LMFDB - Embedded newform 384.2.v.a.229.5

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			229.5
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23474 - 0.689501i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.04918 + 1.70271i) q^{4} +(-0.913716 - 1.11337i) q^{5} +(-1.41397 - 0.0260320i) q^{6} +(3.00931 - 2.01075i) q^{7} +(-0.121442 - 2.82582i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(-1.23474 - 0.689501i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.04918 + 1.70271i) q^{4} +(-0.913716 - 1.11337i) q^{5} +(-1.41397 - 0.0260320i) q^{6} +(3.00931 - 2.01075i) q^{7} +(-0.121442 - 2.82582i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.360537 + 2.00473i) q^{10} +(-2.39307 + 0.725929i) q^{11} +(1.72794 + 1.00708i) q^{12} +(1.40718 + 1.15484i) q^{13} +(-5.10214 + 0.407844i) q^{14} +(-1.33066 - 0.551179i) q^{15} +(-1.79845 + 3.57289i) q^{16} +(0.984758 - 0.407900i) q^{17} +(-1.25929 + 0.643585i) q^{18} +(-0.506757 - 5.14519i) q^{19} +(0.937092 - 2.72391i) q^{20} +(1.70611 - 3.19191i) q^{21} +(3.45535 + 0.753687i) q^{22} +(3.05869 - 0.608412i) q^{23} +(-1.43918 - 2.43490i) q^{24} +(0.570744 - 2.86932i) q^{25} +(-0.941240 - 2.39619i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(6.58103 + 3.01435i) q^{28} +(-0.237506 + 0.782952i) q^{29} +(1.26299 + 1.59806i) q^{30} +(0.899529 + 0.899529i) q^{31} +(4.68414 - 3.17157i) q^{32} +(-1.76830 + 1.76830i) q^{33} +(-1.49717 - 0.175340i) q^{34} +(-4.98836 - 1.51320i) q^{35} +(1.99864 + 0.0736171i) q^{36} +(-8.18993 - 0.806638i) q^{37} +(-2.92190 + 6.70240i) q^{38} +(1.78541 + 0.355141i) q^{39} +(-3.03521 + 2.71721i) q^{40} +(-2.17991 - 10.9592i) q^{41} +(-4.30743 + 2.76482i) q^{42} +(2.89114 + 1.54535i) q^{43} +(-3.74680 - 3.31308i) q^{44} +(-1.43336 + 0.141174i) q^{45} +(-4.19620 - 1.35774i) q^{46} +(2.42721 + 5.85980i) q^{47} +(0.0981544 + 3.99880i) q^{48} +(2.33401 - 5.63480i) q^{49} +(-2.68312 + 3.14935i) q^{50} +(0.676197 - 0.823948i) q^{51} +(-0.489984 + 3.60766i) q^{52} +(-0.598980 - 1.97457i) q^{53} +(-0.807207 + 1.16121i) q^{54} +(2.99481 + 2.00107i) q^{55} +(-6.04749 - 8.25957i) q^{56} +(-2.87235 - 4.29877i) q^{57} +(0.833104 - 0.802983i) q^{58} +(2.14800 - 1.76282i) q^{59} +(-0.457603 - 2.84402i) q^{60} +(2.46184 + 4.60578i) q^{61} +(-0.490460 - 1.73091i) q^{62} -3.61926i q^{63} +(-7.97050 + 0.686347i) q^{64} -2.62191i q^{65} +(3.40263 - 0.964149i) q^{66} +(6.78262 + 12.6894i) q^{67} +(1.72772 + 1.24880i) q^{68} +(2.41072 - 1.97843i) q^{69} +(5.11599 + 5.30789i) q^{70} +(5.12102 + 7.66415i) q^{71} +(-2.41705 - 1.46897i) q^{72} +(-8.14530 - 5.44251i) q^{73} +(9.55628 + 6.64295i) q^{74} +(-0.849239 - 2.79956i) q^{75} +(8.22911 - 6.26108i) q^{76} +(-5.74181 + 6.99642i) q^{77} +(-1.95965 - 1.66955i) q^{78} +(-2.22145 + 5.36305i) q^{79} +(5.62122 - 1.26227i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-4.86472 + 15.0348i) q^{82} +(3.06469 - 0.301846i) q^{83} +(7.22491 - 0.443862i) q^{84} +(-1.35393 - 0.723692i) q^{85} +(-2.50430 - 3.90155i) q^{86} +(0.159619 + 0.802461i) q^{87} +(2.34196 + 6.67422i) q^{88} +(14.1419 + 2.81300i) q^{89} +(1.86717 + 0.813992i) q^{90} +(6.55675 + 0.645783i) q^{91} +(4.24506 + 4.56974i) q^{92} +(1.21735 + 0.369279i) q^{93} +(1.04336 - 8.90890i) q^{94} +(-5.26546 + 5.26546i) q^{95} +(2.63598 - 5.00516i) q^{96} +(-6.26004 - 6.26004i) q^{97} +(-6.76710 + 5.34823i) q^{98} +(-0.725929 + 2.39307i) 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 $

$2$	−1.23474	−	0.689501i	−0.873095	−	0.487551i
$2$	−1.23474	−	0.689501i	−0.873095	−	0.487551i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	1.04918	+	1.70271i	0.524589	+	0.851356i
$5$	−0.913716	−	1.11337i	−0.408626	−	0.497913i	0.527511	−	0.849549i	$-0.323126\pi$
$5$	−0.913716	−	1.11337i	−0.408626	−	0.497913i	−0.936137	+	0.351636i	$0.885626\pi$
$6$	−1.41397	−	0.0260320i	−0.577252	−	0.0106275i
$7$	3.00931	−	2.01075i	1.13741	−	0.759994i	0.163415	−	0.986557i	$-0.447749\pi$
$7$	3.00931	−	2.01075i	1.13741	−	0.759994i	0.973996	+	0.226563i	$0.0727491\pi$
$8$	−0.121442	−	2.82582i	−0.0429363	−	0.999078i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	0.360537	+	2.00473i	0.114012	+	0.633951i
$11$	−2.39307	+	0.725929i	−0.721537	+	0.218876i	−0.629634	−	0.776892i	$-0.716795\pi$
$11$	−2.39307	+	0.725929i	−0.721537	+	0.218876i	−0.0919033	+	0.995768i	$0.529295\pi$
$12$	1.72794	+	1.00708i	0.498815	+	0.290719i
$13$	1.40718	+	1.15484i	0.390282	+	0.320296i	0.808987	−	0.587826i	$-0.200016\pi$
$13$	1.40718	+	1.15484i	0.390282	+	0.320296i	−0.418706	+	0.908122i	$0.637516\pi$
$14$	−5.10214	+	0.407844i	−1.36360	+	0.109001i
$15$	−1.33066	−	0.551179i	−0.343576	−	0.142314i
$16$	−1.79845	+	3.57289i	−0.449614	+	0.893223i
$17$	0.984758	−	0.407900i	0.238839	−	0.0989303i	−0.260054	−	0.965594i	$-0.583740\pi$
$17$	0.984758	−	0.407900i	0.238839	−	0.0989303i	0.498893	+	0.866664i	$0.333740\pi$
$18$	−1.25929	+	0.643585i	−0.296816	+	0.151694i
$19$	−0.506757	−	5.14519i	−0.116258	−	1.18039i	−0.859418	−	0.511274i	$-0.829174\pi$
$19$	−0.506757	−	5.14519i	−0.116258	−	1.18039i	0.743159	−	0.669114i	$-0.233326\pi$
$20$	0.937092	−	2.72391i	0.209540	−	0.609086i
$21$	1.70611	−	3.19191i	0.372303	−	0.696531i
$22$	3.45535	+	0.753687i	0.736683	+	0.160687i
$23$	3.05869	−	0.608412i	0.637782	−	0.126863i	0.134400	−	0.990927i	$-0.457089\pi$
$23$	3.05869	−	0.608412i	0.637782	−	0.126863i	0.503381	+	0.864064i	$0.332089\pi$
$24$	−1.43918	−	2.43490i	−0.293772	−	0.497022i
$25$	0.570744	−	2.86932i	0.114149	−	0.573865i
$26$	−0.941240	−	2.39619i	−0.184592	−	0.469931i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	6.58103	+	3.01435i	1.24370	+	0.569658i
$29$	−0.237506	+	0.782952i	−0.0441037	+	0.145390i	−0.976227	−	0.216751i	$-0.930454\pi$
$29$	−0.237506	+	0.782952i	−0.0441037	+	0.145390i	0.932123	+	0.362141i	$0.117954\pi$
$30$	1.26299	+	1.59806i	0.230589	+	0.291764i
$31$	0.899529	+	0.899529i	0.161560	+	0.161560i	0.783258	−	0.621697i	$-0.213557\pi$
$31$	0.899529	+	0.899529i	0.161560	+	0.161560i	−0.621697	+	0.783258i	$0.713557\pi$
$32$	4.68414	−	3.17157i	0.828047	−	0.560659i
$33$	−1.76830	+	1.76830i	−0.307821	+	0.307821i
$34$	−1.49717	−	0.175340i	−0.256763	−	0.0300706i
$35$	−4.98836	−	1.51320i	−0.843187	−	0.255778i
$36$	1.99864	+	0.0736171i	0.333107	+	0.0122695i
$37$	−8.18993	−	0.806638i	−1.34642	−	0.132610i	−0.601021	−	0.799233i	$-0.705239\pi$
$37$	−8.18993	−	0.806638i	−1.34642	−	0.132610i	−0.745395	+	0.666623i	$0.767739\pi$
$38$	−2.92190	+	6.70240i	−0.473995	+	1.08727i
$39$	1.78541	+	0.355141i	0.285895	+	0.0568680i
$40$	−3.03521	+	2.71721i	−0.479909	+	0.429628i
$41$	−2.17991	−	10.9592i	−0.340445	−	1.71153i	−0.649393	−	0.760453i	$-0.724977\pi$
$41$	−2.17991	−	10.9592i	−0.340445	−	1.71153i	0.308948	−	0.951079i	$-0.400023\pi$
$42$	−4.30743	+	2.76482i	−0.664650	+	0.426621i
$43$	2.89114	+	1.54535i	0.440895	+	0.235663i	0.676880	−	0.736093i	$-0.263332\pi$
$43$	2.89114	+	1.54535i	0.440895	+	0.235663i	−0.235985	+	0.971757i	$0.575832\pi$
$44$	−3.74680	−	3.31308i	−0.564851	−	0.499465i
$45$	−1.43336	+	0.141174i	−0.213673	+	0.0210450i
$46$	−4.19620	−	1.35774i	−0.618696	−	0.200188i
$47$	2.42721	+	5.85980i	0.354045	+	0.854739i	0.996112	+	0.0880915i	$0.0280768\pi$
$47$	2.42721	+	5.85980i	0.354045	+	0.854739i	−0.642068	+	0.766648i	$0.721923\pi$
$48$	0.0981544	+	3.99880i	0.0141674	+	0.577176i
$49$	2.33401	−	5.63480i	0.333430	−	0.804972i
$50$	−2.68312	+	3.14935i	−0.379451	+	0.445385i
