LMFDB - Embedded newform 531.2.i.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	531.19
Dual form			531.2.i.c.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31462 + 2.47964i) q^{2} +(-3.29802 - 4.86421i) q^{4} +(-1.27307 + 0.280224i) q^{5} +(1.14406 - 0.869689i) q^{7} +(10.8169 - 1.17641i) q^{8} +O(q^{10})$	\(q+(-1.31462 + 2.47964i) q^{2} +(-3.29802 - 4.86421i) q^{4} +(-1.27307 + 0.280224i) q^{5} +(1.14406 - 0.869689i) q^{7} +(10.8169 - 1.17641i) q^{8} +(0.978753 - 3.52515i) q^{10} +(0.0135957 + 0.0341225i) q^{11} +(0.218202 + 4.02450i) q^{13} +(0.652515 + 3.98017i) q^{14} +(-6.95259 + 17.4497i) q^{16} +(0.583795 + 0.443789i) q^{17} +(6.08516 - 2.05033i) q^{19} +(5.56168 + 5.26830i) q^{20} +(-0.102485 - 0.0111459i) q^{22} +(-6.43762 + 3.87339i) q^{23} +(-2.99569 + 1.38596i) q^{25} +(-10.2662 - 4.74964i) q^{26} +(-8.00348 - 2.69668i) q^{28} +(0.0464669 + 0.0876458i) q^{29} +(7.34222 + 2.47388i) q^{31} +(-20.0409 - 23.5940i) q^{32} +(-1.86791 + 0.864187i) q^{34} +(-1.21276 + 1.42777i) q^{35} +(-6.46531 - 0.703145i) q^{37} +(-2.91561 + 17.7844i) q^{38} +(-13.4410 + 4.52881i) q^{40} +(5.56926 + 3.35091i) q^{41} +(-4.42571 + 11.1077i) q^{43} +(0.121141 - 0.178669i) q^{44} +(-1.14157 - 21.0550i) q^{46} +(3.28620 + 0.723348i) q^{47} +(-1.32019 + 4.75490i) q^{49} +(0.501535 - 9.25026i) q^{50} +(18.8564 - 14.3343i) q^{52} +(0.432398 + 1.55736i) q^{53} +(-0.0268702 - 0.0396306i) q^{55} +(11.3521 - 10.7532i) q^{56} -0.278417 q^{58} +(7.05093 - 3.04703i) q^{59} +(-1.59366 + 3.00597i) q^{61} +(-15.7866 + 14.9539i) q^{62} +(48.1617 - 10.6012i) q^{64} +(-1.40555 - 5.06233i) q^{65} +(1.45362 - 0.158091i) q^{67} +(0.233320 - 4.30333i) q^{68} +(-1.94604 - 4.88418i) q^{70} +(1.67909 + 0.369596i) q^{71} +(-0.286609 - 1.74824i) q^{73} +(10.2430 - 15.1073i) q^{74} +(-30.0422 - 22.8375i) q^{76} +(0.0452302 + 0.0272141i) q^{77} +(-0.945647 - 0.895764i) q^{79} +(3.96132 - 24.1630i) q^{80} +(-15.6306 + 9.40459i) q^{82} +(-5.63272 + 6.63135i) q^{83} +(-0.867572 - 0.401382i) q^{85} +(-21.7250 - 25.5766i) q^{86} +(0.187205 + 0.353107i) q^{88} +(5.15817 + 9.72934i) q^{89} +(3.74970 + 4.41449i) q^{91} +(40.0724 + 18.5395i) q^{92} +(-6.11377 + 7.19768i) q^{94} +(-7.17229 + 4.31542i) q^{95} +(-0.416944 + 2.54325i) q^{97} +(-10.0549 - 9.52451i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{19}{29}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.31462	+	2.47964i	−0.929579	+	1.75337i	−0.355176	+	0.934799i	$0.615579\pi$
$2$	−1.31462	+	2.47964i	−0.929579	+	1.75337i	−0.574403	+	0.818573i	$0.694766\pi$
$3$		0			0
$3$		0			0
$4$	−3.29802	−	4.86421i	−1.64901	−	2.43211i
$5$	−1.27307	+	0.280224i	−0.569334	+	0.125320i	−0.490303	−	0.871552i	$-0.663114\pi$
$5$	−1.27307	+	0.280224i	−0.569334	+	0.125320i	−0.0790316	+	0.996872i	$0.525183\pi$
$6$		0			0
$7$	1.14406	−	0.869689i	0.432413	−	0.328712i	−0.366222	−	0.930527i	$-0.619349\pi$
$7$	1.14406	−	0.869689i	0.432413	−	0.328712i	0.798635	+	0.601816i	$0.205556\pi$
$8$	10.8169	−	1.17641i	3.82436	−	0.415924i
$9$		0			0
$10$	0.978753	−	3.52515i	0.309509	−	1.11475i
$11$	0.0135957	+	0.0341225i	0.00409925	+	0.0102883i	0.931012	−	0.364988i	$-0.118927\pi$
$11$	0.0135957	+	0.0341225i	0.00409925	+	0.0102883i	−0.926913	+	0.375277i	$0.877548\pi$
$12$		0			0
$13$	0.218202	+	4.02450i	0.0605184	+	1.11620i	0.858266	+	0.513205i	$0.171542\pi$
$13$	0.218202	+	4.02450i	0.0605184	+	1.11620i	−0.797748	+	0.602991i	$0.793975\pi$
$14$	0.652515	+	3.98017i	0.174392	+	1.06374i
$15$		0			0
$16$	−6.95259	+	17.4497i	−1.73815	+	4.36242i
$17$	0.583795	+	0.443789i	0.141591	+	0.107635i	0.673572	−	0.739122i	$-0.264759\pi$
$17$	0.583795	+	0.443789i	0.141591	+	0.107635i	−0.531981	+	0.846756i	$0.678552\pi$
$18$		0			0
$19$	6.08516	−	2.05033i	1.39603	−	0.470378i	0.482054	−	0.876142i	$-0.339891\pi$
$19$	6.08516	−	2.05033i	1.39603	−	0.470378i	0.913978	+	0.405764i	$0.132995\pi$
$20$	5.56168	+	5.26830i	1.24363	+	1.17803i
$21$		0			0
$22$	−0.102485	−	0.0111459i	−0.0218499	−	0.00237632i
$23$	−6.43762	+	3.87339i	−1.34234	+	0.807657i	−0.991665	−	0.128841i	$-0.958874\pi$
$23$	−6.43762	+	3.87339i	−1.34234	+	0.807657i	−0.350672	+	0.936498i	$0.614047\pi$
$24$		0			0
$25$	−2.99569	+	1.38596i	−0.599139	+	0.277191i
$26$	−10.2662	−	4.74964i	−2.01336	−	0.931481i
$27$		0			0
$28$	−8.00348	−	2.69668i	−1.51251	−	0.509626i
$29$	0.0464669	+	0.0876458i	0.00862868	+	0.0162754i	0.887789	−	0.460251i	$-0.152241\pi$
$29$	0.0464669	+	0.0876458i	0.00862868	+	0.0162754i	−0.879160	+	0.476526i	$0.841896\pi$
$30$		0			0
$31$	7.34222	+	2.47388i	1.31870	+	0.444322i	0.888693	−	0.458503i	$-0.151614\pi$
$31$	7.34222	+	2.47388i	1.31870	+	0.444322i	0.430008	+	0.902825i	$0.358511\pi$
$32$	−20.0409	−	23.5940i	−3.54277	−	4.17087i
$33$		0			0
$34$	−1.86791	+	0.864187i	−0.320344	+	0.148207i
$35$	−1.21276	+	1.42777i	−0.204993	+	0.241337i
$36$		0			0
$37$	−6.46531	−	0.703145i	−1.06289	−	0.115596i	−0.440072	−	0.897963i	$-0.645047\pi$
$37$	−6.46531	−	0.703145i	−1.06289	−	0.115596i	−0.622819	+	0.782366i	$0.714013\pi$
$38$	−2.91561	+	17.7844i	−0.472974	+	2.88502i
$39$		0			0
$40$	−13.4410	+	4.52881i	−2.12522	+	0.716068i
$41$	5.56926	+	3.35091i	0.869773	+	0.523325i	0.879103	−	0.476632i	$-0.158142\pi$
$41$	5.56926	+	3.35091i	0.869773	+	0.523325i	−0.00933048	+	0.999956i	$0.502970\pi$
$42$		0			0
$43$	−4.42571	+	11.1077i	−0.674914	+	1.69391i	0.0442080	+	0.999022i	$0.485924\pi$
$43$	−4.42571	+	11.1077i	−0.674914	+	1.69391i	−0.719122	+	0.694884i	$0.755456\pi$
$44$	0.121141	−	0.178669i	0.0182626	−	0.0269354i
$45$		0			0
$46$	−1.14157	−	21.0550i	−0.168316	−	3.10440i
$47$	3.28620	+	0.723348i	0.479342	+	0.105511i	0.448068	−	0.894000i	$-0.352112\pi$
$47$	3.28620	+	0.723348i	0.479342	+	0.105511i	0.0312745	+	0.999511i	$0.490043\pi$
$48$		0			0
$49$	−1.32019	+	4.75490i	−0.188599	+	0.679272i
$50$	0.501535	−	9.25026i	0.0709277	−	1.30818i
$51$		0			0
$52$	18.8564	−	14.3343i	2.61491	−	1.98780i
$53$	0.432398	+	1.55736i	0.0593944	+	0.213919i	0.987292	−	0.158915i	$-0.0507997\pi$
$53$	0.432398	+	1.55736i	0.0593944	+	0.213919i	−0.927898	+	0.372835i	$0.878386\pi$
$54$		0			0
$55$	−0.0268702	−	0.0396306i	−0.00362318	−	0.00534379i
$56$	11.3521	−	10.7532i	1.51698	−	1.43696i
$57$		0			0
$58$	−0.278417			−0.0365579
$59$	7.05093	−	3.04703i	0.917953	−	0.396689i
$59$	7.05093	−	3.04703i	0.917953	−	0.396689i
$60$		0			0
$61$	−1.59366	+	3.00597i	−0.204048	+	0.384875i	−0.964324	−	0.264725i	$-0.914719\pi$
$61$	−1.59366	+	3.00597i	−0.204048	+	0.384875i	0.760276	+	0.649600i	$0.225064\pi$
$62$	−15.7866	+	14.9539i	−2.00490	+	1.89914i
$63$		0			0
$64$	48.1617	−	10.6012i	6.02022	−	1.32515i
$65$	−1.40555	−	5.06233i	−0.174337	−	0.627905i
$66$		0			0
$67$	1.45362	−	0.158091i	0.177588	−	0.0193139i	−0.0188928	−	0.999822i	$-0.506014\pi$
$67$	1.45362	−	0.158091i	0.177588	−	0.0193139i	0.196481	+	0.980508i	$0.437049\pi$
$68$	0.233320	−	4.30333i	0.0282942	−	0.521855i
$69$		0			0
$70$	−1.94604	−	4.88418i	−0.232596	−	0.583771i
$71$	1.67909	+	0.369596i	0.199272	+	0.0438630i	0.313485	−	0.949593i	$-0.398504\pi$
$71$	1.67909	+	0.369596i	0.199272	+	0.0438630i	−0.114213	+	0.993456i	$0.536435\pi$
$72$		0			0
$73$	−0.286609	−	1.74824i	−0.0335451	−	0.204616i	0.964736	−	0.263218i	$-0.0847839\pi$
$73$	−0.286609	−	1.74824i	−0.0335451	−	0.204616i	−0.998281	+	0.0586023i	$0.981336\pi$
$74$	10.2430	−	15.1073i	1.19072	−	1.75619i
$75$		0			0
$76$	−30.0422	−	22.8375i	−3.44608	−	2.61964i
$77$	0.0452302	+	0.0272141i	0.00515446	+	0.00310134i
$78$		0			0
$79$	−0.945647	−	0.895764i	−0.106394	−	0.100781i	0.632654	−	0.774435i	$-0.281966\pi$
$79$	−0.945647	−	0.895764i	−0.106394	−	0.100781i	−0.739048	+	0.673653i	$0.764724\pi$
