LMFDB - Embedded newform 882.4.g.t.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.t.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -8.00000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(15.0000 - 25.9808i) q^{11} +2.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(33.0000 - 57.1577i) q^{17} +(26.0000 + 45.0333i) q^{19} -24.0000 q^{20} +60.0000 q^{22} +(57.0000 + 98.7269i) q^{23} +(44.5000 - 77.0763i) q^{25} +(2.00000 + 3.46410i) q^{26} -72.0000 q^{29} +(98.0000 - 169.741i) q^{31} +(16.0000 - 27.7128i) q^{32} +132.000 q^{34} +(143.000 + 247.683i) q^{37} +(-52.0000 + 90.0666i) q^{38} +(-24.0000 - 41.5692i) q^{40} +378.000 q^{41} +164.000 q^{43} +(60.0000 + 103.923i) q^{44} +(-114.000 + 197.454i) q^{46} +(-114.000 - 197.454i) q^{47} +178.000 q^{50} +(-4.00000 + 6.92820i) q^{52} +(-174.000 + 301.377i) q^{53} +180.000 q^{55} +(-72.0000 - 124.708i) q^{58} +(-174.000 + 301.377i) q^{59} +(53.0000 + 91.7987i) q^{61} +392.000 q^{62} +64.0000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-298.000 + 516.151i) q^{67} +(132.000 + 228.631i) q^{68} -630.000 q^{71} +(521.000 - 902.398i) q^{73} +(-286.000 + 495.367i) q^{74} -208.000 q^{76} +(44.0000 + 76.2102i) q^{79} +(48.0000 - 83.1384i) q^{80} +(378.000 + 654.715i) q^{82} +1440.00 q^{83} +396.000 q^{85} +(164.000 + 284.056i) q^{86} +(-120.000 + 207.846i) q^{88} +(687.000 + 1189.92i) q^{89} -456.000 q^{92} +(228.000 - 394.908i) q^{94} +(-156.000 + 270.200i) q^{95} -34.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} + 6 q^{5} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 + 6 * q^5 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} + 6 q^{5} - 16 q^{8} - 12 q^{10} + 30 q^{11} + 4 q^{13} - 16 q^{16} + 66 q^{17} + 52 q^{19} - 48 q^{20} + 120 q^{22} + 114 q^{23} + 89 q^{25} + 4 q^{26} - 144 q^{29} + 196 q^{31} + 32 q^{32} + 264 q^{34} + 286 q^{37} - 104 q^{38} - 48 q^{40} + 756 q^{41} + 328 q^{43} + 120 q^{44} - 228 q^{46} - 228 q^{47} + 356 q^{50} - 8 q^{52} - 348 q^{53} + 360 q^{55} - 144 q^{58} - 348 q^{59} + 106 q^{61} + 784 q^{62} + 128 q^{64} + 12 q^{65} - 596 q^{67} + 264 q^{68} - 1260 q^{71} + 1042 q^{73} - 572 q^{74} - 416 q^{76} + 88 q^{79} + 96 q^{80} + 756 q^{82} + 2880 q^{83} + 792 q^{85} + 328 q^{86} - 240 q^{88} + 1374 q^{89} - 912 q^{92} + 456 q^{94} - 312 q^{95} - 68 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 + 6 * q^5 - 16 * q^8 - 12 * q^10 + 30 * q^11 + 4 * q^13 - 16 * q^16 + 66 * q^17 + 52 * q^19 - 48 * q^20 + 120 * q^22 + 114 * q^23 + 89 * q^25 + 4 * q^26 - 144 * q^29 + 196 * q^31 + 32 * q^32 + 264 * q^34 + 286 * q^37 - 104 * q^38 - 48 * q^40 + 756 * q^41 + 328 * q^43 + 120 * q^44 - 228 * q^46 - 228 * q^47 + 356 * q^50 - 8 * q^52 - 348 * q^53 + 360 * q^55 - 144 * q^58 - 348 * q^59 + 106 * q^61 + 784 * q^62 + 128 * q^64 + 12 * q^65 - 596 * q^67 + 264 * q^68 - 1260 * q^71 + 1042 * q^73 - 572 * q^74 - 416 * q^76 + 88 * q^79 + 96 * q^80 + 756 * q^82 + 2880 * q^83 + 792 * q^85 + 328 * q^86 - 240 * q^88 + 1374 * q^89 - 912 * q^92 + 456 * q^94 - 312 * q^95 - 68 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	3.00000	+	5.19615i	0.268328	+	0.464758i	0.968430	−	0.249285i	$-0.0801955\pi$
$5$	3.00000	+	5.19615i	0.268328	+	0.464758i	−0.700102	+	0.714043i	$0.746862\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−6.00000	+	10.3923i	−0.189737	+	0.328634i
$11$	15.0000	−	25.9808i	0.411152	−	0.712136i	−0.583864	−	0.811851i	$-0.698460\pi$
$11$	15.0000	−	25.9808i	0.411152	−	0.712136i	0.995016	+	0.0997155i	$0.0317933\pi$
$12$		0			0
$13$	2.00000			0.0426692			0.0213346	−	0.999772i	$-0.493208\pi$
$13$	2.00000			0.0426692			0.0213346	+	0.999772i	$0.493208\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	33.0000	−	57.1577i	0.470804	−	0.815457i	−0.528638	−	0.848847i	$-0.677297\pi$
$17$	33.0000	−	57.1577i	0.470804	−	0.815457i	0.999442	+	0.0333902i	$0.0106304\pi$
$18$		0			0
$19$	26.0000	+	45.0333i	0.313937	+	0.543755i	0.979211	−	0.202844i	$-0.0650185\pi$
$19$	26.0000	+	45.0333i	0.313937	+	0.543755i	−0.665274	+	0.746600i	$0.731685\pi$
$20$	−24.0000			−0.268328
$21$		0			0
$22$	60.0000			0.581456
$23$	57.0000	+	98.7269i	0.516753	+	0.895043i	0.999811	+	0.0194541i	$0.00619282\pi$
$23$	57.0000	+	98.7269i	0.516753	+	0.895043i	−0.483058	+	0.875589i	$0.660474\pi$
$24$		0			0
$25$	44.5000	−	77.0763i	0.356000	−	0.616610i
$26$	2.00000	+	3.46410i	0.0150859	+	0.0261295i
$27$		0			0
$28$		0			0
$29$	−72.0000			−0.461037			−0.230518	−	0.973068i	$-0.574042\pi$
$29$	−72.0000			−0.461037			−0.230518	+	0.973068i	$0.574042\pi$
$30$		0			0
$31$	98.0000	−	169.741i	0.567785	−	0.983432i	−0.429000	−	0.903304i	$-0.641134\pi$
$31$	98.0000	−	169.741i	0.567785	−	0.983432i	0.996785	−	0.0801272i	$-0.0255326\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	132.000			0.665818
$35$		0			0
$36$		0			0
$37$	143.000	+	247.683i	0.635380	+	1.10051i	0.986435	+	0.164155i	$0.0524898\pi$
$37$	143.000	+	247.683i	0.635380	+	1.10051i	−0.351055	+	0.936355i	$0.614177\pi$
$38$	−52.0000	+	90.0666i	−0.221987	+	0.384493i
$39$		0			0
$40$	−24.0000	−	41.5692i	−0.0948683	−	0.164317i
$41$	378.000			1.43985			0.719923	−	0.694054i	$-0.244177\pi$
$41$	378.000			1.43985			0.719923	+	0.694054i	$0.244177\pi$
$42$		0			0
$43$	164.000			0.581622			0.290811	−	0.956780i	$-0.406075\pi$
$43$	164.000			0.581622			0.290811	+	0.956780i	$0.406075\pi$
$44$	60.0000	+	103.923i	0.205576	+	0.356068i
$45$		0			0
$46$	−114.000	+	197.454i	−0.365400	+	0.632891i
$47$	−114.000	−	197.454i	−0.353800	−	0.612800i	0.633112	−	0.774060i	$-0.281777\pi$
$47$	−114.000	−	197.454i	−0.353800	−	0.612800i	−0.986912	+	0.161261i	$0.948444\pi$
$48$		0			0
$49$		0			0
$50$	178.000			0.503460
$51$		0			0
$52$	−4.00000	+	6.92820i	−0.0106673	+	0.0184763i
$53$	−174.000	+	301.377i	−0.450957	+	0.781081i	−0.998446	−	0.0557323i	$-0.982251\pi$
$53$	−174.000	+	301.377i	−0.450957	+	0.781081i	0.547488	+	0.836813i	$0.315584\pi$
$54$		0			0
$55$	180.000			0.441294
$56$		0			0
$57$		0			0
$58$	−72.0000	−	124.708i	−0.163001	−	0.282326i
$59$	−174.000	+	301.377i	−0.383947	+	0.665016i	−0.991622	−	0.129170i	$-0.958769\pi$
$59$	−174.000	+	301.377i	−0.383947	+	0.665016i	0.607676	+	0.794185i	$0.292102\pi$
$60$		0			0
$61$	53.0000	+	91.7987i	0.111245	+	0.192682i	0.916273	−	0.400555i	$-0.131183\pi$
$61$	53.0000	+	91.7987i	0.111245	+	0.192682i	−0.805027	+	0.593238i	$0.797849\pi$
$62$	392.000			0.802969
$63$		0			0
$64$	64.0000			0.125000
$65$	6.00000	+	10.3923i	0.0114494	+	0.0198309i
$66$		0			0
$67$	−298.000	+	516.151i	−0.543381	+	0.941163i	0.455326	+	0.890325i	$0.349523\pi$
$67$	−298.000	+	516.151i	−0.543381	+	0.941163i	−0.998707	+	0.0508381i	$0.983811\pi$
$68$	132.000	+	228.631i	0.235402	+	0.407729i
$69$		0			0
$70$		0			0
$71$	−630.000			−1.05306			−0.526530	−	0.850157i	$-0.676507\pi$
$71$	−630.000			−1.05306			−0.526530	+	0.850157i	$0.676507\pi$
