	+	5.78926i	0.503255	+	0.290554i	0.730057	−	0.683387i	$-0.239494\pi$
$397$	10.0273	+	5.78926i	0.503255	+	0.290554i	−0.226802	+	0.973941i	$0.572827\pi$
$398$	−1.46270	−	14.0019i	−0.0733184	−	0.701851i
$399$		0			0
$400$	33.5690	−	14.8441i	1.67845	−	0.742207i
$401$	31.1453	+	17.9818i	1.55532	+	0.897967i	0.997694	+	0.0678773i	$0.0216226\pi$
$401$	31.1453	+	17.9818i	1.55532	+	0.897967i	0.557630	+	0.830089i	$0.311711\pi$
$402$		0			0
$403$	−15.4768	−	26.8065i	−0.770953	−	1.33533i
$404$	0.965282	−	2.95809i	0.0480246	−	0.147170i
$405$		0			0
$406$	3.69926	+	25.2086i	0.183591	+	1.25108i
$407$	−10.2000			−0.505595
$408$		0			0
$409$	12.1615	+	21.0644i	0.601349	+	1.04157i	0.992617	+	0.121290i	$0.0387031\pi$
$409$	12.1615	+	21.0644i	0.601349	+	1.04157i	−0.391268	+	0.920277i	$0.627964\pi$
$410$	26.3091	−	19.0892i	1.29931	−	0.942751i
$411$		0			0
$412$	−3.31272	−	15.6827i	−0.163206	−	0.772631i
$413$	−9.45111	+	18.0665i	−0.465059	+	0.888993i
$414$		0			0
$415$	−38.7580	−	22.3769i	−1.90256	−	1.09844i
$416$	16.0460	−	27.5905i	0.786720	−	1.35273i
$417$		0			0
$418$	5.18024	+	2.31032i	0.253374	+	0.113001i
$419$		−	6.92954i		−	0.338530i	−0.985571	−	0.169265i	$-0.945861\pi$
$419$		−	6.92954i		−	0.338530i	0.985571	−	0.169265i	$-0.0541394\pi$
$420$		0			0
$421$		−	12.6192i		−	0.615024i	−0.951544	−	0.307512i	$-0.900504\pi$
$421$		−	12.6192i		−	0.615024i	0.951544	−	0.307512i	$-0.0994965\pi$
$422$	−8.05043	+	18.0508i	−0.391889	+	0.878700i
$423$		0			0
$424$	2.05180	+	1.85452i	0.0996444	+	0.0900634i
$425$	20.7391	+	11.9737i	1.00600	+	0.580812i
$426$		0			0
$427$	−23.3352	+	0.971750i	−1.12927	+	0.0470263i
$428$	−6.02612	−	28.5282i	−0.291284	−	1.37896i
$429$		0			0
$430$	20.3197	+	28.0049i	0.979902	+	1.35052i
$431$	11.1759	+	19.3571i	0.538322	+	0.932401i	0.998995	+	0.0448306i	$0.0142748\pi$
$431$	11.1759	+	19.3571i	0.538322	+	0.932401i	−0.460673	+	0.887570i	$0.652392\pi$
$432$		0			0
$433$	−32.2813			−1.55134			−0.775671	−	0.631138i	$-0.782588\pi$
$433$	−32.2813			−1.55134			−0.775671	+	0.631138i	$0.782588\pi$
$434$	12.7358	+	16.0983i	0.611336	+	0.772745i
$435$		0			0
$436$	1.43844	+	0.469393i	0.0688889	+	0.0224798i
$437$	−1.54413	−	2.67451i	−0.0738658	−	0.127939i
$438$		0			0
$439$	−2.42798	−	1.40180i	−0.115881	−	0.0669041i	0.440939	−	0.897537i	$-0.354645\pi$
$439$	−2.42798	−	1.40180i	−0.115881	−	0.0669041i	−0.556820	+	0.830633i	$0.687979\pi$
$440$	5.55643	+	17.2121i	0.264892	+	0.820554i
$441$		0			0
$442$	20.7113	−	2.16359i	0.985137	−	0.102912i
$443$	−16.2066	−	9.35689i	−0.769999	−	0.444559i	0.0628752	−	0.998021i	$-0.479973\pi$
$443$	−16.2066	−	9.35689i	−0.769999	−	0.444559i	−0.832874	+	0.553462i	$0.813306\pi$
$444$		0			0
$445$	36.0940	−	20.8389i	1.71102	−	0.987859i
$446$	20.5126	+	9.14834i	0.971298	+	0.433187i
$447$		0			0
$448$	−7.87170	+	19.6478i	−0.371903	+	0.928272i
$449$		−	13.8950i		−	0.655747i	−0.944722	−	0.327874i	$-0.893668\pi$
$449$		−	13.8950i		−	0.655747i	0.944722	−	0.327874i	$-0.106332\pi$
$450$		0			0
$451$	5.18395	+	8.97886i	0.244103	+	0.422798i
$452$	−14.6922	+	13.1953i	−0.691063	+	0.620653i
$453$		0			0
$454$	0.105203	+	1.00707i	0.00493742	+	0.0472642i
$455$	56.1567	−	2.33854i	2.63267	−	0.109633i
$456$		0			0
$457$	2.88922	−	5.00428i	0.135152	−	0.234090i	−0.790503	−	0.612458i	$-0.790181\pi$
$457$	2.88922	−	5.00428i	0.135152	−	0.234090i	0.925656	+	0.378367i	$0.123514\pi$
$458$	5.15359	−	3.73932i	0.240811	−	0.174727i
$459$		0			0
$460$	3.05494	−	9.36181i	0.142438	−	0.436496i
$461$	15.4222			0.718285			0.359142	−	0.933283i	$-0.383069\pi$
$461$	15.4222			0.718285			0.359142	+	0.933283i	$0.383069\pi$
$462$		0			0
$463$		−	11.5902i		−	0.538644i	−0.963050	−	0.269322i	$-0.913200\pi$
$463$		−	11.5902i		−	0.538644i	0.963050	−	0.269322i	$-0.0867996\pi$
$464$	−2.91570	+	27.0813i	−0.135358	+	1.25722i
$465$		0			0
$466$	−8.85033	+	6.42159i	−0.409984	+	0.297474i
$467$	1.98153	+	1.14404i	0.0916943	+	0.0529397i	0.545146	−	0.838341i	$-0.316474\pi$
$467$	1.98153	+	1.14404i	0.0916943	+	0.0529397i	−0.453452	+	0.891281i	$0.649808\pi$
$468$		0			0
$469$	−31.4061	−	16.4295i	−1.45020	−	0.758643i
$470$	−37.4270	+	3.90978i	−1.72638	+	0.180345i
$471$		0			0
$472$	−14.6158	+	16.1706i	−0.672746	+	0.744313i
$473$	−9.55761	+	5.51809i	−0.439459	+	0.253722i
$474$		0			0
$475$	21.6696			0.994270
