LMFDB - Embedded newform 882.3.s.d.557.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,3,Mod(557,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.557"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	882.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,4,0,0,0,0,0,12,0,0,-32,0,0,-8,0,0,-32,0,0,-96,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(25)] == traces)

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

Self dual:	no
Analytic conductor:	$24.0327593166$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.557
Dual form			882.3.s.d.863.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 - 2.12132i) q^{5} -2.82843i q^{8} +(3.00000 - 5.19615i) q^{10} +(-14.6969 - 8.48528i) q^{11} -8.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-11.0227 - 6.36396i) q^{17} +(-8.00000 - 13.8564i) q^{19} -8.48528i q^{20} -24.0000 q^{22} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(-9.79796 + 5.65685i) q^{26} +4.24264i q^{29} +(22.0000 - 38.1051i) q^{31} +(-4.89898 - 2.82843i) q^{32} -18.0000 q^{34} +(17.0000 + 29.4449i) q^{37} +(-19.5959 - 11.3137i) q^{38} +(-6.00000 - 10.3923i) q^{40} -46.6690i q^{41} -40.0000 q^{43} +(-29.3939 + 16.9706i) q^{44} +(-12.0000 + 20.7846i) q^{46} +(73.4847 - 42.4264i) q^{47} +9.89949i q^{50} +(-8.00000 + 13.8564i) q^{52} +(-33.0681 - 19.0919i) q^{53} -72.0000 q^{55} +(3.00000 + 5.19615i) q^{58} +(29.3939 + 16.9706i) q^{59} +(25.0000 + 43.3013i) q^{61} -62.2254i q^{62} -8.00000 q^{64} +(-29.3939 + 16.9706i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-22.0454 + 12.7279i) q^{68} -50.9117i q^{71} +(-8.00000 + 13.8564i) q^{73} +(41.6413 + 24.0416i) q^{74} -32.0000 q^{76} +(38.0000 + 65.8179i) q^{79} +(-14.6969 - 8.48528i) q^{80} +(-33.0000 - 57.1577i) q^{82} -118.794i q^{83} -54.0000 q^{85} +(-48.9898 + 28.2843i) q^{86} +(-24.0000 + 41.5692i) q^{88} +(-11.0227 + 6.36396i) q^{89} +33.9411i q^{92} +(60.0000 - 103.923i) q^{94} +(-58.7878 - 33.9411i) q^{95} -176.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 12 q^{10} - 32 q^{13} - 8 q^{16} - 32 q^{19} - 96 q^{22} - 14 q^{25} + 88 q^{31} - 72 q^{34} + 68 q^{37} - 24 q^{40} - 160 q^{43} - 48 q^{46} - 32 q^{52} - 288 q^{55} + 12 q^{58} + 100 q^{61}+ \cdots - 704 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 + 12 * q^10 - 32 * q^13 - 8 * q^16 - 32 * q^19 - 96 * q^22 - 14 * q^25 + 88 * q^31 - 72 * q^34 + 68 * q^37 - 24 * q^40 - 160 * q^43 - 48 * q^46 - 32 * q^52 - 288 * q^55 + 12 * q^58 + 100 * q^61 - 32 * q^64 - 16 * q^67 - 32 * q^73 - 128 * q^76 + 152 * q^79 - 132 * q^82 - 216 * q^85 - 96 * q^88 + 240 * q^94 - 704 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	3.67423	−	2.12132i	0.734847	−	0.424264i	−0.0853458	−	0.996351i	$-0.527199\pi$
$5$	3.67423	−	2.12132i	0.734847	−	0.424264i	0.820193	+	0.572087i	$0.193866\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	3.00000	−	5.19615i	0.300000	−	0.519615i
$11$	−14.6969	−	8.48528i	−1.33609	−	0.771389i	−0.349861	−	0.936802i	$-0.613771\pi$
$11$	−14.6969	−	8.48528i	−1.33609	−	0.771389i	−0.986224	+	0.165412i	$0.947104\pi$
$12$		0			0
$13$	−8.00000			−0.615385			−0.307692	−	0.951486i	$-0.599557\pi$
$13$	−8.00000			−0.615385			−0.307692	+	0.951486i	$0.599557\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−11.0227	−	6.36396i	−0.648394	−	0.374351i	0.139446	−	0.990230i	$-0.455468\pi$
$17$	−11.0227	−	6.36396i	−0.648394	−	0.374351i	−0.787841	+	0.615879i	$0.788801\pi$
$18$		0			0
$19$	−8.00000	−	13.8564i	−0.421053	−	0.729285i	0.574990	−	0.818160i	$-0.305006\pi$
$19$	−8.00000	−	13.8564i	−0.421053	−	0.729285i	−0.996043	+	0.0888758i	$0.971673\pi$
$20$		−	8.48528i		−	0.424264i
$21$		0			0
$22$	−24.0000			−1.09091
$23$	−14.6969	+	8.48528i	−0.638997	+	0.368925i	−0.784228	−	0.620473i	$-0.786941\pi$
$23$	−14.6969	+	8.48528i	−0.638997	+	0.368925i	0.145231	+	0.989398i	$0.453608\pi$
$24$		0			0
$25$	−3.50000	+	6.06218i	−0.140000	+	0.242487i
$26$	−9.79796	+	5.65685i	−0.376845	+	0.217571i
$27$		0			0
$28$		0			0
$29$			4.24264i			0.146298i	0.997321	+	0.0731490i	$0.0233049\pi$
$29$			4.24264i			0.146298i	−0.997321	+	0.0731490i	$0.976695\pi$
$30$		0			0
$31$	22.0000	−	38.1051i	0.709677	−	1.22920i	−0.255299	−	0.966862i	$-0.582174\pi$
$31$	22.0000	−	38.1051i	0.709677	−	1.22920i	0.964977	−	0.262335i	$-0.0844926\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−18.0000			−0.529412
$35$		0			0
$36$		0			0
$37$	17.0000	+	29.4449i	0.459459	+	0.795807i	0.998932	−	0.0461958i	$-0.0147098\pi$
$37$	17.0000	+	29.4449i	0.459459	+	0.795807i	−0.539473	+	0.842003i	$0.681376\pi$
$38$	−19.5959	−	11.3137i	−0.515682	−	0.297729i
$39$		0			0
$40$	−6.00000	−	10.3923i	−0.150000	−	0.259808i
$41$		−	46.6690i		−	1.13827i	−0.822244	−	0.569135i	$-0.807278\pi$
$41$		−	46.6690i		−	1.13827i	0.822244	−	0.569135i	$-0.192722\pi$
$42$		0			0
$43$	−40.0000			−0.930233			−0.465116	−	0.885250i	$-0.653987\pi$
$43$	−40.0000			−0.930233			−0.465116	+	0.885250i	$0.653987\pi$
$44$	−29.3939	+	16.9706i	−0.668043	+	0.385695i
$45$		0			0
$46$	−12.0000	+	20.7846i	−0.260870	+	0.451839i
$47$	73.4847	−	42.4264i	1.56350	−	0.902690i	0.566606	−	0.823989i	$-0.308256\pi$
$47$	73.4847	−	42.4264i	1.56350	−	0.902690i	0.996898	−	0.0787005i	$-0.0250771\pi$
$48$		0			0
$49$		0			0
$50$			9.89949i			0.197990i
$51$		0			0
$52$	−8.00000	+	13.8564i	−0.153846	+	0.266469i
$53$	−33.0681	−	19.0919i	−0.623927	−	0.360224i	0.154470	−	0.987998i	$-0.450633\pi$
$53$	−33.0681	−	19.0919i	−0.623927	−	0.360224i	−0.778396	+	0.627773i	$0.783966\pi$
$54$		0			0
$55$	−72.0000			−1.30909
$56$		0			0
$57$		0			0
$58$	3.00000	+	5.19615i	0.0517241	+	0.0895888i
$59$	29.3939	+	16.9706i	0.498201	+	0.287637i	0.727970	−	0.685609i	$-0.240464\pi$
$59$	29.3939	+	16.9706i	0.498201	+	0.287637i	−0.229769	+	0.973245i	$0.573797\pi$
$60$		0			0
$61$	25.0000	+	43.3013i	0.409836	+	0.709857i	0.994871	−	0.101151i	$-0.0322526\pi$
$61$	25.0000	+	43.3013i	0.409836	+	0.709857i	−0.585035	+	0.811008i	$0.698919\pi$
$62$		−	62.2254i		−	1.00364i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−29.3939	+	16.9706i	−0.452213	+	0.261086i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.0597015	+	0.103406i	−0.894331	−	0.447405i	$-0.852348\pi$
$67$	−4.00000	+	6.92820i	−0.0597015	+	0.103406i	0.834630	+	0.550811i	$0.185682\pi$
$68$	−22.0454	+	12.7279i	−0.324197	+	0.187175i
$69$		0			0
$70$		0			0
$71$		−	50.9117i		−	0.717066i	−0.933517	−	0.358533i	$-0.883277\pi$
$71$		−	50.9117i		−	0.717066i	0.933517	−	0.358533i	$-0.116723\pi$
$72$		0			0
$73$	−8.00000	+	13.8564i	−0.109589	+	0.189814i	−0.915604	−	0.402082i	$-0.868287\pi$
$73$	−8.00000	+	13.8564i	−0.109589	+	0.189814i	0.806015	+	0.591895i	$0.201620\pi$
$74$	41.6413	+	24.0416i	0.562721	+	0.324887i
$75$		0			0
$76$	−32.0000			−0.421053
$77$		0			0
$78$		0			0
$79$	38.0000	+	65.8179i	0.481013	+	0.833138i	0.999763	−	0.0217876i	$-0.00693577\pi$
$79$	38.0000	+	65.8179i	0.481013	+	0.833138i	−0.518750	+	0.854926i	$0.673602\pi$
$80$	−14.6969	−	8.48528i	−0.183712	−	0.106066i
$81$		0			0
$82$	−33.0000	−	57.1577i	−0.402439	−	0.697045i
