LMFDB - Embedded newform 504.2.ch.b.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30255 - 0.550794i) q^{2} +(1.39325 + 1.43487i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 - 2.63638i) q^{8} +O(q^{10})$	\(q+(-1.30255 - 0.550794i) q^{2} +(1.39325 + 1.43487i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 - 2.63638i) q^{8} +(1.62769 - 0.202118i) q^{10} +(-1.41560 + 2.45188i) q^{11} -3.11725 q^{13} +(-0.334143 - 3.72671i) q^{14} +(-0.117700 + 3.99827i) q^{16} +(0.782206 - 1.35482i) q^{17} +(-2.15042 - 3.72463i) q^{19} +(-2.23147 - 0.633255i) q^{20} +(3.19436 - 2.41399i) q^{22} +(-4.05782 + 2.34278i) q^{23} +(-1.82744 + 3.16522i) q^{25} +(4.06037 + 1.71697i) q^{26} +(-1.61741 + 5.03825i) q^{28} -4.08861 q^{29} +(2.40452 + 1.38825i) q^{31} +(2.35553 - 5.14310i) q^{32} +(-1.76509 + 1.33388i) q^{34} +(-2.60353 - 1.62402i) q^{35} +(-4.96358 + 2.86572i) q^{37} +(0.749512 + 6.03594i) q^{38} +(2.55780 + 2.05392i) q^{40} -2.19421 q^{41} -6.52977i q^{43} +(-5.49042 + 1.38490i) q^{44} +(6.57589 - 0.816559i) q^{46} +(5.34609 + 9.25971i) q^{47} +(-3.90521 + 5.80942i) q^{49} +(4.12371 - 3.11630i) q^{50} +(-4.34312 - 4.47285i) q^{52} +(-5.61902 + 9.73242i) q^{53} -3.28359i q^{55} +(4.88179 - 5.67169i) q^{56} +(5.32560 + 2.25198i) q^{58} +(11.9042 + 6.87289i) q^{59} +(5.09458 + 8.82407i) q^{61} +(-2.36736 - 3.13266i) q^{62} +(-5.90098 + 5.40171i) q^{64} +(3.13100 - 1.80768i) q^{65} +(-5.01037 - 2.89274i) q^{67} +(3.03380 - 0.765242i) q^{68} +(2.49672 + 3.54937i) q^{70} -4.72781i q^{71} +(-14.0619 - 8.11863i) q^{73} +(8.04371 - 0.998826i) q^{74} +(2.34829 - 8.27492i) q^{76} +(-7.48627 - 0.255528i) q^{77} +(2.89324 + 5.01124i) q^{79} +(-2.20036 - 4.08415i) q^{80} +(2.85806 + 1.20856i) q^{82} +5.93150i q^{83} +1.81439i q^{85} +(-3.59656 + 8.50533i) q^{86} +(7.91431 + 1.22020i) q^{88} +(1.33902 + 2.31925i) q^{89} +(-3.87769 - 7.27904i) q^{91} +(-9.01515 - 2.55836i) q^{92} +(-1.86334 - 15.0058i) q^{94} +(4.31980 + 2.49404i) q^{95} -11.2024i q^{97} +(8.28651 - 5.41606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Display 100 coefficients 10 coefficients

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 $

$2$	−1.30255	−	0.550794i	−0.921039	−	0.389470i
$2$	−1.30255	−	0.550794i	−0.921039	−	0.389470i
$3$		0			0
$3$		0			0
$4$	1.39325	+	1.43487i	0.696626	+	0.717435i
$5$	−1.00441	+	0.579896i	−0.449185	+	0.259337i	−0.707486	−	0.706727i	$-0.750171\pi$
$5$	−1.00441	+	0.579896i	−0.449185	+	0.259337i	0.258301	+	0.966065i	$0.416837\pi$
$6$		0			0
$7$	1.24394	+	2.33508i	0.470166	+	0.882578i
$7$	1.24394	+	2.33508i	0.470166	+	0.882578i
$8$	−1.02446	−	2.63638i	−0.362200	−	0.932100i
$9$		0			0
$10$	1.62769	−	0.202118i	0.514721	−	0.0639154i
$11$	−1.41560	+	2.45188i	−0.426818	+	0.739271i	−0.996588	−	0.0825332i	$-0.973699\pi$
$11$	−1.41560	+	2.45188i	−0.426818	+	0.739271i	0.569770	+	0.821804i	$0.307032\pi$
$12$		0			0
$13$	−3.11725			−0.864571			−0.432285	−	0.901737i	$-0.642293\pi$
$13$	−3.11725			−0.864571			−0.432285	+	0.901737i	$0.642293\pi$
$14$	−0.334143	−	3.72671i	−0.0893036	−	0.996004i
$15$		0			0
$16$	−0.117700	+	3.99827i	−0.0294251	+	0.999567i
$17$	0.782206	−	1.35482i	0.189713	−	0.328592i	−0.755442	−	0.655216i	$-0.772578\pi$
$17$	0.782206	−	1.35482i	0.189713	−	0.328592i	0.945154	+	0.326624i	$0.105911\pi$
$18$		0			0
$19$	−2.15042	−	3.72463i	−0.493340	−	0.854489i	0.506631	−	0.862163i	$-0.330891\pi$
$19$	−2.15042	−	3.72463i	−0.493340	−	0.854489i	−0.999971	+	0.00767364i	$0.997557\pi$
$20$	−2.23147	−	0.633255i	−0.498972	−	0.141600i
$21$		0			0
$22$	3.19436	−	2.41399i	0.681040	−	0.514664i
$23$	−4.05782	+	2.34278i	−0.846114	+	0.488504i	−0.859338	−	0.511408i	$-0.829124\pi$
$23$	−4.05782	+	2.34278i	−0.846114	+	0.488504i	0.0132237	+	0.999913i	$0.495791\pi$
$24$		0			0
$25$	−1.82744	+	3.16522i	−0.365488	+	0.633044i
$26$	4.06037	+	1.71697i	0.796303	+	0.336725i
$27$		0			0
$28$	−1.61741	+	5.03825i	−0.305662	+	0.952140i
$29$	−4.08861			−0.759235			−0.379618	−	0.925143i	$-0.623944\pi$
$29$	−4.08861			−0.759235			−0.379618	+	0.925143i	$0.623944\pi$
$30$		0			0
$31$	2.40452	+	1.38825i	0.431865	+	0.249337i	0.700141	−	0.714005i	$-0.253121\pi$
$31$	2.40452	+	1.38825i	0.431865	+	0.249337i	−0.268276	+	0.963342i	$0.586454\pi$
$32$	2.35553	−	5.14310i	0.416403	−	0.909180i
$33$		0			0
$34$	−1.76509	+	1.33388i	−0.302710	+	0.228759i
$35$	−2.60353	−	1.62402i	−0.440077	−	0.274509i
$36$		0			0
$37$	−4.96358	+	2.86572i	−0.816008	+	0.471122i	−0.849038	−	0.528332i	$-0.822818\pi$
$37$	−4.96358	+	2.86572i	−0.816008	+	0.471122i	0.0330302	+	0.999454i	$0.489484\pi$
$38$	0.749512	+	6.03594i	0.121587	+	0.979159i
$39$		0			0
$40$	2.55780	+	2.05392i	0.404423	+	0.324754i
$41$	−2.19421			−0.342678			−0.171339	−	0.985212i	$-0.554809\pi$
$41$	−2.19421			−0.342678			−0.171339	+	0.985212i	$0.554809\pi$
$42$		0			0
$43$		−	6.52977i		−	0.995781i	−0.867240	−	0.497891i	$-0.834108\pi$
$43$		−	6.52977i		−	0.995781i	0.867240	−	0.497891i	$-0.165892\pi$
$44$	−5.49042	+	1.38490i	−0.827711	+	0.208781i
$45$		0			0
$46$	6.57589	−	0.816559i	0.969562	−	0.120395i
$47$	5.34609	+	9.25971i	0.779808	+	1.35067i	0.932052	+	0.362324i	$0.118017\pi$
$47$	5.34609	+	9.25971i	0.779808	+	1.35067i	−0.152244	+	0.988343i	$0.548650\pi$
$48$		0			0
$49$	−3.90521	+	5.80942i	−0.557887	+	0.829917i
$50$	4.12371	−	3.11630i	0.583181	−	0.440712i
$51$		0			0
$52$	−4.34312	−	4.47285i	−0.602282	−	0.620273i
$53$	−5.61902	+	9.73242i	−0.771831	+	1.33685i	0.164727	+	0.986339i	$0.447326\pi$
$53$	−5.61902	+	9.73242i	−0.771831	+	1.33685i	−0.936558	+	0.350512i	$0.886008\pi$
$54$		0			0
$55$		−	3.28359i		−	0.442760i
$56$	4.88179	−	5.67169i	0.652357	−	0.757912i
$57$		0			0
$58$	5.32560	+	2.25198i	0.699285	+	0.295700i
$59$	11.9042	+	6.87289i	1.54980	+	0.894775i	0.998157	+	0.0606912i	$0.0193305\pi$
$59$	11.9042	+	6.87289i	1.54980	+	0.894775i	0.551638	+	0.834083i	$0.314003\pi$
$60$		0			0
$61$	5.09458	+	8.82407i	0.652294	+	1.12981i	0.982565	+	0.185920i	$0.0595265\pi$
$61$	5.09458	+	8.82407i	0.652294	+	1.12981i	−0.330271	+	0.943886i	$0.607140\pi$
$62$	−2.36736	−	3.13266i	−0.300655	−	0.397848i
$63$		0			0
$64$	−5.90098	+	5.40171i	−0.737622	+	0.675214i
$65$	3.13100	−	1.80768i	0.388352	−	0.224215i
$66$		0			0
$67$	−5.01037	−	2.89274i	−0.612114	−	0.353404i	0.161678	−	0.986844i	$-0.448309\pi$
$67$	−5.01037	−	2.89274i	−0.612114	−	0.353404i	−0.773793	+	0.633439i	$0.781643\pi$
$68$	3.03380	−	0.765242i	0.367902	−	0.0927992i
$69$		0			0
$70$	2.49672	+	3.54937i	0.298415	+	0.424231i
$71$		−	4.72781i		−	0.561088i	−0.959841	−	0.280544i	$-0.909485\pi$
$71$		−	4.72781i		−	0.561088i	0.959841	−	0.280544i	$-0.0905149\pi$
$72$		0			0
$73$	−14.0619	−	8.11863i	−1.64582	−	0.950213i	−0.978709	−	0.205254i	$-0.934198\pi$
$73$	−14.0619	−	8.11863i	−1.64582	−	0.950213i	−0.667109	−	0.744960i	$-0.732469\pi$
$74$	8.04371	−	0.998826i	0.935063	−	0.116111i
$75$		0			0
$76$	2.34829	−	8.27492i	0.269367	−	0.949198i
$77$	−7.48627	−	0.255528i	−0.853140	−	0.0291201i
$78$		0			0
$79$	2.89324	+	5.01124i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$79$	2.89324	+	5.01124i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$80$	−2.20036	−	4.08415i	−0.246008	−	0.456622i
$81$		0			0
$82$	2.85806	+	1.20856i	0.315620	+	0.133463i
$83$			5.93150i			0.651066i	0.945531	+	0.325533i	$0.105544\pi$
$83$			5.93150i			0.651066i	−0.945531	+	0.325533i	$0.894456\pi$
$84$		0			0
$85$			1.81439i			0.196798i