$51$	0.676197	−	0.823948i	0.0946864	−	0.115376i
$52$	−0.489984	+	3.60766i	−0.0679485	+	0.500292i
$53$	−0.598980	−	1.97457i	−0.0822762	−	0.271228i	0.906144	−	0.422969i	$-0.139012\pi$
$53$	−0.598980	−	1.97457i	−0.0822762	−	0.271228i	−0.988420	+	0.151741i	$0.951512\pi$
$54$	−0.807207	+	1.16121i	−0.109847	+	0.158021i
$55$	2.99481	+	2.00107i	0.403820	+	0.269824i
$56$	−6.04749	−	8.25957i	−0.808129	−	1.10373i
$57$	−2.87235	−	4.29877i	−0.380452	−	0.569386i
$58$	0.833104	−	0.802983i	0.109392	−	0.105437i
$59$	2.14800	−	1.76282i	0.279645	−	0.229499i	−0.484106	−	0.875009i	$-0.660855\pi$
$59$	2.14800	−	1.76282i	0.279645	−	0.229499i	0.763752	+	0.645510i	$0.223355\pi$
$60$	−0.457603	−	2.84402i	−0.0590763	−	0.367161i
$61$	2.46184	+	4.60578i	0.315207	+	0.589710i	0.988775	−	0.149415i	$-0.0477391\pi$
$61$	2.46184	+	4.60578i	0.315207	+	0.589710i	−0.673568	+	0.739125i	$0.735239\pi$
$62$	−0.490460	−	1.73091i	−0.0622885	−	0.219826i
$63$		−	3.61926i		−	0.455984i
$64$	−7.97050	+	0.686347i	−0.996313	+	0.0857934i
$65$		−	2.62191i		−	0.325208i
$66$	3.40263	−	0.964149i	0.418835	−	0.118678i
$67$	6.78262	+	12.6894i	0.828629	+	1.55026i	0.834983	+	0.550275i	$0.185477\pi$
$67$	6.78262	+	12.6894i	0.828629	+	1.55026i	−0.00635457	+	0.999980i	$0.502023\pi$
$68$	1.72772	+	1.24880i	0.209517	+	0.151439i
$69$	2.41072	−	1.97843i	0.290217	−	0.238175i
$70$	5.11599	+	5.30789i	0.611477	+	0.634415i
$71$	5.12102	+	7.66415i	0.607753	+	0.909567i	0.999947	−	0.0103159i	$-0.00328371\pi$
$71$	5.12102	+	7.66415i	0.607753	+	0.909567i	−0.392194	+	0.919883i	$0.628284\pi$
$72$	−2.41705	−	1.46897i	−0.284852	−	0.173119i
$73$	−8.14530	−	5.44251i	−0.953335	−	0.636998i	−0.0214569	−	0.999770i	$-0.506830\pi$
$73$	−8.14530	−	5.44251i	−0.953335	−	0.636998i	−0.931878	+	0.362772i	$0.881830\pi$
$74$	9.55628	+	6.64295i	1.11089	+	0.772228i
$75$	−0.849239	−	2.79956i	−0.0980616	−	0.323266i
$76$	8.22911	−	6.26108i	0.943943	−	0.718195i
$77$	−5.74181	+	6.99642i	−0.654340	+	0.797316i
$78$	−1.95965	−	1.66955i	−0.221887	−	0.189039i
$79$	−2.22145	+	5.36305i	−0.249933	+	0.603391i	−0.998198	−	0.0600091i	$-0.980887\pi$
$79$	−2.22145	+	5.36305i	−0.249933	+	0.603391i	0.748265	+	0.663400i	$0.230887\pi$
$80$	5.62122	−	1.26227i	0.628471	−	0.141126i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−4.86472	+	15.0348i	−0.537218	+	1.66031i
$83$	3.06469	−	0.301846i	0.336394	−	0.0331319i	0.0715897	−	0.997434i	$-0.477193\pi$
$83$	3.06469	−	0.301846i	0.336394	−	0.0331319i	0.264804	+	0.964302i	$0.414693\pi$
$84$	7.22491	−	0.443862i	0.788302	−	0.0484293i
$85$	−1.35393	−	0.723692i	−0.146855	−	0.0784954i
$86$	−2.50430	−	3.90155i	−0.270045	−	0.420715i
$87$	0.159619	+	0.802461i	0.0171130	+	0.0860329i
$88$	2.34196	+	6.67422i	0.249654	+	0.711474i
$89$	14.1419	+	2.81300i	1.49904	+	0.298178i	0.875349	−	0.483492i	$-0.160632\pi$
$89$	14.1419	+	2.81300i	1.49904	+	0.298178i	0.623692	+	0.781670i	$0.285632\pi$
$90$	1.86717	+	0.813992i	0.196818	+	0.0858023i
$91$	6.55675	+	0.645783i	0.687334	+	0.0676965i
$92$	4.24506	+	4.56974i	0.442578	+	0.476428i
$93$	1.21735	+	0.369279i	0.126233	+	0.0382924i
$94$	1.04336	−	8.90890i	0.107614	−	0.918883i
$95$	−5.26546	+	5.26546i	−0.540224	+	0.540224i
$96$	2.63598	−	5.00516i	0.269033	−	0.510837i
$97$	−6.26004	−	6.26004i	−0.635610	−	0.635610i	0.313859	−	0.949470i	$-0.398378\pi$
$97$	−6.26004	−	6.26004i	−0.635610	−	0.635610i	−0.949470	+	0.313859i	$0.898378\pi$
$98$	−6.76710	+	5.34823i	−0.683581	+	0.540252i
$99$	−0.725929	+	2.39307i	−0.0729586	+	0.240512i
$100$	5.48444	−	2.03862i	0.548444	−	0.203862i
$101$	−1.61813	+	16.4292i	−0.161010	+	1.63477i	0.487189	+	0.873296i	$0.338022\pi$
$101$	−1.61813	+	16.4292i	−0.161010	+	1.63477i	−0.648200	+	0.761470i	$0.724478\pi$
$102$	−1.40304	+	0.551125i	−0.138922	+	0.0545695i
$103$	−2.92128	+	14.6863i	−0.287843	+	1.44708i	0.518218	+	0.855249i	$0.326596\pi$
$103$	−2.92128	+	14.6863i	−0.287843	+	1.44708i	−0.806060	+	0.591834i	$0.798404\pi$
$104$	3.09249	−	4.11669i	0.303243	−	0.403674i
$105$	−5.11266	+	1.01697i	−0.498945	+	0.0992462i
$106$	−0.621883	+	2.85108i	−0.0604026	+	0.276922i
$107$	−3.25519	+	6.09003i	−0.314691	+	0.588745i	−0.988688	−	0.149989i	$-0.952076\pi$
$107$	−3.25519	+	6.09003i	−0.314691	+	0.588745i	0.673997	+	0.738734i	$0.264576\pi$
$108$	1.79735	−	0.877230i	0.172950	−	0.0844115i
$109$	0.680219	+	6.90638i	0.0651532	+	0.661511i	0.971189	+	0.238310i	$0.0765936\pi$
$109$	0.680219	+	6.90638i	0.0651532	+	0.661511i	−0.906036	+	0.423201i	$0.860906\pi$
$110$	−2.31808	−	4.53573i	−0.221020	−	0.432465i
$111$	−7.60312	+	3.14932i	−0.721656	+	0.298920i
$112$	1.77211	+	14.3682i	0.167448	+	1.35767i
$113$	14.6311	+	6.06040i	1.37638	+	0.570114i	0.943510	−	0.331343i	$-0.107502\pi$
$113$	14.6311	+	6.06040i	1.37638	+	0.570114i	0.432867	+	0.901458i	$0.357502\pi$
$114$	0.582602	+	7.28836i	0.0545657	+	0.682618i
$115$	−3.47216	−	2.84953i	−0.323781	−	0.265720i
$116$	−1.58233	+	0.417051i	−0.146915	+	0.0387222i
$117$	1.74201	−	0.528432i	0.161048	−	0.0488535i
$118$	−3.86769	+	0.695577i	−0.356049	+	0.0640331i
$119$	2.14325	−	3.20761i	0.196472	−	0.294041i
$120$	−1.39593	+	3.82715i	−0.127431	+	0.349369i
$121$	−3.94637	+	2.63688i	−0.358760	+	0.239716i
$122$	0.135950	−	7.38440i	0.0123084	−	0.668552i
$123$	−7.08862	−	8.63751i	−0.639159	−	0.778818i
$124$	−0.587873	+	2.47540i	−0.0527926	+	0.222298i
$125$	−10.0673	+	5.38106i	−0.900443	+	0.481297i
$126$	−2.49549	+	4.46886i	−0.222315	+	0.398117i
$127$	20.9170			1.85608			0.928040	−	0.372481i	$-0.121493\pi$
$127$	20.9170			1.85608			0.928040	+	0.372481i	$0.121493\pi$
$128$	10.3148	+	4.64821i	0.911704	+	0.410847i
$129$	3.27823			0.288632
$130$	−1.80781	+	3.23738i	−0.158555	+	0.283937i
$131$	−8.25978	+	4.41494i	−0.721660	+	0.385735i	−0.790966	−	0.611860i	$-0.790422\pi$
$131$	−8.25978	+	4.41494i	−0.721660	+	0.385735i	0.0693060	+	0.997595i	$0.477922\pi$
$132$	−4.86616	−	1.15564i	−0.423545	−	0.100586i
$133$	−11.8707	−	14.4645i	−1.02932	−	1.25423i
$134$	0.374557	−	20.3447i	0.0323568	−	1.75752i
$135$	−1.19757	+	0.800188i	−0.103070	+	0.0688692i
$136$	−1.27224	−	2.73321i	−0.109094	−	0.234371i
$137$	−6.10800	+	9.14126i	−0.521841	+	0.780991i	−0.994988	−	0.0999929i	$-0.968118\pi$
$137$	−6.10800	+	9.14126i	−0.521841	+	0.780991i	0.473147	+	0.880984i	$0.343118\pi$
$138$	−4.34075	+	0.780655i	−0.369509	+	0.0664537i
$139$	19.4552	−	5.90167i	1.65017	−	0.500573i	0.678040	−	0.735025i	$-0.262830\pi$
$139$	19.4552	−	5.90167i	1.65017	−	0.500573i	0.972128	+	0.234452i	$0.0753295\pi$
$140$	−2.65713	−	10.0814i	−0.224568	−	0.852030i
$141$	4.90290	+	4.02370i	0.412898	+	0.338857i
$142$	−1.03870	−	12.9942i	−0.0871660	−	1.09045i
$143$	−4.20581	−	1.74211i	−0.351708	−	0.145682i
$144$	1.97158	+	3.48035i	0.164299	+	0.290029i
$145$	1.08873	−	0.450965i	0.0904137	−	0.0374506i
$146$	6.30473	+	12.3363i	0.521783	+	1.02096i
$147$	−0.597813	−	6.06970i	−0.0493068	−	0.500620i
$148$	−7.21922	−	14.7914i	−0.593416	−	1.21585i
$149$	6.41130	−	11.9947i	0.525234	−	0.982644i	−0.469768	−	0.882790i	$-0.655662\pi$
$149$	6.41130	−	11.9947i	0.525234	−	0.982644i	0.995002	−	0.0998540i	$-0.0318376\pi$
$150$	−0.881711	+	4.04229i	−0.0719914	+	0.330052i
$151$	0.789886	−	0.157118i	0.0642800	−	0.0127861i	−0.162846	−	0.986652i	$-0.552067\pi$
$151$	0.789886	−	0.157118i	0.0642800	−	0.0127861i	0.227126	+	0.973865i	$0.427067\pi$
$152$	−14.4778	+	2.05685i	−1.17431	+	0.166832i
$153$	0.207946	−	1.04541i	0.0168114	−	0.0845167i
$154$	11.9137	−	4.67979i	0.960033	−	0.377108i
