LMFDB - Embedded newform 360.2.bs.a.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(113,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("360.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bs (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37710 + 1.05053i) q^{3} +(2.15536 - 0.595338i) q^{5} +(0.205487 + 0.0550600i) q^{7} +(0.792791 - 2.89335i) q^{9} +O(q^{10})$	\(q+(-1.37710 + 1.05053i) q^{3} +(2.15536 - 0.595338i) q^{5} +(0.205487 + 0.0550600i) q^{7} +(0.792791 - 2.89335i) q^{9} +(1.07045 - 0.618027i) q^{11} +(1.61453 - 0.432612i) q^{13} +(-2.34272 + 3.08410i) q^{15} +(3.44214 + 3.44214i) q^{17} +1.17868i q^{19} +(-0.340817 + 0.140046i) q^{21} +(1.68957 + 6.30557i) q^{23} +(4.29115 - 2.56633i) q^{25} +(1.94779 + 4.81727i) q^{27} +(-1.11541 - 1.93195i) q^{29} +(3.60355 - 6.24153i) q^{31} +(-0.824866 + 1.97562i) q^{33} +(0.475677 - 0.00366001i) q^{35} +(-3.01616 + 3.01616i) q^{37} +(-1.76889 + 2.29185i) q^{39} +(8.24325 + 4.75924i) q^{41} +(1.19664 - 4.46591i) q^{43} +(-0.0137729 - 6.70819i) q^{45} +(0.137142 - 0.511821i) q^{47} +(-6.02298 - 3.47737i) q^{49} +(-8.35621 - 1.12410i) q^{51} +(-5.52081 + 5.52081i) q^{53} +(1.93928 - 1.96935i) q^{55} +(-1.23824 - 1.62316i) q^{57} +(-5.83746 + 10.1108i) q^{59} +(-6.60746 - 11.4445i) q^{61} +(0.322216 - 0.550894i) q^{63} +(3.22234 - 1.89363i) q^{65} +(-1.22176 - 4.55967i) q^{67} +(-8.95087 - 6.90844i) q^{69} -15.7215i q^{71} +(-2.55375 - 2.55375i) q^{73} +(-3.21332 + 8.04205i) q^{75} +(0.253993 - 0.0680572i) q^{77} +(-3.27872 + 1.89297i) q^{79} +(-7.74296 - 4.58765i) q^{81} +(-15.0549 - 4.03395i) q^{83} +(9.46827 + 5.36980i) q^{85} +(3.56559 + 1.48871i) q^{87} +10.4067 q^{89} +0.355584 q^{91} +(1.59445 + 12.3808i) q^{93} +(0.701715 + 2.54049i) q^{95} +(-13.8972 - 3.72373i) q^{97} +(-0.939523 - 3.58717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−1.37710	+	1.05053i	−0.795067	+	0.606521i
$3$	−1.37710	+	1.05053i	−0.795067	+	0.606521i
$4$		0			0
$5$	2.15536	−	0.595338i	0.963906	−	0.266243i
$5$	2.15536	−	0.595338i	0.963906	−	0.266243i
$6$		0			0
$7$	0.205487	+	0.0550600i	0.0776667	+	0.0208107i	0.297443	−	0.954740i	$-0.403866\pi$
$7$	0.205487	+	0.0550600i	0.0776667	+	0.0208107i	−0.219776	+	0.975550i	$0.570533\pi$
$8$		0			0
$9$	0.792791	−	2.89335i	0.264264	−	0.964450i
$10$		0			0
$11$	1.07045	−	0.618027i	0.322754	−	0.186342i	−0.329865	−	0.944028i	$-0.607003\pi$
$11$	1.07045	−	0.618027i	0.322754	−	0.186342i	0.652620	+	0.757686i	$0.273670\pi$
$12$		0			0
$13$	1.61453	−	0.432612i	0.447790	−	0.119985i	−0.0278750	−	0.999611i	$-0.508874\pi$
