LMFDB - Embedded newform 504.2.ch.b.269.25

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			269.25
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.25

$q$-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	−0.258301	−	0.966065i	$-0.583163\pi$
$5$	1.00441	−	0.579896i	0.449185	−	0.259337i	0.707486	+	0.706727i	$0.249829\pi$
$6$		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	−0.569770	−	0.821804i	$-0.692968\pi$
$11$	1.41560	−	2.45188i	0.426818	−	0.739271i	0.996588	+	0.0825332i	$0.0263011\pi$
$12$		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	−0.945154	−	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	0.506631	−	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	−0.0132237	−	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
$26$	−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	$-0.376056\pi$
$29$	4.08861			0.759235			0.379618	+	0.925143i	$0.376056\pi$
$30$		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	$-0.445191\pi$
$41$	2.19421			0.342678			0.171339	+	0.985212i	$0.445191\pi$
$42$		0			0
$43$		−	6.52977i		−	0.995781i	−0.867240	−	0.497891i	$-0.834108\pi$
$43$		−	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	$-0.881983\pi$
$47$	−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
$52$	−4.34312	−	4.47285i	−0.602282	−	0.620273i
$53$	5.61902	−	9.73242i	0.771831	−	1.33685i	−0.164727	−	0.986339i	$-0.552674\pi$
$53$	5.61902	−	9.73242i	0.771831	−	1.33685i	0.936558	−	0.350512i	$-0.113992\pi$
$54$		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	$-0.980670\pi$
$59$	−11.9042	−	6.87289i	−1.54980	−	0.894775i	−0.551638	−	0.834083i	$-0.685997\pi$
$60$		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	$0.0905149\pi$
$71$			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	$-0.732469\pi$
$74$	−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	$-0.894456\pi$
$83$		−	5.93150i		−	0.651066i	0.945531	−	0.325533i	$-0.105544\pi$
$84$		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	0.786290	−	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
$94$	−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	0.476270	−	0.879299i	$-0.341989\pi$
$101$	−0.473259	−	0.273236i	−0.0470911	−	0.0271880i	−0.523361	+	0.852111i	$0.675322\pi$
$102$		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	0.926569	−	0.376125i	$-0.122744\pi$
$107$	1.42284	+	2.46443i	0.137551	+	0.238246i	−0.789018	+	0.614370i	$0.789410\pi$
$108$		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	$0.227277\pi$
$113$			13.9228i			1.30974i	−0.755741	+	0.654871i	$0.772723\pi$
$114$		0			0
$115$	2.71714	−	4.70623i	0.253375	−	0.438858i
$116$	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	−0.885006	−	0.465579i	$-0.845846\pi$
$131$	−10.5792	+	6.10788i	−0.924306	+	0.533648i	−0.0392997	+	0.999227i	$0.512513\pi$
$132$		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	0.0898684	−	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	$-0.230874\pi$
$139$	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	0.993700	−	0.112071i	$-0.0357484\pi$
$149$	4.88010	+	8.45259i	0.399794	+	0.692463i	−0.593906	+	0.804534i	$0.702415\pi$
$150$		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	$-0.282826\pi$
$167$	16.2972			1.26112			0.630559	+	0.776142i	$0.282826\pi$
$168$		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	−0.499087	−	0.866552i	$-0.666331\pi$
$173$	0.0240052	−	0.0138594i	0.00182508	−	0.00105371i	0.500912	+	0.865498i	$0.332998\pi$
$174$		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	−0.941562	−	0.336841i	$-0.890642\pi$
$179$	−2.39577	+	4.14959i	−0.179068	+	0.310155i	0.762493	+	0.646996i	$0.223975\pi$
$180$		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	0.000629171	−	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	$0.215076\pi$
$194$	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	$-0.834296\pi$
$197$	−24.3528			−1.73507			−0.867534	+	0.497378i	$0.834296\pi$
$198$		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	−0.140641	−	0.990061i	$-0.544916\pi$
$227$	−16.0967	−	9.29346i	−1.06838	−	0.616829i	−0.927738	+	0.373232i	$0.878250\pi$
$228$		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	0.385987	−	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
$236$	−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	$-0.975741\pi$
$239$		−	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	$0.528734\pi$
$242$	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	$0.274293\pi$
$251$			24.0484i			1.51792i	−0.651136	+	0.758961i	$0.725707\pi$
$252$		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	0.995890	−	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
$262$	−17.1440	+	2.12886i	−1.05916	+	0.131521i
