LMFDB - Embedded newform 882.2.m.c.587.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([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("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			587.11
Character	$\chi$	$=$	882.587
Dual form			882.2.m.c.293.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.54269 + 0.787461i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.724499 + 1.25487i) q^{5} +(-0.942282 - 1.45331i) q^{6} -1.00000i q^{8} +(1.75981 + 2.42962i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.54269 + 0.787461i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.724499 + 1.25487i) q^{5} +(-0.942282 - 1.45331i) q^{6} -1.00000i q^{8} +(1.75981 + 2.42962i) q^{9} -1.44900i q^{10} +(-1.21051 - 0.698887i) q^{11} +(0.0893856 + 1.72974i) q^{12} +(-3.03494 + 1.75222i) q^{13} +(0.129520 + 2.50640i) q^{15} +(-0.500000 + 0.866025i) q^{16} +7.90553 q^{17} +(-0.309228 - 2.98402i) q^{18} +4.16869i q^{19} +(-0.724499 + 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(-3.13371 + 1.80925i) q^{23} +(0.787461 - 1.54269i) q^{24} +(1.45020 - 2.51182i) q^{25} +3.50444 q^{26} +(0.801614 + 5.13395i) q^{27} +(4.06467 + 2.34674i) q^{29} +(1.14103 - 2.23536i) q^{30} +(0.794387 - 0.458640i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.31710 - 2.03140i) q^{33} +(-6.84639 - 3.95277i) q^{34} +(-1.22421 + 2.73885i) q^{36} -4.28351 q^{37} +(2.08434 - 3.61019i) q^{38} +(-6.06179 + 0.313247i) q^{39} +(1.25487 - 0.724499i) q^{40} +(-0.343727 - 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} -1.39777i q^{44} +(-1.77388 + 3.96859i) q^{45} +3.61850 q^{46} +(4.15872 - 7.20312i) q^{47} +(-1.45331 + 0.942282i) q^{48} +(-2.51182 + 1.45020i) q^{50} +(12.1958 + 6.22530i) q^{51} +(-3.03494 - 1.75222i) q^{52} +5.96029i q^{53} +(1.87276 - 4.84694i) q^{54} -2.02537i q^{55} +(-3.28268 + 6.43101i) q^{57} +(-2.34674 - 4.06467i) q^{58} +(4.72065 + 8.17641i) q^{59} +(-2.10584 + 1.36536i) q^{60} +(-8.53864 - 4.92979i) q^{61} -0.917280 q^{62} -1.00000 q^{64} +(-4.39762 - 2.53897i) q^{65} +(0.124941 + 2.41779i) q^{66} +(1.48540 + 2.57278i) q^{67} +(3.95277 + 6.84639i) q^{68} +(-6.25907 + 0.323442i) q^{69} -12.9436i q^{71} +(2.42962 - 1.75981i) q^{72} -11.3053i q^{73} +(3.70963 + 2.14176i) q^{74} +(4.21518 - 2.73300i) q^{75} +(-3.61019 + 2.08434i) q^{76} +(5.40629 + 2.75961i) q^{78} +(-7.81709 + 13.5396i) q^{79} -1.44900 q^{80} +(-2.80614 + 8.55135i) q^{81} +0.687454i q^{82} +(4.11183 - 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(10.4182 - 6.01497i) q^{86} +(4.42258 + 6.82107i) q^{87} +(-0.698887 + 1.21051i) q^{88} -1.06683 q^{89} +(3.52052 - 2.54996i) q^{90} +(-3.13371 - 1.80925i) q^{92} +(1.58666 - 0.0819916i) q^{93} +(-7.20312 + 4.15872i) q^{94} +(-5.23116 + 3.02021i) q^{95} +(1.72974 - 0.0893856i) q^{96} +(10.9670 + 6.33179i) q^{97} +(-0.432231 - 4.17099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 32 * q^9	$ 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 32 * q^9 + 48 * q^11 + 48 * q^15 - 24 * q^16 + 16 * q^18 + 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 - 64 * q^39 - 48 * q^50 - 80 * q^57 - 48 * q^64 + 32 * q^72 + 32 * q^78 + 48 * q^79 + 48 * q^85 + 96 * q^86 + 48 * q^92 + 96 * q^93 - 192 * q^95 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.54269	+	0.787461i	0.890675	+	0.454641i
$3$	1.54269	+	0.787461i	0.890675	+	0.454641i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.724499	+	1.25487i	0.324006	+	0.561195i	0.981311	−	0.192430i	$-0.0616369\pi$
$5$	0.724499	+	1.25487i	0.324006	+	0.561195i	−0.657305	+	0.753625i	$0.728304\pi$
$6$	−0.942282	−	1.45331i	−0.384685	−	0.593311i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.75981	+	2.42962i	0.586603	+	0.809874i
$10$		−	1.44900i		−	0.458214i
$11$	−1.21051	−	0.698887i	−0.364982	−	0.210722i	0.306282	−	0.951941i	$-0.400915\pi$
$11$	−1.21051	−	0.698887i	−0.364982	−	0.210722i	−0.671264	+	0.741218i	$0.734248\pi$
$12$	0.0893856	+	1.72974i	0.0258034	+	0.499334i
$13$	−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
$15$	0.129520	+	2.50640i	0.0334418	+	0.647148i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	7.90553			1.91737			0.958687	−	0.284464i	$-0.0918158\pi$
$17$	7.90553			1.91737			0.958687	+	0.284464i	$0.0918158\pi$
$18$	−0.309228	−	2.98402i	−0.0728858	−	0.703340i
$19$			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	−0.789767	−	0.613407i	$-0.789798\pi$
$23$	−3.13371	+	1.80925i	−0.653424	+	0.377255i	0.136343	+	0.990662i	$0.456465\pi$
$24$	0.787461	−	1.54269i	0.160740	−	0.314901i
$25$	1.45020	−	2.51182i	0.290040	−	0.502364i
$26$	3.50444			0.687278
$27$	0.801614	+	5.13395i	0.154271	+	0.988029i
$28$		0			0
$29$	4.06467	+	2.34674i	0.754791	+	0.435779i	0.827422	−	0.561580i	$-0.189806\pi$
$29$	4.06467	+	2.34674i	0.754791	+	0.435779i	−0.0726316	+	0.997359i	$0.523140\pi$
$30$	1.14103	−	2.23536i	0.208323	−	0.408119i
$31$	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
$33$	−1.31710	−	2.03140i	−0.229277	−	0.353621i
$34$	−6.84639	−	3.95277i	−1.17415	−	0.677894i
$35$		0			0
$36$	−1.22421	+	2.73885i	−0.204035	+	0.456475i
$37$	−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
$39$	−6.06179	+	0.313247i	−0.970663	+	0.0501597i
$40$	1.25487	−	0.724499i	0.198412	−	0.114553i
$41$	−0.343727	−	0.595352i	−0.0536811	−	0.0929784i	0.837936	−	0.545768i	$-0.183762\pi$
$41$	−0.343727	−	0.595352i	−0.0536811	−	0.0929784i	−0.891617	+	0.452790i	$0.850429\pi$
$42$		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
$45$	−1.77388	+	3.96859i	−0.264434	+	0.591603i
$46$	3.61850			0.533519
$47$	4.15872	−	7.20312i	0.606612	−	1.05068i	−0.385182	−	0.922840i	$-0.625861\pi$
$47$	4.15872	−	7.20312i	0.606612	−	1.05068i	0.991794	−	0.127842i	$-0.0408052\pi$
$48$	−1.45331	+	0.942282i	−0.209767	+	0.136007i
$49$		0			0
$50$	−2.51182	+	1.45020i	−0.355225	+	0.205089i
$51$	12.1958	+	6.22530i	1.70776	+	0.871716i
$52$	−3.03494	−	1.75222i	−0.420870	−	0.242990i
$53$			5.96029i			0.818709i	0.912375	+	0.409354i	$0.134246\pi$
$53$			5.96029i			0.818709i	−0.912375	+	0.409354i	$0.865754\pi$
$54$	1.87276	−	4.84694i	0.254850	−	0.659584i
$55$		−	2.02537i		−	0.273101i
$56$		0			0
$57$	−3.28268	+	6.43101i	−0.434802	+	0.851808i
$58$	−2.34674	−	4.06467i	−0.308142	−	0.533718i
$59$	4.72065	+	8.17641i	0.614577	+	1.06448i	0.990459	+	0.137810i	$0.0440064\pi$