$72$		0			0
$73$	521.000	−	902.398i	0.835321	−	1.44682i	−0.0584477	−	0.998290i	$-0.518615\pi$
$73$	521.000	−	902.398i	0.835321	−	1.44682i	0.893769	−	0.448528i	$-0.148052\pi$
$74$	−286.000	+	495.367i	−0.449281	+	0.778178i
$75$		0			0
$76$	−208.000			−0.313937
$77$		0			0
$78$		0			0
$79$	44.0000	+	76.2102i	0.0626631	+	0.108536i	0.895655	−	0.444750i	$-0.146707\pi$
$79$	44.0000	+	76.2102i	0.0626631	+	0.108536i	−0.832992	+	0.553285i	$0.813374\pi$
$80$	48.0000	−	83.1384i	0.0670820	−	0.116190i
$81$		0			0
$82$	378.000	+	654.715i	0.509062	+	0.881722i
$83$	1440.00			1.90434			0.952172	−	0.305563i	$-0.0988446\pi$
$83$	1440.00			1.90434			0.952172	+	0.305563i	$0.0988446\pi$
$84$		0			0
$85$	396.000			0.505320
$86$	164.000	+	284.056i	0.205635	+	0.356170i
$87$		0			0
$88$	−120.000	+	207.846i	−0.145364	+	0.251778i
$89$	687.000	+	1189.92i	0.818223	+	1.41720i	0.906990	+	0.421152i	$0.138374\pi$
$89$	687.000	+	1189.92i	0.818223	+	1.41720i	−0.0887672	+	0.996052i	$0.528293\pi$
$90$		0			0
$91$		0			0
$92$	−456.000			−0.516753
$93$		0			0
$94$	228.000	−	394.908i	0.250175	−	0.433315i
$95$	−156.000	+	270.200i	−0.168476	+	0.291810i
$96$		0			0
$97$	−34.0000			−0.0355895			−0.0177947	−	0.999842i	$-0.505665\pi$
$97$	−34.0000			−0.0355895			−0.0177947	+	0.999842i	$0.505665\pi$
$98$		0			0
$99$		0			0
$100$	178.000	+	308.305i	0.178000	+	0.308305i
$101$	−219.000	+	379.319i	−0.215756	+	0.373700i	−0.953506	−	0.301374i	$-0.902555\pi$
$101$	−219.000	+	379.319i	−0.215756	+	0.373700i	0.737750	+	0.675074i	$0.235888\pi$
$102$		0			0
$103$	−838.000	−	1451.46i	−0.801656	−	1.38851i	−0.918525	−	0.395362i	$-0.870619\pi$
$103$	−838.000	−	1451.46i	−0.801656	−	1.38851i	0.116869	−	0.993147i	$-0.462714\pi$
$104$	−16.0000			−0.0150859
$105$		0			0
$106$	−696.000			−0.637750
$107$	1011.00	+	1751.10i	0.913430	+	1.58211i	0.809183	+	0.587557i	$0.199910\pi$
$107$	1011.00	+	1751.10i	0.913430	+	1.58211i	0.104247	+	0.994551i	$0.466757\pi$
$108$		0			0
$109$	251.000	−	434.745i	0.220564	−	0.382027i	−0.734416	−	0.678700i	$-0.762544\pi$
$109$	251.000	−	434.745i	0.220564	−	0.382027i	0.954979	+	0.296673i	$0.0958770\pi$
$110$	180.000	+	311.769i	0.156021	+	0.270237i
$111$		0			0
$112$		0			0
$113$	−2016.00			−1.67831			−0.839156	−	0.543890i	$-0.816951\pi$
$113$	−2016.00			−1.67831			−0.839156	+	0.543890i	$0.816951\pi$
$114$		0			0
$115$	−342.000	+	592.361i	−0.277319	+	0.480330i
$116$	144.000	−	249.415i	0.115259	−	0.199635i
$117$		0			0
$118$	−696.000			−0.542983
$119$		0			0
$120$		0			0
$121$	215.500	+	373.257i	0.161908	+	0.280433i
$122$	−106.000	+	183.597i	−0.0786622	+	0.136247i
$123$		0			0
$124$	392.000	+	678.964i	0.283892	+	0.491716i
$125$	1284.00			0.918756
$126$		0			0
$127$	1784.00			1.24649			0.623246	−	0.782026i	$-0.285814\pi$
$127$	1784.00			1.24649			0.623246	+	0.782026i	$0.285814\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−12.0000	+	20.7846i	−0.00809592	+	0.0140225i
$131$	804.000	+	1392.57i	0.536228	+	0.928773i	0.999103	+	0.0423499i	$0.0134844\pi$
$131$	804.000	+	1392.57i	0.536228	+	0.928773i	−0.462875	+	0.886423i	$0.653182\pi$
$132$		0			0
$133$		0			0
$134$	−1192.00			−0.768456
$135$		0			0
$136$	−264.000	+	457.261i	−0.166455	+	0.288308i
$137$	−1290.00	+	2234.35i	−0.804468	+	1.39338i	0.112181	+	0.993688i	$0.464216\pi$
$137$	−1290.00	+	2234.35i	−0.804468	+	1.39338i	−0.916650	+	0.399692i	$0.869117\pi$
$138$		0			0
$139$	2144.00			1.30829			0.654143	−	0.756371i	$-0.273030\pi$
$139$	2144.00			1.30829			0.654143	+	0.756371i	$0.273030\pi$
$140$		0			0
$141$		0			0
$142$	−630.000	−	1091.19i	−0.372313	−	0.644865i
$143$	30.0000	−	51.9615i	0.0175435	−	0.0303863i
$144$		0			0
$145$	−216.000	−	374.123i	−0.123709	−	0.214270i
$146$	2084.00			1.18132
$147$		0			0
$148$	−1144.00			−0.635380
$149$	750.000	+	1299.04i	0.412365	+	0.714237i	0.995148	−	0.0983907i	$-0.0313695\pi$
$149$	750.000	+	1299.04i	0.412365	+	0.714237i	−0.582783	+	0.812628i	$0.698036\pi$
$150$		0			0
$151$	620.000	−	1073.87i	0.334138	−	0.578745i	−0.649181	−	0.760634i	$-0.724888\pi$
$151$	620.000	−	1073.87i	0.334138	−	0.578745i	0.983319	+	0.181890i	$0.0582214\pi$
$152$	−208.000	−	360.267i	−0.110994	−	0.192247i
$153$		0			0
$154$		0			0
$155$	1176.00			0.609410
$156$		0			0
$157$	−307.000	+	531.740i	−0.156059	+	0.270302i	−0.933444	−	0.358723i	$-0.883212\pi$
$157$	−307.000	+	531.740i	−0.156059	+	0.270302i	0.777385	+	0.629025i	$0.216546\pi$
$158$	−88.0000	+	152.420i	−0.0443095	+	0.0767463i
$159$		0			0
$160$	192.000			0.0948683
$161$		0			0
$162$		0			0
$163$	−46.0000	−	79.6743i	−0.0221043	−	0.0382857i	0.854762	−	0.519021i	$-0.173703\pi$
$163$	−46.0000	−	79.6743i	−0.0221043	−	0.0382857i	−0.876866	+	0.480735i	$0.840370\pi$
$164$	−756.000	+	1309.43i	−0.359961	+	0.623472i
$165$		0			0
$166$	1440.00	+	2494.15i	0.673287	+	1.16617i
$167$	3924.00			1.81825			0.909126	−	0.416520i	$-0.136750\pi$
$167$	3924.00			1.81825			0.909126	+	0.416520i	$0.136750\pi$
$168$		0			0
$169$	−2193.00			−0.998179
$170$	396.000	+	685.892i	0.178658	+	0.309444i
$171$		0			0
$172$	−328.000	+	568.113i	−0.145406	+	0.251850i
$173$	−951.000	−	1647.18i	−0.417938	−	0.723889i	0.577794	−	0.816182i	$-0.303914\pi$
$173$	−951.000	−	1647.18i	−0.417938	−	0.723889i	−0.995732	+	0.0922934i	$0.970580\pi$
$174$		0			0
$175$		0			0
$176$	−480.000			−0.205576
$177$		0			0
$178$	−1374.00	+	2379.84i	−0.578571	+	1.00211i
$179$	−3.00000	+	5.19615i	−0.00125268	+	0.00216971i	−0.866651	−	0.498915i	$-0.833732\pi$
$179$	−3.00000	+	5.19615i	−0.00125268	+	0.00216971i	0.865398	+	0.501084i	$0.167065\pi$
$180$		0			0
$181$	−2878.00			−1.18188			−0.590939	−	0.806716i	$-0.701243\pi$
$181$	−2878.00			−1.18188			−0.590939	+	0.806716i	$0.701243\pi$
$182$		0			0
$183$		0			0
$184$	−456.000	−	789.815i	−0.182700	−	0.316445i
$185$	−858.000	+	1486.10i	−0.340981	+	0.590596i
$186$		0			0
$187$	−990.000	−	1714.73i	−0.387144	−	0.670553i
$188$	912.000			0.353800
$189$		0			0
$190$	−624.000			−0.238262
$191$	−177.000	−	306.573i	−0.0670538	−	0.116141i	0.830549	−	0.556945i	$-0.188027\pi$
$191$	−177.000	−	306.573i	−0.0670538	−	0.116141i	−0.897603	+	0.440804i	$0.854693\pi$
$192$		0			0
$193$	2429.00	−	4207.15i	0.905924	−	1.56911i	0.0862509	−	0.996273i	$-0.472511\pi$
$193$	2429.00	−	4207.15i	0.905924	−	1.56911i	0.819673	−	0.572832i	$-0.194155\pi$
$194$	−34.0000	−	58.8897i	−0.0125828	−	0.0217940i
$195$		0			0
$196$		0			0
$197$	396.000			0.143217			0.0716087	−	0.997433i	$-0.477187\pi$
$197$	396.000			0.143217			0.0716087	+	0.997433i	$0.477187\pi$
$198$		0			0
$199$	−856.000	+	1482.64i	−0.304926	+	0.528147i	−0.977245	−	0.212115i	$-0.931965\pi$
$199$	−856.000	+	1482.64i	−0.304926	+	0.528147i	0.672319	+	0.740262i	$0.265298\pi$
$200$	−356.000	+	616.610i	−0.125865	+	0.218005i
$201$		0			0
$202$	−876.000			−0.305124
$203$		0			0
$204$		0			0
$205$	1134.00	+	1964.15i	0.386351	+	0.669180i
