LMFDB - Embedded newform 1620.2.e.a.971.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.16
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.a.971.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.821961 + 1.15082i) q^{2} +(-0.648762 - 1.89185i) q^{4} -1.00000i q^{5} +1.74129i q^{7} +(2.71043 + 0.808422i) q^{8} +O(q^{10})$	\(q+(-0.821961 + 1.15082i) q^{2} +(-0.648762 - 1.89185i) q^{4} -1.00000i q^{5} +1.74129i q^{7} +(2.71043 + 0.808422i) q^{8} +(1.15082 + 0.821961i) q^{10} -1.35950 q^{11} -1.15926 q^{13} +(-2.00391 - 1.43127i) q^{14} +(-3.15822 + 2.45472i) q^{16} -5.00950i q^{17} +5.40540i q^{19} +(-1.89185 + 0.648762i) q^{20} +(1.11746 - 1.56454i) q^{22} -2.88925 q^{23} -1.00000 q^{25} +(0.952868 - 1.33410i) q^{26} +(3.29426 - 1.12968i) q^{28} -3.97150i q^{29} -1.11895i q^{31} +(-0.229010 - 5.65222i) q^{32} +(5.76502 + 4.11761i) q^{34} +1.74129 q^{35} -3.01838 q^{37} +(-6.22063 - 4.44303i) q^{38} +(0.808422 - 2.71043i) q^{40} +9.26947i q^{41} +11.6746i q^{43} +(0.881995 + 2.57198i) q^{44} +(2.37485 - 3.32500i) q^{46} -8.27157 q^{47} +3.96791 q^{49} +(0.821961 - 1.15082i) q^{50} +(0.752085 + 2.19315i) q^{52} -4.96612i q^{53} +1.35950i q^{55} +(-1.40770 + 4.71965i) q^{56} +(4.57047 + 3.26442i) q^{58} +3.49943 q^{59} -2.56067 q^{61} +(1.28770 + 0.919731i) q^{62} +(6.69291 + 4.38235i) q^{64} +1.15926i q^{65} -5.64710i q^{67} +(-9.47724 + 3.24997i) q^{68} +(-1.43127 + 2.00391i) q^{70} -13.9484 q^{71} -10.7264 q^{73} +(2.48099 - 3.47361i) q^{74} +(10.2262 - 3.50682i) q^{76} -2.36729i q^{77} +11.0336i q^{79} +(2.45472 + 3.15822i) q^{80} +(-10.6675 - 7.61914i) q^{82} -11.0896 q^{83} -5.00950 q^{85} +(-13.4354 - 9.59610i) q^{86} +(-3.68485 - 1.09905i) q^{88} -9.36881i q^{89} -2.01861i q^{91} +(1.87444 + 5.46604i) q^{92} +(6.79890 - 9.51906i) q^{94} +5.40540 q^{95} -13.2368 q^{97} +(-3.26147 + 4.56634i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) $ 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.821961	+	1.15082i	−0.581214	+	0.813751i
$2$	−0.821961	+	1.15082i	−0.581214	+	0.813751i
$3$		0			0
$3$		0			0
$4$	−0.648762	−	1.89185i	−0.324381	−	0.945927i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			1.74129i			0.658145i	0.944305	+	0.329073i	$0.106736\pi$
$7$			1.74129i			0.658145i	−0.944305	+	0.329073i	$0.893264\pi$
$8$	2.71043	+	0.808422i	0.958283	+	0.285820i
$9$		0			0
$10$	1.15082	+	0.821961i	0.363920	+	0.259927i
$11$	−1.35950			−0.409906			−0.204953	−	0.978772i	$-0.565704\pi$
$11$	−1.35950			−0.409906			−0.204953	+	0.978772i	$0.565704\pi$
$12$		0			0
$13$	−1.15926			−0.321522			−0.160761	−	0.986993i	$-0.551395\pi$
$13$	−1.15926			−0.321522			−0.160761	+	0.986993i	$0.551395\pi$
$14$	−2.00391	−	1.43127i	−0.535566	−	0.382523i
$15$		0			0
$16$	−3.15822	+	2.45472i	−0.789554	+	0.613681i
$17$		−	5.00950i		−	1.21498i	−0.794326	−	0.607492i	$-0.792176\pi$
$17$		−	5.00950i		−	1.21498i	0.794326	−	0.607492i	$-0.207824\pi$
$18$		0			0
$19$			5.40540i			1.24008i	0.784568	+	0.620042i	$0.212885\pi$
$19$			5.40540i			1.24008i	−0.784568	+	0.620042i	$0.787115\pi$
$20$	−1.89185	+	0.648762i	−0.423031	+	0.145068i
$21$		0			0
$22$	1.11746	−	1.56454i	0.238243	−	0.333561i
$23$	−2.88925			−0.602451			−0.301226	−	0.953553i	$-0.597396\pi$
$23$	−2.88925			−0.602451			−0.301226	+	0.953553i	$0.597396\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	0.952868	−	1.33410i	0.186873	−	0.261638i
$27$		0			0
$28$	3.29426	−	1.12968i	0.622557	−	0.213490i
$29$		−	3.97150i		−	0.737489i	−0.929531	−	0.368745i	$-0.879788\pi$
$29$		−	3.97150i		−	0.737489i	0.929531	−	0.368745i	$-0.120212\pi$
$30$		0			0
$31$		−	1.11895i		−	0.200969i	−0.994939	−	0.100485i	$-0.967961\pi$
$31$		−	1.11895i		−	0.200969i	0.994939	−	0.100485i	$-0.0320393\pi$
$32$	−0.229010	−	5.65222i	−0.0404837	−	0.999180i
$33$		0			0
$34$	5.76502	+	4.11761i	0.988693	+	0.706165i
$35$	1.74129			0.294332
$36$		0			0
$37$	−3.01838			−0.496219			−0.248110	−	0.968732i	$-0.579809\pi$
$37$	−3.01838			−0.496219			−0.248110	+	0.968732i	$0.579809\pi$
$38$	−6.22063	−	4.44303i	−1.00912	−	0.720754i
$39$		0			0
$40$	0.808422	−	2.71043i	0.127823	−	0.428557i
$41$			9.26947i			1.44765i	0.689985	+	0.723824i	$0.257617\pi$
$41$			9.26947i			1.44765i	−0.689985	+	0.723824i	$0.742383\pi$
$42$		0			0
$43$			11.6746i			1.78037i	0.455603	+	0.890183i	$0.349424\pi$
$43$			11.6746i			1.78037i	−0.455603	+	0.890183i	$0.650576\pi$
$44$	0.881995	+	2.57198i	0.132966	+	0.387741i
$45$		0			0
$46$	2.37485	−	3.32500i	0.350153	−	0.490245i
$47$	−8.27157			−1.20653			−0.603266	−	0.797540i	$-0.706134\pi$
$47$	−8.27157			−1.20653			−0.603266	+	0.797540i	$0.706134\pi$
$48$		0			0
$49$	3.96791			0.566845
$50$	0.821961	−	1.15082i	0.116243	−	0.162750i
$51$		0			0
$52$	0.752085	+	2.19315i	0.104295	+	0.304136i
$53$		−	4.96612i		−	0.682150i	−0.940036	−	0.341075i	$-0.889209\pi$
$53$		−	4.96612i		−	0.682150i	0.940036	−	0.341075i	$-0.110791\pi$
$54$		0			0
$55$			1.35950i			0.183316i
$56$	−1.40770	+	4.71965i	−0.188111	+	0.630690i
$57$		0			0
$58$	4.57047	+	3.26442i	0.600132	+	0.428639i
$59$	3.49943			0.455587			0.227793	−	0.973709i	$-0.426849\pi$
$59$	3.49943			0.455587			0.227793	+	0.973709i	$0.426849\pi$
$60$		0			0
$61$	−2.56067			−0.327861			−0.163930	−	0.986472i	$-0.552417\pi$
$61$	−2.56067			−0.327861			−0.163930	+	0.986472i	$0.552417\pi$
$62$	1.28770	+	0.919731i	0.163539	+	0.116806i
$63$		0			0
$64$	6.69291	+	4.38235i	0.836613	+	0.547794i
$65$			1.15926i			0.143789i
$66$		0			0
$67$		−	5.64710i		−	0.689903i	−0.938620	−	0.344952i	$-0.887895\pi$
$67$		−	5.64710i		−	0.689903i	0.938620	−	0.344952i	$-0.112105\pi$
$68$	−9.47724	+	3.24997i	−1.14928	+	0.394117i
$69$		0			0
$70$	−1.43127	+	2.00391i	−0.171070	+	0.239513i
$71$	−13.9484			−1.65537			−0.827686	−	0.561191i	$-0.810343\pi$
$71$	−13.9484			−1.65537			−0.827686	+	0.561191i	$0.810343\pi$
$72$		0			0
$73$	−10.7264			−1.25543			−0.627716	−	0.778443i	$-0.716010\pi$
$73$	−10.7264			−1.25543			−0.627716	+	0.778443i	$0.716010\pi$
$74$	2.48099	−	3.47361i	0.288409	−	0.403799i
$75$		0			0
$76$	10.2262	−	3.50682i	1.17303	−	0.402260i
$77$		−	2.36729i		−	0.269778i
$78$		0			0
$79$			11.0336i			1.24137i	0.784058	+	0.620687i	$0.213146\pi$
$79$			11.0336i			1.24137i	−0.784058	+	0.620687i	$0.786854\pi$
$80$	2.45472	+	3.15822i	0.274446	+	0.353099i
$81$		0			0
$82$	−10.6675	−	7.61914i	−1.17802	−	0.841393i
