LMFDB - Embedded newform 504.2.ch.b.269.16

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			269.16
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.174271 - 1.40343i) q^{2} +(-1.93926 - 0.489157i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 + 2.63638i) q^{8} +O(q^{10})$	\(q+(0.174271 - 1.40343i) q^{2} +(-1.93926 - 0.489157i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 + 2.63638i) q^{8} +(0.638806 + 1.51068i) q^{10} +(-1.41560 + 2.45188i) q^{11} +3.11725 q^{13} +(3.49392 - 1.33886i) q^{14} +(3.52145 + 1.89720i) q^{16} +(-0.782206 + 1.35482i) q^{17} +(2.15042 + 3.72463i) q^{19} +(2.23147 - 0.633255i) q^{20} +(3.19436 + 2.41399i) q^{22} +(4.05782 - 2.34278i) q^{23} +(-1.82744 + 3.16522i) q^{25} +(0.543248 - 4.37486i) q^{26} +(-1.27011 - 5.13681i) q^{28} -4.08861 q^{29} +(2.40452 + 1.38825i) q^{31} +(3.27629 - 4.61150i) q^{32} +(1.76509 + 1.33388i) q^{34} +(-2.60353 - 1.62402i) q^{35} +(4.96358 - 2.86572i) q^{37} +(5.60204 - 2.36888i) q^{38} +(-0.499851 - 3.24208i) q^{40} +2.19421 q^{41} +6.52977i q^{43} +(3.94456 - 4.06239i) q^{44} +(-2.58078 - 6.10317i) q^{46} +(-5.34609 - 9.25971i) q^{47} +(-3.90521 + 5.80942i) q^{49} +(4.12371 + 3.11630i) q^{50} +(-6.04516 - 1.52483i) q^{52} +(-5.61902 + 9.73242i) q^{53} -3.28359i q^{55} +(-7.43052 + 0.887315i) q^{56} +(-0.712527 + 5.73810i) q^{58} +(11.9042 + 6.87289i) q^{59} +(-5.09458 - 8.82407i) q^{61} +(2.36736 - 3.13266i) q^{62} +(-5.90098 - 5.40171i) q^{64} +(-3.13100 + 1.80768i) q^{65} +(5.01037 + 2.89274i) q^{67} +(2.17962 - 2.24473i) q^{68} +(-2.73293 + 3.37087i) q^{70} +4.72781i q^{71} +(-14.0619 - 8.11863i) q^{73} +(-3.15685 - 7.46547i) q^{74} +(-2.34829 - 8.27492i) q^{76} +(-7.48627 - 0.255528i) q^{77} +(2.89324 + 5.01124i) q^{79} +(-4.63716 + 0.136508i) q^{80} +(0.382388 - 3.07943i) q^{82} +5.93150i q^{83} -1.81439i q^{85} +(9.16411 + 1.13795i) q^{86} +(-5.01388 - 6.24390i) q^{88} +(-1.33902 - 2.31925i) q^{89} +(3.87769 + 7.27904i) q^{91} +(-9.01515 + 2.55836i) q^{92} +(-13.9271 + 5.88919i) q^{94} +(-4.31980 - 2.49404i) q^{95} -11.2024i q^{97} +(7.47257 + 6.49312i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.174271	−	1.40343i	0.123228	−	0.992378i
$2$	0.174271	−	1.40343i	0.123228	−	0.992378i
$3$		0			0
$3$		0			0
$4$	−1.93926	−	0.489157i	−0.969630	−	0.244578i
$5$	−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
$10$	0.638806	+	1.51068i	0.202008	+	0.477719i
$11$	−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	$-0.357707\pi$
$13$	3.11725			0.864571			0.432285	+	0.901737i	$0.357707\pi$
$14$	3.49392	−	1.33886i	0.933789	−	0.357824i
$15$		0			0
$16$	3.52145	+	1.89720i	0.880363	+	0.474301i
$17$	−0.782206	+	1.35482i	−0.189713	+	0.328592i	−0.945154	−	0.326624i	$-0.894089\pi$
$17$	−0.782206	+	1.35482i	−0.189713	+	0.328592i	0.755442	+	0.655216i	$0.227422\pi$
$18$		0			0
$19$	2.15042	+	3.72463i	0.493340	+	0.854489i	0.999971	−	0.00767364i	$-0.00244262\pi$
$19$	2.15042	+	3.72463i	0.493340	+	0.854489i	−0.506631	+	0.862163i	$0.669109\pi$
$20$	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	−0.0132237	−	0.999913i	$-0.504209\pi$
$23$	4.05782	−	2.34278i	0.846114	−	0.488504i	0.859338	+	0.511408i	$0.170876\pi$
$24$		0			0
$25$	−1.82744	+	3.16522i	−0.365488	+	0.633044i
$26$	0.543248	−	4.37486i	0.106540	−	0.857981i
$27$		0			0
$28$	−1.27011	−	5.13681i	−0.240028	−	0.970766i
$29$	−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	$0.586454\pi$
$32$	3.27629	−	4.61150i	0.579171	−	0.815206i
$33$		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	−0.0330302	−	0.999454i	$-0.510516\pi$
$37$	4.96358	−	2.86572i	0.816008	−	0.471122i	0.849038	+	0.528332i	$0.177182\pi$
$38$	5.60204	−	2.36888i	0.908770	−	0.384282i
$39$		0			0
$40$	−0.499851	−	3.24208i	−0.0790334	−	0.512618i
$41$	2.19421			0.342678			0.171339	−	0.985212i	$-0.445191\pi$
$41$	2.19421			0.342678			0.171339	+	0.985212i	$0.445191\pi$
$42$		0			0
$43$			6.52977i			0.995781i	0.867240	+	0.497891i	$0.165892\pi$
$43$			6.52977i			0.995781i	−0.867240	+	0.497891i	$0.834108\pi$
$44$	3.94456	−	4.06239i	0.594665	−	0.612429i
$45$		0			0
$46$	−2.58078	−	6.10317i	−0.380516	−	0.899863i
$47$	−5.34609	−	9.25971i	−0.779808	−	1.35067i	−0.932052	−	0.362324i	$-0.881983\pi$
$47$	−5.34609	−	9.25971i	−0.779808	−	1.35067i	0.152244	−	0.988343i	$-0.451350\pi$
$48$		0			0
$49$	−3.90521	+	5.80942i	−0.557887	+	0.829917i
$50$	4.12371	+	3.11630i	0.583181	+	0.440712i
$51$		0			0
$52$	−6.04516	−	1.52483i	−0.838313	−	0.211455i
$53$	−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
$56$	−7.43052	+	0.887315i	−0.992945	+	0.118572i
$57$		0			0
$58$	−0.712527	+	5.73810i	−0.0935593	+	0.753449i
$59$	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	$-0.940474\pi$
$61$	−5.09458	−	8.82407i	−0.652294	−	1.12981i	0.330271	−	0.943886i	$-0.392860\pi$
$62$	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	0.773793	−	0.633439i	$-0.218357\pi$
$67$	5.01037	+	2.89274i	0.612114	+	0.353404i	−0.161678	+	0.986844i	$0.551691\pi$
