LMFDB - Embedded newform 668.2.e.a.21.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			21.6
Character	$\chi$	$=$	668.21
Dual form			668.2.e.a.509.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.537235 - 0.0819657i) q^{3} +(-1.19475 - 1.41779i) q^{5} +(0.821536 - 1.13980i) q^{7} +(-2.58161 - 0.806524i) q^{9} +O(q^{10})$	\(q+(-0.537235 - 0.0819657i) q^{3} +(-1.19475 - 1.41779i) q^{5} +(0.821536 - 1.13980i) q^{7} +(-2.58161 - 0.806524i) q^{9} +(-0.0156941 + 0.0148274i) q^{11} +(-0.255201 + 1.91510i) q^{13} +(0.525653 + 0.859613i) q^{15} +(-2.08237 + 3.13251i) q^{17} +(-5.72303 - 1.32253i) q^{19} +(-0.534782 + 0.545000i) q^{21} +(1.10797 + 5.24513i) q^{23} +(0.264842 - 1.53983i) q^{25} +(2.78587 + 1.36021i) q^{27} +(0.217852 - 1.03131i) q^{29} +(-8.62801 + 1.65265i) q^{31} +(0.00964676 - 0.00667943i) q^{33} +(-2.59752 + 0.197011i) q^{35} +(-5.97084 + 1.86536i) q^{37} +(0.294075 - 1.00794i) q^{39} +(-0.246121 + 0.0978776i) q^{41} +(-9.13328 - 3.23751i) q^{43} +(1.94091 + 4.62377i) q^{45} +(2.82948 - 11.2676i) q^{47} +(1.58924 + 4.76806i) q^{49} +(1.37548 - 1.51221i) q^{51} +(3.05790 + 2.29323i) q^{53} +(0.0397728 + 0.00453577i) q^{55} +(2.96621 + 1.17960i) q^{57} +(-4.22102 - 6.34967i) q^{59} +(-0.243249 - 0.311885i) q^{61} +(-3.04016 + 2.27992i) q^{63} +(3.02010 - 1.92625i) q^{65} +(-3.18850 + 3.78372i) q^{67} +(-0.165320 - 2.90868i) q^{69} +(0.352493 + 3.71398i) q^{71} +(0.568238 - 1.01354i) q^{73} +(-0.268496 + 0.805544i) q^{75} +(0.00400696 + 0.0300694i) q^{77} +(-16.4267 - 0.622057i) q^{79} +(5.28578 + 3.65988i) q^{81} +(3.72234 - 1.00999i) q^{83} +(6.92915 - 0.790215i) q^{85} +(-0.201569 + 0.536198i) q^{87} +(6.11244 - 9.99581i) q^{89} +(1.97316 + 1.86420i) q^{91} +(4.77073 - 0.180661i) q^{93} +(4.96254 + 9.69413i) q^{95} +(8.19386 + 1.56949i) q^{97} +(0.0524748 - 0.0256210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{23}{83}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.537235	−	0.0819657i	−0.310173	−	0.0473229i	−0.00612953	−	0.999981i	$-0.501951\pi$
$3$	−0.537235	−	0.0819657i	−0.310173	−	0.0473229i	−0.304043	+	0.952658i	$0.598337\pi$
$4$		0			0
$5$	−1.19475	−	1.41779i	−0.534310	−	0.634054i	0.428723	−	0.903436i	$-0.358964\pi$
$5$	−1.19475	−	1.41779i	−0.534310	−	0.634054i	−0.963033	+	0.269382i	$0.913180\pi$
$6$		0			0
$7$	0.821536	−	1.13980i	0.310512	−	0.430802i	−0.626861	−	0.779131i	$-0.715661\pi$
$7$	0.821536	−	1.13980i	0.310512	−	0.430802i	0.937372	+	0.348329i	$0.113251\pi$
$8$		0			0
$9$	−2.58161	−	0.806524i	−0.860537	−	0.268841i
$10$		0			0
$11$	−0.0156941	+	0.0148274i	−0.00473195	+	0.00447064i	−0.689114	−	0.724653i	$-0.742000\pi$
$11$	−0.0156941	+	0.0148274i	−0.00473195	+	0.00447064i	0.684382	+	0.729124i	$0.260072\pi$
$12$		0			0
$13$	−0.255201	+	1.91510i	−0.0707800	+	0.531153i	0.919608	+	0.392837i	$0.128506\pi$
$13$	−0.255201	+	1.91510i	−0.0707800	+	0.531153i	−0.990388	+	0.138316i	$0.955831\pi$
$14$		0			0
$15$	0.525653	+	0.859613i	0.135723	+	0.221951i
$16$		0			0
$17$	−2.08237	+	3.13251i	−0.505050	+	0.759745i	−0.993620	−	0.112780i	$-0.964025\pi$
$17$	−2.08237	+	3.13251i	−0.505050	+	0.759745i	0.488570	+	0.872525i	$0.337519\pi$
$18$		0			0
$19$	−5.72303	−	1.32253i	−1.31295	−	0.303410i	−0.490101	−	0.871666i	$-0.663040\pi$
$19$	−5.72303	−	1.32253i	−1.31295	−	0.303410i	−0.822852	+	0.568256i	$0.807618\pi$
$20$		0			0
$21$	−0.534782	+	0.545000i	−0.116699	+	0.118929i
$22$		0			0
$23$	1.10797	+	5.24513i	0.231028	+	1.09369i	0.926839	+	0.375460i	$0.122515\pi$
$23$	1.10797	+	5.24513i	0.231028	+	1.09369i	−0.695811	+	0.718225i	$0.744955\pi$
$24$		0			0
$25$	0.264842	−	1.53983i	0.0529684	−	0.307967i
$26$		0			0
$27$	2.78587	+	1.36021i	0.536142	+	0.261773i
$28$		0			0
$29$	0.217852	−	1.03131i	0.0404540	−	0.191509i	−0.953485	−	0.301440i	$-0.902533\pi$
$29$	0.217852	−	1.03131i	0.0404540	−	0.191509i	0.993939	+	0.109931i	$0.0350629\pi$
$30$		0			0
$31$	−8.62801	+	1.65265i	−1.54964	+	0.296825i	−0.890424	−	0.455132i	$-0.849592\pi$
$31$	−8.62801	+	1.65265i	−1.54964	+	0.296825i	−0.659212	+	0.751957i	$0.729110\pi$
$32$		0			0
$33$	0.00964676	−	0.00667943i	0.00167929	−	0.00116274i
$34$		0			0
$35$	−2.59752	+	0.197011i	−0.439061	+	0.0333010i
$36$		0			0
$37$	−5.97084	+	1.86536i	−0.981600	+	0.306663i	−0.746556	−	0.665322i	$-0.768294\pi$
$37$	−5.97084	+	1.86536i	−0.981600	+	0.306663i	−0.235043	+	0.971985i	$0.575523\pi$
$38$		0			0
$39$	0.294075	−	1.00794i	0.0470897	−	0.161399i
$40$		0			0
$41$	−0.246121	+	0.0978776i	−0.0384377	+	0.0152859i	−0.388672	−	0.921376i	$-0.627066\pi$
$41$	−0.246121	+	0.0978776i	−0.0384377	+	0.0152859i	0.350234	+	0.936662i	$0.386102\pi$
$42$		0			0
$43$	−9.13328	−	3.23751i	−1.39281	−	0.493715i	−0.471269	−	0.881990i	$-0.656204\pi$
$43$	−9.13328	−	3.23751i	−1.39281	−	0.493715i	−0.921544	+	0.388274i	$0.873071\pi$
$44$		0			0
$45$	1.94091	+	4.62377i	0.289334	+	0.689271i
$46$		0			0
$47$	2.82948	−	11.2676i	0.412722	−	1.64355i	−0.308773	−	0.951136i	$-0.599918\pi$
$47$	2.82948	−	11.2676i	0.412722	−	1.64355i	0.721495	−	0.692419i	$-0.243455\pi$
$48$		0			0
$49$	1.58924	+	4.76806i	0.227035	+	0.681152i
$50$		0			0
$51$	1.37548	−	1.51221i	0.192606	−	0.211752i
$52$		0			0
$53$	3.05790	+	2.29323i	0.420035	+	0.314999i	0.788942	−	0.614468i	$-0.210629\pi$
$53$	3.05790	+	2.29323i	0.420035	+	0.314999i	−0.368907	+	0.929466i	$0.620268\pi$
$54$		0			0
$55$	0.0397728	+	0.00453577i	0.00536296	+	0.000611603i
$56$		0			0
$57$	2.96621	+	1.17960i	0.392883	+	0.156242i
$58$		0			0
$59$	−4.22102	−	6.34967i	−0.549530	−	0.826657i	0.448204	−	0.893931i	$-0.352064\pi$
$59$	−4.22102	−	6.34967i	−0.549530	−	0.826657i	−0.997735	+	0.0672745i	$0.978570\pi$
$60$		0			0
$61$	−0.243249	−	0.311885i	−0.0311448	−	0.0399328i	0.772703	−	0.634768i	$-0.218904\pi$
$61$	−0.243249	−	0.311885i	−0.0311448	−	0.0399328i	−0.803848	+	0.594835i	$0.797217\pi$
$62$		0			0
$63$	−3.04016	+	2.27992i	−0.383024	+	0.287243i
$64$		0			0
$65$	3.02010	−	1.92625i	0.374598	−	0.238922i
$66$		0			0
$67$	−3.18850	+	3.78372i	−0.389538	+	0.462255i	−0.923694	−	0.383130i	$-0.874846\pi$
$67$	−3.18850	+	3.78372i	−0.389538	+	0.462255i	0.534157	+	0.845385i	$0.320629\pi$
$68$		0			0
$69$	−0.165320	−	2.90868i	−0.0199022	−	0.350164i
$70$		0			0
$71$	0.352493	+	3.71398i	0.0418332	+	0.440768i	0.991743	+	0.128243i	$0.0409338\pi$
$71$	0.352493	+	3.71398i	0.0418332	+	0.440768i	−0.949910	+	0.312525i	$0.898825\pi$
$72$		0			0
$73$	0.568238	−	1.01354i	0.0665072	−	0.118625i	−0.836992	−	0.547215i	$-0.815688\pi$
$73$	0.568238	−	1.01354i	0.0665072	−	0.118625i	0.903499	+	0.428589i	$0.140989\pi$
$74$		0			0
$75$	−0.268496	+	0.805544i	−0.0310032	+	0.0930162i
$76$		0			0
$77$	0.00400696	+	0.0300694i	0.000456635	+	0.00342672i
$78$		0			0
$79$	−16.4267	−	0.622057i	−1.84815	−	0.0699869i	−0.909673	−	0.415326i	$-0.863668\pi$
$79$	−16.4267	−	0.622057i	−1.84815	−	0.0699869i	−0.938478	+	0.345339i	$0.887764\pi$
$80$		0			0
$81$	5.28578	+	3.65988i	0.587309	+	0.406654i
