LMFDB - Embedded newform 504.2.bk.c.451.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(19,504)] 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, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.19"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [32,2] 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.13
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.c.19.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03162 + 0.967346i) q^{2} +(0.128485 + 1.99587i) q^{4} +(1.25150 + 2.16767i) q^{5} +(-1.36321 - 2.26752i) q^{7} +(-1.79815 + 2.18327i) q^{8} +(-0.805806 + 3.44685i) q^{10} +(-2.83809 + 4.91572i) q^{11} +5.31228 q^{13} +(0.787162 - 3.65792i) q^{14} +(-3.96698 + 0.512879i) q^{16} +(0.393919 + 0.227429i) q^{17} +(-3.19938 + 1.84716i) q^{19} +(-4.16558 + 2.77635i) q^{20} +(-7.68304 + 2.32575i) q^{22} +(4.43443 - 2.56022i) q^{23} +(-0.632521 + 1.09556i) q^{25} +(5.48026 + 5.13881i) q^{26} +(4.35053 - 3.01213i) q^{28} -2.57962i q^{29} +(-3.00333 + 5.20192i) q^{31} +(-4.58856 - 3.30835i) q^{32} +(0.186372 + 0.615676i) q^{34} +(3.20917 - 5.79280i) q^{35} +(7.80778 - 4.50782i) q^{37} +(-5.08739 - 1.18933i) q^{38} +(-6.98299 - 1.16541i) q^{40} -4.65692i q^{41} +3.66703 q^{43} +(-10.1758 - 5.03286i) q^{44} +(7.05126 + 1.64845i) q^{46} +(-0.478841 - 0.829377i) q^{47} +(-3.28332 + 6.18222i) q^{49} +(-1.71230 + 0.518335i) q^{50} +(0.682549 + 10.6026i) q^{52} +(-5.41124 - 3.12418i) q^{53} -14.2075 q^{55} +(7.40187 + 1.10108i) q^{56} +(2.49539 - 2.66119i) q^{58} +(8.76604 + 5.06108i) q^{59} +(2.50184 + 4.33331i) q^{61} +(-8.13036 + 2.46115i) q^{62} +(-1.53334 - 7.85168i) q^{64} +(6.64834 + 11.5153i) q^{65} +(4.65133 - 8.05634i) q^{67} +(-0.403306 + 0.815431i) q^{68} +(8.91429 - 2.87159i) q^{70} -7.35240i q^{71} +(5.93541 + 3.42681i) q^{73} +(12.4153 + 2.90245i) q^{74} +(-4.09777 - 6.14821i) q^{76} +(15.0154 - 0.265718i) q^{77} +(7.71882 - 4.45646i) q^{79} +(-6.07644 - 7.95723i) q^{80} +(4.50485 - 4.80418i) q^{82} -1.96259i q^{83} +1.13851i q^{85} +(3.78299 + 3.54728i) q^{86} +(-5.62904 - 15.0355i) q^{88} +(-5.91361 + 3.41423i) q^{89} +(-7.24175 - 12.0457i) q^{91} +(5.67961 + 8.52158i) q^{92} +(0.308312 - 1.31881i) q^{94} +(-8.00807 - 4.62346i) q^{95} +3.71270i q^{97} +(-9.36748 + 3.20160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	1.03162	+	0.967346i	0.729466	+	0.684017i
$2$	1.03162	+	0.967346i	0.729466	+	0.684017i
$3$		0			0
$3$		0			0
$4$	0.128485	+	1.99587i	0.0642426	+	0.997934i
$5$	1.25150	+	2.16767i	0.559689	+	0.969410i	0.997522	+	0.0703538i	$0.0224128\pi$
$5$	1.25150	+	2.16767i	0.559689	+	0.969410i	−0.437833	+	0.899056i	$0.644254\pi$
$6$		0			0
$7$	−1.36321	−	2.26752i	−0.515245	−	0.857043i
$7$	−1.36321	−	2.26752i	−0.515245	−	0.857043i
$8$	−1.79815	+	2.18327i	−0.635741	+	0.771903i
$9$		0			0
$10$	−0.805806	+	3.44685i	−0.254818	+	1.08999i
$11$	−2.83809	+	4.91572i	−0.855717	+	1.48215i	0.0202603	+	0.999795i	$0.493550\pi$
$11$	−2.83809	+	4.91572i	−0.855717	+	1.48215i	−0.875978	+	0.482351i	$0.839783\pi$
$12$		0			0
$13$	5.31228			1.47336			0.736681	−	0.676241i	$-0.236392\pi$
$13$	5.31228			1.47336			0.736681	+	0.676241i	$0.236392\pi$
$14$	0.787162	−	3.65792i	0.210378	−	0.977620i
$15$		0			0
$16$	−3.96698	+	0.512879i	−0.991746	+	0.128220i
$17$	0.393919	+	0.227429i	0.0955393	+	0.0551596i	0.547008	−	0.837127i	$-0.315767\pi$
$17$	0.393919	+	0.227429i	0.0955393	+	0.0551596i	−0.451469	+	0.892287i	$0.649100\pi$
$18$		0			0
$19$	−3.19938	+	1.84716i	−0.733988	+	0.423768i	−0.819879	−	0.572536i	$-0.805960\pi$
$19$	−3.19938	+	1.84716i	−0.733988	+	0.423768i	0.0858912	+	0.996305i	$0.472626\pi$
$20$	−4.16558	+	2.77635i	−0.931452	+	0.620811i
$21$		0			0
$22$	−7.68304	+	2.32575i	−1.63803	+	0.495851i
$23$	4.43443	−	2.56022i	0.924642	−	0.533842i	0.0395287	−	0.999218i	$-0.487414\pi$
$23$	4.43443	−	2.56022i	0.924642	−	0.533842i	0.885113	+	0.465376i	$0.154081\pi$
$24$		0			0
$25$	−0.632521	+	1.09556i	−0.126504	+	0.219112i
$26$	5.48026	+	5.13881i	1.07477	+	1.00780i
$27$		0			0
$28$	4.35053	−	3.01213i	0.822172	−	0.569239i
$29$		−	2.57962i		−	0.479024i	−0.970893	−	0.239512i	$-0.923013\pi$
$29$		−	2.57962i		−	0.479024i	0.970893	−	0.239512i	$-0.0769874\pi$
$30$		0			0
$31$	−3.00333	+	5.20192i	−0.539414	+	0.934293i	0.459521	+	0.888167i	$0.348021\pi$
$31$	−3.00333	+	5.20192i	−0.539414	+	0.934293i	−0.998936	+	0.0461260i	$0.985312\pi$
$32$	−4.58856	−	3.30835i	−0.811150	−	0.584839i
$33$		0			0
$34$	0.186372	+	0.615676i	0.0319626	+	0.105588i
$35$	3.20917	−	5.79280i	0.542449	−	0.979161i
$36$		0			0
$37$	7.80778	−	4.50782i	1.28359	−	0.741082i	0.306088	−	0.952003i	$-0.400980\pi$
$37$	7.80778	−	4.50782i	1.28359	−	0.741082i	0.977503	+	0.210922i	$0.0676465\pi$
$38$	−5.08739	−	1.18933i	−0.825284	−	0.192935i
$39$		0			0
$40$	−6.98299	−	1.16541i	−1.10411	−	0.184268i
$41$		−	4.65692i		−	0.727289i	−0.931538	−	0.363644i	$-0.881532\pi$
$41$		−	4.65692i		−	0.727289i	0.931538	−	0.363644i	$-0.118468\pi$
$42$		0			0
$43$	3.66703			0.559217			0.279608	−	0.960114i	$-0.409795\pi$
$43$	3.66703			0.559217			0.279608	+	0.960114i	$0.409795\pi$
$44$	−10.1758	−	5.03286i	−1.53406	−	0.758733i
$45$		0			0
$46$	7.05126	+	1.64845i	1.03965	+	0.243050i
$47$	−0.478841	−	0.829377i	−0.0698461	−	0.120977i	0.828987	−	0.559267i	$-0.188918\pi$
$47$	−0.478841	−	0.829377i	−0.0698461	−	0.120977i	−0.898833	+	0.438290i	$0.855584\pi$
$48$		0			0
$49$	−3.28332	+	6.18222i	−0.469046	+	0.883174i
$50$	−1.71230	+	0.518335i	−0.242156	+	0.0733036i
$51$		0			0
$52$	0.682549	+	10.6026i	0.0946526	+	1.47032i
$53$	−5.41124	−	3.12418i	−0.743290	−	0.429139i	0.0799741	−	0.996797i	$-0.474516\pi$
$53$	−5.41124	−	3.12418i	−0.743290	−	0.429139i	−0.823264	+	0.567658i	$0.807850\pi$
$54$		0			0
$55$	−14.2075			−1.91574
$56$	7.40187	+	1.10108i	0.989116	+	0.147138i
$57$		0			0
$58$	2.49539	−	2.66119i	0.327660	−	0.349432i
$59$	8.76604	+	5.06108i	1.14124	+	0.658896i	0.946738	−	0.322006i	$-0.104357\pi$
$59$	8.76604	+	5.06108i	1.14124	+	0.658896i	0.194503	+	0.980902i	$0.437690\pi$
$60$		0			0
$61$	2.50184	+	4.33331i	0.320327	+	0.554823i	0.980555	−	0.196242i	$-0.0628738\pi$
$61$	2.50184	+	4.33331i	0.320327	+	0.554823i	−0.660228	+	0.751065i	$0.729540\pi$
$62$	−8.13036	+	2.46115i	−1.03256	+	0.312567i
$63$		0			0
$64$	−1.53334	−	7.85168i	−0.191667	−	0.981460i
$65$	6.64834	+	11.5153i	0.824625	+	1.42829i
$66$		0			0
$67$	4.65133	−	8.05634i	0.568251	−	0.984239i	−0.428489	−	0.903547i	$-0.640954\pi$
$67$	4.65133	−	8.05634i	0.568251	−	0.984239i	0.996739	−	0.0806916i	$-0.0257129\pi$
$68$	−0.403306	+	0.815431i	−0.0489080	+	0.0988856i
$69$		0			0
$70$	8.91429	−	2.87159i	1.06546	−	0.343221i
$71$		−	7.35240i		−	0.872569i	−0.899809	−	0.436285i	$-0.856294\pi$
$71$		−	7.35240i		−	0.872569i	0.899809	−	0.436285i	$-0.143706\pi$
$72$		0			0
$73$	5.93541	+	3.42681i	0.694687	+	0.401078i	0.805366	−	0.592779i	$-0.201969\pi$
$73$	5.93541	+	3.42681i	0.694687	+	0.401078i	−0.110678	+	0.993856i	$0.535302\pi$
$74$	12.4153	+	2.90245i	1.44325	+	0.337403i
$75$		0			0
$76$	−4.09777	−	6.14821i	−0.470046	−	0.705248i
$77$	15.0154	−	0.265718i	1.71117	−	0.0302814i
$78$		0			0
$79$	7.71882	−	4.45646i	0.868435	−	0.501391i	0.00160740	−	0.999999i	$-0.499488\pi$
$79$	7.71882	−	4.45646i	0.868435	−	0.501391i	0.866828	+	0.498607i	$0.166155\pi$
$80$	−6.07644	−	7.95723i	−0.679367	−	0.889645i
$81$		0			0
$82$	4.50485	−	4.80418i	0.497478	−	0.530533i
$83$		−	1.96259i		−	0.215423i	−0.994182	−	0.107711i	$-0.965648\pi$
