LMFDB - Embedded newform 588.2.e.d.491.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.312013725601644544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} - 2x^{8} + 8x^{6} - 8x^{4} - 16x^{2} + 64 $ x^12 - x^10 - 2x^8 + 8x^6 - 8x^4 - 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.4
Root			$-1.13556 + 0.842913i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.d.491.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13556 + 0.842913i) q^{2} +(-1.65140 - 0.522368i) q^{3} +(0.578995 - 1.91436i) q^{4} +0.499464i q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(2.45426 + 1.72528i) q^{9} +O(q^{10})$	\(q+(-1.13556 + 0.842913i) q^{2} +(-1.65140 - 0.522368i) q^{3} +(0.578995 - 1.91436i) q^{4} +0.499464i q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(2.45426 + 1.72528i) q^{9} +(-0.421005 - 0.567172i) q^{10} -1.39050 q^{11} +(-1.95615 + 2.85893i) q^{12} -2.75054 q^{13} +(0.260904 - 0.824817i) q^{15} +(-3.32953 - 2.21681i) q^{16} -5.82329i q^{17} +(-4.24123 + 0.109569i) q^{18} +2.48153i q^{19} +(0.956154 + 0.289187i) q^{20} +(1.57899 - 1.17207i) q^{22} +5.06405 q^{23} +(-0.188496 - 4.89535i) q^{24} +4.75054 q^{25} +(3.12340 - 2.31846i) q^{26} +(-3.15174 - 4.13116i) q^{27} +6.32275i q^{29} +(0.398976 + 1.15655i) q^{30} +6.91514i q^{31} +(5.64946 - 0.289187i) q^{32} +(2.29627 + 0.726352i) q^{33} +(4.90852 + 6.61269i) q^{34} +(4.72381 - 3.69941i) q^{36} +7.34308 q^{37} +(-2.09171 - 2.81793i) q^{38} +(4.54224 + 1.43679i) q^{39} +(-1.32953 + 0.477565i) q^{40} +5.74438i q^{41} +3.52627i q^{43} +(-0.805091 + 2.66191i) q^{44} +(-0.861717 + 1.22582i) q^{45} +(-5.75054 + 4.26855i) q^{46} +5.06405 q^{47} +(4.34041 + 5.40008i) q^{48} +(-5.39452 + 4.00429i) q^{50} +(-3.04190 + 9.61659i) q^{51} +(-1.59255 + 5.26551i) q^{52} -5.24491i q^{53} +(7.06121 + 2.03454i) q^{54} -0.694505i q^{55} +(1.29627 - 4.09801i) q^{57} +(-5.32953 - 7.17987i) q^{58} +3.15174 q^{59} +(-1.42793 - 0.977029i) q^{60} +4.90852 q^{61} +(-5.82886 - 7.85256i) q^{62} +(-6.17154 + 5.09039i) q^{64} -1.37379i q^{65} +(-3.21981 + 1.11074i) q^{66} +10.7439i q^{67} +(-11.1479 - 3.37165i) q^{68} +(-8.36279 - 2.64530i) q^{69} +4.54224 q^{71} +(-2.24589 + 8.18266i) q^{72} +9.97504 q^{73} +(-8.33851 + 6.18958i) q^{74} +(-7.84505 - 2.48153i) q^{75} +(4.75054 + 1.43679i) q^{76} +(-6.36908 + 2.19715i) q^{78} +2.13130i q^{79} +(1.10722 - 1.66298i) q^{80} +(3.04681 + 8.46859i) q^{81} +(-4.84201 - 6.52309i) q^{82} +12.0165 q^{83} +2.90852 q^{85} +(-2.97234 - 4.00429i) q^{86} +(3.30281 - 10.4414i) q^{87} +(-1.32953 - 3.70138i) q^{88} -2.45163i q^{89} +(-0.0547257 - 2.11834i) q^{90} +(2.93206 - 9.69440i) q^{92} +(3.61225 - 11.4197i) q^{93} +(-5.75054 + 4.26855i) q^{94} -1.23944 q^{95} +(-9.48059 - 2.47353i) q^{96} -0.526031 q^{97} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} + 2 q^{9}+O(q^{10}) $ 12 * q + 2 * q^4 + 2 * q^9	$ 12 q + 2 q^{4} + 2 q^{9} - 10 q^{10} - 12 q^{12} + 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} - 14 q^{24} + 12 q^{25} + 14 q^{30} + 10 q^{33} + 4 q^{34} + 22 q^{36} + 8 q^{37} + 34 q^{40} - 18 q^{45} - 24 q^{46} - 4 q^{48} + 16 q^{52} + 38 q^{54} - 2 q^{57} - 14 q^{58} - 14 q^{60} + 4 q^{61} - 34 q^{64} + 30 q^{66} - 18 q^{69} - 20 q^{72} + 12 q^{76} - 52 q^{78} - 26 q^{81} - 68 q^{82} - 20 q^{85} + 34 q^{88} + 20 q^{90} + 6 q^{93} - 24 q^{94} - 62 q^{96} - 36 q^{97}+O(q^{100}) $ 12 * q + 2 * q^4 + 2 * q^9 - 10 * q^10 - 12 * q^12 + 12 * q^13 + 10 * q^16 + 10 * q^18 + 14 * q^22 - 14 * q^24 + 12 * q^25 + 14 * q^30 + 10 * q^33 + 4 * q^34 + 22 * q^36 + 8 * q^37 + 34 * q^40 - 18 * q^45 - 24 * q^46 - 4 * q^48 + 16 * q^52 + 38 * q^54 - 2 * q^57 - 14 * q^58 - 14 * q^60 + 4 * q^61 - 34 * q^64 + 30 * q^66 - 18 * q^69 - 20 * q^72 + 12 * q^76 - 52 * q^78 - 26 * q^81 - 68 * q^82 - 20 * q^85 + 34 * q^88 + 20 * q^90 + 6 * q^93 - 24 * q^94 - 62 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.13556	+	0.842913i	−0.802962	+	0.596030i
$2$	−1.13556	+	0.842913i	−0.802962	+	0.596030i
$3$	−1.65140	−	0.522368i	−0.953438	−	0.301590i
$3$	−1.65140	−	0.522368i	−0.953438	−	0.301590i
$4$	0.578995	−	1.91436i	0.289497	−	0.957179i
$5$			0.499464i			0.223367i	0.993744	+	0.111684i	$0.0356243\pi$
$5$			0.499464i			0.223367i	−0.993744	+	0.111684i	$0.964376\pi$
$6$	2.31558	−	0.798808i	0.945331	−	0.326112i
$7$		0			0
$7$		0			0
$8$	0.956154	+	2.66191i	0.338051	+	0.941128i
$9$	2.45426	+	1.72528i	0.818087	+	0.575094i
$10$	−0.421005	−	0.567172i	−0.133134	−	0.179356i
$11$	−1.39050			−0.419251			−0.209626	−	0.977782i	$-0.567224\pi$
$11$	−1.39050			−0.419251			−0.209626	+	0.977782i	$0.567224\pi$
$12$	−1.95615	+	2.85893i	−0.564693	+	0.825301i
$13$	−2.75054			−0.762861			−0.381431	−	0.924397i	$-0.624568\pi$
$13$	−2.75054			−0.762861			−0.381431	+	0.924397i	$0.624568\pi$
$14$		0			0
$15$	0.260904	−	0.824817i	0.0673652	−	0.212967i
$16$	−3.32953	−	2.21681i	−0.832383	−	0.554202i
$17$		−	5.82329i		−	1.41235i	−0.708035	−	0.706177i	$-0.750418\pi$
$17$		−	5.82329i		−	1.41235i	0.708035	−	0.706177i	$-0.249582\pi$
$18$	−4.24123	+	0.109569i	−0.999666	+	0.0258256i
$19$			2.48153i			0.569302i	0.958631	+	0.284651i	$0.0918777\pi$
$19$			2.48153i			0.569302i	−0.958631	+	0.284651i	$0.908122\pi$
$20$	0.956154	+	0.289187i	0.213802	+	0.0646643i
$21$		0			0
$22$	1.57899	−	1.17207i	0.336643	−	0.249886i
$23$	5.06405			1.05593			0.527964	−	0.849267i	$-0.322956\pi$
$23$	5.06405			1.05593			0.527964	+	0.849267i	$0.322956\pi$
$24$	−0.188496	−	4.89535i	−0.0384767	−	0.999259i
$25$	4.75054			0.950107
$26$	3.12340	−	2.31846i	0.612549	−	0.454688i
$27$	−3.15174	−	4.13116i	−0.606553	−	0.795043i
$28$		0			0
$29$			6.32275i			1.17411i	0.809549	+	0.587053i	$0.199712\pi$
$29$			6.32275i			1.17411i	−0.809549	+	0.587053i	$0.800288\pi$
$30$	0.398976	+	1.15655i	0.0728428	+	0.211156i
$31$			6.91514i			1.24200i	0.783812	+	0.620998i	$0.213273\pi$
$31$			6.91514i			1.24200i	−0.783812	+	0.620998i	$0.786727\pi$
$32$	5.64946	−	0.289187i	0.998692	−	0.0511216i
$33$	2.29627	+	0.726352i	0.399730	+	0.126442i
$34$	4.90852	+	6.61269i	0.841805	+	1.13407i
$35$		0			0
$36$	4.72381	−	3.69941i	0.787302	−	0.616568i
$37$	7.34308			1.20720			0.603598	−	0.797289i	$-0.293733\pi$
$37$	7.34308			1.20720			0.603598	+	0.797289i	$0.293733\pi$
$38$	−2.09171	−	2.81793i	−0.339321	−	0.457128i
$39$	4.54224	+	1.43679i	0.727341	+	0.230071i
$40$	−1.32953	+	0.477565i	−0.210217	+	0.0755096i
$41$			5.74438i			0.897121i	0.893753	+	0.448560i	$0.148063\pi$
$41$			5.74438i			0.897121i	−0.893753	+	0.448560i	$0.851937\pi$
$42$		0			0
$43$			3.52627i			0.537751i	0.963175	+	0.268875i	$0.0866520\pi$
$43$			3.52627i			0.537751i	−0.963175	+	0.268875i	$0.913348\pi$
$44$	−0.805091	+	2.66191i	−0.121372	+	0.401298i
$45$	−0.861717	+	1.22582i	−0.128457	+	0.182734i
$46$	−5.75054	+	4.26855i	−0.847870	+	0.629364i
$47$	5.06405			0.738668			0.369334	−	0.929297i	$-0.379586\pi$
$47$	5.06405			0.738668			0.369334	+	0.929297i	$0.379586\pi$
$48$	4.34041	+	5.40008i	0.626484	+	0.779435i
$49$		0			0
$50$	−5.39452	+	4.00429i	−0.762900	+	0.566292i
$51$	−3.04190	+	9.61659i	−0.425951	+	1.34659i
$52$	−1.59255	+	5.26551i	−0.220846	+	0.730195i
$53$		−	5.24491i		−	0.720444i	−0.932867	−	0.360222i	$-0.882701\pi$
$53$		−	5.24491i		−	0.720444i	0.932867	−	0.360222i	$-0.117299\pi$
$54$	7.06121	+	2.03454i	0.960909	+	0.276866i
$55$		−	0.694505i		−	0.0936470i
$56$		0			0
$57$	1.29627	−	4.09801i	0.171696	−	0.542794i
$58$	−5.32953	−	7.17987i	−0.699802	−	0.942763i
$59$	3.15174			0.410322			0.205161	−	0.978728i	$-0.434228\pi$
$59$	3.15174			0.410322			0.205161	+	0.978728i	$0.434228\pi$
$60$	−1.42793	−	0.977029i	−0.184345	−	0.126134i
$61$	4.90852			0.628472			0.314236	−	0.949345i	$-0.398252\pi$
$61$	4.90852			0.628472			0.314236	+	0.949345i	$0.398252\pi$
$62$	−5.82886	−	7.85256i	−0.740267	−	0.997276i
$63$		0			0
$64$	−6.17154	+	5.09039i	−0.771443	+	0.636299i
$65$		−	1.37379i		−	0.170398i
$66$	−3.21981	+	1.11074i	−0.396331	+	0.136723i