$13$	1.61453	−	0.432612i	0.447790	−	0.119985i	0.475665	+	0.879626i	$0.342207\pi$
$14$		0			0
$15$	−2.34272	+	3.08410i	−0.604888	+	0.796311i
$16$		0			0
$17$	3.44214	+	3.44214i	0.834841	+	0.834841i	0.988174	−	0.153334i	$-0.0490010\pi$
$17$	3.44214	+	3.44214i	0.834841	+	0.834841i	−0.153334	+	0.988174i	$0.549001\pi$
$18$		0			0
$19$			1.17868i			0.270408i	0.990818	+	0.135204i	$0.0431691\pi$
$19$			1.17868i			0.270408i	−0.990818	+	0.135204i	$0.956831\pi$
$20$		0			0
$21$	−0.340817	+	0.140046i	−0.0743724	+	0.0305606i
$22$		0			0
$23$	1.68957	+	6.30557i	0.352300	+	1.31480i	0.883848	+	0.467774i	$0.154944\pi$
$23$	1.68957	+	6.30557i	0.352300	+	1.31480i	−0.531547	+	0.847029i	$0.678389\pi$
$24$		0			0
$25$	4.29115	−	2.56633i	0.858229	−	0.513267i
$26$		0			0
$27$	1.94779	+	4.81727i	0.374852	+	0.927085i
$28$		0			0
$29$	−1.11541	−	1.93195i	−0.207127	−	0.358754i	0.743682	−	0.668534i	$-0.233078\pi$
$29$	−1.11541	−	1.93195i	−0.207127	−	0.358754i	−0.950808	+	0.309780i	$0.899745\pi$
$30$		0			0
$31$	3.60355	−	6.24153i	0.647216	−	1.12101i	−0.336569	−	0.941659i	$-0.609266\pi$
$31$	3.60355	−	6.24153i	0.647216	−	1.12101i	0.983785	−	0.179352i	$-0.0574002\pi$
$32$		0			0
$33$	−0.824866	+	1.97562i	−0.143591	+	0.343912i
$34$		0			0
$35$	0.475677	−	0.00366001i	0.0804041	−	0.000618655i
$36$		0			0
$37$	−3.01616	+	3.01616i	−0.495853	+	0.495853i	−0.910144	−	0.414291i	$-0.864030\pi$
$37$	−3.01616	+	3.01616i	−0.495853	+	0.495853i	0.414291	+	0.910144i	$0.364030\pi$
$38$		0			0
$39$	−1.76889	+	2.29185i	−0.283250	+	0.366990i
$40$		0			0
$41$	8.24325	+	4.75924i	1.28738	+	0.743269i	0.978186	−	0.207730i	$-0.0666077\pi$
$41$	8.24325	+	4.75924i	1.28738	+	0.743269i	0.309193	+	0.950999i	$0.399941\pi$
$42$		0			0
$43$	1.19664	−	4.46591i	0.182486	−	0.681045i	−0.812669	−	0.582725i	$-0.801986\pi$
$43$	1.19664	−	4.46591i	0.182486	−	0.681045i	0.995155	−	0.0983202i	$-0.0313469\pi$
$44$		0			0
$45$	−0.0137729	−	6.70819i	−0.00205314	−	0.999998i
$46$		0			0
$47$	0.137142	−	0.511821i	0.0200042	−	0.0746568i	−0.955202	−	0.295954i	$-0.904362\pi$
$47$	0.137142	−	0.511821i	0.0200042	−	0.0746568i	0.975206	+	0.221297i	$0.0710291\pi$
$48$		0			0
$49$	−6.02298	−	3.47737i	−0.860426	−	0.496767i
$50$		0			0
$51$	−8.35621	−	1.12410i	−1.17010	−	0.157406i
$52$		0			0
$53$	−5.52081	+	5.52081i	−0.758341	+	0.758341i	−0.976020	−	0.217679i	$-0.930151\pi$
$53$	−5.52081	+	5.52081i	−0.758341	+	0.758341i	0.217679	+	0.976020i	$0.430151\pi$
$54$		0			0
$55$	1.93928	−	1.96935i	0.261492	−	0.265547i
$56$		0			0
$57$	−1.23824	−	1.62316i	−0.164009	−	0.214993i
$58$		0			0