$476$	−13.3809	+	3.41376i	−0.613314	+	0.156469i
$477$		0			0
$478$	−12.3148	+	27.6125i	−0.563268	+	1.26297i
$479$	−9.42948	−	16.3323i	−0.430844	−	0.746244i	0.566102	−	0.824335i	$-0.308451\pi$
$479$	−9.42948	−	16.3323i	−0.430844	−	0.746244i	−0.996946	+	0.0780912i	$0.975117\pi$
$480$		0			0
$481$	−16.9427	+	29.3457i	−0.772522	+	1.33805i
$482$	11.9751	−	1.25097i	0.545451	−	0.0569802i
$483$		0			0
$484$	15.8806	−	3.35451i	0.721843	−	0.152478i
$485$	28.3573	−	49.1162i	1.28764	−	2.23025i
$486$		0			0
$487$	−26.9019	+	15.5318i	−1.21904	+	0.703813i	−0.964713	−	0.263305i	$-0.915187\pi$
$487$	−26.9019	+	15.5318i	−1.21904	+	0.703813i	−0.254327	+	0.967118i	$0.581854\pi$
$488$	−24.4124	−	5.23750i	−1.10510	−	0.237090i
$489$		0			0
$490$	−36.6207	+	6.94136i	−1.65436	+	0.313579i
$491$			7.52948i			0.339801i	0.985461	+	0.169900i	$0.0543446\pi$
$491$			7.52948i			0.339801i	−0.985461	+	0.169900i	$0.945655\pi$
$492$		0			0
$493$	−15.3901	+	8.88549i	−0.693136	+	0.400182i
$494$	15.2515	−	11.0661i	0.686198	−	0.497889i
$495$		0			0
$496$	8.87474	+	20.0696i	0.398487	+	0.901151i
$497$	−21.0142	+	13.3281i	−0.942617	+	0.597848i
$498$		0			0
$499$	−0.883277	+	1.52988i	−0.0395409	+	0.0684869i	−0.885119	−	0.465366i	$-0.845923\pi$
$499$	−0.883277	+	1.52988i	−0.0395409	+	0.0684869i	0.845578	+	0.533852i	$0.179256\pi$
$500$	21.0128	+	23.3966i	0.939720	+	1.04633i
$501$		0			0
$502$	−1.00598	−	0.448653i	−0.0448990	−	0.0200244i
$503$	−16.9584			−0.756136			−0.378068	−	0.925778i	$-0.623411\pi$
$503$	−16.9584			−0.756136			−0.378068	+	0.925778i	$0.623411\pi$
$504$		0			0
$505$	5.85777			0.260667
$506$	2.86868	+	1.27940i	0.127528	+	0.0568760i
$507$		0			0
$508$	6.70853	−	6.02503i	0.297643	−	0.267317i
$509$	−5.13114	+	8.88739i	−0.227434	+	0.393927i	−0.957047	−	0.289934i	$-0.906367\pi$
$509$	−5.13114	+	8.88739i	−0.227434	+	0.393927i	0.729613	+	0.683860i	$0.239700\pi$
$510$		0			0
$511$	5.11079	+	2.67361i	0.226088	+	0.118273i
$512$	−13.4041	+	18.2299i	−0.592385	+	0.805655i
$513$		0			0
$514$	14.1294	−	10.2520i	0.623223	−	0.452195i
$515$	26.1324	−	15.0876i	1.15153	−	0.664837i
$516$		0			0
$517$		−	12.0028i		−	0.527884i
$518$	8.29107	−	20.8858i	0.364289	−	0.917669i
$519$		0			0
$520$	58.7492	+	12.6042i	2.57632	+	0.552730i
$521$	32.7368	−	18.9006i	1.43423	−	0.828051i	0.436787	−	0.899565i	$-0.356116\pi$
$521$	32.7368	−	18.9006i	1.43423	−	0.828051i	0.997440	+	0.0715138i	$0.0227830\pi$
$522$		0			0
$523$	19.6691	−	34.0679i	0.860070	−	1.48968i	−0.0117911	−	0.999930i	$-0.503753\pi$
$523$	19.6691	−	34.0679i	0.860070	−	1.48968i	0.871861	−	0.489754i	$-0.162913\pi$
$524$	−6.71420	−	31.7856i	−0.293311	−	1.38856i
$525$		0			0
$526$	−2.85341	+	0.298080i	−0.124415	+	0.0129969i
$527$	−7.15864	+	12.3991i	−0.311835	+	0.540114i
$528$		0			0
$529$	10.6449	+	18.4375i	0.462822	+	0.801631i
$530$	−2.12073	+	4.75514i	−0.0921186	+	0.206550i
$531$		0			0
$532$	−8.94144	+	8.72926i	−0.387661	+	0.378461i
$533$	34.4433			1.49190
$534$		0			0
$535$	47.5372	−	27.4456i	2.05521	−	1.18658i
$536$	−28.1104	−	25.4076i	−1.21419	−	1.09744i
$537$		0			0
$538$	36.9493	−	3.85988i	1.59300	−	0.166411i
$539$	−0.988451	−	11.8475i	−0.0425756	−	0.510309i
$540$		0			0
$541$	12.8385	+	7.41231i	0.551970	+	0.318680i	0.749916	−	0.661533i	$-0.230094\pi$
$541$	12.8385	+	7.41231i	0.551970	+	0.318680i	−0.197946	+	0.980213i	$0.563427\pi$
$542$	−9.27311	+	6.72834i	−0.398314	+	0.289007i
$543$		0			0
$544$	−14.7629	−	0.0467261i	−0.632956	−	0.00200337i
$545$			2.84849i			0.122016i
$546$		0			0
$547$	−16.2017			−0.692736			−0.346368	−	0.938099i	$-0.612585\pi$
$547$	−16.2017			−0.692736			−0.346368	+	0.938099i	$0.612585\pi$
$548$	−7.97986	−	2.60399i	−0.340883	−	0.111237i
$549$		0			0
$550$	−17.8389	+	12.9435i	−0.760654	+	0.551912i
$551$	−8.04030	+	13.9262i	−0.342528	+	0.593277i
$552$		0			0
$553$	46.0632	−	1.91822i	1.95881	−	0.0815708i
$554$	1.43485	+	13.7354i	0.0609611	+	0.583560i
$555$		0			0
$556$	7.62102	+	8.48558i	0.323203	+	0.359869i
$557$	1.17534	+	2.03574i	0.0498006	+	0.0862572i	0.889851	−	0.456251i	$-0.150808\pi$
$557$	1.17534	+	2.03574i	0.0498006	+	0.0862572i	−0.840051	+	0.542508i	$0.817475\pi$
$558$		0			0
$559$			36.6634i			1.55070i
$560$	−39.7605	−	2.61334i	−1.68019	−	0.110434i
$561$		0			0
$562$	2.43789	+	1.08727i	0.102836	+	0.0458636i
$563$	6.40537	−	3.69814i	0.269954	−	0.155858i	−0.358913	−	0.933371i	$-0.616852\pi$
