LMFDB - Embedded newform 540.2.y.a.127.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,2,Mod(127,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 3]))

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

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

chi := DirichletCharacter("540.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.y (of order $12$, degree $4$, not 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			127.15
Character	$\chi$	$=$	540.127
Dual form			540.2.y.a.523.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0534584 - 1.41320i) q^{2} +(-1.99428 + 0.151095i) q^{4} +(-0.795868 + 2.08964i) q^{5} +(-0.659597 - 2.46165i) q^{7} +(0.320139 + 2.81025i) q^{8} +O(q^{10})$	\(q+(-0.0534584 - 1.41320i) q^{2} +(-1.99428 + 0.151095i) q^{4} +(-0.795868 + 2.08964i) q^{5} +(-0.659597 - 2.46165i) q^{7} +(0.320139 + 2.81025i) q^{8} +(2.99563 + 1.01301i) q^{10} +(3.01796 + 1.74242i) q^{11} +(5.09493 + 1.36518i) q^{13} +(-3.44355 + 1.06374i) q^{14} +(3.95434 - 0.602653i) q^{16} +(-2.16382 - 2.16382i) q^{17} +3.88577 q^{19} +(1.27145 - 4.28759i) q^{20} +(2.30106 - 4.35813i) q^{22} +(0.991920 - 3.70190i) q^{23} +(-3.73319 - 3.32615i) q^{25} +(1.65691 - 7.27315i) q^{26} +(1.68737 + 4.80957i) q^{28} +(3.85118 + 2.22348i) q^{29} +(1.86992 - 1.07960i) q^{31} +(-1.06306 - 5.55607i) q^{32} +(-2.94224 + 3.17359i) q^{34} +(5.66891 + 0.580828i) q^{35} +(3.67542 + 3.67542i) q^{37} +(-0.207727 - 5.49138i) q^{38} +(-6.12720 - 1.56761i) q^{40} +(4.04792 + 7.01121i) q^{41} +(5.08248 - 1.36185i) q^{43} +(-6.28194 - 3.01888i) q^{44} +(-5.28456 - 1.20389i) q^{46} +(-0.0620436 - 0.231550i) q^{47} +(0.437526 - 0.252606i) q^{49} +(-4.50096 + 5.45356i) q^{50} +(-10.3670 - 1.95274i) q^{52} +(-0.265818 + 0.265818i) q^{53} +(-6.04292 + 4.91971i) q^{55} +(6.70669 - 2.64170i) q^{56} +(2.93635 - 5.56137i) q^{58} +(-5.69158 - 9.85810i) q^{59} +(-4.61792 + 7.99848i) q^{61} +(-1.62566 - 2.58487i) q^{62} +(-7.79502 + 1.79934i) q^{64} +(-6.90763 + 9.56007i) q^{65} +(-0.719566 - 0.192807i) q^{67} +(4.64221 + 3.98832i) q^{68} +(0.517777 - 8.04237i) q^{70} +2.06980i q^{71} +(8.97449 - 8.97449i) q^{73} +(4.99763 - 5.39060i) q^{74} +(-7.74933 + 0.587121i) q^{76} +(2.29859 - 8.57845i) q^{77} +(-7.56173 + 13.0973i) q^{79} +(-1.88780 + 8.74278i) q^{80} +(9.69186 - 6.09534i) q^{82} +(-14.9925 + 4.01723i) q^{83} +(6.24371 - 2.79948i) q^{85} +(-2.19627 - 7.10978i) q^{86} +(-3.93047 + 9.03903i) q^{88} +3.61495i q^{89} -13.4424i q^{91} +(-1.41883 + 7.53251i) q^{92} +(-0.323910 + 0.100059i) q^{94} +(-3.09256 + 8.11986i) q^{95} +(3.05651 - 0.818990i) q^{97} +(-0.380373 - 0.604809i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0534584	−	1.41320i	−0.0378008	−	0.999285i
$2$	−0.0534584	−	1.41320i	−0.0378008	−	0.999285i
$3$		0			0
$3$		0			0
$4$	−1.99428	+	0.151095i	−0.997142	+	0.0755476i
$5$	−0.795868	+	2.08964i	−0.355923	+	0.934515i
$5$	−0.795868	+	2.08964i	−0.355923	+	0.934515i
$6$		0			0
$7$	−0.659597	−	2.46165i	−0.249304	−	0.930416i	−0.971171	−	0.238384i	$-0.923382\pi$
$7$	−0.659597	−	2.46165i	−0.249304	−	0.930416i	0.721867	−	0.692032i	$-0.243284\pi$
$8$	0.320139	+	2.81025i	0.113186	+	0.993574i
$9$		0			0
$10$	2.99563	+	1.01301i	0.947302	+	0.320343i
$11$	3.01796	+	1.74242i	0.909948	+	0.525359i	0.880415	−	0.474205i	$-0.157264\pi$
$11$	3.01796	+	1.74242i	0.909948	+	0.525359i	0.0295338	+	0.999564i	$0.490598\pi$
$12$		0			0
$13$	5.09493	+	1.36518i	1.41308	+	0.378634i	0.883024	−	0.469329i	$-0.155504\pi$
$13$	5.09493	+	1.36518i	1.41308	+	0.378634i	0.530057	+	0.847962i	$0.322171\pi$
$14$	−3.44355	+	1.06374i	−0.920327	+	0.284297i
$15$		0			0
$16$	3.95434	−	0.602653i	0.988585	−	0.150663i
$17$	−2.16382	−	2.16382i	−0.524802	−	0.524802i	0.394216	−	0.919018i	$-0.371016\pi$
$17$	−2.16382	−	2.16382i	−0.524802	−	0.524802i	−0.919018	+	0.394216i	$0.871016\pi$
$18$		0			0
$19$	3.88577			0.891456			0.445728	−	0.895168i	$-0.352945\pi$
$19$	3.88577			0.891456			0.445728	+	0.895168i	$0.352945\pi$
$20$	1.27145	−	4.28759i	0.284305	−	0.958734i
$21$		0			0
$22$	2.30106	−	4.35813i	0.490587	−	0.929157i
$23$	0.991920	−	3.70190i	0.206830	−	0.771899i	−0.782054	−	0.623210i	$-0.785828\pi$
$23$	0.991920	−	3.70190i	0.206830	−	0.771899i	0.988884	−	0.148689i	$-0.0475052\pi$
$24$		0			0
$25$	−3.73319	−	3.32615i	−0.746638	−	0.665231i
$26$	1.65691	−	7.27315i	0.324947	−	1.42638i
$27$		0			0
$28$	1.68737	+	4.80957i	0.318883	+	0.908923i
$29$	3.85118	+	2.22348i	0.715147	+	0.412890i	0.812964	−	0.582314i	$-0.197853\pi$
$29$	3.85118	+	2.22348i	0.715147	+	0.412890i	−0.0978169	+	0.995204i	$0.531186\pi$
$30$		0			0
$31$	1.86992	−	1.07960i	0.335848	−	0.193902i	−0.322586	−	0.946540i	$-0.604552\pi$
$31$	1.86992	−	1.07960i	0.335848	−	0.193902i	0.658434	+	0.752638i	$0.271219\pi$
$32$	−1.06306	−	5.55607i	−0.187925	−	0.982183i
$33$		0			0
$34$	−2.94224	+	3.17359i	−0.504589	+	0.544265i
$35$	5.66891	+	0.580828i	0.958221	+	0.0981779i
$36$		0			0
$37$	3.67542	+	3.67542i	0.604235	+	0.604235i	0.941434	−	0.337198i	$-0.109479\pi$
$37$	3.67542	+	3.67542i	0.604235	+	0.604235i	−0.337198	+	0.941434i	$0.609479\pi$
$38$	−0.207727	−	5.49138i	−0.0336978	−	0.890819i
$39$		0			0
$40$	−6.12720	−	1.56761i	−0.968796	−	0.247861i
$41$	4.04792	+	7.01121i	0.632179	+	1.09497i	0.987105	+	0.160072i	$0.0511727\pi$
$41$	4.04792	+	7.01121i	0.632179	+	1.09497i	−0.354926	+	0.934894i	$0.615494\pi$
$42$		0			0
$43$	5.08248	−	1.36185i	0.775071	−	0.207680i	0.150461	−	0.988616i	$-0.451924\pi$
$43$	5.08248	−	1.36185i	0.775071	−	0.207680i	0.624611	+	0.780936i	$0.285258\pi$
$44$	−6.28194	−	3.01888i	−0.947037	−	0.455113i
$45$		0			0
$46$	−5.28456	−	1.20389i	−0.779165	−	0.177503i
$47$	−0.0620436	−	0.231550i	−0.00904999	−	0.0337750i	0.961253	−	0.275667i	$-0.0888987\pi$
$47$	−0.0620436	−	0.231550i	−0.00904999	−	0.0337750i	−0.970303	+	0.241892i	$0.922232\pi$
$48$		0			0
$49$	0.437526	−	0.252606i	0.0625037	−	0.0360865i
$50$	−4.50096	+	5.45356i	−0.636532	+	0.771250i
$51$		0			0
$52$	−10.3670	−	1.95274i	−1.43765	−	0.270797i
$53$	−0.265818	+	0.265818i	−0.0365129	+	0.0365129i	−0.725127	−	0.688615i	$-0.758219\pi$
$53$	−0.265818	+	0.265818i	−0.0365129	+	0.0365129i	0.688615	+	0.725127i	$0.258219\pi$
$54$		0			0
$55$	−6.04292	+	4.91971i	−0.814827	+	0.663373i
$56$	6.70669	−	2.64170i	0.896219	−	0.353013i
$57$		0			0
$58$	2.93635	−	5.56137i	0.385562	−	0.730243i
$59$	−5.69158	−	9.85810i	−0.740980	−	1.28342i	−0.952049	−	0.305944i	$-0.901028\pi$
$59$	−5.69158	−	9.85810i	−0.740980	−	1.28342i	0.211069	−	0.977471i	$-0.432305\pi$
$60$		0			0
$61$	−4.61792	+	7.99848i	−0.591264	+	1.02410i	0.402798	+	0.915289i	$0.368038\pi$
$61$	−4.61792	+	7.99848i	−0.591264	+	1.02410i	−0.994062	+	0.108811i	$0.965296\pi$
$62$	−1.62566	−	2.58487i	−0.206459	−	0.328278i
$63$		0			0
$64$	−7.79502	+	1.79934i	−0.974378	+	0.224918i
$65$	−6.90763	+	9.56007i	−0.856787	+	1.18578i
$66$		0			0
$67$	−0.719566	−	0.192807i	−0.0879089	−	0.0235551i	0.214596	−	0.976703i	$-0.431156\pi$
$67$	−0.719566	−	0.192807i	−0.0879089	−	0.0235551i	−0.302505	+	0.953148i	$0.597823\pi$
$68$	4.64221	+	3.98832i	0.562950	+	0.483655i
$69$		0			0
$70$	0.517777	−	8.04237i	0.0618862	−	0.961248i
$71$			2.06980i			0.245640i	0.992429	+	0.122820i	$0.0391938\pi$
$71$			2.06980i			0.245640i	−0.992429	+	0.122820i	$0.960806\pi$
$72$		0			0
$73$	8.97449	−	8.97449i	1.05038	−	1.05038i	0.0517232	−	0.998661i	$-0.483529\pi$
$73$	8.97449	−	8.97449i	1.05038	−	1.05038i	0.998661	−	0.0517232i	$-0.0164714\pi$
$74$	4.99763	−	5.39060i	0.580963	−	0.626644i
$75$		0			0
$76$	−7.74933	+	0.587121i	−0.888909	+	0.0673474i
$77$	2.29859	−	8.57845i	0.261948	−	0.977605i
$78$		0			0
$79$	−7.56173	+	13.0973i	−0.850761	+	1.47356i	0.0297623	+	0.999557i	$0.490525\pi$