$155$	0.179591	−	1.82342i	0.0144251	−	0.146461i
$156$	1.26851	+	3.41265i	0.101562	+	0.273231i
$157$	1.51462	−	4.99302i	0.120879	−	0.398486i	−0.875529	−	0.483166i	$-0.839487\pi$
$157$	1.51462	−	4.99302i	0.120879	−	0.398486i	0.996408	+	0.0846799i	$0.0269868\pi$
$158$	6.44075	−	5.09030i	0.512398	−	0.404962i
$159$	−1.45906	−	1.45906i	−0.115711	−	0.115711i
$160$	−7.81109	−	2.31725i	−0.617521	−	0.183195i
$161$	7.98118	−	7.98118i	0.629005	−	0.629005i
$162$	−0.164500	+	1.40461i	−0.0129244	+	0.110357i
$163$	−23.9792	−	7.27402i	−1.87820	−	0.569745i	−0.994892	−	0.100948i	$-0.967812\pi$
$163$	−23.9792	−	7.27402i	−1.87820	−	0.569745i	−0.883306	−	0.468797i	$-0.844688\pi$
$164$	16.3732	−	15.2099i	1.27853	−	1.18769i
$165$	3.58448	+	0.353041i	0.279052	+	0.0274842i
$166$	−3.99223	−	1.74041i	−0.309857	−	0.135082i
$167$	6.41810	+	1.27664i	0.496647	+	0.0987893i	0.437057	−	0.899434i	$-0.356021\pi$
$167$	6.41810	+	1.27664i	0.496647	+	0.0987893i	0.0595899	+	0.998223i	$0.481021\pi$
$168$	−9.22694	−	4.43352i	−0.711874	−	0.342054i
$169$	−1.88968	−	9.50006i	−0.145360	−	0.730774i
$170$	1.17277	+	1.82711i	0.0899475	+	0.140133i
$171$	−4.55961	−	2.43716i	−0.348682	−	0.186375i
$172$	0.402039	+	6.54413i	0.0306552	+	0.498985i
$173$	−16.3847	+	1.61375i	−1.24571	+	0.122691i	−0.699299	−	0.714829i	$-0.746504\pi$
$173$	−16.3847	+	1.61375i	−1.24571	+	0.122691i	−0.546406	+	0.837520i	$0.684004\pi$
$174$	0.356209	−	1.10089i	0.0270041	−	0.0834583i
$175$	−4.05196	−	9.78230i	−0.306300	−	0.739473i
$176$	1.71016	−	9.85572i	0.128908	−	0.742903i
$177$	1.06338	−	2.56722i	0.0799285	−	0.192964i
$178$	−15.5221	−	13.2242i	−1.16343	−	0.991196i
$179$	−10.0065	+	12.1929i	−0.747920	+	0.911343i	−0.998387	−	0.0567823i	$-0.981916\pi$
$179$	−10.0065	+	12.1929i	−0.747920	+	0.911343i	0.250467	+	0.968125i	$0.419416\pi$
$180$	−1.74423	−	2.29249i	−0.130007	−	0.170872i
$181$	−3.33835	−	11.0051i	−0.248138	−	0.818000i	−0.989201	−	0.146565i	$-0.953178\pi$
$181$	−3.33835	−	11.0051i	−0.248138	−	0.818000i	0.741063	−	0.671435i	$-0.234322\pi$
$182$	−7.65063	−	5.31826i	−0.567102	−	0.394216i
$183$	4.34230	+	2.90143i	0.320992	+	0.214480i
$184$	−2.09072	−	8.56943i	−0.154130	−	0.631746i
$185$	6.58519	+	9.85543i	0.484153	+	0.724586i
$186$	−1.24849	−	1.29533i	−0.0915440	−	0.0949780i
$187$	−2.06049	+	1.69100i	−0.150678	+	0.123658i
$188$	−7.43098	+	10.2808i	−0.541960	+	0.749805i
$189$	−1.70611	−	3.19191i	−0.124101	−	0.232177i
$190$	10.1320	−	2.87094i	0.735054	−	0.208280i
$191$		−	1.39585i		−	0.101000i	−0.998724	−	0.0505000i	$-0.983919\pi$
$191$		−	1.39585i		−	0.101000i	0.998724	−	0.0505000i	$-0.0160815\pi$
$192$	−6.70581	+	4.36257i	−0.483951	+	0.314842i
$193$		−	5.97250i		−	0.429910i	−0.976624	−	0.214955i	$-0.931040\pi$
$193$		−	5.97250i		−	0.429910i	0.976624	−	0.214955i	$-0.0689605\pi$
$194$	3.41323	+	12.0458i	0.245056	+	0.864840i
$195$	−1.23596	−	2.31232i	−0.0885088	−	0.165588i
$196$	12.0432	−	1.93776i	0.860231	−	0.138411i
$197$	−0.937743	+	0.769586i	−0.0668114	+	0.0548307i	−0.667206	−	0.744873i	$-0.732510\pi$
$197$	−0.937743	+	0.769586i	−0.0668114	+	0.0548307i	0.600395	+	0.799704i	$0.295010\pi$
$198$	2.54636	−	2.45429i	0.180962	−	0.174419i
$199$	6.88095	+	10.2981i	0.487778	+	0.730011i	0.990958	−	0.134170i	$-0.0428369\pi$
$199$	6.88095	+	10.2981i	0.487778	+	0.730011i	−0.503180	+	0.864181i	$0.667837\pi$
$200$	−8.17750	−	1.26436i	−0.578237	−	0.0894039i
$201$	11.9635	+	7.99374i	0.843838	+	0.563835i
$202$	13.3259	−	19.1701i	0.937609	−	1.34881i
$203$	0.859596	+	2.83371i	0.0603318	+	0.198887i
$204$	2.11240	+	0.286901i	0.147897	+	0.0200871i
$205$	−10.2097	+	12.4406i	−0.713079	+	0.868889i
$206$	13.7332	−	16.1195i	0.956840	−	1.12310i
$207$	1.19344	−	2.88123i	0.0829500	−	0.200259i
$208$	−6.65688	+	2.95077i	−0.461572	+	0.204599i
$209$	4.94775	+	11.9449i	0.342243	+	0.826248i
$210$	7.01402	+	2.26949i	0.484013	+	0.156609i
$211$	−0.734121	+	0.0723046i	−0.0505390	+	0.00497766i	−0.123255	−	0.992375i	$-0.539333\pi$
$211$	−0.734121	+	0.0723046i	−0.0505390	+	0.00497766i	0.0727160	+	0.997353i	$0.476833\pi$
$212$	2.73369	−	3.09157i	0.187751	−	0.212330i
$213$	8.12919	+	4.34514i	0.557003	+	0.297724i
$214$	8.21840	−	5.27516i	0.561798	−	0.360603i
$215$	−0.921145	−	4.63091i	−0.0628216	−	0.315825i
$216$	−2.82412	−	0.156121i	−0.192157	−	0.0106227i
$217$	4.51569	+	0.898227i	0.306545	+	0.0609756i
$218$	3.92206	−	8.99661i	0.265635	−	0.609328i
$219$	−9.74909	−	0.960202i	−0.658783	−	0.0648844i
$220$	−0.265156	+	7.19877i	−0.0178768	+	0.485341i
$221$	1.85679	+	0.563252i	0.124902	+	0.0378885i
$222$	11.5594	+	1.35377i	0.775813	+	0.0908588i
$223$	−10.6890	+	10.6890i	−0.715786	+	0.715786i	−0.967739	−	0.251953i	$-0.918927\pi$
$223$	−10.6890	+	10.6890i	−0.715786	+	0.715786i	0.251953	+	0.967739i	$0.418927\pi$
$224$	7.71878	−	18.9629i	0.515733	−	1.26701i
$225$	−2.06867	−	2.06867i	−0.137911	−	0.137911i
$226$	−13.8870	−	17.5712i	−0.923748	−	1.16882i
$227$	−4.28102	+	14.1126i	−0.284141	+	0.936689i	0.692428	+	0.721487i	$0.256541\pi$
$227$	−4.28102	+	14.1126i	−0.284141	+	0.936689i	−0.976570	+	0.215202i	$0.930959\pi$
$228$	4.30597	−	9.40096i	0.285170	−	0.622593i
$229$	1.06581	−	10.8213i	0.0704306	−	0.715094i	−0.893522	−	0.449020i	$-0.851773\pi$
$229$	1.06581	−	10.8213i	0.0704306	−	0.715094i	0.963953	−	0.266074i	$-0.0857267\pi$
$230$	2.32247	+	5.91250i	0.153139	+	0.389858i
$231$	−1.76574	+	8.87696i	−0.116177	+	0.584061i
$232$	2.24132	+	0.576065i	0.147150	+	0.0378205i
$233$	−23.0141	+	4.57779i	−1.50770	+	0.299901i	−0.878652	−	0.477463i	$-0.841556\pi$
$233$	−23.0141	+	4.57779i	−1.50770	+	0.299901i	−0.629051	+	0.777364i	$0.716556\pi$
$234$	−2.51528	−	0.548637i	−0.164429	−	0.0358655i
$235$	4.30632	−	8.05657i	0.280914	−	0.525552i
$236$	5.25520	+	1.80791i	0.342084	+	0.117685i
$237$	0.568982	+	5.77697i	0.0369594	+	0.375255i
$238$	−4.85801	+	2.48279i	−0.314898	+	0.160935i
$239$	19.4468	−	8.05511i	1.25791	−	0.521042i	0.348640	−	0.937257i	$-0.386644\pi$
$239$	19.4468	−	8.05511i	1.25791	−	0.521042i	0.909266	+	0.416215i	$0.136644\pi$
$240$	4.36244	−	3.76305i	0.281594	−	0.242904i
$241$	−3.19672	−	1.32412i	−0.205919	−	0.0852943i	0.277340	−	0.960772i	$-0.410547\pi$
$241$	−3.19672	−	1.32412i	−0.205919	−	0.0852943i	−0.483259	+	0.875477i	$0.660547\pi$
$242$	6.69087	−	0.534841i	0.430106	−	0.0343809i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	−5.25941	+	9.02409i	−0.336699	+	0.577708i
$245$	−8.40623	+	2.55000i	−0.537054	+	0.162914i
$246$	2.79705	+	15.5527i	0.178333	+	0.991604i
$247$	5.22880	−	7.82545i	0.332700	−	0.497921i
$248$	2.43266	−	2.65115i	0.154474	−	0.168348i
$249$	2.56053	−	1.71089i	0.162267	−	0.108423i
$250$	16.1407	+	0.297159i	1.02083	+	0.0187940i
$251$	−11.6082	−	14.1446i	−0.732704	−	0.892802i	0.264735	−	0.964321i	$-0.414715\pi$
$251$	−11.6082	−	14.1446i	−0.732704	−	0.892802i	−0.997439	+	0.0715189i	$0.977215\pi$
$252$	6.16256	−	3.79725i	0.388205	−	0.239204i
$253$	−6.87800	+	3.67637i	−0.432416	+	0.231131i
$254$	−25.8270	−	14.4223i	−1.62053	−	0.904933i
$255$	−1.53521			−0.0961384
$256$	−9.53112	−	12.8514i	−0.595695	−	0.803211i
$257$	20.8656			1.30156			0.650779	−	0.759267i	$-0.274442\pi$
$257$	20.8656			1.30156			0.650779	+	0.759267i	$0.274442\pi$
$258$	−4.04777	−	2.26034i	−0.252003	−	0.140723i
$259$	−26.2680	+	14.0405i	−1.63221	+	0.872436i
$260$	4.46435	−	2.75085i	0.276867	−	0.170600i
$261$	0.519049	+	0.632464i	0.0321284	+	0.0391485i
$262$	13.2428	+	0.243807i	0.818143	+	0.0150624i
$263$	16.1506	−	10.7915i	0.995889	−	0.665432i	0.0530194	−	0.998593i	$-0.483115\pi$
