LMFDB - Embedded newform 882.2.g.k.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,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, 2, names="a")

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.2.g.k.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{8} +(-0.707107 + 1.22474i) q^{10} +(-2.00000 + 3.46410i) q^{11} +4.24264 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.53553 - 6.12372i) q^{17} +(2.82843 + 4.89898i) q^{19} +1.41421 q^{20} +4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(1.50000 - 2.59808i) q^{25} +(-2.12132 - 3.67423i) q^{26} +2.00000 q^{29} +(-0.500000 + 0.866025i) q^{32} -7.07107 q^{34} +(-2.00000 - 3.46410i) q^{37} +(2.82843 - 4.89898i) q^{38} +(-0.707107 - 1.22474i) q^{40} +9.89949 q^{41} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-4.00000 + 6.92820i) q^{46} +(-2.82843 - 4.89898i) q^{47} -3.00000 q^{50} +(-2.12132 + 3.67423i) q^{52} +(-2.00000 + 3.46410i) q^{53} +5.65685 q^{55} +(-1.00000 - 1.73205i) q^{58} +(5.65685 - 9.79796i) q^{59} +(-0.707107 - 1.22474i) q^{61} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(6.00000 - 10.3923i) q^{67} +(3.53553 + 6.12372i) q^{68} +(7.77817 - 13.4722i) q^{73} +(-2.00000 + 3.46410i) q^{74} -5.65685 q^{76} +(8.00000 + 13.8564i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-4.94975 - 8.57321i) q^{82} -5.65685 q^{83} -10.0000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.53553 - 6.12372i) q^{89} +8.00000 q^{92} +(-2.82843 + 4.89898i) q^{94} +(4.00000 - 6.92820i) q^{95} +7.07107 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 8 q^{11} - 2 q^{16} + 16 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{29} - 2 q^{32} - 8 q^{37} - 16 q^{43} - 8 q^{44} - 16 q^{46} - 12 q^{50} - 8 q^{53} - 4 q^{58} + 4 q^{64} - 12 q^{65} + 24 q^{67} - 8 q^{74} + 32 q^{79} - 40 q^{85} + 8 q^{86} - 8 q^{88} + 32 q^{92} + 16 q^{95}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 8 * q^11 - 2 * q^16 + 16 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^29 - 2 * q^32 - 8 * q^37 - 16 * q^43 - 8 * q^44 - 16 * q^46 - 12 * q^50 - 8 * q^53 - 4 * q^58 + 4 * q^64 - 12 * q^65 + 24 * q^67 - 8 * q^74 + 32 * q^79 - 40 * q^85 + 8 * q^86 - 8 * q^88 + 32 * q^92 + 16 * q^95

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	0.663470	−	0.748203i	$-0.269083\pi$
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	−0.979698	+	0.200480i	$0.935750\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	4.24264			1.17670			0.588348	−	0.808608i	$-0.299778\pi$
$13$	4.24264			1.17670			0.588348	+	0.808608i	$0.299778\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.53553	−	6.12372i	0.857493	−	1.48522i	−0.0168199	−	0.999859i	$-0.505354\pi$
$17$	3.53553	−	6.12372i	0.857493	−	1.48522i	0.874313	−	0.485363i	$-0.161312\pi$
$18$		0			0
$19$	2.82843	+	4.89898i	0.648886	+	1.12390i	0.983389	+	0.181509i	$0.0580980\pi$
$19$	2.82843	+	4.89898i	0.648886	+	1.12390i	−0.334504	+	0.942394i	$0.608569\pi$
$20$	1.41421			0.316228
$21$		0			0
$22$	4.00000			0.852803
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$		0			0
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$	−2.12132	−	3.67423i	−0.416025	−	0.720577i
$27$		0			0
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−7.07107			−1.21268
$35$		0			0
$36$		0			0
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	2.82843	−	4.89898i	0.458831	−	0.794719i
$39$		0			0
$40$	−0.707107	−	1.22474i	−0.111803	−	0.193649i
$41$	9.89949			1.54604			0.773021	−	0.634381i	$-0.218745\pi$
$41$	9.89949			1.54604			0.773021	+	0.634381i	$0.218745\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$		0			0
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	−2.82843	−	4.89898i	−0.412568	−	0.714590i	0.582601	−	0.812758i	$-0.302035\pi$
$47$	−2.82843	−	4.89898i	−0.412568	−	0.714590i	−0.995170	+	0.0981685i	$0.968702\pi$
$48$		0			0
$49$		0			0
$50$	−3.00000			−0.424264
$51$		0			0
$52$	−2.12132	+	3.67423i	−0.294174	+	0.509525i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	5.65685			0.762770
$56$		0			0
$57$		0			0
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	5.65685	−	9.79796i	0.736460	−	1.27559i	−0.217620	−	0.976034i	$-0.569829\pi$
$59$	5.65685	−	9.79796i	0.736460	−	1.27559i	0.954080	−	0.299552i	$-0.0968372\pi$
$60$		0			0
$61$	−0.707107	−	1.22474i	−0.0905357	−	0.156813i	0.817201	−	0.576353i	$-0.195525\pi$
$61$	−0.707107	−	1.22474i	−0.0905357	−	0.156813i	−0.907737	+	0.419540i	$0.862191\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	3.53553	+	6.12372i	0.428746	+	0.742611i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	7.77817	−	13.4722i	0.910366	−	1.57680i	0.0968194	−	0.995302i	$-0.469133\pi$
$73$	7.77817	−	13.4722i	0.910366	−	1.57680i	0.813547	−	0.581499i	$-0.197534\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−5.65685			−0.648886
$77$		0			0
$78$		0			0
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.827401	+	0.561611i	$0.189818\pi$
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.0726692	+	0.997356i	$0.476848\pi$
$80$	−0.707107	+	1.22474i	−0.0790569	+	0.136931i
$81$		0			0
$82$	−4.94975	−	8.57321i	−0.546608	−	0.946753i
$83$	−5.65685			−0.620920			−0.310460	−	0.950586i	$-0.600483\pi$
$83$	−5.65685			−0.620920			−0.310460	+	0.950586i	$0.600483\pi$
$84$		0			0
$85$	−10.0000			−1.08465
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	0.615526	−	0.788116i	$-0.288944\pi$
