LMFDB - Embedded newform 882.2.m.c.293.11

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			293.11
Character	$\chi$	$=$	882.293
Dual form			882.2.m.c.587.11

$q$-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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.657305	−	0.753625i	$-0.728304\pi$
$5$	0.724499	−	1.25487i	0.324006	−	0.561195i	0.981311	+	0.192430i	$0.0616369\pi$
$6$	−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	−0.671264	−	0.741218i	$-0.734248\pi$
$11$	−1.21051	+	0.698887i	−0.364982	+	0.210722i	0.306282	+	0.951941i	$0.400915\pi$
$12$	0.0893856	−	1.72974i	0.0258034	−	0.499334i
$13$	−3.03494	−	1.75222i	−0.841740	−	0.485979i	0.0161150	−	0.999870i	$-0.494870\pi$
$13$	−3.03494	−	1.75222i	−0.841740	−	0.485979i	−0.857855	+	0.513891i	$0.828204\pi$
$14$		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	$-0.841296\pi$
$19$		−	4.16869i		−	0.956363i	0.878261	−	0.478181i	$-0.158704\pi$
$20$	−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	$-0.456465\pi$
$23$	−3.13371	−	1.80925i	−0.653424	−	0.377255i	−0.789767	+	0.613407i	$0.789798\pi$
$24$	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	−0.0726316	−	0.997359i	$-0.523140\pi$
$29$	4.06467	−	2.34674i	0.754791	−	0.435779i	0.827422	+	0.561580i	$0.189806\pi$
$30$	1.14103	+	2.23536i	0.208323	+	0.408119i
$31$	0.794387	+	0.458640i	0.142676	+	0.0823741i	0.569639	−	0.821895i	$-0.307083\pi$
$31$	0.794387	+	0.458640i	0.142676	+	0.0823741i	−0.426963	+	0.904269i	$0.640416\pi$
$32$	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	−0.891617	−	0.452790i	$-0.850429\pi$
$41$	−0.343727	+	0.595352i	−0.0536811	+	0.0929784i	0.837936	+	0.545768i	$0.183762\pi$
$42$		0			0
$43$	−6.01497	−	10.4182i	−0.917275	−	1.58877i	−0.803536	−	0.595256i	$-0.797051\pi$
$43$	−6.01497	−	10.4182i	−0.917275	−	1.58877i	−0.113739	−	0.993511i	$-0.536283\pi$
$44$			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	0.991794	+	0.127842i	$0.0408052\pi$
$47$	4.15872	+	7.20312i	0.606612	+	1.05068i	−0.385182	+	0.922840i	$0.625861\pi$
$48$	−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	$-0.865754\pi$
$53$		−	5.96029i		−	0.818709i	0.912375	−	0.409354i	$-0.134246\pi$
$54$	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	−0.375882	−	0.926668i	$-0.622660\pi$
$59$	4.72065	−	8.17641i	0.614577	−	1.06448i	0.990459	−	0.137810i	$-0.0440064\pi$
$60$	−2.10584	−	1.36536i	−0.271863	−	0.176268i
$61$	−8.53864	+	4.92979i	−1.09326	+	0.631194i	−0.934443	−	0.356113i	$-0.884102\pi$
$61$	−8.53864	+	4.92979i	−1.09326	+	0.631194i	−0.158818	+	0.987308i	$0.550768\pi$
$62$	−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	−0.760911	−	0.648856i	$-0.775248\pi$
$67$	1.48540	−	2.57278i	0.181470	−	0.314315i	0.942381	+	0.334541i	$0.108581\pi$
$68$	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	$0.278778\pi$
$71$			12.9436i			1.53612i	−0.640377	+	0.768061i	$0.721222\pi$
$72$	2.42962	+	1.75981i	0.286334	+	0.207396i
$73$			11.3053i			1.32319i	0.749862	+	0.661595i	$0.230120\pi$
$73$			11.3053i			1.32319i	−0.749862	+	0.661595i	$0.769880\pi$
$74$	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	−0.851900	−	0.523704i	$-0.824550\pi$
$79$	−7.81709	−	13.5396i	−0.879491	−	1.52332i	−0.0275906	−	0.999619i	$-0.508783\pi$
$80$	−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	0.998469	−	0.0553135i	$-0.0176158\pi$