$263$	16.1506	−	10.7915i	0.995889	−	0.665432i	0.942870	+	0.333162i	$0.108115\pi$
$264$	5.21163	+	4.78214i	0.320754	+	0.294320i
$265$	−1.65112	+	2.47108i	−0.101428	+	0.151797i
$266$	4.68398	+	26.0448i	0.287193	+	1.59691i
$267$	13.7981	−	4.18561i	0.844430	−	0.256155i
$268$	−14.4902	+	24.8623i	−0.885130	+	1.51870i
$269$	16.1575	+	13.2601i	0.985140	+	0.808484i	0.981491	−	0.191510i	$-0.0613384\pi$
$269$	16.1575	+	13.2601i	0.985140	+	0.808484i	0.00364930	+	0.999993i	$0.498838\pi$
$270$	2.03041	−	0.162303i	0.123567	−	0.00987745i
$271$	6.41613	+	2.65765i	0.389752	+	0.161441i	0.568949	−	0.822373i	$-0.307350\pi$
$271$	6.41613	+	2.65765i	0.389752	+	0.161441i	−0.179197	+	0.983813i	$0.557350\pi$
$272$	−0.313660	+	4.25203i	−0.0190184	+	0.257817i
$273$	6.08696	−	2.52130i	0.368399	−	0.152596i
$274$	13.8447	−	7.07563i	0.836389	−	0.427455i
$275$	0.717097	+	7.28081i	0.0432426	+	0.439049i
$276$	5.89797	+	2.02904i	0.355016	+	0.122134i
$277$	−11.2470	+	21.0417i	−0.675767	+	1.26427i	0.277089	+	0.960844i	$0.410630\pi$
$277$	−11.2470	+	21.0417i	−0.675767	+	1.26427i	−0.952855	+	0.303426i	$0.901870\pi$
$278$	−28.0914	−	6.12733i	−1.68481	−	0.367493i
$279$	1.24768	−	0.248179i	0.0746968	−	0.0148581i
$280$	−3.67024	+	14.2800i	−0.219339	+	0.853391i
$281$	−0.586137	+	2.94671i	−0.0349660	+	0.175786i	−0.994322	−	0.106412i	$-0.966064\pi$
$281$	−0.586137	+	2.94671i	−0.0349660	+	0.175786i	0.959356	+	0.282198i	$0.0910637\pi$
$282$	−3.27947	−	8.34879i	−0.195289	−	0.497163i
$283$	1.43106	−	14.5298i	0.0850676	−	0.863706i	−0.854068	−	0.520161i	$-0.825872\pi$
$283$	1.43106	−	14.5298i	0.0850676	−	0.863706i	0.939136	−	0.343545i	$-0.111628\pi$
$284$	−7.67698	+	16.7607i	−0.455545	+	0.994562i
$285$	−2.16160	+	7.12584i	−0.128042	+	0.422098i
$286$	3.99191	+	5.05096i	0.236047	+	0.298670i
$287$	−28.5962	−	28.5962i	−1.68798	−	1.68798i
$288$	−0.0346911	−	5.65675i	−0.00204420	−	0.333327i
$289$	−11.2174	+	11.2174i	−0.659850	+	0.659850i
$290$	−1.65524	−	0.193852i	−0.0971988	−	0.0113834i
$291$	−8.47182	−	2.56990i	−0.496627	−	0.150650i
$292$	0.721173	−	19.5793i	0.0422034	−	1.14579i
$293$	16.7797	+	1.65266i	0.980282	+	0.0965493i	0.575446	−	0.817840i	$-0.304829\pi$
$293$	16.7797	+	1.65266i	0.980282	+	0.0965493i	0.404836	+	0.914389i	$0.367329\pi$
$294$	−3.44692	+	7.90671i	−0.201028	+	0.461128i
$295$	−3.92532	−	0.780795i	−0.228541	−	0.0454596i
$296$	−1.28481	+	23.2412i	−0.0746780	+	1.35087i
$297$	0.487872	+	2.45270i	0.0283092	+	0.142320i
$298$	−16.1867	+	10.3898i	−0.937668	+	0.601863i
$299$	5.00676	+	2.67617i	0.289548	+	0.154767i
$300$	3.87585	−	4.38325i	0.223772	−	0.253067i
$301$	11.8077	−	1.16295i	0.680582	−	0.0670315i
$302$	−1.08364	−	0.350627i	−0.0623564	−	0.0201763i
$303$	6.31760	+	15.2520i	0.362937	+	0.876207i
$304$	19.2946	+	7.44281i	1.10662	+	0.426874i
$305$	2.87850	−	6.94931i	0.164822	−	0.397916i
$306$	−0.977573	+	1.14744i	−0.0558841	+	0.0655947i
$307$	9.43732	−	11.4994i	0.538616	−	0.656306i	−0.430592	−	0.902546i	$-0.641695\pi$
$307$	9.43732	−	11.4994i	0.538616	−	0.656306i	0.969209	+	0.246241i	$0.0791954\pi$
$308$	−17.9371	−	2.43617i	−1.02206	−	0.138814i
$309$	4.34672	+	14.3292i	0.247276	+	0.815161i
$310$	−1.47900	+	2.12762i	−0.0840014	+	0.120841i
$311$	−14.5379	−	9.71388i	−0.824366	−	0.550824i	0.0703173	−	0.997525i	$-0.477599\pi$
$311$	−14.5379	−	9.71388i	−0.824366	−	0.550824i	−0.894683	+	0.446701i	$0.852599\pi$
$312$	0.786739	−	5.08838i	0.0445403	−	0.288073i
$313$	−9.49147	−	14.2050i	−0.536489	−	0.802913i	0.459886	−	0.887978i	$-0.347890\pi$
$313$	−9.49147	−	14.2050i	−0.536489	−	0.802913i	−0.996375	+	0.0850649i	$0.972890\pi$
$314$	−5.31285	+	5.12076i	−0.299821	+	0.288981i
$315$	−4.02957	+	3.30698i	−0.227040	+	0.186327i
$316$	−11.4624	+	1.84430i	−0.644812	+	0.103750i
$317$	−11.3164	−	21.1714i	−0.635590	−	1.18910i	−0.969172	−	0.246384i	$-0.920758\pi$
$317$	−11.3164	−	21.1714i	−0.635590	−	1.18910i	0.333583	−	0.942721i	$-0.391742\pi$
$318$	0.795540	+	2.80759i	0.0446117	+	0.157442i
$319$		−	2.04607i		−	0.114558i
$320$	8.04693	+	8.24697i	0.449837	+	0.461019i
$321$			6.90541i			0.385423i
$322$	−15.3577	+	4.35167i	−0.855853	+	0.242509i
$323$	−2.59776	−	4.86007i	−0.144543	−	0.270421i
$324$	1.17160	−	1.62091i	0.0650888	−	0.0900507i
$325$	4.11676	−	3.37854i	0.228357	−	0.187408i
$326$	24.5927	+	25.5152i	1.36206	+	1.41316i
$327$	3.85555	+	5.77023i	0.213212	+	0.319095i
$328$	−30.7038	+	7.49094i	−1.69534	+	0.413618i
$329$	19.0868	+	12.7534i	1.05229	+	0.703118i
$330$	−4.18249	−	2.90742i	−0.230239	−	0.160048i
$331$	−7.62369	−	25.1319i	−0.419036	−	1.38138i	−0.871851	−	0.489772i	$-0.837080\pi$
$331$	−7.62369	−	25.1319i	−0.419036	−	1.38138i	0.452814	−	0.891605i	$-0.350420\pi$
$332$	3.72936	+	4.90160i	0.204675	+	0.269010i
$333$	−5.22078	+	6.36154i	−0.286097	+	0.348610i
$334$	−7.04445	−	6.00160i	−0.385455	−	0.328393i
$335$	7.93055	−	19.1460i	0.433292	−	1.04606i
$336$	8.33597	+	11.8362i	0.454765	+	0.645720i
$337$	12.0662	+	29.1305i	0.657290	+	1.58684i	0.801973	+	0.597361i	$0.203784\pi$
$337$	12.0662	+	29.1305i	0.657290	+	1.58684i	−0.144682	+	0.989478i	$0.546216\pi$
$338$	−4.21703	+	13.0331i	−0.229376	+	0.708905i
$339$	15.7603	−	1.55226i	0.855983	−	0.0843070i
$340$	−0.188276	−	3.06464i	−0.0102107	−	0.166203i
$341$	−2.80563	−	1.49964i	−0.151933	−	0.0812100i
$342$	3.94952	+	6.15313i	0.213566	+	0.332723i
$343$	0.636134	+	3.19806i	0.0343480	+	0.172679i
$344$	4.01577	−	8.35751i	0.216516	−	0.450607i
$345$	−4.40543	−	0.876295i	−0.237181	−	0.0471782i
$346$	21.3436	+	9.30469i	1.14744	+	0.500223i
$347$	18.2161	+	1.79413i	0.977890	+	0.0963138i	0.574316	−	0.818633i	$-0.305268\pi$
$347$	18.2161	+	1.79413i	0.977890	+	0.0963138i	0.403574	+	0.914947i	$0.367768\pi$
$348$	−1.19889	+	1.11371i	−0.0642673	+	0.0597011i
$349$	32.1144	+	9.74179i	1.71904	+	0.521466i	0.987128	−	0.159929i	$-0.0511267\pi$
$349$	32.1144	+	9.74179i	1.71904	+	0.521466i	0.731915	+	0.681396i	$0.238627\pi$
$350$	−1.74178	+	14.8725i	−0.0931019	+	0.794966i
$351$	1.28721	−	1.28721i	0.0687062	−	0.0687062i
$352$	−8.90713	+	10.9901i	−0.474752	+	0.585776i
$353$	−9.80004	−	9.80004i	−0.521603	−	0.521603i	0.396452	−	0.918055i	$-0.370241\pi$
$353$	−9.80004	−	9.80004i	−0.521603	−	0.521603i	−0.918055	+	0.396452i	$0.870241\pi$
$354$	−3.08310	+	2.43666i	−0.163865	+	0.129507i
$355$	3.85385	−	12.7044i	0.204541	−	0.674281i
$356$	10.0477	+	27.0310i	0.532524	+	1.43264i
$357$	0.378126	−	3.83918i	0.0200126	−	0.203191i
$358$	20.7625	−	8.15565i	1.09733	−	0.431040i
$359$	−2.71298	+	13.6391i	−0.143186	+	0.719843i	0.840765	+	0.541401i	$0.182106\pi$
$359$	−2.71298	+	13.6391i	−0.143186	+	0.719843i	−0.983950	+	0.178442i	$0.942894\pi$
$360$	0.573003	+	4.03328i	0.0301999	+	0.212573i
$361$	−7.58131	+	1.50802i	−0.399016	+	0.0793692i
$362$	−3.46600	+	15.8902i	−0.182169	+	0.835171i
$363$	−2.23737	+	4.18582i	−0.117431	+	0.219699i
$364$	5.77961	+	11.8418i	0.302934	+	0.620679i
$365$	1.38298	+	14.0416i	0.0723884	+	0.734972i
$366$	−3.36108	−	6.57654i	−0.175687	−	0.343761i
$367$	28.4631	−	11.7898i	1.48576	−	0.615422i	0.515370	−	0.856968i	$-0.327654\pi$
$367$	28.4631	−	11.7898i	1.48576	−	0.615422i	0.970389	+	0.241546i	$0.0776544\pi$
$368$	−3.32713	+	12.0226i	−0.173439	+	0.626720i
$369$	−10.3233	−	4.27605i	−0.537409	−	0.222602i
$370$	−1.33568	−	16.7094i	−0.0694389	−	0.868681i
$371$	−5.77289	−	4.73769i	−0.299714	−	0.245969i
$372$	0.648439	+	2.46023i	0.0336200	+	0.127557i
$373$	1.31435	−	0.398704i	0.0680545	−	0.0206441i	−0.256074	−	0.966657i	$-0.582429\pi$