$68$	2.17962	−	2.24473i	0.264318	−	0.272213i
$69$		0			0
$70$	−2.73293	+	3.37087i	−0.326647	+	0.402896i
$71$			4.72781i			0.561088i	0.959841	+	0.280544i	$0.0905149\pi$
$71$			4.72781i			0.561088i	−0.959841	+	0.280544i	$0.909485\pi$
$72$		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	$-0.732469\pi$
$74$	−3.15685	−	7.46547i	−0.366976	−	0.867844i
$75$		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	$0.727796\pi$
$80$	−4.63716	+	0.136508i	−0.518450	+	0.0152620i
$81$		0			0
$82$	0.382388	−	3.07943i	0.0422277	−	0.340066i
$83$			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
$86$	9.16411	+	1.13795i	0.988192	+	0.122708i
$87$		0			0
$88$	−5.01388	−	6.24390i	−0.534481	−	0.665601i
$89$	−1.33902	−	2.31925i	−0.141936	−	0.245840i	0.786290	−	0.617858i	$-0.211999\pi$
$89$	−1.33902	−	2.31925i	−0.141936	−	0.245840i	−0.928226	+	0.372018i	$0.878666\pi$
$90$		0			0
$91$	3.87769	+	7.27904i	0.406492	+	0.763051i
$92$	−9.01515	+	2.55836i	−0.939895	+	0.266727i
$93$		0			0
$94$	−13.9271	+	5.88919i	−1.43647	+	0.607424i
$95$	−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	$-0.192560\pi$
$98$	7.47257	+	6.49312i	0.754844	+	0.655905i
$99$		0			0
$100$	5.09217	−	5.24428i	0.509217	−	0.524428i
$101$	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	0.538104	−	0.842879i	$-0.319141\pi$
$109$	0.806006	+	0.465348i	0.0772014	+	0.0445722i	−0.460902	+	0.887451i	$0.652474\pi$
$110$	−4.60831	−	0.572236i	−0.439385	−	0.0545605i
$111$		0			0
$112$	−0.0496374	+	10.5829i	−0.00469030	+	0.999989i
$113$			13.9228i			1.30974i	0.755741	+	0.654871i	$0.227277\pi$
$113$			13.9228i			1.30974i	−0.755741	+	0.654871i	$0.772723\pi$
$114$		0			0
$115$	−2.71714	+	4.70623i	−0.253375	+	0.438858i
$116$	7.92887	+	1.99997i	0.736177	+	0.185692i
$117$		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
$122$	−13.2718	+	5.61213i	−1.20158	+	0.508098i
$123$		0			0
$124$	−3.98392	−	3.86836i	−0.357766	−	0.347389i
$125$		−	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	$0.530429\pi$
$128$	−8.60932	+	7.34028i	−0.760963	+	0.648795i
$129$		0			0
$130$	1.99132	+	4.70918i	0.174650	+	0.413022i
$131$	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
$136$	−2.77048	−	3.45014i	−0.237567	−	0.295847i
$137$	−8.51773	−	4.91771i	−0.727718	−	0.420148i	0.0898684	−	0.995954i	$-0.471355\pi$
$137$	−8.51773	−	4.91771i	−0.727718	−	0.420148i	−0.817587	+	0.575805i	$0.804689\pi$
$138$		0			0
$139$	−17.6445			−1.49658			−0.748292	−	0.663369i	$-0.769126\pi$
$139$	−17.6445			−1.49658			−0.748292	+	0.663369i	$0.769126\pi$
$140$	4.25452	+	4.42293i	0.359573	+	0.373806i
$141$		0			0
$142$	6.63518	+	0.823922i	0.556812	+	0.0691420i
$143$	−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	$0.110953\pi$
$152$	−12.0226	+	1.85359i	−0.975158	+	0.150346i
$153$		0			0
$154$	−1.66326	+	10.4620i	−0.134029	+	0.843049i
$155$	−3.22016			−0.258650
$156$		0			0
$157$	12.1053	−	20.9671i	0.966111	−	1.67335i	0.259512	−	0.965740i	$-0.416438\pi$
$157$	12.1053	−	20.9671i	0.966111	−	1.67335i	0.706599	−	0.707614i	$-0.250228\pi$
$158$	7.53716	−	3.18716i	0.599625	−	0.253557i
$159$		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	−0.773892	−	0.633318i	$-0.781693\pi$
$163$	−7.81820	+	4.51384i	−0.612369	+	0.353551i	0.161523	+	0.986869i	$0.448359\pi$
$164$	−4.25514	−	1.07331i	−0.332271	−	0.0838116i
$165$		0			0
$166$	8.32447	+	1.03369i	0.646104	+	0.0802298i
$167$	16.2972			1.26112			0.630559	−	0.776142i	$-0.282826\pi$
$167$	16.2972			1.26112			0.630559	+	0.776142i	$0.282826\pi$
$168$		0			0
$169$	−3.28273			−0.252518
$170$	−2.54638	−	0.316196i	−0.195298	−	0.0242511i
$171$		0			0
$172$	3.19408	−	12.6629i	0.243546	−	0.965539i
$173$	−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
$178$	−3.48827	+	1.47505i	−0.261457	+	0.110560i
$179$	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	$-0.584174\pi$
$181$	−7.03270			−0.522736			−0.261368	+	0.965239i	$0.584174\pi$
$182$	10.8914	−	4.17355i	0.807327	−	0.309364i
$183$		0			0
$184$	2.01940	+	13.0980i	0.148872	+	0.965600i
$185$	−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	0.000629171	−	1.00000i	$-0.499800\pi$
$191$	11.9817	−	6.91767i	0.866969	−	0.500545i	0.866340	+	0.499455i	$0.166466\pi$
$192$		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	$0.215076\pi$
$194$	−15.7219	−	1.95226i	−1.12876	−	0.140164i
$195$		0			0
$196$	10.4149	−	9.35570i	0.743924	−	0.668265i
$197$	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	$0.688047\pi$
$200$	−6.47259	−	8.06046i	−0.457681	−	0.569961i
$201$		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
$206$	−8.29287	−	19.6114i	−0.577792	−	1.36639i
$207$		0			0
$208$	10.9773	+	5.91406i	0.761136	+	0.410066i
$209$	−12.1765			−0.842266
$210$		0			0
$211$		−	25.0597i		−	1.72518i	−0.505901	−	0.862592i	$-0.668840\pi$
$211$		−	25.0597i		−	1.72518i	0.505901	−	0.862592i	$-0.331160\pi$
$212$	15.6574	−	16.1251i	1.07536	−	1.10748i
$213$		0			0
$214$	−3.70663	+	1.56738i	−0.253380	+	0.107144i