$83$	4.11183	+	7.12189i	0.451332	+	0.781729i	−0.547137	+	0.837043i	$0.684282\pi$
$84$		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	0.173787	−	0.984783i	$-0.444400\pi$
$97$	10.9670	−	6.33179i	1.11353	−	0.642895i	0.939741	+	0.341888i	$0.111066\pi$
$98$		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	0.858489	+	0.512831i	$0.171403\pi$
$101$	8.77726	+	15.2027i	0.873370	+	1.51272i	0.0148801	+	0.999889i	$0.495263\pi$
$102$	−7.44924	+	11.4892i	−0.737584	+	1.13760i
$103$	3.86082	+	2.22905i	0.380418	+	0.219635i	0.678000	−	0.735062i	$-0.262847\pi$
$103$	3.86082	+	2.22905i	0.380418	+	0.219635i	−0.297582	+	0.954696i	$0.596180\pi$
$104$	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	$0.963577\pi$
$108$	−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	0.630426	−	0.776249i	$-0.282880\pi$
$113$	2.90616	+	1.67787i	0.273388	+	0.157841i	−0.357038	+	0.934090i	$0.616213\pi$
$114$	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	−0.627364	−	0.778726i	$-0.715866\pi$
$131$	4.12856	−	7.15088i	0.360714	−	0.624775i	0.988079	+	0.153951i	$0.0491996\pi$
$132$	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	0.0691676	−	0.997605i	$-0.477966\pi$
$137$	11.3267	−	6.53946i	0.967703	−	0.558703i	0.898535	+	0.438902i	$0.144632\pi$
$138$	5.58224	−	2.84943i	0.475192	−	0.242559i
$139$	10.6722	+	6.16162i	0.905207	+	0.522621i	0.878886	−	0.477032i	$-0.158287\pi$
$139$	10.6722	+	6.16162i	0.905207	+	0.522621i	0.0263210	+	0.999654i	$0.491621\pi$
$140$		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	0.477772	−	0.878484i	$-0.341445\pi$
$149$	−0.538692	−	0.311014i	−0.0441314	−	0.0254792i	−0.521903	+	0.853005i	$0.674778\pi$
$150$	−5.01695	−	0.259254i	−0.409632	−	0.0211680i
$151$	10.5911	+	18.3443i	0.861889	+	1.49284i	0.870103	+	0.492870i	$0.164052\pi$
$151$	10.5911	+	18.3443i	0.861889	+	1.49284i	−0.00821353	+	0.999966i	$0.502614\pi$
$152$	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	−0.119289	−	0.992860i	$-0.538062\pi$
$157$	−13.0158	−	7.51469i	−1.03878	−	0.599737i	−0.919486	+	0.393122i	$0.871395\pi$
$158$	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	−0.959768	−	0.280794i	$-0.909402\pi$
$167$	−3.05895	+	5.29826i	−0.236709	+	0.409992i	0.723059	+	0.690786i	$0.242735\pi$
$168$		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	0.819099	−	0.573653i	$-0.194474\pi$
$173$	−1.14757	−	1.98766i	−0.0872484	−	0.151119i	−0.906347	+	0.422534i	$0.861141\pi$
$174$	−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	$-0.959733\pi$
$179$		−	3.37592i		−	0.252328i	0.992009	−	0.126164i	$-0.0402666\pi$
$180$	−4.32384	−	0.448071i	−0.322280	−	0.0333973i
$181$			1.68857i			0.125511i	0.998029	+	0.0627553i	$0.0199888\pi$
$181$			1.68857i			0.125511i	−0.998029	+	0.0627553i	$0.980011\pi$
$182$		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	−0.753439	−	0.657517i	$-0.771607\pi$
$191$	−7.74947	+	4.47416i	−0.560732	+	0.323739i	0.192707	+	0.981256i	$0.438273\pi$
$192$	−1.54269	+	0.787461i	−0.111334	+	0.0568301i
$193$	−12.8028	+	22.1751i	−0.921564	+	1.59620i	−0.124568	+	0.992211i	$0.539754\pi$
$193$	−12.8028	+	22.1751i	−0.921564	+	1.59620i	−0.796996	+	0.603984i	$0.793579\pi$
$194$	−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	$0.317034\pi$
$197$			23.5602i			1.67860i	−0.543670	+	0.839299i	$0.682966\pi$