$83$		−	118.794i		−	1.43125i	−0.698484	−	0.715626i	$-0.746141\pi$
$83$		−	118.794i		−	1.43125i	0.698484	−	0.715626i	$-0.253859\pi$
$84$		0			0
$85$	−54.0000			−0.635294
$86$	−48.9898	+	28.2843i	−0.569649	+	0.328887i
$87$		0			0
$88$	−24.0000	+	41.5692i	−0.272727	+	0.472377i
$89$	−11.0227	+	6.36396i	−0.123851	+	0.0715052i	−0.560645	−	0.828056i	$-0.689447\pi$
$89$	−11.0227	+	6.36396i	−0.123851	+	0.0715052i	0.436795	+	0.899561i	$0.356114\pi$
$90$		0			0
$91$		0			0
$92$			33.9411i			0.368925i
$93$		0			0
$94$	60.0000	−	103.923i	0.638298	−	1.10556i
$95$	−58.7878	−	33.9411i	−0.618818	−	0.357275i
$96$		0			0
$97$	−176.000			−1.81443			−0.907216	−	0.420664i	$-0.861797\pi$
$97$	−176.000			−1.81443			−0.907216	+	0.420664i	$0.861797\pi$
$98$		0			0
$99$		0			0
$100$	7.00000	+	12.1244i	0.0700000	+	0.121244i
$101$	25.7196	+	14.8492i	0.254650	+	0.147022i	0.621892	−	0.783103i	$-0.286364\pi$
$101$	25.7196	+	14.8492i	0.254650	+	0.147022i	−0.367242	+	0.930126i	$0.619698\pi$
$102$		0			0
$103$	−14.0000	−	24.2487i	−0.135922	−	0.235424i	0.790027	−	0.613072i	$-0.210066\pi$
$103$	−14.0000	−	24.2487i	−0.135922	−	0.235424i	−0.925949	+	0.377648i	$0.876733\pi$
$104$			22.6274i			0.217571i
$105$		0			0
$106$	−54.0000			−0.509434
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$		0			0
$109$	−28.0000	+	48.4974i	−0.256881	+	0.444930i	−0.965405	−	0.260756i	$-0.916028\pi$
$109$	−28.0000	+	48.4974i	−0.256881	+	0.444930i	0.708524	+	0.705687i	$0.249361\pi$
$110$	−88.1816	+	50.9117i	−0.801651	+	0.462834i
$111$		0			0
$112$		0			0
$113$		−	156.978i		−	1.38918i	−0.719404	−	0.694592i	$-0.755585\pi$
$113$		−	156.978i		−	1.38918i	0.719404	−	0.694592i	$-0.244415\pi$
$114$		0			0
$115$	−36.0000	+	62.3538i	−0.313043	+	0.542207i
$116$	7.34847	+	4.24264i	0.0633489	+	0.0365745i
$117$		0			0
$118$	48.0000			0.406780
$119$		0			0
$120$		0			0
$121$	83.5000	+	144.626i	0.690083	+	1.19526i
$122$	61.2372	+	35.3553i	0.501945	+	0.289798i
$123$		0			0
$124$	−44.0000	−	76.2102i	−0.354839	−	0.614599i
$125$			135.765i			1.08612i
$126$		0			0
$127$	92.0000			0.724409			0.362205	−	0.932099i	$-0.382024\pi$
$127$	92.0000			0.724409			0.362205	+	0.932099i	$0.382024\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−24.0000	+	41.5692i	−0.184615	+	0.319763i
$131$	146.969	−	84.8528i	1.12190	−	0.647731i	0.180017	−	0.983663i	$-0.442385\pi$
$131$	146.969	−	84.8528i	1.12190	−	0.647731i	0.941886	+	0.335932i	$0.109051\pi$
$132$		0			0
$133$		0			0
$134$			11.3137i			0.0844307i
$135$		0			0
$136$	−18.0000	+	31.1769i	−0.132353	+	0.229242i
$137$	−135.947	−	78.4889i	−0.992312	−	0.572911i	−0.0863471	−	0.996265i	$-0.527519\pi$
$137$	−135.947	−	78.4889i	−0.992312	−	0.572911i	−0.905964	+	0.423354i	$0.860853\pi$
$138$		0			0
$139$	−152.000			−1.09353			−0.546763	−	0.837288i	$-0.684140\pi$
$139$	−152.000			−1.09353			−0.546763	+	0.837288i	$0.684140\pi$
$140$		0			0
$141$		0			0
$142$	−36.0000	−	62.3538i	−0.253521	−	0.439111i
$143$	117.576	+	67.8823i	0.822206	+	0.474701i
$144$		0			0
$145$	9.00000	+	15.5885i	0.0620690	+	0.107507i
$146$			22.6274i			0.154982i
$147$		0			0
$148$	68.0000			0.459459
$149$	238.825	−	137.886i	1.60285	−	0.925408i	0.611941	−	0.790903i	$-0.290389\pi$
$149$	238.825	−	137.886i	1.60285	−	0.925408i	0.990913	−	0.134505i	$-0.0429444\pi$
$150$		0			0
$151$	74.0000	−	128.172i	0.490066	−	0.848820i	−0.509868	−	0.860252i	$-0.670306\pi$
$151$	74.0000	−	128.172i	0.490066	−	0.848820i	0.999935	+	0.0114328i	$0.00363925\pi$
$152$	−39.1918	+	22.6274i	−0.257841	+	0.148865i
$153$		0			0
$154$		0			0
$155$		−	186.676i		−	1.20436i
$156$		0			0
$157$	−41.0000	+	71.0141i	−0.261146	+	0.452319i	−0.966547	−	0.256490i	$-0.917434\pi$
$157$	−41.0000	+	71.0141i	−0.261146	+	0.452319i	0.705400	+	0.708809i	$0.250767\pi$
$158$	93.0806	+	53.7401i	0.589118	+	0.340127i
$159$		0			0
$160$	−24.0000			−0.150000
$161$		0			0
$162$		0			0
$163$	−28.0000	−	48.4974i	−0.171779	−	0.297530i	0.767263	−	0.641333i	$-0.221618\pi$
$163$	−28.0000	−	48.4974i	−0.171779	−	0.297530i	−0.939042	+	0.343803i	$0.888285\pi$
$164$	−80.8332	−	46.6690i	−0.492885	−	0.284567i
$165$		0			0
$166$	−84.0000	−	145.492i	−0.506024	−	0.876459i
$167$		−	33.9411i		−	0.203240i	−0.994823	−	0.101620i	$-0.967597\pi$
$167$		−	33.9411i		−	0.203240i	0.994823	−	0.101620i	$-0.0324026\pi$
$168$		0			0
$169$	−105.000			−0.621302
$170$	−66.1362	+	38.1838i	−0.389037	+	0.224610i
$171$		0			0
$172$	−40.0000	+	69.2820i	−0.232558	+	0.402803i
$173$	150.644	−	86.9741i	0.870772	−	0.502741i	0.00316754	−	0.999995i	$-0.498992\pi$
$173$	150.644	−	86.9741i	0.870772	−	0.502741i	0.867605	+	0.497254i	$0.165658\pi$
$174$		0			0
$175$		0			0
$176$			67.8823i			0.385695i
$177$		0			0
$178$	−9.00000	+	15.5885i	−0.0505618	+	0.0875756i
$179$	176.363	+	101.823i	0.985270	+	0.568846i	0.903857	−	0.427835i	$-0.140723\pi$
$179$	176.363	+	101.823i	0.985270	+	0.568846i	0.0814127	+	0.996680i	$0.474057\pi$
$180$		0			0
$181$	232.000			1.28177			0.640884	−	0.767638i	$-0.278568\pi$
$181$	232.000			1.28177			0.640884	+	0.767638i	$0.278568\pi$
$182$		0			0
$183$		0			0
$184$	24.0000	+	41.5692i	0.130435	+	0.225920i
$185$	124.924	+	72.1249i	0.675265	+	0.389864i
$186$		0			0
$187$	108.000	+	187.061i	0.577540	+	1.00033i
$188$		−	169.706i		−	0.902690i
$189$		0			0
$190$	−96.0000			−0.505263
$191$	−29.3939	+	16.9706i	−0.153895	+	0.0888511i	−0.574970	−	0.818175i	$-0.694986\pi$
$191$	−29.3939	+	16.9706i	−0.153895	+	0.0888511i	0.421075	+	0.907026i	$0.361653\pi$
$192$		0			0
$193$	−103.000	+	178.401i	−0.533679	+	0.924359i	0.465547	+	0.885023i	$0.345858\pi$
$193$	−103.000	+	178.401i	−0.533679	+	0.924359i	−0.999226	+	0.0393357i	$0.987476\pi$
$194$	−215.555	+	124.451i	−1.11111	+	0.641499i
$195$		0			0
$196$		0			0
$197$			165.463i			0.839914i	0.907544	+	0.419957i	$0.137955\pi$
$197$			165.463i			0.839914i	−0.907544	+	0.419957i	$0.862045\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.0502513	−	0.0870377i	−0.839806	−	0.542887i	$-0.817331\pi$
$199$	10.0000	−	17.3205i	0.0502513	−	0.0870377i	0.890057	+	0.455849i	$0.150664\pi$
$200$	17.1464	+	9.89949i	0.0857321	+	0.0494975i
$201$		0			0
$202$	42.0000			0.207921
$203$		0			0
$204$		0			0
$205$	−99.0000	−	171.473i	−0.482927	−	0.836454i
$206$	−34.2929	−	19.7990i	−0.166470	−	0.0961116i
$207$		0			0
$208$	16.0000	+	27.7128i	0.0769231	+	0.133235i
$209$			271.529i			1.29918i
$210$		0			0
$211$	296.000			1.40284			0.701422	−	0.712746i	$-0.252549\pi$
$211$	296.000			1.40284			0.701422	+	0.712746i	$0.252549\pi$
$212$	−66.1362	+	38.1838i	−0.311963	+	0.180112i
$213$		0			0
$214$		0			0
$215$	−146.969	+	84.8528i	−0.683579	+	0.394664i
$216$		0			0
$217$		0			0
$218$			79.1960i			0.363284i
$219$		0			0
$220$	−72.0000	+	124.708i	−0.327273	+	0.566853i
$221$	88.1816	+	50.9117i	0.399012	+	0.230370i
$222$		0			0
$223$	436.000			1.95516			0.977578	−	0.210571i	$-0.0675325\pi$
$223$	436.000			1.95516			0.977578	+	0.210571i	$0.0675325\pi$
$224$		0			0
$225$		0			0
$226$	−111.000	−	192.258i	−0.491150	−	0.850698i
