LMFDB - Embedded newform 2646.2.m.c.1763.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1763.21
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.c.881.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.724499 - 1.25487i) q^{5} +1.00000i q^{8} -1.44900i q^{10} +(1.21051 + 0.698887i) q^{11} +(-3.03494 + 1.75222i) q^{13} +(-0.500000 + 0.866025i) q^{16} -7.90553 q^{17} +4.16869i q^{19} +(0.724499 - 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(3.13371 - 1.80925i) q^{23} +(1.45020 - 2.51182i) q^{25} -3.50444 q^{26} +(-4.06467 - 2.34674i) q^{29} +(0.794387 - 0.458640i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.84639 - 3.95277i) q^{34} -4.28351 q^{37} +(-2.08434 + 3.61019i) q^{38} +(1.25487 - 0.724499i) q^{40} +(0.343727 + 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +1.39777i q^{44} +3.61850 q^{46} +(-4.15872 + 7.20312i) q^{47} +(2.51182 - 1.45020i) q^{50} +(-3.03494 - 1.75222i) q^{52} -5.96029i q^{53} -2.02537i q^{55} +(-2.34674 - 4.06467i) q^{58} +(-4.72065 - 8.17641i) q^{59} +(-8.53864 - 4.92979i) q^{61} +0.917280 q^{62} -1.00000 q^{64} +(4.39762 + 2.53897i) q^{65} +(1.48540 + 2.57278i) q^{67} +(-3.95277 - 6.84639i) q^{68} +12.9436i q^{71} -11.3053i q^{73} +(-3.70963 - 2.14176i) q^{74} +(-3.61019 + 2.08434i) q^{76} +(-7.81709 + 13.5396i) q^{79} +1.44900 q^{80} +0.687454i q^{82} +(-4.11183 + 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(-10.4182 + 6.01497i) q^{86} +(-0.698887 + 1.21051i) q^{88} +1.06683 q^{89} +(3.13371 + 1.80925i) q^{92} +(-7.20312 + 4.15872i) q^{94} +(5.23116 - 3.02021i) q^{95} +(10.9670 + 6.33179i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 48 * q^11 - 24 * q^16 - 48 * q^23 - 24 * q^25 + 48 * q^50 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 96 * q^86 - 48 * q^92 + 192 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.724499	−	1.25487i	−0.324006	−	0.561195i	0.657305	−	0.753625i	$-0.271696\pi$
$5$	−0.724499	−	1.25487i	−0.324006	−	0.561195i	−0.981311	+	0.192430i	$0.938363\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$		−	1.44900i		−	0.458214i
$11$	1.21051	+	0.698887i	0.364982	+	0.210722i	0.671264	−	0.741218i	$-0.265752\pi$
$11$	1.21051	+	0.698887i	0.364982	+	0.210722i	−0.306282	+	0.951941i	$0.599085\pi$
$12$		0			0
$13$	−3.03494	+	1.75222i	−0.841740	+	0.485979i	−0.857855	−	0.513891i	$-0.828204\pi$
$13$	−3.03494	+	1.75222i	−0.841740	+	0.485979i	0.0161150	+	0.999870i	$0.494870\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−7.90553			−1.91737			−0.958687	−	0.284464i	$-0.908184\pi$
$17$	−7.90553			−1.91737			−0.958687	+	0.284464i	$0.908184\pi$
$18$		0			0
$19$			4.16869i			0.956363i	0.878261	+	0.478181i	$0.158704\pi$
$19$			4.16869i			0.956363i	−0.878261	+	0.478181i	$0.841296\pi$
$20$	0.724499	−	1.25487i	0.162003	−	0.280597i
$21$		0			0
$22$	0.698887	+	1.21051i	0.149003	+	0.258081i
$23$	3.13371	−	1.80925i	0.653424	−	0.377255i	−0.136343	−	0.990662i	$-0.543535\pi$
$23$	3.13371	−	1.80925i	0.653424	−	0.377255i	0.789767	+	0.613407i	$0.210202\pi$
$24$		0			0
$25$	1.45020	−	2.51182i	0.290040	−	0.502364i
$26$	−3.50444			−0.687278
$27$		0			0
$28$		0			0
$29$	−4.06467	−	2.34674i	−0.754791	−	0.435779i	0.0726316	−	0.997359i	$-0.476860\pi$
$29$	−4.06467	−	2.34674i	−0.754791	−	0.435779i	−0.827422	+	0.561580i	$0.810194\pi$
$30$		0			0
$31$	0.794387	−	0.458640i	0.142676	−	0.0823741i	−0.426963	−	0.904269i	$-0.640416\pi$
$31$	0.794387	−	0.458640i	0.142676	−	0.0823741i	0.569639	+	0.821895i	$0.307083\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−6.84639	−	3.95277i	−1.17415	−	0.677894i
$35$		0			0
$36$		0			0
$37$	−4.28351			−0.704205			−0.352103	−	0.935961i	$-0.614533\pi$
$37$	−4.28351			−0.704205			−0.352103	+	0.935961i	$0.614533\pi$
$38$	−2.08434	+	3.61019i	−0.338125	+	0.585650i
$39$		0			0
$40$	1.25487	−	0.724499i	0.198412	−	0.114553i
$41$	0.343727	+	0.595352i	0.0536811	+	0.0929784i	0.891617	−	0.452790i	$-0.149571\pi$
$41$	0.343727	+	0.595352i	0.0536811	+	0.0929784i	−0.837936	+	0.545768i	$0.816238\pi$
$42$		0			0
$43$	−6.01497	+	10.4182i	−0.917275	+	1.58877i	−0.113739	+	0.993511i	$0.536283\pi$
$43$	−6.01497	+	10.4182i	−0.917275	+	1.58877i	−0.803536	+	0.595256i	$0.797051\pi$
$44$			1.39777i			0.210722i
$45$		0			0
$46$	3.61850			0.533519
$47$	−4.15872	+	7.20312i	−0.606612	+	1.05068i	0.385182	+	0.922840i	$0.374139\pi$
$47$	−4.15872	+	7.20312i	−0.606612	+	1.05068i	−0.991794	+	0.127842i	$0.959195\pi$
$48$		0			0
$49$		0			0
$50$	2.51182	−	1.45020i	0.355225	−	0.205089i
$51$		0			0
$52$	−3.03494	−	1.75222i	−0.420870	−	0.242990i
$53$		−	5.96029i		−	0.818709i	−0.912375	−	0.409354i	$-0.865754\pi$
$53$		−	5.96029i		−	0.818709i	0.912375	−	0.409354i	$-0.134246\pi$
$54$		0			0
$55$		−	2.02537i		−	0.273101i
$56$		0			0
$57$		0			0
$58$	−2.34674	−	4.06467i	−0.308142	−	0.533718i
$59$	−4.72065	−	8.17641i	−0.614577	−	1.06448i	−0.990459	−	0.137810i	$-0.955994\pi$
$59$	−4.72065	−	8.17641i	−0.614577	−	1.06448i	0.375882	−	0.926668i	$-0.377340\pi$
$60$		0			0
$61$	−8.53864	−	4.92979i	−1.09326	−	0.631194i	−0.158818	−	0.987308i	$-0.550768\pi$
$61$	−8.53864	−	4.92979i	−1.09326	−	0.631194i	−0.934443	+	0.356113i	$0.884102\pi$
$62$	0.917280			0.116495
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.39762	+	2.53897i	0.545458	+	0.314920i
$66$		0			0
$67$	1.48540	+	2.57278i	0.181470	+	0.314315i	0.942381	−	0.334541i	$-0.108581\pi$
$67$	1.48540	+	2.57278i	0.181470	+	0.314315i	−0.760911	+	0.648856i	$0.775248\pi$
$68$	−3.95277	−	6.84639i	−0.479343	−	0.830247i
$69$		0			0
$70$		0			0
$71$			12.9436i			1.53612i	0.640377	+	0.768061i	$0.278778\pi$
$71$			12.9436i			1.53612i	−0.640377	+	0.768061i	$0.721222\pi$
$72$		0			0
$73$		−	11.3053i		−	1.32319i	−0.749862	−	0.661595i	$-0.769880\pi$
$73$		−	11.3053i		−	1.32319i	0.749862	−	0.661595i	$-0.230120\pi$
$74$	−3.70963	−	2.14176i	−0.431236	−	0.248974i
$75$		0			0
$76$	−3.61019	+	2.08434i	−0.414117	+	0.239091i
$77$		0			0
$78$		0			0
$79$	−7.81709	+	13.5396i	−0.879491	+	1.52332i	−0.0275906	+	0.999619i	$0.508783\pi$
$79$	−7.81709	+	13.5396i	−0.879491	+	1.52332i	−0.851900	+	0.523704i	$0.824550\pi$
$80$	1.44900			0.162003
$81$		0			0
$82$			0.687454i			0.0759166i
$83$	−4.11183	+	7.12189i	−0.451332	+	0.781729i	−0.998469	−	0.0553135i	$-0.982384\pi$
$83$	−4.11183	+	7.12189i	−0.451332	+	0.781729i	0.547137	+	0.837043i	$0.315718\pi$
$84$		0			0
$85$	5.72755	+	9.92041i	0.621240	+	1.07602i
$86$	−10.4182	+	6.01497i	−1.12343	+	0.648611i
$87$		0			0
$88$	−0.698887	+	1.21051i	−0.0745016	+	0.129041i
$89$	1.06683			0.113084			0.0565421	−	0.998400i	$-0.481992\pi$
$89$	1.06683			0.113084			0.0565421	+	0.998400i	$0.481992\pi$
$90$		0			0
$91$		0			0
$92$	3.13371	+	1.80925i	0.326712	+	0.188627i
