LMFDB - Embedded newform 384.2.v.a.229.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			229.32
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41343 - 0.0470411i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.99557 - 0.132979i) q^{4} +(-2.41721 - 2.94538i) q^{5} +(1.22436 - 0.707773i) q^{6} +(-0.253541 + 0.169410i) q^{7} +(2.81435 - 0.281830i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(1.41343 - 0.0470411i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.99557 - 0.132979i) q^{4} +(-2.41721 - 2.94538i) q^{5} +(1.22436 - 0.707773i) q^{6} +(-0.253541 + 0.169410i) q^{7} +(2.81435 - 0.281830i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-3.55512 - 4.04939i) q^{10} +(-0.265657 + 0.0805862i) q^{11} +(1.69725 - 1.05798i) q^{12} +(1.32231 + 1.08519i) q^{13} +(-0.350393 + 0.251377i) q^{14} +(-3.52024 - 1.45813i) q^{15} +(3.96463 - 0.530737i) q^{16} +(4.25100 - 1.76082i) q^{17} +(0.746147 - 1.20136i) q^{18} +(0.116081 + 1.17859i) q^{19} +(-5.21540 - 5.55629i) q^{20} +(-0.143743 + 0.268925i) q^{21} +(-0.371697 + 0.126400i) q^{22} +(-7.69105 + 1.52985i) q^{23} +(2.34918 - 1.57523i) q^{24} +(-1.85691 + 9.33531i) q^{25} +(1.92005 + 1.47164i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-0.483431 + 0.371787i) q^{28} +(0.259270 - 0.854697i) q^{29} +(-5.04420 - 1.89537i) q^{30} +(7.54481 + 7.54481i) q^{31} +(5.57877 - 0.936661i) q^{32} +(-0.196300 + 0.196300i) q^{33} +(5.92566 - 2.68877i) q^{34} +(1.11184 + 0.337273i) q^{35} +(0.998114 - 1.73314i) q^{36} +(-11.1755 - 1.10069i) q^{37} +(0.219515 + 1.66040i) q^{38} +(1.67773 + 0.333722i) q^{39} +(-7.63298 - 7.60810i) q^{40} +(0.635690 + 3.19583i) q^{41} +(-0.190521 + 0.386869i) q^{42} +(6.03772 + 3.22723i) q^{43} +(-0.519422 + 0.196142i) q^{44} +(-3.79193 + 0.373472i) q^{45} +(-10.7988 + 2.52413i) q^{46} +(3.17864 + 7.67391i) q^{47} +(3.24631 - 2.33698i) q^{48} +(-2.64320 + 6.38125i) q^{49} +(-2.18547 + 13.2822i) q^{50} +(2.91900 - 3.55681i) q^{51} +(2.78308 + 1.98974i) q^{52} +(-0.522948 - 1.72393i) q^{53} +(0.0917259 - 1.41124i) q^{54} +(0.879507 + 0.587668i) q^{55} +(-0.665807 + 0.548236i) q^{56} +(0.657959 + 0.984705i) q^{57} +(0.326254 - 1.22025i) q^{58} +(1.79439 - 1.47262i) q^{59} +(-7.21879 - 2.44169i) q^{60} +(-3.97939 - 7.44491i) q^{61} +(11.0190 + 10.3091i) q^{62} +0.304931i q^{63} +(7.84114 - 1.58634i) q^{64} -6.51786i q^{65} +(-0.268223 + 0.286691i) q^{66} +(-1.29293 - 2.41889i) q^{67} +(8.24903 - 4.07914i) q^{68} +(-6.06174 + 4.97474i) q^{69} +(1.58738 + 0.424410i) q^{70} +(-4.04516 - 6.05400i) q^{71} +(1.32924 - 2.49662i) q^{72} +(-3.57334 - 2.38763i) q^{73} +(-15.8476 - 1.03005i) q^{74} +(2.76299 + 9.10835i) q^{75} +(0.388376 + 2.33653i) q^{76} +(0.0537027 - 0.0654369i) q^{77} +(2.38706 + 0.392770i) q^{78} +(2.38560 - 5.75934i) q^{79} +(-11.1466 - 10.3945i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(1.04884 + 4.48718i) q^{82} +(9.70409 - 0.955769i) q^{83} +(-0.251089 + 0.555774i) q^{84} +(-15.4619 - 8.26453i) q^{85} +(8.68571 + 4.27744i) q^{86} +(-0.174246 - 0.875994i) q^{87} +(-0.724940 + 0.301668i) q^{88} +(-6.03919 - 1.20127i) q^{89} +(-5.34206 + 0.706254i) q^{90} +(-0.519103 - 0.0511272i) q^{91} +(-15.1446 + 4.07567i) q^{92} +(10.2105 + 3.09733i) q^{93} +(4.85377 + 10.6970i) q^{94} +(3.19081 - 3.19081i) q^{95} +(4.47850 - 3.45587i) q^{96} +(7.57970 + 7.57970i) q^{97} +(-3.43580 + 9.14380i) q^{98} +(-0.0805862 + 0.265657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	1.41343	−	0.0470411i	0.999447	−	0.0332631i
$2$	1.41343	−	0.0470411i	0.999447	−	0.0332631i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	1.99557	−	0.132979i	0.997787	−	0.0664893i
$5$	−2.41721	−	2.94538i	−1.08101	−	1.31722i	−0.945204	−	0.326480i	$-0.894137\pi$
$5$	−2.41721	−	2.94538i	−1.08101	−	1.31722i	−0.135807	−	0.990735i	$-0.543363\pi$
$6$	1.22436	−	0.707773i	0.499843	−	0.288947i
$7$	−0.253541	+	0.169410i	−0.0958294	+	0.0640311i	−0.602562	−	0.798072i	$-0.705853\pi$
$7$	−0.253541	+	0.169410i	−0.0958294	+	0.0640311i	0.506732	+	0.862103i	$0.330853\pi$
$8$	2.81435	−	0.281830i	0.995023	−	0.0996419i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−3.55512	−	4.04939i	−1.12423	−	1.28053i
$11$	−0.265657	+	0.0805862i	−0.0800986	+	0.0242976i	−0.330080	−	0.943953i	$-0.607076\pi$
$11$	−0.265657	+	0.0805862i	−0.0800986	+	0.0242976i	0.249981	+	0.968251i	$0.419576\pi$
$12$	1.69725	−	1.05798i	0.489955	−	0.305414i
$13$	1.32231	+	1.08519i	0.366743	+	0.300978i	0.799657	−	0.600457i	$-0.205015\pi$
$13$	1.32231	+	1.08519i	0.366743	+	0.300978i	−0.432914	+	0.901435i	$0.642515\pi$
$14$	−0.350393	+	0.251377i	−0.0936465	+	0.0671833i
$15$	−3.52024	−	1.45813i	−0.908921	−	0.376487i
$16$	3.96463	−	0.530737i	0.991158	−	0.132684i
$17$	4.25100	−	1.76082i	1.03102	−	0.427062i	0.197938	−	0.980215i	$-0.436575\pi$
$17$	4.25100	−	1.76082i	1.03102	−	0.427062i	0.833080	+	0.553153i	$0.186575\pi$
$18$	0.746147	−	1.20136i	0.175869	−	0.283163i
$19$	0.116081	+	1.17859i	0.0266308	+	0.270388i	0.999274	+	0.0380853i	$0.0121258\pi$
$19$	0.116081	+	1.17859i	0.0266308	+	0.270388i	−0.972644	+	0.232302i	$0.925374\pi$
$20$	−5.21540	−	5.55629i	−1.16620	−	1.24242i
$21$	−0.143743	+	0.268925i	−0.0313674	+	0.0586842i
$22$	−0.371697	+	0.126400i	−0.0792460	+	0.0269485i
$23$	−7.69105	+	1.52985i	−1.60370	+	0.318995i	−0.914190	−	0.405285i	$-0.867172\pi$
$23$	−7.69105	+	1.52985i	−1.60370	+	0.318995i	−0.689506	+	0.724280i	$0.742172\pi$
$24$	2.34918	−	1.57523i	0.479525	−	0.321542i
$25$	−1.85691	+	9.33531i	−0.371382	+	1.86706i
$26$	1.92005	+	1.47164i	0.376552	+	0.288613i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−0.483431	+	0.371787i	−0.0913599	+	0.0702611i
$29$	0.259270	−	0.854697i	0.0481451	−	0.158713i	−0.929572	−	0.368641i	$-0.879823\pi$
$29$	0.259270	−	0.854697i	0.0481451	−	0.158713i	0.977717	+	0.209928i	$0.0673230\pi$
$30$	−5.04420	−	1.89537i	−0.920941	−	0.346046i
$31$	7.54481	+	7.54481i	1.35509	+	1.35509i	0.879867	+	0.475220i	$0.157632\pi$
$31$	7.54481	+	7.54481i	1.35509	+	1.35509i	0.475220	+	0.879867i	$0.342368\pi$
$32$	5.57877	−	0.936661i	0.986196	−	0.165580i
$33$	−0.196300	+	0.196300i	−0.0341715	+	0.0341715i
$34$	5.92566	−	2.68877i	1.01624	−	0.461120i
$35$	1.11184	+	0.337273i	0.187935	+	0.0570096i
$36$	0.998114	−	1.73314i	0.166352	−	0.288856i
$37$	−11.1755	−	1.10069i	−1.83725	−	0.180953i	−0.880923	−	0.473260i	$-0.843077\pi$
$37$	−11.1755	−	1.10069i	−1.83725	−	0.180953i	−0.956325	+	0.292306i	$0.905577\pi$
$38$	0.219515	+	1.66040i	0.0356100	+	0.269352i
$39$	1.67773	+	0.333722i	0.268652	+	0.0534382i
$40$	−7.63298	−	7.60810i	−1.20688	−	1.20295i
$41$	0.635690	+	3.19583i	0.0992781	+	0.499104i	0.998145	+	0.0608827i	$0.0193916\pi$
$41$	0.635690	+	3.19583i	0.0992781	+	0.499104i	−0.898867	+	0.438222i	$0.855608\pi$
$42$	−0.190521	+	0.386869i	−0.0293980	+	0.0596951i
$43$	6.03772	+	3.22723i	0.920744	+	0.492148i	0.862445	−	0.506151i	$-0.168932\pi$
$43$	6.03772	+	3.22723i	0.920744	+	0.492148i	0.0582990	+	0.998299i	$0.481432\pi$
$44$	−0.519422	+	0.196142i	−0.0783058	+	0.0295696i
$45$	−3.79193	+	0.373472i	−0.565267	+	0.0556740i
$46$	−10.7988	+	2.52413i	−1.59220	+	0.372162i
$47$	3.17864	+	7.67391i	0.463652	+	1.11936i	0.966887	+	0.255205i	$0.0821431\pi$
$47$	3.17864	+	7.67391i	0.463652	+	1.11936i	−0.503235	+	0.864150i	$0.667857\pi$
$48$	3.24631	−	2.33698i	0.468564	−	0.337315i
$49$	−2.64320	+	6.38125i	−0.377600	+	0.911607i
$50$	−2.18547	+	13.2822i	−0.309072	+	1.87838i
$51$	2.91900	−	3.55681i	0.408742	−	0.498053i