$227$	14.6969	+	8.48528i	0.0647442	+	0.0373801i	0.532023	−	0.846730i	$-0.321432\pi$
$227$	14.6969	+	8.48528i	0.0647442	+	0.0373801i	−0.467278	+	0.884110i	$0.654765\pi$
$228$		0			0
$229$	4.00000	+	6.92820i	0.0174672	+	0.0302542i	0.874627	−	0.484797i	$-0.161106\pi$
$229$	4.00000	+	6.92820i	0.0174672	+	0.0302542i	−0.857160	+	0.515051i	$0.827773\pi$
$230$			101.823i			0.442710i
$231$		0			0
$232$	12.0000			0.0517241
$233$	−11.0227	+	6.36396i	−0.0473077	+	0.0273131i	−0.523467	−	0.852046i	$-0.675362\pi$
$233$	−11.0227	+	6.36396i	−0.0473077	+	0.0273131i	0.476160	+	0.879359i	$0.342028\pi$
$234$		0			0
$235$	180.000	−	311.769i	0.765957	−	1.32668i
$236$	58.7878	−	33.9411i	0.249101	−	0.143818i
$237$		0			0
$238$		0			0
$239$			135.765i			0.568052i	0.958817	+	0.284026i	$0.0916703\pi$
$239$			135.765i			0.568052i	−0.958817	+	0.284026i	$0.908330\pi$
$240$		0			0
$241$	16.0000	−	27.7128i	0.0663900	−	0.114991i	−0.830920	−	0.556392i	$-0.812185\pi$
$241$	16.0000	−	27.7128i	0.0663900	−	0.114991i	0.897310	+	0.441401i	$0.145519\pi$
$242$	204.532	+	118.087i	0.845175	+	0.487962i
$243$		0			0
$244$	100.000			0.409836
$245$		0			0
$246$		0			0
$247$	64.0000	+	110.851i	0.259109	+	0.448790i
$248$	−107.778	−	62.2254i	−0.434587	−	0.250909i
$249$		0			0
$250$	96.0000	+	166.277i	0.384000	+	0.665108i
$251$		−	50.9117i		−	0.202835i	−0.994844	−	0.101418i	$-0.967662\pi$
$251$		−	50.9117i		−	0.202835i	0.994844	−	0.101418i	$-0.0323379\pi$
$252$		0			0
$253$	288.000			1.13834
$254$	112.677	−	65.0538i	0.443608	−	0.256117i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	157.992	−	91.2168i	0.614755	−	0.354929i	−0.160069	−	0.987106i	$-0.551172\pi$
$257$	157.992	−	91.2168i	0.614755	−	0.354929i	0.774824	+	0.632177i	$0.217838\pi$
$258$		0			0
$259$		0			0
$260$			67.8823i			0.261086i
$261$		0			0
$262$	120.000	−	207.846i	0.458015	−	0.793306i
$263$	−323.333	−	186.676i	−1.22940	−	0.709795i	−0.262497	−	0.964933i	$-0.584546\pi$
$263$	−323.333	−	186.676i	−1.22940	−	0.709795i	−0.966905	+	0.255137i	$0.917879\pi$
$264$		0			0
$265$	−162.000			−0.611321
$266$		0			0
$267$		0			0
$268$	8.00000	+	13.8564i	0.0298507	+	0.0517030i
$269$	−297.613	−	171.827i	−1.10637	−	0.638762i	−0.168482	−	0.985705i	$-0.553886\pi$
$269$	−297.613	−	171.827i	−1.10637	−	0.638762i	−0.937886	+	0.346943i	$0.887220\pi$
$270$		0			0
$271$	190.000	+	329.090i	0.701107	+	1.21435i	0.968078	+	0.250648i	$0.0806438\pi$
$271$	190.000	+	329.090i	0.701107	+	1.21435i	−0.266971	+	0.963705i	$0.586023\pi$
$272$			50.9117i			0.187175i
$273$		0			0
$274$	−222.000			−0.810219
$275$	102.879	−	59.3970i	0.374104	−	0.215989i
$276$		0			0
$277$	164.000	−	284.056i	0.592058	−	1.02547i	−0.401897	−	0.915685i	$-0.631649\pi$
$277$	164.000	−	284.056i	0.592058	−	1.02547i	0.993955	−	0.109789i	$-0.0350176\pi$
$278$	−186.161	+	107.480i	−0.669645	+	0.386620i
$279$		0			0
$280$		0			0
$281$			284.257i			1.01159i	0.862654	+	0.505795i	$0.168801\pi$
$281$			284.257i			1.01159i	−0.862654	+	0.505795i	$0.831199\pi$
$282$		0			0
$283$	−104.000	+	180.133i	−0.367491	+	0.636513i	−0.989173	−	0.146757i	$-0.953117\pi$
$283$	−104.000	+	180.133i	−0.367491	+	0.636513i	0.621681	+	0.783270i	$0.286450\pi$
$284$	−88.1816	−	50.9117i	−0.310499	−	0.179267i
$285$		0			0
$286$	192.000			0.671329
$287$		0			0
$288$		0			0
$289$	−63.5000	−	109.985i	−0.219723	−	0.380572i
$290$	22.0454	+	12.7279i	0.0760186	+	0.0438894i
$291$		0			0
$292$	16.0000	+	27.7128i	0.0547945	+	0.0949069i
$293$			436.992i			1.49144i	0.666259	+	0.745720i	$0.267894\pi$
$293$			436.992i			1.49144i	−0.666259	+	0.745720i	$0.732106\pi$
$294$		0			0
$295$	144.000			0.488136
$296$	83.2827	−	48.0833i	0.281360	−	0.162443i
$297$		0			0
$298$	195.000	−	337.750i	0.654362	−	1.13339i
$299$	117.576	−	67.8823i	0.393229	−	0.227031i
$300$		0			0
$301$		0			0
$302$		−	209.304i		−	0.693058i
$303$		0			0
$304$	−32.0000	+	55.4256i	−0.105263	+	0.182321i
$305$	183.712	+	106.066i	0.602334	+	0.347757i
$306$		0			0
$307$	520.000			1.69381			0.846906	−	0.531743i	$-0.178463\pi$
$307$	520.000			1.69381			0.846906	+	0.531743i	$0.178463\pi$
$308$		0			0
$309$		0			0
$310$	−132.000	−	228.631i	−0.425806	−	0.737518i
$311$	−323.333	−	186.676i	−1.03965	−	0.600245i	−0.119919	−	0.992784i	$-0.538264\pi$
$311$	−323.333	−	186.676i	−1.03965	−	0.600245i	−0.919736	+	0.392539i	$0.871597\pi$
$312$		0			0
$313$	−47.0000	−	81.4064i	−0.150160	−	0.260084i	0.781126	−	0.624373i	$-0.214645\pi$
$313$	−47.0000	−	81.4064i	−0.150160	−	0.260084i	−0.931286	+	0.364289i	$0.881312\pi$
$314$			115.966i			0.369317i
$315$		0			0
$316$	152.000			0.481013
$317$	290.265	−	167.584i	0.915661	−	0.528657i	0.0334128	−	0.999442i	$-0.489362\pi$
$317$	290.265	−	167.584i	0.915661	−	0.528657i	0.882248	+	0.470785i	$0.156029\pi$
$318$		0			0
$319$	36.0000	−	62.3538i	0.112853	−	0.195467i
$320$	−29.3939	+	16.9706i	−0.0918559	+	0.0530330i
$321$		0			0
$322$		0			0
$323$			203.647i			0.630485i
$324$		0			0
$325$	28.0000	−	48.4974i	0.0861538	−	0.149223i
$326$	−68.5857	−	39.5980i	−0.210386	−	0.121466i
$327$		0			0
$328$	−132.000			−0.402439
$329$		0			0
$330$		0			0
$331$	−268.000	−	464.190i	−0.809668	−	1.40239i	−0.913094	−	0.407748i	$-0.866314\pi$
$331$	−268.000	−	464.190i	−0.809668	−	1.40239i	0.103427	−	0.994637i	$-0.467019\pi$
$332$	−205.757	−	118.794i	−0.619750	−	0.357813i
$333$		0			0
$334$	−24.0000	−	41.5692i	−0.0718563	−	0.124459i
$335$			33.9411i			0.101317i
$336$		0			0
$337$	−208.000			−0.617211			−0.308605	−	0.951190i	$-0.599862\pi$
$337$	−208.000			−0.617211			−0.308605	+	0.951190i	$0.599862\pi$
$338$	−128.598	+	74.2462i	−0.380468	+	0.219663i
$339$		0			0
$340$	−54.0000	+	93.5307i	−0.158824	+	0.275090i
$341$	−646.665	+	373.352i	−1.89638	+	1.09488i
$342$		0			0
$343$		0			0
$344$			113.137i			0.328887i
$345$		0			0
$346$	123.000	−	213.042i	0.355491	−	0.615729i
$347$	−249.848	−	144.250i	−0.720023	−	0.415705i	0.0947382	−	0.995502i	$-0.469799\pi$
$347$	−249.848	−	144.250i	−0.720023	−	0.415705i	−0.814761	+	0.579797i	$0.803132\pi$
$348$		0			0
$349$	238.000			0.681948			0.340974	−	0.940073i	$-0.389243\pi$
$349$	238.000			0.681948			0.340974	+	0.940073i	$0.389243\pi$
$350$		0			0
$351$		0			0
$352$	48.0000	+	83.1384i	0.136364	+	0.236189i
$353$	−194.734	−	112.430i	−0.551656	−	0.318499i	0.198134	−	0.980175i	$-0.436512\pi$
$353$	−194.734	−	112.430i	−0.551656	−	0.318499i	−0.749789	+	0.661676i	$0.769845\pi$
$354$		0			0
$355$	−108.000	−	187.061i	−0.304225	−	0.526934i
$356$			25.4558i			0.0715052i
$357$		0			0
$358$	288.000			0.804469
$359$	−484.999	+	280.014i	−1.35097	+	0.779984i	−0.988386	−	0.151966i	$-0.951440\pi$
$359$	−484.999	+	280.014i	−1.35097	+	0.779984i	−0.362586	+	0.931950i	$0.618106\pi$
$360$		0			0
$361$	52.5000	−	90.9327i	0.145429	−	0.251891i
$362$	284.141	−	164.049i	0.784919	−	0.453173i
$363$		0			0
$364$		0			0
$365$			67.8823i			0.185979i
$366$		0			0
$367$	142.000	−	245.951i	0.386921	−	0.670167i	−0.605113	−	0.796140i	$-0.706872\pi$
$367$	142.000	−	245.951i	0.386921	−	0.670167i	0.992034	+	0.125973i	$0.0402053\pi$
$368$	58.7878	+	33.9411i	0.159749	+	0.0922313i