$263$	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
$266$	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	−0.00594471	−	0.999982i	$-0.501892\pi$
$269$	−14.3499	−	8.28490i	−0.874927	−	0.505139i	−0.868982	+	0.494843i	$0.835226\pi$
$270$		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	$-0.685662\pi$
$281$		−	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	$0.361958\pi$
$283$	−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	$0.253173\pi$
$293$			24.4475i			1.42824i	−0.700024	+	0.714119i	$0.746827\pi$
$294$		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	−0.873748	−	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	0.987275	−	0.159022i	$-0.0508340\pi$
$317$	6.33699	+	10.9760i	0.355921	+	0.616472i	−0.631355	+	0.775494i	$0.717501\pi$
$318$		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	$-0.478641\pi$
$347$	16.7205	−	28.9607i	0.897602	−	1.55469i	0.830551	−	0.556943i	$-0.188026\pi$
$348$		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	$0.432506\pi$
$353$	−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
$362$	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	$0.160097\pi$
$383$	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
$388$	16.0740	−	15.6078i	0.816033	−	0.792365i
$389$	11.7772	−	20.3988i	0.597130	−	1.03426i	−0.396113	−	0.918202i	$-0.629641\pi$
$389$	11.7772	−	20.3988i	0.597130	−	1.03426i	0.993243	−	0.116057i	$-0.0370256\pi$
$390$		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	−0.734251	−	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
$404$	−0.267311	−	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	$-0.932349\pi$
$419$		−	8.63546i		−	0.421870i	0.977500	−	0.210935i	$-0.0676508\pi$
$420$		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	0.315290	−	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	$-0.0587424\pi$
$434$	−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	$-0.992767\pi$
$443$	−10.9352	−	18.9404i	−0.519549	−	0.899885i	0.480193	−	0.877163i	$-0.340567\pi$
$444$		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	$-0.871434\pi$
$449$		−	16.6555i		−	0.786020i	0.919534	−	0.393010i	$-0.128566\pi$
$450$		0			0
$451$	3.10612	−	5.37995i	0.146261	−	0.253332i
$452$	−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	$0.262457\pi$
$461$			31.5292i			1.46846i	−0.678901	+	0.734230i	$0.737543\pi$
$462$		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	−0.246195	−	0.969220i	$-0.579180\pi$
$467$	10.1585	−	5.86499i	0.470077	−	0.271399i	0.716272	+	0.697821i	$0.245847\pi$
$468$		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	−0.859109	−	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	$0.322806\pi$
$488$	−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	$-0.330965\pi$
$491$	22.4435			1.01286			0.506430	+	0.862281i	$0.330965\pi$
$492$		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	$-0.521894\pi$
$503$	−3.08281			−0.137456			−0.0687278	+	0.997635i	$0.521894\pi$
$504$		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	−0.585843	−	0.810425i	$-0.699236\pi$
$509$	−3.99141	+	2.30444i	−0.176916	+	0.102143i	0.408927	+	0.912567i	$0.365903\pi$
$510$		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	$-0.513799\pi$
$521$	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	$-0.845761\pi$
$523$	−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	−0.521335	−	0.853352i	$-0.674566\pi$
$557$	11.2896	−	19.5542i	0.478357	−	0.828538i	0.999692	+	0.0248137i	$0.00789926\pi$
$558$		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	0.125593	−	0.992082i	$-0.459917\pi$
$563$	−15.9160	−	9.18909i	−0.670778	−	0.387274i	−0.796371	+	0.604808i	$0.793250\pi$
$564$		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	0.450056	−	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	$-0.765388\pi$
$587$		−	32.5679i		−	1.34422i	0.740451	−	0.672110i	$-0.234612\pi$
$588$		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	$0.0498359\pi$
$593$	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
$598$	−20.4987	+	2.54542i	−0.838255	+	0.104090i
$599$	−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	$0.962690\pi$
$602$	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	$-0.765351\pi$
$617$		−	33.3940i		−	1.34439i	0.740373	−	0.672196i	$-0.234649\pi$
$618$		0			0
$619$	0.347094	−	0.601184i	0.0139509	−	0.0241636i	−0.858966	−	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	0.852862	−	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	$-0.549329\pi$
$643$	−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	−0.655163	−	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	0.600576	−	0.799568i	$-0.294938\pi$
$653$	−10.0211	−	17.3571i	−0.392158	−	0.679237i	−0.992734	+	0.120331i	$0.961605\pi$