$198$	−1.71117	−	3.82829i	−0.121608	−	0.272065i
$199$			13.6242i			0.965796i	0.875677	+	0.482898i	$0.160416\pi$
$199$			13.6242i			0.965796i	−0.875677	+	0.482898i	$0.839584\pi$
$200$	−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	0.207780	+	0.978176i	$0.433376\pi$
$211$	−10.7961	+	18.6994i	−0.743235	+	1.28732i	−0.951015	+	0.309145i	$0.899957\pi$
$212$	−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	0.0747620	−	0.997201i	$-0.476180\pi$
$223$	14.5710	−	8.41256i	0.975745	−	0.563347i	0.900983	+	0.433855i	$0.142847\pi$
$224$		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	0.588810	−	0.808271i	$-0.299596\pi$
$227$	−6.11065	−	10.5840i	−0.405578	−	0.702482i	−0.994389	+	0.105789i	$0.966263\pi$
$228$	−7.21076	−	0.372621i	−0.477544	−	0.0246774i
$229$	16.8458	+	9.72591i	1.11320	+	0.642706i	0.939656	−	0.342120i	$-0.111145\pi$
$229$	16.8458	+	9.72591i	1.11320	+	0.642706i	0.173543	+	0.984826i	$0.444478\pi$
$230$	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	$0.614787\pi$
$234$	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	0.140322	−	0.990106i	$-0.455186\pi$
$239$	−10.0020	−	5.77465i	−0.646975	−	0.373531i	−0.787296	+	0.616575i	$0.788520\pi$
$240$	−2.23536	+	1.14103i	−0.144292	+	0.0736532i
$241$	0.0299000	−	0.0172628i	0.00192603	−	0.00111199i	−0.499037	−	0.866581i	$-0.666313\pi$
$241$	0.0299000	−	0.0172628i	0.00192603	−	0.00111199i	0.500963	+	0.865469i	$0.332979\pi$
$242$		−	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	0.372497	+	0.928034i	$0.378502\pi$
$257$	−9.89851	+	17.1447i	−0.617452	+	1.06946i	−0.989949	+	0.141425i	$0.954832\pi$
$258$	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	−0.890218	−	0.455535i	$-0.849448\pi$
$263$	−15.2576	+	8.80897i	−0.940823	+	0.543184i	−0.0506045	+	0.998719i	$0.516115\pi$
$264$	−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	$-0.931469\pi$
$271$		−	7.03381i		−	0.427273i	0.976913	−	0.213637i	$-0.0685309\pi$
$272$	−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	−0.999731	−	0.0231880i	$-0.992618\pi$
$277$	−8.65364	−	14.9885i	−0.519947	−	0.900575i	0.479784	−	0.877387i	$-0.340715\pi$
$278$	−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	−0.00800273	−	0.999968i	$-0.502547\pi$
$281$	14.3155	−	8.26508i	0.853994	−	0.493053i	0.861996	+	0.506915i	$0.169214\pi$
$282$	−14.3870	−	0.743460i	−0.856736	−	0.0442724i
$283$	−2.73910	−	1.58142i	−0.162823	−	0.0940057i	0.416374	−	0.909193i	$-0.363301\pi$
$283$	−2.73910	−	1.58142i	−0.162823	−	0.0940057i	−0.579197	+	0.815187i	$0.696634\pi$
$284$	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	−0.963220	−	0.268713i	$-0.913402\pi$
$293$	−4.26045	+	7.37932i	−0.248898	+	0.431104i	0.714322	+	0.699817i	$0.246735\pi$
$294$		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	$0.253897\pi$
$307$			25.0805i			1.43142i	−0.698398	+	0.715710i	$0.746103\pi$
$308$		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	−0.912228	−	0.409682i	$-0.865640\pi$
$311$	−1.78678	+	3.09479i	−0.101319	+	0.175489i	0.810909	+	0.585172i	$0.198973\pi$
$312$	0.313247	−	6.06179i	0.0177341	−	0.343181i
$313$	11.8033	−	6.81464i	0.667162	−	0.385186i	−0.127838	−	0.991795i	$-0.540804\pi$
$313$	11.8033	−	6.81464i	0.667162	−	0.385186i	0.795000	+	0.606609i	$0.207471\pi$
$314$	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	$-0.628225\pi$