$93$		0			0
$94$	−7.20312	+	4.15872i	−0.742945	+	0.428939i
$95$	5.23116	−	3.02021i	0.536706	−	0.309867i
$96$		0			0
$97$	10.9670	+	6.33179i	1.11353	+	0.642895i	0.939741	−	0.341888i	$-0.111066\pi$
$97$	10.9670	+	6.33179i	1.11353	+	0.642895i	0.173787	+	0.984783i	$0.444400\pi$
$98$		0			0
$99$		0			0
$100$	2.90040			0.290040
$101$	−8.77726	+	15.2027i	−0.873370	+	1.51272i	−0.0148801	+	0.999889i	$0.504737\pi$
$101$	−8.77726	+	15.2027i	−0.873370	+	1.51272i	−0.858489	+	0.512831i	$0.828597\pi$
$102$		0			0
$103$	3.86082	−	2.22905i	0.380418	−	0.219635i	−0.297582	−	0.954696i	$-0.596180\pi$
$103$	3.86082	−	2.22905i	0.380418	−	0.219635i	0.678000	+	0.735062i	$0.262847\pi$
$104$	−1.75222	−	3.03494i	−0.171820	−	0.297600i
$105$		0			0
$106$	2.98014	−	5.16176i	0.289457	−	0.501355i
$107$			2.36213i			0.228356i	0.993460	+	0.114178i	$0.0364233\pi$
$107$			2.36213i			0.228356i	−0.993460	+	0.114178i	$0.963577\pi$
$108$		0			0
$109$	12.9955			1.24475			0.622373	−	0.782721i	$-0.286169\pi$
$109$	12.9955			1.24475			0.622373	+	0.782721i	$0.286169\pi$
$110$	1.01269	−	1.75402i	0.0965558	−	0.167240i
$111$		0			0
$112$		0			0
$113$	−2.90616	+	1.67787i	−0.273388	+	0.157841i	−0.630426	−	0.776249i	$-0.717120\pi$
$113$	−2.90616	+	1.67787i	−0.273388	+	0.157841i	0.357038	+	0.934090i	$0.383787\pi$
$114$		0			0
$115$	−4.54074	−	2.62160i	−0.423427	−	0.244465i
$116$		−	4.69348i		−	0.435779i
$117$		0			0
$118$		−	9.44130i		−	0.869143i
$119$		0			0
$120$		0			0
$121$	−4.52311	−	7.83426i	−0.411192	−	0.712206i
$122$	−4.92979	−	8.53864i	−0.446322	−	0.773052i
$123$		0			0
$124$	0.794387	+	0.458640i	0.0713381	+	0.0411871i
$125$	−11.4477			−1.02391
$126$		0			0
$127$	−12.9075			−1.14535			−0.572677	−	0.819781i	$-0.694095\pi$
$127$	−12.9075			−1.14535			−0.572677	+	0.819781i	$0.694095\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	2.53897	+	4.39762i	0.222682	+	0.385697i
$131$	−4.12856	−	7.15088i	−0.360714	−	0.624775i	0.627364	−	0.778726i	$-0.284134\pi$
$131$	−4.12856	−	7.15088i	−0.360714	−	0.624775i	−0.988079	+	0.153951i	$0.950800\pi$
$132$		0			0
$133$		0			0
$134$			2.97079i			0.256637i
$135$		0			0
$136$		−	7.90553i		−	0.677894i
$137$	−11.3267	−	6.53946i	−0.967703	−	0.558703i	−0.0691676	−	0.997605i	$-0.522034\pi$
$137$	−11.3267	−	6.53946i	−0.967703	−	0.558703i	−0.898535	+	0.438902i	$0.855368\pi$
$138$		0			0
$139$	10.6722	−	6.16162i	0.905207	−	0.522621i	0.0263210	−	0.999654i	$-0.491621\pi$
$139$	10.6722	−	6.16162i	0.905207	−	0.522621i	0.878886	+	0.477032i	$0.158287\pi$
$140$		0			0
$141$		0			0
$142$	−6.47179	+	11.2095i	−0.543101	+	0.940678i
$143$	−4.89842			−0.409627
$144$		0			0
$145$			6.80085i			0.564780i
$146$	5.65267	−	9.79071i	0.467818	−	0.810285i
$147$		0			0
$148$	−2.14176	−	3.70963i	−0.176051	−	0.304930i
$149$	0.538692	−	0.311014i	0.0441314	−	0.0254792i	−0.477772	−	0.878484i	$-0.658555\pi$
$149$	0.538692	−	0.311014i	0.0441314	−	0.0254792i	0.521903	+	0.853005i	$0.325222\pi$
$150$		0			0
$151$	10.5911	−	18.3443i	0.861889	−	1.49284i	−0.00821353	−	0.999966i	$-0.502614\pi$
$151$	10.5911	−	18.3443i	0.861889	−	1.49284i	0.870103	−	0.492870i	$-0.164052\pi$
$152$	−4.16869			−0.338125
$153$		0			0
$154$		0			0
$155$	−1.15107	−	0.664569i	−0.0924559	−	0.0533794i
$156$		0			0
$157$	−13.0158	+	7.51469i	−1.03878	+	0.599737i	−0.919486	−	0.393122i	$-0.871395\pi$
$157$	−13.0158	+	7.51469i	−1.03878	+	0.599737i	−0.119289	+	0.992860i	$0.538062\pi$
$158$	−13.5396	+	7.81709i	−1.07715	+	0.621894i
$159$		0			0
$160$	1.25487	+	0.724499i	0.0992062	+	0.0572767i
$161$		0			0
$162$		0			0
$163$	−3.03527			−0.237741			−0.118871	−	0.992910i	$-0.537927\pi$
$163$	−3.03527			−0.237741			−0.118871	+	0.992910i	$0.537927\pi$
$164$	−0.343727	+	0.595352i	−0.0268406	+	0.0464892i
$165$		0			0
$166$	−7.12189	+	4.11183i	−0.552766	+	0.319140i
$167$	3.05895	+	5.29826i	0.236709	+	0.409992i	0.959768	−	0.280794i	$-0.0905979\pi$
$167$	3.05895	+	5.29826i	0.236709	+	0.409992i	−0.723059	+	0.690786i	$0.757265\pi$
$168$		0			0
$169$	−0.359433	+	0.622557i	−0.0276487	+	0.0478890i
$170$			11.4551i			0.878567i
$171$		0			0
$172$	−12.0299			−0.917275
$173$	1.14757	−	1.98766i	0.0872484	−	0.151119i	−0.819099	−	0.573653i	$-0.805526\pi$
$173$	1.14757	−	1.98766i	0.0872484	−	0.151119i	0.906347	+	0.422534i	$0.138859\pi$
$174$		0			0
$175$		0			0
$176$	−1.21051	+	0.698887i	−0.0912454	+	0.0526806i
$177$		0			0
$178$	0.923906	+	0.533417i	0.0692497	+	0.0399813i
$179$		−	3.37592i		−	0.252328i	−0.992009	−	0.126164i	$-0.959733\pi$
$179$		−	3.37592i		−	0.252328i	0.992009	−	0.126164i	$-0.0402666\pi$
$180$		0			0
$181$		−	1.68857i		−	0.125511i	−0.998029	−	0.0627553i	$-0.980011\pi$
$181$		−	1.68857i		−	0.125511i	0.998029	−	0.0627553i	$-0.0199888\pi$
$182$		0			0
$183$		0			0
$184$	1.80925	+	3.13371i	0.133380	+	0.231020i
$185$	3.10340	+	5.37525i	0.228167	+	0.395196i
$186$		0			0
$187$	−9.56971	−	5.52507i	−0.699806	−	0.404033i
$188$	−8.31745			−0.606612
$189$		0			0
$190$	6.04043			0.438219
$191$	7.74947	+	4.47416i	0.560732	+	0.323739i	0.753439	−	0.657517i	$-0.228393\pi$
$191$	7.74947	+	4.47416i	0.560732	+	0.323739i	−0.192707	+	0.981256i	$0.561727\pi$
$192$		0			0
$193$	−12.8028	−	22.1751i	−0.921564	−	1.59620i	−0.796996	−	0.603984i	$-0.793579\pi$
$193$	−12.8028	−	22.1751i	−0.921564	−	1.59620i	−0.124568	−	0.992211i	$-0.539754\pi$
$194$	6.33179	+	10.9670i	0.454596	+	0.787383i
$195$		0			0
$196$		0			0
$197$			23.5602i			1.67860i	0.543670	+	0.839299i	$0.317034\pi$
$197$			23.5602i			1.67860i	−0.543670	+	0.839299i	$0.682966\pi$
$198$		0			0
$199$		−	13.6242i		−	0.965796i	−0.875677	−	0.482898i	$-0.839584\pi$
$199$		−	13.6242i		−	0.965796i	0.875677	−	0.482898i	$-0.160416\pi$
$200$	2.51182	+	1.45020i	0.177613	+	0.102545i
$201$		0			0
$202$	−15.2027	+	8.77726i	−1.06965	+	0.617566i
$203$		0			0
$204$		0			0
$205$	0.498060	−	0.862665i	0.0347860	−	0.0602511i
$206$	4.45810			0.310610
$207$		0			0
$208$		−	3.50444i		−	0.242990i
$209$	−2.91344	+	5.04623i	−0.201527	+	0.349055i
$210$		0			0
$211$	−10.7961	−	18.6994i	−0.743235	−	1.28732i	−0.951015	−	0.309145i	$-0.899957\pi$
$211$	−10.7961	−	18.6994i	−0.743235	−	1.28732i	0.207780	−	0.978176i	$-0.433376\pi$
$212$	5.16176	−	2.98014i	0.354511	−	0.204677i
$213$		0			0
$214$	−1.18106	+	2.04566i	−0.0807359	+	0.139839i
$215$	17.4314			1.18881
$216$		0			0
$217$		0			0
$218$	11.2545	+	6.49776i	0.762248	+	0.440084i
$219$		0			0
$220$	1.75402	−	1.01269i	0.118256	−	0.0682753i
$221$	23.9928	−	13.8523i	1.61393	−	0.931803i
$222$		0			0
$223$	14.5710	+	8.41256i	0.975745	+	0.563347i	0.900983	−	0.433855i	$-0.142847\pi$
$223$	14.5710	+	8.41256i	0.975745	+	0.563347i	0.0747620	+	0.997201i	$0.476180\pi$
$224$		0			0
$225$		0			0
