LMFDB - Embedded newform 450.2.l.d.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.2
Root			$-0.917186 + 1.66637i$ of defining polynomial
Character	$\chi$	$=$	450.19
Dual form			450.2.l.d.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.420099 + 2.19625i) q^{5} -0.407162i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.420099 + 2.19625i) q^{5} -0.407162i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.07822 - 1.95894i) q^{10} +(0.930123 + 2.86263i) q^{11} +(-0.172519 - 0.0560547i) q^{13} +(0.125820 + 0.387234i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-1.82018 + 2.50527i) q^{17} +(1.15643 + 0.840198i) q^{19} +(1.63079 + 1.52988i) q^{20} +(-1.76920 - 2.43509i) q^{22} +(-1.06192 + 0.345037i) q^{23} +(-4.64703 + 1.84529i) q^{25} +0.181397 q^{26} +(-0.239324 - 0.329401i) q^{28} +(0.127844 - 0.0928839i) q^{29} +(6.96457 + 5.06006i) q^{31} +1.00000i q^{32} +(0.956927 - 2.94512i) q^{34} +(0.894229 - 0.171048i) q^{35} +(-4.19300 - 1.36239i) q^{37} +(-1.35947 - 0.441718i) q^{38} +(-2.02373 - 0.951057i) q^{40} +(-2.54673 + 7.83802i) q^{41} +10.6902i q^{43} +(2.43509 + 1.76920i) q^{44} +(0.903319 - 0.656300i) q^{46} +(1.62460 + 2.23607i) q^{47} +6.83422 q^{49} +(3.84937 - 3.19098i) q^{50} +(-0.172519 + 0.0560547i) q^{52} +(-4.93299 - 6.78968i) q^{53} +(-5.89630 + 3.24537i) q^{55} +(0.329401 + 0.239324i) q^{56} +(-0.0928839 + 0.127844i) q^{58} +(2.21780 - 6.82570i) q^{59} +(2.09288 + 6.44123i) q^{61} +(-8.18735 - 2.66023i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(0.0506353 - 0.402443i) q^{65} +(2.32046 - 3.19384i) q^{67} +3.09668i q^{68} +(-0.797605 + 0.439008i) q^{70} +(-2.49317 + 1.81140i) q^{71} +(-8.18781 + 2.66038i) q^{73} +4.40878 q^{74} +1.42943 q^{76} +(1.16555 - 0.378710i) q^{77} +(5.59113 - 4.06219i) q^{79} +(2.21858 + 0.279141i) q^{80} -8.24138i q^{82} +(8.70043 - 11.9751i) q^{83} +(-6.26685 - 2.94512i) q^{85} +(-3.30345 - 10.1670i) q^{86} +(-2.86263 - 0.930123i) q^{88} +(-4.52785 - 13.9353i) q^{89} +(-0.0228233 + 0.0702429i) q^{91} +(-0.656300 + 0.903319i) q^{92} +(-2.23607 - 1.62460i) q^{94} +(-1.35947 + 2.89278i) q^{95} +(-9.59110 - 13.2010i) q^{97} +(-6.49973 + 2.11189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.420099	+	2.19625i	0.187874	+	0.982193i
$5$	0.420099	+	2.19625i	0.187874	+	0.982193i
$6$		0			0
$7$		−	0.407162i		−	0.153893i	−0.997035	−	0.0769463i	$-0.975483\pi$
$7$		−	0.407162i		−	0.153893i	0.997035	−	0.0769463i	$-0.0245170\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$		0			0
$10$	−1.07822	−	1.95894i	−0.340962	−	0.619471i
$11$	0.930123	+	2.86263i	0.280443	+	0.863114i	0.987728	+	0.156185i	$0.0499198\pi$
$11$	0.930123	+	2.86263i	0.280443	+	0.863114i	−0.707285	+	0.706928i	$0.750080\pi$
$12$		0			0
$13$	−0.172519	−	0.0560547i	−0.0478480	−	0.0155468i	0.284995	−	0.958529i	$-0.408008\pi$
$13$	−0.172519	−	0.0560547i	−0.0478480	−	0.0155468i	−0.332843	+	0.942982i	$0.608008\pi$
$14$	0.125820	+	0.387234i	0.0336268	+	0.103493i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.82018	+	2.50527i	−0.441459	+	0.607617i	−0.970536	−	0.240958i	$-0.922539\pi$
$17$	−1.82018	+	2.50527i	−0.441459	+	0.607617i	0.529076	+	0.848574i	$0.322539\pi$
$18$		0			0
$19$	1.15643	+	0.840198i	0.265304	+	0.192755i	0.712482	−	0.701690i	$-0.247571\pi$
$19$	1.15643	+	0.840198i	0.265304	+	0.192755i	−0.447178	+	0.894445i	$0.647571\pi$
$20$	1.63079	+	1.52988i	0.364656	+	0.342091i
$21$		0			0
$22$	−1.76920	−	2.43509i	−0.377195	−	0.519164i
$23$	−1.06192	+	0.345037i	−0.221425	+	0.0719452i	−0.417628	−	0.908618i	$-0.637139\pi$
$23$	−1.06192	+	0.345037i	−0.221425	+	0.0719452i	0.196204	+	0.980563i	$0.437139\pi$
$24$		0			0
$25$	−4.64703	+	1.84529i	−0.929407	+	0.369057i
$26$	0.181397			0.0355748
$27$		0			0
$28$	−0.239324	−	0.329401i	−0.0452279	−	0.0622509i
$29$	0.127844	−	0.0928839i	0.0237400	−	0.0172481i	−0.575852	−	0.817554i	$-0.695330\pi$
$29$	0.127844	−	0.0928839i	0.0237400	−	0.0172481i	0.599592	+	0.800306i	$0.295330\pi$
$30$		0			0
$31$	6.96457	+	5.06006i	1.25087	+	0.908813i	0.998272	−	0.0587568i	$-0.0187137\pi$
$31$	6.96457	+	5.06006i	1.25087	+	0.908813i	0.252602	+	0.967570i	$0.418714\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.956927	−	2.94512i	0.164112	−	0.505084i
$35$	0.894229	−	0.171048i	0.151152	−	0.0289124i
$36$		0			0
$37$	−4.19300	−	1.36239i	−0.689324	−	0.223975i	−0.0566511	−	0.998394i	$-0.518042\pi$
$37$	−4.19300	−	1.36239i	−0.689324	−	0.223975i	−0.632673	+	0.774419i	$0.718042\pi$
$38$	−1.35947	−	0.441718i	−0.220535	−	0.0716562i
$39$		0			0
$40$	−2.02373	−	0.951057i	−0.319980	−	0.150375i
$41$	−2.54673	+	7.83802i	−0.397732	+	1.22409i	0.529082	+	0.848571i	$0.322536\pi$
$41$	−2.54673	+	7.83802i	−0.397732	+	1.22409i	−0.926814	+	0.375522i	$0.877464\pi$
$42$		0			0
$43$			10.6902i			1.63024i	0.579294	+	0.815119i	$0.303328\pi$
$43$			10.6902i			1.63024i	−0.579294	+	0.815119i	$0.696672\pi$
$44$	2.43509	+	1.76920i	0.367104	+	0.266717i
$45$		0			0
$46$	0.903319	−	0.656300i	0.133187	−	0.0967661i
$47$	1.62460	+	2.23607i	0.236972	+	0.326164i	0.910895	−	0.412637i	$-0.135392\pi$
$47$	1.62460	+	2.23607i	0.236972	+	0.326164i	−0.673923	+	0.738801i	$0.735392\pi$
$48$		0			0
$49$	6.83422			0.976317
$50$	3.84937	−	3.19098i	0.544383	−	0.451273i
$51$		0			0
$52$	−0.172519	+	0.0560547i	−0.0239240	+	0.00777339i
$53$	−4.93299	−	6.78968i	−0.677598	−	0.932634i	0.322304	−	0.946636i	$-0.395543\pi$
$53$	−4.93299	−	6.78968i	−0.677598	−	0.932634i	−0.999902	+	0.0140025i	$0.995543\pi$
$54$		0			0
$55$	−5.89630	+	3.24537i	−0.795057	+	0.437606i
$56$	0.329401	+	0.239324i	0.0440180	+	0.0319810i
$57$		0			0
$58$	−0.0928839	+	0.127844i	−0.0121962	+	0.0167867i
$59$	2.21780	−	6.82570i	0.288733	−	0.888630i	−0.696521	−	0.717536i	$-0.745270\pi$
$59$	2.21780	−	6.82570i	0.288733	−	0.888630i	0.985255	−	0.171094i	$-0.0547301\pi$
$60$		0			0
$61$	2.09288	+	6.44123i	0.267966	+	0.824716i	0.990995	+	0.133898i	$0.0427494\pi$
$61$	2.09288	+	6.44123i	0.267966	+	0.824716i	−0.723029	+	0.690818i	$0.757251\pi$
$62$	−8.18735	−	2.66023i	−1.03979	−	0.337850i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.0506353	−	0.402443i	0.00628053	−	0.0499169i
$66$		0			0
$67$	2.32046	−	3.19384i	0.283489	−	0.390190i	−0.643396	−	0.765533i	$-0.722475\pi$
$67$	2.32046	−	3.19384i	0.283489	−	0.390190i	0.926886	+	0.375344i	$0.122475\pi$
$68$			3.09668i			0.375528i
$69$		0			0
$70$	−0.797605	+	0.439008i	−0.0953321	+	0.0524715i
$71$	−2.49317	+	1.81140i	−0.295885	+	0.214973i	−0.725816	−	0.687888i	$-0.758538\pi$
$71$	−2.49317	+	1.81140i	−0.295885	+	0.214973i	0.429931	+	0.902862i	$0.358538\pi$
$72$		0			0
$73$	−8.18781	+	2.66038i	−0.958311	+	0.311374i	−0.746088	−	0.665847i	$-0.768070\pi$
$73$	−8.18781	+	2.66038i	−0.958311	+	0.311374i	−0.212223	+	0.977221i	$0.568070\pi$
$74$	4.40878			0.512510
$75$		0			0
$76$	1.42943			0.163967
$77$	1.16555	−	0.378710i	0.132827	−	0.0431581i
$78$		0			0
$79$	5.59113	−	4.06219i	0.629051	−	0.457033i	−0.227020	−	0.973890i	$-0.572898\pi$
$79$	5.59113	−	4.06219i	0.629051	−	0.457033i	0.856071	+	0.516857i	$0.172898\pi$
$80$	2.21858	+	0.279141i	0.248044	+	0.0312089i
$81$		0			0
$82$		−	8.24138i		−	0.910108i
$83$	8.70043	−	11.9751i	0.954996	−	1.31444i	0.00572357	−	0.999984i	$-0.498178\pi$
$83$	8.70043	−	11.9751i	0.954996	−	1.31444i	0.949272	−	0.314455i	$-0.101822\pi$
$84$		0			0