$206$	1676.00	−	2902.92i	0.566857	−	0.981824i
$207$		0			0
$208$	−16.0000	−	27.7128i	−0.00533366	−	0.00923816i
$209$	1560.00			0.516304
$210$		0			0
$211$	−772.000			−0.251880			−0.125940	−	0.992038i	$-0.540195\pi$
$211$	−772.000			−0.251880			−0.125940	+	0.992038i	$0.540195\pi$
$212$	−696.000	−	1205.51i	−0.225479	−	0.390540i
$213$		0			0
$214$	−2022.00	+	3502.21i	−0.645893	+	1.11872i
$215$	492.000	+	852.169i	0.156066	+	0.270314i
$216$		0			0
$217$		0			0
$218$	1004.00			0.311924
$219$		0			0
$220$	−360.000	+	623.538i	−0.110324	+	0.191086i
$221$	66.0000	−	114.315i	0.0200889	−	0.0347949i
$222$		0			0
$223$	776.000			0.233026			0.116513	−	0.993189i	$-0.462828\pi$
$223$	776.000			0.233026			0.116513	+	0.993189i	$0.462828\pi$
$224$		0			0
$225$		0			0
$226$	−2016.00	−	3491.81i	−0.593373	−	1.02775i
$227$	−894.000	+	1548.45i	−0.261396	+	0.452751i	−0.966613	−	0.256240i	$-0.917516\pi$
$227$	−894.000	+	1548.45i	−0.261396	+	0.452751i	0.705217	+	0.708991i	$0.250849\pi$
$228$		0			0
$229$	−2701.00	−	4678.27i	−0.779420	−	1.34999i	−0.932277	−	0.361746i	$-0.882181\pi$
$229$	−2701.00	−	4678.27i	−0.779420	−	1.34999i	0.152857	−	0.988248i	$-0.451153\pi$
$230$	−1368.00			−0.392188
$231$		0			0
$232$	576.000			0.163001
$233$	1506.00	+	2608.47i	0.423439	+	0.733418i	0.996273	−	0.0862531i	$-0.0274894\pi$
$233$	1506.00	+	2608.47i	0.423439	+	0.733418i	−0.572834	+	0.819671i	$0.694156\pi$
$234$		0			0
$235$	684.000	−	1184.72i	0.189869	−	0.328863i
$236$	−696.000	−	1205.51i	−0.191973	−	0.332508i
$237$		0			0
$238$		0			0
$239$	−3546.00			−0.959714			−0.479857	−	0.877347i	$-0.659311\pi$
$239$	−3546.00			−0.959714			−0.479857	+	0.877347i	$0.659311\pi$
$240$		0			0
$241$	1781.00	−	3084.78i	0.476034	−	0.824516i	−0.523589	−	0.851971i	$-0.675407\pi$
$241$	1781.00	−	3084.78i	0.476034	−	0.824516i	0.999623	+	0.0274554i	$0.00874043\pi$
$242$	−431.000	+	746.514i	−0.114486	+	0.198296i
$243$		0			0
$244$	−424.000			−0.111245
$245$		0			0
$246$		0			0
$247$	52.0000	+	90.0666i	0.0133955	+	0.0232016i
$248$	−784.000	+	1357.93i	−0.200742	+	0.347696i
$249$		0			0
$250$	1284.00	+	2223.95i	0.324829	+	0.562621i
$251$	−3348.00			−0.841928			−0.420964	−	0.907077i	$-0.638308\pi$
$251$	−3348.00			−0.841928			−0.420964	+	0.907077i	$0.638308\pi$
$252$		0			0
$253$	3420.00			0.849856
$254$	1784.00	+	3089.98i	0.440701	+	0.763317i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	183.000	+	316.965i	0.0444172	+	0.0769329i	0.887379	−	0.461040i	$-0.152524\pi$
$257$	183.000	+	316.965i	0.0444172	+	0.0769329i	−0.842962	+	0.537973i	$0.819190\pi$
$258$		0			0
$259$		0			0
$260$	−48.0000			−0.0114494
$261$		0			0
$262$	−1608.00	+	2785.14i	−0.379170	+	0.656742i
$263$	2085.00	−	3611.33i	0.488846	−	0.846707i	−0.511071	−	0.859538i	$-0.670751\pi$
$263$	2085.00	−	3611.33i	0.488846	−	0.846707i	0.999918	+	0.0128315i	$0.00408451\pi$
$264$		0			0
$265$	−2088.00			−0.484018
$266$		0			0
$267$		0			0
$268$	−1192.00	−	2064.60i	−0.271690	−	0.470581i
$269$	3039.00	−	5263.70i	0.688814	−	1.19306i	−0.283407	−	0.959000i	$-0.591465\pi$
$269$	3039.00	−	5263.70i	0.688814	−	1.19306i	0.972222	−	0.234062i	$-0.0752019\pi$
$270$		0			0
$271$	−1234.00	−	2137.35i	−0.276606	−	0.479095i	0.693933	−	0.720039i	$-0.255876\pi$
$271$	−1234.00	−	2137.35i	−0.276606	−	0.479095i	−0.970539	+	0.240944i	$0.922543\pi$
$272$	−1056.00			−0.235402
$273$		0			0
$274$	−5160.00			−1.13769
$275$	−1335.00	−	2312.29i	−0.292740	−	0.507041i
$276$		0			0
$277$	197.000	−	341.214i	0.0427313	−	0.0740129i	−0.843869	−	0.536550i	$-0.819727\pi$
$277$	197.000	−	341.214i	0.0427313	−	0.0740129i	0.886600	+	0.462537i	$0.153061\pi$
$278$	2144.00	+	3713.52i	0.462549	+	0.801158i
$279$		0			0
$280$		0			0
$281$	396.000			0.0840690			0.0420345	−	0.999116i	$-0.486616\pi$
$281$	396.000			0.0840690			0.0420345	+	0.999116i	$0.486616\pi$
$282$		0			0
$283$	674.000	−	1167.40i	0.141573	−	0.245212i	−0.786516	−	0.617570i	$-0.788117\pi$
$283$	674.000	−	1167.40i	0.141573	−	0.245212i	0.928089	+	0.372358i	$0.121451\pi$
$284$	1260.00	−	2182.38i	0.263265	−	0.455988i
$285$		0			0
$286$	120.000			0.0248103
$287$		0			0
$288$		0			0
$289$	278.500	+	482.376i	0.0566863	+	0.0981836i
$290$	432.000	−	748.246i	0.0874756	−	0.151512i
$291$		0			0
$292$	2084.00	+	3609.59i	0.417661	+	0.723409i
$293$	−7506.00			−1.49660			−0.748302	−	0.663358i	$-0.769131\pi$
$293$	−7506.00			−1.49660			−0.748302	+	0.663358i	$0.769131\pi$
$294$		0			0
$295$	−2088.00			−0.412095
$296$	−1144.00	−	1981.47i	−0.224641	−	0.389089i
$297$		0			0
$298$	−1500.00	+	2598.08i	−0.291586	+	0.505042i
$299$	114.000	+	197.454i	0.0220495	+	0.0381908i
$300$		0			0
$301$		0			0
$302$	2480.00			0.472543
$303$		0			0
$304$	416.000	−	720.533i	0.0784843	−	0.135939i
$305$	−318.000	+	550.792i	−0.0597004	+	0.103404i
$306$		0			0
$307$	1748.00			0.324963			0.162481	−	0.986712i	$-0.448050\pi$
$307$	1748.00			0.324963			0.162481	+	0.986712i	$0.448050\pi$
$308$		0			0
$309$		0			0
$310$	1176.00	+	2036.89i	0.215459	+	0.373186i
$311$	−570.000	+	987.269i	−0.103928	+	0.180009i	−0.913300	−	0.407288i	$-0.866475\pi$
$311$	−570.000	+	987.269i	−0.103928	+	0.180009i	0.809371	+	0.587297i	$0.199808\pi$
$312$		0			0
$313$	−73.0000	−	126.440i	−0.0131828	−	0.0228332i	0.859359	−	0.511373i	$-0.170863\pi$
$313$	−73.0000	−	126.440i	−0.0131828	−	0.0228332i	−0.872542	+	0.488540i	$0.837530\pi$
$314$	−1228.00			−0.220701
$315$		0			0
$316$	−352.000			−0.0626631
$317$	−4074.00	−	7056.37i	−0.721825	−	1.25024i	−0.960267	−	0.279081i	$-0.909970\pi$
$317$	−4074.00	−	7056.37i	−0.721825	−	1.25024i	0.238442	−	0.971157i	$-0.423363\pi$
$318$		0			0
$319$	−1080.00	+	1870.61i	−0.189556	+	0.328321i
$320$	192.000	+	332.554i	0.0335410	+	0.0580948i
$321$		0			0
$322$		0			0
$323$	3432.00			0.591212
$324$		0			0
$325$	89.0000	−	154.153i	0.0151903	−	0.0263103i
$326$	92.0000	−	159.349i	0.0156301	−	0.0270721i
$327$		0			0
$328$	−3024.00			−0.509062
$329$		0			0
$330$		0			0
$331$	4850.00	+	8400.45i	0.805378	+	1.39496i	0.916036	+	0.401097i	$0.131371\pi$
$331$	4850.00	+	8400.45i	0.805378	+	1.39496i	−0.110658	+	0.993859i	$0.535296\pi$
$332$	−2880.00	+	4988.31i	−0.476086	+	0.824605i
$333$		0			0
$334$	3924.00	+	6796.57i	0.642849	+	1.11345i
$335$	−3576.00			−0.583217
$336$		0			0
$337$	8174.00			1.32126			0.660632	−	0.750710i	$-0.270288\pi$
$337$	8174.00			1.32126			0.660632	+	0.750710i	$0.270288\pi$
$338$	−2193.00	−	3798.39i	−0.352910	−	0.611258i
$339$		0			0
$340$	−792.000	+	1371.78i	−0.126330	+	0.218810i
$341$	−2940.00	−	5092.23i	−0.466891	−	0.808679i
$342$		0			0
$343$		0			0
$344$	−1312.00			−0.205635
$345$		0			0
$346$	1902.00	−	3294.36i	0.295526	−	0.511867i
$347$	−2019.00	+	3497.01i	−0.312350	+	0.541007i	−0.978871	−	0.204480i	$-0.934450\pi$
$347$	−2019.00	+	3497.01i	−0.312350	+	0.541007i	0.666520	+	0.745487i	$0.267783\pi$
$348$		0			0
