LMFDB - Embedded newform 384.2.v.a.13.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [384,2,Mod(13,384)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			13.9
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.922626 + 1.07180i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-0.297523 - 1.97775i) q^{4} +(-0.0692954 - 0.703568i) q^{5} +(1.29348 + 0.571770i) q^{6} +(-2.09840 + 3.14048i) q^{7} +(2.39426 + 1.50583i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(0.818020 + 0.574859i) q^{10} +(2.74124 - 1.46523i) q^{11} +(-1.80622 + 0.858821i) q^{12} +(0.988056 + 0.0973150i) q^{13} +(-1.42993 - 5.14656i) q^{14} +(-0.653157 + 0.270546i) q^{15} +(-3.82296 + 1.17685i) q^{16} +(5.69460 + 2.35878i) q^{17} +(0.171674 - 1.40376i) q^{18} +(4.13124 - 3.39042i) q^{19} +(-1.37086 + 0.346376i) q^{20} +(3.61438 + 1.09641i) q^{21} +(-0.958710 + 4.28993i) q^{22} +(1.75976 - 8.84689i) q^{23} +(0.745978 - 2.72828i) q^{24} +(4.41372 - 0.877944i) q^{25} +(-1.01591 + 0.969216i) q^{26} +(0.773010 + 0.634393i) q^{27} +(6.83539 + 3.21574i) q^{28} +(4.38728 - 8.20803i) q^{29} +(0.312647 - 0.949669i) q^{30} +(-6.32341 + 6.32341i) q^{31} +(2.26581 - 5.18325i) q^{32} +(-2.19787 - 2.19787i) q^{33} +(-7.78214 + 3.92722i) q^{34} +(2.35495 + 1.25875i) q^{35} +(1.34616 + 1.47914i) q^{36} +(0.539535 - 0.657425i) q^{37} +(-0.177726 + 7.55596i) q^{38} +(-0.193693 - 0.973759i) q^{39} +(0.893545 - 1.78887i) q^{40} +(4.53327 + 0.901723i) q^{41} +(-4.50986 + 2.86233i) q^{42} +(-3.21185 + 10.5881i) q^{43} +(-3.71343 - 4.98555i) q^{44} +(0.448498 + 0.546497i) q^{45} +(7.85853 + 10.0485i) q^{46} +(-3.20109 + 7.72811i) q^{47} +(2.23592 + 3.31672i) q^{48} +(-2.78054 - 6.71281i) q^{49} +(-3.13123 + 5.54065i) q^{50} +(0.604157 - 6.13411i) q^{51} +(-0.101505 - 1.98308i) q^{52} +(3.54717 + 6.63629i) q^{53} +(-1.39314 + 0.243207i) q^{54} +(-1.22084 - 1.82712i) q^{55} +(-9.75315 + 4.35927i) q^{56} +(-4.44366 - 2.96916i) q^{57} +(4.74957 + 12.2752i) q^{58} +(-4.92635 + 0.485203i) q^{59} +(0.729401 + 1.21128i) q^{60} +(5.12187 - 1.55370i) q^{61} +(-0.943307 - 12.6116i) q^{62} -3.77702i q^{63} +(3.46493 + 7.21071i) q^{64} -0.701908i q^{65} +(4.38350 - 0.327872i) q^{66} +(3.72518 - 1.13002i) q^{67} +(2.97080 - 11.9643i) q^{68} +(-8.97678 + 0.884136i) q^{69} +(-3.52186 + 1.36269i) q^{70} +(-5.87698 - 3.92687i) q^{71} +(-2.82735 + 0.0781222i) q^{72} +(-3.51161 - 5.25550i) q^{73} +(0.206841 + 1.18483i) q^{74} +(-2.12138 - 3.96881i) q^{75} +(-7.93453 - 7.16181i) q^{76} +(-1.15072 + 11.6834i) q^{77} +(1.22238 + 0.690815i) q^{78} +(-2.98662 - 7.21034i) q^{79} +(1.09291 + 2.60816i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-5.14898 + 4.02682i) q^{82} +(0.745612 + 0.908531i) q^{83} +(1.09306 - 7.47454i) q^{84} +(1.26495 - 4.16999i) q^{85} +(-8.38497 - 13.2113i) q^{86} +(-9.12815 - 1.81570i) q^{87} +(8.76963 + 0.619734i) q^{88} +(-0.652421 - 3.27994i) q^{89} +(-0.999533 - 0.0235103i) q^{90} +(-2.37895 + 2.89876i) q^{91} +(-18.0205 - 0.848199i) q^{92} +(7.88672 + 4.21554i) q^{93} +(-5.32961 - 10.5611i) q^{94} +(-2.67167 - 2.67167i) q^{95} +(-5.61779 - 0.663628i) q^{96} +(3.71723 - 3.71723i) q^{97} +(9.76020 + 3.21322i) q^{98} +(-1.46523 + 2.74124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.922626	+	1.07180i	−0.652395	+	0.757879i
$2$	−0.922626	+	1.07180i	−0.652395	+	0.757879i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	−0.297523	−	1.97775i	−0.148761	−	0.988873i
$5$	−0.0692954	−	0.703568i	−0.0309898	−	0.314645i	−0.998166	−	0.0605379i	$-0.980718\pi$
$5$	−0.0692954	−	0.703568i	−0.0309898	−	0.314645i	0.967176	−	0.254107i	$-0.0817816\pi$
$6$	1.29348	+	0.571770i	0.528059	+	0.233424i
$7$	−2.09840	+	3.14048i	−0.793121	+	1.18699i	0.185768	+	0.982594i	$0.440523\pi$
$7$	−2.09840	+	3.14048i	−0.793121	+	1.18699i	−0.978888	+	0.204395i	$0.934477\pi$
$8$	2.39426	+	1.50583i	0.846497	+	0.532393i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	0.818020	+	0.574859i	0.258680	+	0.181786i
$11$	2.74124	−	1.46523i	0.826516	−	0.441782i	−0.00318153	−	0.999995i	$-0.501013\pi$
$11$	2.74124	−	1.46523i	0.826516	−	0.441782i	0.829698	+	0.558213i	$0.188513\pi$
$12$	−1.80622	+	0.858821i	−0.521410	+	0.247920i
$13$	0.988056	+	0.0973150i	0.274037	+	0.0269903i	0.234102	−	0.972212i	$-0.424785\pi$
$13$	0.988056	+	0.0973150i	0.274037	+	0.0269903i	0.0399350	+	0.999202i	$0.487285\pi$
$14$	−1.42993	−	5.14656i	−0.382166	−	1.37548i
$15$	−0.653157	+	0.270546i	−0.168644	+	0.0698548i
$16$	−3.82296	+	1.17685i	−0.955740	+	0.294212i
$17$	5.69460	+	2.35878i	1.38114	+	0.572089i	0.944787	−	0.327685i	$-0.106269\pi$
$17$	5.69460	+	2.35878i	1.38114	+	0.572089i	0.436357	+	0.899774i	$0.356269\pi$
$18$	0.171674	−	1.40376i	0.0404639	−	0.330868i
$19$	4.13124	−	3.39042i	0.947771	−	0.777816i	−0.0273186	−	0.999627i	$-0.508697\pi$
$19$	4.13124	−	3.39042i	0.947771	−	0.777816i	0.975090	+	0.221811i	$0.0711969\pi$
$20$	−1.37086	+	0.346376i	−0.306534	+	0.0774520i
$21$	3.61438	+	1.09641i	0.788723	+	0.239257i
$22$	−0.958710	+	4.28993i	−0.204398	+	0.914616i
$23$	1.75976	−	8.84689i	0.366935	−	1.84470i	−0.150008	−	0.988685i	$-0.547930\pi$
$23$	1.75976	−	8.84689i	0.366935	−	1.84470i	0.516943	−	0.856020i	$-0.327070\pi$
$24$	0.745978	−	2.72828i	0.152272	−	0.556908i
$25$	4.41372	−	0.877944i	0.882744	−	0.175589i
$26$	−1.01591	+	0.969216i	−0.199236	+	0.190079i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	6.83539	+	3.21574i	1.29177	+	0.607718i
$29$	4.38728	−	8.20803i	0.814698	−	1.52419i	−0.0364915	−	0.999334i	$-0.511618\pi$
$29$	4.38728	−	8.20803i	0.814698	−	1.52419i	0.851189	−	0.524859i	$-0.175882\pi$
$30$	0.312647	−	0.949669i	0.0570813	−	0.173385i
$31$	−6.32341	+	6.32341i	−1.13572	+	1.13572i	−0.146509	+	0.989209i	$0.546804\pi$
$31$	−6.32341	+	6.32341i	−1.13572	+	1.13572i	−0.989209	+	0.146509i	$0.953196\pi$
$32$	2.26581	−	5.18325i	0.400543	−	0.916278i
$33$	−2.19787	−	2.19787i	−0.382601	−	0.382601i
$34$	−7.78214	+	3.92722i	−1.33463	+	0.673512i
$35$	2.35495	+	1.25875i	0.398059	+	0.212767i
$36$	1.34616	+	1.47914i	0.224360	+	0.246524i
$37$	0.539535	−	0.657425i	0.0886989	−	0.108080i	−0.726770	−	0.686881i	$-0.758979\pi$
$37$	0.539535	−	0.657425i	0.0886989	−	0.108080i	0.815469	+	0.578801i	$0.196479\pi$
$38$	−0.177726	+	7.55596i	−0.0288310	+	1.22574i
$39$	−0.193693	−	0.973759i	−0.0310157	−	0.155926i
$40$	0.893545	−	1.78887i	0.141282	−	0.282845i
$41$	4.53327	+	0.901723i	0.707977	+	0.140825i	0.535929	−	0.844263i	$-0.319961\pi$
$41$	4.53327	+	0.901723i	0.707977	+	0.140825i	0.172048	+	0.985089i	$0.444961\pi$
$42$	−4.50986	+	2.86233i	−0.695887	+	0.441667i
$43$	−3.21185	+	10.5881i	−0.489803	+	1.61466i	0.268859	+	0.963180i	$0.413353\pi$
$43$	−3.21185	+	10.5881i	−0.489803	+	1.61466i	−0.758662	+	0.651485i	$0.774147\pi$
$44$	−3.71343	−	4.98555i	−0.559820	−	0.751600i
$45$	0.448498	+	0.546497i	0.0668582	+	0.0814669i
$46$	7.85853	+	10.0485i	1.15868	+	1.48157i
$47$	−3.20109	+	7.72811i	−0.466927	+	1.12726i	0.498571	+	0.866849i	$0.333858\pi$
$47$	−3.20109	+	7.72811i	−0.466927	+	1.12726i	−0.965498	+	0.260412i	$0.916142\pi$
$48$	2.23592	+	3.31672i	0.322727	+	0.478728i
$49$	−2.78054	−	6.71281i	−0.397219	−	0.958972i
$50$	−3.13123	+	5.54065i	−0.442823	+	0.783567i
$51$	0.604157	−	6.13411i	0.0845990	−	0.858948i
$52$	−0.101505	−	1.98308i	−0.0140762	−	0.275003i
$53$	3.54717	+	6.63629i	0.487241	+	0.911565i	0.998636	+	0.0522184i	$0.0166292\pi$
$53$	3.54717	+	6.63629i	0.487241	+	0.911565i	−0.511394	+	0.859346i	$0.670871\pi$
$54$	−1.39314	+	0.243207i	−0.189583	+	0.0330963i
$55$	−1.22084	−	1.82712i	−0.164618	−	0.246368i
$56$	−9.75315	+	4.35927i	−1.30332	+	0.582532i
$57$	−4.44366	−	2.96916i	−0.588578	−	0.393275i
$58$	4.74957	+	12.2752i	0.623649	+	1.61182i
$59$	−4.92635	+	0.485203i	−0.641357	+	0.0631681i	−0.413467	−	0.910519i	$-0.635682\pi$
$59$	−4.92635	+	0.485203i	−0.641357	+	0.0631681i	−0.227889	+	0.973687i	$0.573182\pi$
$60$	0.729401	+	1.21128i	0.0941653	+	0.156376i
$61$	5.12187	−	1.55370i	0.655789	−	0.198931i	0.0551825	−	0.998476i	$-0.482426\pi$
$61$	5.12187	−	1.55370i	0.655789	−	0.198931i	0.600606	+	0.799545i	$0.294926\pi$
$62$	−0.943307	−	12.6116i	−0.119800	−	1.60167i
$63$		−	3.77702i		−	0.475860i
$64$	3.46493	+	7.21071i	0.433116	+	0.901338i
$65$		−	0.701908i		−	0.0870609i
$66$	4.38350	−	0.327872i	0.539572	−	0.0403583i
$67$	3.72518	−	1.13002i	0.455103	−	0.138054i	−0.0544070	−	0.998519i	$-0.517327\pi$
$67$	3.72518	−	1.13002i	0.455103	−	0.138054i	0.509510	+	0.860465i	$0.329827\pi$
$68$	2.97080	−	11.9643i	0.360262	−	1.45088i
$69$	−8.97678	+	0.884136i	−1.08068	+	0.106437i
$70$	−3.52186	+	1.36269i	−0.420943	+	0.162872i
$71$	−5.87698	−	3.92687i	−0.697469	−	0.466034i	0.155608	−	0.987819i	$-0.450266\pi$
$71$	−5.87698	−	3.92687i	−0.697469	−	0.466034i	−0.853077	+	0.521785i	$0.825266\pi$
$72$	−2.82735	+	0.0781222i	−0.333206	+	0.00920679i
$73$	−3.51161	−	5.25550i	−0.411003	−	0.615110i	0.566995	−	0.823721i	$-0.308106\pi$
$73$	−3.51161	−	5.25550i	−0.411003	−	0.615110i	−0.977999	+	0.208611i	$0.933106\pi$
$74$	0.206841	+	1.18483i	0.0240448	+	0.137734i
$75$	−2.12138	−	3.96881i	−0.244955	−	0.458279i
$76$	−7.93453	−	7.16181i	−0.910153	−	0.821516i
$77$	−1.15072	+	11.6834i	−0.131137	+	1.33145i
$78$	1.22238	+	0.690815i	0.138408	+	0.0782194i
$79$	−2.98662	−	7.21034i	−0.336021	−	0.811227i	−0.998090	−	0.0617836i	$-0.980321\pi$