$80$	3.96132	−	24.1630i	0.442889	−	2.70150i
$81$		0			0
$82$	−15.6306	+	9.40459i	−1.72611	+	1.03856i
$83$	−5.63272	+	6.63135i	−0.618271	+	0.727885i	−0.978790	−	0.204867i	$-0.934324\pi$
$83$	−5.63272	+	6.63135i	−0.618271	+	0.727885i	0.360519	+	0.932752i	$0.382600\pi$
$84$		0			0
$85$	−0.867572	−	0.401382i	−0.0941014	−	0.0435360i
$86$	−21.7250	−	25.5766i	−2.34266	−	2.75800i
$87$		0			0
$88$	0.187205	+	0.353107i	0.0199562	+	0.0376413i
$89$	5.15817	+	9.72934i	0.546765	+	1.03131i	0.990805	+	0.135301i	$0.0432001\pi$
$89$	5.15817	+	9.72934i	0.546765	+	1.03131i	−0.444040	+	0.896007i	$0.646455\pi$
$90$		0			0
$91$	3.74970	+	4.41449i	0.393075	+	0.462764i
$92$	40.0724	+	18.5395i	4.17784	+	1.93287i
$93$		0			0
$94$	−6.11377	+	7.19768i	−0.630587	+	0.742384i
$95$	−7.17229	+	4.31542i	−0.735861	+	0.442753i
$96$		0			0
$97$	−0.416944	+	2.54325i	−0.0423343	+	0.258228i	−0.999511	−	0.0312775i	$-0.990042\pi$
$97$	−0.416944	+	2.54325i	−0.0423343	+	0.258228i	0.957176	+	0.289505i	$0.0934907\pi$
$98$	−10.0549	−	9.52451i	−1.01570	−	0.962121i
$99$		0			0
$100$	16.6214	+	10.0008i	1.66214	+	1.00008i
$101$	−3.61927	−	2.75130i	−0.360131	−	0.273765i	0.409425	−	0.912344i	$-0.365729\pi$
$101$	−3.61927	−	2.75130i	−0.360131	−	0.273765i	−0.769556	+	0.638579i	$0.779522\pi$
$102$		0			0
$103$	−5.86371	+	8.64833i	−0.577769	+	0.852145i	−0.998484	−	0.0550477i	$-0.982469\pi$
$103$	−5.86371	+	8.64833i	−0.577769	+	0.852145i	0.420715	+	0.907193i	$0.361779\pi$
$104$	7.09474	+	43.2760i	0.695697	+	4.24356i
$105$		0			0
$106$	−4.43013	−	0.975145i	−0.430292	−	0.0947144i
$107$	−0.845630	−	2.12237i	−0.0817502	−	0.205177i	0.882420	−	0.470463i	$-0.155913\pi$
$107$	−0.845630	−	2.12237i	−0.0817502	−	0.205177i	−0.964170	+	0.265286i	$0.914534\pi$
$108$		0			0
$109$	−0.295752	+	5.45483i	−0.0283279	+	0.522478i	0.949591	+	0.313492i	$0.101499\pi$
$109$	−0.295752	+	5.45483i	−0.0283279	+	0.522478i	−0.977919	+	0.208986i	$0.932984\pi$
$110$	0.133594	−	0.0145292i	0.0127377	−	0.00138531i
$111$		0			0
$112$	7.22165	+	26.0100i	0.682382	+	2.45772i
$113$	4.54970	−	1.00146i	0.427999	−	0.0942098i	0.00425359	−	0.999991i	$-0.498646\pi$
$113$	4.54970	−	1.00146i	0.427999	−	0.0942098i	0.423746	+	0.905781i	$0.360715\pi$
$114$		0			0
$115$	7.11013	−	6.73507i	0.663023	−	0.628049i
$116$	0.273079	−	0.515082i	0.0253548	−	0.0478242i
$117$		0			0
$118$	−1.71378	+	21.4895i	−0.157766	+	1.97827i
$119$	1.05385			0.0966066
$120$		0			0
$121$	7.98497	−	7.56377i	0.725906	−	0.687615i
$122$	−5.35866	−	7.90343i	−0.485150	−	0.715543i
$123$		0			0
$124$	−12.1813	−	43.8730i	−1.09391	−	3.93991i
$125$	8.61407	−	6.54825i	0.770466	−	0.585693i
$126$		0			0
$127$	0.269602	−	4.97252i	0.0239233	−	0.441240i	−0.961894	−	0.273421i	$-0.911845\pi$
$127$	0.269602	−	4.97252i	0.0239233	−	0.441240i	0.985818	−	0.167819i	$-0.0536724\pi$
$128$	−20.4638	+	73.7039i	−1.80876	+	6.51456i
$129$		0			0
$130$	14.4005	+	3.16980i	1.26301	+	0.278010i
$131$	0.681745	+	12.5741i	0.0595644	+	1.09860i	0.863652	+	0.504089i	$0.168172\pi$
$131$	0.681745	+	12.5741i	0.0595644	+	1.09860i	−0.804087	+	0.594511i	$0.797346\pi$
$132$		0			0
$133$	5.17862	−	7.63789i	0.449043	−	0.662289i
$134$	−1.51896	+	3.81229i	−0.131218	+	0.329332i
$135$		0			0
$136$	6.83694	+	4.11365i	0.586263	+	0.352743i
$137$	5.76708	−	1.94316i	0.492715	−	0.166015i	−0.0619658	−	0.998078i	$-0.519737\pi$
$137$	5.76708	−	1.94316i	0.492715	−	0.166015i	0.554681	+	0.832063i	$0.312840\pi$
$138$		0			0
$139$	1.97846	−	12.0681i	0.167811	−	1.02360i	−0.759828	−	0.650124i	$-0.774717\pi$
$139$	1.97846	−	12.0681i	0.167811	−	1.02360i	0.927639	−	0.373478i	$-0.121835\pi$
$140$	10.9447	+	1.19030i	0.924993	+	0.100599i
$141$		0			0
$142$	−3.12384	+	3.67767i	−0.262147	+	0.308623i
$143$	−0.134360	+	0.0621614i	−0.0112357	+	0.00519820i
$144$		0			0
$145$	−0.0837160	−	0.0985581i	−0.00695224	−	0.00818481i
$146$	4.71179	+	1.58759i	0.389951	+	0.131390i
$147$		0			0
$148$	17.9025	+	33.7676i	1.47157	+	2.77568i
$149$	−3.24907	−	1.09474i	−0.266174	−	0.0896845i	0.183050	−	0.983104i	$-0.441403\pi$
$149$	−3.24907	−	1.09474i	−0.266174	−	0.0896845i	−0.449224	+	0.893419i	$0.648300\pi$
$150$		0			0
$151$	−12.2024	−	5.64543i	−0.993017	−	0.459419i	−0.145025	−	0.989428i	$-0.546326\pi$
$151$	−12.2024	−	5.64543i	−0.993017	−	0.459419i	−0.847992	+	0.530009i	$0.822188\pi$
$152$	63.4107	−	29.3369i	5.14328	−	2.37954i
$153$		0			0
$154$	−0.126942	+	0.0763785i	−0.0102293	+	0.00615475i
$155$	−10.0404	−	1.09196i	−0.806464	−	0.0877083i
$156$		0			0
$157$	7.28190	+	6.89778i	0.581159	+	0.550503i	0.920792	−	0.390055i	$-0.127544\pi$
$157$	7.28190	+	6.89778i	0.581159	+	0.550503i	−0.339632	+	0.940558i	$0.610303\pi$
$158$	3.46434	−	1.16727i	0.275608	−	0.0928633i
$159$		0			0
$160$	32.1251	+	24.4209i	2.53971	+	1.93064i
$161$	−3.99636	+	10.0301i	−0.314957	+	0.790483i
$162$		0			0
$163$	2.50915	+	15.3051i	0.196532	+	1.19879i	0.882200	+	0.470876i	$0.156062\pi$
$163$	2.50915	+	15.3051i	0.196532	+	1.19879i	−0.685668	+	0.727915i	$0.740490\pi$
$164$	−2.06797	−	38.1415i	−0.161481	−	2.97835i
$165$		0			0
$166$	−9.03847	−	22.6848i	−0.701521	−	1.76069i
$167$	−0.608168	+	2.19042i	−0.0470615	+	0.169500i	−0.983346	−	0.181741i	$-0.941827\pi$
$167$	−0.608168	+	2.19042i	−0.0470615	+	0.169500i	0.936285	+	0.351242i	$0.114240\pi$
$168$		0			0
$169$	−3.22520	+	0.350762i	−0.248093	+	0.0269817i
$170$	2.13581	−	1.62360i	0.163809	−	0.124525i
$171$		0			0
$172$	68.6262	−	15.1058i	5.23270	−	1.15180i
$173$	−2.13983	−	3.15601i	−0.162688	−	0.239947i	0.737604	−	0.675234i	$-0.235957\pi$
$173$	−2.13983	−	3.15601i	−0.162688	−	0.239947i	−0.900292	+	0.435287i	$0.856647\pi$
$174$		0			0
$175$	−2.22189	+	4.19093i	−0.167959	+	0.316805i
$176$	−0.689953			−0.0520072
$177$		0			0
$178$	−30.9063			−2.31653
$179$	−1.46289	+	2.75930i	−0.109341	+	0.206239i	−0.932144	−	0.362087i	$-0.882064\pi$
$179$	−1.46289	+	2.75930i	−0.109341	+	0.206239i	0.822803	+	0.568327i	$0.192409\pi$
$180$		0			0
$181$	−4.67958	−	6.90186i	−0.347830	−	0.513011i	0.613024	−	0.790064i	$-0.289953\pi$
$181$	−4.67958	−	6.90186i	−0.347830	−	0.513011i	−0.960855	+	0.277053i	$0.910642\pi$
$182$	−15.8758	+	3.49453i	−1.17679	+	0.259032i
$183$		0			0
$184$	−65.0785	+	49.4714i	−4.79765	+	3.64708i
$185$	8.42783	−	0.916582i	0.619627	−	0.0673885i
$186$		0			0
$187$	−0.00720614	+	0.0259542i	−0.000526965	+	0.00189796i
$188$	−7.31944	−	18.3704i	−0.533825	−	1.33980i
$189$		0			0
$190$	−1.27185	−	23.4579i	−0.0922696	−	1.70181i
$191$	2.01000	+	12.2604i	0.145438	+	0.887134i	0.954238	+	0.299049i	$0.0966695\pi$
$191$	2.01000	+	12.2604i	0.145438	+	0.887134i	−0.808800	+	0.588084i	$0.799882\pi$
$192$		0			0
$193$	3.15003	−	7.90598i	0.226744	−	0.569085i	−0.770954	−	0.636890i	$-0.780220\pi$
$193$	3.15003	−	7.90598i	0.226744	−	0.569085i	0.997699	+	0.0678054i	$0.0215997\pi$
$194$	−5.75822	−	4.37728i	−0.413416	−	0.314271i
$195$		0			0
$196$	27.4829	−	9.26006i	1.96306	−	0.661433i
$197$	−11.5263	−	10.9183i	−0.821215	−	0.777896i	0.156535	−	0.987672i	$-0.449968\pi$
$197$	−11.5263	−	10.9183i	−0.821215	−	0.777896i	−0.977749	+	0.209776i	$0.932726\pi$
$198$		0			0
$199$	−2.51155	−	0.273148i	−0.178039	−	0.0193629i	0.0186650	−	0.999826i	$-0.494058\pi$
$199$	−2.51155	−	0.273148i	−0.178039	−	0.0193629i	−0.196704	+	0.980463i	$0.563024\pi$
$200$	−30.7737	+	18.5159i	−2.17603	+	1.30927i
$201$		0			0
$202$	11.5802	−	5.35758i	0.814781	−	0.376958i
$203$	0.129385	+	0.0598600i	0.00908107	+	0.00420135i
$204$		0			0
$205$	−8.02907	−	2.70531i	−0.560775	−	0.188947i
$206$	−13.7362	−	25.9092i	−0.957046	−	1.80518i
$207$		0			0
$208$	−71.7434	−	24.1732i	−4.97451	−	1.67611i
$209$	0.152694	+	0.179766i	0.0105621	+	0.0124346i
