LMFDB - Embedded newform 882.3.n.a.325.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,3,Mod(19,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.19"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,-12,0,0,0,0,12,-12,0,0,0,0,-8,12,0,12,0,0,-24,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == 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 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			325.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.325
Dual form			882.3.n.a.19.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.878680 + 0.507306i) q^{5} -2.82843 q^{8} +(-1.24264 - 0.717439i) q^{10} +(-5.12132 + 8.87039i) q^{11} -8.95743i q^{13} +(-2.00000 - 3.46410i) q^{16} +(26.3345 + 15.2042i) q^{17} +(-13.9706 + 8.06591i) q^{19} -2.02922i q^{20} -14.4853 q^{22} +(-3.36396 - 5.82655i) q^{23} +(-11.9853 + 20.7591i) q^{25} +(10.9706 - 6.33386i) q^{26} -30.0000 q^{29} +(-43.4558 - 25.0892i) q^{31} +(2.82843 - 4.89898i) q^{32} +43.0041i q^{34} +(-15.4558 - 26.7703i) q^{37} +(-19.7574 - 11.4069i) q^{38} +(2.48528 - 1.43488i) q^{40} +7.10228i q^{41} -74.4264 q^{43} +(-10.2426 - 17.7408i) q^{44} +(4.75736 - 8.23999i) q^{46} +(50.4853 - 29.1477i) q^{47} -33.8995 q^{50} +(15.5147 + 8.95743i) q^{52} +(-35.4853 + 61.4623i) q^{53} -10.3923i q^{55} +(-21.2132 - 36.7423i) q^{58} +(-0.426407 - 0.246186i) q^{59} +(2.48528 - 1.43488i) q^{61} -70.9631i q^{62} +8.00000 q^{64} +(4.54416 + 7.87071i) q^{65} +(-13.5147 + 23.4082i) q^{67} +(-52.6690 + 30.4085i) q^{68} -50.6102 q^{71} +(61.1543 + 35.3075i) q^{73} +(21.8579 - 37.8589i) q^{74} -32.2636i q^{76} +(-66.9117 - 115.894i) q^{79} +(3.51472 + 2.02922i) q^{80} +(-8.69848 + 5.02207i) q^{82} +104.415i q^{83} -30.8528 q^{85} +(-52.6274 - 91.1534i) q^{86} +(14.4853 - 25.0892i) q^{88} +(-125.548 + 72.4850i) q^{89} +13.4558 q^{92} +(71.3970 + 41.2211i) q^{94} +(8.18377 - 14.1747i) q^{95} -100.705i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 12 q^{5} + 12 q^{10} - 12 q^{11} - 8 q^{16} + 12 q^{17} + 12 q^{19} - 24 q^{22} + 12 q^{23} - 14 q^{25} - 24 q^{26} - 120 q^{29} - 72 q^{31} + 40 q^{37} - 96 q^{38} - 24 q^{40} - 128 q^{43}+ \cdots - 120 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 12 * q^5 + 12 * q^10 - 12 * q^11 - 8 * q^16 + 12 * q^17 + 12 * q^19 - 24 * q^22 + 12 * q^23 - 14 * q^25 - 24 * q^26 - 120 * q^29 - 72 * q^31 + 40 * q^37 - 96 * q^38 - 24 * q^40 - 128 * q^43 - 24 * q^44 + 36 * q^46 + 168 * q^47 - 96 * q^50 + 96 * q^52 - 108 * q^53 + 168 * q^59 - 24 * q^61 + 32 * q^64 + 120 * q^65 - 88 * q^67 - 24 * q^68 + 120 * q^71 + 24 * q^73 + 144 * q^74 - 64 * q^79 + 48 * q^80 + 84 * q^82 + 216 * q^85 - 120 * q^86 + 24 * q^88 - 324 * q^89 - 48 * q^92 + 48 * q^94 - 120 * q^95

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−0.878680	+	0.507306i	−0.175736	+	0.101461i	−0.585288	−	0.810826i	$-0.699018\pi$
$5$	−0.878680	+	0.507306i	−0.175736	+	0.101461i	0.409552	+	0.912287i	$0.365685\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−1.24264	−	0.717439i	−0.124264	−	0.0717439i
$11$	−5.12132	+	8.87039i	−0.465575	+	0.806399i	−0.999227	−	0.0393049i	$-0.987486\pi$
$11$	−5.12132	+	8.87039i	−0.465575	+	0.806399i	0.533653	+	0.845704i	$0.320819\pi$
$12$		0			0
$13$		−	8.95743i		−	0.689033i	−0.938780	−	0.344516i	$-0.888043\pi$
$13$		−	8.95743i		−	0.689033i	0.938780	−	0.344516i	$-0.111957\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	26.3345	+	15.2042i	1.54909	+	0.894367i	0.998211	+	0.0597816i	$0.0190404\pi$
$17$	26.3345	+	15.2042i	1.54909	+	0.894367i	0.550878	+	0.834586i	$0.314293\pi$
$18$		0			0
$19$	−13.9706	+	8.06591i	−0.735293	+	0.424521i	−0.820355	−	0.571854i	$-0.806224\pi$
$19$	−13.9706	+	8.06591i	−0.735293	+	0.424521i	0.0850625	+	0.996376i	$0.472891\pi$
$20$		−	2.02922i		−	0.101461i
$21$		0			0
$22$	−14.4853			−0.658422
$23$	−3.36396	−	5.82655i	−0.146259	−	0.253328i	0.783583	−	0.621287i	$-0.213390\pi$
$23$	−3.36396	−	5.82655i	−0.146259	−	0.253328i	−0.929842	+	0.367959i	$0.880057\pi$
$24$		0			0
$25$	−11.9853	+	20.7591i	−0.479411	+	0.830365i
$26$	10.9706	−	6.33386i	0.421945	−	0.243610i
$27$		0			0
$28$		0			0
$29$	−30.0000			−1.03448			−0.517241	−	0.855840i	$-0.673041\pi$
$29$	−30.0000			−1.03448			−0.517241	+	0.855840i	$0.673041\pi$
$30$		0			0
$31$	−43.4558	−	25.0892i	−1.40180	−	0.809330i	−0.407224	−	0.913328i	$-0.633503\pi$
$31$	−43.4558	−	25.0892i	−1.40180	−	0.809330i	−0.994578	+	0.103998i	$0.966836\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$			43.0041i			1.26483i
$35$		0			0
$36$		0			0
$37$	−15.4558	−	26.7703i	−0.417726	−	0.723522i	0.577985	−	0.816048i	$-0.303839\pi$
$37$	−15.4558	−	26.7703i	−0.417726	−	0.723522i	−0.995710	+	0.0925257i	$0.970506\pi$
$38$	−19.7574	−	11.4069i	−0.519931	−	0.300182i
$39$		0			0
$40$	2.48528	−	1.43488i	0.0621320	−	0.0358719i
$41$			7.10228i			0.173226i	0.996242	+	0.0866132i	$0.0276044\pi$
$41$			7.10228i			0.173226i	−0.996242	+	0.0866132i	$0.972396\pi$
$42$		0			0
$43$	−74.4264			−1.73085			−0.865423	−	0.501041i	$-0.832950\pi$
$43$	−74.4264			−1.73085			−0.865423	+	0.501041i	$0.832950\pi$
$44$	−10.2426	−	17.7408i	−0.232787	−	0.403199i
$45$		0			0
$46$	4.75736	−	8.23999i	0.103421	−	0.179130i
$47$	50.4853	−	29.1477i	1.07415	−	0.620164i	0.144841	−	0.989455i	$-0.453733\pi$
$47$	50.4853	−	29.1477i	1.07415	−	0.620164i	0.929314	+	0.369291i	$0.120400\pi$
$48$		0			0
$49$		0			0
$50$	−33.8995			−0.677990
$51$		0			0
$52$	15.5147	+	8.95743i	0.298360	+	0.172258i
$53$	−35.4853	+	61.4623i	−0.669534	+	1.15967i	0.308501	+	0.951224i	$0.400173\pi$
$53$	−35.4853	+	61.4623i	−0.669534	+	1.15967i	−0.978035	+	0.208442i	$0.933161\pi$
$54$		0			0
$55$		−	10.3923i		−	0.188951i
$56$		0			0
$57$		0			0
$58$	−21.2132	−	36.7423i	−0.365745	−	0.633489i
$59$	−0.426407	−	0.246186i	−0.00722724	−	0.00417265i	0.496382	−	0.868104i	$-0.334662\pi$
$59$	−0.426407	−	0.246186i	−0.00722724	−	0.00417265i	−0.503609	+	0.863932i	$0.667995\pi$
$60$		0			0
$61$	2.48528	−	1.43488i	0.0407423	−	0.0235226i	−0.479490	−	0.877547i	$-0.659179\pi$
$61$	2.48528	−	1.43488i	0.0407423	−	0.0235226i	0.520233	+	0.854024i	$0.325845\pi$
$62$		−	70.9631i		−	1.14457i
$63$		0			0
$64$	8.00000			0.125000
$65$	4.54416	+	7.87071i	0.0699101	+	0.121088i
$66$		0			0
$67$	−13.5147	+	23.4082i	−0.201712	+	0.349376i	−0.949080	−	0.315035i	$-0.897984\pi$
$67$	−13.5147	+	23.4082i	−0.201712	+	0.349376i	0.747368	+	0.664410i	$0.231317\pi$
$68$	−52.6690	+	30.4085i	−0.774545	+	0.447184i
$69$		0			0
$70$		0			0
$71$	−50.6102			−0.712819			−0.356410	−	0.934330i	$-0.615999\pi$
$71$	−50.6102			−0.712819			−0.356410	+	0.934330i	$0.615999\pi$
$72$		0			0
$73$	61.1543	+	35.3075i	0.837731	+	0.483664i	0.856492	−	0.516160i	$-0.172639\pi$
$73$	61.1543	+	35.3075i	0.837731	+	0.483664i	−0.0187616	+	0.999824i	$0.505972\pi$
$74$	21.8579	−	37.8589i	0.295377	−	0.511607i
$75$		0			0
$76$		−	32.2636i		−	0.424521i