$82$		0			0
$83$	3.72234	−	1.00999i	0.408580	−	0.110861i	−0.0516405	−	0.998666i	$-0.516445\pi$
$83$	3.72234	−	1.00999i	0.408580	−	0.110861i	0.460221	+	0.887805i	$0.347770\pi$
$84$		0			0
$85$	6.92915	−	0.790215i	0.751572	−	0.0857109i
$86$		0			0
$87$	−0.201569	+	0.536198i	−0.0216105	+	0.0574864i
$88$		0			0
$89$	6.11244	−	9.99581i	0.647917	−	1.05955i	−0.344752	−	0.938694i	$-0.612037\pi$
$89$	6.11244	−	9.99581i	0.647917	−	1.05955i	0.992670	−	0.120860i	$-0.0385653\pi$
$90$		0			0
$91$	1.97316	+	1.86420i	0.206844	+	0.195421i
$92$		0			0
$93$	4.77073	−	0.180661i	0.494701	−	0.0187336i
$94$		0			0
$95$	4.96254	+	9.69413i	0.509146	+	0.994597i
$96$		0			0
$97$	8.19386	+	1.56949i	0.831961	+	0.159358i	0.586398	−	0.810023i	$-0.300545\pi$
$97$	8.19386	+	1.56949i	0.831961	+	0.159358i	0.245563	+	0.969381i	$0.421027\pi$
$98$		0			0
$99$	0.0524748	−	0.0256210i	0.00527391	−	0.00257501i
$100$		0			0
$101$	−0.669183	+	0.237208i	−0.0665862	+	0.0236030i	−0.367189	−	0.930146i	$-0.619680\pi$
$101$	−0.669183	+	0.237208i	−0.0665862	+	0.0236030i	0.300603	+	0.953749i	$0.402812\pi$
$102$		0			0
$103$	−0.0234315	+	1.23796i	−0.00230877	+	0.121980i	0.996805	+	0.0798787i	$0.0254533\pi$
$103$	−0.0234315	+	1.23796i	−0.00230877	+	0.121980i	−0.999113	+	0.0421009i	$0.986595\pi$
$104$		0			0
$105$	1.41163	+	0.107066i	0.137761	+	0.0104486i
$106$		0			0
$107$	−0.210171	−	11.1040i	−0.0203180	−	1.07347i	−0.853699	−	0.520767i	$-0.825646\pi$
$107$	−0.210171	−	11.1040i	−0.0203180	−	1.07347i	0.833381	−	0.552699i	$-0.186402\pi$
$108$		0			0
$109$	9.00852	−	17.5978i	0.862860	−	1.68556i	0.144939	−	0.989441i	$-0.453701\pi$
$109$	9.00852	−	17.5978i	0.862860	−	1.68556i	0.717921	−	0.696124i	$-0.245094\pi$
$110$		0			0
$111$	3.36064	−	0.512731i	0.318977	−	0.0486663i
$112$		0			0
$113$	12.1953	+	10.6780i	1.14724	+	1.00450i	0.999881	+	0.0154191i	$0.00490824\pi$
$113$	12.1953	+	10.6780i	1.14724	+	1.00450i	0.147358	+	0.989083i	$0.452923\pi$
$114$		0			0
$115$	6.11272	−	7.83751i	0.570014	−	0.730851i
$116$		0			0
$117$	2.20340	−	4.73821i	0.203705	−	0.438048i
$118$		0			0
$119$	1.85967	+	4.94695i	0.170476	+	0.453486i
$120$		0			0
$121$	−0.624172	+	10.9818i	−0.0567429	+	0.998346i
$122$		0			0
$123$	0.140247	−	0.0324098i	0.0126457	−	0.00292229i
$124$		0			0
$125$	−10.4985	+	6.14995i	−0.939016	+	0.550068i
$126$		0			0
$127$	0.110867	−	1.16813i	0.00983783	−	0.103655i	−0.989257	−	0.146184i	$-0.953301\pi$
$127$	0.110867	−	1.16813i	0.00983783	−	0.103655i	0.999095	+	0.0425297i	$0.0135417\pi$
$128$		0			0
$129$	4.64135	+	2.48792i	0.408648	+	0.219049i
$130$		0			0
$131$	−0.775050	−	0.852092i	−0.0677164	−	0.0744476i	0.704963	−	0.709244i	$-0.250964\pi$
$131$	−0.775050	−	0.852092i	−0.0677164	−	0.0744476i	−0.772680	+	0.634796i	$0.781084\pi$
$132$		0			0
$133$	−6.20909	+	5.43657i	−0.538396	+	0.471410i
$134$		0			0
$135$	−1.39994	−	5.57490i	−0.120488	−	0.479811i
$136$		0			0
$137$	−1.69616	−	5.81356i	−0.144912	−	0.496686i	0.854841	−	0.518890i	$-0.173655\pi$
$137$	−1.69616	−	5.81356i	−0.144912	−	0.496686i	−0.999753	+	0.0222039i	$0.992932\pi$
$138$		0			0
$139$	−4.76339	+	2.10641i	−0.404025	+	0.178664i	−0.596454	−	0.802648i	$-0.703424\pi$
$139$	−4.76339	+	2.10641i	−0.404025	+	0.178664i	0.192428	+	0.981311i	$0.438364\pi$
$140$		0			0
$141$	−2.44365	+	5.82145i	−0.205793	+	0.490254i
$142$		0			0
$143$	−0.0243909	−	0.0338397i	−0.00203967	−	0.00282982i
$144$		0			0
$145$	−1.72245	+	0.923291i	−0.143042	+	0.0766752i
$146$		0			0
$147$	−0.462978	−	2.69183i	−0.0381858	−	0.222019i
$148$		0			0
$149$	15.1733	+	9.67765i	1.24304	+	0.792824i	0.984873	−	0.173276i	$-0.0554352\pi$
$149$	15.1733	+	9.67765i	1.24304	+	0.792824i	0.258169	+	0.966100i	$0.416881\pi$
$150$		0			0
$151$	2.56035	+	4.56676i	0.208358	+	0.371638i	0.956421	−	0.291990i	$-0.0943173\pi$
$151$	2.56035	+	4.56676i	0.208358	+	0.371638i	−0.748063	+	0.663627i	$0.769016\pi$
$152$		0			0
$153$	7.90232	−	6.40743i	0.638865	−	0.518010i
$154$		0			0
$155$	12.6515	+	10.2582i	1.01619	+	0.823956i
$156$		0			0
$157$	−8.36277	−	17.9834i	−0.667422	−	1.43523i	−0.887993	−	0.459857i	$-0.847901\pi$
$157$	−8.36277	−	17.9834i	−0.667422	−	1.43523i	0.220571	−	0.975371i	$-0.429208\pi$
$158$		0			0
$159$	−1.45485	−	1.48264i	−0.115377	−	0.117581i
$160$		0			0
$161$	6.88861	+	3.04620i	0.542899	+	0.240074i
$162$		0			0
$163$	−13.9693	−	8.18311i	−1.09416	−	0.640950i	−0.156211	−	0.987724i	$-0.549928\pi$
$163$	−13.9693	−	8.18311i	−1.09416	−	0.640950i	−0.937949	+	0.346773i	$0.887277\pi$
$164$		0			0
$165$	−0.0209955	−	0.00569677i	−0.00163450	−	0.000443493i
$166$		0			0
$167$	6.11298	−	11.3856i	0.473036	−	0.881043i
$167$	6.11298	−	11.3856i	0.473036	−	0.881043i
$168$		0			0
$169$	8.94389	+	2.42677i	0.687991	+	0.186675i
$170$		0			0
$171$	13.7080	+	8.03002i	1.04827	+	0.614071i
$172$		0			0
$173$	−20.1801	−	8.92382i	−1.53427	−	0.678465i	−0.546940	−	0.837172i	$-0.684207\pi$
$173$	−20.1801	−	8.92382i	−1.53427	−	0.678465i	−0.987326	+	0.158707i	$0.949267\pi$
$174$		0			0
$175$	−1.53752	−	1.56689i	−0.116225	−	0.118446i
$176$		0			0
$177$	1.74722	+	3.75724i	0.131329	+	0.282411i
$178$		0			0
$179$	8.73479	+	7.08242i	0.652869	+	0.529365i	0.897928	−	0.440143i	$-0.145072\pi$
$179$	8.73479	+	7.08242i	0.652869	+	0.529365i	−0.245059	+	0.969508i	$0.578807\pi$
$180$		0			0
$181$	7.82730	−	6.34661i	0.581799	−	0.471739i	−0.293076	−	0.956089i	$-0.594679\pi$
$181$	7.82730	−	6.34661i	0.581799	−	0.471739i	0.874874	+	0.484350i	$0.160944\pi$
$182$		0			0
$183$	0.105118	+	0.187493i	0.00777054	+	0.0138599i
$184$		0			0
$185$	9.77836	+	6.23673i	0.718919	+	0.458534i
$186$		0			0
$187$	−0.0137661	−	0.0800382i	−0.00100668	−	0.00585297i
$188$		0			0
$189$	3.83906	−	2.05786i	0.279251	−	0.149687i
$190$		0			0
$191$	−11.9954	−	16.6423i	−0.867954	−	1.20419i	−0.977652	−	0.210230i	$-0.932579\pi$
$191$	−11.9954	−	16.6423i	−0.867954	−	1.20419i	0.109698	−	0.993965i	$-0.465012\pi$
$192$		0			0
$193$	−2.31222	+	5.50833i	−0.166437	+	0.396498i	−0.983712	−	0.179749i	$-0.942471\pi$
$193$	−2.31222	+	5.50833i	−0.166437	+	0.396498i	0.817275	+	0.576247i	$0.195483\pi$
$194$		0			0
$195$	−1.78039	+	0.787304i	−0.127496	+	0.0563800i
$196$		0			0
$197$	−1.24039	−	4.25144i	−0.0883745	−	0.302903i	0.903767	−	0.428025i	$-0.140791\pi$
$197$	−1.24039	−	4.25144i	−0.0883745	−	0.302903i	−0.992141	+	0.125122i	$0.960068\pi$
$198$		0			0
$199$	1.82807	+	7.27979i	0.129588	+	0.516051i	0.999730	+	0.0232485i	$0.00740089\pi$
$199$	1.82807	+	7.27979i	0.129588	+	0.516051i	−0.870141	+	0.492802i	$0.835973\pi$
$200$		0			0
$201$	2.02311	−	1.77140i	0.142699	−	0.124945i
$202$		0			0
$203$	−0.996506	−	1.09556i	−0.0699410	−	0.0768934i
$204$		0			0
$205$	0.432824	+	0.232008i	0.0302297	+	0.0162041i
$206$		0			0
$207$	1.36997	−	14.4345i	0.0952197	−	1.00327i
$208$		0			0
$209$	0.109428	−	0.0641018i	0.00756926	−	0.00443402i
$210$		0			0
$211$	14.9184	−	3.44750i	1.02703	−	0.237335i	0.322168	−	0.946683i	$-0.395588\pi$