$210$		0			0
$211$	18.9138	−	8.75045i	1.30208	−	0.602406i	0.358493	−	0.933533i	$-0.383291\pi$
$211$	18.9138	−	8.75045i	1.30208	−	0.602406i	0.943586	+	0.331127i	$0.107429\pi$
$212$	6.14926	−	7.23946i	0.422333	−	0.497208i
$213$		0			0
$214$	6.37441	+	0.693259i	0.435746	+	0.0473902i
$215$	2.52160	−	15.3811i	0.171971	−	1.04898i
$216$		0			0
$217$	10.5514	−	3.55519i	0.716277	−	0.241342i
$218$	−13.1372	−	7.90440i	−0.889765	−	0.535354i
$219$		0			0
$220$	−0.104153	+	0.261405i	−0.00702201	+	0.0176239i
$221$	−1.65865	+	2.44632i	−0.111573	+	0.164557i
$222$		0			0
$223$	−0.595157	−	10.9770i	−0.0398546	−	0.735076i	−0.948359	−	0.317200i	$-0.897257\pi$
$223$	−0.595157	−	10.9770i	−0.0398546	−	0.735076i	0.908504	−	0.417876i	$-0.137225\pi$
$224$	−43.4474	−	9.56350i	−2.90295	−	0.638988i
$225$		0			0
$226$	−3.49786	+	12.5982i	−0.232674	+	0.838018i
$227$	1.02311	−	18.8702i	0.0679065	−	1.25246i	−0.743803	−	0.668399i	$-0.766980\pi$
$227$	1.02311	−	18.8702i	0.0679065	−	1.25246i	0.811709	−	0.584062i	$-0.198537\pi$
$228$		0			0
$229$	16.9706	−	12.9007i	1.12145	−	0.852505i	0.131139	−	0.991364i	$-0.458136\pi$
$229$	16.9706	−	12.9007i	1.12145	−	0.852505i	0.990312	+	0.138859i	$0.0443434\pi$
$230$	7.35343	+	26.4847i	0.484871	+	1.74635i
$231$		0			0
$232$	0.605736	+	0.893393i	0.0397685	+	0.0586541i
$233$	12.7574	−	12.0844i	0.835764	−	0.791678i	−0.144472	−	0.989509i	$-0.546148\pi$
$233$	12.7574	−	12.0844i	0.835764	−	0.791678i	0.980236	+	0.197831i	$0.0633897\pi$
$234$		0			0
$235$	−4.38627			−0.286129
$236$	−38.0755	−	24.2481i	−2.47850	−	1.57842i
$237$		0			0
$238$	−1.38542	+	2.61318i	−0.0898034	+	0.169387i
$239$	7.63987	−	7.23686i	0.494182	−	0.468114i	−0.399553	−	0.916710i	$-0.630835\pi$
$239$	7.63987	−	7.23686i	0.494182	−	0.468114i	0.893734	+	0.448596i	$0.148076\pi$
$240$		0			0
$241$	7.89970	−	1.73886i	0.508865	−	0.112010i	0.0468854	−	0.998900i	$-0.485070\pi$
$241$	7.89970	−	1.73886i	0.508865	−	0.112010i	0.461979	+	0.886891i	$0.347139\pi$
$242$	8.25821	+	29.7434i	0.530858	+	1.91198i
$243$		0			0
$244$	19.8776	−	2.16182i	1.27253	−	0.138396i
$245$	0.348260	−	6.42328i	0.0222495	−	0.410368i
$246$		0			0
$247$	9.57935	+	24.0423i	0.609519	+	1.52978i
$248$	82.3305	+	18.1223i	5.22799	+	1.15077i
$249$		0			0
$250$	4.91305	+	29.9683i	0.310729	+	1.89536i
$251$	−13.1610	+	19.4110i	−0.830713	+	1.22521i	0.141226	+	0.989977i	$0.454895\pi$
$251$	−13.1610	+	19.4110i	−0.830713	+	1.22521i	−0.971939	+	0.235232i	$0.924415\pi$
$252$		0			0
$253$	−0.219694	−	0.167007i	−0.0138120	−	0.0104996i
$254$	11.9756	+	7.20551i	0.751419	+	0.452114i
$255$		0			0
$256$	−84.2526	−	79.8083i	−5.26579	−	4.98802i
$257$	1.77496	−	10.8268i	0.110719	−	0.675355i	−0.871895	−	0.489693i	$-0.837109\pi$
$257$	1.77496	−	10.8268i	0.110719	−	0.675355i	0.982614	−	0.185662i	$-0.0594428\pi$
$258$		0			0
$259$	−8.00820	+	4.81837i	−0.497605	+	0.299399i
$260$	−19.9887	+	23.5325i	−1.23965	+	1.45943i
$261$		0			0
$262$	−32.0754	−	14.8397i	−1.98162	−	0.916797i
$263$	11.0285	+	12.9838i	0.680049	+	0.800615i	0.988596	−	0.150594i	$-0.0481185\pi$
$263$	11.0285	+	12.9838i	0.680049	+	0.800615i	−0.308547	+	0.951209i	$0.599843\pi$
$264$		0			0
$265$	−0.986881	−	1.86146i	−0.0606236	−	0.114348i
$266$	12.1313	+	22.8821i	0.743818	+	1.40299i
$267$		0			0
$268$	−5.56306	−	6.54934i	−0.339818	−	0.400065i
$269$	−13.5294	−	6.25939i	−0.824905	−	0.381642i	−0.0384279	−	0.999261i	$-0.512235\pi$
$269$	−13.5294	−	6.25939i	−0.824905	−	0.381642i	−0.786477	+	0.617620i	$0.788097\pi$
$270$		0			0
$271$	0.607704	−	0.715445i	0.0369154	−	0.0434602i	−0.743395	−	0.668853i	$-0.766785\pi$
$271$	0.607704	−	0.715445i	0.0369154	−	0.0434602i	0.780310	+	0.625393i	$0.215061\pi$
$272$	−11.8029	+	7.10156i	−0.715655	+	0.430595i
$273$		0			0
$274$	−2.76321	+	16.8548i	−0.166931	+	1.01824i
$275$	−0.0880208	−	0.0833777i	−0.00530785	−	0.00502787i
$276$		0			0
$277$	−26.6047	−	16.0075i	−1.59852	−	0.961798i	−0.985088	−	0.172050i	$-0.944961\pi$
$277$	−26.6047	−	16.0075i	−1.59852	−	0.961798i	−0.613432	−	0.789747i	$-0.710212\pi$
$278$	27.3236	+	20.7709i	1.63876	+	1.24576i
$279$		0			0
$280$	−11.4387	+	16.8708i	−0.683590	+	1.00822i
$281$	−2.78993	−	17.0178i	−0.166433	−	1.01520i	−0.929485	−	0.368860i	$-0.879748\pi$
$281$	−2.78993	−	17.0178i	−0.166433	−	1.01520i	0.763052	−	0.646337i	$-0.223700\pi$
$282$		0			0
$283$	10.7983	+	2.37690i	0.641895	+	0.141292i	0.523978	−	0.851732i	$-0.324447\pi$
$283$	10.7983	+	2.37690i	0.641895	+	0.141292i	0.117917	+	0.993023i	$0.462378\pi$
$284$	−3.73988	−	9.38640i	−0.221921	−	0.556980i
$285$		0			0
$286$	0.0224943	−	0.414883i	0.00133012	−	0.0245325i
$287$	9.28581	−	1.00989i	0.548124	−	0.0596121i
$288$		0			0
$289$	−4.40411	−	15.8622i	−0.259066	−	0.933070i
$290$	0.354444	−	0.0780190i	0.0208137	−	0.00458143i
$291$		0			0
$292$	−7.55856	+	7.15985i	−0.442332	+	0.418999i
$293$	11.3369	−	21.3836i	0.662307	−	1.24924i	−0.293699	−	0.955898i	$-0.594886\pi$
$293$	11.3369	−	21.3836i	0.662307	−	1.24924i	0.956006	−	0.293346i	$-0.0947687\pi$
$294$		0			0
$295$	−8.12248	+	5.85492i	−0.472909	+	0.340887i
$296$	−70.7619			−4.11295
$297$		0			0
$298$	6.98587	−	6.61736i	0.404680	−	0.383334i
$299$	−16.9932	−	25.0630i	−0.982740	−	1.44943i
$300$		0			0
$301$	4.59698	+	16.5568i	0.264965	+	0.954319i
$302$	30.0402	−	22.8360i	1.72862	−	1.31406i
$303$		0			0
$304$	−6.53003	+	120.439i	−0.374523	+	6.90767i
$305$	1.18650	−	4.27339i	0.0679389	−	0.244694i
$306$		0			0
$307$	−13.2695	−	2.92085i	−0.757333	−	0.166702i	−0.180513	−	0.983573i	$-0.557776\pi$
$307$	−13.2695	−	2.92085i	−0.757333	−	0.166702i	−0.576820	+	0.816871i	$0.695707\pi$
$308$	−0.0167948	−	0.309762i	−0.000956974	−	0.0176503i
$309$		0			0
$310$	15.9070	−	23.4611i	0.903458	−	1.33250i
$311$	−2.89840	+	7.27444i	−0.164353	+	0.412496i	−0.987969	−	0.154653i	$-0.950574\pi$
$311$	−2.89840	+	7.27444i	−0.164353	+	0.412496i	0.823616	+	0.567148i	$0.191953\pi$
$312$		0			0
$313$	−9.41911	−	5.66729i	−0.532400	−	0.320334i	0.223843	−	0.974625i	$-0.428140\pi$
$313$	−9.41911	−	5.66729i	−0.532400	−	0.320334i	−0.756243	+	0.654291i	$0.772967\pi$
$314$	−26.6770	+	8.98853i	−1.50547	+	0.507252i
$315$		0			0
$316$	−1.23843	+	7.55407i	−0.0696670	+	0.424950i
$317$	17.8894	+	1.94559i	1.00477	+	0.109275i	0.595683	−	0.803220i	$-0.296881\pi$
$317$	17.8894	+	1.94559i	1.00477	+	0.109275i	0.409088	+	0.912495i	$0.365847\pi$
$318$		0			0
$319$	−0.00235895	+	0.00277717i	−0.000132076	+	0.000155492i
$320$	−58.3426	+	26.9921i	−3.26145	+	1.50891i
$321$		0			0
$322$	−19.6174	−	23.0954i	−1.09323	−	1.28705i
$323$	4.46240	+	1.50356i	0.248295	+	0.0836602i
$324$		0			0
$325$	−6.23145	−	11.7538i	−0.345659	−	0.651981i
$326$	−41.2498	−	13.8987i	−2.28462	−	0.769777i
$327$		0			0
$328$	64.1843	+	29.6948i	3.54399	+	1.63962i
$329$	4.38869	−	2.03042i	0.241956	−	0.111941i
$330$		0			0
$331$	−4.13584	+	2.48845i	−0.227326	+	0.136778i	−0.624661	−	0.780896i	$-0.714763\pi$
$331$	−4.13584	+	2.48845i	−0.227326	+	0.136778i	0.397335	+	0.917674i	$0.369935\pi$
$332$	50.8331	+	5.52843i	2.78983	+	0.303412i
$333$		0			0
$334$	−4.63195	−	4.38762i	−0.253449	−	0.240080i
$335$	−1.80626	+	0.608600i	−0.0986866	+	0.0332514i
$336$		0			0
$337$	21.4554	+	16.3100i	1.16875	+	0.888461i	0.995344	−	0.0963888i	$-0.0307292\pi$
$337$	21.4554	+	16.3100i	1.16875	+	0.888461i	0.173407	+	0.984850i	$0.444522\pi$
$338$	3.37016	−	8.45847i	0.183313	−	0.460080i
$339$		0			0
$340$	0.908864	+	5.54382i	0.0492900	+	0.300656i
$341$	0.0154072	+	0.284169i	0.000834347	+	0.0153886i
$342$		0			0
$343$	6.34836	+	15.9332i	0.342779	+	0.860311i
$344$	−34.8053	+	125.357i	−1.87658	+	6.75882i
$345$		0			0
$346$	10.6388	−	1.15704i	0.571948	−	0.0622031i