$83$	−11.0896			−1.21724			−0.608621	−	0.793461i	$-0.708277\pi$
$83$	−11.0896			−1.21724			−0.608621	+	0.793461i	$0.708277\pi$
$84$		0			0
$85$	−5.00950			−0.543357
$86$	−13.4354	−	9.59610i	−1.44877	−	1.03477i
$87$		0			0
$88$	−3.68485	−	1.09905i	−0.392806	−	0.117160i
$89$		−	9.36881i		−	0.993092i	−0.868010	−	0.496546i	$-0.834601\pi$
$89$		−	9.36881i		−	0.993092i	0.868010	−	0.496546i	$-0.165399\pi$
$90$		0			0
$91$		−	2.01861i		−	0.211608i
$92$	1.87444	+	5.46604i	0.195424	+	0.569875i
$93$		0			0
$94$	6.79890	−	9.51906i	0.701253	−	0.981816i
$95$	5.40540			0.554583
$96$		0			0
$97$	−13.2368			−1.34400			−0.671999	−	0.740552i	$-0.734564\pi$
$97$	−13.2368			−1.34400			−0.671999	+	0.740552i	$0.734564\pi$
$98$	−3.26147	+	4.56634i	−0.329458	+	0.461270i
$99$		0			0
$100$	0.648762	+	1.89185i	0.0648762	+	0.189185i
$101$			5.33510i			0.530862i	0.964130	+	0.265431i	$0.0855142\pi$
$101$			5.33510i			0.530862i	−0.964130	+	0.265431i	$0.914486\pi$
$102$		0			0
$103$			14.9529i			1.47336i	0.676243	+	0.736679i	$0.263607\pi$
$103$			14.9529i			1.47336i	−0.676243	+	0.736679i	$0.736393\pi$
$104$	−3.14210	−	0.937173i	−0.308109	−	0.0918974i
$105$		0			0
$106$	5.71510	+	4.08196i	0.555100	+	0.396475i
$107$	−15.7052			−1.51827			−0.759137	−	0.650931i	$-0.774379\pi$
$107$	−15.7052			−1.51827			−0.759137	+	0.650931i	$0.774379\pi$
$108$		0			0
$109$	4.34742			0.416407			0.208204	−	0.978085i	$-0.433238\pi$
$109$	4.34742			0.416407			0.208204	+	0.978085i	$0.433238\pi$
$110$	−1.56454	−	1.11746i	−0.149173	−	0.106546i
$111$		0			0
$112$	−4.27438	−	5.49937i	−0.403891	−	0.519641i
$113$			10.6598i			1.00279i	0.865218	+	0.501396i	$0.167180\pi$
$113$			10.6598i			1.00279i	−0.865218	+	0.501396i	$0.832820\pi$
$114$		0			0
$115$			2.88925i			0.269424i
$116$	−7.51350	+	2.57656i	−0.697611	+	0.239227i
$117$		0			0
$118$	−2.87639	+	4.02720i	−0.264793	+	0.370734i
$119$	8.72299			0.799635
$120$		0			0
$121$	−9.15175			−0.831977
$122$	2.10477	−	2.94687i	0.190557	−	0.266797i
$123$		0			0
$124$	−2.11689	+	0.725931i	−0.190102	+	0.0651905i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	4.04665i		−	0.359082i	−0.983751	−	0.179541i	$-0.942539\pi$
$127$		−	4.04665i		−	0.359082i	0.983751	−	0.179541i	$-0.0574612\pi$
$128$	−10.5446	+	4.10020i	−0.932019	+	0.362410i
$129$		0			0
$130$	−1.33410	−	0.952868i	−0.117008	−	0.0835721i
$131$	2.11548			0.184830			0.0924152	−	0.995721i	$-0.470541\pi$
$131$	2.11548			0.184830			0.0924152	+	0.995721i	$0.470541\pi$
$132$		0			0
$133$	−9.41237			−0.816156
$134$	6.49878	+	4.64170i	0.561409	+	0.400981i
$135$		0			0
$136$	4.04979	−	13.5779i	0.347267	−	1.16430i
$137$			5.47699i			0.467930i	0.972245	+	0.233965i	$0.0751702\pi$
$137$			5.47699i			0.467930i	−0.972245	+	0.233965i	$0.924830\pi$
$138$		0			0
$139$		−	22.0116i		−	1.86700i	−0.358576	−	0.933500i	$-0.616738\pi$
$139$		−	22.0116i		−	1.86700i	0.358576	−	0.933500i	$-0.383262\pi$
$140$	−1.12968	−	3.29426i	−0.0954755	−	0.278416i
$141$		0			0
$142$	11.4650	−	16.0521i	0.962125	−	1.34706i
$143$	1.57602			0.131794
$144$		0			0
$145$	−3.97150			−0.329815
$146$	8.81669	−	12.3441i	0.729674	−	1.02161i
$147$		0			0
$148$	1.95821	+	5.71034i	0.160964	+	0.469387i
$149$			12.7425i			1.04390i	0.852975	+	0.521952i	$0.174796\pi$
$149$			12.7425i			1.04390i	−0.852975	+	0.521952i	$0.825204\pi$
$150$		0			0
$151$		−	14.9159i		−	1.21383i	−0.794765	−	0.606917i	$-0.792406\pi$
$151$		−	14.9159i		−	1.21383i	0.794765	−	0.606917i	$-0.207594\pi$
$152$	−4.36985	+	14.6510i	−0.354441	+	1.18835i
$153$		0			0
$154$	2.72432	+	1.94582i	0.219532	+	0.156799i
$155$	−1.11895			−0.0898761
$156$		0			0
$157$	0.158102			0.0126180			0.00630898	−	0.999980i	$-0.497992\pi$
$157$	0.158102			0.0126180			0.00630898	+	0.999980i	$0.497992\pi$
$158$	−12.6976	−	9.06916i	−1.01017	−	0.721504i
$159$		0			0
$160$	−5.65222	+	0.229010i	−0.446847	+	0.0181049i
$161$		−	5.03103i		−	0.396500i
$162$		0			0
$163$		−	6.97722i		−	0.546498i	−0.961943	−	0.273249i	$-0.911902\pi$
$163$		−	6.97722i		−	0.546498i	0.961943	−	0.273249i	$-0.0880983\pi$
$164$	17.5365	−	6.01368i	1.36937	−	0.469589i
$165$		0			0
$166$	9.11522	−	12.7621i	0.707478	−	0.990532i
$167$	8.41426			0.651115			0.325557	−	0.945522i	$-0.394448\pi$
$167$	8.41426			0.651115			0.325557	+	0.945522i	$0.394448\pi$
$168$		0			0
$169$	−11.6561			−0.896624
$170$	4.11761	−	5.76502i	0.315807	−	0.442157i
$171$		0			0
$172$	22.0867	−	7.57406i	1.68410	−	0.577517i
$173$		−	19.3782i		−	1.47330i	−0.676275	−	0.736649i	$-0.736407\pi$
$173$		−	19.3782i		−	1.47330i	0.676275	−	0.736649i	$-0.263593\pi$
$174$		0			0
$175$		−	1.74129i		−	0.131629i
$176$	4.29361	−	3.33721i	0.323643	−	0.251552i
$177$		0			0
$178$	10.7818	+	7.70079i	0.808130	+	0.577199i
$179$	−10.0067			−0.747935			−0.373967	−	0.927442i	$-0.622003\pi$
$179$	−10.0067			−0.747935			−0.373967	+	0.927442i	$0.622003\pi$
$180$		0			0
$181$	−6.51340			−0.484137			−0.242069	−	0.970259i	$-0.577826\pi$
$181$	−6.51340			−0.484137			−0.242069	+	0.970259i	$0.577826\pi$
$182$	2.32305	+	1.65922i	0.172196	+	0.122989i
$183$		0			0
$184$	−7.83113	−	2.33574i	−0.577319	−	0.172193i
$185$			3.01838i			0.221916i
$186$		0			0
$187$			6.81044i			0.498029i
$188$	5.36628	+	15.6486i	0.391376	+	1.14129i
$189$		0			0
$190$	−4.44303	+	6.22063i	−0.322331	+	0.451292i
$191$	26.8190			1.94055			0.970277	−	0.241996i	$-0.0778023\pi$
$191$	26.8190			1.94055			0.970277	+	0.241996i	$0.0778023\pi$
$192$		0			0
$193$	5.72474			0.412076			0.206038	−	0.978544i	$-0.433943\pi$
$193$	5.72474			0.412076			0.206038	+	0.978544i	$0.433943\pi$
$194$	10.8802	−	15.2332i	0.781150	−	1.09368i
$195$		0			0
$196$	−2.57423	−	7.50671i	−0.183874	−	0.536194i
$197$		−	15.0858i		−	1.07482i	−0.843323	−	0.537408i	$-0.819404\pi$
$197$		−	15.0858i		−	1.07482i	0.843323	−	0.537408i	$-0.180596\pi$
$198$		0			0
$199$			17.4336i			1.23584i	0.786242	+	0.617919i	$0.212024\pi$
$199$			17.4336i			1.23584i	−0.786242	+	0.617919i	$0.787976\pi$
$200$	−2.71043	−	0.808422i	−0.191657	−	0.0571641i
$201$		0			0
$202$	−6.13972	−	4.38524i	−0.431989	−	0.308544i
$203$	6.91553			0.485375
$204$		0			0
$205$	9.26947			0.647408
$206$	−17.2081	−	12.2907i	−1.19895	−	0.856336i
$207$		0			0
$208$	3.66120	−	2.84567i	0.253859	−	0.197312i
$209$		−	7.34867i		−	0.508318i
$210$		0			0
$211$			17.5682i			1.20944i	0.796436	+	0.604722i	$0.206716\pi$
$211$			17.5682i			1.20944i	−0.796436	+	0.604722i	$0.793284\pi$