$211$	14.9184	−	3.44750i	1.02703	−	0.237335i	0.704859	+	0.709347i	$0.251010\pi$
$212$		0			0
$213$	0.115047	−	2.02417i	0.00788292	−	0.138694i
$214$		0			0
$215$	6.32193	+	16.8171i	0.431152	+	1.14692i
$216$		0			0
$217$	−5.20454	+	11.1919i	−0.353307	+	0.759754i
$218$		0			0
$219$	−0.388352	+	0.497931i	−0.0262424	+	0.0336470i
$220$		0			0
$221$	−5.46764	−	4.78737i	−0.367793	−	0.322033i
$222$		0			0
$223$	3.36103	−	0.512790i	0.225071	−	0.0343390i	−0.0373084	−	0.999304i	$-0.511878\pi$
$223$	3.36103	−	0.512790i	0.225071	−	0.0343390i	0.262379	+	0.964965i	$0.415493\pi$
$224$		0			0
$225$	−1.92563	+	3.76165i	−0.128375	+	0.250776i
$226$		0			0
$227$	0.102663	+	5.42403i	0.00681401	+	0.360006i	0.986891	+	0.161388i	$0.0515970\pi$
$227$	0.102663	+	5.42403i	0.00681401	+	0.360006i	−0.980077	+	0.198618i	$0.936355\pi$
$228$		0			0
$229$	−3.72243	−	0.282331i	−0.245985	−	0.0186570i	−0.0479412	−	0.998850i	$-0.515266\pi$
$229$	−3.72243	−	0.282331i	−0.245985	−	0.0186570i	−0.198044	+	0.980193i	$0.563459\pi$
$230$		0			0
$231$	0.000311977	−	0.0164827i	2.05266e−5	−	0.00108448i
$232$		0			0
$233$	15.6115	−	5.53386i	1.02274	−	0.362535i	0.230716	−	0.973021i	$-0.425893\pi$
$233$	15.6115	−	5.53386i	1.02274	−	0.362535i	0.792027	+	0.610486i	$0.209026\pi$
$234$		0			0
$235$	−19.3557	+	9.45046i	−1.26262	+	0.616480i
$236$		0			0
$237$	8.77402	+	1.68062i	0.569934	+	0.109168i
$238$		0			0
$239$	−1.75138	−	3.42126i	−0.113287	−	0.221303i	0.826598	−	0.562793i	$-0.190273\pi$
$239$	−1.75138	−	3.42126i	−0.113287	−	0.221303i	−0.939885	+	0.341490i	$0.889068\pi$
$240$		0			0
$241$	−5.18330	+	0.196284i	−0.333886	+	0.0126438i	−0.204252	−	0.978918i	$-0.565476\pi$
$241$	−5.18330	+	0.196284i	−0.333886	+	0.0126438i	−0.129633	+	0.991562i	$0.541380\pi$
$242$		0			0
$243$	−9.30027	−	8.78668i	−0.596612	−	0.563666i
$244$		0			0
$245$	4.86135	−	7.94987i	0.310580	−	0.507899i
$246$		0			0
$247$	3.99330	−	10.6226i	0.254088	−	0.675903i
$248$		0			0
$249$	−2.08256	+	0.237499i	−0.131977	+	0.0150509i
$250$		0			0
$251$	−13.0665	+	3.54536i	−0.824748	+	0.223781i	−0.649130	−	0.760677i	$-0.724867\pi$
$251$	−13.0665	+	3.54536i	−0.824748	+	0.223781i	−0.175618	+	0.984458i	$0.556192\pi$
$252$		0			0
$253$	−0.0951605	−	0.0658893i	−0.00598269	−	0.00414242i
$254$		0			0
$255$	−3.78735	−	0.143422i	−0.237173	−	0.00898142i
$256$		0			0
$257$	−0.479864	−	3.60104i	−0.0299331	−	0.224626i	0.969888	−	0.243552i	$-0.0783127\pi$
$257$	−0.479864	−	3.60104i	−0.0299331	−	0.224626i	−0.999821	+	0.0189258i	$0.993975\pi$
$258$		0			0
$259$	−2.77913	+	8.33799i	−0.172687	+	0.518097i
$260$		0			0
$261$	−1.39418	+	2.48673i	−0.0862977	+	0.153925i
$262$		0			0
$263$	0.0374928	+	0.395037i	0.00231191	+	0.0243590i	0.996608	−	0.0822986i	$-0.0262261\pi$
$263$	0.0374928	+	0.395037i	0.00231191	+	0.0243590i	−0.994296	+	0.106658i	$0.965985\pi$
$264$		0			0
$265$	−0.402138	−	7.07530i	−0.0247031	−	0.434632i
$266$		0			0
$267$	−4.10313	+	4.86909i	−0.251107	+	0.297983i
$268$		0			0
$269$	−23.0591	+	14.7073i	−1.40594	+	0.896722i	−0.999854	−	0.0171121i	$-0.994553\pi$
$269$	−23.0591	+	14.7073i	−1.40594	+	0.896722i	−0.406087	+	0.913834i	$0.633107\pi$
$270$		0			0
$271$	−7.79534	+	5.84599i	−0.473533	+	0.355118i	−0.809856	−	0.586628i	$-0.800455\pi$
$271$	−7.79534	+	5.84599i	−0.473533	+	0.355118i	0.336323	+	0.941747i	$0.390816\pi$
$272$		0			0
$273$	−0.907251	−	1.16324i	−0.0549093	−	0.0704027i
$274$		0			0
$275$	0.0186753	+	0.0280932i	0.00112616	+	0.00169409i
$276$		0			0
$277$	−23.3664	−	9.29234i	−1.40395	−	0.558323i	−0.459853	−	0.887995i	$-0.652098\pi$
$277$	−23.3664	−	9.29234i	−1.40395	−	0.558323i	−0.944095	+	0.329672i	$0.893062\pi$
$278$		0			0
$279$	23.6071	+	2.69220i	1.41332	+	0.161178i
$280$		0			0
$281$	19.3178	+	14.4870i	1.15240	+	0.864224i	0.992420	−	0.122896i	$-0.0392182\pi$
$281$	19.3178	+	14.4870i	1.15240	+	0.864224i	0.159981	+	0.987120i	$0.448857\pi$
$282$		0			0
$283$	3.52158	−	3.87163i	0.209336	−	0.230145i	−0.626086	−	0.779754i	$-0.715344\pi$
$283$	3.52158	−	3.87163i	0.209336	−	0.230145i	0.835422	+	0.549610i	$0.185224\pi$
$284$		0			0
$285$	−1.87146	−	5.61478i	−0.110856	−	0.332591i
$286$		0			0
$287$	−0.0906371	+	0.360938i	−0.00535014	+	0.0213055i
$288$		0			0
$289$	1.10352	+	2.62889i	0.0649131	+	0.154641i
$290$		0			0
$291$	−4.27338	−	1.51480i	−0.250510	−	0.0887992i
$292$		0			0
$293$	−18.8458	+	7.49460i	−1.10098	+	0.437839i	−0.848196	−	0.529683i	$-0.822311\pi$
$293$	−18.8458	+	7.49460i	−1.10098	+	0.437839i	−0.252787	+	0.967522i	$0.581347\pi$
$294$		0			0
$295$	−3.95940	+	13.5708i	−0.230525	+	0.790123i
$296$		0			0
$297$	−0.0638903	+	0.0199601i	−0.00370729	+	0.00115820i
$298$		0			0
$299$	−10.3277	+	0.783314i	−0.597266	+	0.0453002i
$300$		0			0
$301$	−11.1934	+	7.75034i	−0.645178	+	0.446722i
$302$		0			0
$303$	0.378951	−	0.0725861i	0.0217702	−	0.00416997i
$304$		0			0
$305$	−0.151564	+	0.717501i	−0.00867851	+	0.0410840i
$306$		0			0
$307$	−22.7174	−	11.0918i	−1.29655	−	0.633045i	−0.344442	−	0.938807i	$-0.611932\pi$
$307$	−22.7174	−	11.0918i	−1.29655	−	0.633045i	−0.952108	+	0.305762i	$0.901089\pi$
$308$		0			0
$309$	0.114058	−	0.663153i	0.00648855	−	0.0377255i
$310$		0			0
$311$	−0.168612	−	0.798207i	−0.00956110	−	0.0452622i	0.973367	−	0.229253i	$-0.0736284\pi$
$311$	−0.168612	−	0.798207i	−0.00956110	−	0.0452622i	−0.982928	+	0.183991i	$0.941098\pi$
$312$		0			0
$313$	−21.3324	+	21.7400i	−1.20578	+	1.22882i	−0.239621	+	0.970867i	$0.577023\pi$
$313$	−21.3324	+	21.7400i	−1.20578	+	1.22882i	−0.966158	+	0.257951i	$0.916953\pi$
$314$		0			0
$315$	6.86468	+	1.58636i	0.386781	+	0.0893811i
$316$		0			0
$317$	−0.832361	+	1.25212i	−0.0467500	+	0.0703260i	−0.855414	−	0.517945i	$-0.826697\pi$
$317$	−0.832361	+	1.25212i	−0.0467500	+	0.0703260i	0.808664	+	0.588271i	$0.200191\pi$
$318$		0			0
$319$	0.0118727	+	0.0194156i	0.000664741	+	0.00108707i
$320$		0			0
$321$	−0.797237	+	5.98269i	−0.0444974	+	0.333921i
$322$		0			0
$323$	16.0603	−	15.1734i	0.893620	−	0.844272i
$324$		0			0
$325$	2.88134	+	0.900165i	0.159828	+	0.0499321i
$326$		0			0
$327$	−6.28211	+	8.71576i	−0.347401	+	0.481983i
$328$		0			0
$329$	−10.5183	−	12.4818i	−0.579892	−	0.688144i
$330$		0			0
$331$	−20.4856	−	3.12548i	−1.12599	−	0.171792i	−0.439020	−	0.898477i	$-0.644674\pi$
$331$	−20.4856	−	3.12548i	−1.12599	−	0.171792i	−0.686971	+	0.726685i	$0.741060\pi$
$332$		0			0
$333$	16.9188			0.927146
$334$		0			0
$335$	9.17399			0.501229
$336$		0			0
$337$	−15.0449	−	2.29540i	−0.819548	−	0.125038i	−0.272518	−	0.962151i	$-0.587856\pi$
$337$	−15.0449	−	2.29540i	−0.819548	−	0.125038i	−0.547031	+	0.837113i	$0.684242\pi$
$338$		0			0
$339$	−5.67652	−	6.73619i	−0.308306	−	0.365860i
$340$		0			0
$341$	0.110904	−	0.153868i	0.00600581	−	0.00833243i
$342$		0			0
$343$	16.1279	+	5.03852i	0.870822	+	0.272055i
$344$		0			0
$345$	−3.92637	+	3.70955i	−0.211389	+	0.199715i
$346$		0			0