$83$		−	1.96259i		−	0.215423i	0.994182	−	0.107711i	$-0.0343522\pi$
$84$		0			0
$85$			1.13851i			0.123489i
$86$	3.78299	+	3.54728i	0.407930	+	0.382514i
$87$		0			0
$88$	−5.62904	−	15.0355i	−0.600058	−	1.60279i
$89$	−5.91361	+	3.41423i	−0.626842	+	0.361907i	−0.779528	−	0.626367i	$-0.784541\pi$
$89$	−5.91361	+	3.41423i	−0.626842	+	0.361907i	0.152686	+	0.988275i	$0.451208\pi$
$90$		0			0
$91$	−7.24175	−	12.0457i	−0.759142	−	1.26273i
$92$	5.67961	+	8.52158i	0.592141	+	0.888436i
$93$		0			0
$94$	0.308312	−	1.31881i	0.0317999	−	0.136025i
$95$	−8.00807	−	4.62346i	−0.821611	−	0.474357i
$96$		0			0
$97$			3.71270i			0.376967i	0.982076	+	0.188484i	$0.0603573\pi$
$97$			3.71270i			0.376967i	−0.982076	+	0.188484i	$0.939643\pi$
$98$	−9.36748	+	3.20160i	−0.946259	+	0.323411i
$99$		0			0
$100$	−2.26786	−	1.12167i	−0.226786	−	0.112167i
$101$	2.84077	−	4.92036i	0.282667	−	0.489594i	−0.689373	−	0.724406i	$-0.742114\pi$
$101$	2.84077	−	4.92036i	0.282667	−	0.489594i	0.972041	+	0.234812i	$0.0754474\pi$
$102$		0			0
$103$	−2.95345	−	5.11553i	−0.291013	−	0.504049i	0.683037	−	0.730384i	$-0.260659\pi$
$103$	−2.95345	−	5.11553i	−0.291013	−	0.504049i	−0.974049	+	0.226335i	$0.927325\pi$
$104$	−9.55226	+	11.5981i	−0.936676	+	1.13729i
$105$		0			0
$106$	−2.56019	−	8.45750i	−0.248667	−	0.821465i
$107$	−5.33045	−	9.23261i	−0.515314	−	0.892550i	−0.999842	−	0.0177741i	$-0.994342\pi$
$107$	−5.33045	−	9.23261i	−0.515314	−	0.892550i	0.484528	−	0.874776i	$-0.338991\pi$
$108$		0			0
$109$	−2.75319	−	1.58956i	−0.263708	−	0.152252i	0.362317	−	0.932055i	$-0.381986\pi$
$109$	−2.75319	−	1.58956i	−0.263708	−	0.152252i	−0.626025	+	0.779803i	$0.715319\pi$
$110$	−14.6568	−	13.7436i	−1.39747	−	1.31040i
$111$		0			0
$112$	6.57079	+	8.29606i	0.620882	+	0.783904i
$113$	0.302446			0.0284518			0.0142259	−	0.999899i	$-0.495472\pi$
$113$	0.302446			0.0284518			0.0142259	+	0.999899i	$0.495472\pi$
$114$		0			0
$115$	11.0994	+	6.40824i	1.03502	+	0.597571i
$116$	5.14859	−	0.331443i	0.478034	−	0.0307737i
$117$		0			0
$118$	4.14742	+	13.7009i	0.381801	+	1.26127i
$119$	−0.0212932	−	1.20325i	−0.00195194	−	0.110302i
$120$		0			0
$121$	−10.6096	−	18.3763i	−0.964505	−	1.67057i
$122$	−1.61086	+	6.89047i	−0.145840	+	0.623834i
$123$		0			0
$124$	−10.7682	−	5.32588i	−0.967016	−	0.478278i
$125$	9.34863			0.836167
$126$		0			0
$127$		−	6.39751i		−	0.567687i	−0.958871	−	0.283843i	$-0.908390\pi$
$127$		−	6.39751i		−	0.567687i	0.958871	−	0.283843i	$-0.0916096\pi$
$128$	6.01346	−	9.58323i	0.531520	−	0.847046i
$129$		0			0
$130$	−4.28067	+	18.3106i	−0.375439	+	1.60595i
$131$	12.5596	−	7.25130i	1.09734	−	0.633549i	0.161818	−	0.986821i	$-0.448264\pi$
$131$	12.5596	−	7.25130i	1.09734	−	0.633549i	0.935521	+	0.353272i	$0.114931\pi$
$132$		0			0
$133$	8.54991	+	4.73660i	0.741371	+	0.410715i
$134$	12.5917	−	3.81165i	1.08776	−	0.329276i
$135$		0			0
$136$	−1.20486	+	0.451080i	−0.103316	+	0.0386798i
$137$	0.615559	−	1.06618i	0.0525908	−	0.0910899i	−0.838532	−	0.544853i	$-0.816585\pi$
$137$	0.615559	−	1.06618i	0.0525908	−	0.0910899i	0.891122	+	0.453763i	$0.149919\pi$
$138$		0			0
$139$			15.7788i			1.33834i	0.743108	+	0.669172i	$0.233351\pi$
$139$			15.7788i			1.33834i	−0.743108	+	0.669172i	$0.766649\pi$
$140$	11.9740	+	5.66080i	1.01199	+	0.478425i
$141$		0			0
$142$	7.11231	−	7.58489i	0.596852	−	0.636510i
$143$	−15.0768	+	26.1137i	−1.26078	+	2.18374i
$144$		0			0
$145$	5.59176	−	3.22841i	0.464371	−	0.268104i
$146$	2.80819	+	9.27676i	0.232407	+	0.767750i
$147$		0			0
$148$	10.0002	+	15.0041i	0.822012	+	1.23333i
$149$	−5.15767	+	2.97778i	−0.422532	+	0.243949i	−0.696160	−	0.717886i	$-0.745110\pi$
$149$	−5.15767	+	2.97778i	−0.422532	+	0.243949i	0.273628	+	0.961836i	$0.411776\pi$
$150$		0			0
$151$	−3.11126	−	1.79629i	−0.253191	−	0.146180i	0.368034	−	0.929812i	$-0.380031\pi$
$151$	−3.11126	−	1.79629i	−0.253191	−	0.146180i	−0.621224	+	0.783633i	$0.713364\pi$
$152$	1.72010	−	10.3066i	0.139518	−	0.835974i
$153$		0			0
$154$	15.7473	+	14.2510i	1.26895	+	1.14838i
$155$	−15.0347			−1.20762
$156$		0			0
$157$	0.491762	−	0.851757i	0.0392469	−	0.0679776i	−0.845735	−	0.533604i	$-0.820837\pi$
$157$	0.491762	−	0.851757i	0.0392469	−	0.0679776i	0.884982	+	0.465626i	$0.154171\pi$
$158$	12.2738	+	2.86939i	0.976455	+	0.228276i
$159$		0			0
$160$	1.42880	−	14.0869i	0.112957	−	1.11366i
$161$	−11.8504	−	6.56505i	−0.933942	−	0.517398i
$162$		0			0
$163$	−1.26083	−	2.18383i	−0.0987562	−	0.171051i	0.812414	−	0.583081i	$-0.198153\pi$
$163$	−1.26083	−	2.18383i	−0.0987562	−	0.171051i	−0.911170	+	0.412030i	$0.864820\pi$
$164$	9.29460	−	0.598345i	0.725787	−	0.0467229i
$165$		0			0
$166$	1.89851	−	2.02465i	0.147353	−	0.157144i
$167$	−5.26232			−0.407211			−0.203605	−	0.979053i	$-0.565266\pi$
$167$	−5.26232			−0.407211			−0.203605	+	0.979053i	$0.565266\pi$
$168$		0			0
$169$	15.2203			1.17079
$170$	−1.10134	+	1.17451i	−0.0844686	+	0.0900811i
$171$		0			0
$172$	0.471159	+	7.31891i	0.0359255	+	0.558062i
$173$	−0.0718117	−	0.124381i	−0.00545974	−	0.00945654i	0.863283	−	0.504721i	$-0.168405\pi$
$173$	−0.0718117	−	0.124381i	−0.00545974	−	0.00945654i	−0.868742	+	0.495264i	$0.835071\pi$
$174$		0			0
$175$	3.34646	−	0.0592202i	0.252969	−	0.00447662i
$176$	8.73750	−	20.9562i	0.658614	−	1.57963i
$177$		0			0
$178$	−9.40335	−	2.19832i	−0.704811	−	0.164771i
$179$	−9.46239	+	16.3893i	−0.707252	+	1.22500i	0.258621	+	0.965979i	$0.416732\pi$
$179$	−9.46239	+	16.3893i	−0.707252	+	1.22500i	−0.965873	+	0.259018i	$0.916601\pi$
$180$		0			0
$181$	−22.2260			−1.65204			−0.826022	−	0.563637i	$-0.809402\pi$
$181$	−22.2260			−1.65204			−0.826022	+	0.563637i	$0.809402\pi$
$182$	4.18163	−	19.4319i	0.309963	−	1.44039i
$183$		0			0
$184$	−2.38410	+	14.2852i	−0.175758	+	1.05312i
$185$	19.5429	+	11.2831i	1.43682	+	0.829551i
$186$		0			0
$187$	−2.23596	+	1.29093i	−0.163509	+	0.0944021i
$188$	1.59380	−	1.06227i	0.116240	−	0.0774737i
$189$		0			0
$190$	−3.78881	−	12.5162i	−0.274869	−	0.908023i
$191$	−10.2112	+	5.89547i	−0.738860	+	0.426581i	−0.821655	−	0.569986i	$-0.806949\pi$
$191$	−10.2112	+	5.89547i	−0.738860	+	0.426581i	0.0827947	+	0.996567i	$0.473615\pi$
$192$		0			0
$193$	−13.4112	+	23.2289i	−0.965361	+	1.67205i	−0.256719	+	0.966486i	$0.582641\pi$
$193$	−13.4112	+	23.2289i	−0.965361	+	1.67205i	−0.708642	+	0.705568i	$0.750692\pi$
$194$	−3.59146	+	3.83010i	−0.257852	+	0.274985i
$195$		0			0
$196$	−12.7608	−	5.75875i	−0.911482	−	0.411339i
$197$			16.5842i			1.18157i	0.806828	+	0.590786i	$0.201182\pi$
$197$			16.5842i			1.18157i	−0.806828	+	0.590786i	$0.798818\pi$
$198$		0			0
$199$	−5.70420	+	9.87996i	−0.404360	+	0.700372i	−0.994247	−	0.107114i	$-0.965839\pi$
$199$	−5.70420	+	9.87996i	−0.404360	+	0.700372i	0.589887	+	0.807486i	$0.299172\pi$
$200$	−1.25453	−	3.35094i	−0.0887090	−	0.236947i
$201$		0			0
$202$	7.69029	−	2.32794i	0.541087	−	0.163793i
$203$	−5.84935	+	3.51657i	−0.410544	+	0.246815i
$204$		0			0
$205$	10.0947	−	5.82815i	0.705041	−	0.407056i
$206$	1.90164	−	8.13430i	0.132494	−	0.566744i
$207$		0			0
$208$	−21.0737	+	2.72456i	−1.46120	+	0.188914i
$209$		−	20.9697i		−	1.45050i
$210$		0			0
$211$	−4.13300			−0.284527			−0.142264	−	0.989829i	$-0.545438\pi$
$211$	−4.13300			−0.284527			−0.142264	+	0.989829i	$0.545438\pi$
$212$	5.54019	−	11.2015i	0.380502	−	0.769324i
$213$		0			0
$214$	3.43212	−	14.6809i	0.234615	−	1.00357i
$215$	4.58930	+	7.94890i	0.312988	+	0.542110i
$216$		0			0
$217$	15.8896	−	0.281189i	1.07866	−	0.0190883i