$212$	−9.39518	+	3.22183i	−0.645263	+	0.221276i
$213$		0			0
$214$	12.9090	−	18.0738i	0.882442	−	1.23550i
$215$	11.6746			0.796204
$216$		0			0
$217$	1.94841			0.132267
$218$	−3.57341	+	5.00309i	−0.242022	+	0.338852i
$219$		0			0
$220$	2.57198	−	0.881995i	0.173403	−	0.0594641i
$221$			5.80733i			0.390643i
$222$		0			0
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	9.84214	−	0.398773i	0.657606	−	0.0266442i
$225$		0			0
$226$	−12.2675	−	8.76195i	−0.816022	−	0.582836i
$227$	14.8726			0.987131			0.493565	−	0.869709i	$-0.335693\pi$
$227$	14.8726			0.987131			0.493565	+	0.869709i	$0.335693\pi$
$228$		0			0
$229$	−23.2055			−1.53346			−0.766731	−	0.641968i	$-0.778118\pi$
$229$	−23.2055			−1.53346			−0.766731	+	0.641968i	$0.778118\pi$
$230$	−3.32500	−	2.37485i	−0.219244	−	0.156593i
$231$		0			0
$232$	3.21065	−	10.7645i	0.210789	−	0.706724i
$233$			10.4597i			0.685237i	0.939475	+	0.342619i	$0.111314\pi$
$233$			10.4597i			0.685237i	−0.939475	+	0.342619i	$0.888686\pi$
$234$		0			0
$235$			8.27157i			0.539577i
$236$	−2.27030	−	6.62041i	−0.147784	−	0.430952i
$237$		0			0
$238$	−7.16995	+	10.0386i	−0.464759	+	0.650704i
$239$	4.27838			0.276745			0.138373	−	0.990380i	$-0.455813\pi$
$239$	4.27838			0.276745			0.138373	+	0.990380i	$0.455813\pi$
$240$		0			0
$241$	27.2579			1.75583			0.877917	−	0.478812i	$-0.158932\pi$
$241$	27.2579			1.75583			0.877917	+	0.478812i	$0.158932\pi$
$242$	7.52237	−	10.5320i	0.483557	−	0.677022i
$243$		0			0
$244$	1.66127	+	4.84442i	0.106352	+	0.310132i
$245$		−	3.96791i		−	0.253501i
$246$		0			0
$247$		−	6.26628i		−	0.398714i
$248$	0.904582	−	3.03284i	0.0574410	−	0.192585i
$249$		0			0
$250$	−1.15082	−	0.821961i	−0.0727841	−	0.0519853i
$251$	−14.5359			−0.917500			−0.458750	−	0.888565i	$-0.651703\pi$
$251$	−14.5359			−0.917500			−0.458750	+	0.888565i	$0.651703\pi$
$252$		0			0
$253$	3.92795			0.246948
$254$	4.65695	+	3.32618i	0.292203	+	0.208703i
$255$		0			0
$256$	3.94866	−	15.5051i	0.246791	−	0.969069i
$257$			7.12993i			0.444753i	0.974961	+	0.222376i	$0.0713814\pi$
$257$			7.12993i			0.444753i	−0.974961	+	0.222376i	$0.928619\pi$
$258$		0			0
$259$		−	5.25588i		−	0.326584i
$260$	2.19315	−	0.752085i	0.136014	−	0.0466423i
$261$		0			0
$262$	−1.73884	+	2.43453i	−0.107426	+	0.150406i
$263$	−21.5707			−1.33011			−0.665054	−	0.746795i	$-0.731592\pi$
$263$	−21.5707			−1.33011			−0.665054	+	0.746795i	$0.731592\pi$
$264$		0			0
$265$	−4.96612			−0.305067
$266$	7.73660	−	10.8319i	0.474361	−	0.664148i
$267$		0			0
$268$	−10.6835	+	3.66362i	−0.652598	+	0.223791i
$269$		−	9.13678i		−	0.557079i	−0.960425	−	0.278540i	$-0.910150\pi$
$269$		−	9.13678i		−	0.557079i	0.960425	−	0.278540i	$-0.0898504\pi$
$270$		0			0
$271$		−	9.94313i		−	0.604002i	−0.953308	−	0.302001i	$-0.902345\pi$
$271$		−	9.94313i		−	0.604002i	0.953308	−	0.302001i	$-0.0976547\pi$
$272$	12.2969	+	15.8211i	0.745612	+	0.959295i
$273$		0			0
$274$	−6.30301	−	4.50187i	−0.380779	−	0.271968i
$275$	1.35950			0.0819812
$276$		0			0
$277$	−21.6281			−1.29951			−0.649754	−	0.760145i	$-0.725128\pi$
$277$	−21.6281			−1.29951			−0.649754	+	0.760145i	$0.725128\pi$
$278$	25.3314	+	18.0927i	1.51927	+	1.08513i
$279$		0			0
$280$	4.71965	+	1.40770i	0.282053	+	0.0841259i
$281$			23.3650i			1.39384i	0.717151	+	0.696918i	$0.245446\pi$
$281$			23.3650i			1.39384i	−0.717151	+	0.696918i	$0.754554\pi$
$282$		0			0
$283$			29.6975i			1.76533i	0.470001	+	0.882666i	$0.344254\pi$
$283$			29.6975i			1.76533i	−0.470001	+	0.882666i	$0.655746\pi$
$284$	9.04920	+	26.3884i	0.536971	+	1.56586i
$285$		0			0
$286$	−1.29543	+	1.81371i	−0.0766003	+	0.107247i
$287$	−16.1408			−0.952762
$288$		0			0
$289$	−8.09512			−0.476184
$290$	3.26442	−	4.57047i	0.191693	−	0.268387i
$291$		0			0
$292$	6.95888	+	20.2928i	0.407238	+	1.18755i
$293$		−	4.44017i		−	0.259397i	−0.991553	−	0.129699i	$-0.958599\pi$
$293$		−	4.44017i		−	0.259397i	0.991553	−	0.129699i	$-0.0414010\pi$
$294$		0			0
$295$		−	3.49943i		−	0.203745i
$296$	−8.18113	−	2.44013i	−0.475518	−	0.141830i
$297$		0			0
$298$	−14.6643	−	10.4738i	−0.849477	−	0.606731i
$299$	3.34940			0.193701
$300$		0			0
$301$	−20.3289			−1.17174
$302$	17.1654	+	12.2602i	0.987759	+	0.705498i
$303$		0			0
$304$	−13.2688	−	17.0714i	−0.761016	−	0.979114i
$305$			2.56067i			0.146624i
$306$		0			0
$307$			4.96065i			0.283119i	0.989930	+	0.141560i	$0.0452117\pi$
$307$			4.96065i			0.283119i	−0.989930	+	0.141560i	$0.954788\pi$
$308$	−4.47857	+	1.53581i	−0.255190	+	0.0875108i
$309$		0			0
$310$	0.919731	−	1.28770i	0.0522372	−	0.0731367i
$311$	22.9852			1.30337			0.651685	−	0.758489i	$-0.274062\pi$
$311$	22.9852			1.30337			0.651685	+	0.758489i	$0.274062\pi$
$312$		0			0
$313$	5.60425			0.316771			0.158385	−	0.987377i	$-0.449371\pi$
$313$	5.60425			0.316771			0.158385	+	0.987377i	$0.449371\pi$
$314$	−0.129954	+	0.181947i	−0.00733373	+	0.0102679i
$315$		0			0
$316$	20.8739	−	7.15816i	1.17425	−	0.402678i
$317$		−	18.7505i		−	1.05313i	−0.850134	−	0.526567i	$-0.823479\pi$
$317$		−	18.7505i		−	1.05313i	0.850134	−	0.526567i	$-0.176521\pi$
$318$		0			0
$319$			5.39927i			0.302301i
$320$	4.38235	−	6.69291i	0.244981	−	0.374145i
$321$		0			0
$322$	5.78979	+	4.13530i	0.322653	+	0.230452i
$323$	27.0784			1.50668
$324$		0			0
$325$	1.15926			0.0643043
$326$	8.02951	+	5.73500i	0.444713	+	0.317632i
$327$		0			0
$328$	−7.49364	+	25.1243i	−0.413767	+	1.38726i
$329$		−	14.4032i		−	0.794073i
$330$		0			0
$331$		−	29.6495i		−	1.62969i	−0.579681	−	0.814843i	$-0.696823\pi$
$331$		−	29.6495i		−	1.62969i	0.579681	−	0.814843i	$-0.303177\pi$
$332$	7.19451	+	20.9799i	0.394850	+	1.15142i
$333$		0			0
$334$	−6.91619	+	9.68328i	−0.378437	+	0.529845i
$335$	−5.64710			−0.308534
$336$		0			0
$337$	33.8222			1.84241			0.921207	−	0.389073i	$-0.127205\pi$
$337$	33.8222			1.84241			0.921207	+	0.389073i	$0.127205\pi$
$338$	9.58086	−	13.4141i	0.521130	−	0.729628i
$339$		0			0
$340$	3.24997	+	9.47724i	0.176255	+	0.513976i
$341$			1.52122i			0.0823784i
$342$		0			0
$343$			19.0983i			1.03121i
$344$	−9.43804	+	31.6434i	−0.508865	+	1.70610i
$345$		0			0
$346$	22.3008	+	15.9281i	1.19890	+	0.856301i
$347$	−22.9318			−1.23104			−0.615521	−	0.788120i	$-0.711055\pi$
$347$	−22.9318			−1.23104			−0.615521	+	0.788120i	$0.711055\pi$
$348$		0			0
$349$	−2.20201			−0.117871			−0.0589355	−	0.998262i	$-0.518771\pi$
$349$	−2.20201			−0.117871			−0.0589355	+	0.998262i	$0.518771\pi$