$347$	−0.598016	+	4.48768i	−0.0321032	+	0.240911i	−0.999943	−	0.0106551i	$-0.996608\pi$
$347$	−0.598016	+	4.48768i	−0.0321032	+	0.240911i	0.967840	+	0.251566i	$0.0809457\pi$
$348$		0			0
$349$	−7.14101	−	11.6779i	−0.382249	−	0.625101i	0.602695	−	0.797971i	$-0.294093\pi$
$349$	−7.14101	−	11.6779i	−0.382249	−	0.625101i	−0.984945	+	0.172870i	$0.944696\pi$
$350$		0			0
$351$	−3.31590	+	4.98810i	−0.176990	+	0.266245i
$352$		0			0
$353$	−7.83684	−	1.81101i	−0.417113	−	0.0963905i	0.0113808	−	0.999935i	$-0.496377\pi$
$353$	−7.83684	−	1.81101i	−0.417113	−	0.0963905i	−0.428494	+	0.903545i	$0.640956\pi$
$354$		0			0
$355$	4.84449	−	4.93705i	0.257119	−	0.262031i
$356$		0			0
$357$	−0.593601	−	2.81010i	−0.0314167	−	0.148726i
$358$		0			0
$359$	1.35446	−	7.87505i	0.0714857	−	0.415629i	−0.927627	−	0.373508i	$-0.878155\pi$
$359$	1.35446	−	7.87505i	0.0714857	−	0.415629i	0.999113	−	0.0421211i	$-0.0134115\pi$
$360$		0			0
$361$	13.9304	+	6.80154i	0.733176	+	0.357976i
$362$		0			0
$363$	1.23546	−	5.84865i	0.0648447	−	0.306974i
$364$		0			0
$365$	−2.11588	+	0.405286i	−0.110750	+	0.0212137i
$366$		0			0
$367$	0.167156	−	0.115739i	0.00872545	−	0.00604152i	−0.564891	−	0.825165i	$-0.691082\pi$
$367$	0.167156	−	0.115739i	0.00872545	−	0.00604152i	0.573617	+	0.819124i	$0.305540\pi$
$368$		0			0
$369$	0.714330	−	0.0541790i	0.0371865	−	0.00282045i
$370$		0			0
$371$	5.12599	−	1.60142i	0.266128	−	0.0831414i
$372$		0			0
$373$	3.03599	−	10.4058i	0.157197	−	0.538793i	−0.842802	−	0.538223i	$-0.819096\pi$
$373$	3.03599	−	10.4058i	0.157197	−	0.538793i	1.00000		0.000569571i	$-0.000181300\pi$
$374$		0			0
$375$	6.14425	−	2.44345i	0.317288	−	0.126179i
$376$		0			0
$377$	1.91946	+	0.680398i	0.0988572	+	0.0350423i
$378$		0			0
$379$	−7.43388	−	17.7095i	−0.381853	−	0.909676i	−0.992995	−	0.118156i	$-0.962302\pi$
$379$	−7.43388	−	17.7095i	−0.381853	−	0.909676i	0.611142	−	0.791521i	$-0.290710\pi$
$380$		0			0
$381$	−0.155308	+	0.618471i	−0.00795666	+	0.0316852i
$382$		0			0
$383$	1.51416	+	4.54280i	0.0773700	+	0.232126i	0.980249	−	0.197769i	$-0.0633696\pi$
$383$	1.51416	+	4.54280i	0.0773700	+	0.232126i	−0.902879	+	0.429896i	$0.858550\pi$
$384$		0			0
$385$	0.0378446	−	0.0416065i	0.00192874	−	0.00212046i
$386$		0			0
$387$	20.9674	+	15.7242i	1.06584	+	0.799306i
$388$		0			0
$389$	−0.815848	−	0.0930411i	−0.0413652	−	0.00471737i	0.0926005	−	0.995703i	$-0.470482\pi$
$389$	−0.815848	−	0.0930411i	−0.0413652	−	0.00471737i	−0.133966	+	0.990986i	$0.542771\pi$
$390$		0			0
$391$	−18.7376	−	7.45159i	−0.947603	−	0.376843i
$392$		0			0
$393$	0.346541	+	0.521301i	0.0174807	+	0.0262961i
$394$		0			0
$395$	18.7440	+	24.0328i	0.943110	+	1.20922i
$396$		0			0
$397$	22.2756	−	16.7052i	1.11798	−	0.838411i	0.129774	−	0.991544i	$-0.458575\pi$
$397$	22.2756	−	16.7052i	1.11798	−	0.838411i	0.988206	+	0.153133i	$0.0489362\pi$
$398$		0			0
$399$	3.78135	−	2.41178i	0.189304	−	0.120740i
$400$		0			0
$401$	−24.6170	+	29.2124i	−1.22931	+	1.45880i	−0.385027	+	0.922905i	$0.625808\pi$
$401$	−24.6170	+	29.2124i	−1.22931	+	1.45880i	−0.844286	+	0.535893i	$0.819975\pi$
$402$		0			0
$403$	−0.963114	−	16.9452i	−0.0479761	−	0.844103i
$404$		0			0
$405$	−1.12627	−	11.8668i	−0.0559649	−	0.589665i
$406$		0			0
$407$	0.0660485	−	0.117807i	0.00327390	−	0.00583949i
$408$		0			0
$409$	−4.44758	+	13.3437i	−0.219918	+	0.659802i	0.779523	+	0.626374i	$0.215462\pi$
$409$	−4.44758	+	13.3437i	−0.219918	+	0.659802i	−0.999441	+	0.0334280i	$0.989358\pi$
$410$		0			0
$411$	0.434722	+	3.26227i	0.0214432	+	0.160916i
$412$		0			0
$413$	−10.7050	−	0.405385i	−0.526761	−	0.0199477i
$414$		0			0
$415$	−5.87924	−	4.07080i	−0.288600	−	0.199827i
$416$		0			0
$417$	2.73171	−	0.741203i	0.133772	−	0.0362969i
$418$		0			0
$419$	−16.4949	+	1.88111i	−0.805828	+	0.0918983i	−0.506487	−	0.862248i	$-0.669056\pi$
$419$	−16.4949	+	1.88111i	−0.805828	+	0.0918983i	−0.299341	+	0.954146i	$0.596767\pi$
$420$		0			0
$421$	−6.56422	+	17.4616i	−0.319920	+	0.851026i	0.673777	+	0.738934i	$0.264671\pi$
$421$	−6.56422	+	17.4616i	−0.319920	+	0.851026i	−0.993698	+	0.112092i	$0.964245\pi$
$422$		0			0
$423$	−16.3922	+	26.8066i	−0.797018	+	1.30338i
$424$		0			0
$425$	4.27204	+	4.03613i	0.207224	+	0.195781i
$426$		0			0
$427$	−0.555323	+	0.0210293i	−0.0268739	+	0.00101768i
$428$		0			0
$429$	0.0103299	+	0.0201791i	0.000498733	+	0.000974256i
$430$		0			0
$431$	1.93652	+	0.370930i	0.0932788	+	0.0178671i	0.234552	−	0.972104i	$-0.424638\pi$
$431$	1.93652	+	0.370930i	0.0932788	+	0.0178671i	−0.141273	+	0.989971i	$0.545120\pi$
$432$		0			0
$433$	27.7595	−	13.5537i	1.33404	−	0.651349i	0.373018	−	0.927824i	$-0.378323\pi$
$433$	27.7595	−	13.5537i	1.33404	−	0.651349i	0.961021	+	0.276476i	$0.0891665\pi$
$434$		0			0
$435$	1.00104	−	0.354842i	0.0479962	−	0.0170134i
$436$		0			0
$437$	0.595902	−	31.4833i	0.0285058	−	1.50605i
$438$		0			0
$439$	−20.3343	−	1.54227i	−0.970501	−	0.0736086i	−0.419181	−	0.907903i	$-0.637683\pi$
$439$	−20.3343	−	1.54227i	−0.970501	−	0.0736086i	−0.551320	+	0.834294i	$0.685876\pi$
$440$		0			0
$441$	−0.257245	−	13.5910i	−0.0122497	−	0.647192i
$442$		0			0
$443$	−7.63294	+	14.9107i	−0.362652	+	0.708427i	−0.997961	−	0.0638314i	$-0.979668\pi$
$443$	−7.63294	+	14.9107i	−0.362652	+	0.708427i	0.635309	+	0.772258i	$0.280873\pi$
$444$		0			0
$445$	−21.4748	+	3.27640i	−1.01800	+	0.155316i
$446$		0			0
$447$	−7.35836	−	6.44285i	−0.348039	−	0.304737i
$448$		0			0
$449$	2.78414	−	3.56973i	0.131392	−	0.168466i	−0.718320	−	0.695712i	$-0.755089\pi$
$449$	2.78414	−	3.56973i	0.131392	−	0.168466i	0.849712	+	0.527247i	$0.176776\pi$
$450$		0			0
$451$	0.00241138	−	0.00518545i	0.000113548	−	0.000244173i
$452$		0			0
$453$	−1.00119	−	2.66328i	−0.0470400	−	0.125132i
$454$		0			0
$455$	0.285593	−	5.02478i	0.0133888	−	0.235566i
$456$		0			0
$457$	−10.3615	+	2.39443i	−0.484690	+	0.112007i	−0.460425	−	0.887699i	$-0.652303\pi$
$457$	−10.3615	+	2.39443i	−0.484690	+	0.112007i	−0.0242651	+	0.999706i	$0.507725\pi$
$458$		0			0
$459$	−10.0621	+	5.89431i	−0.469659	+	0.275123i
$460$		0			0
$461$	−0.927989	+	9.77759i	−0.0432208	+	0.455388i	0.947527	+	0.319675i	$0.103574\pi$
$461$	−0.927989	+	9.77759i	−0.0432208	+	0.455388i	−0.990748	+	0.135713i	$0.956667\pi$
$462$		0			0
$463$	−25.8051	−	13.8324i	−1.19927	−	0.642846i	−0.253387	−	0.967365i	$-0.581545\pi$
$463$	−25.8051	−	13.8324i	−1.19927	−	0.642846i	−0.945879	+	0.324519i	$0.894798\pi$
$464$		0			0
$465$	−5.95598	−	6.54803i	−0.276202	−	0.303658i
$466$		0			0
$467$	8.31584	−	7.28120i	0.384811	−	0.336934i	−0.444441	−	0.895808i	$-0.646598\pi$
$467$	8.31584	−	7.28120i	0.384811	−	0.336934i	0.829253	+	0.558874i	$0.188766\pi$
$468$		0			0
$469$	1.69320	+	6.74270i	0.0781846	+	0.311349i
$470$		0			0
$471$	3.01875	+	10.3467i	0.139097	+	0.476753i
$472$		0			0
$473$	0.191343	−	0.0846134i	0.00879795	−	0.00389053i
$474$		0			0
$475$	−3.55218	+	8.46224i	−0.162985	+	0.388274i
$476$		0			0
$477$	−6.04477	−	8.38649i	−0.276771	−	0.383991i