$67$			10.7439i			1.31257i	0.754513	+	0.656286i	$0.227873\pi$
$67$			10.7439i			1.31257i	−0.754513	+	0.656286i	$0.772127\pi$
$68$	−11.1479	−	3.37165i	−1.35188	−	0.408873i
$69$	−8.36279	−	2.64530i	−1.00676	−	0.318457i
$70$		0			0
$71$	4.54224			0.539065			0.269532	−	0.962991i	$-0.413131\pi$
$71$	4.54224			0.539065			0.269532	+	0.962991i	$0.413131\pi$
$72$	−2.24589	+	8.18266i	−0.264681	+	0.964336i
$73$	9.97504			1.16749			0.583745	−	0.811937i	$-0.301587\pi$
$73$	9.97504			1.16749			0.583745	+	0.811937i	$0.301587\pi$
$74$	−8.33851	+	6.18958i	−0.969332	+	0.719524i
$75$	−7.84505	−	2.48153i	−0.905868	−	0.286542i
$76$	4.75054	+	1.43679i	0.544924	+	0.164811i
$77$		0			0
$78$	−6.36908	+	2.19715i	−0.721156	+	0.248778i
$79$			2.13130i			0.239790i	0.992787	+	0.119895i	$0.0382557\pi$
$79$			2.13130i			0.239790i	−0.992787	+	0.119895i	$0.961744\pi$
$80$	1.10722	−	1.66298i	0.123791	−	0.185927i
$81$	3.04681	+	8.46859i	0.338534	+	0.940954i
$82$	−4.84201	−	6.52309i	−0.534711	−	0.720354i
$83$	12.0165			1.31899			0.659493	−	0.751710i	$-0.270771\pi$
$83$	12.0165			1.31899			0.659493	+	0.751710i	$0.270771\pi$
$84$		0			0
$85$	2.90852			0.315474
$86$	−2.97234	−	4.00429i	−0.320515	−	0.431794i
$87$	3.30281	−	10.4414i	0.354098	−	1.11944i
$88$	−1.32953	−	3.70138i	−0.141728	−	0.394569i
$89$		−	2.45163i		−	0.259873i	−0.991522	−	0.129936i	$-0.958523\pi$
$89$		−	2.45163i		−	0.259873i	0.991522	−	0.129936i	$-0.0414773\pi$
$90$	−0.0547257	−	2.11834i	−0.00576860	−	0.223293i
$91$		0			0
$92$	2.93206	−	9.69440i	0.305688	−	1.01071i
$93$	3.61225	−	11.4197i	0.374573	−	1.18417i
$94$	−5.75054	+	4.26855i	−0.593122	+	0.440268i
$95$	−1.23944			−0.127163
$96$	−9.48059	−	2.47353i	−0.967609	−	0.252454i
$97$	−0.526031			−0.0534104			−0.0267052	−	0.999643i	$-0.508502\pi$
$97$	−0.526031			−0.0534104			−0.0267052	+	0.999643i	$0.508502\pi$
$98$		0			0
$99$	−3.41265	−	2.39900i	−0.342984	−	0.241109i
$100$	2.75054	−	9.09422i	0.275054	−	0.909422i
$101$			16.0961i			1.60162i	0.598920	+	0.800809i	$0.295597\pi$
$101$			16.0961i			1.60162i	−0.598920	+	0.800809i	$0.704403\pi$
$102$	−4.65169	−	13.4843i	−0.460586	−	1.33514i
$103$		−	1.87663i		−	0.184910i	−0.995717	−	0.0924550i	$-0.970529\pi$
$103$		−	1.87663i		−	0.184910i	0.995717	−	0.0924550i	$-0.0294714\pi$
$104$	−2.62993	−	7.32168i	−0.257886	−	0.717950i
$105$		0			0
$106$	4.42101	+	5.95591i	0.429406	+	0.578490i
$107$	−7.27848			−0.703637			−0.351819	−	0.936068i	$-0.614437\pi$
$107$	−7.27848			−0.703637			−0.351819	+	0.936068i	$0.614437\pi$
$108$	−9.73337	+	3.64164i	−0.936594	+	0.350417i
$109$	−1.84201			−0.176433			−0.0882163	−	0.996101i	$-0.528117\pi$
$109$	−1.84201			−0.176433			−0.0882163	+	0.996101i	$0.528117\pi$
$110$	0.585407	+	0.788652i	0.0558164	+	0.0751950i
$111$	−12.1264	−	3.83579i	−1.15099	−	0.364077i
$112$		0			0
$113$		−	10.2728i		−	0.966382i	−0.875515	−	0.483191i	$-0.839478\pi$
$113$		−	10.2728i		−	0.966382i	0.875515	−	0.483191i	$-0.160522\pi$
$114$	1.98227	+	5.74618i	0.185656	+	0.538179i
$115$			2.52931i			0.235860i
$116$	12.1040	+	3.66084i	1.12383	+	0.339900i
$117$	−6.75054	−	4.74545i	−0.624087	−	0.438717i
$118$	−3.57899	+	2.65665i	−0.329473	+	0.244564i
$119$		0			0
$120$	2.44505	−	0.0941473i	0.223202	−	0.00859443i
$121$	−9.06651			−0.824229
$122$	−5.57393	+	4.13746i	−0.504640	+	0.374588i
$123$	3.00068	−	9.48628i	0.270562	−	0.855349i
$124$	13.2381	+	4.00383i	1.18881	+	0.359555i
$125$			4.87005i			0.435590i
$126$		0			0
$127$			1.51224i			0.134190i	0.997747	+	0.0670949i	$0.0213730\pi$
$127$			1.51224i			0.134190i	−0.997747	+	0.0670949i	$0.978627\pi$
$128$	2.71740	−	10.9825i	0.240186	−	0.970727i
$129$	1.84201	−	5.82329i	0.162180	−	0.512712i
$130$	1.15799	+	1.56003i	0.101562	+	0.136823i
$131$	6.65037			0.581045			0.290523	−	0.956868i	$-0.406171\pi$
$131$	6.65037			0.581045			0.290523	+	0.956868i	$0.406171\pi$
$132$	2.72003	−	3.97533i	0.236748	−	0.346008i
$133$		0			0
$134$	−9.05614	−	12.2003i	−0.782331	−	1.05395i
$135$	2.06337	−	1.57418i	0.177587	−	0.135484i
$136$	15.5011	−	5.56796i	1.32921	−	0.477448i
$137$		−	12.1917i		−	1.04161i	−0.853676	−	0.520805i	$-0.825632\pi$
$137$		−	12.1917i		−	1.04161i	0.853676	−	0.520805i	$-0.174368\pi$
$138$	11.7262	−	4.04521i	0.998201	−	0.344351i
$139$		−	0.0477837i		−	0.00405296i	−0.999998	−	0.00202648i	$-0.999355\pi$
$139$		−	0.0477837i		−	0.00405296i	0.999998	−	0.00202648i	$-0.000645050\pi$
$140$		0			0
$141$	−8.36279	−	2.64530i	−0.704274	−	0.222774i
$142$	−5.15799	+	3.82872i	−0.432849	+	0.321299i
$143$	3.82461			0.319830
$144$	−4.34693	−	11.1850i	−0.362244	−	0.932083i
$145$	−3.15799			−0.262257
$146$	−11.3273	+	8.40809i	−0.937451	+	0.695859i
$147$		0			0
$148$	4.25161	−	14.0573i	0.349480	−	1.15550i
$149$			2.29381i			0.187917i	0.995576	+	0.0939583i	$0.0299520\pi$
$149$			2.29381i			0.187917i	−0.995576	+	0.0939583i	$0.970048\pi$
$150$	11.0002	−	3.79477i	0.898166	−	0.309841i
$151$		−	13.1358i		−	1.06897i	−0.845177	−	0.534487i	$-0.820505\pi$
$151$		−	13.1358i		−	1.06897i	0.845177	−	0.534487i	$-0.179495\pi$
$152$	−6.60561	+	2.37272i	−0.535786	+	0.192453i
$153$	10.0468	−	14.2919i	0.812236	−	1.15543i
$154$		0			0
$155$	−3.45387			−0.277421
$156$	5.38047	−	7.86358i	0.430782	−	0.629590i
$157$	−8.40960			−0.671159			−0.335579	−	0.942012i	$-0.608932\pi$
$157$	−8.40960			−0.671159			−0.335579	+	0.942012i	$0.608932\pi$
$158$	−1.79650	−	2.42022i	−0.142922	−	0.192542i
$159$	−2.73978	+	8.66146i	−0.217278	+	0.686899i
$160$	0.144439	+	2.82170i	0.0114189	+	0.223075i
$161$		0			0
$162$	−10.5981	−	7.04840i	−0.832667	−	0.553774i
$163$		−	12.3599i		−	0.968099i	−0.875041	−	0.484050i	$-0.839165\pi$
$163$		−	12.3599i		−	0.968099i	0.875041	−	0.484050i	$-0.160835\pi$
$164$	10.9968	+	3.32596i	0.858705	+	0.259714i
$165$	−0.362787	+	1.14691i	−0.0282429	+	0.0892866i
$166$	−13.6455	+	10.1289i	−1.05910	+	0.786155i
$167$	−2.36549			−0.183047			−0.0915237	−	0.995803i	$-0.529174\pi$
$167$	−2.36549			−0.183047			−0.0915237	+	0.995803i	$0.529174\pi$
$168$		0			0
$169$	−5.43456			−0.418043
$170$	−3.30281	+	2.45163i	−0.253314	+	0.188032i
$171$	−4.28134	+	6.09033i	−0.327402	+	0.465739i
$172$	6.75054	+	2.04169i	0.514723	+	0.155677i
$173$			9.56980i			0.727579i	0.931481	+	0.363789i	$0.118517\pi$
$173$			9.56980i			0.727579i	−0.931481	+	0.363789i	$0.881483\pi$
$174$	5.05067	+	14.6408i	0.382890	+	1.10992i
$175$		0			0
$176$	4.62971	+	3.08247i	0.348977	+	0.232350i
$177$	−5.20480	−	1.64637i	−0.391217	−	0.123749i
$178$	2.06651	+	2.78398i	0.154892	+	0.208668i
$179$	−20.7541			−1.55124			−0.775619	−	0.631202i	$-0.782562\pi$
$179$	−20.7541			−1.55124			−0.775619	+	0.631202i	$0.782562\pi$
$180$	1.84772	+	2.35938i	0.137721	+	0.175857i
$181$	6.43456			0.478277			0.239138	−	0.970985i	$-0.423135\pi$
$181$	6.43456			0.478277			0.239138	+	0.970985i	$0.423135\pi$
$182$		0			0
$183$	−8.10595	−	2.56406i	−0.599209	−	0.189541i
$184$	4.84201	+	13.4801i	0.356958	+	0.993763i
$185$			3.66761i			0.269648i
$186$	5.52387	+	16.0126i	0.405030	+	1.17410i
$187$			8.09727i			0.592131i
$188$	2.93206	−	9.69440i	0.213842	−	0.707037i
$189$		0			0
$190$	1.40745	−	1.04474i	0.102107	−	0.0757932i
$191$	17.5338			1.26870			0.634350	−	0.773046i	$-0.281268\pi$
$191$	17.5338			1.26870			0.634350	+	0.773046i	$0.281268\pi$
$192$	12.8508	−	5.18247i	0.927424	−	0.374013i
$193$	−2.18509			−0.157286			−0.0786432	−	0.996903i	$-0.525059\pi$
$193$	−2.18509			−0.157286			−0.0786432	+	0.996903i	$0.525059\pi$
$194$	0.597340	−	0.443399i	0.0428865	−	0.0318342i
$195$	−0.717627	+	2.26869i	−0.0513903	+	0.162464i
$196$		0			0
$197$		−	6.27706i		−	0.447222i	−0.974678	−	0.223611i	$-0.928215\pi$
$197$		−	6.27706i		−	0.447222i	0.974678	−	0.223611i	$-0.0717845\pi$
$198$	5.89742	−	0.152355i	0.419111	−	0.0108274i
$199$		−	0.865522i		−	0.0613552i	−0.999529	−	0.0306776i	$-0.990233\pi$
$199$		−	0.865522i		−	0.0613552i	0.999529	−	0.0306776i	$-0.00976652\pi$
$200$	4.54224	+	12.6455i	0.321185	+	0.894172i
$201$	5.61225	−	17.7424i	0.395858	−	1.25145i
$202$	−13.5676	−	18.2781i	−0.954612	−	1.28604i