$79$	−7.56173	+	13.0973i	−0.850761	+	1.47356i	−0.880523	+	0.474004i	$0.842808\pi$
$80$	−1.88780	+	8.74278i	−0.211063	+	0.977472i
$81$		0			0
$82$	9.69186	−	6.09534i	1.07029	−	0.673118i
$83$	−14.9925	+	4.01723i	−1.64564	+	0.440949i	−0.958388	−	0.285468i	$-0.907851\pi$
$83$	−14.9925	+	4.01723i	−1.64564	+	0.440949i	−0.687255	+	0.726417i	$0.741184\pi$
$84$		0			0
$85$	6.24371	−	2.79948i	0.677225	−	0.303647i
$86$	−2.19627	−	7.10978i	−0.236830	−	0.766667i
$87$		0			0
$88$	−3.93047	+	9.03903i	−0.418989	+	0.963564i
$89$			3.61495i			0.383184i	0.981475	+	0.191592i	$0.0613650\pi$
$89$			3.61495i			0.383184i	−0.981475	+	0.191592i	$0.938635\pi$
$90$		0			0
$91$		−	13.4424i		−	1.40915i
$92$	−1.41883	+	7.53251i	−0.147923	+	0.785318i
$93$		0			0
$94$	−0.323910	+	0.100059i	−0.0334088	+	0.0103203i
$95$	−3.09256	+	8.11986i	−0.317290	+	0.833080i
$96$		0			0
$97$	3.05651	−	0.818990i	0.310342	−	0.0831559i	−0.100287	−	0.994959i	$-0.531976\pi$
$97$	3.05651	−	0.818990i	0.310342	−	0.0831559i	0.410629	+	0.911803i	$0.365309\pi$
$98$	−0.380373	−	0.604809i	−0.0384234	−	0.0610949i
$99$		0			0
$100$	7.94760	+	6.06923i	0.794760	+	0.606923i
$101$	−2.15969	+	3.74069i	−0.214897	+	0.372213i	−0.953241	−	0.302212i	$-0.902275\pi$
$101$	−2.15969	+	3.74069i	−0.214897	+	0.372213i	0.738344	+	0.674425i	$0.235608\pi$
$102$		0			0
$103$	−0.353529	+	1.31939i	−0.0348342	+	0.130003i	−0.981153	−	0.193231i	$-0.938103\pi$
$103$	−0.353529	+	1.31939i	−0.0348342	+	0.130003i	0.946319	+	0.323234i	$0.104770\pi$
$104$	−2.20542	+	14.7551i	−0.216259	+	1.44686i
$105$		0			0
$106$	0.389864	+	0.361444i	0.0378670	+	0.0351065i
$107$	5.32781	−	5.32781i	0.515059	−	0.515059i	−0.401013	−	0.916072i	$-0.631342\pi$
$107$	5.32781	−	5.32781i	0.515059	−	0.515059i	0.916072	+	0.401013i	$0.131342\pi$
$108$		0			0
$109$			14.1851i			1.35869i	0.733820	+	0.679344i	$0.237736\pi$
$109$			14.1851i			1.35869i	−0.733820	+	0.679344i	$0.762264\pi$
$110$	7.27559	+	8.27687i	0.693700	+	0.789169i
$111$		0			0
$112$	−4.09179	−	9.33669i	−0.386638	−	0.882235i
$113$	−0.437551	−	0.117242i	−0.0411614	−	0.0110292i	0.238180	−	0.971221i	$-0.423449\pi$
$113$	−0.437551	−	0.117242i	−0.0411614	−	0.0110292i	−0.279341	+	0.960192i	$0.590116\pi$
$114$		0			0
$115$	6.94619	+	5.01898i	0.647736	+	0.468022i
$116$	−8.01631	−	3.85236i	−0.744296	−	0.357683i
$117$		0			0
$118$	−13.6272	+	8.57035i	−1.25449	+	0.788965i
$119$	−3.89931	+	6.75380i	−0.357449	+	0.619120i
$120$		0			0
$121$	0.572043	+	0.990808i	0.0520040	+	0.0900735i
$122$	11.5503	+	6.09848i	1.04572	+	0.552130i
$123$		0			0
$124$	−3.56603	+	2.43557i	−0.320239	+	0.218720i
$125$	9.92159	−	5.15384i	0.887414	−	0.460973i
$126$		0			0
$127$	2.66261	−	2.66261i	0.236269	−	0.236269i	−0.579034	−	0.815303i	$-0.696570\pi$
$127$	2.66261	−	2.66261i	0.236269	−	0.236269i	0.815303	+	0.579034i	$0.196570\pi$
$128$	2.95955	+	10.9198i	0.261590	+	0.965179i
$129$		0			0
$130$	13.8796	+	9.25082i	1.21732	+	0.811351i
$131$	10.6177	−	6.13011i	0.927670	−	0.535590i	0.0415959	−	0.999135i	$-0.486756\pi$
$131$	10.6177	−	6.13011i	0.927670	−	0.535590i	0.886074	+	0.463544i	$0.153422\pi$
$132$		0			0
$133$	−2.56304	−	9.56540i	−0.222244	−	0.829425i
$134$	−0.234009	+	1.02720i	−0.0202153	+	0.0887365i
$135$		0			0
$136$	5.38814	−	6.77359i	0.462029	−	0.580830i
$137$	8.93538	−	2.39423i	0.763401	−	0.204553i	0.143947	−	0.989585i	$-0.454021\pi$
$137$	8.93538	−	2.39423i	0.763401	−	0.204553i	0.619454	+	0.785033i	$0.287354\pi$
$138$		0			0
$139$	−8.95460	−	15.5098i	−0.759520	−	1.31553i	−0.943096	−	0.332521i	$-0.892101\pi$
$139$	−8.95460	−	15.5098i	−0.759520	−	1.31553i	0.183576	−	0.983005i	$-0.441233\pi$
$140$	−11.3932	−	0.301791i	−0.962900	−	0.0255060i
$141$		0			0
$142$	2.92504	−	0.110648i	0.245464	−	0.00928539i
$143$	12.9976	+	12.9976i	1.08691	+	1.08691i
$144$		0			0
$145$	−7.71131	+	6.27799i	−0.640389	+	0.521359i
$146$	−13.1625	−	12.2030i	−1.08934	−	1.00993i
$147$		0			0
$148$	−7.88517	−	6.77450i	−0.648157	−	0.556860i
$149$	−2.39752	+	1.38421i	−0.196413	+	0.113399i	−0.594981	−	0.803740i	$-0.702840\pi$
$149$	−2.39752	+	1.38421i	−0.196413	+	0.113399i	0.398568	+	0.917139i	$0.369507\pi$
$150$		0			0
$151$	−6.51667	−	3.76240i	−0.530319	−	0.306180i	0.210827	−	0.977523i	$-0.432384\pi$
$151$	−6.51667	−	3.76240i	−0.530319	−	0.306180i	−0.741146	+	0.671343i	$0.765718\pi$
$152$	1.24399	+	10.9200i	0.100901	+	0.885728i
$153$		0			0
$154$	−12.2460	−	2.78978i	−0.986808	−	0.224807i
$155$	0.767764	+	4.76668i	0.0616683	+	0.382869i
$156$		0			0
$157$	0.969291	−	3.61744i	0.0773578	−	0.288703i	−0.916400	−	0.400264i	$-0.868918\pi$
$157$	0.969291	−	3.61744i	0.0773578	−	0.288703i	0.993758	+	0.111561i	$0.0355850\pi$
$158$	18.9134	+	9.98609i	1.50467	+	0.794451i
$159$		0			0
$160$	12.4562	+	2.20048i	0.984752	+	0.173963i
$161$	−9.76704			−0.769751
$162$		0			0
$163$	6.76935	+	6.76935i	0.530216	+	0.530216i	0.920637	−	0.390420i	$-0.127670\pi$
$163$	6.76935	+	6.76935i	0.530216	+	0.530216i	−0.390420	+	0.920637i	$0.627670\pi$
$164$	−9.13207	−	13.3707i	−0.713095	−	1.04408i
$165$		0			0
$166$	6.47864	+	20.9727i	0.502840	+	1.62780i
$167$	3.57315	+	0.957423i	0.276499	+	0.0740876i	0.394404	−	0.918937i	$-0.370951\pi$
$167$	3.57315	+	0.957423i	0.276499	+	0.0740876i	−0.117905	+	0.993025i	$0.537618\pi$
$168$		0			0
$169$	12.8363	+	7.41103i	0.987406	+	0.570079i
$170$	−4.29002	−	8.67397i	−0.329029	−	0.665263i
$171$		0			0
$172$	−9.93015	+	3.48385i	−0.757167	+	0.265641i
$173$	−6.00167	−	22.3985i	−0.456299	−	1.70293i	−0.684242	−	0.729255i	$-0.739867\pi$
$173$	−6.00167	−	22.3985i	−0.456299	−	1.70293i	0.227943	−	0.973674i	$-0.426800\pi$
$174$		0			0
$175$	−5.72543	+	11.3837i	−0.432802	+	0.860529i
$176$	12.9841	+	5.07133i	0.978714	+	0.382266i
$177$		0			0
$178$	5.10866	−	0.193249i	0.382910	−	0.0144847i
$179$	−10.0185			−0.748819			−0.374410	−	0.927263i	$-0.622155\pi$
$179$	−10.0185			−0.748819			−0.374410	+	0.927263i	$0.622155\pi$
$180$		0			0
$181$	−19.9811			−1.48518			−0.742590	−	0.669746i	$-0.766403\pi$
$181$	−19.9811			−1.48518			−0.742590	+	0.669746i	$0.766403\pi$
$182$	−18.9969	+	0.718610i	−1.40814	+	0.0532669i
$183$		0			0
$184$	10.7208	+	1.60242i	0.790349	+	0.118132i
$185$	−10.6055	+	4.75515i	−0.779728	+	0.349606i
$186$		0			0
$187$	−2.76003	−	10.3006i	−0.201833	−	0.753253i
$188$	0.158719	+	0.452402i	0.0115758	+	0.0329948i
$189$		0			0
$190$	11.6403	+	3.93634i	0.844478	+	0.285572i
$191$	−13.5705	−	7.83490i	−0.981923	−	0.566914i	−0.0790731	−	0.996869i	$-0.525196\pi$
$191$	−13.5705	−	7.83490i	−0.981923	−	0.566914i	−0.902850	+	0.429955i	$0.858529\pi$
$192$		0			0
$193$	−20.8469	−	5.58592i	−1.50060	−	0.402083i	−0.587296	−	0.809372i	$-0.699807\pi$
$193$	−20.8469	−	5.58592i	−1.50060	−	0.402083i	−0.913299	+	0.407289i	$0.866474\pi$
$194$	−1.32080	−	4.27569i	−0.0948276	−	0.306977i
$195$		0			0
$196$	−0.834384	+	0.569876i	−0.0595988	+	0.0407054i
$197$	9.44630	+	9.44630i	0.673021	+	0.673021i	0.958411	−	0.285390i	$-0.0921232\pi$
$197$	9.44630	+	9.44630i	0.673021	+	0.673021i	−0.285390	+	0.958411i	$0.592123\pi$
$198$		0			0
$199$	2.06079			0.146085			0.0730427	−	0.997329i	$-0.476729\pi$
$199$	2.06079			0.146085			0.0730427	+	0.997329i	$0.476729\pi$
$200$	8.15219	−	11.5560i	0.576447	−	0.817135i
$201$		0			0
$202$	5.40181	+	2.85211i	0.380070	+	0.200674i
$203$	2.93320	−	10.9469i	0.205871	−	0.768320i
$204$		0			0
$205$	−17.8725	+	2.87870i	−1.24827	+	0.201057i
$206$	1.88346	+	0.429076i	0.131227	+	0.0298951i
$207$		0			0
$208$	20.9698	+	2.32792i	1.45400	+	0.161412i
$209$	11.7271	+	6.77063i	0.811179	+	0.468335i
$210$		0			0
$211$	−1.99458	+	1.15157i	−0.137313	+	0.0792776i	−0.567083	−	0.823661i	$-0.691928\pi$
$211$	−1.99458	+	1.15157i	−0.137313	+	0.0792776i	0.429770	+	0.902938i	$0.358595\pi$
$212$	0.489952	−	0.570280i	0.0336500	−	0.0391670i
$213$		0			0