$478$		0			0
$479$	16.8774	−	9.04682i	0.771146	−	0.413360i	−0.0392594	−	0.999229i	$-0.512500\pi$
$479$	16.8774	−	9.04682i	0.771146	−	0.413360i	0.810405	+	0.585869i	$0.199247\pi$
$480$		0			0
$481$	−2.04858	−	11.9108i	−0.0934072	−	0.543085i
$482$		0			0
$483$	−3.45112	−	2.20116i	−0.157031	−	0.100156i
$484$		0			0
$485$	−7.56444	−	13.4923i	−0.343484	−	0.612654i
$486$		0			0
$487$	8.11520	−	6.58004i	0.367735	−	0.298170i	−0.428044	−	0.903758i	$-0.640797\pi$
$487$	8.11520	−	6.58004i	0.367735	−	0.298170i	0.795778	+	0.605588i	$0.207062\pi$
$488$		0			0
$489$	6.83406	+	5.54125i	0.309047	+	0.250584i
$490$		0			0
$491$	13.9651	+	30.0307i	0.630238	+	1.35527i	0.917623	+	0.397452i	$0.130106\pi$
$491$	13.9651	+	30.0307i	0.630238	+	1.35527i	−0.287385	+	0.957815i	$0.592786\pi$
$492$		0			0
$493$	2.77693	+	2.82999i	0.125067	+	0.127456i
$494$		0			0
$495$	−0.0990195	−	0.0437873i	−0.00445060	−	0.00196809i
$496$		0			0
$497$	4.52276	+	2.64940i	0.202873	+	0.118842i
$498$		0			0
$499$	32.8170	+	8.90432i	1.46909	+	0.398612i	0.904398	−	0.426689i	$-0.140320\pi$
$499$	32.8170	+	8.90432i	1.46909	+	0.398612i	0.564692	+	0.825302i	$0.308995\pi$
$500$		0			0
$501$	−4.21733	+	5.61567i	−0.188416	+	0.250890i
$502$		0			0
$503$	36.5620	+	9.92046i	1.63022	+	0.442332i	0.955319	−	0.295578i	$-0.0955121\pi$
$503$	36.5620	+	9.92046i	1.63022	+	0.442332i	0.674900	+	0.737909i	$0.264187\pi$
$504$		0			0
$505$	1.13582	+	0.665354i	0.0505433	+	0.0296079i
$506$		0			0
$507$	−4.60605	−	2.03684i	−0.204562	−	0.0904591i
$508$		0			0
$509$	−17.0594	−	17.3853i	−0.756143	−	0.770590i	0.222770	−	0.974871i	$-0.428490\pi$
$509$	−17.0594	−	17.3853i	−0.756143	−	0.770590i	−0.978912	+	0.204281i	$0.934514\pi$
$510$		0			0
$511$	−0.688396	−	1.48033i	−0.0304528	−	0.0654860i
$512$		0			0
$513$	−14.1447	−	11.4689i	−0.624504	−	0.506366i
$514$		0			0
$515$	1.78316	−	1.44583i	0.0785752	−	0.0637111i
$516$		0			0
$517$	0.122664	+	0.218790i	0.00539476	+	0.00962236i
$518$		0			0
$519$	10.1100	+	6.44826i	0.443780	+	0.283047i
$520$		0			0
$521$	6.85805	+	39.8738i	0.300457	+	1.74690i	0.606682	+	0.794945i	$0.292500\pi$
$521$	6.85805	+	39.8738i	0.300457	+	1.74690i	−0.306225	+	0.951959i	$0.599066\pi$
$522$		0			0
$523$	18.2091	−	9.76067i	0.796228	−	0.426804i	−0.0233820	−	0.999727i	$-0.507443\pi$
$523$	18.2091	−	9.76067i	0.796228	−	0.426804i	0.819610	+	0.572922i	$0.194190\pi$
$524$		0			0
$525$	0.697576	+	0.967813i	0.0304447	+	0.0422388i
$526$		0			0
$527$	12.7898	−	30.4688i	0.557132	−	1.32724i
$528$		0			0
$529$	−5.24870	+	2.32102i	−0.228204	+	0.100914i
$530$		0			0
$531$	5.77586	+	19.7967i	0.250651	+	0.859105i
$532$		0			0
$533$	−0.124635	−	0.496325i	−0.00539854	−	0.0214982i
$534$		0			0
$535$	−15.4920	+	13.5645i	−0.669779	+	0.586447i
$536$		0			0
$537$	−4.11211	−	4.52087i	−0.177451	−	0.195090i
$538$		0			0
$539$	−0.0956399	−	0.0512661i	−0.00411950	−	0.00220819i
$540$		0			0
$541$	0.211581	−	2.22929i	0.00909658	−	0.0958446i	−0.989824	−	0.142298i	$-0.954551\pi$
$541$	0.211581	−	2.22929i	0.00909658	−	0.0958446i	0.998920	+	0.0464533i	$0.0147919\pi$
$542$		0			0
$543$	−4.72530	+	2.76805i	−0.202782	+	0.118788i
$544$		0			0
$545$	−35.7129	+	8.25289i	−1.52977	+	0.353515i
$546$		0			0
$547$	−1.94052	+	34.1420i	−0.0829708	+	1.45981i	0.639706	+	0.768620i	$0.279056\pi$
$547$	−1.94052	+	34.1420i	−0.0829708	+	1.45981i	−0.722676	+	0.691187i	$0.757088\pi$
$548$		0			0
$549$	0.376431	+	1.00135i	0.0160657	+	0.0427366i
$550$		0			0
$551$	−2.61071	+	5.61408i	−0.111220	+	0.239168i
$552$		0			0
$553$	−14.2042	+	18.2121i	−0.604023	+	0.774455i
$554$		0			0
$555$	−4.74208	−	4.15208i	−0.201290	−	0.176246i
$556$		0			0
$557$	23.2366	−	3.54520i	0.984568	−	0.150215i	0.361491	−	0.932376i	$-0.382268\pi$
$557$	23.2366	−	3.54520i	0.984568	−	0.150215i	0.623077	+	0.782161i	$0.285882\pi$
$558$		0			0
$559$	8.53097	−	16.6649i	0.360821	−	0.704851i
$560$		0			0
$561$	0.000835227		0.0441276i	3.52633e−5		0.00186307i
$562$		0			0
$563$	21.7020	+	1.64601i	0.914629	+	0.0693709i	0.524520	−	0.851398i	$-0.324245\pi$
$563$	21.7020	+	1.64601i	0.914629	+	0.0693709i	0.390108	+	0.920769i	$0.372438\pi$
$564$		0			0
$565$	0.568733	−	30.0480i	0.0239268	−	1.26413i
$566$		0			0
$567$	8.51398	−	3.01798i	0.357554	−	0.126743i
$568$		0			0
$569$	17.3526	−	8.47246i	0.727459	−	0.355184i	−0.0374712	−	0.999298i	$-0.511930\pi$
$569$	17.3526	−	8.47246i	0.727459	−	0.355184i	0.764930	+	0.644114i	$0.222774\pi$
$570$		0			0
$571$	44.2094	+	8.46808i	1.85011	+	0.354378i	0.988259	−	0.152791i	$-0.0488262\pi$
$571$	44.2094	+	8.46808i	1.85011	+	0.354378i	0.861847	+	0.507169i	$0.169308\pi$
$572$		0			0
$573$	5.08022	+	9.92403i	0.212229	+	0.414582i
$574$		0			0
$575$	8.37006	−	0.316963i	0.349056	−	0.0132183i
$576$		0			0
$577$	−3.73955	−	3.53304i	−0.155679	−	0.147082i	0.604963	−	0.796254i	$-0.293188\pi$
$577$	−3.73955	−	3.53304i	−0.155679	−	0.147082i	−0.760642	+	0.649172i	$0.775116\pi$
$578$		0			0
$579$	1.69370	−	2.76974i	0.0703876	−	0.115107i
$580$		0			0
$581$	1.90685	−	5.07245i	0.0791096	−	0.210441i
$582$		0			0
$583$	−0.0819938	+	0.00935074i	−0.00339583	+	0.000387268i
$584$		0			0
$585$	−9.35030	+	2.53704i	−0.386587	+	0.104894i
$586$		0			0
$587$	−15.0266	−	10.4044i	−0.620212	−	0.429436i	0.217109	−	0.976147i	$-0.430337\pi$
$587$	−15.0266	−	10.4044i	−0.620212	−	0.429436i	−0.837321	+	0.546711i	$0.815880\pi$
$588$		0			0
$589$	51.5640	+	1.95266i	2.12466	+	0.0804578i
$590$		0			0
$591$	0.317911	+	2.38569i	0.0130771	+	0.0981342i
$592$		0			0
$593$	11.9129	−	35.7413i	0.489205	−	1.46772i	−0.356617	−	0.934251i	$-0.616070\pi$
$593$	11.9129	−	35.7413i	0.489205	−	1.46772i	0.845821	−	0.533467i	$-0.179111\pi$
$594$		0			0
$595$	4.79187	−	8.54701i	0.196447	−	0.350393i
$596$		0			0
$597$	−0.385409	−	4.06079i	−0.0157737	−	0.166197i
$598$		0			0
$599$	1.32497	+	23.3118i	0.0541368	+	0.952495i	0.904547	+	0.426374i	$0.140209\pi$
$599$	1.32497	+	23.3118i	0.0541368	+	0.952495i	−0.850410	+	0.526121i	$0.823646\pi$
$600$		0			0
$601$	−11.4615	+	13.6011i	−0.467525	+	0.554802i	−0.946364	−	0.323101i	$-0.895275\pi$
$601$	−11.4615	+	13.6011i	−0.467525	+	0.554802i	0.478839	+	0.877903i	$0.341058\pi$
$602$		0			0
$603$	11.2831	−	7.19649i	0.459485	−	0.293064i
$604$		0			0
$605$	16.3156	−	12.2356i	0.663323	−	0.497449i
$606$		0			0
$607$	−10.6921	−	13.7091i	−0.433981	−	0.556434i	0.520825	−	0.853663i	$-0.325624\pi$
$607$	−10.6921	−	13.7091i	−0.433981	−	0.556434i	−0.954806	+	0.297229i	$0.903938\pi$
$608$		0			0
$609$	0.445559	+	0.670253i	0.0180550	+	0.0271600i
$610$		0			0
$611$	20.8566	+	8.29425i	0.843766	+	0.335549i
$612$		0			0
$613$	16.0311	+	1.82822i	0.647492	+	0.0738413i	0.430870	−	0.902414i	$-0.358207\pi$
$613$	16.0311	+	1.82822i	0.647492	+	0.0738413i	0.216622	+	0.976256i	$0.430496\pi$
$614$		0			0
$615$	−0.213511	−	0.160119i	−0.00860961	−	0.00645664i
$616$		0			0
$617$	25.9944	−	28.5784i	1.04650	−	1.15052i	0.0581493	−	0.998308i	$-0.481480\pi$