$350$	2.00391	+	1.43127i	0.107113	+	0.0765046i
$351$		0			0
$352$	0.311341	+	7.68422i	0.0165945	+	0.409570i
$353$			22.0545i			1.17384i	0.809645	+	0.586920i	$0.199660\pi$
$353$			22.0545i			1.17384i	−0.809645	+	0.586920i	$0.800340\pi$
$354$		0			0
$355$			13.9484i			0.740305i
$356$	−17.7244	+	6.07813i	−0.939392	+	0.322140i
$357$		0			0
$358$	8.22510	−	11.5159i	0.434710	−	0.608633i
$359$	19.8808			1.04927			0.524633	−	0.851328i	$-0.324202\pi$
$359$	19.8808			1.04927			0.524633	+	0.851328i	$0.324202\pi$
$360$		0			0
$361$	−10.2184			−0.537810
$362$	5.35376	−	7.49573i	0.281387	−	0.393967i
$363$		0			0
$364$	−3.81891	+	1.30960i	−0.200166	+	0.0686416i
$365$			10.7264i			0.561446i
$366$		0			0
$367$		−	6.76071i		−	0.352906i	−0.984309	−	0.176453i	$-0.943538\pi$
$367$		−	6.76071i		−	0.352906i	0.984309	−	0.176453i	$-0.0564624\pi$
$368$	9.12489	−	7.09232i	0.475668	−	0.369713i
$369$		0			0
$370$	−3.47361	−	2.48099i	−0.180584	−	0.128981i
$371$	8.64746			0.448954
$372$		0			0
$373$	−13.3772			−0.692646			−0.346323	−	0.938115i	$-0.612570\pi$
$373$	−13.3772			−0.692646			−0.346323	+	0.938115i	$0.612570\pi$
$374$	−7.83758	−	5.59792i	−0.405271	−	0.289461i
$375$		0			0
$376$	−22.4195	−	6.68692i	−1.15620	−	0.344851i
$377$			4.60401i			0.237119i
$378$		0			0
$379$		−	15.3512i		−	0.788537i	−0.918995	−	0.394269i	$-0.870998\pi$
$379$		−	15.3512i		−	0.788537i	0.918995	−	0.394269i	$-0.129002\pi$
$380$	−3.50682	−	10.2262i	−0.179896	−	0.524595i
$381$		0			0
$382$	−22.0442	+	30.8638i	−1.12788	+	1.57913i
$383$	−11.4736			−0.586275			−0.293137	−	0.956070i	$-0.594699\pi$
$383$	−11.4736			−0.586275			−0.293137	+	0.956070i	$0.594699\pi$
$384$		0			0
$385$	−2.36729			−0.120648
$386$	−4.70551	+	6.58813i	−0.239504	+	0.335327i
$387$		0			0
$388$	8.58755	+	25.0422i	0.435967	+	1.27132i
$389$			9.76634i			0.495173i	0.968866	+	0.247587i	$0.0796375\pi$
$389$			9.76634i			0.495173i	−0.968866	+	0.247587i	$0.920363\pi$
$390$		0			0
$391$			14.4737i			0.731968i
$392$	10.7548	+	3.20775i	0.543198	+	0.162016i
$393$		0			0
$394$	17.3609	+	12.3999i	0.874632	+	0.624698i
$395$	11.0336			0.555159
$396$		0			0
$397$	4.14351			0.207957			0.103978	−	0.994580i	$-0.466843\pi$
$397$	4.14351			0.207957			0.103978	+	0.994580i	$0.466843\pi$
$398$	−20.0629	−	14.3298i	−1.00566	−	0.718286i
$399$		0			0
$400$	3.15822	−	2.45472i	0.157911	−	0.122736i
$401$			25.9587i			1.29632i	0.761506	+	0.648158i	$0.224460\pi$
$401$			25.9587i			1.29632i	−0.761506	+	0.648158i	$0.775540\pi$
$402$		0			0
$403$			1.29715i			0.0646159i
$404$	10.0932	−	3.46121i	0.502156	−	0.172201i
$405$		0			0
$406$	−5.68429	+	7.95851i	−0.282107	+	0.394974i
$407$	4.10351			0.203403
$408$		0			0
$409$	36.7101			1.81520			0.907600	−	0.419836i	$-0.137912\pi$
$409$	36.7101			1.81520			0.907600	+	0.419836i	$0.137912\pi$
$410$	−7.61914	+	10.6675i	−0.376282	+	0.526829i
$411$		0			0
$412$	28.2888	−	9.70090i	1.39369	−	0.477929i
$413$			6.09352i			0.299842i
$414$		0			0
$415$			11.0896i			0.544367i
$416$	0.265483	+	6.55240i	0.0130164	+	0.321258i
$417$		0			0
$418$	8.45698	+	6.04032i	0.413644	+	0.295442i
$419$	23.1443			1.13067			0.565336	−	0.824861i	$-0.308747\pi$
$419$	23.1443			1.13067			0.565336	+	0.824861i	$0.308747\pi$
$420$		0			0
$421$	38.3585			1.86948			0.934739	−	0.355336i	$-0.115633\pi$
$421$	38.3585			1.86948			0.934739	+	0.355336i	$0.115633\pi$
$422$	−20.2178	−	14.4404i	−0.984187	−	0.702946i
$423$		0			0
$424$	4.01472	−	13.4604i	0.194972	−	0.653693i
$425$			5.00950i			0.242997i
$426$		0			0
$427$		−	4.45887i		−	0.215780i
$428$	10.1889	+	29.7118i	0.492499	+	1.43618i
$429$		0			0
$430$	−9.59610	+	13.4354i	−0.462765	+	0.647912i
$431$	25.1032			1.20918			0.604589	−	0.796538i	$-0.293338\pi$
$431$	25.1032			1.20918			0.604589	+	0.796538i	$0.293338\pi$
$432$		0			0
$433$	−14.2379			−0.684229			−0.342115	−	0.939658i	$-0.611143\pi$
$433$	−14.2379			−0.684229			−0.342115	+	0.939658i	$0.611143\pi$
$434$	−1.60152	+	2.24227i	−0.0768753	+	0.107632i
$435$		0			0
$436$	−2.82044	−	8.22468i	−0.135075	−	0.393891i
$437$		−	15.6176i		−	0.747090i
$438$		0			0
$439$		−	9.40530i		−	0.448890i	−0.974487	−	0.224445i	$-0.927943\pi$
$439$		−	9.40530i		−	0.448890i	0.974487	−	0.224445i	$-0.0720570\pi$
$440$	−1.09905	+	3.68485i	−0.0523953	+	0.175668i
$441$		0			0
$442$	−6.68318	−	4.77340i	−0.317886	−	0.227047i
$443$	−33.9700			−1.61396			−0.806981	−	0.590577i	$-0.798900\pi$
$443$	−33.9700			−1.61396			−0.806981	+	0.590577i	$0.798900\pi$
$444$		0			0
$445$	−9.36881			−0.444124
$446$	−4.60327	−	3.28784i	−0.217971	−	0.155684i
$447$		0			0
$448$	−7.63094	+	11.6543i	−0.360528	+	0.550613i
$449$		−	2.34426i		−	0.110632i	−0.998469	−	0.0553161i	$-0.982383\pi$
$449$		−	2.34426i		−	0.110632i	0.998469	−	0.0553161i	$-0.0176167\pi$
$450$		0			0
$451$		−	12.6019i		−	0.593400i
$452$	20.1668	−	6.91568i	0.948567	−	0.325286i
$453$		0			0
$454$	−12.2247	+	17.1157i	−0.573734	+	0.803279i
$455$	−2.01861			−0.0946339
$456$		0			0
$457$	20.3496			0.951912			0.475956	−	0.879469i	$-0.342102\pi$
$457$	20.3496			0.951912			0.475956	+	0.879469i	$0.342102\pi$
$458$	19.0740	−	26.7053i	0.891270	−	1.24786i
$459$		0			0
$460$	5.46604	−	1.87444i	0.254856	−	0.0873961i
$461$			15.8303i			0.737290i	0.929570	+	0.368645i	$0.120178\pi$
$461$			15.8303i			0.737290i	−0.929570	+	0.368645i	$0.879822\pi$
$462$		0			0
$463$		−	5.75697i		−	0.267549i	−0.991012	−	0.133775i	$-0.957290\pi$
$463$		−	5.75697i		−	0.267549i	0.991012	−	0.133775i	$-0.0427098\pi$
$464$	9.74894	+	12.5429i	0.452583	+	0.582288i
$465$		0			0
$466$	−12.0372	−	8.59745i	−0.557612	−	0.398269i
$467$	13.5706			0.627973			0.313987	−	0.949427i	$-0.398335\pi$
$467$	13.5706			0.627973			0.313987	+	0.949427i	$0.398335\pi$
$468$		0			0
$469$	9.83324			0.454057
$470$	−9.51906	−	6.79890i	−0.439082	−	0.313610i
$471$		0			0
$472$	9.48497	+	2.82902i	0.436581	+	0.130216i
$473$		−	15.8717i		−	0.729783i
$474$		0			0
$475$		−	5.40540i		−	0.248017i
$476$	−5.65914	−	16.5026i	−0.259386	−	0.756396i
$477$		0			0
$478$	−3.51666	+	4.92363i	−0.160848	+	0.225202i
$479$	−14.2028			−0.648941			−0.324471	−	0.945896i	$-0.605186\pi$
$479$	−14.2028			−0.648941			−0.324471	+	0.945896i	$0.605186\pi$
$480$		0			0
$481$	3.49910			0.159545
$482$	−22.4049	+	31.3689i	−1.02052	+	1.42881i
$483$		0			0
$484$	5.93730	+	17.3138i	0.269877	+	0.786989i
$485$			13.2368i			0.601054i
$486$		0			0