$203$		0			0
$204$	16.6484	+	11.3912i	1.16562	+	0.797547i
$205$	−2.86911			−0.200387
$206$	1.58184	+	2.13103i	0.110212	+	0.148476i
$207$	12.4285	+	8.73691i	0.863841	+	0.607257i
$208$	9.15799	+	6.09740i	0.634992	+	0.422779i
$209$		−	3.45056i		−	0.238680i
$210$		0			0
$211$		−	3.90417i		−	0.268774i	−0.990929	−	0.134387i	$-0.957094\pi$
$211$		−	3.90417i		−	0.268774i	0.990929	−	0.134387i	$-0.0429065\pi$
$212$	−10.0406	−	3.03678i	−0.689594	−	0.208567i
$213$	−7.50107	−	2.37272i	−0.513965	−	0.162576i
$214$	8.26516	−	6.13513i	0.564994	−	0.419389i
$215$	−1.76124			−0.120116
$216$	7.98324	−	12.3397i	0.543191	−	0.839609i
$217$		0			0
$218$	2.09171	−	1.55265i	0.141669	−	0.105159i
$219$	−16.4728	−	5.21065i	−1.11313	−	0.352103i
$220$	−1.32953	−	0.402115i	−0.0896369	−	0.0271106i
$221$			16.0172i			1.07743i
$222$	17.0035	−	5.86571i	1.14120	−	0.393681i
$223$			23.5017i			1.57379i	0.617085	+	0.786896i	$0.288313\pi$
$223$			23.5017i			1.57379i	−0.617085	+	0.786896i	$0.711687\pi$
$224$		0			0
$225$	11.6591	+	8.19601i	0.777271	+	0.546401i
$226$	8.65906	+	11.6654i	0.575992	+	0.775968i
$227$	−19.1678			−1.27221			−0.636107	−	0.771601i	$-0.719456\pi$
$227$	−19.1678			−1.27221			−0.636107	+	0.771601i	$0.719456\pi$
$228$	−7.09451	−	4.85425i	−0.469846	−	0.321481i
$229$	−11.4761			−0.758363			−0.379181	−	0.925322i	$-0.623794\pi$
$229$	−11.4761			−0.758363			−0.379181	+	0.925322i	$0.623794\pi$
$230$	−2.13199	−	2.87219i	−0.140579	−	0.189386i
$231$		0			0
$232$	−16.8306	+	6.04552i	−1.10498	+	0.396908i
$233$			20.2174i			1.32449i	0.749288	+	0.662245i	$0.230396\pi$
$233$			20.2174i			1.32449i	−0.749288	+	0.662245i	$0.769604\pi$
$234$	11.6656	−	0.301373i	0.762607	−	0.0197014i
$235$			2.52931i			0.164994i
$236$	1.82484	−	6.03356i	0.118787	−	0.392752i
$237$	1.11332	−	3.51963i	0.0723181	−	0.228625i
$238$		0			0
$239$	6.90774			0.446824			0.223412	−	0.974724i	$-0.428280\pi$
$239$	6.90774			0.446824			0.223412	+	0.974724i	$0.428280\pi$
$240$	−2.69715	+	2.16788i	−0.174100	+	0.139936i
$241$	−8.06651			−0.519610			−0.259805	−	0.965661i	$-0.583658\pi$
$241$	−8.06651			−0.519610			−0.259805	+	0.965661i	$0.583658\pi$
$242$	10.2956	−	7.64228i	0.661825	−	0.491265i
$243$	−0.607785	−	15.5766i	−0.0389894	−	0.999240i
$244$	2.84201	−	9.39667i	0.181941	−	0.601560i
$245$		0			0
$246$	4.58866	+	13.3016i	0.292562	+	0.848076i
$247$		−	6.82553i		−	0.434298i
$248$	−18.4075	+	6.61194i	−1.16888	+	0.419859i
$249$	−19.8442	−	6.27706i	−1.25757	−	0.397793i
$250$	−4.10503	−	5.53023i	−0.259625	−	0.349763i
$251$	20.4073			1.28810			0.644048	−	0.764985i	$-0.277254\pi$
$251$	20.4073			1.28810			0.644048	+	0.764985i	$0.277254\pi$
$252$		0			0
$253$	−7.04155			−0.442699
$254$	−1.27469	−	1.71724i	−0.0799811	−	0.107749i
$255$	−4.80315	−	1.51932i	−0.300785	−	0.0951436i
$256$	6.17154	+	14.7618i	0.385721	+	0.922615i
$257$			27.2100i			1.69731i	0.528947	+	0.848655i	$0.322587\pi$
$257$			27.2100i			1.69731i	−0.528947	+	0.848655i	$0.677413\pi$
$258$	2.81681	+	8.16535i	0.175367	+	0.508352i
$259$		0			0
$260$	−2.62993	−	0.795420i	−0.163102	−	0.0493299i
$261$	−10.9085	+	15.5177i	−0.675221	+	0.960521i
$262$	−7.55189	+	5.60568i	−0.466558	+	0.346320i
$263$	3.60493			0.222290			0.111145	−	0.993804i	$-0.464548\pi$
$263$	3.60493			0.222290			0.111145	+	0.993804i	$0.464548\pi$
$264$	0.262104	+	6.80698i	0.0161314	+	0.418941i
$265$	2.61965			0.160924
$266$		0			0
$267$	−1.28066	+	4.04864i	−0.0783749	+	0.247772i
$268$	20.5676	+	6.22064i	1.25637	+	0.379986i
$269$		−	26.1653i		−	1.59533i	−0.603102	−	0.797664i	$-0.706069\pi$
$269$		−	26.1653i		−	1.59533i	0.603102	−	0.797664i	$-0.293931\pi$
$270$	−1.01618	+	3.52682i	−0.0618428	+	0.214636i
$271$		−	23.0619i		−	1.40091i	−0.713696	−	0.700455i	$-0.752980\pi$
$271$		−	23.0619i		−	1.40091i	0.713696	−	0.700455i	$-0.247020\pi$
$272$	−12.9091	+	19.3888i	−0.782729	+	1.17562i
$273$		0			0
$274$	10.2766	+	13.8444i	0.620830	+	0.836373i
$275$	−6.60561			−0.398333
$276$	−9.90606	+	14.4778i	−0.596275	+	0.871458i
$277$	−20.2910			−1.21917			−0.609585	−	0.792721i	$-0.708664\pi$
$277$	−20.2910			−1.21917			−0.609585	+	0.792721i	$0.708664\pi$
$278$	0.0402775	+	0.0542613i	0.00241569	+	0.00325438i
$279$	−11.9306	+	16.9716i	−0.714264	+	1.01606i
$280$		0			0
$281$			27.6637i			1.65028i	0.564929	+	0.825140i	$0.308904\pi$
$281$			27.6637i			1.65028i	−0.564929	+	0.825140i	$0.691096\pi$
$282$	11.7262	−	4.04521i	0.698286	−	0.240888i
$283$		−	17.3707i		−	1.03258i	−0.856413	−	0.516291i	$-0.827312\pi$
$283$		−	17.3707i		−	1.03258i	0.856413	−	0.516291i	$-0.172688\pi$
$284$	2.62993	−	8.69547i	0.156058	−	0.515981i
$285$	2.04681	+	0.647442i	0.121242	+	0.0383512i
$286$	−4.34308	+	3.22382i	−0.256812	+	0.190628i
$287$		0			0
$288$	14.3642	+	9.03716i	0.846417	+	0.532520i
$289$	−16.9107			−0.994745
$290$	3.58609	−	2.66191i	0.210582	−	0.156313i
$291$	0.868689	+	0.274782i	0.0509235	+	0.0161080i
$292$	5.77550	−	19.0958i	0.337985	−	1.11750i
$293$			19.9672i			1.16650i	0.812294	+	0.583248i	$0.198218\pi$
$293$			19.9672i			1.16650i	−0.812294	+	0.583248i	$0.801782\pi$
$294$		0			0
$295$			1.57418i			0.0916525i
$296$	7.02111	+	19.5466i	0.408094	+	1.13612i
$297$	4.38249	+	5.74438i	0.254298	+	0.333323i
$298$	−1.93349	−	2.60476i	−0.112004	−	0.150890i
$299$	−13.9288			−0.805526
$300$	−9.29278	+	13.5814i	−0.536519	+	0.784124i
$301$		0			0
$302$	11.0723	+	14.9165i	0.637141	+	0.858346i
$303$	8.40808	−	26.5811i	0.483031	−	1.52704i
$304$	5.50107	−	8.26233i	0.315508	−	0.473877i
$305$			2.45163i			0.140380i
$306$	0.638051	+	24.6979i	0.0364749	+	1.41188i
$307$		−	14.1529i		−	0.807746i	−0.914815	−	0.403873i	$-0.867664\pi$
$307$		−	14.1529i		−	0.807746i	0.914815	−	0.403873i	$-0.132336\pi$
$308$		0			0
$309$	−0.980294	+	3.09908i	−0.0557670	+	0.176300i
$310$	3.92208	−	2.91131i	0.222759	−	0.165351i
$311$	24.5549			1.39238			0.696190	−	0.717857i	$-0.254877\pi$
$311$	24.5549			1.39238			0.696190	+	0.717857i	$0.254877\pi$
$312$	0.518466	+	13.4648i	0.0293524	+	0.762296i
$313$	−0.0520623			−0.00294274			−0.00147137	−	0.999999i	$-0.500468\pi$
$313$	−0.0520623			−0.00294274			−0.00147137	+	0.999999i	$0.500468\pi$
$314$	9.54960	−	7.08856i	0.538915	−	0.400031i
$315$		0			0
$316$	4.08007	+	1.23401i	0.229522	+	0.0694185i
$317$		−	6.77653i		−	0.380608i	−0.981725	−	0.190304i	$-0.939053\pi$
$317$		−	6.77653i		−	0.380608i	0.981725	−	0.190304i	$-0.0609473\pi$
$318$	−4.18968	−	12.1450i	−0.234946	−	0.681058i
$319$		−	8.79177i		−	0.492245i
$320$	−2.54247	−	3.08247i	−0.142128	−	0.172315i
$321$	12.0197	+	3.80205i	0.670875	+	0.212210i
$322$		0			0
$323$	14.4507			0.804056
$324$	17.9760	−	0.929412i	0.998666	−	0.0516340i
$325$	−13.0665			−0.724800
$326$	10.4183	+	14.0354i	0.577016	+	0.777347i
$327$	3.04190	+	0.962208i	0.168218	+	0.0532102i
$328$	−15.2910	+	5.49251i	−0.844305	+	0.303273i
$329$		0			0
$330$	−0.554776	−	1.60818i	−0.0305394	−	0.0885274i
$331$			17.8920i			0.983431i	0.870756	+	0.491715i	$0.163630\pi$
$331$			17.8920i			0.983431i	−0.870756	+	0.491715i	$0.836370\pi$
$332$	6.95752	−	23.0040i	0.381843	−	1.26251i
$333$	18.0218	+	12.6689i	0.987591	+	0.694250i
$334$	2.68616	−	1.99391i	0.146980	−	0.109102i
$335$	−5.36618			−0.293185
$336$		0			0
$337$	7.09362			0.386414			0.193207	−	0.981158i	$-0.438111\pi$
$337$	7.09362			0.386414			0.193207	+	0.981158i	$0.438111\pi$
$338$	6.17127	−	4.58086i	0.335673	−	0.249166i
$339$	−5.36618	+	16.9645i	−0.291451	+	0.921385i
$340$	1.68402	−	5.56796i	0.0913288	−	0.301965i
$341$		−	9.61549i		−	0.520708i
$342$	−0.271898	−	10.5247i	−0.0147026	−	0.569112i
$343$		0			0
$344$	−9.38661	+	3.37165i	−0.506092	+	0.181787i
$345$	1.32123	−	4.17692i	0.0711328	−	0.224878i
$346$	−8.06651	−	10.8671i	−0.433659	−	0.584218i
$347$	−9.19079			−0.493387			−0.246694	−	0.969093i	$-0.579344\pi$
$347$	−9.19079			−0.493387			−0.246694	+	0.969093i	$0.579344\pi$
$348$	−18.0763	−	12.3683i	−0.968990	−	0.663009i
$349$	22.1330			1.18475			0.592377	−	0.805661i	$-0.298190\pi$
$349$	22.1330			1.18475			0.592377	+	0.805661i	$0.298190\pi$