$215$	−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
$220$	−1.60619	+	6.36774i	−0.108289	+	0.429313i
$221$	−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	$0.897800\pi$
$224$	14.8437	+	1.91396i	0.991789	+	0.127882i
$225$		0			0
$226$	19.5397	+	2.42633i	1.29976	+	0.161397i
$227$	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	$-0.806217\pi$
$229$	−13.7016	−	23.7319i	−0.905428	−	1.56825i	−0.0850862	−	0.996374i	$-0.527117\pi$
$230$	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	0.385987	−	0.922504i	$-0.373861\pi$
$233$	21.0326	−	12.1432i	1.37789	−	0.795526i	0.991906	+	0.126978i	$0.0405278\pi$
$234$		0			0
$235$	10.7393	+	6.20035i	0.700556	+	0.404466i
$236$	−19.7234	−	19.1513i	−1.28388	−	1.24665i
$237$		0			0
$238$	−0.919055	+	5.78089i	−0.0595735	+	0.374719i
$239$		−	2.35413i		−	0.152276i	−0.997097	−	0.0761380i	$-0.975741\pi$
$239$		−	2.35413i		−	0.152276i	0.997097	−	0.0761380i	$-0.0242590\pi$
$240$		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	$0.528734\pi$
$242$	3.88725	−	1.64376i	0.249882	−	0.105665i
$243$		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
$248$	−6.12328	+	4.91702i	−0.388829	+	0.312231i
$249$		0			0
$250$	−14.0875	−	1.74931i	−0.890971	−	0.110636i
$251$		−	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
$254$	−0.374918	+	3.01928i	−0.0235244	+	0.189446i
$255$		0			0
$256$	8.80125	+	13.3618i	0.550078	+	0.835113i
$257$	6.72517	+	11.6483i	0.419504	+	0.726603i	0.995890	−	0.0905752i	$-0.0288706\pi$
$257$	6.72517	+	11.6483i	0.419504	+	0.726603i	−0.576385	+	0.817178i	$0.695537\pi$
$258$		0			0
$259$	12.8661	+	8.02557i	0.799461	+	0.498684i
$260$	6.95605	−	1.97402i	0.431396	−	0.122423i
$261$		0			0
$262$	−6.72837	−	15.9116i	−0.415680	−	0.983022i
$263$	1.35260	+	0.780923i	0.0834048	+	0.0481538i	0.541122	−	0.840944i	$-0.318000\pi$
$263$	1.35260	+	0.780923i	0.0834048	+	0.0481538i	−0.457718	+	0.889098i	$0.651333\pi$
$264$		0			0
$265$		−	13.0338i		−	0.800658i
$266$	12.5001	+	10.1345i	0.766432	+	0.621384i
$267$		0			0
$268$	−8.30141	−	8.06063i	−0.507089	−	0.492381i
$269$	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	0.807006	−	0.590544i	$-0.201087\pi$
$277$	11.6351	+	6.71750i	0.699083	+	0.403616i	−0.107923	+	0.994159i	$0.534420\pi$
$278$	−3.07492	+	24.7629i	−0.184422	+	1.48518i
$279$		0			0
$280$	6.94873	−	5.20016i	0.415266	−	0.310769i
$281$		−	27.9830i		−	1.66933i	−0.550761	−	0.834663i	$-0.685662\pi$
$281$		−	27.9830i		−	1.66933i	0.550761	−	0.834663i	$-0.314338\pi$
$282$		0			0
$283$	9.68568	−	16.7761i	0.575754	−	0.997235i	−0.420205	−	0.907429i	$-0.638042\pi$
$283$	9.68568	−	16.7761i	0.575754	−	0.997235i	0.995959	−	0.0898063i	$-0.0286248\pi$
$284$	2.31264	−	9.16846i	0.137230	−	0.544048i
$285$		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
$290$	−2.61183	−	6.17658i	−0.153372	−	0.362702i
$291$		0			0
$292$	23.2983	+	22.6226i	1.36343	+	1.32389i
$293$		−	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
$296$	2.47016	+	16.0217i	0.143575	+	0.931241i
$297$		0			0
$298$	−12.7131	+	5.37587i	−0.736451	+	0.311416i
$299$	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
$304$	0.506210	+	17.1959i	0.0290331	+	0.986252i
$305$	10.2341	+	5.90865i	0.586001	+	0.338328i
$306$		0			0
$307$	−27.0446			−1.54352			−0.771758	−	0.635917i	$-0.780622\pi$
$307$	−27.0446			−1.54352			−0.771758	+	0.635917i	$0.780622\pi$
$308$	14.3928	+	4.15749i	0.820107	+	0.236895i
$309$		0			0
$310$	−0.561182	+	4.51929i	−0.0318730	+	0.256678i
$311$	−0.276139	+	0.478286i	−0.0156584	+	0.0271211i	−0.873748	−	0.486378i	$-0.838318\pi$
$311$	−0.276139	+	0.478286i	−0.0156584	+	0.0271211i	0.858090	+	0.513499i	$0.171651\pi$
$312$		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
$320$	9.05942	+	2.00357i	0.506437	+	0.112003i
$321$		0			0
$322$	11.0410	−	13.6183i	0.615293	−	0.758920i
$323$	−6.72828			−0.374371
$324$		0			0
$325$	−5.69660	+	9.86680i	−0.315991	+	0.547312i
$326$	4.97240	+	11.7590i	0.275396	+	0.651269i
$327$		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	−0.436375	−	0.899765i	$-0.643738\pi$
$331$	2.26793	−	1.30939i	0.124657	−	0.0719706i	0.561032	+	0.827794i	$0.310405\pi$
$332$	2.90143	−	11.5027i	0.159237	−	0.631293i
$333$		0			0
$334$	2.84014	−	22.8721i	0.155405	−	1.25151i
$335$	−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	$0.0992542\pi$
$338$	−0.572085	+	4.60709i	−0.0311173	+	0.250593i
$339$		0			0
$340$	−0.887521	+	3.51857i	−0.0481326	+	0.190821i
$341$	−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
$346$	0.0152674	+	0.0361051i	0.000820780	+	0.00194102i
$347$	−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	$-0.437179\pi$
$349$	7.32611			0.392158			0.196079	+	0.980588i	$0.437179\pi$
$350$	−2.14716	+	13.5057i	−0.114770	+	0.721911i
$351$		0			0
$352$	6.66897	+	14.5611i	0.355457	+	0.776109i
$353$	−13.9297	+	24.1269i	−0.741402	+	1.28415i	0.210454	+	0.977604i	$0.432506\pi$
$353$	−13.9297	+	24.1269i	−0.741402	+	1.28415i	−0.951857	+	0.306543i	$0.900828\pi$