$214$	−7.81409	−	7.24446i	−0.534161	−	0.495221i
$215$	−1.19922	+	11.7044i	−0.0817858	+	0.798234i
$216$		0			0
$217$	−3.89099	−	3.89099i	−0.264138	−	0.264138i
$218$	20.0465	−	0.758314i	1.35772	−	0.0513595i
$219$		0			0
$220$	11.3080	−	10.7244i	0.762383	−	0.723036i
$221$	−8.07049	−	13.9785i	−0.542880	−	0.940296i
$222$		0			0
$223$	−16.1225	+	4.32002i	−1.07964	+	0.289290i	−0.754450	−	0.656357i	$-0.772096\pi$
$223$	−16.1225	+	4.32002i	−1.07964	+	0.289290i	−0.325194	+	0.945647i	$0.605430\pi$
$224$	−12.9759	+	6.28166i	−0.866989	+	0.419711i
$225$		0			0
$226$	−0.142295	+	0.624617i	−0.00946534	+	0.0415489i
$227$	1.30473	+	4.86933i	0.0865981	+	0.323189i	0.995612	−	0.0935772i	$-0.0298302\pi$
$227$	1.30473	+	4.86933i	0.0865981	+	0.323189i	−0.909014	+	0.416766i	$0.863164\pi$
$228$		0			0
$229$	−6.71866	+	3.87902i	−0.443981	+	0.256333i	−0.705285	−	0.708924i	$-0.749181\pi$
$229$	−6.71866	+	3.87902i	−0.443981	+	0.256333i	0.261304	+	0.965257i	$0.415848\pi$
$230$	6.72150	−	10.0847i	0.443203	−	0.664964i
$231$		0			0
$232$	−5.01563	+	11.5346i	−0.329292	+	0.757285i
$233$	4.15335	−	4.15335i	0.272095	−	0.272095i	−0.557848	−	0.829943i	$-0.688373\pi$
$233$	4.15335	−	4.15335i	0.272095	−	0.272095i	0.829943	+	0.557848i	$0.188373\pi$
$234$		0			0
$235$	0.533235	+	0.0546344i	0.0347844	+	0.00356396i
$236$	12.8401	+	18.7999i	0.835822	+	1.22377i
$237$		0			0
$238$	9.75295	+	5.14947i	0.632190	+	0.333791i
$239$	−1.28058	−	2.21802i	−0.0828335	−	0.143472i	0.821632	−	0.570018i	$-0.193064\pi$
$239$	−1.28058	−	2.21802i	−0.0828335	−	0.143472i	−0.904466	+	0.426546i	$0.859730\pi$
$240$		0			0
$241$	6.89420	−	11.9411i	0.444094	−	0.769194i	−0.553894	−	0.832587i	$-0.686859\pi$
$241$	6.89420	−	11.9411i	0.444094	−	0.769194i	0.997989	+	0.0633929i	$0.0201921\pi$
$242$	1.36963	−	0.861381i	0.0880433	−	0.0553716i
$243$		0			0
$244$	8.00092	−	16.6490i	0.512206	−	1.06584i
$245$	0.179642	+	1.11531i	0.0114769	+	0.0712547i
$246$		0			0
$247$	19.7977	+	5.30478i	1.25970	+	0.337535i
$248$	3.63258	+	4.90933i	0.230669	+	0.311743i
$249$		0			0
$250$	−7.81381	−	13.7457i	−0.494189	−	0.869355i
$251$			11.4799i			0.724602i	0.932061	+	0.362301i	$0.118009\pi$
$251$			11.4799i			0.724602i	−0.932061	+	0.362301i	$0.881991\pi$
$252$		0			0
$253$	9.44382	−	9.44382i	0.593728	−	0.593728i
$254$	−3.90515	−	3.62047i	−0.245031	−	0.227169i
$255$		0			0
$256$	15.2736	−	4.76619i	0.954601	−	0.297887i
$257$	3.79760	−	14.1728i	0.236888	−	0.884077i	−0.740401	−	0.672165i	$-0.765364\pi$
$257$	3.79760	−	14.1728i	0.236888	−	0.884077i	0.977289	−	0.211912i	$-0.0679689\pi$
$258$		0			0
$259$	6.62330	−	11.4719i	0.411552	−	0.712829i
$260$	12.3313	−	20.1092i	0.764755	−	1.24712i
$261$		0			0
$262$	−9.23070	−	14.6772i	−0.570274	−	0.906761i
$263$	−1.77189	+	0.474777i	−0.109259	+	0.0292760i	−0.313034	−	0.949742i	$-0.601346\pi$
$263$	−1.77189	+	0.474777i	−0.109259	+	0.0292760i	0.203775	+	0.979018i	$0.434679\pi$
$264$		0			0
$265$	−0.343907	−	0.767019i	−0.0211261	−	0.0471176i
$266$	−13.3808	+	4.13345i	−0.820432	+	0.253438i
$267$		0			0
$268$	1.46415	+	0.275789i	0.0894372	+	0.0168465i
$269$		−	13.4031i		−	0.817201i	−0.912713	−	0.408600i	$-0.866017\pi$
$269$		−	13.4031i		−	0.817201i	0.912713	−	0.408600i	$-0.133983\pi$
$270$		0			0
$271$			19.1919i			1.16582i	0.812536	+	0.582911i	$0.198086\pi$
$271$			19.1919i			1.16582i	−0.812536	+	0.582911i	$0.801914\pi$
$272$	−9.86050	−	7.25243i	−0.597880	−	0.439743i
$273$		0			0
$274$	−3.86120	−	12.4995i	−0.233264	−	0.755123i
$275$	−5.47105	−	16.5430i	−0.329917	−	0.997579i
$276$		0			0
$277$	7.21889	−	1.93430i	0.433741	−	0.116221i	−0.0353406	−	0.999375i	$-0.511252\pi$
$277$	7.21889	−	1.93430i	0.433741	−	0.116221i	0.469082	+	0.883155i	$0.344585\pi$
$278$	−21.4398	+	13.4838i	−1.28588	+	0.808705i
$279$		0			0
$280$	0.182570	+	16.1170i	0.0109106	+	0.963176i
$281$	6.99536	−	12.1163i	0.417308	−	0.722799i	−0.578360	−	0.815782i	$-0.696307\pi$
$281$	6.99536	−	12.1163i	0.417308	−	0.722799i	0.995668	+	0.0929831i	$0.0296403\pi$
$282$		0			0
$283$	0.480944	−	1.79491i	0.0285891	−	0.106696i	−0.950157	−	0.311772i	$-0.899077\pi$
$283$	0.480944	−	1.79491i	0.0285891	−	0.106696i	0.978746	+	0.205076i	$0.0657441\pi$
$284$	−0.312737	−	4.12777i	−0.0185575	−	0.244938i
$285$		0			0
$286$	17.6734	−	19.0630i	1.04505	−	1.12722i
$287$	14.5891	−	14.5891i	0.861170	−	0.861170i
$288$		0			0
$289$		−	7.63580i		−	0.449165i
$290$	9.28431	+	10.5620i	0.545193	+	0.620224i
$291$		0			0
$292$	−16.5417	+	19.2537i	−0.968029	+	1.12674i
$293$	−25.4808	−	6.82756i	−1.48860	−	0.398870i	−0.579339	−	0.815087i	$-0.696689\pi$
$293$	−25.4808	−	6.82756i	−1.48860	−	0.398870i	−0.909266	+	0.416217i	$0.863356\pi$
$294$		0			0
$295$	25.1296	−	4.04760i	1.46310	−	0.235660i
$296$	−9.15221	+	11.5055i	−0.531961	+	0.668744i
$297$		0			0
$298$	2.08434	+	3.31419i	0.120742	+	0.191986i
$299$	10.1075	−	17.5068i	0.584534	−	1.01244i
$300$		0			0
$301$	−6.70478	−	11.6130i	−0.386457	−	0.669363i
$302$	−4.96867	+	9.41051i	−0.285915	+	0.541514i
$303$		0			0
$304$	15.3657	−	2.34177i	0.881280	−	0.134310i
$305$	−13.0387	−	16.0155i	−0.746593	−	0.917046i
$306$		0			0
$307$	−13.9421	+	13.9421i	−0.795717	+	0.795717i	−0.982417	−	0.186700i	$-0.940221\pi$
$307$	−13.9421	+	13.9421i	−0.795717	+	0.795717i	0.186700	+	0.982417i	$0.440221\pi$
$308$	−3.28788	+	17.4552i	−0.187344	+	0.994601i
$309$		0			0
$310$	6.69525	−	1.33983i	0.380264	−	0.0760970i
$311$	0.701482	−	0.405001i	0.0397774	−	0.0229655i	−0.479979	−	0.877280i	$-0.659356\pi$
$311$	0.701482	−	0.405001i	0.0397774	−	0.0229655i	0.519757	+	0.854314i	$0.326023\pi$
$312$		0			0
$313$	−1.63805	−	6.11329i	−0.0925882	−	0.345544i	0.904055	−	0.427417i	$-0.140576\pi$
$313$	−1.63805	−	6.11329i	−0.0925882	−	0.345544i	−0.996643	+	0.0818732i	$0.973910\pi$
$314$	−5.16400	−	1.17642i	−0.291421	−	0.0663893i
$315$		0			0
$316$	13.1013	−	27.2623i	0.737005	−	1.53362i
$317$	−19.5297	+	5.23297i	−1.09690	+	0.293913i	−0.761501	−	0.648164i	$-0.775537\pi$
$317$	−19.5297	+	5.23297i	−1.09690	+	0.293913i	−0.335397	+	0.942077i	$0.608871\pi$
$318$		0			0
$319$	7.74847	+	13.4207i	0.433831	+	0.751418i
$320$	2.44383	−	17.7208i	0.136614	−	0.990624i
$321$		0			0
$322$	0.522130	+	13.8028i	0.0290972	+	0.769200i
$323$	−8.40809	−	8.40809i	−0.467838	−	0.467838i
$324$		0			0
$325$	−14.4795	−	22.0430i	−0.803180	−	1.22273i
$326$	9.20458	−	9.92834i	0.509795	−	0.549880i
$327$		0			0
$328$	−18.4073	+	13.6202i	−1.01638	+	0.752052i
$329$	−0.529071	+	0.305459i	−0.0291686	+	0.0168405i
$330$		0			0
$331$	16.9166	+	9.76680i	0.929821	+	0.536832i	0.886755	−	0.462240i	$-0.152954\pi$
$331$	16.9166	+	9.76680i	0.929821	+	0.536832i	0.0430657	+	0.999072i	$0.486288\pi$
$332$	29.2924	−	10.2768i	1.60763	−	0.564013i
$333$		0			0
$334$	1.16202	−	5.10077i	0.0635828	−	0.279102i
$335$	0.975577	−	1.35018i	0.0533014	−	0.0737684i
$336$		0			0
$337$	−2.61793	+	9.77024i	−0.142608	+	0.532219i	0.857243	+	0.514913i	$0.172176\pi$
$337$	−2.61793	+	9.77024i	−0.142608	+	0.532219i	−0.999850	+	0.0173061i	$0.994491\pi$
$338$	9.78708	−	18.5365i	0.532347	−	1.00825i
$339$		0			0
$340$	−12.0287	+	6.52636i	−0.652350	+	0.353942i
$341$	7.52446			0.407472
$342$		0			0
$343$	−13.5248	−	13.5248i	−0.730270	−	0.730270i
$344$	5.45423	+	13.8471i	0.294073	+	0.746584i
$345$		0			0
$346$	−31.3328	+	9.67897i	−1.68446	+	0.520345i
$347$	−24.2713	−	6.50347i	−1.30295	−	0.349125i	−0.460386	−	0.887719i	$-0.652289\pi$
$347$	−24.2713	−	6.50347i	−1.30295	−	0.349125i	−0.842565	+	0.538594i	$0.818956\pi$
$348$		0			0
$349$	15.0315	+	8.67844i	0.804617	+	0.464546i	0.845083	−	0.534635i	$-0.179551\pi$
$349$	15.0315	+	8.67844i	0.804617	+	0.464546i	−0.0404658	+	0.999181i	$0.512884\pi$
$350$	16.3936	+	7.48264i	0.876274	+	0.399964i
$351$		0			0
$352$	6.47271	−	18.6203i	0.344997	−	0.992464i