$617$	25.9944	−	28.5784i	1.04650	−	1.15052i	0.988348	−	0.152214i	$-0.0486404\pi$
$618$		0			0
$619$	1.86170	+	5.58551i	0.0748282	+	0.224501i	0.979440	−	0.201736i	$-0.0646584\pi$
$619$	1.86170	+	5.58551i	0.0748282	+	0.224501i	−0.904612	+	0.426237i	$0.859839\pi$
$620$		0			0
$621$	−4.04782	+	16.1193i	−0.162433	+	0.646847i
$622$		0			0
$623$	−6.37159	−	15.1789i	−0.255272	−	0.608128i
$624$		0			0
$625$	13.8992	+	4.92689i	0.555967	+	0.197075i
$626$		0			0
$627$	−0.0640424	+	0.0254684i	−0.00255761	+	0.00101711i
$628$		0			0
$629$	6.59026	−	22.5881i	0.262771	−	0.900645i
$630$		0			0
$631$	−39.4877	+	12.3364i	−1.57198	+	0.491105i	−0.955183	−	0.296016i	$-0.904342\pi$
$631$	−39.4877	+	12.3364i	−1.57198	+	0.491105i	−0.616799	+	0.787121i	$0.711571\pi$
$632$		0			0
$633$	−8.29727	+	0.629315i	−0.329787	+	0.0250130i
$634$		0			0
$635$	−1.78861	+	1.23844i	−0.0709790	+	0.0491460i
$636$		0			0
$637$	−9.53689	+	1.82674i	−0.377865	+	0.0723781i
$638$		0			0
$639$	2.08541	−	9.87233i	0.0824977	−	0.390544i
$640$		0			0
$641$	26.4512	+	12.9149i	1.04476	+	0.510106i	0.879378	−	0.476124i	$-0.157959\pi$
$641$	26.4512	+	12.9149i	1.04476	+	0.510106i	0.165379	+	0.986230i	$0.447115\pi$
$642$		0			0
$643$	2.95691	−	17.1919i	0.116609	−	0.677984i	−0.867089	−	0.498154i	$-0.834011\pi$
$643$	2.95691	−	17.1919i	0.116609	−	0.677984i	0.983698	−	0.179830i	$-0.0575548\pi$
$644$		0			0
$645$	−2.01794	−	9.55290i	−0.0794562	−	0.376145i
$646$		0			0
$647$	5.74689	−	5.85670i	0.225934	−	0.230251i	−0.591454	−	0.806339i	$-0.701446\pi$
$647$	5.74689	−	5.85670i	0.225934	−	0.230251i	0.817387	+	0.576088i	$0.195422\pi$
$648$		0			0
$649$	0.160395	+	0.0370655i	0.00629604	+	0.00145495i
$650$		0			0
$651$	3.71341	−	5.58607i	0.145540	−	0.218935i
$652$		0			0
$653$	−16.8134	−	27.4953i	−0.657959	−	1.07598i	−0.991103	−	0.133099i	$-0.957507\pi$
$653$	−16.8134	−	27.4953i	−0.657959	−	1.07598i	0.333144	−	0.942876i	$-0.391890\pi$
$654$		0			0
$655$	−0.282092	+	2.11690i	−0.0110222	+	0.0827140i
$656$		0			0
$657$	−2.28441	+	2.15826i	−0.0891233	+	0.0842016i
$658$		0			0
$659$	−14.9801	−	4.67994i	−0.583540	−	0.182305i	−0.00784528	−	0.999969i	$-0.502497\pi$
$659$	−14.9801	−	4.67994i	−0.583540	−	0.182305i	−0.575695	+	0.817665i	$0.695268\pi$
$660$		0			0
$661$	−18.5016	+	25.6691i	−0.719630	+	0.998410i	0.279637	+	0.960106i	$0.409786\pi$
$661$	−18.5016	+	25.6691i	−0.719630	+	0.998410i	−0.999266	+	0.0383044i	$0.987804\pi$
$662$		0			0
$663$	2.54500	+	3.02010i	0.0988398	+	0.117291i
$664$		0			0
$665$	15.1262	+	2.30780i	0.586570	+	0.0894928i
$666$		0			0
$667$	5.65071			0.218797
$668$		0			0
$669$	−1.84769			−0.0714358
$670$		0			0
$671$	0.00844203	+	0.00128800i	0.000325901	+	4.97226e-5i
$672$		0			0
$673$	25.0036	+	29.6712i	0.963818	+	1.14374i	0.989567	+	0.144072i	$0.0460197\pi$
$673$	25.0036	+	29.6712i	0.963818	+	1.14374i	−0.0257494	+	0.999668i	$0.508197\pi$
$674$		0			0
$675$	2.83232	−	3.92954i	0.109016	−	0.151248i
$676$		0			0
$677$	−1.21676	−	0.380129i	−0.0467638	−	0.0146095i	0.274727	−	0.961522i	$-0.411413\pi$
$677$	−1.21676	−	0.380129i	−0.0467638	−	0.0146095i	−0.321490	+	0.946913i	$0.604184\pi$
$678$		0			0
$679$	8.52046	−	8.04993i	0.326985	−	0.308928i
$680$		0			0
$681$	0.389430	−	2.92239i	0.0149230	−	0.111986i
$682$		0			0
$683$	13.5056	+	22.0860i	0.516776	+	0.845096i	0.999530	−	0.0306599i	$-0.00976089\pi$
$683$	13.5056	+	22.0860i	0.516776	+	0.845096i	−0.482754	+	0.875756i	$0.660363\pi$
$684$		0			0
$685$	−6.21590	+	9.35057i	−0.237497	+	0.357267i
$686$		0			0
$687$	1.97667	+	0.456789i	0.0754148	+	0.0174276i
$688$		0			0
$689$	−5.17213	+	5.27095i	−0.197043	+	0.200807i
$690$		0			0
$691$	−6.11891	−	28.9669i	−0.232774	−	1.10195i	−0.924910	−	0.380185i	$-0.875860\pi$
$691$	−6.11891	−	28.9669i	−0.232774	−	1.10195i	0.692136	−	0.721767i	$-0.256670\pi$
$692$		0			0
$693$	0.0139073	−	0.0808590i	0.000528293	−	0.00307158i
$694$		0			0
$695$	8.67752	+	4.23683i	0.329157	+	0.160712i
$696$		0			0
$697$	0.205914	−	0.974795i	0.00779955	−	0.0369230i
$698$		0			0
$699$	−8.84062	+	1.69338i	−0.334383	+	0.0640494i
$700$		0			0
$701$	−12.5728	+	8.70542i	−0.474868	+	0.328799i	−0.782440	−	0.622725i	$-0.786025\pi$
$701$	−12.5728	+	8.70542i	−0.474868	+	0.328799i	0.307573	+	0.951525i	$0.400483\pi$
$702$		0			0
$703$	36.6383	−	2.77886i	1.38184	−	0.104807i
$704$		0			0
$705$	11.1731	−	3.49062i	0.420805	−	0.131464i
$706$		0			0
$707$	−0.279390	+	0.957606i	−0.0105075	+	0.0360145i
$708$		0			0
$709$	23.3386	−	9.28129i	0.876498	−	0.348566i	0.112397	−	0.993663i	$-0.464147\pi$
$709$	23.3386	−	9.28129i	0.876498	−	0.348566i	0.764100	+	0.645097i	$0.223183\pi$
$710$		0			0
$711$	41.9057	+	14.8545i	1.57159	+	0.557086i
$712$		0			0
$713$	−18.2280	−	43.4239i	−0.682643	−	1.62624i
$714$		0			0
$715$	−0.0188365	+	0.0750112i	−0.000704445	+	0.00280526i
$716$		0			0
$717$	0.660477	+	1.98157i	0.0246660	+	0.0740031i
$718$		0			0
$719$	−4.50640	+	4.95435i	−0.168060	+	0.184766i	−0.817997	−	0.575222i	$-0.804916\pi$
$719$	−4.50640	+	4.95435i	−0.168060	+	0.184766i	0.649937	+	0.759988i	$0.274795\pi$
$720$		0			0
$721$	1.39177	+	1.04373i	0.0518322	+	0.0388707i
$722$		0			0
$723$	2.80074	+	0.319402i	0.104160	+	0.0118787i
$724$		0			0
$725$	−1.53035	−	0.608588i	−0.0568356	−	0.0226024i
$726$		0			0
$727$	−6.10499	−	9.18372i	−0.226422	−	0.340605i	0.701972	−	0.712205i	$-0.252303\pi$
$727$	−6.10499	−	9.18372i	−0.226422	−	0.340605i	−0.928393	+	0.371600i	$0.878809\pi$
$728$		0			0
$729$	−7.58557	−	9.72594i	−0.280947	−	0.360220i
$730$		0			0
$731$	29.1604	−	21.8684i	1.07854	−	0.808832i
$732$		0			0
$733$	8.25612	−	5.26583i	0.304947	−	0.194498i	−0.376403	−	0.926456i	$-0.622839\pi$
$733$	8.25612	−	5.26583i	0.304947	−	0.194498i	0.681350	+	0.731958i	$0.261393\pi$
$734$		0			0
$735$	−3.26330	+	3.87248i	−0.120369	+	0.142839i
$736$		0			0
$737$	−0.00606219	−	0.106659i	−0.000223304	−	0.00392885i
$738$		0			0
$739$	2.25248	+	23.7328i	0.0828587	+	0.873026i	0.936152	+	0.351595i	$0.114361\pi$
$739$	2.25248	+	23.7328i	0.0828587	+	0.873026i	−0.853293	+	0.521431i	$0.825398\pi$
$740$		0			0
$741$	−3.01603	+	5.37954i	−0.110797	+	0.197622i
$742$		0			0
$743$	−10.2220	+	30.6681i	−0.375008	+	1.12510i	0.576399	+	0.817168i	$0.304457\pi$
$743$	−10.2220	+	30.6681i	−0.375008	+	1.12510i	−0.951407	+	0.307935i	$0.900362\pi$
$744$		0			0
$745$	−4.40747	−	33.0749i	−0.161477	−	1.21177i
$746$		0			0
$747$	−10.4242	−	0.394751i	−0.381402	−	0.0144432i
$748$		0			0
$749$	−12.8290	−	8.88280i	−0.468760	−	0.324570i
$750$		0			0
$751$	1.26310	−	0.342719i	0.0460910	−	0.0125060i	−0.238744	−	0.971082i	$-0.576736\pi$
$751$	1.26310	−	0.342719i	0.0460910	−	0.0125060i	0.284835	+	0.958576i	$0.408061\pi$
$752$		0			0
$753$	7.31035	−	0.833688i	0.266404	−	0.0303813i
$754$		0			0
$755$	3.41571	−	9.08618i	0.124310	−	0.330680i
$756$		0			0
$757$	−12.1114	+	19.8060i	−0.440195	+	0.719861i	−0.993588	−	0.113059i	$-0.963935\pi$