$59$	4.72065	+	8.17641i	0.614577	+	1.06448i	−0.375882	+	0.926668i	$0.622660\pi$
$60$	−2.10584	+	1.36536i	−0.271863	+	0.176268i
$61$	−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
$66$	0.124941	+	2.41779i	0.0153792	+	0.297609i
$67$	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
$69$	−6.25907	+	0.323442i	−0.753504	+	0.0389378i
$70$		0			0
$71$		−	12.9436i		−	1.53612i	−0.640377	−	0.768061i	$-0.721222\pi$
$71$		−	12.9436i		−	1.53612i	0.640377	−	0.768061i	$-0.278778\pi$
$72$	2.42962	−	1.75981i	0.286334	−	0.207396i
$73$		−	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
$75$	4.21518	−	2.73300i	0.486727	−	0.315579i
$76$	−3.61019	+	2.08434i	−0.414117	+	0.239091i
$77$		0			0
$78$	5.40629	+	2.75961i	0.612141	+	0.312465i
$79$	−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
$81$	−2.80614	+	8.55135i	−0.311793	+	0.950150i
$82$			0.687454i			0.0759166i
$83$	4.11183	−	7.12189i	0.451332	−	0.781729i	−0.547137	−	0.837043i	$-0.684282\pi$
$83$	4.11183	−	7.12189i	0.451332	−	0.781729i	0.998469	+	0.0553135i	$0.0176158\pi$
$84$		0			0
$85$	5.72755	+	9.92041i	0.621240	+	1.07602i
$86$	10.4182	−	6.01497i	1.12343	−	0.648611i
$87$	4.42258	+	6.82107i	0.474150	+	0.731296i
$88$	−0.698887	+	1.21051i	−0.0745016	+	0.129041i
$89$	−1.06683			−0.113084			−0.0565421	−	0.998400i	$-0.518008\pi$
$89$	−1.06683			−0.113084			−0.0565421	+	0.998400i	$0.518008\pi$
$90$	3.52052	−	2.54996i	0.371096	−	0.268790i
$91$		0			0
$92$	−3.13371	−	1.80925i	−0.326712	−	0.188627i
$93$	1.58666	−	0.0819916i	0.164529	−	0.00850213i
$94$	−7.20312	+	4.15872i	−0.742945	+	0.428939i
$95$	−5.23116	+	3.02021i	−0.536706	+	0.309867i
$96$	1.72974	−	0.0893856i	0.176541	−	0.00912288i
$97$	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
$99$	−0.432231	−	4.17099i	−0.0434409	−	0.419200i
$100$	2.90040			0.290040
$101$	8.77726	−	15.2027i	0.873370	−	1.51272i	0.0148801	−	0.999889i	$-0.495263\pi$
$101$	8.77726	−	15.2027i	0.873370	−	1.51272i	0.858489	−	0.512831i	$-0.171403\pi$
$102$	−7.44924	−	11.4892i	−0.737584	−	1.13760i
$103$	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	$-0.963577\pi$
$107$		−	2.36213i		−	0.228356i	0.993460	−	0.114178i	$-0.0364233\pi$
$108$	−4.04532	+	3.26119i	−0.389261	+	0.313808i
$109$	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
$111$	−6.60815	−	3.37310i	−0.627218	−	0.320161i
$112$		0			0
$113$	2.90616	−	1.67787i	0.273388	−	0.157841i	−0.357038	−	0.934090i	$-0.616213\pi$
$113$	2.90616	−	1.67787i	0.273388	−	0.157841i	0.630426	+	0.776249i	$0.282880\pi$
$114$	6.05839	−	3.92808i	0.567420	−	0.367898i
$115$	−4.54074	−	2.62160i	−0.423427	−	0.244465i
$116$			4.69348i			0.435779i
$117$	−9.59815	−	4.29018i	−0.887350	−	0.396627i
$118$		−	9.44130i		−	0.869143i
$119$		0			0
$120$	2.50640	−	0.129520i	0.228802	−	0.0118235i
$121$	−4.52311	−	7.83426i	−0.411192	−	0.712206i
$122$	4.92979	+	8.53864i	0.446322	+	0.773052i
$123$	−0.0614485	−	1.18912i	−0.00554062	−	0.107219i
$124$	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
$129$	−17.4832	+	11.3356i	−1.53931	+	0.998044i
$130$	2.53897	+	4.39762i	0.222682	+	0.385697i
$131$	4.12856	+	7.15088i	0.360714	+	0.624775i	0.988079	−	0.153951i	$-0.0491996\pi$
$131$	4.12856	+	7.15088i	0.360714	+	0.624775i	−0.627364	+	0.778726i	$0.715866\pi$
$132$	1.10069	−	2.15634i	0.0958030	−	0.187685i
$133$		0			0
$134$		−	2.97079i		−	0.256637i
$135$	−5.86167	+	4.72546i	−0.504492	+	0.406703i
$136$		−	7.90553i		−	0.677894i
$137$	11.3267	+	6.53946i	0.967703	+	0.558703i	0.898535	−	0.438902i	$-0.144632\pi$
$137$	11.3267	+	6.53946i	0.967703	+	0.558703i	0.0691676	+	0.997605i	$0.477966\pi$
$138$	5.58224	+	2.84943i	0.475192	+	0.242559i
$139$	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
$141$	12.0878	−	7.83738i	1.01798	−	0.660026i
$142$	−6.47179	+	11.2095i	−0.543101	+	0.940678i
$143$	4.89842			0.409627
$144$	−2.98402	+	0.309228i	−0.248668	+	0.0257690i
$145$			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	−0.521903	−	0.853005i	$-0.674778\pi$
$149$	−0.538692	+	0.311014i	−0.0441314	+	0.0254792i	0.477772	+	0.878484i	$0.341445\pi$
$150$	−5.01695	+	0.259254i	−0.409632	+	0.0211680i
$151$	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
$153$	13.9122	+	19.2075i	1.12474	+	1.55283i
$154$		0			0
$155$	1.15107	+	0.664569i	0.0924559	+	0.0533794i
$156$	−3.30217	−	5.09304i	−0.264386	−	0.407769i
$157$	−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
$159$	−4.69350	+	9.19490i	−0.372218	+	0.729203i
$160$	1.25487	+	0.724499i	0.0992062	+	0.0572767i
$161$		0			0
$162$	6.70586	−	6.00262i	0.526862	−	0.471610i
$163$	−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
$165$	1.59490	−	3.12453i	0.124163	−	0.243244i
$166$	−7.12189	+	4.11183i	−0.552766	+	0.319140i
$167$	−3.05895	−	5.29826i	−0.236709	−	0.409992i	0.723059	−	0.690786i	$-0.242735\pi$
$167$	−3.05895	−	5.29826i	−0.236709	−	0.409992i	−0.959768	+	0.280794i	$0.909402\pi$
$168$		0			0
$169$	−0.359433	+	0.622557i	−0.0276487	+	0.0478890i
$170$		−	11.4551i		−	0.878567i
$171$	−10.1283	+	7.33610i	−0.774534	+	0.561006i
$172$	−12.0299			−0.917275
$173$	−1.14757	+	1.98766i	−0.0872484	+	0.151119i	−0.906347	−	0.422534i	$-0.861141\pi$
$173$	−1.14757	+	1.98766i	−0.0872484	+	0.151119i	0.819099	+	0.573653i	$0.194474\pi$
$174$	−0.419530	−	8.11851i	−0.0318045	−	0.615463i
$175$		0			0
$176$	1.21051	−	0.698887i	0.0912454	−	0.0526806i
$177$	0.843917	+	16.3310i	0.0634327	+	1.22752i
$178$	0.923906	+	0.533417i	0.0692497	+	0.0399813i
$179$			3.37592i			0.252328i	0.992009	+	0.126164i	$0.0402666\pi$
$179$			3.37592i			0.252328i	−0.992009	+	0.126164i	$0.959733\pi$
$180$	−4.32384	+	0.448071i	−0.322280	+	0.0333973i
$181$		−	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
$183$	−9.29049	−	14.3290i	−0.686773	−	1.05923i
$184$	1.80925	+	3.13371i	0.133380	+	0.231020i
$185$	−3.10340	−	5.37525i	−0.228167	−	0.395196i
$186$	−1.41508	−	0.722322i	−0.103759	−	0.0529632i
$187$	−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	0.192707	−	0.981256i	$-0.438273\pi$
$191$	−7.74947	−	4.47416i	−0.560732	−	0.323739i	−0.753439	+	0.657517i	$0.771607\pi$
$192$	−1.54269	−	0.787461i	−0.111334	−	0.0568301i
$193$	−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
$195$	−4.78485	−	7.37981i	−0.342650	−	0.528479i
$196$		0			0
$197$		−	23.5602i		−	1.67860i	−0.543670	−	0.839299i	$-0.682966\pi$