$487$		−	25.3676i		−	1.14952i	−0.818323	−	0.574759i	$-0.805096\pi$
$487$		−	25.3676i		−	1.14952i	0.818323	−	0.574759i	$-0.194904\pi$
$488$	−6.94054	−	2.07011i	−0.314183	−	0.0937093i
$489$		0			0
$490$	4.56634	+	3.26147i	0.206286	+	0.147338i
$491$	3.69314			0.166669			0.0833346	−	0.996522i	$-0.473443\pi$
$491$	3.69314			0.166669			0.0833346	+	0.996522i	$0.473443\pi$
$492$		0			0
$493$	−19.8952			−0.896037
$494$	7.21135	+	5.15064i	0.324454	+	0.231738i
$495$		0			0
$496$	2.74671	+	3.53388i	0.123331	+	0.158676i
$497$		−	24.2882i		−	1.08948i
$498$		0			0
$499$			2.10274i			0.0941315i	0.998892	+	0.0470658i	$0.0149870\pi$
$499$			2.10274i			0.0941315i	−0.998892	+	0.0470658i	$0.985013\pi$
$500$	1.89185	−	0.648762i	0.0846062	−	0.0290135i
$501$		0			0
$502$	11.9480	−	16.7282i	0.533264	−	0.746616i
$503$	10.1166			0.451079			0.225539	−	0.974234i	$-0.427586\pi$
$503$	10.1166			0.451079			0.225539	+	0.974234i	$0.427586\pi$
$504$		0			0
$505$	5.33510			0.237409
$506$	−3.22862	+	4.52036i	−0.143530	+	0.200954i
$507$		0			0
$508$	−7.65566	+	2.62531i	−0.339665	+	0.116479i
$509$		−	39.8463i		−	1.76616i	−0.469225	−	0.883079i	$-0.655467\pi$
$509$		−	39.8463i		−	1.76616i	0.469225	−	0.883079i	$-0.344533\pi$
$510$		0			0
$511$		−	18.6778i		−	0.826256i
$512$	14.5979	+	17.2888i	0.645142	+	0.764063i
$513$		0			0
$514$	−8.20525	−	5.86052i	−0.361918	−	0.258497i
$515$	14.9529			0.658906
$516$		0			0
$517$	11.2452			0.494565
$518$	6.04855	+	4.32012i	0.265758	+	0.189815i
$519$		0			0
$520$	−0.937173	+	3.14210i	−0.0410978	+	0.137790i
$521$			37.2574i			1.63227i	0.577858	+	0.816137i	$0.303889\pi$
$521$			37.2574i			1.63227i	−0.577858	+	0.816137i	$0.696111\pi$
$522$		0			0
$523$			33.5724i			1.46802i	0.679140	+	0.734008i	$0.262353\pi$
$523$			33.5724i			1.46802i	−0.679140	+	0.734008i	$0.737647\pi$
$524$	−1.37244	−	4.00218i	−0.0599555	−	0.174836i
$525$		0			0
$526$	17.7303	−	24.8240i	0.773078	−	1.08238i
$527$	−5.60537			−0.244174
$528$		0			0
$529$	−14.6522			−0.637053
$530$	4.08196	−	5.71510i	0.177309	−	0.248248i
$531$		0			0
$532$	6.10639	+	17.8068i	0.264745	+	0.772023i
$533$		−	10.7457i		−	0.465450i
$534$		0			0
$535$			15.7052i			0.678993i
$536$	4.56524	−	15.3061i	0.197188	−	0.661123i
$537$		0			0
$538$	10.5148	+	7.51007i	0.453324	+	0.323782i
$539$	−5.39440			−0.232353
$540$		0			0
$541$	45.6679			1.96342			0.981709	−	0.190387i	$-0.0609744\pi$
$541$	45.6679			1.96342			0.981709	+	0.190387i	$0.0609744\pi$
$542$	11.4427	+	8.17286i	0.491507	+	0.351055i
$543$		0			0
$544$	−28.3148	+	1.14723i	−1.21399	+	0.0491870i
$545$		−	4.34742i		−	0.186223i
$546$		0			0
$547$			32.0547i			1.37056i	0.728279	+	0.685281i	$0.240321\pi$
$547$			32.0547i			1.37056i	−0.728279	+	0.685281i	$0.759679\pi$
$548$	10.3617	−	3.55326i	0.442628	−	0.151788i
$549$		0			0
$550$	−1.11746	+	1.56454i	−0.0476486	+	0.0667123i
$551$	21.4676			0.914549
$552$		0			0
$553$	−19.2126			−0.817004
$554$	17.7775	−	24.8900i	0.755292	−	1.05748i
$555$		0			0
$556$	−41.6427	+	14.2803i	−1.76605	+	0.605619i
$557$		−	26.7136i		−	1.13189i	−0.824442	−	0.565946i	$-0.808511\pi$
$557$		−	26.7136i		−	1.13189i	0.824442	−	0.565946i	$-0.191489\pi$
$558$		0			0
$559$		−	13.5340i		−	0.572426i
$560$	−5.49937	+	4.27438i	−0.232391	+	0.180626i
$561$		0			0
$562$	−26.8888	−	19.2051i	−1.13424	−	0.810117i
$563$	−19.1364			−0.806504			−0.403252	−	0.915089i	$-0.632120\pi$
$563$	−19.1364			−0.806504			−0.403252	+	0.915089i	$0.632120\pi$
$564$		0			0
$565$	10.6598			0.448462
$566$	−34.1764	−	24.4102i	−1.43654	−	1.02604i
$567$		0			0
$568$	−37.8063	−	11.2762i	−1.58632	−	0.473139i
$569$			5.57968i			0.233912i	0.993137	+	0.116956i	$0.0373137\pi$
$569$			5.57968i			0.233912i	−0.993137	+	0.116956i	$0.962686\pi$
$570$		0			0
$571$		−	19.1782i		−	0.802582i	−0.915951	−	0.401291i	$-0.868562\pi$
$571$		−	19.1782i		−	0.802582i	0.915951	−	0.401291i	$-0.131438\pi$
$572$	−1.02246	−	2.98160i	−0.0427513	−	0.124667i
$573$		0			0
$574$	13.2671	−	18.5751i	0.553759	−	0.775311i
$575$	2.88925			0.120490
$576$		0			0
$577$	3.36261			0.139987			0.0699935	−	0.997547i	$-0.477702\pi$
$577$	3.36261			0.139987			0.0699935	+	0.997547i	$0.477702\pi$
$578$	6.65387	−	9.31601i	0.276765	−	0.387495i
$579$		0			0
$580$	2.57656	+	7.51350i	0.106986	+	0.311981i
$581$		−	19.3102i		−	0.801122i
$582$		0			0
$583$			6.75147i			0.279617i
$584$	−29.0732	−	8.67147i	−1.20306	−	0.358828i
$585$		0			0
$586$	5.10982	+	3.64964i	0.211085	+	0.150765i
$587$	−3.50152			−0.144523			−0.0722616	−	0.997386i	$-0.523022\pi$
$587$	−3.50152			−0.144523			−0.0722616	+	0.997386i	$0.523022\pi$
$588$		0			0
$589$	6.04837			0.249219
$590$	4.02720	+	2.87639i	0.165797	+	0.118419i
$591$		0			0
$592$	9.53271	−	7.40930i	0.391792	−	0.304520i
$593$			17.5704i			0.721528i	0.932657	+	0.360764i	$0.117484\pi$
$593$			17.5704i			0.721528i	−0.932657	+	0.360764i	$0.882516\pi$
$594$		0			0
$595$		−	8.72299i		−	0.357608i
$596$	24.1069	−	8.26683i	0.987456	−	0.338622i
$597$		0			0
$598$	−2.75308	+	3.85455i	−0.112582	+	0.157624i
$599$	−38.6768			−1.58029			−0.790146	−	0.612919i	$-0.789995\pi$
$599$	−38.6768			−1.58029			−0.790146	+	0.612919i	$0.789995\pi$
$600$		0			0
$601$	21.4186			0.873685			0.436842	−	0.899538i	$-0.356097\pi$
$601$	21.4186			0.873685			0.436842	+	0.899538i	$0.356097\pi$
$602$	16.7096	−	23.3949i	0.681031	−	0.953504i
$603$		0			0
$604$	−28.2186	+	9.67684i	−1.14820	+	0.393745i
$605$			9.15175i			0.372071i
$606$		0			0
$607$		−	30.3914i		−	1.23355i	−0.787140	−	0.616775i	$-0.788439\pi$
$607$		−	30.3914i		−	1.23355i	0.787140	−	0.616775i	$-0.211561\pi$
$608$	30.5525	−	1.23789i	1.23907	−	0.0502032i
$609$		0			0
$610$	−2.94687	−	2.10477i	−0.119315	−	0.0852198i
$611$	9.58892			0.387926
$612$		0			0
$613$	22.5432			0.910513			0.455256	−	0.890360i	$-0.349548\pi$
$613$	22.5432			0.910513			0.455256	+	0.890360i	$0.349548\pi$
$614$	−5.70880	−	4.07746i	−0.230388	−	0.164553i
$615$		0			0
$616$	1.91377	−	6.41638i	0.0771080	−	0.258523i
$617$		−	16.1234i		−	0.649105i	−0.945868	−	0.324552i	$-0.894786\pi$
$617$		−	16.1234i		−	0.649105i	0.945868	−	0.324552i	$-0.105214\pi$
$618$		0			0
$619$		−	0.140171i		−	0.00563395i	−0.999996	−	0.00281697i	$-0.999103\pi$
$619$		−	0.140171i		−	0.00563395i	0.999996	−	0.00281697i	$-0.000896672\pi$
$620$	0.725931	+	2.11689i	0.0291541	+	0.0850162i
$621$		0			0
$622$	−18.8929	+	26.4518i	−0.757537	+	1.06062i
$623$	16.3138			0.653599