$347$	−17.1241	+	13.0174i	−0.919270	+	0.698811i	−0.953752	−	0.300595i	$-0.902815\pi$
$347$	−17.1241	+	13.0174i	−0.919270	+	0.698811i	0.0344821	+	0.999405i	$0.489022\pi$
$348$		0			0
$349$	1.04890	−	0.230881i	0.0561466	−	0.0123588i	−0.186808	−	0.982396i	$-0.559814\pi$
$349$	1.04890	−	0.230881i	0.0561466	−	0.0123588i	0.242955	+	0.970038i	$0.421883\pi$
$350$	−7.47107	−	11.0190i	−0.399345	−	0.588990i
$351$		0			0
$352$	0.532618	−	1.00462i	0.0283886	−	0.0535466i
$353$	12.2525			0.652134			0.326067	−	0.945347i	$-0.394277\pi$
$353$	12.2525			0.652134			0.326067	+	0.945347i	$0.394277\pi$
$354$		0			0
$355$	−2.24117			−0.118949
$356$	30.3139	−	57.1780i	1.60663	−	3.03043i
$357$		0			0
$358$	−4.91892	−	7.25487i	−0.259973	−	0.383432i
$359$	33.4112	−	7.35436i	1.76338	−	0.388148i	0.789236	−	0.614091i	$-0.210477\pi$
$359$	33.4112	−	7.35436i	1.76338	−	0.388148i	0.974141	+	0.225942i	$0.0725460\pi$
$360$		0			0
$361$	17.6996	−	13.4549i	0.931555	−	0.708150i
$362$	23.2660	−	2.53033i	1.22284	−	0.132991i
$363$		0			0
$364$	9.10644	−	32.7984i	0.477307	−	1.71910i
$365$	0.854772	+	2.14532i	0.0447408	+	0.112291i
$366$		0			0
$367$	−0.463399	−	8.54690i	−0.0241893	−	0.446145i	−0.985392	−	0.170302i	$-0.945526\pi$
$367$	−0.463399	−	8.54690i	−0.0241893	−	0.446145i	0.961203	−	0.275843i	$-0.0889570\pi$
$368$	−22.8313	−	139.265i	−1.19016	−	7.25967i
$369$		0			0
$370$	−8.80663	+	22.1030i	−0.457835	+	1.14908i
$371$	1.84910	+	1.40565i	0.0960007	+	0.0729778i
$372$		0			0
$373$	−25.3490	+	8.54108i	−1.31252	+	0.442240i	−0.886607	−	0.462523i	$-0.846944\pi$
$373$	−25.3490	+	8.54108i	−1.31252	+	0.442240i	−0.425915	+	0.904763i	$0.640048\pi$
$374$	−0.0548837	−	0.0519886i	−0.00283797	−	0.00268827i
$375$		0			0
$376$	36.3976	+	3.95847i	1.87706	+	0.204143i
$377$	−0.342591	+	0.206130i	−0.0176444	+	0.0106163i
$378$		0			0
$379$	−16.0655	+	7.43269i	−0.825229	+	0.381792i	−0.786601	−	0.617462i	$-0.788161\pi$
$379$	−16.0655	+	7.43269i	−0.825229	+	0.381792i	−0.0386286	+	0.999254i	$0.512299\pi$
$380$	44.6455	+	20.6552i	2.29026	+	1.05959i
$381$		0			0
$382$	−33.0439	−	11.1338i	−1.69067	−	0.569654i
$383$	7.71987	+	14.5612i	0.394467	+	0.744043i	0.998603	−	0.0528376i	$-0.0168266\pi$
$383$	7.71987	+	14.5612i	0.394467	+	0.744043i	−0.604136	+	0.796881i	$0.706482\pi$
$384$		0			0
$385$	−0.0652073	−	0.0219709i	−0.00332327	−	0.00111974i
$386$	15.4629	+	18.2043i	0.787041	+	0.926576i
$387$		0			0
$388$	13.7460	−	6.35957i	0.697847	−	0.322858i
$389$	−5.53137	+	6.51203i	−0.280452	+	0.330173i	−0.884294	−	0.466931i	$-0.845360\pi$
$389$	−5.53137	+	6.51203i	−0.280452	+	0.330173i	0.603842	+	0.797104i	$0.293636\pi$
$390$		0			0
$391$	−5.47722	−	0.595683i	−0.276995	−	0.0301250i
$392$	−8.68669	+	52.9865i	−0.438744	+	2.67622i
$393$		0			0
$394$	42.2262	−	14.2277i	2.12733	−	0.716779i
$395$	1.45489	+	0.875378i	0.0732034	+	0.0440450i
$396$		0			0
$397$	1.72865	−	4.33858i	0.0867584	−	0.217747i	−0.879196	−	0.476461i	$-0.841919\pi$
$397$	1.72865	−	4.33858i	0.0867584	−	0.217747i	0.965954	+	0.258714i	$0.0832986\pi$
$398$	3.97906	−	5.86867i	0.199452	−	0.294170i
$399$		0			0
$400$	−3.35666	−	61.9099i	−0.167833	−	3.09550i
$401$	−28.3915	−	6.24945i	−1.41781	−	0.312083i	−0.561040	−	0.827789i	$-0.689599\pi$
$401$	−28.3915	−	6.24945i	−1.41781	−	0.312083i	−0.856765	+	0.515706i	$0.827530\pi$
$402$		0			0
$403$	−8.35405	+	30.0886i	−0.416145	+	1.49882i
$404$	−1.44648	+	26.6788i	−0.0719651	+	1.32732i
$405$		0			0
$406$	−0.318524	+	0.242136i	−0.0158081	+	0.0120170i
$407$	−0.0639071	−	0.230173i	−0.00316776	−	0.0114092i
$408$		0			0
$409$	−10.0222	−	14.7816i	−0.495564	−	0.730903i	0.494858	−	0.868974i	$-0.335220\pi$
$409$	−10.0222	−	14.7816i	−0.495564	−	0.730903i	−0.990422	+	0.138071i	$0.955910\pi$
$410$	17.2634	−	16.3528i	0.852579	−	0.807605i
$411$		0			0
$412$	61.4060			3.02525
$413$	5.41670	−	9.61809i	0.266538	−	0.473275i
$414$		0			0
$415$	5.31258	−	10.0206i	0.260784	−	0.491892i
$416$	90.5812	−	85.8030i	4.44111	−	4.20684i
$417$		0			0
$418$	−0.646490	+	0.142303i	−0.0316209	+	0.00696028i
$419$	−7.65622	−	27.5752i	−0.374031	−	1.34714i	−0.876025	−	0.482266i	$-0.839814\pi$
$419$	−7.65622	−	27.5752i	−0.374031	−	1.34714i	0.501994	−	0.864871i	$-0.332600\pi$
$420$		0			0
$421$	−18.6848	+	2.03210i	−0.910642	+	0.0990383i	−0.551433	−	0.834219i	$-0.685919\pi$
$421$	−18.6848	+	2.03210i	−0.910642	+	0.0990383i	−0.359209	+	0.933257i	$0.616953\pi$
$422$	−3.16652	+	58.4030i	−0.154144	+	2.84301i
$423$		0			0
$424$	6.50930	+	16.3371i	0.316120	+	0.793401i
$425$	−2.36394	−	0.520343i	−0.114668	−	0.0252404i
$426$		0			0
$427$	0.791017	+	4.82499i	0.0382800	+	0.233498i
$428$	−7.53477	+	11.1130i	−0.364207	+	0.537165i
$429$		0			0
$430$	34.8246	+	26.4730i	1.67939	+	1.27664i
$431$	29.0565	+	17.4827i	1.39960	+	0.842113i	0.997303	−	0.0733948i	$-0.0233833\pi$
$431$	29.0565	+	17.4827i	1.39960	+	0.842113i	0.402300	+	0.915508i	$0.368211\pi$
$432$		0			0
$433$	10.9578	+	10.3798i	0.526597	+	0.498819i	0.904177	−	0.427158i	$-0.140485\pi$
$433$	10.9578	+	10.3798i	0.526597	+	0.498819i	−0.377580	+	0.925977i	$0.623244\pi$
$434$	−5.05555	+	30.8375i	−0.242674	+	1.48025i
$435$		0			0
$436$	27.5088	−	16.5515i	1.31743	−	0.792674i
$437$	−31.2322	+	36.7694i	−1.49404	+	1.75892i
$438$		0			0
$439$	−9.94298	−	4.60011i	−0.474552	−	0.219551i	0.168009	−	0.985785i	$-0.446266\pi$
$439$	−9.94298	−	4.60011i	−0.474552	−	0.219551i	−0.642561	+	0.766234i	$0.722128\pi$
$440$	−0.337275	−	0.397070i	−0.0160789	−	0.0189296i
$441$		0			0
$442$	−3.88550	−	7.32884i	−0.184815	−	0.348597i
$443$	−10.2733	−	19.3775i	−0.488100	−	0.920654i	−0.998167	−	0.0605196i	$-0.980724\pi$
$443$	−10.2733	−	19.3775i	−0.488100	−	0.920654i	0.510067	−	0.860135i	$-0.329621\pi$
$444$		0			0
$445$	−9.29311	−	10.9407i	−0.440536	−	0.518639i
$446$	28.0015	+	12.9549i	1.32591	+	0.613431i
$447$		0			0
$448$	45.8800	−	54.0141i	2.16763	−	2.55193i
$449$	18.9443	−	11.3984i	0.894039	−	0.537925i	0.00718437	−	0.999974i	$-0.497713\pi$
$449$	18.9443	−	11.3984i	0.894039	−	0.537925i	0.886854	+	0.462049i	$0.152886\pi$
$450$		0			0
$451$	−0.0386239	+	0.235595i	−0.00181873	+	0.0110938i
$452$	−19.8763	−	18.8278i	−0.934903	−	0.885587i
$453$		0			0
$454$	45.4464	+	27.3442i	2.13291	+	1.28333i
$455$	−6.01068	−	4.56920i	−0.281785	−	0.214207i
$456$		0			0
$457$	7.34530	−	10.8335i	0.343599	−	0.506770i	−0.616151	−	0.787628i	$-0.711309\pi$
$457$	7.34530	−	10.8335i	0.343599	−	0.506770i	0.959749	+	0.280858i	$0.0906191\pi$
$458$	9.67924	+	59.0407i	0.452281	+	2.75879i
$459$		0			0
$460$	−56.2102	−	12.3728i	−2.62081	−	0.576885i
$461$	9.12304	+	22.8971i	0.424903	+	1.06642i	0.973163	+	0.230117i	$0.0739110\pi$
$461$	9.12304	+	22.8971i	0.424903	+	1.06642i	−0.548260	+	0.836308i	$0.684710\pi$
$462$		0			0
$463$	−0.829924	+	15.3070i	−0.0385698	+	0.711379i	0.913750	+	0.406277i	$0.133173\pi$
$463$	−0.829924	+	15.3070i	−0.0385698	+	0.711379i	−0.952320	+	0.305102i	$0.901310\pi$
$464$	−1.85246	+	0.201467i	−0.0859982	+	0.00935287i
$465$		0			0
$466$	13.1939	+	47.5203i	0.611197	+	2.20133i
$467$	−30.0830	+	6.62178i	−1.39208	+	0.306419i	−0.846834	−	0.531858i	$-0.821494\pi$
$467$	−30.0830	+	6.62178i	−1.39208	+	0.306419i	−0.545244	+	0.838277i	$0.683563\pi$
$468$		0			0
$469$	1.52554	−	1.44506i	0.0704427	−	0.0667269i
$470$	5.76629	−	10.8764i	0.265979	−	0.501690i
$471$		0			0
$472$	72.6848	−	41.2542i	3.34559	−	1.89888i
$473$	−0.439193			−0.0201941
$474$		0			0
$475$	−15.3876	+	14.5759i	−0.706032	+	0.668789i
$476$	−3.47563	−	5.12617i	−0.159305	−	0.234957i
$477$		0			0
$478$	7.90129	+	28.4579i	0.361397	+	1.30163i
$479$	−28.9241	+	21.9876i	−1.32158	+	1.00464i	−0.323280	+	0.946303i	$0.604786\pi$