$373$	1.31435	−	0.398704i	0.0680545	−	0.0206441i	0.324128	+	0.946013i	$0.394929\pi$
$374$	3.71011	−	0.667239i	0.191845	−	0.0345021i
$375$	−6.34192	+	9.49135i	−0.327495	+	0.490131i
$376$	16.2640	−	7.57048i	0.838750	−	0.390417i
$377$	−1.23840	+	0.827473i	−0.0637809	+	0.0426170i
$378$	−0.0942166	+	5.11754i	−0.00484598	+	0.263218i
$379$	−6.00725	−	7.31986i	−0.308572	−	0.375996i	0.595515	−	0.803344i	$-0.296948\pi$
$379$	−6.00725	−	7.31986i	−0.308572	−	0.375996i	−0.904087	+	0.427348i	$0.859448\pi$
$380$	−14.4899	−	3.44116i	−0.743319	−	0.176528i
$381$	18.4471	−	9.86018i	0.945074	−	0.505153i
$382$	−0.962438	+	1.72351i	−0.0492426	+	0.0881826i
$383$	−34.9807			−1.78743			−0.893715	−	0.448635i	$-0.851910\pi$
$383$	−34.9807			−1.78743			−0.893715	+	0.448635i	$0.851910\pi$
$384$	11.2880	−	0.762989i	0.576036	−	0.0389361i
$385$	13.0360			0.664374
$386$	−4.11804	+	7.37450i	−0.209603	+	0.375352i
$387$	2.89114	−	1.54535i	0.146965	−	0.0785544i
$388$	4.09115	−	17.2269i	0.207697	−	0.874565i
$389$	−14.2747	−	17.3938i	−0.723756	−	0.881899i	0.273030	−	0.962005i	$-0.411974\pi$
$389$	−14.2747	−	17.3938i	−0.723756	−	0.881899i	−0.996786	+	0.0801062i	$0.974474\pi$
$390$	−0.0682535	+	3.70731i	−0.00345615	+	0.187727i
$391$	2.76390	−	1.84678i	0.139777	−	0.0933957i
$392$	−16.2064	−	5.91119i	−0.818546	−	0.298560i
$393$	−5.20328	+	7.78726i	−0.262471	+	0.392815i
$394$	1.68850	−	0.303666i	0.0850655	−	0.0152985i
$395$	8.00082	−	2.42702i	0.402565	−	0.122117i
$396$	−4.83633	+	1.27470i	−0.243035	+	0.0640563i
$397$	17.7473	+	14.5649i	0.890713	+	0.730989i	0.963882	−	0.266330i	$-0.0858112\pi$
$397$	17.7473	+	14.5649i	0.890713	+	0.730989i	−0.0731690	+	0.997320i	$0.523311\pi$
$398$	−1.39567	−	17.4599i	−0.0699588	−	0.875185i
$399$	−17.2876	−	7.16074i	−0.865460	−	0.358485i
$400$	9.22533	+	7.19956i	0.461266	+	0.359978i
$401$	18.6145	−	7.71037i	0.929562	−	0.385037i	0.134050	−	0.990975i	$-0.457202\pi$
$401$	18.6145	−	7.71037i	0.929562	−	0.385037i	0.795512	+	0.605937i	$0.207202\pi$
$402$	−9.26012	−	18.1190i	−0.461853	−	0.903695i
$403$	0.226985	+	2.30461i	0.0113069	+	0.114801i
$404$	−29.6719	+	14.4819i	−1.47623	+	0.720503i
$405$	−0.678952	+	1.27023i	−0.0337374	+	0.0631183i
$406$	0.892465	−	4.09159i	0.0442923	−	0.203062i
$407$	20.1846	−	4.01497i	1.00051	−	0.199015i
$408$	−2.41045	−	1.81075i	−0.119335	−	0.0896453i
$409$	1.90165	−	9.56024i	0.0940306	−	0.472724i	−0.904863	−	0.425702i	$-0.860027\pi$
$409$	1.90165	−	9.56024i	0.0940306	−	0.472724i	0.998894	−	0.0470213i	$-0.0149729\pi$
$410$	21.1842	−	8.32131i	1.04621	−	0.410960i
$411$	−1.07761	+	10.9412i	−0.0531546	+	0.539688i
$412$	−28.0715	+	10.4344i	−1.38298	+	0.514066i
$413$	2.91939	−	9.62395i	0.143654	−	0.473564i
$414$	−3.46020	+	2.73469i	−0.170060	+	0.134403i
$415$	−3.13632	−	3.13632i	−0.153956	−	0.153956i
$416$	10.2541	+	0.946483i	0.502748	+	0.0464052i
$417$	14.3759	−	14.3759i	0.703992	−	0.703992i
$418$	2.12684	−	18.1604i	0.104027	−	0.888254i
$419$	4.36742	+	1.32484i	0.213363	+	0.0647228i	0.395156	−	0.918614i	$-0.370690\pi$
$419$	4.36742	+	1.32484i	0.213363	+	0.0647228i	−0.181794	+	0.983337i	$0.558190\pi$
$420$	−7.09569	−	7.63840i	−0.346234	−	0.372716i
$421$	−16.8256	−	1.65718i	−0.820031	−	0.0807660i	−0.320704	−	0.947180i	$-0.603919\pi$
$421$	−16.8256	−	1.65718i	−0.820031	−	0.0807660i	−0.499327	+	0.866414i	$0.666419\pi$
$422$	0.956304	+	0.416900i	0.0465522	+	0.0202944i
$423$	6.22073	+	1.23738i	0.302462	+	0.0601635i
$424$	−5.50704	+	1.93240i	−0.267446	+	0.0938459i
$425$	−0.608353	−	3.05840i	−0.0295095	−	0.148354i
$426$	−7.04147	−	10.9702i	−0.341161	−	0.531509i
$427$	16.6695	+	8.91005i	0.806695	+	0.431188i
$428$	−13.7848	+	0.846872i	−0.666315	+	0.0409351i
$429$	−4.53042	+	0.446207i	−0.218731	+	0.0215431i
$430$	−2.05564	+	6.35311i	−0.0991318	+	0.306374i
$431$	−15.4973	−	37.4138i	−0.746479	−	1.80216i	−0.577223	−	0.816586i	$-0.695864\pi$
$431$	−15.4973	−	37.4138i	−0.746479	−	1.80216i	−0.169255	−	0.985572i	$-0.554136\pi$
$432$	3.37941	+	2.14000i	0.162592	+	0.102961i
$433$	−4.89333	+	11.8135i	−0.235158	+	0.567723i	−0.996770	−	0.0803113i	$-0.974409\pi$
$433$	−4.89333	+	11.8135i	−0.235158	+	0.567723i	0.761611	+	0.648034i	$0.224409\pi$
$434$	−4.95639	−	4.22265i	−0.237914	−	0.202694i
$435$	0.747587	−	0.910937i	0.0358440	−	0.0436761i
$436$	−11.0459	+	8.40424i	−0.529003	+	0.402490i
$437$	−4.68041	−	15.4293i	−0.223895	−	0.738081i
$438$	11.3756	+	7.90761i	0.543545	+	0.377840i
$439$	−7.63787	−	5.10346i	−0.364536	−	0.243575i	0.359790	−	0.933033i	$-0.382849\pi$
$439$	−7.63787	−	5.10346i	−0.364536	−	0.243575i	−0.724325	+	0.689459i	$0.757849\pi$
$440$	5.29096	−	8.70581i	0.252237	−	0.415033i
$441$	−3.38846	−	5.07119i	−0.161355	−	0.241485i
$442$	−1.90430	−	1.97573i	−0.0905783	−	0.0939760i
$443$	−10.9620	+	8.99626i	−0.520819	+	0.427425i	−0.857722	−	0.514114i	$-0.828121\pi$
$443$	−10.9620	+	8.99626i	−0.520819	+	0.427425i	0.336902	+	0.941540i	$0.390621\pi$
$444$	−13.3394	−	9.64173i	−0.633060	−	0.457576i
$445$	−9.78980	−	18.3154i	−0.464081	−	0.868235i
$446$	20.5682	−	5.82807i	0.973932	−	0.275967i
$447$		−	13.6006i		−	0.643288i
$448$	−22.6056	+	18.0922i	−1.06802	+	0.854774i
$449$		−	15.4977i		−	0.731381i	−0.930736	−	0.365691i	$-0.880833\pi$
$449$		−	15.4977i		−	0.731381i	0.930736	−	0.365691i	$-0.119167\pi$
$450$	1.12792	+	3.98062i	0.0531708	+	0.187648i
$451$	13.1722	+	24.6435i	0.620257	+	1.16042i
$452$	5.03150	+	31.2710i	0.236662	+	1.47086i
$453$	0.622552	−	0.510915i	0.0292501	−	0.0240049i
$454$	15.0166	−	14.4737i	0.704766	−	0.679285i
$455$	−5.27201	−	7.89013i	−0.247156	−	0.369895i
$456$	−11.7987	+	8.63879i	−0.552526	+	0.404548i
$457$	−19.9192	−	13.3096i	−0.931781	−	0.622596i	−0.00572586	−	0.999984i	$-0.501823\pi$
$457$	−19.9192	−	13.3096i	−0.931781	−	0.622596i	−0.926056	+	0.377387i	$0.876823\pi$
$458$	−8.77732	+	12.6267i	−0.410137	+	0.590006i
$459$	−0.309413	−	1.02000i	−0.0144422	−	0.0476094i
$460$	1.20902	−	8.90176i	0.0563706	−	0.415046i
$461$	−0.618984	+	0.754234i	−0.0288289	+	0.0351282i	−0.787225	−	0.616665i	$-0.788483\pi$
$461$	−0.618984	+	0.754234i	−0.0288289	+	0.0351282i	0.758396	+	0.651794i	$0.225983\pi$
$462$	8.30090	−	9.74328i	0.386193	−	0.453298i
$463$	−16.3259	+	39.4142i	−0.758728	+	1.83173i	−0.257942	+	0.966161i	$0.583044\pi$
$463$	−16.3259	+	39.4142i	−0.758728	+	1.83173i	−0.500786	+	0.865571i	$0.666956\pi$
$464$	−2.37026	−	2.25669i	−0.110036	−	0.104764i
$465$	−0.701169	−	1.69277i	−0.0325159	−	0.0785004i
$466$	31.5728	+	10.2158i	1.46258	+	0.473240i
$467$	−9.27997	+	0.913997i	−0.429426	+	0.0422948i	−0.310422	−	0.950599i	$-0.600470\pi$
$467$	−9.27997	+	0.913997i	−0.429426	+	0.0422948i	−0.119004	+	0.992894i	$0.537970\pi$
$468$	2.72744	+	2.41171i	0.126076	+	0.111482i
$469$	45.9262	+	24.5481i	2.12068	+	1.13353i
$470$	−10.8722	+	6.97857i	−0.501498	+	0.321897i
$471$	−1.01792	−	5.11743i	−0.0469033	−	0.235799i
$472$	−5.24226	−	5.85577i	−0.241294	−	0.269534i
$473$	−8.04051	−	1.59936i	−0.369703	−	0.0735385i
$474$	3.28068	−	7.52539i	0.150687	−	0.345653i
$475$	−15.0525	−	1.48254i	−0.690654	−	0.0680235i
$476$	7.71028	+	0.283997i	0.353400	+	0.0130170i
$477$	−1.97457	−	0.598980i	−0.0904094	−	0.0274254i
$478$	−29.5657	−	3.46257i	−1.35231	−	0.158374i
$479$	3.52234	−	3.52234i	0.160940	−	0.160940i	−0.622043	−	0.782983i	$-0.713697\pi$
$479$	3.52234	−	3.52234i	0.160940	−	0.160940i	0.782983	+	0.622043i	$0.213697\pi$
$480$	−7.98111	+	1.63849i	−0.364286	+	0.0747863i