$197$		−	23.5602i		−	1.67860i	0.543670	−	0.839299i	$-0.317034\pi$
$198$	−1.71117	+	3.82829i	−0.121608	+	0.272065i
$199$		−	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
$201$	0.265546	+	5.13871i	0.0187302	+	0.362456i
$202$	−15.2027	+	8.77726i	−1.06965	+	0.617566i
$203$		0			0
$204$	0.706641	+	13.6745i	0.0494748	+	0.957409i
$205$	0.498060	−	0.862665i	0.0347860	−	0.0602511i
$206$	−4.45810			−0.310610
$207$	−9.91053	−	4.42980i	−0.688830	−	0.307893i
$208$		−	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
$213$	10.1926	−	19.9680i	0.698384	−	1.36818i
$214$	−1.18106	+	2.04566i	−0.0807359	+	0.139839i
$215$	−17.4314			−1.18881
$216$	5.13395	−	0.801614i	0.349321	−	0.0545429i
$217$		0			0
$218$	−11.2545	−	6.49776i	−0.762248	−	0.440084i
$219$	8.90251	−	17.4407i	0.601576	−	1.17853i
$220$	1.75402	−	1.01269i	0.118256	−	0.0682753i
$221$	−23.9928	+	13.8523i	−1.61393	+	0.931803i
$222$	4.03628	+	6.22527i	0.270897	+	0.417813i
$223$	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
$225$	8.65486	−	0.896887i	0.576991	−	0.0597924i
$226$	−3.35574			−0.223221
$227$	−6.11065	+	10.5840i	−0.405578	+	0.702482i	−0.994389	−	0.105789i	$-0.966263\pi$
$227$	−6.11065	+	10.5840i	−0.405578	+	0.702482i	0.588810	+	0.808271i	$0.299596\pi$
$228$	−7.21076	+	0.372621i	−0.477544	+	0.0246774i
$229$	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	$-0.614787\pi$
$233$		−	28.5651i		−	1.87136i	0.352848	−	0.935681i	$-0.385213\pi$
$234$	6.16716	+	8.51448i	0.403160	+	0.556609i
$235$	12.0520			0.786184
$236$	−4.72065	+	8.17641i	−0.307288	+	0.532239i
$237$	−22.7213	+	14.7318i	−1.47591	+	0.956933i
$238$		0			0
$239$	−10.0020	+	5.77465i	−0.646975	+	0.373531i	−0.787296	−	0.616575i	$-0.788520\pi$
$239$	−10.0020	+	5.77465i	−0.646975	+	0.373531i	0.140322	+	0.990106i	$0.455186\pi$
$240$	−2.23536	−	1.14103i	−0.144292	−	0.0736532i
$241$	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
$243$	−11.0629	+	10.9824i	−0.709683	+	0.704521i
$244$		−	9.85957i		−	0.631194i
$245$		0			0
$246$	−0.541343	+	1.06053i	−0.0345148	+	0.0676170i
$247$	−7.30447	−	12.6517i	−0.464772	−	0.805009i
$248$	−0.458640	−	0.794387i	−0.0291237	−	0.0504437i
$249$	11.9515	−	7.74900i	0.757396	−	0.491073i
$250$	−9.91398	−	5.72384i	−0.627015	−	0.362007i
$251$	−3.26317			−0.205969			−0.102985	−	0.994683i	$-0.532839\pi$
$251$	−3.26317			−0.205969			−0.102985	+	0.994683i	$0.532839\pi$
$252$		0			0
$253$	5.05784			0.317984
$254$	11.1782	+	6.45374i	0.701383	+	0.404944i
$255$	1.02392	+	19.8144i	0.0641205	+	1.24083i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.89851	−	17.1447i	−0.617452	−	1.06946i	−0.989949	−	0.141425i	$-0.954832\pi$
$257$	−9.89851	−	17.1447i	−0.617452	−	1.06946i	0.372497	−	0.928034i	$-0.378502\pi$
$258$	20.8087	−	1.07530i	1.29549	−	0.0669455i
$259$		0			0
$260$		−	5.07794i		−	0.314920i
$261$	1.45136	+	14.0054i	0.0898367	+	0.866915i
$262$		−	8.25713i		−	0.510127i
$263$	−15.2576	−	8.80897i	−0.940823	−	0.543184i	−0.0506045	−	0.998719i	$-0.516115\pi$
$263$	−15.2576	−	8.80897i	−0.940823	−	0.543184i	−0.890218	+	0.455535i	$0.849448\pi$
$264$	−2.03140	+	1.31710i	−0.125024	+	0.0810617i
$265$	−7.47939	+	4.31823i	−0.459455	+	0.265266i
$266$		0			0
$267$	−1.64580	−	0.840091i	−0.100721	−	0.0514127i
$268$	−1.48540	+	2.57278i	−0.0907350	+	0.157158i
$269$	−7.67344			−0.467858			−0.233929	−	0.972254i	$-0.575158\pi$
$269$	−7.67344			−0.467858			−0.233929	+	0.972254i	$0.575158\pi$
$270$	7.43908	−	1.16154i	0.452728	−	0.0706889i
$271$			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
$276$	−3.40965	−	5.25879i	−0.205237	−	0.316542i
$277$	−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
$279$	2.51229	+	1.12294i	0.150407	+	0.0672289i
$280$		0			0
$281$	14.3155	+	8.26508i	0.853994	+	0.493053i	0.861996	−	0.506915i	$-0.169214\pi$
$281$	14.3155	+	8.26508i	0.853994	+	0.493053i	−0.00800273	+	0.999968i	$0.502547\pi$
$282$	−14.3870	+	0.743460i	−0.856736	+	0.0442724i
$283$	−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
$285$	−10.4484	+	0.539927i	−0.618909	+	0.0319825i
$286$	−4.24216	−	2.44921i	−0.250844	−	0.144825i
$287$		0			0
$288$	2.73885	+	1.22421i	0.161388	+	0.0721373i
$289$	45.4974			2.67632
$290$	3.40042	−	5.88971i	0.199680	−	0.345855i
$291$	11.9327	+	18.4041i	0.699504	+	1.07887i
$292$	9.79071	−	5.65267i	0.572958	−	0.330797i
$293$	−4.26045	−	7.37932i	−0.248898	−	0.431104i	0.714322	−	0.699817i	$-0.246735\pi$
$293$	−4.26045	−	7.37932i	−0.248898	−	0.431104i	−0.963220	+	0.268713i	$0.913402\pi$
$294$		0			0
$295$	−6.84022	+	11.8476i	−0.398253	+	0.689794i
$296$			4.28351i			0.248974i
$297$	2.61769	−	6.77492i	0.151894	−	0.393121i
$298$	0.622028			0.0360331
$299$	6.34042	−	10.9819i	0.366676	−	0.635101i
$300$	4.47443	+	2.28395i	0.258332	+	0.131864i
$301$		0			0
$302$	−18.3443	+	10.5911i	−1.05559	+	0.609448i
$303$	25.5121	−	16.5413i	1.46563	−	0.950273i
$304$	−3.61019	−	2.08434i	−0.207059	−	0.119545i
$305$		−	14.2865i		−	0.818043i
$306$	−2.44461	−	23.5903i	−0.139749	−	1.34857i
$307$		−	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
$309$	7.71136	−	0.398490i	0.438684	−	0.0226693i
$310$	−0.664569	−	1.15107i	−0.0377450	−	0.0653762i
$311$	−1.78678	−	3.09479i	−0.101319	−	0.175489i	0.810909	−	0.585172i	$-0.198973\pi$
$311$	−1.78678	−	3.09479i	−0.101319	−	0.175489i	−0.912228	+	0.409682i	$0.865640\pi$
$312$	0.313247	+	6.06179i	0.0177341	+	0.343181i
$313$	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	0.600692	−	0.799481i	$-0.294892\pi$
$317$	3.71520	+	2.14497i	0.208666	+	0.120474i	−0.392025	+	0.919955i	$0.628225\pi$
$318$	8.66214	−	5.61627i	0.485749	−	0.314945i
$319$	−3.28021	−	5.68149i	−0.183657	−	0.318102i
$320$	−0.724499	−	1.25487i	−0.0405007	−	0.0701494i
$321$	1.86008	−	3.64404i	0.103820	−	0.203391i
$322$		0			0
$323$			32.9557i			1.83370i
$324$	−8.80876	+	1.84549i	−0.489375	+	0.102527i
$325$			10.1643i			0.563814i
$326$	2.62863	+	1.51764i	0.145586	+	0.0840542i
$327$	20.0481	+	10.2335i	1.10866	+	0.565912i
$328$	−0.595352	+	0.343727i	−0.0328728	+	0.0189791i
$329$		0			0
$330$	−2.94349	+	1.90847i	−0.162034	+	0.105058i
$331$	−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
$333$	−7.53817	−	10.4073i	−0.413089	−	0.570318i
$334$			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
$339$	5.80457	−	0.299955i	0.315261	−	0.0162913i
$340$	−5.72755	+	9.92041i	−0.310620	+	0.538010i