$353$	−7.72886	−	28.8445i	−0.411366	−	1.53524i	−0.792006	−	0.610514i	$-0.790963\pi$
$353$	−7.72886	−	28.8445i	−0.411366	−	1.53524i	0.380640	−	0.924723i	$-0.375704\pi$
$354$		0			0
$355$	−4.32513	−	1.64729i	−0.229554	−	0.0874289i
$356$	−0.546201	−	7.20924i	−0.0289486	−	0.382089i
$357$		0			0
$358$	0.535574	+	14.1582i	0.0283060	+	0.748284i
$359$	26.1394			1.37959			0.689794	−	0.724006i	$-0.257701\pi$
$359$	26.1394			1.37959			0.689794	+	0.724006i	$0.257701\pi$
$360$		0			0
$361$	−3.90081			−0.205306
$362$	1.06816	+	28.2373i	0.0561410	+	1.48412i
$363$		0			0
$364$	2.03108	+	26.8080i	0.106458	+	1.40512i
$365$	11.6109	+	25.8960i	0.607744	+	1.35546i
$366$		0			0
$367$	−5.95191	−	22.2128i	−0.310687	−	1.15950i	−0.927938	−	0.372734i	$-0.878420\pi$
$367$	−5.95191	−	22.2128i	−0.310687	−	1.15950i	0.617251	−	0.786766i	$-0.288246\pi$
$368$	1.69143	−	15.2363i	0.0881718	−	0.794249i
$369$		0			0
$370$	7.28695	+	14.7335i	0.378830	+	0.765956i
$371$	0.829682	+	0.479017i	0.0430750	+	0.0248693i
$372$		0			0
$373$	12.8388	+	3.44016i	0.664770	+	0.178125i	0.575398	−	0.817874i	$-0.304847\pi$
$373$	12.8388	+	3.44016i	0.664770	+	0.178125i	0.0893722	+	0.995998i	$0.471514\pi$
$374$	−14.4093	+	4.45114i	−0.745085	+	0.230163i
$375$		0			0
$376$	0.630851	−	0.248486i	0.0325337	−	0.0128147i
$377$	16.5861	+	16.5861i	0.854226	+	0.854226i
$378$		0			0
$379$	12.7657			0.655730			0.327865	−	0.944725i	$-0.393671\pi$
$379$	12.7657			0.655730			0.327865	+	0.944725i	$0.393671\pi$
$380$	4.94057	−	16.6606i	0.253446	−	0.854669i
$381$		0			0
$382$	−10.3469	+	19.5966i	−0.529391	+	1.00265i
$383$	−9.09327	+	33.9365i	−0.464644	+	1.73408i	0.193422	+	0.981116i	$0.438041\pi$
$383$	−9.09327	+	33.9365i	−0.464644	+	1.73408i	−0.658066	+	0.752960i	$0.728625\pi$
$384$		0			0
$385$	16.0965	+	11.6305i	0.820353	+	0.592747i
$386$	−6.77959	+	29.7596i	−0.345072	+	1.51472i
$387$		0			0
$388$	−5.97181	+	2.09512i	−0.303173	+	0.106364i
$389$	15.4675	+	8.93019i	0.784236	+	0.452779i	0.837929	−	0.545779i	$-0.183766\pi$
$389$	15.4675	+	8.93019i	0.784236	+	0.452779i	−0.0536937	+	0.998557i	$0.517099\pi$
$390$		0			0
$391$	−10.1566	+	5.86389i	−0.513639	+	0.296550i
$392$	0.849955	+	1.14869i	0.0429292	+	0.0580175i
$393$		0			0
$394$	12.8446	−	13.8545i	0.647099	−	0.697981i
$395$	−21.3505	−	26.2250i	−1.07426	−	1.31952i
$396$		0			0
$397$	22.9050	+	22.9050i	1.14957	+	1.14957i	0.986637	+	0.162934i	$0.0520959\pi$
$397$	22.9050	+	22.9050i	1.14957	+	1.14957i	0.162934	+	0.986637i	$0.447904\pi$
$398$	−0.110166	−	2.91231i	−0.00552215	−	0.145981i
$399$		0			0
$400$	−16.7668	−	10.9029i	−0.838341	−	0.545147i
$401$	15.2608	+	26.4324i	0.762087	+	1.31997i	0.941773	+	0.336249i	$0.109159\pi$
$401$	15.2608	+	26.4324i	0.762087	+	1.31997i	−0.179686	+	0.983724i	$0.557508\pi$
$402$		0			0
$403$	11.0010	−	2.94770i	0.547998	−	0.146836i
$404$	3.74183	−	7.78632i	0.186163	−	0.387384i
$405$		0			0
$406$	−15.6270	−	3.56001i	−0.775553	−	0.176680i
$407$	4.68814	+	17.4964i	0.232383	+	0.867263i
$408$		0			0
$409$	−14.2191	+	8.20942i	−0.703091	+	0.405930i	−0.808498	−	0.588499i	$-0.799719\pi$
$409$	−14.2191	+	8.20942i	−0.703091	+	0.405930i	0.105407	+	0.994429i	$0.466386\pi$
$410$	5.02363	+	25.1036i	0.248099	+	1.23978i
$411$		0			0
$412$	0.505684	−	2.68465i	0.0249133	−	0.132263i
$413$	−20.5130	+	20.5130i	−1.00938	+	1.00938i
$414$		0			0
$415$	3.53750	−	34.5262i	0.173649	−	1.69482i
$416$	2.16881	−	29.7591i	0.106335	−	1.45906i
$417$		0			0
$418$	8.94137	−	16.9347i	0.437337	−	0.828303i
$419$	5.01036	+	8.67820i	0.244772	+	0.423958i	0.962068	−	0.272811i	$-0.0879535\pi$
$419$	5.01036	+	8.67820i	0.244772	+	0.423958i	−0.717295	+	0.696769i	$0.754620\pi$
$420$		0			0
$421$	−3.68335	+	6.37975i	−0.179515	+	0.310930i	−0.941715	−	0.336413i	$-0.890786\pi$
$421$	−3.68335	+	6.37975i	−0.179515	+	0.310930i	0.762199	+	0.647342i	$0.224120\pi$
$422$	1.73403	+	2.75719i	0.0844115	+	0.134218i
$423$		0			0
$424$	−0.832113	−	0.661915i	−0.0404110	−	0.0321455i
$425$	0.880745	+	15.2751i	0.0427224	+	0.740952i
$426$		0			0
$427$	22.7354	+	6.09194i	1.10024	+	0.294810i
$428$	−9.82017	+	11.4302i	−0.474676	+	0.552499i
$429$		0			0
$430$	16.6048	+	1.06904i	0.800755	+	0.0515535i
$431$		−	16.4473i		−	0.792237i	−0.918199	−	0.396119i	$-0.870357\pi$
$431$		−	16.4473i		−	0.792237i	0.918199	−	0.396119i	$-0.129643\pi$
$432$		0			0
$433$	−3.78112	+	3.78112i	−0.181709	+	0.181709i	−0.792100	−	0.610391i	$-0.791012\pi$
$433$	−3.78112	+	3.78112i	−0.181709	+	0.181709i	0.610391	+	0.792100i	$0.291012\pi$
$434$	−5.29076	+	5.70677i	−0.253964	+	0.273934i
$435$		0			0
$436$	−2.14330	−	28.2892i	−0.102646	−	1.35481i
$437$	3.85437	−	14.3847i	0.184380	−	0.688114i
$438$		0			0
$439$	−18.4104	+	31.8878i	−0.878683	+	1.52192i	−0.0258954	+	0.999665i	$0.508244\pi$
$439$	−18.4104	+	31.8878i	−0.878683	+	1.52192i	−0.852787	+	0.522258i	$0.825090\pi$
$440$	−15.7602	−	15.4071i	−0.751338	−	0.734506i
$441$		0			0
$442$	−19.3230	+	12.1525i	−0.919102	+	0.578036i
$443$	11.6926	−	3.13302i	0.555532	−	0.148854i	0.0298790	−	0.999554i	$-0.490488\pi$
$443$	11.6926	−	3.13302i	0.555532	−	0.148854i	0.525653	+	0.850699i	$0.323821\pi$
$444$		0			0
$445$	−7.55394	−	2.87702i	−0.358091	−	0.136384i
$446$	6.96695	+	22.5535i	0.329895	+	1.06794i
$447$		0			0
$448$	9.57093	+	18.0018i	0.452184	+	0.850504i
$449$			1.04828i			0.0494715i	0.999694	+	0.0247357i	$0.00787443\pi$
$449$			1.04828i			0.0494715i	−0.999694	+	0.0247357i	$0.992126\pi$
$450$		0			0
$451$			28.2127i			1.32848i
$452$	0.890317	+	0.167701i	0.0418770	+	0.00788800i
$453$		0			0
$454$	6.81160	−	2.10416i	0.319684	−	0.0987530i
$455$	28.0898	+	10.6984i	1.31687	+	0.501548i
$456$		0			0
$457$	−13.1438	+	3.52188i	−0.614843	+	0.164747i	−0.552782	−	0.833326i	$-0.686434\pi$
$457$	−13.1438	+	3.52188i	−0.614843	+	0.164747i	−0.0620609	+	0.998072i	$0.519767\pi$
$458$	5.84101	+	9.28746i	0.272932	+	0.433974i
$459$		0			0
$460$	−14.6110	−	8.95973i	−0.681242	−	0.417750i
$461$	−5.72422	+	9.91464i	−0.266604	+	0.461771i	−0.967983	−	0.251018i	$-0.919235\pi$
$461$	−5.72422	+	9.91464i	−0.266604	+	0.461771i	0.701379	+	0.712789i	$0.252568\pi$
$462$		0			0
$463$	−1.21606	+	4.53841i	−0.0565153	+	0.210918i	−0.988409	−	0.151813i	$-0.951489\pi$
$463$	−1.21606	+	4.53841i	−0.0565153	+	0.210918i	0.931894	+	0.362731i	$0.118156\pi$
$464$	16.5689	+	6.47148i	0.769191	+	0.300431i
$465$		0			0
$466$	−6.09155	−	5.64749i	−0.282186	−	0.261615i
$467$	−25.5411	+	25.5411i	−1.18190	+	1.18190i	−0.202651	+	0.979251i	$0.564956\pi$
$467$	−25.5411	+	25.5411i	−1.18190	+	1.18190i	−0.979251	+	0.202651i	$0.935044\pi$
$468$		0			0
$469$			1.89849i			0.0876643i
$470$	0.0487036	−	0.756489i	0.00224653	−	0.0348943i
$471$		0			0
$472$	25.8816	−	19.1507i	1.19130	−	0.881484i
$473$	17.7116	+	4.74581i	0.814381	+	0.218213i
$474$		0			0
$475$	−14.5063	−	12.9247i	−0.665595	−	0.593024i
$476$	6.75587	−	14.0582i	0.309655	−	0.644355i
$477$		0			0
$478$	−3.06606	+	1.92828i	−0.140238	+	0.0881977i
$479$	−6.06234	+	10.5003i	−0.276995	+	0.479770i	−0.970637	−	0.240551i	$-0.922672\pi$
$479$	−6.06234	+	10.5003i	−0.276995	+	0.479770i	0.693641	+	0.720321i	$0.256005\pi$
$480$		0			0
$481$	13.7084	+	23.7436i	0.625049	+	1.08262i
$482$	−17.2438	−	9.10455i	−0.785431	−	0.414701i
$483$		0			0
$484$	−1.29052	−	1.88952i	−0.0586602	−	0.0858873i
$485$	−0.721187	+	7.03882i	−0.0327474	+	0.319616i
$486$		0			0
$487$	−12.5621	+	12.5621i	−0.569243	+	0.569243i	−0.931916	−	0.362673i	$-0.881864\pi$
$487$	−12.5621	+	12.5621i	−0.569243	+	0.569243i	0.362673	+	0.931916i	$0.381864\pi$
$488$	−23.9561	−	10.4169i	−1.08444	−	0.471551i
$489$		0			0
$490$	1.56656	−	0.313493i	0.0707699	−	0.0141622i
$491$	−0.109289	+	0.0630982i	−0.00493215	+	0.00284758i	−0.502464	−	0.864598i	$-0.667573\pi$