$77$		0			0
$78$		0			0
$79$	−66.9117	−	115.894i	−0.846983	−	1.46702i	−0.883888	−	0.467699i	$-0.845083\pi$
$79$	−66.9117	−	115.894i	−0.846983	−	1.46702i	0.0369042	−	0.999319i	$-0.488250\pi$
$80$	3.51472	+	2.02922i	0.0439340	+	0.0253653i
$81$		0			0
$82$	−8.69848	+	5.02207i	−0.106079	+	0.0612448i
$83$			104.415i			1.25802i	0.777398	+	0.629009i	$0.216539\pi$
$83$			104.415i			1.25802i	−0.777398	+	0.629009i	$0.783461\pi$
$84$		0			0
$85$	−30.8528			−0.362974
$86$	−52.6274	−	91.1534i	−0.611947	−	1.05992i
$87$		0			0
$88$	14.4853	−	25.0892i	0.164605	−	0.285105i
$89$	−125.548	+	72.4850i	−1.41065	+	0.814438i	−0.995449	−	0.0952921i	$-0.969621\pi$
$89$	−125.548	+	72.4850i	−1.41065	+	0.814438i	−0.415199	+	0.909730i	$0.636288\pi$
$90$		0			0
$91$		0			0
$92$	13.4558			0.146259
$93$		0			0
$94$	71.3970	+	41.2211i	0.759542	+	0.438522i
$95$	8.18377	−	14.1747i	0.0861449	−	0.149207i
$96$		0			0
$97$		−	100.705i		−	1.03820i	−0.854714	−	0.519099i	$-0.826268\pi$
$97$		−	100.705i		−	1.03820i	0.854714	−	0.519099i	$-0.173732\pi$
$98$		0			0
$99$		0			0
$100$	−23.9706	−	41.5182i	−0.239706	−	0.415182i
$101$	−120.276	−	69.4412i	−1.19085	−	0.687536i	−0.232349	−	0.972632i	$-0.574641\pi$
$101$	−120.276	−	69.4412i	−1.19085	−	0.687536i	−0.958499	+	0.285096i	$0.907975\pi$
$102$		0			0
$103$	68.3087	−	39.4380i	0.663191	−	0.382893i	−0.130301	−	0.991475i	$-0.541594\pi$
$103$	68.3087	−	39.4380i	0.663191	−	0.382893i	0.793492	+	0.608581i	$0.208261\pi$
$104$			25.3354i			0.243610i
$105$		0			0
$106$	−100.368			−0.946864
$107$	−18.8787	−	32.6988i	−0.176436	−	0.305597i	0.764221	−	0.644954i	$-0.223124\pi$
$107$	−18.8787	−	32.6988i	−0.176436	−	0.305597i	−0.940657	+	0.339358i	$0.889790\pi$
$108$		0			0
$109$	−15.9706	+	27.6618i	−0.146519	+	0.253778i	−0.929939	−	0.367715i	$-0.880140\pi$
$109$	−15.9706	+	27.6618i	−0.146519	+	0.253778i	0.783420	+	0.621493i	$0.213474\pi$
$110$	12.7279	−	7.34847i	0.115708	−	0.0668043i
$111$		0			0
$112$		0			0
$113$	106.971			0.946642			0.473321	−	0.880890i	$-0.343055\pi$
$113$	106.971			0.946642			0.473321	+	0.880890i	$0.343055\pi$
$114$		0			0
$115$	5.91169	+	3.41311i	0.0514060	+	0.0296793i
$116$	30.0000	−	51.9615i	0.258621	−	0.447944i
$117$		0			0
$118$		−	0.696320i		−	0.00590101i
$119$		0			0
$120$		0			0
$121$	8.04416	+	13.9329i	0.0664806	+	0.115148i
$122$	3.51472	+	2.02922i	0.0288092	+	0.0166330i
$123$		0			0
$124$	86.9117	−	50.1785i	0.700901	−	0.404665i
$125$		−	49.6861i		−	0.397489i
$126$		0			0
$127$	22.0589			0.173692			0.0868460	−	0.996222i	$-0.472321\pi$
$127$	22.0589			0.173692			0.0868460	+	0.996222i	$0.472321\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−6.42641	+	11.1309i	−0.0494339	+	0.0856220i
$131$	61.4558	−	35.4815i	0.469129	−	0.270852i	−0.246746	−	0.969080i	$-0.579361\pi$
$131$	61.4558	−	35.4815i	0.469129	−	0.270852i	0.715875	+	0.698229i	$0.246028\pi$
$132$		0			0
$133$		0			0
$134$	−38.2254			−0.285264
$135$		0			0
$136$	−74.4853	−	43.0041i	−0.547686	−	0.316207i
$137$	−52.8823	+	91.5947i	−0.386002	+	0.668575i	−0.991908	−	0.126962i	$-0.959477\pi$
$137$	−52.8823	+	91.5947i	−0.386002	+	0.668575i	0.605906	+	0.795536i	$0.292811\pi$
$138$		0			0
$139$			181.322i			1.30447i	0.758015	+	0.652237i	$0.226169\pi$
$139$			181.322i			1.30447i	−0.758015	+	0.652237i	$0.773831\pi$
$140$		0			0
$141$		0			0
$142$	−35.7868	−	61.9845i	−0.252020	−	0.436511i
$143$	79.4558	+	45.8739i	0.555635	+	0.320796i
$144$		0			0
$145$	26.3604	−	15.2192i	0.181796	−	0.104960i
$146$			99.8646i			0.684004i
$147$		0			0
$148$	61.8234			0.417726
$149$	20.5736	+	35.6345i	0.138078	+	0.239158i	0.926769	−	0.375632i	$-0.122574\pi$
$149$	20.5736	+	35.6345i	0.138078	+	0.239158i	−0.788691	+	0.614790i	$0.789241\pi$
$150$		0			0
$151$	−40.1838	+	69.6003i	−0.266118	+	0.460929i	−0.967856	−	0.251506i	$-0.919074\pi$
$151$	−40.1838	+	69.6003i	−0.266118	+	0.460929i	0.701738	+	0.712435i	$0.252408\pi$
$152$	39.5147	−	22.8138i	0.259965	−	0.150091i
$153$		0			0
$154$		0			0
$155$	50.9117			0.328463
$156$		0			0
$157$	49.6325	+	28.6553i	0.316130	+	0.182518i	0.649666	−	0.760219i	$-0.274909\pi$
$157$	49.6325	+	28.6553i	0.316130	+	0.182518i	−0.333536	+	0.942737i	$0.608242\pi$
$158$	94.6274	−	163.899i	0.598908	−	1.03734i
$159$		0			0
$160$			5.73951i			0.0358719i
$161$		0			0
$162$		0			0
$163$	87.4558	+	151.478i	0.536539	+	0.929313i	0.999087	+	0.0427185i	$0.0136019\pi$
$163$	87.4558	+	151.478i	0.536539	+	0.929313i	−0.462548	+	0.886594i	$0.653065\pi$
$164$	−12.3015	−	7.10228i	−0.0750092	−	0.0433066i
$165$		0			0
$166$	−127.882	+	73.8329i	−0.770375	+	0.444776i
$167$		−	196.163i		−	1.17463i	−0.809359	−	0.587315i	$-0.800185\pi$
$167$		−	196.163i		−	1.17463i	0.809359	−	0.587315i	$-0.199815\pi$
$168$		0			0
$169$	88.7645			0.525234
$170$	−21.8162	−	37.7868i	−0.128331	−	0.222275i
$171$		0			0
$172$	74.4264	−	128.910i	0.432712	−	0.749479i
$173$	33.3640	−	19.2627i	0.192855	−	0.111345i	−0.400463	−	0.916313i	$-0.631151\pi$
$173$	33.3640	−	19.2627i	0.192855	−	0.111345i	0.593319	+	0.804968i	$0.297817\pi$
$174$		0			0
$175$		0			0
$176$	40.9706			0.232787
$177$		0			0
$178$	−177.551	−	102.509i	−0.997479	−	0.575895i
$179$	−95.5477	+	165.494i	−0.533786	+	0.924545i	0.465435	+	0.885082i	$0.345898\pi$
$179$	−95.5477	+	165.494i	−0.533786	+	0.924545i	−0.999221	+	0.0394627i	$0.987435\pi$
$180$		0			0
$181$			120.793i			0.667367i	0.942685	+	0.333683i	$0.108292\pi$
$181$			120.793i			0.667367i	−0.942685	+	0.333683i	$0.891708\pi$
$182$		0			0
$183$		0			0
$184$	9.51472	+	16.4800i	0.0517104	+	0.0895651i
$185$	27.1615	+	15.6817i	0.146819	+	0.0847659i
$186$		0			0
$187$	−269.735	+	155.732i	−1.44243	+	0.832789i
$188$			116.591i			0.620164i
$189$		0			0
$190$	23.1472			0.121827
$191$	56.0330	+	97.0520i	0.293367	+	0.508126i	0.974604	−	0.223937i	$-0.0718910\pi$
$191$	56.0330	+	97.0520i	0.293367	+	0.508126i	−0.681237	+	0.732063i	$0.738558\pi$
$192$		0			0
$193$	11.4558	−	19.8421i	0.0593567	−	0.102809i	−0.834820	−	0.550523i	$-0.814428\pi$
$193$	11.4558	−	19.8421i	0.0593567	−	0.102809i	0.894177	+	0.447714i	$0.147762\pi$
$194$	123.338	−	71.2093i	0.635763	−	0.367058i
$195$		0			0
$196$		0			0
$197$	116.059			0.589131			0.294566	−	0.955631i	$-0.404825\pi$
$197$	116.059			0.589131			0.294566	+	0.955631i	$0.404825\pi$
$198$		0			0
$199$	−141.250	−	81.5506i	−0.709798	−	0.409802i	0.101188	−	0.994867i	$-0.467736\pi$
$199$	−141.250	−	81.5506i	−0.709798	−	0.409802i	−0.810986	+	0.585065i	$0.801069\pi$
$200$	33.8995	−	58.7156i	0.169497	−	0.293578i
$201$		0			0
$202$		−	196.409i		−	0.972323i
$203$		0			0
$204$		0			0
$205$	−3.60303	−	6.24063i	−0.0175758	−	0.0304421i
$206$	96.6030	+	55.7738i	0.468947	+	0.270747i
$207$		0			0
$208$	−31.0294	+	17.9149i	−0.149180	+	0.0861291i
$209$		−	165.232i		−	0.790586i
$210$		0			0
$211$	106.426			0.504391			0.252195	−	0.967676i	$-0.418847\pi$
$211$	106.426			0.504391			0.252195	+	0.967676i	$0.418847\pi$
