LMFDB - Embedded newform 504.2.bm.c.179.17

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			179.17
Character	$\chi$	$=$	504.179
Dual form			504.2.bm.c.107.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.830529 + 1.14465i) q^{2} +(-0.620442 + 1.90133i) q^{4} +(1.88256 + 3.26069i) q^{5} +(2.23426 + 1.41706i) q^{7} +(-2.69165 + 0.868922i) q^{8} +(-2.16882 + 4.86297i) q^{10} +(-1.47084 - 0.849192i) q^{11} -5.64222i q^{13} +(0.233580 + 3.73436i) q^{14} +(-3.23010 - 2.35933i) q^{16} +(2.26012 + 1.30488i) q^{17} +(-1.18076 - 2.04513i) q^{19} +(-7.36767 + 1.55630i) q^{20} +(-0.249553 - 2.38888i) q^{22} +(-0.653873 - 1.13254i) q^{23} +(-4.58807 + 7.94677i) q^{25} +(6.45836 - 4.68603i) q^{26} +(-4.08053 + 3.36886i) q^{28} +6.80944 q^{29} +(-4.75107 - 2.74303i) q^{31} +(0.0179044 - 5.65683i) q^{32} +(0.383465 + 3.67078i) q^{34} +(-0.414472 + 9.95295i) q^{35} +(5.20109 - 3.00285i) q^{37} +(1.36030 - 3.05010i) q^{38} +(-7.90048 - 7.14084i) q^{40} +6.10456i q^{41} -6.49804 q^{43} +(2.52717 - 2.26968i) q^{44} +(0.753301 - 1.68906i) q^{46} +(3.53360 + 6.12038i) q^{47} +(2.98386 + 6.33219i) q^{49} +(-12.9068 + 1.34830i) q^{50} +(10.7277 + 3.50067i) q^{52} +(-0.488913 + 0.846821i) q^{53} -6.39462i q^{55} +(-7.24517 - 1.87284i) q^{56} +(5.65544 + 7.79442i) q^{58} +(-6.67395 - 3.85320i) q^{59} +(-7.64484 + 4.41375i) q^{61} +(-0.806095 - 7.71647i) q^{62} +(6.48995 - 4.67767i) q^{64} +(18.3975 - 10.6218i) q^{65} +(6.69828 - 11.6018i) q^{67} +(-3.88327 + 3.48762i) q^{68} +(-11.7369 + 7.79179i) q^{70} +9.40544 q^{71} +(-1.09003 + 1.88798i) q^{73} +(7.75687 + 3.45947i) q^{74} +(4.62106 - 0.976124i) q^{76} +(-2.08289 - 3.98160i) q^{77} +(15.0908 - 8.71267i) q^{79} +(1.61217 - 14.9739i) q^{80} +(-6.98758 + 5.07002i) q^{82} -11.8864i q^{83} +9.82605i q^{85} +(-5.39682 - 7.43798i) q^{86} +(4.69688 + 1.00768i) q^{88} +(-9.58642 + 5.53472i) q^{89} +(7.99538 - 12.6062i) q^{91} +(2.55902 - 0.540552i) q^{92} +(-4.07092 + 9.12788i) q^{94} +(4.44570 - 7.70018i) q^{95} +15.0631 q^{97} +(-4.76995 + 8.67454i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	0.830529	+	1.14465i	0.587273	+	0.809389i
$2$	0.830529	+	1.14465i	0.587273	+	0.809389i
$3$		0			0
$3$		0			0
$4$	−0.620442	+	1.90133i	−0.310221	+	0.950665i
$5$	1.88256	+	3.26069i	0.841907	+	1.45823i	0.888281	+	0.459301i	$0.151900\pi$
$5$	1.88256	+	3.26069i	0.841907	+	1.45823i	−0.0463738	+	0.998924i	$0.514767\pi$
$6$		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
$10$	−2.16882	+	4.86297i	−0.685842	+	1.53781i
$11$	−1.47084	−	0.849192i	−0.443476	−	0.256041i	0.261595	−	0.965178i	$-0.415752\pi$
$11$	−1.47084	−	0.849192i	−0.443476	−	0.256041i	−0.705071	+	0.709137i	$0.749085\pi$
$12$		0			0
$13$		−	5.64222i		−	1.56487i	−0.622733	−	0.782435i	$-0.713978\pi$
$13$		−	5.64222i		−	1.56487i	0.622733	−	0.782435i	$-0.286022\pi$
$14$	0.233580	+	3.73436i	0.0624270	+	0.998050i
$15$		0			0
$16$	−3.23010	−	2.35933i	−0.807526	−	0.589832i
$17$	2.26012	+	1.30488i	0.548158	+	0.316479i	0.748379	−	0.663271i	$-0.230833\pi$
$17$	2.26012	+	1.30488i	0.548158	+	0.316479i	−0.200220	+	0.979751i	$0.564166\pi$
$18$		0			0
$19$	−1.18076	−	2.04513i	−0.270885	−	0.469186i	0.698204	−	0.715899i	$-0.253983\pi$
$19$	−1.18076	−	2.04513i	−0.270885	−	0.469186i	−0.969089	+	0.246713i	$0.920649\pi$
$20$	−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	0.789767	−	0.613406i	$-0.210201\pi$
$23$	−0.653873	−	1.13254i	−0.136342	−	0.236151i	−0.926109	+	0.377255i	$0.876868\pi$
$24$		0			0
$25$	−4.58807	+	7.94677i	−0.917614	+	1.58935i
$26$	6.45836	−	4.68603i	1.26659	−	0.919006i
$27$		0			0
$28$	−4.08053	+	3.36886i	−0.771149	+	0.636655i
$29$	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	$-0.497310\pi$
$31$	−4.75107	−	2.74303i	−0.853317	−	0.492663i	−0.861769	+	0.507302i	$0.830643\pi$
$32$	0.0179044	−	5.65683i	0.00316508	−	0.999995i
$33$		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	$-0.502323\pi$
$37$	5.20109	−	3.00285i	0.855054	−	0.493666i	0.862353	+	0.506308i	$0.168990\pi$
$38$	1.36030	−	3.05010i	0.220671	−	0.494791i
$39$		0			0
$40$	−7.90048	−	7.14084i	−1.24918	−	1.12907i
$41$			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	$0.665005\pi$
$44$	2.52717	−	2.26968i	0.380985	−	0.342168i
$45$		0			0
$46$	0.753301	−	1.68906i	0.111068	−	0.249039i
$47$	3.53360	+	6.12038i	0.515429	+	0.892749i	0.999840	+	0.0179081i	$0.00570062\pi$
$47$	3.53360	+	6.12038i	0.515429	+	0.892749i	−0.484411	+	0.874841i	$0.660966\pi$
$48$		0			0
$49$	2.98386	+	6.33219i	0.426266	+	0.904598i
$50$	−12.9068	+	1.34830i	−1.82530	+	0.190678i
$51$		0			0
$52$	10.7277	+	3.50067i	1.48767	+	0.485455i
$53$	−0.488913	+	0.846821i	−0.0671573	+	0.116320i	−0.897649	−	0.440711i	$-0.854726\pi$
$53$	−0.488913	+	0.846821i	−0.0671573	+	0.116320i	0.830492	+	0.557031i	$0.188060\pi$
$54$		0			0
$55$		−	6.39462i		−	0.862251i
$56$	−7.24517	−	1.87284i	−0.968176	−	0.250269i
$57$		0			0
$58$	5.65544	+	7.79442i	0.742596	+	1.02346i
$59$	−6.67395	−	3.85320i	−0.868874	−	0.501645i	−0.00190001	−	0.999998i	$-0.500605\pi$
$59$	−6.67395	−	3.85320i	−0.868874	−	0.501645i	−0.866974	+	0.498354i	$0.833938\pi$
$60$		0			0
$61$	−7.64484	+	4.41375i	−0.978822	+	0.565123i	−0.901914	−	0.431915i	$-0.857838\pi$
$61$	−7.64484	+	4.41375i	−0.978822	+	0.565123i	−0.0769075	+	0.997038i	$0.524505\pi$
$62$	−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	−0.0885910	−	0.996068i	$-0.528236\pi$
$67$	6.69828	−	11.6018i	0.818325	−	1.41738i	0.906916	−	0.421312i	$-0.138430\pi$
$68$	−3.88327	+	3.48762i	−0.470916	+	0.422936i
$69$		0			0
$70$	−11.7369	+	7.79179i	−1.40282	+	0.931297i
$71$	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	−0.922738	−	0.385429i	$-0.874054\pi$
$73$	−1.09003	+	1.88798i	−0.127578	+	0.220971i	0.795160	+	0.606400i	$0.207387\pi$