$563$	6.40537	−	3.69814i	0.269954	−	0.155858i	0.628867	+	0.777513i	$0.283519\pi$
$564$		0			0
$565$	−32.1957	−	18.5882i	−1.35449	−	0.782012i
$566$	9.25211	−	0.966515i	0.388895	−	0.0406257i
$567$		0			0
$568$	−25.3161	+	8.17260i	−1.06224	+	0.342914i
$569$	30.2952	+	17.4909i	1.27004	+	0.733258i	0.974995	−	0.222226i	$-0.0713322\pi$
$569$	30.2952	+	17.4909i	1.27004	+	0.733258i	0.295045	+	0.955483i	$0.404666\pi$
$570$		0			0
$571$	16.4081	+	28.4197i	0.686659	+	1.18933i	0.972912	+	0.231174i	$0.0742567\pi$
$571$	16.4081	+	28.4197i	0.686659	+	1.18933i	−0.286254	+	0.958154i	$0.592410\pi$
$572$	−5.94548	+	18.2198i	−0.248593	+	0.761807i
$573$		0			0
$574$	−22.5992	+	3.31633i	−0.943271	+	0.138421i
$575$	12.0001			0.500437
$576$		0			0
$577$	4.58139	+	7.93520i	0.190726	+	0.330347i	0.945491	−	0.325648i	$-0.105583\pi$
$577$	4.58139	+	7.93520i	0.190726	+	0.330347i	−0.754765	+	0.655995i	$0.772249\pi$
$578$	8.46241	+	11.6630i	0.351990	+	0.485118i
$579$		0			0
$580$	−50.1697	+	10.5975i	−2.08318	+	0.440038i
$581$	16.8438	+	26.5574i	0.698800	+	1.10179i
$582$		0			0
$583$	−1.43823	−	0.830362i	−0.0595653	−	0.0343901i
$584$	4.57447	+	4.13463i	0.189293	+	0.171092i
$585$		0			0
$586$	−8.13991	+	18.2514i	−0.336257	+	0.753960i
$587$			17.4528i			0.720354i	0.932884	+	0.360177i	$0.117284\pi$
$587$			17.4528i			0.720354i	−0.932884	+	0.360177i	$0.882716\pi$
$588$		0			0
$589$			12.9554i			0.533819i
$590$	−37.4760	−	16.7138i	−1.54286	−	0.688098i
$591$		0			0
$592$	14.1694	−	19.3990i	0.582359	−	0.797296i
$593$	17.0385	+	9.83721i	0.699689	+	0.403966i	0.807232	−	0.590235i	$-0.200965\pi$
$593$	17.0385	+	9.83721i	0.699689	+	0.403966i	−0.107542	+	0.994200i	$0.534298\pi$
$594$		0			0
$595$	−13.9241	−	21.9540i	−0.570834	−	0.900025i
$596$	−26.3856	+	5.57352i	−1.08079	+	0.228300i
$597$		0			0
$598$	8.44589	−	6.12813i	0.345378	−	0.250598i
$599$	2.68048	+	4.64273i	0.109521	+	0.189697i	0.915576	−	0.402144i	$-0.131735\pi$
$599$	2.68048	+	4.64273i	0.109521	+	0.189697i	−0.806055	+	0.591841i	$0.798402\pi$
$600$		0			0
$601$	12.4609			0.508291			0.254145	−	0.967166i	$-0.418206\pi$
$601$	12.4609			0.508291			0.254145	+	0.967166i	$0.418206\pi$
$602$	−3.53009	−	24.0558i	−0.143876	−	0.980442i
$603$		0			0
$604$	40.5562	+	13.2343i	1.65021	+	0.538496i
$605$	15.2779	+	26.4621i	0.621135	+	1.07584i
$606$		0			0
$607$	10.6807	+	6.16649i	0.433515	+	0.250290i	0.700843	−	0.713315i	$-0.252807\pi$
$607$	10.6807	+	6.16649i	0.433515	+	0.250290i	−0.267328	+	0.963606i	$0.586141\pi$
$608$	−11.5901	+	6.64273i	−0.470041	+	0.269398i
$609$		0			0
$610$	−4.88363	−	46.7493i	−0.197732	−	1.89282i
$611$	−34.5325	−	19.9373i	−1.39704	−	0.806579i
$612$		0			0
$613$	3.55744	−	2.05389i	0.143683	−	0.0829557i	−0.426435	−	0.904518i	$-0.640231\pi$
$613$	3.55744	−	2.05389i	0.143683	−	0.0829557i	0.570118	+	0.821563i	$0.306897\pi$
$614$	−10.1366	+	22.7284i	−0.409080	+	0.917245i
$615$		0			0
$616$	2.14672	−	12.5269i	0.0864937	−	0.504725i
$617$		−	36.1255i		−	1.45436i	−0.686447	−	0.727180i	$-0.740831\pi$
$617$		−	36.1255i		−	1.45436i	0.686447	−	0.727180i	$-0.259169\pi$
$618$		0			0
$619$	−0.802674	−	1.39027i	−0.0322622	−	0.0558798i	0.849443	−	0.527680i	$-0.176938\pi$
$619$	−0.802674	−	1.39027i	−0.0322622	−	0.0558798i	−0.881706	+	0.471800i	$0.843604\pi$
$620$	−30.7353	+	27.6038i	−1.23436	+	1.10860i
$621$		0			0
$622$	−15.3226	+	1.60066i	−0.614379	+	0.0641807i
$623$	−29.2616	+	1.21855i	−1.17234	+	0.0488201i
$624$		0			0
$625$	−6.66043	+	11.5362i	−0.266417	+	0.461448i
$626$	2.93235	+	4.04141i	0.117200	+	0.161527i
$627$		0			0
$628$	17.5034	+	5.71170i	0.698461	+	0.227922i
$629$	15.6734			0.624940
$630$		0			0
$631$		−	8.98270i		−	0.357596i	−0.983886	−	0.178798i	$-0.942779\pi$
$631$		−	8.98270i		−	0.357596i	0.983886	−	0.178798i	$-0.0572208\pi$
$632$	48.1897	+	10.3387i	1.91688	+	0.411253i
$633$		0			0
$634$	13.4450	+	18.5302i	0.533971	+	0.735927i
$635$	14.7007	+	8.48748i	0.583381	+	0.336815i
$636$		0			0
$637$	−35.7276	−	16.8356i	−1.41558	−	0.667050i
$638$	−1.69931	−	16.2669i	−0.0672764	−	0.644014i
$639$		0			0
$640$	−40.4539	−	13.3427i	−1.59908	−	0.527418i
$641$	−34.1214	+	19.7000i	−1.34772	+	0.778104i	−0.987926	−	0.154929i	$-0.950485\pi$
$641$	−34.1214	+	19.7000i	−1.34772	+	0.778104i	−0.359790	+	0.933033i	$0.617152\pi$
$642$		0			0