$85$	−6.26685	−	2.94512i	−0.679736	−	0.319443i
$86$	−3.30345	−	10.1670i	−0.356220	−	1.09633i
$87$		0			0
$88$	−2.86263	−	0.930123i	−0.305157	−	0.0991515i
$89$	−4.52785	−	13.9353i	−0.479951	−	1.47714i	−0.839162	−	0.543882i	$-0.816954\pi$
$89$	−4.52785	−	13.9353i	−0.479951	−	1.47714i	0.359211	−	0.933256i	$-0.383046\pi$
$90$		0			0
$91$	−0.0228233	+	0.0702429i	−0.00239253	+	0.00736346i
$92$	−0.656300	+	0.903319i	−0.0684240	+	0.0941775i
$93$		0			0
$94$	−2.23607	−	1.62460i	−0.230633	−	0.167565i
$95$	−1.35947	+	2.89278i	−0.139479	+	0.296793i
$96$		0			0
$97$	−9.59110	−	13.2010i	−0.973829	−	1.34036i	−0.940089	−	0.340929i	$-0.889258\pi$
$97$	−9.59110	−	13.2010i	−0.973829	−	1.34036i	−0.0337396	−	0.999431i	$-0.510742\pi$
$98$	−6.49973	+	2.11189i	−0.656572	+	0.213333i
$99$		0			0
$100$	−2.67490	+	4.22433i	−0.267490	+	0.422433i
$101$	15.6979			1.56200			0.781000	−	0.624530i	$-0.214710\pi$
$101$	15.6979			1.56200			0.781000	+	0.624530i	$0.214710\pi$
$102$		0			0
$103$	10.2205	+	14.0673i	1.00706	+	1.38610i	0.920893	+	0.389816i	$0.127461\pi$
$103$	10.2205	+	14.0673i	1.00706	+	1.38610i	0.0861654	+	0.996281i	$0.472539\pi$
$104$	0.146753	−	0.106622i	0.0143903	−	0.0104552i
$105$		0			0
$106$	6.78968	+	4.93299i	0.659472	+	0.479134i
$107$		−	7.64086i		−	0.738670i	−0.929296	−	0.369335i	$-0.879586\pi$
$107$		−	7.64086i		−	0.738670i	0.929296	−	0.369335i	$-0.120414\pi$
$108$		0			0
$109$	5.67399	−	17.4627i	0.543470	−	1.67263i	−0.181132	−	0.983459i	$-0.557976\pi$
$109$	5.67399	−	17.4627i	0.543470	−	1.67263i	0.724601	−	0.689168i	$-0.242024\pi$
$110$	4.60484	−	4.90859i	0.439054	−	0.468015i
$111$		0			0
$112$	−0.387234	−	0.125820i	−0.0365901	−	0.0118889i
$113$	4.99871	+	1.62418i	0.470239	+	0.152790i	0.534544	−	0.845140i	$-0.320483\pi$
$113$	4.99871	+	1.62418i	0.470239	+	0.152790i	−0.0643056	+	0.997930i	$0.520483\pi$
$114$		0			0
$115$	−1.20390	−	2.18728i	−0.112264	−	0.203965i
$116$	0.0488319	−	0.150289i	0.00453393	−	0.0139540i
$117$		0			0
$118$			7.17696i			0.660693i
$119$	1.02005	+	0.741109i	0.0935077	+	0.0679373i
$120$		0			0
$121$	1.56969	−	1.14045i	0.142699	−	0.103677i
$122$	−3.98090	−	5.47924i	−0.360414	−	0.496067i
$123$		0			0
$124$	8.60869			0.773083
$125$	−6.00492	−	9.43085i	−0.537097	−	0.843521i
$126$		0			0
$127$	8.29206	−	2.69425i	0.735801	−	0.239076i	0.0829406	−	0.996554i	$-0.473569\pi$
$127$	8.29206	−	2.69425i	0.735801	−	0.239076i	0.652860	+	0.757478i	$0.273569\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$		0			0
$130$	0.0762046	+	0.398393i	0.00668358	+	0.0349414i
$131$	−9.89185	−	7.18685i	−0.864255	−	0.627918i	0.0647841	−	0.997899i	$-0.479364\pi$
$131$	−9.89185	−	7.18685i	−0.864255	−	0.627918i	−0.929039	+	0.369981i	$0.879364\pi$
$132$		0			0
$133$	0.342096	−	0.470855i	0.0296635	−	0.0408283i
$134$	−1.21994	+	3.75458i	−0.105387	+	0.324347i
$135$		0			0
$136$	−0.956927	−	2.94512i	−0.0820558	−	0.252542i
$137$	10.4728	+	3.40281i	0.894749	+	0.290722i	0.720068	−	0.693903i	$-0.244111\pi$
$137$	10.4728	+	3.40281i	0.894749	+	0.290722i	0.174681	+	0.984625i	$0.444111\pi$
$138$		0			0
$139$	0.640857	+	1.97236i	0.0543568	+	0.167293i	0.974549	−	0.224173i	$-0.0719681\pi$
$139$	0.640857	+	1.97236i	0.0543568	+	0.167293i	−0.920193	+	0.391466i	$0.871968\pi$
$140$	0.622907	−	0.663995i	0.0526452	−	0.0561179i
$141$		0			0
$142$	1.81140	−	2.49317i	0.152009	−	0.209222i
$143$		−	0.545994i		−	0.0456583i
$144$		0			0
$145$	0.257703	+	0.241756i	0.0214011	+	0.0200768i
$146$	6.96497	−	5.06035i	0.576425	−	0.418797i
$147$		0			0
$148$	−4.19300	+	1.36239i	−0.344662	+	0.111987i
$149$	−6.96358			−0.570479			−0.285239	−	0.958456i	$-0.592073\pi$
$149$	−6.96358			−0.570479			−0.285239	+	0.958456i	$0.592073\pi$
$150$		0			0
$151$	13.2401			1.07746			0.538732	−	0.842477i	$-0.318904\pi$
$151$	13.2401			1.07746			0.538732	+	0.842477i	$0.318904\pi$
$152$	−1.35947	+	0.441718i	−0.110267	+	0.0358281i
$153$		0			0
$154$	−0.991477	+	0.720350i	−0.0798955	+	0.0580475i
$155$	−8.18735	+	17.4217i	−0.657624	+	1.39934i
$156$		0			0
$157$		−	6.96025i		−	0.555488i	−0.960655	−	0.277744i	$-0.910413\pi$
$157$		−	6.96025i		−	0.555488i	0.960655	−	0.277744i	$-0.0895867\pi$
$158$	−4.06219	+	5.59113i	−0.323171	+	0.444807i
$159$		0			0
$160$	−2.19625	+	0.420099i	−0.173629	+	0.0332117i
$161$	0.140486	+	0.432371i	0.0110718	+	0.0340756i
$162$		0			0
$163$	−16.0703	−	5.22155i	−1.25872	−	0.408984i	−0.397683	−	0.917523i	$-0.630186\pi$
$163$	−16.0703	−	5.22155i	−1.25872	−	0.408984i	−0.861039	+	0.508539i	$0.830186\pi$
$164$	2.54673	+	7.83802i	0.198866	+	0.612046i
$165$		0			0
$166$	−4.57408	+	14.0776i	−0.355018	+	1.09263i
$167$	1.32498	−	1.82368i	0.102530	−	0.141121i	−0.754669	−	0.656106i	$-0.772202\pi$
$167$	1.32498	−	1.82368i	0.102530	−	0.141121i	0.857199	+	0.514985i	$0.172202\pi$
$168$		0			0
$169$	−10.4906	−	7.62187i	−0.806969	−	0.586297i
$170$	6.87022	+	0.864410i	0.526922	+	0.0662972i
$171$		0			0
$172$	6.28353	+	8.64854i	0.479115	+	0.659445i
$173$	−1.05017	+	0.341220i	−0.0798427	+	0.0259425i	−0.348666	−	0.937247i	$-0.613365\pi$
$173$	−1.05017	+	0.341220i	−0.0798427	+	0.0259425i	0.268823	+	0.963190i	$0.413365\pi$
$174$		0			0
$175$	0.751329	+	1.89209i	0.0567952	+	0.143029i
$176$	3.00994			0.226883
$177$		0			0
$178$	8.61248	+	11.8541i	0.645533	+	0.888500i
$179$	−11.0774	+	8.04823i	−0.827967	+	0.601553i	−0.918983	−	0.394296i	$-0.870988\pi$
$179$	−11.0774	+	8.04823i	−0.827967	+	0.601553i	0.0910165	+	0.995849i	$0.470988\pi$
$180$		0			0
$181$	−8.04367	−	5.84407i	−0.597881	−	0.434386i	0.247245	−	0.968953i	$-0.420475\pi$
$181$	−8.04367	−	5.84407i	−0.597881	−	0.434386i	−0.845126	+	0.534567i	$0.820475\pi$
$182$		−	0.0738578i		−	0.00547470i
$183$		0			0
$184$	0.345037	−	1.06192i	0.0254365	−	0.0782854i
$185$	1.23067	−	9.78121i	0.0904806	−	0.719129i
$186$		0			0
$187$	−8.86464	−	2.88030i	−0.648246	−	0.210628i
$188$	2.62866	+	0.854102i	0.191714	+	0.0622918i
$189$		0			0
$190$	0.399012	−	3.17130i	0.0289474	−	0.230070i
$191$	−8.04149	+	24.7492i	−0.581862	+	1.79079i	0.0296620	+	0.999560i	$0.490557\pi$
$191$	−8.04149	+	24.7492i	−0.581862	+	1.79079i	−0.611524	+	0.791226i	$0.709443\pi$
$192$		0			0
$193$			3.52671i			0.253858i	0.991912	+	0.126929i	$0.0405121\pi$
$193$			3.52671i			0.253858i	−0.991912	+	0.126929i	$0.959488\pi$
$194$	13.2010	+	9.59110i	0.947778	+	0.688601i
$195$		0			0
$196$	5.52900	−	4.01705i	0.394929	−	0.286932i
$197$	8.56510	+	11.7889i	0.610238	+	0.839921i	0.996597	−	0.0824276i	$-0.0262673\pi$
$197$	8.56510	+	11.7889i	0.610238	+	0.839921i	−0.386359	+	0.922349i	$0.626267\pi$
$198$		0			0
$199$	14.2079			1.00717			0.503586	−	0.863945i	$-0.332014\pi$
$199$	14.2079			1.00717			0.503586	+	0.863945i	$0.332014\pi$
$200$	1.23859	−	4.84416i	0.0875816	−	0.342534i
$201$		0			0
$202$	−14.9296	+	4.85092i	−1.05044	+	0.341310i
$203$	−0.0378187	−	0.0520530i	−0.00265436	−	0.00365341i
$204$		0			0
$205$	−18.2841	−	2.30051i	−1.27702	−	0.160674i
$206$	−14.0673	−	10.2205i	−0.980118	−	0.712098i
$207$		0			0
$208$	−0.106622	+	0.146753i	−0.00739293	+	0.0101755i
$209$	−1.32955	+	4.09192i	−0.0919666	+	0.283044i
$210$		0			0
$211$	3.71472	+	11.4327i	0.255732	+	0.787061i	0.993685	+	0.112209i	$0.0357925\pi$
$211$	3.71472	+	11.4327i	0.255732	+	0.787061i	−0.737953	+	0.674852i	$0.764207\pi$
$212$	−7.98174	−	2.59343i	−0.548188	−	0.178117i
$213$		0			0
$214$	2.36115	+	7.26689i	0.161405	+	0.496754i