$74$	7.75687	+	3.45947i	0.901717	+	0.402155i
$75$		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	0.750045	−	0.661386i	$-0.230032\pi$
$79$	15.0908	−	8.71267i	1.69785	−	0.980252i	0.947800	−	0.318865i	$-0.103302\pi$
$80$	1.61217	−	14.9739i	0.180246	−	1.67414i
$81$		0			0
$82$	−6.98758	+	5.07002i	−0.771649	+	0.559890i
$83$		−	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
$86$	−5.39682	−	7.43798i	−0.581954	−	0.802058i
$87$		0			0
$88$	4.69688	+	1.00768i	0.500689	+	0.107419i
$89$	−9.58642	+	5.53472i	−1.01616	+	0.586679i	−0.912989	−	0.407984i	$-0.866232\pi$
$89$	−9.58642	+	5.53472i	−1.01616	+	0.586679i	−0.103170	+	0.994664i	$0.532898\pi$
$90$		0			0
$91$	7.99538	−	12.6062i	0.838144	−	1.32149i
$92$	2.55902	−	0.540552i	0.266797	−	0.0563564i
$93$		0			0
$94$	−4.07092	+	9.12788i	−0.419883	+	0.941469i
$95$	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	$0.222880\pi$
$98$	−4.76995	+	8.67454i	−0.481837	+	0.876261i
$99$		0			0
$100$	−12.2628	−	13.6539i	−1.22628	−	1.36539i
$101$	0.777899	−	1.34736i	0.0774039	−	0.134067i	−0.824725	−	0.565534i	$-0.808670\pi$
$101$	0.777899	−	1.34736i	0.0774039	−	0.134067i	0.902129	+	0.431466i	$0.142004\pi$
$102$		0			0
$103$	−6.94066	+	4.00719i	−0.683883	+	0.394840i	−0.801317	−	0.598240i	$-0.795867\pi$
$103$	−6.94066	+	4.00719i	−0.683883	+	0.394840i	0.117433	+	0.993081i	$0.462533\pi$
$104$	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	$-0.915583\pi$
$107$	−12.6257	+	7.28943i	−1.22057	+	0.704696i	−0.255530	+	0.966801i	$0.582250\pi$
$108$		0			0
$109$	0.655188	+	0.378273i	0.0627556	+	0.0362320i	0.531050	−	0.847341i	$-0.321798\pi$
$109$	0.655188	+	0.378273i	0.0627556	+	0.0362320i	−0.468294	+	0.883573i	$0.655131\pi$
$110$	7.31960	−	5.31092i	0.697896	−	0.506377i
$111$		0			0
$112$	−3.87358	−	9.84862i	−0.366019	−	0.930607i
$113$		−	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
$116$	−4.22486	+	12.9470i	−0.392268	+	1.20210i
$117$		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
$122$	−11.4015	−	5.08491i	−1.03224	−	0.460366i
$123$		0			0
$124$	8.16316	−	7.33145i	0.733074	−	0.658384i
$125$	−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	$0.935896\pi$
$128$	10.7444	+	3.54377i	0.949678	+	0.313228i
$129$		0			0
$130$	27.4379	+	12.2370i	2.40647	+	1.07325i
$131$	−14.0673	+	8.12176i	−1.22907	+	0.709601i	−0.966835	−	0.255404i	$-0.917792\pi$
$131$	−14.0673	+	8.12176i	−1.22907	+	0.709601i	−0.262231	+	0.965005i	$0.584458\pi$
$132$		0			0
$133$	0.259961	−	6.24258i	0.0225414	−	0.541300i
$134$	18.8431	−	1.96843i	1.62779	−	0.170046i
$135$		0			0
$136$	−7.21727	−	1.54841i	−0.618876	−	0.132775i
$137$	−3.63470	−	2.09849i	−0.310533	−	0.179286i	0.336632	−	0.941636i	$-0.390712\pi$
$137$	−3.63470	−	2.09849i	−0.310533	−	0.179286i	−0.647165	+	0.762350i	$0.724046\pi$
$138$		0			0
$139$	−5.70274			−0.483700			−0.241850	−	0.970314i	$-0.577754\pi$
$139$	−5.70274			−0.483700			−0.241850	+	0.970314i	$0.577754\pi$
$140$	−18.6667	−	6.96327i	−1.57762	−	0.588504i
$141$		0			0
$142$	7.81150	+	10.7659i	0.655526	+	0.903457i
$143$	−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	0.998106	+	0.0615095i	$0.0195915\pi$
$149$	6.74195	+	11.6774i	0.552322	+	0.956650i	−0.445784	+	0.895140i	$0.647075\pi$
$150$		0			0
$151$	18.4727	+	10.6652i	1.50329	+	0.867924i	0.999993	+	0.00380878i	$0.00121238\pi$
$151$	18.4727	+	10.6652i	1.50329	+	0.867924i	0.503295	+	0.864115i	$0.332121\pi$
$152$	4.95525	+	4.47879i	0.401924	+	0.363278i
$153$		0			0
$154$	2.82763	−	5.69102i	0.227857	−	0.458595i
$155$		−	20.6557i		−	1.65910i
$156$		0			0
$157$	7.97251	+	4.60293i	0.636276	+	0.367354i	0.783179	−	0.621797i	$-0.213597\pi$
$157$	7.97251	+	4.60293i	0.636276	+	0.367354i	−0.146903	+	0.989151i	$0.546930\pi$
$158$	22.5063	+	10.0375i	1.79050	+	0.798542i
$159$		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	0.868367	−	0.495922i	$-0.165170\pi$
$163$	0.0600325	+	0.103979i	0.00470211	+	0.00814429i	−0.863665	+	0.504067i	$0.831837\pi$
$164$	−11.6068	−	3.78753i	−0.906338	−	0.295756i
$165$		0			0
$166$	13.6058	−	9.87204i	1.05601	−	0.766219i
$167$	−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
$170$	−11.2474	+	8.16082i	−0.862634	+	0.625907i
$171$		0			0
$172$	4.03166	−	12.3549i	0.307411	−	0.942054i
$173$	−3.44458	−	5.96618i	−0.261886	−	0.453600i	0.704857	−	0.709350i	$-0.251011\pi$
$173$	−3.44458	−	5.96618i	−0.261886	−	0.453600i	−0.966743	+	0.255749i	$0.917678\pi$
$174$		0			0
$175$	−21.5120	+	11.2536i	−1.62616	+	0.850691i
$176$	2.74746	+	6.21318i	0.207097	+	0.468336i
$177$		0			0
$178$	−14.2971	−	6.37634i	−1.07161	−	0.477927i
$179$	13.6043	+	7.85445i	1.01683	+	0.587070i	0.913185	−	0.407544i	$-0.133615\pi$
$179$	13.6043	+	7.85445i	1.01683	+	0.587070i	0.103649	+	0.994614i	$0.466948\pi$
$180$		0			0
$181$		−	15.6714i		−	1.16485i	−0.812886	−	0.582423i	$-0.802105\pi$
$181$		−	15.6714i		−	1.16485i	0.812886	−	0.582423i	$-0.197895\pi$
$182$	21.0701	−	1.31791i	1.56182	−	0.0976901i
$183$		0			0
$184$	2.74409	+	2.48024i	0.202297	+	0.182846i
$185$	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	−0.859011	−	0.511957i	$-0.828921\pi$
$191$	−12.0633	−	20.8943i	−0.872873	−	1.51186i	−0.0138617	−	0.999904i	$-0.504412\pi$
$192$		0			0
$193$	−4.80306	+	8.31914i	−0.345732	+	0.598825i	−0.985486	−	0.169754i	$-0.945703\pi$
$193$	−4.80306	+	8.31914i	−0.345732	+	0.598825i	0.639755	+	0.768579i	$0.279036\pi$
$194$	12.5104	+	17.2420i	0.898193	+	1.23790i
$195$		0			0
$196$	−13.8909	+	1.74455i	−0.992206	+	0.124610i
$197$	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	$-0.448116\pi$
$199$	−8.62103	−	4.97735i	−0.611128	−	0.352835i	−0.773407	+	0.633910i	$0.781449\pi$
$200$	5.44435	−	25.3766i	0.384974	−	1.79440i