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	−0.990292	+	0.139003i	$0.955610\pi$
$90$		0			0
$91$		0			0
$92$	8.00000			0.834058
$93$		0			0
$94$	−2.82843	+	4.89898i	−0.291730	+	0.505291i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	7.07107			0.717958			0.358979	−	0.933346i	$-0.383125\pi$
$97$	7.07107			0.717958			0.358979	+	0.933346i	$0.383125\pi$
$98$		0			0
$99$		0			0
$100$	1.50000	+	2.59808i	0.150000	+	0.259808i
$101$	−6.36396	+	11.0227i	−0.633238	+	1.09680i	0.353648	+	0.935379i	$0.384941\pi$
$101$	−6.36396	+	11.0227i	−0.633238	+	1.09680i	−0.986886	+	0.161421i	$0.948392\pi$
$102$		0			0
$103$	−2.82843	−	4.89898i	−0.278693	−	0.482711i	0.692367	−	0.721545i	$-0.256568\pi$
$103$	−2.82843	−	4.89898i	−0.278693	−	0.482711i	−0.971060	+	0.238835i	$0.923235\pi$
$104$	4.24264			0.416025
$105$		0			0
$106$	4.00000			0.388514
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$	−2.82843	−	4.89898i	−0.269680	−	0.467099i
$111$		0			0
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−5.65685	+	9.79796i	−0.527504	+	0.913664i
$116$	−1.00000	+	1.73205i	−0.0928477	+	0.160817i
$117$		0			0
$118$	−11.3137			−1.04151
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−0.707107	+	1.22474i	−0.0640184	+	0.110883i
$123$		0			0
$124$		0			0
$125$	−11.3137			−1.01193
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	8.48528	+	14.6969i	0.741362	+	1.28408i	0.951875	+	0.306486i	$0.0991534\pi$
$131$	8.48528	+	14.6969i	0.741362	+	1.28408i	−0.210513	+	0.977591i	$0.567513\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		0			0
$136$	3.53553	−	6.12372i	0.303170	−	0.525105i
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−5.65685			−0.479808			−0.239904	−	0.970797i	$-0.577116\pi$
$139$	−5.65685			−0.479808			−0.239904	+	0.970797i	$0.577116\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.48528	+	14.6969i	−0.709575	+	1.22902i
$144$		0			0
$145$	−1.41421	−	2.44949i	−0.117444	−	0.203419i
$146$	−15.5563			−1.28745
$147$		0			0
$148$	4.00000			0.328798
$149$	10.0000	+	17.3205i	0.819232	+	1.41895i	0.906249	+	0.422744i	$0.138933\pi$
$149$	10.0000	+	17.3205i	0.819232	+	1.41895i	−0.0870170	+	0.996207i	$0.527733\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	2.82843	+	4.89898i	0.229416	+	0.397360i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.19239	−	15.9217i	0.733632	−	1.27069i	−0.221688	−	0.975118i	$-0.571157\pi$
$157$	9.19239	−	15.9217i	0.733632	−	1.27069i	0.955321	−	0.295571i	$-0.0955099\pi$
$158$	8.00000	−	13.8564i	0.636446	−	1.10236i
$159$		0			0
$160$	1.41421			0.111803
$161$		0			0
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−4.94975	+	8.57321i	−0.386510	+	0.669456i
$165$		0			0
$166$	2.82843	+	4.89898i	0.219529	+	0.380235i
$167$	11.3137			0.875481			0.437741	−	0.899101i	$-0.355779\pi$
$167$	11.3137			0.875481			0.437741	+	0.899101i	$0.355779\pi$
$168$		0			0
$169$	5.00000			0.384615
$170$	5.00000	+	8.66025i	0.383482	+	0.664211i
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	6.36396	+	11.0227i	0.483843	+	0.838041i	0.999828	−	0.0185571i	$-0.00590724\pi$
$173$	6.36396	+	11.0227i	0.483843	+	0.838041i	−0.515985	+	0.856598i	$0.672574\pi$
$174$		0			0
$175$		0			0
$176$	4.00000			0.301511
$177$		0			0
$178$	−3.53553	+	6.12372i	−0.264999	+	0.458993i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	12.7279			0.946059			0.473029	−	0.881047i	$-0.343160\pi$
$181$	12.7279			0.946059			0.473029	+	0.881047i	$0.343160\pi$
$182$		0			0
$183$		0			0
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	−2.82843	+	4.89898i	−0.207950	+	0.360180i
$186$		0			0
$187$	14.1421	+	24.4949i	1.03418	+	1.79124i
$188$	5.65685			0.412568
$189$		0			0
$190$	−8.00000			−0.580381
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−3.53553	−	6.12372i	−0.253837	−	0.439658i
$195$		0			0
$196$		0			0
$197$	−4.00000			−0.284988			−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000			−0.284988			−0.142494	+	0.989796i	$0.545512\pi$
$198$		0			0
$199$	−8.48528	+	14.6969i	−0.601506	+	1.04184i	0.391088	+	0.920353i	$0.372099\pi$
$199$	−8.48528	+	14.6969i	−0.601506	+	1.04184i	−0.992593	+	0.121485i	$0.961234\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$		0			0
$202$	12.7279			0.895533
$203$		0			0
$204$		0			0
$205$	−7.00000	−	12.1244i	−0.488901	−	0.846802i
$206$	−2.82843	+	4.89898i	−0.197066	+	0.341328i
$207$		0			0
$208$	−2.12132	−	3.67423i	−0.147087	−	0.254762i
$209$	−22.6274			−1.56517
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	2.82843	+	4.89898i	0.192897	+	0.334108i
$216$		0			0
$217$		0			0
$218$	4.00000			0.270914
$219$		0			0
$220$	−2.82843	+	4.89898i	−0.190693	+	0.330289i
$221$	15.0000	−	25.9808i	1.00901	−	1.74766i
$222$		0			0
$223$	−16.9706			−1.13643			−0.568216	−	0.822879i	$-0.692366\pi$
$223$	−16.9706			−1.13643			−0.568216	+	0.822879i	$0.692366\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.48528	+	14.6969i	−0.563188	+	0.975470i	0.434028	+	0.900899i	$0.357092\pi$
$227$	−8.48528	+	14.6969i	−0.563188	+	0.975470i	−0.997216	+	0.0745706i	$0.976241\pi$
$228$		0			0
$229$	−6.36396	−	11.0227i	−0.420542	−	0.728401i	0.575450	−	0.817837i	$-0.304827\pi$
$229$	−6.36396	−	11.0227i	−0.420542	−	0.728401i	−0.995993	+	0.0894361i	$0.971494\pi$
$230$	11.3137			0.746004
$231$		0			0
$232$	2.00000			0.131306
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	5.65685	+	9.79796i	0.368230	+	0.637793i
$237$		0			0