$52$	2.78308	+	1.98974i	0.385944	+	0.275928i
$53$	−0.522948	−	1.72393i	−0.0718325	−	0.236800i	0.913671	−	0.406454i	$-0.133235\pi$
$53$	−0.522948	−	1.72393i	−0.0718325	−	0.236800i	−0.985504	+	0.169654i	$0.945735\pi$
$54$	0.0917259	−	1.41124i	0.0124823	−	0.192045i
$55$	0.879507	+	0.587668i	0.118593	+	0.0792411i
$56$	−0.665807	+	0.548236i	−0.0889723	+	0.0732611i
$57$	0.657959	+	0.984705i	0.0871488	+	0.130427i
$58$	0.326254	−	1.22025i	0.0428392	−	0.160227i
$59$	1.79439	−	1.47262i	0.233610	−	0.191718i	−0.510304	−	0.859994i	$-0.670467\pi$
$59$	1.79439	−	1.47262i	0.233610	−	0.191718i	0.743914	+	0.668275i	$0.232967\pi$
$60$	−7.21879	−	2.44169i	−0.931942	−	0.315221i
$61$	−3.97939	−	7.44491i	−0.509509	−	0.953223i	−0.996796	−	0.0799820i	$-0.974514\pi$
$61$	−3.97939	−	7.44491i	−0.509509	−	0.953223i	0.487288	−	0.873241i	$-0.337986\pi$
$62$	11.0190	+	10.3091i	1.39941	+	1.30926i
$63$			0.304931i			0.0384177i
$64$	7.84114	−	1.58634i	0.980143	−	0.198292i
$65$		−	6.51786i		−	0.808441i
$66$	−0.268223	+	0.286691i	−0.0330160	+	0.0352893i
$67$	−1.29293	−	2.41889i	−0.157956	−	0.295515i	0.790477	−	0.612491i	$-0.209832\pi$
$67$	−1.29293	−	2.41889i	−0.157956	−	0.295515i	−0.948434	+	0.316976i	$0.897332\pi$
$68$	8.24903	−	4.07914i	1.00034	−	0.494668i
$69$	−6.06174	+	4.97474i	−0.729748	+	0.598889i
$70$	1.58738	+	0.424410i	0.189728	+	0.0507267i
$71$	−4.04516	−	6.05400i	−0.480072	−	0.718478i	0.509824	−	0.860279i	$-0.329711\pi$
$71$	−4.04516	−	6.05400i	−0.480072	−	0.718478i	−0.989895	+	0.141801i	$0.954711\pi$
$72$	1.32924	−	2.49662i	0.156652	−	0.294230i
$73$	−3.57334	−	2.38763i	−0.418228	−	0.279451i	0.328599	−	0.944470i	$-0.393424\pi$
$73$	−3.57334	−	2.38763i	−0.418228	−	0.279451i	−0.746827	+	0.665019i	$0.768424\pi$
$74$	−15.8476	−	1.03005i	−1.84225	−	0.119741i
$75$	2.76299	+	9.10835i	0.319042	+	1.05174i
$76$	0.388376	+	2.33653i	0.0445498	+	0.268019i
$77$	0.0537027	−	0.0654369i	0.00611999	−	0.00745723i
$78$	2.38706	+	0.392770i	0.270281	+	0.0444725i
$79$	2.38560	−	5.75934i	0.268401	−	0.647977i	−0.731008	−	0.682369i	$-0.760950\pi$
$79$	2.38560	−	5.75934i	0.268401	−	0.647977i	0.999408	+	0.0343924i	$0.0109496\pi$
$80$	−11.1466	−	10.3945i	−1.24623	−	1.16214i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	1.04884	+	4.48718i	0.115825	+	0.495526i
$83$	9.70409	−	0.955769i	1.06516	−	0.104909i	0.449781	−	0.893139i	$-0.351502\pi$
$83$	9.70409	−	0.955769i	1.06516	−	0.104909i	0.615381	+	0.788230i	$0.289002\pi$
$84$	−0.251089	+	0.555774i	−0.0273961	+	0.0606400i
$85$	−15.4619	−	8.26453i	−1.67707	−	0.896414i
$86$	8.68571	+	4.27744i	0.936604	+	0.461249i
$87$	−0.174246	−	0.875994i	−0.0186811	−	0.0939164i
$88$	−0.724940	+	0.301668i	−0.0772789	+	0.0321579i
$89$	−6.03919	−	1.20127i	−0.640153	−	0.127334i	−0.135667	−	0.990754i	$-0.543318\pi$
$89$	−6.03919	−	1.20127i	−0.640153	−	0.127334i	−0.504485	+	0.863420i	$0.668318\pi$
$90$	−5.34206	+	0.706254i	−0.563103	+	0.0744457i
$91$	−0.519103	−	0.0511272i	−0.0544168	−	0.00535958i
$92$	−15.1446	+	4.07567i	−1.57894	+	0.424918i
$93$	10.2105	+	3.09733i	1.05878	+	0.321178i
$94$	4.85377	+	10.6970i	0.500629	+	1.10331i
$95$	3.19081	−	3.19081i	0.327370	−	0.327370i
$96$	4.47850	−	3.45587i	0.457085	−	0.352714i
$97$	7.57970	+	7.57970i	0.769602	+	0.769602i	0.978036	−	0.208434i	$-0.0668367\pi$
$97$	7.57970	+	7.57970i	0.769602	+	0.769602i	−0.208434	+	0.978036i	$0.566837\pi$
$98$	−3.43580	+	9.14380i	−0.347068	+	0.923663i
$99$	−0.0805862	+	0.265657i	−0.00809921	+	0.0266995i
$100$	−2.46420	+	18.8762i	−0.246420	+	1.88762i
$101$	0.969036	−	9.83879i	0.0964227	−	0.978996i	−0.818267	−	0.574839i	$-0.805065\pi$
$101$	0.969036	−	9.83879i	0.0964227	−	0.978996i	0.914689	−	0.404158i	$-0.132435\pi$
$102$	3.95849	−	5.16462i	0.391949	−	0.511373i
$103$	−0.694336	+	3.49066i	−0.0684149	+	0.343945i	−0.999798	−	0.0200954i	$-0.993603\pi$
$103$	−0.694336	+	3.49066i	−0.0684149	+	0.343945i	0.931383	+	0.364040i	$0.118603\pi$
$104$	4.02729	+	2.68145i	0.394908	+	0.262938i
$105$	1.13955	−	0.226670i	0.111208	−	0.0221207i
$106$	−0.820247	−	2.41205i	−0.0796694	−	0.234279i
$107$	1.52702	−	2.85685i	0.147622	−	0.276182i	−0.797232	−	0.603673i	$-0.793703\pi$
$107$	1.52702	−	2.85685i	0.147622	−	0.276182i	0.944854	+	0.327491i	$0.106203\pi$
$108$	0.0632622	−	1.99900i	0.00608741	−	0.192354i
$109$	0.637583	+	6.47349i	0.0610694	+	0.620048i	0.976197	+	0.216884i	$0.0695894\pi$
$109$	0.637583	+	6.47349i	0.0610694	+	0.620048i	−0.915128	+	0.403164i	$0.867911\pi$
$110$	1.27077	+	0.789255i	0.121163	+	0.0752525i
$111$	−10.3748	+	4.29739i	−0.984734	+	0.407890i
$112$	−0.915283	+	0.806214i	−0.0864861	+	0.0761800i
$113$	−16.3034	−	6.75309i	−1.53369	−	0.635277i	−0.553417	−	0.832904i	$-0.686676\pi$
$113$	−16.3034	−	6.75309i	−1.53369	−	0.635277i	−0.980277	+	0.197627i	$0.936676\pi$
$114$	0.976301	+	1.36086i	0.0914390	+	0.127456i
$115$	23.0969	+	18.9551i	2.15380	+	1.76758i
$116$	0.403735	−	1.74009i	0.0374859	−	0.161563i
$117$	1.63694	−	0.496561i	0.151335	−	0.0459071i
$118$	2.46697	−	2.16585i	0.227103	−	0.199383i
$119$	−0.779499	+	1.16660i	−0.0714565	+	0.106942i
$120$	−10.3181	−	3.11158i	−0.941912	−	0.284047i
$121$	−9.08209	+	6.06846i	−0.825644	+	0.551678i
$122$	−5.97481	−	10.3357i	−0.540934	−	0.935748i
$123$	2.06713	+	2.51881i	0.186387	+	0.227113i
$124$	16.0595	+	14.0529i	1.44219	+	1.26199i
$125$	15.1828	−	8.11537i	1.35799	−	0.725861i
$126$	0.0143443	+	0.430999i	0.00127789	+	0.0383964i
$127$	−12.9264			−1.14704			−0.573518	−	0.819193i	$-0.694422\pi$
$127$	−12.9264			−1.14704			−0.573518	+	0.819193i	$0.694422\pi$
$128$	11.0083	−	2.61103i	0.973005	−	0.230785i
$129$	6.84610			0.602765
$130$	−0.306607	−	9.21254i	−0.0268912	−	0.807994i
$131$	−11.7129	+	6.26065i	−1.02336	+	0.546996i	−0.895624	−	0.444813i	$-0.853270\pi$
$131$	−11.7129	+	6.26065i	−1.02336	+	0.546996i	−0.127734	+	0.991809i	$0.540770\pi$
$132$	−0.365628	+	0.417836i	−0.0318239	+	0.0363679i
$133$	−0.229097	−	0.279156i	−0.0198652	−	0.0242059i
$134$	−1.94125	−	3.35812i	−0.167698	−	0.290097i
$135$	−3.16813	+	2.11688i	−0.272669	+	0.182192i
$136$	11.4675	−	6.15362i	0.983334	−	0.527669i
$137$	−0.158020	+	0.236494i	−0.0135006	+	0.0202050i	−0.838159	−	0.545427i	$-0.816368\pi$
$137$	−0.158020	+	0.236494i	−0.0135006	+	0.0202050i	0.824658	+	0.565632i	$0.191368\pi$
$138$	−8.33383	+	7.31660i	−0.709423	+	0.622831i
$139$	−11.5672	+	3.50886i	−0.981115	+	0.297618i	−0.739799	−	0.672828i	$-0.765079\pi$
$139$	−11.5672	+	3.50886i	−0.981115	+	0.297618i	−0.241316	+	0.970446i	$0.577579\pi$
$140$	2.26361	+	0.525203i	0.191310	+	0.0443877i
$141$	6.42077	+	5.26939i	0.540726	+	0.443762i
$142$	−6.00233	−	8.36663i	−0.503705	−	0.702112i
$143$	−0.438733	−	0.181729i	−0.0366887	−	0.0151970i
$144$	1.76134	−	3.59133i	0.146778	−	0.299278i
$145$	−3.14412	+	1.30234i	−0.261105	+	0.108153i
$146$	−5.16299	−	3.20666i	−0.427292	−	0.265385i
$147$	0.677006	+	6.87376i	0.0558385	+	0.566938i
$148$	−22.4480	−	0.710410i	−1.84521	−	0.0583954i
$149$	8.90366	−	16.6576i	0.729416	−	1.36464i	−0.194061	−	0.980989i	$-0.562166\pi$
$149$	8.90366	−	16.6576i	0.729416	−	1.36464i	0.923477	−	0.383653i	$-0.125334\pi$
$150$	4.33376	+	12.7441i	0.353850	+	1.04055i
$151$	20.3884	−	4.05551i	1.65919	−	0.330033i	0.725526	−	0.688195i	$-0.241596\pi$
$151$	20.3884	−	4.05551i	1.65919	−	0.330033i	0.933659	+	0.358162i	$0.116596\pi$
$152$	0.658856	+	3.28426i	0.0534403	+	0.266388i
$153$	0.897658	−	4.51283i	0.0725714	−	0.364841i
$154$	0.0728268	−	0.0950168i	0.00586855	−	0.00765667i
$155$	3.98494	−	40.4597i	0.320078	−	3.24981i