$201$		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
$206$	−10.3512	−	4.61653i	−0.721206	−	0.321649i
$207$		0			0
$208$	−13.3118	+	18.2249i	−0.923010	+	1.26367i
$209$			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	$0.659750\pi$
$212$	−1.30674	−	1.45499i	−0.0897476	−	0.0999289i
$213$		0			0
$214$	−18.8298	−	8.39787i	−1.28718	−	0.574066i
$215$	−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
$220$	12.1583	+	3.96749i	0.819711	+	0.267488i
$221$	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	$0.821531\pi$
$224$	8.05609	−	12.6135i	0.538270	−	0.842772i
$225$		0			0
$226$	11.3022	−	8.20057i	0.751808	−	0.545494i
$227$	0.620059	+	0.357991i	0.0411548	+	0.0237607i	0.520436	−	0.853901i	$-0.325769\pi$
$227$	0.620059	+	0.357991i	0.0411548	+	0.0237607i	−0.479281	+	0.877661i	$0.659103\pi$
$228$		0			0
$229$	−3.89913	+	2.25117i	−0.257662	+	0.148761i	−0.623268	−	0.782009i	$-0.714195\pi$
$229$	−3.89913	+	2.25117i	−0.257662	+	0.148761i	0.365606	+	0.930770i	$0.380862\pi$
$230$	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	$-0.585161\pi$
$233$	6.69604	−	3.86596i	0.438672	−	0.253267i	0.703034	+	0.711156i	$0.251828\pi$
$234$		0			0
$235$	−13.3044	+	23.0440i	−0.867886	+	1.50322i
$236$	11.4670	−	10.2987i	0.746438	−	0.670387i
$237$		0			0
$238$	−4.34496	+	8.74488i	−0.281642	+	0.566846i
$239$	−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	−0.695726	−	0.718308i	$-0.744917\pi$
$241$	4.25688	−	7.37313i	0.274210	−	0.474945i	0.969935	+	0.243362i	$0.0782504\pi$
$242$	4.67477	−	10.4818i	0.300505	−	0.673798i
$243$		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
$248$	15.1717	+	3.25497i	0.963403	+	0.206691i
$249$		0			0
$250$	−13.0590	−	17.9981i	−0.825922	−	1.13830i
$251$		−	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
$254$	−5.16062	+	3.74442i	−0.323806	+	0.234946i
$255$		0			0
$256$	4.86715	+	15.2417i	0.304197	+	0.952609i
$257$	−10.6901	+	6.17195i	−0.666832	+	0.384996i	−0.794875	−	0.606773i	$-0.792464\pi$
$257$	−10.6901	+	6.17195i	−0.666832	+	0.384996i	0.128043	+	0.991769i	$0.459130\pi$
$258$		0			0
$259$	15.8758	+	0.661120i	0.986476	+	0.0410800i
$260$	8.78098	+	41.5700i	0.544573	+	2.57806i
$261$		0			0
$262$	−20.9799	−	9.35676i	−1.29614	−	0.578062i
$263$	−1.01432	+	1.75686i	−0.0625458	+	0.108333i	−0.895603	−	0.444855i	$-0.853255\pi$
$263$	−1.01432	+	1.75686i	−0.0625458	+	0.108333i	0.833057	+	0.553187i	$0.186589\pi$
$264$		0			0
$265$	−3.68163			−0.226161
$266$	7.36146	−	4.88708i	0.451360	−	0.299646i
$267$		0			0
$268$	17.9029	+	19.9338i	1.09359	+	1.21765i
$269$	13.1346	−	22.7498i	0.800833	−	1.38708i	−0.118236	−	0.992986i	$-0.537724\pi$
$269$	13.1346	−	22.7498i	0.800833	−	1.38708i	0.919069	−	0.394097i	$-0.128943\pi$
$270$		0			0
$271$	7.01591	−	4.05064i	0.426186	−	0.246059i	−0.271535	−	0.962429i	$-0.587531\pi$
$271$	7.01591	−	4.05064i	0.426186	−	0.246059i	0.697720	+	0.716370i	$0.254198\pi$
$272$	−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	$-0.238557\pi$
$277$	8.45693	+	4.88261i	0.508127	+	0.293368i	−0.223936	+	0.974604i	$0.571891\pi$
$278$	−4.73630	−	6.52764i	−0.284064	−	0.391502i
$279$		0			0
$280$	−7.53272	−	27.1500i	−0.450166	−	1.62252i
$281$			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	−0.751560	−	0.659664i	$-0.770698\pi$
$283$	3.28892	−	5.69657i	0.195506	−	0.338626i	0.947066	+	0.321038i	$0.104032\pi$
$284$	−5.83553	+	17.8828i	−0.346275	+	1.06115i
$285$		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
$290$	−14.7685	+	33.1141i	−0.867235	+	1.94453i
$291$		0			0
$292$	−2.91337	−	3.24388i	−0.170492	−	0.189834i
$293$	−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
$296$	−11.3903	+	12.6020i	−0.662046	+	0.732474i
$297$		0			0
$298$	−7.76713	+	17.4156i	−0.449938	+	1.00886i
$299$	−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
$304$	−1.01117	+	9.39179i	−0.0579944	+	0.538656i
$305$	−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	$0.667464\pi$
$308$	8.86264	−	1.48991i	0.504996	−	0.0848958i
$309$		0			0
$310$	23.6435	−	17.1552i	1.34286	−	0.974347i
$311$	−5.44683	+	9.43418i	−0.308861	+	0.534963i	−0.978114	−	0.208072i	$-0.933281\pi$
$311$	−5.44683	+	9.43418i	−0.308861	+	0.534963i	0.669252	+	0.743035i	$0.266615\pi$
$312$		0			0
$313$	−1.76535	−	3.05768i	−0.0997835	−	0.172830i	0.811811	−	0.583920i	$-0.198482\pi$
$313$	−1.76535	−	3.05768i	−0.0997835	−	0.172830i	−0.911595	+	0.411090i	$0.865148\pi$
$314$	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	0.544047	−	0.839055i	$-0.316891\pi$
$317$	−8.09426	−	14.0197i	−0.454619	−	0.787423i	−0.998666	+	0.0516316i	$0.983558\pi$
$318$		0			0
$319$	−10.0156	−	5.78252i	−0.560767	−	0.323759i
$320$	27.4701	+	12.3557i	1.53563	+	0.690706i
$321$		0			0
$322$	4.07658	−	2.70634i	0.227179	−	0.150818i
$323$		−	6.16298i		−	0.342918i
$324$		0			0
$325$	44.8374	+	25.8869i	2.48713	+	1.43595i
$326$	−0.0691610	+	0.155074i	−0.00383048	+	0.00858875i
$327$		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	0.980218	−	0.197919i	$-0.0634183\pi$
$331$	5.79835	+	10.0430i	0.318706	+	0.552016i	−0.661512	+	0.749935i	$0.730085\pi$
$332$	22.6000	+	7.37484i	1.24034	+	0.404747i
$333$		0			0
$334$	−10.7811	−	14.8587i	−0.589917	−	0.813033i
$335$	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	$0.475608\pi$
$338$	−15.6427	−	21.5590i	−0.850851	−	1.17266i
$339$		0			0
$340$	−18.6826	−	6.09649i	−1.01320	−	0.330629i
$341$	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
$346$	3.96836	−	8.89792i	0.213340	−	0.478355i
$347$	−18.7883	−	10.8474i	−1.00861	−	0.582320i	−0.0978242	−	0.995204i	$-0.531188\pi$
$347$	−18.7883	−	10.8474i	−1.00861	−	0.582320i	−0.910784	+	0.412884i	$0.864522\pi$
$348$		0			0
$349$		−	7.44465i		−	0.398503i	−0.979948	−	0.199251i	$-0.936149\pi$