$79$	−2.98662	−	7.21034i	−0.336021	−	0.811227i	0.662068	−	0.749443i	$-0.269679\pi$
$80$	1.09291	+	2.60816i	0.122191	+	0.291601i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−5.14898	+	4.02682i	−0.568610	+	0.444687i
$83$	0.745612	+	0.908531i	0.0818415	+	0.0997242i	0.812321	−	0.583210i	$-0.198204\pi$
$83$	0.745612	+	0.908531i	0.0818415	+	0.0997242i	−0.730480	+	0.682934i	$0.760704\pi$
$84$	1.09306	−	7.47454i	0.119263	−	0.815539i
$85$	1.26495	−	4.16999i	0.137203	−	0.452299i
$86$	−8.38497	−	13.2113i	−0.904175	−	1.42461i
$87$	−9.12815	−	1.81570i	−0.978641	−	0.194664i
$88$	8.76963	+	0.619734i	0.934846	+	0.0660638i
$89$	−0.652421	−	3.27994i	−0.0691564	−	0.347673i	0.930679	−	0.365838i	$-0.119218\pi$
$89$	−0.652421	−	3.27994i	−0.0691564	−	0.347673i	−0.999835	+	0.0181650i	$0.994218\pi$
$90$	−0.999533	−	0.0235103i	−0.105360	−	0.00247820i
$91$	−2.37895	+	2.89876i	−0.249382	+	0.303873i
$92$	−18.0205	−	0.848199i	−1.87876	−	0.0884309i
$93$	7.88672	+	4.21554i	0.817814	+	0.437131i
$94$	−5.32961	−	10.5611i	−0.549707	−	1.08929i
$95$	−2.67167	−	2.67167i	−0.274107	−	0.274107i
$96$	−5.61779	−	0.663628i	−0.573364	−	0.0677313i
$97$	3.71723	−	3.71723i	0.377427	−	0.377427i	−0.492746	−	0.870173i	$-0.664007\pi$
$97$	3.71723	−	3.71723i	0.377427	−	0.377427i	0.870173	+	0.492746i	$0.164007\pi$
$98$	9.76020	+	3.21322i	0.985929	+	0.324585i
$99$	−1.46523	+	2.74124i	−0.147261	+	0.275505i
$100$	−3.04953	−	8.46801i	−0.304953	−	0.846801i
$101$	6.57714	+	5.39772i	0.654450	+	0.537093i	0.901975	−	0.431788i	$-0.142117\pi$
$101$	6.57714	+	5.39772i	0.654450	+	0.537093i	−0.247525	+	0.968881i	$0.579617\pi$
$102$	6.01715	+	6.30703i	0.595786	+	0.624489i
$103$	14.0512	−	2.79496i	1.38451	−	0.275395i	0.554052	−	0.832482i	$-0.313081\pi$
$103$	14.0512	−	2.79496i	1.38451	−	0.275395i	0.830454	+	0.557087i	$0.188081\pi$
$104$	2.21912	+	1.72085i	0.217602	+	0.168743i
$105$	0.520940	−	2.61894i	0.0508385	−	0.255582i
$106$	−10.3855	−	2.32095i	−1.00873	−	0.225430i
$107$	15.1525	+	4.59647i	1.46485	+	0.444358i	0.919246	−	0.393684i	$-0.128800\pi$
$107$	15.1525	+	4.59647i	1.46485	+	0.444358i	0.545606	+	0.838042i	$0.316300\pi$
$108$	1.02468	−	1.71756i	0.0985999	−	0.165273i
$109$	−10.3164	+	8.46646i	−0.988133	+	0.810940i	−0.981969	−	0.189041i	$-0.939462\pi$
$109$	−10.3164	+	8.46646i	−0.988133	+	0.810940i	−0.00616383	+	0.999981i	$0.501962\pi$
$110$	3.08469	+	0.377245i	0.294114	+	0.0359689i
$111$	−0.785735	−	0.325462i	−0.0745787	−	0.0308915i
$112$	4.32623	−	14.4754i	0.408791	−	1.36780i
$113$	3.19473	−	1.32330i	0.300535	−	0.124486i	−0.227320	−	0.973820i	$-0.572996\pi$
$113$	3.19473	−	1.32330i	0.300535	−	0.124486i	0.527855	+	0.849334i	$0.322996\pi$
$114$	7.28220	−	2.02331i	0.682040	−	0.189500i
$115$	−6.34633	−	0.625059i	−0.591798	−	0.0582871i
$116$	−17.5387	−	6.23486i	−1.62843	−	0.578892i
$117$	−0.875604	+	0.468020i	−0.0809496	+	0.0432685i
$118$	4.02514	−	5.72774i	0.370544	−	0.527281i
$119$	−19.3573	+	12.9341i	−1.77448	+	1.18567i
$120$	−1.97122	−	0.335788i	−0.179947	−	0.0306531i
$121$	−0.743738	+	1.11308i	−0.0676125	+	0.101189i
$122$	−3.06031	+	6.92313i	−0.277067	+	0.626790i
$123$	−0.453043	−	4.59982i	−0.0408495	−	0.414752i
$124$	14.3875	+	10.6247i	1.29203	+	0.954130i
$125$	−1.94966	−	6.42716i	−0.174383	−	0.574863i
$126$	4.04822	+	3.48478i	0.360644	+	0.310449i
$127$	−13.9765			−1.24021			−0.620107	−	0.784517i	$-0.712911\pi$
$127$	−13.9765			−1.24021			−0.620107	+	0.784517i	$0.712911\pi$
$128$	−10.9253	−	2.93907i	−0.965668	−	0.259779i
$129$	11.0645			0.974174
$130$	0.752307	+	0.647598i	0.0659816	+	0.0567981i
$131$	−3.68669	−	12.1534i	−0.322108	−	1.06185i	−0.957204	−	0.289414i	$-0.906539\pi$
$131$	−3.68669	−	12.1534i	−0.322108	−	1.06185i	0.635096	−	0.772433i	$-0.280961\pi$
$132$	−3.69292	+	5.00076i	−0.321428	+	0.435260i
$133$	1.97855	+	20.0885i	0.171562	+	1.74190i
$134$	−2.22579	+	5.03524i	−0.192279	+	0.434978i
$135$	0.392773	−	0.587826i	0.0338045	−	0.0505920i
$136$	10.0824	+	14.2227i	0.864559	+	1.21958i
$137$	−10.8690	+	7.26243i	−0.928601	+	0.620471i	−0.925182	−	0.379523i	$-0.876088\pi$
$137$	−10.8690	+	7.26243i	−0.928601	+	0.620471i	−0.00341868	+	0.999994i	$0.501088\pi$
$138$	7.33459	−	10.4371i	0.624362	−	0.888462i
$139$	1.37280	−	0.733775i	0.116439	−	0.0622380i	−0.412149	−	0.911116i	$-0.635222\pi$
$139$	1.37280	−	0.733775i	0.116439	−	0.0622380i	0.528588	+	0.848879i	$0.322722\pi$
$140$	1.78883	−	5.03200i	0.151184	−	0.425281i
$141$	8.32457	+	0.819899i	0.701055	+	0.0690479i
$142$	9.63109	−	2.67593i	0.808223	−	0.224559i
$143$	2.85109	−	1.18096i	0.238420	−	0.0987569i
$144$	2.52485	−	3.10244i	0.210404	−	0.258536i
$145$	−6.07892	−	2.51797i	−0.504827	−	0.209106i
$146$	8.87277	+	1.08510i	0.734315	+	0.0898038i
$147$	−5.61661	+	4.60943i	−0.463250	+	0.380179i
$148$	−1.46074	−	0.871464i	−0.120072	−	0.0716339i
$149$	−8.37139	−	2.53943i	−0.685811	−	0.208038i	−0.0718978	−	0.997412i	$-0.522906\pi$
$149$	−8.37139	−	2.53943i	−0.685811	−	0.208038i	−0.613913	+	0.789374i	$0.710406\pi$
$150$	6.21102	+	1.38803i	0.507128	+	0.113333i
$151$	0.175335	−	0.881470i	0.0142686	−	0.0717330i	−0.972995	−	0.230826i	$-0.925857\pi$
$151$	0.175335	−	0.881470i	0.0142686	−	0.0717330i	0.987264	+	0.159093i	$0.0508571\pi$
$152$	14.9967	−	1.89657i	1.21639	−	0.153832i
$153$	−6.04536	+	1.20250i	−0.488738	+	0.0972161i
$154$	−11.4607	−	12.0128i	−0.923527	−	0.968019i
$155$	4.88713	+	4.01076i	0.392544	+	0.322152i
$156$	−1.86822	+	0.672791i	−0.149577	+	0.0538664i
$157$	−2.92559	+	5.47340i	−0.233488	+	0.436825i	−0.971192	−	0.238300i	$-0.923410\pi$
$157$	−2.92559	+	5.47340i	−0.233488	+	0.436825i	0.737704	+	0.675124i	$0.235910\pi$
$158$	10.4836	+	3.45138i	0.834031	+	0.274577i
$159$	5.32084	−	5.32084i	0.421970	−	0.421970i
$160$	−3.80378	−	1.23498i	−0.300715	−	0.0976335i
$161$	24.0908	+	24.0908i	1.89862	+	1.89862i
$162$	0.637143	+	1.26256i	0.0500587	+	0.0991958i
$163$	−15.8546	−	8.47448i	−1.24183	−	0.663773i	−0.286153	−	0.958184i	$-0.592376\pi$
$163$	−15.8546	−	8.47448i	−1.24183	−	0.663773i	−0.955679	+	0.294411i	$0.904876\pi$
$164$	0.434629	−	9.23393i	0.0339388	−	0.721049i
$165$	−1.39405	+	1.69866i	−0.108527	+	0.132240i
$166$	−1.66169	−	0.0390850i	−0.128972	−	0.00303359i
$167$	−0.349862	−	1.75888i	−0.0270732	−	0.136106i	0.964885	−	0.262673i	$-0.0846041\pi$
$167$	−0.349862	−	1.75888i	−0.0270732	−	0.136106i	−0.991958	+	0.126567i	$0.959604\pi$
$168$	7.00275	+	8.06775i	0.540274	+	0.622441i
$169$	−11.7834	−	2.34387i	−0.906417	−	0.180298i
$170$	3.30233	+	5.20312i	0.253277	+	0.399061i
$171$	−1.55138	+	5.11422i	−0.118637	+	0.391094i
$172$	21.8961	+	3.20204i	1.66956	+	0.244153i
$173$	0.660707	+	0.805074i	0.0502327	+	0.0612087i	0.797521	−	0.603292i	$-0.206144\pi$
$173$	0.660707	+	0.805074i	0.0502327	+	0.0612087i	−0.747288	+	0.664500i	$0.768644\pi$
$174$	10.3679	−	8.10837i	0.785992	−	0.614694i
$175$	−6.50459	+	15.7035i	−0.491701	+	1.18707i
$176$	−8.75532	+	8.82753i	−0.659957	+	0.665400i
$177$	1.89436	+	4.57338i	0.142388	+	0.343756i
$178$	4.11739	+	2.32689i	0.308611	+	0.174408i
$179$	0.166175	−	1.68720i	0.0124205	−	0.126107i	−0.986975	−	0.160874i	$-0.948569\pi$
$179$	0.166175	−	1.68720i	0.0124205	−	0.126107i	0.999395	+	0.0347666i	$0.0110688\pi$
$180$	0.947393	−	1.04961i	0.0706145	−	0.0782334i
$181$	−1.87942	−	3.51615i	−0.139696	−	0.261353i	0.802338	−	0.596870i	$-0.203589\pi$
$181$	−1.87942	−	3.51615i	−0.139696	−	0.261353i	−0.942034	+	0.335517i	$0.891089\pi$
$182$	−0.912018	−	5.22424i	−0.0676033	−	0.387246i
$183$	−2.97360	−	4.45031i	−0.219815	−	0.328976i
$184$	17.5353	−	18.5318i	1.29272	−	1.36618i
$185$	−0.499930	−	0.334043i	−0.0367556	−	0.0245593i
$186$	−11.7947	+	4.56364i	−0.864830	+	0.334622i
$187$	19.0664	−	1.87788i	1.39428	−	0.137324i
$188$	16.2366	+	4.03165i	1.18418	+	0.294039i
$189$	−3.61438	+	1.09641i	−0.262908	+	0.0797522i
$190$	5.32845	−	0.398551i	0.386566	−	0.0289139i
$191$			2.12689i			0.153896i	0.997035	+	0.0769482i	$0.0245176\pi$
$191$			2.12689i			0.153896i	−0.997035	+	0.0769482i	$0.975482\pi$
$192$	5.89440	−	5.40889i	0.425392	−	0.390353i
$193$		−	19.6060i		−	1.41127i	−0.708574	−	0.705636i	$-0.750661\pi$
$193$		−	19.6060i		−	1.41127i	0.708574	−	0.705636i	$-0.249339\pi$
$194$	0.554525	+	7.41375i	0.0398126	+	0.532276i
$195$	−0.671684	+	0.203753i	−0.0481003	+	0.0145911i
$196$	−12.4490	+	7.49641i	−0.889211	+	0.535458i
$197$	−10.4182	+	1.02610i	−0.742264	+	0.0731066i	−0.462078	−	0.886839i	$-0.652896\pi$
$197$	−10.4182	+	1.02610i	−0.742264	+	0.0731066i	−0.280186	+	0.959946i	$0.590396\pi$
$198$	−1.58622	−	4.09958i	−0.112728	−	0.291344i
$199$	17.5150	+	11.7032i	1.24161	+	0.829615i	0.990388	−	0.138316i	$-0.0441689\pi$
$199$	17.5150	+	11.7032i	1.24161	+	0.829615i	0.251218	+	0.967931i	$0.419169\pi$
$200$	11.8896	+	4.54431i	0.840723	+	0.321331i
$201$	−2.16272	−	3.23674i	−0.152547	−	0.228302i
$202$	−11.8535	+	2.06932i	−0.834011	+	0.145597i
$203$	16.5709	+	31.0019i	1.16305	+	2.17591i
$204$	−12.3115	+	0.630168i	−0.861975	+	0.0441206i
$205$	0.320289	−	3.25195i	0.0223699	−	0.227126i
$206$	−9.96836	+	17.6388i	−0.694529	+	1.22896i
$207$	3.45189	+	8.33359i	0.239923	+	0.579225i
$208$	−3.89182	+	0.790761i	−0.269849	+	0.0548294i
$209$	6.35700	−	15.3472i	0.439723	−	1.06159i
$210$	2.32635	+	2.97465i	0.160534	+	0.205270i
$211$	10.2562	+	12.4972i	0.706066	+	0.860344i	0.995292	−	0.0969169i	$-0.0308981\pi$