$218$	−1.30260	−	4.30311i	−0.0882233	−	0.291443i
$219$		0			0
$220$	−1.82546	−	28.3564i	−0.123072	−	1.91179i
$221$	2.09261	+	1.20817i	0.140764	+	0.0812701i
$222$		0			0
$223$	18.1063			1.21249			0.606245	−	0.795278i	$-0.292675\pi$
$223$	18.1063			1.21249			0.606245	+	0.795278i	$0.292675\pi$
$224$	−1.24659	+	14.9146i	−0.0832911	+	0.996525i
$225$		0			0
$226$	0.312010	+	0.292570i	0.0207546	+	0.0194615i
$227$	−6.86343	−	3.96260i	−0.455542	−	0.263007i	0.254626	−	0.967040i	$-0.418048\pi$
$227$	−6.86343	−	3.96260i	−0.455542	−	0.263007i	−0.710168	+	0.704032i	$0.751381\pi$
$228$		0			0
$229$	−1.07787	−	1.86692i	−0.0712274	−	0.123370i	0.828212	−	0.560415i	$-0.189358\pi$
$229$	−1.07787	−	1.86692i	−0.0712274	−	0.123370i	−0.899440	+	0.437045i	$0.856025\pi$
$230$	5.25139	+	17.3478i	0.346266	+	1.14388i
$231$		0			0
$232$	5.63201	+	4.63854i	0.369760	+	0.304535i
$233$	−10.0072	−	17.3330i	−0.655594	−	1.13552i	−0.981745	−	0.190204i	$-0.939085\pi$
$233$	−10.0072	−	17.3330i	−0.655594	−	1.13552i	0.326151	−	0.945318i	$-0.394248\pi$
$234$		0			0
$235$	1.19854	−	2.07594i	0.0781843	−	0.135419i
$236$	−8.97493	+	18.1461i	−0.584219	+	1.18121i
$237$		0			0
$238$	1.14199	−	1.26190i	0.0740245	−	0.0817968i
$239$		−	18.8923i		−	1.22204i	−0.791614	−	0.611021i	$-0.790759\pi$
$239$		−	18.8923i		−	1.22204i	0.791614	−	0.611021i	$-0.209241\pi$
$240$		0			0
$241$	−15.8555	−	9.15417i	−1.02134	−	0.589672i	−0.106849	−	0.994275i	$-0.534076\pi$
$241$	−15.8555	−	9.15417i	−1.02134	−	0.589672i	−0.914492	+	0.404603i	$0.867410\pi$
$242$	6.83118	−	29.2205i	0.439125	−	1.87836i
$243$		0			0
$244$	−8.32726	+	5.55010i	−0.533098	+	0.355309i
$245$	−17.5101	+	0.619923i	−1.11868	+	0.0396054i
$246$		0			0
$247$	−16.9960	+	9.81265i	−1.08143	+	0.624364i
$248$	−5.95677	−	15.9109i	−0.378255	−	1.01034i
$249$		0			0
$250$	9.64424	+	9.04335i	0.609955	+	0.571952i
$251$		−	3.43251i		−	0.216658i	−0.994115	−	0.108329i	$-0.965450\pi$
$251$		−	3.43251i		−	0.216658i	0.994115	−	0.108329i	$-0.0345500\pi$
$252$		0			0
$253$			29.0645i			1.82727i
$254$	6.18860	−	6.59981i	0.388307	−	0.414109i
$255$		0			0
$256$	15.4739	−	4.06917i	0.967119	−	0.254323i
$257$	−21.7104	+	12.5345i	−1.35426	+	0.781882i	−0.988843	−	0.148962i	$-0.952407\pi$
$257$	−21.7104	+	12.5345i	−1.35426	+	0.781882i	−0.365417	+	0.930844i	$0.619073\pi$
$258$		0			0
$259$	−20.8652	−	11.5592i	−1.29650	−	0.718254i
$260$	−22.1287	+	14.7487i	−1.37237	+	0.914678i
$261$		0			0
$262$	19.9713	+	4.66890i	1.23383	+	0.288445i
$263$	13.4314	+	7.75460i	0.828214	+	0.478169i	0.853241	−	0.521517i	$-0.174634\pi$
$263$	13.4314	+	7.75460i	0.828214	+	0.478169i	−0.0250270	+	0.999687i	$0.507967\pi$
$264$		0			0
$265$		−	15.6397i		−	0.960738i
$266$	4.23834	+	13.1571i	0.259870	+	0.806713i
$267$		0			0
$268$	16.6770	+	8.24832i	1.01871	+	0.503847i
$269$	−11.8667	+	20.5537i	−0.723523	+	1.25318i	0.236055	+	0.971740i	$0.424145\pi$
$269$	−11.8667	+	20.5537i	−0.723523	+	1.25318i	−0.959579	+	0.281440i	$0.909188\pi$
$270$		0			0
$271$	−7.35684	−	12.7424i	−0.446896	−	0.774047i	0.551286	−	0.834316i	$-0.314137\pi$
$271$	−7.35684	−	12.7424i	−0.446896	−	0.774047i	−0.998182	+	0.0602693i	$0.980804\pi$
$272$	−1.67931	−	0.700175i	−0.101823	−	0.0424543i
$273$		0			0
$274$	1.66639	−	0.504436i	0.100670	−	0.0304741i
$275$	−3.59031	−	6.21859i	−0.216504	−	0.374995i
$276$		0			0
$277$	−6.16822	−	3.56123i	−0.370613	−	0.213973i	0.303113	−	0.952954i	$-0.401974\pi$
$277$	−6.16822	−	3.56123i	−0.370613	−	0.213973i	−0.673726	+	0.738981i	$0.735307\pi$
$278$	−15.2636	+	16.2778i	−0.915449	+	0.976277i
$279$		0			0
$280$	6.87668	+	17.4228i	0.410960	+	1.04121i
$281$	13.0561			0.778861			0.389430	−	0.921056i	$-0.372672\pi$
$281$	13.0561			0.778861			0.389430	+	0.921056i	$0.372672\pi$
$282$		0			0
$283$	−1.83051	−	1.05685i	−0.108813	−	0.0628230i	0.444606	−	0.895726i	$-0.353344\pi$
$283$	−1.83051	−	1.05685i	−0.108813	−	0.0628230i	−0.553419	+	0.832903i	$0.686677\pi$
$284$	14.6744	−	0.944674i	0.870767	−	0.0560561i
$285$		0			0
$286$	−40.8145	+	12.3550i	−2.41341	+	0.730568i
$287$	−10.5597	+	6.34836i	−0.623318	+	0.374732i
$288$		0			0
$289$	−8.39655	−	14.5433i	−0.493915	−	0.855486i
$290$	8.89156	+	2.07867i	0.522131	+	0.122064i
$291$		0			0
$292$	−6.07685	+	12.2866i	−0.355621	+	0.719018i
$293$	0.334002			0.0195126			0.00975630	−	0.999952i	$-0.496894\pi$
$293$	0.334002			0.0195126			0.00975630	+	0.999952i	$0.496894\pi$
$294$		0			0
$295$			25.3358i			1.47511i
$296$	−4.19774	+	25.1522i	−0.243988	+	1.46194i
$297$		0			0
$298$	−8.20130	−	1.91730i	−0.475089	−	0.111066i
$299$	23.5569	−	13.6006i	1.36233	−	0.786542i
$300$		0			0
$301$	−4.99893	−	8.31507i	−0.288134	−	0.479273i
$302$	−1.47201	−	4.86275i	−0.0847047	−	0.279820i
$303$		0			0
$304$	11.7445	−	8.96856i	0.673594	−	0.514382i
$305$	−6.26211	+	10.8463i	−0.358567	+	0.621057i
$306$		0			0
$307$		−	9.39141i		−	0.535996i	−0.963419	−	0.267998i	$-0.913638\pi$
$307$		−	9.39141i		−	0.535996i	0.963419	−	0.267998i	$-0.0863621\pi$
$308$	2.45960	+	29.9347i	0.140149	+	1.70569i
$309$		0			0
$310$	−15.5101	−	14.5438i	−0.880916	−	0.826030i
$311$	7.93750	−	13.7482i	0.450095	−	0.779587i	−0.548297	−	0.836284i	$-0.684724\pi$
$311$	7.93750	−	13.7482i	0.450095	−	0.779587i	0.998391	+	0.0566971i	$0.0180569\pi$
$312$		0			0
$313$	−27.8562	+	16.0828i	−1.57453	+	0.909054i	−0.578924	+	0.815381i	$0.696527\pi$
$313$	−27.8562	+	16.0828i	−1.57453	+	0.909054i	−0.995603	+	0.0936727i	$0.970139\pi$
$314$	1.33125	−	0.402987i	0.0751271	−	0.0227418i
$315$		0			0
$316$	9.88627	+	14.8332i	0.556146	+	0.834431i
$317$	13.2252	−	7.63558i	0.742802	−	0.428857i	−0.0802854	−	0.996772i	$-0.525583\pi$
$317$	13.2252	−	7.63558i	0.742802	−	0.428857i	0.823087	+	0.567915i	$0.192250\pi$
$318$		0			0
$319$	12.6807	+	7.32121i	0.709983	+	0.409909i
$320$	15.1009	−	13.1502i	0.844163	−	0.735117i
$321$		0			0
$322$	−5.87446	−	18.2361i	−0.327371	−	1.01626i
$323$	−1.68039			−0.0934996
$324$		0			0
$325$	−3.36013	+	5.81991i	−0.186386	+	0.322831i
$326$	0.811814	−	3.47255i	0.0449622	−	0.192327i
$327$		0			0
$328$	10.1673	+	8.37383i	0.561396	+	0.462367i
$329$	−1.22787	+	2.21640i	−0.0676947	+	0.122194i
$330$		0			0
$331$	10.5189	+	18.2193i	0.578174	+	1.00143i	0.995689	+	0.0927561i	$0.0295677\pi$
$331$	10.5189	+	18.2193i	0.578174	+	1.00143i	−0.417515	+	0.908670i	$0.637099\pi$
$332$	3.91708	−	0.252164i	0.214978	−	0.0138393i
$333$		0			0
$334$	−5.42872	−	5.09048i	−0.297046	−	0.278539i
$335$	23.2846			1.27217
$336$		0			0
$337$	1.18351			0.0644697			0.0322348	−	0.999480i	$-0.489738\pi$
$337$	1.18351			0.0644697			0.0322348	+	0.999480i	$0.489738\pi$
$338$	15.7016	+	14.7233i	0.854056	+	0.800843i
$339$		0			0
$340$	−2.27232	+	0.146282i	−0.123234	+	0.00793326i
$341$	−17.0475	−	29.5271i	−0.923172	−	1.59898i
$342$		0			0
$343$	18.4942	−	0.982659i	0.998591	−	0.0530586i
$344$	−6.59386	+	8.00612i	−0.355517	+	0.431661i
$345$		0			0
$346$	0.0462374	−	0.197781i	0.00248574	−	0.0106328i
$347$	−2.40670	+	4.16854i	−0.129199	+	0.223779i	−0.923366	−	0.383920i	$-0.874574\pi$
$347$	−2.40670	+	4.16854i	−0.129199	+	0.223779i	0.794168	+	0.607699i	$0.207907\pi$
$348$		0			0
$349$	35.4792			1.89916			0.949578	−	0.313530i	$-0.101512\pi$
$349$	35.4792			1.89916			0.949578	+	0.313530i	$0.101512\pi$
$350$	3.50957	+	3.17609i	0.187594	+	0.169769i
$351$		0			0
$352$	29.2857	−	13.1667i	1.56093	−	0.701786i
$353$	4.13712	+	2.38857i	0.220197	+	0.127131i	0.606041	−	0.795433i	$-0.292757\pi$
$353$	4.13712	+	2.38857i	0.220197	+	0.127131i	−0.385845	+	0.922564i	$0.626090\pi$