$86$	−3.59656	+	8.50533i	−0.387827	+	0.917153i
$87$		0			0
$88$	7.91431	+	1.22020i	0.843668	+	0.130074i
$89$	1.33902	+	2.31925i	0.141936	+	0.245840i	0.928226	−	0.372018i	$-0.121334\pi$
$89$	1.33902	+	2.31925i	0.141936	+	0.245840i	−0.786290	+	0.617858i	$0.788001\pi$
$90$		0			0
$91$	−3.87769	−	7.27904i	−0.406492	−	0.763051i
$92$	−9.01515	−	2.55836i	−0.939895	−	0.266727i
$93$		0			0
$94$	−1.86334	−	15.0058i	−0.192189	−	1.54773i
$95$	4.31980	+	2.49404i	0.443202	+	0.255883i
$96$		0			0
$97$		−	11.2024i		−	1.13743i	−0.822534	−	0.568716i	$-0.807440\pi$
$97$		−	11.2024i		−	1.13743i	0.822534	−	0.568716i	$-0.192560\pi$
$98$	8.28651	−	5.41606i	0.837064	−	0.547105i
$99$		0			0
$100$	−7.08777	+	1.78781i	−0.708777	+	0.178781i
$101$	0.473259	+	0.273236i	0.0470911	+	0.0271880i	0.523361	−	0.852111i	$-0.324678\pi$
$101$	0.473259	+	0.273236i	0.0470911	+	0.0271880i	−0.476270	+	0.879299i	$0.658011\pi$
$102$		0			0
$103$	13.0391	−	7.52810i	1.28478	−	0.741766i	0.307059	−	0.951691i	$-0.400655\pi$
$103$	13.0391	−	7.52810i	1.28478	−	0.741766i	0.977718	+	0.209925i	$0.0673219\pi$
$104$	3.19349	+	8.21826i	0.313148	+	0.805867i
$105$		0			0
$106$	12.6796	−	9.58201i	1.23155	−	0.930687i
$107$	−1.42284	−	2.46443i	−0.137551	−	0.238246i	0.789018	−	0.614370i	$-0.210590\pi$
$107$	−1.42284	−	2.46443i	−0.137551	−	0.238246i	−0.926569	+	0.376125i	$0.877256\pi$
$108$		0			0
$109$	−0.806006	−	0.465348i	−0.0772014	−	0.0445722i	0.460902	−	0.887451i	$-0.347526\pi$
$109$	−0.806006	−	0.465348i	−0.0772014	−	0.0445722i	−0.538104	+	0.842879i	$0.680859\pi$
$110$	−1.80858	+	4.27703i	−0.172442	+	0.407799i
$111$		0			0
$112$	−9.48269	+	4.69878i	−0.896030	+	0.443993i
$113$		−	13.9228i		−	1.30974i	−0.755741	−	0.654871i	$-0.772723\pi$
$113$		−	13.9228i		−	1.30974i	0.755741	−	0.654871i	$-0.227277\pi$
$114$		0			0
$115$	2.71714	−	4.70623i	0.253375	−	0.438858i
$116$	−5.69646	−	5.86662i	−0.528903	−	0.544702i
$117$		0			0
$118$	−11.7202	−	15.5090i	−1.07893	−	1.42772i
$119$	4.13663	+	0.141195i	0.379205	+	0.0129434i
$120$		0			0
$121$	1.49218	+	2.58452i	0.135652	+	0.234957i
$122$	−1.77568	−	14.2998i	−0.160762	−	1.29464i
$123$		0			0
$124$	1.35814	+	5.38436i	0.121965	+	0.483529i
$125$		−	10.0379i		−	0.897813i
$126$		0			0
$127$	−2.15135			−0.190901			−0.0954506	−	0.995434i	$-0.530429\pi$
$127$	−2.15135			−0.190901			−0.0954506	+	0.995434i	$0.530429\pi$
$128$	10.6615	−	3.78575i	0.942355	−	0.334616i
$129$		0			0
$130$	−5.07393	+	0.630054i	−0.445013	+	0.0552594i
$131$	10.5792	−	6.10788i	0.924306	−	0.533648i	0.0392997	−	0.999227i	$-0.487487\pi$
$131$	10.5792	−	6.10788i	0.924306	−	0.533648i	0.885006	+	0.465579i	$0.154154\pi$
$132$		0			0
$133$	6.02233	−	9.65463i	0.522202	−	0.837163i
$134$	4.93294	+	6.52761i	0.426141	+	0.563900i
$135$		0			0
$136$	−4.37315	−	0.674236i	−0.374995	−	0.0578153i
$137$	8.51773	+	4.91771i	0.727718	+	0.420148i	0.817587	−	0.575805i	$-0.195311\pi$
$137$	8.51773	+	4.91771i	0.727718	+	0.420148i	−0.0898684	+	0.995954i	$0.528645\pi$
$138$		0			0
$139$	17.6445			1.49658			0.748292	−	0.663369i	$-0.230874\pi$
$139$	17.6445			1.49658			0.748292	+	0.663369i	$0.230874\pi$
$140$	−1.29712	−	5.99839i	−0.109626	−	0.506957i
$141$		0			0
$142$	−2.60405	+	6.15819i	−0.218527	+	0.516784i
$143$	4.41277	−	7.64315i	0.369015	−	0.639152i
$144$		0			0
$145$	4.10663	−	2.37097i	0.341037	−	0.196898i
$146$	13.8445	+	18.3201i	1.14578	+	1.51618i
$147$		0			0
$148$	−11.0275	−	3.12941i	−0.906451	−	0.257236i
$149$	−4.88010	−	8.45259i	−0.399794	−	0.692463i	0.593906	−	0.804534i	$-0.297585\pi$
$149$	−4.88010	−	8.45259i	−0.399794	−	0.692463i	−0.993700	+	0.112071i	$0.964252\pi$
$150$		0			0
$151$	2.13984	−	3.70631i	0.174138	−	0.301615i	−0.765725	−	0.643168i	$-0.777620\pi$
$151$	2.13984	−	3.70631i	0.174138	−	0.301615i	0.939862	+	0.341553i	$0.110953\pi$
$152$	−7.61653	+	9.48504i	−0.617782	+	0.769338i
$153$		0			0
$154$	9.61047	+	4.45623i	0.774434	+	0.359093i
$155$	−3.22016			−0.258650
$156$		0			0
$157$	−12.1053	+	20.9671i	−0.966111	+	1.67335i	−0.259512	+	0.965740i	$0.583562\pi$
$157$	−12.1053	+	20.9671i	−0.966111	+	1.67335i	−0.706599	+	0.707614i	$0.749772\pi$
$158$	−1.00842	−	8.12096i	−0.0802254	−	0.646069i
$159$		0			0
$160$	0.616543	+	6.53174i	0.0487420	+	0.516379i
$161$	−10.5183	−	6.56105i	−0.828957	−	0.517083i
$162$		0			0
$163$	7.81820	−	4.51384i	0.612369	−	0.353551i	−0.161523	−	0.986869i	$-0.551641\pi$
$163$	7.81820	−	4.51384i	0.612369	−	0.353551i	0.773892	+	0.633318i	$0.218307\pi$
$164$	−3.05709	−	3.14841i	−0.238718	−	0.245849i
$165$		0			0
$166$	3.26703	−	7.72605i	0.253571	−	0.599658i
$167$	−16.2972			−1.26112			−0.630559	−	0.776142i	$-0.717174\pi$
$167$	−16.2972			−1.26112			−0.630559	+	0.776142i	$0.717174\pi$
$168$		0			0
$169$	−3.28273			−0.252518
$170$	0.999356	−	2.36333i	0.0766471	−	0.181259i
$171$		0			0
$172$	9.36937	−	9.09762i	0.714408	−	0.693687i
$173$	−0.0240052	+	0.0138594i	−0.00182508	+	0.00105371i	−0.500912	−	0.865498i	$-0.667002\pi$
$173$	−0.0240052	+	0.0138594i	−0.00182508	+	0.00105371i	0.499087	+	0.866552i	$0.333669\pi$
$174$		0			0
$175$	−9.66429	−	0.329870i	−0.730551	−	0.0249358i
$176$	−9.63667	−	5.94852i	−0.726392	−	0.448387i
$177$		0			0
$178$	−0.466706	−	3.75846i	−0.0349811	−	0.281708i
$179$	2.39577	−	4.14959i	0.179068	−	0.310155i	−0.762493	−	0.646996i	$-0.776025\pi$
$179$	2.39577	−	4.14959i	0.179068	−	0.310155i	0.941562	+	0.336841i	$0.109358\pi$
$180$		0			0
$181$	7.03270			0.522736			0.261368	−	0.965239i	$-0.415826\pi$
$181$	7.03270			0.522736			0.261368	+	0.965239i	$0.415826\pi$
$182$	1.04161	+	11.6171i	0.0772093	+	0.861116i
$183$		0			0
$184$	10.3335	+	8.29787i	0.761798	+	0.611727i
$185$	3.32364	−	5.75672i	0.244359	−	0.423242i
$186$		0			0
$187$	2.21457	+	3.83576i	0.161946	+	0.280498i
$188$	−5.83801	+	20.5720i	−0.425781	+	1.50037i
$189$		0			0
$190$	−4.25303	−	5.62792i	−0.308547	−	0.408292i
$191$	−11.9817	+	6.91767i	−0.866969	+	0.500545i	−0.866340	−	0.499455i	$-0.833534\pi$
$191$	−11.9817	+	6.91767i	−0.866969	+	0.500545i	−0.000629171		1.00000i	$0.500200\pi$
$192$		0			0
$193$	−2.10467	+	3.64540i	−0.151498	+	0.262402i	−0.931778	−	0.363028i	$-0.881743\pi$
$193$	−2.10467	+	3.64540i	−0.151498	+	0.262402i	0.780280	+	0.625430i	$0.215076\pi$
$194$	−6.17022	+	14.5917i	−0.442996	+	1.04762i
$195$		0			0
$196$	−13.7767	+	2.49051i	−0.984050	+	0.177894i
$197$	24.3528			1.73507			0.867534	−	0.497378i	$-0.165704\pi$
$197$	24.3528			1.73507			0.867534	+	0.497378i	$0.165704\pi$
$198$		0			0
$199$	−1.63996	−	0.946831i	−0.116254	−	0.0671191i	0.440746	−	0.897632i	$-0.354714\pi$
$199$	−1.63996	−	0.946831i	−0.116254	−	0.0671191i	−0.556999	+	0.830513i	$0.688047\pi$
$200$	10.2169	+	1.57520i	0.722441	+	0.111383i
$201$		0			0
$202$	−0.465945	−	0.616571i	−0.0327838	−	0.0433818i
$203$	−5.08600	−	9.54723i	−0.356967	−	0.670084i
$204$		0			0
$205$	2.20389	−	1.27241i	0.153926	−	0.0888692i
$206$	−21.1304	+	2.62386i	−1.47222	+	0.182813i
$207$		0			0
$208$	0.366902	−	12.4636i	0.0254401	−	0.864196i
$209$	12.1765			0.842266
$210$		0			0
$211$			25.0597i			1.72518i	0.505901	+	0.862592i	$0.331160\pi$
$211$			25.0597i			1.72518i	−0.505901	+	0.862592i	$0.668840\pi$
$212$	−21.7935	+	5.49716i	−1.49678	+	0.377546i
$213$		0			0
$214$	0.495920	+	3.99373i	0.0339004	+	0.273006i
$215$	3.78659	+	6.55856i	0.258243	+	0.447290i
$216$		0			0
$217$	−0.250592	+	7.34166i	−0.0170113	+	0.498384i
$218$	0.793549	+	1.05008i	0.0537459	+	0.0711204i