$369$		0			0
$370$	204.000			0.551351
$371$		0			0
$372$		0			0
$373$	95.0000	+	164.545i	0.254692	+	0.441139i	0.964812	−	0.262942i	$-0.0846927\pi$
$373$	95.0000	+	164.545i	0.254692	+	0.441139i	−0.710120	+	0.704081i	$0.751359\pi$
$374$	264.545	+	152.735i	0.707339	+	0.408383i
$375$		0			0
$376$	−120.000	−	207.846i	−0.319149	−	0.552782i
$377$		−	33.9411i		−	0.0900295i
$378$		0			0
$379$	−160.000			−0.422164			−0.211082	−	0.977468i	$-0.567699\pi$
$379$	−160.000			−0.422164			−0.211082	+	0.977468i	$0.567699\pi$
$380$	−117.576	+	67.8823i	−0.309409	+	0.178638i
$381$		0			0
$382$	−24.0000	+	41.5692i	−0.0628272	+	0.108820i
$383$	235.151	−	135.765i	0.613971	−	0.354477i	−0.160547	−	0.987028i	$-0.551326\pi$
$383$	235.151	−	135.765i	0.613971	−	0.354477i	0.774518	+	0.632552i	$0.217992\pi$
$384$		0			0
$385$		0			0
$386$			291.328i			0.754736i
$387$		0			0
$388$	−176.000	+	304.841i	−0.453608	+	0.785673i
$389$	349.052	+	201.525i	0.897307	+	0.518060i	0.876325	−	0.481720i	$-0.159988\pi$
$389$	349.052	+	201.525i	0.897307	+	0.518060i	0.0209813	+	0.999780i	$0.493321\pi$
$390$		0			0
$391$	216.000			0.552430
$392$		0			0
$393$		0			0
$394$	117.000	+	202.650i	0.296954	+	0.514340i
$395$	279.242	+	161.220i	0.706941	+	0.408153i
$396$		0			0
$397$	73.0000	+	126.440i	0.183879	+	0.318488i	0.943198	−	0.332230i	$-0.107801\pi$
$397$	73.0000	+	126.440i	0.183879	+	0.318488i	−0.759319	+	0.650718i	$0.774468\pi$
$398$		−	28.2843i		−	0.0710660i
$399$		0			0
$400$	28.0000			0.0700000
$401$	282.916	−	163.342i	0.705526	−	0.407336i	−0.103876	−	0.994590i	$-0.533125\pi$
$401$	282.916	−	163.342i	0.705526	−	0.407336i	0.809402	+	0.587254i	$0.199791\pi$
$402$		0			0
$403$	−176.000	+	304.841i	−0.436725	+	0.756429i
$404$	51.4393	−	29.6985i	0.127325	−	0.0735111i
$405$		0			0
$406$		0			0
$407$		−	576.999i		−	1.41769i
$408$		0			0
$409$	184.000	−	318.697i	0.449878	−	0.779211i	−0.548500	−	0.836151i	$-0.684801\pi$
$409$	184.000	−	318.697i	0.449878	−	0.779211i	0.998378	+	0.0569395i	$0.0181342\pi$
$410$	−242.499	−	140.007i	−0.591462	−	0.341481i
$411$		0			0
$412$	−56.0000			−0.135922
$413$		0			0
$414$		0			0
$415$	−252.000	−	436.477i	−0.607229	−	1.05175i
$416$	39.1918	+	22.6274i	0.0942111	+	0.0543928i
$417$		0			0
$418$	192.000	+	332.554i	0.459330	+	0.795583i
$419$		−	390.323i		−	0.931558i	−0.884901	−	0.465779i	$-0.845774\pi$
$419$		−	390.323i		−	0.931558i	0.884901	−	0.465779i	$-0.154226\pi$
$420$		0			0
$421$	−40.0000			−0.0950119			−0.0475059	−	0.998871i	$-0.515127\pi$
$421$	−40.0000			−0.0950119			−0.0475059	+	0.998871i	$0.515127\pi$
$422$	362.524	−	209.304i	0.859063	−	0.495980i
$423$		0			0
$424$	−54.0000	+	93.5307i	−0.127358	+	0.220591i
$425$	77.1589	−	44.5477i	0.181550	−	0.104818i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−120.000	+	207.846i	−0.279070	+	0.483363i
$431$	132.272	+	76.3675i	0.306897	+	0.177187i	0.645537	−	0.763729i	$-0.276634\pi$
$431$	132.272	+	76.3675i	0.306897	+	0.177187i	−0.338640	+	0.940916i	$0.609967\pi$
$432$		0			0
$433$	−542.000			−1.25173			−0.625866	−	0.779931i	$-0.715254\pi$
$433$	−542.000			−1.25173			−0.625866	+	0.779931i	$0.715254\pi$
$434$		0			0
$435$		0			0
$436$	56.0000	+	96.9948i	0.128440	+	0.222465i
$437$	235.151	+	135.765i	0.538103	+	0.310674i
$438$		0			0
$439$	−2.00000	−	3.46410i	−0.00455581	−	0.00789089i	0.863739	−	0.503940i	$-0.168117\pi$
$439$	−2.00000	−	3.46410i	−0.00455581	−	0.00789089i	−0.868294	+	0.496049i	$0.834783\pi$
$440$			203.647i			0.462834i
$441$		0			0
$442$	144.000			0.325792
$443$	279.242	−	161.220i	0.630343	−	0.363929i	−0.150542	−	0.988604i	$-0.548102\pi$
$443$	279.242	−	161.220i	0.630343	−	0.363929i	0.780885	+	0.624675i	$0.214769\pi$
$444$		0			0
$445$	−27.0000	+	46.7654i	−0.0606742	+	0.105091i
$446$	533.989	−	308.299i	1.19728	−	0.691252i
$447$		0			0
$448$		0			0
$449$			216.375i			0.481904i	0.970537	+	0.240952i	$0.0774596\pi$
$449$			216.375i			0.481904i	−0.970537	+	0.240952i	$0.922540\pi$
$450$		0			0
$451$	−396.000	+	685.892i	−0.878049	+	1.52083i
$452$	−271.893	−	156.978i	−0.601534	−	0.347296i
$453$		0			0
$454$	24.0000			0.0528634
$455$		0			0
$456$		0			0
$457$	200.000	+	346.410i	0.437637	+	0.758009i	0.997507	−	0.0705714i	$-0.0224823\pi$
$457$	200.000	+	346.410i	0.437637	+	0.758009i	−0.559870	+	0.828580i	$0.689149\pi$
$458$	9.79796	+	5.65685i	0.0213929	+	0.0123512i
$459$		0			0
$460$	72.0000	+	124.708i	0.156522	+	0.271104i
$461$			301.227i			0.653422i	0.945124	+	0.326711i	$0.105940\pi$
$461$			301.227i			0.653422i	−0.945124	+	0.326711i	$0.894060\pi$
$462$		0			0
$463$	−604.000			−1.30454			−0.652268	−	0.757989i	$-0.726182\pi$
$463$	−604.000			−1.30454			−0.652268	+	0.757989i	$0.726182\pi$
$464$	14.6969	−	8.48528i	0.0316744	−	0.0182872i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.0193133	+	0.0334516i
$467$	−308.636	+	178.191i	−0.660890	+	0.381565i	−0.792616	−	0.609721i	$-0.791281\pi$
$467$	−308.636	+	178.191i	−0.660890	+	0.381565i	0.131726	+	0.991286i	$0.457948\pi$
$468$		0			0
$469$		0			0
$470$		−	509.117i		−	1.08323i
$471$		0			0
$472$	48.0000	−	83.1384i	0.101695	−	0.176141i
$473$	587.878	+	339.411i	1.24287	+	0.717571i
$474$		0			0
$475$	112.000			0.235789
$476$		0			0
$477$		0			0
$478$	96.0000	+	166.277i	0.200837	+	0.347860i
$479$	455.605	+	263.044i	0.951159	+	0.549152i	0.893441	−	0.449181i	$-0.148284\pi$
$479$	455.605	+	263.044i	0.951159	+	0.549152i	0.0577181	+	0.998333i	$0.481618\pi$
$480$		0			0
$481$	−136.000	−	235.559i	−0.282744	−	0.489727i
$482$		−	45.2548i		−	0.0938897i
$483$		0			0
$484$	334.000			0.690083
$485$	−646.665	+	373.352i	−1.33333	+	0.769799i
$486$		0			0
$487$	−298.000	+	516.151i	−0.611910	+	1.05986i	0.379009	+	0.925393i	$0.376265\pi$
$487$	−298.000	+	516.151i	−0.611910	+	1.05986i	−0.990918	+	0.134465i	$0.957068\pi$
$488$	122.474	−	70.7107i	0.250972	−	0.144899i
$489$		0			0
$490$		0			0
$491$		−	271.529i		−	0.553012i	−0.961012	−	0.276506i	$-0.910823\pi$
$491$		−	271.529i		−	0.553012i	0.961012	−	0.276506i	$-0.0891766\pi$
$492$		0			0
$493$	27.0000	−	46.7654i	0.0547667	−	0.0948588i
$494$	156.767	+	90.5097i	0.317343	+	0.183218i
$495$		0			0
$496$	−176.000			−0.354839
$497$		0			0
$498$		0			0
$499$	−112.000	−	193.990i	−0.224449	−	0.388757i	0.731705	−	0.681621i	$-0.238725\pi$
$499$	−112.000	−	193.990i	−0.224449	−	0.388757i	−0.956154	+	0.292864i	$0.905392\pi$
$500$	235.151	+	135.765i	0.470302	+	0.271529i
$501$		0			0
$502$	−36.0000	−	62.3538i	−0.0717131	−	0.124211i
$503$		−	865.499i		−	1.72067i	−0.509726	−	0.860337i	$-0.670253\pi$
$503$		−	865.499i		−	1.72067i	0.509726	−	0.860337i	$-0.329747\pi$
$504$		0			0
$505$	126.000			0.249505
$506$	352.727	−	203.647i	0.697088	−	0.402464i
$507$		0			0
$508$	92.0000	−	159.349i	0.181102	−	0.313678i
$509$	−415.189	+	239.709i	−0.815695	+	0.470941i	−0.848929	−	0.528506i	$-0.822752\pi$
$509$	−415.189	+	239.709i	−0.815695	+	0.470941i	0.0332350	+	0.999448i	$0.489419\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	129.000	−	223.435i	0.250973	−	0.434698i
$515$	−102.879	−	59.3970i	−0.199764	−	0.115334i