$349$	10766.0			1.65126			0.825631	−	0.564210i	$-0.190819\pi$
$349$	10766.0			1.65126			0.825631	+	0.564210i	$0.190819\pi$
$350$		0			0
$351$		0			0
$352$	−480.000	−	831.384i	−0.0726821	−	0.125889i
$353$	1833.00	−	3174.85i	0.276376	−	0.478697i	−0.694105	−	0.719873i	$-0.744200\pi$
$353$	1833.00	−	3174.85i	0.276376	−	0.478697i	0.970481	+	0.241176i	$0.0775331\pi$
$354$		0			0
$355$	−1890.00	−	3273.58i	−0.282566	−	0.489418i
$356$	−5496.00			−0.818223
$357$		0			0
$358$	−12.0000			−0.00177156
$359$	−2553.00	−	4421.93i	−0.375326	−	0.650084i	0.615049	−	0.788489i	$-0.289136\pi$
$359$	−2553.00	−	4421.93i	−0.375326	−	0.650084i	−0.990376	+	0.138404i	$0.955803\pi$
$360$		0			0
$361$	2077.50	−	3598.34i	0.302887	−	0.524615i
$362$	−2878.00	−	4984.84i	−0.417857	−	0.723750i
$363$		0			0
$364$		0			0
$365$	6252.00			0.896561
$366$		0			0
$367$	2888.00	−	5002.16i	0.410769	−	0.711473i	−0.584205	−	0.811606i	$-0.698593\pi$
$367$	2888.00	−	5002.16i	0.410769	−	0.711473i	0.994974	+	0.100133i	$0.0319268\pi$
$368$	912.000	−	1579.63i	0.129188	−	0.223761i
$369$		0			0
$370$	−3432.00			−0.482219
$371$		0			0
$372$		0			0
$373$	−4231.00	−	7328.31i	−0.587327	−	1.01728i	−0.994581	−	0.103965i	$-0.966847\pi$
$373$	−4231.00	−	7328.31i	−0.587327	−	1.01728i	0.407254	−	0.913315i	$-0.366486\pi$
$374$	1980.00	−	3429.46i	0.273752	−	0.474153i
$375$		0			0
$376$	912.000	+	1579.63i	0.125087	+	0.216657i
$377$	−144.000			−0.0196721
$378$		0			0
$379$	6860.00			0.929748			0.464874	−	0.885377i	$-0.346100\pi$
$379$	6860.00			0.929748			0.464874	+	0.885377i	$0.346100\pi$
$380$	−624.000	−	1080.80i	−0.0842382	−	0.145905i
$381$		0			0
$382$	354.000	−	613.146i	0.0474142	−	0.0821238i
$383$	−348.000	−	602.754i	−0.0464281	−	0.0804159i	0.841877	−	0.539669i	$-0.181451\pi$
$383$	−348.000	−	602.754i	−0.0464281	−	0.0804159i	−0.888306	+	0.459253i	$0.848117\pi$
$384$		0			0
$385$		0			0
$386$	9716.00			1.28117
$387$		0			0
$388$	68.0000	−	117.779i	0.00889736	−	0.0154107i
$389$	5568.00	−	9644.06i	0.725730	−	1.25700i	−0.232943	−	0.972490i	$-0.574836\pi$
$389$	5568.00	−	9644.06i	0.725730	−	1.25700i	0.958673	−	0.284510i	$-0.0918310\pi$
$390$		0			0
$391$	7524.00			0.973159
$392$		0			0
$393$		0			0
$394$	396.000	+	685.892i	0.0506350	+	0.0877024i
$395$	−264.000	+	457.261i	−0.0336286	+	0.0582464i
$396$		0			0
$397$	−5419.00	−	9385.98i	−0.685068	−	1.18657i	−0.973416	−	0.229046i	$-0.926439\pi$
$397$	−5419.00	−	9385.98i	−0.685068	−	1.18657i	0.288348	−	0.957526i	$-0.406894\pi$
$398$	−3424.00			−0.431230
$399$		0			0
$400$	−1424.00			−0.178000
$401$	−4182.00	−	7243.44i	−0.520796	−	0.902045i	−0.999708	−	0.0241817i	$-0.992302\pi$
$401$	−4182.00	−	7243.44i	−0.520796	−	0.902045i	0.478912	−	0.877863i	$-0.341031\pi$
$402$		0			0
$403$	196.000	−	339.482i	0.0242269	−	0.0419623i
$404$	−876.000	−	1517.28i	−0.107878	−	0.186850i
$405$		0			0
$406$		0			0
$407$	8580.00			1.04495
$408$		0			0
$409$	881.000	−	1525.94i	0.106510	−	0.184481i	−0.807844	−	0.589396i	$-0.799366\pi$
$409$	881.000	−	1525.94i	0.106510	−	0.184481i	0.914354	+	0.404915i	$0.132699\pi$
$410$	−2268.00	+	3928.29i	−0.273192	+	0.473182i
$411$		0			0
$412$	6704.00			0.801656
$413$		0			0
$414$		0			0
$415$	4320.00	+	7482.46i	0.510989	+	0.885059i
$416$	32.0000	−	55.4256i	0.00377146	−	0.00653237i
$417$		0			0
$418$	1560.00	+	2702.00i	0.182541	+	0.316170i
$419$	−14580.0			−1.69995			−0.849976	−	0.526822i	$-0.823383\pi$
$419$	−14580.0			−1.69995			−0.849976	+	0.526822i	$0.823383\pi$
$420$		0			0
$421$	8534.00			0.987938			0.493969	−	0.869480i	$-0.335546\pi$
$421$	8534.00			0.987938			0.493969	+	0.869480i	$0.335546\pi$
$422$	−772.000	−	1337.14i	−0.0890530	−	0.154244i
$423$		0			0
$424$	1392.00	−	2411.01i	0.159437	−	0.276154i
$425$	−2937.00	−	5087.03i	−0.335213	−	0.580606i
$426$		0			0
$427$		0			0
$428$	−8088.00			−0.913430
$429$		0			0
$430$	−984.000	+	1704.34i	−0.110355	+	0.191141i
$431$	2967.00	−	5138.99i	0.331590	−	0.574331i	−0.651234	−	0.758877i	$-0.725748\pi$
$431$	2967.00	−	5138.99i	0.331590	−	0.574331i	0.982824	+	0.184546i	$0.0590816\pi$
$432$		0			0
$433$	−14758.0			−1.63793			−0.818966	−	0.573843i	$-0.805452\pi$
$433$	−14758.0			−1.63793			−0.818966	+	0.573843i	$0.805452\pi$
$434$		0			0
$435$		0			0
$436$	1004.00	+	1738.98i	0.110282	+	0.191014i
$437$	−2964.00	+	5133.80i	−0.324456	+	0.561975i
$438$		0			0
$439$	5696.00	+	9865.76i	0.619260	+	1.07259i	0.989621	+	0.143702i	$0.0459007\pi$
$439$	5696.00	+	9865.76i	0.619260	+	1.07259i	−0.370361	+	0.928888i	$0.620766\pi$
$440$	−1440.00			−0.156021
$441$		0			0
$442$	264.000			0.0284100
$443$	3513.00	+	6084.69i	0.376767	+	0.652579i	0.990590	−	0.136865i	$-0.0437025\pi$
$443$	3513.00	+	6084.69i	0.376767	+	0.652579i	−0.613823	+	0.789444i	$0.710369\pi$
$444$		0			0
$445$	−4122.00	+	7139.51i	−0.439105	+	0.760551i
$446$	776.000	+	1344.07i	0.0823871	+	0.142699i
$447$		0			0
$448$		0			0
$449$	3384.00			0.355681			0.177841	−	0.984059i	$-0.443089\pi$
$449$	3384.00			0.355681			0.177841	+	0.984059i	$0.443089\pi$
$450$		0			0
$451$	5670.00	−	9820.73i	0.591995	−	1.02537i
$452$	4032.00	−	6983.63i	0.419578	−	0.726731i
$453$		0			0
$454$	−3576.00			−0.369670
$455$		0			0
$456$		0			0
$457$	2141.00	+	3708.32i	0.219150	+	0.379580i	0.954548	−	0.298056i	$-0.0963381\pi$
$457$	2141.00	+	3708.32i	0.219150	+	0.379580i	−0.735398	+	0.677635i	$0.763005\pi$
$458$	5402.00	−	9356.54i	0.551133	−	0.954590i
$459$		0			0
$460$	−1368.00	−	2369.45i	−0.138659	−	0.240165i
$461$	−16650.0			−1.68214			−0.841071	−	0.540924i	$-0.818075\pi$
$461$	−16650.0			−1.68214			−0.841071	+	0.540924i	$0.818075\pi$
$462$		0			0
$463$	−9664.00			−0.970031			−0.485015	−	0.874506i	$-0.661186\pi$
$463$	−9664.00			−0.970031			−0.485015	+	0.874506i	$0.661186\pi$
$464$	576.000	+	997.661i	0.0576296	+	0.0998174i
$465$		0			0
$466$	−3012.00	+	5216.94i	−0.299417	+	0.518605i
$467$	−6162.00	−	10672.9i	−0.610585	−	1.05756i	−0.991142	−	0.132807i	$-0.957601\pi$
$467$	−6162.00	−	10672.9i	−0.610585	−	1.05756i	0.380557	−	0.924758i	$-0.375732\pi$
$468$		0			0
$469$		0			0
$470$	2736.00			0.268515
$471$		0			0
$472$	1392.00	−	2411.01i	0.135746	−	0.235119i
$473$	2460.00	−	4260.84i	0.239135	−	0.414194i
$474$		0			0
$475$	4628.00			0.447047
$476$		0			0
$477$		0			0
$478$	−3546.00	−	6141.85i	−0.339310	−	0.587702i
$479$	9330.00	−	16160.0i	0.889976	−	1.54148i	0.0500744	−	0.998745i	$-0.484054\pi$
$479$	9330.00	−	16160.0i	0.889976	−	1.54148i	0.839902	−	0.542738i	$-0.182613\pi$
$480$		0			0
$481$	286.000	+	495.367i	0.0271112	+	0.0469579i
$482$	7124.00			0.673214
$483$		0			0
$484$	−1724.00			−0.161908
$485$	−102.000	−	176.669i	−0.00954965	−	0.0165405i
$486$		0			0
$487$	1700.00	−	2944.49i	0.158181	−	0.273978i	−0.776031	−	0.630694i	$-0.782770\pi$
$487$	1700.00	−	2944.49i	0.158181	−	0.273978i	0.934213	+	0.356716i	$0.116104\pi$
$488$	−424.000	−	734.390i	−0.0393311	−	0.0681235i
$489$		0			0
$490$		0			0