$349$		−	7.44465i		−	0.398503i	0.979948	−	0.199251i	$-0.0638511\pi$
$350$	−30.7478	−	15.2773i	−1.64354	−	0.816606i
$351$		0			0
$352$	−4.83007	+	8.30511i	−0.257443	+	0.442664i
$353$	13.0365	+	7.52665i	0.693865	+	0.400603i	0.805058	−	0.593196i	$-0.202134\pi$
$353$	13.0365	+	7.52665i	0.693865	+	0.400603i	−0.111193	+	0.993799i	$0.535467\pi$
$354$		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	0.999622	−	0.0275035i	$-0.00875575\pi$
$359$	9.01876	+	15.6210i	0.475992	+	0.824442i	−0.523630	+	0.851946i	$0.675422\pi$
$360$		0			0
$361$	6.71162	−	11.6249i	0.353243	−	0.611835i
$362$	17.9383	−	13.0156i	0.942814	−	0.684083i
$363$		0			0
$364$	19.0079	+	23.0233i	0.996282	+	1.20675i
$365$	−8.20816			−0.429635
$366$		0			0
$367$	3.38897	+	1.95662i	0.176903	+	0.102135i	0.585837	−	0.810429i	$-0.300766\pi$
$367$	3.38897	+	1.95662i	0.176903	+	0.102135i	−0.408934	+	0.912564i	$0.634099\pi$
$368$	−0.559958	+	5.20093i	−0.0291898	+	0.271117i
$369$		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	$-0.823807\pi$
$373$	−15.8513	+	9.15178i	−0.820752	+	0.473861i	0.0299239	+	0.999552i	$0.490473\pi$
$374$	2.55318	−	5.72478i	0.132022	−	0.296021i
$375$		0			0
$376$	−14.8293	−	13.4035i	−0.764765	−	0.691232i
$377$		−	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	$0.269361\pi$
$380$	11.8823	+	13.2302i	0.609548	+	0.678697i
$381$		0			0
$382$	13.8977	−	31.1616i	0.711068	−	1.59437i
$383$	7.37665	+	12.7767i	0.376929	+	0.652860i	0.990614	−	0.136691i	$-0.0436467\pi$
$383$	7.37665	+	12.7767i	0.376929	+	0.652860i	−0.613685	+	0.789551i	$0.710313\pi$
$384$		0			0
$385$	9.06159	−	14.2873i	0.461822	−	0.728147i
$386$	−13.5116	+	1.41148i	−0.687721	+	0.0718423i
$387$		0			0
$388$	−9.34580	+	28.6400i	−0.474461	+	1.45397i
$389$	−8.70264	+	15.0734i	−0.441242	+	0.764253i	−0.997782	−	0.0665677i	$-0.978795\pi$
$389$	−8.70264	+	15.0734i	−0.441242	+	0.764253i	0.556540	+	0.830821i	$0.312128\pi$
$390$		0			0
$391$		−	3.41290i		−	0.172598i
$392$	−13.5337	−	14.4513i	−0.683554	−	0.729900i
$393$		0			0
$394$	1.70512	+	2.35003i	0.0859028	+	0.118393i
$395$	56.8186	+	32.8042i	2.85886	+	1.65056i
$396$		0			0
$397$	−10.0273	+	5.78926i	−0.503255	+	0.290554i	−0.730057	−	0.683387i	$-0.760506\pi$
$397$	−10.0273	+	5.78926i	−0.503255	+	0.290554i	0.226802	+	0.973941i	$0.427173\pi$
$398$	−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	−0.557630	+	0.830089i	$0.688289\pi$
$401$	−31.1453	+	17.9818i	−1.55532	+	0.897967i	−0.997694	+	0.0678773i	$0.978377\pi$
$402$		0			0
$403$	−15.4768	+	26.8065i	−0.770953	+	1.33533i
$404$	2.07914	+	2.31500i	0.103441	+	0.115176i
$405$		0			0
$406$	1.59055	+	25.4289i	0.0789378	+	1.26201i
$407$	−10.2000			−0.505595
$408$		0			0
$409$	12.1615	−	21.0644i	0.601349	−	1.04157i	−0.391268	−	0.920277i	$-0.627964\pi$
$409$	12.1615	−	21.0644i	0.601349	−	1.04157i	0.992617	−	0.121290i	$-0.0387031\pi$
$410$	−29.6863	−	13.2397i	−1.46610	−	0.653863i
$411$		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
$416$	−31.9170	−	0.101021i	−1.56486	−	0.00495294i
$417$		0			0
$418$	−4.59092	+	3.33106i	−0.224549	+	0.162927i
$419$		−	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	$-0.0994965\pi$
$422$	−11.6072	−	15.9973i	−0.565032	−	0.778736i
$423$		0			0
$424$	0.580159	−	2.70417i	0.0281750	−	0.131326i
$425$	−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
$430$	14.0931	−	31.5998i	0.679630	−	1.52388i
$431$	11.1759	−	19.3571i	0.538322	−	0.932401i	−0.460673	−	0.887570i	$-0.652392\pi$
$431$	11.1759	−	19.3571i	0.538322	−	0.932401i	0.998995	−	0.0448306i	$-0.0142748\pi$
$432$		0			0
$433$	−32.2813			−1.55134			−0.775671	−	0.631138i	$-0.782588\pi$
$433$	−32.2813			−1.55134			−0.775671	+	0.631138i	$0.782588\pi$
$434$	9.13370	−	18.3829i	0.438432	−	0.882408i
$435$		0			0
$436$	−1.12573	+	1.01103i	−0.0539126	+	0.0484196i
$437$	−1.54413	+	2.67451i	−0.0738658	+	0.127939i
$438$		0			0
$439$	2.42798	−	1.40180i	0.115881	−	0.0669041i	−0.440939	−	0.897537i	$-0.645355\pi$
$439$	2.42798	−	1.40180i	0.115881	−	0.0669041i	0.556820	+	0.830633i	$0.312021\pi$
$440$	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	$-0.520027\pi$
$443$	16.2066	−	9.35689i	0.769999	−	0.444559i	0.832874	+	0.553462i	$0.186694\pi$
$444$		0			0
$445$	−36.0940	−	20.8389i	−1.71102	−	0.987859i
$446$	−18.1790	+	13.1902i	−0.860799	+	0.624575i
$447$		0			0
$448$	21.1288	−	1.25446i	0.998242	−	0.0592678i
$449$		−	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
$452$	18.7735	+	6.12618i	0.883033	+	0.288151i
$453$		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	0.925656	−	0.378367i	$-0.123514\pi$
$457$	2.88922	+	5.00428i	0.135152	+	0.234090i	−0.790503	+	0.612458i	$0.790181\pi$
$458$	−5.81514	−	2.59348i	−0.271724	−	0.121185i
$459$		0			0
$460$	6.58009	+	7.32656i	0.306798	+	0.341603i
$461$	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	$-0.0867996\pi$
$464$	−21.9952	−	16.0657i	−1.02110	−	0.745831i
$465$		0			0
$466$	9.98642	+	4.45382i	0.462612	+	0.206319i
$467$	−1.98153	+	1.14404i	−0.0916943	+	0.0529397i	−0.545146	−	0.838341i	$-0.683526\pi$
$467$	−1.98153	+	1.14404i	−0.0916943	+	0.0529397i	0.453452	+	0.891281i	$0.350192\pi$
$468$		0			0
$469$	31.4061	−	16.4295i	1.45020	−	0.758643i
$470$	−37.4270	+	3.90978i	−1.72638	+	0.180345i
$471$		0			0
$472$	21.3121	+	4.57234i	0.980967	+	0.210459i
$473$	9.55761	+	5.51809i	0.439459	+	0.253722i
$474$		0			0
$475$	21.6696			0.994270
$476$	−13.6184	+	2.28942i	−0.624200	+	0.104935i
$477$		0			0
$478$	−17.7557	−	24.4712i	−0.812129	−	1.11929i
$479$	−9.42948	+	16.3323i	−0.430844	+	0.746244i	−0.996946	−	0.0780912i	$-0.975117\pi$
$479$	−9.42948	+	16.3323i	−0.430844	+	0.746244i	0.566102	+	0.824335i	$0.308451\pi$
$480$		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	$-0.0848126\pi$