$350$		0			0
$351$	8.66898	+	11.3629i	0.462716	+	0.606507i
$352$	−7.85556	+	0.402115i	−0.418703	+	0.0214328i
$353$			10.7266i			0.570917i	0.958391	+	0.285458i	$0.0921459\pi$
$353$			10.7266i			0.570917i	−0.958391	+	0.285458i	$0.907854\pi$
$354$	7.29811	−	2.51764i	0.387890	−	0.133811i
$355$			2.26869i			0.120409i
$356$	−4.69330	−	1.41948i	−0.248745	−	0.0752325i
$357$		0			0
$358$	23.5676	−	17.4939i	1.24559	−	0.924584i
$359$	3.60493			0.190261			0.0951305	−	0.995465i	$-0.469673\pi$
$359$	3.60493			0.190261			0.0951305	+	0.995465i	$0.469673\pi$
$360$	−4.08695	−	1.12174i	−0.215401	−	0.0591211i
$361$	12.8420			0.675895
$362$	−7.30683	+	5.42377i	−0.384038	+	0.285067i
$363$	14.9725	+	4.73606i	0.785851	+	0.248579i
$364$		0			0
$365$			4.98218i			0.260779i
$366$	11.3661	−	3.92097i	0.594114	−	0.204952i
$367$		−	15.0266i		−	0.784381i	−0.919884	−	0.392190i	$-0.871717\pi$
$367$		−	15.0266i		−	0.784381i	0.919884	−	0.392190i	$-0.128283\pi$
$368$	−16.8609	−	11.2260i	−0.878936	−	0.585197i
$369$	−9.91067	+	14.0982i	−0.515929	+	0.733923i
$370$	−3.09148	−	4.16479i	−0.160718	−	0.216517i
$371$		0			0
$372$	−19.7699	−	13.5271i	−1.02502	−	0.701346i
$373$	2.65692			0.137570			0.0687850	−	0.997632i	$-0.478088\pi$
$373$	2.65692			0.137570			0.0687850	+	0.997632i	$0.478088\pi$
$374$	−6.82530	−	9.19494i	−0.352928	−	0.475459i
$375$	2.54396	−	8.04241i	0.131369	−	0.415308i
$376$	4.84201	+	13.4801i	0.249708	+	0.695181i
$377$		−	17.3909i		−	0.895679i
$378$		0			0
$379$		−	17.7150i		−	0.909957i	−0.890502	−	0.454979i	$-0.849647\pi$
$379$		−	17.7150i		−	0.909957i	0.890502	−	0.454979i	$-0.150353\pi$
$380$	−0.717627	+	2.37272i	−0.0368135	+	0.121718i
$381$	0.789948	−	2.49732i	0.0404703	−	0.127942i
$382$	−19.9107	+	14.7795i	−1.01872	+	0.756183i
$383$	32.9217			1.68222			0.841111	−	0.540862i	$-0.181902\pi$
$383$	32.9217			1.68222			0.841111	+	0.540862i	$0.181902\pi$
$384$	−10.2244	+	16.7171i	−0.521764	+	0.853090i
$385$		0			0
$386$	2.48130	−	1.84184i	0.126295	−	0.0937473i
$387$	−6.08380	+	8.65438i	−0.309257	+	0.439927i
$388$	−0.304569	+	1.00701i	−0.0154622	+	0.0511233i
$389$		−	6.82222i		−	0.345900i	−0.984931	−	0.172950i	$-0.944670\pi$
$389$		−	6.82222i		−	0.345900i	0.984931	−	0.172950i	$-0.0553299\pi$
$390$	−1.09740	−	3.18113i	−0.0555689	−	0.161083i
$391$		−	29.4894i		−	1.49134i
$392$		0			0
$393$	−10.9824	−	3.47394i	−0.553991	−	0.175237i
$394$	5.29102	+	7.12798i	0.266558	+	0.359103i
$395$	−1.06451			−0.0535612
$396$	−6.56845	+	5.14402i	−0.330077	+	0.258497i
$397$	20.8442			1.04614			0.523069	−	0.852290i	$-0.324787\pi$
$397$	20.8442			1.04614			0.523069	+	0.852290i	$0.324787\pi$
$398$	0.729560	+	0.982853i	0.0365695	+	0.0492660i
$399$		0			0
$400$	−15.8170	−	10.5310i	−0.790852	−	0.526551i
$401$		−	3.82543i		−	0.191033i	−0.995428	−	0.0955164i	$-0.969550\pi$
$401$		−	3.82543i		−	0.191033i	0.995428	−	0.0955164i	$-0.0304502\pi$
$402$	8.58228	+	24.8782i	0.428045	+	1.24081i
$403$		−	19.0203i		−	0.947471i
$404$	30.8136	+	9.31954i	1.53304	+	0.463664i
$405$	−4.22976	+	1.52177i	−0.210178	+	0.0756175i
$406$		0			0
$407$	−10.2105			−0.506118
$408$	−28.5070	+	1.09767i	−1.41131	+	0.0543427i
$409$	3.86911			0.191315			0.0956576	−	0.995414i	$-0.469505\pi$
$409$	3.86911			0.191315			0.0956576	+	0.995414i	$0.469505\pi$
$410$	3.25805	−	2.41841i	0.160904	−	0.119437i
$411$	−6.36857	+	20.1335i	−0.314139	+	0.993110i
$412$	−3.59255	−	1.08656i	−0.176992	−	0.0535310i
$413$		0			0
$414$	−21.4778	+	0.554862i	−1.05558	+	0.0272700i
$415$			6.00184i			0.294619i
$416$	−15.5390	+	0.795420i	−0.761864	+	0.0389987i
$417$	−0.0249607	+	0.0789102i	−0.00122233	+	0.00386425i
$418$	2.90852	+	3.91832i	0.142261	+	0.191651i
$419$	13.5133			0.660170			0.330085	−	0.943951i	$-0.392923\pi$
$419$	13.5133			0.660170			0.330085	+	0.943951i	$0.392923\pi$
$420$		0			0
$421$	11.3825			0.554749			0.277374	−	0.960762i	$-0.410536\pi$
$421$	11.3825			0.554749			0.277374	+	0.960762i	$0.410536\pi$
$422$	3.29087	+	4.43342i	0.160197	+	0.215815i
$423$	12.4285	+	8.73691i	0.604295	+	0.424803i
$424$	13.9615	−	5.01494i	0.678030	−	0.243547i
$425$		−	27.6637i		−	1.34189i
$426$	10.5179	−	3.62838i	0.509595	−	0.175796i
$427$		0			0
$428$	−4.21420	+	13.9336i	−0.203701	+	0.673507i
$429$	−6.31598	−	1.99786i	−0.304938	−	0.0964575i
$430$	2.00000	−	1.48458i	0.0964486	−	0.0715926i
$431$	25.9245			1.24874			0.624370	−	0.781129i	$-0.285356\pi$
$431$	25.9245			1.24874			0.624370	+	0.781129i	$0.285356\pi$
$432$	1.33583	+	20.7416i	0.0642704	+	0.997933i
$433$	−23.3825			−1.12369			−0.561845	−	0.827242i	$-0.689908\pi$
$433$	−23.3825			−1.12369			−0.561845	+	0.827242i	$0.689908\pi$
$434$		0			0
$435$	5.21511	+	1.64963i	0.250046	+	0.0790939i
$436$	−1.06651	+	3.52627i	−0.0510768	+	0.168878i
$437$			12.5666i			0.601142i
$438$	23.0980	−	7.96814i	1.10366	−	0.380733i
$439$			17.6732i			0.843494i	0.906714	+	0.421747i	$0.138583\pi$
$439$			17.6732i			0.843494i	−0.906714	+	0.421747i	$0.861417\pi$
$440$	1.84871	−	0.664053i	0.0881338	−	0.0316575i
$441$		0			0
$442$	−13.5011	−	18.1884i	−0.642180	−	0.865136i
$443$	−35.1362			−1.66937			−0.834685	−	0.550727i	$-0.814350\pi$
$443$	−35.1362			−1.66937			−0.834685	+	0.550727i	$0.814350\pi$
$444$	−14.3642	+	20.9933i	−0.681694	+	0.996299i
$445$	1.22450			0.0580471
$446$	−19.8099	−	26.6876i	−0.938027	−	1.26370i
$447$	1.19822	−	3.78801i	0.0566737	−	0.179167i
$448$		0			0
$449$		−	5.52733i		−	0.260851i	−0.991458	−	0.130425i	$-0.958366\pi$
$449$		−	5.52733i		−	0.260851i	0.991458	−	0.130425i	$-0.0416343\pi$
$450$	−20.1481	+	0.520511i	−0.949790	+	0.0245371i
$451$		−	7.98755i		−	0.376119i
$452$	−19.6658	−	5.94789i	−0.925000	−	0.279765i
$453$	−6.86172	+	21.6925i	−0.322392	+	1.01920i
$454$	21.7662	−	16.1568i	1.02154	−	0.758277i
$455$		0			0
$456$	12.1480	−	0.467760i	0.568880	−	0.0219049i
$457$	23.9522			1.12044			0.560219	−	0.828345i	$-0.310717\pi$
$457$	23.9522			1.12044			0.560219	+	0.828345i	$0.310717\pi$
$458$	13.0318	−	9.67336i	0.608937	−	0.452007i
$459$	−24.0570	+	18.3535i	−1.12288	+	0.856668i
$460$	4.84201	+	1.46446i	0.225760	+	0.0682808i
$461$		−	2.99679i		−	0.139574i	−0.997562	−	0.0697871i	$-0.977768\pi$
$461$		−	2.99679i		−	0.139574i	0.997562	−	0.0697871i	$-0.0222320\pi$
$462$		0			0
$463$		−	22.4152i		−	1.04172i	−0.853642	−	0.520861i	$-0.825611\pi$
$463$		−	22.4152i		−	1.04172i	0.853642	−	0.520861i	$-0.174389\pi$
$464$	14.0163	−	21.0518i	0.650691	−	0.977305i
$465$	5.70373	+	1.80419i	0.264504	+	0.0836674i
$466$	−17.0416	−	22.9581i	−0.789435	−	1.06352i
$467$	−12.0613			−0.558130			−0.279065	−	0.960272i	$-0.590025\pi$
$467$	−12.0613			−0.558130			−0.279065	+	0.960272i	$0.590025\pi$
$468$	−12.9930	+	10.1753i	−0.600602	+	0.470356i
$469$		0			0
$470$	−2.13199	−	2.87219i	−0.0983414	−	0.132484i
$471$	13.8876	+	4.39291i	0.639908	+	0.202414i
$472$	3.01355	+	8.38966i	0.138710	+	0.386165i
$473$		−	4.90327i		−	0.225452i
$474$	1.70250	+	4.93519i	0.0781983	+	0.226681i
$475$			11.7886i			0.540898i
$476$		0			0
$477$	9.04895	−	12.8724i	0.414323	−	0.589386i
$478$	−7.84415	+	5.82262i	−0.358783	+	0.266321i
$479$	−13.4070			−0.612583			−0.306292	−	0.951938i	$-0.599088\pi$
$479$	−13.4070			−0.612583			−0.306292	+	0.951938i	$0.599088\pi$
$480$	1.23544	−	4.73522i	0.0563900	−	0.216132i
$481$	−20.1974			−0.920922
$482$	9.16001	−	6.79937i	0.417227	−	0.309703i
$483$		0			0
$484$	−5.24946	+	17.3566i	−0.238612	+	0.788934i
$485$		−	0.262734i		−	0.0119301i
$486$	13.8199	+	17.1759i	0.626883	+	0.779113i
$487$			12.2083i			0.553212i	0.960983	+	0.276606i	$0.0892096\pi$
$487$			12.2083i			0.553212i	−0.960983	+	0.276606i	$0.910790\pi$
$488$	4.69330	+	13.0661i	0.212456	+	0.591473i
$489$	−6.45640	+	20.4111i	−0.291969	+	0.923023i
$490$		0			0
$491$	−39.8981			−1.80058			−0.900288	−	0.435294i	$-0.856644\pi$
$491$	−39.8981			−1.80058			−0.900288	+	0.435294i	$0.856644\pi$
$492$	−16.4228	−	11.2369i	−0.740395	−	0.506598i
$493$	36.8192			1.65825
$494$	5.75333	+	7.75081i	0.258855	+	0.348725i
$495$	1.19822	−	1.70450i	0.0538558	−	0.0766114i