$226$	−3.35574			−0.223221
$227$	6.11065	−	10.5840i	0.405578	−	0.702482i	−0.588810	−	0.808271i	$-0.700404\pi$
$227$	6.11065	−	10.5840i	0.405578	−	0.702482i	0.994389	+	0.105789i	$0.0337369\pi$
$228$		0			0
$229$	16.8458	−	9.72591i	1.11320	−	0.642706i	0.173543	−	0.984826i	$-0.444478\pi$
$229$	16.8458	−	9.72591i	1.11320	−	0.642706i	0.939656	+	0.342120i	$0.111145\pi$
$230$	−2.62160	−	4.54074i	−0.172863	−	0.299408i
$231$		0			0
$232$	2.34674	−	4.06467i	0.154071	−	0.266859i
$233$			28.5651i			1.87136i	0.352848	+	0.935681i	$0.385213\pi$
$233$			28.5651i			1.87136i	−0.352848	+	0.935681i	$0.614787\pi$
$234$		0			0
$235$	12.0520			0.786184
$236$	4.72065	−	8.17641i	0.307288	−	0.532239i
$237$		0			0
$238$		0			0
$239$	10.0020	−	5.77465i	0.646975	−	0.373531i	−0.140322	−	0.990106i	$-0.544814\pi$
$239$	10.0020	−	5.77465i	0.646975	−	0.373531i	0.787296	+	0.616575i	$0.211480\pi$
$240$		0			0
$241$	0.0299000	+	0.0172628i	0.00192603	+	0.00111199i	0.500963	−	0.865469i	$-0.332979\pi$
$241$	0.0299000	+	0.0172628i	0.00192603	+	0.00111199i	−0.499037	+	0.866581i	$0.666313\pi$
$242$		−	9.04623i		−	0.581514i
$243$		0			0
$244$		−	9.85957i		−	0.631194i
$245$		0			0
$246$		0			0
$247$	−7.30447	−	12.6517i	−0.464772	−	0.805009i
$248$	0.458640	+	0.794387i	0.0291237	+	0.0504437i
$249$		0			0
$250$	−9.91398	−	5.72384i	−0.627015	−	0.362007i
$251$	3.26317			0.205969			0.102985	−	0.994683i	$-0.467161\pi$
$251$	3.26317			0.205969			0.102985	+	0.994683i	$0.467161\pi$
$252$		0			0
$253$	5.05784			0.317984
$254$	−11.1782	−	6.45374i	−0.701383	−	0.404944i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.89851	+	17.1447i	0.617452	+	1.06946i	0.989949	+	0.141425i	$0.0451685\pi$
$257$	9.89851	+	17.1447i	0.617452	+	1.06946i	−0.372497	+	0.928034i	$0.621498\pi$
$258$		0			0
$259$		0			0
$260$			5.07794i			0.314920i
$261$		0			0
$262$		−	8.25713i		−	0.510127i
$263$	15.2576	+	8.80897i	0.940823	+	0.543184i	0.890218	−	0.455535i	$-0.150552\pi$
$263$	15.2576	+	8.80897i	0.940823	+	0.543184i	0.0506045	+	0.998719i	$0.483885\pi$
$264$		0			0
$265$	−7.47939	+	4.31823i	−0.459455	+	0.265266i
$266$		0			0
$267$		0			0
$268$	−1.48540	+	2.57278i	−0.0907350	+	0.157158i
$269$	7.67344			0.467858			0.233929	−	0.972254i	$-0.424842\pi$
$269$	7.67344			0.467858			0.233929	+	0.972254i	$0.424842\pi$
$270$		0			0
$271$			7.03381i			0.427273i	0.976913	+	0.213637i	$0.0685309\pi$
$271$			7.03381i			0.427273i	−0.976913	+	0.213637i	$0.931469\pi$
$272$	3.95277	−	6.84639i	0.239672	−	0.415123i
$273$		0			0
$274$	−6.53946	−	11.3267i	−0.395063	−	0.684269i
$275$	3.51096	−	2.02705i	0.211719	−	0.122236i
$276$		0			0
$277$	−8.65364	+	14.9885i	−0.519947	+	0.900575i	0.479784	+	0.877387i	$0.340715\pi$
$277$	−8.65364	+	14.9885i	−0.519947	+	0.900575i	−0.999731	+	0.0231880i	$0.992618\pi$
$278$	12.3232			0.739098
$279$		0			0
$280$		0			0
$281$	−14.3155	−	8.26508i	−0.853994	−	0.493053i	0.00800273	−	0.999968i	$-0.497453\pi$
$281$	−14.3155	−	8.26508i	−0.853994	−	0.493053i	−0.861996	+	0.506915i	$0.830786\pi$
$282$		0			0
$283$	−2.73910	+	1.58142i	−0.162823	+	0.0940057i	−0.579197	−	0.815187i	$-0.696634\pi$
$283$	−2.73910	+	1.58142i	−0.162823	+	0.0940057i	0.416374	+	0.909193i	$0.363301\pi$
$284$	−11.2095	+	6.47179i	−0.665160	+	0.384030i
$285$		0			0
$286$	−4.24216	−	2.44921i	−0.250844	−	0.144825i
$287$		0			0
$288$		0			0
$289$	45.4974			2.67632
$290$	−3.40042	+	5.88971i	−0.199680	+	0.345855i
$291$		0			0
$292$	9.79071	−	5.65267i	0.572958	−	0.330797i
$293$	4.26045	+	7.37932i	0.248898	+	0.431104i	0.963220	−	0.268713i	$-0.0865982\pi$
$293$	4.26045	+	7.37932i	0.248898	+	0.431104i	−0.714322	+	0.699817i	$0.753265\pi$
$294$		0			0
$295$	−6.84022	+	11.8476i	−0.398253	+	0.689794i
$296$		−	4.28351i		−	0.248974i
$297$		0			0
$298$	0.622028			0.0360331
$299$	−6.34042	+	10.9819i	−0.366676	+	0.635101i
$300$		0			0
$301$		0			0
$302$	18.3443	−	10.5911i	1.05559	−	0.609448i
$303$		0			0
$304$	−3.61019	−	2.08434i	−0.207059	−	0.119545i
$305$			14.2865i			0.818043i
$306$		0			0
$307$		−	25.0805i		−	1.43142i	−0.698398	−	0.715710i	$-0.746103\pi$
$307$		−	25.0805i		−	1.43142i	0.698398	−	0.715710i	$-0.253897\pi$
$308$		0			0
$309$		0			0
$310$	−0.664569	−	1.15107i	−0.0377450	−	0.0653762i
$311$	1.78678	+	3.09479i	0.101319	+	0.175489i	0.912228	−	0.409682i	$-0.134360\pi$
$311$	1.78678	+	3.09479i	0.101319	+	0.175489i	−0.810909	+	0.585172i	$0.801027\pi$
$312$		0			0
$313$	11.8033	+	6.81464i	0.667162	+	0.385186i	0.795000	−	0.606609i	$-0.207471\pi$
$313$	11.8033	+	6.81464i	0.667162	+	0.385186i	−0.127838	+	0.991795i	$0.540804\pi$
$314$	−15.0294			−0.848157
$315$		0			0
$316$	−15.6342			−0.879491
$317$	−3.71520	−	2.14497i	−0.208666	−	0.120474i	0.392025	−	0.919955i	$-0.371775\pi$
$317$	−3.71520	−	2.14497i	−0.208666	−	0.120474i	−0.600692	+	0.799481i	$0.705108\pi$
$318$		0			0
$319$	−3.28021	−	5.68149i	−0.183657	−	0.318102i
$320$	0.724499	+	1.25487i	0.0405007	+	0.0701494i
$321$		0			0
$322$		0			0
$323$		−	32.9557i		−	1.83370i
$324$		0			0
$325$			10.1643i			0.563814i
$326$	−2.62863	−	1.51764i	−0.145586	−	0.0840542i
$327$		0			0
$328$	−0.595352	+	0.343727i	−0.0328728	+	0.0189791i
$329$		0			0
$330$		0			0
$331$	−4.46962	+	7.74160i	−0.245672	+	0.425517i	−0.962320	−	0.271918i	$-0.912342\pi$
$331$	−4.46962	+	7.74160i	−0.245672	+	0.425517i	0.716648	+	0.697435i	$0.245675\pi$
$332$	−8.22365			−0.451332
$333$		0			0
$334$			6.11791i			0.334757i
$335$	2.15234	−	3.72796i	0.117595	−	0.203680i
$336$		0			0
$337$	0.0729773	+	0.126400i	0.00397532	+	0.00688546i	0.868006	−	0.496553i	$-0.165401\pi$
$337$	0.0729773	+	0.126400i	0.00397532	+	0.00688546i	−0.864031	+	0.503439i	$0.832068\pi$
$338$	−0.622557	+	0.359433i	−0.0338626	+	0.0195506i
$339$		0			0
$340$	−5.72755	+	9.92041i	−0.310620	+	0.538010i
$341$	1.28215			0.0694323
$342$		0			0
$343$		0			0
$344$	−10.4182	−	6.01497i	−0.561714	−	0.324306i
$345$		0			0
$346$	1.98766	−	1.14757i	0.106857	−	0.0616939i
$347$	19.2988	−	11.1422i	1.03602	−	0.598144i	0.117313	−	0.993095i	$-0.462572\pi$
$347$	19.2988	−	11.1422i	1.03602	−	0.598144i	0.918702	+	0.394951i	$0.129238\pi$
$348$		0			0
$349$	2.79851	+	1.61572i	0.149801	+	0.0864876i	0.573027	−	0.819537i	$-0.305769\pi$
$349$	2.79851	+	1.61572i	0.149801	+	0.0864876i	−0.423226	+	0.906024i	$0.639102\pi$
$350$		0			0
$351$		0			0
$352$	−1.39777			−0.0745016
$353$	−3.13232	+	5.42533i	−0.166716	+	0.288761i	−0.937263	−	0.348622i	$-0.886650\pi$
$353$	−3.13232	+	5.42533i	−0.166716	+	0.288761i	0.770547	+	0.637383i	$0.219983\pi$
$354$		0			0
$355$	16.2425	−	9.37762i	0.862063	−	0.497712i
$356$	0.533417	+	0.923906i	0.0282711	+	0.0489669i
$357$		0			0
$358$	1.68796	−	2.92364i	0.0892116	−	0.154519i