$643$	40.0002			1.57745			0.788726	−	0.614745i	$-0.210741\pi$
$643$	40.0002			1.57745			0.788726	+	0.614745i	$0.210741\pi$
$644$	−4.95153	+	4.83403i	−0.195118	+	0.190488i
$645$		0			0
$646$	−7.96001	−	3.55006i	−0.313182	−	0.139675i
$647$	−19.8854	−	34.4425i	−0.781775	−	1.35407i	−0.930907	−	0.365257i	$-0.880981\pi$
$647$	−19.8854	−	34.4425i	−0.781775	−	1.35407i	0.149132	−	0.988817i	$-0.452352\pi$
$648$		0			0
$649$	6.54422	−	11.3349i	0.256883	−	0.444935i
$650$	7.60739	+	72.8229i	0.298386	+	2.85635i
$651$		0			0
$652$	−0.234946	+	0.0496284i	−0.00920118	+	0.00194360i
$653$	1.64003	−	2.84061i	0.0641792	−	0.111162i	−0.832150	−	0.554550i	$-0.812890\pi$
$653$	1.64003	−	2.84061i	0.0641792	−	0.111162i	0.896330	+	0.443388i	$0.146224\pi$
$654$		0			0
$655$	52.9651	−	30.5794i	2.06952	−	1.19484i
$656$	−24.2780	−	2.61388i	−0.947895	−	0.102055i
$657$		0			0
$658$	24.5773	+	9.75650i	0.958124	+	0.380348i
$659$		−	16.7484i		−	0.652425i	−0.945297	−	0.326212i	$-0.894228\pi$
$659$		−	16.7484i		−	0.652425i	0.945297	−	0.326212i	$-0.105772\pi$
$660$		0			0
$661$	4.50164	−	2.59902i	0.175093	−	0.101090i	−0.409892	−	0.912134i	$-0.634434\pi$
$661$	4.50164	−	2.59902i	0.175093	−	0.101090i	0.584985	+	0.811044i	$0.301100\pi$
$662$	−9.63141	−	13.2742i	−0.374335	−	0.515915i
$663$		0			0
$664$	10.3284	+	31.9941i	0.400819	+	1.24161i
$665$	−20.8445	−	10.9044i	−0.808315	−	0.422854i
$666$		0			0
$667$	−4.45251	+	7.71197i	−0.172402	+	0.298609i
$668$	17.3476	+	19.3156i	0.671198	+	0.747341i
$669$		0			0
$670$	29.0548	−	65.1471i	1.12248	−	2.51685i
$671$	14.9925			0.578779
$672$		0			0
$673$	−29.9571			−1.15476			−0.577380	−	0.816475i	$-0.695925\pi$
$673$	−29.9571			−1.15476			−0.577380	+	0.816475i	$0.695925\pi$
$674$	1.61906	−	3.63029i	0.0623640	−	0.139833i
$675$		0			0
$676$	25.1702	+	28.0256i	0.968083	+	1.07791i
$677$	15.2704	−	26.4492i	0.586891	−	1.01652i	−0.407746	−	0.913095i	$-0.633685\pi$
$677$	15.2704	−	26.4492i	0.586891	−	1.01652i	0.994637	−	0.103429i	$-0.0329816\pi$
$678$		0			0
$679$	−33.6550	+	21.3454i	−1.29156	+	0.819162i
$680$	−8.53807	−	26.4483i	−0.327420	−	1.01425i
$681$		0			0
$682$	−7.73841	−	10.6652i	−0.296319	−	0.408391i
$683$	−11.1942	+	6.46296i	−0.428333	+	0.247298i	−0.698636	−	0.715477i	$-0.746209\pi$
$683$	−11.1942	+	6.46296i	−0.428333	+	0.247298i	0.270303	+	0.962775i	$0.412876\pi$
$684$		0			0
$685$		−	15.8022i		−	0.603770i
$686$	25.0628	+	7.60629i	0.956902	+	0.290409i
$687$		0			0
$688$	2.78237	−	25.8428i	0.106077	−	0.985249i
$689$	−4.77795	+	2.75855i	−0.182025	+	0.105092i
$690$		0			0
$691$	−8.33676	+	14.4397i	−0.317145	+	0.549312i	−0.979891	−	0.199533i	$-0.936058\pi$
$691$	−8.33676	+	14.4397i	−0.317145	+	0.549312i	0.662746	+	0.748844i	$0.269391\pi$
$692$	13.4808	−	2.84761i	0.512464	−	0.108250i
$693$		0			0
$694$	−3.18774	−	30.5151i	−0.121005	−	1.15834i
$695$	−10.7358	+	18.5949i	−0.407231	+	0.705344i
$696$		0			0
$697$	−7.96571	−	13.7970i	−0.301723	−	0.522599i
$698$	−9.61539	−	4.28834i	−0.363948	−	0.162316i
$699$		0			0
$700$	−12.0031	−	47.0486i	−0.453674	−	1.77827i
$701$	24.5914			0.928805			0.464403	−	0.885624i	$-0.346269\pi$
$701$	24.5914			0.928805			0.464403	+	0.885624i	$0.346269\pi$
$702$		0			0
$703$	12.2825	−	7.09128i	0.463242	−	0.267453i
$704$	5.57347	−	12.3913i	0.210058	−	0.467016i
$705$		0			0
$706$	2.21186	+	21.1734i	0.0832444	+	0.796870i
$707$	−3.64733	−	1.90803i	−0.137172	−	0.0717587i
$708$		0			0
$709$	−4.59843	−	2.65490i	−0.172698	−	0.0997070i	0.411160	−	0.911563i	$-0.365124\pi$
$709$	−4.59843	−	2.65490i	−0.172698	−	0.0997070i	−0.583857	+	0.811856i	$0.698457\pi$
$710$	−29.4112	−	40.5350i	−1.10378	−	1.52125i
$711$		0			0
$712$	−30.6125	−	6.56768i	−1.14725	−	0.246134i
$713$			7.17437i			0.268682i
$714$		0			0
$715$	−36.0799			−1.34931
$716$	29.8678	+	9.74646i	1.11621	+	0.364242i
$717$		0			0
$718$	−14.9807	−	20.6466i	−0.559075	−	0.770525i
$719$	5.16456	−	8.94528i	0.192606	−	0.333603i	−0.753507	−	0.657439i	$-0.771640\pi$
$719$	5.16456	−	8.94528i	0.192606	−	0.333603i	0.946113	+	0.323837i	$0.104973\pi$
$720$		0			0
$721$	−21.1857	+	0.882240i	−0.788997	+	0.0328563i
$722$	18.8806	−	1.97235i	0.702663	−	0.0734031i
$723$		0			0
$724$	−23.3188	+	20.9429i	−0.866636	+	0.778338i
$725$	−31.2422	−	54.1131i	−1.16031	−	2.00971i
$726$		0			0
$727$			28.6727i			1.06341i	0.846929	+	0.531706i	$0.178449\pi$