$212$	−70.9706	−	122.925i	−0.334767	−	0.579833i
$213$		0			0
$214$	26.6985	−	46.2431i	0.124759	−	0.216089i
$215$	65.3970	−	37.7570i	0.304172	−	0.175614i
$216$		0			0
$217$		0			0
$218$	−45.1716			−0.207209
$219$		0			0
$220$	18.0000	+	10.3923i	0.0818182	+	0.0472377i
$221$	136.191	−	235.890i	0.616248	−	1.06737i
$222$		0			0
$223$		−	57.0047i		−	0.255627i	−0.991798	−	0.127813i	$-0.959204\pi$
$223$		−	57.0047i		−	0.255627i	0.991798	−	0.127813i	$-0.0407958\pi$
$224$		0			0
$225$		0			0
$226$	75.6396	+	131.012i	0.334689	+	0.579698i
$227$	248.912	+	143.709i	1.09653	+	0.633080i	0.935307	−	0.353838i	$-0.115124\pi$
$227$	248.912	+	143.709i	1.09653	+	0.633080i	0.161221	+	0.986918i	$0.448457\pi$
$228$		0			0
$229$	120.728	−	69.7023i	0.527196	−	0.304377i	−0.212678	−	0.977122i	$-0.568218\pi$
$229$	120.728	−	69.7023i	0.527196	−	0.304377i	0.739874	+	0.672746i	$0.234885\pi$
$230$			9.65375i			0.0419728i
$231$		0			0
$232$	84.8528			0.365745
$233$	181.368	+	314.138i	0.778401	+	1.34823i	0.932863	+	0.360232i	$0.117302\pi$
$233$	181.368	+	314.138i	0.778401	+	1.34823i	−0.154461	+	0.987999i	$0.549364\pi$
$234$		0			0
$235$	−29.5736	+	51.2230i	−0.125845	+	0.217970i
$236$	0.852814	−	0.492372i	0.00361362	−	0.00208632i
$237$		0			0
$238$		0			0
$239$	−18.4781			−0.0773144			−0.0386572	−	0.999253i	$-0.512308\pi$
$239$	−18.4781			−0.0773144			−0.0386572	+	0.999253i	$0.512308\pi$
$240$		0			0
$241$	154.243	+	89.0520i	0.640011	+	0.369510i	0.784619	−	0.619979i	$-0.212859\pi$
$241$	154.243	+	89.0520i	0.640011	+	0.369510i	−0.144608	+	0.989489i	$0.546192\pi$
$242$	−11.3762	+	19.7041i	−0.0470089	+	0.0814218i
$243$		0			0
$244$			5.73951i			0.0235226i
$245$		0			0
$246$		0			0
$247$	72.2498	+	125.140i	0.292509	+	0.506641i
$248$	122.912	+	70.9631i	0.495612	+	0.286142i
$249$		0			0
$250$	60.8528	−	35.1334i	0.243411	−	0.140534i
$251$		−	50.6709i		−	0.201876i	−0.994893	−	0.100938i	$-0.967816\pi$
$251$		−	50.6709i		−	0.201876i	0.994893	−	0.100938i	$-0.0321844\pi$
$252$		0			0
$253$	68.9117			0.272378
$254$	15.5980	+	27.0165i	0.0614094	+	0.106364i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−162.452	+	93.7919i	−0.632110	+	0.364949i	−0.781569	−	0.623819i	$-0.785580\pi$
$257$	−162.452	+	93.7919i	−0.632110	+	0.364949i	0.149459	+	0.988768i	$0.452247\pi$
$258$		0			0
$259$		0			0
$260$	−18.1766			−0.0699101
$261$		0			0
$262$	86.9117	+	50.1785i	0.331724	+	0.191521i
$263$	−201.489	+	348.989i	−0.766117	+	1.32695i	0.173537	+	0.984827i	$0.444481\pi$
$263$	−201.489	+	348.989i	−0.766117	+	1.32695i	−0.939654	+	0.342127i	$0.888853\pi$
$264$		0			0
$265$		−	72.0076i		−	0.271727i
$266$		0			0
$267$		0			0
$268$	−27.0294	−	46.8164i	−0.100856	−	0.174688i
$269$	−416.158	−	240.269i	−1.54706	−	0.893193i	−0.998365	−	0.0571675i	$-0.981793\pi$
$269$	−416.158	−	240.269i	−1.54706	−	0.893193i	−0.548691	−	0.836025i	$-0.684874\pi$
$270$		0			0
$271$	−32.3087	+	18.6534i	−0.119220	+	0.0688318i	−0.558424	−	0.829556i	$-0.688594\pi$
$271$	−32.3087	+	18.6534i	−0.119220	+	0.0688318i	0.439204	+	0.898387i	$0.355261\pi$
$272$		−	121.634i		−	0.447184i
$273$		0			0
$274$	−149.574			−0.545889
$275$	−122.761	−	212.628i	−0.446403	−	0.773193i
$276$		0			0
$277$	41.3381	−	71.5997i	0.149235	−	0.258483i	−0.781710	−	0.623642i	$-0.785652\pi$
$277$	41.3381	−	71.5997i	0.149235	−	0.258483i	0.930945	+	0.365160i	$0.118986\pi$
$278$	−222.073	+	128.214i	−0.798824	+	0.461201i
$279$		0			0
$280$		0			0
$281$	150.853			0.536843			0.268421	−	0.963302i	$-0.413498\pi$
$281$	150.853			0.536843			0.268421	+	0.963302i	$0.413498\pi$
$282$		0			0
$283$	−246.088	−	142.079i	−0.869570	−	0.502046i	−0.00236468	−	0.999997i	$-0.500753\pi$
$283$	−246.088	−	142.079i	−0.869570	−	0.502046i	−0.867205	+	0.497951i	$0.834086\pi$
$284$	50.6102	−	87.6594i	0.178205	−	0.308660i
$285$		0			0
$286$			129.751i			0.453674i
$287$		0			0
$288$		0			0
$289$	317.838	+	550.512i	1.09979	+	1.90488i
$290$	37.2792	+	21.5232i	0.128549	+	0.0742178i
$291$		0			0
$292$	−122.309	+	70.6149i	−0.418865	+	0.241832i
$293$			537.237i			1.83357i	0.399379	+	0.916786i	$0.369226\pi$
$293$			537.237i			1.83357i	−0.399379	+	0.916786i	$0.630774\pi$
$294$		0			0
$295$	0.499567			0.00169345
$296$	43.7157	+	75.7179i	0.147688	+	0.255804i
$297$		0			0
$298$	−29.0955	+	50.3948i	−0.0976358	+	0.169110i
$299$	−52.1909	+	30.1324i	−0.174552	+	0.100777i
$300$		0			0
$301$		0			0
$302$	−113.657			−0.376347
$303$		0			0
$304$	55.8823	+	32.2636i	0.183823	+	0.106130i
$305$	−1.45584	+	2.52160i	−0.00477326	+	0.00826753i
$306$		0			0
$307$		−	34.7430i		−	0.113169i	−0.998398	−	0.0565847i	$-0.981979\pi$
$307$		−	34.7430i		−	0.113169i	0.998398	−	0.0565847i	$-0.0180211\pi$
$308$		0			0
$309$		0			0
$310$	36.0000	+	62.3538i	0.116129	+	0.201141i
$311$	−77.2203	−	44.5832i	−0.248297	−	0.143354i	0.370687	−	0.928758i	$-0.379122\pi$
$311$	−77.2203	−	44.5832i	−0.248297	−	0.143354i	−0.618984	+	0.785403i	$0.712456\pi$
$312$		0			0
$313$	450.073	−	259.850i	1.43793	−	0.830191i	0.440227	−	0.897886i	$-0.354898\pi$
$313$	450.073	−	259.850i	1.43793	−	0.830191i	0.997706	+	0.0676951i	$0.0215645\pi$
$314$			81.0495i			0.258119i
$315$		0			0
$316$	267.647			0.846983
$317$	271.014	+	469.411i	0.854935	+	1.48079i	0.876706	+	0.481027i	$0.159736\pi$
$317$	271.014	+	469.411i	0.854935	+	1.48079i	−0.0217710	+	0.999763i	$0.506930\pi$
$318$		0			0
$319$	153.640	−	266.112i	0.481629	−	0.834206i
$320$	−7.02944	+	4.05845i	−0.0219670	+	0.0126826i
$321$		0			0
$322$		0			0
$323$	−490.544			−1.51871
$324$		0			0
$325$	185.948	+	107.357i	0.572149	+	0.330330i
$326$	−123.681	+	214.222i	−0.379390	+	0.657123i
$327$		0			0
$328$		−	20.0883i		−	0.0612448i
$329$		0			0
$330$		0			0
$331$	−89.8162	−	155.566i	−0.271348	−	0.469989i	0.697859	−	0.716235i	$-0.254136\pi$
$331$	−89.8162	−	155.566i	−0.271348	−	0.469989i	−0.969207	+	0.246246i	$0.920803\pi$
$332$	−180.853	−	104.415i	−0.544737	−	0.314504i
$333$		0			0
$334$	240.250	−	138.708i	0.719311	−	0.415294i
$335$		−	27.4244i		−	0.0818638i
$336$		0			0
$337$	291.823			0.865945			0.432972	−	0.901407i	$-0.357465\pi$
$337$	291.823			0.865945			0.432972	+	0.901407i	$0.357465\pi$
$338$	62.7660	+	108.714i	0.185698	+	0.321639i
$339$		0			0
$340$	30.8528	−	53.4386i	0.0907436	−	0.157172i
$341$	445.103	−	256.980i	1.30529	−	0.753607i
$342$		0			0
$343$		0			0
$344$	210.510			0.611947
$345$		0			0
$346$	47.1838	+	27.2416i	0.136369	+	0.0787328i
$347$	226.040	−	391.513i	0.651413	−	1.12828i	−0.331368	−	0.943502i	$-0.607510\pi$
$347$	226.040	−	391.513i	0.651413	−	1.12828i	0.982780	−	0.184778i	$-0.0591566\pi$
$348$		0			0
$349$			235.067i			0.673543i	0.941586	+	0.336772i	$0.109335\pi$
$349$			235.067i			0.673543i	−0.941586	+	0.336772i	$0.890665\pi$
$350$		0			0
$351$		0			0
$352$	28.9706	+	50.1785i	0.0823027	+	0.142553i
$353$	−21.8635	−	12.6229i	−0.0619363	−	0.0357590i	0.468712	−	0.883351i	$-0.344718\pi$