$481$	−10.5932	−	10.5932i	−0.483007	−	0.483007i
$482$	3.03414	+	3.83909i	0.138201	+	0.174866i
$483$	3.27647	−	10.8011i	0.149085	−	0.491466i
$484$	−8.63028	−	3.95297i	−0.392285	−	0.179681i
$485$	−1.24982	+	12.6896i	−0.0567513	+	0.576206i
$486$	0.517054	+	1.31630i	0.0234540	+	0.0597087i
$487$	−1.76932	+	8.89499i	−0.0801757	+	0.403070i	0.919768	+	0.392462i	$0.128377\pi$
$487$	−1.76932	+	8.89499i	−0.0801757	+	0.403070i	−0.999944	+	0.0106079i	$0.996623\pi$
$488$	12.7161	−	7.51605i	0.575632	−	0.340236i
$489$	−24.5767	+	4.88862i	−1.11140	+	0.221071i
$490$	12.1378	+	2.64751i	0.548328	+	0.119602i
$491$	−8.65486	+	16.1921i	−0.390588	+	0.730740i	−0.997971	−	0.0636699i	$-0.979720\pi$
$491$	−8.65486	+	16.1921i	−0.390588	+	0.730740i	0.607383	+	0.794409i	$0.292220\pi$
$492$	7.26997	−	21.1322i	0.327756	−	0.952711i
$493$	0.0854804	+	0.867897i	0.00384984	+	0.0390881i
$494$	−11.8519	+	6.05715i	−0.533241	+	0.272524i
$495$	3.32766	−	1.37836i	0.149567	−	0.0619527i
$496$	−4.83168	+	1.59616i	−0.216949	+	0.0716696i
$497$	30.8214	+	12.7667i	1.38253	+	0.572663i
$498$	−4.34125	+	0.347022i	−0.194536	+	0.0155504i
$499$	21.6794	+	17.7919i	0.970505	+	0.796473i	0.979077	−	0.203490i	$-0.0652285\pi$
$499$	21.6794	+	17.7919i	0.970505	+	0.796473i	−0.00857167	+	0.999963i	$0.502728\pi$
$500$	−19.7247	−	11.4960i	−0.882117	−	0.514115i
$501$	6.26206	−	1.89957i	0.279768	−	0.0848667i
$502$	4.58040	+	25.4689i	0.204433	+	1.13673i
$503$	−18.1384	+	27.1460i	−0.808752	+	1.21038i	0.165787	+	0.986162i	$0.446984\pi$
$503$	−18.1384	+	27.1460i	−0.808752	+	1.21038i	−0.974538	+	0.224221i	$0.928016\pi$
$504$	−10.2274	+	0.439531i	−0.455564	+	0.0195783i
$505$	19.7702	−	13.2101i	0.879764	−	0.587840i
$506$	11.0274	+	0.203020i	0.490228	+	0.00902535i
$507$	−6.14485	−	7.48752i	−0.272902	−	0.332532i
$508$	21.9456	+	35.6155i	0.973678	+	1.58018i
$509$	19.0395	−	10.1768i	0.843910	−	0.451079i	0.00801424	−	0.999968i	$-0.497449\pi$
$509$	19.0395	−	10.1768i	0.843910	−	0.451079i	0.835895	+	0.548889i	$0.184949\pi$
$510$	1.89559	+	1.05853i	0.0839380	+	0.0468724i
$511$	−35.4553			−1.56845
$512$	2.90745	+	22.4398i	0.128492	+	0.991711i
$513$	−5.17009			−0.228265
$514$	−25.7636	−	14.3868i	−1.13638	−	0.634576i
$515$	19.0204	−	10.1666i	0.838141	−	0.447996i
$516$	3.43945	+	5.58188i	0.151413	+	0.245729i
$517$	−10.0623	−	12.2609i	−0.442538	−	0.539234i
$518$	42.1151	+	0.775361i	1.85043	+	0.0340674i
$519$	−13.6893	+	9.14689i	−0.600893	+	0.401504i
$520$	−7.40904	+	0.318410i	−0.324908	+	0.0139632i
$521$	4.94935	−	7.40722i	0.216835	−	0.324516i	−0.707066	−	0.707147i	$-0.749982\pi$
$521$	4.94935	−	7.40722i	0.216835	−	0.324516i	0.923901	+	0.382631i	$0.124982\pi$
$522$	−0.204808	−	1.13881i	−0.00896421	−	0.0498446i
$523$	9.84535	−	2.98655i	0.430507	−	0.130593i	−0.0675920	−	0.997713i	$-0.521532\pi$
$523$	9.84535	−	2.98655i	0.430507	−	0.130593i	0.498099	+	0.867120i	$0.334032\pi$
$524$	−16.1833	−	9.43196i	−0.706973	−	0.412037i
$525$	−8.18486	−	6.71714i	−0.357217	−	0.293160i
$526$	−27.3826	+	2.18885i	−1.19394	+	0.0954385i
$527$	1.25274	+	0.518900i	0.0545701	+	0.0226037i
$528$	−3.13773	−	9.49814i	−0.136552	−	0.413353i
$529$	−12.2638	+	5.07983i	−0.533208	+	0.220862i
$530$	3.74253	−	1.91270i	0.162565	−	0.0830823i
$531$	−0.272364	−	2.76536i	−0.0118196	−	0.120007i
$532$	12.1744	−	35.3882i	0.527827	−	1.53427i
$533$	9.58858	−	17.9390i	0.415327	−	0.777023i
$534$	−19.9231	−	4.34566i	−0.862156	−	0.188055i
$535$	9.75476	−	1.94034i	0.421735	−	0.0838883i
$536$	35.0342	−	20.7075i	1.51325	−	0.894427i
$537$	−3.07722	+	15.4702i	−0.132792	+	0.667590i
$538$	−10.8075	−	27.5134i	−0.465944	−	1.18619i
$539$	−1.49498	+	15.1788i	−0.0643934	+	0.653797i
$540$	−2.61895	−	1.19957i	−0.112702	−	0.0516213i
$541$	−0.611541	+	2.01598i	−0.0262922	+	0.0866737i	−0.969105	−	0.246650i	$-0.920670\pi$
$541$	−0.611541	+	2.01598i	−0.0262922	+	0.0866737i	0.942812	+	0.333324i	$0.108170\pi$
$542$	−6.08982	−	7.70544i	−0.261580	−	0.330977i
$543$	−8.13191	−	8.13191i	−0.348974	−	0.348974i
$544$	3.31906	−	5.03389i	0.142304	−	0.215826i
$545$	7.06781	−	7.06781i	0.302752	−	0.302752i
$546$	−9.25426	−	1.08381i	−0.396046	−	0.0463826i
$547$	11.7470	+	3.56340i	0.502264	+	0.152360i	0.531242	−	0.847220i	$-0.321725\pi$
$547$	11.7470	+	3.56340i	0.502264	+	0.152360i	−0.0289784	+	0.999580i	$0.509225\pi$
$548$	−21.9733	−	0.809354i	−0.938653	−	0.0345739i
$549$	5.19729	+	0.511889i	0.221815	+	0.0218469i
$550$	4.13469	−	9.48436i	0.176304	−	0.404414i
$551$	4.14880	+	0.825247i	0.176745	+	0.0351567i
$552$	−5.88345	−	6.57200i	−0.250416	−	0.279723i
$553$	4.09876	+	20.6059i	0.174297	+	0.876250i
$554$	28.3954	−	18.2262i	1.20640	−	0.774357i
$555$	10.4534	+	5.58748i	0.443724	+	0.237175i
$556$	30.4608	+	26.9347i	1.29182	+	1.14229i
$557$	−33.8679	+	3.33570i	−1.43503	+	0.141338i	−0.785436	−	0.618943i	$-0.787561\pi$
$557$	−33.8679	+	3.33570i	−1.43503	+	0.141338i	−0.649594	+	0.760281i	$0.725061\pi$
$558$	−1.71169	−	0.553840i	−0.0724614	−	0.0234459i
$559$	2.28373	+	5.51340i	0.0965913	+	0.233192i
$560$	14.3779	−	15.1014i	0.607575	−	0.638153i
$561$	−1.02006	+	2.46263i	−0.0430668	+	0.103972i
$562$	2.75549	−	3.23429i	0.116233	−	0.136430i
$563$	24.4301	−	29.7681i	1.02960	−	1.25458i	0.0630780	−	0.998009i	$-0.479908\pi$
$563$	24.4301	−	29.7681i	1.02960	−	1.25458i	0.966526	−	0.256568i	$-0.0825917\pi$
$564$	−1.70720	+	12.5698i	−0.0718861	+	0.529284i
$565$	−6.62123	−	21.8273i	−0.278557	−	0.918280i
$566$	−11.7853	+	16.9538i	−0.495373	+	0.712622i
$567$	−3.00931	−	2.01075i	−0.126379	−	0.0844438i
$568$	21.0356	−	15.4018i	0.882633	−	0.646246i
$569$	−8.92893	−	13.3631i	−0.374320	−	0.560210i	0.595708	−	0.803201i	$-0.296871\pi$
$569$	−8.92893	−	13.3631i	−0.374320	−	0.560210i	−0.970029	+	0.242991i	$0.921871\pi$
$570$	7.58229	−	7.30815i	0.317587	−	0.306105i
$571$	26.8715	−	22.0529i	1.12454	−	0.922883i	0.126922	−	0.991913i	$-0.459490\pi$
$571$	26.8715	−	22.0529i	1.12454	−	0.922883i	0.997615	+	0.0690294i	$0.0219902\pi$
$572$	−1.44634	−	8.98907i	−0.0604746	−	0.375852i
$573$	−0.657998	−	1.23103i	−0.0274883	−	0.0514269i
$574$	15.5918	+	55.0260i	0.650790	+	2.29674i
$575$		−	9.12363i		−	0.380482i
$576$	−3.85750	+	7.00855i	−0.160729	+	0.292023i
$577$			15.3269i			0.638067i	0.947743	+	0.319033i	$0.103358\pi$
$577$			15.3269i			0.638067i	−0.947743	+	0.319033i	$0.896642\pi$
$578$	21.5851	−	6.11622i	0.897822	−	0.254401i
$579$	−2.81542	−	5.26727i	−0.117005	−	0.218900i
$580$	1.91013	+	1.38064i	0.0793138	+	0.0573281i
$581$	8.61566	−	7.07069i	0.357438	−	0.293342i
$582$	8.68857	+	9.01449i	0.360153	+	0.373663i
$583$	2.86680	+	4.29047i	0.118731	+	0.177693i
$584$	−14.3904	+	23.6781i	−0.595478	+	0.979806i
$585$	−2.18004	−	1.45665i	−0.0901334	−	0.0602252i
$586$	−19.5791	−	13.6102i	−0.808806	−	0.562234i
$587$	0.257727	+	0.849613i	0.0106375	+	0.0350673i	0.962098	−	0.272702i	$-0.0879174\pi$
$587$	0.257727	+	0.849613i	0.0106375	+	0.0350673i	−0.951461	+	0.307770i	$0.900417\pi$
$588$	9.70773	−	7.38609i	0.400340	−	0.304597i
$589$	4.17241	−	5.08409i	0.171921	−	0.209486i
$590$	4.30840	+	3.67059i	0.177374	+	0.151116i
$591$	−0.464235	+	1.12076i	−0.0190961	+	0.0461020i
$592$	17.6113	−	27.8110i	0.723818	−	1.14303i
$593$	9.15074	+	22.0918i	0.375776	+	0.907203i	0.992748	+	0.120218i	$0.0383593\pi$
$593$	9.15074	+	22.0918i	0.375776	+	0.907203i	−0.616972	+	0.786985i	$0.711641\pi$
$594$	1.08874	−	3.36484i	0.0446716	−	0.138061i
$595$	−5.52957	+	0.544615i	−0.226690	+	0.0223270i
$596$	27.1501	−	1.66797i	1.11211	−	0.0683226i