$211$	10.2562	+	12.4972i	0.706066	+	0.860344i	−0.289227	+	0.957261i	$0.593398\pi$
$212$	12.0695	−	8.98985i	0.828939	−	0.617426i
$213$	−2.05179	+	6.76383i	−0.140586	+	0.463450i
$214$	−18.9066	+	11.9997i	−1.29243	+	0.820284i
$215$	7.67198	+	1.52605i	0.523225	+	0.104076i
$216$	0.895494	+	2.68293i	0.0609307	+	0.182550i
$217$	−6.58949	−	33.1276i	−0.447323	−	2.24885i
$218$	0.443812	−	18.8685i	0.0300588	−	1.27794i
$219$	−4.00983	+	4.88600i	−0.270959	+	0.330165i
$220$	−3.25035	+	2.95812i	−0.219138	+	0.199437i
$221$	5.39704	+	2.88478i	0.363044	+	0.194051i
$222$	1.07377	−	0.541873i	0.0720668	−	0.0363681i
$223$	6.18991	+	6.18991i	0.414507	+	0.414507i	0.883305	−	0.468798i	$-0.155313\pi$
$223$	6.18991	+	6.18991i	0.414507	+	0.414507i	−0.468798	+	0.883305i	$0.655313\pi$
$224$	11.5233	+	17.9923i	0.769933	+	1.20216i
$225$	−3.18212	+	3.18212i	−0.212141	+	0.212141i
$226$	−1.52922	+	4.64503i	−0.101722	+	0.308983i
$227$	9.27411	−	17.3506i	0.615544	−	1.15160i	−0.360238	−	0.932860i	$-0.617305\pi$
$227$	9.27411	−	17.3506i	0.615544	−	1.15160i	0.975783	−	0.218742i	$-0.0701953\pi$
$228$	−4.55016	+	9.67183i	−0.301342	+	0.640533i
$229$	3.76531	+	3.09011i	0.248819	+	0.204200i	0.750533	−	0.660833i	$-0.229797\pi$
$229$	3.76531	+	3.09011i	0.248819	+	0.204200i	−0.501714	+	0.865034i	$0.667297\pi$
$230$	6.52523	−	6.22532i	0.430261	−	0.410485i
$231$	11.5144	−	2.29036i	0.757592	−	0.150694i
$232$	22.8642	−	13.0456i	1.50111	−	0.856486i
$233$	−3.54010	+	17.7973i	−0.231919	+	1.16594i	0.672765	+	0.739856i	$0.265106\pi$
$233$	−3.54010	+	17.7973i	−0.231919	+	1.16594i	−0.904685	+	0.426082i	$0.859894\pi$
$234$	0.306230	−	1.37028i	0.0200189	−	0.0895781i
$235$	5.65907	+	1.71666i	0.369157	+	0.111983i
$236$	2.42531	+	9.59872i	0.157874	+	0.624823i
$237$	−6.03290	+	4.95107i	−0.391879	+	0.321607i
$238$	3.99670	−	32.6805i	0.259067	−	2.11836i
$239$	−14.9580	−	6.19580i	−0.967552	−	0.400773i	−0.157752	−	0.987479i	$-0.550425\pi$
$239$	−14.9580	−	6.19580i	−0.967552	−	0.400773i	−0.809800	+	0.586705i	$0.800425\pi$
$240$	2.17860	−	1.80296i	0.140628	−	0.116380i
$241$	−4.24119	+	1.75676i	−0.273199	+	0.113163i	−0.515077	−	0.857144i	$-0.672237\pi$
$241$	−4.24119	+	1.75676i	−0.273199	+	0.113163i	0.241878	+	0.970307i	$0.422237\pi$
$242$	−0.506813	−	1.82410i	−0.0325792	−	0.117257i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−4.59671	−	9.66750i	−0.294274	−	0.618899i
$245$	−4.53023	+	2.42146i	−0.289426	+	0.154701i
$246$	5.34809	+	3.75834i	0.340982	+	0.239623i
$247$	4.41183	−	2.94789i	0.280718	−	0.187570i
$248$	−24.6619	+	5.61786i	−1.56603	+	0.356734i
$249$	0.652970	−	0.977239i	0.0413803	−	0.0619300i
$250$	8.68746	+	3.84022i	0.549443	+	0.242877i
$251$	−2.59605	−	26.3581i	−0.163861	−	1.66371i	−0.628199	−	0.778053i	$-0.716208\pi$
$251$	−2.59605	−	26.3581i	−0.163861	−	1.66371i	0.464338	−	0.885658i	$-0.346292\pi$
$252$	−7.46999	+	1.12375i	−0.470565	+	0.0707896i
$253$	−8.13877	−	26.8299i	−0.511680	−	1.68678i
$254$	12.8951	−	14.9801i	0.809110	−	0.939933i
$255$	−4.35763			−0.272885
$256$	13.2301	−	8.99810i	0.826878	−	0.562381i
$257$	−5.71535			−0.356514			−0.178257	−	0.983984i	$-0.557046\pi$
$257$	−5.71535			−0.356514			−0.178257	+	0.983984i	$0.557046\pi$
$258$	−10.2084	+	11.8590i	−0.635547	+	0.738306i
$259$	0.932469	+	3.07394i	0.0579408	+	0.191005i
$260$	−1.38820	+	0.208834i	−0.0860922	+	0.0129513i
$261$	0.912244	+	9.26217i	0.0564665	+	0.573314i
$262$	16.4275	+	7.26163i	1.01489	+	0.448625i
$263$	−2.40272	+	3.59593i	−0.148158	+	0.221735i	−0.898124	−	0.439742i	$-0.855070\pi$
$263$	−2.40272	+	3.59593i	−0.148158	+	0.221735i	0.749966	+	0.661477i	$0.230070\pi$
$264$	−1.95264	−	8.57191i	−0.120177	−	0.527565i
$265$	4.42328	−	2.95554i	0.271720	−	0.181557i
$266$	−23.3564	−	16.4136i	−1.43207	−	1.00638i
$267$	−2.94932	+	1.57644i	−0.180495	+	0.0964768i
$268$	−3.34322	−	7.03125i	−0.204219	−	0.429502i
$269$	0.538695	+	0.0530569i	0.0328448	+	0.00323493i	0.114426	−	0.993432i	$-0.463497\pi$
$269$	0.538695	+	0.0530569i	0.0328448	+	0.00323493i	−0.0815814	+	0.996667i	$0.525997\pi$
$270$	0.267651	+	0.963318i	0.0162887	+	0.0586257i
$271$	−24.1138	+	9.98824i	−1.46481	+	0.606743i	−0.965668	−	0.259780i	$-0.916350\pi$
$271$	−24.1138	+	9.98824i	−1.46481	+	0.606743i	−0.499138	+	0.866522i	$0.666350\pi$
$272$	−24.5462	−	2.31584i	−1.48833	−	0.140418i
$273$	3.46452	+	1.43505i	0.209682	+	0.0868531i
$274$	2.24412	−	18.3499i	0.135572	−	1.10856i
$275$	10.8127	−	8.87376i	0.652030	−	0.535108i
$276$	4.41939	+	17.4907i	0.266016	+	1.05282i
$277$	12.3173	+	3.73641i	0.740074	+	0.224499i	0.637741	−	0.770251i	$-0.279869\pi$
$277$	12.3173	+	3.73641i	0.740074	+	0.224499i	0.102333	+	0.994750i	$0.467369\pi$
$278$	−0.480116	+	2.14837i	−0.0287954	+	0.128851i
$279$	1.74463	−	8.77082i	0.104448	−	0.525095i
$280$	3.74289	+	6.55992i	0.223680	+	0.392030i
$281$	−11.5372	+	2.29490i	−0.688255	+	0.136902i	−0.526815	−	0.849980i	$-0.676614\pi$
$281$	−11.5372	+	2.29490i	−0.688255	+	0.136902i	−0.161440	+	0.986883i	$0.551614\pi$
$282$	−8.55924	+	8.16584i	−0.509695	+	0.486269i
$283$	−1.82777	−	1.50001i	−0.108650	−	0.0891666i	0.578500	−	0.815683i	$-0.303638\pi$
$283$	−1.82777	−	1.50001i	−0.108650	−	0.0891666i	−0.687150	+	0.726516i	$0.741138\pi$
$284$	−6.01782	+	12.7915i	−0.357092	+	0.759036i
$285$	−1.78108	+	3.33217i	−0.105502	+	0.197381i
$286$	−1.36473	+	4.14539i	−0.0806984	+	0.245122i
$287$	−12.3445	+	12.3445i	−0.728670	+	0.728670i
$288$	0.995706	+	5.56853i	0.0586726	+	0.328129i
$289$	14.8438	+	14.8438i	0.873166	+	0.873166i
$290$	8.30734	−	4.19226i	0.487824	−	0.246178i
$291$	−4.63622	−	2.47811i	−0.271780	−	0.145269i
$292$	−9.34926	+	8.50871i	−0.547124	+	0.497935i
$293$	0.140076	−	0.170683i	0.00818334	−	0.00997143i	−0.768903	−	0.639366i	$-0.779197\pi$
$293$	0.140076	−	0.170683i	0.00818334	−	0.00997143i	0.777086	+	0.629394i	$0.216697\pi$
$294$	0.241627	−	10.2727i	0.0140920	−	0.599115i
$295$	0.682747	+	3.43240i	0.0397511	+	0.199842i
$296$	2.28176	−	0.761594i	0.132624	−	0.0442667i
$297$	3.04854	+	0.606392i	0.176894	+	0.0351865i
$298$	10.4454	−	6.62953i	0.605088	−	0.384039i
$299$	2.59967	−	8.56997i	0.150343	−	0.495614i
$300$	−7.21815	+	5.37635i	−0.416740	+	0.310404i
$301$	−26.5118	−	32.3047i	−1.52812	−	1.86201i
$302$	0.782993	+	1.00119i	0.0450562	+	0.0576121i
$303$	3.25605	−	7.86080i	0.187055	−	0.451591i
$304$	−11.8035	+	17.8233i	−0.676980	+	1.02224i
$305$	−1.44806	−	3.49592i	−0.0829155	−	0.200176i
$306$	4.28876	−	7.58889i	0.245172	−	0.433828i
$307$	−2.36263	+	23.9882i	−0.134842	+	1.36908i	0.654935	+	0.755685i	$0.272696\pi$
$307$	−2.36263	+	23.9882i	−0.134842	+	1.36908i	−0.789778	+	0.613393i	$0.789804\pi$
$308$	23.4493	−	1.20026i	1.33615	−	0.0683913i
$309$	−6.75346	−	12.6348i	−0.384191	−	0.718770i
$310$	−8.80774	+	1.53761i	−0.500246	+	0.0873301i
$311$	0.320102	+	0.479066i	0.0181513	+	0.0271654i	0.840434	−	0.541913i	$-0.182300\pi$
$311$	0.320102	+	0.479066i	0.0181513	+	0.0271654i	−0.822283	+	0.569079i	$0.807300\pi$
$312$	1.00257	−	2.62310i	0.0567594	−	0.148504i
$313$	−7.03901	−	4.70332i	−0.397869	−	0.265847i	0.340500	−	0.940244i	$-0.389404\pi$
$313$	−7.03901	−	4.70332i	−0.397869	−	0.265847i	−0.738369	+	0.674397i	$0.764404\pi$
$314$	−3.16718	−	8.18556i	−0.178734	−	0.461938i
$315$	−2.65739	+	0.261730i	−0.149727	+	0.0147468i
$316$	−13.3716	+	8.05202i	−0.752214	+	0.452962i
$317$	11.2304	−	3.40672i	0.630764	−	0.191340i	0.0413157	−	0.999146i	$-0.486845\pi$
$317$	11.2304	−	3.40672i	0.630764	−	0.191340i	0.589449	+	0.807806i	$0.299345\pi$
$318$	0.793747	+	10.6120i	0.0445111	+	0.595094i
$319$		−	28.9286i		−	1.61969i
$320$	4.83312	−	2.93748i	0.270179	−	0.164210i
$321$		−	15.8344i		−	0.883788i
$322$	−48.0474	+	3.59379i	−2.67758	+	0.200274i
$323$	31.5230	−	9.56240i	1.75399	−	0.532066i
$324$	−1.94106	−	0.481975i	−0.107836	−	0.0267764i
$325$	4.44644	−	0.437936i	0.246644	−	0.0242923i
$326$	23.7109	−	9.17427i	1.31322	−	0.508116i
$327$	11.0966	+	7.41451i	0.613643	+	0.410023i
$328$	9.49596	+	8.98530i	0.524327	+	0.496130i
$329$	−17.5528	−	26.2696i	−0.967718	−	1.44829i
$330$	−0.534437	−	3.06137i	−0.0294198	−	0.168523i
$331$	−12.8496	−	24.0399i	−0.706277	−	1.32135i	−0.937341	−	0.348413i	$-0.886721\pi$
$331$	−12.8496	−	24.0399i	−0.706277	−	1.32135i	0.231064	−	0.972939i	$-0.425779\pi$
$332$	1.57501	−	1.74494i	0.0864397	−	0.0957660i
$333$	−0.0833610	+	0.846378i	−0.00456815	+	0.0463812i
$334$	2.20796	+	1.24780i	0.120814	+	0.0682767i
$335$	−1.05318	−	2.54261i	−0.0575415	−	0.138918i
$336$	−15.1080	+	0.0620477i	−0.824207	+	0.00338498i
$337$	−5.77417	+	13.9401i	−0.314539	+	0.759364i	0.684986	+	0.728556i	$0.259808\pi$
$337$	−5.77417	+	13.9401i	−0.314539	+	0.759364i	−0.999525	+	0.0308082i	$0.990192\pi$
$338$	13.3839	−	10.4670i	0.727986	−	0.569329i
$339$	−2.19370	−	2.67303i	−0.119146	−	0.145179i
$340$	−8.62354	−	1.26109i	−0.467677	−	0.0683921i
$341$	−8.06879	+	26.5992i	−0.436950	+	1.44043i
$342$	−4.05009	−	6.38129i	−0.219004	−	0.345061i
$343$	0.984969	+	0.195922i	0.0531833	+	0.0105788i
$344$	−23.6339	+	20.5140i	−1.27425	+	1.10604i
$345$	1.24410	+	6.25450i	0.0669800	+	0.336731i
$346$	−1.47247	−	0.0346343i	−0.0791603	−	0.00186195i
$347$	−2.30319	+	2.80644i	−0.123641	+	0.150658i	−0.831152	−	0.556045i	$-0.812318\pi$
$347$	−2.30319	+	2.80644i	−0.123641	+	0.150658i	0.707511	+	0.706703i	$0.249818\pi$