$317$	3.71520	−	2.14497i	0.208666	−	0.120474i	0.600692	+	0.799481i	$0.294892\pi$
$318$	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	0.716648	−	0.697435i	$-0.245675\pi$
$331$	−4.46962	−	7.74160i	−0.245672	−	0.425517i	−0.962320	+	0.271918i	$0.912342\pi$
$332$	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	−0.864031	−	0.503439i	$-0.832068\pi$
$337$	0.0729773	−	0.126400i	0.00397532	−	0.00688546i	0.868006	+	0.496553i	$0.165401\pi$
$338$	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	−0.117313	−	0.993095i	$-0.537428\pi$
$347$	−19.2988	−	11.1422i	−1.03602	−	0.598144i	−0.918702	+	0.394951i	$0.870762\pi$
$348$	−3.69593	−	7.24060i	−0.198123	−	0.388137i
$349$	2.79851	−	1.61572i	0.149801	−	0.0864876i	−0.423226	−	0.906024i	$-0.639102\pi$
$349$	2.79851	−	1.61572i	0.149801	−	0.0864876i	0.573027	+	0.819537i	$0.305769\pi$
$350$		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	0.937263	−	0.348622i	$-0.113350\pi$
$353$	3.13232	+	5.42533i	0.166716	+	0.288761i	−0.770547	+	0.637383i	$0.780017\pi$
$354$	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	$-0.896822\pi$
$359$		−	12.0693i		−	0.636991i	0.947924	−	0.318496i	$-0.103178\pi$
$360$	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	−0.0615446	−	0.998104i	$-0.519603\pi$
$367$	14.7907	−	8.53940i	0.772067	−	0.445753i	0.833611	+	0.552351i	$0.186269\pi$
$368$			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	−0.911801	−	0.410631i	$-0.865308\pi$
$373$	−1.93680	+	3.35463i	−0.100284	+	0.173696i	0.811518	+	0.584328i	$0.198642\pi$
$374$	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	−0.161050	−	0.986946i	$-0.551488\pi$
$383$	15.1513	−	26.2428i	0.774195	−	1.34095i	0.935246	−	0.353999i	$-0.115179\pi$
$384$	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	0.0394744	−	0.999221i	$-0.487432\pi$
$389$	18.2352	−	10.5281i	0.924562	−	0.533796i	0.885088	+	0.465424i	$0.154098\pi$
$390$	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	$-0.995236\pi$
$397$		−	0.596428i		−	0.0299338i	0.999888	−	0.0149669i	$-0.00476430\pi$
$398$	−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	$-0.351911\pi$
$401$	−2.02316	−	1.16807i	−0.101032	−	0.0583309i	−0.549665	+	0.835385i	$0.685245\pi$
$402$	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	0.692098	−	0.721803i	$-0.256686\pi$
$409$	8.35337	+	4.82282i	0.413048	+	0.238473i	−0.279051	+	0.960276i	$0.590020\pi$
$410$	−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	0.261775	+	0.965129i	$0.415692\pi$
$419$	−14.4297	+	24.9930i	−0.704939	+	1.22099i	−0.966714	+	0.255861i	$0.917641\pi$
$420$		0			0
$421$	6.14672	+	10.6464i	0.299573	+	0.518875i	0.976038	−	0.217599i	$-0.0698226\pi$
$421$	6.14672	+	10.6464i	0.299573	+	0.518875i	−0.676466	+	0.736474i	$0.736489\pi$
$422$		−	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	$0.233128\pi$
$431$			27.7631i			1.33730i	−0.743577	+	0.668650i	$0.766872\pi$
$432$	−4.84694	+	1.87276i	−0.233198	+	0.0901030i
$433$		−	21.3927i		−	1.02807i	−0.857769	−	0.514035i	$-0.828150\pi$
$433$		−	21.3927i		−	1.02807i	0.857769	−	0.514035i	$-0.171850\pi$
$434$		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	−0.444465	−	0.895796i	$-0.646606\pi$
$439$	2.28558	−	1.31958i	0.109085	−	0.0629801i	0.553550	+	0.832816i	$0.313273\pi$
$440$	−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	$-0.573269\pi$