$491$	−2970.00			−0.272982			−0.136491	−	0.990641i	$-0.543582\pi$
$491$	−2970.00			−0.272982			−0.136491	+	0.990641i	$0.543582\pi$
$492$		0			0
$493$	−2376.00	+	4115.35i	−0.217058	+	0.375956i
$494$	−104.000	+	180.133i	−0.00947203	+	0.0164060i
$495$		0			0
$496$	−3136.00			−0.283892
$497$		0			0
$498$		0			0
$499$	494.000	+	855.633i	0.0443176	+	0.0767603i	0.887333	−	0.461129i	$-0.152555\pi$
$499$	494.000	+	855.633i	0.0443176	+	0.0767603i	−0.843016	+	0.537889i	$0.819222\pi$
$500$	−2568.00	+	4447.91i	−0.229689	+	0.397833i
$501$		0			0
$502$	−3348.00	−	5798.91i	−0.297666	−	0.515573i
$503$	−5184.00			−0.459529			−0.229765	−	0.973246i	$-0.573796\pi$
$503$	−5184.00			−0.459529			−0.229765	+	0.973246i	$0.573796\pi$
$504$		0			0
$505$	−2628.00			−0.231573
$506$	3420.00	+	5923.61i	0.300469	+	0.520428i
$507$		0			0
$508$	−3568.00	+	6179.96i	−0.311623	+	0.539747i
$509$	8427.00	+	14596.0i	0.733831	+	1.27103i	0.955234	+	0.295851i	$0.0956032\pi$
$509$	8427.00	+	14596.0i	0.733831	+	1.27103i	−0.221403	+	0.975182i	$0.571064\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−366.000	+	633.931i	−0.0314077	+	0.0543998i
$515$	5028.00	−	8708.75i	0.430214	−	0.745152i
$516$		0			0
$517$	−6840.00			−0.581862
$518$		0			0
$519$		0			0
$520$	−48.0000	−	83.1384i	−0.00404796	−	0.00701127i
$521$	−2199.00	+	3808.78i	−0.184914	+	0.320280i	−0.943547	−	0.331238i	$-0.892534\pi$
$521$	−2199.00	+	3808.78i	−0.184914	+	0.320280i	0.758634	+	0.651517i	$0.225867\pi$
$522$		0			0
$523$	5336.00	+	9242.22i	0.446132	+	0.772723i	0.998130	−	0.0611220i	$-0.0194679\pi$
$523$	5336.00	+	9242.22i	0.446132	+	0.772723i	−0.551998	+	0.833845i	$0.686135\pi$
$524$	−6432.00			−0.536228
$525$		0			0
$526$	8340.00			0.691333
$527$	−6468.00	−	11202.9i	−0.534631	−	0.926008i
$528$		0			0
$529$	−414.500	+	717.935i	−0.0340676	+	0.0590067i
$530$	−2088.00	−	3616.52i	−0.171126	−	0.296399i
$531$		0			0
$532$		0			0
$533$	756.000			0.0614371
$534$		0			0
$535$	−6066.00	+	10506.6i	−0.490198	+	0.849048i
$536$	2384.00	−	4129.21i	0.192114	−	0.332751i
$537$		0			0
$538$	12156.0			0.974131
$539$		0			0
$540$		0			0
$541$	−10351.0	−	17928.5i	−0.822596	−	1.42478i	−0.903743	−	0.428075i	$-0.859192\pi$
$541$	−10351.0	−	17928.5i	−0.822596	−	1.42478i	0.0811474	−	0.996702i	$-0.474142\pi$
$542$	2468.00	−	4274.70i	0.195590	−	0.338771i
$543$		0			0
$544$	−1056.00	−	1829.05i	−0.0832273	−	0.144154i
$545$	3012.00			0.236734
$546$		0			0
$547$	−22876.0			−1.78813			−0.894065	−	0.447937i	$-0.852159\pi$
$547$	−22876.0			−1.78813			−0.894065	+	0.447937i	$0.852159\pi$
$548$	−5160.00	−	8937.38i	−0.402234	−	0.696690i
$549$		0			0
$550$	2670.00	−	4624.58i	0.206999	−	0.358532i
$551$	−1872.00	−	3242.40i	−0.144737	−	0.250691i
$552$		0			0
$553$		0			0
$554$	788.000			0.0604312
$555$		0			0
$556$	−4288.00	+	7427.03i	−0.327071	+	0.566504i
$557$	−6438.00	+	11150.9i	−0.489743	+	0.848260i	−0.999930	−	0.0118036i	$-0.996243\pi$
$557$	−6438.00	+	11150.9i	−0.489743	+	0.848260i	0.510187	+	0.860063i	$0.329576\pi$
$558$		0			0
$559$	328.000			0.0248174
$560$		0			0
$561$		0			0
$562$	396.000	+	685.892i	0.0297229	+	0.0514815i
$563$	−3450.00	+	5975.58i	−0.258260	+	0.447319i	−0.965776	−	0.259378i	$-0.916482\pi$
$563$	−3450.00	+	5975.58i	−0.258260	+	0.447319i	0.707516	+	0.706697i	$0.249816\pi$
$564$		0			0
$565$	−6048.00	−	10475.4i	−0.450339	−	0.780009i
$566$	2696.00			0.200214
$567$		0			0
$568$	5040.00			0.372313
$569$	7338.00	+	12709.8i	0.540641	+	0.936418i	0.998867	+	0.0475826i	$0.0151517\pi$
$569$	7338.00	+	12709.8i	0.540641	+	0.936418i	−0.458226	+	0.888836i	$0.651515\pi$
$570$		0			0
$571$	−190.000	+	329.090i	−0.0139251	+	0.0241190i	−0.872904	−	0.487892i	$-0.837766\pi$
$571$	−190.000	+	329.090i	−0.0139251	+	0.0241190i	0.858979	+	0.512011i	$0.171099\pi$
$572$	120.000	+	207.846i	0.00877177	+	0.0151932i
$573$		0			0
$574$		0			0
$575$	10146.0			0.735856
$576$		0			0
$577$	5903.00	−	10224.3i	0.425901	−	0.737683i	−0.570603	−	0.821226i	$-0.693290\pi$
$577$	5903.00	−	10224.3i	0.425901	−	0.737683i	0.996504	+	0.0835434i	$0.0266237\pi$
$578$	−557.000	+	964.752i	−0.0400833	+	0.0694263i
$579$		0			0
$580$	1728.00			0.123709
$581$		0			0
$582$		0			0
$583$	5220.00	+	9041.31i	0.370824	+	0.642286i
$584$	−4168.00	+	7219.19i	−0.295331	+	0.511528i
$585$		0			0
$586$	−7506.00	−	13000.8i	−0.529130	−	0.916480i
$587$	19188.0			1.34919			0.674594	−	0.738189i	$-0.264319\pi$
$587$	19188.0			1.34919			0.674594	+	0.738189i	$0.264319\pi$
$588$		0			0
$589$	10192.0			0.712995
$590$	−2088.00	−	3616.52i	−0.145698	−	0.252356i
$591$		0			0
$592$	2288.00	−	3962.93i	0.158845	−	0.275128i
$593$	345.000	+	597.558i	0.0238912	+	0.0413807i	0.877724	−	0.479167i	$-0.159061\pi$
$593$	345.000	+	597.558i	0.0238912	+	0.0413807i	−0.853833	+	0.520548i	$0.825728\pi$
$594$		0			0
$595$		0			0
$596$	−6000.00			−0.412365
$597$		0			0
$598$	−228.000	+	394.908i	−0.0155913	+	0.0270050i
$599$	−10245.0	+	17744.9i	−0.698830	+	1.21041i	0.270042	+	0.962849i	$0.412962\pi$
$599$	−10245.0	+	17744.9i	−0.698830	+	1.21041i	−0.968872	+	0.247561i	$0.920371\pi$
$600$		0			0
$601$	−11590.0			−0.786632			−0.393316	−	0.919403i	$-0.628672\pi$
$601$	−11590.0			−0.786632			−0.393316	+	0.919403i	$0.628672\pi$
$602$		0			0
$603$		0			0
$604$	2480.00	+	4295.49i	0.167069	+	0.289372i
$605$	−1293.00	+	2239.54i	−0.0868891	+	0.150496i
$606$		0			0
$607$	3212.00	+	5563.35i	0.214779	+	0.372009i	0.953204	−	0.302327i	$-0.0977634\pi$
$607$	3212.00	+	5563.35i	0.214779	+	0.372009i	−0.738425	+	0.674336i	$0.764430\pi$
$608$	1664.00			0.110994
$609$		0			0
$610$	−1272.00			−0.0844291
$611$	−228.000	−	394.908i	−0.0150964	−	0.0261477i
$612$		0			0
$613$	4841.00	−	8384.86i	0.318966	−	0.552465i	−0.661307	−	0.750116i	$-0.729998\pi$
$613$	4841.00	−	8384.86i	0.318966	−	0.552465i	0.980273	+	0.197650i	$0.0633311\pi$
$614$	1748.00	+	3027.62i	0.114892	+	0.198998i
$615$		0			0
$616$		0			0
$617$	−5076.00			−0.331203			−0.165601	−	0.986193i	$-0.552956\pi$
$617$	−5076.00			−0.331203			−0.165601	+	0.986193i	$0.552956\pi$
$618$		0			0
$619$	−11332.0	+	19627.6i	−0.735818	+	1.27447i	0.218545	+	0.975827i	$0.429869\pi$
$619$	−11332.0	+	19627.6i	−0.735818	+	1.27447i	−0.954363	+	0.298648i	$0.903464\pi$
$620$	−2352.00	+	4073.78i	−0.152353	+	0.263882i
$621$		0			0
$622$	−2280.00			−0.146977
$623$		0			0
$624$		0			0
$625$	−1710.50	−	2962.67i	−0.109472	−	0.189611i
$626$	146.000	−	252.879i	0.00932162	−	0.0161455i
$627$		0			0
$628$	−1228.00	−	2126.96i	−0.0780295	−	0.135151i
$629$	18876.0			1.19656
$630$		0			0
$631$	−8584.00			−0.541559			−0.270779	−	0.962641i	$-0.587281\pi$
$631$	−8584.00			−0.541559			−0.270779	+	0.962641i	$0.587281\pi$
$632$	−352.000	−	609.682i	−0.0221548	−	0.0383732i
$633$		0			0
$634$	8148.00	−	14112.7i	0.510408	−	0.884052i
$635$	5352.00	+	9269.94i	0.334469	+	0.579317i
$636$		0			0
$637$		0			0
$638$	−4320.00			−0.268073