$359$		−	12.0693i		−	0.636991i	−0.947924	−	0.318496i	$-0.896822\pi$
$359$		−	12.0693i		−	0.636991i	0.947924	−	0.318496i	$-0.103178\pi$
$360$		0			0
$361$	1.62203			0.0853700
$362$	0.844286	−	1.46235i	0.0443747	−	0.0768592i
$363$		0			0
$364$		0			0
$365$	−14.1867	+	8.19071i	−0.742567	+	0.428721i
$366$		0			0
$367$	14.7907	+	8.53940i	0.772067	+	0.445753i	0.833611	−	0.552351i	$-0.186269\pi$
$367$	14.7907	+	8.53940i	0.772067	+	0.445753i	−0.0615446	+	0.998104i	$0.519603\pi$
$368$			3.61850i			0.188627i
$369$		0			0
$370$			6.20681i			0.322677i
$371$		0			0
$372$		0			0
$373$	−1.93680	−	3.35463i	−0.100284	−	0.173696i	0.811518	−	0.584328i	$-0.198642\pi$
$373$	−1.93680	−	3.35463i	−0.100284	−	0.173696i	−0.911801	+	0.410631i	$0.865308\pi$
$374$	−5.52507	−	9.56971i	−0.285695	−	0.494838i
$375$		0			0
$376$	−7.20312	−	4.15872i	−0.371472	−	0.214470i
$377$	16.4480			0.847117
$378$		0			0
$379$	8.21884			0.422173			0.211087	−	0.977467i	$-0.432300\pi$
$379$	8.21884			0.422173			0.211087	+	0.977467i	$0.432300\pi$
$380$	5.23116	+	3.02021i	0.268353	+	0.154934i
$381$		0			0
$382$	4.47416	+	7.74947i	0.228918	+	0.396498i
$383$	−15.1513	−	26.2428i	−0.774195	−	1.34095i	−0.935246	−	0.353999i	$-0.884821\pi$
$383$	−15.1513	−	26.2428i	−0.774195	−	1.34095i	0.161050	−	0.986946i	$-0.448512\pi$
$384$		0			0
$385$		0			0
$386$		−	25.6055i		−	1.30329i
$387$		0			0
$388$			12.6636i			0.642895i
$389$	−18.2352	−	10.5281i	−0.924562	−	0.533796i	−0.0394744	−	0.999221i	$-0.512568\pi$
$389$	−18.2352	−	10.5281i	−0.924562	−	0.533796i	−0.885088	+	0.465424i	$0.845902\pi$
$390$		0			0
$391$	−24.7737	+	14.3031i	−1.25286	+	0.723338i
$392$		0			0
$393$		0			0
$394$	−11.7801	+	20.4038i	−0.593474	+	1.02793i
$395$	22.6539			1.13984
$396$		0			0
$397$			0.596428i			0.0299338i	0.999888	+	0.0149669i	$0.00476430\pi$
$397$			0.596428i			0.0299338i	−0.999888	+	0.0149669i	$0.995236\pi$
$398$	6.81212	−	11.7989i	0.341461	−	0.591427i
$399$		0			0
$400$	1.45020	+	2.51182i	0.0725101	+	0.125591i
$401$	2.02316	−	1.16807i	0.101032	−	0.0583309i	−0.448633	−	0.893716i	$-0.648089\pi$
$401$	2.02316	−	1.16807i	0.101032	−	0.0583309i	0.549665	+	0.835385i	$0.314755\pi$
$402$		0			0
$403$	−1.60728	+	2.78389i	−0.0800642	+	0.138675i
$404$	−17.5545			−0.873370
$405$		0			0
$406$		0			0
$407$	−5.18523	−	2.99369i	−0.257022	−	0.148392i
$408$		0			0
$409$	8.35337	−	4.82282i	0.413048	−	0.238473i	−0.279051	−	0.960276i	$-0.590020\pi$
$409$	8.35337	−	4.82282i	0.413048	−	0.238473i	0.692098	+	0.721803i	$0.256686\pi$
$410$	0.862665	−	0.498060i	0.0426040	−	0.0245974i
$411$		0			0
$412$	3.86082	+	2.22905i	0.190209	+	0.109817i
$413$		0			0
$414$		0			0
$415$	11.9161			0.584937
$416$	1.75222	−	3.03494i	0.0859098	−	0.148800i
$417$		0			0
$418$	−5.04623	+	2.91344i	−0.246819	+	0.142501i
$419$	14.4297	+	24.9930i	0.704939	+	1.22099i	0.966714	+	0.255861i	$0.0823590\pi$
$419$	14.4297	+	24.9930i	0.704939	+	1.22099i	−0.261775	+	0.965129i	$0.584308\pi$
$420$		0			0
$421$	6.14672	−	10.6464i	0.299573	−	0.518875i	−0.676466	−	0.736474i	$-0.736489\pi$
$421$	6.14672	−	10.6464i	0.299573	−	0.518875i	0.976038	+	0.217599i	$0.0698226\pi$
$422$		−	21.5922i		−	1.05109i
$423$		0			0
$424$	5.96029			0.289457
$425$	−11.4646	+	19.8573i	−0.556115	+	0.963220i
$426$		0			0
$427$		0			0
$428$	−2.04566	+	1.18106i	−0.0988808	+	0.0570889i
$429$		0			0
$430$	15.0960	+	8.71569i	0.727995	+	0.420308i
$431$			27.7631i			1.33730i	0.743577	+	0.668650i	$0.233128\pi$
$431$			27.7631i			1.33730i	−0.743577	+	0.668650i	$0.766872\pi$
$432$		0			0
$433$			21.3927i			1.02807i	0.857769	+	0.514035i	$0.171850\pi$
$433$			21.3927i			1.02807i	−0.857769	+	0.514035i	$0.828150\pi$
$434$		0			0
$435$		0			0
$436$	6.49776	+	11.2545i	0.311186	+	0.538990i
$437$	7.54220	+	13.0635i	0.360792	+	0.624911i
$438$		0			0
$439$	2.28558	+	1.31958i	0.109085	+	0.0629801i	0.553550	−	0.832816i	$-0.313273\pi$
$439$	2.28558	+	1.31958i	0.109085	+	0.0629801i	−0.444465	+	0.895796i	$0.646606\pi$
$440$	2.02537			0.0965558
$441$		0			0
$442$	27.7045			1.31777
$443$	−10.5439	−	6.08750i	−0.500954	−	0.289226i	0.228153	−	0.973625i	$-0.426731\pi$
$443$	−10.5439	−	6.08750i	−0.500954	−	0.289226i	−0.729107	+	0.684399i	$0.760065\pi$
$444$		0			0
$445$	−0.772921	−	1.33874i	−0.0366400	−	0.0634623i
$446$	8.41256	+	14.5710i	0.398346	+	0.689956i
$447$		0			0
$448$		0			0
$449$		−	14.2454i		−	0.672283i	−0.941811	−	0.336142i	$-0.890878\pi$
$449$		−	14.2454i		−	0.672283i	0.941811	−	0.336142i	$-0.109122\pi$
$450$		0			0
$451$			0.960905i			0.0452472i
$452$	−2.90616	−	1.67787i	−0.136694	−	0.0789204i
$453$		0			0
$454$	10.5840	−	6.11065i	0.496730	−	0.286787i
$455$		0			0
$456$		0			0
$457$	5.78156	−	10.0140i	0.270450	−	0.468433i	−0.698527	−	0.715583i	$-0.746161\pi$
$457$	5.78156	−	10.0140i	0.270450	−	0.468433i	0.968977	+	0.247151i	$0.0794942\pi$
$458$	19.4518			0.908924
$459$		0			0
$460$		−	5.24320i		−	0.244465i
$461$	−11.0041	+	19.0597i	−0.512513	+	0.887698i	0.487382	+	0.873189i	$0.337952\pi$
$461$	−11.0041	+	19.0597i	−0.512513	+	0.887698i	−0.999895	+	0.0145095i	$0.995381\pi$
$462$		0			0
$463$	6.47862	+	11.2213i	0.301087	+	0.521498i	0.976382	−	0.216049i	$-0.0693171\pi$
$463$	6.47862	+	11.2213i	0.301087	+	0.521498i	−0.675295	+	0.737547i	$0.735984\pi$
$464$	4.06467	−	2.34674i	0.188698	−	0.108945i
$465$		0			0
$466$	−14.2825	+	24.7381i	−0.661626	+	1.14597i
$467$	2.85090			0.131924			0.0659619	−	0.997822i	$-0.478988\pi$
$467$	2.85090			0.131924			0.0659619	+	0.997822i	$0.478988\pi$
$468$		0			0
$469$		0			0
$470$	10.4373	+	6.02598i	0.481437	+	0.277958i
$471$		0			0
$472$	8.17641	−	4.72065i	0.376350	−	0.217286i
$473$	−14.5623	+	8.40757i	−0.669577	+	0.386581i
$474$		0			0
$475$	10.4710	+	6.04544i	0.480443	+	0.277384i
$476$		0			0
$477$		0			0
$478$	11.5493			0.528253
$479$	16.6352	−	28.8130i	0.760081	−	1.31650i	−0.182727	−	0.983164i	$-0.558492\pi$
$479$	16.6352	−	28.8130i	0.760081	−	1.31650i	0.942808	−	0.333336i	$-0.108174\pi$
$480$		0			0
$481$	13.0002	−	7.50567i	0.592758	−	0.342229i
$482$	0.0172628	+	0.0299000i	0.000786298	+	0.00136191i
$483$		0			0
$484$	4.52311	−	7.83426i	0.205596	−	0.356103i
$485$		−	18.3495i		−	0.833208i
$486$		0			0
$487$	−10.4500			−0.473535			−0.236767	−	0.971566i	$-0.576088\pi$
$487$	−10.4500			−0.473535			−0.236767	+	0.971566i	$0.576088\pi$
$488$	4.92979	−	8.53864i	0.223161	−	0.386526i
$489$		0			0
$490$		0			0
$491$	−2.03404	+	1.17436i	−0.0917952	+	0.0529980i	−0.545195	−	0.838309i	$-0.683544\pi$
$491$	−2.03404	+	1.17436i	−0.0917952	+	0.0529980i	0.453400	+	0.891307i	$0.350211\pi$
$492$		0			0
$493$	32.1334	+	18.5522i	1.44722	+	0.835550i
$494$		−	14.6089i		−	0.657287i
$495$		0			0
$496$			0.917280i			0.0411871i
$497$		0			0
$498$		0			0