$348$	−0.875165	+	18.5934i	−0.0469138	+	0.996710i
$349$	21.9842	+	11.7508i	1.17679	+	0.629005i	0.939538	−	0.342444i	$-0.111255\pi$
$349$	21.9842	+	11.7508i	1.17679	+	0.629005i	0.237247	+	0.971449i	$0.423755\pi$
$350$	−10.8297	−	21.4601i	−0.578873	−	1.14709i
$351$	0.702041	+	0.702041i	0.0374722	+	0.0374722i
$352$	−1.38349	−	17.5285i	−0.0737402	−	0.934271i
$353$	−10.7933	+	10.7933i	−0.574467	+	0.574467i	−0.933374	−	0.358906i	$-0.883150\pi$
$353$	−10.7933	+	10.7933i	−0.574467	+	0.574467i	0.358906	+	0.933374i	$0.383150\pi$
$354$	−6.64954	−	2.18914i	−0.353419	−	0.116352i
$355$	−2.35557	+	4.40697i	−0.125021	+	0.233897i
$356$	−6.29278	+	2.26618i	−0.333517	+	0.120107i
$357$	17.9963	+	14.7692i	0.952464	+	0.781667i
$358$	1.65503	+	1.73476i	0.0874710	+	0.0916849i
$359$	4.32575	−	0.860444i	0.228304	−	0.0454125i	−0.0796124	−	0.996826i	$-0.525368\pi$
$359$	4.32575	−	0.860444i	0.228304	−	0.0454125i	0.307916	+	0.951413i	$0.400368\pi$
$360$	0.250886	+	1.98382i	0.0132229	+	0.104556i
$361$	1.86547	−	9.37834i	0.0981826	−	0.493597i
$362$	5.50262	+	1.22972i	0.289211	+	0.0646328i
$363$	1.28105	+	0.388602i	0.0672376	+	0.0203963i
$364$	6.44081	+	3.84252i	0.337590	+	0.201403i
$365$	−3.45426	+	2.83484i	−0.180804	+	0.148382i
$366$	7.51338	+	0.918856i	0.392731	+	0.0480294i
$367$	26.8946	+	11.1401i	1.40389	+	0.581510i	0.950758	−	0.309935i	$-0.100307\pi$
$367$	26.8946	+	11.1401i	1.40389	+	0.581510i	0.453131	+	0.891444i	$0.350307\pi$
$368$	3.68398	+	35.8923i	0.192041	+	1.87101i
$369$	−4.27024	+	1.76879i	−0.222300	+	0.0920797i
$370$	0.819276	−	0.227630i	0.0425921	−	0.0118339i
$371$	−28.2845	−	2.78578i	−1.46846	−	0.144631i
$372$	5.99079	−	16.8521i	0.310608	−	0.873743i
$373$	−4.20134	+	2.24566i	−0.217537	+	0.116276i	−0.576566	−	0.817050i	$-0.695608\pi$
$373$	−4.20134	+	2.24566i	−0.217537	+	0.116276i	0.359029	+	0.933326i	$0.383108\pi$
$374$	−15.5785	+	22.1681i	−0.805544	+	1.14628i
$375$	−5.58446	+	3.73141i	−0.288380	+	0.192689i
$376$	−19.3015	+	13.6828i	−0.995398	+	0.705635i
$377$	5.13364	−	7.68304i	0.264396	−	0.395697i
$378$	2.15959	−	4.88548i	0.111077	−	0.251282i
$379$	2.34190	+	23.7777i	0.120295	+	1.22138i	0.845928	+	0.533297i	$0.179047\pi$
$379$	2.34190	+	23.7777i	0.120295	+	1.22138i	−0.725633	+	0.688082i	$0.758453\pi$
$380$	−4.48899	+	6.07876i	−0.230281	+	0.311834i
$381$	4.05717	+	13.3747i	0.207855	+	0.685206i
$382$	−2.27961	−	1.96232i	−0.116635	−	0.100401i
$383$	13.4215			0.685807			0.342904	−	0.939371i	$-0.388590\pi$
$383$	13.4215			0.685807			0.342904	+	0.939371i	$0.388590\pi$
$384$	0.358933	+	11.3080i	0.0183167	+	0.577060i
$385$	8.29984			0.422999
$386$	21.0138	+	18.0890i	1.06957	+	0.920707i
$387$	−3.21185	−	10.5881i	−0.163268	−	0.538221i
$388$	−8.45769	−	6.24577i	−0.429374	−	0.317081i
$389$	−0.811687	−	8.24120i	−0.0411542	−	0.417845i	−0.993585	−	0.113090i	$-0.963925\pi$
$389$	−0.811687	−	8.24120i	−0.0411542	−	0.417845i	0.952431	−	0.304756i	$-0.0985748\pi$
$390$	0.401330	−	0.907900i	0.0203221	−	0.0459733i
$391$	30.8890	−	46.2287i	1.56212	−	2.33788i
$392$	3.45106	−	20.2592i	0.174305	−	1.02324i
$393$	−10.5599	+	7.05589i	−0.532676	+	0.355923i
$394$	8.51230	−	12.1129i	0.428843	−	0.610241i
$395$	−4.86601	+	2.60093i	−0.244835	+	0.130867i
$396$	5.85742	+	2.08226i	0.294347	+	0.104638i
$397$	−15.8954	−	1.56556i	−0.797765	−	0.0785730i	−0.309083	−	0.951035i	$-0.600022\pi$
$397$	−15.8954	−	1.56556i	−0.797765	−	0.0785730i	−0.488682	+	0.872462i	$0.662522\pi$
$398$	−28.7033	+	7.97500i	−1.43877	+	0.399751i
$399$	18.6492	−	7.72474i	0.933627	−	0.386721i
$400$	−15.8403	+	8.55063i	−0.792014	+	0.427531i
$401$	−24.9817	−	10.3477i	−1.24752	−	0.516742i	−0.341466	−	0.939894i	$-0.610923\pi$
$401$	−24.9817	−	10.3477i	−1.24752	−	0.516742i	−0.906059	+	0.423152i	$0.860923\pi$
$402$	5.46454	+	0.668291i	0.272546	+	0.0333313i
$403$	−6.86324	+	5.63252i	−0.341883	+	0.280576i
$404$	8.71847	−	14.6139i	0.433760	−	0.727066i
$405$	−0.676530	−	0.205223i	−0.0336170	−	0.0101976i
$406$	−48.5166	−	10.8425i	−2.40784	−	0.538102i
$407$	0.515720	−	2.59270i	0.0255633	−	0.128515i
$408$	10.6835	−	13.7769i	0.528910	−	0.682057i
$409$	−1.76482	+	0.351044i	−0.0872647	+	0.0173580i	−0.238530	−	0.971135i	$-0.576665\pi$
$409$	−1.76482	+	0.351044i	−0.0872647	+	0.0173580i	0.151265	+	0.988493i	$0.451665\pi$
$410$	3.18994	+	3.34362i	0.157540	+	0.165129i
$411$	10.1048	+	8.29281i	0.498434	+	0.409054i
$412$	−9.70827	−	26.9582i	−0.478292	−	1.32813i
$413$	8.81369	−	16.4893i	0.433693	−	0.811383i
$414$	−12.1168	−	3.98905i	−0.595507	−	0.196051i
$415$	0.587545	−	0.587545i	0.0288415	−	0.0288415i
$416$	2.74316	−	4.90084i	0.134494	−	0.240284i
$417$	−1.10068	−	1.10068i	−0.0539006	−	0.0539006i
$418$	10.5840	+	20.9731i	0.517680	+	1.02583i
$419$	4.39131	+	2.34720i	0.214529	+	0.114668i	0.575162	−	0.818040i	$-0.304939\pi$
$419$	4.39131	+	2.34720i	0.214529	+	0.114668i	−0.360632	+	0.932708i	$0.617439\pi$
$420$	−5.33459	−	0.251092i	−0.260301	−	0.0122520i
$421$	−14.2951	+	17.4186i	−0.696700	+	0.848931i	−0.994395	−	0.105730i	$-0.966282\pi$
$421$	−14.2951	+	17.4186i	−0.696700	+	0.848931i	0.297695	+	0.954661i	$0.403782\pi$
$422$	−22.8572	−	0.537631i	−1.11267	−	0.0261715i
$423$	−1.63190	−	8.20412i	−0.0793458	−	0.398898i
$424$	−1.50032	+	21.2304i	−0.0728618	+	1.03104i
$425$	27.2053	+	5.41146i	1.31965	+	0.262495i
$426$	−5.35646	−	8.43959i	−0.259521	−	0.408900i
$427$	−5.86837	+	19.3454i	−0.283990	+	0.936191i
$428$	4.58243	−	31.3354i	0.221500	−	1.51466i
$429$	−1.95774	−	2.38551i	−0.0945204	−	0.115173i
$430$	−8.71400	+	6.81488i	−0.420226	+	0.328643i
$431$	−2.19171	+	5.29126i	−0.105571	+	0.254871i	−0.967834	−	0.251590i	$-0.919047\pi$
$431$	−2.19171	+	5.29126i	−0.105571	+	0.254871i	0.862263	+	0.506461i	$0.169047\pi$
$432$	−3.70177	−	1.51554i	−0.178102	−	0.0729166i
$433$	1.80138	+	4.34891i	0.0865686	+	0.208995i	0.961235	−	0.275730i	$-0.0889196\pi$
$433$	1.80138	+	4.34891i	0.0865686	+	0.208995i	−0.874666	+	0.484725i	$0.838920\pi$
$434$	41.5859	+	23.5017i	1.99619	+	1.12812i
$435$	−0.644931	+	6.54809i	−0.0309221	+	0.313957i
$436$	19.8139	+	17.8843i	0.948913	+	0.856502i
$437$	−22.7247	−	42.5149i	−1.08707	−	2.03377i
$438$	−1.53725	−	8.80570i	−0.0734526	−	0.420752i
$439$	13.9407	+	20.8638i	0.665355	+	0.995774i	0.998598	+	0.0529333i	$0.0168571\pi$
$439$	13.9407	+	20.8638i	0.665355	+	0.995774i	−0.333243	+	0.942841i	$0.608143\pi$
$440$	−0.171670	−	6.21297i	−0.00818405	−	0.296192i
$441$	6.04137	+	4.03671i	0.287684	+	0.192224i
$442$	−8.07136	+	3.12299i	−0.383916	+	0.148546i
$443$	7.05921	−	0.695272i	0.335393	−	0.0330334i	0.0710811	−	0.997471i	$-0.477355\pi$
$443$	7.05921	−	0.695272i	0.335393	−	0.0330334i	0.264312	+	0.964437i	$0.414855\pi$
$444$	−0.409907	+	1.65082i	−0.0194533	+	0.0783443i
$445$	−2.26245	+	0.686307i	−0.107250	+	0.0325341i
$446$	−12.3453	+	0.923392i	−0.584568	+	0.0437239i
$447$			8.74808i			0.413770i
$448$	−29.9159	−	4.24942i	−1.41339	−	0.200766i
$449$			28.8634i			1.36215i	0.732215	+	0.681073i	$0.238486\pi$
$449$			28.8634i			1.36215i	−0.732215	+	0.681073i	$0.761514\pi$
$450$	−0.474698	−	6.34650i	−0.0223775	−	0.299177i
$451$	13.7480	−	4.17042i	0.647369	−	0.196377i
$452$	−3.56766	−	5.92465i	−0.167809	−	0.278672i
$453$	−0.894411	+	0.0880918i	−0.0420231	+	0.00413891i
$454$	10.0399	+	25.9482i	0.471197	+	1.21781i
$455$	2.20433	+	1.47288i	0.103340	+	0.0690498i
$456$	−6.16821	−	13.8004i	−0.288853	−	0.646261i
$457$	3.51197	+	5.25604i	0.164283	+	0.245867i	0.904473	−	0.426531i	$-0.140264\pi$
$457$	3.51197	+	5.25604i	0.164283	+	0.245867i	−0.740190	+	0.672398i	$0.765264\pi$
$458$	−6.78597	+	1.18466i	−0.317087	+	0.0553553i
$459$	2.90559	+	5.43598i	0.135621	+	0.253730i
$460$	0.651970	+	12.7374i	0.0303983	+	0.593884i
$461$	2.48141	−	25.1941i	0.115571	−	1.17341i	−0.746062	−	0.665876i	$-0.768058\pi$
$461$	2.48141	−	25.1941i	0.115571	−	1.17341i	0.861633	−	0.507532i	$-0.169442\pi$
$462$	−8.16867	+	14.4543i	−0.380041	+	0.672475i
$463$	1.82855	+	4.41451i	0.0849800	+	0.205160i	0.960657	−	0.277737i	$-0.0895845\pi$
$463$	1.82855	+	4.41451i	0.0849800	+	0.205160i	−0.875677	+	0.482897i	$0.839584\pi$
$464$	−7.11280	+	36.5421i	−0.330203	+	1.69643i
$465$	2.41940	−	5.84096i	0.112197	−	0.270868i
$466$	−15.8090	−	20.2145i	−0.732337	−	0.936419i
$467$	−4.32997	−	5.27608i	−0.200367	−	0.244148i	0.663127	−	0.748507i	$-0.269229\pi$
$467$	−4.32997	−	5.27608i	−0.200367	−	0.244148i	−0.863494	+	0.504359i	$0.831729\pi$
$468$	1.18614	+	1.59248i	0.0548292	+	0.0736122i
$469$	−4.26811	+	14.0701i	−0.197083	+	0.649695i
$470$	−7.06113	+	4.48157i	−0.325706	+	0.206720i
$471$	6.08697	+	1.21077i	0.280473	+	0.0557895i
$472$	−12.5256	−	6.25657i	−0.576537	−	0.287982i
$473$	6.70942	+	33.7306i	0.308500	+	1.55093i
$474$	0.259536	−	11.0341i	0.0119209	−	0.506811i
$475$	15.2575	−	18.5914i	0.700064	−	0.853030i
$476$	31.3396	+	34.4356i	1.43645	+	1.57835i
$477$	−6.63629	−	3.54717i	−0.303855	−	0.162414i
$478$	20.4413	−	10.3156i	0.934964	−	0.471825i
$479$	5.01229	+	5.01229i	0.229018	+	0.229018i	0.812282	−	0.583265i	$-0.198225\pi$
$479$	5.01229	+	5.01229i	0.229018	+	0.229018i	−0.583265	+	0.812282i	$0.698225\pi$
$480$	−0.0776204	+	3.99848i	−0.00354287	+	0.182505i
$481$	0.597068	−	0.597068i	0.0272239	−	0.0272239i
$482$	2.03013	−	6.16656i	0.0924701	−	0.280879i
$483$	16.0603	−	30.0466i	0.730768	−	1.36717i
$484$	2.42267	+	1.13976i	0.110121	+	0.0518071i