$219$		0			0
$220$	4.71153	−	4.57487i	0.317651	−	0.308438i
$221$	−2.43833	+	4.22332i	−0.164020	+	0.284091i
$222$		0			0
$223$			9.42532i			0.631166i	0.948898	+	0.315583i	$0.102200\pi$
$223$			9.42532i			0.631166i	−0.948898	+	0.315583i	$0.897800\pi$
$224$	14.9397	−	0.897360i	0.998201	−	0.0599574i
$225$		0			0
$226$	−7.66857	+	18.1350i	−0.510106	+	1.20632i
$227$	16.0967	+	9.29346i	1.06838	+	0.616829i	0.927738	−	0.373232i	$-0.121750\pi$
$227$	16.0967	+	9.29346i	1.06838	+	0.616829i	0.140641	+	0.990061i	$0.455084\pi$
$228$		0			0
$229$	13.7016	+	23.7319i	0.905428	+	1.56825i	0.820342	+	0.571874i	$0.193783\pi$
$229$	13.7016	+	23.7319i	0.905428	+	1.56825i	0.0850862	+	0.996374i	$0.472883\pi$
$230$	−6.13136	+	4.63349i	−0.404290	+	0.305523i
$231$		0			0
$232$	4.18860	+	10.7791i	0.274995	+	0.707684i
$233$	−21.0326	+	12.1432i	−1.37789	+	0.795526i	−0.991906	−	0.126978i	$-0.959472\pi$
$233$	−21.0326	+	12.1432i	−1.37789	+	0.795526i	−0.385987	+	0.922504i	$0.626139\pi$
$234$		0			0
$235$	−10.7393	−	6.20035i	−0.700556	−	0.404466i
$236$	6.72384	+	26.6566i	0.437685	+	1.73520i
$237$		0			0
$238$	−5.31039	−	2.46235i	−0.344221	−	0.159610i
$239$			2.35413i			0.152276i	0.997097	+	0.0761380i	$0.0242590\pi$
$239$			2.35413i			0.152276i	−0.997097	+	0.0761380i	$0.975741\pi$
$240$		0			0
$241$	11.2904	+	6.51850i	0.727277	+	0.419893i	0.817425	−	0.576035i	$-0.195401\pi$
$241$	11.2904	+	6.51850i	0.727277	+	0.419893i	−0.0901483	+	0.995928i	$0.528734\pi$
$242$	−0.520086	−	4.18834i	−0.0334324	−	0.269237i
$243$		0			0
$244$	−5.56336	+	19.6042i	−0.356157	+	1.25503i
$245$	0.553574	−	8.09964i	0.0353665	−	0.517467i
$246$		0			0
$247$	6.70340	+	11.6106i	0.426527	+	0.738767i
$248$	1.19663	−	7.76143i	0.0759859	−	0.492851i
$249$		0			0
$250$	−5.52879	+	13.0748i	−0.349672	+	0.826921i
$251$		−	24.0484i		−	1.51792i	−0.651136	−	0.758961i	$-0.725707\pi$
$251$		−	24.0484i		−	1.51792i	0.651136	−	0.758961i	$-0.274293\pi$
$252$		0			0
$253$		−	13.2657i		−	0.834010i
$254$	2.80223	+	1.18495i	0.175828	+	0.0743504i
$255$		0			0
$256$	−15.9723	−	0.941195i	−0.998268	−	0.0588247i
$257$	−6.72517	−	11.6483i	−0.419504	−	0.726603i	0.576385	−	0.817178i	$-0.304463\pi$
$257$	−6.72517	−	11.6483i	−0.419504	−	0.726603i	−0.995890	+	0.0905752i	$0.971129\pi$
$258$		0			0
$259$	−12.8661	−	8.02557i	−0.799461	−	0.498684i
$260$	6.95605	+	1.97402i	0.431396	+	0.122423i
$261$		0			0
$262$	−17.1440	+	2.12886i	−1.05916	+	0.131521i
$263$	−1.35260	−	0.780923i	−0.0834048	−	0.0481538i	0.457718	−	0.889098i	$-0.348667\pi$
$263$	−1.35260	−	0.780923i	−0.0834048	−	0.0481538i	−0.541122	+	0.840944i	$0.682000\pi$
$264$		0			0
$265$		−	13.0338i		−	0.800658i
$266$	−13.1621	+	9.25854i	−0.807018	+	0.567678i
$267$		0			0
$268$	−2.83001	−	11.2195i	−0.172870	−	0.685343i
$269$	14.3499	+	8.28490i	0.874927	+	0.505139i	0.868982	−	0.494843i	$-0.164774\pi$
$269$	14.3499	+	8.28490i	0.874927	+	0.505139i	0.00594471	+	0.999982i	$0.498108\pi$
$270$		0			0
$271$	11.9658	−	6.90846i	0.726871	−	0.419659i	−0.0904054	−	0.995905i	$-0.528816\pi$
$271$	11.9658	−	6.90846i	0.726871	−	0.419659i	0.817276	+	0.576246i	$0.195483\pi$
$272$	5.32487	+	3.28693i	0.322867	+	0.199299i
$273$		0			0
$274$	−8.38608	−	11.0971i	−0.506622	−	0.670398i
$275$	−5.17384	−	8.96135i	−0.311994	−	0.540390i
$276$		0			0
$277$	−11.6351	−	6.71750i	−0.699083	−	0.403616i	0.107923	−	0.994159i	$-0.465580\pi$
$277$	−11.6351	−	6.71750i	−0.699083	−	0.403616i	−0.807006	+	0.590544i	$0.798913\pi$
$278$	−22.9827	−	9.71847i	−1.37841	−	0.582875i
$279$		0			0
$280$	−1.61433	+	8.52763i	−0.0964744	+	0.509623i
$281$			27.9830i			1.66933i	0.550761	+	0.834663i	$0.314338\pi$
$281$			27.9830i			1.66933i	−0.550761	+	0.834663i	$0.685662\pi$
$282$		0			0
$283$	−9.68568	+	16.7761i	−0.575754	+	0.997235i	0.420205	+	0.907429i	$0.361958\pi$
$283$	−9.68568	+	16.7761i	−0.575754	+	0.997235i	−0.995959	+	0.0898063i	$0.971375\pi$
$284$	6.78380	−	6.58703i	0.402544	−	0.390869i
$285$		0			0
$286$	−9.95764	+	7.52502i	−0.588808	+	0.444964i
$287$	−2.72947	−	5.12366i	−0.161116	−	0.302440i
$288$		0			0
$289$	7.27631	+	12.6029i	0.428018	+	0.741349i
$290$	−6.65499	+	0.826382i	−0.390795	+	0.0485268i
$291$		0			0
$292$	−7.94256	−	31.4882i	−0.464803	−	1.84271i
$293$		−	24.4475i		−	1.42824i	−0.700024	−	0.714119i	$-0.746827\pi$
$293$		−	24.4475i		−	1.42824i	0.700024	−	0.714119i	$-0.253173\pi$
$294$		0			0
$295$	−15.9422			−0.928193
$296$	12.6401	+	10.1501i	0.734691	+	0.589960i
$297$		0			0
$298$	1.70092	+	13.6978i	0.0985318	+	0.793493i
$299$	12.6493	−	7.30305i	0.731525	−	0.422346i
$300$		0			0
$301$	15.2476	−	8.12267i	0.878855	−	0.468183i
$302$	−4.82865	+	3.64903i	−0.277858	+	0.209978i
$303$		0			0
$304$	15.1452	−	8.15956i	0.868636	−	0.467983i
$305$	−10.2341	−	5.90865i	−0.586001	−	0.338328i
$306$		0			0
$307$	27.0446			1.54352			0.771758	−	0.635917i	$-0.219378\pi$
$307$	27.0446			1.54352			0.771758	+	0.635917i	$0.219378\pi$
$308$	−10.0636	−	11.0978i	−0.573427	−	0.632358i
$309$		0			0
$310$	4.19441	+	1.77365i	0.238226	+	0.100736i
$311$	0.276139	−	0.478286i	0.0156584	−	0.0271211i	−0.858090	−	0.513499i	$-0.828349\pi$
$311$	0.276139	−	0.478286i	0.0156584	−	0.0271211i	0.873748	+	0.486378i	$0.161682\pi$
$312$		0			0
$313$	−13.5478	+	7.82183i	−0.765768	+	0.442116i	−0.831363	−	0.555730i	$-0.812439\pi$
$313$	−13.5478	+	7.82183i	−0.765768	+	0.442116i	0.0655951	+	0.997846i	$0.479105\pi$
$314$	27.3163	−	20.6430i	1.54155	−	1.16495i
$315$		0			0
$316$	−3.15947	+	11.1334i	−0.177734	+	0.626300i
$317$	−6.33699	−	10.9760i	−0.355921	−	0.616472i	0.631355	−	0.775494i	$-0.282499\pi$
$317$	−6.33699	−	10.9760i	−0.355921	−	0.616472i	−0.987275	+	0.159022i	$0.949166\pi$
$318$		0			0
$319$	5.78782	−	10.0248i	0.324056	−	0.561281i
$320$	2.79457	−	8.84748i	0.156221	−	0.494589i
$321$		0			0
$322$	10.0868	+	14.3395i	0.562113	+	0.799108i
$323$	−6.72828			−0.374371
$324$		0			0
$325$	5.69660	−	9.86680i	0.315991	−	0.547312i
$326$	−12.6698	+	1.57327i	−0.701713	+	0.0871351i
$327$		0			0
$328$	2.24787	+	5.78477i	0.124118	+	0.319411i
$329$	−14.9719	+	24.0021i	−0.825429	+	1.32328i
$330$		0			0
$331$	−2.26793	+	1.30939i	−0.124657	+	0.0719706i	−0.561032	−	0.827794i	$-0.689595\pi$
$331$	−2.26793	+	1.30939i	−0.124657	+	0.0719706i	0.436375	+	0.899765i	$0.356262\pi$
$332$	−8.51092	+	8.26407i	−0.467098	+	0.453550i
$333$		0			0
$334$	21.2279	+	8.97642i	1.16154	+	0.491168i
$335$	6.70995			0.366604
$336$		0			0
$337$	34.9446			1.90356			0.951778	−	0.306788i	$-0.0992542\pi$
$337$	34.9446			1.90356			0.951778	+	0.306788i	$0.0992542\pi$
$338$	4.27590	+	1.80811i	0.232578	+	0.0983481i
$339$		0			0
$340$	−2.60341	+	2.52790i	−0.141190	+	0.137095i
$341$	−6.80766	+	3.93040i	−0.368656	+	0.212843i
$342$		0			0
$343$	−18.4233	−	1.89241i	−0.994766	−	0.102180i
$344$	−17.2150	+	6.68947i	−0.928168	+	0.360672i
$345$		0			0
$346$	0.0389016	−	0.00483060i	0.00209136	−	0.000259695i
$347$	−16.7205	+	28.9607i	−0.897602	+	1.55469i	−0.0670515	+	0.997750i	$0.521359\pi$
$347$	−16.7205	+	28.9607i	−0.897602	+	1.55469i	−0.830551	+	0.556943i	$0.811974\pi$
$348$		0			0
$349$	−7.32611			−0.392158			−0.196079	−	0.980588i	$-0.562821\pi$
$349$	−7.32611			−0.392158			−0.196079	+	0.980588i	$0.562821\pi$
$350$	12.4065	+	5.75270i	0.663155	+	0.307495i
$351$		0			0
$352$	9.27580	+	13.0560i	0.494402	+	0.695890i
$353$	13.9297	−	24.1269i	0.741402	−	1.28415i	−0.210454	−	0.977604i	$-0.567494\pi$