$516$		0			0
$517$	−1440.00			−2.78530
$518$		0			0
$519$		0			0
$520$	48.0000	+	83.1384i	0.0923077	+	0.159882i
$521$	−451.931	−	260.922i	−0.867430	−	0.500811i	−0.000936430	−	1.00000i	$-0.500298\pi$
$521$	−451.931	−	260.922i	−0.867430	−	0.500811i	−0.866493	+	0.499189i	$0.833631\pi$
$522$		0			0
$523$	−368.000	−	637.395i	−0.703633	−	1.21873i	−0.967183	−	0.254082i	$-0.918227\pi$
$523$	−368.000	−	637.395i	−0.703633	−	1.21873i	0.263550	−	0.964646i	$-0.415107\pi$
$524$		−	339.411i		−	0.647731i
$525$		0			0
$526$	−528.000			−1.00380
$527$	−484.999	+	280.014i	−0.920302	+	0.531336i
$528$		0			0
$529$	−120.500	+	208.712i	−0.227788	+	0.394541i
$530$	−198.409	+	114.551i	−0.374356	+	0.216135i
$531$		0			0
$532$		0			0
$533$			373.352i			0.700474i
$534$		0			0
$535$		0			0
$536$	19.5959	+	11.3137i	0.0365595	+	0.0211077i
$537$		0			0
$538$	−486.000			−0.903346
$539$		0			0
$540$		0			0
$541$	404.000	+	699.749i	0.746765	+	1.29344i	0.949365	+	0.314174i	$0.101727\pi$
$541$	404.000	+	699.749i	0.746765	+	1.29344i	−0.202600	+	0.979262i	$0.564939\pi$
$542$	465.403	+	268.701i	0.858677	+	0.495758i
$543$		0			0
$544$	36.0000	+	62.3538i	0.0661765	+	0.114621i
$545$			237.588i			0.435941i
$546$		0			0
$547$	536.000			0.979890			0.489945	−	0.871753i	$-0.337017\pi$
$547$	536.000			0.979890			0.489945	+	0.871753i	$0.337017\pi$
$548$	−271.893	+	156.978i	−0.496156	+	0.286456i
$549$		0			0
$550$	84.0000	−	145.492i	0.152727	−	0.264531i
$551$	58.7878	−	33.9411i	0.106693	−	0.0615991i
$552$		0			0
$553$		0			0
$554$		−	463.862i		−	0.837296i
$555$		0			0
$556$	−152.000	+	263.272i	−0.273381	+	0.473510i
$557$	143.295	+	82.7315i	0.257262	+	0.148531i	0.623085	−	0.782154i	$-0.285879\pi$
$557$	143.295	+	82.7315i	0.257262	+	0.148531i	−0.365823	+	0.930685i	$0.619212\pi$
$558$		0			0
$559$	320.000			0.572451
$560$		0			0
$561$		0			0
$562$	201.000	+	348.142i	0.357651	+	0.619470i
$563$	−279.242	−	161.220i	−0.495989	−	0.286359i	0.231067	−	0.972938i	$-0.425778\pi$
$563$	−279.242	−	161.220i	−0.495989	−	0.286359i	−0.727056	+	0.686579i	$0.759112\pi$
$564$		0			0
$565$	−333.000	−	576.773i	−0.589381	−	1.02084i
$566$			294.156i			0.519711i
$567$		0			0
$568$	−144.000			−0.253521
$569$	135.947	−	78.4889i	0.238922	−	0.137942i	−0.375759	−	0.926717i	$-0.622618\pi$
$569$	135.947	−	78.4889i	0.238922	−	0.137942i	0.614681	+	0.788776i	$0.289285\pi$
$570$		0			0
$571$	−184.000	+	318.697i	−0.322242	+	0.558139i	−0.980950	−	0.194259i	$-0.937770\pi$
$571$	−184.000	+	318.697i	−0.322242	+	0.558139i	0.658709	+	0.752398i	$0.271103\pi$
$572$	235.151	−	135.765i	0.411103	−	0.237351i
$573$		0			0
$574$		0			0
$575$		−	118.794i		−	0.206598i
$576$		0			0
$577$	−71.0000	+	122.976i	−0.123050	+	0.213129i	−0.920969	−	0.389636i	$-0.872601\pi$
$577$	−71.0000	+	122.976i	−0.123050	+	0.213129i	0.797919	+	0.602765i	$0.205934\pi$
$578$	−155.543	−	89.8026i	−0.269105	−	0.155368i
$579$		0			0
$580$	36.0000			0.0620690
$581$		0			0
$582$		0			0
$583$	324.000	+	561.184i	0.555746	+	0.962581i
$584$	39.1918	+	22.6274i	0.0671093	+	0.0387456i
$585$		0			0
$586$	309.000	+	535.204i	0.527304	+	0.913317i
$587$		−	373.352i		−	0.636035i	−0.948085	−	0.318017i	$-0.896983\pi$
$587$		−	373.352i		−	0.636035i	0.948085	−	0.318017i	$-0.103017\pi$
$588$		0			0
$589$	−704.000			−1.19525
$590$	176.363	−	101.823i	0.298921	−	0.172582i
$591$		0			0
$592$	68.0000	−	117.779i	0.114865	−	0.198952i
$593$	−958.975	+	553.665i	−1.61716	+	0.933667i	−0.629508	+	0.776994i	$0.716744\pi$
$593$	−958.975	+	553.665i	−1.61716	+	0.933667i	−0.987650	+	0.156674i	$0.949923\pi$
$594$		0			0
$595$		0			0
$596$		−	551.543i		−	0.925408i
$597$		0			0
$598$	96.0000	−	166.277i	0.160535	−	0.278055i
$599$	−690.756	−	398.808i	−1.15318	−	0.665790i	−0.203521	−	0.979070i	$-0.565239\pi$
$599$	−690.756	−	398.808i	−1.15318	−	0.665790i	−0.949661	+	0.313280i	$0.898572\pi$
$600$		0			0
$601$	−158.000			−0.262895			−0.131448	−	0.991323i	$-0.541963\pi$
$601$	−158.000			−0.262895			−0.131448	+	0.991323i	$0.541963\pi$
$602$		0			0
$603$		0			0
$604$	−148.000	−	256.344i	−0.245033	−	0.424410i
$605$	613.597	+	354.260i	1.01421	+	0.585555i
$606$		0			0
$607$	166.000	+	287.520i	0.273476	+	0.473675i	0.969750	−	0.244102i	$-0.0784932\pi$
$607$	166.000	+	287.520i	0.273476	+	0.473675i	−0.696273	+	0.717777i	$0.745160\pi$
$608$			90.5097i			0.148865i
$609$		0			0
$610$	300.000			0.491803
$611$	−587.878	+	339.411i	−0.962156	+	0.555501i
$612$		0			0
$613$	−289.000	+	500.563i	−0.471452	+	0.816579i	−0.999467	−	0.0326566i	$-0.989603\pi$
$613$	−289.000	+	500.563i	−0.471452	+	0.816579i	0.528015	+	0.849235i	$0.322937\pi$
$614$	636.867	−	367.696i	1.03724	−	0.598853i
$615$		0			0
$616$		0			0
$617$		−	55.1543i		−	0.0893911i	−0.999001	−	0.0446956i	$-0.985768\pi$
$617$		−	55.1543i		−	0.0893911i	0.999001	−	0.0446956i	$-0.0142318\pi$
$618$		0			0
$619$	448.000	−	775.959i	0.723748	−	1.25357i	−0.235739	−	0.971816i	$-0.575751\pi$
$619$	448.000	−	775.959i	0.723748	−	1.25357i	0.959487	−	0.281752i	$-0.0909155\pi$
$620$	−323.333	−	186.676i	−0.521504	−	0.301091i
$621$		0			0
$622$	−528.000			−0.848875
$623$		0			0
$624$		0			0
$625$	200.500	+	347.276i	0.320800	+	0.555642i
$626$	−115.126	−	66.4680i	−0.183907	−	0.106179i
$627$		0			0
$628$	82.0000	+	142.028i	0.130573	+	0.226160i
$629$		−	432.749i		−	0.687996i
$630$		0			0
$631$	20.0000			0.0316957			0.0158479	−	0.999874i	$-0.494955\pi$
$631$	20.0000			0.0316957			0.0158479	+	0.999874i	$0.494955\pi$
$632$	186.161	−	107.480i	0.294559	−	0.170064i
$633$		0			0
$634$	237.000	−	410.496i	0.373817	−	0.647470i
$635$	338.030	−	195.161i	0.532330	−	0.307341i
$636$		0			0
$637$		0			0
$638$		−	101.823i		−	0.159598i
$639$		0			0
$640$	−24.0000	+	41.5692i	−0.0375000	+	0.0649519i
$641$	−224.128	−	129.401i	−0.349654	−	0.201873i	0.314879	−	0.949132i	$-0.398036\pi$
$641$	−224.128	−	129.401i	−0.349654	−	0.201873i	−0.664533	+	0.747259i	$0.731369\pi$
$642$		0			0
$643$	−728.000			−1.13219			−0.566096	−	0.824339i	$-0.691547\pi$
$643$	−728.000			−1.13219			−0.566096	+	0.824339i	$0.691547\pi$
$644$		0			0
$645$		0			0
$646$	144.000	+	249.415i	0.222910	+	0.386092i
$647$	−396.817	−	229.103i	−0.613319	−	0.354100i	0.160944	−	0.986963i	$-0.448546\pi$
$647$	−396.817	−	229.103i	−0.613319	−	0.354100i	−0.774263	+	0.632864i	$0.781879\pi$
$648$		0			0
$649$	−288.000	−	498.831i	−0.443760	−	0.768614i
$650$		−	79.1960i		−	0.121840i
$651$		0			0
$652$	−112.000			−0.171779
$653$	260.871	−	150.614i	0.399496	−	0.230649i	−0.286771	−	0.957999i	$-0.592582\pi$
$653$	260.871	−	150.614i	0.399496	−	0.230649i	0.686266	+	0.727350i	$0.259248\pi$
$654$		0			0
$655$	360.000	−	623.538i	0.549618	−	0.951967i
$656$	−161.666	+	93.3381i	−0.246443	+	0.142284i
$657$		0			0
$658$		0			0
$659$		−	1052.17i		−	1.59662i	−0.602244	−	0.798312i	$-0.705727\pi$
$659$		−	1052.17i		−	1.59662i	0.602244	−	0.798312i	$-0.294273\pi$
$660$		0			0
$661$	31.0000	−	53.6936i	0.0468986	−	0.0812308i	−0.841623	−	0.540065i	$-0.818400\pi$
$661$	31.0000	−	53.6936i	0.0468986	−	0.0812308i	0.888522	+	0.458834i	$0.151733\pi$