$156$	3.39242	+	0.442864i	0.271611	+	0.0354575i
$157$	5.26513	−	17.3568i	0.420203	−	1.38522i	−0.450219	−	0.892918i	$-0.648654\pi$
$157$	5.26513	−	17.3568i	0.420203	−	1.38522i	0.870422	−	0.492306i	$-0.163846\pi$
$158$	3.10095	−	8.25266i	0.246699	−	0.656546i
$159$	−1.27385	−	1.27385i	−0.101023	−	0.101023i
$160$	−16.2439	−	14.1675i	−1.28419	−	1.12004i
$161$	1.69082	−	1.69082i	0.133256	−	0.133256i
$162$	−0.584357	−	1.28784i	−0.0459114	−	0.101182i
$163$	−2.97340	−	0.901972i	−0.232895	−	0.0706479i	0.171680	−	0.985153i	$-0.445081\pi$
$163$	−2.97340	−	0.901972i	−0.232895	−	0.0706479i	−0.404575	+	0.914505i	$0.632581\pi$
$164$	1.69354	+	6.29298i	0.132243	+	0.491399i
$165$	1.05268	+	0.103680i	0.0819510	+	0.00807147i
$166$	13.6711	−	1.80740i	1.06108	−	0.140282i
$167$	13.2953	+	2.64461i	1.02882	+	0.204646i	0.680515	−	0.732734i	$-0.261756\pi$
$167$	13.2953	+	2.64461i	1.02882	+	0.204646i	0.348309	+	0.937380i	$0.386756\pi$
$168$	−0.328753	+	0.797360i	−0.0253639	+	0.0615177i
$169$	−1.96531	−	9.88028i	−0.151178	−	0.760022i
$170$	−22.2430	−	10.9540i	−1.70596	−	0.840134i
$171$	1.04445	+	0.558273i	0.0798714	+	0.0426922i
$172$	12.4779	+	5.63729i	0.951429	+	0.429839i
$173$	−7.59205	+	0.747751i	−0.577213	+	0.0568505i	−0.382411	−	0.923992i	$-0.624906\pi$
$173$	−7.59205	+	0.747751i	−0.577213	+	0.0568505i	−0.194801	+	0.980843i	$0.562406\pi$
$174$	−0.287493	−	1.22996i	−0.0217948	−	0.0932431i
$175$	−1.11070	−	2.68146i	−0.0839608	−	0.202699i
$176$	−1.01046	+	0.460489i	−0.0761665	+	0.0347106i
$177$	0.888323	−	2.14460i	0.0667705	−	0.161198i
$178$	−8.59248	−	1.41382i	−0.644034	−	0.105970i
$179$	−4.49736	+	5.48005i	−0.336148	+	0.409598i	−0.913462	−	0.406925i	$-0.866601\pi$
$179$	−4.49736	+	5.48005i	−0.336148	+	0.409598i	0.577313	+	0.816523i	$0.304101\pi$
$180$	−7.51741	+	1.24954i	−0.560315	+	0.0931350i
$181$	6.91261	+	22.7878i	0.513811	+	1.69381i	0.702427	+	0.711756i	$0.252100\pi$
$181$	6.91261	+	22.7878i	0.513811	+	1.69381i	−0.188616	+	0.982051i	$0.560400\pi$
$182$	−0.736121	−	0.0478456i	−0.0545649	−	0.00354655i
$183$	−7.01902	−	4.68996i	−0.518861	−	0.346692i
$184$	−21.2142	+	6.47309i	−1.56393	+	0.477203i
$185$	23.7717	+	35.5769i	1.74773	+	2.61566i
$186$	14.5776	+	3.89755i	1.06888	+	0.285782i
$187$	−0.987409	+	0.810345i	−0.0722065	+	0.0592583i
$188$	7.36367	+	14.8912i	0.537051	+	1.08605i
$189$	0.143743	+	0.268925i	0.0104558	+	0.0195614i
$190$	4.35989	−	4.66009i	0.316300	−	0.338079i
$191$			8.50701i			0.615546i	0.951460	+	0.307773i	$0.0995837\pi$
$191$			8.50701i			0.615546i	−0.951460	+	0.307773i	$0.900416\pi$
$192$	6.16748	−	5.09531i	0.445099	−	0.367723i
$193$		−	24.4589i		−	1.76059i	−0.474427	−	0.880295i	$-0.657345\pi$
$193$		−	24.4589i		−	1.76059i	0.474427	−	0.880295i	$-0.342655\pi$
$194$	11.0699	+	10.3568i	0.794776	+	0.743577i
$195$	−3.07250	−	5.74824i	−0.220026	−	0.411640i
$196$	−4.42613	+	13.0858i	−0.316152	+	0.934697i
$197$	−10.6534	+	8.74305i	−0.759026	+	0.622917i	−0.932187	−	0.361977i	$-0.882102\pi$
$197$	−10.6534	+	8.74305i	−0.759026	+	0.622917i	0.173161	+	0.984894i	$0.444602\pi$
$198$	−0.101406	+	0.379279i	−0.00720662	+	0.0269542i
$199$	−6.90873	−	10.3396i	−0.489747	−	0.732958i	0.501474	−	0.865173i	$-0.332791\pi$
$199$	−6.90873	−	10.3396i	−0.489747	−	0.732958i	−0.991221	+	0.132215i	$0.957791\pi$
$200$	−2.59502	+	26.7962i	−0.183496	+	1.89478i
$201$	−2.28052	−	1.52379i	−0.160855	−	0.107480i
$202$	0.906839	−	13.9520i	0.0638050	−	0.981662i
$203$	0.0790592	+	0.260623i	0.00554887	+	0.0182922i
$204$	5.35210	−	7.48604i	0.374722	−	0.524128i
$205$	7.87634	−	9.59735i	0.550107	−	0.670308i
$206$	−0.817191	+	4.96647i	−0.0569364	+	0.346030i
$207$	−3.00090	+	7.24482i	−0.208577	+	0.503549i
$208$	5.81843	+	3.60059i	0.403436	+	0.249656i
$209$	−0.125816	−	0.303747i	−0.00870287	−	0.0210106i
$210$	1.60001	−	0.373987i	0.110411	−	0.0258076i
$211$	18.4423	−	1.81641i	1.26962	−	0.125047i	0.559324	−	0.828949i	$-0.311061\pi$
$211$	18.4423	−	1.81641i	1.26962	−	0.125047i	0.710297	+	0.703902i	$0.248561\pi$
$212$	−1.27283	−	3.37069i	−0.0874182	−	0.231500i
$213$	−6.42135	−	3.43228i	−0.439983	−	0.235176i
$214$	2.02394	−	4.10979i	0.138354	−	0.280939i
$215$	−5.08903	−	25.5843i	−0.347069	−	1.74483i
$216$	−0.00461825	−	2.82842i	−0.000314232	−	0.192450i
$217$	−3.19108	−	0.634746i	−0.216625	−	0.0430894i
$218$	1.20570	+	9.11984i	0.0816603	+	0.617673i
$219$	−4.27693	−	0.421241i	−0.289008	−	0.0284648i
$220$	1.83327	+	1.05578i	0.123599	+	0.0711806i
$221$	7.53197	+	2.28480i	0.506655	+	0.153692i
$222$	−14.4619	+	6.56210i	−0.970621	+	0.440420i
$223$	−5.81613	+	5.81613i	−0.389477	+	0.389477i	−0.874501	−	0.485024i	$-0.838811\pi$
$223$	−5.81613	+	5.81613i	−0.389477	+	0.389477i	0.485024	+	0.874501i	$0.338811\pi$
$224$	−1.25576	+	1.18258i	−0.0839043	+	0.0790147i
$225$	6.73038	+	6.73038i	0.448692	+	0.448692i
$226$	−23.3614	−	8.77809i	−1.55398	−	0.583910i
$227$	1.98614	−	6.54744i	0.131825	−	0.434569i	−0.866033	−	0.499987i	$-0.833338\pi$
$227$	1.98614	−	6.54744i	0.131825	−	0.434569i	0.997858	+	0.0654183i	$0.0208382\pi$
$228$	1.44395	+	1.87756i	0.0956279	+	0.124344i
$229$	2.03161	−	20.6273i	0.134253	−	1.36309i	−0.658055	−	0.752970i	$-0.728621\pi$
$229$	2.03161	−	20.6273i	0.134253	−	1.36309i	0.792308	−	0.610122i	$-0.208879\pi$
$230$	33.5375	+	25.7053i	2.21140	+	1.69496i
$231$	0.0165148	−	0.0830255i	0.00108659	−	0.00546268i
$232$	0.488796	−	2.47849i	0.0320910	−	0.162721i
$233$	3.58964	−	0.714024i	0.235165	−	0.0467773i	−0.0761006	−	0.997100i	$-0.524247\pi$
$233$	3.58964	−	0.714024i	0.235165	−	0.0467773i	0.311266	+	0.950323i	$0.399247\pi$
$234$	2.29035	−	0.778858i	0.149725	−	0.0509156i
$235$	14.9192	−	27.9118i	0.973219	−	1.82076i
$236$	3.38501	−	3.17733i	0.220345	−	0.206827i
$237$	−0.611026	−	6.20385i	−0.0396904	−	0.402983i
$238$	−1.04689	+	1.68558i	−0.0678598	+	0.109260i
$239$	−24.2794	+	10.0569i	−1.57050	+	0.650524i	−0.986874	−	0.161495i	$-0.948368\pi$
$239$	−24.2794	+	10.0569i	−1.57050	+	0.650524i	−0.583631	+	0.812019i	$0.698368\pi$
$240$	−14.7303	−	3.91263i	−0.950839	−	0.252559i
$241$	16.6511	+	6.89710i	1.07259	+	0.444281i	0.847904	−	0.530150i	$-0.177865\pi$
$241$	16.6511	+	6.89710i	1.07259	+	0.444281i	0.224685	+	0.974431i	$0.427865\pi$
$242$	−12.5514	+	9.00457i	−0.806837	+	0.578836i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	−8.93118	−	14.3277i	−0.571760	−	0.917237i
$245$	25.1844	−	7.63961i	1.60897	−	0.488077i
$246$	3.04023	+	3.46292i	0.193838	+	0.220788i
$247$	−1.12550	+	1.68444i	−0.0716141	+	0.107178i
$248$	23.3601	+	19.1074i	1.48337	+	1.21332i
$249$	8.10770	−	5.41739i	0.513804	−	0.343313i
$250$	21.0781	−	12.1847i	1.33309	−	0.770630i
$251$	0.553541	+	0.674491i	0.0349392	+	0.0425735i	0.790187	−	0.612866i	$-0.209983\pi$
$251$	0.553541	+	0.674491i	0.0349392	+	0.0425735i	−0.755248	+	0.655439i	$0.772483\pi$
$252$	0.0405493	+	0.608512i	0.00255436	+	0.0383326i
$253$	1.91990	−	1.02621i	0.120703	−	0.0645171i
$254$	−18.2706	+	0.608074i	−1.14640	+	0.0381539i
$255$	−17.5320			−1.09790
$256$	15.4366	−	4.20836i	0.964790	−	0.263022i
$257$	−11.2540			−0.702005			−0.351002	−	0.936375i	$-0.614159\pi$
$257$	−11.2540			−0.702005			−0.351002	+	0.936375i	$0.614159\pi$
$258$	9.67649	−	0.322048i	0.602432	−	0.0200498i
$259$	3.01992	−	1.61418i	0.187649	−	0.100300i
$260$	−0.866736	−	13.0069i	−0.0537527	−	0.806652i
$261$	−0.566612	−	0.690419i	−0.0350724	−	0.0427359i
$262$	−16.2608	+	9.39999i	−1.00460	+	0.580733i
$263$	3.00757	−	2.00960i	0.185455	−	0.123917i	−0.459377	−	0.888241i	$-0.651927\pi$