$479$	−28.9241	+	21.9876i	−1.32158	+	1.00464i	−0.998297	+	0.0583338i	$0.981421\pi$
$480$		0			0
$481$	1.41906	−	26.1731i	0.0647037	−	1.19339i
$482$	−6.07339	+	21.8744i	−0.276635	+	0.996351i
$483$		0			0
$484$	−63.1264	−	13.8952i	−2.86938	−	0.631598i
$485$	−0.181879	−	3.35457i	−0.00825872	−	0.152323i
$486$		0			0
$487$	−3.45577	+	5.09688i	−0.156596	+	0.230962i	−0.897891	−	0.440217i	$-0.854901\pi$
$487$	−3.45577	+	5.09688i	−0.156596	+	0.230962i	0.741295	+	0.671179i	$0.234212\pi$
$488$	−13.7023	+	34.3901i	−0.620273	+	1.55677i
$489$		0			0
$490$	15.4696	+	9.30775i	0.698845	+	0.420481i
$491$	−27.8230	+	9.37466i	−1.25564	+	0.423073i	−0.866995	−	0.498317i	$-0.833952\pi$
$491$	−27.8230	+	9.37466i	−1.25564	+	0.423073i	−0.388640	+	0.921390i	$0.627055\pi$
$492$		0			0
$493$	−0.0117692	+	0.0717886i	−0.000530056	+	0.00323320i
$494$	−72.2097	−	7.85327i	−3.24887	−	0.353335i
$495$		0			0
$496$	−94.2159	+	110.920i	−4.23042	+	4.98044i
$497$	2.24241	−	1.03745i	0.100586	−	0.0465360i
$498$		0			0
$499$	28.2428	+	33.2499i	1.26432	+	1.48847i	0.796488	+	0.604655i	$0.206689\pi$
$499$	28.2428	+	33.2499i	1.26432	+	1.48847i	0.467832	+	0.883817i	$0.345035\pi$
$500$	−60.2615	−	20.3045i	−2.69497	−	0.908043i
$501$		0			0
$502$	−30.8306	−	58.1526i	−1.37604	−	2.59548i
$503$	2.25892	+	0.761119i	0.100720	+	0.0339366i	0.369211	−	0.929346i	$-0.379628\pi$
$503$	2.25892	+	0.761119i	0.100720	+	0.0339366i	−0.268490	+	0.963282i	$0.586525\pi$
$504$		0			0
$505$	5.37857	+	2.48839i	0.239343	+	0.110732i
$506$	0.702931	−	0.325211i	0.0312491	−	0.0144574i
$507$		0			0
$508$	−25.0766	+	15.0881i	−1.11259	+	0.669425i
$509$	−38.3004	−	4.16542i	−1.69764	−	0.184629i	−0.792535	−	0.609827i	$-0.791239\pi$
$509$	−38.3004	−	4.16542i	−1.69764	−	0.184629i	−0.905101	+	0.425198i	$0.860205\pi$
$510$		0			0
$511$	−1.84832	−	1.75082i	−0.0817649	−	0.0774519i
$512$	163.681	−	55.1504i	7.23373	−	2.43733i
$513$		0			0
$514$	24.5131	+	18.6344i	1.08123	+	0.821927i
$515$	5.04145	−	12.6531i	0.222153	−	0.557562i
$516$		0			0
$517$	0.0199956	+	0.121968i	0.000879408	+	0.00536415i
$518$	−1.42008	−	26.1918i	−0.0623947	−	1.15080i
$519$		0			0
$520$	−21.1591	−	53.1053i	−0.927887	−	2.32882i
$521$	1.06799	−	3.84657i	0.0467897	−	0.168521i	−0.936464	−	0.350764i	$-0.885922\pi$
$521$	1.06799	−	3.84657i	0.0467897	−	0.168521i	0.983254	+	0.182243i	$0.0583357\pi$
$522$		0			0
$523$	5.33882	−	0.580632i	0.233450	−	0.0253893i	0.00935399	−	0.999956i	$-0.497022\pi$
$523$	5.33882	−	0.580632i	0.233450	−	0.0253893i	0.224096	+	0.974567i	$0.428057\pi$
$524$	58.9145	−	44.7856i	2.57369	−	1.95647i
$525$		0			0
$526$	−46.6936	+	10.2780i	−2.03594	+	0.448143i
$527$	3.18847	+	4.70264i	0.138892	+	0.204850i
$528$		0			0
$529$	15.6664	−	29.5500i	0.681149	−	1.28478i
$530$	5.91312			0.256850
$531$		0			0
$532$	−54.2315			−2.35123
$533$	−12.2705	+	23.1447i	−0.531496	+	1.00251i
$534$		0			0
$535$	1.67129	+	2.46496i	0.0722560	+	0.106570i
$536$	15.5377	−	3.42011i	0.671128	−	0.147726i
$537$		0			0
$538$	33.3072	−	25.3194i	1.43597	−	1.09160i
$539$	−0.180198	+	0.0195977i	−0.00776169	+	0.000844135i
$540$		0			0
$541$	−2.62518	+	9.45503i	−0.112865	+	0.406503i	−0.998302	−	0.0582569i	$-0.981446\pi$
$541$	−2.62518	+	9.45503i	−0.112865	+	0.406503i	0.885436	+	0.464760i	$0.153860\pi$
$542$	0.975145	+	2.44743i	0.0418861	+	0.105126i
$543$		0			0
$544$	−1.22902	−	22.6680i	−0.0526940	−	0.971883i
$545$	−1.15206	−	7.02725i	−0.0493488	−	0.301015i
$546$		0			0
$547$	−4.68519	+	11.7589i	−0.200324	+	0.502776i	−0.994479	−	0.104940i	$-0.966535\pi$
$547$	−4.68519	+	11.7589i	−0.200324	+	0.502776i	0.794154	+	0.607716i	$0.207914\pi$
$548$	−28.4719	−	21.6437i	−1.21626	−	0.924575i
$549$		0			0
$550$	0.322461	−	0.108650i	0.0137498	−	0.00463284i
$551$	0.462461	+	0.438066i	0.0197015	+	0.0186622i
$552$		0			0
$553$	−1.86091	−	0.202386i	−0.0791339	−	0.00860633i
$554$	74.6680	−	44.9263i	3.17234	−	1.90873i
$555$		0			0
$556$	−65.2268	+	30.1771i	−2.76623	+	1.27980i
$557$	4.96242	+	2.29586i	0.210264	+	0.0972787i	0.522195	−	0.852826i	$-0.325113\pi$
$557$	4.96242	+	2.29586i	0.210264	+	0.0972787i	−0.311930	+	0.950105i	$0.600976\pi$
$558$		0			0
$559$	−45.6686	−	15.3875i	−1.93158	−	0.650824i
$560$	−16.4823	−	31.0889i	−0.696505	−	1.31375i
$561$		0			0
$562$	45.8658	+	15.4540i	1.93473	+	0.651887i
$563$	22.4104	+	26.3835i	0.944485	+	1.11193i	0.993579	+	0.113139i	$0.0360907\pi$
$563$	22.4104	+	26.3835i	0.944485	+	1.11193i	−0.0490942	+	0.998794i	$0.515633\pi$
$564$		0			0
$565$	−5.51145	+	2.54987i	−0.231868	+	0.107274i
$566$	−20.0896	+	23.6513i	−0.844429	+	0.994139i
$567$		0			0
$568$	18.5974	+	2.02259i	0.780330	+	0.0848660i
$569$	−1.46975	+	8.96507i	−0.0616150	+	0.375835i	0.937962	+	0.346739i	$0.112711\pi$
$569$	−1.46975	+	8.96507i	−0.0616150	+	0.375835i	−0.999577	+	0.0290959i	$0.990737\pi$
$570$		0			0
$571$	−8.41697	+	2.83601i	−0.352239	+	0.118683i	−0.489858	−	0.871802i	$-0.662952\pi$
$571$	−8.41697	+	2.83601i	−0.352239	+	0.118683i	0.137619	+	0.990485i	$0.456055\pi$
$572$	0.745487	+	0.448545i	0.0311704	+	0.0187546i
$573$		0			0
$574$	−9.70316	+	24.3531i	−0.405002	+	1.01648i
$575$	13.9168	−	20.5257i	0.580371	−	0.855983i
$576$		0			0
$577$	0.922146	+	17.0080i	0.0383895	+	0.708052i	0.952862	+	0.303404i	$0.0981232\pi$
$577$	0.922146	+	17.0080i	0.0383895	+	0.708052i	−0.914473	+	0.404648i	$0.867394\pi$
$578$	45.1223	+	9.93217i	1.87684	+	0.413124i
$579$		0			0
$580$	−0.203311	+	0.732259i	−0.00844202	+	0.0304054i
$581$	−0.676936	+	12.4854i	−0.0280840	+	0.517980i
$582$		0			0
$583$	−0.0472622	+	0.0359278i	−0.00195740	+	0.00148798i
$584$	−5.15688	−	18.5734i	−0.213393	−	0.768572i
$585$		0			0
$586$	38.1200	+	56.2228i	1.57472	+	2.32254i
$587$	−23.6925	+	22.4428i	−0.977896	+	0.926312i	−0.997295	−	0.0734996i	$-0.976583\pi$
$587$	−23.6925	+	22.4428i	−0.977896	+	0.926312i	0.0193993	+	0.999812i	$0.493825\pi$
$588$		0			0
$589$	49.7508			2.04995
$590$	−3.84010	−	27.8379i	−0.158095	−	1.14607i
$591$		0			0
$592$	57.2203	−	107.929i	2.35174	−	4.43586i
$593$	−10.2524	+	9.71161i	−0.421016	+	0.398808i	−0.868664	−	0.495402i	$-0.835021\pi$
$593$	−10.2524	+	9.71161i	−0.421016	+	0.398808i	0.447647	+	0.894210i	$0.352262\pi$
$594$		0			0
$595$	−1.34163	+	0.295315i	−0.0550014	+	0.0121067i
$596$	5.39045	+	19.4146i	0.220801	+	0.795255i
$597$		0			0
$598$	84.4870	−	9.18851i	3.45493	−	0.375746i
$599$	−1.81453	+	33.4671i	−0.0741397	+	1.36743i	0.690670	+	0.723170i	$0.257316\pi$
$599$	−1.81453	+	33.4671i	−0.0741397	+	1.36743i	−0.764809	+	0.644257i	$0.777167\pi$
$600$		0			0
$601$	−12.0913	−	30.3469i	−0.493215	−	1.23788i	−0.939365	−	0.342918i	$-0.888585\pi$
$601$	−12.0913	−	30.3469i	−0.493215	−	1.23788i	0.446150	−	0.894958i	$-0.352795\pi$
$602$	−47.0983	−	10.3671i	−1.91958	−	0.422532i
$603$		0			0
$604$	12.7832	+	77.9738i	0.520139	+	3.17271i
$605$	−8.04588	+	11.8668i	−0.327112	+	0.482454i
$606$		0			0
$607$	12.7652	+	9.70384i	0.518123	+	0.393867i	0.831297	−	0.555829i	$-0.187599\pi$
$607$	12.7652	+	9.70384i	0.518123	+	0.393867i	−0.313174	+	0.949696i	$0.601392\pi$
$608$	−170.328	−	102.483i	−6.90770	−	4.15623i
$609$		0			0
$610$	9.03669	+	8.56000i	0.365885	+	0.346584i
$611$	−2.19406	+	13.3832i	−0.0887621	+	0.541425i
$612$		0			0
$613$	18.6457	−	11.2188i	0.753094	−	0.453122i	−0.0865574	−	0.996247i	$-0.527587\pi$
$613$	18.6457	−	11.2188i	0.753094	−	0.453122i	0.839652	+	0.543125i	$0.182759\pi$
$614$	24.6871	−	29.0639i	0.996291	−	1.17292i
$615$		0			0
$616$	0.521267	+	0.241164i	0.0210024	+	0.00971676i
$617$	−4.14417	−	4.87890i	−0.166838	−	0.196417i	0.672389	−	0.740198i	$-0.265268\pi$
$617$	−4.14417	−	4.87890i	−0.166838	−	0.196417i	−0.839227	+	0.543781i	$0.816992\pi$
$618$		0			0