$353$	−21.8635	−	12.6229i	−0.0619363	−	0.0357590i	−0.530648	+	0.847592i	$0.678052\pi$
$354$		0			0
$355$	44.4701	−	25.6748i	0.125268	−	0.0723235i
$356$		−	289.940i		−	0.814438i
$357$		0			0
$358$	−270.250			−0.754888
$359$	−53.1213	−	92.0088i	−0.147970	−	0.256292i	0.782507	−	0.622642i	$-0.213941\pi$
$359$	−53.1213	−	92.0088i	−0.147970	−	0.256292i	−0.930477	+	0.366350i	$0.880607\pi$
$360$		0			0
$361$	−50.3823	+	87.2646i	−0.139563	+	0.241730i
$362$	−147.941	+	85.4138i	−0.408677	+	0.235950i
$363$		0			0
$364$		0			0
$365$	−71.6468			−0.196292
$366$		0			0
$367$	248.044	+	143.208i	0.675868	+	0.390213i	0.798297	−	0.602265i	$-0.205735\pi$
$367$	248.044	+	143.208i	0.675868	+	0.390213i	−0.122428	+	0.992477i	$0.539068\pi$
$368$	−13.4558	+	23.3062i	−0.0365648	+	0.0633321i
$369$		0			0
$370$			44.3545i			0.119877i
$371$		0			0
$372$		0			0
$373$	211.735	+	366.736i	0.567654	+	0.983206i	0.996797	+	0.0799696i	$0.0254823\pi$
$373$	211.735	+	366.736i	0.567654	+	0.983206i	−0.429143	+	0.903237i	$0.641184\pi$
$374$	−381.463	−	220.238i	−1.01995	−	0.588871i
$375$		0			0
$376$	−142.794	+	82.4421i	−0.379771	+	0.219261i
$377$			268.723i			0.712793i
$378$		0			0
$379$	101.103			0.266761			0.133381	−	0.991065i	$-0.457417\pi$
$379$	101.103			0.266761			0.133381	+	0.991065i	$0.457417\pi$
$380$	16.3675	+	28.3494i	0.0430725	+	0.0746037i
$381$		0			0
$382$	−79.2426	+	137.252i	−0.207441	+	0.359299i
$383$	−190.867	+	110.197i	−0.498348	+	0.287721i	−0.728031	−	0.685544i	$-0.759564\pi$
$383$	−190.867	+	110.197i	−0.498348	+	0.287721i	0.229683	+	0.973265i	$0.426231\pi$
$384$		0			0
$385$		0			0
$386$	32.4020			0.0839431
$387$		0			0
$388$	174.426	+	100.705i	0.449553	+	0.259549i
$389$	−191.735	+	332.095i	−0.492892	+	0.853714i	−0.999966	−	0.00818803i	$-0.997394\pi$
$389$	−191.735	+	332.095i	−0.492892	+	0.853714i	0.507074	+	0.861902i	$0.330727\pi$
$390$		0			0
$391$		−	204.586i		−	0.523238i
$392$		0			0
$393$		0			0
$394$	82.0660	+	142.143i	0.208289	+	0.360768i
$395$	117.588	+	67.8894i	0.297691	+	0.171872i
$396$		0			0
$397$	−420.177	+	242.589i	−1.05838	+	0.611056i	−0.924984	−	0.380007i	$-0.875922\pi$
$397$	−420.177	+	242.589i	−1.05838	+	0.611056i	−0.133396	+	0.991063i	$0.542588\pi$
$398$		−	230.660i		−	0.579548i
$399$		0			0
$400$	95.8823			0.239706
$401$	−126.588	−	219.257i	−0.315680	−	0.546775i	0.663901	−	0.747820i	$-0.268899\pi$
$401$	−126.588	−	219.257i	−0.315680	−	0.546775i	−0.979582	+	0.201045i	$0.935566\pi$
$402$		0			0
$403$	−224.735	+	389.253i	−0.557655	+	0.965887i
$404$	240.551	−	138.882i	0.595424	−	0.343768i
$405$		0			0
$406$		0			0
$407$	316.617			0.777930
$408$		0			0
$409$	−4.66905	−	2.69568i	−0.0114158	−	0.00659089i	0.494281	−	0.869302i	$-0.335431\pi$
$409$	−4.66905	−	2.69568i	−0.0114158	−	0.00659089i	−0.505697	+	0.862711i	$0.668765\pi$
$410$	5.09545	−	8.82559i	0.0124279	−	0.0215258i
$411$		0			0
$412$			157.752i			0.382893i
$413$		0			0
$414$		0			0
$415$	−52.9706	−	91.7477i	−0.127640	−	0.221079i
$416$	−43.8823	−	25.3354i	−0.105486	−	0.0609025i
$417$		0			0
$418$	202.368	−	116.837i	0.484133	−	0.279514i
$419$		−	294.431i		−	0.702700i	−0.936244	−	0.351350i	$-0.885723\pi$
$419$		−	294.431i		−	0.702700i	0.936244	−	0.351350i	$-0.114277\pi$
$420$		0			0
$421$	−290.441			−0.689883			−0.344941	−	0.938624i	$-0.612101\pi$
$421$	−290.441			−0.689883			−0.344941	+	0.938624i	$0.612101\pi$
$422$	75.2548	+	130.345i	0.178329	+	0.308875i
$423$		0			0
$424$	100.368	−	173.842i	0.236716	−	0.410004i
$425$	−631.253	+	364.454i	−1.48530	+	0.857540i
$426$		0			0
$427$		0			0
$428$	75.5147			0.176436
$429$		0			0
$430$	92.4853	+	53.3964i	0.215082	+	0.124178i
$431$	25.3568	−	43.9193i	0.0588325	−	0.101901i	−0.835109	−	0.550084i	$-0.814596\pi$
$431$	25.3568	−	43.9193i	0.0588325	−	0.101901i	0.893942	+	0.448183i	$0.147929\pi$
$432$		0			0
$433$		−	724.761i		−	1.67381i	−0.547347	−	0.836906i	$-0.684362\pi$
$433$		−	724.761i		−	1.67381i	0.547347	−	0.836906i	$-0.315638\pi$
$434$		0			0
$435$		0			0
$436$	−31.9411	−	55.3237i	−0.0732595	−	0.126889i
$437$	93.9929	+	54.2668i	0.215087	+	0.124180i
$438$		0			0
$439$	−321.926	+	185.864i	−0.733317	+	0.423381i	−0.819634	−	0.572887i	$-0.805823\pi$
$439$	−321.926	+	185.864i	−0.733317	+	0.423381i	0.0863177	+	0.996268i	$0.472490\pi$
$440$			29.3939i			0.0668043i
$441$		0			0
$442$	385.206			0.871507
$443$	−114.629	−	198.543i	−0.258756	−	0.448178i	0.707153	−	0.707061i	$-0.249979\pi$
$443$	−114.629	−	198.543i	−0.258756	−	0.448178i	−0.965909	+	0.258882i	$0.916646\pi$
$444$		0			0
$445$	73.5442	−	127.382i	0.165268	−	0.286252i
$446$	69.8162	−	40.3084i	0.156539	−	0.0903776i
$447$		0			0
$448$		0			0
$449$	600.323			1.33702			0.668511	−	0.743702i	$-0.266932\pi$
$449$	600.323			1.33702			0.668511	+	0.743702i	$0.266932\pi$
$450$		0			0
$451$	−63.0000	−	36.3731i	−0.139690	−	0.0806498i
$452$	−106.971	+	185.278i	−0.236661	+	0.409908i
$453$		0			0
$454$			406.471i			0.895311i
$455$		0			0
$456$		0			0
$457$	−241.912	−	419.003i	−0.529347	−	0.916856i	−0.999414	−	0.0342255i	$-0.989104\pi$
$457$	−241.912	−	419.003i	−0.529347	−	0.916856i	0.470067	−	0.882631i	$-0.344230\pi$
$458$	170.735	+	98.5739i	0.372784	+	0.215227i
$459$		0			0
$460$	−11.8234	+	6.82623i	−0.0257030	+	0.0148396i
$461$		−	274.661i		−	0.595794i	−0.954598	−	0.297897i	$-0.903715\pi$
$461$		−	274.661i		−	0.595794i	0.954598	−	0.297897i	$-0.0962852\pi$
$462$		0			0
$463$	−153.470			−0.331469			−0.165734	−	0.986170i	$-0.552999\pi$
$463$	−153.470			−0.331469			−0.165734	+	0.986170i	$0.552999\pi$
$464$	60.0000	+	103.923i	0.129310	+	0.223972i
$465$		0			0
$466$	−256.492	+	444.258i	−0.550413	+	0.953343i
$467$	53.4701	−	30.8710i	0.114497	−	0.0661049i	−0.441658	−	0.897184i	$-0.645609\pi$
$467$	53.4701	−	30.8710i	0.114497	−	0.0661049i	0.556155	+	0.831079i	$0.312276\pi$
$468$		0			0
$469$		0			0
$470$	−83.6468			−0.177972
$471$		0			0
$472$	1.20606	+	0.696320i	0.00255521	+	0.00147525i
$473$	381.161	−	660.191i	0.805838	−	1.39575i
$474$		0			0
$475$		−	386.689i		−	0.814082i
$476$		0			0
$477$		0			0
$478$	−13.0660	−	22.6310i	−0.0273348	−	0.0473452i
$479$	481.955	+	278.257i	1.00617	+	0.580912i	0.910068	−	0.414459i	$-0.136029\pi$
$479$	481.955	+	278.257i	1.00617	+	0.580912i	0.0961020	+	0.995371i	$0.469363\pi$
$480$		0			0
$481$	−239.793	+	138.445i	−0.498530	+	0.287827i
$482$			251.877i			0.522567i
$483$		0			0
$484$	−32.1766			−0.0664806
$485$	51.0883	+	88.4876i	0.105337	+	0.182449i
$486$		0			0
$487$	162.610	−	281.649i	0.333902	−	0.578335i	−0.649371	−	0.760471i	$-0.724968\pi$
$487$	162.610	−	281.649i	0.333902	−	0.578335i	0.983273	+	0.182136i	$0.0583013\pi$
$488$	−7.02944	+	4.05845i	−0.0144046	+	0.00831649i
$489$		0			0
$490$		0			0
$491$	−643.477			−1.31054			−0.655272	−	0.755393i	$-0.727446\pi$
$491$	−643.477			−1.31054			−0.655272	+	0.755393i	$0.727446\pi$
$492$		0			0
$493$	−790.036	−	456.127i	−1.60251	−	0.925208i