$215$	−23.4783	+	4.49094i	−1.60121	+	0.306279i
$216$		0			0
$217$	2.06026	−	2.83571i	0.139860	−	0.192500i
$218$			18.3614i			1.24359i
$219$		0			0
$220$	−2.86263	+	6.09132i	−0.192998	+	0.410676i
$221$	0.454447	−	0.330175i	0.0305694	−	0.0222100i
$222$		0			0
$223$	2.81341	−	0.914132i	0.188400	−	0.0612148i	−0.213298	−	0.976987i	$-0.568420\pi$
$223$	2.81341	−	0.914132i	0.188400	−	0.0612148i	0.401697	+	0.915772i	$0.368420\pi$
$224$	0.407162			0.0272046
$225$		0			0
$226$	−5.25595			−0.349621
$227$	20.7044	−	6.72726i	1.37420	−	0.446504i	0.473440	−	0.880826i	$-0.343012\pi$
$227$	20.7044	−	6.72726i	1.37420	−	0.446504i	0.900758	+	0.434322i	$0.143012\pi$
$228$		0			0
$229$	−10.6063	+	7.70596i	−0.700887	+	0.509224i	−0.880221	−	0.474564i	$-0.842606\pi$
$229$	−10.6063	+	7.70596i	−0.700887	+	0.509224i	0.179334	+	0.983788i	$0.442606\pi$
$230$	1.82088	+	1.70820i	0.120065	+	0.112636i
$231$		0			0
$232$			0.158023i			0.0103747i
$233$	3.17852	−	4.37486i	0.208232	−	0.286607i	−0.692108	−	0.721794i	$-0.743318\pi$
$233$	3.17852	−	4.37486i	0.208232	−	0.286607i	0.900340	+	0.435187i	$0.143318\pi$
$234$		0			0
$235$	−4.22847	+	4.50740i	−0.275835	+	0.294030i
$236$	−2.21780	−	6.82570i	−0.144367	−	0.444315i
$237$		0			0
$238$	−1.19914	−	0.389624i	−0.0777286	−	0.0252556i
$239$	2.97796	+	9.16522i	0.192628	+	0.592849i	0.999996	+	0.00280018i	$0.000891326\pi$
$239$	2.97796	+	9.16522i	0.192628	+	0.592849i	−0.807368	+	0.590048i	$0.799109\pi$
$240$		0			0
$241$	2.09756	−	6.45562i	0.135116	−	0.415843i	−0.860492	−	0.509463i	$-0.829844\pi$
$241$	2.09756	−	6.45562i	0.135116	−	0.415843i	0.995608	+	0.0936203i	$0.0298440\pi$
$242$	−1.14045	+	1.56969i	−0.0733108	+	0.100904i
$243$		0			0
$244$	5.47924	+	3.98090i	0.350772	+	0.254851i
$245$	2.87105	+	15.0097i	0.183425	+	0.958932i
$246$		0			0
$247$	−0.152409	−	0.209773i	−0.00969756	−	0.0133476i
$248$	−8.18735	+	2.66023i	−0.519897	+	0.168925i
$249$		0			0
$250$	8.62531	+	7.11365i	0.545513	+	0.449906i
$251$	14.8097			0.934783			0.467391	−	0.884051i	$-0.345194\pi$
$251$	14.8097			0.934783			0.467391	+	0.884051i	$0.345194\pi$
$252$		0			0
$253$	−1.97542	−	2.71894i	−0.124194	−	0.170938i
$254$	−7.05364	+	5.12477i	−0.442585	+	0.321557i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			13.8365i			0.863097i	0.902090	+	0.431548i	$0.142033\pi$
$257$			13.8365i			0.863097i	−0.902090	+	0.431548i	$0.857967\pi$
$258$		0			0
$259$	−0.554711	+	1.70723i	−0.0344681	+	0.106082i
$260$	−0.195585	−	0.355345i	−0.0121297	−	0.0220376i
$261$		0			0
$262$	11.6286	+	3.77835i	0.718415	+	0.233427i
$263$	28.4672	+	9.24954i	1.75536	+	0.570351i	0.996703	−	0.0811378i	$-0.0258554\pi$
$263$	28.4672	+	9.24954i	1.75536	+	0.570351i	0.758658	+	0.651489i	$0.225855\pi$
$264$		0			0
$265$	12.8395	−	13.6864i	0.788723	−	0.840750i
$266$	−0.179851	+	0.553523i	−0.0110274	+	0.0339387i
$267$		0			0
$268$		−	3.94780i		−	0.241151i
$269$	−13.3561	−	9.70379i	−0.814337	−	0.591650i	0.100748	−	0.994912i	$-0.467876\pi$
$269$	−13.3561	−	9.70379i	−0.814337	−	0.591650i	−0.915085	+	0.403262i	$0.867876\pi$
$270$		0			0
$271$	−0.291377	+	0.211697i	−0.0176999	+	0.0128597i	−0.596600	−	0.802539i	$-0.703482\pi$
$271$	−0.291377	+	0.211697i	−0.0176999	+	0.0128597i	0.578900	+	0.815398i	$0.303482\pi$
$272$	1.82018	+	2.50527i	0.110365	+	0.151904i
$273$		0			0
$274$	−11.0117			−0.665243
$275$	−9.60467	−	11.5864i	−0.579184	−	0.698685i
$276$		0			0
$277$	3.51696	−	1.14273i	0.211314	−	0.0686600i	−0.201447	−	0.979499i	$-0.564564\pi$
$277$	3.51696	−	1.14273i	0.211314	−	0.0686600i	0.412761	+	0.910839i	$0.364564\pi$
$278$	−1.21898	−	1.67779i	−0.0731097	−	0.100627i
$279$		0			0
$280$	−0.387234	+	0.823986i	−0.0231416	+	0.0492426i
$281$	−0.615107	−	0.446901i	−0.0366942	−	0.0266599i	0.569287	−	0.822139i	$-0.307219\pi$
$281$	−0.615107	−	0.446901i	−0.0366942	−	0.0266599i	−0.605981	+	0.795479i	$0.707219\pi$
$282$		0			0
$283$	15.5916	−	21.4601i	0.926827	−	1.27567i	−0.0342577	−	0.999413i	$-0.510907\pi$
$283$	15.5916	−	21.4601i	0.926827	−	1.27567i	0.961084	−	0.276255i	$-0.0890933\pi$
$284$	−0.952307	+	2.93090i	−0.0565090	+	0.173917i
$285$		0			0
$286$	0.168721	+	0.519271i	0.00997670	+	0.0307051i
$287$	3.19134	+	1.03693i	0.188379	+	0.0612080i
$288$		0			0
$289$	2.28999	+	7.04787i	0.134705	+	0.414580i
$290$	−0.319797	−	0.150289i	−0.0187791	−	0.00882529i
$291$		0			0
$292$	−5.06035	+	6.96497i	−0.296134	+	0.407594i
$293$			24.0344i			1.40411i	0.712124	+	0.702054i	$0.247733\pi$
$293$			24.0344i			1.40411i	−0.712124	+	0.702054i	$0.752267\pi$
$294$		0			0
$295$	15.9226	+	2.00338i	0.927052	+	0.116641i
$296$	3.56677	−	2.59141i	0.207315	−	0.150623i
$297$		0			0
$298$	6.62276	−	2.15187i	0.383646	−	0.124654i
$299$	0.202541			0.0117132
$300$		0			0
$301$	4.35263			0.250882
$302$	−12.5921	+	4.09141i	−0.724593	+	0.235434i
$303$		0			0
$304$	1.15643	−	0.840198i	0.0663260	−	0.0481887i
$305$	−13.2673	+	7.30245i	−0.759686	+	0.418137i
$306$		0			0
$307$			24.6543i			1.40710i	0.710647	+	0.703549i	$0.248402\pi$
$307$			24.6543i			1.40710i	−0.710647	+	0.703549i	$0.751598\pi$
$308$	0.720350	−	0.991477i	0.0410458	−	0.0564946i
$309$		0			0
$310$	2.40304	−	19.0990i	0.136483	−	1.08475i
$311$	−9.20357	−	28.3257i	−0.521887	−	1.60620i	−0.770392	−	0.637571i	$-0.779939\pi$
$311$	−9.20357	−	28.3257i	−0.521887	−	1.60620i	0.248505	−	0.968631i	$-0.420061\pi$
$312$		0			0
$313$	−11.8228	−	3.84145i	−0.668262	−	0.217131i	−0.0448127	−	0.998995i	$-0.514269\pi$
$313$	−11.8228	−	3.84145i	−0.668262	−	0.217131i	−0.623449	+	0.781864i	$0.714269\pi$
$314$	2.15083	+	6.61959i	0.121379	+	0.373565i
$315$		0			0
$316$	2.13562	−	6.57277i	0.120138	−	0.369747i
$317$	3.70333	−	5.09719i	0.207999	−	0.286287i	−0.692253	−	0.721655i	$-0.743382\pi$
$317$	3.70333	−	5.09719i	0.207999	−	0.286287i	0.900253	+	0.435368i	$0.143382\pi$
$318$		0			0
$319$	0.384802	+	0.279575i	0.0215448	+	0.0156532i
$320$	1.95894	−	1.07822i	0.109508	−	0.0602741i
$321$		0			0
$322$	−0.267220	−	0.367797i	−0.0148916	−	0.0204965i
$323$	−4.20984	+	1.36786i	−0.234242	+	0.0761098i
$324$		0			0
$325$	0.905136	−	0.0578580i	0.0502079	−	0.00320938i
$326$	16.8973			0.935855
$327$		0			0
$328$	−4.84416	−	6.66742i	−0.267474	−	0.368146i
$329$	0.910441	−	0.661474i	0.0501942	−	0.0364682i
$330$		0			0
$331$	−16.9917	−	12.3452i	−0.933950	−	0.678555i	0.0130065	−	0.999915i	$-0.495860\pi$
$331$	−16.9917	−	12.3452i	−0.933950	−	0.678555i	−0.946957	+	0.321361i	$0.895860\pi$
$332$		−	14.8020i		−	0.812368i
$333$		0			0
$334$	−0.696585	+	2.14387i	−0.0381155	+	0.117307i
$335$	7.98930	+	3.75458i	0.436502	+	0.205135i
$336$		0			0
$337$	−6.61679	−	2.14993i	−0.360440	−	0.117114i	0.123198	−	0.992382i	$-0.460685\pi$
$337$	−6.61679	−	2.14993i	−0.360440	−	0.117114i	−0.483638	+	0.875268i	$0.660685\pi$
$338$	12.3324	+	4.00705i	0.670796	+	0.217955i
$339$		0			0
$340$	−6.80109	+	1.30091i	−0.368841	+	0.0705519i
$341$	−8.00714	+	24.6434i	−0.433611	+	1.33452i
$342$		0			0
$343$		−	5.63276i		−	0.304141i
$344$	−8.64854	−	6.28353i	−0.466298	−	0.338785i
$345$		0			0
$346$	0.893325	−	0.649039i	0.0480255	−	0.0348925i
$347$	−4.82104	−	6.63559i	−0.258807	−	0.356217i	0.659764	−	0.751473i	$-0.270656\pi$
$347$	−4.82104	−	6.63559i	−0.258807	−	0.356217i	−0.918571	+	0.395255i	$0.870656\pi$
$348$		0			0
$349$	−7.36978			−0.394495			−0.197248	−	0.980354i	$-0.563200\pi$
$349$	−7.36978			−0.394495			−0.197248	+	0.980354i	$0.563200\pi$