$59$	−5.83746	+	10.1108i	−0.759973	+	1.31631i	0.182891	+	0.983133i	$0.441455\pi$
$59$	−5.83746	+	10.1108i	−0.759973	+	1.31631i	−0.942864	+	0.333179i	$0.891879\pi$
$60$		0			0
$61$	−6.60746	−	11.4445i	−0.845999	−	1.46531i	−0.884751	−	0.466065i	$-0.845671\pi$
$61$	−6.60746	−	11.4445i	−0.845999	−	1.46531i	0.0387516	−	0.999249i	$-0.487662\pi$
$62$		0			0
$63$	0.322216	−	0.550894i	0.0405954	−	0.0694062i
$64$		0			0
$65$	3.22234	−	1.89363i	0.399682	−	0.234875i
$66$		0			0
$67$	−1.22176	−	4.55967i	−0.149262	−	0.557053i	−0.999529	−	0.0307007i	$-0.990226\pi$
$67$	−1.22176	−	4.55967i	−0.149262	−	0.557053i	0.850267	−	0.526352i	$-0.176441\pi$
$68$		0			0
$69$	−8.95087	−	6.90844i	−1.07756	−	0.831679i
$70$		0			0
$71$		−	15.7215i		−	1.86580i	−0.360135	−	0.932900i	$-0.617269\pi$
$71$		−	15.7215i		−	1.86580i	0.360135	−	0.932900i	$-0.382731\pi$
$72$		0			0
$73$	−2.55375	−	2.55375i	−0.298893	−	0.298893i	0.541687	−	0.840580i	$-0.317786\pi$
$73$	−2.55375	−	2.55375i	−0.298893	−	0.298893i	−0.840580	+	0.541687i	$0.817786\pi$
$74$		0			0
$75$	−3.21332	+	8.04205i	−0.371042	+	0.928616i
$76$		0			0
$77$	0.253993	−	0.0680572i	0.0289452	−	0.00775583i
$78$		0			0
$79$	−3.27872	+	1.89297i	−0.368885	+	0.212976i	−0.672971	−	0.739669i	$-0.734982\pi$
$79$	−3.27872	+	1.89297i	−0.368885	+	0.212976i	0.304086	+	0.952644i	$0.401649\pi$
$80$		0			0
$81$	−7.74296	−	4.58765i	−0.860329	−	0.509739i
$82$		0			0
$83$	−15.0549	−	4.03395i	−1.65249	−	0.442784i	−0.692182	−	0.721723i	$-0.743351\pi$
$83$	−15.0549	−	4.03395i	−1.65249	−	0.442784i	−0.960309	+	0.278939i	$0.910017\pi$
$84$		0			0
$85$	9.46827	+	5.36980i	1.02698	+	0.582437i
$86$		0			0
$87$	3.56559	+	1.48871i	0.382272	+	0.159607i
$88$		0			0
$89$	10.4067			1.10311			0.551555	−	0.834138i	$-0.314035\pi$
$89$	10.4067			1.10311			0.551555	+	0.834138i	$0.314035\pi$
$90$		0			0
$91$	0.355584			0.0372754
$92$		0			0
$93$	1.59445	+	12.3808i	0.165337	+	1.28383i
$94$		0			0
$95$	0.701715	+	2.54049i	0.0719944	+	0.260648i
$96$		0			0
$97$	−13.8972	−	3.72373i	−1.41104	−	0.378088i	−0.528746	−	0.848780i	$-0.677338\pi$
$97$	−13.8972	−	3.72373i	−1.41104	−	0.378088i	−0.882298	+	0.470692i	$0.844004\pi$
$98$		0			0
$99$	−0.939523	−	3.58717i	−0.0944256	−	0.360524i
$100$		0			0
$101$	2.25771	−	1.30349i	0.224650	−	0.129702i	−0.383451	−	0.923561i	$-0.625265\pi$
$101$	2.25771	−	1.30349i	0.224650	−	0.129702i	0.608102	+	0.793859i	$0.291931\pi$
$102$		0			0
$103$	11.9939	−	3.21375i	1.18179	−	0.316661i	0.386156	−	0.922434i	$-0.373803\pi$
$103$	11.9939	−	3.21375i	1.18179	−	0.316661i	0.795637	+	0.605773i	$0.207136\pi$
$104$		0			0