$443$	10.5439	−	6.08750i	0.500954	−	0.289226i	0.729107	+	0.684399i	$0.239935\pi$
$444$	−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	$-0.890878\pi$
$449$		−	14.2454i		−	0.672283i	0.941811	−	0.336142i	$-0.109122\pi$
$450$	−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	0.968977	−	0.247151i	$-0.0794942\pi$
$457$	5.78156	+	10.0140i	0.270450	+	0.468433i	−0.698527	+	0.715583i	$0.746161\pi$
$458$	−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	0.999895	+	0.0145095i	$0.00461867\pi$
$461$	11.0041	+	19.0597i	0.512513	+	0.887698i	−0.487382	+	0.873189i	$0.662048\pi$
$462$		0			0
$463$	6.47862	−	11.2213i	0.301087	−	0.521498i	−0.675295	−	0.737547i	$-0.735984\pi$
$463$	6.47862	−	11.2213i	0.301087	−	0.521498i	0.976382	+	0.216049i	$0.0693171\pi$
$464$	−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	−0.942808	−	0.333336i	$-0.891826\pi$
$479$	−16.6352	−	28.8130i	−0.760081	−	1.31650i	0.182727	−	0.983164i	$-0.441508\pi$
$480$	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	0.545195	−	0.838309i	$-0.316456\pi$
$491$	2.03404	+	1.17436i	0.0917952	+	0.0529980i	−0.453400	+	0.891307i	$0.649789\pi$
$492$	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	0.154366	+	0.988014i	$0.450667\pi$
$499$	−17.3895	+	30.1195i	−0.778462	+	1.34834i	−0.932828	+	0.360322i	$0.882667\pi$
$500$	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	−0.640461	−	0.767991i	$-0.721257\pi$
$509$	7.78061	−	13.4764i	0.344869	−	0.597331i	0.985330	+	0.170660i	$0.0545899\pi$
$510$	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	$-0.838597\pi$
$523$		−	22.2110i		−	0.971220i	0.874176	−	0.485610i	$-0.161403\pi$
$524$	−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	−0.989286	−	0.145987i	$-0.953364\pi$
$547$	−14.5256	−	25.1592i	−0.621072	−	1.07573i	0.368215	−	0.929741i	$-0.379969\pi$
$548$		−	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	$0.119552\pi$
$557$			17.3143i			0.733632i	−0.930294	+	0.366816i	$0.880448\pi$
$558$	−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	−0.997504	−	0.0706035i	$-0.977507\pi$
$563$	−10.3834	+	17.9846i	−0.437608	+	0.757959i	0.559897	+	0.828562i	$0.310841\pi$
$564$	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	−0.207524	−	0.978230i	$-0.566540\pi$
$569$	12.7829	−	7.38020i	0.535887	−	0.309394i	0.743410	+	0.668836i	$0.233207\pi$
$570$	9.31853	−	4.75660i	0.390310	−	0.199232i
$571$	11.1208	−	19.2618i	0.465390	−	0.806080i	−0.533829	−	0.845593i	$-0.679247\pi$
$571$	11.1208	−	19.2618i	0.465390	−	0.806080i	0.999219	+	0.0395130i	$0.0125806\pi$
$572$	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	$-0.872605\pi$
$577$		−	18.7182i		−	0.779249i	0.920974	−	0.389625i	$-0.127395\pi$
$578$	−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	0.554518	−	0.832172i	$-0.312903\pi$
$587$	−10.7433	−	18.6079i	−0.443423	−	0.768031i	−0.997941	+	0.0641405i	$0.979569\pi$
$588$		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	0.799235	−	0.601019i	$-0.205239\pi$
$599$	16.6024	+	9.58537i	0.678354	+	0.391648i	−0.120881	+	0.992667i	$0.538572\pi$
$600$	−2.73300	+	4.21518i	−0.111574	+	0.172084i
$601$	34.6795	−	20.0222i	1.41460	−	0.816723i	0.418787	−	0.908084i	$-0.362455\pi$
$601$	34.6795	−	20.0222i	1.41460	−	0.816723i	0.995818	+	0.0913619i	$0.0291220\pi$
$602$		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	−0.989490	−	0.144599i	$-0.953811\pi$