$654$		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	$-0.465588\pi$
$659$	5.53973			0.215797			0.107899	+	0.994162i	$0.465588\pi$
$660$		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	−0.289405	−	0.957207i	$-0.593457\pi$
$677$	10.2739	−	5.93164i	0.394858	−	0.227971i	0.684263	+	0.729235i	$0.260124\pi$
$678$		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	−0.974236	−	0.225530i	$-0.927589\pi$
$683$	−7.62606	+	13.2087i	−0.291803	+	0.505418i	0.682433	+	0.730948i	$0.260922\pi$
$684$		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	$-0.529265\pi$
$701$	−4.86157			−0.183619			−0.0918096	+	0.995777i	$0.529265\pi$
$702$		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	0.607806	−	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
$724$	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	$0.189306\pi$
$743$			30.5441i			1.12056i	−0.828305	+	0.560278i	$0.810694\pi$
$744$		0			0
$745$	9.80324	+	5.65990i	0.359163	+	0.207363i
$746$	−0.955434	+	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	0.702620	−	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
$766$	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	0.779765	−	0.626073i	$-0.215339\pi$
$773$	17.4450	+	10.0719i	0.627452	+	0.362259i	−0.152313	+	0.988332i	$0.548672\pi$
$774$		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	$0.0916468\pi$
$797$			16.0328i			0.567911i	−0.958838	+	0.283955i	$0.908353\pi$
$798$		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	0.795400	−	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	$-0.247521\pi$
$811$	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	$0.111556\pi$
$821$	21.9753	+	38.0623i	0.766942	+	1.32838i	−0.172272	+	0.985049i	$0.555111\pi$
$822$		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	$-0.459168\pi$
$827$	7.35761			0.255849			0.127925	+	0.991784i	$0.459168\pi$
$828$		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	$-0.161417\pi$
$839$	50.6405			1.74831			0.874153	+	0.485651i	$0.161417\pi$
$840$		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	$-0.634377\pi$
$857$	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	0.738649	−	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	−0.967940	−	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
$866$	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	$-0.425544\pi$
$881$	13.7595			0.463569			0.231785	+	0.972767i	$0.425544\pi$
$882$		0			0
$883$			31.7680i			1.06908i	0.845144	+	0.534539i	$0.179515\pi$
$883$			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	0.666965	−	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
$892$	−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	$-0.808790\pi$
$911$		−	34.1200i		−	1.13044i	0.824939	−	0.565222i	$-0.191210\pi$
$912$		0			0
$913$	−14.5433	−	8.39660i	−0.481314	−	0.277887i
$914$	−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	$0.243182\pi$
$929$	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
$934$	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	$0.0152390\pi$
$941$	47.2322	+	27.2695i	1.53973	+	0.888961i	0.540872	+	0.841105i	$0.318094\pi$
$942$		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	$-0.719156\pi$
$947$	−30.3559	−	52.5780i	−0.986435	−	1.70856i	−0.351056	−	0.936355i	$-0.614177\pi$
$948$		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	$-0.919822\pi$
$953$		−	15.3879i		−	0.498463i	0.968444	−	0.249232i	$-0.0801781\pi$
$954$		0			0
$955$	8.02305	−	13.8963i	0.259620	−	0.449675i
$956$	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	−0.926689	−	0.375830i	$-0.877358\pi$
$971$	−33.1725	+	19.1521i	−1.06456	+	0.614621i	−0.137866	+	0.990451i	$0.544024\pi$
$972$		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	0.155801	−	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
$980$	−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	−0.549550	−	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	$-0.0248543\pi$
$992$	−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.269.25	yes	56
3.2	odd	2	inner	504.2.ch.b.269.4	✓	56
4.3	odd	2		2016.2.cp.b.17.19		56
7.5	odd	6	inner	504.2.ch.b.341.13	yes	56
8.3	odd	2		2016.2.cp.b.17.10		56
8.5	even	2	inner	504.2.ch.b.269.16	yes	56
12.11	even	2		2016.2.cp.b.17.9		56
21.5	even	6	inner	504.2.ch.b.341.16	yes	56
24.5	odd	2	inner	504.2.ch.b.269.13	yes	56
24.11	even	2		2016.2.cp.b.17.20		56
28.19	even	6		2016.2.cp.b.593.20		56
56.5	odd	6	inner	504.2.ch.b.341.4	yes	56
56.19	even	6		2016.2.cp.b.593.9		56
84.47	odd	6		2016.2.cp.b.593.10		56
168.5	even	6	inner	504.2.ch.b.341.25	yes	56
168.131	odd	6		2016.2.cp.b.593.19		56

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

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