$350$	−1.29925	−	1.56731i	−0.0694476	−	0.0837765i
$351$		0			0
$352$	−2.86263	+	0.930123i	−0.152578	+	0.0495757i
$353$	−17.4021	−	23.9520i	−0.926222	−	1.27483i	−0.961315	−	0.275451i	$-0.911173\pi$
$353$	−17.4021	−	23.9520i	−0.926222	−	1.27483i	0.0350935	−	0.999384i	$-0.488827\pi$
$354$		0			0
$355$	−5.02566	−	4.71467i	−0.266734	−	0.250229i
$356$	−11.8541	−	8.61248i	−0.628264	−	0.456461i
$357$		0			0
$358$	8.04823	−	11.0774i	0.425362	−	0.585461i
$359$	0.615389	−	1.89397i	0.0324790	−	0.0999600i	−0.933503	−	0.358570i	$-0.883264\pi$
$359$	0.615389	−	1.89397i	0.0324790	−	0.0999600i	0.965982	+	0.258610i	$0.0832644\pi$
$360$		0			0
$361$	−5.23992	−	16.1268i	−0.275785	−	0.848779i
$362$	9.45590	+	3.07241i	0.496991	+	0.161482i
$363$		0			0
$364$	0.0228233	+	0.0702429i	0.00119627	+	0.00368173i
$365$	−9.28256	−	16.8649i	−0.485871	−	0.882747i
$366$		0			0
$367$	−3.06409	+	4.21736i	−0.159944	+	0.220144i	−0.881466	−	0.472247i	$-0.843443\pi$
$367$	−3.06409	+	4.21736i	−0.159944	+	0.220144i	0.721522	+	0.692392i	$0.243443\pi$
$368$			1.11656i			0.0582049i
$369$		0			0
$370$	1.85212	+	9.68278i	0.0962873	+	0.503384i
$371$	−2.76450	+	2.00852i	−0.143525	+	0.104277i
$372$		0			0
$373$	20.7985	−	6.75786i	1.07691	−	0.349909i	0.283733	−	0.958903i	$-0.408427\pi$
$373$	20.7985	−	6.75786i	1.07691	−	0.349909i	0.793174	+	0.608995i	$0.208427\pi$
$374$	9.32083			0.481969
$375$		0			0
$376$	−2.76393			−0.142539
$377$	−0.0272620	+	0.00885796i	−0.00140406	+	0.000456208i
$378$		0			0
$379$	−11.0703	+	8.04303i	−0.568642	+	0.413143i	−0.834612	−	0.550839i	$-0.814308\pi$
$379$	−11.0703	+	8.04303i	−0.568642	+	0.413143i	0.265969	+	0.963981i	$0.414308\pi$
$380$	0.600502	+	3.13939i	0.0308051	+	0.161047i
$381$		0			0
$382$		−	26.0228i		−	1.33144i
$383$	18.0171	−	24.7984i	0.920629	−	1.26714i	−0.0427747	−	0.999085i	$-0.513620\pi$
$383$	18.0171	−	24.7984i	0.920629	−	1.26714i	0.963404	−	0.268053i	$-0.0863802\pi$
$384$		0			0
$385$	1.32139	+	2.40075i	0.0673443	+	0.122353i
$386$	−1.08981	−	3.35410i	−0.0554701	−	0.170719i
$387$		0			0
$388$	−15.5187	−	5.04234i	−0.787844	−	0.255986i
$389$	−5.07712	−	15.6258i	−0.257420	−	0.792258i	−0.993343	−	0.115193i	$-0.963251\pi$
$389$	−5.07712	−	15.6258i	−0.257420	−	0.792258i	0.735923	−	0.677065i	$-0.236749\pi$
$390$		0			0
$391$	1.06847	−	3.28841i	0.0540348	−	0.166302i
$392$	−4.01705	+	5.52900i	−0.202892	+	0.279257i
$393$		0			0
$394$	−11.7889	−	8.56510i	−0.593914	−	0.431504i
$395$	11.2704	+	10.5730i	0.567077	+	0.531985i
$396$		0			0
$397$	20.6819	+	28.4662i	1.03800	+	1.42868i	0.898771	+	0.438417i	$0.144461\pi$
$397$	20.6819	+	28.4662i	1.03800	+	1.42868i	0.139224	+	0.990261i	$0.455539\pi$
$398$	−13.5125	+	4.39049i	−0.677322	+	0.220075i
$399$		0			0
$400$	0.318958	+	4.98982i	0.0159479	+	0.249491i
$401$	34.4884			1.72227			0.861134	−	0.508378i	$-0.169755\pi$
$401$	34.4884			1.72227			0.861134	+	0.508378i	$0.169755\pi$
$402$		0			0
$403$	−0.917878	−	1.26335i	−0.0457228	−	0.0629320i
$404$	12.6999	−	9.22700i	0.631843	−	0.459061i
$405$		0			0
$406$	0.0520530	+	0.0378187i	0.00258335	+	0.00187691i
$407$		−	13.2702i		−	0.657777i
$408$		0			0
$409$	−5.92852	+	18.2461i	−0.293147	+	0.902212i	0.690691	+	0.723150i	$0.257306\pi$
$409$	−5.92852	+	18.2461i	−0.293147	+	0.902212i	−0.983838	+	0.179062i	$0.942694\pi$
$410$	18.1001	−	3.46219i	0.893902	−	0.170986i
$411$		0			0
$412$	16.5372	+	5.37325i	0.814727	+	0.264721i
$413$	−2.77916	−	0.903004i	−0.136754	−	0.0444339i
$414$		0			0
$415$	29.9554	+	14.0776i	1.47045	+	0.691041i
$416$	0.0560547	−	0.172519i	0.00274831	−	0.00845842i
$417$		0			0
$418$		−	4.30250i		−	0.210442i
$419$	8.89016	+	6.45908i	0.434313	+	0.315547i	0.783371	−	0.621554i	$-0.213498\pi$
$419$	8.89016	+	6.45908i	0.434313	+	0.315547i	−0.349058	+	0.937101i	$0.613498\pi$
$420$		0			0
$421$	−23.5263	+	17.0929i	−1.14660	+	0.833056i	−0.988026	−	0.154290i	$-0.950691\pi$
$421$	−23.5263	+	17.0929i	−1.14660	+	0.833056i	−0.158578	+	0.987346i	$0.550691\pi$
$422$	−7.06581	−	9.72525i	−0.343958	−	0.473418i
$423$		0			0
$424$	8.39250			0.407576
$425$	3.83552	−	15.0008i	0.186050	−	0.727647i
$426$		0			0
$427$	2.62262	−	0.852142i	0.126918	−	0.0412380i
$428$	−4.49118	−	6.18158i	−0.217090	−	0.298798i
$429$		0			0
$430$	20.9414	−	11.5263i	1.00989	−	0.555849i
$431$	−23.4783	−	17.0580i	−1.13091	−	0.821655i	−0.145084	−	0.989419i	$-0.546345\pi$
$431$	−23.4783	−	17.0580i	−1.13091	−	0.821655i	−0.985827	+	0.167764i	$0.946345\pi$
$432$		0			0
$433$	4.71547	−	6.49029i	0.226611	−	0.311903i	−0.680538	−	0.732713i	$-0.738254\pi$
$433$	4.71547	−	6.49029i	0.226611	−	0.311903i	0.907149	+	0.420809i	$0.138254\pi$
$434$	−1.08314	+	3.33357i	−0.0519926	+	0.160017i
$435$		0			0
$436$	−5.67399	−	17.4627i	−0.271735	−	0.836314i
$437$	−1.51793	−	0.493206i	−0.0726126	−	0.0235933i
$438$		0			0
$439$	4.85101	+	14.9299i	0.231526	+	0.712563i	0.997563	+	0.0697675i	$0.0222257\pi$
$439$	4.85101	+	14.9299i	0.231526	+	0.712563i	−0.766037	+	0.642796i	$0.777774\pi$
$440$	0.840198	−	6.67779i	0.0400549	−	0.318351i
$441$		0			0
$442$	−0.330175	+	0.454447i	−0.0157048	+	0.0216159i
$443$		−	18.1541i		−	0.862528i	−0.902226	−	0.431264i	$-0.858068\pi$
$443$		−	18.1541i		−	0.862528i	0.902226	−	0.431264i	$-0.141932\pi$
$444$		0			0
$445$	28.7032	−	15.7985i	1.36066	−	0.748921i
$446$	−2.39323	+	1.73878i	−0.113323	+	0.0823337i
$447$		0			0
$448$	−0.387234	+	0.125820i	−0.0182951	+	0.00594443i
$449$	−12.2292			−0.577133			−0.288567	−	0.957460i	$-0.593179\pi$
$449$	−12.2292			−0.577133			−0.288567	+	0.957460i	$0.593179\pi$
$450$		0			0
$451$	−24.8061			−1.16807
$452$	4.99871	−	1.62418i	0.235119	−	0.0763949i
$453$		0			0
$454$	−17.6122	+	12.7960i	−0.826582	+	0.600547i
$455$	−0.163859	−	0.0206167i	−0.00768183	−	0.000966527i
$456$		0			0
$457$			40.1425i			1.87779i	0.344209	+	0.938893i	$0.388147\pi$
$457$			40.1425i			1.87779i	−0.344209	+	0.938893i	$0.611853\pi$
$458$	7.70596	−	10.6063i	0.360076	−	0.495602i
$459$		0			0
$460$	−2.25963	−	1.06192i	−0.105356	−	0.0495120i
$461$	0.106910	+	0.329037i	0.00497932	+	0.0153248i	0.953515	−	0.301345i	$-0.0974354\pi$
$461$	0.106910	+	0.329037i	0.00497932	+	0.0153248i	−0.948536	+	0.316669i	$0.897435\pi$
$462$		0			0
$463$	10.4401	+	3.39218i	0.485191	+	0.157648i	0.541390	−	0.840771i	$-0.317898\pi$
$463$	10.4401	+	3.39218i	0.485191	+	0.157648i	−0.0561991	+	0.998420i	$0.517898\pi$
$464$	−0.0488319	−	0.150289i	−0.00226697	−	0.00697700i
$465$		0			0
$466$	−1.67105	+	5.14296i	−0.0774098	+	0.238243i
$467$	11.7878	−	16.2245i	0.545472	−	0.750778i	−0.443917	−	0.896068i	$-0.646411\pi$
$467$	11.7878	−	16.2245i	0.545472	−	0.750778i	0.989389	+	0.145290i	$0.0464114\pi$
$468$		0			0
$469$	−1.30041	−	0.944802i	−0.0600473	−	0.0436269i
$470$	2.62866	−	5.59346i	0.121251	−	0.258007i
$471$		0			0
$472$	4.21851	+	5.80628i	0.194173	+	0.267256i
$473$	−30.6020	+	9.94319i	−1.40708	+	0.457188i
$474$		0			0
$475$	−6.92439	−	1.77048i	−0.317713	−	0.0812351i
$476$	1.26085			0.0577909
$477$		0			0
$478$	−5.66441	−	7.79640i	−0.259084	−	0.356599i
$479$	19.5813	−	14.2267i	0.894693	−	0.650033i	−0.0424044	−	0.999101i	$-0.513502\pi$
$479$	19.5813	−	14.2267i	0.894693	−	0.650033i	0.937097	+	0.349068i	$0.113502\pi$
$480$		0			0
$481$	0.647001	+	0.470074i	0.0295007	+	0.0214335i
$482$			6.78784i			0.309178i
$483$		0			0
$484$	0.599570	−	1.84529i	0.0272532	−	0.0838766i