$491$	−0.109289	+	0.0630982i	−0.00493215	+	0.00284758i	0.497532	+	0.867446i	$0.334240\pi$
$492$		0			0
$493$	−3.52205	−	13.1445i	−0.158625	−	0.591997i
$494$	6.43838	−	28.2618i	0.289677	−	1.27156i
$495$		0			0
$496$	6.74369	−	5.39602i	0.302800	−	0.242289i
$497$	5.09512	−	1.36523i	0.228547	−	0.0612391i
$498$		0			0
$499$	−20.2868	−	35.1377i	−0.908161	−	1.57298i	−0.816618	−	0.577179i	$-0.804153\pi$
$499$	−20.2868	−	35.1377i	−0.908161	−	1.57298i	−0.0915430	−	0.995801i	$-0.529180\pi$
$500$	−19.0078	+	11.7773i	−0.850053	+	0.526698i
$501$		0			0
$502$	16.2234	−	0.613695i	0.724084	−	0.0273905i
$503$	6.97397	+	6.97397i	0.310954	+	0.310954i	0.845279	−	0.534325i	$-0.179434\pi$
$503$	6.97397	+	6.97397i	0.310954	+	0.310954i	−0.534325	+	0.845279i	$0.679434\pi$
$504$		0			0
$505$	−6.09787	−	7.49007i	−0.271352	−	0.333304i
$506$	−13.8509	−	12.8412i	−0.615747	−	0.570860i
$507$		0			0
$508$	−4.90770	+	5.71231i	−0.217744	+	0.253443i
$509$	27.6387	−	15.9572i	1.22507	−	0.707292i	0.259072	−	0.965858i	$-0.416583\pi$
$509$	27.6387	−	15.9572i	1.22507	−	0.707292i	0.965994	+	0.258566i	$0.0832499\pi$
$510$		0			0
$511$	−28.0116	−	16.1725i	−1.23916	−	0.715430i
$512$	−7.55210	−	21.3299i	−0.333759	−	0.942658i
$513$		0			0
$514$	−20.2321	−	4.60912i	−0.892400	−	0.203300i
$515$	−2.47568	−	1.78881i	−0.109092	−	0.0788243i
$516$		0			0
$517$	0.216212	−	0.806914i	0.00950899	−	0.0354880i
$518$	−16.5662	−	8.74680i	−0.727876	−	0.384312i
$519$		0			0
$520$	−29.0776	−	16.3516i	−1.27514	−	0.717067i
$521$	−34.5815			−1.51504			−0.757521	−	0.652811i	$-0.773590\pi$
$521$	−34.5815			−1.51504			−0.757521	+	0.652811i	$0.773590\pi$
$522$		0			0
$523$	−31.6445	−	31.6445i	−1.38372	−	1.38372i	−0.837915	−	0.545801i	$-0.816225\pi$
$523$	−31.6445	−	31.6445i	−1.38372	−	1.38372i	−0.545801	−	0.837915i	$-0.683775\pi$
$524$	−20.2484	+	13.8295i	−0.884556	+	0.604143i
$525$		0			0
$526$	0.765678	+	2.47866i	0.0333851	+	0.108075i
$527$	−6.38222	−	1.71011i	−0.278014	−	0.0744936i
$528$		0			0
$529$	7.19846	+	4.15603i	0.312976	+	0.180697i
$530$	−1.06557	+	0.527014i	−0.0462853	+	0.0228920i
$531$		0			0
$532$	6.55672	+	18.6889i	0.284270	+	0.810265i
$533$	11.0523	+	41.2478i	0.478729	+	1.78664i
$534$		0			0
$535$	6.89297	+	15.3734i	0.298009	+	0.664652i
$536$	0.311475	−	2.08389i	0.0134537	−	0.0900101i
$537$		0			0
$538$	−18.9413	+	0.716508i	−0.816617	+	0.0308908i
$539$	1.76058			0.0758335
$540$		0			0
$541$	35.6814			1.53407			0.767033	−	0.641608i	$-0.221732\pi$
$541$	35.6814			1.53407			0.767033	+	0.641608i	$0.221732\pi$
$542$	27.1220	−	1.02597i	1.16499	−	0.0440690i
$543$		0			0
$544$	−9.72203	+	14.3226i	−0.416829	+	0.614076i
$545$	−29.6418	−	11.2895i	−1.26972	−	0.483588i
$546$		0			0
$547$	4.27345	+	15.9487i	0.182720	+	0.681919i	0.995107	+	0.0988010i	$0.0315007\pi$
$547$	4.27345	+	15.9487i	0.182720	+	0.681919i	−0.812388	+	0.583118i	$0.801833\pi$
$548$	−17.4579	+	6.12487i	−0.745766	+	0.261641i
$549$		0			0
$550$	−23.0861	+	8.61606i	−0.984394	+	0.367390i
$551$	14.9648	+	8.63994i	0.637522	+	0.368074i
$552$		0			0
$553$	37.2286	+	9.97538i	1.58312	+	0.424197i
$554$	−3.11946	−	10.0984i	−0.132533	−	0.429038i
$555$		0			0
$556$	20.2015	+	29.5780i	0.856734	+	1.25439i
$557$	−1.96120	−	1.96120i	−0.0830989	−	0.0830989i	0.664336	−	0.747434i	$-0.268715\pi$
$557$	−1.96120	−	1.96120i	−0.0830989	−	0.0830989i	−0.747434	+	0.664336i	$0.768715\pi$
$558$		0			0
$559$	27.7541			1.17387
$560$	22.7669	−	1.11960i	0.962075	−	0.0473116i
$561$		0			0
$562$	−17.4968	−	9.23814i	−0.738057	−	0.389687i
$563$	3.43039	−	12.8024i	0.144574	−	0.539557i	−0.855200	−	0.518298i	$-0.826566\pi$
$563$	3.43039	−	12.8024i	0.144574	−	0.539557i	0.999774	−	0.0212589i	$-0.00676742\pi$
$564$		0			0
$565$	0.593226	−	0.821016i	0.0249572	−	0.0345404i
$566$	−2.56228	−	0.583718i	−0.107701	−	0.0245355i
$567$		0			0
$568$	−5.81665	+	0.662624i	−0.244061	+	0.0278031i
$569$	−9.89594	−	5.71342i	−0.414859	−	0.239519i	0.278016	−	0.960576i	$-0.410323\pi$
$569$	−9.89594	−	5.71342i	−0.414859	−	0.239519i	−0.692876	+	0.721057i	$0.743656\pi$
$570$		0			0
$571$	32.2228	−	18.6038i	1.34848	−	0.778546i	0.360447	−	0.932780i	$-0.382624\pi$
$571$	32.2228	−	18.6038i	1.34848	−	0.778546i	0.988034	+	0.154234i	$0.0492908\pi$
$572$	−27.8847	−	23.9570i	−1.16592	−	1.00169i
$573$		0			0
$574$	−21.3973	−	19.8375i	−0.893107	−	0.828001i
$575$	−16.0161	+	10.5206i	−0.667918	+	0.438739i
$576$		0			0
$577$	−8.63696	−	8.63696i	−0.359561	−	0.359561i	0.504090	−	0.863651i	$-0.331828\pi$
$577$	−8.63696	−	8.63696i	−0.359561	−	0.359561i	−0.863651	+	0.504090i	$0.831828\pi$
$578$	−10.7909	+	0.408198i	−0.448844	+	0.0169788i
$579$		0			0
$580$	14.4300	−	13.6852i	0.599172	−	0.568249i
$581$	19.7780	+	34.2566i	0.820532	+	1.42120i
$582$		0			0
$583$	−1.26539	+	0.339061i	−0.0524072	+	0.0140425i
$584$	28.0937	+	22.3475i	1.16252	+	0.924745i
$585$		0			0
$586$	−8.28656	+	36.3745i	−0.342315	+	1.50262i
$587$	−2.05297	−	7.66180i	−0.0847352	−	0.316236i	0.910529	−	0.413446i	$-0.135675\pi$
$587$	−2.05297	−	7.66180i	−0.0847352	−	0.316236i	−0.995264	+	0.0972097i	$0.969008\pi$
$588$		0			0
$589$	7.26609	−	4.19508i	0.299394	−	0.172855i
$590$	−7.06347	−	35.2969i	−0.290798	−	1.45315i
$591$		0			0
$592$	16.7489	+	12.3189i	0.688374	+	0.506302i
$593$	17.4824	−	17.4824i	0.717918	−	0.717918i	−0.250261	−	0.968178i	$-0.580516\pi$
$593$	17.4824	−	17.4824i	0.717918	−	0.717918i	0.968178	+	0.250261i	$0.0805164\pi$
$594$		0			0
$595$	−11.0097	−	13.5233i	−0.451353	−	0.554401i
$596$	4.57219	−	3.12276i	0.187284	−	0.127913i
$597$		0			0
$598$	−25.2809	−	13.3481i	−1.03381	−	0.545845i
$599$	15.1365	+	26.2172i	0.618461	+	1.07121i	0.989767	+	0.142696i	$0.0455770\pi$
$599$	15.1365	+	26.2172i	0.618461	+	1.07121i	−0.371305	+	0.928511i	$0.621090\pi$
$600$		0			0
$601$	−1.15030	+	1.99238i	−0.0469219	+	0.0812710i	−0.888532	−	0.458814i	$-0.848275\pi$
$601$	−1.15030	+	1.99238i	−0.0469219	+	0.0812710i	0.841611	+	0.540085i	$0.181608\pi$
$602$	−16.0531	+	10.0960i	−0.654277	+	0.411483i
$603$		0			0
$604$	13.5646	+	6.51866i	0.551935	+	0.265241i
$605$	−2.52570	+	0.406812i	−0.102684	+	0.0165393i
$606$		0			0
$607$	−42.3071	−	11.3362i	−1.71719	−	0.460120i	−0.740023	−	0.672581i	$-0.765185\pi$
$607$	−42.3071	−	11.3362i	−1.71719	−	0.460120i	−0.977170	+	0.212461i	$0.931852\pi$
$608$	−4.13082	−	21.5896i	−0.167527	−	0.875574i
$609$		0			0
$610$	−21.9362	+	19.2825i	−0.888169	+	0.780724i
$611$		−	1.26443i		−	0.0511535i
$612$		0			0
$613$	5.01756	−	5.01756i	0.202657	−	0.202657i	−0.598480	−	0.801138i	$-0.704228\pi$
$613$	5.01756	−	5.01756i	0.202657	−	0.202657i	0.801138	+	0.598480i	$0.204228\pi$
$614$	20.4483	+	18.9577i	0.825227	+	0.765070i
$615$		0			0
$616$	24.8435	+	3.71331i	1.00097	+	0.149614i
$617$	−1.85628	+	6.92773i	−0.0747310	+	0.278900i	−0.993172	−	0.116658i	$-0.962782\pi$
$617$	−1.85628	+	6.92773i	−0.0747310	+	0.278900i	0.918441	+	0.395558i	$0.129449\pi$
$618$		0			0
$619$	6.11352	−	10.5889i	0.245723	−	0.425605i	−0.716612	−	0.697473i	$-0.754308\pi$
$619$	6.11352	−	10.5889i	0.245723	−	0.425605i	0.962335	+	0.271868i	$0.0876413\pi$
$620$	−2.25136	−	9.39012i	−0.0904169	−	0.377116i
$621$		0			0
$622$	−0.609848	−	0.969686i	−0.0244527	−	0.0388809i
$623$	8.89874	−	2.38441i	0.356521	−	0.0955294i
$624$		0			0
$625$	2.87339	+	24.8343i	0.114936	+	0.993373i
$626$	−8.55176	+	2.64171i	−0.341797	+	0.105584i
$627$		0			0
$628$	−1.38646	+	7.36066i	−0.0553259	+	0.293723i
$629$		−	15.9059i		−	0.634208i
$630$		0			0
$631$			8.53598i			0.339812i	0.985460	+	0.169906i	$0.0543464\pi$
$631$			8.53598i			0.339812i	−0.985460	+	0.169906i	$0.945654\pi$
$632$	−39.2275	−	17.0574i	−1.56039	−	0.678506i
$633$		0			0
$634$	8.43928	+	27.3197i	0.335167	+	1.08500i
$635$	3.44481	+	7.68299i	0.136703	+	0.304890i
$636$		0			0
$637$	2.57402	−	0.689706i	0.101986	−	0.0273272i