$354$		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	−0.851930	−	0.523656i	$-0.824568\pi$
$359$	−15.6201	+	9.01825i	−0.824396	+	0.475965i	0.0275343	+	0.999621i	$0.491234\pi$
$360$		0			0
$361$	0.251405	−	0.435447i	0.0132319	−	0.0229182i
$362$	−1.22560	+	9.86994i	−0.0644159	+	0.518752i
$363$		0			0
$364$	−3.95925	−	16.0127i	−0.207521	−	0.839296i
$365$	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	$0.626588\pi$
$368$	18.7342	−	0.551493i	0.976585	−	0.0287486i
$369$		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	−0.484659	−	0.874703i	$-0.661056\pi$
$373$	0.589575	−	0.340391i	0.0305270	−	0.0176248i	0.515186	+	0.857078i	$0.327723\pi$
$374$	−5.76917	+	2.43955i	−0.298317	+	0.126146i
$375$		0			0
$376$	29.8889	−	4.60816i	1.54140	−	0.237648i
$377$	−12.7452			−0.656413
$378$		0			0
$379$		−	23.7081i		−	1.21780i	−0.793245	−	0.608902i	$-0.791610\pi$
$379$		−	23.7081i		−	1.21780i	0.793245	−	0.608902i	$-0.208390\pi$
$380$	7.15723	+	6.94964i	0.367158	+	0.356509i
$381$		0			0
$382$	−7.62042	−	18.0212i	−0.389895	−	0.922043i
$383$	16.7429	+	28.9996i	0.855522	+	1.48181i	0.876160	+	0.482021i	$0.160097\pi$
$383$	16.7429	+	28.9996i	0.855522	+	1.48181i	−0.0206373	+	0.999787i	$0.506570\pi$
$384$		0			0
$385$	7.66746	−	4.08460i	0.390770	−	0.208171i
$386$	4.74930	+	3.58906i	0.241733	+	0.182679i
$387$		0			0
$388$	−5.47973	+	21.7244i	−0.278191	+	1.10289i
$389$	−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
$392$	−11.3151	−	16.2471i	−0.571499	−	0.820603i
$393$		0			0
$394$	4.24400	−	34.1776i	0.213810	−	1.72184i
$395$	−5.81200	−	3.35556i	−0.292433	−	0.168836i
$396$		0			0
$397$	12.7489	+	22.0817i	0.639849	+	1.10825i	0.985466	+	0.169875i	$0.0543364\pi$
$397$	12.7489	+	22.0817i	0.639849	+	1.10825i	−0.345617	+	0.938376i	$0.612330\pi$
$398$	−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	−0.734251	−	0.678878i	$-0.762467\pi$
$401$	−10.2818	+	5.93623i	−0.513451	+	0.296441i	0.220800	+	0.975319i	$0.429133\pi$
$402$		0			0
$403$	7.49550	+	4.32753i	0.373378	+	0.215570i
$404$	−0.784117	−	0.761374i	−0.0390113	−	0.0378798i
$405$		0			0
$406$	−14.2853	+	5.47406i	−0.708966	+	0.271673i
$407$			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	$0.707372\pi$
$410$	1.40168	+	3.31475i	0.0692238	+	0.163704i
$411$		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
$416$	10.2130	−	14.3752i	0.500735	−	0.704803i
$417$		0			0
$418$	−2.12201	+	17.0889i	−0.103791	+	0.835846i
$419$			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	$0.361820\pi$
$421$			37.2303i			1.81449i	−0.420599	+	0.907247i	$0.638180\pi$
$422$	−35.1697	−	4.36719i	−1.71203	−	0.212591i
$423$		0			0
$424$	−19.9019	−	24.7843i	−0.966522	−	1.20363i
$425$	−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
$430$	−9.86441	+	4.17126i	−0.475704	+	0.201156i
$431$	−7.24374	−	4.18217i	−0.348919	−	0.201448i	0.315290	−	0.948995i	$-0.397898\pi$
$431$	−7.24374	−	4.18217i	−0.348919	−	0.201448i	−0.664209	+	0.747547i	$0.731231\pi$
$432$		0			0
$433$		−	7.63673i		−	0.366998i	−0.983020	−	0.183499i	$-0.941258\pi$
$433$		−	7.63673i		−	0.366998i	0.983020	−	0.183499i	$-0.0587424\pi$
$434$	10.2599	+	1.63113i	0.492489	+	0.0782967i
$435$		0			0
$436$	−1.33543	−	1.29669i	−0.0639553	−	0.0621003i
$437$	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
$446$	13.2278	+	1.64256i	0.626356	+	0.0777775i
$447$		0			0
$448$	5.27295	−	20.4987i	0.249123	−	0.968472i
$449$		−	16.6555i		−	0.786020i	−0.919534	−	0.393010i	$-0.871434\pi$
$449$		−	16.6555i		−	0.786020i	0.919534	−	0.393010i	$-0.128566\pi$
$450$		0			0
$451$	−3.10612	+	5.37995i	−0.146261	+	0.253332i
$452$	6.81040	−	26.9998i	0.320334	−	1.26996i
$453$		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	$0.993601\pi$
$458$	−35.6940	+	15.0935i	−1.66787	+	0.705275i
$459$		0			0
$460$	7.57132	−	7.79748i	0.353015	−	0.363560i
$461$		−	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	$0.887701\pi$
$464$	−14.3978	−	7.75692i	−0.668403	−	0.360106i
$465$		0			0
$466$	−13.3768	−	31.6341i	−0.619668	−	1.46542i
$467$	−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
$472$	−30.3149	+	24.3430i	−1.39536	+	1.12048i
$473$	−16.0103	−	9.24352i	−0.736152	−	0.425018i
$474$		0			0
$475$	−15.7191			−0.721240
$476$	7.95294	+	2.29728i	0.364522	+	0.105295i
$477$		0			0
$478$	−3.30387	−	0.410257i	−0.151115	−	0.0187647i
$479$	0.299198	−	0.518227i	0.0136707	−	0.0236784i	−0.859109	−	0.511792i	$-0.828982\pi$
$479$	0.299198	−	0.518227i	0.0136707	−	0.0236784i	0.872780	+	0.488114i	$0.162315\pi$
$480$		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	$0.322806\pi$
$488$	28.4827	−	4.39136i	1.28935	−	0.198788i
$489$		0			0
$490$	−11.2709	−	2.18844i	−0.509165	−	0.0988636i
$491$	−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
$494$	17.4630	−	7.38439i	0.785696	−	0.332239i
$495$		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	−0.253320	−	0.967383i	$-0.581522\pi$
$499$	10.2264	−	5.90424i	0.457799	−	0.264310i	0.711118	+	0.703072i	$0.248189\pi$