$727$			28.6727i			1.06341i	−0.846929	+	0.531706i	$0.821551\pi$
$728$	−32.4746	−	26.9841i	−1.20359	−	1.00010i
$729$		0			0
$730$	−4.72815	+	10.6015i	−0.174997	+	0.392380i
$731$	14.6863	−	8.47916i	0.543193	−	0.313613i
$732$		0			0
$733$	33.6091	+	19.4042i	1.24138	+	0.716710i	0.969375	−	0.245586i	$-0.0789803\pi$
$733$	33.6091	+	19.4042i	1.24138	+	0.716710i	0.272004	+	0.962296i	$0.412314\pi$
$734$	0.574993	+	5.50421i	0.0212234	+	0.203164i
$735$		0			0
$736$	−6.41830	+	3.67857i	−0.236582	+	0.135594i
$737$	19.7042	+	11.3763i	0.725815	+	0.419050i
$738$		0			0
$739$	−5.59773	−	9.69556i	−0.205916	−	0.356657i	0.744508	−	0.667613i	$-0.232684\pi$
$739$	−5.59773	−	9.69556i	−0.205916	−	0.356657i	−0.950424	+	0.310956i	$0.899351\pi$
$740$	42.9932	+	14.0295i	1.58046	+	0.515736i
$741$		0			0
$742$	2.86934	−	2.27000i	0.105337	−	0.0833343i
$743$	6.68201			0.245139			0.122570	−	0.992460i	$-0.460887\pi$
$743$	6.68201			0.245139			0.122570	+	0.992460i	$0.460887\pi$
$744$		0			0
$745$	−25.3843	−	43.9668i	−0.930007	−	1.61082i
$746$	20.9511	−	15.2016i	0.767076	−	0.556572i
$747$		0			0
$748$	8.67335	−	1.83210i	0.317129	−	0.0669883i
$749$	−38.5387	+	1.60487i	−1.40817	+	0.0586407i
$750$		0			0
$751$	−43.2883	−	24.9925i	−1.57961	−	0.911990i	−0.994913	−	0.100741i	$-0.967879\pi$
$751$	−43.2883	−	24.9925i	−1.57961	−	0.911990i	−0.584701	−	0.811249i	$-0.698788\pi$
$752$	22.8278	+	16.6738i	0.832444	+	0.608032i
$753$		0			0
$754$	−49.6231	−	22.1313i	−1.80717	−	0.805973i
$755$			80.3117i			2.92284i
$756$		0			0
$757$			32.8378i			1.19351i	0.802424	+	0.596755i	$0.203543\pi$
$757$			32.8378i			1.19351i	−0.802424	+	0.596755i	$0.796457\pi$
$758$	14.8658	−	33.3323i	0.539949	−	1.21068i
$759$		0			0
$760$	−18.6571	−	16.8632i	−0.676765	−	0.611693i
$761$	−28.7157	−	16.5790i	−1.04094	−	0.600988i	−0.120842	−	0.992672i	$-0.538560\pi$
$761$	−28.7157	−	16.5790i	−1.04094	−	0.600988i	−0.920100	+	0.391683i	$0.871893\pi$
$762$		0			0
$763$	0.927825	−	1.77360i	0.0335895	−	0.0642088i
$764$	47.2116	−	9.97268i	1.70806	−	0.360799i
$765$		0			0
$766$	−12.2530	−	16.8873i	−0.442721	−	0.610165i
$767$	−21.7406	−	37.6559i	−0.785008	−	1.35967i
$768$		0			0
$769$	−48.1183			−1.73519			−0.867596	−	0.497270i	$-0.834336\pi$
$769$	−48.1183			−1.73519			−0.867596	+	0.497270i	$0.834336\pi$
$770$	23.6730	−	3.47391i	0.853114	−	0.125191i
$771$		0			0
$772$	−5.96004	+	18.2644i	−0.214506	+	0.657350i
$773$	−14.2293	−	24.6458i	−0.511791	−	0.886449i	−0.999907	−	0.0136695i	$-0.995649\pi$
$773$	−14.2293	−	24.6458i	−0.511791	−	0.886449i	0.488115	−	0.872779i	$-0.337685\pi$
$774$		0			0
$775$	−43.5965	−	25.1704i	−1.56603	−	0.904148i
$776$	−40.5447	+	13.0887i	−1.45547	+	0.469857i
$777$		0			0
$778$	−24.4816	+	2.55745i	−0.877707	+	0.0916890i
$779$	−12.4847	−	7.20802i	−0.447309	−	0.258254i
$780$		0			0
$781$	13.8339	−	7.98703i	0.495017	−	0.285798i
$782$	−4.40804	−	1.96593i	−0.157631	−	0.0703016i
$783$		0			0
$784$	23.9056	+	14.5782i	0.853770	+	0.520650i
$785$			34.6612i			1.23711i
$786$		0			0
$787$	−11.0597	−	19.1559i	−0.394234	−	0.682834i	0.598769	−	0.800922i	$-0.295657\pi$
$787$	−11.0597	−	19.1559i	−0.394234	−	0.682834i	−0.993003	+	0.118088i	$0.962323\pi$
$788$	−2.74366	−	3.05491i	−0.0977388	−	0.108827i
$789$		0			0
$790$	9.64020	+	92.2823i	0.342983	+	3.28326i
$791$	13.9920	+	22.0609i	0.497497	+	0.784395i
$792$		0			0
$793$	24.9033	−	43.1339i	0.884344	−	1.53173i
$794$	13.2533	−	9.61629i	0.470343	−	0.341270i
$795$		0			0
$796$	−18.9272	−	6.17631i	−0.670856	−	0.218914i
$797$	−25.7820			−0.913247			−0.456623	−	0.889660i	$-0.650941\pi$
$797$	−25.7820			−0.913247			−0.456623	+	0.889660i	$0.650941\pi$
$798$		0			0
$799$			18.4437i			0.652490i
$800$	0.164293	−	51.9078i	0.00580864	−	1.83522i
$801$		0			0
$802$	41.1656	−	29.8688i	1.45361	−	1.05470i
$803$	−3.20652	−	1.85128i	−0.113156	−	0.0653304i
$804$		0			0
$805$	−11.5431	−	6.03856i	−0.406842	−	0.212831i
$806$	−43.5380	+	4.54816i	−1.53356	+	0.160202i
$807$		0			0
$808$	−3.26458	−	2.95069i	−0.114848	−	0.103805i
$809$	−2.56573	+	1.48132i	−0.0902062	+	0.0520806i	−0.544425	−	0.838810i	$-0.683252\pi$
$809$	−2.56573	+	1.48132i	−0.0902062	+	0.0520806i	0.454218	+	0.890890i	$0.349919\pi$
$810$		0			0
$811$	−51.9174			−1.82307			−0.911533	−	0.411228i	$-0.865100\pi$
$811$	−51.9174			−1.82307			−0.911533	+	0.411228i	$0.865100\pi$