$607$	−39.6529	−	22.8936i	−1.60946	−	0.929223i	−0.619971	−	0.784625i	$-0.712856\pi$
$608$	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	−0.203149	−	0.979148i	$-0.565118\pi$
$617$	−28.6323	−	16.5308i	−1.15269	−	0.665506i	−0.949542	+	0.313641i	$0.898451\pi$
$618$	−6.87748	+	3.51058i	−0.276653	+	0.141216i
$619$	9.35801	−	5.40285i	0.376130	−	0.217159i	−0.300003	−	0.953938i	$-0.596988\pi$
$619$	9.35801	−	5.40285i	0.376130	−	0.217159i	0.676133	+	0.736779i	$0.263654\pi$
$620$		−	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	−0.678655	−	0.734457i	$-0.737437\pi$
$641$	−9.66957	+	5.58273i	−0.381925	+	0.220505i	0.296730	+	0.954961i	$0.404104\pi$
$642$	−3.43290	−	2.22579i	−0.135486	−	0.0878449i
$643$	−4.40588	−	2.54373i	−0.173751	−	0.100315i	0.410602	−	0.911814i	$-0.365318\pi$
$643$	−4.40588	−	2.54373i	−0.173751	−	0.100315i	−0.584353	+	0.811499i	$0.698652\pi$
$644$		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	−0.267716	−	0.963498i	$-0.586269\pi$
$653$	−31.5843	−	18.2352i	−1.23599	−	0.713598i	−0.968272	+	0.249900i	$0.919602\pi$
$654$	−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	−0.459718	−	0.888065i	$-0.652049\pi$
$659$	2.04111	−	1.17844i	0.0795104	−	0.0459054i	0.539228	+	0.842160i	$0.318716\pi$
$660$	3.50337	+	0.181039i	0.136369	+	0.00704694i
$661$	−6.72135	−	3.88057i	−0.261430	−	0.150937i	0.363557	−	0.931572i	$-0.381562\pi$
$661$	−6.72135	−	3.88057i	−0.261430	−	0.150937i	−0.624987	+	0.780635i	$0.714896\pi$
$662$	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	0.975703	+	0.219096i	$0.0703106\pi$
$673$	17.5783	+	30.4465i	0.677594	+	1.17363i	−0.298109	+	0.954532i	$0.596356\pi$
$674$			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	0.968916	−	0.247389i	$-0.0795724\pi$
$677$	7.03074	+	12.1776i	0.270213	+	0.468023i	−0.698703	+	0.715412i	$0.746239\pi$
$678$	−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	$0.222530\pi$
$683$			33.6363i			1.28706i	−0.765422	+	0.643529i	$0.777470\pi$
$684$	−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	−0.425723	−	0.904854i	$-0.639980\pi$
$691$	3.81269	−	2.20126i	0.145042	−	0.0837399i	0.570765	+	0.821114i	$0.306647\pi$
$692$	−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	$0.203113\pi$
$701$			31.5424i			1.19134i	−0.803229	+	0.595670i	$0.796887\pi$
$702$	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	0.822339	−	0.568998i	$-0.192669\pi$
$709$	−2.17269	−	3.76320i	−0.0815970	−	0.141330i	−0.903936	+	0.427668i	$0.859335\pi$
$710$	−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	−0.702233	−	0.711948i	$-0.747813\pi$
$727$	−11.7770	+	6.79945i	−0.436784	+	0.252178i	0.265448	+	0.964125i	$0.414480\pi$
$728$		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	−0.999840	−	0.0178757i	$-0.994310\pi$
$733$	−41.0236	−	23.6850i	−1.51524	−	0.874825i	−0.515401	−	0.856949i	$-0.672357\pi$
$734$	−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	0.620571	−	0.784151i	$-0.286901\pi$
$743$	6.86253	+	3.96208i	0.251762	+	0.145355i	−0.368809	+	0.929505i	$0.620234\pi$
$744$	−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	−0.901298	−	0.433201i	$-0.857384\pi$
$751$	−2.06865	+	3.58301i	−0.0754861	+	0.130746i	0.825811	+	0.563946i	$0.190718\pi$
$752$	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	−0.762585	−	0.646888i	$-0.776070\pi$