$341$	−1.28215			−0.0694323
$342$	12.4395	−	1.28908i	0.672649	−	0.0697053i
$343$		0			0
$344$	10.4182	+	6.01497i	0.561714	+	0.324306i
$345$	−4.94057	−	7.61999i	−0.265991	−	0.410246i
$346$	1.98766	−	1.14757i	0.106857	−	0.0616939i
$347$	−19.2988	+	11.1422i	−1.03602	+	0.598144i	−0.918702	−	0.394951i	$-0.870762\pi$
$347$	−19.2988	+	11.1422i	−1.03602	+	0.598144i	−0.117313	+	0.993095i	$0.537428\pi$
$348$	−3.69593	+	7.24060i	−0.198123	+	0.388137i
$349$	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
$351$	−11.4287	−	14.1766i	−0.610017	−	0.756691i
$352$	−1.39777			−0.0745016
$353$	3.13232	−	5.42533i	0.166716	−	0.288761i	−0.770547	−	0.637383i	$-0.780017\pi$
$353$	3.13232	−	5.42533i	0.166716	−	0.288761i	0.937263	+	0.348622i	$0.113350\pi$
$354$	7.43466	−	14.5650i	0.395148	−	0.774123i
$355$	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	$0.103178\pi$
$359$			12.0693i			0.636991i	−0.947924	+	0.318496i	$0.896822\pi$
$360$	3.96859	+	1.77388i	0.209163	+	0.0934917i
$361$	1.62203			0.0853700
$362$	−0.844286	+	1.46235i	−0.0443747	+	0.0768592i
$363$	−0.808603	−	15.6476i	−0.0424406	−	0.821289i
$364$		0			0
$365$	14.1867	−	8.19071i	0.742567	−	0.428721i
$366$	0.881304	+	17.0545i	0.0460665	+	0.891454i
$367$	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
$369$	0.841588	−	1.88283i	0.0438113	−	0.0980164i
$370$			6.20681i			0.322677i
$371$		0			0
$372$	0.864336	+	1.33309i	0.0448137	+	0.0691175i
$373$	−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
$375$	17.6603	+	9.01460i	0.911972	+	0.465512i
$376$	−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
$381$	−19.9123	−	10.1641i	−1.02014	−	0.520725i
$382$	4.47416	+	7.74947i	0.228918	+	0.396498i
$383$	15.1513	+	26.2428i	0.774195	+	1.34095i	0.935246	+	0.353999i	$0.115179\pi$
$383$	15.1513	+	26.2428i	0.774195	+	1.34095i	−0.161050	+	0.986946i	$0.551488\pi$
$384$	0.942282	+	1.45331i	0.0480856	+	0.0741638i
$385$		0			0
$386$			25.6055i			1.30329i
$387$	−35.8976	+	3.72000i	−1.82478	+	0.189098i
$388$			12.6636i			0.642895i
$389$	18.2352	+	10.5281i	0.924562	+	0.533796i	0.885088	−	0.465424i	$-0.154098\pi$
$389$	18.2352	+	10.5281i	0.924562	+	0.533796i	0.0394744	+	0.999221i	$0.487432\pi$
$390$	0.453895	+	8.78352i	0.0229838	+	0.444771i
$391$	−24.7737	+	14.3031i	−1.25286	+	0.723338i
$392$		0			0
$393$	0.738068	+	14.2827i	0.0372306	+	0.720467i
$394$	−11.7801	+	20.4038i	−0.593474	+	1.02793i
$395$	−22.6539			−1.13984
$396$	3.39606	−	2.45982i	0.170659	−	0.123610i
$397$			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	−0.549665	−	0.835385i	$-0.685245\pi$
$401$	−2.02316	+	1.16807i	−0.101032	+	0.0583309i	0.448633	+	0.893716i	$0.351911\pi$
$402$	2.33938	−	4.58302i	0.116678	−	0.228580i
$403$	−1.60728	+	2.78389i	−0.0800642	+	0.138675i
$404$	17.5545			0.873370
$405$	−12.7639	+	2.67411i	−0.634242	+	0.132878i
$406$		0			0
$407$	5.18523	+	2.99369i	0.257022	+	0.148392i
$408$	6.22530	−	12.1958i	0.308198	−	0.603783i
$409$	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
$411$	12.3240	+	19.0077i	0.607899	+	0.937580i
$412$	3.86082	+	2.22905i	0.190209	+	0.109817i
$413$		0			0
$414$	6.36787	+	8.79159i	0.312964	+	0.432083i
$415$	11.9161			0.584937
$416$	−1.75222	+	3.03494i	−0.0859098	+	0.148800i
$417$	21.3160	−	1.10152i	1.04385	−	0.0539417i
$418$	−5.04623	+	2.91344i	−0.246819	+	0.142501i
$419$	−14.4297	−	24.9930i	−0.704939	−	1.22099i	−0.966714	−	0.255861i	$-0.917641\pi$
$419$	−14.4297	−	24.9930i	−0.704939	−	1.22099i	0.261775	−	0.965129i	$-0.415692\pi$
$420$		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
$423$	24.8194	−	2.57199i	1.20676	−	0.125054i
$424$	5.96029			0.289457
$425$	11.4646	−	19.8573i	0.556115	−	0.963220i
$426$	−18.8110	+	12.1965i	−0.911397	+	0.590923i
$427$		0			0
$428$	2.04566	−	1.18106i	0.0988808	−	0.0570889i
$429$	7.55676	+	3.85732i	0.364844	+	0.186233i
$430$	15.0960	+	8.71569i	0.727995	+	0.420308i
$431$		−	27.7631i		−	1.33730i	−0.743577	−	0.668650i	$-0.766872\pi$
$431$		−	27.7631i		−	1.33730i	0.743577	−	0.668650i	$-0.233128\pi$
$432$	−4.84694	−	1.87276i	−0.233198	−	0.0901030i
$433$			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
$435$	−5.35540	+	10.4916i	−0.256772	+	0.503035i
$436$	6.49776	+	11.2545i	0.311186	+	0.538990i
$437$	−7.54220	−	13.0635i	−0.360792	−	0.624911i
$438$	−16.4301	+	10.6528i	−0.785062	+	0.509011i
$439$	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	0.729107	−	0.684399i	$-0.239935\pi$
$443$	10.5439	+	6.08750i	0.500954	+	0.289226i	−0.228153	+	0.973625i	$0.573269\pi$
$444$	−0.382885	−	7.40938i	−0.0181709	−	0.351634i
$445$	−0.772921	−	1.33874i	−0.0366400	−	0.0634623i
$446$	−8.41256	−	14.5710i	−0.398346	−	0.689956i
$447$	−1.07595	+	0.0556003i	−0.0508906	+	0.00262981i
$448$		0			0
$449$			14.2454i			0.672283i	0.941811	+	0.336142i	$0.109122\pi$
$449$			14.2454i			0.672283i	−0.941811	+	0.336142i	$0.890878\pi$
$450$	−7.94377	−	3.55070i	−0.374473	−	0.167382i
$451$			0.960905i			0.0452472i
$452$	2.90616	+	1.67787i	0.136694	+	0.0789204i
$453$	30.7842	−	19.9596i	1.44637	−	0.937781i
$454$	10.5840	−	6.11065i	0.496730	−	0.286787i
$455$		0			0
$456$	6.43101	+	3.28268i	0.301160	+	0.153726i
$457$	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
$459$	6.33719	+	40.5866i	0.295794	+	1.89442i
$460$		−	5.24320i		−	0.244465i
$461$	11.0041	−	19.0597i	0.512513	−	0.887698i	−0.487382	−	0.873189i	$-0.662048\pi$
$461$	11.0041	−	19.0597i	0.512513	−	0.887698i	0.999895	−	0.0145095i	$-0.00461867\pi$
$462$		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
$465$	1.25242	+	1.93165i	0.0580797	+	0.0895779i
$466$	−14.2825	+	24.7381i	−0.661626	+	1.14597i
$467$	−2.85090			−0.131924			−0.0659619	−	0.997822i	$-0.521012\pi$
$467$	−2.85090			−0.131924			−0.0659619	+	0.997822i	$0.521012\pi$
$468$	−1.08367	−	10.4573i	−0.0500928	−	0.483390i
$469$		0			0
$470$	−10.4373	−	6.02598i	−0.481437	−	0.277958i
$471$	−25.9970	+	1.34341i	−1.19788	+	0.0619011i
$472$	8.17641	−	4.72065i	0.376350	−	0.217286i
$473$	14.5623	−	8.40757i	0.669577	−	0.386581i
$474$	27.0431	−	1.39747i	1.24213	−	0.0641879i
$475$	10.4710	+	6.04544i	0.480443	+	0.277384i
$476$		0			0
$477$	−14.4813	+	10.4890i	−0.663051	+	0.480257i
$478$	11.5493			0.528253
$479$	−16.6352	+	28.8130i	−0.760081	+	1.31650i	0.182727	+	0.983164i	$0.441508\pi$
$479$	−16.6352	+	28.8130i	−0.760081	+	1.31650i	−0.942808	+	0.333336i	$0.891826\pi$