$487$	26.9019	+	15.5318i	1.21904	+	0.703813i	0.254327	+	0.967118i	$0.418146\pi$
$488$	16.7420	−	18.5230i	0.757876	−	0.838499i
$489$		0			0
$490$	−37.2647	+	0.777026i	−1.68345	+	0.0351025i
$491$			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
$494$	−17.2093	−	7.67514i	−0.774283	−	0.345321i
$495$		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	0.845578	−	0.533852i	$-0.179256\pi$
$499$	−0.883277	−	1.52988i	−0.0395409	−	0.0684869i	−0.885119	+	0.465366i	$0.845923\pi$
$500$	9.75562	−	29.8959i	0.436285	−	1.33698i
$501$		0			0
$502$	0.891534	−	0.646876i	0.0397911	−	0.0288715i
$503$	−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
$506$	−2.54233	+	1.84465i	−0.113020	+	0.0820048i
$507$		0			0
$508$	−8.57209	−	2.79724i	−0.380325	−	0.124108i
$509$	−5.13114	−	8.88739i	−0.227434	−	0.393927i	0.729613	−	0.683860i	$-0.239700\pi$
$509$	−5.13114	−	8.88739i	−0.227434	−	0.393927i	−0.957047	+	0.289934i	$0.906367\pi$
$510$		0			0
$511$	−5.11079	+	2.67361i	−0.226088	+	0.118273i
$512$	−13.4041	+	18.2299i	−0.592385	+	0.805655i
$513$		0			0
$514$	−15.9432	−	7.11046i	−0.703224	−	0.313629i
$515$	−26.1324	−	15.0876i	−1.15153	−	0.664837i
$516$		0			0
$517$		−	12.0028i		−	0.527884i
$518$	12.4286	+	18.7213i	0.546081	+	0.822568i
$519$		0			0
$520$	−40.2902	+	44.5762i	−1.76684	+	1.95480i
$521$	−32.7368	−	18.9006i	−1.43423	−	0.828051i	−0.436787	−	0.899565i	$-0.643884\pi$
$521$	−32.7368	−	18.9006i	−1.43423	−	0.828051i	−0.997440	+	0.0715138i	$0.977217\pi$
$522$		0			0
$523$	19.6691	+	34.0679i	0.860070	+	1.48968i	0.871861	+	0.489754i	$0.162913\pi$
$523$	19.6691	+	34.0679i	0.860070	+	1.48968i	−0.0117911	+	0.999930i	$0.503753\pi$
$524$	−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
$530$	−3.05770	−	4.21417i	−0.132818	−	0.183052i
$531$		0			0
$532$	11.7079	+	4.36742i	0.507602	+	0.189352i
$533$	34.4433			1.49190
$534$		0			0
$535$	−47.5372	−	27.4456i	−2.05521	−	1.18658i
$536$	−7.94839	+	37.0481i	−0.343318	+	1.60024i
$537$		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	$-0.769906\pi$
$541$	−12.8385	+	7.41231i	−0.551970	+	0.318680i	0.197946	+	0.980213i	$0.436573\pi$
$542$	10.4635	+	4.66658i	0.449445	+	0.200447i
$543$		0			0
$544$	7.42193	−	12.7617i	0.318213	−	0.547154i
$545$			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	$0.612585\pi$
$548$	6.24505	−	5.60876i	0.266775	−	0.239595i
$549$		0			0
$550$	20.1288	+	8.97721i	0.858297	+	0.382790i
$551$	−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
$556$	3.53822	−	10.8428i	0.150054	−	0.459837i
$557$	1.17534	−	2.03574i	0.0498006	−	0.0862572i	−0.840051	−	0.542508i	$-0.817475\pi$
$557$	1.17534	−	2.03574i	0.0498006	−	0.0862572i	0.889851	+	0.456251i	$0.150808\pi$
$558$		0			0
$559$			36.6634i			1.55070i
$560$	24.8211	−	31.1712i	1.04888	−	1.31722i
$561$		0			0
$562$	−2.16054	+	1.56764i	−0.0911370	+	0.0661268i
$563$	−6.40537	−	3.69814i	−0.269954	−	0.155858i	0.358913	−	0.933371i	$-0.383148\pi$
$563$	−6.40537	−	3.69814i	−0.269954	−	0.155858i	−0.628867	+	0.777513i	$0.716481\pi$
$564$		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	$-0.928668\pi$
$569$	−30.2952	+	17.4909i	−1.27004	+	0.733258i	−0.295045	+	0.955483i	$0.595334\pi$
$570$		0			0
$571$	16.4081	−	28.4197i	0.686659	−	1.18933i	−0.286254	−	0.958154i	$-0.592410\pi$
$571$	16.4081	−	28.4197i	0.686659	−	1.18933i	0.972912	−	0.231174i	$-0.0742567\pi$
$572$	−12.8061	−	14.2588i	−0.535448	−	0.596191i
$573$		0			0
$574$	−22.7966	+	1.42591i	−0.951513	+	0.0595162i
$575$	12.0001			0.500437
$576$		0			0
$577$	4.58139	−	7.93520i	0.190726	−	0.330347i	−0.754765	−	0.655995i	$-0.772249\pi$
$577$	4.58139	−	7.93520i	0.190726	−	0.330347i	0.945491	+	0.325648i	$0.105583\pi$
$578$	5.86927	−	13.1602i	0.244130	−	0.547391i
$579$		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
$584$	1.29346	−	6.02893i	0.0535237	−	0.249479i
$585$		0			0
$586$	−11.7363	−	16.1751i	−0.484820	−	0.668187i
$587$			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
$590$	33.2126	−	24.0983i	1.36734	−	0.992111i
$591$		0			0
$592$	−23.8848	−	2.57155i	−0.981658	−	0.105690i
$593$	−17.0385	+	9.83721i	−0.699689	+	0.403966i	−0.807232	−	0.590235i	$-0.799035\pi$
$593$	−17.0385	+	9.83721i	−0.699689	+	0.403966i	0.107542	+	0.994200i	$0.465702\pi$
$594$		0			0
$595$	−13.9241	+	21.9540i	−0.570834	+	0.900025i
$596$	−26.3856	+	5.57352i	−1.08079	+	0.228300i
$597$		0			0
$598$	−9.53006	−	4.25029i	−0.389713	−	0.173807i
$599$	2.68048	−	4.64273i	0.109521	−	0.189697i	−0.806055	−	0.591841i	$-0.798402\pi$
$599$	2.68048	−	4.64273i	0.109521	−	0.189697i	0.915576	+	0.402144i	$0.131735\pi$
$600$		0			0
$601$	12.4609			0.508291			0.254145	−	0.967166i	$-0.418206\pi$
$601$	12.4609			0.508291			0.254145	+	0.967166i	$0.418206\pi$
$602$	−1.51782	−	24.2660i	−0.0618616	−	0.989010i
$603$		0			0
$604$	−31.7393	+	28.5055i	−1.29146	+	1.15987i
$605$	15.2779	−	26.4621i	0.621135	−	1.07584i
$606$		0			0
$607$	−10.6807	+	6.16649i	−0.433515	+	0.250290i	−0.700843	−	0.713315i	$-0.747193\pi$
$607$	−10.6807	+	6.16649i	−0.433515	+	0.250290i	0.267328	+	0.963606i	$0.413859\pi$
$608$	−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	$-0.359769\pi$
$613$	−3.55744	−	2.05389i	−0.143683	−	0.0829557i	−0.570118	+	0.821563i	$0.693103\pi$
$614$	−14.6151	−	20.1428i	−0.589818	−	0.812896i
$615$		0			0
$616$	9.06612	+	8.90720i	0.365284	+	0.358881i
$617$		−	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	−0.881706	−	0.471800i	$-0.843604\pi$
$619$	−0.802674	+	1.39027i	−0.0322622	+	0.0558798i	0.849443	+	0.527680i	$0.176938\pi$
$620$	39.2732	+	12.8156i	1.57725	+	0.514689i
$621$		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
$626$	2.03379	−	4.56020i	0.0812866	−	0.182262i
$627$		0			0
$628$	−13.6982	+	12.3025i	−0.546616	+	0.490924i
$629$	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	$-0.0572208\pi$