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.60647	+	6.44947i	−0.184112	+	0.257773i
$627$		0			0
$628$	−0.102571	−	0.299107i	−0.00409302	−	0.0119357i
$629$			15.1206i			0.602898i
$630$		0			0
$631$		−	15.6203i		−	0.621833i	−0.950437	−	0.310917i	$-0.899364\pi$
$631$		−	15.6203i		−	0.621833i	0.950437	−	0.310917i	$-0.100636\pi$
$632$	−8.91978	+	29.9058i	−0.354810	+	1.18959i
$633$		0			0
$634$	21.5784	+	15.4122i	0.856988	+	0.612096i
$635$	−4.04665			−0.160586
$636$		0			0
$637$	−4.59985			−0.182253
$638$	−6.21358	−	4.43799i	−0.245998	−	0.175702i
$639$		0			0
$640$	4.10020	+	10.5446i	0.162074	+	0.416812i
$641$			8.17846i			0.323030i	0.986870	+	0.161515i	$0.0516380\pi$
$641$			8.17846i			0.323030i	−0.986870	+	0.161515i	$0.948362\pi$
$642$		0			0
$643$		−	29.6547i		−	1.16947i	−0.811226	−	0.584733i	$-0.801199\pi$
$643$		−	29.6547i		−	1.16947i	0.811226	−	0.584733i	$-0.198801\pi$
$644$	−9.51796	+	3.26394i	−0.375060	+	0.128617i
$645$		0			0
$646$	−22.2574	+	31.1623i	−0.875704	+	1.22606i
$647$	−18.4489			−0.725299			−0.362650	−	0.931926i	$-0.618128\pi$
$647$	−18.4489			−0.725299			−0.362650	+	0.931926i	$0.618128\pi$
$648$		0			0
$649$	−4.75749			−0.186748
$650$	−0.952868	+	1.33410i	−0.0373746	+	0.0523277i
$651$		0			0
$652$	−13.1999	+	4.52655i	−0.516947	+	0.177274i
$653$		−	5.25538i		−	0.205659i	−0.994699	−	0.102829i	$-0.967210\pi$
$653$		−	5.25538i		−	0.205659i	0.994699	−	0.102829i	$-0.0327896\pi$
$654$		0			0
$655$		−	2.11548i		−	0.0826587i
$656$	−22.7540	−	29.2750i	−0.888394	−	1.14300i
$657$		0			0
$658$	16.5754	+	11.8388i	0.646178	+	0.461526i
$659$	−5.12900			−0.199798			−0.0998988	−	0.994998i	$-0.531852\pi$
$659$	−5.12900			−0.199798			−0.0998988	+	0.994998i	$0.531852\pi$
$660$		0			0
$661$	−51.0402			−1.98523			−0.992617	−	0.121288i	$-0.961297\pi$
$661$	−51.0402			−1.98523			−0.992617	+	0.121288i	$0.961297\pi$
$662$	34.1212	+	24.3708i	1.32616	+	0.947196i
$663$		0			0
$664$	−30.0576	−	8.96508i	−1.16646	−	0.347913i
$665$			9.41237i			0.364996i
$666$		0			0
$667$			11.4747i			0.444301i
$668$	−5.45885	−	15.9185i	−0.211209	−	0.615907i
$669$		0			0
$670$	4.64170	−	6.49878i	0.179324	−	0.251070i
$671$	3.48125			0.134392
$672$		0			0
$673$	−21.5381			−0.830232			−0.415116	−	0.909769i	$-0.636259\pi$
$673$	−21.5381			−0.830232			−0.415116	+	0.909769i	$0.636259\pi$
$674$	−27.8005	+	38.9232i	−1.07084	+	1.49927i
$675$		0			0
$676$	7.56204	+	22.0516i	0.290848	+	0.848140i
$677$		−	13.6880i		−	0.526071i	−0.964786	−	0.263036i	$-0.915276\pi$
$677$		−	13.6880i		−	0.526071i	0.964786	−	0.263036i	$-0.0847237\pi$
$678$		0			0
$679$		−	23.0492i		−	0.884545i
$680$	−13.5779	−	4.04979i	−0.520690	−	0.155302i
$681$		0			0
$682$	−1.75064	−	1.25038i	−0.0670355	−	0.0478795i
$683$	35.3198			1.35148			0.675738	−	0.737142i	$-0.263825\pi$
$683$	35.3198			1.35148			0.675738	+	0.737142i	$0.263825\pi$
$684$		0			0
$685$	5.47699			0.209265
$686$	−21.9787	−	15.6981i	−0.839149	−	0.599354i
$687$		0			0
$688$	−28.6580	−	36.8710i	−1.09258	−	1.40570i
$689$			5.75704i			0.219326i
$690$		0			0
$691$		−	27.6204i		−	1.05073i	−0.850877	−	0.525365i	$-0.823929\pi$
$691$		−	27.6204i		−	1.05073i	0.850877	−	0.525365i	$-0.176071\pi$
$692$	−36.6607	+	12.5718i	−1.39363	+	0.477910i
$693$		0			0
$694$	18.8490	−	26.3903i	0.715499	−	1.00176i
$695$	−22.0116			−0.834948
$696$		0			0
$697$	46.4354			1.75887
$698$	1.80997	−	2.53412i	0.0685083	−	0.0959177i
$699$		0			0
$700$	−3.29426	+	1.12968i	−0.124511	+	0.0426980i
$701$			10.3877i			0.392338i	0.980570	+	0.196169i	$0.0628501\pi$
$701$			10.3877i			0.392338i	−0.980570	+	0.196169i	$0.937150\pi$
$702$		0			0
$703$		−	16.3156i		−	0.615354i
$704$	−9.09904	−	5.95783i	−0.342933	−	0.224544i
$705$		0			0
$706$	−25.3807	−	18.1279i	−0.955214	−	0.682252i
$707$	−9.28994			−0.349384
$708$		0			0
$709$	9.35085			0.351179			0.175589	−	0.984464i	$-0.443817\pi$
$709$	9.35085			0.351179			0.175589	+	0.984464i	$0.443817\pi$
$710$	−16.0521	−	11.4650i	−0.602424	−	0.430276i
$711$		0			0
$712$	7.57396	−	25.3936i	0.283846	−	0.951664i
$713$			3.23293i			0.121074i
$714$		0			0
$715$		−	1.57602i		−	0.0589399i
$716$	6.49196	+	18.9312i	0.242616	+	0.707492i
$717$		0			0
$718$	−16.3412	+	22.8791i	−0.609849	+	0.853842i
$719$	−39.1679			−1.46072			−0.730358	−	0.683064i	$-0.760647\pi$
$719$	−39.1679			−1.46072			−0.730358	+	0.683064i	$0.760647\pi$
$720$		0			0
$721$	−26.0374			−0.969683
$722$	8.39911	−	11.7595i	0.312583	−	0.437643i
$723$		0			0
$724$	4.22564	+	12.3224i	0.157045	+	0.457958i
$725$			3.97150i			0.147498i
$726$		0			0
$727$			20.9691i			0.777700i	0.921301	+	0.388850i	$0.127128\pi$
$727$			20.9691i			0.777700i	−0.921301	+	0.388850i	$0.872872\pi$
$728$	1.63189	−	5.47131i	0.0604818	−	0.202780i
$729$		0			0
$730$	−12.3441	−	8.81669i	−0.456877	−	0.326320i
$731$	58.4842			2.16311
$732$		0			0
$733$	52.1208			1.92513			0.962564	−	0.271055i	$-0.0873727\pi$
$733$	52.1208			1.92513			0.962564	+	0.271055i	$0.0873727\pi$
$734$	7.78035	+	5.55704i	0.287178	+	0.205114i
$735$		0			0
$736$	0.661669	+	16.3307i	0.0243894	+	0.601957i
$737$			7.67726i			0.282796i
$738$		0			0
$739$		−	26.2861i		−	0.966950i	−0.875358	−	0.483475i	$-0.839374\pi$
$739$		−	26.2861i		−	0.966950i	0.875358	−	0.483475i	$-0.160626\pi$
$740$	5.71034	−	1.95821i	0.209916	−	0.0719853i
$741$		0			0
$742$	−7.10787	+	9.95164i	−0.260938	+	0.365336i
$743$	2.21190			0.0811466			0.0405733	−	0.999177i	$-0.487082\pi$
$743$	2.21190			0.0811466			0.0405733	+	0.999177i	$0.487082\pi$
$744$		0			0
$745$	12.7425			0.466848
$746$	10.9955	−	15.3947i	0.402575	−	0.563641i
$747$		0			0
$748$	12.8844	−	4.41836i	0.471099	−	0.161551i
$749$		−	27.3472i		−	0.999245i
$750$		0			0
$751$		−	6.63335i		−	0.242054i	−0.992649	−	0.121027i	$-0.961381\pi$
$751$		−	6.63335i		−	0.242054i	0.992649	−	0.121027i	$-0.0386188\pi$
$752$	26.1234	−	20.3044i	0.952622	−	0.740426i
$753$		0			0
$754$	−5.29838	−	3.78432i	−0.192956	−	0.137817i
$755$	−14.9159			−0.542843
$756$		0			0
$757$	48.2838			1.75490			0.877452	−	0.479664i	$-0.159241\pi$
$757$	48.2838			1.75490			0.877452	+	0.479664i	$0.159241\pi$
$758$	17.6664	+	12.6181i	0.641673	+	0.458309i
$759$		0			0
$760$	14.6510	+	4.36985i	0.531447	+	0.158511i
$761$			32.1481i			1.16537i	0.812699	+	0.582684i	$0.197998\pi$
$761$			32.1481i			1.16537i	−0.812699	+	0.582684i	$0.802002\pi$
$762$		0			0
$763$			7.57012i			0.274057i