$480$	1.36536	+	2.10584i	0.0623201	+	0.0961181i
$481$	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
$486$	15.0719	−	3.97959i	0.683676	−	0.180518i
$487$	−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
$489$	−4.68250	−	2.39016i	−0.211750	−	0.108087i
$490$		0			0
$491$	2.03404	−	1.17436i	0.0917952	−	0.0529980i	−0.453400	−	0.891307i	$-0.649789\pi$
$491$	2.03404	−	1.17436i	0.0917952	−	0.0529980i	0.545195	+	0.838309i	$0.316456\pi$
$492$	0.999082	−	0.647775i	0.0450421	−	0.0292040i
$493$	32.1334	+	18.5522i	1.44722	+	0.835550i
$494$			14.6089i			0.657287i
$495$	4.92089	−	3.56427i	0.221178	−	0.160202i
$496$			0.917280i			0.0411871i
$497$		0			0
$498$	−14.2248	+	0.735076i	−0.637429	+	0.0329396i
$499$	−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
$501$	−0.546853	−	10.5824i	−0.0244316	−	0.472787i
$502$	2.82599	+	1.63158i	0.126130	+	0.0728211i
$503$	−17.8290			−0.794956			−0.397478	−	0.917612i	$-0.630114\pi$
$503$	−17.8290			−0.794956			−0.397478	+	0.917612i	$0.630114\pi$
$504$		0			0
$505$	25.4365			1.13191
$506$	−4.38022	−	2.52892i	−0.194725	−	0.112424i
$507$	−1.04473	+	0.677375i	−0.0463983	+	0.0300833i
$508$	−6.45374	−	11.1782i	−0.286338	−	0.495953i
$509$	7.78061	+	13.4764i	0.344869	+	0.597331i	0.985330	−	0.170660i	$-0.0545899\pi$
$509$	7.78061	+	13.4764i	0.344869	+	0.597331i	−0.640461	+	0.767991i	$0.721257\pi$
$510$	9.02045	−	17.6717i	0.399432	−	0.782517i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−21.4018	+	3.34168i	−0.944914	+	0.147539i
$514$			19.7970i			0.873209i
$515$	5.59433	+	3.22989i	0.246516	+	0.142326i
$516$	−18.5585	−	9.47312i	−0.816994	−	0.417031i
$517$	−10.0683	+	5.81295i	−0.442805	+	0.255653i
$518$		0			0
$519$	−3.33556	+	2.16267i	−0.146415	+	0.0949309i
$520$	−2.53897	+	4.39762i	−0.111341	+	0.192848i
$521$	29.6376			1.29844			0.649222	−	0.760599i	$-0.275094\pi$
$521$	29.6376			1.29844			0.649222	+	0.760599i	$0.275094\pi$
$522$	5.74581	−	12.8547i	0.251487	−	0.562637i
$523$			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
$528$	2.41779	−	0.124941i	0.105221	−	0.00543735i
$529$	−4.95323	+	8.57925i	−0.215358	+	0.373011i
$530$	8.63645			0.375143
$531$	−11.5581	+	25.8583i	−0.501581	+	1.12216i
$532$		0			0
$533$	2.08638	+	1.20457i	0.0903711	+	0.0521758i
$534$	1.00526	+	1.55044i	0.0435018	+	0.0670941i
$535$	2.96416	−	1.71136i	0.128152	−	0.0739886i
$536$	2.57278	−	1.48540i	0.111127	−	0.0641593i
$537$	−2.65841	+	5.20802i	−0.114719	+	0.224743i
$538$	6.64540	+	3.83672i	0.286503	+	0.165413i
$539$		0			0
$540$	−7.02320	−	2.71362i	−0.302231	−	0.116776i
$541$	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
$543$	1.32968	−	2.60495i	0.0570622	−	0.111789i
$544$	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
$549$	−3.04886	−	29.4212i	−0.130122	−	1.25566i
$550$	4.05411			0.172868
$551$	−9.78283	+	16.9444i	−0.416762	+	0.721854i
$552$	0.323442	+	6.25907i	0.0137666	+	0.266404i
$553$		0			0
$554$	14.9885	−	8.65364i	0.636802	−	0.367658i
$555$	−0.554799	−	10.7362i	−0.0235499	−	0.455725i
$556$	10.6722	+	6.16162i	0.452603	+	0.261311i
$557$		−	17.3143i		−	0.733632i	−0.930294	−	0.366816i	$-0.880448\pi$
$557$		−	17.3143i		−	0.733632i	0.930294	−	0.366816i	$-0.119552\pi$
$558$	−1.61424	−	2.22864i	−0.0683361	−	0.0943460i
$559$		−	42.1583i		−	1.78311i
$560$		0			0
$561$	−10.4123	−	16.0593i	−0.439610	−	0.678023i
$562$	−8.26508	−	14.3155i	−0.348641	−	0.603865i
$563$	−10.3834	−	17.9846i	−0.437608	−	0.757959i	0.559897	−	0.828562i	$-0.310841\pi$
$563$	−10.3834	−	17.9846i	−0.437608	−	0.757959i	−0.997504	+	0.0706035i	$0.977507\pi$
$564$	12.8313	+	6.54967i	0.540294	+	0.275791i
$565$	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	0.743410	−	0.668836i	$-0.233207\pi$
$569$	12.7829	+	7.38020i	0.535887	+	0.309394i	−0.207524	+	0.978230i	$0.566540\pi$
$570$	9.31853	+	4.75660i	0.390310	+	0.199232i
$571$	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
$573$	−8.43184	−	13.0047i	−0.352245	−	0.543278i
$574$		0			0
$575$			10.4951i			0.437676i
$576$	−1.75981	−	2.42962i	−0.0733254	−	0.101234i
$577$			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
$579$	−2.28877	−	44.2910i	−0.0951180	−	1.84067i
$580$	−5.88971	+	3.40042i	−0.244557	+	0.141195i
$581$		0			0
$582$	−1.13194	−	21.9047i	−0.0469205	−	0.907980i
$583$	4.16557	−	7.21497i	0.172520	−	0.298814i
$584$	−11.3053			−0.467818
$585$	−1.57024	−	15.1527i	−0.0649215	−	0.626486i
$586$			8.52090i			0.351995i
$587$	−10.7433	+	18.6079i	−0.443423	+	0.768031i	−0.997941	−	0.0641405i	$-0.979569\pi$
$587$	−10.7433	+	18.6079i	−0.443423	+	0.768031i	0.554518	+	0.832172i	$0.312903\pi$
$588$		0			0
$589$	1.91193	+	3.31155i	0.0787796	+	0.136450i
$590$	11.8476	−	6.84022i	0.487758	−	0.281607i
$591$	18.5528	−	36.3462i	0.763159	−	1.49508i
$592$	2.14176	−	3.70963i	0.0880257	−	0.152465i
$593$	14.0949			0.578809			0.289404	−	0.957207i	$-0.406543\pi$
$593$	14.0949			0.578809			0.289404	+	0.957207i	$0.406543\pi$
$594$	−5.65444	+	4.55841i	−0.232005	+	0.187034i
$595$		0			0
$596$	−0.538692	−	0.311014i	−0.0220657	−	0.0127396i
$597$	10.7286	−	21.0180i	0.439091	−	0.860210i
$598$	−10.9819	+	6.34042i	−0.449084	+	0.259279i
$599$	16.6024	−	9.58537i	0.678354	−	0.391648i	−0.120881	−	0.992667i	$-0.538572\pi$
$599$	16.6024	−	9.58537i	0.678354	−	0.391648i	0.799235	+	0.601019i	$0.205239\pi$
$600$	−2.73300	−	4.21518i	−0.111574	−	0.172084i
$601$	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
$603$	−3.63688	+	8.13656i	−0.148105	+	0.331346i
$604$	21.1821			0.861889
$605$	6.55399	−	11.3518i	0.266457	−	0.461518i
$606$	−30.3648	+	1.56912i	−1.23349	+	0.0637412i
$607$	−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
$612$	−9.67804	+	21.6521i	−0.391211	+	0.875233i
$613$	−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
$615$	1.44767	−	0.938625i	0.0583756	−	0.0378490i
$616$		0			0
$617$	−28.6323	+	16.5308i	−1.15269	+	0.665506i	−0.949542	−	0.313641i	$-0.898451\pi$
$617$	−28.6323	+	16.5308i	−1.15269	+	0.665506i	−0.203149	+	0.979148i	$0.565118\pi$
$618$	−6.87748	−	3.51058i	−0.276653	−	0.141216i
$619$	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
$621$	−11.8006	−	14.6380i	−0.473543	−	0.587402i
$622$			3.57355i			0.143286i
$623$		0			0
$624$	2.75961	−	5.40629i	0.110473	−	0.216425i
$625$	1.04283	+	1.80623i	0.0417131	+	0.0722491i