$638$	18.5520	−	11.6676i	0.734481	−	0.461925i
$639$		0			0
$640$	−25.1738	−	2.50630i	−0.995080	−	0.0990701i
$641$	−5.32828	+	9.22886i	−0.210454	+	0.364518i	−0.951857	−	0.306543i	$-0.900828\pi$
$641$	−5.32828	+	9.22886i	−0.210454	+	0.364518i	0.741402	+	0.671061i	$0.234161\pi$
$642$		0			0
$643$	0.0850425	−	0.317383i	0.00335375	−	0.0125164i	−0.964229	−	0.265072i	$-0.914604\pi$
$643$	0.0850425	−	0.317383i	0.00335375	−	0.0125164i	0.967582	+	0.252555i	$0.0812710\pi$
$644$	19.4783	−	1.47575i	0.767551	−	0.0581528i
$645$		0			0
$646$	−11.4328	+	12.3318i	−0.449819	+	0.485189i
$647$	−1.08970	+	1.08970i	−0.0428405	+	0.0428405i	−0.728203	−	0.685362i	$-0.759644\pi$
$647$	−1.08970	+	1.08970i	−0.0428405	+	0.0428405i	0.685362	+	0.728203i	$0.259644\pi$
$648$		0			0
$649$		−	39.6684i		−	1.55712i
$650$	−30.3772	+	21.6409i	−1.19149	+	0.848826i
$651$		0			0
$652$	−14.5228	−	12.4772i	−0.568758	−	0.488644i
$653$	22.1285	+	5.92931i	0.865954	+	0.232032i	0.664337	−	0.747433i	$-0.268714\pi$
$653$	22.1285	+	5.92931i	0.865954	+	0.232032i	0.201617	+	0.979465i	$0.435380\pi$
$654$		0			0
$655$	4.35947	+	27.0659i	0.170338	+	1.05755i
$656$	20.2322	+	25.2852i	0.789934	+	0.987221i
$657$		0			0
$658$	0.459959	+	0.731356i	0.0179311	+	0.0285112i
$659$	6.24819	−	10.8222i	0.243395	−	0.421572i	−0.718284	−	0.695750i	$-0.755072\pi$
$659$	6.24819	−	10.8222i	0.243395	−	0.421572i	0.961679	+	0.274177i	$0.0884055\pi$
$660$		0			0
$661$	−2.84081	−	4.92043i	−0.110495	−	0.191382i	0.805475	−	0.592630i	$-0.201910\pi$
$661$	−2.84081	−	4.92043i	−0.110495	−	0.191382i	−0.915970	+	0.401247i	$0.868577\pi$
$662$	12.8981	−	24.4287i	0.501300	−	0.949449i
$663$		0			0
$664$	−16.0891	−	40.8467i	−0.624379	−	1.58516i
$665$	22.0281	+	2.25696i	0.854212	+	0.0875213i
$666$		0			0
$667$	12.0512	−	12.0512i	0.466623	−	0.466623i
$668$	−7.27054	−	1.36949i	−0.281306	−	0.0529871i
$669$		0			0
$670$	−1.96024	−	1.30651i	−0.0757306	−	0.0504748i
$671$	−27.8734	+	16.0927i	−1.07604	+	0.621252i
$672$		0			0
$673$	7.75138	+	28.9286i	0.298794	+	1.11511i	0.938157	+	0.346209i	$0.112531\pi$
$673$	7.75138	+	28.9286i	0.298794	+	1.11511i	−0.639363	+	0.768905i	$0.720802\pi$
$674$	13.9473	+	3.17736i	0.537229	+	0.122387i
$675$		0			0
$676$	−26.7190	−	12.8402i	−1.02765	−	0.493854i
$677$	−2.56951	+	0.688499i	−0.0987544	+	0.0264612i	−0.307858	−	0.951432i	$-0.599612\pi$
$677$	−2.56951	+	0.688499i	−0.0987544	+	0.0264612i	0.209103	+	0.977894i	$0.432945\pi$
$678$		0			0
$679$	−4.03213	−	6.98386i	−0.154739	−	0.268016i
$680$	9.86611	+	16.6502i	0.378348	+	0.638505i
$681$		0			0
$682$	−0.402246	−	10.6336i	−0.0154028	−	0.407181i
$683$	−31.3443	−	31.3443i	−1.19936	−	1.19936i	−0.974359	−	0.224999i	$-0.927762\pi$
$683$	−31.3443	−	31.3443i	−1.19936	−	1.19936i	−0.224999	−	0.974359i	$-0.572238\pi$
$684$		0			0
$685$	−2.10831	+	20.5772i	−0.0805544	+	0.786215i
$686$	−18.3903	+	19.8363i	−0.702143	+	0.757353i
$687$		0			0
$688$	19.2771	−	8.44818i	0.734934	−	0.322084i
$689$	−1.71721	+	0.991433i	−0.0654206	+	0.0377706i
$690$		0			0
$691$	−1.44150	−	0.832251i	−0.0548373	−	0.0316603i	0.472331	−	0.881421i	$-0.343413\pi$
$691$	−1.44150	−	0.832251i	−0.0548373	−	0.0316603i	−0.527168	+	0.849761i	$0.676746\pi$
$692$	15.3534	+	43.7622i	0.583647	+	1.66359i
$693$		0			0
$694$	−7.89322	+	34.6479i	−0.299623	+	1.31522i
$695$	39.5366	−	6.36812i	1.49971	−	0.241557i
$696$		0			0
$697$	6.41200	−	23.9299i	0.242872	−	0.906410i
$698$	11.4608	−	21.7065i	0.433799	−	0.821603i
$699$		0			0
$700$	9.69811	−	23.5675i	0.366554	−	0.890767i
$701$	6.95642			0.262740			0.131370	−	0.991333i	$-0.458062\pi$
$701$	6.95642			0.262740			0.131370	+	0.991333i	$0.458062\pi$
$702$		0			0
$703$	14.2818	+	14.2818i	0.538649	+	0.538649i
$704$	−26.6603	−	8.15185i	−1.00480	−	0.307234i
$705$		0			0
$706$	−40.3499	+	12.4644i	−1.51859	+	0.469105i
$707$	10.6328	+	2.84905i	0.399888	+	0.107150i
$708$		0			0
$709$	−41.5369	−	23.9814i	−1.55995	−	0.900639i	−0.997260	−	0.0739729i	$-0.976432\pi$
$709$	−41.5369	−	23.9814i	−1.55995	−	0.900639i	−0.562693	−	0.826666i	$-0.690235\pi$
$710$	−2.09673	+	6.20035i	−0.0786891	+	0.232695i
$711$		0			0
$712$	−10.1589	+	1.15729i	−0.380722	+	0.0433712i
$713$	−2.14175	−	7.99314i	−0.0802093	−	0.299345i
$714$		0			0
$715$	−37.5046	+	16.8159i	−1.40259	+	0.628878i
$716$	19.9798	−	1.51375i	0.746679	−	0.0565715i
$717$		0			0
$718$	−1.39737	−	36.9403i	−0.0521495	−	1.37860i
$719$	−27.9555			−1.04257			−0.521283	−	0.853384i	$-0.674546\pi$
$719$	−27.9555			−1.04257			−0.521283	+	0.853384i	$0.674546\pi$
$720$		0			0
$721$	3.48106			0.129641
$722$	0.208531	+	5.51263i	0.00776072	+	0.205159i
$723$		0			0
$724$	39.8479	−	3.01904i	1.48094	−	0.112202i
$725$	−6.98155	−	21.1103i	−0.259288	−	0.784017i
$726$		0			0
$727$	8.62843	+	32.2018i	0.320011	+	1.19430i	0.919233	+	0.393714i	$0.128810\pi$
$727$	8.62843	+	32.2018i	0.320011	+	1.19430i	−0.599222	+	0.800583i	$0.704523\pi$
$728$	37.7766	−	4.30345i	1.40009	−	0.159496i
$729$		0			0
$730$	35.9755	−	17.7930i	1.33151	−	0.658547i
$731$	−13.9443	−	8.05077i	−0.515750	−	0.297768i
$732$		0			0
$733$	1.63983	+	0.439391i	0.0605685	+	0.0162293i	0.288976	−	0.957336i	$-0.406685\pi$
$733$	1.63983	+	0.439391i	0.0605685	+	0.0162293i	−0.228408	+	0.973566i	$0.573352\pi$
$734$	−31.0731	+	9.59872i	−1.14693	+	0.354295i
$735$		0			0
$736$	−21.6225	−	1.57582i	−0.797014	−	0.0580856i
$737$	−1.83567	−	1.83567i	−0.0676177	−	0.0676177i
$738$		0			0
$739$	48.7588			1.79362			0.896811	−	0.442414i	$-0.145878\pi$
$739$	48.7588			1.79362			0.896811	+	0.442414i	$0.145878\pi$
$740$	20.4318	−	11.0856i	0.751088	−	0.407513i
$741$		0			0
$742$	0.632595	−	1.19812i	0.0232233	−	0.0439843i
$743$	5.51322	−	20.5756i	0.202260	−	0.754846i	−0.788007	−	0.615667i	$-0.788887\pi$
$743$	5.51322	−	20.5756i	0.202260	−	0.754846i	0.990267	−	0.139179i	$-0.0444465\pi$
$744$		0			0
$745$	−0.984389	−	6.11161i	−0.0360652	−	0.223912i
$746$	4.17530	−	18.3278i	0.152868	−	0.671028i
$747$		0			0
$748$	7.06065	+	20.1253i	0.258163	+	0.735852i
$749$	−16.6294	−	9.60100i	−0.607626	−	0.350813i
$750$		0			0
$751$	30.0558	−	17.3527i	1.09675	−	0.633209i	0.161385	−	0.986892i	$-0.448404\pi$
$751$	30.0558	−	17.3527i	1.09675	−	0.633209i	0.935366	+	0.353682i	$0.115071\pi$
$752$	−0.384886	−	0.878237i	−0.0140354	−	0.0320260i
$753$		0			0
$754$	22.5528	−	24.3261i	0.821325	−	0.885906i
$755$	13.0485	−	10.6231i	0.474883	−	0.386615i
$756$		0			0
$757$	21.6732	+	21.6732i	0.787727	+	0.787727i	0.981121	−	0.193394i	$-0.0619496\pi$
$757$	21.6732	+	21.6732i	0.787727	+	0.787727i	−0.193394	+	0.981121i	$0.561950\pi$
$758$	−0.682434	−	18.0405i	−0.0247871	−	0.655262i
$759$		0			0
$760$	−23.8089	−	6.09138i	−0.863639	−	0.220958i
$761$	−13.2539	−	22.9564i	−0.480452	−	0.832167i	0.519297	−	0.854594i	$-0.326194\pi$
$761$	−13.2539	−	22.9564i	−0.480452	−	0.832167i	−0.999748	+	0.0224270i	$0.992861\pi$
$762$		0			0
$763$	34.9188	−	9.35647i	1.26415	−	0.338727i
$764$	28.2472	+	13.5746i	1.02195	+	0.491112i
$765$		0			0
$766$	48.4453	+	11.0364i	1.75040	+	0.398763i
$767$	−15.5401	−	57.9964i	−0.561120	−	2.09413i
$768$		0			0
$769$	−10.2142	+	5.89716i	−0.368333	+	0.212657i	−0.672730	−	0.739888i	$-0.734878\pi$
$769$	−10.2142	+	5.89716i	−0.368333	+	0.212657i	0.304397	+	0.952545i	$0.401545\pi$
$770$	15.5758	−	23.3694i	0.561313	−	0.842173i
$771$		0			0
$772$	42.4187	+	7.99004i	1.52668	+	0.287568i
$773$	−7.36402	+	7.36402i	−0.264865	+	0.264865i	−0.827027	−	0.562162i	$-0.809970\pi$
$773$	−7.36402	+	7.36402i	−0.264865	+	0.264865i	0.562162	+	0.827027i	$0.309970\pi$
$774$		0			0
$775$	−10.5717	−	2.18930i	−0.379746	−	0.0786420i
$776$	3.28008	+	8.32738i	0.117748	+	0.298935i
$777$		0			0
$778$	11.7933	−	22.3362i	0.422810	−	0.800791i
$779$	15.7293	+	27.2439i	0.563560	+	0.976115i
$780$		0			0