$105$	−0.651208	+	0.504751i	−0.0635514	+	0.0492587i
$106$		0			0
$107$	5.34549	+	5.34549i	0.516768	+	0.516768i	0.916592	−	0.399824i	$-0.130929\pi$
$107$	5.34549	+	5.34549i	0.516768	+	0.516768i	−0.399824	+	0.916592i	$0.630929\pi$
$108$		0			0
$109$			12.2032i			1.16885i	0.811446	+	0.584427i	$0.198681\pi$
$109$			12.2032i			1.16885i	−0.811446	+	0.584427i	$0.801319\pi$
$110$		0			0
$111$	0.984990	−	7.32209i	0.0934911	−	0.694982i
$112$		0			0
$113$	2.34940	+	8.76807i	0.221013	+	0.824831i	0.983963	+	0.178374i	$0.0570836\pi$
$113$	2.34940	+	8.76807i	0.221013	+	0.824831i	−0.762950	+	0.646457i	$0.776250\pi$
$114$		0			0
$115$	7.39559	+	12.5849i	0.689642	+	1.17355i
$116$		0			0
$117$	0.0282865	−	5.01438i	0.00261509	−	0.463579i
$118$		0			0
$119$	0.517789	+	0.896838i	0.0474657	+	0.0822130i
$120$		0			0
$121$	−4.73608	+	8.20314i	−0.430553	+	0.745740i
$122$		0			0
$123$	−16.3515	+	2.10581i	−1.47436	+	0.189874i
$124$		0			0
$125$	7.72112	−	8.08606i	0.690598	−	0.723239i
$126$		0			0
$127$	9.69876	−	9.69876i	0.860626	−	0.860626i	−0.130785	−	0.991411i	$-0.541750\pi$
$127$	9.69876	−	9.69876i	0.860626	−	0.860626i	0.991411	+	0.130785i	$0.0417498\pi$
$128$		0			0
$129$	3.04367	+	7.40709i	0.267980	+	0.652158i
$130$		0			0
$131$	−13.1901	−	7.61530i	−1.15242	−	0.665352i	−0.202947	−	0.979190i	$-0.565052\pi$
$131$	−13.1901	−	7.61530i	−1.15242	−	0.665352i	−0.949477	+	0.313838i	$0.898385\pi$
$132$		0			0
$133$	−0.0648983	+	0.242204i	−0.00562740	+	0.0210017i
$134$		0			0
$135$	7.06609	+	9.22336i	0.608152	+	0.793820i
$136$		0			0
$137$	−2.11654	+	7.89905i	−0.180829	+	0.674861i	0.814657	+	0.579944i	$0.196925\pi$
$137$	−2.11654	+	7.89905i	−0.180829	+	0.674861i	−0.995485	+	0.0949177i	$0.969741\pi$
$138$		0			0
$139$	−5.75765	−	3.32418i	−0.488357	−	0.281953i	0.235535	−	0.971866i	$-0.424316\pi$
$139$	−5.75765	−	3.32418i	−0.488357	−	0.281953i	−0.723893	+	0.689912i	$0.757649\pi$
$140$		0			0
$141$	0.348824	+	0.848899i	0.0293762	+	0.0714902i
$142$		0			0
$143$	1.46092	−	1.46092i	0.122168	−	0.122168i
$144$		0			0
$145$	−3.55428	−	3.50000i	−0.295167	−	0.290659i
$146$		0			0
$147$	11.9473	−	1.53862i	0.985397	−	0.126903i
$148$		0			0
$149$	0.834718	−	1.44577i	0.0683828	−	0.118442i	−0.829807	−	0.558051i	$-0.811549\pi$
$149$	0.834718	−	1.44577i	0.0683828	−	0.118442i	0.898190	+	0.439608i	$0.144883\pi$
$150$		0			0
$151$	6.69358	+	11.5936i	0.544716	+	0.943475i	0.998625	+	0.0524272i	$0.0166958\pi$
$151$	6.69358	+	11.5936i	0.544716	+	0.943475i	−0.453909	+	0.891048i	$0.649971\pi$
$152$		0			0
$153$	12.6882	−	7.23041i	1.02578	−	0.584544i
$154$		0			0
$155$	4.05112	−	15.5981i	0.325394	−	1.25287i