$500$	−4.91008	+	19.4660i	−0.219586	+	0.870546i
$501$		0			0
$502$	−33.7504	−	4.19095i	−1.50635	−	0.187051i
$503$	−3.08281			−0.137456			−0.0687278	−	0.997635i	$-0.521894\pi$
$503$	−3.08281			−0.137456			−0.0687278	+	0.997635i	$0.521894\pi$
$504$		0			0
$505$	−0.633794			−0.0282035
$506$	18.6176	+	2.31184i	0.827654	+	0.102774i
$507$		0			0
$508$	4.17202	+	1.05235i	0.185104	+	0.0466903i
$509$	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
$514$	17.5197	−	7.40837i	0.772760	−	0.326769i
$515$	−8.73103	+	15.1226i	−0.384735	+	0.666381i
$516$		0			0
$517$	30.2716			1.33135
$518$	13.5056	−	16.6581i	0.593400	−	0.731916i
$519$		0			0
$520$	−1.55816	−	10.1064i	−0.0683300	−	0.443194i
$521$	19.2542	−	33.3493i	0.843542	−	1.46106i	−0.0433388	−	0.999060i	$-0.513799\pi$
$521$	19.2542	−	33.3493i	0.843542	−	1.46106i	0.886881	−	0.461998i	$-0.152867\pi$
$522$		0			0
$523$	19.3439	+	33.5046i	0.845849	+	1.46505i	0.884882	+	0.465815i	$0.154239\pi$
$523$	19.3439	+	33.5046i	0.845849	+	1.46505i	−0.0390332	+	0.999238i	$0.512428\pi$
$524$	−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
$530$	−18.2921	−	2.27141i	−0.794556	−	0.0986638i
$531$		0			0
$532$	16.4015	−	15.7770i	0.711094	−	0.684019i
$533$	6.83991			0.296270
$534$		0			0
$535$	2.85823	+	1.65020i	0.123572	+	0.0713443i
$536$	−12.7593	+	10.2458i	−0.551116	+	0.442549i
$537$		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	−0.928883	−	0.370374i	$-0.879230\pi$
$541$	−24.9474	+	14.4034i	−1.07257	+	0.619249i	−0.143688	+	0.989623i	$0.545896\pi$
$542$	−7.61028	−	17.9972i	−0.326890	−	0.773045i
$543$		0			0
$544$	3.68502	+	8.04592i	0.157994	+	0.344966i
$545$	−1.07941			−0.0462370
$546$		0			0
$547$		−	26.0874i		−	1.11541i	−0.830038	−	0.557707i	$-0.811681\pi$
$547$		−	26.0874i		−	1.11541i	0.830038	−	0.557707i	$-0.188319\pi$
$548$	14.1125	+	13.7032i	0.602858	+	0.585372i
$549$		0			0
$550$	−13.4783	+	5.69944i	−0.574718	+	0.243025i
$551$	−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
$556$	34.2172	+	8.63091i	1.45113	+	0.366032i
$557$	−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
$560$	−6.08712	−	10.6583i	−0.257228	−	0.450397i
$561$		0			0
$562$	−39.2723	−	4.87663i	−1.65660	−	0.205708i
$563$	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	−0.801161	−	0.598449i	$-0.795784\pi$
$569$	−16.3033	+	9.41272i	−0.683470	+	0.394602i	0.117691	+	0.993050i	$0.462451\pi$
$570$		0			0
$571$	2.34839	+	1.35584i	0.0982770	+	0.0567403i	0.548333	−	0.836260i	$-0.315263\pi$
$571$	2.34839	+	1.35584i	0.0982770	+	0.0567403i	−0.450056	+	0.893000i	$0.648596\pi$
$572$	12.2962	−	12.6635i	0.514130	−	0.529488i
$573$		0			0
$574$	7.66639	−	2.93773i	0.319989	−	0.122619i
$575$			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	$0.542607\pi$
$578$	18.9555	−	8.01550i	0.788443	−	0.333401i
$579$		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
$584$	35.8095	−	28.7552i	1.48181	−	1.18990i
$585$		0			0
$586$	−34.3105	−	4.26049i	−1.41735	−	0.175999i
$587$			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
$590$	−2.77827	+	22.3739i	−0.114380	+	0.921119i
$591$		0			0
$592$	22.9159	−	0.674593i	0.941836	−	0.0277256i
$593$	15.3152	+	26.5267i	0.628920	+	1.08932i	0.987769	+	0.155925i	$0.0498359\pi$
$593$	15.3152	+	26.5267i	0.628920	+	1.08932i	−0.358849	+	0.933396i	$0.616831\pi$
$594$		0			0
$595$	4.23675	−	2.25700i	0.173690	−	0.0925279i
$596$	5.32915	+	18.7789i	0.218290	+	0.769214i
$597$		0			0
$598$	−8.04496	−	19.0251i	−0.328983	−	0.777995i
$599$	−28.4250	−	16.4112i	−1.16141	−	0.670543i	−0.209772	−	0.977750i	$-0.567272\pi$
$599$	−28.4250	−	16.4112i	−1.16141	−	0.670543i	−0.951643	+	0.307207i	$0.900606\pi$
$600$		0			0
$601$			5.73393i			0.233892i	0.993138	+	0.116946i	$0.0373104\pi$
$601$			5.73393i			0.233892i	−0.993138	+	0.116946i	$0.962690\pi$
$602$	8.74243	+	22.8145i	0.356315	+	0.929850i
$603$		0			0
$604$	−5.96267	+	6.14078i	−0.242618	+	0.249865i
$605$	−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	0.515330	−	0.856992i	$-0.327670\pi$
$613$	0.763004	+	0.440521i	0.0308174	+	0.0177925i	−0.484512	+	0.874785i	$0.661003\pi$
$614$	−4.71309	+	37.9553i	−0.190205	+	1.53175i
$615$		0			0
$616$	8.34303	−	19.4749i	0.336150	−	0.784665i
$617$		−	33.3940i		−	1.34439i	−0.740373	−	0.672196i	$-0.765351\pi$
$617$		−	33.3940i		−	1.34439i	0.740373	−	0.672196i	$-0.234649\pi$
$618$		0			0
$619$	−0.347094	+	0.601184i	−0.0139509	+	0.0241636i	−0.872917	−	0.487870i	$-0.837774\pi$
$619$	−0.347094	+	0.601184i	−0.0139509	+	0.0241636i	0.858966	+	0.512033i	$0.171108\pi$
$620$	6.24473	+	1.57516i	0.250794	+	0.0632601i
$621$		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
$626$	8.61644	+	20.3766i	0.344382	+	0.814412i
$627$		0			0
$628$	−33.7316	+	34.7392i	−1.34604	+	1.38624i
$629$			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	$0.476690\pi$
$632$	−16.1755	+	2.49388i	−0.643428	+	0.0992013i
$633$		0			0
$634$	−16.5084	+	6.98075i	−0.655633	+	0.277241i
$635$	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