$485$	−2.87291	−	2.35773i	−0.130452	−	0.107059i
$486$	1.02324	−	0.976209i	0.0464150	−	0.0442817i
$487$	2.42480	−	0.482322i	0.109878	−	0.0218561i	−0.139845	−	0.990173i	$-0.544660\pi$
$487$	2.42480	−	0.482322i	0.109878	−	0.0218561i	0.249723	+	0.968317i	$0.419660\pi$
$488$	14.6027	+	3.99273i	0.661033	+	0.180742i
$489$	−3.50721	+	17.6320i	−0.158602	+	0.797345i
$490$	1.58438	−	7.08962i	0.0715751	−	0.320276i
$491$	29.0704	+	8.81840i	1.31193	+	0.397969i	0.867317	−	0.497755i	$-0.165842\pi$
$491$	29.0704	+	8.81840i	1.31193	+	0.397969i	0.444610	+	0.895724i	$0.353342\pi$
$492$	−8.96249	+	2.26456i	−0.404060	+	0.102094i
$493$	44.3448	−	36.3928i	1.99719	−	1.63905i
$494$	−0.910912	+	7.44842i	−0.0409839	+	0.335120i
$495$	2.03018	+	0.840930i	0.0912500	+	0.0377970i
$496$	16.7324	−	31.6158i	0.751309	−	1.41959i
$497$	24.6645	−	10.2164i	1.10635	−	0.458267i
$498$	0.444960	+	1.60148i	0.0199391	+	0.0717641i
$499$	−33.5924	−	3.30856i	−1.50380	−	0.148112i	−0.687690	−	0.726004i	$-0.741375\pi$
$499$	−33.5924	−	3.30856i	−1.50380	−	0.148112i	−0.816113	+	0.577892i	$0.803875\pi$
$500$	−12.1312	+	5.76816i	−0.542525	+	0.257960i
$501$	−1.58158	+	0.845372i	−0.0706598	+	0.0377685i
$502$	30.6459	+	21.5362i	1.36779	+	0.961210i
$503$	−7.64146	+	5.10586i	−0.340716	+	0.227659i	−0.714142	−	0.700001i	$-0.753183\pi$
$503$	−7.64146	+	5.10586i	−0.340716	+	0.227659i	0.373426	+	0.927660i	$0.378183\pi$
$504$	5.68757	−	9.04316i	0.253344	−	0.402814i
$505$	3.34189	−	5.00150i	0.148712	−	0.222564i
$506$	36.2654	+	16.0308i	1.61220	+	0.712658i
$507$	1.17760	+	11.9564i	0.0522993	+	0.531003i
$508$	4.15833	+	27.6420i	0.184496	+	1.22641i
$509$	−6.58694	−	21.7142i	−0.291961	−	0.962466i	−0.973114	−	0.230325i	$-0.926021\pi$
$509$	−6.58694	−	21.7142i	−0.291961	−	0.962466i	0.681153	−	0.732141i	$-0.261479\pi$
$510$	4.02046	−	4.67052i	0.178029	−	0.206814i
$511$	23.8736			1.05610
$512$	−2.56220	+	22.4819i	−0.113234	+	0.993568i
$513$	5.34435			0.235959
$514$	5.27313	−	6.12573i	0.232588	−	0.270194i
$515$	−2.94013	−	9.69230i	−0.129557	−	0.427094i
$516$	−3.29194	−	21.8828i	−0.144920	−	0.963335i
$517$	2.54846	+	25.8750i	0.112081	+	1.13798i
$518$	−4.15497	−	1.83667i	−0.182559	−	0.0806987i
$519$	0.578615	−	0.865958i	0.0253984	−	0.0380114i
$520$	1.05696	−	1.68055i	0.0463506	−	0.0736968i
$521$	−15.1150	+	10.0995i	−0.662201	+	0.442469i	−0.840722	−	0.541468i	$-0.817869\pi$
$521$	−15.1150	+	10.0995i	−0.662201	+	0.442469i	0.178521	+	0.983936i	$0.442869\pi$
$522$	−10.7689	−	7.56777i	−0.471341	−	0.331232i
$523$	−1.69414	+	0.905535i	−0.0740795	+	0.0395963i	−0.508021	−	0.861345i	$-0.669623\pi$
$523$	−1.69414	+	0.905535i	−0.0740795	+	0.0395963i	0.433941	+	0.900941i	$0.357123\pi$
$524$	−22.9395	+	10.9073i	−1.00212	+	0.476486i
$525$	16.9155	+	1.66603i	0.738252	+	0.0727114i
$526$	−1.63731	−	5.89295i	−0.0713903	−	0.256945i
$527$	−50.9248	+	21.0938i	−2.21832	+	0.918859i
$528$	10.9890	+	5.81582i	0.478233	+	0.253101i
$529$	−53.9215	−	22.3350i	−2.34441	−	0.971088i
$530$	−0.913275	+	7.46774i	−0.0396701	+	0.324378i
$531$	3.82655	−	3.14037i	0.166058	−	0.136280i
$532$	39.1413	−	9.88986i	1.69699	−	0.428780i
$533$	4.39137	+	1.33211i	0.190211	+	0.0577000i
$534$	1.03148	−	4.61556i	0.0446366	−	0.199735i
$535$	2.18393	−	10.9794i	0.0944195	−	0.474679i
$536$	10.6206	+	2.90394i	0.458742	+	0.125431i
$537$	−1.66279	+	0.330749i	−0.0717546	+	0.0142729i
$538$	−0.553881	+	0.528424i	−0.0238795	+	0.0227820i
$539$	−17.4579	−	14.3273i	−0.751965	−	0.617122i
$540$	−1.27943	−	0.601913i	−0.0550579	−	0.0259022i
$541$	8.42979	−	15.7710i	0.362425	−	0.678049i	−0.632942	−	0.774199i	$-0.718153\pi$
$541$	8.42979	−	15.7710i	0.362425	−	0.678049i	0.995367	+	0.0961500i	$0.0306528\pi$
$542$	11.5425	−	35.0606i	0.495795	−	1.50598i
$543$	−2.81918	+	2.81918i	−0.120983	+	0.120983i
$544$	25.1291	−	24.1720i	1.07740	−	1.03637i
$545$	6.67161	+	6.67161i	0.285780	+	0.285780i
$546$	−4.73454	+	2.38926i	−0.202620	+	0.102251i
$547$	6.08330	+	3.25159i	0.260103	+	0.139028i	0.596295	−	0.802766i	$-0.296639\pi$
$547$	6.08330	+	3.25159i	0.260103	+	0.139028i	−0.336192	+	0.941794i	$0.609139\pi$
$548$	17.5970	+	19.3354i	0.751707	+	0.825966i
$549$	−3.39549	+	4.13742i	−0.144916	+	0.176581i
$550$	−0.465163	+	19.7762i	−0.0198346	+	0.843262i
$551$	−9.70375	−	48.7841i	−0.413394	−	2.07827i
$552$	−22.8241	−	11.4007i	−0.971457	−	0.485246i
$553$	28.9111	+	5.75077i	1.22942	+	0.244547i
$554$	−15.3689	+	9.75439i	−0.652963	+	0.414424i
$555$	−0.174537	+	0.575371i	−0.00740867	+	0.0244231i
$556$	−1.85966	−	2.49673i	−0.0788671	−	0.105885i
$557$	−12.9359	−	15.7624i	−0.548111	−	0.667876i	0.423103	−	0.906081i	$-0.360941\pi$
$557$	−12.9359	−	15.7624i	−0.548111	−	0.667876i	−0.971215	+	0.238206i	$0.923441\pi$
$558$	7.79096	+	9.96208i	0.329817	+	0.421729i
$559$	−4.20387	+	10.1490i	−0.177805	+	0.429258i
$560$	−10.4842	−	2.04072i	−0.443040	−	0.0862361i
$561$	−7.33172	−	17.7003i	−0.309545	−	0.747308i
$562$	8.18488	−	14.4830i	0.345258	−	0.610928i
$563$	1.52977	−	15.5320i	0.0644721	−	0.654596i	−0.907588	−	0.419862i	$-0.862078\pi$
$563$	1.52977	−	15.5320i	0.0644721	−	0.654596i	0.972060	−	0.234733i	$-0.0754217\pi$
$564$	−0.855198	−	16.7078i	−0.0360103	−	0.703526i
$565$	−1.15241	−	2.15601i	−0.0484823	−	0.0907041i
$566$	3.29407	−	0.575060i	0.138460	−	0.0241716i
$567$	2.09840	+	3.14048i	0.0881245	+	0.131888i
$568$	−8.15778	−	18.2517i	−0.342293	−	0.765824i
$569$	−27.0824	−	18.0959i	−1.13535	−	0.758620i	−0.161743	−	0.986833i	$-0.551712\pi$
$569$	−27.0824	−	18.0959i	−1.13535	−	0.758620i	−0.973611	+	0.228213i	$0.926712\pi$
$570$	−1.92816	−	4.98331i	−0.0807616	−	0.208728i
$571$	−17.6576	+	1.73912i	−0.738946	+	0.0727798i	−0.460485	−	0.887668i	$-0.652324\pi$
$571$	−17.6576	+	1.73912i	−0.738946	+	0.0727798i	−0.278461	+	0.960448i	$0.589824\pi$
$572$	−3.18390	−	5.28737i	−0.133126	−	0.221076i
$573$	2.03531	−	0.617404i	0.0850262	−	0.0257924i
$574$	−1.84151	−	24.6201i	−0.0768630	−	1.02762i
$575$		−	40.5927i		−	1.69283i
$576$	−6.88704	−	4.07047i	−0.286960	−	0.169603i
$577$			42.1617i			1.75522i	0.479380	+	0.877608i	$0.340862\pi$
$577$			42.1617i			1.75522i	−0.479380	+	0.877608i	$0.659138\pi$
$578$	−29.6050	+	2.21436i	−1.23140	+	0.0921051i
$579$	−18.7618	+	5.69133i	−0.779713	+	0.236523i
$580$	−3.17129	+	12.7717i	−0.131681	+	0.530317i
$581$	−4.41781	+	0.435117i	−0.183282	+	0.0180517i
$582$	6.93354	−	2.68274i	0.287405	−	0.111203i
$583$	19.4473	+	12.9943i	0.805426	+	0.538168i
$584$	−0.493790	−	17.8709i	−0.0204332	−	0.739504i
$585$	0.389959	+	0.583615i	0.0161228	+	0.0241295i
$586$	0.0537010	+	0.307611i	0.00221837	+	0.0127073i
$587$	−11.8208	−	22.1152i	−0.487897	−	0.912791i	−0.998593	−	0.0530296i	$-0.983112\pi$
$587$	−11.8208	−	22.1152i	−0.487897	−	0.912791i	0.510696	−	0.859761i	$-0.329388\pi$
$588$	10.7874	+	9.73681i	0.444863	+	0.401539i
$589$	−4.68450	+	47.5625i	−0.193021	+	1.95978i
$590$	−4.30878	−	2.43505i	−0.177390	−	0.100249i
$591$	4.00615	+	9.67170i	0.164791	+	0.397841i
$592$	−1.28893	+	3.14826i	−0.0529747	+	0.129393i
$593$	−7.47719	+	18.0515i	−0.307051	+	0.741287i	0.692747	+	0.721181i	$0.256400\pi$
$593$	−7.47719	+	18.0515i	−0.307051	+	0.741287i	−0.999798	+	0.0201061i	$0.993600\pi$
$594$	−3.46260	+	2.70796i	−0.142072	+	0.111109i
$595$	10.4414	+	12.7229i	0.428055	+	0.521587i
$596$	−2.53168	+	17.3120i	−0.103701	+	0.709128i
$597$	6.11488	−	20.1581i	0.250266	−	0.825015i
$598$	6.78680	+	10.6932i	0.277533	+	0.437278i
$599$	5.82748	+	1.15916i	0.238104	+	0.0473619i	0.312700	−	0.949852i	$-0.398767\pi$
$599$	5.82748	+	1.15916i	0.238104	+	0.0473619i	−0.0745955	+	0.997214i	$0.523767\pi$
$600$	0.897259	−	12.6968i	0.0366305	−	0.518345i
$601$	−0.179462	−	0.902216i	−0.00732040	−	0.0368021i	0.976952	−	0.213457i	$-0.0684723\pi$
$601$	−0.179462	−	0.902216i	−0.00732040	−	0.0368021i	−0.984273	+	0.176655i	$0.943472\pi$
$602$	59.0848	+	1.38975i	2.40812	+	0.0566420i
$603$	−2.46957	+	3.00917i	−0.100568	+	0.122543i
$604$	−1.79549	−	0.0845112i	−0.0730574	−	0.00343871i
$605$	0.834666	+	0.446138i	0.0339340	+	0.0181381i
$606$	5.42111	+	10.7424i	0.220218	+	0.436381i
$607$	−31.1905	−	31.1905i	−1.26598	−	1.26598i	−0.948145	−	0.317837i	$-0.897044\pi$
$607$	−31.1905	−	31.1905i	−1.26598	−	1.26598i	−0.317837	−	0.948145i	$-0.602956\pi$
$608$	−8.21279	−	29.0953i	−0.333073	−	1.17997i
$609$	24.8567	−	24.8567i	1.00724	−	1.00724i
$610$	5.08295	+	1.67339i	0.205803	+	0.0677538i
$611$	−3.91492	+	7.32429i	−0.158381	+	0.296309i
$612$	4.17686	+	11.5984i	0.168840	+	0.468838i
$613$	5.21850	+	4.28271i	0.210773	+	0.172977i	0.733857	−	0.679304i	$-0.237718\pi$
$613$	5.21850	+	4.28271i	0.210773	+	0.172977i	−0.523084	+	0.852281i	$0.675218\pi$
$614$	−23.5308	−	24.6644i	−0.949625	−	0.995374i
$615$	−3.20489	+	0.637493i	−0.129234	+	0.0257062i
$616$	−20.3485	+	26.2404i	−0.819863	+	1.05726i
$617$	−6.88240	+	34.6002i	−0.277075	+	1.39295i	0.552014	+	0.833835i	$0.313859\pi$
$617$	−6.88240	+	34.6002i	−0.277075	+	1.39295i	−0.829089	+	0.559116i	$0.811141\pi$
$618$	19.7730	+	4.41885i	0.795385	+	0.177752i
$619$	45.7498	+	13.8780i	1.83884	+	0.557806i	0.999908	+	0.0135675i	$0.00431882\pi$
$619$	45.7498	+	13.8780i	1.83884	+	0.557806i	0.838931	+	0.544238i	$0.183181\pi$
$620$	6.47824	−	10.8588i	0.260172	−	0.436100i
$621$	6.97272	−	5.72236i	0.279806	−	0.229631i
$622$	−0.808799	−	0.0989129i	−0.0324299	−	0.00396605i