$353$	13.9297	−	24.1269i	0.741402	−	1.28415i	0.951857	−	0.306543i	$-0.0991723\pi$
$354$		0			0
$355$	2.74164	+	4.74866i	0.145511	+	0.252033i
$356$	−1.46223	+	5.15262i	−0.0774981	+	0.273088i
$357$		0			0
$358$	−5.40617	+	4.08546i	−0.285725	+	0.215923i
$359$	15.6201	−	9.01825i	0.824396	−	0.475965i	−0.0275343	−	0.999621i	$-0.508766\pi$
$359$	15.6201	−	9.01825i	0.824396	−	0.475965i	0.851930	+	0.523656i	$0.175432\pi$
$360$		0			0
$361$	0.251405	−	0.435447i	0.0132319	−	0.0229182i
$362$	−9.16041	−	3.87357i	−0.481461	−	0.203590i
$363$		0			0
$364$	5.04188	−	15.7055i	0.264266	−	0.823192i
$365$	18.8318			0.985703
$366$		0			0
$367$	4.16683	+	2.40572i	0.217507	+	0.125578i	0.604795	−	0.796381i	$-0.293255\pi$
$367$	4.16683	+	2.40572i	0.217507	+	0.125578i	−0.387288	+	0.921959i	$0.626588\pi$
$368$	−8.88947	−	16.5000i	−0.463396	−	0.860122i
$369$		0			0
$370$	−7.49996	+	5.66775i	−0.389904	+	0.294652i
$371$	−29.7157	−	1.01428i	−1.54276	−	0.0526590i
$372$		0			0
$373$	−0.589575	+	0.340391i	−0.0305270	+	0.0176248i	−0.515186	−	0.857078i	$-0.672277\pi$
$373$	−0.589575	+	0.340391i	−0.0305270	+	0.0176248i	0.484659	+	0.874703i	$0.338944\pi$
$374$	−0.771873	−	6.21602i	−0.0399126	−	0.321423i
$375$		0			0
$376$	18.9352	−	23.5805i	0.976511	−	1.21607i
$377$	12.7452			0.656413
$378$		0			0
$379$			23.7081i			1.21780i	0.793245	+	0.608902i	$0.208390\pi$
$379$			23.7081i			1.21780i	−0.793245	+	0.608902i	$0.791610\pi$
$380$	2.43995	+	9.67316i	0.125167	+	0.496223i
$381$		0			0
$382$	19.4170	−	2.41110i	0.993460	−	0.123363i
$383$	−16.7429	−	28.9996i	−0.855522	−	1.48181i	−0.876160	−	0.482021i	$-0.839903\pi$
$383$	−16.7429	−	28.9996i	−0.855522	−	1.48181i	0.0206373	−	0.999787i	$-0.493430\pi$
$384$		0			0
$385$	7.66746	−	4.08460i	0.390770	−	0.208171i
$386$	4.74930	−	3.58906i	0.241733	−	0.182679i
$387$		0			0
$388$	16.0740	−	15.6078i	0.816033	−	0.792365i
$389$	−11.7772	+	20.3988i	−0.597130	+	1.03426i	0.396113	+	0.918202i	$0.370359\pi$
$389$	−11.7772	+	20.3988i	−0.597130	+	1.03426i	−0.993243	+	0.116057i	$0.962974\pi$
$390$		0			0
$391$			7.33015i			0.370702i
$392$	19.3165	+	4.34412i	0.975632	+	0.219411i
$393$		0			0
$394$	−31.7207	−	13.4134i	−1.59807	−	0.675757i
$395$	−5.81200	−	3.35556i	−0.292433	−	0.168836i
$396$		0			0
$397$	−12.7489	−	22.0817i	−0.639849	−	1.10825i	−0.985466	−	0.169875i	$-0.945664\pi$
$397$	−12.7489	−	22.0817i	−0.639849	−	1.10825i	0.345617	−	0.938376i	$-0.387670\pi$
$398$	1.61461	+	2.13657i	0.0809332	+	0.107097i
$399$		0			0
$400$	−12.4403	−	7.67915i	−0.622016	−	0.383958i
$401$	10.2818	−	5.93623i	0.513451	−	0.296441i	−0.220800	−	0.975319i	$-0.570867\pi$
$401$	10.2818	−	5.93623i	0.513451	−	0.296441i	0.734251	+	0.678878i	$0.237533\pi$
$402$		0			0
$403$	−7.49550	−	4.32753i	−0.373378	−	0.215570i
$404$	0.267311	+	1.05975i	0.0132992	+	0.0527247i
$405$		0			0
$406$	1.36618	+	15.2370i	0.0678024	+	0.756202i
$407$		−	16.2268i		−	0.804334i
$408$		0			0
$409$	−4.46727	−	2.57918i	−0.220892	−	0.127532i	0.385471	−	0.922720i	$-0.374039\pi$
$409$	−4.46727	−	2.57918i	−0.220892	−	0.127532i	−0.606363	+	0.795188i	$0.707372\pi$
$410$	−3.57150	+	0.443490i	−0.176384	+	0.0219024i
$411$		0			0
$412$	28.9685	+	8.22080i	1.42718	+	0.405010i
$413$	−1.24062	+	36.3468i	−0.0610469	+	1.78851i
$414$		0			0
$415$	−3.43965	−	5.95765i	−0.168846	−	0.292449i
$416$	−7.34279	+	16.0323i	−0.360010	+	0.786050i
$417$		0			0
$418$	−15.8604	−	6.70674i	−0.775760	−	0.328037i
$419$			8.63546i			0.421870i	0.977500	+	0.210935i	$0.0676508\pi$
$419$			8.63546i			0.421870i	−0.977500	+	0.210935i	$0.932349\pi$
$420$		0			0
$421$		−	37.2303i		−	1.81449i	−0.420599	−	0.907247i	$-0.638180\pi$
$421$		−	37.2303i		−	1.81449i	0.420599	−	0.907247i	$-0.361820\pi$
$422$	13.8028	−	32.6415i	0.671908	−	1.58896i
$423$		0			0
$424$	31.4148	+	4.84341i	1.52564	+	0.235217i
$425$	2.85887	+	4.95171i	0.138676	+	0.240193i
$426$		0			0
$427$	−14.2676	+	22.8729i	−0.690455	+	1.10690i
$428$	1.55376	−	5.47516i	0.0751040	−	0.264652i
$429$		0			0
$430$	−1.31979	−	10.6285i	−0.0636458	−	0.512550i
$431$	7.24374	+	4.18217i	0.348919	+	0.201448i	0.664209	−	0.747547i	$-0.268769\pi$
$431$	7.24374	+	4.18217i	0.348919	+	0.201448i	−0.315290	+	0.948995i	$0.602102\pi$
$432$		0			0
$433$		−	7.63673i		−	0.366998i	−0.983020	−	0.183499i	$-0.941258\pi$
$433$		−	7.63673i		−	0.366998i	0.983020	−	0.183499i	$-0.0587424\pi$
$434$	4.37015	−	9.42482i	0.209774	−	0.452406i
$435$		0			0
$436$	−0.455256	−	1.80486i	−0.0218028	−	0.0864371i
$437$	17.4520	+	10.0759i	0.834843	+	0.481997i
$438$		0			0
$439$	−8.42793	+	4.86587i	−0.402243	+	0.232235i	−0.687451	−	0.726230i	$-0.741271\pi$
$439$	−8.42793	+	4.86587i	−0.402243	+	0.232235i	0.285208	+	0.958466i	$0.407937\pi$
$440$	−8.65679	+	3.36390i	−0.412696	+	0.160367i
$441$		0			0
$442$	5.50222	−	4.15804i	0.261714	−	0.197778i
$443$	10.9352	+	18.9404i	0.519549	+	0.899885i	0.999742	+	0.0227221i	$0.00723330\pi$
$443$	10.9352	+	18.9404i	0.519549	+	0.899885i	−0.480193	+	0.877163i	$0.659433\pi$
$444$		0			0
$445$	−2.68985	−	1.55299i	−0.127511	−	0.0736186i
$446$	5.19141	−	12.2769i	0.245820	−	0.581329i
$447$		0			0
$448$	−19.9539	−	7.05985i	−0.942734	−	0.333547i
$449$			16.6555i			0.786020i	0.919534	+	0.393010i	$0.128566\pi$
$449$			16.6555i			0.786020i	−0.919534	+	0.393010i	$0.871434\pi$
$450$		0			0
$451$	3.10612	−	5.37995i	0.146261	−	0.253332i
$452$	19.9773	−	19.3979i	0.939655	−	0.912400i
$453$		0			0
$454$	−15.8480	−	20.9712i	−0.743782	−	0.984225i
$455$	8.11587	+	5.06248i	0.380478	+	0.237333i
$456$		0			0
$457$	−10.3145	−	17.8652i	−0.482490	−	0.835698i	0.517307	−	0.855800i	$-0.326934\pi$
$457$	−10.3145	−	17.8652i	−0.482490	−	0.835698i	−0.999798	+	0.0201016i	$0.993601\pi$
$458$	−4.77559	−	38.4586i	−0.223149	−	1.79705i
$459$		0			0
$460$	10.5385	−	2.65821i	0.491359	−	0.123940i
$461$		−	31.5292i		−	1.46846i	−0.678901	−	0.734230i	$-0.737543\pi$
$461$		−	31.5292i		−	1.46846i	0.678901	−	0.734230i	$-0.262457\pi$
$462$		0			0
$463$	−40.3843			−1.87682			−0.938409	−	0.345526i	$-0.887701\pi$
$463$	−40.3843			−1.87682			−0.938409	+	0.345526i	$0.887701\pi$
$464$	0.481231	−	16.3474i	0.0223406	−	0.758907i
$465$		0			0
$466$	34.0843	−	4.23241i	1.57893	−	0.196063i
$467$	−10.1585	+	5.86499i	−0.470077	+	0.271399i	−0.716272	−	0.697821i	$-0.754153\pi$
$467$	−10.1585	+	5.86499i	−0.470077	+	0.271399i	0.246195	+	0.969220i	$0.420820\pi$
$468$		0			0
$469$	0.522166	−	15.2980i	0.0241114	−	0.706398i
$470$	10.5733	+	13.9914i	0.487712	+	0.645375i
$471$		0			0
$472$	5.92421	−	38.4250i	0.272684	−	1.76865i
$473$	16.0103	+	9.24352i	0.736152	+	0.425018i
$474$		0			0
$475$	15.7191			0.721240
$476$	5.56077	+	6.13225i	0.254878	+	0.281071i
$477$		0			0
$478$	1.29664	−	3.06636i	0.0593070	−	0.140252i
$479$	−0.299198	+	0.518227i	−0.0136707	+	0.0236784i	−0.872780	−	0.488114i	$-0.837685\pi$
$479$	−0.299198	+	0.518227i	−0.0136707	+	0.0236784i	0.859109	+	0.511792i	$0.171018\pi$
$480$		0			0
$481$	15.4727	−	8.93319i	0.705496	−	0.407318i
$482$	−11.1159	−	14.7093i	−0.506314	−	0.669991i
$483$		0			0
$484$	−1.62948	+	5.74197i	−0.0740672	+	0.260998i
$485$	6.49623	+	11.2518i	0.294979	+	0.510918i
$486$		0			0
$487$	−10.3961	+	18.0065i	−0.471090	+	0.815952i	−0.999453	−	0.0330665i	$-0.989473\pi$
$487$	−10.3961	+	18.0065i	−0.471090	+	0.815952i	0.528363	+	0.849019i	$0.322806\pi$
$488$	18.0444	−	22.4711i	0.816832	−	1.01722i
$489$		0			0
$490$	−5.18229	+	10.2453i	−0.234112	+	0.462833i
$491$	−22.4435			−1.01286			−0.506430	−	0.862281i	$-0.669035\pi$