$485$	24.9635	−	26.6102i	1.13354	−	1.20831i
$486$		0			0
$487$	15.1890	+	4.93519i	0.688278	+	0.223635i	0.632216	−	0.774792i	$-0.282146\pi$
$487$	15.1890	+	4.93519i	0.688278	+	0.223635i	0.0560619	+	0.998427i	$0.482146\pi$
$488$	−6.44123	−	2.09288i	−0.291581	−	0.0947404i
$489$		0			0
$490$	−7.36877	−	13.3878i	−0.332887	−	0.604801i
$491$	−9.86671	+	30.3666i	−0.445278	+	1.37043i	0.436900	+	0.899510i	$0.356076\pi$
$491$	−9.86671	+	30.3666i	−0.445278	+	1.37043i	−0.882178	+	0.470916i	$0.843924\pi$
$492$		0			0
$493$			0.489348i			0.0220391i
$494$	0.209773	+	0.152409i	0.00943814	+	0.00685721i
$495$		0			0
$496$	6.96457	−	5.06006i	0.312719	−	0.227203i
$497$	0.737531	+	1.01512i	0.0330828	+	0.0455345i
$498$		0			0
$499$	−32.2566			−1.44400			−0.722001	−	0.691892i	$-0.756778\pi$
$499$	−32.2566			−1.44400			−0.722001	+	0.691892i	$0.756778\pi$
$500$	−10.4014	−	4.10011i	−0.465165	−	0.183363i
$501$		0			0
$502$	−14.0849	+	4.57646i	−0.628640	+	0.204258i
$503$	−2.12383	−	2.92320i	−0.0946969	−	0.130339i	0.759039	−	0.651045i	$-0.225669\pi$
$503$	−2.12383	−	2.92320i	−0.0946969	−	0.130339i	−0.853736	+	0.520706i	$0.825669\pi$
$504$		0			0
$505$	6.59468	+	34.4766i	0.293459	+	1.53419i
$506$	2.71894	+	1.97542i	0.120872	+	0.0878183i
$507$		0			0
$508$	5.12477	−	7.05364i	0.227375	−	0.312955i
$509$	5.20479	−	16.0187i	0.230698	−	0.710016i	−0.766965	−	0.641689i	$-0.778234\pi$
$509$	5.20479	−	16.0187i	0.230698	−	0.710016i	0.997663	−	0.0683268i	$-0.0217661\pi$
$510$		0			0
$511$	1.08321	+	3.33376i	0.0479182	+	0.147477i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$		0			0
$514$	−4.27571	−	13.1593i	−0.188594	−	0.580431i
$515$	−26.6018	+	28.3565i	−1.17221	+	1.24954i
$516$		0			0
$517$	−4.88995	+	6.73044i	−0.215060	+	0.296004i
$518$		−	1.79508i		−	0.0788715i
$519$		0			0
$520$	0.295820	+	0.277515i	0.0129726	+	0.0121698i
$521$	23.8458	−	17.3250i	1.04471	−	0.759023i	0.0735066	−	0.997295i	$-0.476581\pi$
$521$	23.8458	−	17.3250i	1.04471	−	0.759023i	0.971198	+	0.238272i	$0.0765810\pi$
$522$		0			0
$523$	−29.7235	+	9.65775i	−1.29972	+	0.422304i	−0.875483	−	0.483248i	$-0.839457\pi$
$523$	−29.7235	+	9.65775i	−1.29972	+	0.422304i	−0.424235	+	0.905552i	$0.639457\pi$
$524$	−12.2270			−0.534139
$525$		0			0
$526$	−29.9322			−1.30510
$527$	−25.3536	+	8.23789i	−1.10442	+	0.358848i
$528$		0			0
$529$	−17.5988	+	12.7863i	−0.765164	+	0.555924i
$530$	−7.98174	+	16.9842i	−0.346705	+	0.737745i
$531$		0			0
$532$		−	0.582009i		−	0.0252333i
$533$	0.878715	−	1.20945i	0.0380614	−	0.0523870i
$534$		0			0
$535$	16.7812	−	3.20992i	0.725516	−	0.138777i
$536$	1.21994	+	3.75458i	0.0526933	+	0.162173i
$537$		0			0
$538$	15.7011	+	5.10158i	0.676921	+	0.219945i
$539$	6.35667	+	19.5638i	0.273801	+	0.842673i
$540$		0			0
$541$	8.04024	−	24.7453i	0.345677	−	1.06388i	−0.615544	−	0.788103i	$-0.711064\pi$
$541$	8.04024	−	24.7453i	0.345677	−	1.06388i	0.961220	−	0.275781i	$-0.0889365\pi$
$542$	0.211697	−	0.291377i	0.00909319	−	0.0125157i
$543$		0			0
$544$	−2.50527	−	1.82018i	−0.107412	−	0.0780397i
$545$	40.7362	+	5.12542i	1.74495	+	0.219549i
$546$		0			0
$547$	−10.5699	−	14.5482i	−0.451936	−	0.622037i	0.520876	−	0.853632i	$-0.325605\pi$
$547$	−10.5699	−	14.5482i	−0.451936	−	0.622037i	−0.972812	+	0.231595i	$0.925605\pi$
$548$	10.4728	−	3.40281i	0.447375	−	0.145361i
$549$		0			0
$550$	12.7150	+	8.05129i	0.542168	+	0.343308i
$551$	0.225884			0.00962296
$552$		0			0
$553$	−1.65397	−	2.27649i	−0.0703339	−	0.0968064i
$554$	−2.99171	+	2.17360i	−0.127105	+	0.0923475i
$555$		0			0
$556$	1.67779	+	1.21898i	0.0711540	+	0.0516964i
$557$			37.9619i			1.60850i	0.594292	+	0.804250i	$0.297432\pi$
$557$			37.9619i			1.60850i	−0.594292	+	0.804250i	$0.702568\pi$
$558$		0			0
$559$	0.599235	−	1.84426i	0.0253449	−	0.0780037i
$560$	0.113655	−	0.903319i	0.00480282	−	0.0381722i
$561$		0			0
$562$	0.723101	+	0.234950i	0.0305022	+	0.00991076i
$563$	15.3020	+	4.97191i	0.644901	+	0.209541i	0.613164	−	0.789955i	$-0.289896\pi$
$563$	15.3020	+	4.97191i	0.644901	+	0.209541i	0.0317364	+	0.999496i	$0.489896\pi$
$564$		0			0
$565$	−1.46715	+	11.6607i	−0.0617235	+	0.490570i
$566$	−8.19701	+	25.2278i	−0.344546	+	1.06040i
$567$		0			0
$568$		−	3.08173i		−	0.129307i
$569$	−20.4202	−	14.8362i	−0.856060	−	0.621964i	0.0707501	−	0.997494i	$-0.477461\pi$
$569$	−20.4202	−	14.8362i	−0.856060	−	0.621964i	−0.926810	+	0.375530i	$0.877461\pi$
$570$		0			0
$571$	−17.9321	+	13.0284i	−0.750435	+	0.545223i	−0.895962	−	0.444132i	$-0.853512\pi$
$571$	−17.9321	+	13.0284i	−0.750435	+	0.545223i	0.145527	+	0.989354i	$0.453512\pi$
$572$	−0.320927	−	0.441718i	−0.0134186	−	0.0184692i
$573$		0			0
$574$	−3.35557			−0.140059
$575$	4.29806	−	3.56294i	0.179242	−	0.148585i
$576$		0			0
$577$	36.7915	−	11.9543i	1.53165	−	0.497663i	0.582591	−	0.812766i	$-0.302039\pi$
$577$	36.7915	−	11.9543i	1.53165	−	0.497663i	0.949058	+	0.315103i	$0.102039\pi$
$578$	−4.35582	−	5.99527i	−0.181178	−	0.249371i
$579$		0			0
$580$	0.350587	+	0.0441108i	0.0145573	+	0.00183160i
$581$	−4.87580	−	3.54248i	−0.202282	−	0.146967i
$582$		0			0
$583$	14.8480	−	20.4365i	0.614942	−	0.846395i
$584$	2.66038	−	8.18781i	0.110087	−	0.338814i
$585$		0			0
$586$	−7.42705	−	22.8581i	−0.306809	−	0.944260i
$587$	−26.2756	−	8.53747i	−1.08451	−	0.352379i	−0.288388	−	0.957514i	$-0.593119\pi$
$587$	−26.2756	−	8.53747i	−1.08451	−	0.352379i	−0.796123	+	0.605134i	$0.793119\pi$
$588$		0			0
$589$	3.80261	+	11.7032i	0.156684	+	0.482224i
$590$	−15.7624	+	3.01503i	−0.648928	+	0.124127i
$591$		0			0
$592$	−2.59141	+	3.56677i	−0.106506	+	0.146594i
$593$			30.9606i			1.27140i	0.771936	+	0.635701i	$0.219289\pi$
$593$			30.9606i			1.27140i	−0.771936	+	0.635701i	$0.780711\pi$
$594$		0			0
$595$	−1.19914	+	2.55162i	−0.0491599	+	0.104606i
$596$	−5.63366	+	4.09309i	−0.230764	+	0.167660i
$597$		0			0
$598$	−0.192628	+	0.0625886i	−0.00787714	+	0.00255944i
$599$	29.2581			1.19545			0.597727	−	0.801700i	$-0.296071\pi$
$599$	29.2581			1.19545			0.597727	+	0.801700i	$0.296071\pi$
$600$		0			0
$601$	−1.13536			−0.0463124			−0.0231562	−	0.999732i	$-0.507372\pi$
$601$	−1.13536			−0.0463124			−0.0231562	+	0.999732i	$0.507372\pi$
$602$	−4.13960	+	1.34504i	−0.168717	+	0.0548196i
$603$		0			0
$604$	10.7115	−	7.78233i	0.435843	−	0.316659i
$605$	3.16414	+	2.96834i	0.128641	+	0.120680i
$606$		0			0
$607$			20.7485i			0.842157i	0.907024	+	0.421079i	$0.138348\pi$
$607$			20.7485i			0.842157i	−0.907024	+	0.421079i	$0.861652\pi$
$608$	−0.840198	+	1.15643i	−0.0340745	+	0.0468996i
$609$		0			0
$610$	10.3614	−	11.0449i	0.419521	−	0.447194i
$611$	−0.154931	−	0.476830i	−0.00626785	−	0.0192905i
$612$		0			0
$613$	−2.25065	−	0.731279i	−0.0909027	−	0.0295361i	0.263213	−	0.964738i	$-0.415218\pi$
$613$	−2.25065	−	0.731279i	−0.0909027	−	0.0295361i	−0.354115	+	0.935202i	$0.615218\pi$
$614$	−7.61861	−	23.4477i	−0.307462	−	0.946271i
$615$		0			0
$616$	−0.378710	+	1.16555i	−0.0152587	+	0.0469614i
$617$	−17.0025	+	23.4019i	−0.684493	+	0.942124i	−0.999977	−	0.00680691i	$-0.997833\pi$
$617$	−17.0025	+	23.4019i	−0.684493	+	0.942124i	0.315484	+	0.948931i	$0.397833\pi$
$618$		0			0
$619$	−12.5443	−	9.11400i	−0.504200	−	0.366323i	0.306419	−	0.951897i	$-0.400869\pi$
$619$	−12.5443	−	9.11400i	−0.504200	−	0.366323i	−0.810619	+	0.585574i	$0.800869\pi$
$620$	3.61650	+	18.9068i	0.145242	+	0.759317i
$621$		0			0