$496$	15.3295	−	23.0242i	0.688316	−	1.03382i
$497$		0			0
$498$	27.8253	−	9.59891i	1.24688	−	0.430138i
$499$			8.47517i			0.379401i	0.981842	+	0.189700i	$0.0607516\pi$
$499$			8.47517i			0.379401i	−0.981842	+	0.189700i	$0.939248\pi$
$500$	9.32301	+	2.81973i	0.416938	+	0.126102i
$501$	3.90638	+	1.23566i	0.174524	+	0.0552052i
$502$	−23.1737	+	17.2016i	−1.03429	+	0.767743i
$503$	−42.5519			−1.89730			−0.948648	−	0.316334i	$-0.897548\pi$
$503$	−42.5519			−1.89730			−0.948648	+	0.316334i	$0.897548\pi$
$504$		0			0
$505$	−8.03941			−0.357749
$506$	7.99611	−	5.93542i	0.355470	−	0.263862i
$507$	8.97464	+	2.83884i	0.398578	+	0.126077i
$508$	2.89497	+	0.875581i	0.128444	+	0.0388476i
$509$		−	17.2071i		−	0.762692i	−0.924432	−	0.381346i	$-0.875461\pi$
$509$		−	17.2071i		−	0.762692i	0.924432	−	0.381346i	$-0.124539\pi$
$510$	6.73492	−	2.32335i	0.298227	−	0.102880i
$511$		0			0
$512$	−19.4511	−	11.5609i	−0.859626	−	0.510924i
$513$	10.2516	−	7.82114i	0.452619	−	0.345312i
$514$	−22.9356	−	30.8985i	−1.01165	−	1.36288i
$515$	0.937311			0.0413029
$516$	−10.0813	−	6.89792i	−0.443806	−	0.303664i
$517$	−7.04155			−0.309687
$518$		0			0
$519$	4.99896	−	15.8036i	0.219430	−	0.693701i
$520$	3.65692	−	1.31356i	0.160367	−	0.0576034i
$521$		−	10.9436i		−	0.479448i	−0.970841	−	0.239724i	$-0.922943\pi$
$521$		−	10.9436i		−	0.479448i	0.970841	−	0.239724i	$-0.0770569\pi$
$522$	−0.692777	−	26.8162i	−0.0303220	−	1.17371i
$523$		−	5.53433i		−	0.241999i	−0.992653	−	0.121000i	$-0.961390\pi$
$523$		−	5.53433i		−	0.241999i	0.992653	−	0.121000i	$-0.0386100\pi$
$524$	3.85053	−	12.7312i	0.168211	−	0.556164i
$525$		0			0
$526$	−4.09362	+	3.03864i	−0.178490	+	0.132491i
$527$	40.2689			1.75414
$528$	−6.03533	−	7.50880i	−0.262654	−	0.326779i
$529$	2.64461			0.114983
$530$	−2.97477	+	2.20814i	−0.129216	+	0.0959153i
$531$	7.73521	+	5.43764i	0.335679	+	0.235974i
$532$		0			0
$533$		−	15.8001i		−	0.684379i
$534$	−1.95839	−	5.67695i	−0.0847476	−	0.245666i
$535$		−	3.63534i		−	0.157170i
$536$	−28.5992	+	10.2728i	−1.23530	+	0.443716i
$537$	34.2735	+	10.8413i	1.47901	+	0.467837i
$538$	22.0551	+	29.7123i	0.950863	+	1.28099i
$539$		0			0
$540$	−1.81887	−	4.86147i	−0.0782717	−	0.209204i
$541$	12.5282			0.538628			0.269314	−	0.963052i	$-0.413203\pi$
$541$	12.5282			0.538628			0.269314	+	0.963052i	$0.413203\pi$
$542$	19.4392	+	26.1882i	0.834984	+	1.12488i
$543$	−10.6260	−	3.36121i	−0.456007	−	0.144243i
$544$	−1.68402	−	32.8984i	−0.0722018	−	1.41051i
$545$		−	0.920019i		−	0.0394093i
$546$		0			0
$547$			37.4911i			1.60300i	0.597992	+	0.801502i	$0.295966\pi$
$547$			37.4911i			1.60300i	−0.597992	+	0.801502i	$0.704034\pi$
$548$	−23.3393	−	7.05895i	−0.997006	−	0.301543i
$549$	12.0468	+	8.46859i	0.514145	+	0.361430i
$550$	7.50107	−	5.56796i	0.319847	−	0.237418i
$551$	−15.6901			−0.668420
$552$	−0.954556	−	24.7903i	−0.0406286	−	1.05515i
$553$		0			0
$554$	23.0417	−	17.1036i	0.978947	−	0.726661i
$555$	1.91584	−	6.05670i	0.0813230	−	0.257093i
$556$	−0.0914752	−	0.0276665i	−0.00387941	−	0.00117332i
$557$		−	30.0697i		−	1.27409i	−0.770825	−	0.637046i	$-0.780156\pi$
$557$		−	30.0697i		−	1.27409i	0.770825	−	0.637046i	$-0.219844\pi$
$558$	−0.757684	−	29.3287i	−0.0320753	−	1.24158i
$559$		−	9.69912i		−	0.410229i
$560$		0			0
$561$	4.22976	−	13.3719i	0.178581	−	0.564560i
$562$	−23.3181	−	31.4138i	−0.983616	−	1.32511i
$563$	−6.83911			−0.288234			−0.144117	−	0.989561i	$-0.546034\pi$
$563$	−6.83911			−0.288234			−0.144117	+	0.989561i	$0.546034\pi$
$564$	−9.90606	+	14.4778i	−0.417120	+	0.609623i
$565$	5.13089			0.215858
$566$	14.6420	+	19.7255i	0.615449	+	0.829124i
$567$		0			0
$568$	4.34308	+	12.0910i	0.182232	+	0.507329i
$569$		−	33.4870i		−	1.40385i	−0.712252	−	0.701924i	$-0.752324\pi$
$569$		−	33.4870i		−	1.40385i	0.712252	−	0.701924i	$-0.247676\pi$
$570$	−2.87001	+	0.990072i	−0.120212	+	0.0414695i
$571$			27.9973i			1.17165i	0.810438	+	0.585825i	$0.199229\pi$
$571$			27.9973i			1.17165i	−0.810438	+	0.585825i	$0.800771\pi$
$572$	2.21443	−	7.32168i	0.0925901	−	0.306135i
$573$	−28.9553	−	9.15909i	−1.20963	−	0.382627i
$574$		0			0
$575$	24.0570			1.00324
$576$	−23.9289	+	1.84551i	−0.997039	+	0.0768964i
$577$	−37.6362			−1.56682			−0.783409	−	0.621507i	$-0.786521\pi$
$577$	−37.6362			−1.56682			−0.783409	+	0.621507i	$0.786521\pi$
$578$	19.2031	−	14.2542i	0.798743	−	0.592898i
$579$	3.60847	+	1.14142i	0.149963	+	0.0474359i
$580$	−1.82846	+	6.04552i	−0.0759227	+	0.251027i
$581$		0			0
$582$	−1.21807	+	0.420198i	−0.0504905	+	0.0174178i
$583$			7.29304i			0.302047i
$584$	9.53767	+	26.5527i	0.394672	+	1.09876i
$585$	2.37018	−	3.37165i	0.0979950	−	0.139401i
$586$	−16.8306	−	22.6739i	−0.695266	−	0.936652i
$587$	−19.7791			−0.816373			−0.408186	−	0.912899i	$-0.633839\pi$
$587$	−19.7791			−0.816373			−0.408186	+	0.912899i	$0.633839\pi$
$588$		0			0
$589$	−17.1601			−0.707071
$590$	−1.32690	−	1.78758i	−0.0546276	−	0.0735935i
$591$	−3.27894	+	10.3660i	−0.134878	+	0.426399i
$592$	−24.4490	−	16.2782i	−1.00485	−	0.669029i
$593$		−	22.5237i		−	0.924939i	−0.886635	−	0.462469i	$-0.846964\pi$
$593$		−	22.5237i		−	0.924939i	0.886635	−	0.462469i	$-0.153036\pi$
$594$	−9.81860	−	2.82902i	−0.402862	−	0.116076i
$595$		0			0
$596$	4.39118	+	1.32811i	0.179870	+	0.0544013i
$597$	−0.452122	+	1.42933i	−0.0185041	+	0.0584984i
$598$	15.8170	−	11.7408i	0.646807	−	0.480117i
$599$	26.7316			1.09223			0.546113	−	0.837712i	$-0.316107\pi$
$599$	26.7316			1.09223			0.546113	+	0.837712i	$0.316107\pi$
$600$	−0.895459	−	23.2555i	−0.0365570	−	0.949403i
$601$	−31.1478			−1.27055			−0.635273	−	0.772288i	$-0.719112\pi$
$601$	−31.1478			−1.27055			−0.635273	+	0.772288i	$0.719112\pi$
$602$		0			0
$603$	−18.5362	+	26.3682i	−0.754851	+	1.07380i
$604$	−25.1466	−	7.60555i	−1.02320	−	0.309465i
$605$		−	4.52840i		−	0.184106i
$606$	12.8577	+	37.2717i	0.522307	+	1.51406i
$607$		−	12.5787i		−	0.510552i	−0.966868	−	0.255276i	$-0.917834\pi$
$607$		−	12.5787i		−	0.510552i	0.966868	−	0.255276i	$-0.0821664\pi$
$608$	0.717627	+	14.0193i	0.0291036	+	0.568558i
$609$		0			0
$610$	−2.06651	−	2.78398i	−0.0836707	−	0.112720i
$611$	−13.9288			−0.563501
$612$	−21.5427	−	27.5081i	−0.870812	−	1.11195i
$613$	4.54262			0.183475			0.0917374	−	0.995783i	$-0.470758\pi$
$613$	4.54262			0.183475			0.0917374	+	0.995783i	$0.470758\pi$
$614$	11.9296	+	16.0714i	0.481440	+	0.648590i
$615$	4.73806	+	1.49873i	0.191057	+	0.0604348i
$616$		0			0
$617$		−	35.4652i		−	1.42777i	−0.700261	−	0.713887i	$-0.746933\pi$
$617$		−	35.4652i		−	1.42777i	0.700261	−	0.713887i	$-0.253067\pi$
$618$	−1.49907	−	4.34549i	−0.0603014	−	0.174801i
$619$			41.4572i			1.66631i	0.553042	+	0.833153i	$0.313467\pi$
$619$			41.4572i			1.66631i	−0.553042	+	0.833153i	$0.686533\pi$
$620$	−1.99977	+	6.61194i	−0.0803128	+	0.265542i
$621$	−15.9606	−	20.9204i	−0.640476	−	0.839508i
$622$	−27.8836	+	20.6976i	−1.11803	+	0.829900i
$623$		0			0
$624$	−11.9384	−	14.8531i	−0.477920	−	0.594600i
$625$	21.3203			0.852810
$626$	0.0591199	−	0.0438840i	0.00236291	−	0.00175396i
$627$	−1.80247	+	5.69827i	−0.0719835	+	0.227567i
$628$	−4.86911	+	16.0990i	−0.194299	+	0.642419i
$629$		−	42.7609i		−	1.70499i
$630$		0			0
$631$			22.2919i			0.887428i	0.896168	+	0.443714i	$0.146339\pi$
$631$			22.2919i			0.887428i	−0.896168	+	0.443714i	$0.853661\pi$
$632$	−5.67332	+	2.03785i	−0.225673	+	0.0810612i
$633$	−2.03941	+	6.44735i	−0.0810594	+	0.256259i
$634$	5.71202	+	7.69516i	0.226853	+	0.305614i
$635$	−0.755312			−0.0299736
$636$	14.9948	+	10.2599i	0.594583	+	0.406830i
$637$		0			0
$638$	7.41070	+	9.98359i	0.293393	+	0.395254i
$639$	11.1479	+	7.83664i	0.441002	+	0.310013i
$640$	5.48538	+	1.35724i	0.216829	+	0.0536498i
$641$			34.1111i			1.34731i	0.739048	+	0.673653i	$0.235276\pi$
$641$			34.1111i			1.34731i	−0.739048	+	0.673653i	$0.764724\pi$
$642$	−16.8539	+	5.81411i	−0.665170	+	0.229465i
$643$		−	24.2299i		−	0.955533i	−0.878487	−	0.477766i	$-0.841447\pi$
$643$		−	24.2299i		−	0.955533i	0.878487	−	0.477766i	$-0.158553\pi$