$156$		0			0
$157$	3.48702	+	13.0137i	0.278294	+	1.03861i	0.953601	+	0.301072i	$0.0973444\pi$
$157$	3.48702	+	13.0137i	0.278294	+	1.03861i	−0.675307	+	0.737537i	$0.735989\pi$
$158$		0			0
$159$	1.80293	−	13.4024i	0.142982	−	1.06288i
$160$		0			0
$161$			1.38874i			0.109448i
$162$		0			0
$163$	−12.7035	−	12.7035i	−0.995015	−	0.995015i	0.00497235	−	0.999988i	$-0.498417\pi$
$163$	−12.7035	−	12.7035i	−0.995015	−	0.995015i	−0.999988	+	0.00497235i	$0.998417\pi$
$164$		0			0
$165$	−0.601718	+	4.74925i	−0.0468437	+	0.369729i
$166$		0			0
$167$	9.58124	−	2.56729i	0.741419	−	0.198663i	0.131710	−	0.991288i	$-0.457953\pi$
$167$	9.58124	−	2.56729i	0.741419	−	0.198663i	0.609708	+	0.792626i	$0.291287\pi$
$168$		0			0
$169$	−8.83877	+	5.10307i	−0.679906	+	0.392544i
$170$		0			0
$171$	3.41034	+	0.934450i	0.260796	+	0.0714591i
$172$		0			0
$173$	−25.3108	−	6.78201i	−1.92434	−	0.515626i	−0.984968	−	0.172738i	$-0.944739\pi$
$173$	−25.3108	−	6.78201i	−1.92434	−	0.515626i	−0.939376	−	0.342889i	$-0.888595\pi$
$174$		0			0
$175$	1.02308	−	0.291077i	0.0773373	−	0.0220034i
$176$		0			0
$177$	−2.58289	−	20.0559i	−0.194142	−	1.50750i
$178$		0			0
$179$	4.73803			0.354137			0.177069	−	0.984199i	$-0.443339\pi$
$179$	4.73803			0.354137			0.177069	+	0.984199i	$0.443339\pi$
$180$		0			0
$181$	13.6660			1.01578			0.507892	−	0.861421i	$-0.330425\pi$
$181$	13.6660			1.01578			0.507892	+	0.861421i	$0.330425\pi$
$182$		0			0
$183$	21.1218	+	8.81882i	1.56137	+	0.651906i
$184$		0			0
$185$	−4.70527	+	8.29654i	−0.345938	+	0.609974i
$186$		0			0
$187$	5.81198	+	1.55732i	0.425014	+	0.113882i
$188$		0			0
$189$	0.135006	+	1.09713i	0.00982024	+	0.0798045i
$190$		0			0
$191$	−3.95184	+	2.28160i	−0.285945	+	0.165090i	−0.636112	−	0.771597i	$-0.719458\pi$
$191$	−3.95184	+	2.28160i	−0.285945	+	0.165090i	0.350167	+	0.936687i	$0.386125\pi$
$192$		0			0
$193$	−15.2945	+	4.09816i	−1.10092	+	0.294992i	−0.763141	−	0.646232i	$-0.776344\pi$
$193$	−15.2945	+	4.09816i	−1.10092	+	0.294992i	−0.337783	+	0.941224i	$0.609677\pi$
$194$		0			0
$195$	−2.44817	+	5.99286i	−0.175317	+	0.429158i
$196$		0			0
$197$	−0.539482	−	0.539482i	−0.0384365	−	0.0384365i	0.687627	−	0.726064i	$-0.258652\pi$
$197$	−0.539482	−	0.539482i	−0.0384365	−	0.0384365i	−0.726064	+	0.687627i	$0.758652\pi$
$198$		0			0
$199$			0.658213i			0.0466595i	0.999728	+	0.0233298i	$0.00742676\pi$
$199$			0.658213i			0.0466595i	−0.999728	+	0.0233298i	$0.992573\pi$
$200$		0			0
$201$	6.47253	+	4.99562i	0.456537	+	0.352364i
$202$		0			0
$203$	−0.122829	−	0.458405i	−0.00862092	−	0.0321737i
$204$		0			0