$632$	−33.0485	+	36.5642i	−1.31460	+	1.45444i
$633$		0			0
$634$	9.32507	−	20.9088i	0.370346	−	0.830396i
$635$	−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
$640$	8.67180	+	41.7055i	0.342783	+	1.64855i
$641$	34.1214	+	19.7000i	1.34772	+	0.778104i	0.987926	−	0.154929i	$-0.0495149\pi$
$641$	34.1214	+	19.7000i	1.34772	+	0.778104i	0.359790	+	0.933033i	$0.382848\pi$
$642$		0			0
$643$	40.0002			1.57745			0.788726	−	0.614745i	$-0.210741\pi$
$643$	40.0002			1.57745			0.788726	+	0.614745i	$0.210741\pi$
$644$	6.48353	+	2.41856i	0.255487	+	0.0953048i
$645$		0			0
$646$	7.05445	−	5.11854i	0.277554	−	0.201386i
$647$	−19.8854	+	34.4425i	−0.781775	+	1.35407i	0.149132	+	0.988817i	$0.452352\pi$
$647$	−19.8854	+	34.4425i	−0.781775	+	1.35407i	−0.930907	+	0.365257i	$0.880981\pi$
$648$		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	0.896330	−	0.443388i	$-0.146224\pi$
$653$	1.64003	+	2.84061i	0.0641792	+	0.111162i	−0.832150	+	0.554550i	$0.812890\pi$
$654$		0			0
$655$	−52.9651	−	30.5794i	−2.06952	−	1.19484i
$656$	14.4027	−	19.7184i	0.562330	−	0.769873i
$657$		0			0
$658$	−22.0303	+	14.6253i	−0.858831	+	0.570155i
$659$		−	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	$-0.365566\pi$
$661$	−4.50164	−	2.59902i	−0.175093	−	0.101090i	−0.584985	+	0.811044i	$0.698900\pi$
$662$	−6.68005	+	14.9781i	−0.259628	+	0.582141i
$663$		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
$668$	8.05397	−	24.6812i	0.311618	−	0.954945i
$669$		0			0
$670$	41.8916	+	57.7357i	1.61841	+	2.23052i
$671$	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	$0.695925\pi$
$674$	2.33439	+	3.21729i	0.0899174	+	0.123926i
$675$		0			0
$676$	11.6858	−	35.8108i	0.449453	−	1.37734i
$677$	15.2704	+	26.4492i	0.586891	+	1.01652i	0.994637	+	0.103429i	$0.0329816\pi$
$677$	15.2704	+	26.4492i	0.586891	+	1.01652i	−0.407746	+	0.913095i	$0.633685\pi$
$678$		0			0
$679$	33.6550	+	21.3454i	1.29156	+	0.819162i
$680$	−8.53807	−	26.4483i	−0.327420	−	1.01425i
$681$		0			0
$682$	−5.36713	+	12.0343i	−0.205518	+	0.460815i
$683$	11.1942	+	6.46296i	0.428333	+	0.247298i	0.698636	−	0.715477i	$-0.253791\pi$
$683$	11.1942	+	6.46296i	0.428333	+	0.247298i	−0.270303	+	0.962775i	$0.587124\pi$
$684$		0			0
$685$		−	15.8022i		−	0.603770i
$686$	−22.9497	+	12.6219i	−0.876223	+	0.481906i
$687$		0			0
$688$	20.9894	+	15.3310i	0.800212	+	0.584489i
$689$	4.77795	+	2.75855i	0.182025	+	0.105092i
$690$		0			0
$691$	−8.33676	−	14.4397i	−0.317145	−	0.549312i	0.662746	−	0.748844i	$-0.269391\pi$
$691$	−8.33676	−	14.4397i	−0.317145	−	0.549312i	−0.979891	+	0.199533i	$0.936058\pi$
$692$	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
$698$	8.52151	−	6.18300i	0.322544	−	0.234030i
$699$		0			0
$700$	−8.04980	−	47.8837i	−0.304254	−	1.80983i
$701$	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
$704$	−13.5179	+	1.36890i	−0.509477	+	0.0515925i
$705$		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	$-0.634876\pi$
$709$	4.59843	−	2.65490i	0.172698	−	0.0997070i	0.583857	+	0.811856i	$0.301543\pi$
$710$	−20.3987	+	45.7384i	−0.765551	+	1.71653i
$711$		0			0
$712$	20.9940	−	23.2274i	0.786785	−	0.870483i
$713$			7.17437i			0.268682i
$714$		0			0
$715$	−36.0799			−1.34931
$716$	−23.3746	+	20.9930i	−0.873549	+	0.784547i
$717$		0			0
$718$	−10.3902	+	23.2970i	−0.387757	+	0.869436i
$719$	5.16456	+	8.94528i	0.192606	+	0.333603i	0.946113	−	0.323837i	$-0.104973\pi$
$719$	5.16456	+	8.94528i	0.192606	+	0.333603i	−0.753507	+	0.657439i	$0.771640\pi$
$720$		0			0
$721$	−21.1857	−	0.882240i	−0.788997	−	0.0328563i
$722$	18.8806	−	1.97235i	0.702663	−	0.0734031i
$723$		0			0
$724$	29.7965	+	9.72319i	1.10738	+	0.361360i
$725$	−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	$0.821551\pi$
$728$	−10.5670	+	40.8788i	−0.391638	+	1.51507i
$729$		0			0
$730$	−6.81712	−	9.39546i	−0.252313	−	0.347742i
$731$	−14.6863	−	8.47916i	−0.543193	−	0.313613i
$732$		0			0
$733$	−33.6091	+	19.4042i	−1.24138	+	0.716710i	−0.969375	−	0.245586i	$-0.921020\pi$
$733$	−33.6091	+	19.4042i	−1.24138	+	0.716710i	−0.272004	+	0.962296i	$0.587686\pi$
$734$	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	−0.950424	−	0.310956i	$-0.899351\pi$
$739$	−5.59773	+	9.69556i	−0.205916	+	0.356657i	0.744508	+	0.667613i	$0.232684\pi$
$740$	−33.6466	+	30.2184i	−1.23687	+	1.11085i
$741$		0			0
$742$	−3.27654	−	1.62797i	−0.120285	−	0.0597648i
$743$	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
$746$	−23.6406	−	10.5434i	−0.865543	−	0.386021i
$747$		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	0.584701	−	0.811249i	$-0.301212\pi$
$751$	43.2883	−	24.9925i	1.57961	−	0.911990i	0.994913	−	0.100741i	$-0.0321215\pi$
$752$	3.02607	−	28.1064i	0.110349	−	1.02493i
$753$		0			0
$754$	43.9778	−	31.9092i	1.60158	−	1.16207i
$755$			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	$0.796457\pi$
$758$	21.4337	+	29.5403i	0.778507	+	1.07295i
$759$		0			0
$760$	−5.27541	+	24.5891i	−0.191359	+	0.891942i
$761$	28.7157	−	16.5790i	1.04094	−	0.600988i	0.120842	−	0.992672i	$-0.461440\pi$
$761$	28.7157	−	16.5790i	1.04094	−	0.600988i	0.920100	+	0.391683i	$0.128107\pi$
$762$		0			0
$763$	0.927825	+	1.77360i	0.0335895	+	0.0642088i
$764$	47.2116	−	9.97268i	1.70806	−	0.360799i
$765$		0			0
$766$	−8.49835	+	19.0551i	−0.307058	+	0.688490i
$767$	−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	$0.834336\pi$
$770$	23.8798	−	1.49366i	0.860569	−	0.0538277i
$771$		0			0
$772$	−12.8374	−	14.2937i	−0.462028	−	0.514443i
$773$	−14.2293	+	24.6458i	−0.511791	+	0.886449i	0.488115	+	0.872779i	$0.337685\pi$
$773$	−14.2293	+	24.6458i	−0.511791	+	0.886449i	−0.999907	+	0.0136695i	$0.995649\pi$
$774$		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