$644$		0			0
$645$	2.90852	+	0.920019i	0.114523	+	0.0362257i
$646$	−16.4096	+	12.1807i	−0.645627	+	0.479241i
$647$	1.42818			0.0561477			0.0280738	−	0.999606i	$-0.491063\pi$
$647$	1.42818			0.0561477			0.0280738	+	0.999606i	$0.491063\pi$
$648$	−19.6294	+	16.2076i	−0.771116	+	0.636695i
$649$	−4.38249			−0.172028
$650$	14.8378	−	11.0139i	0.581987	−	0.432002i
$651$		0			0
$652$	−23.6612	−	7.15630i	−0.926644	−	0.280262i
$653$			5.02787i			0.196756i	0.995149	+	0.0983778i	$0.0313654\pi$
$653$			5.02787i			0.196756i	−0.995149	+	0.0983778i	$0.968635\pi$
$654$	−4.26532	+	1.47141i	−0.166787	+	0.0575368i
$655$			3.32162i			0.129787i
$656$	12.7342	−	19.1261i	0.497186	−	0.746748i
$657$	24.4814	+	17.2097i	0.955109	+	0.671416i
$658$		0			0
$659$	19.7930			0.771025			0.385512	−	0.922703i	$-0.374025\pi$
$659$	19.7930			0.771025			0.385512	+	0.922703i	$0.374025\pi$
$660$	1.98554	+	1.35856i	0.0772869	+	0.0528818i
$661$	22.6612			0.881419			0.440709	−	0.897650i	$-0.354727\pi$
$661$	22.6612			0.881419			0.440709	+	0.897650i	$0.354727\pi$
$662$	−15.0814	−	20.3174i	−0.586154	−	0.789658i
$663$	8.36686	−	26.4508i	0.324942	−	1.02726i
$664$	11.4897	+	31.9870i	0.445885	+	1.24134i
$665$		0			0
$666$	−31.1437	+	0.804573i	−1.20679	+	0.0311766i
$667$			32.0187i			1.23977i
$668$	−1.36961	+	4.52840i	−0.0529918	+	0.175209i
$669$	12.2766	−	38.8108i	0.474639	−	1.50051i
$670$	6.09362	−	4.52322i	0.235417	−	0.174747i
$671$	−6.82530			−0.263488
$672$		0			0
$673$	−11.2766			−0.434680			−0.217340	−	0.976096i	$-0.569738\pi$
$673$	−11.2766			−0.434680			−0.217340	+	0.976096i	$0.569738\pi$
$674$	−8.05523	+	5.97930i	−0.310276	+	0.230314i
$675$	−14.9725	−	19.6252i	−0.576291	−	0.755376i
$676$	−3.14658	+	10.4037i	−0.121022	+	0.400142i
$677$			10.0890i			0.387750i	0.981026	+	0.193875i	$0.0621056\pi$
$677$			10.0890i			0.387750i	−0.981026	+	0.193875i	$0.937894\pi$
$678$	−8.20598	−	23.7874i	−0.315149	−	0.913551i
$679$		0			0
$680$	2.78100	+	7.74223i	0.106646	+	0.296901i
$681$	31.6538	+	10.0127i	1.21298	+	0.383686i
$682$	8.10503	+	10.9190i	0.310357	+	0.418109i
$683$	−6.23486			−0.238570			−0.119285	−	0.992860i	$-0.538060\pi$
$683$	−6.23486			−0.238570			−0.119285	+	0.992860i	$0.538060\pi$
$684$	9.18019	+	11.7223i	0.351013	+	0.448212i
$685$	6.08933			0.232662
$686$		0			0
$687$	18.9517	+	5.99476i	0.723052	+	0.228714i
$688$	7.81705	−	11.7408i	0.298022	−	0.447614i
$689$			14.4263i			0.549599i
$690$	2.02044	+	5.85682i	0.0769167	+	0.222966i
$691$			17.0676i			0.649283i	0.945837	+	0.324641i	$0.105244\pi$
$691$			17.0676i			0.649283i	−0.945837	+	0.324641i	$0.894756\pi$
$692$	18.3200	+	5.54087i	0.696423	+	0.210632i
$693$		0			0
$694$	10.4367	−	7.74704i	0.396172	−	0.294074i
$695$	0.0238663			0.000905300
$696$	30.9521	−	1.19182i	1.17324	−	0.0451757i
$697$	33.4511			1.26705
$698$	−25.1334	+	18.6562i	−0.951313	+	0.706148i
$699$	10.5610	−	33.3872i	0.399452	−	1.26282i
$700$		0			0
$701$			21.4324i			0.809489i	0.914430	+	0.404744i	$0.132640\pi$
$701$			21.4324i			0.809489i	−0.914430	+	0.404744i	$0.867360\pi$
$702$	−19.4221	−	5.59607i	−0.733040	−	0.211210i
$703$			18.2221i			0.687259i
$704$	8.58152	−	7.07818i	0.323428	−	0.266769i
$705$	1.32123	−	4.17692i	0.0497605	−	0.157312i
$706$	−9.04155	−	12.1807i	−0.340283	−	0.458425i
$707$		0			0
$708$	−6.16529	+	9.01060i	−0.231706	+	0.338639i
$709$	−8.54262			−0.320825			−0.160412	−	0.987050i	$-0.551282\pi$
$709$	−8.54262			−0.320825			−0.160412	+	0.987050i	$0.551282\pi$
$710$	−1.91231	−	2.57623i	−0.0717676	−	0.0966843i
$711$	−3.67709	+	5.23076i	−0.137902	+	0.196169i
$712$	6.52603	−	2.34414i	0.244573	−	0.0878503i
$713$			35.0186i			1.31146i
$714$		0			0
$715$			1.91026i			0.0714396i
$716$	−12.0165	+	39.7309i	−0.449079	+	1.48481i
$717$	−11.4075	−	3.60838i	−0.426019	−	0.134758i
$718$	−4.09362	+	3.03864i	−0.152772	+	0.113401i
$719$	−27.4731			−1.02457			−0.512287	−	0.858814i	$-0.671202\pi$
$719$	−27.4731			−1.02457			−0.512287	+	0.858814i	$0.671202\pi$
$720$	5.58651	−	2.17114i	0.208197	−	0.0809134i
$721$		0			0
$722$	−14.5829	+	10.8247i	−0.542719	+	0.402854i
$723$	13.3211	+	4.21369i	0.495416	+	0.156709i
$724$	3.72557	−	12.3180i	0.138460	−	0.457796i
$725$			30.0365i			1.11553i
$726$	−20.9942	+	7.24241i	−0.779169	+	0.268791i
$727$			45.7930i			1.69837i	0.528096	+	0.849185i	$0.322906\pi$
$727$			45.7930i			1.69837i	−0.528096	+	0.849185i	$0.677094\pi$
$728$		0			0
$729$	−7.13303	+	26.0407i	−0.264186	+	0.964472i
$730$	−4.19954	−	5.65756i	−0.155432	−	0.209396i
$731$	20.5345			0.759494
$732$	−9.60183	+	14.0331i	−0.354894	+	0.518679i
$733$	43.2932			1.59907			0.799535	−	0.600620i	$-0.205080\pi$
$733$	43.2932			1.59907			0.799535	+	0.600620i	$0.205080\pi$
$734$	12.6661	+	17.0636i	0.467514	+	0.629828i
$735$		0			0
$736$	28.6091	−	1.46446i	1.05455	−	0.0539807i
$737$		−	14.9393i		−	0.550297i
$738$	−0.629405	−	24.3632i	−0.0231687	−	0.896822i
$739$			5.17590i			0.190399i	0.995458	+	0.0951993i	$0.0303488\pi$
$739$			5.17590i			0.190399i	−0.995458	+	0.0951993i	$0.969651\pi$
$740$	7.02111	+	2.12353i	0.258101	+	0.0780624i
$741$	−3.56544	+	11.2717i	−0.130980	+	0.414077i
$742$		0			0
$743$	−49.5492			−1.81778			−0.908891	−	0.417034i	$-0.863070\pi$
$743$	−49.5492			−1.81778			−0.908891	+	0.417034i	$0.863070\pi$
$744$	33.8521	−	1.30348i	1.24108	−	0.0477879i
$745$	−1.14568			−0.0419744
$746$	−3.01709	+	2.23955i	−0.110464	+	0.0819958i
$747$	29.4917	+	20.7319i	1.07905	+	0.758541i
$748$	15.5011	+	4.68828i	0.566775	+	0.171420i
$749$		0			0
$750$	3.89023	+	11.2770i	0.142051	+	0.411777i
$751$		−	30.5879i		−	1.11617i	−0.829784	−	0.558084i	$-0.811537\pi$
$751$		−	30.5879i		−	1.11617i	0.829784	−	0.558084i	$-0.188463\pi$
$752$	−16.8609	−	11.2260i	−0.614854	−	0.409371i
$753$	−33.7006	−	10.6601i	−1.22812	−	0.388476i
$754$	14.6591	+	19.7485i	0.533851	+	0.719197i
$755$	6.56086			0.238774
$756$		0			0
$757$	46.4533			1.68837			0.844187	−	0.536049i	$-0.180084\pi$
$757$	46.4533			1.68837			0.844187	+	0.536049i	$0.180084\pi$
$758$	14.9322	+	20.1164i	0.542362	+	0.730662i
$759$	11.6284	+	3.67829i	0.422086	+	0.133513i
$760$	−1.18509	−	3.29927i	−0.0429878	−	0.119677i
$761$			39.4484i			1.43000i	0.699122	+	0.715002i	$0.253574\pi$
$761$			39.4484i			1.43000i	−0.699122	+	0.715002i	$0.746426\pi$
$762$	1.20799	+	3.50172i	0.0437609	+	0.126854i
$763$		0			0
$764$	10.1520	−	33.5659i	0.367285	−	1.21437i
$765$	7.13828	+	5.01802i	0.258085	+	0.181427i
$766$	−37.3846	+	27.7502i	−1.35076	+	1.00265i
$767$	−8.66898			−0.313019
$768$	−2.48058	−	27.6016i	−0.0895101	−	0.995986i
$769$	−39.7256			−1.43254			−0.716270	−	0.697823i	$-0.754152\pi$
$769$	−39.7256			−1.43254			−0.716270	+	0.697823i	$0.754152\pi$
$770$		0			0
$771$	14.2136	−	44.9346i	0.511891	−	1.61828i
$772$	−1.26516	+	4.18305i	−0.0455340	+	0.150551i
$773$		−	21.9318i		−	0.788833i	−0.918932	−	0.394416i	$-0.870947\pi$
$773$		−	21.9318i		−	0.788833i	0.918932	−	0.394416i	$-0.129053\pi$
$774$	−0.386369	−	14.9557i	−0.0138877	−	0.537571i
$775$			32.8506i			1.18003i
$776$	−0.502967	−	1.40025i	−0.0180554	−	0.0502660i
$777$		0			0
$778$	5.75054	+	7.74704i	0.206167	+	0.277745i
$779$	−14.2548			−0.510733
$780$	3.92758	+	2.68735i	0.140630	+	0.0962227i
$781$	−6.31598			−0.226004
$782$	24.8570	+	33.4870i	0.888885	+	1.19749i
$783$	26.1203	−	19.9277i	0.933464	−	0.712157i
$784$		0			0
$785$		−	4.20029i		−	0.149915i
$786$	15.3994	−	5.31237i	0.549280	−	0.189486i
$787$			5.04447i			0.179816i	0.995950	+	0.0899080i	$0.0286573\pi$
$787$			5.04447i			0.179816i	−0.995950	+	0.0899080i	$0.971343\pi$
$788$	−12.0165	−	3.63439i	−0.428072	−	0.129470i
$789$	−5.95319	−	1.88310i	−0.211939	−	0.0670402i
$790$	1.20881	−	0.897287i	0.0430076	−	0.0319240i
$791$		0			0
$792$	3.12291	−	11.3780i	0.110968	−	0.404299i
$793$	−13.5011			−0.479437
$794$	−23.6698	+	17.5698i	−0.840010	+	0.623529i
$795$	−4.32609	−	1.36842i	−0.153431	−	0.0485329i
$796$	−1.65692	−	0.501133i	−0.0587279	−	0.0177622i
$797$		−	28.3335i		−	1.00362i	−0.864977	−	0.501812i	$-0.832667\pi$