$626$	−6.81464	−	11.8033i	−0.272368	−	0.471755i
$627$	8.46826	−	5.49057i	0.338190	−	0.219272i
$628$	−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
$633$	−1.93003	−	37.3490i	−0.0767120	−	1.48449i
$634$	−2.14497	−	3.71520i	−0.0851877	−	0.147549i
$635$	−9.35146	−	16.1972i	−0.371101	−	0.642767i
$636$	−10.3098	+	0.532764i	−0.408809	+	0.0211255i
$637$		0			0
$638$			6.56042i			0.259730i
$639$	31.4480	−	22.7783i	1.24407	−	0.901094i
$640$			1.44900i			0.0572767i
$641$	−9.66957	−	5.58273i	−0.381925	−	0.220505i	0.296730	−	0.954961i	$-0.404104\pi$
$641$	−9.66957	−	5.58273i	−0.381925	−	0.220505i	−0.678655	+	0.734457i	$0.737437\pi$
$642$	−3.43290	+	2.22579i	−0.135486	+	0.0878449i
$643$	−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
$645$	−26.8913	−	13.7265i	−1.05884	−	0.540482i
$646$	16.4779	−	28.5405i	0.648312	−	1.12291i
$647$	−12.9142			−0.507710			−0.253855	−	0.967242i	$-0.581699\pi$
$647$	−12.9142			−0.507710			−0.253855	+	0.967242i	$0.581699\pi$
$648$	8.55135	+	2.80614i	0.335929	+	0.110236i
$649$		−	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	−0.968272	−	0.249900i	$-0.919602\pi$
$653$	−31.5843	+	18.2352i	−1.23599	+	0.713598i	−0.267716	+	0.963498i	$0.586269\pi$
$654$	−12.2454	−	18.8865i	−0.478835	−	0.738521i
$655$	−5.98228	+	10.3616i	−0.233747	+	0.404862i
$656$	0.687454			0.0268406
$657$	27.4677	−	19.8952i	1.07162	−	0.776187i
$658$		0			0
$659$	2.04111	+	1.17844i	0.0795104	+	0.0459054i	0.539228	−	0.842160i	$-0.318716\pi$
$659$	2.04111	+	1.17844i	0.0795104	+	0.0459054i	−0.459718	+	0.888065i	$0.652049\pi$
$660$	3.50337	−	0.181039i	0.136369	−	0.00704694i
$661$	−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
$663$	−47.9217	+	2.47638i	−1.86112	+	0.0961748i
$664$	−7.12189	−	4.11183i	−0.276383	−	0.159570i
$665$		0			0
$666$	1.32458	+	12.7821i	0.0513266	+	0.495296i
$667$	−16.9833			−0.657598
$668$	3.05895	−	5.29826i	0.118354	−	0.204996i
$669$	15.8540	+	24.4521i	0.612951	+	0.945372i
$670$	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
$675$	14.0581	+	5.43174i	0.541095	+	0.209068i
$676$	−0.718866			−0.0276487
$677$	7.03074	−	12.1776i	0.270213	−	0.468023i	−0.698703	−	0.715412i	$-0.746239\pi$
$677$	7.03074	−	12.1776i	0.270213	−	0.468023i	0.968916	+	0.247389i	$0.0795724\pi$
$678$	−5.17688	−	2.64252i	−0.198817	−	0.101485i
$679$		0			0
$680$	9.92041	−	5.72755i	0.380430	−	0.219642i
$681$	−17.7613	+	11.5159i	−0.680615	+	0.441291i
$682$	1.11037	+	0.641075i	0.0425184	+	0.0245480i
$683$		−	33.6363i		−	1.28706i	−0.765422	−	0.643529i	$-0.777470\pi$
$683$		−	33.6363i		−	1.28706i	0.765422	−	0.643529i	$-0.222530\pi$
$684$	−11.4174	−	5.10335i	−0.436556	−	0.195132i
$685$			18.9513i			0.724093i
$686$		0			0
$687$	33.6466	−	1.73871i	1.28370	−	0.0663360i
$688$	−6.01497	−	10.4182i	−0.229319	−	0.397192i
$689$	−10.4438	−	18.0891i	−0.397875	−	0.689140i
$690$	0.468667	+	9.06939i	0.0178418	+	0.345266i
$691$	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
$696$	6.82107	−	4.42258i	0.258552	−	0.167637i
$697$	−2.71734	−	4.70658i	−0.102927	−	0.178274i
$698$	−1.61572	−	2.79851i	−0.0611560	−	0.105925i
$699$	22.4939	−	44.0672i	0.850798	−	1.66677i
$700$		0			0
$701$		−	31.5424i		−	1.19134i	−0.803229	−	0.595670i	$-0.796887\pi$
$701$		−	31.5424i		−	1.19134i	0.803229	−	0.595670i	$-0.203113\pi$
$702$	2.80921	+	17.9916i	0.106027	+	0.679051i
$703$		−	17.8566i		−	0.673476i
$704$	1.21051	+	0.698887i	0.0456227	+	0.0263403i
$705$	18.5925	+	9.49046i	0.700234	+	0.357431i
$706$	−5.42533	+	3.13232i	−0.204185	+	0.117886i
$707$		0			0
$708$	−13.7211	+	8.89637i	−0.515672	+	0.334346i
$709$	−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
$711$	−46.6527	+	4.83453i	−1.74961	+	0.181309i
$712$			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
$717$	−19.9773	+	1.03234i	−0.746066	+	0.0385535i
$718$	6.03463	−	10.4523i	0.225210	−	0.390076i
$719$	−28.3001			−1.05541			−0.527707	−	0.849426i	$-0.676948\pi$
$719$	−28.3001			−1.05541			−0.527707	+	0.849426i	$0.676948\pi$
$720$	−2.54996	−	3.52052i	−0.0950315	−	0.131202i
$721$		0			0
$722$	−1.40472	−	0.811015i	−0.0522782	−	0.0301829i
$723$	0.0325328	+	0.0501763i	0.00120991	+	0.00186608i
$724$	1.46235	−	0.844286i	0.0543477	−	0.0313776i
$725$	11.7892	−	6.80649i	0.437839	−	0.252787i
$726$	−7.12355	+	13.9556i	−0.264380	+	0.517940i
$727$	−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
$729$	−25.7148	+	8.23089i	−0.952401	+	0.304848i
$730$	−16.3814			−0.606303
$731$	−47.5516	+	82.3617i	−1.75876	+	3.04626i
$732$	7.76403	−	15.2103i	0.286967	−	0.562189i
$733$	−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
$738$	−1.67025	+	1.20979i	−0.0614829	+	0.0445329i
$739$	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
$741$	−1.30583	−	25.2697i	−0.0479708	−	0.928306i
$742$		0			0
$743$	6.86253	−	3.96208i	0.251762	−	0.145355i	−0.368809	−	0.929505i	$-0.620234\pi$
$743$	6.86253	−	3.96208i	0.251762	−	0.145355i	0.620571	+	0.784151i	$0.286901\pi$
$744$	−0.0819916	−	1.58666i	−0.00300596	−	0.0581697i
$745$	−0.780564	−	0.450659i	−0.0285976	−	0.0165109i
$746$			3.87360i			0.141822i
$747$	24.5396	−	2.54299i	0.897855	−	0.0930430i
$748$		−	11.0501i		−	0.404033i
$749$		0			0
$750$	−10.7869	−	16.6370i	−0.393883	−	0.607497i
$751$	−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
$753$	−5.03407	−	2.56962i	−0.183452	−	0.0936421i
$754$	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
$759$	7.80270	+	3.98285i	0.283220	+	0.144568i
$760$	3.02021	+	5.23116i	0.109555	+	0.189754i
$761$	4.93597	+	8.54935i	0.178929	+	0.309914i	0.941514	−	0.336974i	$-0.109404\pi$
$761$	4.93597	+	8.54935i	0.178929	+	0.309914i	−0.762585	+	0.646888i	$0.776070\pi$
$762$	12.1625	+	18.7586i	0.440600	+	0.679551i
$763$		0			0
$764$		−	8.94832i		−	0.323739i
$765$	−14.0235	+	31.3738i	−0.507019	+	1.13432i
$766$		−	30.3026i		−	1.09488i
$767$	−28.6538	−	16.5433i	−1.03463	−	0.597343i
$768$	−0.0893856	−	1.72974i	−0.00322543	−	0.0624167i
$769$	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
$771$	−1.76957	−	34.2438i	−0.0637295	−	1.23326i
$772$	12.8028	−	22.1751i	0.460782	−	0.798098i
$773$	7.39549			0.265997			0.132999	−	0.991116i	$-0.457539\pi$
$773$	7.39549			0.265997			0.132999	+	0.991116i	$0.457539\pi$
$774$	32.9482	+	14.7272i	1.18430	+	0.529358i
$775$		−	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
$780$	3.99868	−	7.83370i	0.143176	−	0.280492i