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−2.12132	+	3.67423i	−0.136646	+	0.236678i	−0.926225	−	0.376971i	$-0.876966\pi$
$241$	−2.12132	+	3.67423i	−0.136646	+	0.236678i	0.789579	+	0.613649i	$0.210299\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$		0			0
$244$	1.41421			0.0905357
$245$		0			0
$246$		0			0
$247$	12.0000	+	20.7846i	0.763542	+	1.32249i
$248$		0			0
$249$		0			0
$250$	5.65685	+	9.79796i	0.357771	+	0.619677i
$251$	−5.65685			−0.357057			−0.178529	−	0.983935i	$-0.557134\pi$
$251$	−5.65685			−0.357057			−0.178529	+	0.983935i	$0.557134\pi$
$252$		0			0
$253$	32.0000			2.01182
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.36396	+	11.0227i	0.396973	+	0.687577i	0.993351	−	0.115126i	$-0.0367273\pi$
$257$	6.36396	+	11.0227i	0.396973	+	0.687577i	−0.596378	+	0.802704i	$0.703394\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$		0			0
$262$	8.48528	−	14.6969i	0.524222	−	0.907980i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$	5.65685			0.347498
$266$		0			0
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	0.707107	−	1.22474i	0.0431131	−	0.0746740i	−0.843664	−	0.536872i	$-0.819606\pi$
$269$	0.707107	−	1.22474i	0.0431131	−	0.0746740i	0.886777	+	0.462198i	$0.152939\pi$
$270$		0			0
$271$	2.82843	+	4.89898i	0.171815	+	0.297592i	0.939054	−	0.343769i	$-0.111704\pi$
$271$	2.82843	+	4.89898i	0.171815	+	0.297592i	−0.767240	+	0.641361i	$0.778370\pi$
$272$	−7.07107			−0.428746
$273$		0			0
$274$	6.00000			0.362473
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	−0.976231	−	0.216731i	$-0.930460\pi$
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	0.675810	+	0.737075i	$0.263794\pi$
$278$	2.82843	+	4.89898i	0.169638	+	0.293821i
$279$		0			0
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−11.3137	+	19.5959i	−0.672530	+	1.16486i	0.304654	+	0.952463i	$0.401459\pi$
$283$	−11.3137	+	19.5959i	−0.672530	+	1.16486i	−0.977184	+	0.212393i	$0.931874\pi$
$284$		0			0
$285$		0			0
$286$	16.9706			1.00349
$287$		0			0
$288$		0			0
$289$	−16.5000	−	28.5788i	−0.970588	−	1.68111i
$290$	−1.41421	+	2.44949i	−0.0830455	+	0.143839i
$291$		0			0
$292$	7.77817	+	13.4722i	0.455183	+	0.788400i
$293$	24.0416			1.40453			0.702264	−	0.711917i	$-0.252173\pi$
$293$	24.0416			1.40453			0.702264	+	0.711917i	$0.252173\pi$
$294$		0			0
$295$	−16.0000			−0.931556
$296$	−2.00000	−	3.46410i	−0.116248	−	0.201347i
$297$		0			0
$298$	10.0000	−	17.3205i	0.579284	−	1.00335i
$299$	−16.9706	−	29.3939i	−0.981433	−	1.69989i
$300$		0			0
$301$		0			0
$302$	−16.0000			−0.920697
$303$		0			0
$304$	2.82843	−	4.89898i	0.162221	−	0.280976i
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$		0			0
$307$	5.65685			0.322854			0.161427	−	0.986885i	$-0.448390\pi$
$307$	5.65685			0.322854			0.161427	+	0.986885i	$0.448390\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.82843	−	4.89898i	0.160385	−	0.277796i	−0.774622	−	0.632425i	$-0.782060\pi$
$311$	2.82843	−	4.89898i	0.160385	−	0.277796i	0.935007	+	0.354629i	$0.115393\pi$
$312$		0			0
$313$	−10.6066	−	18.3712i	−0.599521	−	1.03840i	−0.992892	−	0.119020i	$-0.962025\pi$
$313$	−10.6066	−	18.3712i	−0.599521	−	1.03840i	0.393371	−	0.919380i	$-0.371309\pi$
$314$	−18.3848			−1.03751
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−14.0000	−	24.2487i	−0.786318	−	1.36194i	−0.928208	−	0.372061i	$-0.878651\pi$
$317$	−14.0000	−	24.2487i	−0.786318	−	1.36194i	0.141890	−	0.989882i	$-0.454682\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	−0.707107	−	1.22474i	−0.0395285	−	0.0684653i
$321$		0			0
$322$		0			0
$323$	40.0000			2.22566
$324$		0			0
$325$	6.36396	−	11.0227i	0.353009	−	0.611430i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	9.89949			0.546608
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$	2.82843	−	4.89898i	0.155230	−	0.268866i
$333$		0			0
$334$	−5.65685	−	9.79796i	−0.309529	−	0.536120i
$335$	−16.9706			−0.927201
$336$		0			0
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$	−2.50000	−	4.33013i	−0.135982	−	0.235528i
$339$		0			0
$340$	5.00000	−	8.66025i	0.271163	−	0.469668i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−4.00000			−0.215666
$345$		0			0
$346$	6.36396	−	11.0227i	0.342129	−	0.592584i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−29.6985			−1.58972			−0.794862	−	0.606791i	$-0.792457\pi$
$349$	−29.6985			−1.58972			−0.794862	+	0.606791i	$0.792457\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000	−	3.46410i	−0.106600	−	0.184637i
$353$	−0.707107	+	1.22474i	−0.0376355	+	0.0651866i	−0.884230	−	0.467052i	$-0.845316\pi$
$353$	−0.707107	+	1.22474i	−0.0376355	+	0.0651866i	0.846594	+	0.532239i	$0.178649\pi$
$354$		0			0
$355$		0			0
$356$	7.07107			0.374766
$357$		0			0
$358$	−12.0000			−0.634220
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	0.573933	−	0.818902i	$-0.305417\pi$
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	−0.996157	+	0.0875892i	$0.972084\pi$
$360$		0			0
$361$	−6.50000	+	11.2583i	−0.342105	+	0.592544i
$362$	−6.36396	−	11.0227i	−0.334482	−	0.579340i
$363$		0			0
$364$		0			0
$365$	−22.0000			−1.15153
$366$		0			0
$367$	−2.82843	+	4.89898i	−0.147643	+	0.255725i	−0.930356	−	0.366658i	$-0.880502\pi$
$367$	−2.82843	+	4.89898i	−0.147643	+	0.255725i	0.782713	+	0.622383i	$0.213835\pi$
$368$	−4.00000	+	6.92820i	−0.208514	+	0.361158i
$369$		0			0
$370$	5.65685			0.294086
$371$		0			0
$372$		0			0
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	14.1421	−	24.4949i	0.731272	−	1.26660i