$205$	20.6005	+	5.35035i	1.43880	+	0.373685i
$206$		0			0
$207$	19.5837	+	0.110473i	1.36116	+	0.00767843i
$208$		0			0
$209$	0.728458	+	1.26173i	0.0503885	+	0.0872755i
$210$		0			0
$211$	−8.51683	+	14.7516i	−0.586323	+	1.01554i	0.408386	+	0.912809i	$0.366092\pi$
$211$	−8.51683	+	14.7516i	−0.586323	+	1.01554i	−0.994709	+	0.102732i	$0.967242\pi$
$212$		0			0
$213$	16.5159	+	21.6500i	1.13165	+	1.48344i
$214$		0			0
$215$	−0.0795443	−	10.3381i	−0.00542488	−	0.705049i
$216$		0			0
$217$	1.08414	−	1.08414i	0.0735962	−	0.0735962i
$218$		0			0
$219$	6.19953	+	0.833980i	0.418926	+	0.0563551i
$220$		0			0
$221$	7.04654	+	4.06832i	0.474002	+	0.273665i
$222$		0			0
$223$	1.97428	−	7.36810i	0.132207	−	0.493404i	−0.867786	−	0.496937i	$-0.834458\pi$
$223$	1.97428	−	7.36810i	0.132207	−	0.493404i	0.999994	+	0.00353291i	$0.00112456\pi$
$224$		0			0
$225$	−4.02333	−	14.4504i	−0.268222	−	0.963357i
$226$		0			0
$227$	−3.44139	+	12.8434i	−0.228413	+	0.852449i	0.752595	+	0.658483i	$0.228802\pi$
$227$	−3.44139	+	12.8434i	−0.228413	+	0.852449i	−0.981008	+	0.193965i	$0.937865\pi$
$228$		0			0
$229$	−11.0304	−	6.36839i	−0.728908	−	0.420835i	0.0891145	−	0.996021i	$-0.471596\pi$
$229$	−11.0304	−	6.36839i	−0.728908	−	0.420835i	−0.818023	+	0.575186i	$0.804930\pi$
$230$		0			0
$231$	−0.278277	+	0.360547i	−0.0183093	+	0.0237223i
$232$		0			0
$233$	1.95049	−	1.95049i	0.127781	−	0.127781i	−0.640324	−	0.768105i	$-0.721200\pi$
$233$	1.95049	−	1.95049i	0.127781	−	0.127781i	0.768105	+	0.640324i	$0.221200\pi$
$234$		0			0
$235$	−0.00911627	−	1.18480i	−0.000594680	−	0.0772881i
$236$		0			0
$237$	2.52650	−	6.05118i	0.164114	−	0.393067i
$238$		0			0
$239$	−0.616351	+	1.06755i	−0.0398684	+	0.0690541i	−0.885271	−	0.465075i	$-0.846027\pi$
$239$	−0.616351	+	1.06755i	−0.0398684	+	0.0690541i	0.845403	+	0.534130i	$0.179361\pi$
$240$		0			0
$241$	7.13859	+	12.3644i	0.459837	+	0.796461i	0.998952	−	0.0457714i	$-0.0145746\pi$
$241$	7.13859	+	12.3644i	0.459837	+	0.796461i	−0.539115	+	0.842232i	$0.681241\pi$
$242$		0			0
$243$	15.4823	−	1.81655i	0.993187	−	0.116532i
$244$		0			0
$245$	−15.0519	−	3.90927i	−0.961631	−	0.249754i
$246$		0			0
$247$	0.509913	+	1.90302i	0.0324450	+	0.121086i
$248$		0			0
$249$	24.9698	−	10.2604i	1.58240	−	0.650228i
$250$		0			0
$251$		−	7.40573i		−	0.467446i	−0.972303	−	0.233723i	$-0.924909\pi$
$251$		−	7.40573i		−	0.467446i	0.972303	−	0.233723i	$-0.0750908\pi$
$252$		0			0
$253$	5.70563	+	5.70563i	0.358710	+	0.358710i
$254$		0			0
$255$	−18.6798	+	2.55193i	−1.16978	+	0.159808i
$256$		0			0
$257$	−25.8070	+	6.91497i	−1.60980	+	0.431344i	−0.947983	−	0.318322i	$-0.896881\pi$