$797$		−	28.3335i		−	1.00362i	0.864977	−	0.501812i	$-0.167333\pi$
$798$		0			0
$799$		−	29.4894i		−	1.04326i
$800$	26.8379	−	1.37379i	0.948865	−	0.0485710i
$801$	4.22976	−	6.01695i	0.149451	−	0.212599i
$802$	3.22450	+	4.34401i	0.113861	+	0.153392i
$803$	−13.8703			−0.489471
$804$	−30.7159	−	21.0166i	−1.08327	−	0.741200i
$805$		0			0
$806$	16.0325	+	21.5987i	0.564721	+	0.760783i
$807$	−13.6679	+	43.2095i	−0.481134	+	1.52105i
$808$	−42.8463	+	15.3903i	−1.50733	+	0.541429i
$809$			20.2174i			0.710808i	0.934713	+	0.355404i	$0.115657\pi$
$809$			20.2174i			0.710808i	−0.934713	+	0.355404i	$0.884343\pi$
$810$	3.52042	−	5.29338i	0.123695	−	0.185991i
$811$			1.33368i			0.0468317i	0.999726	+	0.0234158i	$0.00745418\pi$
$811$			1.33368i			0.0468317i	−0.999726	+	0.0234158i	$0.992546\pi$
$812$		0			0
$813$	−12.0468	+	38.0845i	−0.422500	+	1.33568i
$814$	11.5947	−	8.60660i	0.406394	−	0.301661i
$815$	6.17331			0.216242
$816$	31.4462	−	25.2754i	1.10084	−	0.884817i
$817$	−8.75054			−0.306142
$818$	−4.39361	+	3.26133i	−0.153619	+	0.114030i
$819$		0			0
$820$	−1.66120	+	5.49251i	−0.0580117	+	0.191807i
$821$			5.31136i			0.185368i	0.995696	+	0.0926838i	$0.0295446\pi$
$821$			5.31136i			0.185368i	−0.995696	+	0.0926838i	$0.970455\pi$
$822$	−9.73885	−	28.2309i	−0.339681	−	0.984666i
$823$			15.3007i			0.533349i	0.963787	+	0.266675i	$0.0859249\pi$
$823$			15.3007i			0.533349i	−0.963787	+	0.266675i	$0.914075\pi$
$824$	4.99543	−	1.79435i	0.174024	−	0.0625091i
$825$	10.9085	+	3.45056i	0.379786	+	0.120133i
$826$		0			0
$827$	0.288306			0.0100254			0.00501270	−	0.999987i	$-0.498404\pi$
$827$	0.288306			0.0100254			0.00501270	+	0.999987i	$0.498404\pi$
$828$	23.9216	−	18.7340i	0.831334	−	0.651051i
$829$	41.1102			1.42782			0.713908	−	0.700239i	$-0.246923\pi$
$829$	41.1102			1.42782			0.713908	+	0.700239i	$0.246923\pi$
$830$	−5.05903	−	6.81545i	−0.175601	−	0.236568i
$831$	33.5086	+	10.5994i	1.16240	+	0.367689i
$832$	16.9750	−	14.0013i	0.588504	−	0.485408i
$833$		0			0
$834$	−0.0381700	−	0.110647i	−0.00132172	−	0.00383139i
$835$		−	1.18148i		−	0.0408868i
$836$	−6.60561	−	1.99786i	−0.228460	−	0.0690974i
$837$	28.5676	−	21.7948i	0.987440	−	0.753337i
$838$	−15.3452	+	11.3906i	−0.530092	+	0.393481i
$839$	−25.7705			−0.889695			−0.444848	−	0.895606i	$-0.646742\pi$
$839$	−25.7705			−0.889695			−0.444848	+	0.895606i	$0.646742\pi$
$840$		0			0
$841$	−10.9772			−0.378523
$842$	−12.9255	+	9.59445i	−0.445442	+	0.330647i
$843$	14.4507	−	45.6840i	0.497707	−	1.57344i
$844$	−7.47397	−	2.26049i	−0.257265	−	0.0778093i
$845$		−	2.71437i		−	0.0933771i
$846$	−21.4778	+	0.554862i	−0.738421	+	0.0190766i
$847$		0			0
$848$	−11.6270	+	17.4631i	−0.399271	+	0.599685i
$849$	−9.07391	+	28.6860i	−0.311416	+	0.984502i
$850$	23.3181	+	31.4138i	0.799805	+	1.07749i
$851$	37.1857			1.27471
$852$	−8.88532	+	12.9859i	−0.304406	+	0.444891i
$853$	51.4656			1.76215			0.881074	−	0.472978i	$-0.156821\pi$
$853$	51.4656			1.76215			0.881074	+	0.472978i	$0.156821\pi$
$854$		0			0
$855$	−3.04190	−	2.13838i	−0.104031	−	0.0731309i
$856$	−6.95935	−	19.3747i	−0.237866	−	0.662213i
$857$		−	35.5762i		−	1.21526i	−0.794220	−	0.607631i	$-0.792120\pi$
$857$		−	35.5762i		−	1.21526i	0.794220	−	0.607631i	$-0.207880\pi$
$858$	8.85620	−	3.05513i	0.302346	−	0.104301i
$859$		−	51.3072i		−	1.75058i	−0.483598	−	0.875290i	$-0.660670\pi$
$859$		−	51.3072i		−	1.75058i	0.483598	−	0.875290i	$-0.339330\pi$
$860$	−1.01975	+	3.37165i	−0.0347732	+	0.114972i
$861$		0			0
$862$	−29.4388	+	21.8521i	−1.00269	+	0.744286i
$863$	−11.7830			−0.401099			−0.200550	−	0.979684i	$-0.564273\pi$
$863$	−11.7830			−0.401099			−0.200550	+	0.979684i	$0.564273\pi$
$864$	−19.0003	−	22.4274i	−0.646404	−	0.762995i
$865$	−4.77978			−0.162517
$866$	26.5522	−	19.7094i	0.902282	−	0.669753i
$867$	27.9263	+	8.83360i	0.948428	+	0.300005i
$868$		0			0
$869$		−	2.96357i		−	0.100532i
$870$	−7.31257	+	2.52263i	−0.247919	+	0.0855251i
$871$		−	29.5514i		−	1.00131i
$872$	−1.76124	−	4.90327i	−0.0596433	−	0.166046i
$873$	−1.29102	−	0.907552i	−0.0436944	−	0.0307160i
$874$	−10.5925	−	14.2701i	−0.358298	−	0.482694i
$875$		0			0
$876$	−19.5127	+	28.5179i	−0.659273	+	0.963531i
$877$	1.32863			0.0448646			0.0224323	−	0.999748i	$-0.492859\pi$
$877$	1.32863			0.0448646			0.0224323	+	0.999748i	$0.492859\pi$
$878$	−14.8969	−	20.0689i	−0.502747	−	0.677294i
$879$	10.4302	−	32.9739i	0.351803	−	1.11218i
$880$	−1.53958	+	2.31237i	−0.0518993	+	0.0779501i
$881$			23.8258i			0.802713i	0.915922	+	0.401356i	$0.131461\pi$
$881$			23.8258i			0.802713i	−0.915922	+	0.401356i	$0.868539\pi$
$882$		0			0
$883$		−	30.2235i		−	1.01710i	−0.861032	−	0.508551i	$-0.830181\pi$
$883$		−	30.2235i		−	1.01710i	0.861032	−	0.508551i	$-0.169819\pi$
$884$	30.6626	+	9.27385i	1.03129	+	0.311913i
$885$	0.822304	−	2.59961i	0.0276414	−	0.0873850i
$886$	39.8993	−	29.6167i	1.34044	−	0.994994i
$887$	21.9111			0.735704			0.367852	−	0.929884i	$-0.380093\pi$
$887$	21.9111			0.735704			0.367852	+	0.929884i	$0.380093\pi$
$888$	−1.38415	−	35.9470i	−0.0464489	−	1.20630i
$889$		0			0
$890$	−1.39050	+	1.03215i	−0.0466096	+	0.0345978i
$891$	−4.23658	−	11.7756i	−0.141931	−	0.394496i
$892$	44.9907	+	13.6074i	1.50640	+	0.455609i
$893$			12.5666i			0.420525i
$894$	1.83232	+	5.31151i	0.0612819	+	0.177643i
$895$		−	10.3660i		−	0.346496i
$896$		0			0
$897$	23.0021	+	7.27599i	0.768019	+	0.242938i
$898$	4.65906	+	6.27662i	0.155475	+	0.209453i
$899$	−43.7227			−1.45823
$900$	22.4406	−	17.5742i	0.748021	−	0.585805i
$901$	−30.5426			−1.01752
$902$	6.73281	+	9.07034i	0.224178	+	0.302009i
$903$		0			0
$904$	27.3452	−	9.82235i	0.909489	−	0.326687i
$905$			3.21383i			0.106831i
$906$	−10.4930	−	30.4169i	−0.348606	−	1.01053i
$907$		−	48.9638i		−	1.62581i	−0.582393	−	0.812907i	$-0.697883\pi$
$907$		−	48.9638i		−	1.62581i	0.582393	−	0.812907i	$-0.302117\pi$
$908$	−11.0981	+	36.6941i	−0.368302	+	1.21774i
$909$	−27.7702	+	39.5040i	−0.921081	+	1.31026i
$910$		0			0
$911$	51.8251			1.71704			0.858522	−	0.512777i	$-0.171383\pi$
$911$	51.8251			1.71704			0.858522	+	0.512777i	$0.171383\pi$
$912$	−13.4005	+	10.7708i	−0.443734	+	0.356658i
$913$	−16.7090			−0.552987
$914$	−27.1992	+	20.1896i	−0.899669	+	0.667814i
$915$	1.28066	−	4.04864i	0.0423372	−	0.133844i
$916$	−6.64461	+	21.9694i	−0.219544	+	0.725889i
$917$		0			0
$918$	11.8477	−	41.1194i	0.391033	−	1.35714i
$919$		−	50.5037i		−	1.66596i	−0.553301	−	0.832981i	$-0.686632\pi$
$919$		−	50.5037i		−	1.66596i	0.553301	−	0.832981i	$-0.313368\pi$
$920$	−6.73281	+	2.41841i	−0.221974	+	0.0797327i
$921$	−7.39300	+	23.3721i	−0.243608	+	0.770135i
$922$	2.52603	+	3.40303i	0.0831904	+	0.112073i
$923$	−12.4936			−0.411232
$924$		0			0
$925$	34.8836			1.14696
$926$	18.8940	+	25.4538i	0.620897	+	0.836463i
$927$	3.23772	−	4.60575i	0.106341	−	0.151273i
$928$	1.82846	+	35.7201i	0.0600221	+	1.17257i
$929$			1.23566i			0.0405407i	0.999795	+	0.0202703i	$0.00645269\pi$
$929$			1.23566i			0.0405407i	−0.999795	+	0.0202703i	$0.993547\pi$
$930$	−7.99770	+	2.75898i	−0.262255	+	0.0904705i
$931$		0			0
$932$	38.7034	+	11.7058i	1.26777	+	0.383436i
$933$	−40.5500	−	12.8267i	−1.32755	−	0.419927i
$934$	13.6963	−	10.1666i	0.448158	−	0.332662i
$935$	−4.04430			−0.132263
$936$	6.17741	−	22.5067i	0.201915	−	0.735655i
$937$	29.4139			0.960909			0.480455	−	0.877020i	$-0.340472\pi$
$937$	29.4139			0.960909			0.480455	+	0.877020i	$0.340472\pi$
$938$		0			0
$939$	0.0859759	+	0.0271957i	0.00280572	+	0.000887499i
$940$	4.84201	+	1.46446i	0.157929	+	0.0477654i
$941$			44.8636i			1.46251i	0.682103	+	0.731256i	$0.261066\pi$
$941$			44.8636i			1.46251i	−0.682103	+	0.731256i	$0.738934\pi$
$942$	−19.4731	+	6.71765i	−0.634467	+	0.218873i
$943$			29.0898i			0.947295i
$944$	−10.4938	−	6.98680i	−0.341545	−	0.227401i
$945$		0			0
$946$	4.13303	+	5.56796i	0.134376	+	0.181030i
$947$	17.5576			0.570547			0.285273	−	0.958446i	$-0.407916\pi$
$947$	17.5576			0.570547			0.285273	+	0.958446i	$0.407916\pi$