$354$		0			0
$355$	15.9375	−	9.20155i	0.845877	−	0.488367i
$356$	−7.57416	−	11.3641i	−0.401430	−	0.602297i
$357$		0			0
$358$	−25.6158	+	7.75419i	−1.35383	+	0.409822i
$359$	31.9690	−	18.4573i	1.68726	−	0.974140i	0.730656	−	0.682745i	$-0.239214\pi$
$359$	31.9690	−	18.4573i	1.68726	−	0.974140i	0.956603	−	0.291394i	$-0.0941192\pi$
$360$		0			0
$361$	−2.67598	+	4.63493i	−0.140841	+	0.243943i
$362$	−22.9288	−	21.5002i	−1.20511	−	1.13003i
$363$		0			0
$364$	23.1112	−	16.0013i	1.21136	−	0.838695i
$365$			17.1547i			0.897916i
$366$		0			0
$367$	−0.284416	+	0.492623i	−0.0148464	+	0.0257147i	−0.873353	−	0.487088i	$-0.838059\pi$
$367$	−0.284416	+	0.492623i	−0.0148464	+	0.0257147i	0.858507	+	0.512802i	$0.171393\pi$
$368$	−16.2782	+	12.4307i	−0.848560	+	0.647993i
$369$		0			0
$370$	9.24623	+	30.5447i	0.480689	+	1.58794i
$371$	0.292503	+	16.5290i	0.0151860	+	0.858143i
$372$		0			0
$373$	−20.2929	+	11.7161i	−1.05073	+	0.606638i	−0.922853	−	0.385153i	$-0.874149\pi$
$373$	−20.2929	+	11.7161i	−1.05073	+	0.606638i	−0.127874	+	0.991790i	$0.540815\pi$
$374$	−3.55544	−	0.831191i	−0.183847	−	0.0429799i
$375$		0			0
$376$	2.67178	+	0.445902i	0.137787	+	0.0229956i
$377$		−	13.7037i		−	0.705775i
$378$		0			0
$379$	−14.7240			−0.756320			−0.378160	−	0.925740i	$-0.623443\pi$
$379$	−14.7240			−0.756320			−0.378160	+	0.925740i	$0.623443\pi$
$380$	8.19890	−	16.5771i	0.420595	−	0.850387i
$381$		0			0
$382$	−16.2371	−	3.79592i	−0.830762	−	0.194216i
$383$	−2.49754	−	4.32587i	−0.127618	−	0.221042i	0.795135	−	0.606432i	$-0.207400\pi$
$383$	−2.49754	−	4.32587i	−0.127618	−	0.221042i	−0.922753	+	0.385391i	$0.874067\pi$
$384$		0			0
$385$	19.3678	+	32.2159i	0.987077	+	1.64187i
$386$	−36.3057	+	10.9902i	−1.84791	+	0.559385i
$387$		0			0
$388$	−7.41006	+	0.477027i	−0.376189	+	0.0242174i
$389$	−27.6098	−	15.9405i	−1.39987	−	0.808216i	−0.405492	−	0.914099i	$-0.632900\pi$
$389$	−27.6098	−	15.9405i	−1.39987	−	0.808216i	−0.994379	+	0.105883i	$0.966233\pi$
$390$		0			0
$391$	2.32907			0.117786
$392$	−7.59356	−	18.2849i	−0.383533	−	0.923527i
$393$		0			0
$394$	−16.0426	+	17.1086i	−0.808215	+	0.861917i
$395$	19.3203	+	11.1546i	0.972108	+	0.561247i
$396$		0			0
$397$	−16.4530	−	28.4975i	−0.825753	−	1.43025i	−0.901343	−	0.433107i	$-0.857417\pi$
$397$	−16.4530	−	28.4975i	−0.825753	−	1.43025i	0.0755896	−	0.997139i	$-0.475916\pi$
$398$	−15.4419	+	4.67445i	−0.774033	+	0.234309i
$399$		0			0
$400$	1.94731	−	4.67047i	0.0973655	−	0.233523i
$401$	0.106236	+	0.184006i	0.00530517	+	0.00918883i	0.868666	−	0.495399i	$-0.164978\pi$
$401$	0.106236	+	0.184006i	0.00530517	+	0.00918883i	−0.863361	+	0.504587i	$0.831645\pi$
$402$		0			0
$403$	−15.9545	+	27.6341i	−0.794752	+	1.37655i
$404$	10.1854	+	5.03762i	0.506742	+	0.250631i
$405$		0			0
$406$	−9.43605	−	2.03058i	−0.468303	−	0.100776i
$407$			51.1745i			2.53663i
$408$		0			0
$409$	17.7288	+	10.2357i	0.876633	+	0.506124i	0.869547	−	0.493851i	$-0.164411\pi$
$409$	17.7288	+	10.2357i	0.876633	+	0.506124i	0.00708628	+	0.999975i	$0.497744\pi$
$410$	16.0517	+	3.75257i	0.792737	+	0.185326i
$411$		0			0
$412$	9.83046	−	6.55198i	0.484312	−	0.322793i
$413$	−0.473847	−	26.7765i	−0.0233165	−	1.31759i
$414$		0			0
$415$	4.25425	−	2.45619i	0.208833	−	0.120570i
$416$	−24.3757	−	17.5749i	−1.19512	−	0.861679i
$417$		0			0
$418$	20.2849	−	21.6328i	0.992169	−	1.05809i
$419$			11.8439i			0.578614i	0.957236	+	0.289307i	$0.0934248\pi$
$419$			11.8439i			0.578614i	−0.957236	+	0.289307i	$0.906575\pi$
$420$		0			0
$421$		−	21.7928i		−	1.06211i	−0.847336	−	0.531057i	$-0.821795\pi$
$421$		−	21.7928i		−	1.06211i	0.847336	−	0.531057i	$-0.178205\pi$
$422$	−4.26369	−	3.99804i	−0.207553	−	0.194621i
$423$		0			0
$424$	16.5511	−	6.19646i	0.803793	−	0.300927i
$425$	−0.498323	+	0.287707i	−0.0241722	+	0.0139558i
$426$		0			0
$427$	6.41534	−	11.5802i	0.310460	−	0.560404i
$428$	17.7422	−	11.8251i	0.857601	−	0.571589i
$429$		0			0
$430$	−2.95491	+	12.6397i	−0.142499	+	0.609540i
$431$	−14.3234	−	8.26964i	−0.689936	−	0.398335i	0.113652	−	0.993521i	$-0.463745\pi$
$431$	−14.3234	−	8.26964i	−0.689936	−	0.398335i	−0.803588	+	0.595186i	$0.797078\pi$
$432$		0			0
$433$		−	39.2724i		−	1.88731i	−0.330929	−	0.943656i	$-0.607362\pi$
$433$		−	39.2724i		−	1.88731i	0.330929	−	0.943656i	$-0.392638\pi$
$434$	16.6641	+	15.0807i	0.799903	+	0.723897i
$435$		0			0
$436$	2.81880	−	5.69924i	0.134996	−	0.272944i
$437$	−9.45828	+	16.3822i	−0.452451	+	0.783668i
$438$		0			0
$439$	15.5165	+	26.8754i	0.740564	+	1.28269i	0.952239	+	0.305355i	$0.0987750\pi$
$439$	15.5165	+	26.8754i	0.740564	+	1.28269i	−0.211674	+	0.977340i	$0.567892\pi$
$440$	25.5472	−	31.0189i	1.21792	−	1.47877i
$441$		0			0
$442$	0.990063	+	3.27064i	0.0470925	+	0.155569i
$443$	−0.422464	−	0.731729i	−0.0200719	−	0.0347655i	0.855815	−	0.517282i	$-0.173056\pi$
$443$	−0.422464	−	0.731729i	−0.0200719	−	0.0347655i	−0.875887	+	0.482517i	$0.839723\pi$
$444$		0			0
$445$	−14.8018	−	8.54583i	−0.701673	−	0.405111i
$446$	18.6789	+	17.5151i	0.884470	+	0.829363i
$447$		0			0
$448$	−15.7136	+	14.1804i	−0.742398	+	0.669959i
$449$	41.7433			1.96999			0.984995	−	0.172585i	$-0.0552119\pi$
$449$	41.7433			1.96999			0.984995	+	0.172585i	$0.0552119\pi$
$450$		0			0
$451$	22.8921	+	13.2168i	1.07795	+	0.622354i
$452$	0.0388599	+	0.603643i	0.00182782	+	0.0283930i
$453$		0			0
$454$	−3.24726	−	10.7272i	−0.152401	−	0.503453i
$455$	17.0480	−	30.7730i	0.799224	−	1.44266i
$456$		0			0
$457$	3.74286	+	6.48282i	0.175083	+	0.303254i	0.940190	−	0.340650i	$-0.110647\pi$
$457$	3.74286	+	6.48282i	0.175083	+	0.303254i	−0.765107	+	0.643904i	$0.777314\pi$
$458$	0.694006	−	2.96862i	0.0324288	−	0.138715i
$459$		0			0
$460$	−11.3639	+	22.9763i	−0.529844	+	1.07128i
$461$	4.33499			0.201901			0.100950	−	0.994891i	$-0.467812\pi$
$461$	4.33499			0.201901			0.100950	+	0.994891i	$0.467812\pi$
$462$		0			0
$463$		−	35.3200i		−	1.64146i	−0.571316	−	0.820730i	$-0.693567\pi$
$463$		−	35.3200i		−	1.64146i	0.571316	−	0.820730i	$-0.306433\pi$
$464$	1.32303	+	10.2333i	0.0614203	+	0.475070i
$465$		0			0
$466$	6.44334	−	27.5615i	0.298482	−	1.27676i
$467$	−9.09213	+	5.24934i	−0.420733	+	0.242911i	−0.695391	−	0.718632i	$-0.744769\pi$
$467$	−9.09213	+	5.24934i	−0.420733	+	0.242911i	0.274658	+	0.961542i	$0.411435\pi$
$468$		0			0
$469$	−24.6087	+	0.435484i	−1.13632	+	0.0201088i
$470$	3.24459	−	0.982175i	0.149662	−	0.0453044i
$471$		0			0
$472$	−26.8123	+	10.0381i	−1.23414	+	0.462040i
$473$	−10.4074	+	18.0261i	−0.478532	+	0.828841i
$474$		0			0
$475$		−	4.67348i		−	0.214434i
$476$	2.39880	−	0.197099i	0.109949	−	0.00903400i
$477$		0			0
$478$	18.2754	−	19.4897i	0.835897	−	0.891439i
$479$	8.46375	−	14.6596i	0.386719	−	0.669816i	−0.605287	−	0.796007i	$-0.706942\pi$
$479$	8.46375	−	14.6596i	0.386719	−	0.669816i	0.992006	+	0.126191i	$0.0402752\pi$
$480$		0			0
$481$	41.4771	−	23.9468i	1.89119	−	1.09188i
$482$	−7.50161	−	24.7814i	−0.341689	−	1.12876i
$483$		0			0
$484$	35.3135	−	23.5364i	1.60516	−	1.06983i
$485$	−8.04790	+	4.64645i	−0.365436	+	0.210985i
$486$		0			0
$487$	−20.5482	−	11.8635i	−0.931127	−	0.537586i	−0.0439591	−	0.999033i	$-0.513997\pi$
$487$	−20.5482	−	11.8635i	−0.931127	−	0.537586i	−0.887168	+	0.461447i	$0.847330\pi$
$488$	−13.9594	−	2.32974i	−0.631914	−	0.105462i
$489$		0			0
$490$	−18.6634	−	16.2988i	−0.843129	−	0.736303i
$491$	3.41198			0.153980			0.0769901	−	0.997032i	$-0.475469\pi$
$491$	3.41198			0.153980			0.0769901	+	0.997032i	$0.475469\pi$