$622$	17.5062	+	24.0953i	0.701936	+	0.966132i
$623$	−5.67391	+	1.84357i	−0.227321	+	0.0738609i
$624$		0			0
$625$	18.1898	−	17.1502i	0.727594	−	0.686008i
$626$	12.4312			0.496850
$627$		0			0
$628$	−4.09113	−	5.63096i	−0.163254	−	0.224700i
$629$	11.0452	−	8.02478i	0.440400	−	0.319969i
$630$		0			0
$631$	−24.2478	−	17.6171i	−0.965289	−	0.701324i	−0.0109162	−	0.999940i	$-0.503475\pi$
$631$	−24.2478	−	17.6171i	−0.965289	−	0.701324i	−0.954373	+	0.298617i	$0.903475\pi$
$632$			6.91102i			0.274906i
$633$		0			0
$634$	−1.94695	+	5.99211i	−0.0773234	+	0.237977i
$635$	9.40074	+	17.0796i	0.373057	+	0.677782i
$636$		0			0
$637$	−1.17903	−	0.383090i	−0.0467149	−	0.0151786i
$638$	−0.452362	−	0.146981i	−0.0179092	−	0.00581905i
$639$		0			0
$640$	−1.52988	+	1.63079i	−0.0604737	+	0.0644627i
$641$	−12.4269	+	38.2460i	−0.490833	+	1.51063i	0.332519	+	0.943096i	$0.392101\pi$
$641$	−12.4269	+	38.2460i	−0.490833	+	1.51063i	−0.823352	+	0.567531i	$0.807899\pi$
$642$		0			0
$643$		−	26.3050i		−	1.03737i	−0.854967	−	0.518683i	$-0.826422\pi$
$643$		−	26.3050i		−	1.03737i	0.854967	−	0.518683i	$-0.173578\pi$
$644$	0.367797	+	0.267220i	0.0144932	+	0.0105299i
$645$		0			0
$646$	3.58111	−	2.60183i	0.140897	−	0.102367i
$647$	−10.8479	−	14.9309i	−0.426476	−	0.586994i	0.540664	−	0.841239i	$-0.318173\pi$
$647$	−10.8479	−	14.9309i	−0.426476	−	0.586994i	−0.967140	+	0.254245i	$0.918173\pi$
$648$		0			0
$649$	21.6022			0.847962
$650$	−0.842957	+	0.334729i	−0.0330635	+	0.0131291i
$651$		0			0
$652$	−16.0703	+	5.22155i	−0.629361	+	0.204492i
$653$	−10.1418	−	13.9590i	−0.396880	−	0.546259i	0.563077	−	0.826404i	$-0.309617\pi$
$653$	−10.1418	−	13.9590i	−0.396880	−	0.546259i	−0.959958	+	0.280145i	$0.909617\pi$
$654$		0			0
$655$	11.6286	−	24.7442i	0.454366	−	0.966835i
$656$	6.66742	+	4.84416i	0.260319	+	0.189133i
$657$		0			0
$658$	−0.661474	+	0.910441i	−0.0257869	+	0.0354927i
$659$	−10.1818	+	31.3364i	−0.396627	+	1.22069i	0.531061	+	0.847334i	$0.321794\pi$
$659$	−10.1818	+	31.3364i	−0.396627	+	1.22069i	−0.927687	+	0.373358i	$0.878206\pi$
$660$		0			0
$661$	7.09419	+	21.8337i	0.275932	+	0.849232i	0.988971	+	0.148108i	$0.0473182\pi$
$661$	7.09419	+	21.8337i	0.275932	+	0.849232i	−0.713039	+	0.701124i	$0.752682\pi$
$662$	19.9750	+	6.49027i	0.776350	+	0.252251i
$663$		0			0
$664$	4.57408	+	14.0776i	0.177509	+	0.546316i
$665$	1.17783	+	0.553523i	0.0456743	+	0.0214647i
$666$		0			0
$667$	−0.103711	+	0.142746i	−0.00401570	+	0.00552713i
$668$		−	2.25420i		−	0.0872175i
$669$		0			0
$670$	−8.75850	−	1.10199i	−0.338371	−	0.0425737i
$671$	−16.4922	+	11.9823i	−0.636674	+	0.462571i
$672$		0			0
$673$	20.6476	−	6.70880i	0.795906	−	0.258605i	0.117289	−	0.993098i	$-0.462580\pi$
$673$	20.6476	−	6.70880i	0.795906	−	0.258605i	0.678617	+	0.734492i	$0.262580\pi$
$674$	6.95731			0.267985
$675$		0			0
$676$	−12.9671			−0.498734
$677$	−18.9782	+	6.16639i	−0.729392	+	0.236994i	−0.650090	−	0.759857i	$-0.725269\pi$
$677$	−18.9782	+	6.16639i	−0.729392	+	0.236994i	−0.0793015	+	0.996851i	$0.525269\pi$
$678$		0			0
$679$	−5.37495	+	3.90513i	−0.206271	+	0.149865i
$680$	6.06621	−	3.33889i	0.232629	−	0.128041i
$681$		0			0
$682$		−	25.9116i		−	0.992208i
$683$	4.78322	−	6.58354i	0.183025	−	0.251912i	−0.707639	−	0.706574i	$-0.750240\pi$
$683$	4.78322	−	6.58354i	0.183025	−	0.251912i	0.890664	+	0.454662i	$0.150240\pi$
$684$		0			0
$685$	−3.07382	+	24.4303i	−0.117445	+	0.933436i
$686$	1.74062	+	5.35708i	0.0664572	+	0.204534i
$687$		0			0
$688$	10.1670	+	3.30345i	0.387612	+	0.125943i
$689$	0.470439	+	1.44786i	0.0179223	+	0.0551592i
$690$		0			0
$691$	6.26649	−	19.2863i	0.238388	−	0.733684i	−0.758265	−	0.651946i	$-0.773953\pi$
$691$	6.26649	−	19.2863i	0.238388	−	0.733684i	0.996654	−	0.0817380i	$-0.0260471\pi$
$692$	−0.649039	+	0.893325i	−0.0246728	+	0.0339591i
$693$		0			0
$694$	6.63559	+	4.82104i	0.251884	+	0.183004i
$695$	−4.06256	+	2.23607i	−0.154102	+	0.0848189i
$696$		0			0
$697$	−15.0008	−	20.6469i	−0.568197	−	0.782056i
$698$	7.00908	−	2.27739i	0.265298	−	0.0862004i
$699$		0			0
$700$	1.71998	+	1.08912i	0.0650092	+	0.0411647i
$701$	43.7615			1.65285			0.826424	−	0.563049i	$-0.190372\pi$
$701$	43.7615			1.65285			0.826424	+	0.563049i	$0.190372\pi$
$702$		0			0
$703$	−3.70424	−	5.09846i	−0.139708	−	0.192292i
$704$	2.43509	−	1.76920i	0.0917761	−	0.0666792i
$705$		0			0
$706$	23.9520	+	17.4021i	0.901444	+	0.654938i
$707$		−	6.39159i		−	0.240380i
$708$		0			0
$709$	−2.80109	+	8.62086i	−0.105197	+	0.323763i	−0.989777	−	0.142626i	$-0.954445\pi$
$709$	−2.80109	+	8.62086i	−0.105197	+	0.323763i	0.884580	+	0.466389i	$0.154445\pi$
$710$	6.23660	+	2.93090i	0.234055	+	0.109995i
$711$		0			0
$712$	13.9353	+	4.52785i	0.522247	+	0.169688i
$713$	−9.14169	−	2.97032i	−0.342359	−	0.111239i
$714$		0			0
$715$	1.19914	−	0.229371i	0.0448453	−	0.00857800i
$716$	−4.23121	+	13.0223i	−0.158128	+	0.486667i
$717$		0			0
$718$			1.99144i			0.0743199i
$719$	13.4116	+	9.74411i	0.500169	+	0.363394i	0.809082	−	0.587696i	$-0.199965\pi$
$719$	13.4116	+	9.74411i	0.500169	+	0.363394i	−0.308912	+	0.951090i	$0.599965\pi$
$720$		0			0
$721$	5.72768	−	4.16140i	0.213310	−	0.154979i
$722$	9.96692	+	13.7183i	0.370930	+	0.510542i
$723$		0			0
$724$	−9.94252			−0.369511
$725$	−0.422697	+	0.667543i	−0.0156986	+	0.0247919i
$726$		0			0
$727$	27.0109	−	8.77637i	1.00178	−	0.325497i	0.238202	−	0.971216i	$-0.423442\pi$
$727$	27.0109	−	8.77637i	1.00178	−	0.325497i	0.763576	+	0.645718i	$0.223442\pi$
$728$	−0.0434125	−	0.0597522i	−0.00160897	−	0.00221456i
$729$		0			0
$730$	14.0398	+	13.1710i	0.519635	+	0.487480i
$731$	−26.7818	−	19.4581i	−0.990560	−	0.719684i
$732$		0			0
$733$	−3.03619	+	4.17896i	−0.112144	+	0.154354i	−0.861400	−	0.507928i	$-0.830412\pi$
$733$	−3.03619	+	4.17896i	−0.112144	+	0.154354i	0.749255	+	0.662281i	$0.230412\pi$
$734$	1.61089	−	4.95780i	0.0594590	−	0.182996i
$735$		0			0
$736$	−0.345037	−	1.06192i	−0.0127182	−	0.0391427i
$737$	11.3011	+	3.67194i	0.416281	+	0.135258i
$738$		0			0
$739$	−10.2940	−	31.6817i	−0.378671	−	1.16543i	−0.940968	−	0.338494i	$-0.890082\pi$
$739$	−10.2940	−	31.6817i	−0.378671	−	1.16543i	0.562297	−	0.826935i	$-0.309918\pi$
$740$	−4.75362	−	8.63653i	−0.174746	−	0.317485i
$741$		0			0
$742$	2.00852	−	2.76450i	0.0737352	−	0.101488i
$743$			41.0018i			1.50421i	0.659043	+	0.752105i	$0.270962\pi$
$743$			41.0018i			1.50421i	−0.659043	+	0.752105i	$0.729038\pi$
$744$		0			0
$745$	−2.92539	−	15.2938i	−0.107178	−	0.560320i
$746$	−17.6923	+	12.8542i	−0.647761	+	0.470626i
$747$		0			0
$748$	−8.86464	+	2.88030i	−0.324123	+	0.105314i
$749$	−3.11106			−0.113676
$750$		0			0
$751$	31.3198			1.14288			0.571438	−	0.820645i	$-0.306386\pi$
$751$	31.3198			1.14288			0.571438	+	0.820645i	$0.306386\pi$
$752$	2.62866	−	0.854102i	0.0958572	−	0.0311459i
$753$		0			0
$754$	0.0231904	−	0.0168488i	0.000844546	−	0.000613598i
$755$	5.56215	+	29.0786i	0.202427	+	1.05828i
$756$		0			0
$757$			20.8083i			0.756291i	0.925746	+	0.378146i	$0.123438\pi$
$757$			20.8083i			0.756291i	−0.925746	+	0.378146i	$0.876562\pi$
$758$	8.04303	−	11.0703i	0.292136	−	0.402091i
$759$		0			0
$760$	−1.54124	−	2.80017i	−0.0559065	−	0.101573i
$761$	−7.74368	−	23.8326i	−0.280708	−	0.863931i	−0.987652	−	0.156661i	$-0.949927\pi$
$761$	−7.74368	−	23.8326i	−0.280708	−	0.863931i	0.706944	−	0.707269i	$-0.250073\pi$
$762$		0			0