$597$	10.9229	+	5.83843i	0.447046	+	0.238951i
$598$	−4.33683	−	6.75654i	−0.177346	−	0.276295i
$599$	−0.728406	−	3.66194i	−0.0297619	−	0.149623i	0.963047	−	0.269333i	$-0.0868034\pi$
$599$	−0.728406	−	3.66194i	−0.0297619	−	0.149623i	−0.992809	+	0.119710i	$0.961803\pi$
$600$	−7.80793	+	2.73978i	−0.318757	+	0.111851i
$601$	−30.2037	−	6.00790i	−1.23204	−	0.245067i	−0.464210	−	0.885725i	$-0.653662\pi$
$601$	−30.2037	−	6.00790i	−1.23204	−	0.245067i	−0.767826	+	0.640658i	$0.778662\pi$
$602$	−15.3813	−	6.70544i	−0.626894	−	0.273293i
$603$	14.3191	+	1.41030i	0.583117	+	0.0574320i
$604$	1.09626	+	1.18010i	0.0446061	+	0.0480177i
$605$	6.54167	+	1.98439i	0.265957	+	0.0806771i
$606$	2.71569	−	23.1883i	0.110317	−	0.941962i
$607$	−11.3604	+	11.3604i	−0.461103	+	0.461103i	−0.899017	−	0.437914i	$-0.855717\pi$
$607$	−11.3604	+	11.3604i	−0.461103	+	0.461103i	0.437914	+	0.899017i	$0.355717\pi$
$608$	−18.6920	−	22.4936i	−0.758063	−	0.912236i
$609$	2.09390	+	2.09390i	0.0848490	+	0.0848490i
$610$	−8.34576	+	6.59588i	−0.337910	+	0.267059i
$611$	−3.35163	+	11.0488i	−0.135592	+	0.446988i
$612$	1.99821	−	0.742753i	0.0807729	−	0.0300240i
$613$	−0.193542	+	1.96507i	−0.00781709	+	0.0793683i	−0.998302	−	0.0582551i	$-0.981446\pi$
$613$	−0.193542	+	1.96507i	−0.00781709	+	0.0793683i	0.990485	+	0.137623i	$0.0439463\pi$
$614$	−19.5815	+	7.69176i	−0.790245	+	0.310414i
$615$	−3.13972	+	15.7845i	−0.126606	+	0.636491i
$616$	20.4679	+	15.3757i	0.824675	+	0.619503i
$617$	−6.73969	+	1.34061i	−0.271330	+	0.0539708i	−0.328880	−	0.944372i	$-0.606671\pi$
$617$	−6.73969	+	1.34061i	−0.271330	+	0.0539708i	0.0575501	+	0.998343i	$0.481671\pi$
$618$	4.51293	−	20.6900i	0.181537	−	0.832273i
$619$	−4.15334	+	7.77036i	−0.166937	+	0.312317i	−0.951454	−	0.307790i	$-0.900411\pi$
$619$	−4.15334	+	7.77036i	−0.166937	+	0.312317i	0.784518	+	0.620107i	$0.212911\pi$
$620$	3.29318	−	1.60730i	0.132257	−	0.0645506i
$621$	−0.305678	−	3.10360i	−0.0122664	−	0.124543i
$622$	11.2528	+	22.0180i	0.451195	+	0.882842i
$623$	48.2137	−	19.9708i	1.93164	−	0.800111i
$624$	−4.47986	+	5.74038i	−0.179338	+	0.229799i
$625$	1.67550	+	0.694013i	0.0670198	+	0.0277605i
$626$	1.92517	+	24.0839i	0.0769451	+	0.962585i
$627$	9.99433	+	8.20213i	0.399135	+	0.327562i
$628$	10.0908	−	2.65961i	0.402665	−	0.106130i
$629$	−8.39413	+	2.54633i	−0.334696	+	0.101529i
$630$	7.25564	−	1.30488i	0.289072	−	0.0519876i
$631$	15.1890	−	22.7319i	0.604663	−	0.904942i	−0.395244	−	0.918576i	$-0.629340\pi$
$631$	15.1890	−	22.7319i	0.604663	−	0.904942i	0.999907	+	0.0136338i	$0.00433991\pi$
$632$	15.4248	+	5.62611i	0.613565	+	0.223795i
$633$	−0.613353	+	0.409829i	−0.0243786	+	0.0162893i
$634$	−0.624924	+	33.9439i	−0.0248189	+	1.34808i
$635$	−19.1122	−	23.2882i	−0.758443	−	0.924165i
$636$	0.953546	−	4.01517i	0.0378106	−	0.159212i
$637$	9.79169	−	5.23377i	0.387961	−	0.207369i
$638$	−1.41077	+	2.52637i	−0.0558528	+	0.100020i
$639$	9.21759			0.364642
$640$	−4.24960	−	15.7312i	−0.167980	−	0.621832i
$641$	−19.8103			−0.782460			−0.391230	−	0.920293i	$-0.627950\pi$
$641$	−19.8103			−0.782460			−0.391230	+	0.920293i	$0.627950\pi$
$642$	4.76129	−	8.52641i	0.187913	−	0.336510i
$643$	−35.5607	+	19.0076i	−1.40238	+	0.749586i	−0.987099	−	0.160109i	$-0.948816\pi$
$643$	−35.5607	+	19.0076i	−1.40238	+	0.749586i	−0.415278	+	0.909695i	$0.636316\pi$
$644$	21.9633	+	5.21598i	0.865476	+	0.205538i
$645$	−2.99537	−	3.64987i	−0.117943	−	0.143714i
$646$	−0.143456	+	7.79209i	−0.00564421	+	0.306576i
$647$	−12.4651	+	8.32894i	−0.490055	+	0.327444i	−0.775926	−	0.630824i	$-0.782717\pi$
$647$	−12.4651	+	8.32894i	−0.490055	+	0.327444i	0.285871	+	0.958268i	$0.407717\pi$
$648$	−2.56424	+	1.19359i	−0.100733	+	0.0468887i
$649$	−3.86062	+	5.77783i	−0.151543	+	0.226800i
$650$	−7.41264	+	1.33311i	−0.290748	+	0.0522890i
$651$	4.40590	−	1.33652i	0.172681	−	0.0523822i
$652$	−12.7729	−	48.4614i	−0.500225	−	1.89790i
$653$	−27.4303	−	22.5115i	−1.07343	−	0.880943i	−0.0801638	−	0.996782i	$-0.525544\pi$
$653$	−27.4303	−	22.5115i	−1.07343	−	0.880943i	−0.993268	+	0.115839i	$0.963044\pi$
$654$	−0.782026	−	9.78315i	−0.0305796	−	0.382552i
$655$	12.4625	+	5.16215i	0.486952	+	0.201702i
$656$	43.0763	+	11.9210i	1.68185	+	0.465435i
$657$	−9.05057	+	3.74887i	−0.353096	+	0.146257i
$658$	−14.7738	−	28.9076i	−0.575944	−	1.12693i
$659$	0.685199	+	6.95694i	0.0266916	+	0.271004i	0.999263	+	0.0383977i	$0.0122254\pi$
$659$	0.685199	+	6.95694i	0.0266916	+	0.271004i	−0.972571	+	0.232606i	$0.925275\pi$
$660$	3.15963	+	6.47375i	0.122989	+	0.251990i
$661$	6.78168	−	12.6876i	0.263777	−	0.493491i	−0.714812	−	0.699317i	$-0.753488\pi$
$661$	6.78168	−	12.6876i	0.263777	−	0.493491i	0.978589	+	0.205825i	$0.0659878\pi$
$662$	−7.91520	+	36.2880i	−0.307633	+	1.41037i
$663$	1.90306	−	0.378543i	0.0739088	−	0.0147014i
$664$	−1.22514	−	8.62361i	−0.0475448	−	0.334661i
$665$	−5.25783	+	26.4329i	−0.203890	+	1.02502i
$666$	10.8326	−	4.25513i	0.419755	−	0.164883i
$667$	−0.250100	+	2.53931i	−0.00968392	+	0.0983225i
$668$	4.55997	+	12.2676i	0.176431	+	0.474647i
$669$	−4.38808	+	14.4656i	−0.169653	+	0.559272i
$670$	−22.9934	+	18.1723i	−0.888312	+	0.702057i
$671$	−9.23483	−	9.23483i	−0.356507	−	0.356507i
$672$	−2.13168	−	20.3624i	−0.0822314	−	0.785495i
$673$	−33.2399	+	33.2399i	−1.28130	+	1.28130i	−0.341377	+	0.939927i	$0.610893\pi$
$673$	−33.2399	+	33.2399i	−1.28130	+	1.28130i	−0.939927	+	0.341377i	$0.889107\pi$
$674$	5.18680	−	44.2883i	0.199788	−	1.70592i
$675$	−2.79956	−	0.849239i	−0.107755	−	0.0326872i
$676$	14.1933	−	13.1848i	0.545894	−	0.507109i
$677$	−19.9924	−	1.96908i	−0.768370	−	0.0756779i	−0.293766	−	0.955877i	$-0.594909\pi$
$677$	−19.9924	−	1.96908i	−0.768370	−	0.0756779i	−0.474604	+	0.880199i	$0.657409\pi$
$678$	−20.5302	−	8.95012i	−0.788459	−	0.343727i
$679$	−31.4258	−	6.25098i	−1.20601	−	0.239890i
$680$	−1.88060	+	3.91385i	−0.0721176	+	0.150089i
$681$	2.87713	+	14.4643i	0.110252	+	0.554273i
$682$	2.43022	+	3.78615i	0.0930581	+	0.144979i
$683$	21.9227	+	11.7179i	0.838848	+	0.448374i	0.834099	−	0.551615i	$-0.185988\pi$
$683$	21.9227	+	11.7179i	0.838848	+	0.448374i	0.00474923	+	0.999989i	$0.498488\pi$
$684$	−0.634054	−	10.3207i	−0.0242437	−	0.394623i
$685$	15.7586	−	1.55208i	0.602103	−	0.0593020i
$686$	1.41960	−	4.38740i	0.0542007	−	0.167512i
$687$	−4.16118	−	10.0460i	−0.158759	−	0.383278i
$688$	−10.7210	+	7.55050i	−0.408732	+	0.287860i
$689$	1.43745	−	3.47031i	0.0547624	−	0.132208i
$690$	4.83537	+	4.11955i	0.184079	+	0.156829i
$691$	3.92876	−	4.78720i	0.149457	−	0.182114i	−0.692900	−	0.721033i	$-0.743667\pi$
$691$	3.92876	−	4.78720i	0.149457	−	0.182114i	0.842357	+	0.538920i	$0.181167\pi$
$692$	−19.9382	−	26.2053i	−0.757937	−	0.996176i
$693$	2.62733	+	8.66114i	0.0998040	+	0.329010i
$694$	−21.2551	−	14.7753i	−0.806833	−	0.560862i
$695$	−24.3472	−	16.2683i	−0.923544	−	0.617092i
$696$	2.24823	−	0.548508i	0.0852188	−	0.0207912i
$697$	−6.61693	−	9.90293i	−0.250634	−	0.375100i
$698$	−32.9360	−	34.1715i	−1.24665	−	1.29341i
$699$	−18.1387	+	14.8860i	−0.686067	+	0.563041i
$700$	12.4052	−	17.1627i	0.468873	−	0.648689i
$701$	−10.8129	−	20.2295i	−0.408396	−	0.764056i	0.590685	−	0.806902i	$-0.298857\pi$
$701$	−10.8129	−	20.2295i	−0.408396	−	0.764056i	−0.999082	+	0.0428461i	$0.986357\pi$
$702$	−2.47691	+	0.701841i	−0.0934848	+	0.0264893i
$703$			42.5476i			1.60471i
$704$	18.5757	−	7.42850i	0.700099	−	0.279972i
$705$		−	9.13524i		−	0.344053i
$706$	5.34339	+	18.8577i	0.201101	+	0.709717i
$707$	28.1656	+	52.6942i	1.05928	+	1.98177i