$494$	−102.177	+	176.975i	−0.206835	+	0.358249i
$495$		0			0
$496$			200.714i			0.404665i
$497$		0			0
$498$		0			0
$499$	−377.713	−	654.218i	−0.756939	−	1.31106i	−0.944404	−	0.328786i	$-0.893360\pi$
$499$	−377.713	−	654.218i	−0.756939	−	1.31106i	0.187465	−	0.982271i	$-0.439973\pi$
$500$	86.0589	+	49.6861i	0.172118	+	0.0993722i
$501$		0			0
$502$	62.0589	−	35.8297i	0.123623	−	0.0713739i
$503$			509.409i			1.01274i	0.862316	+	0.506371i	$0.169013\pi$
$503$			509.409i			1.01274i	−0.862316	+	0.506371i	$0.830987\pi$
$504$		0			0
$505$	140.912			0.279033
$506$	48.7279	+	84.3992i	0.0963002	+	0.166797i
$507$		0			0
$508$	−22.0589	+	38.2071i	−0.0434230	+	0.0752108i
$509$	666.349	−	384.717i	1.30913	−	0.755828i	0.327182	−	0.944961i	$-0.393901\pi$
$509$	666.349	−	384.717i	1.30913	−	0.755828i	0.981951	+	0.189133i	$0.0605677\pi$
$510$		0			0
$511$		0			0
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−229.742	−	132.642i	−0.446969	−	0.258058i
$515$	−40.0143	+	69.3068i	−0.0776976	+	0.134576i
$516$		0			0
$517$			597.099i			1.15493i
$518$		0			0
$519$		0			0
$520$	−12.8528	−	22.2617i	−0.0247169	−	0.0428110i
$521$	463.503	+	267.604i	0.889641	+	0.513635i	0.873825	−	0.486240i	$-0.161632\pi$
$521$	463.503	+	267.604i	0.889641	+	0.513635i	0.0158162	+	0.999875i	$0.494965\pi$
$522$		0			0
$523$	726.999	−	419.733i	1.39006	−	0.802549i	0.396735	−	0.917933i	$-0.370143\pi$
$523$	726.999	−	419.733i	1.39006	−	0.802549i	0.993321	+	0.115384i	$0.0368099\pi$
$524$			141.926i			0.270852i
$525$		0			0
$526$	−569.897			−1.08345
$527$	−762.926	−	1321.43i	−1.44768	−	2.50745i
$528$		0			0
$529$	241.868	−	418.927i	0.457217	−	0.791922i
$530$	88.1909	−	50.9170i	0.166398	−	0.0960699i
$531$		0			0
$532$		0			0
$533$	63.6182			0.119359
$534$		0			0
$535$	33.1766	+	19.1545i	0.0620124	+	0.0358029i
$536$	38.2254	−	66.2083i	0.0713160	−	0.123523i
$537$		0			0
$538$		−	679.583i		−	1.26317i
$539$		0			0
$540$		0			0
$541$	−142.926	−	247.555i	−0.264188	−	0.457588i	0.703162	−	0.711029i	$-0.251771\pi$
$541$	−142.926	−	247.555i	−0.264188	−	0.457588i	−0.967351	+	0.253442i	$0.918437\pi$
$542$	−45.6913	−	26.3799i	−0.0843014	−	0.0486714i
$543$		0			0
$544$	148.971	−	86.0082i	0.273843	−	0.158103i
$545$		−	32.4078i		−	0.0594639i
$546$		0			0
$547$	−741.470			−1.35552			−0.677761	−	0.735283i	$-0.737049\pi$
$547$	−741.470			−1.35552			−0.677761	+	0.735283i	$0.737049\pi$
$548$	−105.765	−	183.189i	−0.193001	−	0.334287i
$549$		0			0
$550$	173.610	−	300.702i	0.315655	−	0.546730i
$551$	419.117	−	241.977i	0.760648	−	0.439160i
$552$		0			0
$553$		0			0
$554$	116.922			0.211050
$555$		0			0
$556$	−314.059	−	181.322i	−0.564854	−	0.326119i
$557$	417.426	−	723.004i	0.749419	−	1.29803i	−0.198682	−	0.980064i	$-0.563666\pi$
$557$	417.426	−	723.004i	0.749419	−	1.29803i	0.948101	−	0.317968i	$-0.103000\pi$
$558$		0			0
$559$			666.669i			1.19261i
$560$		0			0
$561$		0			0
$562$	106.669	+	184.756i	0.189803	+	0.328748i
$563$	−361.809	−	208.891i	−0.642645	−	0.371031i	0.142988	−	0.989724i	$-0.454329\pi$
$563$	−361.809	−	208.891i	−0.642645	−	0.371031i	−0.785633	+	0.618693i	$0.787662\pi$
$564$		0			0
$565$	−93.9929	+	54.2668i	−0.166359	+	0.0960474i
$566$		−	401.861i		−	0.710001i
$567$		0			0
$568$	143.147			0.252020
$569$	336.515	+	582.861i	0.591414	+	1.02436i	0.994042	+	0.108996i	$0.0347635\pi$
$569$	336.515	+	582.861i	0.591414	+	1.02436i	−0.402628	+	0.915364i	$0.631903\pi$
$570$		0			0
$571$	132.544	−	229.573i	0.232126	−	0.402055i	−0.726307	−	0.687370i	$-0.758765\pi$
$571$	132.544	−	229.573i	0.232126	−	0.402055i	0.958434	+	0.285315i	$0.0920984\pi$
$572$	−158.912	+	91.7477i	−0.277818	+	0.160398i
$573$		0			0
$574$		0			0
$575$	161.272			0.280473
$576$		0			0
$577$	−405.941	−	234.370i	−0.703537	−	0.406188i	0.105126	−	0.994459i	$-0.466475\pi$
$577$	−405.941	−	234.370i	−0.703537	−	0.406188i	−0.808664	+	0.588271i	$0.799809\pi$
$578$	−449.491	+	778.541i	−0.777666	+	1.34696i
$579$		0			0
$580$			60.8767i			0.104960i
$581$		0			0
$582$		0			0
$583$	−363.463	−	629.536i	−0.623436	−	1.07982i
$584$	−172.971	−	99.8646i	−0.296182	−	0.171001i
$585$		0			0
$586$	−657.978	+	379.884i	−1.12283	+	0.648266i
$587$			120.530i			0.205332i	0.994716	+	0.102666i	$0.0327372\pi$
$587$			120.530i			0.205332i	−0.994716	+	0.102666i	$0.967263\pi$
$588$		0			0
$589$	809.470			1.37431
$590$	0.353247	+	0.611842i	0.000598724	+	0.00103702i
$591$		0			0
$592$	−61.8234	+	107.081i	−0.104431	+	0.180880i
$593$	−486.245	+	280.734i	−0.819975	+	0.473413i	−0.850408	−	0.526124i	$-0.823645\pi$
$593$	−486.245	+	280.734i	−0.819975	+	0.473413i	0.0304327	+	0.999537i	$0.490311\pi$
$594$		0			0
$595$		0			0
$596$	−82.2944			−0.138078
$597$		0			0
$598$	−73.8091	−	42.6137i	−0.123427	−	0.0712604i
$599$	470.054	−	814.158i	0.784732	−	1.35920i	−0.144427	−	0.989515i	$-0.546134\pi$
$599$	470.054	−	814.158i	0.784732	−	1.35920i	0.929159	−	0.369680i	$-0.120533\pi$
$600$		0			0
$601$			563.527i			0.937649i	0.883291	+	0.468824i	$0.155322\pi$
$601$			563.527i			0.937649i	−0.883291	+	0.468824i	$0.844678\pi$
$602$		0			0
$603$		0			0
$604$	−80.3675	−	139.201i	−0.133059	−	0.230465i
$605$	−14.1365	−	8.16170i	−0.0233661	−	0.0134904i
$606$		0			0
$607$	−265.514	+	153.294i	−0.437420	+	0.252544i	−0.702503	−	0.711681i	$-0.747934\pi$
$607$	−265.514	+	153.294i	−0.437420	+	0.252544i	0.265083	+	0.964226i	$0.414601\pi$
$608$			91.2553i			0.150091i
$609$		0			0
$610$	−4.11775			−0.00675041
$611$	−261.088	−	452.218i	−0.427313	−	0.740128i
$612$		0			0
$613$	−137.794	+	238.666i	−0.224786	+	0.389341i	−0.956255	−	0.292533i	$-0.905502\pi$
$613$	−137.794	+	238.666i	−0.224786	+	0.389341i	0.731469	+	0.681875i	$0.238835\pi$
$614$	42.5513	−	24.5670i	0.0693018	−	0.0400114i
$615$		0			0
$616$		0			0
$617$	−461.294			−0.747639			−0.373820	−	0.927501i	$-0.621952\pi$
$617$	−461.294			−0.747639			−0.373820	+	0.927501i	$0.621952\pi$
$618$		0			0
$619$	324.676	+	187.452i	0.524517	+	0.302830i	0.738781	−	0.673946i	$-0.235402\pi$
$619$	324.676	+	187.452i	0.524517	+	0.302830i	−0.214264	+	0.976776i	$0.568735\pi$
$620$	−50.9117	+	88.1816i	−0.0821156	+	0.142228i
$621$		0			0
$622$		−	126.100i		−	0.202734i
$623$		0			0
$624$		0			0
$625$	−274.426	−	475.320i	−0.439082	−	0.760512i
$626$	636.500	+	367.483i	1.01677	+	0.587034i
$627$		0			0
$628$	−99.2649	+	57.3106i	−0.158065	+	0.0912590i
$629$		−	939.978i		−	1.49440i
$630$		0			0
$631$	−1127.32			−1.78656			−0.893282	−	0.449496i	$-0.851603\pi$
$631$	−1127.32			−1.78656			−0.893282	+	0.449496i	$0.851603\pi$
$632$	189.255	+	327.799i	0.299454	+	0.518669i
$633$		0			0
$634$	−383.272	+	663.847i	−0.604530	+	1.04708i
$635$	−19.3827	+	11.1906i	−0.0305239	+	0.0176230i
$636$		0			0
$637$		0			0
$638$	434.558			0.681126
$639$		0			0
$640$	−9.94113	−	5.73951i	−0.0155330	−	0.00896799i
$641$	−442.176	+	765.871i	−0.689822	+	1.19481i	0.282074	+	0.959393i	$0.408978\pi$