$263$	3.00757	−	2.00960i	0.185455	−	0.123917i	0.644832	+	0.764324i	$0.276927\pi$
$264$	−0.497135	+	0.607782i	−0.0305965	+	0.0374064i
$265$	−3.81355	+	5.70739i	−0.234265	+	0.350602i
$266$	−0.336945	−	0.383790i	−0.0206594	−	0.0235317i
$267$	−5.89236	+	1.78743i	−0.360607	+	0.109389i
$268$	−2.90179	−	4.65515i	−0.177255	−	0.284359i
$269$	−19.7006	−	16.1679i	−1.20117	−	0.985774i	−0.999981	−	0.00622170i	$-0.998020\pi$
$269$	−19.7006	−	16.1679i	−1.20117	−	0.985774i	−0.201189	−	0.979553i	$-0.564480\pi$
$270$	−4.37835	+	3.14109i	−0.266458	+	0.191161i
$271$	8.63166	+	3.57535i	0.524336	+	0.217187i	0.629120	−	0.777308i	$-0.283415\pi$
$271$	8.63166	+	3.57535i	0.524336	+	0.217187i	−0.104784	+	0.994495i	$0.533415\pi$
$272$	15.9191	−	9.23717i	0.965238	−	0.560086i
$273$	−0.481909	+	0.199613i	−0.0291665	+	0.0120811i
$274$	−0.212226	+	0.341701i	−0.0128210	+	0.0206429i
$275$	−0.258996	−	2.62963i	−0.0156181	−	0.158573i
$276$	−11.4351	+	10.7335i	−0.688313	+	0.646084i
$277$	−15.3348	+	28.6893i	−0.921376	+	1.72377i	−0.273777	+	0.961793i	$0.588273\pi$
$277$	−15.3348	+	28.6893i	−0.921376	+	1.72377i	−0.647600	+	0.761981i	$0.724227\pi$
$278$	−16.1843	+	5.50367i	−0.970672	+	0.330088i
$279$	10.4649	−	2.08161i	0.626520	−	0.124623i
$280$	3.22416	+	0.635855i	0.192681	+	0.0379996i
$281$	−3.60224	+	18.1097i	−0.214891	+	1.08033i	0.711187	+	0.703002i	$0.248158\pi$
$281$	−3.60224	+	18.1097i	−0.214891	+	1.08033i	−0.926079	+	0.377330i	$0.876842\pi$
$282$	9.32319	+	7.14587i	0.555188	+	0.425531i
$283$	1.49896	−	15.2192i	0.0891041	−	0.904689i	−0.841889	−	0.539651i	$-0.818556\pi$
$283$	1.49896	−	15.2192i	0.0891041	−	0.904689i	0.930993	−	0.365038i	$-0.118944\pi$
$284$	−8.87746	−	11.5433i	−0.526780	−	0.684968i
$285$	1.30991	−	4.31818i	0.0775922	−	0.255787i
$286$	−0.628667	−	0.236223i	−0.0371739	−	0.0139682i
$287$	−0.702580	−	0.702580i	−0.0414720	−	0.0414720i
$288$	2.32059	−	5.15896i	0.136742	−	0.303995i
$289$	2.94966	−	2.94966i	0.173509	−	0.173509i
$290$	−4.38273	+	1.98867i	−0.257363	+	0.116779i
$291$	10.2577	+	3.11165i	0.601320	+	0.182408i
$292$	−7.44837	−	4.28952i	−0.435883	−	0.251025i
$293$	4.38444	+	0.431829i	0.256142	+	0.0252277i	0.225273	−	0.974296i	$-0.427673\pi$
$293$	4.38444	+	0.431829i	0.256142	+	0.0252277i	0.0308687	+	0.999523i	$0.490173\pi$
$294$	1.28025	+	9.68374i	0.0746657	+	0.564767i
$295$	−8.67485	−	1.72553i	−0.505069	−	0.100464i
$296$	−31.7621	+	0.0518612i	−1.84613	+	0.00301437i
$297$	0.0541592	+	0.272277i	0.00314263	+	0.0157991i
$298$	11.8011	−	23.9632i	0.683621	−	1.38815i
$299$	−11.8302	−	6.32335i	−0.684155	−	0.365689i
$300$	6.72496	+	17.8090i	0.388266	+	1.02820i
$301$	−2.07753	+	0.204619i	−0.119747	+	0.0117941i
$302$	28.6268	−	6.69127i	1.64729	−	0.385039i
$303$	−3.78336	−	9.13384i	−0.217348	−	0.524725i
$304$	1.08574	+	4.61108i	0.0622716	+	0.264463i
$305$	−12.3091	+	29.7168i	−0.704816	+	1.70158i
$306$	1.05649	−	6.42080i	0.0603955	−	0.367053i
$307$	12.6421	−	15.4044i	0.721522	−	0.879177i	−0.275090	−	0.961418i	$-0.588708\pi$
$307$	12.6421	−	15.4044i	0.721522	−	0.879177i	0.996612	+	0.0822412i	$0.0262078\pi$
$308$	0.0984660	−	0.137726i	0.00561062	−	0.00784764i
$309$	1.03314	+	3.40580i	0.0587731	+	0.193749i
$310$	3.72916	−	57.3745i	0.211802	−	3.25865i
$311$	26.0006	+	17.3730i	1.47436	+	0.985135i	0.994153	+	0.107978i	$0.0344377\pi$
$311$	26.0006	+	17.3730i	1.47436	+	0.985135i	0.480205	+	0.877156i	$0.340562\pi$
$312$	4.81578	+	0.466375i	0.272640	+	0.0264033i
$313$	0.301562	+	0.451319i	0.0170453	+	0.0255101i	0.839894	−	0.542750i	$-0.182617\pi$
$313$	0.301562	+	0.451319i	0.0170453	+	0.0255101i	−0.822849	+	0.568260i	$0.807617\pi$
$314$	6.62541	−	24.7803i	0.373894	−	1.39843i
$315$	0.898138	−	0.737083i	0.0506043	−	0.0415299i
$316$	3.99477	−	11.8104i	0.224723	−	0.664389i
$317$	12.0142	+	22.4770i	0.674786	+	1.26243i	0.953306	+	0.302005i	$0.0976558\pi$
$317$	12.0142	+	22.4770i	0.674786	+	1.26243i	−0.278521	+	0.960430i	$0.589844\pi$
$318$	−1.86043	−	1.74058i	−0.104328	−	0.0976069i
$319$			0.247950i			0.0138825i
$320$	−23.6261	−	19.2607i	−1.32074	−	1.07670i
$321$		−	3.23934i		−	0.180803i
$322$	2.31032	−	2.46940i	0.128749	−	0.137614i
$323$	2.56875	+	4.80579i	0.142929	+	0.267401i
$324$	−0.886529	−	1.79278i	−0.0492516	−	0.0995990i
$325$	−12.5860	+	10.3291i	−0.698147	+	0.572955i
$326$	−4.24513	−	1.13500i	−0.235116	−	0.0628620i
$327$	3.61388	+	5.40855i	0.199848	+	0.299094i
$328$	2.68973	+	8.81503i	0.148516	+	0.486728i
$329$	−2.10595	−	1.40715i	−0.116105	−	0.0775789i
$330$	1.49277	+	0.0970253i	0.0821742	+	0.00534106i
$331$	−0.737347	−	2.43071i	−0.0405283	−	0.133604i	0.934342	−	0.356378i	$-0.115989\pi$
$331$	−0.737347	−	2.43071i	−0.0405283	−	0.133604i	−0.974870	+	0.222775i	$0.928489\pi$
$332$	19.2381	−	3.19774i	1.05583	−	0.175499i
$333$	−7.12399	+	8.68061i	−0.390392	+	0.475695i
$334$	18.9164	+	3.11254i	1.03506	+	0.170311i
$335$	−3.99929	+	9.65515i	−0.218505	+	0.527517i
$336$	−0.427161	+	1.14248i	−0.0233036	+	0.0623273i
$337$	1.01266	+	2.44477i	0.0551630	+	0.133175i	0.949058	−	0.315101i	$-0.102038\pi$
$337$	1.01266	+	2.44477i	0.0551630	+	0.133175i	−0.893895	+	0.448276i	$0.852038\pi$
$338$	−3.24261	−	13.8726i	−0.176375	−	0.754572i
$339$	−17.5617	+	1.72968i	−0.953820	+	0.0939431i
$340$	−31.9543	−	14.4364i	−1.73296	−	0.782923i
$341$	−2.61234	−	1.39632i	−0.141466	−	0.0756151i
$342$	1.50253	+	0.739948i	0.0812473	+	0.0400118i
$343$	−0.827315	−	4.15919i	−0.0446708	−	0.224575i
$344$	17.9018	+	7.38094i	0.965200	+	0.397954i
$345$	29.3050	+	5.82913i	1.57773	+	0.313830i
$346$	−10.6957	+	1.41403i	−0.575002	+	0.0760189i
$347$	−21.0844	−	2.07664i	−1.13187	−	0.111480i	−0.485311	−	0.874342i	$-0.661294\pi$
$347$	−21.0844	−	2.07664i	−1.13187	−	0.111480i	−0.646561	+	0.762862i	$0.723794\pi$
$348$	−0.464210	−	1.72494i	−0.0248842	−	0.0924665i
$349$	−2.52716	−	0.766607i	−0.135276	−	0.0410355i	0.221921	−	0.975065i	$-0.428767\pi$
$349$	−2.52716	−	0.766607i	−0.135276	−	0.0410355i	−0.357197	+	0.934029i	$0.616267\pi$
$350$	−1.69603	−	3.73781i	−0.0906568	−	0.199794i
$351$	1.20958	−	1.20958i	0.0645625	−	0.0645625i
$352$	−1.40656	+	0.698402i	−0.0749697	+	0.0372250i
$353$	−1.37562	−	1.37562i	−0.0732169	−	0.0732169i	0.669550	−	0.742767i	$-0.266487\pi$
$353$	−1.37562	−	1.37562i	−0.0732169	−	0.0732169i	−0.742767	+	0.669550i	$0.766487\pi$
$354$	1.15470	−	3.07303i	0.0613716	−	0.163330i
$355$	−8.05335	+	26.5483i	−0.427428	+	1.40904i
$356$	−12.2114	−	1.59414i	−0.647202	−	0.0844892i
$357$	−0.137524	+	1.39630i	−0.00727854	+	0.0739003i
$358$	−6.09892	+	7.95723i	−0.322338	+	0.420553i
$359$	−5.83010	+	29.3099i	−0.307701	+	1.54692i	0.449226	+	0.893418i	$0.351700\pi$
$359$	−5.83010	+	29.3099i	−0.307701	+	1.54692i	−0.756927	+	0.653499i	$0.773300\pi$
$360$	−10.5666	+	2.11976i	−0.556907	+	0.111721i
$361$	17.2593	−	3.43309i	0.908385	−	0.180689i
$362$	10.8425	+	31.8839i	0.569867	+	1.67578i
$363$	−5.14903	+	9.63317i	−0.270254	+	0.505610i
$364$	−1.04271	−	0.0329985i	−0.0546527	−	0.00172959i
$365$	1.60504	+	16.2963i	0.0840118	+	0.852986i
$366$	−10.1415	−	6.29875i	−0.530105	−	0.329241i
$367$	−15.7493	+	6.52359i	−0.822109	+	0.340529i	−0.753774	−	0.657134i	$-0.771769\pi$
$367$	−15.7493	+	6.52359i	−0.822109	+	0.340529i	−0.0683352	+	0.997662i	$0.521769\pi$
$368$	−29.6803	+	10.1472i	−1.54719	+	0.528960i
$369$	3.01040	+	1.24695i	0.156715	+	0.0649136i
$370$	35.2732	+	49.1672i	1.83377	+	2.55608i
$371$	0.424640	+	0.348493i	0.0220462	+	0.0180929i
$372$	20.7877	+	4.82317i	1.07779	+	0.250070i