$623$	11.6696	+	4.83371i	0.467533	+	0.193659i
$624$	1.88645	+	3.49470i	0.0755184	+	0.139900i
$625$	16.4013	−	6.79365i	0.656053	−	0.271746i
$626$	11.5354	−	3.20503i	0.461048	−	0.128099i
$627$	−16.5317	−	1.62823i	−0.660211	−	0.0650251i
$628$	11.6954	+	4.15762i	0.466698	+	0.165907i
$629$	4.62316	−	2.47113i	0.184337	−	0.0985303i
$630$	2.17125	−	3.08968i	0.0865048	−	0.123096i
$631$	2.62126	−	1.75147i	0.104351	−	0.0697249i	−0.502300	−	0.864693i	$-0.667513\pi$
$631$	2.62126	−	1.75147i	0.104351	−	0.0697249i	0.606651	+	0.794969i	$0.292513\pi$
$632$	3.70684	−	21.7608i	0.147450	−	0.865597i
$633$	8.98187	−	13.4423i	0.356997	−	0.534284i
$634$	−6.71016	+	15.1799i	−0.266495	+	0.602872i
$635$	0.968507	+	9.83342i	0.0384340	+	0.390227i
$636$	−12.1064	−	8.94021i	−0.480048	−	0.354502i
$637$	−2.09407	−	6.90321i	−0.0829700	−	0.273515i
$638$	31.0057	+	26.6902i	1.22753	+	1.05668i
$639$	7.06818			0.279613
$640$	−1.31076	+	7.89034i	−0.0518123	+	0.311893i
$641$	21.7727			0.859971			0.429985	−	0.902836i	$-0.358519\pi$
$641$	21.7727			0.859971			0.429985	+	0.902836i	$0.358519\pi$
$642$	16.9713	+	14.6092i	0.669805	+	0.576579i
$643$	8.58897	+	28.3140i	0.338716	+	1.11660i	0.946557	+	0.322537i	$0.104536\pi$
$643$	8.58897	+	28.3140i	0.338716	+	1.11660i	−0.607841	+	0.794059i	$0.707964\pi$
$644$	40.4779	−	54.8131i	1.59505	−	2.15994i
$645$	−0.766718	−	7.78462i	−0.0301895	−	0.306519i
$646$	−18.8349	+	42.6090i	−0.741051	+	1.67643i
$647$	−22.5392	+	33.7323i	−0.886109	+	1.32616i	0.0586128	+	0.998281i	$0.481332\pi$
$647$	−22.5392	+	33.7323i	−0.886109	+	1.32616i	−0.944721	+	0.327874i	$0.893668\pi$
$648$	2.30745	−	1.63575i	0.0906453	−	0.0642582i
$649$	−12.7934	+	8.54828i	−0.502185	+	0.335549i
$650$	−3.63302	+	5.16976i	−0.142499	+	0.202775i
$651$	−29.7883	+	15.9222i	−1.16750	+	0.624039i
$652$	−12.0433	+	33.8778i	−0.471650	+	1.32676i
$653$	−40.4719	−	3.98614i	−1.58379	−	0.155990i	−0.732529	−	0.680735i	$-0.761660\pi$
$653$	−40.4719	−	3.98614i	−1.58379	−	0.155990i	−0.851259	+	0.524746i	$0.824160\pi$
$654$	−18.1849	+	5.05254i	−0.711086	+	0.197570i
$655$	−8.29527	+	3.43601i	−0.324123	+	0.134256i
$656$	−18.3917	+	1.88772i	−0.718075	+	0.0737031i
$657$	5.83960	+	2.41884i	0.227824	+	0.0943680i
$658$	44.3505	+	5.42389i	1.72896	+	0.211445i
$659$	−7.38978	+	6.06464i	−0.287865	+	0.236245i	−0.767232	−	0.641370i	$-0.778366\pi$
$659$	−7.38978	+	6.06464i	−0.287865	+	0.236245i	0.479367	+	0.877615i	$0.340866\pi$
$660$	3.77427	+	2.25169i	0.146913	+	0.0876469i
$661$	10.5173	+	3.19038i	0.409075	+	0.124091i	0.488114	−	0.872780i	$-0.337685\pi$
$661$	10.5173	+	3.19038i	0.409075	+	0.124091i	−0.0790389	+	0.996872i	$0.525185\pi$
$662$	37.6214	+	8.40760i	1.46220	+	0.326771i
$663$	1.19388	−	6.00205i	0.0463665	−	0.233100i
$664$	0.417089	+	3.29802i	0.0161862	+	0.127988i
$665$	13.9965	−	2.78408i	0.542762	−	0.107962i
$666$	−0.830239	−	0.870237i	−0.0321711	−	0.0337210i
$667$	−64.8950	−	53.2579i	−2.51274	−	2.06216i
$668$	−3.37452	+	1.21524i	−0.130564	+	0.0470192i
$669$	4.12654	−	7.72021i	0.159541	−	0.298480i
$670$	3.69687	+	1.21707i	0.142822	+	0.0470196i
$671$	11.7638	−	11.7638i	0.454136	−	0.454136i
$672$	13.8725	−	16.2500i	0.535143	−	0.626857i
$673$	21.9085	+	21.9085i	0.844509	+	0.844509i	0.989442	−	0.144932i	$-0.0462965\pi$
$673$	21.9085	+	21.9085i	0.844509	+	0.844509i	−0.144932	+	0.989442i	$0.546296\pi$
$674$	−9.61361	−	19.0502i	−0.370303	−	0.733788i
$675$	3.96881	+	2.12138i	0.152760	+	0.0816518i
$676$	−1.12974	+	24.0020i	−0.0434516	+	0.923153i
$677$	14.1420	−	17.2321i	0.543521	−	0.662283i	−0.426731	−	0.904379i	$-0.640335\pi$
$677$	14.1420	−	17.2321i	0.543521	−	0.662283i	0.970252	+	0.242096i	$0.0778349\pi$
$678$	4.88893	+	0.114994i	0.187758	+	0.00441632i
$679$	3.87364	+	19.4741i	0.148657	+	0.747348i
$680$	9.30794	−	8.07922i	0.356943	−	0.309824i
$681$	−19.2957	−	3.83815i	−0.739411	−	0.147078i
$682$	−21.0647	−	33.1893i	−0.806608	−	1.27088i
$683$	−11.4011	+	37.5844i	−0.436251	+	1.43813i	0.413287	+	0.910601i	$0.364381\pi$
$683$	−11.4011	+	37.5844i	−0.436251	+	1.43813i	−0.849538	+	0.527527i	$0.823119\pi$
$684$	10.5762	+	1.54664i	0.404391	+	0.0591374i
$685$	5.86278	+	7.14382i	0.224005	+	0.272951i
$686$	−1.11875	+	0.874929i	−0.0427140	+	0.0334050i
$687$	1.86404	−	4.50019i	0.0711176	−	0.171693i
$688$	−0.181764	−	44.2576i	−0.00692969	−	1.68731i
$689$	2.85899	+	6.90222i	0.108919	+	0.262954i
$690$	−7.85143	−	4.43714i	−0.298899	−	0.168919i
$691$	−0.746271	+	7.57702i	−0.0283895	+	0.288243i	0.970499	+	0.241105i	$0.0775100\pi$
$691$	−0.746271	+	7.57702i	−0.0283895	+	0.288243i	−0.998888	+	0.0471378i	$0.984990\pi$
$692$	1.39566	−	1.54624i	0.0530549	−	0.0587792i
$693$	−5.53419	−	10.3537i	−0.210226	−	0.393306i
$694$	−0.882971	−	5.05785i	−0.0335171	−	0.191994i
$695$	−0.611389	−	0.915008i	−0.0231913	−	0.0347082i
$696$	−19.1210	−	18.0927i	−0.724779	−	0.685804i
$697$	23.6882	+	15.8279i	0.897254	+	0.599526i
$698$	−32.8777	+	12.7211i	−1.24444	+	0.481501i
$699$	18.0586	−	1.77861i	0.683037	−	0.0672733i
$700$	32.9927	+	8.19229i	1.24701	+	0.309639i
$701$	12.0810	−	3.66473i	0.456293	−	0.138415i	−0.0537673	−	0.998553i	$-0.517123\pi$
$701$	12.0810	−	3.66473i	0.456293	−	0.138415i	0.510061	+	0.860138i	$0.329623\pi$
$702$	−1.40017	+	0.104728i	−0.0528461	+	0.00395272i
$703$		−	4.54523i		−	0.171426i
$704$	20.0635	+	14.6894i	0.756173	+	0.553628i
$705$		−	5.91371i		−	0.222723i
$706$	−1.61011	−	21.5264i	−0.0605971	−	0.810156i
$707$	−30.7529	+	9.32879i	−1.15658	+	0.350845i
$708$	8.48137	−	5.10724i	0.318749	−	0.191942i
$709$	38.6412	−	3.80583i	1.45120	−	0.142931i	0.658519	−	0.752564i	$-0.271183\pi$
$709$	38.6412	−	3.80583i	1.45120	−	0.142931i	0.792684	+	0.609633i	$0.208683\pi$
$710$	−2.55009	−	6.59069i	−0.0957031	−	0.247344i
$711$	6.48914	+	4.33590i	0.243362	+	0.162609i
$712$	3.37698	−	8.83545i	0.126558	−	0.331123i
$713$	44.8149	+	67.0702i	1.67833	+	2.51180i
$714$	−32.4335	+	5.66205i	−1.21379	+	0.211897i
$715$	−1.02845	−	1.92410i	−0.0384620	−	0.0719573i
$716$	−3.38629	+	0.173329i	−0.126552	+	0.00647761i
$717$	−1.58694	+	16.1125i	−0.0592653	+	0.601731i
$718$	−3.06882	+	5.43021i	−0.114527	+	0.202654i
$719$	7.17769	+	17.3285i	0.267683	+	0.646244i	0.999373	−	0.0353933i	$-0.0112684\pi$
$719$	7.17769	+	17.3285i	0.267683	+	0.646244i	−0.731691	+	0.681637i	$0.761268\pi$
$720$	−2.35774	−	1.56142i	−0.0878676	−	0.0581907i
$721$	−20.7076	+	49.9924i	−0.771189	+	1.86182i
$722$	8.33061	+	10.6521i	0.310033	+	0.396431i
$723$	2.91227	+	3.54861i	0.108308	+	0.131974i
$724$	−6.39488	+	4.76315i	−0.237664	+	0.177021i
$725$	12.1581	−	40.0797i	0.451539	−	1.48852i
$726$	−1.59843	+	1.01450i	−0.0593234	+	0.0376515i
$727$	−6.95754	−	1.38394i	−0.258041	−	0.0513275i	0.0643745	−	0.997926i	$-0.479495\pi$
$727$	−6.95754	−	1.38394i	−0.258041	−	0.0513275i	−0.322415	+	0.946598i	$0.604495\pi$
$728$	−10.0609	+	3.35807i	−0.372881	+	0.124458i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	0.148602	−	6.31778i	0.00550002	−	0.233832i
$731$	−43.2651	+	52.7187i	−1.60022	+	1.94987i
$732$	−7.91687	+	7.20510i	−0.292616	+	0.266308i
$733$	−10.9906	−	5.87462i	−0.405948	−	0.216984i	0.255768	−	0.966738i	$-0.417672\pi$
$733$	−10.9906	−	5.87462i	−0.405948	−	0.216984i	−0.661716	+	0.749754i	$0.730172\pi$
$734$	−36.7537	+	18.5476i	−1.35660	+	0.684604i
$735$	3.63225	+	3.63225i	0.133978	+	0.133978i
$736$	−41.8684	−	29.1667i	−1.54329	−	1.07510i
$737$	8.55588	−	8.55588i	0.315160	−	0.315160i
$738$	2.04404	−	6.20879i	0.0752422	−	0.228549i
$739$	6.76747	−	12.6611i	0.248946	−	0.465744i	−0.726148	−	0.687538i	$-0.758691\pi$
$739$	6.76747	−	12.6611i	0.248946	−	0.465744i	0.975094	+	0.221794i	$0.0711913\pi$
$740$	−0.511911	+	1.08812i	−0.0188182	+	0.0400001i
$741$	−4.10164	−	3.36613i	−0.150678	−	0.123658i
$742$	29.0818	−	27.7452i	1.06763	−	1.01856i
$743$	18.9700	−	3.77336i	0.695941	−	0.138431i	0.165572	−	0.986198i	$-0.447053\pi$
$743$	18.9700	−	3.77336i	0.695941	−	0.138431i	0.530370	+	0.847766i	$0.322053\pi$
$744$	12.5349	+	21.9692i	0.459552	+	0.805429i
$745$	−1.20656	+	6.06581i	−0.0442051	+	0.222234i
$746$	1.46936	−	6.57491i	0.0537969	−	0.240725i
$747$	−1.12471	−	0.341176i	−0.0411509	−	0.0124830i
$748$	−9.38667	−	37.1499i	−0.343211	−	1.35833i
$749$	−46.2312	+	37.9410i	−1.68925	+	1.38633i
$750$	1.15302	−	9.42814i	0.0421025	−	0.344267i
$751$	18.6700	+	7.73335i	0.681277	+	0.282194i	0.696361	−	0.717692i	$-0.254801\pi$
$751$	18.6700	+	7.73335i	0.681277	+	0.282194i	−0.0150837	+	0.999886i	$0.504801\pi$
$752$	3.14281	−	33.3115i	0.114607	−	1.21474i
$753$	−24.4696	+	10.1356i	−0.891721	+	0.369363i
$754$	3.49827	+	12.5908i	0.127400	+	0.458531i
$755$	−0.632324	−	0.0622784i	−0.0230126	−	0.00226654i
$756$	3.24379	+	6.82213i	0.117975	+	0.248118i
$757$	−16.3206	+	8.72352i	−0.593181	+	0.317062i	−0.740531	−	0.672023i	$-0.765426\pi$
$757$	−16.3206	+	8.72352i	−0.593181	+	0.317062i	0.147350	+	0.989084i	$0.452926\pi$
$758$	−27.6457	−	19.4279i	−1.00414	−	0.705652i
$759$	−23.3121	+	15.5766i	−0.846175	+	0.565396i
$760$	−2.37357	−	10.4197i	−0.0860983	−	0.377964i
$761$	26.4158	−	39.5340i	0.957572	−	1.43311i	0.0570137	−	0.998373i	$-0.481842\pi$
$761$	26.4158	−	39.5340i	0.957572	−	1.43311i	0.900559	−	0.434735i	$-0.143158\pi$
$762$	−18.0783	−	7.99135i	−0.654907	−	0.289496i
$763$	−4.94077	−	50.1645i	−0.178868	−	1.81608i
$764$	4.20645	−	0.632798i	0.152184	−	0.0228938i