$492$		0			0
$493$	0.586681	−	1.01616i	0.0264228	−	0.0457656i
$494$	−27.0257	−	6.31807i	−1.21594	−	0.284264i
$495$		0			0
$496$	9.24621	−	22.1763i	0.415167	−	0.995744i
$497$	−16.6717	+	10.0229i	−0.747829	+	0.449587i
$498$		0			0
$499$	8.72998	+	15.1208i	0.390808	+	0.676899i	0.992556	−	0.121787i	$-0.0388624\pi$
$499$	8.72998	+	15.1208i	0.390808	+	0.676899i	−0.601749	+	0.798686i	$0.705529\pi$
$500$	1.20116	+	18.6586i	0.0537175	+	0.834439i
$501$		0			0
$502$	3.32043	−	3.54105i	0.148198	−	0.158045i
$503$	7.08646			0.315970			0.157985	−	0.987442i	$-0.449500\pi$
$503$	7.08646			0.315970			0.157985	+	0.987442i	$0.449500\pi$
$504$		0			0
$505$	14.2209			0.632824
$506$	−28.1155	+	29.9836i	−1.24988	+	1.33293i
$507$		0			0
$508$	12.7686	−	0.821985i	0.566514	−	0.0364697i
$509$	18.9653	+	32.8488i	0.840622	+	1.45600i	0.889370	+	0.457188i	$0.151143\pi$
$509$	18.9653	+	32.8488i	0.840622	+	1.45600i	−0.0487485	+	0.998811i	$0.515523\pi$
$510$		0			0
$511$	−0.320837	−	18.1301i	−0.0141930	−	0.802030i
$512$	19.8995	+	10.7708i	0.879442	+	0.476006i
$513$		0			0
$514$	−34.5222	−	8.07061i	−1.52271	−	0.355979i
$515$	7.39252	−	12.8042i	0.325753	−	0.564221i
$516$		0			0
$517$	5.43598			0.239074
$518$	−10.3433	−	32.1086i	−0.454457	−	1.41077i
$519$		0			0
$520$	−37.0956	−	6.19100i	−1.62675	−	0.271494i
$521$	−6.91166	−	3.99045i	−0.302805	−	0.174825i	0.340897	−	0.940101i	$-0.389269\pi$
$521$	−6.91166	−	3.99045i	−0.302805	−	0.174825i	−0.643702	+	0.765276i	$0.722603\pi$
$522$		0			0
$523$	12.3267	−	7.11681i	0.539008	−	0.311196i	−0.205669	−	0.978622i	$-0.565937\pi$
$523$	12.3267	−	7.11681i	0.539008	−	0.311196i	0.744677	+	0.667425i	$0.232604\pi$
$524$	16.0864	+	24.1357i	0.702736	+	1.05437i
$525$		0			0
$526$	6.35470	+	20.9926i	0.277078	+	0.915320i
$527$	−2.36614	+	1.36609i	−0.103071	+	0.0595078i
$528$		0			0
$529$	1.60942	−	2.78759i	0.0699747	−	0.121200i
$530$	15.1290	−	16.1342i	0.657161	−	0.700826i
$531$		0			0
$532$	−8.35509	+	17.6731i	−0.362239	+	0.766225i
$533$		−	24.7389i		−	1.07156i
$534$		0			0
$535$	13.3421	−	23.1093i	0.576831	−	0.999101i
$536$	9.22540	+	24.6416i	0.398476	+	1.06435i
$537$		0			0
$538$	−32.1244	+	9.72444i	−1.38498	+	0.419250i
$539$	−21.0717	−	33.6856i	−0.907622	−	1.45094i
$540$		0			0
$541$	6.43282	−	3.71399i	0.276569	−	0.159677i	−0.355300	−	0.934752i	$-0.615621\pi$
$541$	6.43282	−	3.71399i	0.276569	−	0.159677i	0.631869	+	0.775075i	$0.282288\pi$
$542$	4.73685	−	20.2620i	0.203465	−	0.870326i
$543$		0			0
$544$	−1.05510	−	2.34679i	−0.0452372	−	0.100618i
$545$		−	7.95734i		−	0.340855i
$546$		0			0
$547$	−28.2287			−1.20697			−0.603485	−	0.797374i	$-0.706222\pi$
$547$	−28.2287			−1.20697			−0.603485	+	0.797374i	$0.706222\pi$
$548$	2.20705	+	1.09159i	0.0942803	+	0.0466303i
$549$		0			0
$550$	2.31169	−	9.88830i	0.0985708	−	0.421638i
$551$	4.76498	+	8.25319i	0.202995	+	0.351598i
$552$		0			0
$553$	−20.6275	−	11.4275i	−0.877171	−	0.485947i
$554$	−2.91834	−	9.64064i	−0.123988	−	0.409592i
$555$		0			0
$556$	−31.4925	+	2.02735i	−1.33558	+	0.0859787i
$557$	29.9378	+	17.2846i	1.26850	+	0.732371i	0.974705	−	0.223496i	$-0.0717470\pi$
$557$	29.9378	+	17.2846i	1.26850	+	0.732371i	0.293799	+	0.955867i	$0.405080\pi$
$558$		0			0
$559$	19.4803			0.823929
$560$	−9.75973	+	24.6258i	−0.412424	+	1.04063i
$561$		0			0
$562$	13.4689	+	12.6297i	0.568153	+	0.532754i
$563$	10.1504	+	5.86033i	0.427788	+	0.246983i	0.698404	−	0.715704i	$-0.253894\pi$
$563$	10.1504	+	5.86033i	0.427788	+	0.246983i	−0.270616	+	0.962687i	$0.587227\pi$
$564$		0			0
$565$	0.378513	+	0.655603i	0.0159242	+	0.0275814i
$566$	−0.866059	−	2.86100i	−0.0364032	−	0.120257i
$567$		0			0
$568$	16.0523	+	13.2207i	0.673538	+	0.554728i
$569$	−5.55324	−	9.61849i	−0.232804	−	0.403228i	0.725828	−	0.687876i	$-0.241457\pi$
$569$	−5.55324	−	9.61849i	−0.232804	−	0.403228i	−0.958632	+	0.284648i	$0.908123\pi$
$570$		0			0
$571$	17.7557	−	30.7537i	0.743052	−	1.28700i	−0.208047	−	0.978119i	$-0.566711\pi$
$571$	17.7557	−	30.7537i	0.743052	−	1.28700i	0.951099	−	0.308885i	$-0.0999558\pi$
$572$	−54.0567	−	26.7360i	−2.26022	−	1.11789i
$573$		0			0
$574$	−17.0346	−	3.66575i	−0.711012	−	0.153005i
$575$			6.47756i			0.270133i
$576$		0			0
$577$	−23.4304	−	13.5276i	−0.975421	−	0.563159i	−0.0745363	−	0.997218i	$-0.523748\pi$
$577$	−23.4304	−	13.5276i	−0.975421	−	0.563159i	−0.900885	+	0.434059i	$0.857081\pi$
$578$	5.40629	−	23.1255i	0.224872	−	0.961894i
$579$		0			0
$580$	7.16193	+	10.7456i	0.297383	+	0.446188i
$581$	−4.45023	+	2.67543i	−0.184627	+	0.110995i
$582$		0			0
$583$	30.7152	−	17.7334i	1.27209	−	0.734443i
$584$	−18.1544	+	6.79669i	−0.751234	+	0.281249i
$585$		0			0
$586$	0.344563	+	0.323095i	0.0142338	+	0.0133469i
$587$			35.3797i			1.46027i	0.683300	+	0.730137i	$0.260544\pi$
$587$			35.3797i			1.46027i	−0.683300	+	0.730137i	$0.739456\pi$
$588$		0			0
$589$		−	22.1906i		−	0.914347i
$590$	−24.5085	+	26.1370i	−1.00900	+	1.07604i
$591$		0			0
$592$	−28.6614	+	21.8869i	−1.17797	+	0.899546i
$593$	33.9659	−	19.6102i	1.39481	−	0.805294i	0.400968	−	0.916092i	$-0.368674\pi$
$593$	33.9659	−	19.6102i	1.39481	−	0.805294i	0.993843	+	0.110798i	$0.0353406\pi$
$594$		0			0
$595$	2.58160	−	1.55203i	0.105835	−	0.0636271i
$596$	−6.60594	−	9.91142i	−0.270590	−	0.405988i
$597$		0			0
$598$	37.4583	+	8.75702i	1.53178	+	0.358101i
$599$	−41.2853	−	23.8361i	−1.68687	−	0.973916i	−0.956890	−	0.290450i	$-0.906195\pi$
$599$	−41.2853	−	23.8361i	−1.68687	−	0.973916i	−0.729982	−	0.683466i	$-0.760472\pi$
$600$		0			0
$601$		−	13.4207i		−	0.547442i	−0.961809	−	0.273721i	$-0.911746\pi$
$601$		−	13.4207i		−	0.547442i	0.961809	−	0.273721i	$-0.0882544\pi$
$602$	2.88655	−	13.4137i	0.117647	−	0.546702i
$603$		0			0
$604$	3.18540	−	6.44046i	0.129612	−	0.262058i
$605$	26.5558	−	45.9960i	1.07965	−	1.87000i
$606$		0			0
$607$	19.1391	+	33.1498i	0.776831	+	1.34551i	0.933760	+	0.357901i	$0.116507\pi$
$607$	19.1391	+	33.1498i	0.776831	+	1.34551i	−0.156929	+	0.987610i	$0.550159\pi$
$608$	20.7916	+	2.10885i	0.843210	+	0.0855251i
$609$		0			0
$610$	−16.9522	+	5.13164i	−0.686376	+	0.207774i
$611$	−2.54374	−	4.40588i	−0.102909	−	0.178243i
$612$		0			0
$613$	−16.9225	−	9.77021i	−0.683493	−	0.394615i	0.117677	−	0.993052i	$-0.462455\pi$
$613$	−16.9225	−	9.77021i	−0.683493	−	0.394615i	−0.801170	+	0.598437i	$0.795789\pi$
$614$	9.08474	−	9.68838i	0.366630	−	0.390991i
$615$		0			0
$616$	−26.4198	+	33.2605i	−1.06448	+	1.34011i
$617$	1.16195			0.0467785			0.0233892	−	0.999726i	$-0.492554\pi$
$617$	1.16195			0.0467785			0.0233892	+	0.999726i	$0.492554\pi$
$618$		0			0
$619$	31.0842	+	17.9465i	1.24938	+	0.721330i	0.970986	−	0.239137i	$-0.0768645\pi$
$619$	31.0842	+	17.9465i	1.24938	+	0.721330i	0.278394	+	0.960467i	$0.410198\pi$
$620$	−1.93174	−	30.0073i	−0.0775805	−	1.20512i
$621$		0			0
$622$	21.4877	−	6.50459i	0.861579	−	0.260810i
$623$	15.8033	+	8.75495i	0.633147	+	0.350759i
$624$		0			0
$625$	14.8624	+	25.7425i	0.594498	+	1.02970i
$626$	−44.2947	−	10.3552i	−1.77037	−	0.413879i
$627$		0			0
$628$	1.76318	+	0.872054i	0.0703585	+	0.0347987i
$629$	4.10084			0.163511
$630$		0			0
$631$		−	8.26460i		−	0.329008i	−0.986376	−	0.164504i	$-0.947398\pi$
$631$		−	8.26460i		−	0.329008i	0.986376	−	0.164504i	$-0.0526024\pi$
$632$	−4.14991	+	24.8657i	−0.165075	+	0.989103i
$633$		0			0
$634$	21.0296	+	4.91632i	0.835194	+	0.195252i
$635$	13.8677	−	8.00650i	0.550322	−	0.317728i
$636$		0			0
$637$	−17.4419	+	32.8417i	−0.691074	+	1.30123i