$757$	−12.1114	+	19.8060i	−0.440195	+	0.719861i	0.553393	+	0.832920i	$0.313333\pi$
$758$		0			0
$759$	0.0457228	+	0.0431979i	0.00165963	+	0.00156798i
$760$		0			0
$761$	−17.6791	+	0.669481i	−0.640865	+	0.0242687i	−0.356276	−	0.934381i	$-0.615954\pi$
$761$	−17.6791	+	0.669481i	−0.640865	+	0.0242687i	−0.284589	+	0.958649i	$0.591857\pi$
$762$		0			0
$763$	−12.6571	−	24.7251i	−0.458217	−	0.895109i
$764$		0			0
$765$	−18.5257	−	3.54850i	−0.669798	−	0.128296i
$766$		0			0
$767$	13.2374	−	6.46323i	0.477977	−	0.233374i
$768$		0			0
$769$	−30.7385	+	10.8960i	−1.10846	+	0.392919i	−0.824469	−	0.565908i	$-0.808526\pi$
$769$	−30.7385	+	10.8960i	−1.10846	+	0.392919i	−0.283990	+	0.958827i	$0.591658\pi$
$770$		0			0
$771$	−0.0373617	+	1.97393i	−0.00134555	+	0.0710895i
$772$		0			0
$773$	27.3958	+	2.07786i	0.985358	+	0.0747354i	0.558431	−	0.829551i	$-0.311404\pi$
$773$	27.3958	+	2.07786i	0.985358	+	0.0747354i	0.426927	+	0.904286i	$0.359596\pi$
$774$		0			0
$775$	0.259750	+	13.7234i	0.00933048	+	0.492959i
$776$		0			0
$777$	2.17648	−	4.25166i	0.0780806	−	0.152528i
$778$		0			0
$779$	1.53801	−	0.234653i	0.0551048	−	0.00840731i
$780$		0			0
$781$	−0.0606008	−	0.0530610i	−0.00216847	−	0.00189867i
$782$		0			0
$783$	2.00970	−	2.57677i	0.0718210	−	0.0920862i
$784$		0			0
$785$	−15.5051	+	33.3423i	−0.553401	+	1.19004i
$786$		0			0
$787$	−8.94723	−	23.8007i	−0.318934	−	0.848403i	−0.993873	−	0.110529i	$-0.964746\pi$
$787$	−8.94723	−	23.8007i	−0.318934	−	0.848403i	0.674939	−	0.737874i	$-0.264170\pi$
$788$		0			0
$789$	0.0122370	−	0.215301i	0.000435649	−	0.00766490i
$790$		0			0
$791$	22.1896	−	5.12780i	0.788973	−	0.182323i
$792$		0			0
$793$	0.659367	−	0.386252i	0.0234148	−	0.0137162i
$794$		0			0
$795$	−0.363889	+	3.83406i	−0.0129058	+	0.135980i
$796$		0			0
$797$	−22.3267	−	11.9678i	−0.790851	−	0.423922i	0.0267970	−	0.999641i	$-0.491469\pi$
$797$	−22.3267	−	11.9678i	−0.790851	−	0.423922i	−0.817648	+	0.575719i	$0.804722\pi$
$798$		0			0
$799$	29.4040	+	32.3268i	1.04024	+	1.14364i
$800$		0			0
$801$	−23.8418	+	20.8755i	−0.842408	+	0.737598i
$802$		0			0
$803$	0.00611016	+	0.0243321i	0.000215623	+	0.000858660i
$804$		0			0
$805$	−3.91133	−	13.4060i	−0.137856	−	0.472501i
$806$		0			0
$807$	13.5937	−	6.01123i	0.478520	−	0.211605i
$808$		0			0
$809$	0.768851	−	1.83161i	0.0270314	−	0.0643960i	−0.907981	−	0.419012i	$-0.862376\pi$
$809$	0.768851	−	1.83161i	0.0270314	−	0.0643960i	0.935012	+	0.354616i	$0.115388\pi$
$810$		0			0
$811$	−3.78235	−	5.24762i	−0.132816	−	0.184269i	0.739579	−	0.673070i	$-0.235025\pi$
$811$	−3.78235	−	5.24762i	−0.132816	−	0.184269i	−0.872395	+	0.488801i	$0.837434\pi$
$812$		0			0
$813$	4.66709	−	2.50172i	0.163682	−	0.0877390i
$814$		0			0
$815$	5.08797	+	29.5823i	0.178224	+	1.03622i
$816$		0			0
$817$	47.9883	+	30.6074i	1.67890	+	1.07082i
$818$		0			0
$819$	−3.59042	−	6.40404i	−0.125459	−	0.223775i
$820$		0			0
$821$	−24.0736	+	19.5196i	−0.840174	+	0.681238i	−0.949842	−	0.312731i	$-0.898756\pi$
$821$	−24.0736	+	19.5196i	−0.840174	+	0.681238i	0.109668	+	0.993968i	$0.465021\pi$
$822$		0			0
$823$	18.6586	+	15.1290i	0.650399	+	0.527363i	0.897155	−	0.441715i	$-0.145630\pi$
$823$	18.6586	+	15.1290i	0.650399	+	0.527363i	−0.246756	+	0.969078i	$0.579365\pi$
$824$		0			0
$825$	−0.00773035	−	0.0166234i	−0.000269136	−	0.000578752i
$826$		0			0
$827$	21.9011	+	22.3196i	0.761576	+	0.776127i	0.979845	−	0.199762i	$-0.0640168\pi$
$827$	21.9011	+	22.3196i	0.761576	+	0.776127i	−0.218269	+	0.975889i	$0.570041\pi$
$828$		0			0
$829$	−17.4739	−	7.72711i	−0.606894	−	0.268374i	0.0780733	−	0.996948i	$-0.475123\pi$
$829$	−17.4739	−	7.72711i	−0.606894	−	0.268374i	−0.684967	+	0.728574i	$0.740183\pi$
$830$		0			0
$831$	11.7916	+	6.90741i	0.409045	+	0.239615i
$832$		0			0
$833$	−18.2454	−	4.95057i	−0.632166	−	0.171527i
$834$		0			0
$835$	−23.4458	+	4.93607i	−0.811377	+	0.170820i
$836$		0			0
$837$	−26.2845	−	7.13185i	−0.908525	−	0.246513i
$838$		0			0
$839$	−28.0908	−	16.4554i	−0.969802	−	0.568102i	−0.0668123	−	0.997766i	$-0.521283\pi$
$839$	−28.0908	−	16.4554i	−0.969802	−	0.568102i	−0.902989	+	0.429663i	$0.858632\pi$
$840$		0			0
$841$	25.5064	+	11.2791i	0.879530	+	0.388936i
$842$		0			0
$843$	−9.19072	−	9.36633i	−0.316545	−	0.322593i
$844$		0			0
$845$	−7.24510	−	15.5799i	−0.249239	−	0.535965i
$846$		0			0
$847$	12.0042	+	9.73338i	0.412470	+	0.334443i
$848$		0			0
$849$	−2.20925	+	1.79133i	−0.0758214	+	0.0614782i
$850$		0			0
$851$	−16.3996	−	29.2511i	−0.562170	−	1.00271i
$852$		0			0
$853$	−3.06333	−	1.95382i	−0.104886	−	0.0668976i	0.484258	−	0.874925i	$-0.339089\pi$
$853$	−3.06333	−	1.95382i	−0.104886	−	0.0668976i	−0.589145	+	0.808027i	$0.700535\pi$
$854$		0			0
$855$	−4.99279	−	29.0289i	−0.170750	−	0.992767i
$856$		0			0
$857$	−9.87953	+	5.29575i	−0.337478	+	0.180899i	−0.632439	−	0.774610i	$-0.717946\pi$
$857$	−9.87953	+	5.29575i	−0.337478	+	0.180899i	0.294961	+	0.955509i	$0.404693\pi$
$858$		0			0
$859$	−18.9068	−	26.2313i	−0.645093	−	0.894999i	0.354098	−	0.935208i	$-0.384788\pi$
$859$	−18.9068	−	26.2313i	−0.645093	−	0.894999i	−0.999191	+	0.0402093i	$0.987198\pi$
$860$		0			0
$861$	0.0782779	−	0.186479i	0.00266770	−	0.00635519i
$862$		0			0
$863$	−28.1360	+	12.4420i	−0.957761	+	0.423530i	−0.823437	−	0.567408i	$-0.807946\pi$
$863$	−28.1360	+	12.4420i	−0.957761	+	0.423530i	−0.134324	+	0.990938i	$0.542886\pi$
$864$		0			0
$865$	11.4582	+	39.2729i	0.389590	+	1.33532i
$866$		0			0
$867$	−0.377372	−	1.50278i	−0.0128162	−	0.0510371i
$868$		0			0
$869$	0.267026	−	0.233804i	0.00905825	−	0.00793124i
$870$		0			0
$871$	−6.43249	−	7.07190i	−0.217957	−	0.239622i
$872$		0			0
$873$	−19.8875	−	10.6604i	−0.673091	−	0.360799i
$874$		0			0
$875$	−1.61523	+	17.0186i	−0.0546046	+	0.575332i
$876$		0			0
$877$	−27.2602	+	15.9688i	−0.920513	+	0.539229i	−0.887797	−	0.460235i	$-0.847765\pi$
$877$	−27.2602	+	15.9688i	−0.920513	+	0.539229i	−0.0327159	+	0.999465i	$0.510416\pi$
$878$		0			0
$879$	10.7389	−	2.48165i	0.362214	−	0.0837040i
$880$		0			0
$881$	−1.46197	+	25.7223i	−0.0492551	+	0.866606i	0.874833	+	0.484425i	$0.160971\pi$
$881$	−1.46197	+	25.7223i	−0.0492551	+	0.866606i	−0.924088	+	0.382180i	$0.875173\pi$
$882$		0			0
$883$	5.43902	+	14.4684i	0.183038	+	0.486902i	0.995350	−	0.0963204i	$-0.0307073\pi$
$883$	5.43902	+	14.4684i	0.183038	+	0.486902i	−0.812313	+	0.583222i	$0.801792\pi$
$884$		0			0
$885$	3.23946	−	6.96617i	0.108893	−	0.234165i
$886$		0			0
$887$	−6.90418	+	8.85229i	−0.231820	+	0.297231i	−0.890307	−	0.455361i	$-0.849510\pi$
$887$	−6.90418	+	8.85229i	−0.231820	+	0.297231i	0.658487	+	0.752592i	$0.271197\pi$
$888$		0			0
$889$	−1.24035	−	1.08602i	−0.0415998	−	0.0364241i
$890$		0			0
$891$	−0.137222	+	0.0209360i	−0.00459712	+	0.000701381i
$892$		0			0
$893$	−31.0950	+	60.7429i	−1.04056	+	2.03269i
$894$		0			0
$895$	−0.394560	−	20.8458i	−0.0131887	−	0.696799i
$896$		0			0
$897$	5.61260	+	0.425693i	0.187399	+	0.0142135i
$898$		0			0