$499$	−17.3895	−	30.1195i	−0.778462	−	1.34834i	−0.932828	−	0.360322i	$-0.882667\pi$
$499$	−17.3895	−	30.1195i	−0.778462	−	1.34834i	0.154366	−	0.988014i	$-0.450667\pi$
$500$	−5.72384	−	9.91398i	−0.255978	−	0.443366i
$501$		0			0
$502$	2.82599	+	1.63158i	0.126130	+	0.0728211i
$503$	17.8290			0.794956			0.397478	−	0.917612i	$-0.369886\pi$
$503$	17.8290			0.794956			0.397478	+	0.917612i	$0.369886\pi$
$504$		0			0
$505$	25.4365			1.13191
$506$	4.38022	+	2.52892i	0.194725	+	0.112424i
$507$		0			0
$508$	−6.45374	−	11.1782i	−0.286338	−	0.495953i
$509$	−7.78061	−	13.4764i	−0.344869	−	0.597331i	0.640461	−	0.767991i	$-0.278743\pi$
$509$	−7.78061	−	13.4764i	−0.344869	−	0.597331i	−0.985330	+	0.170660i	$0.945410\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			19.7970i			0.873209i
$515$	−5.59433	−	3.22989i	−0.246516	−	0.142326i
$516$		0			0
$517$	−10.0683	+	5.81295i	−0.442805	+	0.255653i
$518$		0			0
$519$		0			0
$520$	−2.53897	+	4.39762i	−0.111341	+	0.192848i
$521$	−29.6376			−1.29844			−0.649222	−	0.760599i	$-0.724906\pi$
$521$	−29.6376			−1.29844			−0.649222	+	0.760599i	$0.724906\pi$
$522$		0			0
$523$			22.2110i			0.971220i	0.874176	+	0.485610i	$0.161403\pi$
$523$			22.2110i			0.971220i	−0.874176	+	0.485610i	$0.838597\pi$
$524$	4.12856	−	7.15088i	0.180357	−	0.312388i
$525$		0			0
$526$	8.80897	+	15.2576i	0.384089	+	0.665262i
$527$	−6.28006	+	3.62579i	−0.273564	+	0.157942i
$528$		0			0
$529$	−4.95323	+	8.57925i	−0.215358	+	0.373011i
$530$	−8.63645			−0.375143
$531$		0			0
$532$		0			0
$533$	−2.08638	−	1.20457i	−0.0903711	−	0.0521758i
$534$		0			0
$535$	2.96416	−	1.71136i	0.128152	−	0.0739886i
$536$	−2.57278	+	1.48540i	−0.111127	+	0.0641593i
$537$		0			0
$538$	6.64540	+	3.83672i	0.286503	+	0.165413i
$539$		0			0
$540$		0			0
$541$	22.0342			0.947324			0.473662	−	0.880707i	$-0.342932\pi$
$541$	22.0342			0.947324			0.473662	+	0.880707i	$0.342932\pi$
$542$	−3.51690	+	6.09146i	−0.151064	+	0.261650i
$543$		0			0
$544$	6.84639	−	3.95277i	0.293537	−	0.169473i
$545$	−9.41525	−	16.3077i	−0.403305	−	0.698545i
$546$		0			0
$547$	−14.5256	+	25.1592i	−0.621072	+	1.07573i	0.368215	+	0.929741i	$0.379969\pi$
$547$	−14.5256	+	25.1592i	−0.621072	+	1.07573i	−0.989286	+	0.145987i	$0.953364\pi$
$548$		−	13.0789i		−	0.558703i
$549$		0			0
$550$	4.05411			0.172868
$551$	9.78283	−	16.9444i	0.416762	−	0.721854i
$552$		0			0
$553$		0			0
$554$	−14.9885	+	8.65364i	−0.636802	+	0.367658i
$555$		0			0
$556$	10.6722	+	6.16162i	0.452603	+	0.261311i
$557$			17.3143i			0.733632i	0.930294	+	0.366816i	$0.119552\pi$
$557$			17.3143i			0.733632i	−0.930294	+	0.366816i	$0.880448\pi$
$558$		0			0
$559$		−	42.1583i		−	1.78311i
$560$		0			0
$561$		0			0
$562$	−8.26508	−	14.3155i	−0.348641	−	0.603865i
$563$	10.3834	+	17.9846i	0.437608	+	0.757959i	0.997504	−	0.0706035i	$-0.0224925\pi$
$563$	10.3834	+	17.9846i	0.437608	+	0.757959i	−0.559897	+	0.828562i	$0.689159\pi$
$564$		0			0
$565$	4.21102	+	2.43123i	0.177159	+	0.102283i
$566$	−3.16284			−0.132944
$567$		0			0
$568$	−12.9436			−0.543101
$569$	−12.7829	−	7.38020i	−0.535887	−	0.309394i	0.207524	−	0.978230i	$-0.433460\pi$
$569$	−12.7829	−	7.38020i	−0.535887	−	0.309394i	−0.743410	+	0.668836i	$0.766793\pi$
$570$		0			0
$571$	11.1208	+	19.2618i	0.465390	+	0.806080i	0.999219	−	0.0395130i	$-0.0125806\pi$
$571$	11.1208	+	19.2618i	0.465390	+	0.806080i	−0.533829	+	0.845593i	$0.679247\pi$
$572$	−2.44921	−	4.24216i	−0.102407	−	0.177373i
$573$		0			0
$574$		0			0
$575$		−	10.4951i		−	0.437676i
$576$		0			0
$577$			18.7182i			0.779249i	0.920974	+	0.389625i	$0.127395\pi$
$577$			18.7182i			0.779249i	−0.920974	+	0.389625i	$0.872605\pi$
$578$	39.4019	+	22.7487i	1.63890	+	0.946222i
$579$		0			0
$580$	−5.88971	+	3.40042i	−0.244557	+	0.141195i
$581$		0			0
$582$		0			0
$583$	4.16557	−	7.21497i	0.172520	−	0.298814i
$584$	11.3053			0.467818
$585$		0			0
$586$			8.52090i			0.351995i
$587$	10.7433	−	18.6079i	0.443423	−	0.768031i	−0.554518	−	0.832172i	$-0.687097\pi$
$587$	10.7433	−	18.6079i	0.443423	−	0.768031i	0.997941	+	0.0641405i	$0.0204306\pi$
$588$		0			0
$589$	1.91193	+	3.31155i	0.0787796	+	0.136450i
$590$	−11.8476	+	6.84022i	−0.487758	+	0.281607i
$591$		0			0
$592$	2.14176	−	3.70963i	0.0880257	−	0.152465i
$593$	−14.0949			−0.578809			−0.289404	−	0.957207i	$-0.593457\pi$
$593$	−14.0949			−0.578809			−0.289404	+	0.957207i	$0.593457\pi$
$594$		0			0
$595$		0			0
$596$	0.538692	+	0.311014i	0.0220657	+	0.0127396i
$597$		0			0
$598$	−10.9819	+	6.34042i	−0.449084	+	0.259279i
$599$	−16.6024	+	9.58537i	−0.678354	+	0.391648i	−0.799235	−	0.601019i	$-0.794761\pi$
$599$	−16.6024	+	9.58537i	−0.678354	+	0.391648i	0.120881	+	0.992667i	$0.461428\pi$
$600$		0			0
$601$	34.6795	+	20.0222i	1.41460	+	0.816723i	0.995818	−	0.0913619i	$-0.0291220\pi$
$601$	34.6795	+	20.0222i	1.41460	+	0.816723i	0.418787	+	0.908084i	$0.362455\pi$
$602$		0			0
$603$		0			0
$604$	21.1821			0.861889
$605$	−6.55399	+	11.3518i	−0.266457	+	0.461518i
$606$		0			0
$607$	−39.6529	+	22.8936i	−1.60946	+	0.929223i	−0.619971	+	0.784625i	$0.712856\pi$
$607$	−39.6529	+	22.8936i	−1.60946	+	0.929223i	−0.989490	+	0.144599i	$0.953811\pi$
$608$	−2.08434	−	3.61019i	−0.0845313	−	0.146413i
$609$		0			0
$610$	−7.14325	+	12.3725i	−0.289222	+	0.500947i
$611$		−	29.1480i		−	1.17920i
$612$		0			0
$613$	−45.2962			−1.82950			−0.914748	−	0.404026i	$-0.867611\pi$
$613$	−45.2962			−1.82950			−0.914748	+	0.404026i	$0.867611\pi$
$614$	12.5403	−	21.7204i	0.506083	−	0.876562i
$615$		0			0
$616$		0			0
$617$	28.6323	−	16.5308i	1.15269	−	0.665506i	0.203149	−	0.979148i	$-0.434882\pi$
$617$	28.6323	−	16.5308i	1.15269	−	0.665506i	0.949542	+	0.313641i	$0.101549\pi$
$618$		0			0
$619$	9.35801	+	5.40285i	0.376130	+	0.217159i	0.676133	−	0.736779i	$-0.263654\pi$
$619$	9.35801	+	5.40285i	0.376130	+	0.217159i	−0.300003	+	0.953938i	$0.596988\pi$
$620$		−	1.32914i		−	0.0533794i
$621$		0			0
$622$			3.57355i			0.143286i
$623$		0			0
$624$		0			0
$625$	1.04283	+	1.80623i	0.0417131	+	0.0722491i
$626$	6.81464	+	11.8033i	0.272368	+	0.471755i
$627$		0			0
$628$	−13.0158	−	7.51469i	−0.519388	−	0.299869i
$629$	33.8635			1.35022
$630$		0			0
$631$	−30.0554			−1.19648			−0.598242	−	0.801315i	$-0.704134\pi$
$631$	−30.0554			−1.19648			−0.598242	+	0.801315i	$0.704134\pi$
$632$	−13.5396	−	7.81709i	−0.538576	−	0.310947i
$633$		0			0
$634$	−2.14497	−	3.71520i	−0.0851877	−	0.147549i
$635$	9.35146	+	16.1972i	0.371101	+	0.642767i
$636$		0			0
$637$		0			0
$638$		−	6.56042i		−	0.259730i
$639$		0			0
$640$			1.44900i			0.0572767i
$641$	9.66957	+	5.58273i	0.381925	+	0.220505i	0.678655	−	0.734457i	$-0.262563\pi$
$641$	9.66957	+	5.58273i	0.381925	+	0.220505i	−0.296730	+	0.954961i	$0.595896\pi$