$373$	−28.1976	+	8.55366i	−1.46002	+	0.442892i	−0.917698	−	0.397280i	$-0.869954\pi$
$373$	−28.1976	+	8.55366i	−1.46002	+	0.442892i	−0.542321	+	0.840172i	$0.682454\pi$
$374$	−1.35751	+	1.19182i	−0.0701954	+	0.0616273i
$375$	9.56447	−	14.3142i	0.493907	−	0.739184i
$376$	11.1085	+	20.7012i	0.572879	+	1.06759i
$377$	1.27035	−	0.848819i	0.0654262	−	0.0437164i
$378$	0.215822	+	0.373345i	0.0111007	+	0.0192028i
$379$	−0.808597	−	0.985279i	−0.0415348	−	0.0506104i	0.751829	−	0.659358i	$-0.229172\pi$
$379$	−0.808597	−	0.985279i	−0.0415348	−	0.0506104i	−0.793364	+	0.608748i	$0.791672\pi$
$380$	5.94319	−	6.79181i	0.304879	−	0.348413i
$381$	−11.4001	+	6.09348i	−0.584045	+	0.312179i
$382$	0.400179	+	12.0241i	0.0204749	+	0.615205i
$383$	−16.3844			−0.837204			−0.418602	−	0.908170i	$-0.637480\pi$
$383$	−16.3844			−0.837204			−0.418602	+	0.908170i	$0.637480\pi$
$384$	8.47761	−	7.49200i	0.432621	−	0.382324i
$385$	−0.322548			−0.0164386
$386$	−1.15057	−	34.5710i	−0.0585626	−	1.75962i
$387$	6.03772	−	3.22723i	0.306915	−	0.164049i
$388$	16.1338	+	14.1179i	0.819069	+	0.716729i
$389$	13.9275	+	16.9707i	0.706150	+	0.860447i	0.995300	−	0.0968372i	$-0.0308726\pi$
$389$	13.9275	+	16.9707i	0.706150	+	0.860447i	−0.289150	+	0.957284i	$0.593373\pi$
$390$	−4.61317	−	7.98020i	−0.233597	−	0.404093i
$391$	−30.0009	+	20.0459i	−1.51721	+	1.01377i
$392$	−5.64047	+	18.7040i	−0.284887	+	0.944695i
$393$	−7.37857	+	11.0428i	−0.372199	+	0.557036i
$394$	−14.6466	+	12.8588i	−0.737886	+	0.647819i
$395$	−22.7300	+	6.89506i	−1.14367	+	0.346928i
$396$	−0.125489	+	0.540854i	−0.00630606	+	0.0271790i
$397$	4.90078	+	4.02196i	0.245963	+	0.201857i	0.749295	−	0.662237i	$-0.230393\pi$
$397$	4.90078	+	4.02196i	0.245963	+	0.201857i	−0.503332	+	0.864093i	$0.667893\pi$
$398$	−10.2514	−	14.2894i	−0.513856	−	0.716262i
$399$	−0.333639	−	0.138198i	−0.0167028	−	0.00691853i
$400$	−2.40737	+	37.9966i	−0.120368	+	1.89983i
$401$	10.8317	−	4.48664i	0.540909	−	0.224052i	−0.0954645	−	0.995433i	$-0.530434\pi$
$401$	10.8317	−	4.48664i	0.540909	−	0.224052i	0.636374	+	0.771381i	$0.280434\pi$
$402$	−3.29504	−	2.04650i	−0.164341	−	0.102070i
$403$	1.78901	+	18.1642i	0.0891171	+	0.904821i
$404$	0.625435	−	19.7629i	0.0311166	−	0.983241i
$405$	−1.79615	+	3.36036i	−0.0892515	+	0.166978i
$406$	0.124005	+	0.364654i	0.00615425	+	0.0180975i
$407$	3.05756	−	0.608187i	0.151558	−	0.0301467i
$408$	7.21267	−	10.8328i	0.357080	−	0.536302i
$409$	6.12046	−	30.7697i	0.302637	−	1.52146i	−0.467736	−	0.883868i	$-0.654930\pi$
$409$	6.12046	−	30.7697i	0.302637	−	1.52146i	0.770373	−	0.637593i	$-0.220070\pi$
$410$	10.6812	−	13.9357i	0.527507	−	0.688235i
$411$	−0.0278789	+	0.283059i	−0.00137516	+	0.0139623i
$412$	−0.921415	+	7.05821i	−0.0453949	+	0.347733i
$413$	−0.205474	+	0.677357i	−0.0101107	+	0.0333305i
$414$	−3.90076	+	10.3812i	−0.191712	+	0.510209i
$415$	−26.2720	−	26.2720i	−1.28964	−	1.28964i
$416$	8.39333	+	4.81549i	0.411517	+	0.236099i
$417$	−8.54727	+	8.54727i	−0.418562	+	0.418562i
$418$	−0.192121	−	0.423406i	−0.00939693	−	0.0207095i
$419$	−26.4938	−	8.03680i	−1.29431	−	0.392623i	−0.433314	−	0.901243i	$-0.642656\pi$
$419$	−26.4938	−	8.03680i	−1.29431	−	0.392623i	−0.860991	+	0.508620i	$0.830156\pi$
$420$	2.24390	−	0.603871i	0.109491	−	0.0294659i
$421$	5.11652	+	0.503933i	0.249364	+	0.0245602i	0.221927	−	0.975063i	$-0.428765\pi$
$421$	5.11652	+	0.503933i	0.249364	+	0.0245602i	0.0274371	+	0.999624i	$0.491265\pi$
$422$	25.9815	−	3.43491i	1.26476	−	0.167209i
$423$	8.14658	+	1.62046i	0.396100	+	0.0787893i
$424$	−1.95761	−	4.70436i	−0.0950702	−	0.228464i
$425$	8.54409	+	42.9541i	0.414449	+	2.08358i
$426$	−9.23759	−	4.54923i	−0.447563	−	0.220411i
$427$	2.27018	+	1.21344i	0.109862	+	0.0587224i
$428$	2.66737	−	5.90411i	0.128932	−	0.285386i
$429$	−0.472594	+	0.0465465i	−0.0228171	+	0.00224729i
$430$	−8.39651	−	35.9222i	−0.404916	−	1.73232i
$431$	15.6117	+	37.6901i	0.751991	+	1.81547i	0.547965	+	0.836502i	$0.315403\pi$
$431$	15.6117	+	37.6901i	0.751991	+	1.81547i	0.204026	+	0.978965i	$0.434597\pi$
$432$	−0.139580	−	3.99756i	−0.00671553	−	0.192333i
$433$	−4.89223	+	11.8109i	−0.235106	+	0.567595i	−0.996764	−	0.0803836i	$-0.974385\pi$
$433$	−4.89223	+	11.8109i	−0.235106	+	0.567595i	0.761658	+	0.647979i	$0.224385\pi$
$434$	−4.54024	−	0.747058i	−0.217938	−	0.0358599i
$435$	−2.15895	+	2.63069i	−0.103514	+	0.126132i
$436$	2.13318	+	12.8335i	0.102161	+	0.614615i
$437$	−2.69585	−	8.88703i	−0.128960	−	0.425124i
$438$	−6.06496	−	0.394203i	−0.289795	−	0.0188358i
$439$	11.5818	+	7.73868i	0.552767	+	0.369347i	0.800362	−	0.599516i	$-0.204640\pi$
$439$	11.5818	+	7.73868i	0.552767	+	0.369347i	−0.247596	+	0.968863i	$0.579640\pi$
$440$	2.64086	+	1.40603i	0.125898	+	0.0670299i
$441$	3.83733	+	5.74297i	0.182730	+	0.273475i
$442$	10.7534	+	2.87509i	0.511487	+	0.136754i
$443$	−15.3308	+	12.5817i	−0.728390	+	0.597774i	−0.923767	−	0.382954i	$-0.874907\pi$
$443$	−15.3308	+	12.5817i	−0.728390	+	0.597774i	0.195377	+	0.980728i	$0.437407\pi$
$444$	−20.1322	+	9.95538i	−0.955434	+	0.472462i
$445$	11.0598	+	20.6914i	0.524285	+	0.980869i
$446$	−7.94711	+	8.49430i	−0.376306	+	0.402217i
$447$		−	18.8878i		−	0.893364i
$448$	−1.71931	+	1.73057i	−0.0812296	+	0.0817619i
$449$		−	23.1303i		−	1.09159i	−0.837920	−	0.545793i	$-0.816229\pi$
$449$		−	23.1303i		−	1.09159i	0.837920	−	0.545793i	$-0.183771\pi$
$450$	9.82954	+	9.19633i	0.463369	+	0.433519i
$451$	−0.426415	−	0.797766i	−0.0200791	−	0.0375653i
$452$	−33.4327	−	11.3083i	−1.57254	−	0.531897i
$453$	16.0692	−	13.1877i	0.754998	−	0.619611i
$454$	2.49928	−	9.34778i	0.117297	−	0.438713i
$455$	1.10419	+	1.65254i	0.0517654	+	0.0774724i
$456$	2.12925	+	2.58587i	0.0997111	+	0.121095i
$457$	−23.5139	−	15.7115i	−1.09994	−	0.734953i	−0.133291	−	0.991077i	$-0.542555\pi$
$457$	−23.5139	−	15.7115i	−1.09994	−	0.734953i	−0.966644	+	0.256124i	$0.917555\pi$
$458$	1.90121	−	29.2509i	0.0888379	−	1.36680i
$459$	−1.33567	−	4.40312i	−0.0623438	−	0.205520i
$460$	48.6122	+	34.7550i	2.26656	+	1.62046i
$461$	6.11683	−	7.45338i	0.284889	−	0.347139i	−0.610827	−	0.791764i	$-0.709163\pi$
$461$	6.11683	−	7.45338i	0.284889	−	0.347139i	0.895717	+	0.444625i	$0.146663\pi$
$462$	0.0194369	−	0.118128i	0.000904287	−	0.00549580i
$463$	9.09892	−	21.9667i	0.422863	−	1.02088i	−0.558636	−	0.829413i	$-0.688675\pi$
$463$	9.09892	−	21.9667i	0.422863	−	1.02088i	0.981499	−	0.191468i	$-0.0613249\pi$
$464$	0.574289	−	3.52616i	0.0266607	−	0.163698i
$465$	−15.5582	−	37.5608i	−0.721494	−	1.74184i
$466$	5.04012	−	1.17808i	0.233479	−	0.0545737i
$467$	−11.1659	+	1.09974i	−0.516695	+	0.0508900i	−0.353004	−	0.935622i	$-0.614840\pi$
$467$	−11.1659	+	1.09974i	−0.516695	+	0.0508900i	−0.163691	+	0.986512i	$0.552340\pi$
$468$	3.20061	−	1.20860i	0.147948	−	0.0558677i
$469$	0.737595	+	0.394253i	0.0340590	+	0.0182049i
$470$	19.7742	−	40.1532i	0.912116	−	1.85213i
$471$	−3.53851	−	17.7893i	−0.163046	−	0.819687i
$472$	4.63501	−	4.65018i	0.213344	−	0.214042i
$473$	−1.86403	−	0.370779i	−0.0857083	−	0.0170484i
$474$	−1.15548	−	8.73997i	−0.0530729	−	0.401440i
$475$	−11.2181	−	1.10488i	−0.514721	−	0.0506955i
$476$	−1.40041	+	2.43170i	−0.0641879	+	0.111457i
$477$	−1.72393	−	0.522948i	−0.0789333	−	0.0239442i
$478$	−33.8442	+	15.3568i	−1.54800	+	0.702404i
$479$	−12.2420	+	12.2420i	−0.559353	+	0.559353i	−0.929123	−	0.369770i	$-0.879436\pi$
$479$	−12.2420	+	12.2420i	−0.559353	+	0.559353i	0.369770	+	0.929123i	$0.379436\pi$
$480$	−21.0044	−	4.83730i	−0.958713	−	0.220792i
$481$	−13.5831	−	13.5831i	−0.619335	−	0.619335i