$639$		0			0
$640$	−384.000	+	665.108i	−0.0237171	+	0.0410792i
$641$	186.000	−	322.161i	0.0114611	−	0.0198512i	−0.860238	−	0.509893i	$-0.829685\pi$
$641$	186.000	−	322.161i	0.0114611	−	0.0198512i	0.871699	+	0.490042i	$0.163018\pi$
$642$		0			0
$643$	3188.00			0.195525			0.0977624	−	0.995210i	$-0.468831\pi$
$643$	3188.00			0.195525			0.0977624	+	0.995210i	$0.468831\pi$
$644$		0			0
$645$		0			0
$646$	3432.00	+	5944.40i	0.209025	+	0.362042i
$647$	−6366.00	+	11026.2i	−0.386821	+	0.669994i	−0.992020	−	0.126080i	$-0.959760\pi$
$647$	−6366.00	+	11026.2i	−0.386821	+	0.669994i	0.605199	+	0.796074i	$0.293094\pi$
$648$		0			0
$649$	5220.00	+	9041.31i	0.315721	+	0.546845i
$650$	356.000			0.0214823
$651$		0			0
$652$	368.000			0.0221043
$653$	−1788.00	−	3096.91i	−0.107151	−	0.185592i	0.807464	−	0.589917i	$-0.200840\pi$
$653$	−1788.00	−	3096.91i	−0.107151	−	0.185592i	−0.914615	+	0.404326i	$0.867506\pi$
$654$		0			0
$655$	−4824.00	+	8355.41i	−0.287770	+	0.498432i
$656$	−3024.00	−	5237.72i	−0.179981	−	0.311736i
$657$		0			0
$658$		0			0
$659$	−11430.0			−0.675644			−0.337822	−	0.941210i	$-0.609690\pi$
$659$	−11430.0			−0.675644			−0.337822	+	0.941210i	$0.609690\pi$
$660$		0			0
$661$	−11323.0	+	19612.0i	−0.666284	+	1.15404i	0.312652	+	0.949868i	$0.398783\pi$
$661$	−11323.0	+	19612.0i	−0.666284	+	1.15404i	−0.978936	+	0.204170i	$0.934551\pi$
$662$	−9700.00	+	16800.9i	−0.569488	+	0.986383i
$663$		0			0
$664$	−11520.0			−0.673287
$665$		0			0
$666$		0			0
$667$	−4104.00	−	7108.34i	−0.238242	−	0.412648i
$668$	−7848.00	+	13593.1i	−0.454563	+	0.787327i
$669$		0			0
$670$	−3576.00	−	6193.81i	−0.206198	−	0.357146i
$671$	3180.00			0.182955
$672$		0			0
$673$	−13570.0			−0.777244			−0.388622	−	0.921397i	$-0.627049\pi$
$673$	−13570.0			−0.777244			−0.388622	+	0.921397i	$0.627049\pi$
$674$	8174.00	+	14157.8i	0.467138	+	0.809106i
$675$		0			0
$676$	4386.00	−	7596.77i	0.249545	−	0.432224i
$677$	−1419.00	−	2457.78i	−0.0805563	−	0.139528i	0.822933	−	0.568139i	$-0.192336\pi$
$677$	−1419.00	−	2457.78i	−0.0805563	−	0.139528i	−0.903489	+	0.428611i	$0.859003\pi$
$678$		0			0
$679$		0			0
$680$	−3168.00			−0.178658
$681$		0			0
$682$	5880.00	−	10184.5i	0.330142	−	0.571823i
$683$	−3279.00	+	5679.39i	−0.183701	+	0.318179i	−0.943138	−	0.332402i	$-0.892141\pi$
$683$	−3279.00	+	5679.39i	−0.183701	+	0.318179i	0.759437	+	0.650580i	$0.225474\pi$
$684$		0			0
$685$	−15480.0			−0.863446
$686$		0			0
$687$		0			0
$688$	−1312.00	−	2272.45i	−0.0727028	−	0.125925i
$689$	−348.000	+	602.754i	−0.0192420	+	0.0333281i
$690$		0			0
$691$	10916.0	+	18907.1i	0.600961	+	1.04090i	0.992676	+	0.120809i	$0.0385487\pi$
$691$	10916.0	+	18907.1i	0.600961	+	1.04090i	−0.391715	+	0.920087i	$0.628118\pi$
$692$	7608.00			0.417938
$693$		0			0
$694$	−8076.00			−0.441730
$695$	6432.00	+	11140.6i	0.351050	+	0.608036i
$696$		0			0
$697$	12474.0	−	21605.6i	0.677886	−	1.17413i
$698$	10766.0	+	18647.3i	0.583810	+	1.01119i
$699$		0			0
$700$		0			0
$701$	−16200.0			−0.872847			−0.436423	−	0.899741i	$-0.643755\pi$
$701$	−16200.0			−0.872847			−0.436423	+	0.899741i	$0.643755\pi$
$702$		0			0
$703$	−7436.00	+	12879.5i	−0.398939	+	0.690982i
$704$	960.000	−	1662.77i	0.0513940	−	0.0890170i
$705$		0			0
$706$	7332.00			0.390855
$707$		0			0
$708$		0			0
$709$	−18361.0	−	31802.2i	−0.972584	−	1.68456i	−0.687689	−	0.726006i	$-0.741375\pi$
$709$	−18361.0	−	31802.2i	−0.972584	−	1.68456i	−0.284895	−	0.958559i	$-0.591959\pi$
$710$	3780.00	−	6547.15i	0.199804	−	0.346071i
$711$		0			0
$712$	−5496.00	−	9519.35i	−0.289286	−	0.501057i
$713$	22344.0			1.17362
$714$		0			0
$715$	360.000			0.0188297
$716$	−12.0000	−	20.7846i	−0.000626342	−	0.00108486i
$717$		0			0
$718$	5106.00	−	8843.85i	0.265396	−	0.459679i
$719$	6888.00	+	11930.4i	0.357273	+	0.618814i	0.987504	−	0.157593i	$-0.0503734\pi$
$719$	6888.00	+	11930.4i	0.357273	+	0.618814i	−0.630231	+	0.776407i	$0.717040\pi$
$720$		0			0
$721$		0			0
$722$	8310.00			0.428347
$723$		0			0
$724$	5756.00	−	9969.68i	0.295470	−	0.511769i
$725$	−3204.00	+	5549.49i	−0.164129	+	0.284280i
$726$		0			0
$727$	34220.0			1.74574			0.872868	−	0.487957i	$-0.162258\pi$
$727$	34220.0			1.74574			0.872868	+	0.487957i	$0.162258\pi$
$728$		0			0
$729$		0			0
$730$	6252.00	+	10828.8i	0.316982	+	0.549029i
$731$	5412.00	−	9373.86i	0.273830	−	0.474288i
$732$		0			0
$733$	6875.00	+	11907.8i	0.346431	+	0.600036i	0.985613	−	0.169020i	$-0.0540601\pi$
$733$	6875.00	+	11907.8i	0.346431	+	0.600036i	−0.639182	+	0.769056i	$0.720727\pi$
$734$	11552.0			0.580916
$735$		0			0
$736$	3648.00			0.182700
$737$	8940.00	+	15484.5i	0.446824	+	0.773922i
$738$		0			0
$739$	−19918.0	+	34499.0i	−0.991469	+	1.71727i	−0.382853	+	0.923809i	$0.625059\pi$
$739$	−19918.0	+	34499.0i	−0.991469	+	1.71727i	−0.608616	+	0.793465i	$0.708275\pi$
$740$	−3432.00	−	5944.40i	−0.170490	−	0.295298i
$741$		0			0
$742$		0			0
$743$	−34470.0			−1.70199			−0.850997	−	0.525170i	$-0.824002\pi$
$743$	−34470.0			−1.70199			−0.850997	+	0.525170i	$0.824002\pi$
$744$		0			0
$745$	−4500.00	+	7794.23i	−0.221298	+	0.383300i
$746$	8462.00	−	14656.6i	0.415303	−	0.719325i
$747$		0			0
$748$	7920.00			0.387144
$749$		0			0
$750$		0			0
$751$	−2620.00	−	4537.97i	−0.127304	−	0.220497i	0.795327	−	0.606180i	$-0.207299\pi$
$751$	−2620.00	−	4537.97i	−0.127304	−	0.220497i	−0.922631	+	0.385684i	$0.873966\pi$
$752$	−1824.00	+	3159.26i	−0.0884500	+	0.153200i
$753$		0			0
$754$	−144.000	−	249.415i	−0.00695513	−	0.0120466i
$755$	7440.00			0.358635
$756$		0			0
$757$	18578.0			0.891980			0.445990	−	0.895038i	$-0.352852\pi$
$757$	18578.0			0.891980			0.445990	+	0.895038i	$0.352852\pi$
$758$	6860.00	+	11881.9i	0.328716	+	0.569352i
$759$		0			0
$760$	1248.00	−	2161.60i	0.0595654	−	0.103170i
$761$	15267.0	+	26443.2i	0.727238	+	1.25961i	0.958046	+	0.286614i	$0.0925298\pi$
$761$	15267.0	+	26443.2i	0.727238	+	1.25961i	−0.230808	+	0.972999i	$0.574137\pi$
$762$		0			0
$763$		0			0
$764$	1416.00			0.0670538
$765$		0			0
$766$	696.000	−	1205.51i	0.0328296	−	0.0568626i
$767$	−348.000	+	602.754i	−0.0163827	+	0.0283757i
$768$		0			0
$769$	−39958.0			−1.87376			−0.936881	−	0.349650i	$-0.886301\pi$
$769$	−39958.0			−1.87376			−0.936881	+	0.349650i	$0.886301\pi$
$770$		0			0
$771$		0			0
$772$	9716.00	+	16828.6i	0.452962	+	0.784553i
$773$	−1983.00	+	3434.66i	−0.0922685	+	0.159814i	−0.908465	−	0.417960i	$-0.862745\pi$
$773$	−1983.00	+	3434.66i	−0.0922685	+	0.159814i	0.816197	+	0.577774i	$0.196078\pi$
$774$		0			0
$775$	−8722.00	−	15106.9i	−0.404263	−	0.700203i
$776$	272.000			0.0125828
$777$		0			0
$778$	22272.0			1.02634
$779$	9828.00	+	17022.6i	0.452021	+	0.782924i
$780$		0			0
$781$	−9450.00	+	16367.9i	−0.432967	+	0.749922i
$782$	7524.00	+	13032.0i	0.344064	+	0.595936i
$783$		0			0
$784$		0			0
$785$	−3684.00			−0.167500
$786$		0			0