$491$	−22.4435			−1.01286			−0.506430	+	0.862281i	$0.669035\pi$
$492$		0			0
$493$	−3.19813	+	5.53933i	−0.144037	+	0.249479i
$494$	−2.33642	−	18.8156i	−0.105120	−	0.846552i
$495$		0			0
$496$	−5.83361	+	9.45052i	−0.261937	+	0.424341i
$497$	11.0398	−	5.88113i	0.495204	−	0.263805i
$498$		0			0
$499$	−10.2264	+	5.90424i	−0.457799	+	0.264310i	−0.711118	−	0.703072i	$-0.751811\pi$
$499$	−10.2264	+	5.90424i	−0.457799	+	0.264310i	0.253320	+	0.967383i	$0.418478\pi$
$500$	14.4030	−	13.9853i	0.644123	−	0.625440i
$501$		0			0
$502$	−13.2457	+	31.3242i	−0.591186	+	1.39807i
$503$	3.08281			0.137456			0.0687278	−	0.997635i	$-0.478106\pi$
$503$	3.08281			0.137456			0.0687278	+	0.997635i	$0.478106\pi$
$504$		0			0
$505$	−0.633794			−0.0282035
$506$	−7.30669	+	17.2792i	−0.324822	+	0.768156i
$507$		0			0
$508$	−2.99737	−	3.08690i	−0.132987	−	0.136959i
$509$	3.99141	−	2.30444i	0.176916	−	0.102143i	−0.408927	−	0.912567i	$-0.634097\pi$
$509$	3.99141	−	2.30444i	0.176916	−	0.102143i	0.585843	+	0.810425i	$0.300764\pi$
$510$		0			0
$511$	1.46549	−	42.9347i	0.0648293	−	1.89932i
$512$	20.2862	+	10.0234i	0.896534	+	0.442976i
$513$		0			0
$514$	2.34401	+	18.8767i	0.103390	+	0.832614i
$515$	−8.73103	+	15.1226i	−0.384735	+	0.666381i
$516$		0			0
$517$	−30.2716			−1.33135
$518$	12.3383	+	17.5402i	0.542112	+	0.770674i
$519$		0			0
$520$	−7.97330	−	6.40260i	−0.349652	−	0.280773i
$521$	−19.2542	+	33.3493i	−0.843542	+	1.46106i	0.0433388	+	0.999060i	$0.486201\pi$
$521$	−19.2542	+	33.3493i	−0.843542	+	1.46106i	−0.886881	+	0.461998i	$0.847133\pi$
$522$		0			0
$523$	−19.3439	−	33.5046i	−0.845849	−	1.46505i	−0.884882	−	0.465815i	$-0.845761\pi$
$523$	−19.3439	−	33.5046i	−0.845849	−	1.46505i	0.0390332	−	0.999238i	$-0.487572\pi$
$524$	23.5035	+	6.66990i	1.02675	+	0.291376i
$525$		0			0
$526$	1.33169	+	1.76219i	0.0580646	+	0.0768352i
$527$	3.76166	−	2.17180i	0.163860	−	0.0946049i
$528$		0			0
$529$	−0.522727	+	0.905390i	−0.0227273	+	0.0393648i
$530$	−7.17893	+	16.9771i	−0.311833	+	0.737438i
$531$		0			0
$532$	22.2438	−	4.81008i	0.964389	−	0.208543i
$533$	6.83991			0.296270
$534$		0			0
$535$	2.85823	+	1.65020i	0.123572	+	0.0713443i
$536$	−2.49345	+	16.1727i	−0.107701	+	0.698555i
$537$		0			0
$538$	−14.1281	−	18.6953i	−0.609105	−	0.806011i
$539$	−8.71582	−	17.7989i	−0.375417	−	0.766654i
$540$		0			0
$541$	24.9474	−	14.4034i	1.07257	−	0.619249i	0.143688	−	0.989623i	$-0.454104\pi$
$541$	24.9474	−	14.4034i	1.07257	−	0.619249i	0.928883	+	0.370374i	$0.120770\pi$
$542$	−19.3912	+	2.40789i	−0.832921	+	0.103428i
$543$		0			0
$544$	−5.12546	−	7.21428i	−0.219752	−	0.309310i
$545$	1.07941			0.0462370
$546$		0			0
$547$			26.0874i			1.11541i	0.830038	+	0.557707i	$0.188319\pi$
$547$			26.0874i			1.11541i	−0.830038	+	0.557707i	$0.811681\pi$
$548$	4.81106	+	19.0734i	0.205518	+	0.814777i
$549$		0			0
$550$	1.80330	+	14.5223i	0.0768931	+	0.619233i
$551$	8.79222	+	15.2286i	0.374561	+	0.648759i
$552$		0			0
$553$	−8.10263	+	12.9897i	−0.344559	+	0.552377i
$554$	11.4552	+	15.1584i	0.486686	+	0.644018i
$555$		0			0
$556$	24.5832	+	25.3175i	1.04256	+	1.07370i
$557$	−11.2896	+	19.5542i	−0.478357	+	0.828538i	−0.999692	−	0.0248137i	$-0.992101\pi$
$557$	−11.2896	+	19.5542i	−0.478357	+	0.828538i	0.521335	+	0.853352i	$0.325434\pi$
$558$		0			0
$559$			20.3550i			0.860923i
$560$	6.79970	−	10.2185i	0.287340	−	0.431809i
$561$		0			0
$562$	15.4129	−	36.4491i	0.650153	−	1.53751i
$563$	15.9160	+	9.18909i	0.670778	+	0.387274i	0.796371	−	0.604808i	$-0.206750\pi$
$563$	15.9160	+	9.18909i	0.670778	+	0.387274i	−0.125593	+	0.992082i	$0.540083\pi$
$564$		0			0
$565$	8.07374	+	13.9841i	0.339665	+	0.588317i
$566$	21.8562	−	16.5168i	0.918686	−	0.694254i
$567$		0			0
$568$	−12.4643	+	4.84344i	−0.522991	+	0.203226i
$569$	16.3033	−	9.41272i	0.683470	−	0.394602i	−0.117691	−	0.993050i	$-0.537549\pi$
$569$	16.3033	−	9.41272i	0.683470	−	0.394602i	0.801161	+	0.598449i	$0.204216\pi$
$570$		0			0
$571$	−2.34839	−	1.35584i	−0.0982770	−	0.0567403i	0.450056	−	0.893000i	$-0.351404\pi$
$571$	−2.34839	−	1.35584i	−0.0982770	−	0.0567403i	−0.548333	+	0.836260i	$0.684737\pi$
$572$	17.1150	−	4.31707i	0.715615	−	0.180506i
$573$		0			0
$574$	0.733181	+	8.17718i	0.0306024	+	0.341309i
$575$		−	17.1252i		−	0.714170i
$576$		0			0
$577$	15.8080	+	9.12677i	0.658097	+	0.379952i	0.791551	−	0.611103i	$-0.209274\pi$
$577$	15.8080	+	9.12677i	0.658097	+	0.379952i	−0.133455	+	0.991055i	$0.542607\pi$
$578$	−2.53610	−	20.4237i	−0.105488	−	0.849512i
$579$		0			0
$580$	9.12360	+	2.58913i	0.378837	+	0.107508i
$581$	−13.8505	+	7.37844i	−0.574617	+	0.306109i
$582$		0			0
$583$	−15.9085	−	27.5544i	−0.658863	−	1.14119i
$584$	−6.99799	+	45.3896i	−0.289579	+	1.87823i
$585$		0			0
$586$	−13.4655	+	31.8440i	−0.556256	+	1.31546i
$587$			32.5679i			1.34422i	0.740451	+	0.672110i	$0.234612\pi$
$587$			32.5679i			1.34422i	−0.740451	+	0.672110i	$0.765388\pi$
$588$		0			0
$589$		−	11.9413i		−	0.492032i
$590$	20.7655	+	8.78090i	0.854902	+	0.361504i
$591$		0			0
$592$	−10.8737	−	20.1830i	−0.446907	−	0.829517i
$593$	−15.3152	−	26.5267i	−0.628920	−	1.08932i	−0.987769	−	0.155925i	$-0.950164\pi$
$593$	−15.3152	−	26.5267i	−0.628920	−	1.08932i	0.358849	−	0.933396i	$-0.383169\pi$
$594$		0			0
$595$	−4.23675	+	2.25700i	−0.173690	+	0.0925279i
$596$	5.32915	−	18.7789i	0.218290	−	0.769214i
$597$		0			0
$598$	−20.4987	+	2.54542i	−0.838255	+	0.104090i
$599$	28.4250	+	16.4112i	1.16141	+	0.670543i	0.951643	−	0.307207i	$-0.0993944\pi$
$599$	28.4250	+	16.4112i	1.16141	+	0.670543i	0.209772	+	0.977750i	$0.432728\pi$
$600$		0			0
$601$			5.73393i			0.233892i	0.993138	+	0.116946i	$0.0373104\pi$
$601$			5.73393i			0.233892i	−0.993138	+	0.116946i	$0.962690\pi$
$602$	−24.3346	+	2.18188i	−0.991803	+	0.0889268i
$603$		0			0
$604$	8.29940	−	2.09343i	0.337698	−	0.0851806i
$605$	−2.99751	−	1.73061i	−0.121866	−	0.0703594i
$606$		0			0
$607$	4.62054	−	2.66767i	0.187542	−	0.108277i	−0.403289	−	0.915073i	$-0.632133\pi$
$607$	4.62054	−	2.66767i	0.187542	−	0.108277i	0.590831	+	0.806795i	$0.298800\pi$
$608$	−24.2215	+	2.28632i	−0.982313	+	0.0927224i
$609$		0			0
$610$	10.0759	+	13.3332i	0.407961	+	0.539844i
$611$	−16.6651	−	28.8649i	−0.674199	−	1.16775i
$612$		0			0
$613$	−0.763004	−	0.440521i	−0.0308174	−	0.0177925i	0.484512	−	0.874785i	$-0.338997\pi$
$613$	−0.763004	−	0.440521i	−0.0308174	−	0.0177925i	−0.515330	+	0.856992i	$0.672330\pi$
$614$	−35.2268	−	14.8960i	−1.42164	−	0.601154i
$615$		0			0
$616$	6.99569	+	19.9984i	0.281864	+	0.805759i
$617$			33.3940i			1.34439i	0.740373	+	0.672196i	$0.234649\pi$
$617$			33.3940i			1.34439i	−0.740373	+	0.672196i	$0.765351\pi$
$618$		0			0
$619$	0.347094	−	0.601184i	0.0139509	−	0.0241636i	−0.858966	−	0.512033i	$-0.828892\pi$
$619$	0.347094	−	0.601184i	0.0139509	−	0.0241636i	0.872917	+	0.487870i	$0.162226\pi$
$620$	−4.48650	−	4.62051i	−0.180182	−	0.185564i
$621$		0			0
$622$	−0.623121	+	0.470894i	−0.0249849	+	0.0188811i
$623$	−3.74998	+	6.01174i	−0.150240	+	0.240855i
$624$		0			0
$625$	−3.31630	−	5.74400i	−0.132652	−	0.229760i
$626$	21.9549	−	2.72624i	0.877493	−	0.108962i
$627$		0			0
$628$	−46.9508	+	11.8428i	−1.87354	+	0.472580i
$629$			8.96634i			0.357511i
$630$		0			0
$631$	3.67584			0.146333			0.0731664	−	0.997320i	$-0.476690\pi$
$631$	3.67584			0.146333			0.0731664	+	0.997320i	$0.476690\pi$
$632$	10.2475	−	12.7615i	0.407625	−	0.507625i
$633$		0			0