$642$		0			0
$643$	−4.40588	+	2.54373i	−0.173751	+	0.100315i	−0.584353	−	0.811499i	$-0.698652\pi$
$643$	−4.40588	+	2.54373i	−0.173751	+	0.100315i	0.410602	+	0.911814i	$0.365318\pi$
$644$		0			0
$645$		0			0
$646$	16.4779	−	28.5405i	0.648312	−	1.12291i
$647$	12.9142			0.507710			0.253855	−	0.967242i	$-0.418301\pi$
$647$	12.9142			0.507710			0.253855	+	0.967242i	$0.418301\pi$
$648$		0			0
$649$		−	13.1968i		−	0.518020i
$650$	−5.08215	+	8.80254i	−0.199338	+	0.345264i
$651$		0			0
$652$	−1.51764	−	2.62863i	−0.0594353	−	0.102945i
$653$	31.5843	−	18.2352i	1.23599	−	0.713598i	0.267716	−	0.963498i	$-0.413731\pi$
$653$	31.5843	−	18.2352i	1.23599	−	0.713598i	0.968272	+	0.249900i	$0.0803977\pi$
$654$		0			0
$655$	−5.98228	+	10.3616i	−0.233747	+	0.404862i
$656$	−0.687454			−0.0268406
$657$		0			0
$658$		0			0
$659$	−2.04111	−	1.17844i	−0.0795104	−	0.0459054i	0.459718	−	0.888065i	$-0.347951\pi$
$659$	−2.04111	−	1.17844i	−0.0795104	−	0.0459054i	−0.539228	+	0.842160i	$0.681284\pi$
$660$		0			0
$661$	−6.72135	+	3.88057i	−0.261430	+	0.150937i	−0.624987	−	0.780635i	$-0.714896\pi$
$661$	−6.72135	+	3.88057i	−0.261430	+	0.150937i	0.363557	+	0.931572i	$0.381562\pi$
$662$	−7.74160	+	4.46962i	−0.300886	+	0.173717i
$663$		0			0
$664$	−7.12189	−	4.11183i	−0.276383	−	0.159570i
$665$		0			0
$666$		0			0
$667$	−16.9833			−0.657598
$668$	−3.05895	+	5.29826i	−0.118354	+	0.204996i
$669$		0			0
$670$	3.72796	−	2.15234i	0.144024	−	0.0831520i
$671$	−6.89072	−	11.9351i	−0.266013	−	0.460749i
$672$		0			0
$673$	17.5783	−	30.4465i	0.677594	−	1.17363i	−0.298109	−	0.954532i	$-0.596356\pi$
$673$	17.5783	−	30.4465i	0.677594	−	1.17363i	0.975703	−	0.219096i	$-0.0703106\pi$
$674$			0.145955i			0.00562196i
$675$		0			0
$676$	−0.718866			−0.0276487
$677$	−7.03074	+	12.1776i	−0.270213	+	0.468023i	−0.968916	−	0.247389i	$-0.920428\pi$
$677$	−7.03074	+	12.1776i	−0.270213	+	0.468023i	0.698703	+	0.715412i	$0.253761\pi$
$678$		0			0
$679$		0			0
$680$	−9.92041	+	5.72755i	−0.380430	+	0.219642i
$681$		0			0
$682$	1.11037	+	0.641075i	0.0425184	+	0.0245480i
$683$			33.6363i			1.28706i	0.765422	+	0.643529i	$0.222530\pi$
$683$			33.6363i			1.28706i	−0.765422	+	0.643529i	$0.777470\pi$
$684$		0			0
$685$			18.9513i			0.724093i
$686$		0			0
$687$		0			0
$688$	−6.01497	−	10.4182i	−0.229319	−	0.397192i
$689$	10.4438	+	18.0891i	0.397875	+	0.689140i
$690$		0			0
$691$	3.81269	+	2.20126i	0.145042	+	0.0837399i	0.570765	−	0.821114i	$-0.306647\pi$
$691$	3.81269	+	2.20126i	0.145042	+	0.0837399i	−0.425723	+	0.904854i	$0.639980\pi$
$692$	2.29515			0.0872484
$693$		0			0
$694$	22.2844			0.845903
$695$	−15.4640	−	8.92817i	−0.586585	−	0.338665i
$696$		0			0
$697$	−2.71734	−	4.70658i	−0.102927	−	0.178274i
$698$	1.61572	+	2.79851i	0.0611560	+	0.105925i
$699$		0			0
$700$		0			0
$701$			31.5424i			1.19134i	0.803229	+	0.595670i	$0.203113\pi$
$701$			31.5424i			1.19134i	−0.803229	+	0.595670i	$0.796887\pi$
$702$		0			0
$703$		−	17.8566i		−	0.673476i
$704$	−1.21051	−	0.698887i	−0.0456227	−	0.0263403i
$705$		0			0
$706$	−5.42533	+	3.13232i	−0.204185	+	0.117886i
$707$		0			0
$708$		0			0
$709$	−2.17269	+	3.76320i	−0.0815970	+	0.141330i	−0.903936	−	0.427668i	$-0.859335\pi$
$709$	−2.17269	+	3.76320i	−0.0815970	+	0.141330i	0.822339	+	0.568998i	$0.192669\pi$
$710$	18.7552			0.703872
$711$		0			0
$712$			1.06683i			0.0399813i
$713$	1.65959	−	2.87449i	0.0621520	−	0.107651i
$714$		0			0
$715$	3.54890	+	6.14688i	0.132721	+	0.229880i
$716$	2.92364	−	1.68796i	0.109261	−	0.0630821i
$717$		0			0
$718$	6.03463	−	10.4523i	0.225210	−	0.390076i
$719$	28.3001			1.05541			0.527707	−	0.849426i	$-0.323052\pi$
$719$	28.3001			1.05541			0.527707	+	0.849426i	$0.323052\pi$
$720$		0			0
$721$		0			0
$722$	1.40472	+	0.811015i	0.0522782	+	0.0301829i
$723$		0			0
$724$	1.46235	−	0.844286i	0.0543477	−	0.0313776i
$725$	−11.7892	+	6.80649i	−0.437839	+	0.252787i
$726$		0			0
$727$	−11.7770	−	6.79945i	−0.436784	−	0.252178i	0.265448	−	0.964125i	$-0.414480\pi$
$727$	−11.7770	−	6.79945i	−0.436784	−	0.252178i	−0.702233	+	0.711948i	$0.747813\pi$
$728$		0			0
$729$		0			0
$730$	−16.3814			−0.606303
$731$	47.5516	−	82.3617i	1.75876	−	3.04626i
$732$		0			0
$733$	−41.0236	+	23.6850i	−1.51524	+	0.874825i	−0.515401	+	0.856949i	$0.672357\pi$
$733$	−41.0236	+	23.6850i	−1.51524	+	0.874825i	−0.999840	+	0.0178757i	$0.994310\pi$
$734$	8.53940	+	14.7907i	0.315195	+	0.545934i
$735$		0			0
$736$	−1.80925	+	3.13371i	−0.0666898	+	0.115510i
$737$			4.15250i			0.152959i
$738$		0			0
$739$	33.7203			1.24042			0.620210	−	0.784435i	$-0.287047\pi$
$739$	33.7203			1.24042			0.620210	+	0.784435i	$0.287047\pi$
$740$	−3.10340	+	5.37525i	−0.114083	+	0.197598i
$741$		0			0
$742$		0			0
$743$	−6.86253	+	3.96208i	−0.251762	+	0.145355i	−0.620571	−	0.784151i	$-0.713099\pi$
$743$	−6.86253	+	3.96208i	−0.251762	+	0.145355i	0.368809	+	0.929505i	$0.379766\pi$
$744$		0			0
$745$	−0.780564	−	0.450659i	−0.0285976	−	0.0165109i
$746$		−	3.87360i		−	0.141822i
$747$		0			0
$748$		−	11.0501i		−	0.404033i
$749$		0			0
$750$		0			0
$751$	−2.06865	−	3.58301i	−0.0754861	−	0.130746i	0.825811	−	0.563946i	$-0.190718\pi$
$751$	−2.06865	−	3.58301i	−0.0754861	−	0.130746i	−0.901298	+	0.433201i	$0.857384\pi$
$752$	−4.15872	−	7.20312i	−0.151653	−	0.262671i
$753$		0			0
$754$	14.2444	+	8.22402i	0.518751	+	0.299501i
$755$	−30.6929			−1.11703
$756$		0			0
$757$	35.2411			1.28086			0.640430	−	0.768017i	$-0.278756\pi$
$757$	35.2411			1.28086			0.640430	+	0.768017i	$0.278756\pi$
$758$	7.11772	+	4.10942i	0.258527	+	0.149261i
$759$		0			0
$760$	3.02021	+	5.23116i	0.109555	+	0.189754i
$761$	−4.93597	−	8.54935i	−0.178929	−	0.309914i	0.762585	−	0.646888i	$-0.223930\pi$
$761$	−4.93597	−	8.54935i	−0.178929	−	0.309914i	−0.941514	+	0.336974i	$0.890596\pi$
$762$		0			0
$763$		0			0
$764$			8.94832i			0.323739i
$765$		0			0
$766$		−	30.3026i		−	1.09488i
$767$	28.6538	+	16.5433i	1.03463	+	0.597343i
$768$		0			0
$769$	18.6213	−	10.7510i	0.671503	−	0.387692i	−0.125143	−	0.992139i	$-0.539939\pi$
$769$	18.6213	−	10.7510i	0.671503	−	0.387692i	0.796646	+	0.604446i	$0.206606\pi$
$770$		0			0
$771$		0			0
$772$	12.8028	−	22.1751i	0.460782	−	0.798098i
$773$	−7.39549			−0.265997			−0.132999	−	0.991116i	$-0.542461\pi$
$773$	−7.39549			−0.265997			−0.132999	+	0.991116i	$0.542461\pi$
$774$		0			0
$775$		−	2.66048i		−	0.0955673i
$776$	−6.33179	+	10.9670i	−0.227298	+	0.393691i
$777$		0			0
$778$	−10.5281	−	18.2352i	−0.377451	−	0.653764i
$779$	−2.48184	+	1.43289i	−0.0889211	+	0.0513386i
$780$		0			0
$781$	−9.04610	+	15.6683i	−0.323695	+	0.560656i
$782$	−28.6062			−1.02295
$783$		0			0
$784$		0			0
$785$	18.8599	+	10.8888i	0.673139	+	0.388637i