$948$	−6.09322	−	4.16915i	−0.197899	−	0.135408i
$949$	−27.4367			−0.890633
$950$	−9.93676	−	13.3867i	−0.322391	−	0.434321i
$951$	−3.53984	+	11.1908i	−0.114787	+	0.362886i
$952$		0			0
$953$			37.1546i			1.20356i	0.798663	+	0.601778i	$0.205541\pi$
$953$			37.1546i			1.20356i	−0.798663	+	0.601778i	$0.794459\pi$
$954$	0.574679	+	22.2449i	0.0186059	+	0.720204i
$955$			8.75750i			0.283386i
$956$	3.99954	−	13.2239i	0.129354	−	0.427691i
$957$	−4.59255	+	14.5188i	−0.148456	+	0.469325i
$958$	15.2245	−	11.3010i	0.491881	−	0.365118i
$959$		0			0
$960$	2.58846	+	6.41850i	0.0835422	+	0.207156i
$961$	−16.8192			−0.542555
$962$	22.9354	−	17.0247i	0.739466	−	0.548897i
$963$	−17.8633	−	12.5574i	−0.575637	−	0.404658i
$964$	−4.67047	+	15.4422i	−0.150426	+	0.497360i
$965$		−	1.09138i		−	0.0351326i
$966$		0			0
$967$			53.9045i			1.73345i	0.498786	+	0.866725i	$0.333779\pi$
$967$			53.9045i			1.73345i	−0.498786	+	0.866725i	$0.666221\pi$
$968$	−8.66898	−	24.1343i	−0.278632	−	0.775704i
$969$	−23.8639	−	7.54857i	−0.766618	−	0.242495i
$970$	0.221462	+	0.298350i	0.00711071	+	0.00957945i
$971$	−38.3565			−1.23092			−0.615460	−	0.788168i	$-0.711030\pi$
$971$	−38.3565			−1.23092			−0.615460	+	0.788168i	$0.711030\pi$
$972$	−30.1711	−	7.85526i	−0.967738	−	0.251957i
$973$		0			0
$974$	−10.2906	−	13.8633i	−0.329731	−	0.444208i
$975$	21.5781	+	6.82553i	0.691052	+	0.218592i
$976$	−16.3431	−	10.8812i	−0.523129	−	0.348300i
$977$		−	18.0025i		−	0.575952i	−0.957638	−	0.287976i	$-0.907018\pi$
$977$		−	18.0025i		−	0.575952i	0.957638	−	0.287976i	$-0.0929824\pi$
$978$	−9.87316	−	28.6202i	−0.315709	−	0.915174i
$979$			3.40899i			0.108952i
$980$		0			0
$981$	−4.52078	−	3.17799i	−0.144337	−	0.101465i
$982$	45.3067	−	33.6306i	1.44580	−	1.07320i
$983$	13.7569			0.438777			0.219388	−	0.975638i	$-0.429594\pi$
$983$	13.7569			0.438777			0.219388	+	0.975638i	$0.429594\pi$
$984$	28.1207	−	1.08279i	0.896457	−	0.0345182i
$985$	3.13517			0.0998948
$986$	−41.8104	+	31.0354i	−1.33151	+	0.988368i
$987$		0			0
$988$	−13.0665	−	3.95195i	−0.415701	−	0.125728i
$989$			17.8572i			0.567826i
$990$	0.0760961	+	2.94555i	0.00241849	+	0.0936157i
$991$		−	1.85652i		−	0.0589742i	−0.999565	−	0.0294871i	$-0.990613\pi$
$991$		−	1.85652i		−	0.0589742i	0.999565	−	0.0294871i	$-0.00938739\pi$
$992$	1.99977	+	39.0668i	0.0634928	+	1.24037i
$993$	9.34619	−	29.5468i	0.296593	−	0.937640i
$994$		0			0
$995$	0.432298			0.0137048
$996$	−23.5062	+	34.3544i	−0.744823	+	1.08856i
$997$	−60.3495			−1.91129			−0.955644	−	0.294524i	$-0.904839\pi$
$997$	−60.3495			−1.91129			−0.955644	+	0.294524i	$0.904839\pi$
$998$	−7.14383	−	9.62407i	−0.226134	−	0.304644i
$999$	−23.1435	−	30.3355i	−0.732228	−	0.959772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.d.491.4		12
3.2	odd	2	inner	588.2.e.d.491.9		12
4.3	odd	2	inner	588.2.e.d.491.10		12
7.2	even	3		588.2.n.e.263.11		24
7.3	odd	6		84.2.n.a.23.6	yes	24
7.4	even	3		588.2.n.e.275.6		24
7.5	odd	6		84.2.n.a.11.11	yes	24
7.6	odd	2		588.2.e.e.491.4		12
12.11	even	2	inner	588.2.e.d.491.3		12
21.2	odd	6		588.2.n.e.263.2		24
21.5	even	6		84.2.n.a.11.2	✓	24
21.11	odd	6		588.2.n.e.275.7		24
21.17	even	6		84.2.n.a.23.7	yes	24
21.20	even	2		588.2.e.e.491.9		12
28.3	even	6		84.2.n.a.23.2	yes	24
28.11	odd	6		588.2.n.e.275.2		24
28.19	even	6		84.2.n.a.11.7	yes	24
28.23	odd	6		588.2.n.e.263.7		24
28.27	even	2		588.2.e.e.491.10		12
84.11	even	6		588.2.n.e.275.11		24
84.23	even	6		588.2.n.e.263.6		24
84.47	odd	6		84.2.n.a.11.6	yes	24
84.59	odd	6		84.2.n.a.23.11	yes	24
84.83	odd	2		588.2.e.e.491.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.2	✓	24	21.5	even	6
84.2.n.a.11.6	yes	24	84.47	odd	6
84.2.n.a.11.7	yes	24	28.19	even	6
84.2.n.a.11.11	yes	24	7.5	odd	6
84.2.n.a.23.2	yes	24	28.3	even	6
84.2.n.a.23.6	yes	24	7.3	odd	6
84.2.n.a.23.7	yes	24	21.17	even	6
84.2.n.a.23.11	yes	24	84.59	odd	6
588.2.e.d.491.3		12	12.11	even	2	inner
588.2.e.d.491.4		12	1.1	even	1	trivial
588.2.e.d.491.9		12	3.2	odd	2	inner
588.2.e.d.491.10		12	4.3	odd	2	inner
588.2.e.e.491.3		12	84.83	odd	2
588.2.e.e.491.4		12	7.6	odd	2
588.2.e.e.491.9		12	21.20	even	2
588.2.e.e.491.10		12	28.27	even	2
588.2.n.e.263.2		24	21.2	odd	6
588.2.n.e.263.6		24	84.23	even	6
588.2.n.e.263.7		24	28.23	odd	6
588.2.n.e.263.11		24	7.2	even	3
588.2.n.e.275.2		24	28.11	odd	6
588.2.n.e.275.6		24	7.4	even	3
588.2.n.e.275.7		24	21.11	odd	6
588.2.n.e.275.11		24	84.11	even	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13556 + 0.842913i) q^{2} +(-1.65140 - 0.522368i) q^{3} +(0.578995 - 1.91436i) q^{4} +0.499464i q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(2.45426 + 1.72528i) q^{9} +O(q^{10})\)	\(q+(-1.13556 + 0.842913i) q^{2} +(-1.65140 - 0.522368i) q^{3} +(0.578995 - 1.91436i) q^{4} +0.499464i q^{5} +(2.31558 - 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(2.45426 + 1.72528i) q^{9} +(-0.421005 - 0.567172i) q^{10} -1.39050 q^{11} +(-1.95615 + 2.85893i) q^{12} -2.75054 q^{13} +(0.260904 - 0.824817i) q^{15} +(-3.32953 - 2.21681i) q^{16} -5.82329i q^{17} +(-4.24123 + 0.109569i) q^{18} +2.48153i q^{19} +(0.956154 + 0.289187i) q^{20} +(1.57899 - 1.17207i) q^{22} +5.06405 q^{23} +(-0.188496 - 4.89535i) q^{24} +4.75054 q^{25} +(3.12340 - 2.31846i) q^{26} +(-3.15174 - 4.13116i) q^{27} +6.32275i q^{29} +(0.398976 + 1.15655i) q^{30} +6.91514i q^{31} +(5.64946 - 0.289187i) q^{32} +(2.29627 + 0.726352i) q^{33} +(4.90852 + 6.61269i) q^{34} +(4.72381 - 3.69941i) q^{36} +7.34308 q^{37} +(-2.09171 - 2.81793i) q^{38} +(4.54224 + 1.43679i) q^{39} +(-1.32953 + 0.477565i) q^{40} +5.74438i q^{41} +3.52627i q^{43} +(-0.805091 + 2.66191i) q^{44} +(-0.861717 + 1.22582i) q^{45} +(-5.75054 + 4.26855i) q^{46} +5.06405 q^{47} +(4.34041 + 5.40008i) q^{48} +(-5.39452 + 4.00429i) q^{50} +(-3.04190 + 9.61659i) q^{51} +(-1.59255 + 5.26551i) q^{52} -5.24491i q^{53} +(7.06121 + 2.03454i) q^{54} -0.694505i q^{55} +(1.29627 - 4.09801i) q^{57} +(-5.32953 - 7.17987i) q^{58} +3.15174 q^{59} +(-1.42793 - 0.977029i) q^{60} +4.90852 q^{61} +(-5.82886 - 7.85256i) q^{62} +(-6.17154 + 5.09039i) q^{64} -1.37379i q^{65} +(-3.21981 + 1.11074i) q^{66} +10.7439i q^{67} +(-11.1479 - 3.37165i) q^{68} +(-8.36279 - 2.64530i) q^{69} +4.54224 q^{71} +(-2.24589 + 8.18266i) q^{72} +9.97504 q^{73} +(-8.33851 + 6.18958i) q^{74} +(-7.84505 - 2.48153i) q^{75} +(4.75054 + 1.43679i) q^{76} +(-6.36908 + 2.19715i) q^{78} +2.13130i q^{79} +(1.10722 - 1.66298i) q^{80} +(3.04681 + 8.46859i) q^{81} +(-4.84201 - 6.52309i) q^{82} +12.0165 q^{83} +2.90852 q^{85} +(-2.97234 - 4.00429i) q^{86} +(3.30281 - 10.4414i) q^{87} +(-1.32953 - 3.70138i) q^{88} -2.45163i q^{89} +(-0.0547257 - 2.11834i) q^{90} +(2.93206 - 9.69440i) q^{92} +(3.61225 - 11.4197i) q^{93} +(-5.75054 + 4.26855i) q^{94} -1.23944 q^{95} +(-9.48059 - 2.47353i) q^{96} -0.526031 q^{97} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{9}+O(q^{10}) \) 12 * q + 2 * q^4 + 2 * q^9	\( 12 q + 2 q^{4} + 2 q^{9} - 10 q^{10} - 12 q^{12} + 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} - 14 q^{24} + 12 q^{25} + 14 q^{30} + 10 q^{33} + 4 q^{34} + 22 q^{36} + 8 q^{37} + 34 q^{40} - 18 q^{45} - 24 q^{46} - 4 q^{48} + 16 q^{52} + 38 q^{54} - 2 q^{57} - 14 q^{58} - 14 q^{60} + 4 q^{61} - 34 q^{64} + 30 q^{66} - 18 q^{69} - 20 q^{72} + 12 q^{76} - 52 q^{78} - 26 q^{81} - 68 q^{82} - 20 q^{85} + 34 q^{88} + 20 q^{90} + 6 q^{93} - 24 q^{94} - 62 q^{96} - 36 q^{97}+O(q^{100}) \) 12 * q + 2 * q^4 + 2 * q^9 - 10 * q^10 - 12 * q^12 + 12 * q^13 + 10 * q^16 + 10 * q^18 + 14 * q^22 - 14 * q^24 + 12 * q^25 + 14 * q^30 + 10 * q^33 + 4 * q^34 + 22 * q^36 + 8 * q^37 + 34 * q^40 - 18 * q^45 - 24 * q^46 - 4 * q^48 + 16 * q^52 + 38 * q^54 - 2 * q^57 - 14 * q^58 - 14 * q^60 + 4 * q^61 - 34 * q^64 + 30 * q^66 - 18 * q^69 - 20 * q^72 + 12 * q^76 - 52 * q^78 - 26 * q^81 - 68 * q^82 - 20 * q^85 + 34 * q^88 + 20 * q^90 + 6 * q^93 - 24 * q^94 - 62 * q^96 - 36 * q^97

Introduction

L-functions

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