$764$	−17.3991	−	50.7376i	−0.629479	−	1.83562i
$765$		0			0
$766$	9.43086	−	13.2040i	0.340751	−	0.477081i
$767$	−4.05676			−0.146481
$768$		0			0
$769$	32.5866			1.17510			0.587552	−	0.809187i	$-0.300092\pi$
$769$	32.5866			1.17510			0.587552	+	0.809187i	$0.300092\pi$
$770$	1.94582	−	2.72432i	0.0701225	−	0.0981776i
$771$		0			0
$772$	−3.71399	−	10.8304i	−0.133670	−	0.389793i
$773$		−	1.55573i		−	0.0559558i	−0.999609	−	0.0279779i	$-0.991093\pi$
$773$		−	1.55573i		−	0.0559558i	0.999609	−	0.0279779i	$-0.00890681\pi$
$774$		0			0
$775$			1.11895i			0.0401938i
$776$	−35.8776	−	10.7010i	−1.28793	−	0.384142i
$777$		0			0
$778$	−11.2393	−	8.02755i	−0.402948	−	0.287802i
$779$	−50.1052			−1.79521
$780$		0			0
$781$	18.9629			0.678547
$782$	−16.6566	−	11.8968i	−0.595639	−	0.425430i
$783$		0			0
$784$	−12.5315	+	9.74013i	−0.447555	+	0.347862i
$785$		−	0.158102i		−	0.00564292i
$786$		0			0
$787$		−	23.0137i		−	0.820351i	−0.912007	−	0.410175i	$-0.865467\pi$
$787$		−	23.0137i		−	0.820351i	0.912007	−	0.410175i	$-0.134533\pi$
$788$	−28.5400	+	9.78706i	−1.01670	+	0.348650i
$789$		0			0
$790$	−9.06916	+	12.6976i	−0.322666	+	0.451761i
$791$	−18.5618			−0.659982
$792$		0			0
$793$	2.96849			0.105414
$794$	−3.40580	+	4.76842i	−0.120867	+	0.169225i
$795$		0			0
$796$	32.9819	−	11.3103i	1.16901	−	0.400882i
$797$		−	50.6180i		−	1.79298i	−0.443064	−	0.896490i	$-0.646108\pi$
$797$		−	50.6180i		−	1.79298i	0.443064	−	0.896490i	$-0.353892\pi$
$798$		0			0
$799$			41.4364i			1.46592i
$800$	0.229010	+	5.65222i	0.00809674	+	0.199836i
$801$		0			0
$802$	−29.8737	−	21.3370i	−1.05488	−	0.753436i
$803$	14.5826			0.514609
$804$		0			0
$805$	−5.03103			−0.177320
$806$	−1.49279	−	1.06621i	−0.0525812	−	0.0375556i
$807$		0			0
$808$	−4.31301	+	14.4604i	−0.151731	+	0.508716i
$809$			29.7823i			1.04709i	0.851998	+	0.523545i	$0.175391\pi$
$809$			29.7823i			1.04709i	−0.851998	+	0.523545i	$0.824609\pi$
$810$		0			0
$811$			11.2021i			0.393360i	0.980468	+	0.196680i	$0.0630160\pi$
$811$			11.2021i			0.393360i	−0.980468	+	0.196680i	$0.936984\pi$
$812$	−4.48653	−	13.0832i	−0.157446	−	0.459129i
$813$		0			0
$814$	−3.37292	+	4.72239i	−0.118221	+	0.165520i
$815$	−6.97722			−0.244401
$816$		0			0
$817$	−63.1062			−2.20780
$818$	−30.1743	+	42.2467i	−1.05502	+	1.47712i
$819$		0			0
$820$	−6.01368	−	17.5365i	−0.210007	−	0.612400i
$821$			6.81943i			0.238000i	0.992894	+	0.119000i	$0.0379688\pi$
$821$			6.81943i			0.238000i	−0.992894	+	0.119000i	$0.962031\pi$
$822$		0			0
$823$		−	35.4043i		−	1.23412i	−0.786917	−	0.617059i	$-0.788324\pi$
$823$		−	35.4043i		−	1.23412i	0.786917	−	0.617059i	$-0.211676\pi$
$824$	−12.0883	+	40.5290i	−0.421116	+	1.41189i
$825$		0			0
$826$	−7.01253	−	5.00863i	−0.243997	−	0.174273i
$827$	−22.5867			−0.785418			−0.392709	−	0.919663i	$-0.628462\pi$
$827$	−22.5867			−0.785418			−0.392709	+	0.919663i	$0.628462\pi$
$828$		0			0
$829$	8.09060			0.280998			0.140499	−	0.990081i	$-0.455129\pi$
$829$	8.09060			0.280998			0.140499	+	0.990081i	$0.455129\pi$
$830$	−12.7621	−	9.11522i	−0.442979	−	0.316394i
$831$		0			0
$832$	−7.75884	−	5.08029i	−0.268989	−	0.176127i
$833$		−	19.8773i		−	0.688707i
$834$		0			0
$835$		−	8.41426i		−	0.291187i
$836$	−13.9026	+	4.76754i	−0.480832	+	0.164889i
$837$		0			0
$838$	−19.0237	+	26.6348i	−0.657162	+	0.920085i
$839$	−33.6024			−1.16008			−0.580042	−	0.814586i	$-0.696964\pi$
$839$	−33.6024			−1.16008			−0.580042	+	0.814586i	$0.696964\pi$
$840$		0			0
$841$	13.2272			0.456110
$842$	−31.5291	+	44.1436i	−1.08657	+	1.52129i
$843$		0			0
$844$	33.2364	−	11.3976i	1.14405	−	0.392321i
$845$			11.6561i			0.400982i
$846$		0			0
$847$		−	15.9358i		−	0.547562i
$848$	12.1905	+	15.6841i	0.418622	+	0.538594i
$849$		0			0
$850$	−5.76502	−	4.11761i	−0.197739	−	0.141233i
$851$	8.72087			0.298948
$852$		0			0
$853$	49.9296			1.70956			0.854778	−	0.518993i	$-0.173693\pi$
$853$	49.9296			1.70956			0.854778	+	0.518993i	$0.173693\pi$
$854$	5.13135	+	3.66502i	0.175591	+	0.125414i
$855$		0			0
$856$	−42.5678	−	12.6964i	−1.45494	−	0.433954i
$857$			19.3790i			0.661974i	0.943635	+	0.330987i	$0.107382\pi$
$857$			19.3790i			0.661974i	−0.943635	+	0.330987i	$0.892618\pi$
$858$		0			0
$859$			3.45436i			0.117861i	0.998262	+	0.0589305i	$0.0187690\pi$
$859$			3.45436i			0.117861i	−0.998262	+	0.0589305i	$0.981231\pi$
$860$	−7.57406	−	22.0867i	−0.258273	−	0.753151i
$861$		0			0
$862$	−20.6338	+	28.8892i	−0.702791	+	0.983969i
$863$	−9.29456			−0.316390			−0.158195	−	0.987408i	$-0.550568\pi$
$863$	−9.29456			−0.316390			−0.158195	+	0.987408i	$0.550568\pi$
$864$		0			0
$865$	−19.3782			−0.658879
$866$	11.7030	−	16.3852i	0.397684	−	0.556792i
$867$		0			0
$868$	−1.26406	−	3.68611i	−0.0429048	−	0.125115i
$869$		−	15.0002i		−	0.508847i
$870$		0			0
$871$			6.54647i			0.221819i
$872$	11.7834	+	3.51455i	0.399036	+	0.119018i
$873$		0			0
$874$	17.9730	+	12.8370i	0.607945	+	0.434219i
$875$	−1.74129			−0.0588663
$876$		0			0
$877$	−7.78775			−0.262974			−0.131487	−	0.991318i	$-0.541975\pi$
$877$	−7.78775			−0.262974			−0.131487	+	0.991318i	$0.541975\pi$
$878$	10.8238	+	7.73078i	0.365285	+	0.260901i
$879$		0			0
$880$	−3.33721	−	4.29361i	−0.112497	−	0.144738i
$881$			12.9152i			0.435124i	0.976047	+	0.217562i	$0.0698104\pi$
$881$			12.9152i			0.435124i	−0.976047	+	0.217562i	$0.930190\pi$
$882$		0			0
$883$		−	2.69260i		−	0.0906132i	−0.998973	−	0.0453066i	$-0.985574\pi$
$883$		−	2.69260i		−	0.0906132i	0.998973	−	0.0453066i	$-0.0144265\pi$
$884$	10.9866	−	3.76757i	0.369520	−	0.126717i
$885$		0			0
$886$	27.9220	−	39.0932i	0.938057	−	1.31336i
$887$	−46.9841			−1.57757			−0.788787	−	0.614667i	$-0.789290\pi$
$887$	−46.9841			−1.57757			−0.788787	+	0.614667i	$0.789290\pi$
$888$		0			0
$889$	7.04638			0.236328
$890$	7.70079	−	10.7818i	0.258131	−	0.361407i
$891$		0			0
$892$	7.56742	−	2.59505i	0.253376	−	0.0868887i
$893$		−	44.7112i		−	1.49620i
$894$		0			0
$895$			10.0067i			0.334487i
$896$	−7.13963	−	18.3612i	−0.238518	−	0.613404i
$897$		0			0
$898$	2.69781	+	1.92689i	0.0900271	+	0.0643010i
$899$	−4.44390			−0.148212
$900$		0			0
$901$	−24.8778			−0.828800
$902$	14.5025	+	10.3583i	0.482879	+	0.344892i
$903$		0			0
$904$	−8.61763	+	28.8927i	−0.286618	+	0.960958i
$905$			6.51340i			0.216513i
$906$		0			0
$907$		−	26.3971i		−	0.876501i	−0.898853	−	0.438250i	$-0.855598\pi$
$907$		−	26.3971i		−	0.876501i	0.898853	−	0.438250i	$-0.144402\pi$