$662$	−656.463	−	379.009i	−0.991636	−	0.572522i
$663$		0			0
$664$	−336.000			−0.506024
$665$		0			0
$666$		0			0
$667$	−36.0000	−	62.3538i	−0.0539730	−	0.0934840i
$668$	−58.7878	−	33.9411i	−0.0880056	−	0.0508101i
$669$		0			0
$670$	24.0000	+	41.5692i	0.0358209	+	0.0620436i
$671$		−	848.528i		−	1.26457i
$672$		0			0
$673$	−670.000			−0.995542			−0.497771	−	0.867308i	$-0.665848\pi$
$673$	−670.000			−0.995542			−0.497771	+	0.867308i	$0.665848\pi$
$674$	−254.747	+	147.078i	−0.377963	+	0.218217i
$675$		0			0
$676$	−105.000	+	181.865i	−0.155325	+	0.269032i
$677$	1120.64	−	647.003i	1.65531	−	0.955691i	0.680466	−	0.732779i	$-0.261777\pi$
$677$	1120.64	−	647.003i	1.65531	−	0.955691i	0.974839	−	0.222912i	$-0.0715561\pi$
$678$		0			0
$679$		0			0
$680$			152.735i			0.224610i
$681$		0			0
$682$	−528.000	+	914.523i	−0.774194	+	1.34094i
$683$	484.999	+	280.014i	0.710101	+	0.409977i	0.811098	−	0.584910i	$-0.198870\pi$
$683$	484.999	+	280.014i	0.710101	+	0.409977i	−0.100997	+	0.994887i	$0.532203\pi$
$684$		0			0
$685$	−666.000			−0.972263
$686$		0			0
$687$		0			0
$688$	80.0000	+	138.564i	0.116279	+	0.201401i
$689$	264.545	+	152.735i	0.383955	+	0.221676i
$690$		0			0
$691$	−20.0000	−	34.6410i	−0.0289436	−	0.0501317i	0.851191	−	0.524856i	$-0.175881\pi$
$691$	−20.0000	−	34.6410i	−0.0289436	−	0.0501317i	−0.880134	+	0.474725i	$0.842548\pi$
$692$		−	347.897i		−	0.502741i
$693$		0			0
$694$	−408.000			−0.587896
$695$	−558.484	+	322.441i	−0.803574	+	0.463943i
$696$		0			0
$697$	−297.000	+	514.419i	−0.426112	+	0.738047i
$698$	291.489	−	168.291i	0.417606	−	0.241105i
$699$		0			0
$700$		0			0
$701$			954.594i			1.36176i	0.732395	+	0.680880i	$0.238403\pi$
$701$			954.594i			1.36176i	−0.732395	+	0.680880i	$0.761597\pi$
$702$		0			0
$703$	272.000	−	471.118i	0.386913	−	0.670153i
$704$	117.576	+	67.8823i	0.167011	+	0.0964237i
$705$		0			0
$706$	−318.000			−0.450425
$707$		0			0
$708$		0			0
$709$	−484.000	−	838.313i	−0.682652	−	1.18239i	−0.974169	−	0.225822i	$-0.927493\pi$
$709$	−484.000	−	838.313i	−0.682652	−	1.18239i	0.291517	−	0.956566i	$-0.405840\pi$
$710$	−264.545	−	152.735i	−0.372598	−	0.215120i
$711$		0			0
$712$	18.0000	+	31.1769i	0.0252809	+	0.0437878i
$713$			746.705i			1.04727i
$714$		0			0
$715$	576.000			0.805594
$716$	352.727	−	203.647i	0.492635	−	0.284423i
$717$		0			0
$718$	−396.000	+	685.892i	−0.551532	+	0.955282i
$719$	−1014.09	+	585.484i	−1.41042	+	0.814304i	−0.995427	−	0.0955230i	$-0.969548\pi$
$719$	−1014.09	+	585.484i	−1.41042	+	0.814304i	−0.414988	+	0.909827i	$0.636214\pi$
$720$		0			0
$721$		0			0
$722$		−	148.492i		−	0.205668i
$723$		0			0
$724$	232.000	−	401.836i	0.320442	−	0.555022i
$725$	−25.7196	−	14.8492i	−0.0354754	−	0.0204817i
$726$		0			0
$727$	508.000			0.698762			0.349381	−	0.936981i	$-0.386392\pi$
$727$	508.000			0.698762			0.349381	+	0.936981i	$0.386392\pi$
$728$		0			0
$729$		0			0
$730$	48.0000	+	83.1384i	0.0657534	+	0.113888i
$731$	440.908	+	254.558i	0.603158	+	0.348233i
$732$		0			0
$733$	−572.000	−	990.733i	−0.780355	−	1.35161i	−0.931735	−	0.363138i	$-0.881705\pi$
$733$	−572.000	−	990.733i	−0.780355	−	1.35161i	0.151380	−	0.988476i	$-0.451628\pi$
$734$		−	401.637i		−	0.547189i
$735$		0			0
$736$	96.0000			0.130435
$737$	117.576	−	67.8823i	0.159533	−	0.0921062i
$738$		0			0
$739$	152.000	−	263.272i	0.205683	−	0.356254i	−0.744667	−	0.667436i	$-0.767392\pi$
$739$	152.000	−	263.272i	0.205683	−	0.356254i	0.950350	+	0.311182i	$0.100725\pi$
$740$	249.848	−	144.250i	0.337632	−	0.194932i
$741$		0			0
$742$		0			0
$743$			848.528i			1.14203i	0.820940	+	0.571015i	$0.193450\pi$
$743$			848.528i			1.14203i	−0.820940	+	0.571015i	$0.806550\pi$
$744$		0			0
$745$	585.000	−	1013.25i	0.785235	−	1.36007i
$746$	232.702	+	134.350i	0.311932	+	0.180094i
$747$		0			0
$748$	432.000			0.577540
$749$		0			0
$750$		0			0
$751$	−94.0000	−	162.813i	−0.125166	−	0.216795i	0.796632	−	0.604465i	$-0.206613\pi$
$751$	−94.0000	−	162.813i	−0.125166	−	0.216795i	−0.921798	+	0.387671i	$0.873280\pi$
$752$	−293.939	−	169.706i	−0.390876	−	0.225672i
$753$		0			0
$754$	−24.0000	−	41.5692i	−0.0318302	−	0.0551316i
$755$		−	627.911i		−	0.831670i
$756$		0			0
$757$	−1240.00			−1.63804			−0.819022	−	0.573761i	$-0.805484\pi$
$757$	−1240.00			−1.63804			−0.819022	+	0.573761i	$0.805484\pi$
$758$	−195.959	+	113.137i	−0.258521	+	0.149257i
$759$		0			0
$760$	−96.0000	+	166.277i	−0.126316	+	0.218785i
$761$	135.947	−	78.4889i	0.178642	−	0.103139i	−0.408012	−	0.912976i	$-0.633778\pi$
$761$	135.947	−	78.4889i	0.178642	−	0.103139i	0.586655	+	0.809837i	$0.300445\pi$
$762$		0			0
$763$		0			0
$764$			67.8823i			0.0888511i
$765$		0			0
$766$	192.000	−	332.554i	0.250653	−	0.434143i
$767$	−235.151	−	135.765i	−0.306585	−	0.177007i
$768$		0			0
$769$	910.000			1.18336			0.591678	−	0.806175i	$-0.298466\pi$
$769$	910.000			1.18336			0.591678	+	0.806175i	$0.298466\pi$
$770$		0			0
$771$		0			0
$772$	206.000	+	356.802i	0.266839	+	0.462179i
$773$	−1201.47	−	693.672i	−1.55430	−	0.897376i	−0.997784	−	0.0665401i	$-0.978804\pi$
$773$	−1201.47	−	693.672i	−1.55430	−	0.897376i	−0.556517	−	0.830836i	$-0.687863\pi$
$774$		0			0
$775$	154.000	+	266.736i	0.198710	+	0.344175i
$776$			497.803i			0.641499i
$777$		0			0
$778$	570.000			0.732648
$779$	−646.665	+	373.352i	−0.830122	+	0.479271i
$780$		0			0
$781$	−432.000	+	748.246i	−0.553137	+	0.958061i
$782$	264.545	−	152.735i	0.338293	−	0.195313i
$783$		0			0
$784$		0			0
$785$			347.897i			0.443180i
$786$		0			0
$787$	−680.000	+	1177.79i	−0.864041	+	1.49656i	0.00395593	+	0.999992i	$0.498741\pi$
$787$	−680.000	+	1177.79i	−0.864041	+	1.49656i	−0.867997	+	0.496570i	$0.834593\pi$
$788$	286.590	+	165.463i	0.363693	+	0.209978i
$789$		0			0
$790$	456.000			0.577215
$791$		0			0
$792$		0			0
$793$	−200.000	−	346.410i	−0.252207	−	0.436835i
$794$	178.813	+	103.238i	0.225205	+	0.130022i
$795$		0			0
$796$	−20.0000	−	34.6410i	−0.0251256	−	0.0435189i
$797$			106.066i			0.133082i	0.997784	+	0.0665408i	$0.0211963\pi$
$797$			106.066i			0.133082i	−0.997784	+	0.0665408i	$0.978804\pi$
$798$		0			0
$799$	−1080.00			−1.35169
$800$	34.2929	−	19.7990i	0.0428661	−	0.0247487i
$801$		0			0
$802$	231.000	−	400.104i	0.288030	−	0.498882i
$803$	235.151	−	135.765i	0.292841	−	0.169072i
$804$		0			0
$805$		0			0
$806$			497.803i			0.617622i
$807$		0			0
$808$	42.0000	−	72.7461i	0.0519802	−	0.0900323i
$809$	958.975	+	553.665i	1.18538	+	0.684381i	0.957254	−	0.289249i	$-0.0934057\pi$
$809$	958.975	+	553.665i	1.18538	+	0.684381i	0.228130	+	0.973631i	$0.426739\pi$
$810$		0			0
$811$	160.000			0.197287			0.0986436	−	0.995123i	$-0.468550\pi$
$811$	160.000			0.197287			0.0986436	+	0.995123i	$0.468550\pi$
$812$		0			0
$813$		0			0
$814$	−408.000	−	706.677i	−0.501229	−	0.868153i
$815$	−205.757	−	118.794i	−0.252463	−	0.145759i
$816$		0			0
$817$	320.000	+	554.256i	0.391677	+	0.678404i
$818$		−	520.431i		−	0.636223i
$819$		0			0
$820$	−396.000			−0.482927
$821$	378.446	−	218.496i	0.460958	−	0.266134i	−0.251489	−	0.967860i	$-0.580920\pi$