$638$	5.99955	+	19.8193i	0.237524	+	0.784655i
$639$		0			0
$640$	28.2991	+	1.04175i	1.11862	+	0.0411787i
$641$	14.4955	−	25.1070i	0.572539	−	0.991666i	−0.423766	−	0.905772i	$-0.639292\pi$
$641$	14.4955	−	25.1070i	0.572539	−	0.991666i	0.996304	−	0.0858940i	$-0.0273747\pi$
$642$		0			0
$643$			39.1239i			1.54289i	0.636293	+	0.771447i	$0.280467\pi$
$643$			39.1239i			1.54289i	−0.636293	+	0.771447i	$0.719533\pi$
$644$	11.5804	−	24.4954i	0.456331	−	0.965252i
$645$		0			0
$646$	−1.73353	−	1.62552i	−0.0682049	−	0.0639553i
$647$	6.09491	−	10.5567i	0.239616	−	0.415027i	−0.720988	−	0.692947i	$-0.756312\pi$
$647$	6.09491	−	10.5567i	0.239616	−	0.415027i	0.960604	+	0.277921i	$0.0896452\pi$
$648$		0			0
$649$	−49.7577	+	28.7276i	−1.95316	+	1.12766i
$650$	−9.09624	+	2.75354i	−0.356784	+	0.108003i
$651$		0			0
$652$	4.19664	−	2.79705i	0.164353	−	0.109541i
$653$	8.80194	−	5.08180i	0.344446	−	0.198866i	−0.317790	−	0.948161i	$-0.602941\pi$
$653$	8.80194	−	5.08180i	0.344446	−	0.198866i	0.662237	+	0.749295i	$0.269607\pi$
$654$		0			0
$655$	31.4368	+	18.1500i	1.22834	+	0.709181i
$656$	2.38844	+	18.4739i	0.0932528	+	0.721286i
$657$		0			0
$658$	−3.41072	+	1.09871i	−0.132964	+	0.0428321i
$659$	8.28558			0.322760			0.161380	−	0.986892i	$-0.448405\pi$
$659$	8.28558			0.322760			0.161380	+	0.986892i	$0.448405\pi$
$660$		0			0
$661$	−8.30890	+	14.3914i	−0.323179	+	0.559762i	−0.981142	−	0.193288i	$-0.938085\pi$
$661$	−8.30890	+	14.3914i	−0.323179	+	0.559762i	0.657963	+	0.753050i	$0.271418\pi$
$662$	−6.77284	+	28.9709i	−0.263234	+	1.12599i
$663$		0			0
$664$	4.28487	+	3.52903i	0.166285	+	0.136953i
$665$	0.432875	+	24.4612i	0.0167862	+	0.948566i
$666$		0			0
$667$	−6.60439	−	11.4391i	−0.255723	−	0.442925i
$668$	−0.676130	−	10.5029i	−0.0261603	−	0.406369i
$669$		0			0
$670$	24.0209	+	22.5243i	0.928009	+	0.870189i
$671$	−28.4018			−1.09644
$672$		0			0
$673$	13.1599			0.507278			0.253639	−	0.967299i	$-0.418372\pi$
$673$	13.1599			0.507278			0.253639	+	0.967299i	$0.418372\pi$
$674$	1.22093	+	1.14486i	0.0470285	+	0.0440983i
$675$		0			0
$676$	1.95559	+	30.3778i	0.0752149	+	1.16838i
$677$	−10.2201	−	17.7017i	−0.392790	−	0.680332i	0.600026	−	0.799980i	$-0.295157\pi$
$677$	−10.2201	−	17.7017i	−0.392790	−	0.680332i	−0.992816	+	0.119648i	$0.961823\pi$
$678$		0			0
$679$	8.41863	−	5.06119i	0.323077	−	0.194231i
$680$	−2.48568	−	2.04721i	−0.0953215	−	0.0785070i
$681$		0			0
$682$	10.9764	−	46.9516i	0.420307	−	1.79787i
$683$	−7.87273	+	13.6360i	−0.301242	+	0.521766i	−0.976418	−	0.215891i	$-0.930734\pi$
$683$	−7.87273	+	13.6360i	−0.301242	+	0.521766i	0.675176	+	0.737657i	$0.264068\pi$
$684$		0			0
$685$	3.08150			0.117738
$686$	20.0296	+	16.8765i	0.764732	+	0.644349i
$687$		0			0
$688$	−14.5470	+	1.88074i	−0.554601	+	0.0717026i
$689$	−28.7460	−	16.5965i	−1.09514	−	0.632277i
$690$		0			0
$691$	2.76346	−	1.59549i	0.105127	−	0.0606952i	−0.446515	−	0.894776i	$-0.647335\pi$
$691$	2.76346	−	1.59549i	0.105127	−	0.0606952i	0.551642	+	0.834081i	$0.314002\pi$
$692$	0.239022	−	0.159308i	0.00908626	−	0.00605597i
$693$		0			0
$694$	−6.51522	+	1.97223i	−0.247314	+	0.0748650i
$695$	−34.2033	+	19.7473i	−1.29740	+	0.749057i
$696$		0			0
$697$	1.05912	−	1.83445i	0.0401170	−	0.0694847i
$698$	36.6011	+	34.3206i	1.38537	+	1.29905i
$699$		0			0
$700$	0.548166	+	6.67149i	0.0207187	+	0.252158i
$701$		−	39.2121i		−	1.48102i	−0.672045	−	0.740511i	$-0.734584\pi$
$701$		−	39.2121i		−	1.48102i	0.672045	−	0.740511i	$-0.265416\pi$
$702$		0			0
$703$	−16.6534	+	28.8445i	−0.628094	+	1.08789i
$704$	42.9484	+	14.7463i	1.61868	+	0.555774i
$705$		0			0
$706$	1.95737	+	6.46612i	0.0736666	+	0.243356i
$707$	−15.0296	+	0.265969i	−0.565246	+	0.0100028i
$708$		0			0
$709$	−33.3653	+	19.2635i	−1.25306	+	0.723454i	−0.971716	−	0.236153i	$-0.924113\pi$
$709$	−33.3653	+	19.2635i	−1.25306	+	0.723454i	−0.281343	+	0.959607i	$0.590780\pi$
$710$	25.3426	+	5.92460i	0.951091	+	0.222346i
$711$		0			0
$712$	3.17936	−	19.0503i	0.119152	−	0.713940i
$713$			30.7567i			1.15185i
$714$		0			0
$715$	−75.4744			−2.82258
$716$	−33.9267	−	16.7799i	−1.26790	−	0.627094i
$717$		0			0
$718$	50.8345	+	11.8841i	1.89713	+	0.443511i
$719$	11.5009	+	19.9202i	0.428912	+	0.742897i	0.996777	−	0.0802246i	$-0.0255637\pi$
$719$	11.5009	+	19.9202i	0.428912	+	0.742897i	−0.567865	+	0.823122i	$0.692230\pi$
$720$		0			0
$721$	−7.57341	+	13.6706i	−0.282049	+	0.509119i
$722$	−7.24417	+	2.19289i	−0.269600	+	0.0816111i
$723$		0			0
$724$	−2.85571	−	44.3602i	−0.106132	−	1.64863i
$725$	2.82613	+	1.63166i	0.104960	+	0.0605985i
$726$		0			0
$727$	−21.8433			−0.810125			−0.405062	−	0.914289i	$-0.632750\pi$
$727$	−21.8433			−0.810125			−0.405062	+	0.914289i	$0.632750\pi$
$728$	39.3208	+	5.84926i	1.45733	+	0.216788i
$729$		0			0
$730$	−16.5945	+	17.6971i	−0.614189	+	0.654999i
$731$	1.44451	+	0.833989i	0.0534272	+	0.0308462i
$732$		0			0
$733$	24.0681	+	41.6871i	0.888974	+	1.53975i	0.841089	+	0.540896i	$0.181915\pi$
$733$	24.0681	+	41.6871i	0.888974	+	1.53975i	0.0478850	+	0.998853i	$0.484752\pi$
$734$	−0.769946	+	0.233072i	−0.0284192	+	0.00860283i
$735$		0			0
$736$	−28.8177	−	2.92292i	−1.06223	−	0.107740i
$737$	26.4018	+	45.7293i	0.972524	+	1.68446i
$738$		0			0
$739$	3.23455	−	5.60241i	0.118985	−	0.206088i	−0.800381	−	0.599492i	$-0.795369\pi$
$739$	3.23455	−	5.60241i	0.118985	−	0.206088i	0.919366	+	0.393404i	$0.128703\pi$
$740$	−20.0086	+	40.4548i	−0.735532	+	1.48715i
$741$		0			0
$742$	−15.6875	+	17.3346i	−0.575907	+	0.636374i
$743$		−	16.6709i		−	0.611597i	−0.952096	−	0.305798i	$-0.901077\pi$
$743$		−	16.6709i		−	0.611597i	0.952096	−	0.305798i	$-0.0989234\pi$
$744$		0			0
$745$	−12.9097	−	7.45340i	−0.472974	−	0.273072i
$746$	−32.2681	−	7.54366i	−1.18142	−	0.276193i
$747$		0			0
$748$	−2.86381	−	4.29681i	−0.104711	−	0.157107i
$749$	−13.6686	+	24.6729i	−0.499441	+	0.901528i
$750$		0			0
$751$	−21.2698	+	12.2801i	−0.776145	+	0.448108i	−0.835062	−	0.550155i	$-0.814569\pi$
$751$	−21.2698	+	12.2801i	−0.776145	+	0.448108i	0.0589171	+	0.998263i	$0.481235\pi$
$752$	2.32492	+	3.04454i	0.0847813	+	0.111023i
$753$		0			0
$754$	13.2562	−	14.1370i	0.482762	−	0.514839i
$755$		−	8.99223i		−	0.327261i
$756$		0			0
$757$		−	2.80888i		−	0.102091i	−0.998696	−	0.0510453i	$-0.983745\pi$
$757$		−	2.80888i		−	0.102091i	0.998696	−	0.0510453i	$-0.0162553\pi$
$758$	−15.1896	−	14.2432i	−0.551710	−	0.517335i
$759$		0			0
$760$	24.4940	−	9.17012i	0.888489	−	0.332635i
$761$	17.4708	−	10.0868i	0.633317	−	0.365646i	−0.148718	−	0.988880i	$-0.547515\pi$
$761$	17.4708	−	10.0868i	0.633317	−	0.365646i	0.782036	+	0.623234i	$0.214181\pi$
$762$		0			0
$763$	0.148823	+	8.40982i	0.00538776	+	0.304456i
$764$	−13.0786	−	19.6228i	−0.473166	−	0.709929i
$765$		0			0
$766$	1.60809	−	6.87864i	0.0581028	−	0.248536i
$767$	46.5677	+	26.8859i	1.68146	+	0.970792i
$768$		0			0
$769$		−	32.1388i		−	1.15895i	−0.814988	−	0.579477i	$-0.803257\pi$
$769$		−	32.1388i		−	1.15895i	0.814988	−	0.579477i	$-0.196743\pi$
$770$	−11.1836	+	51.9700i	−0.403030	+	1.87287i
$771$		0			0
$772$	−48.0850	−	23.7825i	−1.73062	−	0.855950i
$773$	−11.2931	+	19.5603i	−0.406186	+	0.703534i	−0.994459	−	0.105128i	$-0.966475\pi$
$773$	−11.2931	+	19.5603i	−0.406186	+	0.703534i	0.588273	+	0.808662i	$0.299808\pi$
$774$		0			0
$775$	−3.79934	−	6.58065i	−0.136476	−	0.236384i
$776$	−8.10583	−	6.67598i	−0.290982	−	0.239654i
$777$		0			0
$778$	−13.0628	−	43.1528i	−0.468326	−	1.54710i
$779$	8.60209	+	14.8993i	0.308202	+	0.533822i