$375$		0			0
$376$	−2.82843	−	4.89898i	−0.145865	−	0.252646i
$377$	8.48528			0.437014
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$		0			0
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	2.82843	+	4.89898i	0.144526	+	0.250326i	0.929196	−	0.369587i	$-0.120501\pi$
$383$	2.82843	+	4.89898i	0.144526	+	0.250326i	−0.784670	+	0.619914i	$0.787168\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$		0			0
$388$	−3.53553	+	6.12372i	−0.179490	+	0.310885i
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$	−56.5685			−2.86079
$392$		0			0
$393$		0			0
$394$	2.00000	+	3.46410i	0.100759	+	0.174519i
$395$	11.3137	−	19.5959i	0.569254	−	0.985978i
$396$		0			0
$397$	−3.53553	−	6.12372i	−0.177443	−	0.307341i	0.763561	−	0.645736i	$-0.223449\pi$
$397$	−3.53553	−	6.12372i	−0.177443	−	0.307341i	−0.941004	+	0.338395i	$0.890116\pi$
$398$	16.9706			0.850657
$399$		0			0
$400$	−3.00000			−0.150000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$		0			0
$404$	−6.36396	−	11.0227i	−0.316619	−	0.548400i
$405$		0			0
$406$		0			0
$407$	16.0000			0.793091
$408$		0			0
$409$	10.6066	−	18.3712i	0.524463	−	0.908396i	−0.475132	−	0.879915i	$-0.657600\pi$
$409$	10.6066	−	18.3712i	0.524463	−	0.908396i	0.999594	−	0.0284813i	$-0.00906711\pi$
$410$	−7.00000	+	12.1244i	−0.345705	+	0.598779i
$411$		0			0
$412$	5.65685			0.278693
$413$		0			0
$414$		0			0
$415$	4.00000	+	6.92820i	0.196352	+	0.340092i
$416$	−2.12132	+	3.67423i	−0.104006	+	0.180144i
$417$		0			0
$418$	11.3137	+	19.5959i	0.553372	+	0.958468i
$419$	22.6274			1.10542			0.552711	−	0.833373i	$-0.313593\pi$
$419$	22.6274			1.10542			0.552711	+	0.833373i	$0.313593\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	−6.00000	−	10.3923i	−0.292075	−	0.505889i
$423$		0			0
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	−10.6066	−	18.3712i	−0.514496	−	0.891133i
$426$		0			0
$427$		0			0
$428$	−4.00000			−0.193347
$429$		0			0
$430$	2.82843	−	4.89898i	0.136399	−	0.236250i
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	−4.24264			−0.203888			−0.101944	−	0.994790i	$-0.532506\pi$
$433$	−4.24264			−0.203888			−0.101944	+	0.994790i	$0.532506\pi$
$434$		0			0
$435$		0			0
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	22.6274	−	39.1918i	1.08242	−	1.87480i
$438$		0			0
$439$	−16.9706	−	29.3939i	−0.809961	−	1.40289i	−0.912890	−	0.408205i	$-0.866155\pi$
$439$	−16.9706	−	29.3939i	−0.809961	−	1.40289i	0.102930	−	0.994689i	$-0.467178\pi$
$440$	5.65685			0.269680
$441$		0			0
$442$	−30.0000			−1.42695
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	8.48528	+	14.6969i	0.401790	+	0.695920i
$447$		0			0
$448$		0			0
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$		0			0
$451$	−19.7990	+	34.2929i	−0.932298	+	1.61479i
$452$		0			0
$453$		0			0
$454$	16.9706			0.796468
$455$		0			0
$456$		0			0
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	0.927622	−	0.373519i	$-0.121849\pi$
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	−0.787288	+	0.616585i	$0.788516\pi$
$458$	−6.36396	+	11.0227i	−0.297368	+	0.515057i
$459$		0			0
$460$	−5.65685	−	9.79796i	−0.263752	−	0.456832i
$461$	−1.41421			−0.0658665			−0.0329332	−	0.999458i	$-0.510485\pi$
$461$	−1.41421			−0.0658665			−0.0329332	+	0.999458i	$0.510485\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−2.82843	−	4.89898i	−0.130884	−	0.226698i	0.793134	−	0.609048i	$-0.208448\pi$
$467$	−2.82843	−	4.89898i	−0.130884	−	0.226698i	−0.924018	+	0.382350i	$0.875115\pi$
$468$		0			0
$469$		0			0
$470$	8.00000			0.369012
$471$		0			0
$472$	5.65685	−	9.79796i	0.260378	−	0.450988i
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$		0			0
$475$	16.9706			0.778663
$476$		0			0
$477$		0			0
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	14.1421	−	24.4949i	0.646171	−	1.11920i	−0.337859	−	0.941197i	$-0.609703\pi$
$479$	14.1421	−	24.4949i	0.646171	−	1.11920i	0.984030	−	0.178004i	$-0.0569639\pi$
$480$		0			0
$481$	−8.48528	−	14.6969i	−0.386896	−	0.670123i
$482$	4.24264			0.193247
$483$		0			0
$484$	5.00000			0.227273
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	12.0000	−	20.7846i	0.543772	−	0.941841i	−0.454911	−	0.890537i	$-0.650329\pi$
$487$	12.0000	−	20.7846i	0.543772	−	0.941841i	0.998683	−	0.0513038i	$-0.0163377\pi$
$488$	−0.707107	−	1.22474i	−0.0320092	−	0.0554416i
$489$		0			0
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	7.07107	−	12.2474i	0.318465	−	0.551597i
$494$	12.0000	−	20.7846i	0.539906	−	0.935144i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	5.65685	−	9.79796i	0.252982	−	0.438178i
$501$		0			0
$502$	2.82843	+	4.89898i	0.126239	+	0.218652i
$503$	28.2843			1.26113			0.630567	−	0.776135i	$-0.282823\pi$
$503$	28.2843			1.26113			0.630567	+	0.776135i	$0.282823\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	−16.0000	−	27.7128i	−0.711287	−	1.23198i
$507$		0			0
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	−16.2635	−	28.1691i	−0.720865	−	1.24857i	−0.960653	−	0.277750i	$-0.910411\pi$
$509$	−16.2635	−	28.1691i	−0.720865	−	1.24857i	0.239788	−	0.970825i	$-0.422922\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.36396	−	11.0227i	0.280702	−	0.486191i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$	22.6274			0.995153
$518$		0			0
$519$		0			0
$520$	−3.00000	−	5.19615i	−0.131559	−	0.227866i
$521$	−0.707107	+	1.22474i	−0.0309789	+	0.0536570i	−0.881099	−	0.472931i	$-0.843196\pi$