$763$	−7.11016	−	2.31023i	−0.257405	−	0.0836359i
$764$	8.04149	+	24.7492i	0.290931	+	0.895393i
$765$		0			0
$766$	−9.47214	+	29.1522i	−0.342242	+	1.05331i
$767$	−0.765224	+	1.05324i	−0.0276307	+	0.0380303i
$768$		0			0
$769$	8.63466	+	6.27345i	0.311374	+	0.226226i	0.732486	−	0.680782i	$-0.238360\pi$
$769$	8.63466	+	6.27345i	0.311374	+	0.226226i	−0.421112	+	0.907009i	$0.638360\pi$
$770$	−1.99859	−	1.87491i	−0.0720241	−	0.0675672i
$771$		0			0
$772$	2.07295	+	2.85317i	0.0746071	+	0.102688i
$773$	−30.9464	+	10.0551i	−1.11306	+	0.361656i	−0.807117	−	0.590392i	$-0.798973\pi$
$773$	−30.9464	+	10.0551i	−1.11306	+	0.361656i	−0.305947	+	0.952048i	$0.598973\pi$
$774$		0			0
$775$	−41.7019	−	10.6626i	−1.49798	−	0.383013i
$776$	16.3174			0.585759
$777$		0			0
$778$	9.65725	+	13.2921i	0.346229	+	0.476544i
$779$	−9.53060	+	6.92439i	−0.341469	+	0.248092i
$780$		0			0
$781$	−7.50431	−	5.45220i	−0.268525	−	0.195095i
$782$			3.45764i			0.123645i
$783$		0			0
$784$	2.11189	−	6.49973i	0.0754246	−	0.232133i
$785$	15.2864	−	2.92399i	0.545597	−	0.104362i
$786$		0			0
$787$	−50.9560	−	16.5566i	−1.81639	−	0.590179i	−0.999918	−	0.0127869i	$-0.995930\pi$
$787$	−50.9560	−	16.5566i	−1.81639	−	0.590179i	−0.816467	−	0.577392i	$-0.804070\pi$
$788$	13.8586	+	4.50294i	0.493693	+	0.160411i
$789$		0			0
$790$	−13.9860	−	6.57277i	−0.497601	−	0.233849i
$791$	0.661303	−	2.03528i	0.0235132	−	0.0723663i
$792$		0			0
$793$		−	1.22855i		−	0.0436270i
$794$	−28.4662	−	20.6819i	−1.01023	−	0.733974i
$795$		0			0
$796$	11.4944	−	8.35121i	0.407410	−	0.296001i
$797$	0.559288	+	0.769794i	0.0198110	+	0.0272675i	0.818808	−	0.574068i	$-0.194636\pi$
$797$	0.559288	+	0.769794i	0.0198110	+	0.0272675i	−0.798997	+	0.601336i	$0.794636\pi$
$798$		0			0
$799$	−8.55902			−0.302796
$800$	−1.84529	−	4.64703i	−0.0652407	−	0.164297i
$801$		0			0
$802$	−32.8004	+	10.6575i	−1.15822	+	0.376329i
$803$	−15.2313	−	20.9642i	−0.537503	−	0.739809i
$804$		0			0
$805$	−0.890577	+	0.490181i	−0.0313887	+	0.0172766i
$806$	1.26335	+	0.917878i	0.0444996	+	0.0323309i
$807$		0			0
$808$	−9.22700	+	12.6999i	−0.324605	+	0.446780i
$809$	−1.01308	+	3.11795i	−0.0356181	+	0.109621i	−0.967285	−	0.253693i	$-0.918355\pi$
$809$	−1.01308	+	3.11795i	−0.0356181	+	0.109621i	0.931667	+	0.363314i	$0.118355\pi$
$810$		0			0
$811$	−10.6011	−	32.6267i	−0.372253	−	1.14568i	−0.945313	−	0.326164i	$-0.894244\pi$
$811$	−10.6011	−	32.6267i	−0.372253	−	1.14568i	0.573060	−	0.819514i	$-0.305756\pi$
$812$	−0.0611920	−	0.0198825i	−0.00214742	−	0.000697739i
$813$		0			0
$814$	4.10071	+	12.6207i	0.143730	+	0.442354i
$815$	4.71673	−	37.4879i	0.165220	−	1.31315i
$816$		0			0
$817$	−8.98187	+	12.3625i	−0.314236	+	0.432509i
$818$		−	19.1851i		−	0.670791i
$819$		0			0
$820$	−16.1444	+	8.88599i	−0.563786	+	0.310312i
$821$	5.66056	−	4.11264i	0.197555	−	0.143532i	−0.484610	−	0.874730i	$-0.661039\pi$
$821$	5.66056	−	4.11264i	0.197555	−	0.143532i	0.682165	+	0.731198i	$0.261039\pi$
$822$		0			0
$823$	7.48293	−	2.43135i	0.260839	−	0.0847516i	−0.175678	−	0.984448i	$-0.556212\pi$
$823$	7.48293	−	2.43135i	0.260839	−	0.0847516i	0.436517	+	0.899696i	$0.356212\pi$
$824$	−17.3882			−0.605746
$825$		0			0
$826$	2.92218			0.101676
$827$	10.1239	−	3.28947i	0.352044	−	0.114386i	−0.127656	−	0.991818i	$-0.540745\pi$
$827$	10.1239	−	3.28947i	0.352044	−	0.114386i	0.479700	+	0.877432i	$0.340745\pi$
$828$		0			0
$829$	27.9649	−	20.3177i	0.971262	−	0.705663i	0.0155230	−	0.999880i	$-0.495059\pi$
$829$	27.9649	−	20.3177i	0.971262	−	0.705663i	0.955739	+	0.294217i	$0.0950587\pi$
$830$	−32.8395	−	4.13186i	−1.13987	−	0.143419i
$831$		0			0
$832$			0.181397i			0.00628880i
$833$	−12.4395	+	17.1215i	−0.431004	+	0.593227i
$834$		0			0
$835$	4.56189	+	2.14387i	0.157871	+	0.0741917i
$836$	1.32955	+	4.09192i	0.0459833	+	0.141522i
$837$		0			0
$838$	−10.4510	−	3.39574i	−0.361024	−	0.117304i
$839$	10.9708	+	33.7646i	0.378754	+	1.16568i	0.940911	+	0.338654i	$0.109972\pi$
$839$	10.9708	+	33.7646i	0.378754	+	1.16568i	−0.562157	+	0.827030i	$0.690028\pi$
$840$		0			0
$841$	−8.95378	+	27.5569i	−0.308751	+	0.950238i
$842$	17.0929	−	23.5263i	0.589060	−	0.810771i
$843$		0			0
$844$	9.72525	+	7.06581i	0.334757	+	0.243215i
$845$	12.3324	−	26.2419i	0.424249	−	0.902750i
$846$		0			0
$847$	−0.464347	−	0.639119i	−0.0159552	−	0.0219604i
$848$	−7.98174	+	2.59343i	−0.274094	+	0.0890586i
$849$		0			0
$850$	0.987712	+	15.4519i	0.0338782	+	0.529995i
$851$	4.92268			0.168747
$852$		0			0
$853$	−13.0820	−	18.0058i	−0.447919	−	0.616507i	0.524030	−	0.851700i	$-0.324428\pi$
$853$	−13.0820	−	18.0058i	−0.447919	−	0.616507i	−0.971949	+	0.235193i	$0.924428\pi$
$854$	−2.23094	+	1.62087i	−0.0763411	+	0.0554650i
$855$		0			0
$856$	6.18158	+	4.49118i	0.211282	+	0.153505i
$857$		−	25.4926i		−	0.870812i	−0.900234	−	0.435406i	$-0.856605\pi$
$857$		−	25.4926i		−	0.870812i	0.900234	−	0.435406i	$-0.143395\pi$
$858$		0			0
$859$	−6.74338	+	20.7540i	−0.230081	+	0.708117i	0.767655	+	0.640864i	$0.221424\pi$
$859$	−6.74338	+	20.7540i	−0.230081	+	0.708117i	−0.997736	+	0.0672534i	$0.978576\pi$
$860$	−16.3547	+	17.4335i	−0.557689	+	0.594476i
$861$		0			0
$862$	27.6004	+	8.96792i	0.940074	+	0.305449i
$863$	30.2920	+	9.84248i	1.03115	+	0.335042i	0.775246	−	0.631659i	$-0.217626\pi$
$863$	30.2920	+	9.84248i	1.03115	+	0.335042i	0.255907	+	0.966701i	$0.417626\pi$
$864$		0			0
$865$	−1.19058	−	2.16308i	−0.0404809	−	0.0735470i
$866$	−2.47907	+	7.62979i	−0.0842422	+	0.259271i
$867$		0			0
$868$		−	3.50513i		−	0.118972i
$869$	16.8290	+	12.2270i	0.570884	+	0.414772i
$870$		0			0
$871$	−0.579352	+	0.420924i	−0.0196306	+	0.0142625i
$872$	10.7926	+	14.8547i	0.365482	+	0.503043i
$873$		0			0
$874$	1.59605			0.0539872
$875$	−3.83988	+	2.44497i	−0.129812	+	0.0826552i
$876$		0			0
$877$	3.79237	−	1.23222i	0.128059	−	0.0416090i	−0.244286	−	0.969703i	$-0.578554\pi$
$877$	3.79237	−	1.23222i	0.128059	−	0.0416090i	0.372345	+	0.928094i	$0.378554\pi$
$878$	−9.22716	−	12.7001i	−0.311402	−	0.428608i
$879$		0			0
$880$	1.26447	+	6.61059i	0.0426254	+	0.222843i
$881$	−3.16475	−	2.29933i	−0.106623	−	0.0774663i	0.533196	−	0.845992i	$-0.320991\pi$
$881$	−3.16475	−	2.29933i	−0.106623	−	0.0774663i	−0.639819	+	0.768525i	$0.720991\pi$
$882$		0			0
$883$	−29.9590	+	41.2350i	−1.00820	+	1.38767i	−0.0880449	+	0.996117i	$0.528062\pi$
$883$	−29.9590	+	41.2350i	−1.00820	+	1.38767i	−0.920156	+	0.391553i	$0.871938\pi$
$884$	0.173583	−	0.534235i	0.00583824	−	0.0179683i
$885$		0			0
$886$	5.60993	+	17.2656i	0.188469	+	0.580049i
$887$	2.76774	+	0.899295i	0.0929318	+	0.0301954i	0.355114	−	0.934823i	$-0.384442\pi$
$887$	2.76774	+	0.899295i	0.0929318	+	0.0301954i	−0.262182	+	0.965018i	$0.584442\pi$
$888$		0			0
$889$	−1.09700	−	3.37621i	−0.0367921	−	0.113234i
$890$	−22.4164	+	23.8951i	−0.751400	+	0.800964i
$891$		0			0
$892$	1.73878	−	2.39323i	0.0582187	−	0.0801312i
$893$			3.95085i			0.132210i
$894$		0			0
$895$	−22.3296	−	20.9478i	−0.746395	−	0.700207i
$896$	0.329401	−	0.239324i	0.0110045	−	0.00799524i
$897$		0			0
$898$	11.6307	−	3.77904i	0.388121	−	0.126108i
$899$	1.36037			0.0453710
$900$		0			0
$901$	25.9889			0.865816
$902$	23.5920	−	7.66550i	0.785527	−	0.255233i
$903$		0			0
$904$	−4.25215	+	3.08937i	−0.141425	+	0.102751i
$905$	9.45590	−	20.1210i	0.314325	−	0.668844i
$906$		0			0
$907$		−	6.26029i		−	0.207870i	−0.994584	−	0.103935i	$-0.966857\pi$