$780$		0			0
$781$	36.1423	+	20.8668i	1.29327	+	0.746673i
$782$	2.40272	+	2.25302i	0.0859210	+	0.0805677i
$783$		0			0
$784$	9.85414	−	26.2087i	0.351934	−	0.936025i
$785$	2.46177			0.0878642
$786$		0			0
$787$	−29.2593	−	16.8929i	−1.04298	−	0.602166i	−0.122306	−	0.992492i	$-0.539029\pi$
$787$	−29.2593	−	16.8929i	−1.04298	−	0.602166i	−0.920677	+	0.390326i	$0.872362\pi$
$788$	−33.0998	+	2.13082i	−1.17913	+	0.0759073i
$789$		0			0
$790$	9.14088	+	30.1967i	0.325218	+	1.07435i
$791$	−0.412298	−	0.685804i	−0.0146596	−	0.0243844i
$792$		0			0
$793$	13.2905	+	23.0197i	0.471958	+	0.817455i
$794$	10.5936	−	45.3143i	0.375953	−	1.60815i
$795$		0			0
$796$	−20.4520	−	10.1154i	−0.724902	−	0.358531i
$797$	27.0472			0.958061			0.479030	−	0.877798i	$-0.340988\pi$
$797$	27.0472			0.958061			0.479030	+	0.877798i	$0.340988\pi$
$798$		0			0
$799$		−	0.435609i		−	0.0154108i
$800$	6.52684	−	2.93443i	0.230759	−	0.103748i
$801$		0			0
$802$	−0.0684022	+	0.292591i	−0.00241536	+	0.0103318i
$803$	−33.6905	+	19.4512i	−1.18891	+	0.686418i
$804$		0			0
$805$	−0.599976	−	33.9039i	−0.0211464	−	1.19496i
$806$	−43.1907	+	13.0743i	−1.52133	+	0.460524i
$807$		0			0
$808$	5.63436	+	15.0497i	0.198216	+	0.529447i
$809$	−24.9224	+	43.1669i	−0.876226	+	1.51767i	−0.0207751	+	0.999784i	$0.506613\pi$
$809$	−24.9224	+	43.1669i	−0.876226	+	1.51767i	−0.855451	+	0.517884i	$0.826720\pi$
$810$		0			0
$811$			36.5330i			1.28285i	0.767188	+	0.641423i	$0.221655\pi$
$811$			36.5330i			1.28285i	−0.767188	+	0.641423i	$0.778345\pi$
$812$	−7.77016	−	11.2227i	−0.272679	−	0.393840i
$813$		0			0
$814$	−49.5034	+	52.7927i	−1.73509	+	1.85038i
$815$	3.15588	−	5.46614i	0.110546	−	0.191470i
$816$		0			0
$817$	−11.7322	+	6.77360i	−0.410459	+	0.236978i
$818$	8.38793	+	27.7093i	0.293277	+	0.968832i
$819$		0			0
$820$	12.9292	+	19.3988i	0.451509	+	0.677435i
$821$	−2.59911	+	1.50060i	−0.0907095	+	0.0523711i	−0.544669	−	0.838651i	$-0.683345\pi$
$821$	−2.59911	+	1.50060i	−0.0907095	+	0.0523711i	0.453959	+	0.891023i	$0.350011\pi$
$822$		0			0
$823$	−13.8543	−	7.99877i	−0.482930	−	0.278820i	0.238707	−	0.971092i	$-0.423277\pi$
$823$	−13.8543	−	7.99877i	−0.482930	−	0.278820i	−0.721637	+	0.692272i	$0.756610\pi$
$824$	16.4793	+	2.75029i	0.574085	+	0.0958109i
$825$		0			0
$826$	25.4133	−	28.0816i	0.884242	−	0.977083i
$827$	−4.57856			−0.159212			−0.0796060	−	0.996826i	$-0.525366\pi$
$827$	−4.57856			−0.159212			−0.0796060	+	0.996826i	$0.525366\pi$
$828$		0			0
$829$	1.53077	−	2.65136i	0.0531657	−	0.0920857i	−0.838218	−	0.545336i	$-0.816402\pi$
$829$	1.53077	−	2.65136i	0.0531657	−	0.0920857i	0.891383	+	0.453250i	$0.149736\pi$
$830$	6.76477	+	1.58147i	0.234808	+	0.0548936i
$831$		0			0
$832$	−8.14552	−	41.7103i	−0.282395	−	1.44605i
$833$	−2.69938	+	1.68857i	−0.0935279	+	0.0585054i
$834$		0			0
$835$	−6.58581	−	11.4070i	−0.227911	−	0.394754i
$836$	41.8527	−	2.69429i	1.44751	−	0.0931841i
$837$		0			0
$838$	−11.4572	+	12.2184i	−0.395781	+	0.422079i
$839$	−39.0864			−1.34941			−0.674706	−	0.738087i	$-0.735730\pi$
$839$	−39.0864			−1.34941			−0.674706	+	0.738087i	$0.735730\pi$
$840$		0			0
$841$	22.3456			0.770536
$842$	21.0811	−	22.4819i	0.726504	−	0.774777i
$843$		0			0
$844$	−0.531029	−	8.24892i	−0.0182788	−	0.283940i
$845$	19.0483	+	32.9926i	0.655281	+	1.13498i
$846$		0			0
$847$	−27.2056	+	49.1081i	−0.934795	+	1.68738i
$848$	23.0686	+	9.61825i	0.792179	+	0.330292i
$849$		0			0
$850$	−0.792393	−	0.185246i	−0.0271789	−	0.00635389i
$851$	23.0820	−	39.9792i	0.791241	−	1.37047i
$852$		0			0
$853$	26.4897			0.906989			0.453495	−	0.891259i	$-0.350177\pi$
$853$	26.4897			0.906989			0.453495	+	0.891259i	$0.350177\pi$
$854$	17.8202	−	5.74050i	0.609796	−	0.196436i
$855$		0			0
$856$	29.7422	+	4.96377i	1.01657	+	0.169658i
$857$	−38.9066	−	22.4627i	−1.32902	−	0.767312i	−0.343875	−	0.939015i	$-0.611740\pi$
$857$	−38.9066	−	22.4627i	−1.32902	−	0.767312i	−0.985149	+	0.171703i	$0.945073\pi$
$858$		0			0
$859$	30.6621	−	17.7028i	1.04618	−	0.604011i	0.124601	−	0.992207i	$-0.460235\pi$
$859$	30.6621	−	17.7028i	1.04618	−	0.604011i	0.921577	+	0.388196i	$0.126902\pi$
$860$	−15.2753	+	10.1810i	−0.520883	+	0.347168i
$861$		0			0
$862$	−6.77677	−	22.3869i	−0.230818	−	0.762499i
$863$	2.40437	−	1.38816i	0.0818456	−	0.0472536i	−0.458519	−	0.888685i	$-0.651620\pi$
$863$	2.40437	−	1.38816i	0.0818456	−	0.0472536i	0.540364	+	0.841431i	$0.318286\pi$
$864$		0			0
$865$	0.179745	−	0.311328i	0.00611151	−	0.0105855i
$866$	37.9900	−	40.5143i	1.29095	−	1.37673i
$867$		0			0
$868$	2.60280	+	31.6775i	0.0883448	+	1.07520i
$869$			50.5915i			1.71620i
$870$		0			0
$871$	24.7092	−	42.7976i	0.837239	−	1.45014i
$872$	8.42107	−	3.15271i	0.285174	−	0.106764i
$873$		0			0
$874$	−25.6046	+	7.75082i	−0.866089	+	0.262175i
$875$	−12.7441	−	21.1982i	−0.430830	−	0.716631i
$876$		0			0
$877$	14.3264	−	8.27135i	0.483768	−	0.279304i	−0.238217	−	0.971212i	$-0.576563\pi$
$877$	14.3264	−	8.27135i	0.483768	−	0.279304i	0.721986	+	0.691908i	$0.243230\pi$
$878$	−9.99064	+	42.7351i	−0.337168	+	1.44224i
$879$		0			0
$880$	56.3610	−	7.28675i	1.89993	−	0.245636i
$881$		−	24.6158i		−	0.829327i	−0.909975	−	0.414664i	$-0.863899\pi$
$881$		−	24.6158i		−	0.829327i	0.909975	−	0.414664i	$-0.136101\pi$
$882$		0			0
$883$	40.4623			1.36167			0.680833	−	0.732439i	$-0.261618\pi$
$883$	40.4623			1.36167			0.680833	+	0.732439i	$0.261618\pi$
$884$	−2.14247	+	4.33180i	−0.0720592	+	0.145694i
$885$		0			0
$886$	0.272012	−	1.16354i	0.00913843	−	0.0390898i
$887$	4.64231	+	8.04072i	0.155873	+	0.269981i	0.933377	−	0.358898i	$-0.116847\pi$
$887$	4.64231	+	8.04072i	0.155873	+	0.269981i	−0.777503	+	0.628879i	$0.783514\pi$
$888$		0			0
$889$	−14.5065	+	8.72114i	−0.486532	+	0.292498i
$890$	−7.00309	−	23.1345i	−0.234744	−	0.775471i
$891$		0			0
$892$	2.32639	+	36.1379i	0.0778935	+	1.20998i
$893$	3.06399	+	1.76900i	0.102533	+	0.0591972i
$894$		0			0
$895$	−47.3688			−1.58337
$896$	−29.9278	−	0.571717i	−0.999818	−	0.0190997i
$897$		0			0
$898$	43.0633	+	40.3802i	1.43704	+	1.34751i
$899$	13.4190	+	7.74746i	0.447548	+	0.258392i
$900$		0			0
$901$	−1.42106	−	2.46134i	−0.0473423	−	0.0819993i
$902$	10.8308	+	35.7793i	0.360627	+	1.19132i
$903$		0			0
$904$	−0.543843	+	0.660322i	−0.0180880	+	0.0219620i
$905$	−27.8159	−	48.1786i	−0.924632	−	1.60151i
$906$		0			0
$907$	−2.55327	+	4.42240i	−0.0847800	+	0.146843i	−0.905297	−	0.424778i	$-0.860352\pi$
$907$	−2.55327	+	4.42240i	−0.0847800	+	0.146843i	0.820517	+	0.571621i	$0.193685\pi$
$908$	7.02699	−	14.2076i	0.233199	−	0.471497i
$909$		0			0
$910$	47.3552	−	15.2547i	1.56981	−	0.505689i
$911$		−	36.3702i		−	1.20500i	−0.798119	−	0.602500i	$-0.794171\pi$
$911$		−	36.3702i		−	1.20500i	0.798119	−	0.602500i	$-0.205829\pi$
$912$		0			0
$913$	9.64757	+	5.57003i	0.319288	+	0.184341i
$914$	−2.40991	+	10.3085i	−0.0797129	+	0.340973i
$915$		0			0
$916$	3.58764	−	2.39115i	0.118539	−	0.0790059i
$917$	−33.5639	−	18.5942i	−1.10838	−	0.614034i
$918$		0			0
$919$	−40.4248	+	23.3393i	−1.33349	+	0.769892i	−0.985833	−	0.167729i	$-0.946357\pi$
$919$	−40.4248	+	23.3393i	−1.33349	+	0.769892i	−0.347659	+	0.937621i	$0.613023\pi$
$920$	−33.9493	+	12.7100i	−1.11927	+	0.419037i
$921$		0			0
$922$	4.47207	+	4.19343i	0.147280	+	0.138103i
$923$		−	39.0580i		−	1.28561i
$924$		0			0
$925$			11.4052i			0.375000i
$926$	34.1666	−	36.4369i	1.12279	−	1.19739i
$927$		0			0
$928$	−8.53428	+	11.8367i	−0.280152	+	0.388560i
$929$	−33.8671	+	19.5532i	−1.11114	+	0.641518i	−0.939125	−	0.343576i	$-0.888362\pi$