$765$	1.26495	+	4.16999i	0.0457345	+	0.150766i
$766$	−12.3830	+	14.3852i	−0.447417	+	0.519759i
$767$	−4.91473			−0.177461
$768$	−12.4511	−	10.0484i	−0.449291	−	0.362589i
$769$	−35.4886			−1.27975			−0.639875	−	0.768479i	$-0.721014\pi$
$769$	−35.4886			−1.27975			−0.639875	+	0.768479i	$0.721014\pi$
$770$	−7.65764	+	8.89579i	−0.275962	+	0.320582i
$771$	1.65908	+	5.46925i	0.0597503	+	0.196970i
$772$	−38.7757	+	5.83324i	−1.39557	+	0.209943i
$773$	−2.30946	−	23.4483i	−0.0830655	−	0.843378i	−0.942960	−	0.332906i	$-0.891971\pi$
$773$	−2.30946	−	23.4483i	−0.0830655	−	0.843378i	0.859895	−	0.510472i	$-0.170529\pi$
$774$	14.3117	+	6.32635i	0.514422	+	0.227396i
$775$	−22.3582	+	33.4614i	−0.803129	+	1.20197i
$776$	14.4975	−	3.30247i	0.520431	−	0.118552i
$777$	2.67089	−	1.78463i	0.0958178	−	0.0640234i
$778$	9.58182	+	6.73357i	0.343525	+	0.241410i
$779$	21.7852	−	11.6444i	0.780537	−	0.417206i
$780$	0.602813	+	1.26780i	0.0215842	+	0.0453945i
$781$	−21.8640	−	2.15341i	−0.782355	−	0.0770552i
$782$	21.0490	+	75.7587i	0.752711	+	2.70912i
$783$	8.59853	−	3.56163i	0.307287	−	0.127282i
$784$	18.5298	+	22.3905i	0.661780	+	0.799661i
$785$	4.05364	+	1.67907i	0.144680	+	0.0599286i
$786$	2.18030	−	17.8281i	0.0777688	−	0.635906i
$787$	−36.8919	+	30.2764i	−1.31505	+	1.07924i	−0.323959	+	0.946071i	$0.605014\pi$
$787$	−36.8919	+	30.2764i	−1.31505	+	1.07924i	−0.991094	+	0.133165i	$0.957486\pi$
$788$	5.12901	+	20.2992i	0.182713	+	0.723129i
$789$	4.13857	+	1.25542i	0.147337	+	0.0446941i
$790$	1.70181	−	7.61509i	0.0605478	−	0.270933i
$791$	−2.54803	+	12.8098i	−0.0905974	+	0.455464i
$792$	−7.63599	+	4.35686i	−0.271333	+	0.154814i
$793$	5.21190	−	1.03671i	0.185080	−	0.0368147i
$794$	16.3434	−	15.5923i	0.580007	−	0.553349i
$795$	−4.11228	−	3.37486i	−0.145848	−	0.119694i
$796$	17.9348	−	38.1222i	0.635681	−	1.35121i
$797$	11.6892	−	21.8689i	0.414051	−	0.774635i	−0.585294	−	0.810821i	$-0.699021\pi$
$797$	11.6892	−	21.8689i	0.414051	−	0.774635i	0.999345	+	0.0361861i	$0.0115209\pi$
$798$	−8.92681	+	27.1153i	−0.316006	+	0.959871i
$799$	−36.4579	+	36.4579i	−1.28979	+	1.28979i
$800$	5.45006	−	24.8667i	0.192689	−	0.879170i
$801$	2.36470	+	2.36470i	0.0835527	+	0.0835527i
$802$	34.1395	−	17.2283i	1.20551	−	0.608353i
$803$	−17.3267	−	9.26131i	−0.611445	−	0.326824i
$804$	−5.75800	+	5.24032i	−0.203069	+	0.184812i
$805$	15.2801	−	18.6189i	0.538554	−	0.656230i
$806$	0.295257	−	12.5528i	0.0104000	−	0.442152i
$807$	−0.105603	−	0.530901i	−0.00371739	−	0.0186886i
$808$	7.61929	+	22.8276i	0.268046	+	0.803072i
$809$	−28.7425	−	5.71724i	−1.01053	−	0.201007i	−0.338056	−	0.941126i	$-0.609769\pi$
$809$	−28.7425	−	5.71724i	−1.01053	−	0.201007i	−0.672476	+	0.740119i	$0.734769\pi$
$810$	0.844143	−	0.535763i	0.0296602	−	0.0188248i
$811$	14.1817	−	46.7507i	0.497985	−	1.64164i	−0.242934	−	0.970043i	$-0.578110\pi$
$811$	14.1817	−	46.7507i	0.497985	−	1.64164i	0.740919	−	0.671594i	$-0.234390\pi$
$812$	56.3837	−	41.9967i	1.97868	−	1.47380i
$813$	16.5580	+	20.1760i	0.580715	+	0.707603i
$814$	2.30305	+	2.94484i	0.0807218	+	0.103217i
$815$	−4.86372	+	11.7421i	−0.170369	+	0.411306i
$816$	4.90926	+	24.1615i	0.171858	+	0.845821i
$817$	22.6290	+	54.6313i	0.791690	+	1.91131i
$818$	1.25202	−	2.21542i	0.0437758	−	0.0774604i
$819$	0.367561	−	3.73191i	0.0128436	−	0.130403i
$820$	−6.52682	+	0.334078i	−0.227926	+	0.0116665i
$821$	−17.5462	−	32.8266i	−0.612366	−	1.14566i	−0.976745	−	0.214405i	$-0.931219\pi$
$821$	−17.5462	−	32.8266i	−0.612366	−	1.14566i	0.364379	−	0.931251i	$-0.381281\pi$
$822$	−18.2112	+	3.17921i	−0.635189	+	0.110888i
$823$	−29.2189	−	43.7291i	−1.01851	−	1.52430i	−0.841619	−	0.540071i	$-0.818397\pi$
$823$	−29.2189	−	43.7291i	−1.01851	−	1.52430i	−0.176887	−	0.984231i	$-0.556603\pi$
$824$	37.8509	+	14.4669i	1.31860	+	0.503980i
$825$	−11.6304	−	7.77120i	−0.404919	−	0.270558i
$826$	9.54149	+	24.6600i	0.331991	+	0.858030i
$827$	−12.5938	+	1.24038i	−0.437928	+	0.0431322i	−0.314579	−	0.949231i	$-0.601863\pi$
$827$	−12.5938	+	1.24038i	−0.437928	+	0.0431322i	−0.123349	+	0.992363i	$0.539363\pi$
$828$	15.4547	−	9.30639i	0.537088	−	0.323419i
$829$	−12.9467	+	3.92733i	−0.449656	+	0.136402i	−0.506987	−	0.861953i	$-0.669241\pi$
$829$	−12.9467	+	3.92733i	−0.449656	+	0.136402i	0.0573311	+	0.998355i	$0.481741\pi$
$830$	0.0876482	+	1.17182i	0.00304231	+	0.0406744i
$831$		−	12.8715i		−	0.446508i
$832$	2.72183	+	7.46177i	0.0943625	+	0.258690i
$833$		−	44.7854i		−	1.55172i
$834$	2.19523	−	0.164196i	0.0760146	−	0.00568565i
$835$	−1.21325	+	0.368034i	−0.0419861	+	0.0127363i
$836$	−32.2442	−	8.00641i	−1.11519	−	0.276907i
$837$	−8.89959	+	0.876533i	−0.307615	+	0.0302974i
$838$	−6.56727	+	2.54103i	−0.226863	+	0.0877783i
$839$	26.0147	+	17.3824i	0.898126	+	0.600109i	0.916637	−	0.399720i	$-0.130893\pi$
$839$	26.0147	+	17.3824i	0.898126	+	0.600109i	−0.0185111	+	0.999829i	$0.505893\pi$
$840$	5.19095	−	5.48596i	0.179105	−	0.189284i
$841$	−32.0119	−	47.9093i	−1.10386	−	1.65204i
$842$	−5.48030	−	31.3924i	−0.188864	−	1.08185i
$843$	5.54517	+	10.3743i	0.190986	+	0.357309i
$844$	21.6649	−	24.0024i	0.745735	−	0.826196i
$845$	−0.832534	+	8.45286i	−0.0286400	+	0.290787i
$846$	10.2988	+	5.82026i	0.354081	+	0.200105i
$847$	−1.93495	−	4.67138i	−0.0664857	−	0.160511i
$848$	−21.3706	−	21.1958i	−0.733870	−	0.727866i
$849$	−0.904850	+	2.18450i	−0.0310544	+	0.0749719i
$850$	−30.9003	+	24.1659i	−1.05987	+	0.828884i
$851$	−4.86672	−	5.93011i	−0.166829	−	0.203282i
$852$	13.9876	+	2.04552i	0.479207	+	0.0700782i
$853$	4.20662	−	13.8674i	0.144032	−	0.474809i	−0.855008	−	0.518614i	$-0.826448\pi$
$853$	4.20662	−	13.8674i	0.144032	−	0.474809i	0.999040	+	0.0438050i	$0.0139480\pi$
$854$	−15.3202	−	24.1383i	−0.524246	−	0.825997i
$855$	3.70571	+	0.737111i	0.126732	+	0.0252087i
$856$	29.3576	+	33.8224i	1.00342	+	1.15602i
$857$	4.83619	+	24.3132i	0.165201	+	0.830522i	0.971138	+	0.238520i	$0.0766622\pi$
$857$	4.83619	+	24.3132i	0.165201	+	0.830522i	−0.805937	+	0.592002i	$0.798338\pi$
$858$	4.36305	+	0.102625i	0.148952	+	0.00350355i
$859$	7.74508	−	9.43741i	0.264259	−	0.322000i	−0.623929	−	0.781481i	$-0.714465\pi$
$859$	7.74508	−	9.43741i	0.264259	−	0.322000i	0.888188	+	0.459481i	$0.151965\pi$
$860$	0.735554	−	15.6273i	0.0250822	−	0.532886i
$861$	15.3963	+	8.22950i	0.524705	+	0.280461i
$862$	−3.64906	−	7.23093i	−0.124287	−	0.246287i
$863$	−8.87130	−	8.87130i	−0.301983	−	0.301983i	0.539807	−	0.841789i	$-0.318497\pi$
$863$	−8.87130	−	8.87130i	−0.301983	−	0.301983i	−0.841789	+	0.539807i	$0.818497\pi$
$864$	5.03972	−	2.56929i	0.171455	−	0.0874091i
$865$	0.520640	−	0.520640i	0.0177023	−	0.0177023i
$866$	−6.32317	−	2.08169i	−0.214870	−	0.0707388i
$867$	9.89572	−	18.5136i	0.336076	−	0.628755i
$868$	−63.5574	+	22.8885i	−2.15728	+	0.776888i
$869$	−18.7518	−	15.3892i	−0.636113	−	0.522044i
$870$	−6.42324	−	6.73268i	−0.217768	−	0.228259i
$871$	3.79065	−	0.754007i	0.128441	−	0.0255486i
$872$	−37.4492	+	4.73607i	−1.26819	+	0.160384i
$873$	−1.02558	+	5.15594i	−0.0347107	+	0.174502i
$874$	66.5340	+	14.8690i	2.25055	+	0.502951i
$875$	24.2755	+	7.36390i	0.820663	+	0.248945i
$876$	10.8563	+	6.47674i	0.366800	+	0.218829i
$877$	8.23005	−	6.75422i	0.277909	−	0.228074i	−0.485105	−	0.874456i	$-0.661219\pi$
$877$	8.23005	−	6.75422i	0.277909	−	0.228074i	0.763014	+	0.646382i	$0.223719\pi$
$878$	−35.2240	−	4.30775i	−1.18875	−	0.145379i
$879$	−0.203996	−	0.0844978i	−0.00688061	−	0.00285004i
$880$	6.81747	+	5.54825i	0.229817	+	0.187032i
$881$	−0.433968	+	0.179755i	−0.0146207	+	0.00605611i	−0.389982	−	0.920823i	$-0.627519\pi$
$881$	−0.433968	+	0.179755i	−0.0146207	+	0.00605611i	0.375361	+	0.926879i	$0.377519\pi$
$882$	−9.90048	+	2.75078i	−0.333366	+	0.0926235i
$883$	−27.1160	−	2.67069i	−0.912525	−	0.0898759i	−0.369154	−	0.929368i	$-0.620352\pi$
$883$	−27.1160	−	2.67069i	−0.912525	−	0.0898759i	−0.543371	+	0.839492i	$0.682852\pi$
$884$	4.09962	−	11.5323i	0.137885	−	0.387872i
$885$	3.08641	−	1.64972i	0.103749	−	0.0554548i
$886$	−5.76782	+	8.20756i	−0.193774	+	0.275738i
$887$	−16.1595	+	10.7974i	−0.542582	+	0.362542i	−0.796457	−	0.604695i	$-0.793295\pi$
$887$	−16.1595	+	10.7974i	−0.542582	+	0.362542i	0.253875	+	0.967237i	$0.418295\pi$
$888$	−1.39116	−	1.96243i	−0.0466842	−	0.0658547i
$889$	29.3283	−	43.8929i	0.983640	−	1.47212i
$890$	1.35181	−	3.05810i	0.0453128	−	0.102508i
$891$	−0.304663	−	3.09330i	−0.0102066	−	0.103629i
$892$	10.4004	−	14.0837i	0.348232	−	0.471557i
$893$	12.9771	+	42.7797i	0.434262	+	1.43157i
$894$	−9.37622	−	8.07121i	−0.313588	−	0.269941i
$895$	−1.19857			−0.0400639
$896$	32.1557	−	28.1433i	1.07425	−	0.940201i
$897$	−8.95560			−0.299019
$898$	−30.9358	−	26.6301i	−1.03234	−	0.888658i
$899$	24.1601	+	79.6453i	0.805786	+	2.65632i
$900$	7.24017	+	5.34666i	0.241339	+	0.178222i
$901$	4.54617	+	46.1580i	0.151455	+	1.53775i
$902$	−8.21442	+	18.5829i	−0.273510	+	0.618743i
$903$	−23.2177	+	34.7478i	−0.772638	+	1.15633i
$904$	9.64168	+	1.64241i	0.320677	+	0.0546259i
$905$	−2.34361	+	1.56595i	−0.0779044	+	0.0520540i
$906$	0.730790	−	1.03991i	0.0242789	−	0.0345486i
$907$	−49.0216	+	26.2026i	−1.62774	+	0.870043i	−0.632289	+	0.774732i	$0.717885\pi$
$907$	−49.0216	+	26.2026i	−1.62774	+	0.870043i	−0.995448	+	0.0953109i	$0.969615\pi$
$908$	−37.0744	−	13.1796i	−1.23036	−	0.437381i
$909$	−8.46750	−	0.833976i	−0.280849	−	0.0276612i