$482$	23.8596	+	8.96528i	1.08677	+	0.408358i
$483$	0.694124	−	2.28822i	0.0315838	−	0.104118i
$484$	−17.3170	+	13.3178i	−0.787137	+	0.605354i
$485$	4.00337	−	40.6469i	0.181784	−	1.84568i
$486$	−1.12244	−	0.860308i	−0.0509149	−	0.0390244i
$487$	5.87251	−	29.5231i	0.266109	−	1.33782i	−0.584231	−	0.811587i	$-0.698604\pi$
$487$	5.87251	−	29.5231i	0.266109	−	1.33782i	0.850340	−	0.526233i	$-0.176396\pi$
$488$	−13.2976	−	19.8311i	−0.601954	−	0.897711i
$489$	−3.04750	+	0.606184i	−0.137812	+	0.0274126i
$490$	35.2371	−	11.9828i	1.59185	−	0.541326i
$491$	−11.9237	+	22.3076i	−0.538108	+	1.00673i	0.455107	+	0.890437i	$0.349601\pi$
$491$	−11.9237	+	22.3076i	−0.538108	+	1.00673i	−0.993215	+	0.116293i	$0.962899\pi$
$492$	4.46006	+	4.75158i	0.201075	+	0.214218i
$493$	−0.402814	−	4.08984i	−0.0181418	−	0.184197i
$494$	−1.51159	+	2.43378i	−0.0680094	+	0.109501i
$495$	0.977255	−	0.404792i	0.0439244	−	0.0181941i
$496$	33.9167	+	25.9081i	1.52290	+	1.16331i
$497$	2.05122	+	0.849644i	0.0920099	+	0.0381118i
$498$	11.2048	−	8.03850i	0.502100	−	0.360214i
$499$	19.0506	+	15.6344i	0.852821	+	0.699892i	0.955554	−	0.294817i	$-0.0952585\pi$
$499$	19.0506	+	15.6344i	0.852821	+	0.699892i	−0.102732	+	0.994709i	$0.532759\pi$
$500$	29.2192	−	18.2138i	1.30672	−	0.814547i
$501$	12.9721	−	3.93504i	0.579550	−	0.175805i
$502$	0.814120	+	0.927308i	0.0363360	+	0.0413878i
$503$	15.5053	−	23.2053i	0.691345	−	1.03467i	−0.305254	−	0.952271i	$-0.598741\pi$
$503$	15.5053	−	23.2053i	0.691345	−	1.03467i	0.996599	−	0.0824005i	$-0.0262587\pi$
$504$	0.0859386	+	0.858182i	0.00382801	+	0.0382265i
$505$	−31.3214	+	20.9283i	−1.39378	+	0.931296i
$506$	2.66537	−	1.54079i	0.118490	−	0.0684963i
$507$	−6.39078	−	7.78719i	−0.283825	−	0.345841i
$508$	−25.7957	+	1.71894i	−1.14450	+	0.0762656i
$509$	29.0181	−	15.5105i	1.28621	−	0.687491i	0.320529	−	0.947239i	$-0.396139\pi$
$509$	29.0181	−	15.5105i	1.28621	−	0.687491i	0.965677	+	0.259747i	$0.0836392\pi$
$510$	−24.7803	+	0.824724i	−1.09729	+	0.0365194i
$511$	1.31048			0.0579721
$512$	21.6207	−	6.67438i	0.955507	−	0.294969i
$513$	1.18429			0.0522879
$514$	−15.9067	+	0.529400i	−0.701616	+	0.0233508i
$515$	11.9597	−	6.39259i	0.527007	−	0.281691i
$516$	13.6619	−	0.910384i	0.601432	−	0.0400774i
$517$	−1.46284	−	1.78247i	−0.0643356	−	0.0783931i
$518$	4.19252	−	2.42360i	0.184209	−	0.106487i
$519$	−6.34310	+	4.23832i	−0.278431	+	0.186042i
$520$	−1.83693	−	18.3435i	−0.0805546	−	0.804418i
$521$	2.48988	−	3.72637i	0.109084	−	0.163255i	−0.772911	−	0.634514i	$-0.781200\pi$
$521$	2.48988	−	3.72637i	0.109084	−	0.163255i	0.881995	+	0.471259i	$0.156200\pi$
$522$	−0.833345	−	0.949205i	−0.0364745	−	0.0415456i
$523$	−12.0654	+	3.66001i	−0.527584	+	0.160041i	−0.542830	−	0.839843i	$-0.682647\pi$
$523$	−12.0654	+	3.66001i	−0.527584	+	0.160041i	0.0152454	+	0.999884i	$0.495147\pi$
$524$	−22.5413	+	14.0512i	−0.984723	+	0.613828i
$525$	−2.24358	−	1.84126i	−0.0979178	−	0.0803591i
$526$	4.15646	−	2.98190i	0.181230	−	0.130017i
$527$	45.3580	+	18.7879i	1.97582	+	0.818413i
$528$	−0.674075	+	0.882443i	−0.0293354	+	0.0384034i
$529$	35.5627	−	14.7305i	1.54620	−	0.640458i
$530$	−5.12171	+	8.24639i	−0.222473	+	0.358200i
$531$	−0.227527	−	2.31012i	−0.00987384	−	0.100251i
$532$	−0.494302	−	0.526611i	−0.0214307	−	0.0228315i
$533$	−2.62751	+	4.91573i	−0.113810	+	0.212924i
$534$	−8.24437	+	2.80359i	−0.356769	+	0.121323i
$535$	−12.1056	+	2.40796i	−0.523372	+	0.104105i
$536$	−4.32047	−	6.44323i	−0.186616	−	0.278305i
$537$	−1.38304	+	6.95301i	−0.0596826	+	0.300045i
$538$	−28.6061	−	21.9255i	−1.23329	−	0.945274i
$539$	0.187944	−	1.90823i	0.00809533	−	0.0821933i
$540$	−6.04074	+	4.64568i	−0.259952	+	0.199918i
$541$	−0.462150	+	1.52350i	−0.0198694	+	0.0655005i	−0.966314	−	0.257364i	$-0.917146\pi$
$541$	−0.462150	+	1.52350i	−0.0198694	+	0.0655005i	0.946445	+	0.322865i	$0.104646\pi$
$542$	12.3684	+	4.64747i	0.531270	+	0.199626i
$543$	16.8385	+	16.8385i	0.722609	+	0.722609i
$544$	22.0660	−	13.8050i	0.946073	−	0.591882i
$545$	17.5257	−	17.5257i	0.750720	−	0.750720i
$546$	−0.671755	+	0.304809i	−0.0287485	+	0.0130446i
$547$	5.04098	+	1.52916i	0.215537	+	0.0653823i	0.396206	−	0.918161i	$-0.370326\pi$
$547$	5.04098	+	1.52916i	0.215537	+	0.0653823i	−0.180670	+	0.983544i	$0.557826\pi$
$548$	−0.283892	+	0.492954i	−0.0121273	+	0.0210580i
$549$	−8.40105	−	0.827431i	−0.358548	−	0.0353139i
$550$	−0.489774	−	3.70462i	−0.0208840	−	0.157965i
$551$	1.03744	+	0.206359i	0.0441962	+	0.00879118i
$552$	−15.6578	+	15.7091i	−0.666442	+	0.668622i
$553$	0.370847	+	1.86437i	0.0157700	+	0.0792812i
$554$	−20.3250	+	41.2717i	−0.863529	+	1.75347i
$555$	37.7356	+	20.1701i	1.60179	+	0.856173i
$556$	−22.6166	+	8.54039i	−0.959156	+	0.362193i
$557$	6.06068	−	0.596925i	0.256799	−	0.0252925i	0.0312018	−	0.999513i	$-0.490067\pi$
$557$	6.06068	−	0.596925i	0.256799	−	0.0252925i	0.225598	+	0.974221i	$0.427567\pi$
$558$	14.6936	−	3.43449i	0.622028	−	0.145394i
$559$	4.48158	+	10.8195i	0.189551	+	0.457616i
$560$	4.58704	+	0.747069i	0.193838	+	0.0315694i
$561$	−0.488823	+	1.18012i	−0.0206381	+	0.0498248i
$562$	−4.23962	+	25.7662i	−0.178837	+	1.08688i
$563$	−5.34202	+	6.50927i	−0.225139	+	0.274333i	−0.873313	−	0.487160i	$-0.838033\pi$
$563$	−5.34202	+	6.50927i	−0.225139	+	0.274333i	0.648174	+	0.761492i	$0.275533\pi$
$564$	13.5138	+	9.66163i	0.569035	+	0.406828i
$565$	19.5184	+	64.3434i	0.821143	+	2.70695i
$566$	1.40275	−	21.5818i	0.0589621	−	0.907153i
$567$	0.253541	+	0.169410i	0.0106477	+	0.00711457i
$568$	−13.0907	−	15.8980i	−0.549273	−	0.667067i
$569$	−16.2956	−	24.3880i	−0.683146	−	1.02240i	−0.997329	−	0.0730377i	$-0.976731\pi$
$569$	−16.2956	−	24.3880i	−0.683146	−	1.02240i	0.314183	−	0.949362i	$-0.398269\pi$
$570$	1.64833	−	6.16507i	0.0690410	−	0.258226i
$571$	−5.71915	+	4.69359i	−0.239339	+	0.196421i	−0.746415	−	0.665481i	$-0.768226\pi$
$571$	−5.71915	+	4.69359i	−0.239339	+	0.196421i	0.507076	+	0.861902i	$0.330726\pi$
$572$	−0.899690	−	0.304312i	−0.0376179	−	0.0127239i
$573$	4.01018	+	7.50251i	0.167528	+	0.313422i
$574$	−1.02610	−	0.959998i	−0.0428285	−	0.0400695i
$575$		−	74.6392i		−	3.11267i
$576$	3.03732	−	7.40099i	0.126555	−	0.308375i
$577$		−	35.1518i		−	1.46339i	−0.681633	−	0.731694i	$-0.738730\pi$
$577$		−	35.1518i		−	1.46339i	0.681633	−	0.731694i	$-0.261270\pi$
$578$	4.03039	−	4.30790i	0.167642	−	0.179185i
$579$	−11.5298	−	21.5708i	−0.479164	−	0.896453i
$580$	−6.10114	+	3.01701i	−0.253336	+	0.125275i
$581$	−2.29846	+	1.88630i	−0.0953563	+	0.0782569i
$582$	14.6450	+	3.91557i	0.607054	+	0.162306i
$583$	0.277850	+	0.415831i	0.0115074	+	0.0172220i
$584$	−10.7295	−	5.71256i	−0.443992	−	0.236387i
$585$	−5.41940	−	3.62113i	−0.224065	−	0.149715i
$586$	6.21741	+	0.404112i	0.256839	+	0.0166937i
$587$	6.52729	+	21.5176i	0.269410	+	0.888126i	0.982374	+	0.186925i	$0.0598522\pi$
$587$	6.52729	+	21.5176i	0.269410	+	0.888126i	−0.712964	+	0.701200i	$0.752648\pi$
$588$	2.26508	+	13.6271i	0.0934103	+	0.561971i
$589$	−8.01644	+	9.76806i	−0.330312	+	0.402486i
$590$	−12.3425	−	2.03085i	−0.508131	−	0.0836087i
$591$	−5.27405	+	12.7327i	−0.216945	+	0.523752i
$592$	−44.8911	+	1.56743i	−1.84501	+	0.0644208i
$593$	5.71437	+	13.7957i	0.234661	+	0.566522i	0.996715	−	0.0809918i	$-0.0258087\pi$
$593$	5.71437	+	13.7957i	0.234661	+	0.566522i	−0.762054	+	0.647514i	$0.775809\pi$
$594$	0.0893584	+	0.382296i	0.00366642	+	0.0156858i
$595$	5.32031	−	0.524004i	0.218111	−	0.0214821i
$596$	15.5528	−	34.4254i	0.637068	−	1.41012i
$597$	−10.9670	−	5.86200i	−0.448851	−	0.239916i