$781$	−9.04610	+	15.6683i	−0.323695	+	0.560656i
$782$	28.6062			1.02295
$783$	−8.78974	+	22.7490i	−0.314120	+	0.812983i
$784$		0			0
$785$	−18.8599	−	10.8888i	−0.673139	−	0.388637i
$786$	6.50217	−	12.7382i	0.231925	−	0.454357i
$787$	−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
$789$	−16.6011	−	25.6043i	−0.591013	−	0.911537i
$790$	19.6189	+	11.3269i	0.698007	+	0.402995i
$791$		0			0
$792$	−4.17099	+	0.432231i	−0.148210	+	0.0153587i
$793$	34.5523			1.22699
$794$	0.298214	−	0.516521i	0.0105832	−	0.0183307i
$795$	−14.9388	+	0.771975i	−0.529826	+	0.0273791i
$796$	11.7989	−	6.81212i	0.418202	−	0.241449i
$797$	27.0403	+	46.8351i	0.957815	+	1.65898i	0.727790	+	0.685800i	$0.240548\pi$
$797$	27.0403	+	46.8351i	0.957815	+	1.65898i	0.230025	+	0.973185i	$0.426119\pi$
$798$		0			0
$799$	32.8769	−	56.9445i	1.16310	−	2.01455i
$800$		−	2.90040i		−	0.102545i
$801$	−1.87743	−	2.59201i	−0.0663356	−	0.0915840i
$802$	2.33615			0.0824923
$803$	−7.90115	+	13.6852i	−0.278825	+	0.482940i
$804$	−4.31748	+	2.79932i	−0.152266	+	0.0987245i
$805$		0			0
$806$	2.78389	−	1.60728i	0.0980582	−	0.0566140i
$807$	−11.8378	−	6.04254i	−0.416709	−	0.212707i
$808$	−15.2027	−	8.77726i	−0.534827	−	0.308783i
$809$			41.6611i			1.46473i	0.680915	+	0.732363i	$0.261582\pi$
$809$			41.6611i			1.46473i	−0.680915	+	0.732363i	$0.738418\pi$
$810$	12.3909	+	4.06609i	0.435372	+	0.142868i
$811$			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
$813$	−5.53885	+	10.8510i	−0.194256	+	0.380562i
$814$	−2.99369	−	5.18523i	−0.104929	−	0.181742i
$815$	−2.19905	−	3.80887i	−0.0770295	−	0.133419i
$816$	−11.4892	+	7.44924i	−0.402202	+	0.260775i
$817$	−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	−0.124234	−	0.992253i	$-0.539647\pi$
$821$	−29.9616	−	17.2983i	−1.04567	−	0.603716i	−0.921433	+	0.388537i	$0.872981\pi$
$822$	−1.16907	−	22.6232i	−0.0407759	−	0.789073i
$823$	−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
$825$	−7.01256	+	0.362379i	−0.244146	+	0.0126164i
$826$		0			0
$827$		−	17.6523i		−	0.613830i	−0.951737	−	0.306915i	$-0.900703\pi$
$827$		−	17.6523i		−	0.613830i	0.951737	−	0.306915i	$-0.0992967\pi$
$828$	−1.11894	−	10.7977i	−0.0388859	−	0.375245i
$829$			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
$831$	−25.1528	+	16.3083i	−0.872542	+	0.565730i
$832$	3.03494	−	1.75222i	0.105218	−	0.0607474i
$833$		0			0
$834$	−19.0110	−	9.70407i	−0.658296	−	0.336024i
$835$	4.43242	−	7.67718i	0.153390	−	0.265680i
$836$	5.82688			0.201527
$837$	2.99142	+	3.71069i	0.103399	+	0.128260i
$838$			28.8595i			0.996934i
$839$	10.5777	−	18.3211i	0.365183	−	0.632516i	−0.623622	−	0.781726i	$-0.714340\pi$
$839$	10.5777	−	18.3211i	0.365183	−	0.632516i	0.988806	+	0.149210i	$0.0476730\pi$
$840$		0			0
$841$	−3.48563	−	6.03728i	−0.120194	−	0.208182i
$842$	−10.6464	+	6.14672i	−0.366900	+	0.211830i
$843$	15.5761	+	24.0234i	0.536468	+	0.827411i
$844$	10.7961	−	18.6994i	0.371617	−	0.643660i
$845$	−1.04164			−0.0358334
$846$	−22.7802	−	10.1823i	−0.783201	−	0.350075i
$847$		0			0
$848$	−5.16176	−	2.98014i	−0.177256	−	0.102339i
$849$	−5.47090	+	0.282713i	−0.187761	+	0.00970267i
$850$	−19.8573	+	11.4646i	−0.681099	+	0.393233i
$851$	13.4233	−	7.74995i	0.460145	−	0.265665i
$852$	22.3891	−	1.15697i	0.767037	−	0.0396372i
$853$	−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
$855$	−16.5438	−	7.39475i	−0.565787	−	0.252895i
$856$	−2.36213			−0.0807359
$857$	3.73018	−	6.46087i	0.127421	−	0.220699i	−0.795256	−	0.606274i	$-0.792664\pi$
$857$	3.73018	−	6.46087i	0.127421	−	0.220699i	0.922677	+	0.385575i	$0.125997\pi$
$858$	−4.61569	−	7.11892i	−0.157577	−	0.243036i
$859$	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	$0.260829\pi$
$863$			42.9343i			1.46150i	−0.682645	+	0.730750i	$0.739171\pi$
$864$	3.26119	+	4.04532i	0.110948	+	0.137625i
$865$	−3.32566			−0.113076
$866$	10.6964	−	18.5267i	0.363478	−	0.629562i
$867$	70.1886	+	35.8275i	2.38373	+	1.21676i
$868$		0			0
$869$	18.9253	−	10.9265i	0.641996	−	0.370657i
$870$	9.88373	−	6.40831i	0.335090	−	0.217262i
$871$	−9.01617	−	5.20549i	−0.305501	−	0.176381i
$872$		−	12.9955i		−	0.440084i
$873$	3.91593	+	37.7884i	0.132534	+	1.27894i
$874$			15.0844i			0.510237i
$875$		0			0
$876$	19.5553	−	1.01053i	0.660713	−	0.0341428i
$877$	−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
$879$	−0.761646	−	14.7390i	−0.0256897	−	0.497133i
$880$	1.75402	+	1.01269i	0.0591281	+	0.0341376i
$881$	11.2385			0.378636			0.189318	−	0.981916i	$-0.439372\pi$
$881$	11.2385			0.378636			0.189318	+	0.981916i	$0.439372\pi$
$882$		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
$885$	−19.8819	+	12.8908i	−0.668323	+	0.433320i
$886$	−6.08750	−	10.5439i	−0.204514	−	0.354228i
$887$	2.86053	+	4.95458i	0.0960472	+	0.166359i	0.910045	−	0.414509i	$-0.136047\pi$
$887$	2.86053	+	4.95458i	0.0960472	+	0.166359i	−0.813998	+	0.580868i	$0.802713\pi$
$888$	−3.37310	+	6.60815i	−0.113194	+	0.221755i
$889$		0			0
$890$			1.54584i			0.0518167i
$891$	9.37328	−	8.39030i	0.314017	−	0.281086i
$892$			16.8251i			0.563347i
$893$	30.0276	+	17.3364i	1.00483	+	0.580141i
$894$	0.959598	+	0.489823i	0.0320938	+	0.0163821i
$895$	−4.23635	+	2.44586i	−0.141605	+	0.0817559i
$896$		0			0
$897$	18.4292	−	11.9489i	0.615332	−	0.398963i
$898$	7.12271	−	12.3369i	0.237688	−	0.411688i
$899$	4.30523			0.143588
$900$	5.10416	+	7.04689i	0.170139	+	0.234896i
$901$			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
$906$	−36.6397	+	1.89338i	−1.21727	+	0.0629033i
$907$	−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
$909$	52.3830	−	5.42835i	1.73744	−	0.180047i
$910$		0			0
$911$	17.0673	+	9.85384i	0.565466	+	0.326472i	0.755337	−	0.655337i	$-0.227473\pi$
$911$	17.0673	+	9.85384i	0.565466	+	0.326472i	−0.189870	+	0.981809i	$0.560807\pi$
$912$	−3.92808	−	6.05839i	−0.130072	−	0.200613i
$913$	−9.95479	+	5.74740i	−0.329456	+	0.190211i
$914$	−10.0140	+	5.78156i	−0.331232	+	0.191237i
$915$	11.2501	−	22.0397i	0.371916	−	0.728610i
$916$	16.8458	+	9.72591i	0.556600	+	0.321353i
$917$		0			0
$918$	14.8051	−	38.3176i	0.488642	−	1.26467i
$919$	−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
$921$	19.7499	−	38.6915i	0.650782	−	1.27493i
$922$	−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
$927$	12.2101	+	5.45765i	0.401031	+	0.179253i
$928$	4.69348			0.154071