$708$	5.48692	−	0.882845i	0.206211	−	0.0331793i
$709$	2.60385	−	2.13692i	0.0977895	−	0.0802538i	−0.584228	−	0.811589i	$-0.698603\pi$
$709$	2.60385	−	2.13692i	0.0977895	−	0.0802538i	0.682018	+	0.731336i	$0.261103\pi$
$710$	−13.5182	+	13.0295i	−0.507330	+	0.488987i
$711$	3.22504	+	4.82662i	0.120949	+	0.181012i
$712$	6.23161	−	40.3041i	0.233540	−	1.51046i
$713$	3.29867	+	2.20410i	0.123536	+	0.0825441i
$714$	−3.11400	+	4.47968i	−0.116539	+	0.167648i
$715$	1.90332	+	6.27440i	0.0711801	+	0.234649i
$716$	−31.2596	−	4.24561i	−1.16823	−	0.158666i
$717$	13.3534	−	16.2711i	0.498690	−	0.607656i
$718$	12.7540	−	14.9701i	0.475975	−	0.558681i
$719$	−2.53128	+	6.11106i	−0.0944010	+	0.227904i	−0.964026	−	0.265809i	$-0.914361\pi$
$719$	−2.53128	+	6.11106i	−0.0944010	+	0.227904i	0.869625	+	0.493713i	$0.164361\pi$
$720$	2.07344	−	5.37515i	0.0772726	−	0.200320i
$721$	20.7395	+	50.0695i	0.772378	+	1.86469i
$722$	10.4007	+	3.36531i	0.387075	+	0.125244i
$723$	−3.44344	+	0.339149i	−0.128063	+	0.0126131i
$724$	15.2359	−	17.2305i	0.566239	−	0.640367i
$725$	2.11099	+	1.12835i	0.0784001	+	0.0419057i
$726$	5.64870	−	3.62574i	0.209643	−	0.134564i
$727$	−8.94893	−	44.9893i	−0.331897	−	1.66856i	−0.681619	−	0.731708i	$-0.738724\pi$
$727$	−8.94893	−	44.9893i	−0.331897	−	1.66856i	0.349721	−	0.936854i	$-0.386276\pi$
$728$	1.02860	−	18.6066i	0.0381225	−	0.689607i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	7.97408	−	18.2913i	0.295134	−	0.676993i
$731$	3.47742	+	0.342496i	0.128617	+	0.0126677i
$732$	−0.384461	+	10.4378i	−0.0142101	+	0.385792i
$733$	9.14574	+	2.77433i	0.337806	+	0.102472i	0.454630	−	0.890680i	$-0.349771\pi$
$733$	9.14574	+	2.77433i	0.337806	+	0.102472i	−0.116824	+	0.993153i	$0.537271\pi$
$734$	−43.2736	−	5.06796i	−1.59726	−	0.187062i
$735$	−6.21157	+	6.21157i	−0.229117	+	0.229117i
$736$	12.3977	−	12.5507i	0.456986	−	0.462626i
$737$	−25.4429	−	25.4429i	−0.937200	−	0.937200i
$738$	9.79827	+	12.3977i	0.360679	+	0.456367i
$739$	−1.99946	+	6.59133i	−0.0735513	+	0.242466i	−0.986006	−	0.166713i	$-0.946685\pi$
$739$	−1.99946	+	6.59133i	−0.0735513	+	0.242466i	0.912454	+	0.409179i	$0.134185\pi$
$740$	−9.87193	+	21.5528i	−0.362899	+	0.792296i
$741$	0.922497	−	9.36626i	0.0338888	−	0.344078i
$742$	3.86139	+	9.83025i	0.141756	+	0.360880i
$743$	1.87773	−	9.43997i	0.0688871	−	0.346319i	−0.930935	−	0.365185i	$-0.881006\pi$
$743$	1.87773	−	9.43997i	0.0688871	−	0.346319i	0.999822	+	0.0188662i	$0.00600566\pi$
$744$	0.895677	−	3.48485i	0.0328371	−	0.127761i
$745$	−19.2126	+	3.82162i	−0.703895	+	0.140013i
$746$	−1.89779	−	0.413949i	−0.0694831	−	0.0151558i
$747$	1.45168	−	2.71589i	0.0531140	−	0.0993694i
$748$	−5.04110	−	1.73426i	−0.184321	−	0.0634108i
$749$	2.44969	+	24.8722i	0.0895099	+	0.908809i
$750$	14.3749	−	7.34661i	0.524898	−	0.268260i
$751$	−12.4505	+	5.15717i	−0.454325	+	0.188188i	−0.598098	−	0.801423i	$-0.704077\pi$
$751$	−12.4505	+	5.15717i	−0.454325	+	0.188188i	0.143772	+	0.989611i	$0.454077\pi$
$752$	−25.3017	−	1.86643i	−0.922656	−	0.0680617i
$753$	−16.9053	−	7.00239i	−0.616062	−	0.255181i
$754$	2.09965	−	0.167837i	0.0764647	−	0.00611228i
$755$	−0.896662	−	0.735871i	−0.0326329	−	0.0267811i
$756$	3.64488	−	6.25389i	0.132563	−	0.227452i
$757$	2.86351	−	0.868637i	0.104076	−	0.0315712i	−0.237817	−	0.971310i	$-0.576432\pi$
$757$	2.86351	−	0.868637i	0.104076	−	0.0315712i	0.341893	+	0.939739i	$0.388932\pi$
$758$	2.37036	+	13.1801i	0.0860954	+	0.478724i
$759$	−4.33282	+	6.48453i	−0.157272	+	0.235374i
$760$	15.5187	+	14.2398i	0.562921	+	0.516531i
$761$	16.0761	−	10.7417i	0.582758	−	0.389387i	−0.228960	−	0.973436i	$-0.573532\pi$
$761$	16.0761	−	10.7417i	0.582758	−	0.389387i	0.811718	+	0.584049i	$0.198532\pi$
$762$	−29.5760	−	0.544510i	−1.07143	−	0.0197255i
$763$	15.9340	+	19.4157i	0.576851	+	0.702895i
$764$	2.37673	−	1.46449i	0.0859869	−	0.0529834i
$765$	−1.35393	+	0.723692i	−0.0489515	+	0.0261651i
$766$	43.1922	+	24.1192i	1.56060	+	0.871463i
$767$	5.05840			0.182648
$768$	−14.4638	−	6.84096i	−0.521917	−	0.246852i

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)

\(f(q)\)	\(=\)	\(q+(-1.23474 - 0.689501i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.04918 + 1.70271i) q^{4} +(-0.913716 - 1.11337i) q^{5} +(-1.41397 - 0.0260320i) q^{6} +(3.00931 - 2.01075i) q^{7} +(-0.121442 - 2.82582i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(-1.23474 - 0.689501i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.04918 + 1.70271i) q^{4} +(-0.913716 - 1.11337i) q^{5} +(-1.41397 - 0.0260320i) q^{6} +(3.00931 - 2.01075i) q^{7} +(-0.121442 - 2.82582i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.360537 + 2.00473i) q^{10} +(-2.39307 + 0.725929i) q^{11} +(1.72794 + 1.00708i) q^{12} +(1.40718 + 1.15484i) q^{13} +(-5.10214 + 0.407844i) q^{14} +(-1.33066 - 0.551179i) q^{15} +(-1.79845 + 3.57289i) q^{16} +(0.984758 - 0.407900i) q^{17} +(-1.25929 + 0.643585i) q^{18} +(-0.506757 - 5.14519i) q^{19} +(0.937092 - 2.72391i) q^{20} +(1.70611 - 3.19191i) q^{21} +(3.45535 + 0.753687i) q^{22} +(3.05869 - 0.608412i) q^{23} +(-1.43918 - 2.43490i) q^{24} +(0.570744 - 2.86932i) q^{25} +(-0.941240 - 2.39619i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(6.58103 + 3.01435i) q^{28} +(-0.237506 + 0.782952i) q^{29} +(1.26299 + 1.59806i) q^{30} +(0.899529 + 0.899529i) q^{31} +(4.68414 - 3.17157i) q^{32} +(-1.76830 + 1.76830i) q^{33} +(-1.49717 - 0.175340i) q^{34} +(-4.98836 - 1.51320i) q^{35} +(1.99864 + 0.0736171i) q^{36} +(-8.18993 - 0.806638i) q^{37} +(-2.92190 + 6.70240i) q^{38} +(1.78541 + 0.355141i) q^{39} +(-3.03521 + 2.71721i) q^{40} +(-2.17991 - 10.9592i) q^{41} +(-4.30743 + 2.76482i) q^{42} +(2.89114 + 1.54535i) q^{43} +(-3.74680 - 3.31308i) q^{44} +(-1.43336 + 0.141174i) q^{45} +(-4.19620 - 1.35774i) q^{46} +(2.42721 + 5.85980i) q^{47} +(0.0981544 + 3.99880i) q^{48} +(2.33401 - 5.63480i) q^{49} +(-2.68312 + 3.14935i) q^{50} +(0.676197 - 0.823948i) q^{51} +(-0.489984 + 3.60766i) q^{52} +(-0.598980 - 1.97457i) q^{53} +(-0.807207 + 1.16121i) q^{54} +(2.99481 + 2.00107i) q^{55} +(-6.04749 - 8.25957i) q^{56} +(-2.87235 - 4.29877i) q^{57} +(0.833104 - 0.802983i) q^{58} +(2.14800 - 1.76282i) q^{59} +(-0.457603 - 2.84402i) q^{60} +(2.46184 + 4.60578i) q^{61} +(-0.490460 - 1.73091i) q^{62} -3.61926i q^{63} +(-7.97050 + 0.686347i) q^{64} -2.62191i q^{65} +(3.40263 - 0.964149i) q^{66} +(6.78262 + 12.6894i) q^{67} +(1.72772 + 1.24880i) q^{68} +(2.41072 - 1.97843i) q^{69} +(5.11599 + 5.30789i) q^{70} +(5.12102 + 7.66415i) q^{71} +(-2.41705 - 1.46897i) q^{72} +(-8.14530 - 5.44251i) q^{73} +(9.55628 + 6.64295i) q^{74} +(-0.849239 - 2.79956i) q^{75} +(8.22911 - 6.26108i) q^{76} +(-5.74181 + 6.99642i) q^{77} +(-1.95965 - 1.66955i) q^{78} +(-2.22145 + 5.36305i) q^{79} +(5.62122 - 1.26227i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-4.86472 + 15.0348i) q^{82} +(3.06469 - 0.301846i) q^{83} +(7.22491 - 0.443862i) q^{84} +(-1.35393 - 0.723692i) q^{85} +(-2.50430 - 3.90155i) q^{86} +(0.159619 + 0.802461i) q^{87} +(2.34196 + 6.67422i) q^{88} +(14.1419 + 2.81300i) q^{89} +(1.86717 + 0.813992i) q^{90} +(6.55675 + 0.645783i) q^{91} +(4.24506 + 4.56974i) q^{92} +(1.21735 + 0.369279i) q^{93} +(1.04336 - 8.90890i) q^{94} +(-5.26546 + 5.26546i) q^{95} +(2.63598 - 5.00516i) q^{96} +(-6.26004 - 6.26004i) q^{97} +(-6.76710 + 5.34823i) q^{98} +(-0.725929 + 2.39307i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more