$598$	−17.0186	−	8.38111i	−0.695941	−	0.342729i
$599$	0.275330	+	1.38418i	0.0112497	+	0.0565560i	0.986002	−	0.166731i	$-0.0533212\pi$
$599$	0.275330	+	1.38418i	0.0112497	+	0.0565560i	−0.974753	+	0.223287i	$0.928321\pi$
$600$	10.3430	+	24.8554i	0.422252	+	1.01472i
$601$	28.9309	+	5.75472i	1.18012	+	0.234740i	0.745893	−	0.666065i	$-0.232023\pi$
$601$	28.9309	+	5.75472i	1.18012	+	0.234740i	0.434223	+	0.900805i	$0.357023\pi$
$602$	−2.92682	+	0.386944i	−0.119288	+	0.0157707i
$603$	−2.72955	−	0.268837i	−0.111156	−	0.0109479i
$604$	40.1473	−	10.8043i	1.63357	−	0.439620i
$605$	39.8273	+	12.0815i	1.61921	+	0.491182i
$606$	−5.77718	−	12.7321i	−0.234682	−	0.517205i
$607$	21.2400	−	21.2400i	0.862106	−	0.862106i	−0.129477	−	0.991582i	$-0.541330\pi$
$607$	21.2400	−	21.2400i	0.862106	−	0.862106i	0.991582	+	0.129477i	$0.0413298\pi$
$608$	1.75153	+	6.46636i	0.0710340	+	0.262246i
$609$	0.192581	+	0.192581i	0.00780378	+	0.00780378i
$610$	−16.0001	+	42.5816i	−0.647827	+	1.72408i
$611$	−4.12453	+	13.5967i	−0.166860	+	0.550065i
$612$	1.19123	−	9.12506i	0.0481528	−	0.368859i
$613$	0.277800	−	2.82055i	0.0112202	−	0.113921i	−0.987943	−	0.154817i	$-0.950521\pi$
$613$	0.277800	−	2.82055i	0.0112202	−	0.113921i	0.999163	+	0.0408960i	$0.0130212\pi$
$614$	17.1441	−	22.3678i	0.691879	−	0.902691i
$615$	2.42215	−	12.1770i	0.0976706	−	0.491023i
$616$	0.132696	−	0.199298i	0.00534648	−	0.00802993i
$617$	−20.3850	+	4.05484i	−0.820671	+	0.163242i	−0.587531	−	0.809202i	$-0.699900\pi$
$617$	−20.3850	+	4.05484i	−0.820671	+	0.163242i	−0.233140	+	0.972443i	$0.574900\pi$
$618$	1.62048	+	4.76526i	0.0651853	+	0.191687i
$619$	2.69417	−	5.04043i	0.108288	−	0.202592i	−0.821941	−	0.569573i	$-0.807109\pi$
$619$	2.69417	−	5.04043i	0.108288	−	0.202592i	0.930228	+	0.366981i	$0.119609\pi$
$620$	2.57196	−	81.2703i	0.103292	−	3.26390i
$621$	0.768624	+	7.80397i	0.0308438	+	0.313163i
$622$	37.5673	+	23.3325i	1.50631	+	0.935548i
$623$	1.73469	−	0.718531i	0.0694988	−	0.0287873i
$624$	6.82871	+	0.432649i	0.273367	+	0.0173198i
$625$	−16.6346	−	6.89027i	−0.665384	−	0.275611i
$626$	0.447467	+	0.623723i	0.0178844	+	0.0249290i
$627$	−0.254145	−	0.208571i	−0.0101496	−	0.00832954i
$628$	8.19887	−	35.3369i	0.327171	−	1.41010i
$629$	−49.4453	+	14.9991i	−1.97151	+	0.598052i
$630$	1.23478	−	1.08406i	0.0491949	−	0.0431902i
$631$	23.8201	−	35.6492i	0.948262	−	1.41917i	0.0407398	−	0.999170i	$-0.487029\pi$
$631$	23.8201	−	35.6492i	0.948262	−	1.41917i	0.907522	−	0.420004i	$-0.137971\pi$
$632$	5.09076	−	16.8812i	0.202499	−	0.671496i
$633$	15.4084	−	10.2956i	0.612429	−	0.409212i
$634$	18.0386	+	31.2045i	0.716405	+	1.23929i
$635$	31.2460	+	38.0733i	1.23996	+	1.51089i
$636$	−2.71146	−	2.37267i	−0.107517	−	0.0940827i
$637$	−10.4200	+	5.56962i	−0.412857	+	0.220676i
$638$	0.0116638	+	0.350460i	0.000461775	+	0.0138748i
$639$	−7.28109			−0.288035
$640$	−34.2999	−	26.1122i	−1.35582	−	1.03218i
$641$	−29.5258			−1.16620			−0.583100	−	0.812401i	$-0.698160\pi$
$641$	−29.5258			−1.16620			−0.583100	+	0.812401i	$0.698160\pi$
$642$	−0.152382	−	4.57859i	−0.00601404	−	0.180702i
$643$	0.454810	−	0.243101i	0.0179360	−	0.00958697i	−0.462404	−	0.886669i	$-0.653013\pi$
$643$	0.454810	−	0.243101i	0.0179360	−	0.00958697i	0.480340	+	0.877082i	$0.340513\pi$
$644$	3.14932	−	3.59901i	0.124101	−	0.141821i
$645$	−16.5485	−	20.1644i	−0.651596	−	0.793972i
$646$	3.85682	+	6.67182i	0.151744	+	0.262499i
$647$	27.2293	−	18.1941i	1.07050	−	0.715282i	0.110099	−	0.993921i	$-0.464883\pi$
$647$	27.2293	−	18.1941i	1.07050	−	0.715282i	0.960396	+	0.278639i	$0.0898832\pi$
$648$	−1.33738	−	2.49227i	−0.0525373	−	0.0979056i
$649$	−0.358020	+	0.535814i	−0.0140535	+	0.0210325i
$650$	−17.3036	+	15.1915i	−0.678703	+	0.595860i
$651$	−3.11350	+	0.944470i	−0.122028	+	0.0370167i
$652$	−6.05359	−	1.40455i	−0.237077	−	0.0550066i
$653$	−24.9106	−	20.4436i	−0.974829	−	0.800021i	0.00497393	−	0.999988i	$-0.498417\pi$
$653$	−24.9106	−	20.4436i	−0.974829	−	0.800021i	−0.979803	+	0.199966i	$0.935917\pi$
$654$	5.36239	+	7.47462i	0.209686	+	0.292281i
$655$	46.7525	+	19.3655i	1.82677	+	0.756673i
$656$	4.21642	+	12.3329i	0.164624	+	0.481519i
$657$	−3.97048	+	1.64463i	−0.154903	+	0.0641631i
$658$	−3.04282	−	1.88985i	−0.118621	−	0.0736740i
$659$	−4.27590	−	43.4140i	−0.166565	−	1.69117i	−0.608050	−	0.793899i	$-0.708048\pi$
$659$	−4.27590	−	43.4140i	−0.166565	−	1.69117i	0.441484	−	0.897269i	$-0.354452\pi$
$660$	2.11449	+	0.0669171i	0.0823064	+	0.00260475i
$661$	6.92977	−	12.9647i	0.269537	−	0.504268i	−0.710343	−	0.703855i	$-0.751460\pi$
$661$	6.92977	−	12.9647i	0.269537	−	0.504268i	0.979880	+	0.199588i	$0.0639603\pi$
$662$	−1.15653	−	3.40095i	−0.0449499	−	0.132182i
$663$	7.71965	−	1.53553i	0.299807	−	0.0596352i
$664$	27.0413	−	5.42477i	1.04941	−	0.210522i
$665$	−0.268444	+	1.34956i	−0.0104098	+	0.0523336i
$666$	−9.66093	+	12.6046i	−0.374353	+	0.488417i
$667$	−0.686501	+	6.97016i	−0.0265814	+	0.269886i
$668$	26.8835	+	3.50951i	1.04015	+	0.135787i
$669$	−2.38767	+	7.87108i	−0.0923125	+	0.304313i
$670$	−5.19854	+	13.8350i	−0.200837	+	0.534493i
$671$	1.65711	+	1.65711i	0.0639720	+	0.0639720i
$672$	−0.550019	+	1.63491i	−0.0212175	+	0.0630680i
$673$	32.5913	−	32.5913i	1.25630	−	1.25630i	0.303460	−	0.952844i	$-0.401858\pi$
$673$	32.5913	−	32.5913i	1.25630	−	1.25630i	0.952844	−	0.303460i	$-0.0981418\pi$
$674$	1.54633	+	3.40788i	0.0595623	+	0.131267i
$675$	9.10835	+	2.76299i	0.350581	+	0.106347i
$676$	−5.23579	−	19.4555i	−0.201376	−	0.748288i
$677$	4.88117	+	0.480754i	0.187599	+	0.0184769i	0.191380	−	0.981516i	$-0.438704\pi$
$677$	4.88117	+	0.480754i	0.187599	+	0.0184769i	−0.00378144	+	0.999993i	$0.501204\pi$
$678$	−24.7409	+	3.27090i	−0.950168	+	0.125618i
$679$	−3.20584	−	0.637682i	−0.123029	−	0.0244720i
$680$	−45.8443	−	18.9017i	−1.75805	−	0.724846i
$681$	−1.33482	−	6.71058i	−0.0511503	−	0.257150i
$682$	−3.75804	−	1.85072i	−0.143903	−	0.0708677i
$683$	−34.5163	−	18.4494i	−1.32073	−	0.705945i	−0.347914	−	0.937526i	$-0.613110\pi$
$683$	−34.5163	−	18.4494i	−1.32073	−	0.705945i	−0.972815	+	0.231582i	$0.925610\pi$
$684$	2.15852	+	0.975184i	0.0825333	+	0.0372871i
$685$	1.07853	−	0.106226i	0.0412086	−	0.00405870i
$686$	−1.36501	−	5.83982i	−0.0521162	−	0.222965i
$687$	−7.93193	−	19.1494i	−0.302622	−	0.730594i
$688$	25.6502	+	9.59033i	0.977903	+	0.365628i
$689$	1.17930	−	2.84707i	0.0449276	−	0.108465i
$690$	41.6949	+	6.86054i	1.58730	+	0.261176i
$691$	−18.7700	+	22.8713i	−0.714044	+	0.870065i	−0.995999	−	0.0893622i	$-0.971517\pi$
$691$	−18.7700	+	22.8713i	−0.714044	+	0.870065i	0.281955	+	0.959428i	$0.409017\pi$
$692$	−15.0511	+	2.50177i	−0.572155	+	0.0951031i
$693$	−0.0245732	−	0.0810070i	−0.000933458	−	0.00307720i
$694$	−29.8991	−	1.94335i	−1.13495	−	0.0737685i
$695$	38.2953	+	25.5881i	1.45262	+	0.970611i
$696$	−0.737271	−	2.41625i	−0.0279462	−	0.0915876i
$697$	8.32959	+	12.4661i	0.315506	+	0.472188i
$698$	−3.60803	−	0.964665i	−0.136566	−	0.0365131i
$699$	2.82919	−	2.32186i	0.107010	−	0.0878208i
$700$	−2.57306	−	5.20335i	−0.0972524	−	0.196668i
$701$	13.0605	+	24.4345i	0.493289	+	0.922878i	0.998215	+	0.0597159i	$0.0190195\pi$
$701$	13.0605	+	24.4345i	0.493289	+	0.922878i	−0.504927	+	0.863162i	$0.668481\pi$
$702$	1.65275	−	1.76655i	0.0623792	−	0.0666743i
$703$		−	13.2992i		−	0.501588i
$704$	−1.95522	+	1.05331i	−0.0736900	+	0.0396981i
$705$		−	31.6488i		−	1.19196i
$706$	−2.00906	−	1.87963i	−0.0756118	−	0.0707410i
$707$	1.42110	+	2.65870i	0.0534461	+	0.0999906i