$781$	−3.60645	+	6.24656i	−0.129049	+	0.223520i
$782$	8.82982	+	14.0398i	0.315754	+	0.502062i
$783$		0			0
$784$	1.57789	−	1.26257i	0.0563533	−	0.0450916i
$785$	6.78772	+	4.90448i	0.242264	+	0.175048i
$786$		0			0
$787$	29.6943	+	7.95656i	1.05849	+	0.283621i	0.745755	−	0.666220i	$-0.232089\pi$
$787$	29.6943	+	7.95656i	1.05849	+	0.283621i	0.312733	+	0.949841i	$0.398756\pi$
$788$	−20.2659	−	17.4113i	−0.721943	−	0.620253i
$789$		0			0
$790$	−35.9199	+	31.5745i	−1.27797	+	1.12337i
$791$			1.15443i			0.0410468i
$792$		0			0
$793$	−34.4474	+	34.4474i	−1.22326	+	1.22326i
$794$	31.1450	−	33.5939i	1.10529	−	1.19220i
$795$		0			0
$796$	−4.10980	+	0.311375i	−0.145668	+	0.0110364i
$797$	−4.77511	+	17.8210i	−0.169143	+	0.631251i	0.828332	+	0.560237i	$0.189290\pi$
$797$	−4.77511	+	17.8210i	−0.169143	+	0.631251i	−0.997475	+	0.0710135i	$0.977377\pi$
$798$		0			0
$799$	−0.366781	+	0.635283i	−0.0129758	+	0.0224747i
$800$	−14.5117	+	24.2778i	−0.513067	+	0.858349i
$801$		0			0
$802$	36.5386	−	22.9796i	1.29022	−	0.811438i
$803$	42.7219	−	11.4473i	1.50762	−	0.403967i
$804$		0			0
$805$	7.77327	−	20.4096i	0.273972	−	0.719344i
$806$	−4.75380	−	15.3890i	−0.167445	−	0.542056i
$807$		0			0
$808$	−11.2037	−	4.87173i	−0.394144	−	0.171387i
$809$			45.3459i			1.59428i	0.603798	+	0.797138i	$0.293653\pi$
$809$			45.3459i			1.59428i	−0.603798	+	0.797138i	$0.706347\pi$
$810$		0			0
$811$			32.6505i			1.14652i	0.819375	+	0.573258i	$0.194321\pi$
$811$			32.6505i			1.14652i	−0.819375	+	0.573258i	$0.805679\pi$
$812$	−4.19563	+	22.2744i	−0.147238	+	0.781677i
$813$		0			0
$814$	24.4753	−	7.56062i	0.857859	−	0.265000i
$815$	−19.5330	+	8.75799i	−0.684211	+	0.306779i
$816$		0			0
$817$	19.7493	−	5.29182i	0.690942	−	0.185137i
$818$	12.3617	+	19.6557i	0.432217	+	0.687244i
$819$		0			0
$820$	35.2079	−	8.44140i	1.22951	−	0.294787i
$821$	14.0278	−	24.2968i	0.489572	−	0.847964i	−0.510356	−	0.859963i	$-0.670486\pi$
$821$	14.0278	−	24.2968i	0.489572	−	0.847964i	0.999928	+	0.0119995i	$0.00381966\pi$
$822$		0			0
$823$	−8.98407	+	33.5290i	−0.313165	+	1.16875i	0.612521	+	0.790454i	$0.290156\pi$
$823$	−8.98407	+	33.5290i	−0.313165	+	1.16875i	−0.925686	+	0.378293i	$0.876511\pi$
$824$	−3.82099	−	0.571117i	−0.133111	−	0.0198958i
$825$		0			0
$826$	30.0857	+	27.8925i	1.04682	+	0.970504i
$827$	−0.244245	+	0.244245i	−0.00849323	+	0.00849323i	−0.711341	−	0.702847i	$-0.751912\pi$
$827$	−0.244245	+	0.244245i	−0.00849323	+	0.00849323i	0.702847	+	0.711341i	$0.251912\pi$
$828$		0			0
$829$			24.5821i			0.853771i	0.904306	+	0.426885i	$0.140389\pi$
$829$			24.5821i			0.853771i	−0.904306	+	0.426885i	$0.859611\pi$
$830$	−48.9816	−	3.15349i	−1.70017	−	0.109459i
$831$		0			0
$832$	−42.1715	−	1.47409i	−1.46204	−	0.0511050i
$833$	−1.49332	−	0.400133i	−0.0517404	−	0.0138638i
$834$		0			0
$835$	−4.84443	+	6.70462i	−0.167648	+	0.232023i
$836$	−24.4101	−	11.7307i	−0.844243	−	0.405713i
$837$		0			0
$838$	11.9962	−	7.54458i	0.414402	−	0.260623i
$839$	4.08967	−	7.08351i	0.141191	−	0.244550i	−0.786754	−	0.617266i	$-0.788240\pi$
$839$	4.08967	−	7.08351i	0.141191	−	0.244550i	0.927945	+	0.372716i	$0.121574\pi$
$840$		0			0
$841$	−4.61225	−	7.98866i	−0.159043	−	0.275471i
$842$	9.21278	+	4.86427i	0.317493	+	0.167634i
$843$		0			0
$844$	3.80377	−	2.59794i	0.130931	−	0.0894247i
$845$	−25.7024	+	20.9250i	−0.884189	+	0.719842i
$846$		0			0
$847$	2.06171	−	2.06171i	0.0708410	−	0.0708410i
$848$	−0.890937	+	1.21133i	−0.0305949	+	0.0415972i
$849$		0			0
$850$	21.5398	−	2.06126i	0.738808	−	0.0707005i
$851$	17.2517	−	9.96030i	0.591382	−	0.341435i
$852$		0			0
$853$	−7.21700	−	26.9342i	−0.247105	−	0.922210i	−0.972314	−	0.233680i	$-0.924923\pi$
$853$	−7.21700	−	26.9342i	−0.247105	−	0.922210i	0.725208	−	0.688530i	$-0.241743\pi$
$854$	7.39374	−	32.4554i	0.253009	−	1.11060i
$855$		0			0
$856$	16.6781	+	13.2668i	0.570047	+	0.453451i
$857$	−42.5245	+	11.3944i	−1.45261	+	0.389226i	−0.896931	−	0.442171i	$-0.854208\pi$
$857$	−42.5245	+	11.3944i	−1.45261	+	0.389226i	−0.555679	+	0.831397i	$0.687542\pi$
$858$		0			0
$859$	−1.47011	−	2.54630i	−0.0501593	−	0.0868785i	0.839856	−	0.542810i	$-0.182640\pi$
$859$	−1.47011	−	2.54630i	−0.0501593	−	0.0868785i	−0.890015	+	0.455931i	$0.849306\pi$
$860$	0.623098	−	23.5231i	0.0212474	−	0.802131i
$861$		0			0
$862$	−23.2433	+	0.879245i	−0.791671	+	0.0299472i
$863$	−7.13386	−	7.13386i	−0.242839	−	0.242839i	0.575184	−	0.818024i	$-0.304930\pi$
$863$	−7.13386	−	7.13386i	−0.242839	−	0.242839i	−0.818024	+	0.575184i	$0.804930\pi$
$864$		0			0
$865$	51.5814	+	5.28495i	1.75382	+	0.179694i
$866$	5.54562	+	5.14136i	0.188448	+	0.174710i
$867$		0			0
$868$	8.34766	+	7.17184i	0.283338	+	0.243428i
$869$	−45.6419	+	26.3514i	−1.54830	+	0.893909i
$870$		0			0
$871$	−3.40292	−	1.96468i	−0.115304	−	0.0665706i
$872$	−39.8638	+	4.54122i	−1.34996	+	0.153785i
$873$		0			0
$874$	−20.5346	−	4.67802i	−0.694592	−	0.158237i
$875$	−19.2312	−	21.0240i	−0.650133	−	0.710742i
$876$		0			0
$877$	6.03921	−	22.5386i	0.203930	−	0.761076i	−0.785843	−	0.618426i	$-0.787771\pi$
$877$	6.03921	−	22.5386i	0.203930	−	0.761076i	0.989773	−	0.142650i	$-0.0455625\pi$
$878$	46.0482	+	24.3130i	1.55405	+	0.820525i
$879$		0			0
$880$	−20.9309	+	23.0960i	−0.705580	+	0.778566i
$881$	42.4590			1.43048			0.715241	−	0.698878i	$-0.246317\pi$
$881$	42.4590			1.43048			0.715241	+	0.698878i	$0.246317\pi$
$882$		0			0
$883$	7.64008	+	7.64008i	0.257109	+	0.257109i	0.823877	−	0.566768i	$-0.191807\pi$
$883$	7.64008	+	7.64008i	0.257109	+	0.257109i	−0.566768	+	0.823877i	$0.691807\pi$
$884$	18.2069	+	26.6577i	0.612366	+	0.896595i
$885$		0			0
$886$	−5.05266	−	16.3565i	−0.169747	−	0.549508i
$887$	4.69064	+	1.25685i	0.157496	+	0.0422010i	0.336706	−	0.941610i	$-0.390687\pi$
$887$	4.69064	+	1.25685i	0.157496	+	0.0422010i	−0.179209	+	0.983811i	$0.557354\pi$
$888$		0			0
$889$	−8.31067	−	4.79817i	−0.278731	−	0.160925i
$890$	−3.66200	+	10.8291i	−0.122750	+	0.362991i
$891$		0			0
$892$	31.5002	−	11.0514i	1.05470	−	0.370028i
$893$	−0.241087	−	0.899750i	−0.00806768	−	0.0301090i
$894$		0			0
$895$	7.97342	−	20.9351i	0.266522	−	0.699783i
$896$	24.9285	−	14.4880i	0.832803	−	0.484010i
$897$		0			0
$898$	1.48143	−	0.0560395i	0.0494361	−	0.00187006i
$899$	9.60189			0.320241
$900$		0			0
$901$	1.15036			0.0383241
$902$	39.8703	−	1.50821i	1.32753	−	0.0502178i
$903$		0			0
$904$	0.189401	−	1.26716i	0.00629938	−	0.0421452i
$905$	15.9023	−	41.7532i	0.528610	−	1.38792i
$906$		0			0
$907$	−15.5709	−	58.1113i	−0.517022	−	1.92955i	−0.305620	−	0.952154i	$-0.598864\pi$
$907$	−15.5709	−	58.1113i	−0.517022	−	1.92955i	−0.211402	−	0.977399i	$-0.567803\pi$
$908$	−3.33774	−	9.51369i	−0.110767	−	0.315723i
$909$		0			0
$910$	13.6174	−	40.2685i	0.451411	−	1.33489i
$911$	2.72513	+	1.57335i	0.0902875	+	0.0521275i	0.544464	−	0.838784i	$-0.316733\pi$
$911$	2.72513	+	1.57335i	0.0902875	+	0.0521275i	−0.454176	+	0.890912i	$0.650066\pi$
$912$		0			0
$913$	−52.2465	−	13.9994i	−1.72911	−	0.463313i
$914$	5.67979	+	18.3867i	0.187871	+	0.608176i
$915$		0			0
$916$	12.8128	−	8.75102i	0.423347	−	0.289142i
$917$	−22.0936	−	22.0936i	−0.729594	−	0.729594i
$918$		0			0
$919$	−31.3326			−1.03357			−0.516783	−	0.856116i	$-0.672871\pi$
$919$	−31.3326			−1.03357			−0.516783	+	0.856116i	$0.672871\pi$
$920$	−11.8808	+	21.1273i	−0.391699	+	0.696547i
$921$		0			0
$922$	14.3174	+	7.55947i	0.471519	+	0.248958i
$923$	−2.82565	+	10.5455i	−0.0930075	+	0.347109i
$924$		0			0
$925$	−1.49602	−	25.9461i	−0.0491888	−	0.853101i
$926$	6.47871	+	1.47593i	0.212904	+	0.0485020i
$927$		0			0
$928$	8.25976	−	23.7611i	0.271140	−	0.779998i
$929$	−10.8495	−	6.26399i	−0.355962	−	0.205515i	0.311346	−	0.950297i	$-0.399220\pi$
$929$	−10.8495	−	6.26399i	−0.355962	−	0.205515i	−0.667308	+	0.744782i	$0.732554\pi$