$521$	−0.707107	+	1.22474i	−0.0309789	+	0.0536570i	0.850120	+	0.526589i	$0.176529\pi$
$522$		0			0
$523$	16.9706	+	29.3939i	0.742071	+	1.28530i	0.951551	+	0.307492i	$0.0994896\pi$
$523$	16.9706	+	29.3939i	0.742071	+	1.28530i	−0.209480	+	0.977813i	$0.567177\pi$
$524$	−16.9706			−0.741362
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−2.82843	−	4.89898i	−0.122859	−	0.212798i
$531$		0			0
$532$		0			0
$533$	42.0000			1.81922
$534$		0			0
$535$	2.82843	−	4.89898i	0.122284	−	0.211801i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$	−1.41421			−0.0609711
$539$		0			0
$540$		0			0
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	0.886721	−	0.462304i	$-0.152977\pi$
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	−0.843728	+	0.536771i	$0.819644\pi$
$542$	2.82843	−	4.89898i	0.121491	−	0.210429i
$543$		0			0
$544$	3.53553	+	6.12372i	0.151585	+	0.262553i
$545$	5.65685			0.242313
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$		0			0
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	5.65685	+	9.79796i	0.240990	+	0.417407i
$552$		0			0
$553$		0			0
$554$	10.0000			0.424859
$555$		0			0
$556$	2.82843	−	4.89898i	0.119952	−	0.207763i
$557$	−18.0000	+	31.1769i	−0.762684	+	1.32101i	0.178778	+	0.983890i	$0.442786\pi$
$557$	−18.0000	+	31.1769i	−0.762684	+	1.32101i	−0.941462	+	0.337119i	$0.890548\pi$
$558$		0			0
$559$	−16.9706			−0.717778
$560$		0			0
$561$		0			0
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	5.65685	−	9.79796i	0.238408	−	0.412935i	−0.721850	−	0.692050i	$-0.756708\pi$
$563$	5.65685	−	9.79796i	0.238408	−	0.412935i	0.960258	+	0.279115i	$0.0900411\pi$
$564$		0			0
$565$		0			0
$566$	22.6274			0.951101
$567$		0			0
$568$		0			0
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	0.998608	+	0.0527519i	$0.0167993\pi$
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	−0.453619	+	0.891196i	$0.649867\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−8.48528	−	14.6969i	−0.354787	−	0.614510i
$573$		0			0
$574$		0			0
$575$	−24.0000			−1.00087
$576$		0			0
$577$	−6.36396	+	11.0227i	−0.264935	+	0.458881i	−0.967547	−	0.252693i	$-0.918684\pi$
$577$	−6.36396	+	11.0227i	−0.264935	+	0.458881i	0.702611	+	0.711574i	$0.252017\pi$
$578$	−16.5000	+	28.5788i	−0.686310	+	1.18872i
$579$		0			0
$580$	2.82843			0.117444
$581$		0			0
$582$		0			0
$583$	−8.00000	−	13.8564i	−0.331326	−	0.573874i
$584$	7.77817	−	13.4722i	0.321863	−	0.557483i
$585$		0			0
$586$	−12.0208	−	20.8207i	−0.496575	−	0.860094i
$587$	−16.9706			−0.700450			−0.350225	−	0.936666i	$-0.613895\pi$
$587$	−16.9706			−0.700450			−0.350225	+	0.936666i	$0.613895\pi$
$588$		0			0
$589$		0			0
$590$	8.00000	+	13.8564i	0.329355	+	0.570459i
$591$		0			0
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	17.6777	+	30.6186i	0.725935	+	1.25736i	0.958588	+	0.284796i	$0.0919260\pi$
$593$	17.6777	+	30.6186i	0.725935	+	1.25736i	−0.232653	+	0.972560i	$0.574741\pi$
$594$		0			0
$595$		0			0
$596$	−20.0000			−0.819232
$597$		0			0
$598$	−16.9706	+	29.3939i	−0.693978	+	1.20201i
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	−0.655018	−	0.755613i	$-0.727339\pi$
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	0.981889	+	0.189456i	$0.0606724\pi$
$600$		0			0
$601$	4.24264			0.173061			0.0865305	−	0.996249i	$-0.472422\pi$
$601$	4.24264			0.173061			0.0865305	+	0.996249i	$0.472422\pi$
$602$		0			0
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	−3.53553	+	6.12372i	−0.143740	+	0.248965i
$606$		0			0
$607$	−8.48528	−	14.6969i	−0.344407	−	0.596530i	0.640839	−	0.767675i	$-0.278587\pi$
$607$	−8.48528	−	14.6969i	−0.344407	−	0.596530i	−0.985246	+	0.171145i	$0.945253\pi$
$608$	−5.65685			−0.229416
$609$		0			0
$610$	2.00000			0.0809776
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$		0			0
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	−2.82843	−	4.89898i	−0.114146	−	0.197707i
$615$		0			0
$616$		0			0
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$		0			0
$619$	−5.65685	+	9.79796i	−0.227368	+	0.393813i	−0.957027	−	0.289998i	$-0.906345\pi$
$619$	−5.65685	+	9.79796i	−0.227368	+	0.393813i	0.729659	+	0.683811i	$0.239679\pi$
$620$		0			0
$621$		0			0
$622$	−5.65685			−0.226819
$623$		0			0
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−10.6066	+	18.3712i	−0.423925	+	0.734260i
$627$		0			0
$628$	9.19239	+	15.9217i	0.366816	+	0.635344i
$629$	−28.2843			−1.12777
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	8.00000	+	13.8564i	0.318223	+	0.551178i
$633$		0			0
$634$	−14.0000	+	24.2487i	−0.556011	+	0.963039i
$635$	5.65685	+	9.79796i	0.224485	+	0.388820i
$636$		0			0
$637$		0			0
$638$	8.00000			0.316723
$639$		0			0
$640$	−0.707107	+	1.22474i	−0.0279508	+	0.0484123i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		0			0
$643$	11.3137			0.446169			0.223085	−	0.974799i	$-0.428387\pi$
$643$	11.3137			0.446169			0.223085	+	0.974799i	$0.428387\pi$
$644$		0			0
$645$		0			0
$646$	−20.0000	−	34.6410i	−0.786889	−	1.36293i
$647$	−16.9706	+	29.3939i	−0.667182	+	1.15559i	0.311507	+	0.950244i	$0.399166\pi$
$647$	−16.9706	+	29.3939i	−0.667182	+	1.15559i	−0.978689	+	0.205349i	$0.934167\pi$
$648$		0			0
$649$	22.6274	+	39.1918i	0.888204	+	1.53841i
$650$	−12.7279			−0.499230
$651$		0			0
$652$	4.00000			0.156652
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	12.0000	−	20.7846i	0.468879	−	0.812122i
$656$	−4.94975	−	8.57321i	−0.193255	−	0.334728i
$657$		0			0