$634$	2.20871	+	17.7871i	0.0877190	+	0.706416i
$635$	2.16083	−	1.24756i	0.0857500	−	0.0495078i
$636$		0			0
$637$	12.1735	−	18.1094i	0.482333	−	0.717522i
$638$	−13.0605	+	9.86986i	−0.517070	+	0.390751i
$639$		0			0
$640$	−8.51319	+	9.98501i	−0.336513	+	0.394692i
$641$	−20.9407	−	12.0901i	−0.827108	−	0.477531i	0.0257532	−	0.999668i	$-0.491802\pi$
$641$	−20.9407	−	12.0901i	−0.827108	−	0.477531i	−0.852862	+	0.522137i	$0.825135\pi$
$642$		0			0
$643$	−7.82797			−0.308705			−0.154352	−	0.988016i	$-0.549329\pi$
$643$	−7.82797			−0.308705			−0.154352	+	0.988016i	$0.549329\pi$
$644$	−5.24037	−	24.2336i	−0.206499	−	0.954936i
$645$		0			0
$646$	8.76389	+	3.70590i	0.344811	+	0.145807i
$647$	−8.30976	+	14.3929i	−0.326690	+	0.565844i	−0.981853	−	0.189644i	$-0.939267\pi$
$647$	−8.30976	+	14.3929i	−0.326690	+	0.565844i	0.655163	+	0.755488i	$0.272600\pi$
$648$		0			0
$649$	−33.7031	+	19.4585i	−1.32296	+	0.763812i
$650$	−12.8547	+	9.71431i	−0.504201	+	0.381026i
$651$		0			0
$652$	17.3695	+	4.92918i	0.680242	+	0.193042i
$653$	10.0211	+	17.3571i	0.392158	+	0.679237i	0.992734	−	0.120331i	$-0.0383954\pi$
$653$	10.0211	+	17.3571i	0.392158	+	0.679237i	−0.600576	+	0.799568i	$0.705062\pi$
$654$		0			0
$655$	−7.08387	+	12.2696i	−0.276790	+	0.479414i
$656$	0.258259	−	8.77304i	0.0100833	−	0.342530i
$657$		0			0
$658$	32.7219	−	23.0174i	1.27563	−	0.897311i
$659$	−5.53973			−0.215797			−0.107899	−	0.994162i	$-0.534412\pi$
$659$	−5.53973			−0.215797			−0.107899	+	0.994162i	$0.534412\pi$
$660$		0			0
$661$	−14.8650	+	25.7470i	−0.578183	+	1.00144i	0.417505	+	0.908675i	$0.362905\pi$
$661$	−14.8650	+	25.7470i	−0.578183	+	1.00144i	−0.995688	+	0.0927674i	$0.970429\pi$
$662$	3.67529	−	0.456378i	0.142844	−	0.0177376i
$663$		0			0
$664$	15.6377	−	6.07656i	0.606859	−	0.235816i
$665$	−0.450196	+	13.1895i	−0.0174579	+	0.511468i
$666$		0			0
$667$	16.5908	−	9.57873i	0.642400	−	0.370890i
$668$	−22.7061	−	23.3844i	−0.878527	−	0.904769i
$669$		0			0
$670$	−8.74002	−	3.69580i	−0.337656	−	0.142781i
$671$	−28.8475			−1.11364
$672$		0			0
$673$	28.0307			1.08050			0.540252	−	0.841503i	$-0.318329\pi$
$673$	28.0307			1.08050			0.540252	+	0.841503i	$0.318329\pi$
$674$	−45.5170	−	19.2473i	−1.75325	−	0.741378i
$675$		0			0
$676$	−4.57367	−	4.71029i	−0.175910	−	0.181165i
$677$	−10.2739	+	5.93164i	−0.394858	+	0.227971i	−0.684263	−	0.729235i	$-0.739876\pi$
$677$	−10.2739	+	5.93164i	−0.394858	+	0.227971i	0.289405	+	0.957207i	$0.406543\pi$
$678$		0			0
$679$	26.1585	−	13.9352i	1.00387	−	0.534782i
$680$	4.78342	−	1.85876i	0.183436	−	0.0712803i
$681$		0			0
$682$	11.0321	−	1.36991i	0.422442	−	0.0524567i
$683$	7.62606	−	13.2087i	0.291803	−	0.505418i	−0.682433	−	0.730948i	$-0.739078\pi$
$683$	7.62606	−	13.2087i	0.291803	−	0.505418i	0.974236	+	0.225530i	$0.0724114\pi$
$684$		0			0
$685$	−11.4070			−0.435841
$686$	22.9549	+	12.6124i	0.876422	+	0.481544i
$687$		0			0
$688$	26.1078	+	0.768557i	0.995350	+	0.0293010i
$689$	17.5159	−	30.3384i	0.667303	−	1.15580i
$690$		0			0
$691$	−3.24122	−	5.61395i	−0.123302	−	0.213565i	0.797766	−	0.602967i	$-0.206015\pi$
$691$	−3.24122	−	5.61395i	−0.123302	−	0.213565i	−0.921068	+	0.389402i	$0.872682\pi$
$692$	−0.0533318	−	0.0151347i	−0.00202737	−	0.000575335i
$693$		0			0
$694$	37.7306	−	28.5131i	1.43223	−	1.08234i
$695$	−17.7223	+	10.2320i	−0.672244	+	0.388120i
$696$		0			0
$697$	−1.71632	+	2.97276i	−0.0650104	+	0.112601i
$698$	9.54259	+	4.03518i	0.361192	+	0.152734i
$699$		0			0
$700$	−12.9915	−	14.3266i	−0.491031	−	0.541494i
$701$	4.86157			0.183619			0.0918096	−	0.995777i	$-0.470735\pi$
$701$	4.86157			0.183619			0.0918096	+	0.995777i	$0.470735\pi$
$702$		0			0
$703$	21.3475	+	12.3250i	0.805138	+	0.464847i
$704$	−4.89096	−	22.1152i	−0.184335	−	0.833496i
$705$		0			0
$706$	−31.4330	+	23.7540i	−1.18300	+	0.893995i
$707$	−0.0493217	+	1.44499i	−0.00185493	+	0.0543444i
$708$		0			0
$709$	−21.3747	+	12.3407i	−0.802744	+	0.463464i	−0.844430	−	0.535667i	$-0.820060\pi$
$709$	−21.3747	+	12.3407i	−0.802744	+	0.463464i	0.0416860	+	0.999131i	$0.486727\pi$
$710$	−0.955577	−	7.69542i	−0.0358622	−	0.288804i
$711$		0			0
$712$	4.74266	−	5.90614i	0.177739	−	0.221342i
$713$	−13.0095			−0.487209
$714$		0			0
$715$			10.2358i			0.382797i
$716$	9.29203	−	2.34381i	0.347260	−	0.0875923i
$717$		0			0
$718$	−25.3131	+	3.14324i	−0.944675	+	0.117305i
$719$	10.2912	+	17.8248i	0.383796	+	0.664754i	0.991601	−	0.129332i	$-0.0412833\pi$
$719$	10.2912	+	17.8248i	0.383796	+	0.664754i	−0.607806	+	0.794086i	$0.707950\pi$
$720$		0			0
$721$	33.7986	+	21.0827i	1.25872	+	0.785162i
$722$	−0.567308	+	0.428717i	−0.0211130	+	0.0159552i
$723$		0			0
$724$	9.79832	+	10.0910i	0.364152	+	0.375029i
$725$	7.47169	−	12.9414i	0.277492	−	0.480630i
$726$		0			0
$727$			27.0889i			1.00467i	0.864673	+	0.502336i	$0.167526\pi$
$727$			27.0889i			1.00467i	−0.864673	+	0.502336i	$0.832474\pi$
$728$	−15.2178	+	17.6801i	−0.564009	+	0.655268i
$729$		0			0
$730$	−24.5293	−	10.3725i	−0.907871	−	0.383902i
$731$	−8.84667	−	5.10763i	−0.327206	−	0.188912i
$732$		0			0
$733$	8.48261	+	14.6923i	0.313312	+	0.542673i	0.979077	−	0.203488i	$-0.0652279\pi$
$733$	8.48261	+	14.6923i	0.313312	+	0.542673i	−0.665765	+	0.746162i	$0.731895\pi$
$734$	−4.10243	−	5.42863i	−0.151424	−	0.200374i
$735$		0			0
$736$	2.49084	+	26.3883i	0.0918135	+	0.972685i
$737$	14.1853	−	8.18990i	0.522523	−	0.301679i
$738$		0			0
$739$	−38.1107	−	22.0032i	−1.40193	−	0.809402i	−0.407336	−	0.913278i	$-0.633542\pi$
$739$	−38.1107	−	22.0032i	−1.40193	−	0.809402i	−0.994590	+	0.103876i	$0.966875\pi$
$740$	12.8908	−	3.25156i	0.473875	−	0.119530i
$741$		0			0
$742$	38.1474	+	17.6884i	1.40044	+	0.649362i
$743$		−	30.5441i		−	1.12056i	−0.828305	−	0.560278i	$-0.810694\pi$
$743$		−	30.5441i		−	1.12056i	0.828305	−	0.560278i	$-0.189306\pi$
$744$		0			0
$745$	9.80324	+	5.65990i	0.359163	+	0.207363i
$746$	0.955434	−	0.118641i	0.0349809	−	0.00434375i
$747$		0			0
$748$	−2.41835	+	8.52180i	−0.0884236	+	0.311588i
$749$	3.98472	−	6.38806i	0.145598	−	0.233415i
$750$		0			0
$751$	8.35120	+	14.4647i	0.304739	+	0.527824i	0.977203	−	0.212306i	$-0.0680973\pi$
$751$	8.35120	+	14.4647i	0.304739	+	0.527824i	−0.672464	+	0.740130i	$0.734764\pi$
$752$	−37.6520	+	20.2852i	−1.37303	+	0.739727i
$753$		0			0
$754$	−16.6012	−	7.02000i	−0.604582	−	0.255653i
$755$			4.96353i			0.180641i
$756$		0			0
$757$		−	1.36258i		−	0.0495237i	−0.999693	−	0.0247618i	$-0.992117\pi$
$757$		−	1.36258i		−	0.0495237i	0.999693	−	0.0247618i	$-0.00788275\pi$
$758$	13.0583	−	30.8809i	0.474299	−	1.12165i
$759$		0			0
$760$	2.14978	−	13.9437i	0.0779807	−	0.505789i
$761$	7.30823	+	12.6582i	0.264923	+	0.458860i	0.967543	−	0.252705i	$-0.0813201\pi$
$761$	7.30823	+	12.6582i	0.264923	+	0.458860i	−0.702620	+	0.711565i	$0.747987\pi$
$762$		0			0
$763$	0.0839995	−	2.46096i	0.00304099	−	0.0890926i
$764$	−26.6195	−	7.55420i	−0.963061	−	0.273301i
$765$		0			0
$766$	5.83561	+	46.9951i	0.210849	+	1.69800i
$767$	−37.1084	−	21.4246i	−1.33991	−	0.773596i
$768$		0			0
$769$			1.23072i			0.0443809i	0.999754	+	0.0221904i	$0.00706402\pi$
$769$			1.23072i			0.0443809i	−0.999754	+	0.0221904i	$0.992936\pi$
$770$	−12.2370	+	1.09719i	−0.440990	+	0.0395400i
$771$		0			0
$772$	−8.16302	+	2.05903i	−0.293794	+	0.0741061i
$773$	−17.4450	−	10.0719i	−0.627452	−	0.362259i	0.152313	−	0.988332i	$-0.451328\pi$
$773$	−17.4450	−	10.0719i	−0.627452	−	0.362259i	−0.779765	+	0.626073i	$0.784661\pi$