$641$	−442.176	+	765.871i	−0.689822	+	1.19481i	−0.971895	+	0.235414i	$0.924356\pi$
$642$		0			0
$643$		−	300.765i		−	0.467753i	−0.972266	−	0.233876i	$-0.924859\pi$
$643$		−	300.765i		−	0.467753i	0.972266	−	0.233876i	$-0.0751411\pi$
$644$		0			0
$645$		0			0
$646$	−346.867	−	600.791i	−0.536946	−	0.930018i
$647$	−814.587	−	470.302i	−1.25902	−	0.726896i	−0.286137	−	0.958189i	$-0.592371\pi$
$647$	−814.587	−	470.302i	−1.25902	−	0.726896i	−0.972884	+	0.231292i	$0.925705\pi$
$648$		0			0
$649$	4.36753	−	2.52160i	0.00672963	−	0.00388536i
$650$			303.652i			0.467157i
$651$		0			0
$652$	−349.823			−0.536539
$653$	−227.985	−	394.881i	−0.349135	−	0.604719i	0.636961	−	0.770896i	$-0.280191\pi$
$653$	−227.985	−	394.881i	−0.349135	−	0.604719i	−0.986096	+	0.166177i	$0.946858\pi$
$654$		0			0
$655$	−36.0000	+	62.3538i	−0.0549618	+	0.0951967i
$656$	24.6030	−	14.2046i	0.0375046	−	0.0216533i
$657$		0			0
$658$		0			0
$659$	−403.684			−0.612571			−0.306285	−	0.951940i	$-0.599086\pi$
$659$	−403.684			−0.612571			−0.306285	+	0.951940i	$0.599086\pi$
$660$		0			0
$661$	998.881	+	576.704i	1.51117	+	0.872473i	0.999915	+	0.0130418i	$0.00415147\pi$
$661$	998.881	+	576.704i	1.51117	+	0.872473i	0.511252	+	0.859431i	$0.329182\pi$
$662$	127.019	−	220.004i	0.191872	−	0.332332i
$663$		0			0
$664$		−	295.331i		−	0.444776i
$665$		0			0
$666$		0			0
$667$	100.919	+	174.797i	0.151303	+	0.262064i
$668$	339.765	+	196.163i	0.508629	+	0.293657i
$669$		0			0
$670$	33.5879	−	19.3920i	0.0501312	−	0.0289432i
$671$			29.3939i			0.0438061i
$672$		0			0
$673$	−607.440			−0.902585			−0.451293	−	0.892376i	$-0.649037\pi$
$673$	−607.440			−0.902585			−0.451293	+	0.892376i	$0.649037\pi$
$674$	206.350	+	357.409i	0.306158	+	0.530281i
$675$		0			0
$676$	−88.7645	+	153.745i	−0.131308	+	0.227433i
$677$	985.180	−	568.794i	1.45521	−	0.840168i	0.456444	−	0.889752i	$-0.349123\pi$
$677$	985.180	−	568.794i	1.45521	−	0.840168i	0.998770	+	0.0495834i	$0.0157894\pi$
$678$		0			0
$679$		0			0
$680$	87.2649			0.128331
$681$		0			0
$682$	629.470	+	363.425i	0.922977	+	0.532881i
$683$	−409.055	+	708.505i	−0.598910	+	1.03734i	0.394073	+	0.919079i	$0.371066\pi$
$683$	−409.055	+	708.505i	−0.598910	+	1.03734i	−0.992982	+	0.118263i	$0.962268\pi$
$684$		0			0
$685$		−	107.310i		−	0.156657i
$686$		0			0
$687$		0			0
$688$	148.853	+	257.821i	0.216356	+	0.374739i
$689$	550.544	+	317.857i	0.799048	+	0.461331i
$690$		0			0
$691$	176.912	−	102.140i	0.256023	−	0.147815i	−0.366496	−	0.930420i	$-0.619443\pi$
$691$	176.912	−	102.140i	0.256023	−	0.147815i	0.622519	+	0.782605i	$0.286109\pi$
$692$			77.0508i			0.111345i
$693$		0			0
$694$	639.338			0.921236
$695$	−91.9857	−	159.324i	−0.132354	−	0.229243i
$696$		0			0
$697$	−107.985	+	187.035i	−0.154928	+	0.268343i
$698$	−287.897	+	166.217i	−0.412459	+	0.238133i
$699$		0			0
$700$		0			0
$701$	318.853			0.454854			0.227427	−	0.973795i	$-0.426969\pi$
$701$	318.853			0.454854			0.227427	+	0.973795i	$0.426969\pi$
$702$		0			0
$703$	431.854	+	249.331i	0.614301	+	0.354667i
$704$	−40.9706	+	70.9631i	−0.0581968	+	0.100800i
$705$		0			0
$706$		−	35.7030i		−	0.0505708i
$707$		0			0
$708$		0			0
$709$	108.823	+	188.488i	0.153489	+	0.265850i	0.932508	−	0.361150i	$-0.117616\pi$
$709$	108.823	+	188.488i	0.153489	+	0.265850i	−0.779019	+	0.627000i	$0.784283\pi$
$710$	62.8903	+	36.3097i	0.0885778	+	0.0511404i
$711$		0			0
$712$	355.103	−	205.019i	0.498740	−	0.287947i
$713$			337.597i			0.473488i
$714$		0			0
$715$	−93.0883			−0.130193
$716$	−191.095	−	330.987i	−0.266893	−	0.462272i
$717$		0			0
$718$	75.1249	−	130.120i	0.104631	−	0.181226i
$719$	−1045.60	+	603.679i	−1.45425	+	0.839609i	−0.998718	−	0.0506134i	$-0.983882\pi$
$719$	−1045.60	+	603.679i	−1.45425	+	0.839609i	−0.455527	+	0.890222i	$0.650549\pi$
$720$		0			0
$721$		0			0
$722$	−142.503			−0.197372
$723$		0			0
$724$	−209.220	−	120.793i	−0.288978	−	0.166842i
$725$	359.558	−	622.773i	0.495943	−	0.858998i
$726$		0			0
$727$			123.231i			0.169506i	0.996402	+	0.0847528i	$0.0270100\pi$
$727$			123.231i			0.169506i	−0.996402	+	0.0847528i	$0.972990\pi$
$728$		0			0
$729$		0			0
$730$	−50.6619	−	87.7490i	−0.0693999	−	0.120204i
$731$	−1959.98	−	1131.60i	−2.68124	−	1.54801i
$732$		0			0
$733$	−325.434	+	187.890i	−0.443976	+	0.256330i	−0.705283	−	0.708926i	$-0.749180\pi$
$733$	−325.434	+	187.890i	−0.443976	+	0.256330i	0.261307	+	0.965256i	$0.415847\pi$
$734$			405.054i			0.551844i
$735$		0			0
$736$	−38.0589			−0.0517104
$737$	−138.426	−	239.762i	−0.187824	−	0.325321i
$738$		0			0
$739$	−361.265	+	625.729i	−0.488856	+	0.846724i	−0.999918	−	0.0128200i	$-0.995919\pi$
$739$	−361.265	+	625.729i	−0.488856	+	0.846724i	0.511061	+	0.859544i	$0.329252\pi$
$740$	−54.3229	+	31.3634i	−0.0734094	+	0.0423829i
$741$		0			0
$742$		0			0
$743$	−1268.48			−1.70724			−0.853618	−	0.520899i	$-0.825597\pi$
$743$	−1268.48			−1.70724			−0.853618	+	0.520899i	$0.825597\pi$
$744$		0			0
$745$	−36.1552	−	20.8742i	−0.0485305	−	0.0280191i
$746$	−299.439	+	518.643i	−0.401392	+	0.695232i
$747$		0			0
$748$		−	622.926i		−	0.832789i
$749$		0			0
$750$		0			0
$751$	−219.581	−	380.325i	−0.292384	−	0.506425i	0.681989	−	0.731363i	$-0.261115\pi$
$751$	−219.581	−	380.325i	−0.292384	−	0.506425i	−0.974373	+	0.224938i	$0.927782\pi$
$752$	−201.941	−	116.591i	−0.268539	−	0.155041i
$753$		0			0
$754$	−329.117	+	190.016i	−0.436495	+	0.252010i
$755$		−	81.5419i		−	0.108002i
$756$		0			0
$757$	−668.530			−0.883131			−0.441565	−	0.897229i	$-0.645577\pi$
$757$	−668.530			−0.883131			−0.441565	+	0.897229i	$0.645577\pi$
$758$	71.4903	+	123.825i	0.0943144	+	0.163357i
$759$		0			0
$760$	−23.1472	+	40.0921i	−0.0304568	+	0.0527528i
$761$	−762.202	+	440.058i	−1.00158	+	0.578263i	−0.908715	−	0.417416i	$-0.862936\pi$
$761$	−762.202	+	440.058i	−1.00158	+	0.578263i	−0.0928647	+	0.995679i	$0.529602\pi$
$762$		0			0
$763$		0			0
$764$	−224.132			−0.293367
$765$		0			0
$766$	−269.927	−	155.842i	−0.352385	−	0.203450i
$767$	−2.20519	+	3.81951i	−0.00287509	+	0.00497980i
$768$		0			0
$769$		−	1163.41i		−	1.51289i	−0.654059	−	0.756444i	$-0.726935\pi$
$769$		−	1163.41i		−	1.51289i	0.654059	−	0.756444i	$-0.273065\pi$
$770$		0			0
$771$		0			0
$772$	22.9117	+	39.6842i	0.0296784	+	0.0514044i
$773$	464.511	+	268.186i	0.600920	+	0.346941i	0.769403	−	0.638763i	$-0.220554\pi$
$773$	464.511	+	268.186i	0.600920	+	0.346941i	−0.168483	+	0.985704i	$0.553887\pi$
$774$		0			0
$775$	1041.66	−	601.403i	1.34408	−	0.776004i
$776$			284.837i			0.367058i
$777$		0			0
$778$	−542.309			−0.697055
$779$	−57.2864	−	99.2229i	−0.0735383	−	0.127372i
$780$		0			0
$781$	259.191	−	448.932i	0.331871	−	0.574817i
$782$	250.566	−	144.664i	0.320416	−	0.184992i
$783$		0			0
$784$		0			0
$785$	−58.1481			−0.0740740
$786$		0			0
$787$	72.6762	+	41.9596i	0.0923459	+	0.0533159i	0.545462	−	0.838136i	$-0.316354\pi$
$787$	72.6762	+	41.9596i	0.0923459	+	0.0533159i	−0.453116	+	0.891452i	$0.649688\pi$