$782$	3.90657	−	2.83451i	0.139699	−	0.101362i
$783$		0			0
$784$	5.30152	−	27.4935i	0.189340	−	0.981912i
$785$			34.6612i			1.23711i
$786$		0			0
$787$	−11.0597	+	19.1559i	−0.394234	+	0.682834i	−0.993003	−	0.118088i	$-0.962323\pi$
$787$	−11.0597	+	19.1559i	−0.394234	+	0.682834i	0.598769	+	0.800922i	$0.295657\pi$
$788$	−1.27380	+	3.90353i	−0.0453773	+	0.139058i
$789$		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
$794$	−14.9546	−	6.66957i	−0.530720	−	0.236694i
$795$		0			0
$796$	14.8124	−	13.3033i	0.525013	−	0.471521i
$797$	−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
$800$	44.8714	+	26.0962i	1.58644	+	0.922640i
$801$		0			0
$802$	−46.4499	−	20.7161i	−1.64020	−	0.731510i
$803$	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
$808$	−0.923080	+	4.30256i	−0.0324738	+	0.151363i
$809$	2.56573	+	1.48132i	0.0902062	+	0.0520806i	0.544425	−	0.838810i	$-0.316748\pi$
$809$	2.56573	+	1.48132i	0.0902062	+	0.0520806i	−0.454218	+	0.890890i	$0.650081\pi$
$810$		0			0
$811$	−51.9174			−1.82307			−0.911533	−	0.411228i	$-0.865100\pi$
$811$	−51.9174			−1.82307			−0.911533	+	0.411228i	$0.865100\pi$
$812$	−27.7862	+	22.9401i	−0.975103	+	0.805039i
$813$		0			0
$814$	−8.47139	−	11.6754i	−0.296922	−	0.409223i
$815$	−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	0.614462	−	0.788947i	$-0.289373\pi$
$821$	−10.7741	−	18.6612i	−0.376017	−	0.651281i	−0.990479	+	0.137666i	$0.956040\pi$
$822$		0			0
$823$	30.0162	+	17.3299i	1.04630	+	0.604082i	0.921611	−	0.388114i	$-0.126873\pi$
$823$	30.0162	+	17.3299i	1.04630	+	0.604082i	0.124689	+	0.992196i	$0.460207\pi$
$824$	15.1999	−	16.8168i	0.529513	−	0.585843i
$825$		0			0
$826$	12.8303	−	25.8229i	0.446425	−	0.898495i
$827$			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	$-0.525288\pi$
$829$	−28.2837	−	16.3296i	−0.982334	−	0.567151i	−0.902974	+	0.429695i	$0.858621\pi$
$830$	57.8034	+	25.7796i	2.00639	+	0.894823i
$831$		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
$836$	−7.62578	−	2.48844i	−0.263743	−	0.0860647i
$837$		0			0
$838$	7.93189	−	5.75519i	0.274002	−	0.198810i
$839$	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
$842$	14.4446	−	10.4807i	0.497794	−	0.361187i
$843$		0			0
$844$	8.67112	−	26.5724i	0.298472	−	0.914661i
$845$	−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
$850$	−30.9302	−	13.7945i	−1.06090	−	0.473147i
$851$	−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	$-0.0156786\pi$
$854$	−18.2682	−	27.5176i	−0.625126	−	0.941634i
$855$		0			0
$856$	27.6499	−	30.5913i	0.945055	−	1.04559i
$857$	5.76468	+	3.32824i	0.196918	+	0.113691i	0.595217	−	0.803565i	$-0.297066\pi$
$857$	5.76468	+	3.32824i	0.196918	+	0.113691i	−0.398299	+	0.917256i	$0.630399\pi$
$858$		0			0
$859$	10.2685	+	17.7855i	0.350355	+	0.606833i	0.986312	−	0.164892i	$-0.0527276\pi$
$859$	10.2685	+	17.7855i	0.350355	+	0.606833i	−0.635956	+	0.771725i	$0.719394\pi$
$860$	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	−0.999100	−	0.0424266i	$-0.986491\pi$
$863$	−15.7546	−	27.2877i	−0.536292	−	0.928886i	0.462807	−	0.886459i	$-0.346842\pi$
$864$		0			0
$865$	12.9692	−	22.4634i	0.440968	−	0.763778i
$866$	−26.8106	−	36.9508i	−0.911061	−	1.25564i
$867$		0			0
$868$	28.6278	−	4.81267i	0.971690	−	0.163353i
$869$	−29.5949			−1.00394
$870$		0			0
$871$	−65.4596	−	37.7931i	−2.21801	−	1.28057i
$872$	−2.09223	−	0.448871i	−0.0708517	−	0.0152007i
$873$		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	−0.647477	+	0.762085i	$0.724176\pi$
$877$	−48.3067	+	27.8899i	−1.63120	+	0.941774i	−0.983723	+	0.179689i	$0.942491\pi$
$878$	3.62107	+	1.61495i	0.122205	+	0.0545020i
$879$		0			0
$880$	−15.0870	+	20.6553i	−0.508583	+	0.696290i
$881$		−	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	$0.309846\pi$
$884$	19.6779	+	21.9103i	0.661840	+	0.736922i
$885$		0			0
$886$	24.1704	+	10.7797i	0.812021	+	0.362151i
$887$	−6.18309	−	10.7094i	−0.207608	−	0.359587i	0.743353	−	0.668900i	$-0.233234\pi$
$887$	−6.18309	−	10.7094i	−0.207608	−	0.359587i	−0.950960	+	0.309313i	$0.899901\pi$
$888$		0			0
$889$	−6.38880	+	10.0731i	−0.214273	+	0.337841i
$890$	−6.12394	−	58.6223i	−0.205275	−	1.96502i
$891$		0			0
$892$	−30.1963	−	9.85367i	−1.01105	−	0.329925i
$893$	8.34466	−	14.4534i	0.279243	−	0.483664i
$894$		0			0
$895$			59.1460i			1.97703i
$896$	18.9840	+	23.1432i	0.634211	+	0.773160i
$897$		0			0
$898$	15.9049	−	11.5402i	0.530755	−	0.385103i
$899$	−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	−0.957142	−	0.289619i	$-0.906471\pi$
$907$	−6.85914	+	11.8804i	−0.227754	+	0.394481i	0.729388	+	0.684100i	$0.239805\pi$
$908$	−1.06537	+	0.956823i	−0.0353555	+	0.0317533i
$909$		0			0
$910$	43.9630	+	66.2219i	1.45736	+	2.19524i
$911$	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
$914$	−3.32856	+	7.46335i	−0.110099	+	0.246866i
$915$		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	$-0.922571\pi$
$919$	−37.8104	+	21.8298i	−1.24725	+	0.720100i	−0.276689	+	0.960959i	$0.589237\pi$
$920$	−2.92138	+	13.6168i	−0.0963151	+	0.448933i
$921$		0			0
$922$	12.8086	+	17.6530i	0.421829	+	0.581372i
$923$		−	53.0675i		−	1.74674i
$924$		0			0
$925$			55.1092i			1.81198i
$926$	13.2668	−	9.62603i	0.435973	−	0.316331i
$927$		0			0
$928$	0.121919	−	38.5198i	0.00400218	−	1.26447i
$929$	43.0944	−	24.8806i	1.41388	−	0.816304i	0.418129	−	0.908387i	$-0.362686\pi$
$929$	43.0944	−	24.8806i	1.41388	−	0.816304i	0.995751	+	0.0920830i	$0.0293525\pi$
$930$		0			0
$931$	9.42695	−	13.5792i	0.308956	−	0.445039i
$932$	3.19596	+	15.1300i	0.104687	+	0.495599i
$933$		0			0
$934$	−2.95524	−	1.31800i	−0.0966984	−	0.0431263i
$935$	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	$0.269616\pi$
$938$	44.8897	+	22.3038i	1.46570	+	0.728246i
$939$		0			0