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−2.12132	+	3.67423i	−0.0825098	+	0.142911i	−0.904327	−	0.426840i	$-0.859627\pi$
$661$	−2.12132	+	3.67423i	−0.0825098	+	0.142911i	0.821818	+	0.569751i	$0.192960\pi$
$662$	10.0000	−	17.3205i	0.388661	−	0.673181i
$663$		0			0
$664$	−5.65685			−0.219529
$665$		0			0
$666$		0			0
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$	−5.65685	+	9.79796i	−0.218870	+	0.379094i
$669$		0			0
$670$	8.48528	+	14.6969i	0.327815	+	0.567792i
$671$	5.65685			0.218380
$672$		0			0
$673$	24.0000			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$674$	8.00000	+	13.8564i	0.308148	+	0.533729i
$675$		0			0
$676$	−2.50000	+	4.33013i	−0.0961538	+	0.166543i
$677$	−2.12132	−	3.67423i	−0.0815290	−	0.141212i	0.822378	−	0.568942i	$-0.192647\pi$
$677$	−2.12132	−	3.67423i	−0.0815290	−	0.141212i	−0.903907	+	0.427729i	$0.859314\pi$
$678$		0			0
$679$		0			0
$680$	−10.0000			−0.383482
$681$		0			0
$682$		0			0
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$	8.48528			0.324206
$686$		0			0
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−8.48528	+	14.6969i	−0.323263	+	0.559909i
$690$		0			0
$691$	25.4558	+	44.0908i	0.968386	+	1.67729i	0.700229	+	0.713918i	$0.253081\pi$
$691$	25.4558	+	44.0908i	0.968386	+	1.67729i	0.268157	+	0.963375i	$0.413585\pi$
$692$	−12.7279			−0.483843
$693$		0			0
$694$	−12.0000			−0.455514
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	35.0000	−	60.6218i	1.32572	−	2.29621i
$698$	14.8492	+	25.7196i	0.562052	+	0.973503i
$699$		0			0
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	11.3137	−	19.5959i	0.426705	−	0.739074i
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	1.41421			0.0532246
$707$		0			0
$708$		0			0
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	−0.999549	−	0.0300298i	$-0.990440\pi$
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	0.473768	−	0.880650i	$-0.342894\pi$
$710$		0			0
$711$		0			0
$712$	−3.53553	−	6.12372i	−0.132500	−	0.229496i
$713$		0			0
$714$		0			0
$715$	24.0000			0.897549
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	−19.7990	−	34.2929i	−0.738378	−	1.27891i	−0.953225	−	0.302260i	$-0.902259\pi$
$719$	−19.7990	−	34.2929i	−0.738378	−	1.27891i	0.214848	−	0.976648i	$-0.431074\pi$
$720$		0			0
$721$		0			0
$722$	13.0000			0.483810
$723$		0			0
$724$	−6.36396	+	11.0227i	−0.236515	+	0.409656i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	28.2843			1.04901			0.524503	−	0.851409i	$-0.324251\pi$
$727$	28.2843			1.04901			0.524503	+	0.851409i	$0.324251\pi$
$728$		0			0
$729$		0			0
$730$	11.0000	+	19.0526i	0.407128	+	0.705167i
$731$	−14.1421	+	24.4949i	−0.523066	+	0.905977i
$732$		0			0
$733$	−6.36396	−	11.0227i	−0.235058	−	0.407133i	0.724231	−	0.689557i	$-0.242195\pi$
$733$	−6.36396	−	11.0227i	−0.235058	−	0.407133i	−0.959290	+	0.282424i	$0.908861\pi$
$734$	5.65685			0.208798
$735$		0			0
$736$	8.00000			0.294884
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$		0			0
$739$	−6.00000	+	10.3923i	−0.220714	+	0.382287i	−0.955025	−	0.296526i	$-0.904172\pi$
$739$	−6.00000	+	10.3923i	−0.220714	+	0.382287i	0.734311	+	0.678813i	$0.237505\pi$
$740$	−2.82843	−	4.89898i	−0.103975	−	0.180090i
$741$		0			0
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$		0			0
$745$	14.1421	−	24.4949i	0.518128	−	0.897424i
$746$	−5.00000	+	8.66025i	−0.183063	+	0.317074i
$747$		0			0
$748$	−28.2843			−1.03418
$749$		0			0
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−2.82843	+	4.89898i	−0.103142	+	0.178647i
$753$		0			0
$754$	−4.24264	−	7.34847i	−0.154508	−	0.267615i
$755$	−22.6274			−0.823496
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$		0			0
$760$	4.00000	−	6.92820i	0.145095	−	0.251312i
$761$	4.94975	+	8.57321i	0.179428	+	0.310779i	0.941685	−	0.336496i	$-0.109242\pi$
$761$	4.94975	+	8.57321i	0.179428	+	0.310779i	−0.762257	+	0.647275i	$0.775909\pi$
$762$		0			0
$763$		0			0
$764$	−16.0000			−0.578860
$765$		0			0
$766$	2.82843	−	4.89898i	0.102195	−	0.177007i
$767$	24.0000	−	41.5692i	0.866590	−	1.50098i
$768$		0			0
$769$	−4.24264			−0.152994			−0.0764968	−	0.997070i	$-0.524373\pi$
$769$	−4.24264			−0.152994			−0.0764968	+	0.997070i	$0.524373\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−16.2635	+	28.1691i	−0.584956	+	1.01317i	0.409925	+	0.912119i	$0.365555\pi$
$773$	−16.2635	+	28.1691i	−0.584956	+	1.01317i	−0.994881	+	0.101054i	$0.967778\pi$
$774$		0			0
$775$		0			0
$776$	7.07107			0.253837
$777$		0			0
$778$	26.0000			0.932145
$779$	28.0000	+	48.4974i	1.00320	+	1.73760i
$780$		0			0
$781$		0			0
$782$	28.2843	+	48.9898i	1.01144	+	1.75187i
$783$		0			0
$784$		0			0
$785$	−26.0000			−0.927980
$786$		0			0
$787$	−2.82843	+	4.89898i	−0.100823	+	0.174630i	−0.912024	−	0.410137i	$-0.865481\pi$
$787$	−2.82843	+	4.89898i	−0.100823	+	0.174630i	0.811201	+	0.584767i	$0.198814\pi$
$788$	2.00000	−	3.46410i	0.0712470	−	0.123404i
$789$		0			0
$790$	−22.6274			−0.805047
$791$		0			0
$792$		0			0
$793$	−3.00000	−	5.19615i	−0.106533	−	0.184521i
$794$	−3.53553	+	6.12372i	−0.125471	+	0.217323i
$795$		0			0
$796$	−8.48528	−	14.6969i	−0.300753	−	0.520919i
$797$	12.7279			0.450846			0.225423	−	0.974261i	$-0.427624\pi$
$797$	12.7279			0.450846			0.225423	+	0.974261i	$0.427624\pi$
$798$		0			0
$799$	−40.0000			−1.41510
$800$	1.50000	+	2.59808i	0.0530330	+	0.0918559i
$801$		0			0
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	31.1127	+	53.8888i	1.09794	+	1.90169i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−6.36396	+	11.0227i	−0.223883	+	0.387777i