$929$	−11.3860	+	19.7211i	−0.373562	+	0.647028i	−0.990111	−	0.140288i	$-0.955197\pi$
$929$	−11.3860	+	19.7211i	−0.373562	+	0.647028i	0.616549	+	0.787317i	$0.288530\pi$
$930$	−0.118806	−	2.29907i	−0.00389579	−	0.0753893i
$931$		0			0
$932$	24.7381	−	14.2825i	0.810323	−	0.467840i
$933$	−0.319424	−	6.18133i	−0.0104575	−	0.202368i
$934$	2.46895	+	1.42545i	0.0807865	+	0.0466421i
$935$		−	16.0116i		−	0.523637i
$936$	−4.29018	+	9.59815i	−0.140229	+	0.313725i
$937$		−	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
$939$	12.8426	+	19.8075i	0.419103	+	0.646395i
$940$	6.02598	+	10.4373i	0.196546	+	0.340428i
$941$	9.73008	+	16.8530i	0.317192	+	0.549392i	0.979901	−	0.199485i	$-0.0639268\pi$
$941$	9.73008	+	16.8530i	0.317192	+	0.549392i	−0.662709	+	0.748877i	$0.730593\pi$
$942$	23.1857	+	11.8350i	0.755432	+	0.385607i
$943$	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	0.861155	−	0.508343i	$-0.169742\pi$
$947$	26.2034	+	15.1285i	0.851495	+	0.491611i	−0.00966017	+	0.999953i	$0.503075\pi$
$948$	−24.1187	−	12.3113i	−0.783341	−	0.399853i
$949$	19.8095	+	34.3110i	0.643042	+	1.11378i
$950$	−6.04544	−	10.4710i	−0.196140	−	0.339724i
$951$	4.04234	+	6.23461i	0.131082	+	0.202171i
$952$		0			0
$953$			21.4885i			0.696082i	0.937479	+	0.348041i	$0.113153\pi$
$953$			21.4885i			0.696082i	−0.937479	+	0.348041i	$0.886847\pi$
$954$	17.7856	−	1.84309i	0.575831	−	0.0596722i
$955$		−	12.9661i		−	0.419573i
$956$	−10.0020	−	5.77465i	−0.323487	−	0.186765i
$957$	−0.586407	−	11.3478i	−0.0189559	−	0.366824i
$958$	28.8130	−	16.6352i	0.930906	−	0.537459i
$959$		0			0
$960$	−0.129520	−	2.50640i	−0.00418023	−	0.0808936i
$961$	−15.0793	+	26.1181i	−0.486429	+	0.842520i
$962$	−15.0113			−0.483985
$963$	5.73908	−	4.15690i	0.184939	−	0.133954i
$964$			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
$969$	−25.9513	+	50.8406i	−0.833677	+	1.63323i
$970$	9.17475	−	15.8911i	0.294583	−	0.510234i
$971$	25.8916			0.830901			0.415451	−	0.909616i	$-0.363624\pi$
$971$	25.8916			0.830901			0.415451	+	0.909616i	$0.363624\pi$
$972$	−15.0425	−	4.08953i	−0.482487	−	0.131172i
$973$		0			0
$974$	9.04997	+	5.22500i	0.289980	+	0.167420i
$975$	−8.00399	+	15.6804i	−0.256333	+	0.502175i
$976$	8.53864	−	4.92979i	0.273315	−	0.157799i
$977$	−47.1235	+	27.2068i	−1.50761	+	0.870421i	−0.507653	+	0.861562i	$0.669487\pi$
$977$	−47.1235	+	27.2068i	−1.50761	+	0.870421i	−0.999961	+	0.00885973i	$0.997180\pi$
$978$	2.86008	+	4.41119i	0.0914554	+	0.141054i
$979$	1.29141	+	0.745597i	0.0412737	+	0.0238294i
$980$		0			0
$981$	22.8696	+	31.5742i	0.730172	+	1.00809i
$982$	−2.34871			−0.0749504
$983$	23.8665	−	41.3379i	0.761222	−	1.31847i	−0.181000	−	0.983483i	$-0.557933\pi$
$983$	23.8665	−	41.3379i	0.761222	−	1.31847i	0.942221	−	0.334991i	$-0.108733\pi$
$984$	−1.18912	+	0.0614485i	−0.0379077	+	0.00195891i
$985$	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
$990$	−6.04375	+	0.626302i	−0.192083	+	0.0199052i
$991$	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
$993$	−12.9915	+	8.42327i	−0.412271	+	0.267304i
$994$		0			0
$995$	17.0966	−	9.87075i	0.542000	−	0.312924i
$996$	12.6866	+	6.47581i	0.401990	+	0.205194i
$997$	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
$999$	−3.43372	−	21.9913i	−0.108638	−	0.695775i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.54269 + 0.787461i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.724499 + 1.25487i) q^{5} +(-0.942282 - 1.45331i) q^{6} -1.00000i q^{8} +(1.75981 + 2.42962i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.54269 + 0.787461i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.724499 + 1.25487i) q^{5} +(-0.942282 - 1.45331i) q^{6} -1.00000i q^{8} +(1.75981 + 2.42962i) q^{9} -1.44900i q^{10} +(-1.21051 - 0.698887i) q^{11} +(0.0893856 + 1.72974i) q^{12} +(-3.03494 + 1.75222i) q^{13} +(0.129520 + 2.50640i) q^{15} +(-0.500000 + 0.866025i) q^{16} +7.90553 q^{17} +(-0.309228 - 2.98402i) q^{18} +4.16869i q^{19} +(-0.724499 + 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(-3.13371 + 1.80925i) q^{23} +(0.787461 - 1.54269i) q^{24} +(1.45020 - 2.51182i) q^{25} +3.50444 q^{26} +(0.801614 + 5.13395i) q^{27} +(4.06467 + 2.34674i) q^{29} +(1.14103 - 2.23536i) q^{30} +(0.794387 - 0.458640i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.31710 - 2.03140i) q^{33} +(-6.84639 - 3.95277i) q^{34} +(-1.22421 + 2.73885i) q^{36} -4.28351 q^{37} +(2.08434 - 3.61019i) q^{38} +(-6.06179 + 0.313247i) q^{39} +(1.25487 - 0.724499i) q^{40} +(-0.343727 - 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} -1.39777i q^{44} +(-1.77388 + 3.96859i) q^{45} +3.61850 q^{46} +(4.15872 - 7.20312i) q^{47} +(-1.45331 + 0.942282i) q^{48} +(-2.51182 + 1.45020i) q^{50} +(12.1958 + 6.22530i) q^{51} +(-3.03494 - 1.75222i) q^{52} +5.96029i q^{53} +(1.87276 - 4.84694i) q^{54} -2.02537i q^{55} +(-3.28268 + 6.43101i) q^{57} +(-2.34674 - 4.06467i) q^{58} +(4.72065 + 8.17641i) q^{59} +(-2.10584 + 1.36536i) q^{60} +(-8.53864 - 4.92979i) q^{61} -0.917280 q^{62} -1.00000 q^{64} +(-4.39762 - 2.53897i) q^{65} +(0.124941 + 2.41779i) q^{66} +(1.48540 + 2.57278i) q^{67} +(3.95277 + 6.84639i) q^{68} +(-6.25907 + 0.323442i) q^{69} -12.9436i q^{71} +(2.42962 - 1.75981i) q^{72} -11.3053i q^{73} +(3.70963 + 2.14176i) q^{74} +(4.21518 - 2.73300i) q^{75} +(-3.61019 + 2.08434i) q^{76} +(5.40629 + 2.75961i) q^{78} +(-7.81709 + 13.5396i) q^{79} -1.44900 q^{80} +(-2.80614 + 8.55135i) q^{81} +0.687454i q^{82} +(4.11183 - 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(10.4182 - 6.01497i) q^{86} +(4.42258 + 6.82107i) q^{87} +(-0.698887 + 1.21051i) q^{88} -1.06683 q^{89} +(3.52052 - 2.54996i) q^{90} +(-3.13371 - 1.80925i) q^{92} +(1.58666 - 0.0819916i) q^{93} +(-7.20312 + 4.15872i) q^{94} +(-5.23116 + 3.02021i) q^{95} +(1.72974 - 0.0893856i) q^{96} +(10.9670 + 6.33179i) q^{97} +(-0.432231 - 4.17099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 32 * q^9	\( 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 32 * q^9 + 48 * q^11 + 48 * q^15 - 24 * q^16 + 16 * q^18 + 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 - 64 * q^39 - 48 * q^50 - 80 * q^57 - 48 * q^64 + 32 * q^72 + 32 * q^78 + 48 * q^79 + 48 * q^85 + 96 * q^86 + 48 * q^92 + 96 * q^93 - 192 * q^95 + 104 * q^99

Introduction

L-functions

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