$908$	−9.64879	−	28.1368i	−0.320206	−	0.933753i
$909$		0			0
$910$	1.65922	−	2.32305i	0.0550026	−	0.0770084i
$911$	−21.9089			−0.725875			−0.362938	−	0.931813i	$-0.618226\pi$
$911$	−21.9089			−0.725875			−0.362938	+	0.931813i	$0.618226\pi$
$912$		0			0
$913$	15.0764			0.498955
$914$	−16.7265	+	23.4186i	−0.553265	+	0.774619i
$915$		0			0
$916$	15.0548	+	43.9014i	0.497426	+	1.45054i
$917$			3.68366i			0.121645i
$918$		0			0
$919$		−	23.7234i		−	0.782564i	−0.920271	−	0.391282i	$-0.872032\pi$
$919$		−	23.7234i		−	0.782564i	0.920271	−	0.391282i	$-0.127968\pi$
$920$	−2.33574	+	7.83113i	−0.0770070	+	0.258185i
$921$		0			0
$922$	−18.2178	−	13.0119i	−0.599970	−	0.428523i
$923$	16.1699			0.532238
$924$		0			0
$925$	3.01838			0.0992438
$926$	6.62522	+	4.73200i	0.217718	+	0.155503i
$927$		0			0
$928$	−22.4478	+	0.909515i	−0.736885	+	0.0298563i
$929$			18.3538i			0.602170i	0.953597	+	0.301085i	$0.0973488\pi$
$929$			18.3538i			0.602170i	−0.953597	+	0.301085i	$0.902651\pi$
$930$		0			0
$931$			21.4482i			0.702936i
$932$	19.7882	−	6.78585i	0.648184	−	0.222278i
$933$		0			0
$934$	−11.1545	+	15.6173i	−0.364987	+	0.511014i
$935$	6.81044			0.222725
$936$		0			0
$937$	−48.9513			−1.59917			−0.799584	−	0.600554i	$-0.794947\pi$
$937$	−48.9513			−1.59917			−0.799584	+	0.600554i	$0.794947\pi$
$938$	−8.08253	+	11.3163i	−0.263904	+	0.369489i
$939$		0			0
$940$	15.6486	−	5.36628i	0.510401	−	0.175029i
$941$		−	55.9548i		−	1.82408i	−0.410106	−	0.912038i	$-0.634508\pi$
$941$		−	55.9548i		−	1.82408i	0.410106	−	0.912038i	$-0.365492\pi$
$942$		0			0
$943$		−	26.7818i		−	0.872137i
$944$	−11.0520	+	8.59013i	−0.359711	+	0.279585i
$945$		0			0
$946$	18.2655	+	13.0459i	0.593862	+	0.424160i
$947$	−44.0368			−1.43101			−0.715503	−	0.698610i	$-0.753802\pi$
$947$	−44.0368			−1.43101			−0.715503	+	0.698610i	$0.753802\pi$
$948$		0			0
$949$	12.4347			0.403648
$950$	6.22063	+	4.44303i	0.201824	+	0.144151i
$951$		0			0
$952$	23.6431	+	7.05186i	0.766277	+	0.228552i
$953$		−	4.87597i		−	0.157948i	−0.996877	−	0.0789741i	$-0.974836\pi$
$953$		−	4.87597i		−	0.157948i	0.996877	−	0.0789741i	$-0.0251644\pi$
$954$		0			0
$955$		−	26.8190i		−	0.867842i
$956$	−2.77565	−	8.09406i	−0.0897709	−	0.261781i
$957$		0			0
$958$	11.6741	−	16.3448i	0.377174	−	0.528076i
$959$	−9.53701			−0.307966
$960$		0			0
$961$	29.7480			0.959611
$962$	−2.87612	+	4.02682i	−0.0927298	+	0.129830i
$963$		0			0
$964$	−17.6839	−	51.5679i	−0.569559	−	1.66089i
$965$		−	5.72474i		−	0.184286i
$966$		0			0
$967$		−	44.9997i		−	1.44709i	−0.690277	−	0.723546i	$-0.742511\pi$
$967$		−	44.9997i		−	1.44709i	0.690277	−	0.723546i	$-0.257489\pi$
$968$	−24.8052	−	7.39847i	−0.797270	−	0.237796i
$969$		0			0
$970$	−15.2332	−	10.8802i	−0.489108	−	0.349341i
$971$	27.0511			0.868110			0.434055	−	0.900886i	$-0.357082\pi$
$971$	27.0511			0.868110			0.434055	+	0.900886i	$0.357082\pi$
$972$		0			0
$973$	38.3286			1.22876
$974$	29.1935	+	20.8512i	0.935421	+	0.668116i
$975$		0			0
$976$	8.08716	−	6.28575i	0.258864	−	0.201202i
$977$		−	24.8309i		−	0.794410i	−0.917730	−	0.397205i	$-0.869980\pi$
$977$		−	24.8309i		−	0.794410i	0.917730	−	0.397205i	$-0.130020\pi$
$978$		0			0
$979$			12.7369i			0.407075i
$980$	−7.50671	+	2.57423i	−0.239793	+	0.0822308i
$981$		0			0
$982$	−3.03562	+	4.25013i	−0.0968704	+	0.135627i
$983$	3.34535			0.106700			0.0533501	−	0.998576i	$-0.483010\pi$
$983$	3.34535			0.106700			0.0533501	+	0.998576i	$0.483010\pi$
$984$		0			0
$985$	−15.0858			−0.480672
$986$	16.3531	−	22.8958i	0.520789	−	0.729151i
$987$		0			0
$988$	−11.8549	+	4.06532i	−0.377154	+	0.129335i
$989$		−	33.7310i		−	1.07258i
$990$		0			0
$991$			19.7659i			0.627884i	0.949442	+	0.313942i	$0.101650\pi$
$991$			19.7659i			0.627884i	−0.949442	+	0.313942i	$0.898350\pi$
$992$	−6.32454	+	0.256251i	−0.200804	+	0.00813597i
$993$		0			0
$994$	27.9513	+	19.9640i	0.886562	+	0.633218i
$995$	17.4336			0.552683
$996$		0			0
$997$	−40.6056			−1.28599			−0.642996	−	0.765870i	$-0.722309\pi$
$997$	−40.6056			−1.28599			−0.642996	+	0.765870i	$0.722309\pi$
$998$	−2.41987	−	1.72837i	−0.0765996	−	0.0547105i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.a.971.16	yes	48
3.2	odd	2	inner	1620.2.e.a.971.33	yes	48
4.3	odd	2	inner	1620.2.e.a.971.34	yes	48
12.11	even	2	inner	1620.2.e.a.971.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.e.a.971.15	✓	48	12.11	even	2	inner
1620.2.e.a.971.16	yes	48	1.1	even	1	trivial
1620.2.e.a.971.33	yes	48	3.2	odd	2	inner
1620.2.e.a.971.34	yes	48	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.821961 + 1.15082i) q^{2} +(-0.648762 - 1.89185i) q^{4} -1.00000i q^{5} +1.74129i q^{7} +(2.71043 + 0.808422i) q^{8} +O(q^{10})\)	\(q+(-0.821961 + 1.15082i) q^{2} +(-0.648762 - 1.89185i) q^{4} -1.00000i q^{5} +1.74129i q^{7} +(2.71043 + 0.808422i) q^{8} +(1.15082 + 0.821961i) q^{10} -1.35950 q^{11} -1.15926 q^{13} +(-2.00391 - 1.43127i) q^{14} +(-3.15822 + 2.45472i) q^{16} -5.00950i q^{17} +5.40540i q^{19} +(-1.89185 + 0.648762i) q^{20} +(1.11746 - 1.56454i) q^{22} -2.88925 q^{23} -1.00000 q^{25} +(0.952868 - 1.33410i) q^{26} +(3.29426 - 1.12968i) q^{28} -3.97150i q^{29} -1.11895i q^{31} +(-0.229010 - 5.65222i) q^{32} +(5.76502 + 4.11761i) q^{34} +1.74129 q^{35} -3.01838 q^{37} +(-6.22063 - 4.44303i) q^{38} +(0.808422 - 2.71043i) q^{40} +9.26947i q^{41} +11.6746i q^{43} +(0.881995 + 2.57198i) q^{44} +(2.37485 - 3.32500i) q^{46} -8.27157 q^{47} +3.96791 q^{49} +(0.821961 - 1.15082i) q^{50} +(0.752085 + 2.19315i) q^{52} -4.96612i q^{53} +1.35950i q^{55} +(-1.40770 + 4.71965i) q^{56} +(4.57047 + 3.26442i) q^{58} +3.49943 q^{59} -2.56067 q^{61} +(1.28770 + 0.919731i) q^{62} +(6.69291 + 4.38235i) q^{64} +1.15926i q^{65} -5.64710i q^{67} +(-9.47724 + 3.24997i) q^{68} +(-1.43127 + 2.00391i) q^{70} -13.9484 q^{71} -10.7264 q^{73} +(2.48099 - 3.47361i) q^{74} +(10.2262 - 3.50682i) q^{76} -2.36729i q^{77} +11.0336i q^{79} +(2.45472 + 3.15822i) q^{80} +(-10.6675 - 7.61914i) q^{82} -11.0896 q^{83} -5.00950 q^{85} +(-13.4354 - 9.59610i) q^{86} +(-3.68485 - 1.09905i) q^{88} -9.36881i q^{89} -2.01861i q^{91} +(1.87444 + 5.46604i) q^{92} +(6.79890 - 9.51906i) q^{94} +5.40540 q^{95} -13.2368 q^{97} +(-3.26147 + 4.56634i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) \) 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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