$809$	20.0000	−	34.6410i	0.703163	−	1.21791i	−0.264188	−	0.964471i	$-0.585104\pi$
$809$	20.0000	−	34.6410i	0.703163	−	1.21791i	0.967351	−	0.253442i	$-0.0815627\pi$
$810$		0			0
$811$	33.9411			1.19183			0.595917	−	0.803046i	$-0.296789\pi$
$811$	33.9411			1.19183			0.595917	+	0.803046i	$0.296789\pi$
$812$		0			0
$813$		0			0
$814$	−8.00000	−	13.8564i	−0.280400	−	0.485667i
$815$	−2.82843	+	4.89898i	−0.0990755	+	0.171604i
$816$		0			0
$817$	−11.3137	−	19.5959i	−0.395817	−	0.685574i
$818$	−21.2132			−0.741702
$819$		0			0
$820$	14.0000			0.488901
$821$	18.0000	+	31.1769i	0.628204	+	1.08808i	0.987912	+	0.155017i	$0.0495431\pi$
$821$	18.0000	+	31.1769i	0.628204	+	1.08808i	−0.359708	+	0.933065i	$0.617124\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−2.82843	−	4.89898i	−0.0985329	−	0.170664i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−21.9203	+	37.9671i	−0.761324	+	1.31865i	0.180845	+	0.983512i	$0.442117\pi$
$829$	−21.9203	+	37.9671i	−0.761324	+	1.31865i	−0.942168	+	0.335140i	$0.891216\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$		0			0
$832$	4.24264			0.147087
$833$		0			0
$834$		0			0
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$	11.3137	−	19.5959i	0.391293	−	0.677739i
$837$		0			0
$838$	−11.3137	−	19.5959i	−0.390826	−	0.676930i
$839$	−45.2548			−1.56237			−0.781185	−	0.624299i	$-0.785385\pi$
$839$	−45.2548			−1.56237			−0.781185	+	0.624299i	$0.785385\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	3.00000	+	5.19615i	0.103387	+	0.179071i
$843$		0			0
$844$	−6.00000	+	10.3923i	−0.206529	+	0.357718i
$845$	−3.53553	−	6.12372i	−0.121626	−	0.210663i
$846$		0			0
$847$		0			0
$848$	4.00000			0.137361
$849$		0			0
$850$	−10.6066	+	18.3712i	−0.363803	+	0.630126i
$851$	−16.0000	+	27.7128i	−0.548473	+	0.949983i
$852$		0			0
$853$	21.2132			0.726326			0.363163	−	0.931726i	$-0.381697\pi$
$853$	21.2132			0.726326			0.363163	+	0.931726i	$0.381697\pi$
$854$		0			0
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	−12.0208	+	20.8207i	−0.410623	+	0.711220i	−0.994958	−	0.100292i	$-0.968022\pi$
$857$	−12.0208	+	20.8207i	−0.410623	+	0.711220i	0.584335	+	0.811513i	$0.301356\pi$
$858$		0			0
$859$	−2.82843	−	4.89898i	−0.0965047	−	0.167151i	0.813731	−	0.581242i	$-0.197433\pi$
$859$	−2.82843	−	4.89898i	−0.0965047	−	0.167151i	−0.910236	+	0.414091i	$0.864100\pi$
$860$	−5.65685			−0.192897
$861$		0			0
$862$	24.0000			0.817443
$863$	−4.00000	−	6.92820i	−0.136162	−	0.235839i	0.789879	−	0.613263i	$-0.210143\pi$
$863$	−4.00000	−	6.92820i	−0.136162	−	0.235839i	−0.926041	+	0.377424i	$0.876810\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	2.12132	+	3.67423i	0.0720854	+	0.124856i
$867$		0			0
$868$		0			0
$869$	−64.0000			−2.17105
$870$		0			0
$871$	25.4558	−	44.0908i	0.862538	−	1.49396i
$872$	−2.00000	+	3.46410i	−0.0677285	+	0.117309i
$873$		0			0
$874$	−45.2548			−1.53077
$875$		0			0
$876$		0			0
$877$	14.0000	+	24.2487i	0.472746	+	0.818821i	0.999514	−	0.0311889i	$-0.00992933\pi$
$877$	14.0000	+	24.2487i	0.472746	+	0.818821i	−0.526767	+	0.850010i	$0.676596\pi$
$878$	−16.9706	+	29.3939i	−0.572729	+	0.991995i
$879$		0			0
$880$	−2.82843	−	4.89898i	−0.0953463	−	0.165145i
$881$	21.2132			0.714691			0.357345	−	0.933972i	$-0.383682\pi$
$881$	21.2132			0.714691			0.357345	+	0.933972i	$0.383682\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	15.0000	+	25.9808i	0.504505	+	0.873828i
$885$		0			0
$886$	−10.0000	+	17.3205i	−0.335957	+	0.581894i
$887$	11.3137	+	19.5959i	0.379877	+	0.657967i	0.991044	−	0.133535i	$-0.0426329\pi$
$887$	11.3137	+	19.5959i	0.379877	+	0.657967i	−0.611167	+	0.791502i	$0.709300\pi$
$888$		0			0
$889$		0			0
$890$	10.0000			0.335201
$891$		0			0
$892$	8.48528	−	14.6969i	0.284108	−	0.492090i
$893$	16.0000	−	27.7128i	0.535420	−	0.927374i
$894$		0			0
$895$	−16.9706			−0.567263
$896$		0			0
$897$		0			0
$898$	12.0000	+	20.7846i	0.400445	+	0.693591i
$899$		0			0
$900$		0			0
$901$	14.1421	+	24.4949i	0.471143	+	0.816043i
$902$	39.5980			1.31847
$903$		0			0
$904$		0			0
$905$	−9.00000	−	15.5885i	−0.299170	−	0.518178i
$906$		0			0
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	−0.650868	−	0.759191i	$-0.725595\pi$
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	0.982913	+	0.184073i	$0.0589282\pi$
$908$	−8.48528	−	14.6969i	−0.281594	−	0.487735i
$909$		0			0
$910$		0			0
$911$	56.0000			1.85536			0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000			1.85536			0.927681	+	0.373373i	$0.121799\pi$
$912$		0			0
$913$	11.3137	−	19.5959i	0.374429	−	0.648530i
$914$	3.00000	−	5.19615i	0.0992312	−	0.171873i
$915$		0			0
$916$	12.7279			0.420542
$917$		0			0
$918$		0			0
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.793742	+	0.608254i	$0.208130\pi$
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.129893	+	0.991528i	$0.458537\pi$
$920$	−5.65685	+	9.79796i	−0.186501	+	0.323029i
$921$		0			0
$922$	0.707107	+	1.22474i	0.0232873	+	0.0403348i
$923$		0			0
$924$		0			0
$925$	−12.0000			−0.394558
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$		0			0
$928$	−1.00000	+	1.73205i	−0.0328266	+	0.0568574i
$929$	−9.19239	−	15.9217i	−0.301592	−	0.522373i	0.674904	−	0.737905i	$-0.264185\pi$
$929$	−9.19239	−	15.9217i	−0.301592	−	0.522373i	−0.976497	+	0.215532i	$0.930852\pi$
$930$		0			0
$931$		0			0
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−2.82843	+	4.89898i	−0.0925490	+	0.160300i