$910$	−3.61241	+	1.00368i	−0.119750	+	0.0332717i
$911$	29.7797	−	12.3351i	0.986645	−	0.408682i	0.169762	−	0.985485i	$-0.445700\pi$
$911$	29.7797	−	12.3351i	0.986645	−	0.408682i	0.816883	+	0.576803i	$0.195700\pi$
$912$	20.4822	+	6.12146i	0.678234	+	0.202702i
$913$	3.37511	+	1.39802i	0.111700	+	0.0462676i
$914$	−8.87367	−	1.08521i	−0.293515	−	0.0358957i
$915$	−2.92504	+	2.40052i	−0.0966988	+	0.0793586i
$916$	4.99119	−	8.36621i	0.164914	−	0.276427i
$917$	45.9036	+	13.9247i	1.51587	+	0.459835i
$918$	−8.50707	−	1.90115i	−0.280775	−	0.0627474i
$919$	−0.198841	+	0.999641i	−0.00655916	+	0.0329751i	−0.983926	−	0.178575i	$-0.942851\pi$
$919$	−0.198841	+	0.999641i	−0.00655916	+	0.0329751i	0.977367	+	0.211550i	$0.0678512\pi$
$920$	−14.2535	−	11.0531i	−0.469924	−	0.364409i
$921$	23.6411	−	4.70251i	0.779001	−	0.154953i
$922$	24.7137	+	25.9044i	0.813904	+	0.853114i
$923$	−5.42464	−	4.45189i	−0.178554	−	0.146536i
$924$	−7.95554	−	22.0911i	−0.261718	−	0.726745i
$925$	1.80417	−	3.37537i	0.0593208	−	0.110981i
$926$	−6.41856	−	2.11310i	−0.210927	−	0.0694407i
$927$	−10.1304	+	10.1304i	−0.332725	+	0.332725i
$928$	−32.6035	−	41.3382i	−1.07026	−	1.35699i
$929$	−9.67232	−	9.67232i	−0.317338	−	0.317338i	0.530406	−	0.847744i	$-0.322040\pi$
$929$	−9.67232	−	9.67232i	−0.317338	−	0.317338i	−0.847744	+	0.530406i	$0.822040\pi$
$930$	4.02815	+	7.98214i	0.132088	+	0.261745i
$931$	−34.2463	−	18.3050i	−1.12238	−	0.599923i
$932$	36.2517	+	1.70632i	1.18746	+	0.0558923i
$933$	0.365517	−	0.445384i	0.0119665	−	0.0145812i
$934$	9.64986	+	0.226977i	0.315753	+	0.00742692i
$935$	−2.64243	−	13.2844i	−0.0864168	−	0.434447i
$936$	−2.80118	−	0.197954i	−0.0915594	−	0.00647034i
$937$	5.17656	+	1.02968i	0.169111	+	0.0336382i	0.278919	−	0.960315i	$-0.410024\pi$
$937$	5.17656	+	1.02968i	0.169111	+	0.0336382i	−0.109809	+	0.993953i	$0.535024\pi$
$938$	−11.1425	−	17.5560i	−0.363815	−	0.573223i
$939$	−2.45748	+	8.10122i	−0.0801968	+	0.264373i
$940$	1.71142	−	11.7030i	0.0558202	−	0.381708i
$941$	−5.96797	−	7.27199i	−0.194550	−	0.237060i	0.666594	−	0.745421i	$-0.267752\pi$
$941$	−5.96797	−	7.27199i	−0.194550	−	0.237060i	−0.861144	+	0.508361i	$0.830252\pi$
$942$	−6.91371	+	5.40694i	−0.225261	+	0.176168i
$943$	15.9549	−	38.5185i	0.519563	−	1.25434i
$944$	18.2622	−	7.65249i	0.594385	−	0.249067i
$945$	1.02186	+	2.46699i	0.0332411	+	0.0802511i
$946$	−42.3428	−	23.9295i	−1.37668	−	0.778015i
$947$	3.74398	−	38.0132i	0.121663	−	1.23526i	−0.719504	−	0.694488i	$-0.755631\pi$
$947$	3.74398	−	38.0132i	0.121663	−	1.23526i	0.841167	−	0.540776i	$-0.181869\pi$
$948$	11.5869	+	10.4585i	0.376325	+	0.339676i
$949$	−2.95823	−	5.53446i	−0.0960282	−	0.179656i
$950$	5.84928	+	33.5059i	0.189776	+	1.08708i
$951$	−6.52005	−	9.75794i	−0.211427	−	0.316423i
$952$	−65.8229	+	1.81875i	−2.13333	+	0.0589459i
$953$	−35.7215	−	23.8684i	−1.15713	−	0.773172i	−0.179556	−	0.983748i	$-0.557466\pi$
$953$	−35.7215	−	23.8684i	−1.15713	−	0.773172i	−0.977578	+	0.210576i	$0.932466\pi$
$954$	9.92468	−	3.84008i	0.321323	−	0.124327i
$955$	1.49641	−	0.147384i	0.0484227	−	0.00476922i
$956$	−7.80338	+	31.4265i	−0.252379	+	1.01641i
$957$	−27.6829	+	8.39752i	−0.894862	+	0.271453i
$958$	−9.99666	+	0.747719i	−0.322977	+	0.0241577i
$959$		−	49.3733i		−	1.59435i
$960$	−4.21397	−	3.77230i	−0.136005	−	0.121750i
$961$		−	48.9710i		−	1.57971i
$962$	0.0890687	+	1.19081i	0.00287169	+	0.0383932i
$963$	−15.1525	+	4.59647i	−0.488284	+	0.148119i
$964$	4.73628	+	7.86533i	0.152545	+	0.253325i
$965$	−13.7942	+	1.35861i	−0.444050	+	0.0437351i
$966$	17.3865	+	44.9353i	0.559400	+	1.44577i
$967$	11.9422	+	7.97952i	0.384035	+	0.256604i	0.732570	−	0.680692i	$-0.238321\pi$
$967$	11.9422	+	7.97952i	0.384035	+	0.256604i	−0.348535	+	0.937296i	$0.613321\pi$
$968$	−3.45682	+	1.54506i	−0.111106	+	0.0496600i
$969$	−18.3013	−	27.3898i	−0.587922	−	0.879888i
$970$	5.17765	−	0.903884i	0.166244	−	0.0290220i
$971$	−9.58248	−	17.9276i	−0.307516	−	0.575323i	0.679930	−	0.733277i	$-0.262010\pi$
$971$	−9.58248	−	17.9276i	−0.307516	−	0.575323i	−0.987446	+	0.157954i	$0.949510\pi$
$972$	0.102237	+	1.99739i	0.00327926	+	0.0640662i
$973$	−0.576272	+	5.85099i	−0.0184744	+	0.187574i
$974$	−1.72023	+	3.04391i	−0.0551196	+	0.0975330i
$975$	−1.70981	−	4.12785i	−0.0547578	−	0.132197i
$976$	−17.7522	+	11.9674i	−0.568236	+	0.383068i
$977$	13.8073	−	33.3338i	0.441735	−	1.06644i	−0.533605	−	0.845734i	$-0.679163\pi$
$977$	13.8073	−	33.3338i	0.441735	−	1.06644i	0.975340	−	0.220709i	$-0.0708370\pi$
$978$	−15.6621	−	20.0267i	−0.500820	−	0.640385i
$979$	−6.59430	−	8.03517i	−0.210755	−	0.256805i
$980$	6.13688	+	8.23921i	0.196036	+	0.263192i
$981$	3.87407	−	12.7711i	0.123690	−	0.407750i
$982$	−36.2727	+	23.0216i	−1.15751	+	0.734650i
$983$	3.35869	+	0.668086i	0.107126	+	0.0213086i	0.248362	−	0.968667i	$-0.420108\pi$
$983$	3.35869	+	0.668086i	0.107126	+	0.0213086i	−0.141236	+	0.989976i	$0.545108\pi$
$984$	5.84187	−	11.6954i	0.186232	−	0.372834i
$985$	1.44386	+	7.25878i	0.0460053	+	0.231284i
$986$	−1.90771	+	81.1058i	−0.0607540	+	2.58294i
$987$	−20.0432	+	24.4227i	−0.637981	+	0.777382i
$988$	−7.14280	−	7.84842i	−0.227243	−	0.249692i
$989$	88.0194	+	47.0473i	2.79885	+	1.49602i
$990$	−2.77441	+	1.40009i	−0.0881766	+	0.0444979i
$991$	12.9356	+	12.9356i	0.410914	+	0.410914i	0.882057	−	0.471143i	$-0.156158\pi$
$991$	12.9356	+	12.9356i	0.410914	+	0.410914i	−0.471143	+	0.882057i	$0.656158\pi$
$992$	18.4482	+	47.1035i	0.585730	+	1.49554i
$993$	−19.2747	+	19.2747i	−0.611664	+	0.611664i
$994$	−11.8062	+	35.8614i	−0.374469	+	1.13745i
$995$	7.02025	−	13.1340i	0.222557	−	0.416375i
$996$	−2.12700	−	1.00066i	−0.0673967	−	0.0317071i
$997$	11.8125	+	9.69425i	0.374105	+	0.307020i	0.802592	−	0.596528i	$-0.203453\pi$
$997$	11.8125	+	9.69425i	0.374105	+	0.307020i	−0.428488	+	0.903548i	$0.640953\pi$
$998$	34.5394	−	32.9519i	1.09332	−	1.04307i
$999$	0.834132	−	0.165919i	0.0263908	−	0.00524945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.9	✓	512
128.69	even	32	inner	384.2.v.a.325.9	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.9	✓	512	1.1	even	1	trivial
384.2.v.a.325.9	yes	512	128.69	even	32	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.922626 + 1.07180i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-0.297523 - 1.97775i) q^{4} +(-0.0692954 - 0.703568i) q^{5} +(1.29348 + 0.571770i) q^{6} +(-2.09840 + 3.14048i) q^{7} +(2.39426 + 1.50583i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(0.818020 + 0.574859i) q^{10} +(2.74124 - 1.46523i) q^{11} +(-1.80622 + 0.858821i) q^{12} +(0.988056 + 0.0973150i) q^{13} +(-1.42993 - 5.14656i) q^{14} +(-0.653157 + 0.270546i) q^{15} +(-3.82296 + 1.17685i) q^{16} +(5.69460 + 2.35878i) q^{17} +(0.171674 - 1.40376i) q^{18} +(4.13124 - 3.39042i) q^{19} +(-1.37086 + 0.346376i) q^{20} +(3.61438 + 1.09641i) q^{21} +(-0.958710 + 4.28993i) q^{22} +(1.75976 - 8.84689i) q^{23} +(0.745978 - 2.72828i) q^{24} +(4.41372 - 0.877944i) q^{25} +(-1.01591 + 0.969216i) q^{26} +(0.773010 + 0.634393i) q^{27} +(6.83539 + 3.21574i) q^{28} +(4.38728 - 8.20803i) q^{29} +(0.312647 - 0.949669i) q^{30} +(-6.32341 + 6.32341i) q^{31} +(2.26581 - 5.18325i) q^{32} +(-2.19787 - 2.19787i) q^{33} +(-7.78214 + 3.92722i) q^{34} +(2.35495 + 1.25875i) q^{35} +(1.34616 + 1.47914i) q^{36} +(0.539535 - 0.657425i) q^{37} +(-0.177726 + 7.55596i) q^{38} +(-0.193693 - 0.973759i) q^{39} +(0.893545 - 1.78887i) q^{40} +(4.53327 + 0.901723i) q^{41} +(-4.50986 + 2.86233i) q^{42} +(-3.21185 + 10.5881i) q^{43} +(-3.71343 - 4.98555i) q^{44} +(0.448498 + 0.546497i) q^{45} +(7.85853 + 10.0485i) q^{46} +(-3.20109 + 7.72811i) q^{47} +(2.23592 + 3.31672i) q^{48} +(-2.78054 - 6.71281i) q^{49} +(-3.13123 + 5.54065i) q^{50} +(0.604157 - 6.13411i) q^{51} +(-0.101505 - 1.98308i) q^{52} +(3.54717 + 6.63629i) q^{53} +(-1.39314 + 0.243207i) q^{54} +(-1.22084 - 1.82712i) q^{55} +(-9.75315 + 4.35927i) q^{56} +(-4.44366 - 2.96916i) q^{57} +(4.74957 + 12.2752i) q^{58} +(-4.92635 + 0.485203i) q^{59} +(0.729401 + 1.21128i) q^{60} +(5.12187 - 1.55370i) q^{61} +(-0.943307 - 12.6116i) q^{62} -3.77702i q^{63} +(3.46493 + 7.21071i) q^{64} -0.701908i q^{65} +(4.38350 - 0.327872i) q^{66} +(3.72518 - 1.13002i) q^{67} +(2.97080 - 11.9643i) q^{68} +(-8.97678 + 0.884136i) q^{69} +(-3.52186 + 1.36269i) q^{70} +(-5.87698 - 3.92687i) q^{71} +(-2.82735 + 0.0781222i) q^{72} +(-3.51161 - 5.25550i) q^{73} +(0.206841 + 1.18483i) q^{74} +(-2.12138 - 3.96881i) q^{75} +(-7.93453 - 7.16181i) q^{76} +(-1.15072 + 11.6834i) q^{77} +(1.22238 + 0.690815i) q^{78} +(-2.98662 - 7.21034i) q^{79} +(1.09291 + 2.60816i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-5.14898 + 4.02682i) q^{82} +(0.745612 + 0.908531i) q^{83} +(1.09306 - 7.47454i) q^{84} +(1.26495 - 4.16999i) q^{85} +(-8.38497 - 13.2113i) q^{86} +(-9.12815 - 1.81570i) q^{87} +(8.76963 + 0.619734i) q^{88} +(-0.652421 - 3.27994i) q^{89} +(-0.999533 - 0.0235103i) q^{90} +(-2.37895 + 2.89876i) q^{91} +(-18.0205 - 0.848199i) q^{92} +(7.88672 + 4.21554i) q^{93} +(-5.32961 - 10.5611i) q^{94} +(-2.67167 - 2.67167i) q^{95} +(-5.61779 - 0.663628i) q^{96} +(3.71723 - 3.71723i) q^{97} +(9.76020 + 3.21322i) q^{98} +(-1.46523 + 2.74124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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