$940$	−35.5595	−	39.5935i	−1.15982	−	1.29140i
$941$	27.1914	−	47.0968i	0.886414	−	1.53531i	0.0423286	−	0.999104i	$-0.486522\pi$
$941$	27.1914	−	47.0968i	0.886414	−	1.53531i	0.844085	−	0.536209i	$-0.180144\pi$
$942$		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	$-0.741097\pi$
$947$	−12.3501	+	7.13032i	−0.401323	+	0.231704i	0.285732	+	0.958310i	$0.407763\pi$
$948$		0			0
$949$	10.6524	+	6.15016i	0.345791	+	0.199643i
$950$	17.9972	+	24.8041i	0.583908	+	0.804751i
$951$		0			0
$952$	−13.9311	−	13.6869i	−0.451509	−	0.443595i
$953$			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
$956$	13.2643	−	40.6482i	0.428998	−	1.31466i
$957$		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
$962$	19.5191	−	43.7659i	0.629319	−	1.41107i
$963$		0			0
$964$	11.3776	+	12.6683i	0.366448	+	0.408019i
$965$	−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	$-0.0970175\pi$
$968$	17.0290	+	15.3916i	0.547333	+	0.494706i
$969$		0			0
$970$	−32.6693	+	73.2516i	−1.04895	+	2.35197i
$971$	4.93811	−	2.85102i	0.158472	−	0.0914936i	−0.418667	−	0.908140i	$-0.637503\pi$
$971$	4.93811	−	2.85102i	0.158472	−	0.0914936i	0.577139	+	0.816646i	$0.304169\pi$
$972$		0			0
$973$	−12.7414	−	8.08115i	−0.408471	−	0.259070i
$974$	4.56434	+	43.6928i	0.146251	+	1.40001i
$975$		0			0
$976$	35.1071	+	3.77981i	1.12375	+	0.120989i
$977$	−3.52730	−	2.03649i	−0.112848	−	0.0651530i	0.442514	−	0.896762i	$-0.354087\pi$
$977$	−3.52730	−	2.03649i	−0.112848	−	0.0651530i	−0.555362	+	0.831609i	$0.687420\pi$
$978$		0			0
$979$	18.8002			0.600856
$980$	−31.8389	−	42.0097i	−1.01705	−	1.34195i
$981$		0			0
$982$	−8.61861	+	6.25345i	−0.275031	+	0.199556i
$983$	−13.6318	+	23.6109i	−0.434786	+	0.753071i	−0.997278	−	0.0737313i	$-0.976509\pi$
$983$	−13.6318	+	23.6109i	−0.434786	+	0.753071i	0.562492	+	0.826803i	$0.309843\pi$
$984$		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	$-0.379732\pi$
$991$	−7.91978	−	4.57249i	−0.251580	−	0.145250i	−0.620488	+	0.784216i	$0.713065\pi$
$992$	−15.6019	+	26.8268i	−0.495361	+	0.851753i
$993$		0			0
$994$	2.19693	+	35.1233i	0.0696823	+	1.11404i
$995$		−	37.4807i		−	1.18822i
$996$		0			0
$997$	40.5025	+	23.3841i	1.28273	+	0.740583i	0.977346	−	0.211647i	$-0.0678827\pi$
$997$	40.5025	+	23.3841i	1.28273	+	0.740583i	0.305381	+	0.952230i	$0.401216\pi$
$998$	1.01759	−	2.28165i	0.0322112	−	0.0722245i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.179.17	yes	48
3.2	odd	2	inner	504.2.bm.c.179.8	yes	48
4.3	odd	2		2016.2.bu.c.431.23		48
7.2	even	3	inner	504.2.bm.c.107.15	yes	48
8.3	odd	2	inner	504.2.bm.c.179.10	yes	48
8.5	even	2		2016.2.bu.c.431.1		48
12.11	even	2		2016.2.bu.c.431.2		48
21.2	odd	6	inner	504.2.bm.c.107.10	yes	48
24.5	odd	2		2016.2.bu.c.431.24		48
24.11	even	2	inner	504.2.bm.c.179.15	yes	48
28.23	odd	6		2016.2.bu.c.1871.24		48
56.37	even	6		2016.2.bu.c.1871.2		48
56.51	odd	6	inner	504.2.bm.c.107.8	✓	48
84.23	even	6		2016.2.bu.c.1871.1		48
168.107	even	6	inner	504.2.bm.c.107.17	yes	48
168.149	odd	6		2016.2.bu.c.1871.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.8	✓	48	56.51	odd	6	inner
504.2.bm.c.107.10	yes	48	21.2	odd	6	inner
504.2.bm.c.107.15	yes	48	7.2	even	3	inner
504.2.bm.c.107.17	yes	48	168.107	even	6	inner
504.2.bm.c.179.8	yes	48	3.2	odd	2	inner
504.2.bm.c.179.10	yes	48	8.3	odd	2	inner
504.2.bm.c.179.15	yes	48	24.11	even	2	inner
504.2.bm.c.179.17	yes	48	1.1	even	1	trivial
2016.2.bu.c.431.1		48	8.5	even	2
2016.2.bu.c.431.2		48	12.11	even	2
2016.2.bu.c.431.23		48	4.3	odd	2
2016.2.bu.c.431.24		48	24.5	odd	2
2016.2.bu.c.1871.1		48	84.23	even	6
2016.2.bu.c.1871.2		48	56.37	even	6
2016.2.bu.c.1871.23		48	168.149	odd	6
2016.2.bu.c.1871.24		48	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.830529 + 1.14465i) q^{2} +(-0.620442 + 1.90133i) q^{4} +(1.88256 + 3.26069i) q^{5} +(2.23426 + 1.41706i) q^{7} +(-2.69165 + 0.868922i) q^{8} +(-2.16882 + 4.86297i) q^{10} +(-1.47084 - 0.849192i) q^{11} -5.64222i q^{13} +(0.233580 + 3.73436i) q^{14} +(-3.23010 - 2.35933i) q^{16} +(2.26012 + 1.30488i) q^{17} +(-1.18076 - 2.04513i) q^{19} +(-7.36767 + 1.55630i) q^{20} +(-0.249553 - 2.38888i) q^{22} +(-0.653873 - 1.13254i) q^{23} +(-4.58807 + 7.94677i) q^{25} +(6.45836 - 4.68603i) q^{26} +(-4.08053 + 3.36886i) q^{28} +6.80944 q^{29} +(-4.75107 - 2.74303i) q^{31} +(0.0179044 - 5.65683i) q^{32} +(0.383465 + 3.67078i) q^{34} +(-0.414472 + 9.95295i) q^{35} +(5.20109 - 3.00285i) q^{37} +(1.36030 - 3.05010i) q^{38} +(-7.90048 - 7.14084i) q^{40} +6.10456i q^{41} -6.49804 q^{43} +(2.52717 - 2.26968i) q^{44} +(0.753301 - 1.68906i) q^{46} +(3.53360 + 6.12038i) q^{47} +(2.98386 + 6.33219i) q^{49} +(-12.9068 + 1.34830i) q^{50} +(10.7277 + 3.50067i) q^{52} +(-0.488913 + 0.846821i) q^{53} -6.39462i q^{55} +(-7.24517 - 1.87284i) q^{56} +(5.65544 + 7.79442i) q^{58} +(-6.67395 - 3.85320i) q^{59} +(-7.64484 + 4.41375i) q^{61} +(-0.806095 - 7.71647i) q^{62} +(6.48995 - 4.67767i) q^{64} +(18.3975 - 10.6218i) q^{65} +(6.69828 - 11.6018i) q^{67} +(-3.88327 + 3.48762i) q^{68} +(-11.7369 + 7.79179i) q^{70} +9.40544 q^{71} +(-1.09003 + 1.88798i) q^{73} +(7.75687 + 3.45947i) q^{74} +(4.62106 - 0.976124i) q^{76} +(-2.08289 - 3.98160i) q^{77} +(15.0908 - 8.71267i) q^{79} +(1.61217 - 14.9739i) q^{80} +(-6.98758 + 5.07002i) q^{82} -11.8864i q^{83} +9.82605i q^{85} +(-5.39682 - 7.43798i) q^{86} +(4.69688 + 1.00768i) q^{88} +(-9.58642 + 5.53472i) q^{89} +(7.99538 - 12.6062i) q^{91} +(2.55902 - 0.540552i) q^{92} +(-4.07092 + 9.12788i) q^{94} +(4.44570 - 7.70018i) q^{95} +15.0631 q^{97} +(-4.76995 + 8.67454i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82}+ \cdots + 240 q^{97}+O(q^{100}) \) 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

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