$787$	1880.00	−	3256.26i	0.0851522	−	0.147488i	−0.820304	−	0.571928i	$-0.806196\pi$
$787$	1880.00	−	3256.26i	0.0851522	−	0.147488i	0.905456	+	0.424440i	$0.139529\pi$
$788$	−792.000	+	1371.78i	−0.0358044	+	0.0620150i
$789$		0			0
$790$	−1056.00			−0.0475580
$791$		0			0
$792$		0			0
$793$	106.000	+	183.597i	0.00474675	+	0.00822161i
$794$	10838.0	−	18772.0i	0.484416	−	0.839033i
$795$		0			0
$796$	−3424.00	−	5930.54i	−0.152463	−	0.264073i
$797$	24102.0			1.07119			0.535594	−	0.844476i	$-0.320088\pi$
$797$	24102.0			1.07119			0.535594	+	0.844476i	$0.320088\pi$
$798$		0			0
$799$	−15048.0			−0.666283
$800$	−1424.00	−	2466.44i	−0.0629325	−	0.109002i
$801$		0			0
$802$	8364.00	−	14486.9i	0.368258	−	0.637842i
$803$	−15630.0	−	27072.0i	−0.686888	−	1.18972i
$804$		0			0
$805$		0			0
$806$	784.000			0.0342621
$807$		0			0
$808$	1752.00	−	3034.55i	0.0762811	−	0.132123i
$809$	5856.00	−	10142.9i	0.254494	−	0.440797i	−0.710264	−	0.703936i	$-0.751424\pi$
$809$	5856.00	−	10142.9i	0.254494	−	0.440797i	0.964758	+	0.263138i	$0.0847576\pi$
$810$		0			0
$811$	37424.0			1.62039			0.810194	−	0.586162i	$-0.199362\pi$
$811$	37424.0			1.62039			0.810194	+	0.586162i	$0.199362\pi$
$812$		0			0
$813$		0			0
$814$	8580.00	+	14861.0i	0.369446	+	0.639899i
$815$	276.000	−	478.046i	0.0118624	−	0.0205463i
$816$		0			0
$817$	4264.00	+	7385.46i	0.182593	+	0.316260i
$818$	3524.00			0.150628
$819$		0			0
$820$	−9072.00			−0.386351
$821$	6726.00	+	11649.8i	0.285918	+	0.495225i	0.972831	−	0.231514i	$-0.0743680\pi$
$821$	6726.00	+	11649.8i	0.285918	+	0.495225i	−0.686913	+	0.726740i	$0.741035\pi$
$822$		0			0
$823$	−10216.0	+	17694.6i	−0.432694	+	0.749448i	−0.997104	−	0.0760461i	$-0.975770\pi$
$823$	−10216.0	+	17694.6i	−0.432694	+	0.749448i	0.564410	+	0.825495i	$0.309104\pi$
$824$	6704.00	+	11611.7i	0.283428	+	0.490912i
$825$		0			0
$826$		0			0
$827$	−24390.0			−1.02554			−0.512771	−	0.858525i	$-0.671381\pi$
$827$	−24390.0			−1.02554			−0.512771	+	0.858525i	$0.671381\pi$
$828$		0			0
$829$	14255.0	−	24690.4i	0.597221	−	1.03442i	−0.396008	−	0.918247i	$-0.629605\pi$
$829$	14255.0	−	24690.4i	0.597221	−	1.03442i	0.993229	−	0.116171i	$-0.0370620\pi$
$830$	−8640.00	+	14964.9i	−0.361324	+	0.625831i
$831$		0			0
$832$	128.000			0.00533366
$833$		0			0
$834$		0			0
$835$	11772.0	+	20389.7i	0.487888	+	0.845048i
$836$	−3120.00	+	5404.00i	−0.129076	+	0.223566i
$837$		0			0
$838$	−14580.0	−	25253.3i	−0.601024	−	1.04100i
$839$	36972.0			1.52135			0.760677	−	0.649131i	$-0.224867\pi$
$839$	36972.0			1.52135			0.760677	+	0.649131i	$0.224867\pi$
$840$		0			0
$841$	−19205.0			−0.787445
$842$	8534.00	+	14781.3i	0.349289	+	0.604986i
$843$		0			0
$844$	1544.00	−	2674.29i	0.0629700	−	0.109067i
$845$	−6579.00	−	11395.2i	−0.267840	−	0.463912i
$846$		0			0
$847$		0			0
$848$	5568.00			0.225479
$849$		0			0
$850$	5874.00	−	10174.1i	0.237031	−	0.410550i
$851$	−16302.0	+	28235.9i	−0.656669	+	1.13738i
$852$		0			0
$853$	−14074.0			−0.564929			−0.282465	−	0.959278i	$-0.591152\pi$
$853$	−14074.0			−0.564929			−0.282465	+	0.959278i	$0.591152\pi$
$854$		0			0
$855$		0			0
$856$	−8088.00	−	14008.8i	−0.322946	−	0.559360i
$857$	−4413.00	+	7643.54i	−0.175899	+	0.304666i	−0.940472	−	0.339871i	$-0.889616\pi$
$857$	−4413.00	+	7643.54i	−0.175899	+	0.304666i	0.764573	+	0.644537i	$0.222950\pi$
$858$		0			0
$859$	10250.0	+	17753.5i	0.407131	+	0.705171i	0.994567	−	0.104099i	$-0.0331959\pi$
$859$	10250.0	+	17753.5i	0.407131	+	0.705171i	−0.587436	+	0.809271i	$0.699863\pi$
$860$	−3936.00			−0.156066
$861$		0			0
$862$	11868.0			0.468939
$863$	3837.00	+	6645.88i	0.151348	+	0.262142i	0.931723	−	0.363169i	$-0.118305\pi$
$863$	3837.00	+	6645.88i	0.151348	+	0.262142i	−0.780375	+	0.625311i	$0.784972\pi$
$864$		0			0
$865$	5706.00	−	9883.08i	0.224289	−	0.388480i
$866$	−14758.0	−	25561.6i	−0.579096	−	1.00302i
$867$		0			0
$868$		0			0
$869$	2640.00			0.103056
$870$		0			0
$871$	−596.000	+	1032.30i	−0.0231856	+	0.0401587i
$872$	−2008.00	+	3477.96i	−0.0779810	+	0.135067i
$873$		0			0
$874$	−11856.0			−0.458850
$875$		0			0
$876$		0			0
$877$	4445.00	+	7698.97i	0.171148	+	0.296437i	0.938822	−	0.344404i	$-0.111919\pi$
$877$	4445.00	+	7698.97i	0.171148	+	0.296437i	−0.767673	+	0.640841i	$0.778586\pi$
$878$	−11392.0	+	19731.5i	−0.437883	+	0.758436i
$879$		0			0
$880$	−1440.00	−	2494.15i	−0.0551618	−	0.0955431i
$881$	−738.000			−0.0282223			−0.0141112	−	0.999900i	$-0.504492\pi$
$881$	−738.000			−0.0282223			−0.0141112	+	0.999900i	$0.504492\pi$
$882$		0			0
$883$	20.0000			0.000762235			0.000381118	−	1.00000i	$-0.499879\pi$
$883$	20.0000			0.000762235			0.000381118		1.00000i	$0.499879\pi$
$884$	264.000	+	457.261i	0.0100444	+	0.0173975i
$885$		0			0
$886$	−7026.00	+	12169.4i	−0.266414	+	0.461443i
$887$	19902.0	+	34471.3i	0.753375	+	1.30488i	0.946178	+	0.323647i	$0.104909\pi$
$887$	19902.0	+	34471.3i	0.753375	+	1.30488i	−0.192803	+	0.981238i	$0.561758\pi$
$888$		0			0
$889$		0			0
$890$	−16488.0			−0.620988
$891$		0			0
$892$	−1552.00	+	2688.14i	−0.0582565	+	0.100903i
$893$	5928.00	−	10267.6i	0.222142	−	0.384762i
$894$		0			0
$895$	−36.0000			−0.00134452
$896$		0			0
$897$		0			0
$898$	3384.00	+	5861.26i	0.125752	+	0.217809i
$899$	−7056.00	+	12221.4i	−0.261769	+	0.453398i
$900$		0			0
$901$	11484.0	+	19890.9i	0.424625	+	0.735473i
$902$	22680.0			0.837208
$903$		0			0
$904$	16128.0			0.593373
$905$	−8634.00	−	14954.5i	−0.317131	−	0.549288i
$906$		0			0
$907$	−14590.0	+	25270.6i	−0.534127	+	0.925135i	0.465078	+	0.885270i	$0.346026\pi$
$907$	−14590.0	+	25270.6i	−0.534127	+	0.925135i	−0.999205	+	0.0398652i	$0.987307\pi$
$908$	−3576.00	−	6193.81i	−0.130698	−	0.226375i
$909$		0			0
$910$		0			0
$911$	48258.0			1.75506			0.877530	−	0.479523i	$-0.159190\pi$
$911$	48258.0			1.75506			0.877530	+	0.479523i	$0.159190\pi$
$912$		0			0
$913$	21600.0	−	37412.3i	0.782974	−	1.35615i
$914$	−4282.00	+	7416.64i	−0.154963	+	0.268403i
$915$		0			0
$916$	21608.0			0.779420
$917$		0			0
$918$		0			0
$919$	−12880.0	−	22308.8i	−0.462320	−	0.800762i	0.536756	−	0.843737i	$-0.319649\pi$
$919$	−12880.0	−	22308.8i	−0.462320	−	0.800762i	−0.999076	+	0.0429758i	$0.986316\pi$
$920$	2736.00	−	4738.89i	0.0980470	−	0.169822i
$921$		0			0
$922$	−16650.0	−	28838.6i	−0.594727	−	1.03010i
$923$	−1260.00			−0.0449333
$924$		0			0
$925$	25454.0			0.904781
$926$	−9664.00	−	16738.5i	−0.342958	−	0.594020i
$927$		0			0
$928$	−1152.00	+	1995.32i	−0.0407503	+	0.0705815i
$929$	−22389.0	−	38778.9i	−0.790699	−	1.36953i	−0.925535	−	0.378663i	$-0.876384\pi$
$929$	−22389.0	−	38778.9i	−0.790699	−	1.36953i	0.134836	−	0.990868i	$-0.456949\pi$
$930$		0			0
$931$		0			0
$932$	−12048.0			−0.423439
$933$		0			0
$934$	12324.0	−	21345.8i	0.431749	−	0.747811i
$935$	5940.00	−	10288.4i	0.207763	−	0.359857i
$936$		0			0
$937$	−44494.0			−1.55129			−0.775643	−	0.631171i	$-0.782574\pi$
$937$	−44494.0			−1.55129			−0.775643	+	0.631171i	$0.782574\pi$