$761$	4.93597	−	8.54935i	0.178929	−	0.309914i	0.941514	+	0.336974i	$0.109404\pi$
$762$	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	0.796646	−	0.604446i	$-0.206606\pi$
$769$	18.6213	+	10.7510i	0.671503	+	0.387692i	−0.125143	+	0.992139i	$0.539939\pi$
$770$		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	0.199141	−	0.979971i	$-0.436185\pi$
$787$	−15.4285	−	8.90768i	−0.549968	−	0.317524i	−0.749109	+	0.662446i	$0.769518\pi$
$788$	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	0.230025	−	0.973185i	$-0.426119\pi$
$797$	27.0403	−	46.8351i	0.957815	−	1.65898i	0.727790	−	0.685800i	$-0.240548\pi$
$798$		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	$-0.738418\pi$
$809$		−	41.6611i		−	1.46473i	0.680915	−	0.732363i	$-0.261582\pi$
$810$	12.3909	−	4.06609i	0.435372	−	0.142868i
$811$		−	24.8645i		−	0.873111i	−0.899677	−	0.436556i	$-0.856198\pi$
$811$		−	24.8645i		−	0.873111i	0.899677	−	0.436556i	$-0.143802\pi$
$812$		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	−0.921433	−	0.388537i	$-0.872981\pi$
$821$	−29.9616	+	17.2983i	−1.04567	+	0.603716i	−0.124234	+	0.992253i	$0.539647\pi$
$822$	−1.16907	+	22.6232i	−0.0407759	+	0.789073i
$823$	−7.88113	+	13.6505i	−0.274719	+	0.475827i	−0.970064	−	0.242849i	$-0.921918\pi$
$823$	−7.88113	+	13.6505i	−0.274719	+	0.475827i	0.695345	+	0.718676i	$0.255251\pi$
$824$	−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	$0.0992967\pi$
$827$			17.6523i			0.613830i	−0.951737	+	0.306915i	$0.900703\pi$
$828$	−1.11894	+	10.7977i	−0.0388859	+	0.375245i
$829$		−	37.6774i		−	1.30859i	−0.756240	−	0.654294i	$-0.772966\pi$
$829$		−	37.6774i		−	1.30859i	0.756240	−	0.654294i	$-0.227034\pi$
$830$	−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	0.988806	−	0.149210i	$-0.0476730\pi$
$839$	10.5777	+	18.3211i	0.365183	+	0.632516i	−0.623622	+	0.781726i	$0.714340\pi$
$840$		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	−0.957923	−	0.287026i	$-0.907334\pi$
$853$	−34.7061	+	20.0376i	−1.18831	+	0.686073i	−0.230390	+	0.973098i	$0.574000\pi$
$854$		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	0.922677	−	0.385575i	$-0.125997\pi$
$857$	3.73018	+	6.46087i	0.127421	+	0.220699i	−0.795256	+	0.606274i	$0.792664\pi$
$858$	−4.61569	+	7.11892i	−0.157577	+	0.243036i
$859$	41.2721	+	23.8285i	1.40819	+	0.813017i	0.995213	−	0.0977257i	$-0.0311568\pi$
$859$	41.2721	+	23.8285i	1.40819	+	0.813017i	0.412974	+	0.910743i	$0.364490\pi$
$860$	−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	$-0.260829\pi$
$864$	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	−0.997790	−	0.0664486i	$-0.978833\pi$
$877$	−13.0702	+	22.6382i	−0.441349	+	0.764438i	0.556441	+	0.830887i	$0.312166\pi$
$878$	−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	−0.813998	−	0.580868i	$-0.802713\pi$
$887$	2.86053	−	4.95458i	0.0960472	−	0.166359i	0.910045	+	0.414509i	$0.136047\pi$
$888$	−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	0.598763	−	0.800926i	$-0.295659\pi$
$907$	−11.8731	−	20.5648i	−0.394241	−	0.682845i	−0.993004	+	0.118081i	$0.962326\pi$
$908$	−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	−0.189870	−	0.981809i	$-0.560807\pi$
$911$	17.0673	−	9.85384i	0.565466	−	0.326472i	0.755337	+	0.655337i	$0.227473\pi$
$912$	−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	0.616549	−	0.787317i	$-0.288530\pi$