$812$	34.6899	+	9.74302i	1.21738	+	0.341913i
$813$		0			0
$814$	−5.87550	+	13.1741i	−0.205936	+	0.461754i
$815$	−0.226030	−	0.391495i	−0.00791747	−	0.0137135i
$816$		0			0
$817$	7.67262	−	13.2894i	0.268431	−	0.464936i
$818$	34.2118	−	3.57391i	1.19619	−	0.124959i
$819$		0			0
$820$	−9.50053	−	44.9764i	−0.331773	−	1.57064i
$821$	−10.7741	+	18.6612i	−0.376017	+	0.651281i	−0.990479	−	0.137666i	$-0.956040\pi$
$821$	−10.7741	+	18.6612i	−0.376017	+	0.651281i	0.614462	+	0.788947i	$0.289373\pi$
$822$		0			0
$823$	−30.0162	+	17.3299i	−1.04630	+	0.604082i	−0.921611	−	0.388114i	$-0.873127\pi$
$823$	−30.0162	+	17.3299i	−1.04630	+	0.604082i	−0.124689	+	0.992196i	$0.539793\pi$
$824$	−22.1638	−	4.75506i	−0.772111	−	0.165650i
$825$		0			0
$826$	17.8903	+	22.6137i	0.622481	+	0.786833i
$827$			40.6029i			1.41190i	0.708260	+	0.705951i	$0.249480\pi$
$827$			40.6029i			1.41190i	−0.708260	+	0.705951i	$0.750520\pi$
$828$		0			0
$829$	28.2837	−	16.3296i	0.982334	−	0.567151i	0.0793604	−	0.996846i	$-0.474712\pi$
$829$	28.2837	−	16.3296i	0.982334	−	0.567151i	0.902974	+	0.429695i	$0.141379\pi$
$830$	−51.2275	+	37.1694i	−1.77813	+	1.29017i
$831$		0			0
$832$	−26.3924	−	36.6177i	−0.914992	−	1.26949i
$833$	1.51886	+	18.2050i	0.0526256	+	0.630767i
$834$		0			0
$835$	−24.4376	+	42.3271i	−0.845697	+	1.46479i
$836$	5.96795	−	5.35990i	0.206406	−	0.185376i
$837$		0			0
$838$	−8.95008	−	3.99162i	−0.309175	−	0.137888i
$839$	35.4704			1.22458			0.612288	−	0.790635i	$-0.290249\pi$
$839$	35.4704			1.22458			0.612288	+	0.790635i	$0.290249\pi$
$840$		0			0
$841$	17.3685			0.598913
$842$	−16.2988	−	7.26906i	−0.561694	−	0.250508i
$843$		0			0
$844$	18.6768	+	20.7956i	0.642884	+	0.715815i
$845$	−35.4573	+	61.4138i	−1.21977	+	2.11270i
$846$		0			0
$847$	−0.893370	−	21.4530i	−0.0306965	−	0.737133i
$848$	3.57717	−	1.58182i	0.122840	−	0.0543198i
$849$		0			0
$850$	27.4115	−	19.8891i	0.940205	−	0.682190i
$851$	6.80170	−	3.92697i	0.233159	−	0.134615i
$852$		0			0
$853$		−	2.87597i		−	0.0984714i	−0.998787	−	0.0492357i	$-0.984321\pi$
$853$		−	2.87597i		−	0.0984714i	0.998787	−	0.0492357i	$-0.0156786\pi$
$854$	−12.1867	+	30.6991i	−0.417019	+	1.05050i
$855$		0			0
$856$	−40.3178	−	8.64987i	−1.37803	−	0.295647i
$857$	−5.76468	+	3.32824i	−0.196918	+	0.113691i	−0.595217	−	0.803565i	$-0.702934\pi$
$857$	−5.76468	+	3.32824i	−0.196918	+	0.113691i	0.398299	+	0.917256i	$0.369601\pi$
$858$		0			0
$859$	10.2685	−	17.7855i	0.350355	−	0.606833i	−0.635956	−	0.771725i	$-0.719394\pi$
$859$	10.2685	−	17.7855i	0.350355	−	0.606833i	0.986312	+	0.164892i	$0.0527276\pi$
$860$	47.8754	−	10.1129i	1.63254	−	0.344847i
$861$		0			0
$862$	31.4390	−	3.28425i	1.07082	−	0.111862i
$863$	−15.7546	+	27.2877i	−0.536292	+	0.928886i	0.462807	+	0.886459i	$0.346842\pi$
$863$	−15.7546	+	27.2877i	−0.536292	+	0.928886i	−0.999100	+	0.0424266i	$0.986491\pi$
$864$		0			0
$865$	12.9692	+	22.4634i	0.440968	+	0.763778i
$866$	−18.5950	+	41.6940i	−0.631884	+	1.41682i
$867$		0			0
$868$	28.1285	−	7.17618i	0.954744	−	0.243575i
$869$	−29.5949			−1.00394
$870$		0			0
$871$	65.4596	−	37.7931i	2.21801	−	1.28057i
$872$	1.43485	−	1.58749i	0.0485900	−	0.0537590i
$873$		0			0
$874$	−4.34383	+	0.453775i	−0.146932	+	0.0153492i
$875$	35.1308	−	22.2815i	1.18764	−	0.753251i
$876$		0			0
$877$	48.3067	+	27.8899i	1.63120	+	0.941774i	0.983723	+	0.179689i	$0.0575091\pi$
$877$	48.3067	+	27.8899i	1.63120	+	0.941774i	0.647477	+	0.762085i	$0.275824\pi$
$878$	−3.20913	+	2.32847i	−0.108303	+	0.0785819i
$879$		0			0
$880$	25.4315	+	2.73808i	0.857297	+	0.0923008i
$881$		−	21.9485i		−	0.739464i	−0.929138	−	0.369732i	$-0.879450\pi$
$881$		−	21.9485i		−	0.739464i	0.929138	−	0.369732i	$-0.120550\pi$
$882$		0			0
$883$	33.4287			1.12497			0.562483	−	0.826809i	$-0.309846\pi$
$883$	33.4287			1.12497			0.562483	+	0.826809i	$0.309846\pi$
$884$	9.13589	−	27.9967i	0.307273	−	0.941631i
$885$		0			0
$886$	−21.4207	+	15.5423i	−0.719643	+	0.522155i
$887$	−6.18309	+	10.7094i	−0.207608	+	0.359587i	−0.950960	−	0.309313i	$-0.899901\pi$
$887$	−6.18309	+	10.7094i	−0.207608	+	0.359587i	0.743353	+	0.668900i	$0.233234\pi$
$888$		0			0
$889$	−6.38880	−	10.0731i	−0.214273	−	0.337841i
$890$	−6.12394	−	58.6223i	−0.205275	−	1.96502i
$891$		0			0
$892$	23.6317	−	21.2240i	0.791248	−	0.710631i
$893$	8.34466	+	14.4534i	0.279243	+	0.483664i