$935$	20.0000	−	34.6410i	0.654070	−	1.13288i
$936$		0			0
$937$	15.5563			0.508204			0.254102	−	0.967177i	$-0.418220\pi$
$937$	15.5563			0.508204			0.254102	+	0.967177i	$0.418220\pi$
$938$		0			0
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	−13.4350	+	23.2702i	−0.437969	+	0.758585i	−0.997533	−	0.0702023i	$-0.977636\pi$
$941$	−13.4350	+	23.2702i	−0.437969	+	0.758585i	0.559563	+	0.828788i	$0.310969\pi$
$942$		0			0
$943$	−39.5980	−	68.5857i	−1.28949	−	2.23346i
$944$	−11.3137			−0.368230
$945$		0			0
$946$	−16.0000			−0.520205
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	33.0000	−	57.1577i	1.07123	−	1.85542i
$950$	−8.48528	−	14.6969i	−0.275299	−	0.476832i
$951$		0			0
$952$		0			0
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		0			0
$955$	11.3137	−	19.5959i	0.366103	−	0.634109i
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$		0			0
$958$	−28.2843			−0.913823
$959$		0			0
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−8.48528	+	14.6969i	−0.273576	+	0.473848i
$963$		0			0
$964$	−2.12132	−	3.67423i	−0.0683231	−	0.118339i
$965$	19.7990			0.637352
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$		0			0
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$	5.65685	+	9.79796i	0.181537	+	0.314431i	0.942404	−	0.334476i	$-0.108559\pi$
$971$	5.65685	+	9.79796i	0.181537	+	0.314431i	−0.760867	+	0.648908i	$0.775226\pi$
$972$		0			0
$973$		0			0
$974$	−24.0000			−0.769010
$975$		0			0
$976$	−0.707107	+	1.22474i	−0.0226339	+	0.0392031i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$		0			0
$979$	28.2843			0.903969
$980$		0			0
$981$		0			0
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	−5.65685	+	9.79796i	−0.180426	+	0.312506i	−0.942026	−	0.335541i	$-0.891081\pi$
$983$	−5.65685	+	9.79796i	−0.180426	+	0.312506i	0.761600	+	0.648047i	$0.224414\pi$
$984$		0			0
$985$	2.82843	+	4.89898i	0.0901212	+	0.156094i
$986$	−14.1421			−0.450377
$987$		0			0
$988$	−24.0000			−0.763542
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	24.0000			0.760851
$996$		0			0
$997$	3.53553	−	6.12372i	0.111971	−	0.193940i	−0.804594	−	0.593826i	$-0.797617\pi$
$997$	3.53553	−	6.12372i	0.111971	−	0.193940i	0.916565	+	0.399886i	$0.130950\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.g.k.361.1		4
3.2	odd	2		882.2.g.m.361.2		4
7.2	even	3	inner	882.2.g.k.667.1		4
7.3	odd	6		882.2.a.o.1.1	yes	2
7.4	even	3		882.2.a.o.1.2	yes	2
7.5	odd	6	inner	882.2.g.k.667.2		4
7.6	odd	2	inner	882.2.g.k.361.2		4
21.2	odd	6		882.2.g.m.667.2		4
21.5	even	6		882.2.g.m.667.1		4
21.11	odd	6		882.2.a.m.1.1	✓	2
21.17	even	6		882.2.a.m.1.2	yes	2
21.20	even	2		882.2.g.m.361.1		4
28.3	even	6		7056.2.a.ci.1.1		2
28.11	odd	6		7056.2.a.ci.1.2		2
84.11	even	6		7056.2.a.cs.1.1		2
84.59	odd	6		7056.2.a.cs.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.a.m.1.1	✓	2	21.11	odd	6
882.2.a.m.1.2	yes	2	21.17	even	6
882.2.a.o.1.1	yes	2	7.3	odd	6
882.2.a.o.1.2	yes	2	7.4	even	3
882.2.g.k.361.1		4	1.1	even	1	trivial
882.2.g.k.361.2		4	7.6	odd	2	inner
882.2.g.k.667.1		4	7.2	even	3	inner
882.2.g.k.667.2		4	7.5	odd	6	inner
882.2.g.m.361.1		4	21.20	even	2
882.2.g.m.361.2		4	3.2	odd	2
882.2.g.m.667.1		4	21.5	even	6
882.2.g.m.667.2		4	21.2	odd	6
7056.2.a.ci.1.1		2	28.3	even	6
7056.2.a.ci.1.2		2	28.11	odd	6
7056.2.a.cs.1.1		2	84.11	even	6
7056.2.a.cs.1.2		2	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{8} +(-0.707107 + 1.22474i) q^{10} +(-2.00000 + 3.46410i) q^{11} +4.24264 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.53553 - 6.12372i) q^{17} +(2.82843 + 4.89898i) q^{19} +1.41421 q^{20} +4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(1.50000 - 2.59808i) q^{25} +(-2.12132 - 3.67423i) q^{26} +2.00000 q^{29} +(-0.500000 + 0.866025i) q^{32} -7.07107 q^{34} +(-2.00000 - 3.46410i) q^{37} +(2.82843 - 4.89898i) q^{38} +(-0.707107 - 1.22474i) q^{40} +9.89949 q^{41} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-4.00000 + 6.92820i) q^{46} +(-2.82843 - 4.89898i) q^{47} -3.00000 q^{50} +(-2.12132 + 3.67423i) q^{52} +(-2.00000 + 3.46410i) q^{53} +5.65685 q^{55} +(-1.00000 - 1.73205i) q^{58} +(5.65685 - 9.79796i) q^{59} +(-0.707107 - 1.22474i) q^{61} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(6.00000 - 10.3923i) q^{67} +(3.53553 + 6.12372i) q^{68} +(7.77817 - 13.4722i) q^{73} +(-2.00000 + 3.46410i) q^{74} -5.65685 q^{76} +(8.00000 + 13.8564i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-4.94975 - 8.57321i) q^{82} -5.65685 q^{83} -10.0000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.53553 - 6.12372i) q^{89} +8.00000 q^{92} +(-2.82843 + 4.89898i) q^{94} +(4.00000 - 6.92820i) q^{95} +7.07107 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 8 q^{11} - 2 q^{16} + 16 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{29} - 2 q^{32} - 8 q^{37} - 16 q^{43} - 8 q^{44} - 16 q^{46} - 12 q^{50} - 8 q^{53} - 4 q^{58} + 4 q^{64} - 12 q^{65} + 24 q^{67} - 8 q^{74} + 32 q^{79} - 40 q^{85} + 8 q^{86} - 8 q^{88} + 32 q^{92} + 16 q^{95}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 8 * q^11 - 2 * q^16 + 16 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^29 - 2 * q^32 - 8 * q^37 - 16 * q^43 - 8 * q^44 - 16 * q^46 - 12 * q^50 - 8 * q^53 - 4 * q^58 + 4 * q^64 - 12 * q^65 + 24 * q^67 - 8 * q^74 + 32 * q^79 - 40 * q^85 + 8 * q^86 - 8 * q^88 + 32 * q^92 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more