$821$	378.446	−	218.496i	0.460958	−	0.266134i	0.712447	+	0.701726i	$0.247587\pi$
$822$		0			0
$823$	−166.000	+	287.520i	−0.201701	+	0.349357i	−0.949077	−	0.315045i	$-0.897980\pi$
$823$	−166.000	+	287.520i	−0.201701	+	0.349357i	0.747376	+	0.664402i	$0.231314\pi$
$824$	−68.5857	+	39.5980i	−0.0832351	+	0.0480558i
$825$		0			0
$826$		0			0
$827$			101.823i			0.123124i	0.998103	+	0.0615619i	$0.0196082\pi$
$827$			101.823i			0.123124i	−0.998103	+	0.0615619i	$0.980392\pi$
$828$		0			0
$829$	316.000	−	547.328i	0.381182	−	0.660227i	−0.610049	−	0.792363i	$-0.708850\pi$
$829$	316.000	−	547.328i	0.381182	−	0.660227i	0.991232	+	0.132137i	$0.0421837\pi$
$830$	−617.271	−	356.382i	−0.743701	−	0.429376i
$831$		0			0
$832$	64.0000			0.0769231
$833$		0			0
$834$		0			0
$835$	−72.0000	−	124.708i	−0.0862275	−	0.149350i
$836$	470.302	+	271.529i	0.562562	+	0.324795i
$837$		0			0
$838$	−276.000	−	478.046i	−0.329356	−	0.570461i
$839$		−	729.734i		−	0.869767i	−0.900487	−	0.434883i	$-0.856790\pi$
$839$		−	729.734i		−	0.869767i	0.900487	−	0.434883i	$-0.143210\pi$
$840$		0			0
$841$	823.000			0.978597
$842$	−48.9898	+	28.2843i	−0.0581827	+	0.0335918i
$843$		0			0
$844$	296.000	−	512.687i	0.350711	−	0.607449i
$845$	−385.795	+	222.739i	−0.456562	+	0.263596i
$846$		0			0
$847$		0			0
$848$			152.735i			0.180112i
$849$		0			0
$850$	63.0000	−	109.119i	0.0741176	−	0.128376i
$851$	−499.696	−	288.500i	−0.587187	−	0.339012i
$852$		0			0
$853$	−446.000			−0.522860			−0.261430	−	0.965222i	$-0.584194\pi$
$853$	−446.000			−0.522860			−0.261430	+	0.965222i	$0.584194\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−371.098	−	214.253i	−0.433019	−	0.250004i	0.267613	−	0.963527i	$-0.413765\pi$
$857$	−371.098	−	214.253i	−0.433019	−	0.250004i	−0.700632	+	0.713523i	$0.747099\pi$
$858$		0			0
$859$	364.000	+	630.466i	0.423749	+	0.733954i	0.996303	−	0.0859129i	$-0.0273807\pi$
$859$	364.000	+	630.466i	0.423749	+	0.733954i	−0.572554	+	0.819867i	$0.694047\pi$
$860$			339.411i			0.394664i
$861$		0			0
$862$	216.000			0.250580
$863$	−793.635	+	458.205i	−0.919623	+	0.530945i	−0.883515	−	0.468403i	$-0.844829\pi$
$863$	−793.635	+	458.205i	−0.919623	+	0.530945i	−0.0361083	+	0.999348i	$0.511496\pi$
$864$		0			0
$865$	369.000	−	639.127i	0.426590	−	0.738875i
$866$	−663.812	+	383.252i	−0.766526	+	0.442554i
$867$		0			0
$868$		0			0
$869$		−	1289.76i		−	1.48419i
$870$		0			0
$871$	32.0000	−	55.4256i	0.0367394	−	0.0636345i
$872$	137.171	+	79.1960i	0.157307	+	0.0908211i
$873$		0			0
$874$	384.000			0.439359
$875$		0			0
$876$		0			0
$877$	455.000	+	788.083i	0.518814	+	0.898612i	0.999761	+	0.0218627i	$0.00695967\pi$
$877$	455.000	+	788.083i	0.518814	+	0.898612i	−0.480947	+	0.876750i	$0.659707\pi$
$878$	−4.89898	−	2.82843i	−0.00557970	−	0.00322144i
$879$		0			0
$880$	144.000	+	249.415i	0.163636	+	0.283426i
$881$			929.138i			1.05464i	0.849667	+	0.527320i	$0.176803\pi$
$881$			929.138i			1.05464i	−0.849667	+	0.527320i	$0.823197\pi$
$882$		0			0
$883$	1064.00			1.20498			0.602492	−	0.798125i	$-0.294175\pi$
$883$	1064.00			1.20498			0.602492	+	0.798125i	$0.294175\pi$
$884$	176.363	−	101.823i	0.199506	−	0.115185i
$885$		0			0
$886$	228.000	−	394.908i	0.257336	−	0.445720i
$887$	1205.15	−	695.793i	1.35868	−	0.784434i	0.369234	−	0.929337i	$-0.379620\pi$
$887$	1205.15	−	695.793i	1.35868	−	0.784434i	0.989446	+	0.144902i	$0.0462868\pi$
$888$		0			0
$889$		0			0
$890$			76.3675i			0.0858062i
$891$		0			0
$892$	436.000	−	755.174i	0.488789	−	0.846608i
$893$	−1175.76	−	678.823i	−1.31664	−	0.760160i
$894$		0			0
$895$	864.000			0.965363
$896$		0			0
$897$		0			0
$898$	153.000	+	265.004i	0.170379	+	0.295104i
$899$	161.666	+	93.3381i	0.179829	+	0.103824i
$900$		0			0
$901$	243.000	+	420.888i	0.269700	+	0.467135i
$902$			1120.06i			1.24175i
$903$		0			0
$904$	−444.000			−0.491150
$905$	852.422	−	492.146i	0.941903	−	0.543808i
$906$		0			0
$907$	884.000	−	1531.13i	0.974642	−	1.68813i	0.293529	−	0.955950i	$-0.405170\pi$
$907$	884.000	−	1531.13i	0.974642	−	1.68813i	0.681112	−	0.732179i	$-0.261496\pi$
$908$	29.3939	−	16.9706i	0.0323721	−	0.0186900i
$909$		0			0
$910$		0			0
$911$		−	237.588i		−	0.260799i	−0.991462	−	0.130399i	$-0.958374\pi$
$911$		−	237.588i		−	0.260799i	0.991462	−	0.130399i	$-0.0416260\pi$
$912$		0			0
$913$	−1008.00	+	1745.91i	−1.10405	+	1.91228i
$914$	489.898	+	282.843i	0.535993	+	0.309456i
$915$		0			0
$916$	16.0000			0.0174672
$917$		0			0
$918$		0			0
$919$	−190.000	−	329.090i	−0.206746	−	0.358095i	0.743941	−	0.668245i	$-0.232954\pi$
$919$	−190.000	−	329.090i	−0.206746	−	0.358095i	−0.950688	+	0.310150i	$0.899621\pi$
$920$	176.363	+	101.823i	0.191699	+	0.110678i
$921$		0			0
$922$	213.000	+	368.927i	0.231020	+	0.400138i
$923$			407.294i			0.441271i
$924$		0			0
$925$	−238.000			−0.257297
$926$	−739.746	+	427.092i	−0.798862	+	0.461223i
$927$		0			0
$928$	12.0000	−	20.7846i	0.0129310	−	0.0223972i
$929$	−576.855	+	333.047i	−0.620942	+	0.358501i	−0.777236	−	0.629210i	$-0.783379\pi$
$929$	−576.855	+	333.047i	−0.620942	+	0.358501i	0.156294	+	0.987711i	$0.450045\pi$
$930$		0			0
$931$		0			0
$932$			25.4558i			0.0273131i
$933$		0			0
$934$	−252.000	+	436.477i	−0.269807	+	0.467320i
$935$	793.635	+	458.205i	0.848807	+	0.490059i
$936$		0			0
$937$	178.000			0.189968			0.0949840	−	0.995479i	$-0.469720\pi$
$937$	178.000			0.189968			0.0949840	+	0.995479i	$0.469720\pi$
$938$		0			0
$939$		0			0
$940$	−360.000	−	623.538i	−0.382979	−	0.663339i
$941$	−378.446	−	218.496i	−0.402174	−	0.232196i	0.285247	−	0.958454i	$-0.407924\pi$
$941$	−378.446	−	218.496i	−0.402174	−	0.232196i	−0.687422	+	0.726258i	$0.741258\pi$
$942$		0			0
$943$	396.000	+	685.892i	0.419936	+	0.727351i
$944$		−	135.765i		−	0.143818i
$945$		0			0
$946$	960.000			1.01480
$947$	1557.88	−	899.440i	1.64506	−	0.949778i	0.666070	−	0.745889i	$-0.267975\pi$
$947$	1557.88	−	899.440i	1.64506	−	0.949778i	0.978994	−	0.203889i	$-0.0653580\pi$
$948$		0			0
$949$	64.0000	−	110.851i	0.0674394	−	0.116808i
$950$	137.171	−	79.1960i	0.144391	−	0.0833642i
$951$		0			0
$952$		0			0
$953$			1310.98i			1.37563i	0.725886	+	0.687815i	$0.241430\pi$
$953$			1310.98i			1.37563i	−0.725886	+	0.687815i	$0.758570\pi$
$954$		0			0
$955$	−72.0000	+	124.708i	−0.0753927	+	0.130584i
$956$	235.151	+	135.765i	0.245974	+	0.142013i
$957$		0			0
$958$	744.000			0.776618
$959$		0			0
$960$		0			0
$961$	−487.500	−	844.375i	−0.507284	−	0.878642i
$962$	−333.131	−	192.333i	−0.346290	−	0.199930i
$963$		0			0
$964$	−32.0000	−	55.4256i	−0.0331950	−	0.0574955i
$965$			873.984i			0.905683i
$966$		0			0
$967$	1700.00			1.75801			0.879007	−	0.476808i	$-0.158206\pi$
$967$	1700.00			1.75801			0.879007	+	0.476808i	$0.158206\pi$
$968$	409.065	−	236.174i	0.422588	−	0.243981i
$969$		0			0
$970$	−528.000	+	914.523i	−0.544330	+	0.942807i
$971$	−396.817	+	229.103i	−0.408669	+	0.235945i	−0.690218	−	0.723602i	$-0.742485\pi$
$971$	−396.817	+	229.103i	−0.408669	+	0.235945i	0.281549	+	0.959547i	$0.409152\pi$
$972$		0			0
$973$		0			0
$974$			842.871i			0.865371i
$975$		0			0
$976$	100.000	−	173.205i	0.102459	−	0.177464i