$786$		0			0
$787$	−15.4285	+	8.90768i	−0.549968	+	0.317524i	−0.749109	−	0.662446i	$-0.769518\pi$
$787$	−15.4285	+	8.90768i	−0.549968	+	0.317524i	0.199141	+	0.979971i	$0.436185\pi$
$788$	−20.4038	+	11.7801i	−0.726854	+	0.419649i
$789$		0			0
$790$	19.6189	+	11.3269i	0.698007	+	0.402995i
$791$		0			0
$792$		0			0
$793$	34.5523			1.22699
$794$	−0.298214	+	0.516521i	−0.0105832	+	0.0183307i
$795$		0			0
$796$	11.7989	−	6.81212i	0.418202	−	0.241449i
$797$	−27.0403	−	46.8351i	−0.957815	−	1.65898i	−0.727790	−	0.685800i	$-0.759452\pi$
$797$	−27.0403	−	46.8351i	−0.957815	−	1.65898i	−0.230025	−	0.973185i	$-0.573881\pi$
$798$		0			0
$799$	32.8769	−	56.9445i	1.16310	−	2.01455i
$800$			2.90040i			0.102545i
$801$		0			0
$802$	2.33615			0.0824923
$803$	7.90115	−	13.6852i	0.278825	−	0.482940i
$804$		0			0
$805$		0			0
$806$	−2.78389	+	1.60728i	−0.0980582	+	0.0566140i
$807$		0			0
$808$	−15.2027	−	8.77726i	−0.534827	−	0.308783i
$809$		−	41.6611i		−	1.46473i	−0.680915	−	0.732363i	$-0.738418\pi$
$809$		−	41.6611i		−	1.46473i	0.680915	−	0.732363i	$-0.261582\pi$
$810$		0			0
$811$			24.8645i			0.873111i	0.899677	+	0.436556i	$0.143802\pi$
$811$			24.8645i			0.873111i	−0.899677	+	0.436556i	$0.856198\pi$
$812$		0			0
$813$		0			0
$814$	−2.99369	−	5.18523i	−0.104929	−	0.181742i
$815$	2.19905	+	3.80887i	0.0770295	+	0.133419i
$816$		0			0
$817$	−43.4304	−	25.0746i	−1.51944	−	0.877248i
$818$	9.64564			0.337252
$819$		0			0
$820$	0.996120			0.0347860
$821$	29.9616	+	17.2983i	1.04567	+	0.603716i	0.921433	−	0.388537i	$-0.127019\pi$
$821$	29.9616	+	17.2983i	1.04567	+	0.603716i	0.124234	+	0.992253i	$0.460353\pi$
$822$		0			0
$823$	−7.88113	−	13.6505i	−0.274719	−	0.475827i	0.695345	−	0.718676i	$-0.255251\pi$
$823$	−7.88113	−	13.6505i	−0.274719	−	0.475827i	−0.970064	+	0.242849i	$0.921918\pi$
$824$	2.22905	+	3.86082i	0.0776526	+	0.134498i
$825$		0			0
$826$		0			0
$827$			17.6523i			0.613830i	0.951737	+	0.306915i	$0.0992967\pi$
$827$			17.6523i			0.613830i	−0.951737	+	0.306915i	$0.900703\pi$
$828$		0			0
$829$			37.6774i			1.30859i	0.756240	+	0.654294i	$0.227034\pi$
$829$			37.6774i			1.30859i	−0.756240	+	0.654294i	$0.772966\pi$
$830$	10.3196	+	5.95803i	0.358199	+	0.206806i
$831$		0			0
$832$	3.03494	−	1.75222i	0.105218	−	0.0607474i
$833$		0			0
$834$		0			0
$835$	4.43242	−	7.67718i	0.153390	−	0.265680i
$836$	−5.82688			−0.201527
$837$		0			0
$838$			28.8595i			0.996934i
$839$	−10.5777	+	18.3211i	−0.365183	+	0.632516i	−0.988806	−	0.149210i	$-0.952327\pi$
$839$	−10.5777	+	18.3211i	−0.365183	+	0.632516i	0.623622	+	0.781726i	$0.285660\pi$
$840$		0			0
$841$	−3.48563	−	6.03728i	−0.120194	−	0.208182i
$842$	10.6464	−	6.14672i	0.366900	−	0.211830i
$843$		0			0
$844$	10.7961	−	18.6994i	0.371617	−	0.643660i
$845$	1.04164			0.0358334
$846$		0			0
$847$		0			0
$848$	5.16176	+	2.98014i	0.177256	+	0.102339i
$849$		0			0
$850$	−19.8573	+	11.4646i	−0.681099	+	0.393233i
$851$	−13.4233	+	7.74995i	−0.460145	+	0.265665i
$852$		0			0
$853$	−34.7061	−	20.0376i	−1.18831	−	0.686073i	−0.230390	−	0.973098i	$-0.574000\pi$
$853$	−34.7061	−	20.0376i	−1.18831	−	0.686073i	−0.957923	+	0.287026i	$0.907334\pi$
$854$		0			0
$855$		0			0
$856$	−2.36213			−0.0807359
$857$	−3.73018	+	6.46087i	−0.127421	+	0.220699i	−0.922677	−	0.385575i	$-0.874003\pi$
$857$	−3.73018	+	6.46087i	−0.127421	+	0.220699i	0.795256	+	0.606274i	$0.207336\pi$
$858$		0			0
$859$	41.2721	−	23.8285i	1.40819	−	0.813017i	0.412974	−	0.910743i	$-0.364490\pi$
$859$	41.2721	−	23.8285i	1.40819	−	0.813017i	0.995213	+	0.0977257i	$0.0311568\pi$
$860$	8.71569	+	15.0960i	0.297203	+	0.514770i
$861$		0			0
$862$	−13.8815	+	24.0435i	−0.472807	+	0.818926i
$863$		−	42.9343i		−	1.46150i	−0.682645	−	0.730750i	$-0.739171\pi$
$863$		−	42.9343i		−	1.46150i	0.682645	−	0.730750i	$-0.260829\pi$
$864$		0			0
$865$	−3.32566			−0.113076
$866$	−10.6964	+	18.5267i	−0.363478	+	0.629562i
$867$		0			0
$868$		0			0
$869$	−18.9253	+	10.9265i	−0.641996	+	0.370657i
$870$		0			0
$871$	−9.01617	−	5.20549i	−0.305501	−	0.176381i
$872$			12.9955i			0.440084i
$873$		0			0
$874$			15.0844i			0.510237i
$875$		0			0
$876$		0			0
$877$	−13.0702	−	22.6382i	−0.441349	−	0.764438i	0.556441	−	0.830887i	$-0.312166\pi$
$877$	−13.0702	−	22.6382i	−0.441349	−	0.764438i	−0.997790	+	0.0664486i	$0.978833\pi$
$878$	1.31958	+	2.28558i	0.0445337	+	0.0771346i
$879$		0			0
$880$	1.75402	+	1.01269i	0.0591281	+	0.0341376i
$881$	−11.2385			−0.378636			−0.189318	−	0.981916i	$-0.560628\pi$
$881$	−11.2385			−0.378636			−0.189318	+	0.981916i	$0.560628\pi$
$882$		0			0
$883$	−0.253239			−0.00852217			−0.00426108	−	0.999991i	$-0.501356\pi$
$883$	−0.253239			−0.00852217			−0.00426108	+	0.999991i	$0.501356\pi$
$884$	23.9928	+	13.8523i	0.806965	+	0.465902i
$885$		0			0
$886$	−6.08750	−	10.5439i	−0.204514	−	0.354228i
$887$	−2.86053	−	4.95458i	−0.0960472	−	0.166359i	0.813998	−	0.580868i	$-0.197287\pi$
$887$	−2.86053	−	4.95458i	−0.0960472	−	0.166359i	−0.910045	+	0.414509i	$0.863953\pi$
$888$		0			0
$889$		0			0
$890$		−	1.54584i		−	0.0518167i
$891$		0			0
$892$			16.8251i			0.563347i
$893$	−30.0276	−	17.3364i	−1.00483	−	0.580141i
$894$		0			0
$895$	−4.23635	+	2.44586i	−0.141605	+	0.0817559i
$896$		0			0
$897$		0			0
$898$	7.12271	−	12.3369i	0.237688	−	0.411688i
$899$	−4.30523			−0.143588
$900$		0			0
$901$			47.1193i			1.56977i
$902$	−0.480452	+	0.832168i	−0.0159973	+	0.0277082i
$903$		0			0
$904$	−1.67787	−	2.90616i	−0.0558052	−	0.0966574i
$905$	−2.11894	+	1.22337i	−0.0704359	+	0.0406662i
$906$		0			0
$907$	−11.8731	+	20.5648i	−0.394241	+	0.682845i	−0.993004	−	0.118081i	$-0.962326\pi$
$907$	−11.8731	+	20.5648i	−0.394241	+	0.682845i	0.598763	+	0.800926i	$0.295659\pi$
$908$	12.2213			0.405578
$909$		0			0
$910$		0			0
$911$	−17.0673	−	9.85384i	−0.565466	−	0.326472i	0.189870	−	0.981809i	$-0.439193\pi$
$911$	−17.0673	−	9.85384i	−0.565466	−	0.326472i	−0.755337	+	0.655337i	$0.772527\pi$
$912$		0			0
$913$	−9.95479	+	5.74740i	−0.329456	+	0.190211i
$914$	10.0140	−	5.78156i	0.331232	−	0.191237i
$915$		0			0
$916$	16.8458	+	9.72591i	0.556600	+	0.321353i
$917$		0			0
$918$		0			0
$919$	−54.6154			−1.80159			−0.900797	−	0.434240i	$-0.857017\pi$
$919$	−54.6154			−1.80159			−0.900797	+	0.434240i	$0.857017\pi$
$920$	2.62160	−	4.54074i	0.0864316	−	0.149704i
$921$		0			0
$922$	−19.0597	+	11.0041i	−0.627698	+	0.362401i
$923$	−22.6800	−	39.2830i	−0.746523	−	1.29302i
$924$		0			0
$925$	−6.21196	+	10.7594i	−0.204248	+	0.353768i
$926$			12.9572i			0.425802i
$927$		0			0
$928$	4.69348			0.154071
$929$	11.3860	−	19.7211i	0.373562	−	0.647028i	−0.616549	−	0.787317i	$-0.711470\pi$
$929$	11.3860	−	19.7211i	0.373562	−	0.647028i	0.990111	+	0.140288i	$0.0448030\pi$