$894$		0			0
$895$			59.1460i			1.97703i
$896$	20.8425	+	21.4847i	0.696298	+	0.717753i
$897$		0			0
$898$	−17.9466	−	8.00396i	−0.598886	−	0.267096i
$899$	32.3521	−	18.6785i	1.07900	−	0.622963i
$900$		0			0
$901$	2.21000	+	1.27594i	0.0736257	+	0.0425078i
$902$	14.5831	−	1.52341i	0.485563	−	0.0507240i
$903$		0			0
$904$	8.57965	+	26.5771i	0.285355	+	0.883941i
$905$	−51.0996	−	29.5024i	−1.69861	−	0.980692i
$906$		0			0
$907$	−6.85914	−	11.8804i	−0.227754	−	0.394481i	0.729388	−	0.684100i	$-0.239805\pi$
$907$	−6.85914	−	11.8804i	−0.227754	−	0.394481i	−0.957142	+	0.289619i	$0.906471\pi$
$908$	1.36132	+	0.444225i	0.0451769	+	0.0147421i
$909$		0			0
$910$	29.3275	−	73.8782i	0.972198	−	2.44904i
$911$	9.02706			0.299080			0.149540	−	0.988756i	$-0.452221\pi$
$911$	9.02706			0.299080			0.149540	+	0.988756i	$0.452221\pi$
$912$		0			0
$913$	−10.0939	−	17.4831i	−0.334058	−	0.578606i
$914$	−4.79917	−	6.61429i	−0.158742	−	0.218781i
$915$		0			0
$916$	−1.86102	−	8.81025i	−0.0614899	−	0.291099i
$917$	−42.9391	+	1.78812i	−1.41797	+	0.0590489i
$918$		0			0
$919$	37.8104	+	21.8298i	1.24725	+	0.720100i	0.970560	−	0.240860i	$-0.0774294\pi$
$919$	37.8104	+	21.8298i	1.24725	+	0.720100i	0.276689	+	0.960959i	$0.410763\pi$
$920$	−10.3318	−	9.33840i	−0.340630	−	0.307878i
$921$		0			0
$922$	8.88367	−	19.9191i	0.292568	−	0.656001i
$923$		−	53.0675i		−	1.74674i
$924$		0			0
$925$			55.1092i			1.81198i
$926$	−14.9698	−	6.67633i	−0.491937	−	0.219398i
$927$		0			0
$928$	33.2982	+	19.3655i	1.09307	+	0.635703i
$929$	−43.0944	−	24.8806i	−1.41388	−	0.816304i	−0.418129	−	0.908387i	$-0.637314\pi$
$929$	−43.0944	−	24.8806i	−1.41388	−	0.816304i	−0.995751	+	0.0920830i	$0.970647\pi$
$930$		0			0
$931$	9.42695	+	13.5792i	0.308956	+	0.445039i
$932$	3.19596	+	15.1300i	0.104687	+	0.495599i
$933$		0			0
$934$	2.61904	−	1.90031i	0.0856977	−	0.0621802i
$935$	8.34421	+	14.4526i	0.272885	+	0.472650i
$936$		0			0
$937$	40.5415			1.32443			0.662216	−	0.749313i	$-0.269616\pi$
$937$	40.5415			1.32443			0.662216	+	0.749313i	$0.269616\pi$
$938$	−39.3109	+	31.0998i	−1.28355	+	1.01544i
$939$		0			0
$940$	−16.5093	+	50.5922i	−0.538472	+	1.65014i
$941$	27.1914	+	47.0968i	0.886414	+	1.53531i	0.844085	+	0.536209i	$0.180144\pi$
$941$	27.1914	+	47.0968i	0.886414	+	1.53531i	0.0423286	+	0.999104i	$0.486522\pi$
$942$		0			0
$943$	−6.91367	−	3.99161i	−0.225140	−	0.129985i
$944$	12.4666	+	28.1923i	0.405752	+	0.917581i
$945$		0			0
$946$	1.62160	+	15.5230i	0.0527229	+	0.504698i
$947$	12.3501	+	7.13032i	0.401323	+	0.231704i	0.687055	−	0.726606i	$-0.258903\pi$
$947$	12.3501	+	7.13032i	0.401323	+	0.231704i	−0.285732	+	0.958310i	$0.592237\pi$
$948$		0			0
$949$	−10.6524	+	6.15016i	−0.345791	+	0.199643i
$950$	12.4823	−	27.9881i	0.404981	−	0.908055i
$951$		0			0
$952$	−3.29867	+	19.2490i	−0.106910	+	0.623865i
$953$			3.31610i			0.107419i	0.998557	+	0.0537095i	$0.0171045\pi$
$953$			3.31610i			0.107419i	−0.998557	+	0.0537095i	$0.982896\pi$
$954$		0			0
$955$	45.4200	+	78.6697i	1.46976	+	2.54569i
$956$	28.5702	+	31.8113i	0.924026	+	1.02885i
$957$		0			0
$958$	−26.5263	+	2.77105i	−0.857025	+	0.0895285i
$959$	−5.14717	+	9.83919i	−0.166211	+	0.317724i
$960$		0			0
$961$	−0.451578	+	0.782157i	−0.0145670	+	0.0252309i
$962$	28.1429	+	38.7870i	0.907363	+	1.25054i
$963$		0			0
$964$	5.28229	−	16.1875i	0.170131	−	0.521363i
$965$	−36.1682			−1.16430
$966$		0			0
$967$		−	18.6637i		−	0.600185i	−0.953910	−	0.300092i	$-0.902982\pi$
$967$		−	18.6637i		−	0.600185i	0.953910	−	0.300092i	$-0.0970175\pi$
$968$	4.81505	−	22.4434i	0.154762	−	0.721357i
$969$		0			0
$970$	−47.1031	−	64.9182i	−1.51239	−	2.08440i
$971$	−4.93811	−	2.85102i	−0.158472	−	0.0914936i	0.418667	−	0.908140i	$-0.362497\pi$
$971$	−4.93811	−	2.85102i	−0.158472	−	0.0914936i	−0.577139	+	0.816646i	$0.695831\pi$
$972$		0			0
$973$	12.7414	−	8.08115i	0.408471	−	0.259070i
$974$	4.56434	+	43.6928i	0.146251	+	1.40001i
$975$		0			0
$976$	−20.8270	+	28.5138i	−0.666655	+	0.912703i
$977$	3.52730	−	2.03649i	0.112848	−	0.0651530i	−0.442514	−	0.896762i	$-0.645913\pi$
$977$	3.52730	−	2.03649i	0.112848	−	0.0651530i	0.555362	+	0.831609i	$0.312580\pi$
$978$		0			0
$979$	18.8002			0.600856
$980$	−12.1293	+	51.2972i	−0.387456	+	1.63863i
$981$		0			0
$982$	9.72496	+	4.33721i	0.310336	+	0.138406i