$899$	−0.175234	+	9.25816i	−0.00584438	+	0.308777i
$900$		0			0
$901$	−13.5512	+	4.80356i	−0.451457	+	0.160030i
$902$		0			0
$903$	6.64875	−	3.24628i	0.221257	−	0.108029i
$904$		0			0
$905$	−18.3498	−	3.51482i	−0.609969	−	0.116836i
$906$		0			0
$907$	6.86137	+	13.4034i	0.227828	+	0.445054i	0.975796	−	0.218681i	$-0.0701754\pi$
$907$	6.86137	+	13.4034i	0.227828	+	0.445054i	−0.747968	+	0.663734i	$0.768971\pi$
$908$		0			0
$909$	1.91888	−	0.0726654i	0.0636453	−	0.00241016i
$910$		0			0
$911$	−28.4647	−	26.8928i	−0.943076	−	0.890997i	0.0511076	−	0.998693i	$-0.483725\pi$
$911$	−28.4647	−	26.8928i	−0.943076	−	0.890997i	−0.994184	+	0.107696i	$0.965653\pi$
$912$		0			0
$913$	−0.0434433	+	0.0710438i	−0.00143776	+	0.00235121i
$914$		0			0
$915$	0.140236	−	0.373043i	0.00463605	−	0.0123324i
$916$		0			0
$917$	−1.60794	+	0.183373i	−0.0530989	+	0.00605551i
$918$		0			0
$919$	−19.4948	+	5.28958i	−0.643074	+	0.174487i	−0.568441	−	0.822724i	$-0.692453\pi$
$919$	−19.4948	+	5.28958i	−0.643074	+	0.174487i	−0.0746330	+	0.997211i	$0.523779\pi$
$920$		0			0
$921$	11.2954	+	7.82097i	0.372197	+	0.257710i
$922$		0			0
$923$	−7.20259	−	0.272752i	−0.237076	−	0.00897774i
$924$		0			0
$925$	1.29101	+	9.68812i	0.0424482	+	0.318543i
$926$		0			0
$927$	1.05893	−	3.17703i	0.0347800	−	0.104347i
$928$		0			0
$929$	4.20096	−	7.49304i	0.137829	−	0.245839i	−0.794646	−	0.607073i	$-0.792343\pi$
$929$	4.20096	−	7.49304i	0.137829	−	0.245839i	0.932475	+	0.361235i	$0.117645\pi$
$930$		0			0
$931$	−2.78936	−	29.3896i	−0.0914175	−	0.963205i
$932$		0			0
$933$	0.0251585	+	0.442645i	0.000823654	+	0.0144915i
$934$		0			0
$935$	−0.0970301	+	0.115143i	−0.00317322	+	0.00376559i
$936$		0			0
$937$	1.51357	−	0.965366i	0.0494460	−	0.0315371i	−0.512789	−	0.858515i	$-0.671388\pi$
$937$	1.51357	−	0.965366i	0.0494460	−	0.0315371i	0.562235	+	0.826978i	$0.309942\pi$
$938$		0			0
$939$	13.2424	−	9.93095i	0.432151	−	0.324084i
$940$		0			0
$941$	−23.0879	−	29.6024i	−0.752644	−	0.965012i	0.247348	−	0.968927i	$-0.420441\pi$
$941$	−23.0879	−	29.6024i	−0.752644	−	0.965012i	−0.999992	+	0.00391437i	$0.998754\pi$
$942$		0			0
$943$	−0.786077	−	1.18249i	−0.0255982	−	0.0385073i
$944$		0			0
$945$	−7.50434	−	2.98433i	−0.244116	−	0.0970803i
$946$		0			0
$947$	3.57007	+	0.407138i	0.116012	+	0.0132302i	0.171120	−	0.985250i	$-0.445261\pi$
$947$	3.57007	+	0.407138i	0.116012	+	0.0132302i	−0.0551086	+	0.998480i	$0.517550\pi$
$948$		0			0
$949$	1.79601	+	1.34689i	0.0583008	+	0.0437218i
$950$		0			0
$951$	0.549804	−	0.604456i	0.0178286	−	0.0196008i
$952$		0			0
$953$	0.864001	+	2.59219i	0.0279877	+	0.0839691i	0.961754	−	0.273913i	$-0.0883181\pi$
$953$	0.864001	+	2.59219i	0.0279877	+	0.0839691i	−0.933767	+	0.357882i	$0.883499\pi$
$954$		0			0
$955$	−9.26373	+	36.8903i	−0.299767	+	1.19374i
$956$		0			0
$957$	−0.00478699	−	0.0114039i	−0.000154741	−	0.000368636i
$958$		0			0
$959$	−8.01973	−	2.84278i	−0.258970	−	0.0917982i
$960$		0			0
$961$	42.9055	−	17.0627i	1.38405	−	0.550409i
$962$		0			0
$963$	−8.41308	+	28.8357i	−0.271108	+	0.929219i
$964$		0			0
$965$	10.5722	−	3.30286i	0.340330	−	0.106323i
$966$		0			0
$967$	21.0666	−	1.59782i	0.677457	−	0.0513824i	0.267597	−	0.963531i	$-0.413770\pi$
$967$	21.0666	−	1.59782i	0.677457	−	0.0513824i	0.409860	+	0.912149i	$0.365578\pi$
$968$		0			0
$969$	−9.87186	+	6.83529i	−0.317130	+	0.219581i
$970$		0			0
$971$	−15.9738	+	3.05970i	−0.512624	+	0.0981905i	−0.437918	−	0.899015i	$-0.644284\pi$
$971$	−15.9738	+	3.05970i	−0.512624	+	0.0981905i	−0.0747062	+	0.997206i	$0.523802\pi$
$972$		0			0
$973$	−1.51242	+	7.15978i	−0.0484860	+	0.229532i
$974$		0			0
$975$	−1.47417	−	0.719771i	−0.0472114	−	0.0230511i
$976$		0			0
$977$	10.1214	−	58.8477i	0.323814	−	1.88271i	−0.129851	−	0.991533i	$-0.541450\pi$
$977$	10.1214	−	58.8477i	0.323814	−	1.88271i	0.453665	−	0.891172i	$-0.350116\pi$
$978$		0			0
$979$	0.0522830	+	0.247507i	0.00167097	+	0.00791037i
$980$		0			0
$981$	−37.4496	+	38.1651i	−1.19567	+	1.21852i
$982$		0			0
$983$	−45.3641	−	10.4832i	−1.44689	−	0.334361i	−0.572628	−	0.819816i	$-0.694076\pi$
$983$	−45.3641	−	10.4832i	−1.44689	−	0.334361i	−0.874262	+	0.485454i	$0.838654\pi$
$984$		0			0
$985$	−4.54567	+	6.83804i	−0.144837	+	0.217878i
$986$		0			0
$987$	4.62771	+	7.56780i	0.147302	+	0.240886i
$988$		0			0
$989$	6.86173	−	51.4923i	0.218190	−	1.63736i
$990$		0			0
$991$	13.2754	−	12.5423i	0.421707	−	0.398419i	−0.446370	−	0.894848i	$-0.647283\pi$
$991$	13.2754	−	12.5423i	0.421707	−	0.398419i	0.868077	+	0.496429i	$0.165356\pi$
$992$		0			0
$993$	10.7494	+	3.35823i	0.341122	+	0.106570i
$994$		0			0
$995$	8.13710	−	11.2894i	0.257963	−	0.357897i
$996$		0			0
$997$	−21.5917	−	25.6224i	−0.683815	−	0.811468i	0.306268	−	0.951945i	$-0.400919\pi$
$997$	−21.5917	−	25.6224i	−0.683815	−	0.811468i	−0.990084	+	0.140477i	$0.955136\pi$
$998$		0			0
$999$	−19.1713	−	2.92496i	−0.606553	−	0.0925415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.21.6	✓	1148
167.8	even	83	inner	668.2.e.a.509.6	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.21.6	✓	1148	1.1	even	1	trivial
668.2.e.a.509.6	yes	1148	167.8	even	83	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537235 - 0.0819657i) q^{3} +(-1.19475 - 1.41779i) q^{5} +(0.821536 - 1.13980i) q^{7} +(-2.58161 - 0.806524i) q^{9} +O(q^{10})\)	\(q+(-0.537235 - 0.0819657i) q^{3} +(-1.19475 - 1.41779i) q^{5} +(0.821536 - 1.13980i) q^{7} +(-2.58161 - 0.806524i) q^{9} +(-0.0156941 + 0.0148274i) q^{11} +(-0.255201 + 1.91510i) q^{13} +(0.525653 + 0.859613i) q^{15} +(-2.08237 + 3.13251i) q^{17} +(-5.72303 - 1.32253i) q^{19} +(-0.534782 + 0.545000i) q^{21} +(1.10797 + 5.24513i) q^{23} +(0.264842 - 1.53983i) q^{25} +(2.78587 + 1.36021i) q^{27} +(0.217852 - 1.03131i) q^{29} +(-8.62801 + 1.65265i) q^{31} +(0.00964676 - 0.00667943i) q^{33} +(-2.59752 + 0.197011i) q^{35} +(-5.97084 + 1.86536i) q^{37} +(0.294075 - 1.00794i) q^{39} +(-0.246121 + 0.0978776i) q^{41} +(-9.13328 - 3.23751i) q^{43} +(1.94091 + 4.62377i) q^{45} +(2.82948 - 11.2676i) q^{47} +(1.58924 + 4.76806i) q^{49} +(1.37548 - 1.51221i) q^{51} +(3.05790 + 2.29323i) q^{53} +(0.0397728 + 0.00453577i) q^{55} +(2.96621 + 1.17960i) q^{57} +(-4.22102 - 6.34967i) q^{59} +(-0.243249 - 0.311885i) q^{61} +(-3.04016 + 2.27992i) q^{63} +(3.02010 - 1.92625i) q^{65} +(-3.18850 + 3.78372i) q^{67} +(-0.165320 - 2.90868i) q^{69} +(0.352493 + 3.71398i) q^{71} +(0.568238 - 1.01354i) q^{73} +(-0.268496 + 0.805544i) q^{75} +(0.00400696 + 0.0300694i) q^{77} +(-16.4267 - 0.622057i) q^{79} +(5.28578 + 3.65988i) q^{81} +(3.72234 - 1.00999i) q^{83} +(6.92915 - 0.790215i) q^{85} +(-0.201569 + 0.536198i) q^{87} +(6.11244 - 9.99581i) q^{89} +(1.97316 + 1.86420i) q^{91} +(4.77073 - 0.180661i) q^{93} +(4.96254 + 9.69413i) q^{95} +(8.19386 + 1.56949i) q^{97} +(0.0524748 - 0.0256210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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