$907$		−	6.26029i		−	0.207870i	0.994584	−	0.103935i	$-0.0331433\pi$
$908$	12.7960	−	17.6122i	0.424651	−	0.584481i
$909$		0			0
$910$	0.162210	−	0.0310276i	0.00537722	−	0.00102855i
$911$	−14.8156	−	45.5978i	−0.490863	−	1.51072i	−0.823306	−	0.567598i	$-0.807873\pi$
$911$	−14.8156	−	45.5978i	−0.490863	−	1.51072i	0.332443	−	0.943123i	$-0.392127\pi$
$912$		0			0
$913$	42.3727	+	13.7677i	1.40233	+	0.455645i
$914$	−12.4047	−	38.1778i	−0.410311	−	1.26281i
$915$		0			0
$916$	−4.05126	+	12.4685i	−0.133857	+	0.411971i
$917$	−2.92621	+	4.02758i	−0.0966319	+	0.133002i
$918$		0			0
$919$	20.4733	+	14.8747i	0.675353	+	0.490672i	0.871813	−	0.489839i	$-0.162945\pi$
$919$	20.4733	+	14.8747i	0.675353	+	0.490672i	−0.196460	+	0.980512i	$0.562945\pi$
$920$	2.47718	+	0.311679i	0.0816703	+	0.0102757i
$921$		0			0
$922$	−0.203356	−	0.279895i	−0.00669717	−	0.00921786i
$923$	0.531656	−	0.172745i	0.0174997	−	0.00568599i
$924$		0			0
$925$	21.9990	−	1.40622i	0.723322	−	0.0462361i
$926$	−10.9773			−0.360738
$927$		0			0
$928$	0.0928839	+	0.127844i	0.00304906	+	0.00419667i
$929$	10.4413	−	7.58605i	0.342568	−	0.248890i	−0.403177	−	0.915122i	$-0.632094\pi$
$929$	10.4413	−	7.58605i	0.342568	−	0.248890i	0.745745	+	0.666232i	$0.232094\pi$
$930$		0			0
$931$	7.90332	+	5.74210i	0.259021	+	0.188190i
$932$		−	5.40763i		−	0.177133i
$933$		0			0
$934$	−6.19719	+	19.0730i	−0.202778	+	0.624087i
$935$	2.60183	−	20.6790i	0.0850888	−	0.676275i
$936$		0			0
$937$	−17.0343	−	5.53478i	−0.556486	−	0.180813i	0.0172533	−	0.999851i	$-0.494508\pi$
$937$	−17.0343	−	5.53478i	−0.556486	−	0.180813i	−0.573740	+	0.819038i	$0.694508\pi$
$938$	1.52872	+	0.496712i	0.0499146	+	0.0162182i
$939$		0			0
$940$	−0.771526	+	6.13199i	−0.0251644	+	0.200004i
$941$	12.1818	−	37.4919i	0.397117	−	1.22220i	−0.530184	−	0.847883i	$-0.677877\pi$
$941$	12.1818	−	37.4919i	0.397117	−	1.22220i	0.927301	−	0.374317i	$-0.122123\pi$
$942$		0			0
$943$		−	9.20202i		−	0.299659i
$944$	−5.80628	−	4.21851i	−0.188978	−	0.137301i
$945$		0			0
$946$	26.0316	−	18.9131i	0.846361	−	0.614917i
$947$	−26.1728	−	36.0238i	−0.850502	−	1.17061i	−0.983752	−	0.179533i	$-0.942541\pi$
$947$	−26.1728	−	36.0238i	−0.850502	−	1.17061i	0.133250	−	0.991082i	$-0.457459\pi$
$948$		0			0
$949$	1.56168			0.0506942
$950$	7.13259	−	0.455929i	0.231412	−	0.0147923i
$951$		0			0
$952$	−1.19914	+	0.389624i	−0.0388643	+	0.0126278i
$953$	14.3919	+	19.8087i	0.466198	+	0.641666i	0.975780	−	0.218756i	$-0.0701999\pi$
$953$	14.3919	+	19.8087i	0.466198	+	0.641666i	−0.509582	+	0.860422i	$0.670200\pi$
$954$		0			0
$955$	−57.7336	−	7.26403i	−1.86821	−	0.235058i
$956$	7.79640	+	5.66441i	0.252154	+	0.183200i
$957$		0			0
$958$	−14.2267	+	19.5813i	−0.459642	+	0.632643i
$959$	1.38549	−	4.26411i	0.0447399	−	0.137695i
$960$		0			0
$961$	13.3216	+	40.9996i	0.429728	+	1.32257i
$962$	−0.760596	−	0.247133i	−0.0245226	−	0.00796787i
$963$		0			0
$964$	−2.09756	−	6.45562i	−0.0675578	−	0.207921i
$965$	−7.74554	+	1.48157i	−0.249338	+	0.0476934i
$966$		0			0
$967$	15.9437	−	21.9446i	0.512714	−	0.705690i	−0.471660	−	0.881780i	$-0.656345\pi$
$967$	15.9437	−	21.9446i	0.512714	−	0.705690i	0.984374	+	0.176090i	$0.0563451\pi$
$968$			1.94025i			0.0623619i
$969$		0			0
$970$	−15.5187	+	33.0219i	−0.498276	+	1.06027i
$971$	34.2011	−	24.8485i	1.09756	−	0.797427i	0.116904	−	0.993143i	$-0.462703\pi$
$971$	34.2011	−	24.8485i	1.09756	−	0.797427i	0.980661	+	0.195716i	$0.0627031\pi$
$972$		0			0
$973$	0.803067	−	0.260932i	0.0257452	−	0.00836511i
$974$	−15.9706			−0.511732
$975$		0			0
$976$	6.77271			0.216789
$977$	−5.48738	+	1.78296i	−0.175557	+	0.0570419i	−0.395476	−	0.918476i	$-0.629421\pi$
$977$	−5.48738	+	1.78296i	−0.175557	+	0.0570419i	0.219920	+	0.975518i	$0.429421\pi$
$978$		0			0
$979$	35.6801	−	25.9231i	1.14034	−	0.828505i
$980$	11.1452	+	10.4555i	0.356020	+	0.333989i
$981$		0			0
$982$		−	31.9294i		−	1.01891i
$983$	15.8663	−	21.8381i	0.506058	−	0.696528i	−0.477191	−	0.878800i	$-0.658345\pi$
$983$	15.8663	−	21.8381i	0.506058	−	0.696528i	0.983248	+	0.182271i	$0.0583449\pi$
$984$		0			0
$985$	−22.2931	+	23.7636i	−0.710317	+	0.757171i
$986$	−0.151217	−	0.465398i	−0.00481573	−	0.0148213i
$987$		0			0
$988$	−0.246603	−	0.0801262i	−0.00784549	−	0.00254916i
$989$	−3.68851	−	11.3521i	−0.117288	−	0.360975i
$990$		0			0
$991$	4.84816	−	14.9211i	0.154007	−	0.473985i	−0.844052	−	0.536261i	$-0.819836\pi$
$991$	4.84816	−	14.9211i	0.154007	−	0.473985i	0.998059	+	0.0622766i	$0.0198361\pi$
$992$	−5.06006	+	6.96457i	−0.160657	+	0.221125i
$993$		0			0
$994$	−1.01512	−	0.737531i	−0.0321978	−	0.0233931i
$995$	5.96873	+	31.2042i	0.189222	+	0.989238i
$996$		0			0
$997$	−25.4580	−	35.0400i	−0.806264	−	1.10973i	−0.991889	−	0.127106i	$-0.959431\pi$
$997$	−25.4580	−	35.0400i	−0.806264	−	1.10973i	0.185625	−	0.982621i	$-0.440569\pi$
$998$	30.6778	−	9.96783i	0.971090	−	0.315526i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.d.19.2	✓	16
3.2	odd	2	inner	450.2.l.d.19.3	yes	16
25.4	even	10	inner	450.2.l.d.379.2	yes	16
75.29	odd	10	inner	450.2.l.d.379.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.l.d.19.2	✓	16	1.1	even	1	trivial
450.2.l.d.19.3	yes	16	3.2	odd	2	inner
450.2.l.d.379.2	yes	16	25.4	even	10	inner
450.2.l.d.379.3	yes	16	75.29	odd	10	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.420099 + 2.19625i) q^{5} -0.407162i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.420099 + 2.19625i) q^{5} -0.407162i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.07822 - 1.95894i) q^{10} +(0.930123 + 2.86263i) q^{11} +(-0.172519 - 0.0560547i) q^{13} +(0.125820 + 0.387234i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-1.82018 + 2.50527i) q^{17} +(1.15643 + 0.840198i) q^{19} +(1.63079 + 1.52988i) q^{20} +(-1.76920 - 2.43509i) q^{22} +(-1.06192 + 0.345037i) q^{23} +(-4.64703 + 1.84529i) q^{25} +0.181397 q^{26} +(-0.239324 - 0.329401i) q^{28} +(0.127844 - 0.0928839i) q^{29} +(6.96457 + 5.06006i) q^{31} +1.00000i q^{32} +(0.956927 - 2.94512i) q^{34} +(0.894229 - 0.171048i) q^{35} +(-4.19300 - 1.36239i) q^{37} +(-1.35947 - 0.441718i) q^{38} +(-2.02373 - 0.951057i) q^{40} +(-2.54673 + 7.83802i) q^{41} +10.6902i q^{43} +(2.43509 + 1.76920i) q^{44} +(0.903319 - 0.656300i) q^{46} +(1.62460 + 2.23607i) q^{47} +6.83422 q^{49} +(3.84937 - 3.19098i) q^{50} +(-0.172519 + 0.0560547i) q^{52} +(-4.93299 - 6.78968i) q^{53} +(-5.89630 + 3.24537i) q^{55} +(0.329401 + 0.239324i) q^{56} +(-0.0928839 + 0.127844i) q^{58} +(2.21780 - 6.82570i) q^{59} +(2.09288 + 6.44123i) q^{61} +(-8.18735 - 2.66023i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(0.0506353 - 0.402443i) q^{65} +(2.32046 - 3.19384i) q^{67} +3.09668i q^{68} +(-0.797605 + 0.439008i) q^{70} +(-2.49317 + 1.81140i) q^{71} +(-8.18781 + 2.66038i) q^{73} +4.40878 q^{74} +1.42943 q^{76} +(1.16555 - 0.378710i) q^{77} +(5.59113 - 4.06219i) q^{79} +(2.21858 + 0.279141i) q^{80} -8.24138i q^{82} +(8.70043 - 11.9751i) q^{83} +(-6.26685 - 2.94512i) q^{85} +(-3.30345 - 10.1670i) q^{86} +(-2.86263 - 0.930123i) q^{88} +(-4.52785 - 13.9353i) q^{89} +(-0.0228233 + 0.0702429i) q^{91} +(-0.656300 + 0.903319i) q^{92} +(-2.23607 - 1.62460i) q^{94} +(-1.35947 + 2.89278i) q^{95} +(-9.59110 - 13.2010i) q^{97} +(-6.49973 + 2.11189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

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