$619$	−13.7814	−	25.9945i	−0.553921	−	1.04481i	−0.989483	−	0.144648i	$-0.953795\pi$
$619$	−13.7814	−	25.9945i	−0.553921	−	1.04481i	0.435562	−	0.900159i	$-0.356550\pi$
$620$	27.8019	+	52.4400i	1.11655	+	2.10604i
$621$		0			0
$622$	−14.2277	−	16.7501i	−0.570479	−	0.671620i
$623$	14.3627	+	6.64491i	0.575431	+	0.266223i
$624$		0			0
$625$	1.55301	−	1.82834i	0.0621203	−	0.0731337i
$626$	26.4354	−	15.9057i	1.05657	−	0.635719i
$627$		0			0
$628$	9.53645	−	58.1698i	0.380546	−	2.32123i
$629$	−3.46237	−	3.27973i	−0.138054	−	0.130771i
$630$		0			0
$631$	−24.4986	−	14.7403i	−0.975275	−	0.586803i	−0.0637136	−	0.997968i	$-0.520294\pi$
$631$	−24.4986	−	14.7403i	−0.975275	−	0.586803i	−0.911561	+	0.411165i	$0.865122\pi$
$632$	−11.2828	−	8.57694i	−0.448805	−	0.341172i
$633$		0			0
$634$	−28.3422	+	41.8017i	−1.12561	+	1.66016i
$635$	1.05020	+	6.40592i	0.0416758	+	0.254211i
$636$		0			0
$637$	−19.4242	−	4.27559i	−0.769614	−	0.169405i
$638$	−0.00378526	−	0.00950028i	−0.000149860	−	0.000376120i
$639$		0			0
$640$	5.39824	−	99.5646i	0.213384	−	3.93564i
$641$	42.1290	−	4.58180i	1.66400	−	0.180970i	0.772819	−	0.634627i	$-0.218846\pi$
$641$	42.1290	−	4.58180i	1.66400	−	0.180970i	0.891177	+	0.453656i	$0.149881\pi$
$642$		0			0
$643$	−8.05075	−	28.9962i	−0.317491	−	1.14350i	−0.934330	−	0.356409i	$-0.884001\pi$
$643$	−8.05075	−	28.9962i	−0.317491	−	1.14350i	0.616840	−	0.787089i	$-0.288413\pi$
$644$	61.9686	−	13.6403i	2.44191	−	0.537504i
$645$		0			0
$646$	−9.59466	+	9.08854i	−0.377497	+	0.357584i
$647$	10.2535	−	19.3401i	0.403107	−	0.760340i	−0.595983	−	0.802997i	$-0.703237\pi$
$647$	10.2535	−	19.3401i	0.403107	−	0.760340i	0.999090	+	0.0426572i	$0.0135823\pi$
$648$		0			0
$649$	0.199834	+	0.199169i	0.00784419	+	0.00781808i
$650$	37.3371			1.46448
$651$		0			0
$652$	66.1722	−	62.6817i	2.59150	−	2.45480i
$653$	−24.2603	−	35.7813i	−0.949380	−	1.40023i	−0.916174	−	0.400782i	$-0.868739\pi$
$653$	−24.2603	−	35.7813i	−0.949380	−	1.40023i	−0.0332060	−	0.999449i	$-0.510572\pi$
$654$		0			0
$655$	−4.39146	−	15.8166i	−0.171589	−	0.618006i
$656$	−97.1933	+	73.8844i	−3.79476	+	2.88470i
$657$		0			0
$658$	−0.734748	+	13.5516i	−0.0286435	+	0.528298i
$659$	12.8044	−	46.1172i	0.498787	−	1.79647i	−0.0993225	−	0.995055i	$-0.531668\pi$
$659$	12.8044	−	46.1172i	0.498787	−	1.79647i	0.598110	−	0.801414i	$-0.295919\pi$
$660$		0			0
$661$	3.99337	+	0.879006i	0.155324	+	0.0341894i	0.291952	−	0.956433i	$-0.405695\pi$
$661$	3.99337	+	0.879006i	0.155324	+	0.0341894i	−0.136628	+	0.990622i	$0.543626\pi$
$662$	−0.733400	−	13.5268i	−0.0285044	−	0.525733i
$663$		0			0
$664$	−53.1275	+	78.3571i	−2.06175	+	3.04085i
$665$	−4.45243	+	11.1747i	−0.172658	+	0.433338i
$666$		0			0
$667$	−0.638622	−	0.384246i	−0.0247275	−	0.0148781i
$668$	12.6604	−	4.26580i	0.489847	−	0.165049i
$669$		0			0
$670$	0.865442	−	5.27896i	0.0334350	−	0.203944i
$671$	−0.124238	−	0.0135117i	−0.00479616	−	0.000521614i
$672$		0			0
$673$	16.1330	−	18.9933i	0.621883	−	0.732137i	−0.357553	−	0.933893i	$-0.616389\pi$
$673$	16.1330	−	18.9933i	0.621883	−	0.732137i	0.979436	+	0.201756i	$0.0646647\pi$
$674$	−68.6487	+	31.7603i	−2.64425	+	1.22336i
$675$		0			0
$676$	12.3430	+	14.5313i	0.474729	+	0.558895i
$677$	26.8722	+	9.05430i	1.03278	+	0.347985i	0.784123	−	0.620606i	$-0.213113\pi$
$677$	26.8722	+	9.05430i	1.03278	+	0.347985i	0.248660	+	0.968591i	$0.420010\pi$
$678$		0			0
$679$	1.73483	+	3.27223i	0.0665765	+	0.125577i
$680$	−9.85665	−	3.32109i	−0.377985	−	0.127358i
$681$		0			0
$682$	−0.724893	−	0.335371i	−0.0277576	−	0.0128420i
$683$	20.1145	−	9.30598i	0.769661	−	0.356083i	0.00455710	−	0.999990i	$-0.498549\pi$
$683$	20.1145	−	9.30598i	0.769661	−	0.356083i	0.765104	+	0.643906i	$0.222687\pi$
$684$		0			0
$685$	−6.79738	+	4.08985i	−0.259715	+	0.156265i
$686$	−47.8543	−	5.20447i	−1.82709	−	0.198708i
$687$		0			0
$688$	−163.056	−	154.454i	−6.21644	−	5.88852i
$689$	−6.17323	+	2.08000i	−0.235181	+	0.0792418i
$690$		0			0
$691$	19.1784	+	14.5791i	0.729582	+	0.554614i	0.902691	−	0.430288i	$-0.141588\pi$
$691$	19.1784	+	14.5791i	0.729582	+	0.554614i	−0.173109	+	0.984903i	$0.555381\pi$
$692$	−8.29432	+	20.8172i	−0.315303	+	0.791350i
$693$		0			0
$694$	−9.76677	−	59.5746i	−0.370741	−	2.26142i
$695$	0.863046	+	15.9180i	0.0327372	+	0.603802i
$696$		0			0
$697$	1.76421	+	4.42783i	0.0668241	+	0.167716i
$698$	−0.806411	+	2.90443i	−0.0305231	+	0.109934i
$699$		0			0
$700$	27.7134	−	3.01402i	1.04747	−	0.113919i
$701$	−11.0706	+	8.41566i	−0.418131	+	0.317855i	−0.792999	−	0.609223i	$-0.791481\pi$
$701$	−11.0706	+	8.41566i	−0.418131	+	0.317855i	0.374867	+	0.927078i	$0.377688\pi$
$702$		0			0
$703$	−40.7841	+	8.97727i	−1.53820	+	0.338584i
$704$	1.01653	+	1.49927i	0.0383119	+	0.0565059i
$705$		0			0
$706$	−16.1074	+	30.3818i	−0.606210	+	1.14343i
$707$	−6.53343			−0.245715
$708$		0			0
$709$	7.26811			0.272960			0.136480	−	0.990643i	$-0.456421\pi$
$709$	7.26811			0.272960			0.136480	+	0.990643i	$0.456421\pi$
$710$	2.94630	−	5.55731i	0.110573	−	0.208562i
$711$		0			0
$712$	67.2412	+	99.1734i	2.51997	+	3.71668i
$713$	−56.8487	+	12.5133i	−2.12900	+	0.468629i
$714$		0			0
$715$	0.153630	−	0.116787i	0.00574544	−	0.00436757i
$716$	18.2464	−	1.98442i	0.681901	−	0.0741612i
$717$		0			0
$718$	−25.6870	+	92.5161i	−0.958629	+	3.45267i
$719$	−16.1434	−	40.5168i	−0.602046	−	1.51102i	−0.841580	−	0.540132i	$-0.818374\pi$
$719$	−16.1434	−	40.5168i	−0.602046	−	1.51102i	0.239535	−	0.970888i	$-0.423005\pi$
$720$		0			0
$721$	0.812939	+	14.9938i	0.0302754	+	0.558398i
$722$	10.0950	+	61.5766i	0.375696	+	2.29164i
$723$		0			0
$724$	−18.1388	+	45.5249i	−0.674123	+	1.69192i
$725$	−0.260674	−	0.198159i	−0.00968118	−	0.00735944i
$726$		0			0
$727$	12.1651	−	4.09890i	0.451178	−	0.152020i	−0.0845333	−	0.996421i	$-0.526940\pi$
$727$	12.1651	−	4.09890i	0.451178	−	0.152020i	0.535712	+	0.844401i	$0.320043\pi$
$728$	45.7535	+	43.3400i	1.69574	+	1.60629i
$729$		0			0
$730$	−6.44332	−	0.700753i	−0.238478	−	0.0259360i
$731$	−7.51318	+	4.52053i	−0.277885	+	0.167198i
$732$		0			0
$733$	−32.2378	+	14.9148i	−1.19073	+	0.550891i	−0.912283	−	0.409560i	$-0.865682\pi$
$733$	−32.2378	+	14.9148i	−1.19073	+	0.550891i	−0.278449	+	0.960451i	$0.589820\pi$
$734$	21.8025	+	10.0869i	0.804743	+	0.372314i
$735$		0			0
$736$	220.405	+	74.2630i	8.12423	+	2.73737i
$737$	0.0251574	+	0.0474519i	0.000926685	+	0.00174791i
$738$		0			0
$739$	20.7213	+	6.98182i	0.762246	+	0.256830i	0.673463	−	0.739221i	$-0.264806\pi$
$739$	20.7213	+	6.98182i	0.762246	+	0.256830i	0.0887823	+	0.996051i	$0.471702\pi$
$740$	−32.2536	−	37.9719i	−1.18567	−	1.39587i
$741$		0			0
$742$	−5.91639	+	2.73721i	−0.217197	+	0.100486i
$743$	3.91021	−	4.60345i	0.143452	−	0.168884i	−0.685744	−	0.727843i	$-0.740523\pi$
$743$	3.91021	−	4.60345i	0.143452	−	0.168884i	0.829196	+	0.558959i	$0.188799\pi$
$744$		0			0
$745$	4.44307	+	0.483213i	0.162781	+	0.0177035i
$746$	12.1456	−	74.0848i	0.444682	−	2.71244i
$747$		0			0
$748$	0.150013	−	0.0505452i	0.00548501	−	0.00184811i
$749$	−2.81325	−	1.69268i	−0.102794	−	0.0618491i
$750$		0			0
$751$	13.7395	−	34.4836i	0.501363	−	1.25833i	−0.432804	−	0.901488i	$-0.642476\pi$
$751$	13.7395	−	34.4836i	0.501363	−	1.25833i	0.934167	−	0.356837i	$-0.116145\pi$
$752$	−35.4699	+	52.3141i	−1.29345	+	1.90770i
$753$		0			0
$754$	−0.0607511	−	1.12049i	−0.00221242	−	0.0408058i
$755$	17.1165	+	3.76763i	0.622933	+	0.137118i
$756$		0			0
$757$	−6.79921	+	24.4886i	−0.247122	+	0.890052i	0.731062	+	0.682311i	$0.239025\pi$
$757$	−6.79921	+	24.4886i	−0.247122	+	0.890052i	−0.978184	+	0.207741i	$0.933389\pi$
$758$	2.68966	−	49.6079i	0.0976929	−	1.80184i
$759$		0			0
$760$	−72.5053	+	55.1171i	−2.63004	+	1.99931i