$774$		0			0
$775$	−8.78824	+	5.07390i	−0.315683	+	0.182260i
$776$	−29.5338	+	11.4764i	−1.06020	+	0.411978i
$777$		0			0
$778$	26.5759	−	20.0835i	0.952793	−	0.720029i
$779$	4.71847	+	8.17263i	0.169057	+	0.292815i
$780$		0			0
$781$	11.5921	+	6.69268i	0.414796	+	0.239483i
$782$	4.03741	−	9.54786i	0.144377	−	0.341431i
$783$		0			0
$784$	−22.7680	−	16.2979i	−0.813141	−	0.582066i
$785$		−	28.0793i		−	1.00219i
$786$		0			0
$787$	−0.411250	+	0.712307i	−0.0146595	+	0.0253910i	−0.873262	−	0.487251i	$-0.838000\pi$
$787$	−0.411250	+	0.712307i	−0.0146595	+	0.0253910i	0.858603	+	0.512642i	$0.171333\pi$
$788$	33.9296	+	34.9431i	1.20869	+	1.24480i
$789$		0			0
$790$	5.72217	+	7.57198i	0.203586	+	0.269399i
$791$	32.5108	−	17.3191i	1.15595	−	0.615797i
$792$		0			0
$793$	−15.8811	−	27.5069i	−0.563954	−	0.976797i
$794$	4.44353	+	35.7845i	0.157695	+	1.26994i
$795$		0			0
$796$	−0.926297	−	3.67230i	−0.0328317	−	0.130161i
$797$		−	16.0328i		−	0.567911i	−0.958838	−	0.283955i	$-0.908353\pi$
$797$		−	16.0328i		−	0.567911i	0.958838	−	0.283955i	$-0.0916468\pi$
$798$		0			0
$799$	16.7270			0.591758
$800$	11.9745	+	16.8545i	0.423361	+	0.595897i
$801$		0			0
$802$	−16.6622	+	2.06903i	−0.588363	+	0.0730599i
$803$	39.8119	−	22.9854i	1.40493	−	0.811137i
$804$		0			0
$805$	14.3694	+	0.490469i	0.506454	+	0.0172868i
$806$	7.37966	+	9.76529i	0.259937	+	0.343968i
$807$		0			0
$808$	0.235521	−	1.52761i	0.00828560	−	0.0537411i
$809$	−19.0060	−	10.9731i	−0.668215	−	0.385794i	0.127185	−	0.991879i	$-0.459406\pi$
$809$	−19.0060	−	10.9731i	−0.668215	−	0.385794i	−0.795400	+	0.606085i	$0.792739\pi$
$810$		0			0
$811$	40.5865			1.42518			0.712592	−	0.701579i	$-0.247521\pi$
$811$	40.5865			1.42518			0.712592	+	0.701579i	$0.247521\pi$
$812$	6.61296	−	20.5994i	0.232069	−	0.722898i
$813$		0			0
$814$	−8.93765	+	21.1362i	−0.313264	+	0.740823i
$815$	−5.23511	+	9.06748i	−0.183378	+	0.317620i
$816$		0			0
$817$	−24.3210	+	14.0417i	−0.850885	+	0.491258i
$818$	4.39822	+	5.82004i	0.153780	+	0.203493i
$819$		0			0
$820$	4.89631	+	1.38949i	0.170987	+	0.0485233i
$821$	−21.9753	−	38.0623i	−0.766942	−	1.32838i	−0.939214	−	0.343333i	$-0.888444\pi$
$821$	−21.9753	−	38.0623i	−0.766942	−	1.32838i	0.172272	−	0.985049i	$-0.444889\pi$
$822$		0			0
$823$	−0.112859	+	0.195478i	−0.00393403	+	0.00681394i	−0.867986	−	0.496589i	$-0.834586\pi$
$823$	−0.112859	+	0.195478i	−0.00393403	+	0.00681394i	0.864052	+	0.503403i	$0.167919\pi$
$824$	−33.2049	−	26.6637i	−1.15675	−	0.928873i
$825$		0			0
$826$	21.6356	−	46.6600i	0.752797	−	1.62351i
$827$	−7.35761			−0.255849			−0.127925	−	0.991784i	$-0.540832\pi$
$827$	−7.35761			−0.255849			−0.127925	+	0.991784i	$0.540832\pi$
$828$		0			0
$829$	−8.03760	+	13.9215i	−0.279157	+	0.483515i	−0.971176	−	0.238365i	$-0.923388\pi$
$829$	−8.03760	+	13.9215i	−0.279157	+	0.483515i	0.692018	+	0.721880i	$0.256722\pi$
$830$	1.19886	+	9.65465i	0.0416132	+	0.335118i
$831$		0			0
$832$	18.3948	−	16.8385i	0.637727	−	0.583770i
$833$	4.81603	+	9.83502i	0.166866	+	0.340763i
$834$		0			0
$835$	16.3691	−	9.45069i	0.566475	−	0.327055i
$836$	16.9649	+	17.4717i	0.586744	+	0.604271i
$837$		0			0
$838$	4.75636	−	11.2481i	0.164306	−	0.388559i
$839$	−50.6405			−1.74831			−0.874153	−	0.485651i	$-0.838583\pi$
$839$	−50.6405			−1.74831			−0.874153	+	0.485651i	$0.838583\pi$
$840$		0			0
$841$	−12.2833			−0.423562
$842$	−20.5062	+	48.4942i	−0.706691	+	1.67122i
$843$		0			0
$844$	−35.9575	+	34.9145i	−1.23771	+	1.20181i
$845$	3.29720	−	1.90364i	0.113427	−	0.0654872i
$846$		0			0
$847$	−4.17889	+	6.69935i	−0.143588	+	0.230192i
$848$	−38.2515	−	23.6118i	−1.31356	−	0.810834i
$849$		0			0
$850$	−0.996438	−	8.02448i	−0.0341775	−	0.275237i
$851$	13.4275	−	23.2572i	0.460290	−	0.797246i
$852$		0			0
$853$	−8.65855			−0.296463			−0.148232	−	0.988953i	$-0.547358\pi$
$853$	−8.65855			−0.296463			−0.148232	+	0.988953i	$0.547358\pi$
$854$	31.1824	−	21.9345i	1.06704	−	0.750583i
$855$		0			0
$856$	−5.03953	+	6.27585i	−0.172248	+	0.214504i
$857$	−17.1294	+	29.6691i	−0.585130	+	1.01348i	0.409729	+	0.912207i	$0.365623\pi$
$857$	−17.1294	+	29.6691i	−0.585130	+	1.01348i	−0.994859	+	0.101268i	$0.967710\pi$
$858$		0			0
$859$	−6.28537	−	10.8866i	−0.214454	−	0.371445i	0.738649	−	0.674090i	$-0.235464\pi$
$859$	−6.28537	−	10.8866i	−0.214454	−	0.371445i	−0.953104	+	0.302644i	$0.902131\pi$
$860$	−4.13501	+	14.5710i	−0.141003	+	0.496867i
$861$		0			0
$862$	−7.13178	−	9.43728i	−0.242910	−	0.321435i
$863$	36.2622	−	20.9360i	1.23438	−	0.712669i	0.266440	−	0.963852i	$-0.414153\pi$
$863$	36.2622	−	20.9360i	1.23438	−	0.712669i	0.967940	+	0.251182i	$0.0808193\pi$
$864$		0			0
$865$	0.0160741	−	0.0278411i	0.000546534	−	0.000946625i
$866$	−4.20627	+	9.94720i	−0.142935	+	0.338019i
$867$		0			0
$868$	−10.8835	+	9.86921i	−0.369409	+	0.334983i
$869$	−16.3827			−0.555744
$870$		0			0
$871$	15.6186	+	9.01741i	0.529216	+	0.305543i
$872$	−0.401115	+	2.60166i	−0.0135835	+	0.0881035i
$873$		0			0
$874$	−17.1823	−	22.7368i	−0.581200	−	0.769085i
$875$	23.4392	−	12.4865i	0.792390	−	0.422122i
$876$		0			0
$877$	−4.04807	+	2.33716i	−0.136694	+	0.0789201i	−0.566787	−	0.823864i	$-0.691814\pi$
$877$	−4.04807	+	2.33716i	−0.136694	+	0.0789201i	0.430094	+	0.902784i	$0.358481\pi$
$878$	13.6579	−	1.69596i	0.460931	−	0.0572359i
$879$		0			0
$880$	13.1287	+	0.386480i	0.442568	+	0.0130282i
$881$	−13.7595			−0.463569			−0.231785	−	0.972767i	$-0.574456\pi$
$881$	−13.7595			−0.463569			−0.231785	+	0.972767i	$0.574456\pi$
$882$		0			0
$883$			31.7680i			1.06908i	0.845144	+	0.534539i	$0.179515\pi$
$883$			31.7680i			1.06908i	−0.845144	+	0.534539i	$0.820485\pi$
$884$	−9.45712	+	2.38545i	−0.318077	+	0.0802315i
$885$		0			0
$886$	−3.81139	−	30.6938i	−0.128046	−	1.03118i
$887$	9.28571	+	16.0833i	0.311784	+	0.540025i	0.978749	−	0.205064i	$-0.0657403\pi$
$887$	9.28571	+	16.0833i	0.311784	+	0.540025i	−0.666965	+	0.745089i	$0.732407\pi$
$888$		0			0
$889$	−2.67615	−	5.02357i	−0.0897553	−	0.168485i
$890$	2.64828	+	3.50439i	0.0887704	+	0.117467i
$891$		0			0
$892$	−13.5241	+	13.1318i	−0.452820	+	0.439687i
$893$	22.9927	−	39.8245i	0.769420	−	1.33268i
$894$		0			0
$895$			5.55718i			0.185756i
$896$	22.1024	+	20.1863i	0.738388	+	0.674376i
$897$		0			0
$898$	9.17373	−	21.6945i	0.306131	−	0.723955i
$899$	−9.83114	−	5.67601i	−0.327887	−	0.189306i
$900$		0			0
$901$	8.79045	+	15.2255i	0.292852	+	0.507235i
$902$	−7.00911	+	5.29680i	−0.233378	+	0.176364i
$903$		0			0
$904$	−36.7056	+	14.2632i	−1.22081	+	0.474389i
$905$	−7.06371	+	4.07823i	−0.234806	+	0.135565i
$906$		0			0
$907$	18.8054	+	10.8573i	0.624423	+	0.360511i	0.778589	−	0.627534i	$-0.215936\pi$
$907$	18.8054	+	10.8573i	0.624423	+	0.360511i	−0.154166	+	0.988045i	$0.549269\pi$
$908$	9.09191	+	36.0449i	0.301726	+	1.19619i
$909$		0			0
$910$	−7.78290	−	11.0643i	−0.258001	−	0.366777i
$911$			34.1200i			1.13044i	0.824939	+	0.565222i	$0.191210\pi$
$911$			34.1200i			1.13044i	−0.824939	+	0.565222i	$0.808790\pi$
$912$		0			0
$913$	−14.5433	−	8.39660i	−0.481314	−	0.277887i
$914$	3.59503	+	28.9514i	0.118913	+	0.957626i
$915$		0			0
$916$	−14.9624	+	52.7245i	−0.494371	+	1.74207i
$917$	27.4223	+	17.1054i	0.905564	+	0.564869i
$918$		0			0
$919$	−5.92493	−	10.2623i	−0.195445	−	0.338521i	0.751601	−	0.659618i	$-0.229282\pi$
$919$	−5.92493	−	10.2623i	−0.195445	−	0.338521i	−0.947046	+	0.321097i	$0.895949\pi$