$929$	−11.3860	−	19.7211i	−0.373562	−	0.647028i	−0.990111	+	0.140288i	$0.955197\pi$
$930$	−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	$0.102872\pi$
$937$			19.4429i			0.635173i	−0.948229	+	0.317587i	$0.897128\pi$
$938$		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	−0.662709	−	0.748877i	$-0.730593\pi$
$941$	9.73008	−	16.8530i	0.317192	−	0.549392i	0.979901	+	0.199485i	$0.0639268\pi$
$942$	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	−0.00966017	−	0.999953i	$-0.503075\pi$
$947$	26.2034	−	15.1285i	0.851495	−	0.491611i	0.861155	+	0.508343i	$0.169742\pi$
$948$	−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	$-0.886847\pi$
$953$		−	21.4885i		−	0.696082i	0.937479	−	0.348041i	$-0.113153\pi$
$954$	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	−0.971853	−	0.235587i	$-0.924299\pi$
$967$	−8.76620	+	15.1835i	−0.281902	+	0.488268i	0.689951	+	0.723856i	$0.257632\pi$
$968$	−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	−0.999961	−	0.00885973i	$-0.997180\pi$
$977$	−47.1235	−	27.2068i	−1.50761	−	0.870421i	−0.507653	−	0.861562i	$-0.669487\pi$
$978$	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	0.942221	+	0.334991i	$0.108733\pi$
$983$	23.8665	+	41.3379i	0.761222	+	1.31847i	−0.181000	+	0.983483i	$0.557933\pi$
$984$	−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	−0.458546	−	0.888671i	$-0.651629\pi$
$997$	2.58264	−	1.49109i	0.0817931	−	0.0472233i	0.540339	+	0.841448i	$0.318296\pi$
$998$		−	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.293.11	yes	48
3.2	odd	2		2646.2.m.c.881.21		48
7.2	even	3		882.2.t.c.815.18		48
7.3	odd	6		882.2.l.c.509.9		48
7.4	even	3		882.2.l.c.509.4		48
7.5	odd	6		882.2.t.c.815.19		48
7.6	odd	2	inner	882.2.m.c.293.2	✓	48
9.2	odd	6	inner	882.2.m.c.587.2	yes	48
9.7	even	3		2646.2.m.c.1763.22		48
21.2	odd	6		2646.2.t.c.2285.2		48
21.5	even	6		2646.2.t.c.2285.1		48
21.11	odd	6		2646.2.l.c.1097.9		48
21.17	even	6		2646.2.l.c.1097.10		48
21.20	even	2		2646.2.m.c.881.22		48
63.2	odd	6		882.2.l.c.227.21		48
63.11	odd	6		882.2.t.c.803.19		48
63.16	even	3		2646.2.l.c.521.10		48
63.20	even	6	inner	882.2.m.c.587.11	yes	48
63.25	even	3		2646.2.t.c.1979.1		48
63.34	odd	6		2646.2.m.c.1763.21		48
63.38	even	6		882.2.t.c.803.18		48
63.47	even	6		882.2.l.c.227.16		48
63.52	odd	6		2646.2.t.c.1979.2		48
63.61	odd	6		2646.2.l.c.521.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.16		48	63.47	even	6
882.2.l.c.227.21		48	63.2	odd	6
882.2.l.c.509.4		48	7.4	even	3
882.2.l.c.509.9		48	7.3	odd	6
882.2.m.c.293.2	✓	48	7.6	odd	2	inner
882.2.m.c.293.11	yes	48	1.1	even	1	trivial
882.2.m.c.587.2	yes	48	9.2	odd	6	inner
882.2.m.c.587.11	yes	48	63.20	even	6	inner
882.2.t.c.803.18		48	63.38	even	6
882.2.t.c.803.19		48	63.11	odd	6
882.2.t.c.815.18		48	7.2	even	3
882.2.t.c.815.19		48	7.5	odd	6
2646.2.l.c.521.9		48	63.61	odd	6
2646.2.l.c.521.10		48	63.16	even	3
2646.2.l.c.1097.9		48	21.11	odd	6
2646.2.l.c.1097.10		48	21.17	even	6
2646.2.m.c.881.21		48	3.2	odd	2
2646.2.m.c.881.22		48	21.20	even	2
2646.2.m.c.1763.21		48	63.34	odd	6
2646.2.m.c.1763.22		48	9.7	even	3
2646.2.t.c.1979.1		48	63.25	even	3
2646.2.t.c.1979.2		48	63.52	odd	6
2646.2.t.c.2285.1		48	21.5	even	6
2646.2.t.c.2285.2		48	21.2	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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