$761$	8.35696	+	30.0990i	0.302940	+	1.09109i	0.945705	+	0.325026i	$0.105373\pi$
$761$	8.35696	+	30.0990i	0.302940	+	1.09109i	−0.642765	+	0.766063i	$0.722213\pi$
$762$		0			0
$763$	4.40565	+	6.49784i	0.159495	+	0.235238i
$764$	53.0084	−	50.2122i	1.91778	−	1.81661i
$765$		0			0
$766$	−46.2553			−1.67127
$767$	13.8013	+	27.7116i	0.498336	+	1.00061i
$768$		0			0
$769$	12.8782	−	24.2908i	0.464399	−	0.875950i	−0.535115	−	0.844779i	$-0.679732\pi$
$769$	12.8782	−	24.2908i	0.464399	−	0.875950i	0.999514	−	0.0311706i	$-0.00992352\pi$
$770$	0.140203	−	0.132807i	0.00505257	−	0.00478605i
$771$		0			0
$772$	−48.8452	+	10.7517i	−1.75798	+	0.386960i
$773$	4.34883	+	15.6631i	0.156416	+	0.563361i	0.999666	+	0.0258390i	$0.00822572\pi$
$773$	4.34883	+	15.6631i	0.156416	+	0.563361i	−0.843250	+	0.537522i	$0.819360\pi$
$774$		0			0
$775$	−25.4237	+	2.76500i	−0.913247	+	0.0993216i
$776$	−1.51815	+	28.0006i	−0.0544983	+	1.00516i
$777$		0			0
$778$	−8.87584	−	22.2767i	−0.318214	−	0.798658i
$779$	40.7603	+	8.97203i	1.46039	+	0.321456i
$780$		0			0
$781$	0.0102168	+	0.0623198i	0.000365586	+	0.00222998i
$782$	8.67756	−	12.7984i	0.310309	−	0.457671i
$783$		0			0
$784$	−73.7928	−	56.0959i	−2.63546	−	2.00342i
$785$	−11.2033	−	6.74080i	−0.399863	−	0.240590i
$786$		0			0
$787$	24.8316	+	23.5218i	0.885152	+	0.838461i	0.987715	−	0.156266i	$-0.0499457\pi$
$787$	24.8316	+	23.5218i	0.885152	+	0.838461i	−0.102563	+	0.994727i	$0.532704\pi$
$788$	−15.0950	+	92.0751i	−0.537735	+	3.28004i
$789$		0			0
$790$	−4.08326	+	2.45681i	−0.145276	+	0.0874095i
$791$	4.33415	−	5.10255i	0.154105	−	0.181426i
$792$		0			0
$793$	−12.4453	−	5.75779i	−0.441944	−	0.204465i
$794$	8.48561	+	9.99004i	0.301143	+	0.354533i
$795$		0			0
$796$	6.95450	+	13.1176i	0.246496	+	0.464940i
$797$	−11.1234	−	20.9810i	−0.394012	−	0.743186i	0.604562	−	0.796558i	$-0.293348\pi$
$797$	−11.1234	−	20.9810i	−0.394012	−	0.743186i	−0.998575	+	0.0533718i	$0.983003\pi$
$798$		0			0
$799$	1.59745	+	1.88067i	0.0565139	+	0.0665333i
$800$	92.7368	+	42.9046i	3.27874	+	1.51691i
$801$		0			0
$802$	52.8206	−	62.1852i	1.86516	−	2.19583i
$803$	0.0557577	−	0.0335483i	0.00196765	−	0.00118389i
$804$		0			0
$805$	2.27697	−	13.8889i	0.0802527	−	0.489520i
$806$	−63.6265	−	60.2702i	−2.24115	−	2.12293i
$807$		0			0
$808$	−42.3860	−	25.5028i	−1.49114	−	0.897187i
$809$	24.2857	+	18.4615i	0.853841	+	0.649073i	0.937716	−	0.347403i	$-0.112937\pi$
$809$	24.2857	+	18.4615i	0.853841	+	0.649073i	−0.0838751	+	0.996476i	$0.526730\pi$
$810$		0			0
$811$	11.3400	−	16.7252i	0.398201	−	0.587302i	−0.574746	−	0.818332i	$-0.694899\pi$
$811$	11.3400	−	16.7252i	0.398201	−	0.587302i	0.972947	+	0.231030i	$0.0742095\pi$
$812$	−0.135543	−	0.826777i	−0.00475664	−	0.0290142i
$813$		0			0
$814$	0.654760	+	0.144123i	0.0229493	+	0.00505153i
$815$	−7.48319	−	18.7814i	−0.262125	−	0.657883i
$816$		0			0
$817$	−4.15672	+	76.6662i	−0.145425	+	2.68221i
$818$	49.8284	−	5.41917i	1.74221	−	0.189477i
$819$		0			0
$820$	13.3208	+	47.9773i	0.465183	+	1.67544i
$821$	38.3330	−	8.43773i	1.33783	−	0.294479i	0.512286	−	0.858815i	$-0.328799\pi$
$821$	38.3330	−	8.43773i	1.33783	−	0.294479i	0.825545	+	0.564336i	$0.190868\pi$
$822$		0			0
$823$	−38.2480	+	36.2304i	−1.33324	+	1.26291i	−0.394238	+	0.919008i	$0.628991\pi$
$823$	−38.2480	+	36.2304i	−1.33324	+	1.26291i	−0.939004	+	0.343906i	$0.888250\pi$
$824$	−53.2533	+	100.446i	−1.85517	+	3.49922i
$825$		0			0
$826$	16.7285	+	26.0756i	0.582059	+	0.907288i
$827$	15.3871			0.535060			0.267530	−	0.963549i	$-0.413792\pi$
$827$	15.3871			0.535060			0.267530	+	0.963549i	$0.413792\pi$
$828$		0			0
$829$	0.254726	−	0.241290i	0.00884702	−	0.00838034i	−0.683263	−	0.730172i	$-0.739440\pi$
$829$	0.254726	−	0.241290i	0.00884702	−	0.00838034i	0.692110	+	0.721792i	$0.256681\pi$
$830$	17.8634	+	26.3466i	0.620049	+	0.914504i
$831$		0			0
$832$	53.1735	+	191.514i	1.84346	+	6.63955i
$833$	−2.88090	+	2.19000i	−0.0998171	+	0.0758790i
$834$		0			0
$835$	0.160432	−	2.95899i	0.00555196	−	0.102400i
$836$	0.370830	−	1.33561i	0.0128254	−	0.0461930i
$837$		0			0
$838$	78.4417	+	17.2663i	2.70972	+	0.596455i
$839$	−0.902105	−	16.6383i	−0.0311441	−	0.574419i	−0.971909	−	0.235359i	$-0.924374\pi$
$839$	−0.902105	−	16.6383i	−0.0311441	−	0.574419i	0.940764	−	0.339061i	$-0.110109\pi$
$840$		0			0
$841$	16.2689	−	23.9948i	0.560997	−	0.827408i
$842$	19.5246	−	49.0031i	0.672863	−	1.68876i
$843$		0			0
$844$	−104.942	−	63.1416i	−3.61226	−	2.17342i
$845$	4.00762	−	1.35032i	0.137866	−	0.0464526i
$846$		0			0
$847$	2.55713	−	15.5978i	0.0878641	−	0.535947i
$848$	−30.1817	−	3.28246i	−1.03644	−	0.112720i
$849$		0			0
$850$	4.39796	−	5.17768i	0.150849	−	0.177593i
$851$	44.3448	−	20.5161i	1.52012	−	0.703282i
$852$		0			0
$853$	−3.64924	−	4.29622i	−0.124948	−	0.147100i	0.696131	−	0.717915i	$-0.254903\pi$
$853$	−3.64924	−	4.29622i	−0.124948	−	0.147100i	−0.821079	+	0.570815i	$0.806627\pi$
$854$	−13.0041	−	4.38161i	−0.444993	−	0.149935i
$855$		0			0
$856$	−11.6439	−	21.9627i	−0.397980	−	0.750670i
$857$	−13.3564	−	4.50031i	−0.456248	−	0.153728i	0.0817881	−	0.996650i	$-0.473937\pi$
$857$	−13.3564	−	4.50031i	−0.456248	−	0.153728i	−0.538036	+	0.842922i	$0.680833\pi$
$858$		0			0
$859$	44.9413	+	20.7921i	1.53338	+	0.709416i	0.991386	−	0.130969i	$-0.0418088\pi$
$859$	44.9413	+	20.7921i	1.53338	+	0.709416i	0.541990	+	0.840385i	$0.317671\pi$
$860$	−83.1330	+	38.4614i	−2.83481	+	1.31152i
$861$		0			0
$862$	−81.5493	+	49.0666i	−2.77758	+	1.67121i
$863$	−19.9481	−	2.16948i	−0.679040	−	0.0738500i	−0.237902	−	0.971289i	$-0.576460\pi$
$863$	−19.9481	−	2.16948i	−0.679040	−	0.0738500i	−0.441138	+	0.897439i	$0.645425\pi$
$864$		0			0
$865$	3.60854	+	3.41819i	0.122694	+	0.116222i
$866$	−40.1434	+	13.5259i	−1.36413	+	0.459629i
$867$		0			0
$868$	−52.0920	−	39.5993i	−1.76812	−	1.34409i
$869$	0.0177091	−	0.0444464i	0.000600739	−	0.00150774i
$870$		0			0
$871$	0.953420	+	5.81561i	0.0323054	+	0.197054i
$872$	3.21799	+	59.3523i	0.108975	+	2.00992i
$873$		0			0
$874$	−50.1164	−	125.783i	−1.69521	−	4.25466i
$875$	4.16005	−	14.9831i	0.140635	−	0.506522i
$876$		0			0
$877$	−38.0964	+	4.14323i	−1.28642	+	0.139907i	−0.725651	−	0.688063i	$-0.758461\pi$
$877$	−38.0964	+	4.14323i	−1.28642	+	0.139907i	−0.560772	+	0.827970i	$0.689496\pi$
$878$	24.4779	−	18.6076i	0.826089	−	0.627977i
$879$		0			0
$880$	0.878359	−	0.193341i	0.0296095	−	0.00651754i
$881$	10.5927	+	15.6230i	0.356876	+	0.526353i	0.963172	−	0.268886i	$-0.0866555\pi$
$881$	10.5927	+	15.6230i	0.356876	+	0.526353i	−0.606296	+	0.795239i	$0.707345\pi$
$882$		0			0
$883$	5.21330	−	9.83333i	0.175442	−	0.330918i	−0.780160	−	0.625580i	$-0.784862\pi$
$883$	5.21330	−	9.83333i	0.175442	−	0.330918i	0.955601	+	0.294662i	$0.0952072\pi$
$884$	17.3697			0.584205
$885$		0			0
$886$	61.5549			2.06798
$887$	5.60340	−	10.5691i	0.188144	−	0.354877i	−0.771439	−	0.636303i	$-0.780463\pi$
$887$	5.60340	−	10.5691i	0.188144	−	0.354877i	0.959583	+	0.281426i	$0.0908075\pi$
$888$		0			0
$889$	−4.01611	−	5.92332i	−0.134696	−	0.198662i
$890$	39.3459	−	8.66070i	1.31888	−	0.290307i
$891$		0			0
$892$	−51.4317	+	39.0974i	−1.72206	+	1.30908i
$893$	21.4802	−	2.33611i	0.718807	−	0.0781749i
$894$		0			0
$895$	1.08914	−	3.92271i	0.0364058	−	0.131122i
$896$	40.6877	+	102.119i	1.35928	+	3.41154i
$897$		0			0
$898$	3.35937	+	61.9598i	0.112103	+	2.06763i
$899$	0.124344	+	0.758468i	0.00414712	+	0.0252963i
$900$		0			0
$901$	−0.438706	+	1.10107i	−0.0146154	+	0.0366820i
$902$	−0.533416	−	0.405493i	−0.0177608	−	0.0135014i
$903$		0			0
$904$	48.0356	−	16.1851i	1.59764	−	0.538307i
$905$	7.89150	+	7.47523i	0.262322	+	0.248485i
$906$		0			0