$930$		0			0
$931$	1.70012	−	0.981567i	0.0557193	−	0.0321696i
$932$	−7.65540	+	8.91050i	−0.250761	+	0.291873i
$933$		0			0
$934$	37.4602	+	34.7294i	1.22573	+	1.13638i
$935$	23.7211	+	2.43043i	0.775763	+	0.0794835i
$936$		0			0
$937$	−27.1824	−	27.1824i	−0.888011	−	0.888011i	0.106321	−	0.994332i	$-0.466093\pi$
$937$	−27.1824	−	27.1824i	−0.888011	−	0.888011i	−0.994332	+	0.106321i	$0.966093\pi$
$938$	2.68296	−	0.101490i	0.0876016	−	0.00331378i
$939$		0			0
$940$	−1.07168	−	0.0283874i	−0.0349542	−	0.000925894i
$941$	−12.5030	−	21.6558i	−0.407585	−	0.705957i	0.587034	−	0.809562i	$-0.300296\pi$
$941$	−12.5030	−	21.6558i	−0.407585	−	0.705957i	−0.994619	+	0.103605i	$0.966962\pi$
$942$		0			0
$943$	29.9700	−	8.03043i	0.975956	−	0.261507i
$944$	−28.4475	−	35.5522i	−0.925886	−	1.15713i
$945$		0			0
$946$	5.75996	−	25.2838i	0.187273	−	0.822048i
$947$	15.5957	+	58.2038i	0.506791	+	1.89137i	0.450098	+	0.892979i	$0.351389\pi$
$947$	15.5957	+	58.2038i	0.506791	+	1.89137i	0.0566928	+	0.998392i	$0.481944\pi$
$948$		0			0
$949$	57.9762	−	33.4726i	1.88199	−	1.08657i
$950$	−17.4897	+	21.1913i	−0.567441	+	0.687536i
$951$		0			0
$952$	−20.2282	−	8.79588i	−0.655600	−	0.285076i
$953$	−7.86673	+	7.86673i	−0.254828	+	0.254828i	−0.822947	−	0.568118i	$-0.807672\pi$
$953$	−7.86673	+	7.86673i	−0.254828	+	0.254828i	0.568118	+	0.822947i	$0.307672\pi$
$954$		0			0
$955$	27.1724	−	22.1218i	0.879279	−	0.715845i
$956$	2.88896	+	4.22988i	0.0934357	+	0.136804i
$957$		0			0
$958$	15.1631	+	8.00599i	0.489898	+	0.258662i
$959$	−11.7875	−	20.4166i	−0.380638	−	0.659285i
$960$		0			0
$961$	−13.1689	+	22.8092i	−0.424804	+	0.735782i
$962$	32.8218	−	20.6420i	1.05822	−	0.665526i
$963$		0			0
$964$	−11.9448	+	24.8556i	−0.384715	+	0.800546i
$965$	28.2640	−	39.1169i	0.909849	−	1.25922i
$966$		0			0
$967$	−15.5687	−	4.17163i	−0.500657	−	0.134151i	−0.000352232	−	1.00000i	$-0.500112\pi$
$967$	−15.5687	−	4.17163i	−0.500657	−	0.134151i	−0.500305	+	0.865849i	$0.666779\pi$
$968$	−2.60129	+	1.92478i	−0.0836085	+	0.0618649i
$969$		0			0
$970$	9.98583	+	0.642899i	0.320626	+	0.0206422i
$971$			51.3038i			1.64642i	0.567739	+	0.823209i	$0.307818\pi$
$971$			51.3038i			1.64642i	−0.567739	+	0.823209i	$0.692182\pi$
$972$		0			0
$973$	−32.2733	+	32.2733i	−1.03464	+	1.03464i
$974$	18.4243	+	17.0812i	0.590354	+	0.547318i
$975$		0			0
$976$	−13.4405	+	34.4117i	−0.430221	+	1.10149i
$977$	0.369048	−	1.37730i	0.0118069	−	0.0440639i	−0.959771	−	0.280784i	$-0.909406\pi$
$977$	0.369048	−	1.37730i	0.0118069	−	0.0440639i	0.971578	+	0.236720i	$0.0760723\pi$
$978$		0			0
$979$	−6.29876	+	10.9098i	−0.201309	+	0.348678i
$980$	−0.526776	−	2.19711i	−0.0168272	−	0.0701840i
$981$		0			0
$982$	0.0950129	+	0.151075i	0.00303198	+	0.00482099i
$983$	−44.4088	+	11.8993i	−1.41642	+	0.379529i	−0.884212	−	0.467085i	$-0.845304\pi$
$983$	−44.4088	+	11.8993i	−1.41642	+	0.379529i	−0.532208	+	0.846614i	$0.678638\pi$
$984$		0			0
$985$	−27.2574	+	12.2214i	−0.868492	+	0.389405i
$986$	−18.3875	+	5.68005i	−0.585577	+	0.180890i
$987$		0			0
$988$	−40.2838	−	7.58791i	−1.28160	−	0.241404i
$989$		−	20.1657i		−	0.641231i
$990$		0			0
$991$		−	47.4822i		−	1.50832i	−0.656689	−	0.754161i	$-0.728044\pi$
$991$		−	47.4822i		−	1.50832i	0.656689	−	0.754161i	$-0.271956\pi$
$992$	−7.98618	−	9.24173i	−0.253561	−	0.293425i
$993$		0			0
$994$	−2.20173	−	7.12745i	−0.0698346	−	0.226069i
$995$	−1.64012	+	4.30631i	−0.0519952	+	0.136519i
$996$		0			0
$997$	−54.8142	+	14.6874i	−1.73598	+	0.465156i	−0.981548	−	0.191218i	$-0.938756\pi$
$997$	−54.8142	+	14.6874i	−1.73598	+	0.465156i	−0.754436	+	0.656373i	$0.772090\pi$
$998$	−48.5722	+	30.5477i	−1.53753	+	0.966971i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.y.a.127.15		128
3.2	odd	2		180.2.x.a.7.18	yes	128
4.3	odd	2	inner	540.2.y.a.127.21		128
5.3	odd	4	inner	540.2.y.a.343.1		128
9.4	even	3	inner	540.2.y.a.307.28		128
9.5	odd	6		180.2.x.a.67.5	yes	128
12.11	even	2		180.2.x.a.7.12	✓	128
15.2	even	4		900.2.bf.e.43.1		128
15.8	even	4		180.2.x.a.43.32	yes	128
15.14	odd	2		900.2.bf.e.7.15		128
20.3	even	4	inner	540.2.y.a.343.28		128
36.23	even	6		180.2.x.a.67.32	yes	128
36.31	odd	6	inner	540.2.y.a.307.1		128
45.13	odd	12	inner	540.2.y.a.523.21		128
45.14	odd	6		900.2.bf.e.607.28		128
45.23	even	12		180.2.x.a.103.12	yes	128
45.32	even	12		900.2.bf.e.643.21		128
60.23	odd	4		180.2.x.a.43.5	yes	128
60.47	odd	4		900.2.bf.e.43.28		128
60.59	even	2		900.2.bf.e.7.21		128
180.23	odd	12		180.2.x.a.103.18	yes	128
180.59	even	6		900.2.bf.e.607.1		128
180.103	even	12	inner	540.2.y.a.523.15		128
180.167	odd	12		900.2.bf.e.643.15		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.12	✓	128	12.11	even	2
180.2.x.a.7.18	yes	128	3.2	odd	2
180.2.x.a.43.5	yes	128	60.23	odd	4
180.2.x.a.43.32	yes	128	15.8	even	4
180.2.x.a.67.5	yes	128	9.5	odd	6
180.2.x.a.67.32	yes	128	36.23	even	6
180.2.x.a.103.12	yes	128	45.23	even	12
180.2.x.a.103.18	yes	128	180.23	odd	12
540.2.y.a.127.15		128	1.1	even	1	trivial
540.2.y.a.127.21		128	4.3	odd	2	inner
540.2.y.a.307.1		128	36.31	odd	6	inner
540.2.y.a.307.28		128	9.4	even	3	inner
540.2.y.a.343.1		128	5.3	odd	4	inner
540.2.y.a.343.28		128	20.3	even	4	inner
540.2.y.a.523.15		128	180.103	even	12	inner
540.2.y.a.523.21		128	45.13	odd	12	inner
900.2.bf.e.7.15		128	15.14	odd	2
900.2.bf.e.7.21		128	60.59	even	2
900.2.bf.e.43.1		128	15.2	even	4
900.2.bf.e.43.28		128	60.47	odd	4
900.2.bf.e.607.1		128	180.59	even	6
900.2.bf.e.607.28		128	45.14	odd	6
900.2.bf.e.643.15		128	180.167	odd	12
900.2.bf.e.643.21		128	45.32	even	12

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0534584 - 1.41320i) q^{2} +(-1.99428 + 0.151095i) q^{4} +(-0.795868 + 2.08964i) q^{5} +(-0.659597 - 2.46165i) q^{7} +(0.320139 + 2.81025i) q^{8} +O(q^{10})\)	\(q+(-0.0534584 - 1.41320i) q^{2} +(-1.99428 + 0.151095i) q^{4} +(-0.795868 + 2.08964i) q^{5} +(-0.659597 - 2.46165i) q^{7} +(0.320139 + 2.81025i) q^{8} +(2.99563 + 1.01301i) q^{10} +(3.01796 + 1.74242i) q^{11} +(5.09493 + 1.36518i) q^{13} +(-3.44355 + 1.06374i) q^{14} +(3.95434 - 0.602653i) q^{16} +(-2.16382 - 2.16382i) q^{17} +3.88577 q^{19} +(1.27145 - 4.28759i) q^{20} +(2.30106 - 4.35813i) q^{22} +(0.991920 - 3.70190i) q^{23} +(-3.73319 - 3.32615i) q^{25} +(1.65691 - 7.27315i) q^{26} +(1.68737 + 4.80957i) q^{28} +(3.85118 + 2.22348i) q^{29} +(1.86992 - 1.07960i) q^{31} +(-1.06306 - 5.55607i) q^{32} +(-2.94224 + 3.17359i) q^{34} +(5.66891 + 0.580828i) q^{35} +(3.67542 + 3.67542i) q^{37} +(-0.207727 - 5.49138i) q^{38} +(-6.12720 - 1.56761i) q^{40} +(4.04792 + 7.01121i) q^{41} +(5.08248 - 1.36185i) q^{43} +(-6.28194 - 3.01888i) q^{44} +(-5.28456 - 1.20389i) q^{46} +(-0.0620436 - 0.231550i) q^{47} +(0.437526 - 0.252606i) q^{49} +(-4.50096 + 5.45356i) q^{50} +(-10.3670 - 1.95274i) q^{52} +(-0.265818 + 0.265818i) q^{53} +(-6.04292 + 4.91971i) q^{55} +(6.70669 - 2.64170i) q^{56} +(2.93635 - 5.56137i) q^{58} +(-5.69158 - 9.85810i) q^{59} +(-4.61792 + 7.99848i) q^{61} +(-1.62566 - 2.58487i) q^{62} +(-7.79502 + 1.79934i) q^{64} +(-6.90763 + 9.56007i) q^{65} +(-0.719566 - 0.192807i) q^{67} +(4.64221 + 3.98832i) q^{68} +(0.517777 - 8.04237i) q^{70} +2.06980i q^{71} +(8.97449 - 8.97449i) q^{73} +(4.99763 - 5.39060i) q^{74} +(-7.74933 + 0.587121i) q^{76} +(2.29859 - 8.57845i) q^{77} +(-7.56173 + 13.0973i) q^{79} +(-1.88780 + 8.74278i) q^{80} +(9.69186 - 6.09534i) q^{82} +(-14.9925 + 4.01723i) q^{83} +(6.24371 - 2.79948i) q^{85} +(-2.19627 - 7.10978i) q^{86} +(-3.93047 + 9.03903i) q^{88} +3.61495i q^{89} -13.4424i q^{91} +(-1.41883 + 7.53251i) q^{92} +(-0.323910 + 0.100059i) q^{94} +(-3.09256 + 8.11986i) q^{95} +(3.05651 - 0.818990i) q^{97} +(-0.380373 - 0.604809i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more