$930$		0			0
$931$		0			0
$932$	−24.7381	+	14.2825i	−0.810323	+	0.467840i
$933$		0			0
$934$	2.46895	+	1.42545i	0.0807865	+	0.0466421i
$935$			16.0116i			0.523637i
$936$		0			0
$937$		−	19.4429i		−	0.635173i	−0.948229	−	0.317587i	$-0.897128\pi$
$937$		−	19.4429i		−	0.635173i	0.948229	−	0.317587i	$-0.102872\pi$
$938$		0			0
$939$		0			0
$940$	6.02598	+	10.4373i	0.196546	+	0.340428i
$941$	−9.73008	−	16.8530i	−0.317192	−	0.549392i	0.662709	−	0.748877i	$-0.269407\pi$
$941$	−9.73008	−	16.8530i	−0.317192	−	0.549392i	−0.979901	+	0.199485i	$0.936073\pi$
$942$		0			0
$943$	2.15428	+	1.24378i	0.0701531	+	0.0405029i
$944$	9.44130			0.307288
$945$		0			0
$946$	−16.8151			−0.546707
$947$	−26.2034	−	15.1285i	−0.851495	−	0.491611i	0.00966017	−	0.999953i	$-0.496925\pi$
$947$	−26.2034	−	15.1285i	−0.851495	−	0.491611i	−0.861155	+	0.508343i	$0.830258\pi$
$948$		0			0
$949$	19.8095	+	34.3110i	0.643042	+	1.11378i
$950$	6.04544	+	10.4710i	0.196140	+	0.339724i
$951$		0			0
$952$		0			0
$953$		−	21.4885i		−	0.696082i	−0.937479	−	0.348041i	$-0.886847\pi$
$953$		−	21.4885i		−	0.696082i	0.937479	−	0.348041i	$-0.113153\pi$
$954$		0			0
$955$		−	12.9661i		−	0.419573i
$956$	10.0020	+	5.77465i	0.323487	+	0.186765i
$957$		0			0
$958$	28.8130	−	16.6352i	0.930906	−	0.537459i
$959$		0			0
$960$		0			0
$961$	−15.0793	+	26.1181i	−0.486429	+	0.842520i
$962$	15.0113			0.483985
$963$		0			0
$964$			0.0345256i			0.00111199i
$965$	−18.5512	+	32.1316i	−0.597184	+	1.03435i
$966$		0			0
$967$	−8.76620	−	15.1835i	−0.281902	−	0.488268i	0.689951	−	0.723856i	$-0.257632\pi$
$967$	−8.76620	−	15.1835i	−0.281902	−	0.488268i	−0.971853	+	0.235587i	$0.924299\pi$
$968$	7.83426	−	4.52311i	0.251803	−	0.145378i
$969$		0			0
$970$	9.17475	−	15.8911i	0.294583	−	0.510234i
$971$	−25.8916			−0.830901			−0.415451	−	0.909616i	$-0.636376\pi$
$971$	−25.8916			−0.830901			−0.415451	+	0.909616i	$0.636376\pi$
$972$		0			0
$973$		0			0
$974$	−9.04997	−	5.22500i	−0.289980	−	0.167420i
$975$		0			0
$976$	8.53864	−	4.92979i	0.273315	−	0.157799i
$977$	47.1235	−	27.2068i	1.50761	−	0.870421i	0.507653	−	0.861562i	$-0.330513\pi$
$977$	47.1235	−	27.2068i	1.50761	−	0.870421i	0.999961	−	0.00885973i	$-0.00282018\pi$
$978$		0			0
$979$	1.29141	+	0.745597i	0.0412737	+	0.0238294i
$980$		0			0
$981$		0			0
$982$	−2.34871			−0.0749504
$983$	−23.8665	+	41.3379i	−0.761222	+	1.31847i	0.181000	+	0.983483i	$0.442067\pi$
$983$	−23.8665	+	41.3379i	−0.761222	+	1.31847i	−0.942221	+	0.334991i	$0.891267\pi$
$984$		0			0
$985$	29.5650	−	17.0694i	0.942020	−	0.543876i
$986$	18.5522	+	32.1334i	0.590823	+	1.02334i
$987$		0			0
$988$	7.30447	−	12.6517i	0.232386	−	0.402505i
$989$			43.5303i			1.38418i
$990$		0			0
$991$	3.78032			0.120086			0.0600430	−	0.998196i	$-0.480876\pi$
$991$	3.78032			0.120086			0.0600430	+	0.998196i	$0.480876\pi$
$992$	−0.458640	+	0.794387i	−0.0145618	+	0.0252218i
$993$		0			0
$994$		0			0
$995$	−17.0966	+	9.87075i	−0.542000	+	0.312924i
$996$		0			0
$997$	2.58264	+	1.49109i	0.0817931	+	0.0472233i	0.540339	−	0.841448i	$-0.318296\pi$
$997$	2.58264	+	1.49109i	0.0817931	+	0.0472233i	−0.458546	+	0.888671i	$0.651629\pi$
$998$		−	34.7791i		−	1.10091i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.c.1763.21		48
3.2	odd	2		882.2.m.c.587.11	yes	48
7.2	even	3		2646.2.l.c.521.9		48
7.3	odd	6		2646.2.t.c.1979.1		48
7.4	even	3		2646.2.t.c.1979.2		48
7.5	odd	6		2646.2.l.c.521.10		48
7.6	odd	2	inner	2646.2.m.c.1763.22		48
9.4	even	3		882.2.m.c.293.2	✓	48
9.5	odd	6	inner	2646.2.m.c.881.22		48
21.2	odd	6		882.2.l.c.227.16		48
21.5	even	6		882.2.l.c.227.21		48
21.11	odd	6		882.2.t.c.803.18		48
21.17	even	6		882.2.t.c.803.19		48
21.20	even	2		882.2.m.c.587.2	yes	48
63.4	even	3		882.2.l.c.509.9		48
63.5	even	6		2646.2.t.c.2285.2		48
63.13	odd	6		882.2.m.c.293.11	yes	48
63.23	odd	6		2646.2.t.c.2285.1		48
63.31	odd	6		882.2.l.c.509.4		48
63.32	odd	6		2646.2.l.c.1097.10		48
63.40	odd	6		882.2.t.c.815.18		48
63.41	even	6	inner	2646.2.m.c.881.21		48
63.58	even	3		882.2.t.c.815.19		48
63.59	even	6		2646.2.l.c.1097.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.16		48	21.2	odd	6
882.2.l.c.227.21		48	21.5	even	6
882.2.l.c.509.4		48	63.31	odd	6
882.2.l.c.509.9		48	63.4	even	3
882.2.m.c.293.2	✓	48	9.4	even	3
882.2.m.c.293.11	yes	48	63.13	odd	6
882.2.m.c.587.2	yes	48	21.20	even	2
882.2.m.c.587.11	yes	48	3.2	odd	2
882.2.t.c.803.18		48	21.11	odd	6
882.2.t.c.803.19		48	21.17	even	6
882.2.t.c.815.18		48	63.40	odd	6
882.2.t.c.815.19		48	63.58	even	3
2646.2.l.c.521.9		48	7.2	even	3
2646.2.l.c.521.10		48	7.5	odd	6
2646.2.l.c.1097.9		48	63.59	even	6
2646.2.l.c.1097.10		48	63.32	odd	6
2646.2.m.c.881.21		48	63.41	even	6	inner
2646.2.m.c.881.22		48	9.5	odd	6	inner
2646.2.m.c.1763.21		48	1.1	even	1	trivial
2646.2.m.c.1763.22		48	7.6	odd	2	inner
2646.2.t.c.1979.1		48	7.3	odd	6
2646.2.t.c.1979.2		48	7.4	even	3
2646.2.t.c.2285.1		48	63.23	odd	6
2646.2.t.c.2285.2		48	63.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.724499 - 1.25487i) q^{5} +1.00000i q^{8} -1.44900i q^{10} +(1.21051 + 0.698887i) q^{11} +(-3.03494 + 1.75222i) q^{13} +(-0.500000 + 0.866025i) q^{16} -7.90553 q^{17} +4.16869i q^{19} +(0.724499 - 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(3.13371 - 1.80925i) q^{23} +(1.45020 - 2.51182i) q^{25} -3.50444 q^{26} +(-4.06467 - 2.34674i) q^{29} +(0.794387 - 0.458640i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.84639 - 3.95277i) q^{34} -4.28351 q^{37} +(-2.08434 + 3.61019i) q^{38} +(1.25487 - 0.724499i) q^{40} +(0.343727 + 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +1.39777i q^{44} +3.61850 q^{46} +(-4.15872 + 7.20312i) q^{47} +(2.51182 - 1.45020i) q^{50} +(-3.03494 - 1.75222i) q^{52} -5.96029i q^{53} -2.02537i q^{55} +(-2.34674 - 4.06467i) q^{58} +(-4.72065 - 8.17641i) q^{59} +(-8.53864 - 4.92979i) q^{61} +0.917280 q^{62} -1.00000 q^{64} +(4.39762 + 2.53897i) q^{65} +(1.48540 + 2.57278i) q^{67} +(-3.95277 - 6.84639i) q^{68} +12.9436i q^{71} -11.3053i q^{73} +(-3.70963 - 2.14176i) q^{74} +(-3.61019 + 2.08434i) q^{76} +(-7.81709 + 13.5396i) q^{79} +1.44900 q^{80} +0.687454i q^{82} +(-4.11183 + 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(-10.4182 + 6.01497i) q^{86} +(-0.698887 + 1.21051i) q^{88} +1.06683 q^{89} +(3.13371 + 1.80925i) q^{92} +(-7.20312 + 4.15872i) q^{94} +(5.23116 - 3.02021i) q^{95} +(10.9670 + 6.33179i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 48 * q^11 - 24 * q^16 - 48 * q^23 - 24 * q^25 + 48 * q^50 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 96 * q^86 - 48 * q^92 + 192 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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