$788$	−116.059	+	201.020i	−0.147283	+	0.255101i
$789$		0			0
$790$			192.020i			0.243064i
$791$		0			0
$792$		0			0
$793$	−12.8528	−	22.2617i	−0.0162078	−	0.0280728i
$794$	−594.219	−	343.073i	−0.748387	−	0.432082i
$795$		0			0
$796$	282.500	−	163.101i	0.354899	−	0.204901i
$797$		−	1005.57i		−	1.26169i	−0.775908	−	0.630846i	$-0.782708\pi$
$797$		−	1005.57i		−	1.26169i	0.775908	−	0.630846i	$-0.217292\pi$
$798$		0			0
$799$	1772.67			2.21862
$800$	67.7990	+	117.431i	0.0847487	+	0.146789i
$801$		0			0
$802$	179.022	−	310.076i	0.223220	−	0.386628i
$803$	−626.382	+	361.642i	−0.780052	+	0.450363i
$804$		0			0
$805$		0			0
$806$	−635.647			−0.788644
$807$		0			0
$808$	340.191	+	196.409i	0.421028	+	0.243081i
$809$	−141.426	+	244.958i	−0.174816	+	0.302791i	−0.940098	−	0.340905i	$-0.889266\pi$
$809$	−141.426	+	244.958i	−0.174816	+	0.302791i	0.765281	+	0.643696i	$0.222600\pi$
$810$		0			0
$811$			923.997i			1.13933i	0.821877	+	0.569665i	$0.192927\pi$
$811$			923.997i			1.13933i	−0.821877	+	0.569665i	$0.807073\pi$
$812$		0			0
$813$		0			0
$814$	223.882	+	387.775i	0.275040	+	0.476383i
$815$	−153.691	−	88.7337i	−0.188578	−	0.108876i
$816$		0			0
$817$	1039.78	−	600.317i	1.27268	−	0.734782i
$818$		−	7.62452i		−	0.00932093i
$819$		0			0
$820$	14.4121			0.0175758
$821$	636.161	+	1101.86i	0.774862	+	1.34210i	0.934872	+	0.354985i	$0.115514\pi$
$821$	636.161	+	1101.86i	0.774862	+	1.34210i	−0.160010	+	0.987115i	$0.551153\pi$
$822$		0			0
$823$	−190.926	+	330.693i	−0.231988	+	0.401815i	−0.958393	−	0.285452i	$-0.907856\pi$
$823$	−190.926	+	330.693i	−0.231988	+	0.401815i	0.726405	+	0.687267i	$0.241190\pi$
$824$	−193.206	+	111.548i	−0.234473	+	0.135373i
$825$		0			0
$826$		0			0
$827$	−653.022			−0.789628			−0.394814	−	0.918761i	$-0.629191\pi$
$827$	−653.022			−0.789628			−0.394814	+	0.918761i	$0.629191\pi$
$828$		0			0
$829$	186.698	+	107.790i	0.225208	+	0.130024i	0.608360	−	0.793662i	$-0.291828\pi$
$829$	186.698	+	107.790i	0.225208	+	0.130024i	−0.383151	+	0.923686i	$0.625161\pi$
$830$	74.9117	−	129.751i	0.0902550	−	0.156326i
$831$		0			0
$832$		−	71.6594i		−	0.0861291i
$833$		0			0
$834$		0			0
$835$	99.5147	+	172.365i	0.119179	+	0.206425i
$836$	286.191	+	165.232i	0.342334	+	0.197646i
$837$		0			0
$838$	360.603	−	208.194i	0.430314	−	0.248442i
$839$			632.267i			0.753596i	0.926295	+	0.376798i	$0.122975\pi$
$839$			632.267i			0.753596i	−0.926295	+	0.376798i	$0.877025\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	−205.373	−	355.716i	−0.243910	−	0.422465i
$843$		0			0
$844$	−106.426	+	184.336i	−0.126098	+	0.218408i
$845$	−77.9956	+	45.0308i	−0.0923024	+	0.0532908i
$846$		0			0
$847$		0			0
$848$	283.882			0.334767
$849$		0			0
$850$	−892.727	−	515.416i	−1.05027	−	0.606372i
$851$	−103.986	+	180.109i	−0.122192	+	0.211643i
$852$		0			0
$853$			919.650i			1.07814i	0.842262	+	0.539068i	$0.181224\pi$
$853$			919.650i			1.07814i	−0.842262	+	0.539068i	$0.818776\pi$
$854$		0			0
$855$		0			0
$856$	53.3970	+	92.4863i	0.0623796	+	0.108045i
$857$	456.525	+	263.575i	0.532702	+	0.307556i	0.742116	−	0.670272i	$-0.233822\pi$
$857$	456.525	+	263.575i	0.532702	+	0.307556i	−0.209414	+	0.977827i	$0.567156\pi$
$858$		0			0
$859$	−207.676	+	119.902i	−0.241765	+	0.139583i	−0.615988	−	0.787756i	$-0.711243\pi$
$859$	−207.676	+	119.902i	−0.241765	+	0.139583i	0.374223	+	0.927339i	$0.377910\pi$
$860$			151.028i			0.175614i
$861$		0			0
$862$	71.7199			0.0832018
$863$	181.253	+	313.940i	0.210027	+	0.363778i	0.951723	−	0.306959i	$-0.0993115\pi$
$863$	181.253	+	313.940i	0.210027	+	0.363778i	−0.741696	+	0.670737i	$0.765978\pi$
$864$		0			0
$865$	−19.5442	+	33.8515i	−0.0225944	+	0.0391346i
$866$	887.647	−	512.483i	1.02500	−	0.591782i
$867$		0			0
$868$		0			0
$869$	1370.70			1.57734
$870$		0			0
$871$	209.677	+	121.057i	0.240731	+	0.138986i
$872$	45.1716	−	78.2395i	0.0518023	−	0.0897242i
$873$		0			0
$874$			153.490i			0.175617i
$875$		0			0
$876$		0			0
$877$	430.823	+	746.208i	0.491247	+	0.850864i	0.999949	−	0.0100781i	$-0.00320801\pi$
$877$	430.823	+	746.208i	0.491247	+	0.850864i	−0.508702	+	0.860942i	$0.669875\pi$
$878$	−455.272	−	262.851i	−0.518533	−	0.299375i
$879$		0			0
$880$	−36.0000	+	20.7846i	−0.0409091	+	0.0236189i
$881$			334.553i			0.379742i	0.981809	+	0.189871i	$0.0608071\pi$
$881$			334.553i			0.379742i	−0.981809	+	0.189871i	$0.939193\pi$
$882$		0			0
$883$	−1488.01			−1.68518			−0.842590	−	0.538555i	$-0.818970\pi$
$883$	−1488.01			−1.68518			−0.842590	+	0.538555i	$0.818970\pi$
$884$	272.382	+	471.779i	0.308124	+	0.533687i
$885$		0			0
$886$	162.110	−	280.782i	0.182968	−	0.316910i
$887$	694.118	−	400.749i	0.782545	−	0.451803i	−0.0547862	−	0.998498i	$-0.517448\pi$
$887$	694.118	−	400.749i	0.782545	−	0.451803i	0.837332	+	0.546695i	$0.184114\pi$
$888$		0			0
$889$		0			0
$890$	208.014			0.233724
$891$		0			0
$892$	98.7351	+	57.0047i	0.110690	+	0.0639066i
$893$	−470.205	+	814.419i	−0.526546	+	0.912004i
$894$		0			0
$895$		−	193.888i		−	0.216634i
$896$		0			0
$897$		0			0
$898$	424.492	+	735.242i	0.472709	+	0.818756i
$899$	1303.68	+	752.677i	1.45014	+	0.837238i
$900$		0			0
$901$	−1868.98	+	1079.05i	−2.07434	+	1.19762i
$902$		−	102.879i		−	0.114056i
$903$		0			0
$904$	−302.558			−0.334689
$905$	−61.2792	−	106.139i	−0.0677118	−	0.117280i
$906$		0			0
$907$	403.640	−	699.124i	0.445027	−	0.770810i	−0.553027	−	0.833163i	$-0.686527\pi$
$907$	403.640	−	699.124i	0.445027	−	0.770810i	0.998054	+	0.0623537i	$0.0198607\pi$
$908$	−497.823	+	287.418i	−0.548264	+	0.316540i
$909$		0			0
$910$		0			0
$911$	442.742			0.485996			0.242998	−	0.970027i	$-0.421869\pi$
$911$	442.742			0.485996			0.242998	+	0.970027i	$0.421869\pi$
$912$		0			0
$913$	−926.205	−	534.745i	−1.01446	−	0.585701i
$914$	342.115	−	592.560i	0.374305	−	0.648315i
$915$		0			0
$916$			278.809i			0.304377i
$917$		0			0
$918$		0			0
$919$	59.2275	+	102.585i	0.0644478	+	0.111627i	0.896449	−	0.443147i	$-0.146138\pi$
$919$	59.2275	+	102.585i	0.0644478	+	0.111627i	−0.832001	+	0.554774i	$0.812805\pi$
$920$	−16.7208	−	9.65375i	−0.0181748	−	0.0104932i
$921$		0			0
$922$	336.390	−	194.215i	0.364848	−	0.210645i
$923$			453.337i			0.491156i
$924$		0			0
$925$	740.971			0.801049
$926$	−108.520	−	187.962i	−0.117192	−	0.202982i
$927$		0			0
$928$	−84.8528	+	146.969i	−0.0914362	+	0.158372i
$929$	544.988	−	314.649i	0.586639	−	0.338696i	−0.177128	−	0.984188i	$-0.556681\pi$
$929$	544.988	−	314.649i	0.586639	−	0.338696i	0.763767	+	0.645492i	$0.223347\pi$
$930$		0			0
$931$		0			0
$932$	−725.470			−0.778401
$933$		0			0
$934$	75.6182	+	43.6582i	0.0809617	+	0.0467432i
$935$	158.007	−	273.676i	0.168992	−	0.292702i
$936$		0			0
$937$		−	210.631i		−	0.224793i	−0.993663	−	0.112397i	$-0.964147\pi$
$937$		−	210.631i		−	0.224793i	0.993663	−	0.112397i	$-0.0358527\pi$
$938$		0			0
$939$		0			0
$940$	−59.1472	−	102.446i	−0.0629225	−	0.108985i