$708$	1.48753	−	4.39784i	0.0559048	−	0.165281i
$709$	25.7701	−	21.1489i	0.967815	−	0.794265i	−0.0108048	−	0.999942i	$-0.503439\pi$
$709$	25.7701	−	21.1489i	0.967815	−	0.794265i	0.978620	+	0.205676i	$0.0659394\pi$
$710$	−10.1340	+	37.9031i	−0.380322	+	1.42248i
$711$	−3.46335	−	5.18327i	−0.129886	−	0.194388i
$712$	−17.3349	−	1.67877i	−0.649655	−	0.0629145i
$713$	−69.5699	−	46.4851i	−2.60541	−	1.74088i
$714$	−0.128697	+	1.98005i	−0.00481637	+	0.0741015i
$715$	0.525249	+	1.73151i	0.0196432	+	0.0647550i
$716$	−8.24609	+	11.5339i	−0.308171	+	0.431042i
$717$	−16.6718	+	20.3146i	−0.622618	+	0.758662i
$718$	−6.86168	+	41.7018i	−0.256076	+	1.55630i
$719$	3.09252	−	7.46600i	0.115331	−	0.278435i	−0.855664	−	0.517531i	$-0.826851\pi$
$719$	3.09252	−	7.46600i	0.115331	−	0.278435i	0.970996	+	0.239096i	$0.0768512\pi$
$720$	−14.8354	+	3.49320i	−0.552882	+	0.130184i
$721$	−0.415312	−	1.00265i	−0.0154670	−	0.0373407i
$722$	24.2334	−	5.66433i	0.901872	−	0.210805i
$723$	17.9362	−	1.76656i	0.667054	−	0.0656991i
$724$	16.8249	+	44.5556i	0.625294	+	1.65590i
$725$	7.49742	+	4.00746i	0.278447	+	0.148833i
$726$	−6.82465	+	13.8580i	−0.253287	+	0.514320i
$727$	2.60903	+	13.1165i	0.0967637	+	0.486464i	0.998528	+	0.0542361i	$0.0172723\pi$
$727$	2.60903	+	13.1165i	0.0967637	+	0.486464i	−0.901764	+	0.432228i	$0.857728\pi$
$728$	−1.47535	+	0.00240895i	−0.0546800	+	8.92815e-5i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	3.03521	+	22.9582i	0.112338	+	0.849719i
$731$	31.3489	+	3.08760i	1.15948	+	0.114199i
$732$	−14.6306	−	8.42578i	−0.540764	−	0.311426i
$733$	0.622169	+	0.188733i	0.0229803	+	0.00697101i	0.301754	−	0.953386i	$-0.402428\pi$
$733$	0.622169	+	0.188733i	0.0229803	+	0.00697101i	−0.278774	+	0.960357i	$0.589928\pi$
$734$	−21.9537	+	9.96152i	−0.810327	+	0.367686i
$735$	18.6094	−	18.6094i	0.686417	−	0.686417i
$736$	−41.4737	+	15.7386i	−1.52874	+	0.580131i
$737$	0.538404	+	0.538404i	0.0198324	+	0.0198324i
$738$	4.31366	+	1.62087i	0.158788	+	0.0596649i
$739$	−7.72873	+	25.4782i	−0.284306	+	0.937231i	0.692194	+	0.721712i	$0.256644\pi$
$739$	−7.72873	+	25.4782i	−0.284306	+	0.937231i	−0.976500	+	0.215519i	$0.930856\pi$
$740$	52.1692	+	67.8351i	1.91778	+	2.49367i
$741$	−0.198568	+	2.01610i	−0.00729460	+	0.0740633i
$742$	0.616593	+	0.472596i	0.0226358	+	0.0173495i
$743$	2.72721	−	13.7106i	0.100052	−	0.502993i	−0.897966	−	0.440064i	$-0.854956\pi$
$743$	2.72721	−	13.7106i	0.100052	−	0.502993i	0.998018	−	0.0629291i	$-0.0200442\pi$
$744$	29.6089	+	5.83934i	1.08552	+	0.214080i
$745$	−70.5850	+	14.0402i	−2.58603	+	0.514394i
$746$	−39.4530	+	13.4165i	−1.44448	+	0.491211i
$747$	4.59661	−	8.59965i	0.168181	−	0.314645i
$748$	−1.86269	+	1.74841i	−0.0681067	+	0.0639282i
$749$	0.0968189	+	0.983019i	0.00353769	+	0.0359187i
$750$	12.8454	−	20.6821i	0.469046	−	0.755204i
$751$	31.8472	−	13.1915i	1.16212	−	0.481366i	0.283540	−	0.958960i	$-0.408491\pi$
$751$	31.8472	−	13.1915i	1.16212	−	0.481366i	0.878581	+	0.477594i	$0.158491\pi$
$752$	16.6750	+	28.7372i	0.608073	+	1.04794i
$753$	0.806132	+	0.333911i	0.0293771	+	0.0121684i
$754$	1.75562	−	1.25950i	0.0639358	−	0.0458685i
$755$	−61.2282	−	50.2487i	−2.22832	−	1.82874i
$756$	0.322612	+	0.517545i	0.0117333	+	0.0188229i
$757$	11.4896	−	3.48532i	0.417595	−	0.126676i	−0.0744927	−	0.997222i	$-0.523734\pi$
$757$	11.4896	−	3.48532i	0.417595	−	0.126676i	0.492088	+	0.870545i	$0.336234\pi$
$758$	−1.18924	−	1.35459i	−0.0431953	−	0.0492008i
$759$	1.20945	−	1.81007i	0.0439002	−	0.0657013i
$760$	8.08080	−	9.87933i	0.293121	−	0.358361i
$761$	27.5016	−	18.3760i	0.996933	−	0.666129i	0.0538023	−	0.998552i	$-0.482866\pi$
$761$	27.5016	−	18.3760i	0.996933	−	0.666129i	0.943131	+	0.332422i	$0.107866\pi$
$762$	−15.8266	+	9.14899i	−0.573338	+	0.331433i
$763$	−1.25833	−	1.53328i	−0.0455546	−	0.0555084i
$764$	1.13125	+	16.9764i	0.0409272	+	0.614184i
$765$	−15.4619	+	8.26453i	−0.559024	+	0.298805i
$766$	−23.1582	+	0.770740i	−0.836741	+	0.0278480i
$767$	3.97082			0.143378
$768$	11.6301	−	10.9882i	0.419665	−	0.396503i

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41343 - 0.0470411i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.99557 - 0.132979i) q^{4} +(-2.41721 - 2.94538i) q^{5} +(1.22436 - 0.707773i) q^{6} +(-0.253541 + 0.169410i) q^{7} +(2.81435 - 0.281830i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.41343 - 0.0470411i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.99557 - 0.132979i) q^{4} +(-2.41721 - 2.94538i) q^{5} +(1.22436 - 0.707773i) q^{6} +(-0.253541 + 0.169410i) q^{7} +(2.81435 - 0.281830i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-3.55512 - 4.04939i) q^{10} +(-0.265657 + 0.0805862i) q^{11} +(1.69725 - 1.05798i) q^{12} +(1.32231 + 1.08519i) q^{13} +(-0.350393 + 0.251377i) q^{14} +(-3.52024 - 1.45813i) q^{15} +(3.96463 - 0.530737i) q^{16} +(4.25100 - 1.76082i) q^{17} +(0.746147 - 1.20136i) q^{18} +(0.116081 + 1.17859i) q^{19} +(-5.21540 - 5.55629i) q^{20} +(-0.143743 + 0.268925i) q^{21} +(-0.371697 + 0.126400i) q^{22} +(-7.69105 + 1.52985i) q^{23} +(2.34918 - 1.57523i) q^{24} +(-1.85691 + 9.33531i) q^{25} +(1.92005 + 1.47164i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-0.483431 + 0.371787i) q^{28} +(0.259270 - 0.854697i) q^{29} +(-5.04420 - 1.89537i) q^{30} +(7.54481 + 7.54481i) q^{31} +(5.57877 - 0.936661i) q^{32} +(-0.196300 + 0.196300i) q^{33} +(5.92566 - 2.68877i) q^{34} +(1.11184 + 0.337273i) q^{35} +(0.998114 - 1.73314i) q^{36} +(-11.1755 - 1.10069i) q^{37} +(0.219515 + 1.66040i) q^{38} +(1.67773 + 0.333722i) q^{39} +(-7.63298 - 7.60810i) q^{40} +(0.635690 + 3.19583i) q^{41} +(-0.190521 + 0.386869i) q^{42} +(6.03772 + 3.22723i) q^{43} +(-0.519422 + 0.196142i) q^{44} +(-3.79193 + 0.373472i) q^{45} +(-10.7988 + 2.52413i) q^{46} +(3.17864 + 7.67391i) q^{47} +(3.24631 - 2.33698i) q^{48} +(-2.64320 + 6.38125i) q^{49} +(-2.18547 + 13.2822i) q^{50} +(2.91900 - 3.55681i) q^{51} +(2.78308 + 1.98974i) q^{52} +(-0.522948 - 1.72393i) q^{53} +(0.0917259 - 1.41124i) q^{54} +(0.879507 + 0.587668i) q^{55} +(-0.665807 + 0.548236i) q^{56} +(0.657959 + 0.984705i) q^{57} +(0.326254 - 1.22025i) q^{58} +(1.79439 - 1.47262i) q^{59} +(-7.21879 - 2.44169i) q^{60} +(-3.97939 - 7.44491i) q^{61} +(11.0190 + 10.3091i) q^{62} +0.304931i q^{63} +(7.84114 - 1.58634i) q^{64} -6.51786i q^{65} +(-0.268223 + 0.286691i) q^{66} +(-1.29293 - 2.41889i) q^{67} +(8.24903 - 4.07914i) q^{68} +(-6.06174 + 4.97474i) q^{69} +(1.58738 + 0.424410i) q^{70} +(-4.04516 - 6.05400i) q^{71} +(1.32924 - 2.49662i) q^{72} +(-3.57334 - 2.38763i) q^{73} +(-15.8476 - 1.03005i) q^{74} +(2.76299 + 9.10835i) q^{75} +(0.388376 + 2.33653i) q^{76} +(0.0537027 - 0.0654369i) q^{77} +(2.38706 + 0.392770i) q^{78} +(2.38560 - 5.75934i) q^{79} +(-11.1466 - 10.3945i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(1.04884 + 4.48718i) q^{82} +(9.70409 - 0.955769i) q^{83} +(-0.251089 + 0.555774i) q^{84} +(-15.4619 - 8.26453i) q^{85} +(8.68571 + 4.27744i) q^{86} +(-0.174246 - 0.875994i) q^{87} +(-0.724940 + 0.301668i) q^{88} +(-6.03919 - 1.20127i) q^{89} +(-5.34206 + 0.706254i) q^{90} +(-0.519103 - 0.0511272i) q^{91} +(-15.1446 + 4.07567i) q^{92} +(10.2105 + 3.09733i) q^{93} +(4.85377 + 10.6970i) q^{94} +(3.19081 - 3.19081i) q^{95} +(4.47850 - 3.45587i) q^{96} +(7.57970 + 7.57970i) q^{97} +(-3.43580 + 9.14380i) q^{98} +(-0.0805862 + 0.265657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

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