$640$	4.39068	−	12.3651i	0.173557	−	0.488775i
$641$	20.9407	+	12.0901i	0.827108	+	0.477531i	0.852862	−	0.522137i	$-0.174865\pi$
$641$	20.9407	+	12.0901i	0.827108	+	0.477531i	−0.0257532	+	0.999668i	$0.508198\pi$
$642$		0			0
$643$	7.82797			0.308705			0.154352	−	0.988016i	$-0.450671\pi$
$643$	7.82797			0.308705			0.154352	+	0.988016i	$0.450671\pi$
$644$	−17.1883	−	17.8687i	−0.677314	−	0.704124i
$645$		0			0
$646$	−1.17254	+	9.44270i	−0.0461332	+	0.371518i
$647$	8.30976	−	14.3929i	0.326690	−	0.565844i	−0.655163	−	0.755488i	$-0.727400\pi$
$647$	8.30976	−	14.3929i	0.326690	−	0.565844i	0.981853	+	0.189644i	$0.0607333\pi$
$648$		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
$656$	7.72681	+	4.16286i	0.301681	+	0.162532i
$657$		0			0
$658$	−31.0762	−	25.1950i	−1.21148	−	0.982204i
$659$	−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	$-0.637095\pi$
$661$	14.8650	−	25.7470i	0.578183	−	1.00144i	0.995688	−	0.0927674i	$-0.0295713\pi$
$662$	−1.44241	−	3.41108i	−0.0560608	−	0.132576i
$663$		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
$668$	−31.6045	−	7.97189i	−1.22282	−	0.308442i
$669$		0			0
$670$	−1.16935	+	9.41698i	−0.0451760	+	0.363810i
$671$	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	$0.318329\pi$
$674$	6.08984	−	49.0425i	0.234572	−	1.88905i
$675$		0			0
$676$	6.36606	+	1.60577i	0.244848	+	0.0617603i
$677$	−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
$682$	4.32969	+	10.2391i	0.165792	+	0.392074i
$683$	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
$686$	−5.86652	+	25.5261i	−0.223985	+	0.974593i
$687$		0			0
$688$	−12.3883	+	22.9943i	−0.472300	+	0.876649i
$689$	−17.5159	+	30.3384i	−0.667303	+	1.15580i
$690$		0			0
$691$	3.24122	+	5.61395i	0.123302	+	0.213565i	0.921068	−	0.389402i	$-0.127318\pi$
$691$	3.24122	+	5.61395i	0.123302	+	0.213565i	−0.797766	+	0.602967i	$0.793985\pi$
$692$	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
$698$	1.27673	−	10.2817i	0.0483249	−	0.389169i
$699$		0			0
$700$	18.5802	+	5.36705i	0.702265	+	0.202856i
$701$	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
$704$	21.5978	−	6.82188i	0.813996	−	0.257109i
$705$		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	−0.0416860	−	0.999131i	$-0.513273\pi$
$709$	21.3747	−	12.3407i	0.802744	−	0.463464i	0.844430	+	0.535667i	$0.179940\pi$
$710$	−7.14222	+	3.02016i	−0.268043	+	0.113344i
$711$		0			0
$712$	7.48619	−	1.15419i	0.280557	−	0.0432552i
$713$	13.0095			0.487209
$714$		0			0
$715$		−	10.2358i		−	0.382797i
$716$	−6.67582	+	6.87523i	−0.249487	+	0.256939i
$717$		0			0
$718$	9.93440	+	23.4934i	0.370748	+	0.876765i
$719$	−10.2912	−	17.8248i	−0.383796	−	0.664754i	0.607806	−	0.794086i	$-0.292050\pi$
$719$	−10.2912	−	17.8248i	−0.383796	−	0.664754i	−0.991601	+	0.129332i	$0.958717\pi$
$720$		0			0
$721$	33.7986	+	21.0827i	1.25872	+	0.785162i
$722$	−0.567308	−	0.428717i	−0.0211130	−	0.0159552i
$723$		0			0
$724$	13.6382	+	3.44009i	0.506861	+	0.127850i
$725$	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	$0.832474\pi$
$728$	−23.1628	+	2.76599i	−0.858471	+	0.102514i
$729$		0			0
$730$	3.28184	−	26.4292i	0.121467	−	0.978190i
$731$	−8.84667	−	5.10763i	−0.327206	−	0.188912i
$732$		0			0
$733$	−8.48261	−	14.6923i	−0.313312	−	0.542673i	0.665765	−	0.746162i	$-0.268105\pi$
$733$	−8.48261	−	14.6923i	−0.313312	−	0.542673i	−0.979077	+	0.203488i	$0.934772\pi$
$734$	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	0.994590	−	0.103876i	$-0.0331245\pi$
$739$	38.1107	+	22.0032i	1.40193	+	0.809402i	0.407336	+	0.913278i	$0.366458\pi$
$740$	9.26134	−	9.53798i	0.340454	−	0.350623i
$741$		0			0
$742$	−6.60208	+	41.5273i	−0.242370	+	1.52452i
$743$			30.5441i			1.12056i	0.828305	+	0.560278i	$0.189306\pi$
$743$			30.5441i			1.12056i	−0.828305	+	0.560278i	$0.810694\pi$
$744$		0			0
$745$	9.80324	+	5.65990i	0.359163	+	0.207363i
$746$	−0.374971	−	0.886750i	−0.0137287	−	0.0324662i
$747$		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	$0.734764\pi$
$752$	−1.25847	−	42.7502i	−0.0458918	−	1.55894i
$753$		0			0
$754$	−2.22113	+	17.8871i	−0.0808886	+	0.651410i
$755$			4.96353i			0.180641i
$756$		0			0
$757$			1.36258i			0.0495237i	0.999693	+	0.0247618i	$0.00788275\pi$
$757$			1.36258i			0.0495237i	−0.999693	+	0.0247618i	$0.992117\pi$
$758$	−33.2728	−	4.13164i	−1.20852	−	0.150068i
$759$		0			0
$760$	11.0007	−	8.83359i	0.399036	−	0.320428i
$761$	−7.30823	−	12.6582i	−0.264923	−	0.458860i	0.702620	−	0.711565i	$-0.252013\pi$
$761$	−7.30823	−	12.6582i	−0.264923	−	0.458860i	−0.967543	+	0.252705i	$0.918680\pi$
$762$		0			0
$763$	−0.0839995	+	2.46096i	−0.00304099	+	0.0890926i
$764$	−26.6195	+	7.55420i	−0.963061	+	0.273301i
$765$		0			0
$766$	43.6168	−	18.4438i	1.57594	−	0.666401i
$767$	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	$0.992936\pi$
$770$	−4.39626	−	11.4726i	−0.158430	−	0.413444i
$771$		0			0
$772$	5.86468	−	6.03987i	0.211075	−	0.217380i
$773$	−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