$941$	−154.518	−	89.2112i	−0.164206	−	0.0948047i	0.415645	−	0.909527i	$-0.363556\pi$
$941$	−154.518	−	89.2112i	−0.164206	−	0.0948047i	−0.579851	+	0.814722i	$0.696889\pi$
$942$		0			0
$943$	41.3818	−	23.8918i	0.0438832	−	0.0253360i
$944$			1.96949i			0.00208632i
$945$		0			0
$946$	1078.09			1.13963
$947$	211.731	+	366.730i	0.223581	+	0.387254i	0.955893	−	0.293716i	$-0.0948918\pi$
$947$	211.731	+	366.730i	0.223581	+	0.387254i	−0.732312	+	0.680970i	$0.761559\pi$
$948$		0			0
$949$	316.264	−	547.785i	0.333260	−	0.577224i
$950$	473.595	−	273.430i	0.498521	−	0.287821i
$951$		0			0
$952$		0			0
$953$	546.706			0.573669			0.286834	−	0.957980i	$-0.407397\pi$
$953$	546.706			0.573669			0.286834	+	0.957980i	$0.407397\pi$
$954$		0			0
$955$	−98.4701	−	56.8518i	−0.103110	−	0.0595306i
$956$	18.4781	−	32.0051i	0.0193286	−	0.0334781i
$957$		0			0
$958$			787.030i			0.821534i
$959$		0			0
$960$		0			0
$961$	778.440	+	1348.30i	0.810031	+	1.40302i
$962$	−339.119	−	195.790i	−0.352514	−	0.203524i
$963$		0			0
$964$	−308.485	+	178.104i	−0.320005	+	0.184755i
$965$			23.2465i			0.0240896i
$966$		0			0
$967$	1262.32			1.30540			0.652701	−	0.757616i	$-0.273636\pi$
$967$	1262.32			1.30540			0.652701	+	0.757616i	$0.273636\pi$
$968$	−22.7523	−	39.4082i	−0.0235045	−	0.0407109i
$969$		0			0
$970$	−72.2498	+	125.140i	−0.0744843	+	0.129011i
$971$	936.116	−	540.467i	0.964074	−	0.556608i	0.0666496	−	0.997776i	$-0.478769\pi$
$971$	936.116	−	540.467i	0.964074	−	0.556608i	0.897425	+	0.441168i	$0.145436\pi$
$972$		0			0
$973$		0			0
$974$	459.931			0.472208
$975$		0			0
$976$	−9.94113	−	5.73951i	−0.0101856	−	0.00588065i
$977$	900.131	−	1559.07i	0.921322	−	1.59578i	0.123949	−	0.992289i	$-0.460444\pi$
$977$	900.131	−	1559.07i	0.921322	−	1.59578i	0.797373	−	0.603487i	$-0.206223\pi$
$978$		0			0
$979$		−	1484.88i		−	1.51673i
$980$		0			0
$981$		0			0
$982$	−455.007	−	788.095i	−0.463347	−	0.802541i
$983$	863.263	+	498.405i	0.878192	+	0.507025i	0.870062	−	0.492942i	$-0.164079\pi$
$983$	863.263	+	498.405i	0.878192	+	0.507025i	0.00813046	+	0.999967i	$0.497412\pi$
$984$		0			0
$985$	−101.979	+	58.8774i	−0.103532	+	0.0597740i
$986$		−	1290.12i		−	1.30844i
$987$		0			0
$988$	−288.999			−0.292509
$989$	250.368	+	433.649i	0.253152	+	0.438472i
$990$		0			0
$991$	−394.360	+	683.052i	−0.397942	+	0.689256i	−0.993472	−	0.114078i	$-0.963609\pi$
$991$	−394.360	+	683.052i	−0.397942	+	0.689256i	0.595530	+	0.803333i	$0.296942\pi$
$992$	−245.823	+	141.926i	−0.247806	+	0.143071i
$993$		0			0
$994$		0			0
$995$	165.484			0.166316
$996$		0			0
$997$	−1682.42	−	971.348i	−1.68749	−	0.974271i	−0.956433	−	0.291952i	$-0.905695\pi$
$997$	−1682.42	−	971.348i	−1.68749	−	0.974271i	−0.731054	−	0.682320i	$-0.760971\pi$
$998$	534.167	−	925.204i	0.535237	−	0.927058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.n.a.325.2		4
3.2	odd	2		294.3.g.b.31.1		4
7.2	even	3		882.3.n.d.19.2		4
7.3	odd	6		126.3.c.b.55.2		4
7.4	even	3		126.3.c.b.55.1		4
7.5	odd	6	inner	882.3.n.a.19.2		4
7.6	odd	2		882.3.n.d.325.2		4
21.2	odd	6		294.3.g.c.19.1		4
21.5	even	6		294.3.g.b.19.1		4
21.11	odd	6		42.3.c.a.13.4	yes	4
21.17	even	6		42.3.c.a.13.3	✓	4
21.20	even	2		294.3.g.c.31.1		4
28.3	even	6		1008.3.f.g.433.3		4
28.11	odd	6		1008.3.f.g.433.2		4
84.11	even	6		336.3.f.c.97.1		4
84.59	odd	6		336.3.f.c.97.4		4
105.17	odd	12		1050.3.h.a.349.5		8
105.32	even	12		1050.3.h.a.349.8		8
105.38	odd	12		1050.3.h.a.349.4		8
105.53	even	12		1050.3.h.a.349.1		8
105.59	even	6		1050.3.f.a.601.2		4
105.74	odd	6		1050.3.f.a.601.1		4
168.11	even	6		1344.3.f.e.769.4		4
168.53	odd	6		1344.3.f.f.769.2		4
168.59	odd	6		1344.3.f.e.769.1		4
168.101	even	6		1344.3.f.f.769.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.3	✓	4	21.17	even	6
42.3.c.a.13.4	yes	4	21.11	odd	6
126.3.c.b.55.1		4	7.4	even	3
126.3.c.b.55.2		4	7.3	odd	6
294.3.g.b.19.1		4	21.5	even	6
294.3.g.b.31.1		4	3.2	odd	2
294.3.g.c.19.1		4	21.2	odd	6
294.3.g.c.31.1		4	21.20	even	2
336.3.f.c.97.1		4	84.11	even	6
336.3.f.c.97.4		4	84.59	odd	6
882.3.n.a.19.2		4	7.5	odd	6	inner
882.3.n.a.325.2		4	1.1	even	1	trivial
882.3.n.d.19.2		4	7.2	even	3
882.3.n.d.325.2		4	7.6	odd	2
1008.3.f.g.433.2		4	28.11	odd	6
1008.3.f.g.433.3		4	28.3	even	6
1050.3.f.a.601.1		4	105.74	odd	6
1050.3.f.a.601.2		4	105.59	even	6
1050.3.h.a.349.1		8	105.53	even	12
1050.3.h.a.349.4		8	105.38	odd	12
1050.3.h.a.349.5		8	105.17	odd	12
1050.3.h.a.349.8		8	105.32	even	12
1344.3.f.e.769.1		4	168.59	odd	6
1344.3.f.e.769.4		4	168.11	even	6
1344.3.f.f.769.2		4	168.53	odd	6
1344.3.f.f.769.3		4	168.101	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.878680 + 0.507306i) q^{5} -2.82843 q^{8} +(-1.24264 - 0.717439i) q^{10} +(-5.12132 + 8.87039i) q^{11} -8.95743i q^{13} +(-2.00000 - 3.46410i) q^{16} +(26.3345 + 15.2042i) q^{17} +(-13.9706 + 8.06591i) q^{19} -2.02922i q^{20} -14.4853 q^{22} +(-3.36396 - 5.82655i) q^{23} +(-11.9853 + 20.7591i) q^{25} +(10.9706 - 6.33386i) q^{26} -30.0000 q^{29} +(-43.4558 - 25.0892i) q^{31} +(2.82843 - 4.89898i) q^{32} +43.0041i q^{34} +(-15.4558 - 26.7703i) q^{37} +(-19.7574 - 11.4069i) q^{38} +(2.48528 - 1.43488i) q^{40} +7.10228i q^{41} -74.4264 q^{43} +(-10.2426 - 17.7408i) q^{44} +(4.75736 - 8.23999i) q^{46} +(50.4853 - 29.1477i) q^{47} -33.8995 q^{50} +(15.5147 + 8.95743i) q^{52} +(-35.4853 + 61.4623i) q^{53} -10.3923i q^{55} +(-21.2132 - 36.7423i) q^{58} +(-0.426407 - 0.246186i) q^{59} +(2.48528 - 1.43488i) q^{61} -70.9631i q^{62} +8.00000 q^{64} +(4.54416 + 7.87071i) q^{65} +(-13.5147 + 23.4082i) q^{67} +(-52.6690 + 30.4085i) q^{68} -50.6102 q^{71} +(61.1543 + 35.3075i) q^{73} +(21.8579 - 37.8589i) q^{74} -32.2636i q^{76} +(-66.9117 - 115.894i) q^{79} +(3.51472 + 2.02922i) q^{80} +(-8.69848 + 5.02207i) q^{82} +104.415i q^{83} -30.8528 q^{85} +(-52.6274 - 91.1534i) q^{86} +(14.4853 - 25.0892i) q^{88} +(-125.548 + 72.4850i) q^{89} +13.4558 q^{92} +(71.3970 + 41.2211i) q^{94} +(8.18377 - 14.1747i) q^{95} -100.705i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 12 q^{5} + 12 q^{10} - 12 q^{11} - 8 q^{16} + 12 q^{17} + 12 q^{19} - 24 q^{22} + 12 q^{23} - 14 q^{25} - 24 q^{26} - 120 q^{29} - 72 q^{31} + 40 q^{37} - 96 q^{38} - 24 q^{40} - 128 q^{43}+ \cdots - 120 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 12 * q^5 + 12 * q^10 - 12 * q^11 - 8 * q^16 + 12 * q^17 + 12 * q^19 - 24 * q^22 + 12 * q^23 - 14 * q^25 - 24 * q^26 - 120 * q^29 - 72 * q^31 + 40 * q^37 - 96 * q^38 - 24 * q^40 - 128 * q^43 - 24 * q^44 + 36 * q^46 + 168 * q^47 - 96 * q^50 + 96 * q^52 - 108 * q^53 + 168 * q^59 - 24 * q^61 + 32 * q^64 + 120 * q^65 - 88 * q^67 - 24 * q^68 + 120 * q^71 + 24 * q^73 + 144 * q^74 - 64 * q^79 + 48 * q^80 + 84 * q^82 + 216 * q^85 - 120 * q^86 + 24 * q^88 - 324 * q^89 - 48 * q^92 + 48 * q^94 - 120 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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