$938$		0			0
$939$		0			0
$940$	2736.00	+	4738.89i	0.0949346	+	0.164431i
$941$	−3729.00	+	6458.82i	−0.129184	+	0.223753i	−0.923361	−	0.383934i	$-0.874569\pi$
$941$	−3729.00	+	6458.82i	−0.129184	+	0.223753i	0.794177	+	0.607687i	$0.207902\pi$
$942$		0			0
$943$	21546.0	+	37318.8i	0.744045	+	1.28872i
$944$	5568.00			0.191973
$945$		0			0
$946$	9840.00			0.338188
$947$	8895.00	+	15406.6i	0.305226	+	0.528666i	0.977312	−	0.211807i	$-0.0679348\pi$
$947$	8895.00	+	15406.6i	0.305226	+	0.528666i	−0.672086	+	0.740473i	$0.734601\pi$
$948$		0			0
$949$	1042.00	−	1804.80i	0.0356425	−	0.0617347i
$950$	4628.00	+	8015.93i	0.158055	+	0.273759i
$951$		0			0
$952$		0			0
$953$	5832.00			0.198234			0.0991170	−	0.995076i	$-0.468398\pi$
$953$	5832.00			0.198234			0.0991170	+	0.995076i	$0.468398\pi$
$954$		0			0
$955$	1062.00	−	1839.44i	0.0359848	−	0.0623276i
$956$	7092.00	−	12283.7i	0.239929	−	0.415568i
$957$		0			0
$958$	37320.0			1.25862
$959$		0			0
$960$		0			0
$961$	−4312.50	−	7469.47i	−0.144758	−	0.250729i
$962$	−572.000	+	990.733i	−0.0191705	+	0.0332043i
$963$		0			0
$964$	7124.00	+	12339.1i	0.238017	+	0.412258i
$965$	29148.0			0.972339
$966$		0			0
$967$	−13264.0			−0.441098			−0.220549	−	0.975376i	$-0.570785\pi$
$967$	−13264.0			−0.441098			−0.220549	+	0.975376i	$0.570785\pi$
$968$	−1724.00	−	2986.06i	−0.0572432	−	0.0991482i
$969$		0			0
$970$	204.000	−	353.338i	0.00675262	−	0.0116959i
$971$	1992.00	+	3450.25i	0.0658356	+	0.114031i	0.897064	−	0.441900i	$-0.145695\pi$
$971$	1992.00	+	3450.25i	0.0658356	+	0.114031i	−0.831229	+	0.555931i	$0.812362\pi$
$972$		0			0
$973$		0			0
$974$	6800.00			0.223702
$975$		0			0
$976$	848.000	−	1468.78i	0.0278113	−	0.0481706i
$977$	−19470.0	+	33723.0i	−0.637564	+	1.10429i	0.348401	+	0.937346i	$0.386725\pi$
$977$	−19470.0	+	33723.0i	−0.637564	+	1.10429i	−0.985966	+	0.166949i	$0.946609\pi$
$978$		0			0
$979$	41220.0			1.34566
$980$		0			0
$981$		0			0
$982$	−2970.00	−	5144.19i	−0.0965138	−	0.167167i
$983$	−4404.00	+	7627.95i	−0.142895	+	0.247501i	−0.928586	−	0.371118i	$-0.878974\pi$
$983$	−4404.00	+	7627.95i	−0.142895	+	0.247501i	0.785691	+	0.618620i	$0.212308\pi$
$984$		0			0
$985$	1188.00	+	2057.68i	0.0384293	+	0.0665614i
$986$	−9504.00			−0.306967
$987$		0			0
$988$	−416.000			−0.0133955
$989$	9348.00	+	16191.2i	0.300555	+	0.520577i
$990$		0			0
$991$	−9244.00	+	16011.1i	−0.296312	+	0.513228i	−0.975289	−	0.220932i	$-0.929090\pi$
$991$	−9244.00	+	16011.1i	−0.296312	+	0.513228i	0.678977	+	0.734159i	$0.262424\pi$
$992$	−3136.00	−	5431.71i	−0.100371	−	0.173848i
$993$		0			0
$994$		0			0
$995$	−10272.0			−0.327281
$996$		0			0
$997$	2501.00	−	4331.86i	0.0794458	−	0.137604i	−0.823565	−	0.567222i	$-0.808018\pi$
$997$	2501.00	−	4331.86i	0.0794458	−	0.137604i	0.903011	+	0.429618i	$0.141352\pi$
$998$	−988.000	+	1711.27i	−0.0313373	+	0.0542777i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.t.361.1		2
3.2	odd	2		882.4.g.e.361.1		2
7.2	even	3	inner	882.4.g.t.667.1		2
7.3	odd	6		882.4.a.e.1.1		1
7.4	even	3		126.4.a.b.1.1	✓	1
7.5	odd	6		882.4.g.q.667.1		2
7.6	odd	2		882.4.g.q.361.1		2
21.2	odd	6		882.4.g.e.667.1		2
21.5	even	6		882.4.g.h.667.1		2
21.11	odd	6		126.4.a.g.1.1	yes	1
21.17	even	6		882.4.a.m.1.1		1
21.20	even	2		882.4.g.h.361.1		2
28.11	odd	6		1008.4.a.g.1.1		1
84.11	even	6		1008.4.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.a.b.1.1	✓	1	7.4	even	3
126.4.a.g.1.1	yes	1	21.11	odd	6
882.4.a.e.1.1		1	7.3	odd	6
882.4.a.m.1.1		1	21.17	even	6
882.4.g.e.361.1		2	3.2	odd	2
882.4.g.e.667.1		2	21.2	odd	6
882.4.g.h.361.1		2	21.20	even	2
882.4.g.h.667.1		2	21.5	even	6
882.4.g.q.361.1		2	7.6	odd	2
882.4.g.q.667.1		2	7.5	odd	6
882.4.g.t.361.1		2	1.1	even	1	trivial
882.4.g.t.667.1		2	7.2	even	3	inner
1008.4.a.g.1.1		1	28.11	odd	6
1008.4.a.n.1.1		1	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -8.00000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(15.0000 - 25.9808i) q^{11} +2.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(33.0000 - 57.1577i) q^{17} +(26.0000 + 45.0333i) q^{19} -24.0000 q^{20} +60.0000 q^{22} +(57.0000 + 98.7269i) q^{23} +(44.5000 - 77.0763i) q^{25} +(2.00000 + 3.46410i) q^{26} -72.0000 q^{29} +(98.0000 - 169.741i) q^{31} +(16.0000 - 27.7128i) q^{32} +132.000 q^{34} +(143.000 + 247.683i) q^{37} +(-52.0000 + 90.0666i) q^{38} +(-24.0000 - 41.5692i) q^{40} +378.000 q^{41} +164.000 q^{43} +(60.0000 + 103.923i) q^{44} +(-114.000 + 197.454i) q^{46} +(-114.000 - 197.454i) q^{47} +178.000 q^{50} +(-4.00000 + 6.92820i) q^{52} +(-174.000 + 301.377i) q^{53} +180.000 q^{55} +(-72.0000 - 124.708i) q^{58} +(-174.000 + 301.377i) q^{59} +(53.0000 + 91.7987i) q^{61} +392.000 q^{62} +64.0000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-298.000 + 516.151i) q^{67} +(132.000 + 228.631i) q^{68} -630.000 q^{71} +(521.000 - 902.398i) q^{73} +(-286.000 + 495.367i) q^{74} -208.000 q^{76} +(44.0000 + 76.2102i) q^{79} +(48.0000 - 83.1384i) q^{80} +(378.000 + 654.715i) q^{82} +1440.00 q^{83} +396.000 q^{85} +(164.000 + 284.056i) q^{86} +(-120.000 + 207.846i) q^{88} +(687.000 + 1189.92i) q^{89} -456.000 q^{92} +(228.000 - 394.908i) q^{94} +(-156.000 + 270.200i) q^{95} -34.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} + 6 q^{5} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 + 6 * q^5 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} + 6 q^{5} - 16 q^{8} - 12 q^{10} + 30 q^{11} + 4 q^{13} - 16 q^{16} + 66 q^{17} + 52 q^{19} - 48 q^{20} + 120 q^{22} + 114 q^{23} + 89 q^{25} + 4 q^{26} - 144 q^{29} + 196 q^{31} + 32 q^{32} + 264 q^{34} + 286 q^{37} - 104 q^{38} - 48 q^{40} + 756 q^{41} + 328 q^{43} + 120 q^{44} - 228 q^{46} - 228 q^{47} + 356 q^{50} - 8 q^{52} - 348 q^{53} + 360 q^{55} - 144 q^{58} - 348 q^{59} + 106 q^{61} + 784 q^{62} + 128 q^{64} + 12 q^{65} - 596 q^{67} + 264 q^{68} - 1260 q^{71} + 1042 q^{73} - 572 q^{74} - 416 q^{76} + 88 q^{79} + 96 q^{80} + 756 q^{82} + 2880 q^{83} + 792 q^{85} + 328 q^{86} - 240 q^{88} + 1374 q^{89} - 912 q^{92} + 456 q^{94} - 312 q^{95} - 68 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 + 6 * q^5 - 16 * q^8 - 12 * q^10 + 30 * q^11 + 4 * q^13 - 16 * q^16 + 66 * q^17 + 52 * q^19 - 48 * q^20 + 120 * q^22 + 114 * q^23 + 89 * q^25 + 4 * q^26 - 144 * q^29 + 196 * q^31 + 32 * q^32 + 264 * q^34 + 286 * q^37 - 104 * q^38 - 48 * q^40 + 756 * q^41 + 328 * q^43 + 120 * q^44 - 228 * q^46 - 228 * q^47 + 356 * q^50 - 8 * q^52 - 348 * q^53 + 360 * q^55 - 144 * q^58 - 348 * q^59 + 106 * q^61 + 784 * q^62 + 128 * q^64 + 12 * q^65 - 596 * q^67 + 264 * q^68 - 1260 * q^71 + 1042 * q^73 - 572 * q^74 - 416 * q^76 + 88 * q^79 + 96 * q^80 + 756 * q^82 + 2880 * q^83 + 792 * q^85 + 328 * q^86 - 240 * q^88 + 1374 * q^89 - 912 * q^92 + 456 * q^94 - 312 * q^95 - 68 * q^97

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