$977$	−657.688	−	379.716i	−0.673171	−	0.388655i	0.124106	−	0.992269i	$-0.460394\pi$
$977$	−657.688	−	379.716i	−0.673171	−	0.388655i	−0.797277	+	0.603614i	$0.793727\pi$
$978$		0			0
$979$	216.000			0.220633
$980$		0			0
$981$		0			0
$982$	−192.000	−	332.554i	−0.195519	−	0.338649i
$983$	−911.210	−	526.087i	−0.926969	−	0.535186i	−0.0411171	−	0.999154i	$-0.513092\pi$
$983$	−911.210	−	526.087i	−0.926969	−	0.535186i	−0.885852	+	0.463969i	$0.846425\pi$
$984$		0			0
$985$	351.000	+	607.950i	0.356345	+	0.617208i
$986$		−	76.3675i		−	0.0774519i
$987$		0			0
$988$	256.000			0.259109
$989$	587.878	−	339.411i	0.594416	−	0.343186i
$990$		0			0
$991$	386.000	−	668.572i	0.389506	−	0.674643i	−0.602878	−	0.797834i	$-0.705979\pi$
$991$	386.000	−	668.572i	0.389506	−	0.674643i	0.992383	+	0.123190i	$0.0393126\pi$
$992$	−215.555	+	124.451i	−0.217293	+	0.125454i
$993$		0			0
$994$		0			0
$995$		−	84.8528i		−	0.0852792i
$996$		0			0
$997$	97.0000	−	168.009i	0.0972919	−	0.168514i	−0.813271	−	0.581885i	$-0.802315\pi$
$997$	97.0000	−	168.009i	0.0972919	−	0.168514i	0.910563	+	0.413371i	$0.135649\pi$
$998$	−274.343	−	158.392i	−0.274893	−	0.158709i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.s.d.557.2		4
3.2	odd	2	inner	882.3.s.d.557.1		4
7.2	even	3	inner	882.3.s.d.863.1		4
7.3	odd	6		18.3.b.a.17.2	yes	2
7.4	even	3		882.3.b.a.197.2		2
7.5	odd	6		882.3.s.b.863.1		4
7.6	odd	2		882.3.s.b.557.2		4
21.2	odd	6	inner	882.3.s.d.863.2		4
21.5	even	6		882.3.s.b.863.2		4
21.11	odd	6		882.3.b.a.197.1		2
21.17	even	6		18.3.b.a.17.1	✓	2
21.20	even	2		882.3.s.b.557.1		4
28.3	even	6		144.3.e.b.17.1		2
35.3	even	12		450.3.b.b.449.4		4
35.17	even	12		450.3.b.b.449.1		4
35.24	odd	6		450.3.d.f.251.1		2
56.3	even	6		576.3.e.f.449.2		2
56.45	odd	6		576.3.e.c.449.2		2
63.31	odd	6		162.3.d.b.107.1		4
63.38	even	6		162.3.d.b.53.1		4
63.52	odd	6		162.3.d.b.53.2		4
63.59	even	6		162.3.d.b.107.2		4
77.10	even	6		2178.3.c.d.485.1		2
84.59	odd	6		144.3.e.b.17.2		2
91.31	even	12		3042.3.d.a.3041.3		4
91.38	odd	6		3042.3.c.e.1691.1		2
91.73	even	12		3042.3.d.a.3041.2		4
105.17	odd	12		450.3.b.b.449.3		4
105.38	odd	12		450.3.b.b.449.2		4
105.59	even	6		450.3.d.f.251.2		2
112.3	even	12		2304.3.h.c.2177.2		4
112.45	odd	12		2304.3.h.f.2177.2		4
112.59	even	12		2304.3.h.c.2177.3		4
112.101	odd	12		2304.3.h.f.2177.3		4
140.3	odd	12		3600.3.c.b.449.1		4
140.59	even	6		3600.3.l.d.1601.1		2
140.87	odd	12		3600.3.c.b.449.3		4
168.59	odd	6		576.3.e.f.449.1		2
168.101	even	6		576.3.e.c.449.1		2
231.164	odd	6		2178.3.c.d.485.2		2
252.31	even	6		1296.3.q.f.593.1		4
252.59	odd	6		1296.3.q.f.593.2		4
252.115	even	6		1296.3.q.f.1025.2		4
252.227	odd	6		1296.3.q.f.1025.1		4
273.38	even	6		3042.3.c.e.1691.2		2
273.122	odd	12		3042.3.d.a.3041.1		4
273.164	odd	12		3042.3.d.a.3041.4		4
336.59	odd	12		2304.3.h.c.2177.1		4
336.101	even	12		2304.3.h.f.2177.1		4
336.227	odd	12		2304.3.h.c.2177.4		4
336.269	even	12		2304.3.h.f.2177.4		4
420.59	odd	6		3600.3.l.d.1601.2		2
420.143	even	12		3600.3.c.b.449.2		4
420.227	even	12		3600.3.c.b.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.b.a.17.1	✓	2	21.17	even	6
18.3.b.a.17.2	yes	2	7.3	odd	6
144.3.e.b.17.1		2	28.3	even	6
144.3.e.b.17.2		2	84.59	odd	6
162.3.d.b.53.1		4	63.38	even	6
162.3.d.b.53.2		4	63.52	odd	6
162.3.d.b.107.1		4	63.31	odd	6
162.3.d.b.107.2		4	63.59	even	6
450.3.b.b.449.1		4	35.17	even	12
450.3.b.b.449.2		4	105.38	odd	12
450.3.b.b.449.3		4	105.17	odd	12
450.3.b.b.449.4		4	35.3	even	12
450.3.d.f.251.1		2	35.24	odd	6
450.3.d.f.251.2		2	105.59	even	6
576.3.e.c.449.1		2	168.101	even	6
576.3.e.c.449.2		2	56.45	odd	6
576.3.e.f.449.1		2	168.59	odd	6
576.3.e.f.449.2		2	56.3	even	6
882.3.b.a.197.1		2	21.11	odd	6
882.3.b.a.197.2		2	7.4	even	3
882.3.s.b.557.1		4	21.20	even	2
882.3.s.b.557.2		4	7.6	odd	2
882.3.s.b.863.1		4	7.5	odd	6
882.3.s.b.863.2		4	21.5	even	6
882.3.s.d.557.1		4	3.2	odd	2	inner
882.3.s.d.557.2		4	1.1	even	1	trivial
882.3.s.d.863.1		4	7.2	even	3	inner
882.3.s.d.863.2		4	21.2	odd	6	inner
1296.3.q.f.593.1		4	252.31	even	6
1296.3.q.f.593.2		4	252.59	odd	6
1296.3.q.f.1025.1		4	252.227	odd	6
1296.3.q.f.1025.2		4	252.115	even	6
2178.3.c.d.485.1		2	77.10	even	6
2178.3.c.d.485.2		2	231.164	odd	6
2304.3.h.c.2177.1		4	336.59	odd	12
2304.3.h.c.2177.2		4	112.3	even	12
2304.3.h.c.2177.3		4	112.59	even	12
2304.3.h.c.2177.4		4	336.227	odd	12
2304.3.h.f.2177.1		4	336.101	even	12
2304.3.h.f.2177.2		4	112.45	odd	12
2304.3.h.f.2177.3		4	112.101	odd	12
2304.3.h.f.2177.4		4	336.269	even	12
3042.3.c.e.1691.1		2	91.38	odd	6
3042.3.c.e.1691.2		2	273.38	even	6
3042.3.d.a.3041.1		4	273.122	odd	12
3042.3.d.a.3041.2		4	91.73	even	12
3042.3.d.a.3041.3		4	91.31	even	12
3042.3.d.a.3041.4		4	273.164	odd	12
3600.3.c.b.449.1		4	140.3	odd	12
3600.3.c.b.449.2		4	420.143	even	12
3600.3.c.b.449.3		4	140.87	odd	12
3600.3.c.b.449.4		4	420.227	even	12
3600.3.l.d.1601.1		2	140.59	even	6
3600.3.l.d.1601.2		2	420.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 - 2.12132i) q^{5} -2.82843i q^{8} +(3.00000 - 5.19615i) q^{10} +(-14.6969 - 8.48528i) q^{11} -8.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-11.0227 - 6.36396i) q^{17} +(-8.00000 - 13.8564i) q^{19} -8.48528i q^{20} -24.0000 q^{22} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(-9.79796 + 5.65685i) q^{26} +4.24264i q^{29} +(22.0000 - 38.1051i) q^{31} +(-4.89898 - 2.82843i) q^{32} -18.0000 q^{34} +(17.0000 + 29.4449i) q^{37} +(-19.5959 - 11.3137i) q^{38} +(-6.00000 - 10.3923i) q^{40} -46.6690i q^{41} -40.0000 q^{43} +(-29.3939 + 16.9706i) q^{44} +(-12.0000 + 20.7846i) q^{46} +(73.4847 - 42.4264i) q^{47} +9.89949i q^{50} +(-8.00000 + 13.8564i) q^{52} +(-33.0681 - 19.0919i) q^{53} -72.0000 q^{55} +(3.00000 + 5.19615i) q^{58} +(29.3939 + 16.9706i) q^{59} +(25.0000 + 43.3013i) q^{61} -62.2254i q^{62} -8.00000 q^{64} +(-29.3939 + 16.9706i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-22.0454 + 12.7279i) q^{68} -50.9117i q^{71} +(-8.00000 + 13.8564i) q^{73} +(41.6413 + 24.0416i) q^{74} -32.0000 q^{76} +(38.0000 + 65.8179i) q^{79} +(-14.6969 - 8.48528i) q^{80} +(-33.0000 - 57.1577i) q^{82} -118.794i q^{83} -54.0000 q^{85} +(-48.9898 + 28.2843i) q^{86} +(-24.0000 + 41.5692i) q^{88} +(-11.0227 + 6.36396i) q^{89} +33.9411i q^{92} +(60.0000 - 103.923i) q^{94} +(-58.7878 - 33.9411i) q^{95} -176.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 12 q^{10} - 32 q^{13} - 8 q^{16} - 32 q^{19} - 96 q^{22} - 14 q^{25} + 88 q^{31} - 72 q^{34} + 68 q^{37} - 24 q^{40} - 160 q^{43} - 48 q^{46} - 32 q^{52} - 288 q^{55} + 12 q^{58} + 100 q^{61}+ \cdots - 704 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 + 12 * q^10 - 32 * q^13 - 8 * q^16 - 32 * q^19 - 96 * q^22 - 14 * q^25 + 88 * q^31 - 72 * q^34 + 68 * q^37 - 24 * q^40 - 160 * q^43 - 48 * q^46 - 32 * q^52 - 288 * q^55 + 12 * q^58 + 100 * q^61 - 32 * q^64 - 16 * q^67 - 32 * q^73 - 128 * q^76 + 152 * q^79 - 132 * q^82 - 216 * q^85 - 96 * q^88 + 240 * q^94 - 704 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more