$983$	−13.6318	−	23.6109i	−0.434786	−	0.753071i	0.562492	−	0.826803i	$-0.309843\pi$
$983$	−13.6318	−	23.6109i	−0.434786	−	0.753071i	−0.997278	+	0.0737313i	$0.976509\pi$
$984$		0			0
$985$	3.86500	−	6.69438i	0.123149	−	0.213301i
$986$	2.61118	+	24.9959i	0.0831570	+	0.796033i
$987$		0			0
$988$	−5.50750	−	26.0730i	−0.175217	−	0.829494i
$989$	4.24890	−	7.35930i	0.135107	−	0.234012i
$990$		0			0
$991$	7.91978	−	4.57249i	0.251580	−	0.145250i	−0.368907	−	0.929466i	$-0.620268\pi$
$991$	7.91978	−	4.57249i	0.251580	−	0.145250i	0.620488	+	0.784216i	$0.286935\pi$
$992$	31.0337	+	0.0982246i	0.985320	+	0.00311863i
$993$		0			0
$994$	5.10955	+	34.8190i	0.162065	+	1.10439i
$995$		−	37.4807i		−	1.18822i
$996$		0			0
$997$	−40.5025	+	23.3841i	−1.28273	+	0.740583i	−0.977346	−	0.211647i	$-0.932117\pi$
$997$	−40.5025	+	23.3841i	−1.28273	+	0.740583i	−0.305381	+	0.952230i	$0.598784\pi$
$998$	1.46718	+	2.02208i	0.0464426	+	0.0640080i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.15	yes	48
3.2	odd	2	inner	504.2.bm.c.107.10	yes	48
4.3	odd	2		2016.2.bu.c.1871.24		48
7.4	even	3	inner	504.2.bm.c.179.17	yes	48
8.3	odd	2	inner	504.2.bm.c.107.8	✓	48
8.5	even	2		2016.2.bu.c.1871.2		48
12.11	even	2		2016.2.bu.c.1871.1		48
21.11	odd	6	inner	504.2.bm.c.179.8	yes	48
24.5	odd	2		2016.2.bu.c.1871.23		48
24.11	even	2	inner	504.2.bm.c.107.17	yes	48
28.11	odd	6		2016.2.bu.c.431.23		48
56.11	odd	6	inner	504.2.bm.c.179.10	yes	48
56.53	even	6		2016.2.bu.c.431.1		48
84.11	even	6		2016.2.bu.c.431.2		48
168.11	even	6	inner	504.2.bm.c.179.15	yes	48
168.53	odd	6		2016.2.bu.c.431.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.8	✓	48	8.3	odd	2	inner
504.2.bm.c.107.10	yes	48	3.2	odd	2	inner
504.2.bm.c.107.15	yes	48	1.1	even	1	trivial
504.2.bm.c.107.17	yes	48	24.11	even	2	inner
504.2.bm.c.179.8	yes	48	21.11	odd	6	inner
504.2.bm.c.179.10	yes	48	56.11	odd	6	inner
504.2.bm.c.179.15	yes	48	168.11	even	6	inner
504.2.bm.c.179.17	yes	48	7.4	even	3	inner
2016.2.bu.c.431.1		48	56.53	even	6
2016.2.bu.c.431.2		48	84.11	even	6
2016.2.bu.c.431.23		48	28.11	odd	6
2016.2.bu.c.431.24		48	168.53	odd	6
2016.2.bu.c.1871.1		48	12.11	even	2
2016.2.bu.c.1871.2		48	8.5	even	2
2016.2.bu.c.1871.23		48	24.5	odd	2
2016.2.bu.c.1871.24		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.576030 - 1.29158i) q^{2} +(-1.33638 - 1.48798i) q^{4} +(1.88256 - 3.26069i) q^{5} +(-2.23426 + 1.41706i) q^{7} +(-2.69165 + 0.868922i) q^{8} +(-3.12704 - 4.30974i) q^{10} +(1.47084 - 0.849192i) q^{11} -5.64222i q^{13} +(0.543254 + 3.70201i) q^{14} +(-0.428185 + 3.97702i) q^{16} +(-2.26012 + 1.30488i) q^{17} +(-1.18076 + 2.04513i) q^{19} +(-7.36767 + 1.55630i) q^{20} +(-0.249553 - 2.38888i) q^{22} +(-0.653873 + 1.13254i) q^{23} +(-4.58807 - 7.94677i) q^{25} +(-7.28740 - 3.25009i) q^{26} +(5.09439 + 1.43081i) q^{28} +6.80944 q^{29} +(4.75107 - 2.74303i) q^{31} +(4.89000 + 2.84392i) q^{32} +(0.383465 + 3.67078i) q^{34} +(0.414472 + 9.95295i) q^{35} +(-5.20109 - 3.00285i) q^{37} +(1.96131 + 2.70311i) q^{38} +(-2.23391 + 10.4124i) q^{40} +6.10456i q^{41} -6.49804 q^{43} +(-3.22919 - 1.05375i) q^{44} +(1.08612 + 1.49691i) q^{46} +(3.53360 - 6.12038i) q^{47} +(2.98386 - 6.33219i) q^{49} +(-12.9068 + 1.34830i) q^{50} +(-8.39552 + 7.54014i) q^{52} +(-0.488913 - 0.846821i) q^{53} -6.39462i q^{55} +(4.78253 - 5.75564i) q^{56} +(3.92244 - 8.79496i) q^{58} +(6.67395 - 3.85320i) q^{59} +(7.64484 + 4.41375i) q^{61} +(-0.806095 - 7.71647i) q^{62} +(6.48995 - 4.67767i) q^{64} +(-18.3975 - 10.6218i) q^{65} +(6.69828 + 11.6018i) q^{67} +(4.96201 + 1.61920i) q^{68} +(13.0938 + 5.19787i) q^{70} +9.40544 q^{71} +(-1.09003 - 1.88798i) q^{73} +(-6.87442 + 4.98791i) q^{74} +(4.62106 - 0.976124i) q^{76} +(-2.08289 + 3.98160i) q^{77} +(-15.0908 - 8.71267i) q^{79} +(12.1617 + 8.88315i) q^{80} +(7.88456 + 3.51641i) q^{82} -11.8864i q^{83} +9.82605i q^{85} +(-3.74307 + 8.39277i) q^{86} +(-3.22111 + 3.56378i) q^{88} +(9.58642 + 5.53472i) q^{89} +(7.99538 + 12.6062i) q^{91} +(2.55902 - 0.540552i) q^{92} +(-5.86952 - 8.08946i) q^{94} +(4.44570 + 7.70018i) q^{95} +15.0631 q^{97} +(-6.45976 - 7.50144i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82}+ \cdots + 240 q^{97}+O(q^{100}) \) 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Introduction

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