$929$	−33.8671	+	19.5532i	−1.11114	+	0.641518i	−0.172017	+	0.985094i	$0.555028\pi$
$930$		0			0
$931$	−0.914979	−	25.8441i	−0.0299872	−	0.847006i
$932$	33.3086	−	22.2001i	1.09106	−	0.727188i
$933$		0			0
$934$	−14.4576	−	3.37990i	−0.473066	−	0.110594i
$935$	−5.59661	−	3.23121i	−0.183029	−	0.105672i
$936$		0			0
$937$		−	14.4038i		−	0.470551i	−0.971929	−	0.235275i	$-0.924401\pi$
$937$		−	14.4038i		−	0.470551i	0.971929	−	0.235275i	$-0.0755992\pi$
$938$	−25.8081	−	23.3558i	−0.842664	−	0.762595i
$939$		0			0
$940$	4.29729	+	2.12541i	0.140162	+	0.0693231i
$941$	−13.1269	+	22.7364i	−0.427924	+	0.741186i	−0.996688	−	0.0813146i	$-0.974088\pi$
$941$	−13.1269	+	22.7364i	−0.427924	+	0.741186i	0.568765	+	0.822500i	$0.307421\pi$
$942$		0			0
$943$	−11.9227	−	20.6508i	−0.388257	−	0.672482i
$944$	−37.3704	−	15.5813i	−1.21630	−	0.507128i
$945$		0			0
$946$	−28.1739	+	8.52858i	−0.916014	+	0.277288i
$947$	7.85354	+	13.6027i	0.255206	+	0.442030i	0.964951	−	0.262429i	$-0.0845234\pi$
$947$	7.85354	+	13.6027i	0.255206	+	0.442030i	−0.709746	+	0.704458i	$0.751190\pi$
$948$		0			0
$949$	31.5306	+	18.2042i	1.02353	+	0.590933i
$950$	4.52087	−	4.82126i	0.146676	−	0.156422i
$951$		0			0
$952$	2.66531	+	2.11714i	0.0863833	+	0.0686168i
$953$	−42.8466			−1.38794			−0.693968	−	0.720006i	$-0.744139\pi$
$953$	−42.8466			−1.38794			−0.693968	+	0.720006i	$0.744139\pi$
$954$		0			0
$955$	−25.5588	−	14.7564i	−0.827064	−	0.477506i
$956$	37.7066	−	2.42738i	1.21952	−	0.0785072i
$957$		0			0
$958$	22.9123	−	6.93583i	0.740264	−	0.224087i
$959$	−3.25672	+	0.0576322i	−0.105165	+	0.00186104i
$960$		0			0
$961$	−2.53999	−	4.39939i	−0.0819352	−	0.141916i
$962$	65.9535	+	15.4187i	2.12643	+	0.497117i
$963$		0			0
$964$	16.2333	−	32.8216i	0.522840	−	1.05711i
$965$	−67.1368			−2.16121
$966$		0			0
$967$			0.672082i			0.0216127i	0.999942	+	0.0108063i	$0.00343983\pi$
$967$			0.672082i			0.0216127i	−0.999942	+	0.0108063i	$0.996560\pi$
$968$	59.1979	+	9.87973i	1.90269	+	0.317547i
$969$		0			0
$970$	−12.7971	−	2.99171i	−0.410890	−	0.0960582i
$971$	6.45838	−	3.72875i	0.207259	−	0.119661i	−0.392778	−	0.919633i	$-0.628486\pi$
$971$	6.45838	−	3.72875i	0.207259	−	0.119661i	0.600037	+	0.799972i	$0.295153\pi$
$972$		0			0
$973$	35.7789	−	21.5099i	1.14702	−	0.689575i
$974$	−9.72184	−	32.1158i	−0.311508	−	1.02906i
$975$		0			0
$976$	−12.1472	−	15.9070i	−0.388822	−	0.509171i
$977$	8.78701	−	15.2195i	0.281121	−	0.486916i	−0.690540	−	0.723294i	$-0.742627\pi$
$977$	8.78701	−	15.2195i	0.281121	−	0.486916i	0.971661	+	0.236378i	$0.0759603\pi$
$978$		0			0
$979$		−	38.7596i		−	1.23876i
$980$	−3.48707	−	34.8682i	−0.111390	−	1.11382i
$981$		0			0
$982$	3.51987	+	3.30056i	0.112323	+	0.105325i
$983$	−21.3661	+	37.0072i	−0.681472	+	1.18034i	0.293059	+	0.956094i	$0.405327\pi$
$983$	−21.3661	+	37.0072i	−0.681472	+	1.18034i	−0.974532	+	0.224250i	$0.928007\pi$
$984$		0			0
$985$	−35.9489	+	20.7551i	−1.14543	+	0.661313i
$986$	1.58821	−	0.480770i	0.0505790	−	0.0153108i
$987$		0			0
$988$	−21.7685	−	32.6610i	−0.692548	−	1.03909i
$989$	16.2612	−	9.38839i	0.517075	−	0.298533i
$990$		0			0
$991$	−39.3373	−	22.7114i	−1.24959	−	0.721451i	−0.278563	−	0.960418i	$-0.589858\pi$
$991$	−39.3373	−	22.7114i	−1.24959	−	0.721451i	−0.971028	+	0.238967i	$0.923191\pi$
$992$	30.9907	−	13.9332i	0.983956	−	0.442381i
$993$		0			0
$994$	−26.8945	−	5.78753i	−0.853041	−	0.183569i
$995$	−28.5553			−0.905264
$996$		0			0
$997$	21.8718	−	37.8831i	0.692687	−	1.19977i	−0.278268	−	0.960504i	$-0.589760\pi$
$997$	21.8718	−	37.8831i	0.692687	−	1.19977i	0.970954	−	0.239265i	$-0.0769065\pi$
$998$	−5.62098	+	24.0438i	−0.177929	+	0.761094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.451.13		32
3.2	odd	2		168.2.t.a.115.4	yes	32
4.3	odd	2		2016.2.bs.c.1711.13		32
7.5	odd	6	inner	504.2.bk.c.19.9		32
8.3	odd	2	inner	504.2.bk.c.451.9		32
8.5	even	2		2016.2.bs.c.1711.4		32
12.11	even	2		672.2.bb.a.367.2		32
21.5	even	6		168.2.t.a.19.8	yes	32
21.11	odd	6		1176.2.p.a.979.25		32
21.17	even	6		1176.2.p.a.979.26		32
24.5	odd	2		672.2.bb.a.367.7		32
24.11	even	2		168.2.t.a.115.8	yes	32
28.19	even	6		2016.2.bs.c.271.4		32
56.5	odd	6		2016.2.bs.c.271.13		32
56.19	even	6	inner	504.2.bk.c.19.13		32
84.11	even	6		4704.2.p.a.3919.2		32
84.47	odd	6		672.2.bb.a.271.7		32
84.59	odd	6		4704.2.p.a.3919.15		32
168.5	even	6		672.2.bb.a.271.2		32
168.11	even	6		1176.2.p.a.979.28		32
168.53	odd	6		4704.2.p.a.3919.16		32
168.59	odd	6		1176.2.p.a.979.27		32
168.101	even	6		4704.2.p.a.3919.1		32
168.131	odd	6		168.2.t.a.19.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.4	✓	32	168.131	odd	6
168.2.t.a.19.8	yes	32	21.5	even	6
168.2.t.a.115.4	yes	32	3.2	odd	2
168.2.t.a.115.8	yes	32	24.11	even	2
504.2.bk.c.19.9		32	7.5	odd	6	inner
504.2.bk.c.19.13		32	56.19	even	6	inner
504.2.bk.c.451.9		32	8.3	odd	2	inner
504.2.bk.c.451.13		32	1.1	even	1	trivial
672.2.bb.a.271.2		32	168.5	even	6
672.2.bb.a.271.7		32	84.47	odd	6
672.2.bb.a.367.2		32	12.11	even	2
672.2.bb.a.367.7		32	24.5	odd	2
1176.2.p.a.979.25		32	21.11	odd	6
1176.2.p.a.979.26		32	21.17	even	6
1176.2.p.a.979.27		32	168.59	odd	6
1176.2.p.a.979.28		32	168.11	even	6
2016.2.bs.c.271.4		32	28.19	even	6
2016.2.bs.c.271.13		32	56.5	odd	6
2016.2.bs.c.1711.4		32	8.5	even	2
2016.2.bs.c.1711.13		32	4.3	odd	2
4704.2.p.a.3919.1		32	168.101	even	6
4704.2.p.a.3919.2		32	84.11	even	6
4704.2.p.a.3919.15		32	84.59	odd	6
4704.2.p.a.3919.16		32	168.53	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03162 + 0.967346i) q^{2} +(0.128485 + 1.99587i) q^{4} +(1.25150 + 2.16767i) q^{5} +(-1.36321 - 2.26752i) q^{7} +(-1.79815 + 2.18327i) q^{8} +(-0.805806 + 3.44685i) q^{10} +(-2.83809 + 4.91572i) q^{11} +5.31228 q^{13} +(0.787162 - 3.65792i) q^{14} +(-3.96698 + 0.512879i) q^{16} +(0.393919 + 0.227429i) q^{17} +(-3.19938 + 1.84716i) q^{19} +(-4.16558 + 2.77635i) q^{20} +(-7.68304 + 2.32575i) q^{22} +(4.43443 - 2.56022i) q^{23} +(-0.632521 + 1.09556i) q^{25} +(5.48026 + 5.13881i) q^{26} +(4.35053 - 3.01213i) q^{28} -2.57962i q^{29} +(-3.00333 + 5.20192i) q^{31} +(-4.58856 - 3.30835i) q^{32} +(0.186372 + 0.615676i) q^{34} +(3.20917 - 5.79280i) q^{35} +(7.80778 - 4.50782i) q^{37} +(-5.08739 - 1.18933i) q^{38} +(-6.98299 - 1.16541i) q^{40} -4.65692i q^{41} +3.66703 q^{43} +(-10.1758 - 5.03286i) q^{44} +(7.05126 + 1.64845i) q^{46} +(-0.478841 - 0.829377i) q^{47} +(-3.28332 + 6.18222i) q^{49} +(-1.71230 + 0.518335i) q^{50} +(0.682549 + 10.6026i) q^{52} +(-5.41124 - 3.12418i) q^{53} -14.2075 q^{55} +(7.40187 + 1.10108i) q^{56} +(2.49539 - 2.66119i) q^{58} +(8.76604 + 5.06108i) q^{59} +(2.50184 + 4.33331i) q^{61} +(-8.13036 + 2.46115i) q^{62} +(-1.53334 - 7.85168i) q^{64} +(6.64834 + 11.5153i) q^{65} +(4.65133 - 8.05634i) q^{67} +(-0.403306 + 0.815431i) q^{68} +(8.91429 - 2.87159i) q^{70} -7.35240i q^{71} +(5.93541 + 3.42681i) q^{73} +(12.4153 + 2.90245i) q^{74} +(-4.09777 - 6.14821i) q^{76} +(15.0154 - 0.265718i) q^{77} +(7.71882 - 4.45646i) q^{79} +(-6.07644 - 7.95723i) q^{80} +(4.50485 - 4.80418i) q^{82} -1.96259i q^{83} +1.13851i q^{85} +(3.78299 + 3.54728i) q^{86} +(-5.62904 - 15.0355i) q^{88} +(-5.91361 + 3.41423i) q^{89} +(-7.24175 - 12.0457i) q^{91} +(5.67961 + 8.52158i) q^{92} +(0.308312 - 1.31881i) q^{94} +(-8.00807 - 4.62346i) q^{95} +3.71270i q^{97} +(-9.36748 + 3.20160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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