$782$	10.2874	+	1.27743i	0.367877	+	0.0456810i
$783$		0			0
$784$	−24.7737	+	13.0486i	−0.884773	+	0.466022i
$785$			28.0793i			1.00219i
$786$		0			0
$787$	0.411250	−	0.712307i	0.0146595	−	0.0253910i	−0.858603	−	0.512642i	$-0.828667\pi$
$787$	0.411250	−	0.712307i	0.0146595	−	0.0253910i	0.873262	+	0.487251i	$0.162000\pi$
$788$	−47.2265	−	11.9124i	−1.68237	−	0.424360i
$789$		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
$794$	33.2121	−	14.0440i	1.17865	−	0.498404i
$795$		0			0
$796$	2.71716	+	2.63835i	0.0963071	+	0.0935137i
$797$		−	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
$800$	8.60920	+	18.7974i	0.304381	+	0.664589i
$801$		0			0
$802$	6.53928	+	15.4644i	0.230910	+	0.546068i
$803$	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
$808$	−1.20519	+	0.967772i	−0.0423984	+	0.0340461i
$809$	19.0060	+	10.9731i	0.668215	+	0.385794i	0.795400	−	0.606085i	$-0.207261\pi$
$809$	19.0060	+	10.9731i	0.668215	+	0.385794i	−0.127185	+	0.991879i	$0.540594\pi$
$810$		0			0
$811$	−40.5865			−1.42518			−0.712592	−	0.701579i	$-0.752479\pi$
$811$	−40.5865			−1.42518			−0.712592	+	0.701579i	$0.752479\pi$
$812$	5.19297	+	21.0024i	0.182238	+	0.737040i
$813$		0			0
$814$	22.7733	+	2.82787i	0.798204	+	0.0991168i
$815$	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	$0.167919\pi$
$824$	6.48898	+	42.0881i	0.226054	+	1.46621i
$825$		0			0
$826$	50.7941	+	8.07532i	1.76735	+	0.280976i
$827$	−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	−0.692018	−	0.721880i	$-0.743278\pi$
$829$	8.03760	−	13.9215i	0.279157	−	0.483515i	0.971176	+	0.238365i	$0.0766116\pi$
$830$	−8.96060	+	3.78908i	−0.311027	+	0.131521i
$831$		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
$836$	23.6134	+	5.95621i	0.816686	+	0.206000i
$837$		0			0
$838$	12.1193	+	1.50491i	0.418655	+	0.0519863i
$839$	50.6405			1.74831			0.874153	−	0.485651i	$-0.161417\pi$
$839$	50.6405			1.74831			0.874153	+	0.485651i	$0.161417\pi$
$840$		0			0
$841$	−12.2833			−0.423562
$842$	52.2503	+	6.48817i	1.80066	+	0.223597i
$843$		0			0
$844$	−12.2581	+	48.5973i	−0.421942	+	1.67279i
$845$	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
$850$	−7.44762	+	3.14930i	−0.255451	+	0.108020i
$851$	13.4275	−	23.2572i	0.460290	−	0.797246i
$852$		0			0
$853$	8.65855			0.296463			0.148232	−	0.988953i	$-0.452642\pi$
$853$	8.65855			0.296463			0.148232	+	0.988953i	$0.452642\pi$
$854$	−29.6142	−	24.0097i	−1.01338	−	0.821594i
$855$		0			0
$856$	7.95481	−	1.22644i	0.271890	−	0.0419189i
$857$	17.1294	−	29.6691i	0.585130	−	1.01348i	−0.409729	−	0.912207i	$-0.634377\pi$
$857$	17.1294	−	29.6691i	0.585130	−	1.01348i	0.994859	−	0.101268i	$-0.0322900\pi$
$858$		0			0
$859$	6.28537	+	10.8866i	0.214454	+	0.371445i	0.953104	−	0.302644i	$-0.0978694\pi$
$859$	6.28537	+	10.8866i	0.214454	+	0.371445i	−0.738649	+	0.674090i	$0.764536\pi$
$860$	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	−0.967940	−	0.251182i	$-0.919181\pi$
$863$	−36.2622	+	20.9360i	−1.23438	+	0.712669i	−0.266440	+	0.963852i	$0.585847\pi$
$864$		0			0
$865$	0.0160741	−	0.0278411i	0.000546534	−	0.000946625i
$866$	−10.7177	−	1.33086i	−0.364201	−	0.0452246i
$867$		0			0
$868$	4.07718	−	14.1148i	0.138389	−	0.479087i
$869$	−16.3827			−0.555744
$870$		0			0
$871$	15.6186	+	9.01741i	0.529216	+	0.305543i
$872$	−2.05255	+	1.64821i	−0.0695081	+	0.0558154i
$873$		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	−0.430094	−	0.902784i	$-0.641519\pi$
$877$	4.04807	−	2.33716i	0.136694	−	0.0789201i	0.566787	+	0.823864i	$0.308186\pi$
$878$	5.36019	+	12.6760i	0.180897	+	0.427796i
$879$		0			0
$880$	6.22964	−	11.5630i	0.210001	−	0.389789i
$881$	13.7595			0.463569			0.231785	−	0.972767i	$-0.425544\pi$
$881$	13.7595			0.463569			0.231785	+	0.972767i	$0.425544\pi$
$882$		0			0
$883$		−	31.7680i		−	1.06908i	−0.845144	−	0.534539i	$-0.820485\pi$
$883$		−	31.7680i		−	1.06908i	0.845144	−	0.534539i	$-0.179515\pi$
$884$	6.79442	−	6.99738i	0.228521	−	0.235347i
$885$		0			0
$886$	28.4873	−	12.0461i	0.957050	−	0.404698i
$887$	−9.28571	−	16.0833i	−0.311784	−	0.540025i	0.666965	−	0.745089i	$-0.267593\pi$
$887$	−9.28571	−	16.0833i	−0.311784	−	0.540025i	−0.978749	+	0.205064i	$0.934260\pi$
$888$		0			0
$889$	−2.67615	−	5.02357i	−0.0897553	−	0.168485i
$890$	2.64828	−	3.50439i	0.0887704	−	0.117467i
$891$		0			0
$892$	4.61046	−	18.2781i	0.154370	−	0.611997i
$893$	22.9927	−	39.8245i	0.769420	−	1.33268i
$894$		0			0
$895$			5.55718i			0.185756i
$896$	−27.8496	−	10.9726i	−0.930391	−	0.366568i
$897$		0			0
$898$	−23.3749	−	2.90257i	−0.780029	−	0.0968599i
$899$	−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	0.154166	−	0.988045i	$-0.450731\pi$
$907$	−18.8054	−	10.8573i	−0.624423	−	0.360511i	−0.778589	+	0.627534i	$0.784064\pi$
$908$	−26.6698	−	25.8963i	−0.885069	−	0.859398i
$909$		0			0
$910$	−8.51922	+	10.5078i	−0.282410	+	0.348332i
$911$		−	34.1200i		−	1.13044i	−0.824939	−	0.565222i	$-0.808790\pi$
$911$		−	34.1200i		−	1.13044i	0.824939	−	0.565222i	$-0.191210\pi$
$912$		0			0