$907$	47.8017	+	5.19875i	1.58723	+	0.172622i	0.858732	−	0.512426i	$-0.171253\pi$
$907$	47.8017	+	5.19875i	1.58723	+	0.172622i	0.728499	+	0.685047i	$0.240218\pi$
$908$	−95.1631	+	57.2577i	−3.15810	+	1.90016i
$909$		0			0
$910$	19.2318	−	8.89756i	0.637527	−	0.294951i
$911$	−26.6121	−	12.3121i	−0.881699	−	0.407917i	−0.0738240	−	0.997271i	$-0.523520\pi$
$911$	−26.6121	−	12.3121i	−0.881699	−	0.407917i	−0.807875	+	0.589354i	$0.799382\pi$
$912$		0			0
$913$	−0.302859	−	0.102045i	−0.0100232	−	0.00337720i
$914$	17.2069	+	32.4557i	0.569154	+	1.07354i
$915$		0			0
$916$	−118.721	−	40.0019i	−3.92267	−	1.32170i
$917$	11.7155	+	13.7925i	0.386879	+	0.455469i
$918$		0			0
$919$	−17.1137	+	7.91765i	−0.564529	+	0.261179i	−0.681330	−	0.731976i	$-0.738598\pi$
$919$	−17.1137	+	7.91765i	−0.564529	+	0.261179i	0.116801	+	0.993155i	$0.462736\pi$
$920$	68.9865	−	81.2172i	2.27442	−	2.67765i
$921$		0			0
$922$	−68.7700	−	7.47919i	−2.26482	−	0.246314i
$923$	−1.12106	+	6.83816i	−0.0369001	+	0.225081i
$924$		0			0
$925$	20.3426	−	6.85423i	0.668861	−	0.225366i
$926$	−36.8650	−	22.1809i	−1.21146	−	0.728910i
$927$		0			0
$928$	1.13668	−	2.85284i	0.0373132	−	0.0936491i
$929$	21.4832	−	31.6853i	0.704840	−	1.03956i	−0.291706	−	0.956508i	$-0.594223\pi$
$929$	21.4832	−	31.6853i	0.704840	−	1.03956i	0.996545	−	0.0830524i	$-0.0264669\pi$
$930$		0			0
$931$	1.71553	+	31.6412i	0.0562244	+	1.03700i
$932$	−100.855	−	22.2000i	−3.30363	−	0.727184i
$933$		0			0
$934$	23.1282	−	83.3004i	0.756779	−	2.72567i
$935$	0.00190094	−	0.0350608i	6.21675e−5	−	0.00114661i
$936$		0			0
$937$	39.2777	−	29.8581i	1.28315	−	0.975422i	0.283280	−	0.959037i	$-0.408577\pi$
$937$	39.2777	−	29.8581i	1.28315	−	0.975422i	0.999866	−	0.0163852i	$-0.00521581\pi$
$938$	1.57774	+	5.68250i	0.0515150	+	0.185540i
$939$		0			0
$940$	14.4660	+	21.3357i	0.471829	+	0.695895i
$941$	−27.5346	+	26.0822i	−0.897602	+	0.850254i	−0.989354	−	0.145528i	$-0.953512\pi$
$941$	−27.5346	+	26.0822i	−0.897602	+	0.850254i	0.0917519	+	0.995782i	$0.470753\pi$
$942$		0			0
$943$	−48.8322			−1.59019
$944$	4.14743	+	144.221i	0.134987	+	4.69401i
$945$		0			0
$946$	0.577373	−	1.08904i	0.0187720	−	0.0354078i
$947$	−20.5536	+	19.4694i	−0.667904	+	0.632672i	−0.944576	−	0.328292i	$-0.893527\pi$
$947$	−20.5536	+	19.4694i	−0.667904	+	0.632672i	0.276672	+	0.960964i	$0.410768\pi$
$948$		0			0
$949$	6.97325	−	1.53493i	0.226361	−	0.0498259i
$950$	−15.9142	−	57.3176i	−0.516324	−	1.85963i
$951$		0			0
$952$	11.3994	−	1.23976i	0.369458	−	0.0401810i
$953$	2.87612	−	53.0470i	0.0931668	−	1.71836i	−0.462217	−	0.886767i	$-0.652946\pi$
$953$	2.87612	−	53.0470i	0.0931668	−	1.71836i	0.555384	−	0.831594i	$-0.312571\pi$
$954$		0			0
$955$	−5.99453	−	15.0451i	−0.193979	−	0.486849i
$956$	−60.3981	−	13.2946i	−1.95341	−	0.429979i
$957$		0			0
$958$	−16.4969	−	100.627i	−0.532992	−	3.25111i
$959$	4.90792	−	7.23865i	0.158485	−	0.233748i
$960$		0			0
$961$	23.1092	+	17.5671i	0.745457	+	0.566682i
$962$	63.0343	+	37.9265i	2.03231	+	1.22280i
$963$		0			0
$964$	−34.5115	−	32.6911i	−1.11154	−	1.05291i
$965$	−1.79477	+	10.9476i	−0.0577755	+	0.352415i
$966$		0			0
$967$	18.9168	−	11.3818i	0.608322	−	0.366015i	−0.177818	−	0.984063i	$-0.556904\pi$
$967$	18.9168	−	11.3818i	0.608322	−	0.366015i	0.786140	+	0.618048i	$0.212076\pi$
$968$	77.4747	−	91.2103i	2.49013	−	2.93161i
$969$		0			0
$970$	8.55724	+	3.95900i	0.274756	+	0.127116i
$971$	−19.7272	−	23.2246i	−0.633075	−	0.745314i	0.348307	−	0.937381i	$-0.386757\pi$
$971$	−19.7272	−	23.2246i	−0.633075	−	0.745314i	−0.981382	+	0.192067i	$0.938481\pi$
$972$		0			0
$973$	−8.23202	−	15.5272i	−0.263906	−	0.497780i
$974$	−8.09541	−	15.2696i	−0.259394	−	0.489268i
$975$		0			0
$976$	−41.3732	−	48.7082i	−1.32432	−	1.55911i
$977$	−7.48675	−	3.46374i	−0.239523	−	0.110815i	0.296456	−	0.955046i	$-0.404195\pi$
$977$	−7.48675	−	3.46374i	−0.239523	−	0.110815i	−0.535979	+	0.844232i	$0.680057\pi$
$978$		0			0
$979$	−0.261861	+	0.308287i	−0.00836912	+	0.00985289i
$980$	−32.3928	+	19.4901i	−1.03475	+	0.622588i
$981$		0			0
$982$	13.3310	−	81.3153i	0.425408	−	2.59488i
$983$	2.49554	+	2.36391i	0.0795955	+	0.0753969i	0.726463	−	0.687205i	$-0.241163\pi$
$983$	2.49554	+	2.36391i	0.0795955	+	0.0753969i	−0.646868	+	0.762602i	$0.723921\pi$
$984$		0			0
$985$	17.7334	+	10.6698i	0.565032	+	0.339968i
$986$	−0.162538	−	0.123558i	−0.00517627	−	0.00393490i
$987$		0			0
$988$	85.3543	−	125.888i	2.71548	−	4.00503i
$989$	−14.5334	−	88.6496i	−0.462134	−	2.81889i
$990$		0			0
$991$	43.8080	+	9.64286i	1.39161	+	0.306316i	0.846650	−	0.532150i	$-0.178616\pi$
$991$	43.8080	+	9.64286i	1.39161	+	0.306316i	0.544955	+	0.838465i	$0.316547\pi$
$992$	−88.7761	−	222.811i	−2.81864	−	7.07426i
$993$		0			0
$994$	−0.375421	+	6.92423i	−0.0119076	+	0.219623i
$995$	3.27393	−	0.356061i	0.103790	−	0.0112879i
$996$		0			0
$997$	−0.943102	−	3.39675i	−0.0298683	−	0.107576i	0.947113	−	0.320899i	$-0.103985\pi$
$997$	−0.943102	−	3.39675i	−0.0298683	−	0.107576i	−0.976982	+	0.213323i	$0.931571\pi$
$998$	−119.577	+	26.3208i	−3.78513	+	0.833170i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.19.1		140
3.2	odd	2		177.2.e.a.19.5	✓	140
59.28	even	29	inner	531.2.i.c.28.1		140
177.146	odd	58		177.2.e.a.28.5	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.19.5	✓	140	3.2	odd	2
177.2.e.a.28.5	yes	140	177.146	odd	58
531.2.i.c.19.1		140	1.1	even	1	trivial
531.2.i.c.28.1		140	59.28	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31462 + 2.47964i) q^{2} +(-3.29802 - 4.86421i) q^{4} +(-1.27307 + 0.280224i) q^{5} +(1.14406 - 0.869689i) q^{7} +(10.8169 - 1.17641i) q^{8} +O(q^{10})\)	\(q+(-1.31462 + 2.47964i) q^{2} +(-3.29802 - 4.86421i) q^{4} +(-1.27307 + 0.280224i) q^{5} +(1.14406 - 0.869689i) q^{7} +(10.8169 - 1.17641i) q^{8} +(0.978753 - 3.52515i) q^{10} +(0.0135957 + 0.0341225i) q^{11} +(0.218202 + 4.02450i) q^{13} +(0.652515 + 3.98017i) q^{14} +(-6.95259 + 17.4497i) q^{16} +(0.583795 + 0.443789i) q^{17} +(6.08516 - 2.05033i) q^{19} +(5.56168 + 5.26830i) q^{20} +(-0.102485 - 0.0111459i) q^{22} +(-6.43762 + 3.87339i) q^{23} +(-2.99569 + 1.38596i) q^{25} +(-10.2662 - 4.74964i) q^{26} +(-8.00348 - 2.69668i) q^{28} +(0.0464669 + 0.0876458i) q^{29} +(7.34222 + 2.47388i) q^{31} +(-20.0409 - 23.5940i) q^{32} +(-1.86791 + 0.864187i) q^{34} +(-1.21276 + 1.42777i) q^{35} +(-6.46531 - 0.703145i) q^{37} +(-2.91561 + 17.7844i) q^{38} +(-13.4410 + 4.52881i) q^{40} +(5.56926 + 3.35091i) q^{41} +(-4.42571 + 11.1077i) q^{43} +(0.121141 - 0.178669i) q^{44} +(-1.14157 - 21.0550i) q^{46} +(3.28620 + 0.723348i) q^{47} +(-1.32019 + 4.75490i) q^{49} +(0.501535 - 9.25026i) q^{50} +(18.8564 - 14.3343i) q^{52} +(0.432398 + 1.55736i) q^{53} +(-0.0268702 - 0.0396306i) q^{55} +(11.3521 - 10.7532i) q^{56} -0.278417 q^{58} +(7.05093 - 3.04703i) q^{59} +(-1.59366 + 3.00597i) q^{61} +(-15.7866 + 14.9539i) q^{62} +(48.1617 - 10.6012i) q^{64} +(-1.40555 - 5.06233i) q^{65} +(1.45362 - 0.158091i) q^{67} +(0.233320 - 4.30333i) q^{68} +(-1.94604 - 4.88418i) q^{70} +(1.67909 + 0.369596i) q^{71} +(-0.286609 - 1.74824i) q^{73} +(10.2430 - 15.1073i) q^{74} +(-30.0422 - 22.8375i) q^{76} +(0.0452302 + 0.0272141i) q^{77} +(-0.945647 - 0.895764i) q^{79} +(3.96132 - 24.1630i) q^{80} +(-15.6306 + 9.40459i) q^{82} +(-5.63272 + 6.63135i) q^{83} +(-0.867572 - 0.401382i) q^{85} +(-21.7250 - 25.5766i) q^{86} +(0.187205 + 0.353107i) q^{88} +(5.15817 + 9.72934i) q^{89} +(3.74970 + 4.41449i) q^{91} +(40.0724 + 18.5395i) q^{92} +(-6.11377 + 7.19768i) q^{94} +(-7.17229 + 4.31542i) q^{95} +(-0.416944 + 2.54325i) q^{97} +(-10.0549 - 9.52451i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more