$920$	−15.1910	−	2.34209i	−0.500832	−	0.0772163i
$921$		0			0
$922$	−17.3661	+	41.0682i	−0.571922	+	1.35251i
$923$			14.7378i			0.485101i
$924$		0			0
$925$		−	20.9478i		−	0.688759i
$926$	52.6024	+	22.2434i	1.72862	+	0.730965i
$927$		0			0
$928$	−9.63085	+	21.0281i	−0.316148	+	0.690282i
$929$	−29.2652	−	50.6888i	−0.960161	−	1.66305i	−0.722090	−	0.691799i	$-0.756818\pi$
$929$	−29.2652	−	50.6888i	−0.960161	−	1.66305i	−0.238071	−	0.971248i	$-0.576515\pi$
$930$		0			0
$931$	30.0358	+	2.05281i	0.984383	+	0.0672781i
$932$	−46.7276	−	13.2605i	−1.53061	−	0.434363i
$933$		0			0
$934$	16.4623	−	2.04420i	0.538661	−	0.0668881i
$935$	−4.44868	−	2.56844i	−0.145487	−	0.0839971i
$936$		0			0
$937$		−	58.2795i		−	1.90391i	−0.306242	−	0.951954i	$-0.599072\pi$
$937$		−	58.2795i		−	1.90391i	0.306242	−	0.951954i	$-0.400928\pi$
$938$	−9.10621	+	19.6388i	−0.297328	+	0.641229i
$939$		0			0
$940$	−6.06589	−	24.0482i	−0.197847	−	0.784365i
$941$	−47.2322	−	27.2695i	−1.53973	−	0.888961i	−0.998854	−	0.0478564i	$-0.984761\pi$
$941$	−47.2322	−	27.2695i	−1.53973	−	0.888961i	−0.540872	−	0.841105i	$-0.681906\pi$
$942$		0			0
$943$	8.90372	−	5.14056i	0.289945	−	0.167400i
$944$	−28.8808	+	46.7872i	−0.939990	+	1.52280i
$945$		0			0
$946$	−15.7628	−	20.8585i	−0.512493	−	0.678167i
$947$	30.3559	+	52.5780i	0.986435	+	1.70856i	0.635379	+	0.772200i	$0.280844\pi$
$947$	30.3559	+	52.5780i	0.986435	+	1.70856i	0.351056	+	0.936355i	$0.385823\pi$
$948$		0			0
$949$	43.8344	+	25.3078i	1.42293	+	0.821527i
$950$	−20.4748	−	8.65796i	−0.664290	−	0.280901i
$951$		0			0
$952$	−3.86556	−	11.0504i	−0.125283	−	0.358145i
$953$			15.3879i			0.498463i	0.968444	+	0.249232i	$0.0801781\pi$
$953$			15.3879i			0.498463i	−0.968444	+	0.249232i	$0.919822\pi$
$954$		0			0
$955$	8.02305	−	13.8963i	0.259620	−	0.449675i
$956$	−3.37787	+	3.27990i	−0.109248	+	0.106079i
$957$		0			0
$958$	0.675156	−	0.510217i	0.0218133	−	0.0164844i
$959$	−0.887692	+	26.0069i	−0.0286651	+	0.839808i
$960$		0			0
$961$	−11.6455	−	20.1706i	−0.375662	−	0.650666i
$962$	−25.0743	+	3.11360i	−0.808428	+	0.100386i
$963$		0			0
$964$	6.37713	+	25.2821i	0.205394	+	0.814282i
$965$		−	4.88197i		−	0.157156i
$966$		0			0
$967$	34.1030			1.09668			0.548339	−	0.836256i	$-0.315260\pi$
$967$	34.1030			1.09668			0.548339	+	0.836256i	$0.315260\pi$
$968$	5.28511	−	6.58167i	0.169870	−	0.211543i
$969$		0			0
$970$	−2.26421	−	18.2341i	−0.0726994	−	0.585461i
$971$	33.1725	−	19.1521i	1.06456	−	0.614621i	0.137866	−	0.990451i	$-0.455976\pi$
$971$	33.1725	−	19.1521i	1.06456	−	0.614621i	0.926689	+	0.375830i	$0.122642\pi$
$972$		0			0
$973$	21.9487	+	41.2013i	0.703644	+	1.32085i
$974$	23.4592	−	17.7282i	0.751682	−	0.568048i
$975$		0			0
$976$	−35.8806	+	19.3309i	−1.14851	+	0.618767i
$977$	19.4340	+	11.2202i	0.621749	+	0.358967i	0.777550	−	0.628822i	$-0.216462\pi$
$977$	19.4340	+	11.2202i	0.621749	+	0.358967i	−0.155801	+	0.987788i	$0.549796\pi$
$978$		0			0
$979$	−7.58205			−0.242323
$980$	12.3932	−	10.4905i	0.395886	−	0.335108i
$981$		0			0
$982$	29.2336	+	12.3617i	0.932883	+	0.394479i
$983$	−14.0698	+	24.3695i	−0.448756	+	0.777268i	−0.998305	−	0.0581932i	$-0.981466\pi$
$983$	−14.0698	+	24.3695i	−0.448756	+	0.777268i	0.549550	+	0.835461i	$0.314799\pi$
$984$		0			0
$985$	−24.4602	+	14.1221i	−0.779367	+	0.449968i
$986$	7.21674	−	5.45372i	0.229828	−	0.173682i
$987$		0			0
$988$	−7.32021	+	25.7950i	−0.232887	+	0.820649i
$989$	15.2979	+	26.4967i	0.486443	+	0.842545i
$990$		0			0
$991$	17.8187	−	30.8629i	0.566029	−	0.980391i	−0.430924	−	0.902388i	$-0.641812\pi$
$991$	17.8187	−	30.8629i	0.566029	−	0.980391i	0.996953	−	0.0780029i	$-0.0248543\pi$
$992$	12.8038	−	9.09662i	0.406522	−	0.288818i
$993$		0			0
$994$	−17.6192	+	1.57977i	−0.558846	+	0.0501072i
$995$	2.19625			0.0696259
$996$		0			0
$997$	−12.1376	+	21.0230i	−0.384402	+	0.665804i	−0.991686	−	0.128681i	$-0.958926\pi$
$997$	−12.1376	+	21.0230i	−0.384402	+	0.665804i	0.607284	+	0.794485i	$0.292259\pi$
$998$	16.5724	−	2.05788i	0.524591	−	0.0651410i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.269.4	✓	56
3.2	odd	2	inner	504.2.ch.b.269.25	yes	56
4.3	odd	2		2016.2.cp.b.17.9		56
7.5	odd	6	inner	504.2.ch.b.341.16	yes	56
8.3	odd	2		2016.2.cp.b.17.20		56
8.5	even	2	inner	504.2.ch.b.269.13	yes	56
12.11	even	2		2016.2.cp.b.17.19		56
21.5	even	6	inner	504.2.ch.b.341.13	yes	56
24.5	odd	2	inner	504.2.ch.b.269.16	yes	56
24.11	even	2		2016.2.cp.b.17.10		56
28.19	even	6		2016.2.cp.b.593.10		56
56.5	odd	6	inner	504.2.ch.b.341.25	yes	56
56.19	even	6		2016.2.cp.b.593.19		56
84.47	odd	6		2016.2.cp.b.593.20		56
168.5	even	6	inner	504.2.ch.b.341.4	yes	56
168.131	odd	6		2016.2.cp.b.593.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.4	✓	56	1.1	even	1	trivial
504.2.ch.b.269.13	yes	56	8.5	even	2	inner
504.2.ch.b.269.16	yes	56	24.5	odd	2	inner
504.2.ch.b.269.25	yes	56	3.2	odd	2	inner
504.2.ch.b.341.4	yes	56	168.5	even	6	inner
504.2.ch.b.341.13	yes	56	21.5	even	6	inner
504.2.ch.b.341.16	yes	56	7.5	odd	6	inner
504.2.ch.b.341.25	yes	56	56.5	odd	6	inner
2016.2.cp.b.17.9		56	4.3	odd	2
2016.2.cp.b.17.10		56	24.11	even	2
2016.2.cp.b.17.19		56	12.11	even	2
2016.2.cp.b.17.20		56	8.3	odd	2
2016.2.cp.b.593.9		56	168.131	odd	6
2016.2.cp.b.593.10		56	28.19	even	6
2016.2.cp.b.593.19		56	56.19	even	6
2016.2.cp.b.593.20		56	84.47	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.30255 - 0.550794i) q^{2} +(1.39325 + 1.43487i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 - 2.63638i) q^{8} +O(q^{10})\)	\(q+(-1.30255 - 0.550794i) q^{2} +(1.39325 + 1.43487i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 - 2.63638i) q^{8} +(1.62769 - 0.202118i) q^{10} +(-1.41560 + 2.45188i) q^{11} -3.11725 q^{13} +(-0.334143 - 3.72671i) q^{14} +(-0.117700 + 3.99827i) q^{16} +(0.782206 - 1.35482i) q^{17} +(-2.15042 - 3.72463i) q^{19} +(-2.23147 - 0.633255i) q^{20} +(3.19436 - 2.41399i) q^{22} +(-4.05782 + 2.34278i) q^{23} +(-1.82744 + 3.16522i) q^{25} +(4.06037 + 1.71697i) q^{26} +(-1.61741 + 5.03825i) q^{28} -4.08861 q^{29} +(2.40452 + 1.38825i) q^{31} +(2.35553 - 5.14310i) q^{32} +(-1.76509 + 1.33388i) q^{34} +(-2.60353 - 1.62402i) q^{35} +(-4.96358 + 2.86572i) q^{37} +(0.749512 + 6.03594i) q^{38} +(2.55780 + 2.05392i) q^{40} -2.19421 q^{41} -6.52977i q^{43} +(-5.49042 + 1.38490i) q^{44} +(6.57589 - 0.816559i) q^{46} +(5.34609 + 9.25971i) q^{47} +(-3.90521 + 5.80942i) q^{49} +(4.12371 - 3.11630i) q^{50} +(-4.34312 - 4.47285i) q^{52} +(-5.61902 + 9.73242i) q^{53} -3.28359i q^{55} +(4.88179 - 5.67169i) q^{56} +(5.32560 + 2.25198i) q^{58} +(11.9042 + 6.87289i) q^{59} +(5.09458 + 8.82407i) q^{61} +(-2.36736 - 3.13266i) q^{62} +(-5.90098 + 5.40171i) q^{64} +(3.13100 - 1.80768i) q^{65} +(-5.01037 - 2.89274i) q^{67} +(3.03380 - 0.765242i) q^{68} +(2.49672 + 3.54937i) q^{70} -4.72781i q^{71} +(-14.0619 - 8.11863i) q^{73} +(8.04371 - 0.998826i) q^{74} +(2.34829 - 8.27492i) q^{76} +(-7.48627 - 0.255528i) q^{77} +(2.89324 + 5.01124i) q^{79} +(-2.20036 - 4.08415i) q^{80} +(2.85806 + 1.20856i) q^{82} +5.93150i q^{83} +1.81439i q^{85} +(-3.59656 + 8.50533i) q^{86} +(7.91431 + 1.22020i) q^{88} +(1.33902 + 2.31925i) q^{89} +(-3.87769 - 7.27904i) q^{91} +(-9.01515 - 2.55836i) q^{92} +(-1.86334 - 15.0058i) q^{94} +(4.31980 + 2.49404i) q^{95} -11.2024i q^{97} +(8.28651 - 5.41606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

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