$913$	−14.5433	−	8.39660i	−0.481314	−	0.277887i
$914$	−26.8701	+	11.3623i	−0.888785	+	0.375831i
$915$		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	$0.895949\pi$
$920$	−9.62380	−	11.9847i	−0.317287	−	0.395125i
$921$		0			0
$922$	−44.2491	−	5.49463i	−1.45727	−	0.180956i
$923$			14.7378i			0.485101i
$924$		0			0
$925$			20.9478i			0.688759i
$926$	−7.03782	+	56.6768i	−0.231277	+	1.86251i
$927$		0			0
$928$	−13.3955	+	18.8546i	−0.439727	+	0.618933i
$929$	29.2652	+	50.6888i	0.960161	+	1.66305i	0.722090	+	0.691799i	$0.243182\pi$
$929$	29.2652	+	50.6888i	0.960161	+	1.66305i	0.238071	+	0.971248i	$0.423485\pi$
$930$		0			0
$931$	−30.0358	−	2.05281i	−0.984383	−	0.0672781i
$932$	−46.7276	+	13.2605i	−1.53061	+	0.434363i
$933$		0			0
$934$	6.46080	+	15.2788i	0.211404	+	0.499938i
$935$	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	$-0.400928\pi$
$938$	21.3788	+	3.39883i	0.698042	+	0.110976i
$939$		0			0
$940$	−17.7934	−	17.2773i	−0.580356	−	0.563523i
$941$	−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
$950$	−2.73938	+	22.0607i	−0.0888772	+	0.715743i
$951$		0			0
$952$	4.61005	−	10.7611i	0.149412	−	0.348769i
$953$		−	15.3879i		−	0.498463i	−0.968444	−	0.249232i	$-0.919822\pi$
$953$		−	15.3879i		−	0.498463i	0.968444	−	0.249232i	$-0.0801781\pi$
$954$		0			0
$955$	−8.02305	+	13.8963i	−0.259620	+	0.449675i
$956$	−1.15154	+	4.56527i	−0.0372434	+	0.147651i
$957$		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
$962$	−9.84070	−	23.2718i	−0.317277	−	0.750312i
$963$		0			0
$964$	−18.7064	−	18.1638i	−0.602492	−	0.585017i
$965$		−	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	$0.315260\pi$
$968$	−8.34245	+	1.28621i	−0.268136	+	0.0413402i
$969$		0			0
$970$	16.9233	−	7.15617i	0.543374	−	0.229771i
$971$	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
$976$	−1.19927	−	40.7390i	−0.0383876	−	1.30402i
$977$	−19.4340	−	11.2202i	−0.621749	−	0.358967i	0.155801	−	0.987788i	$-0.450204\pi$
$977$	−19.4340	−	11.2202i	−0.621749	−	0.358967i	−0.777550	+	0.628822i	$0.783538\pi$
$978$		0			0
$979$	7.58205			0.242323
$980$	−5.03552	+	15.4365i	−0.160854	+	0.493102i
$981$		0			0
$982$	−3.91125	+	31.4979i	−0.124813	+	1.00514i
$983$	14.0698	−	24.3695i	0.448756	−	0.777268i	−0.549550	−	0.835461i	$-0.685201\pi$
$983$	14.0698	−	24.3695i	0.448756	−	0.777268i	0.998305	+	0.0581932i	$0.0185340\pi$
$984$		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	$-0.0248543\pi$
$992$	14.2798	−	6.54014i	0.453385	−	0.207650i
$993$		0			0
$994$	6.32986	+	16.5186i	0.200771	+	0.523938i
$995$	2.19625			0.0696259
$996$		0			0
$997$	12.1376	−	21.0230i	0.384402	−	0.665804i	−0.607284	−	0.794485i	$-0.707741\pi$
$997$	12.1376	−	21.0230i	0.384402	−	0.665804i	0.991686	+	0.128681i	$0.0410742\pi$
$998$	−6.50404	−	15.3811i	−0.205882	−	0.486880i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.174271 - 1.40343i) q^{2} +(-1.93926 - 0.489157i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 + 2.63638i) q^{8} +O(q^{10})\)	\(q+(0.174271 - 1.40343i) q^{2} +(-1.93926 - 0.489157i) q^{4} +(-1.00441 + 0.579896i) q^{5} +(1.24394 + 2.33508i) q^{7} +(-1.02446 + 2.63638i) q^{8} +(0.638806 + 1.51068i) q^{10} +(-1.41560 + 2.45188i) q^{11} +3.11725 q^{13} +(3.49392 - 1.33886i) q^{14} +(3.52145 + 1.89720i) q^{16} +(-0.782206 + 1.35482i) q^{17} +(2.15042 + 3.72463i) q^{19} +(2.23147 - 0.633255i) q^{20} +(3.19436 + 2.41399i) q^{22} +(4.05782 - 2.34278i) q^{23} +(-1.82744 + 3.16522i) q^{25} +(0.543248 - 4.37486i) q^{26} +(-1.27011 - 5.13681i) q^{28} -4.08861 q^{29} +(2.40452 + 1.38825i) q^{31} +(3.27629 - 4.61150i) q^{32} +(1.76509 + 1.33388i) q^{34} +(-2.60353 - 1.62402i) q^{35} +(4.96358 - 2.86572i) q^{37} +(5.60204 - 2.36888i) q^{38} +(-0.499851 - 3.24208i) q^{40} +2.19421 q^{41} +6.52977i q^{43} +(3.94456 - 4.06239i) q^{44} +(-2.58078 - 6.10317i) q^{46} +(-5.34609 - 9.25971i) q^{47} +(-3.90521 + 5.80942i) q^{49} +(4.12371 + 3.11630i) q^{50} +(-6.04516 - 1.52483i) q^{52} +(-5.61902 + 9.73242i) q^{53} -3.28359i q^{55} +(-7.43052 + 0.887315i) q^{56} +(-0.712527 + 5.73810i) q^{58} +(11.9042 + 6.87289i) q^{59} +(-5.09458 - 8.82407i) q^{61} +(2.36736 - 3.13266i) q^{62} +(-5.90098 - 5.40171i) q^{64} +(-3.13100 + 1.80768i) q^{65} +(5.01037 + 2.89274i) q^{67} +(2.17962 - 2.24473i) q^{68} +(-2.73293 + 3.37087i) q^{70} +4.72781i q^{71} +(-14.0619 - 8.11863i) q^{73} +(-3.15685 - 7.46547i) q^{74} +(-2.34829 - 8.27492i) q^{76} +(-7.48627 - 0.255528i) q^{77} +(2.89324 + 5.01124i) q^{79} +(-4.63716 + 0.136508i) q^{80} +(0.382388 - 3.07943i) q^{82} +5.93150i q^{83} -1.81439i q^{85} +(9.16411 + 1.13795i) q^{86} +(-5.01388 - 6.24390i) q^{88} +(-1.33902 - 2.31925i) q^{89} +(3.87769 + 7.27904i) q^{91} +(-9.01515 + 2.55836i) q^{92} +(-13.9271 + 5.88919i) q^{94} +(-4.31980 - 2.49404i) q^{95} -11.2024i q^{97} +(7.47257 + 6.49312i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 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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