$257$	−25.8070	+	6.91497i	−1.60980	+	0.431344i	−0.661816	+	0.749667i	$0.730214\pi$
$258$		0			0
$259$	−0.785850	+	0.453711i	−0.0488304	+	0.0281922i
$260$		0			0
$261$	−6.47410	+	1.69565i	−0.400737	+	0.104958i
$262$		0			0
$263$	−1.63127	−	0.437097i	−0.100588	−	0.0269525i	0.208174	−	0.978092i	$-0.433248\pi$
$263$	−1.63127	−	0.437097i	−0.100588	−	0.0269525i	−0.308762	+	0.951139i	$0.599915\pi$
$264$		0			0
$265$	−8.61257	+	15.1861i	−0.529066	+	0.932872i
$266$		0			0
$267$	−14.3311	+	10.9325i	−0.877047	+	0.669060i
$268$		0			0
$269$	27.2718			1.66279			0.831394	−	0.555683i	$-0.187543\pi$
$269$	27.2718			1.66279			0.831394	+	0.555683i	$0.187543\pi$
$270$		0			0
$271$	−8.58649			−0.521592			−0.260796	−	0.965394i	$-0.583985\pi$
$271$	−8.58649			−0.521592			−0.260796	+	0.965394i	$0.583985\pi$
$272$		0			0
$273$	−0.489674	+	0.373550i	−0.0296364	+	0.0226083i
$274$		0			0
$275$	3.00741	−	5.39919i	0.181354	−	0.325583i
$276$		0			0
$277$	−18.7839	−	5.03312i	−1.12861	−	0.302411i	−0.354249	−	0.935151i	$-0.615263\pi$
$277$	−18.7839	−	5.03312i	−1.12861	−	0.302411i	−0.774364	+	0.632740i	$0.781930\pi$
$278$		0			0
$279$	−15.2021	−	15.3746i	−0.910124	−	0.920450i
$280$		0			0
$281$	4.83957	−	2.79413i	0.288705	−	0.166684i	−0.348653	−	0.937252i	$-0.613361\pi$
$281$	4.83957	−	2.79413i	0.288705	−	0.166684i	0.637357	+	0.770568i	$0.280027\pi$
$282$		0			0
$283$	16.8379	−	4.51171i	1.00091	−	0.268193i	0.279084	−	0.960267i	$-0.409969\pi$
$283$	16.8379	−	4.51171i	1.00091	−	0.268193i	0.721827	+	0.692073i	$0.243303\pi$
$284$		0			0
$285$	−3.63518	−	2.76132i	−0.215329	−	0.163567i
$286$		0			0
$287$	1.43183	+	1.43183i	0.0845185	+	0.0845185i
$288$		0			0
$289$			6.69660i			0.393918i
$290$		0			0
$291$	23.0496	−	9.47139i	1.35119	−	0.555223i
$292$		0			0
$293$	−7.76765	−	28.9893i	−0.453791	−	1.69357i	−0.691618	−	0.722263i	$-0.743102\pi$
$293$	−7.76765	−	28.9893i	−0.453791	−	1.69357i	0.237828	−	0.971307i	$-0.423565\pi$
$294$		0			0
$295$	−6.56249	+	25.2676i	−0.382083	+	1.47114i
$296$		0			0
$297$	5.06223	+	3.95288i	0.293740	+	0.229370i
$298$		0			0
$299$	5.45574	+	9.44961i	0.315513	+	0.546485i
$300$		0			0
$301$	0.491787	−	0.851799i	0.0283461	−	0.0490969i
$302$		0			0
$303$	−1.73973	+	4.16680i	−0.0999450	+	0.239377i
$304$		0			0
$305$	−21.0548	−	20.7333i	−1.20559	−	1.18718i
$306$		0			0
$307$	−21.1488	+	21.1488i	−1.20703	+	1.20703i	−0.235039	+	0.971986i	$0.575522\pi$
$307$	−21.1488	+	21.1488i	−1.20703	+	1.20703i	−0.971986	+	0.235039i	$0.924478\pi$
$308$		0			0
$309$	−13.1406	+	17.0255i	−0.747544	+	0.968549i
$310$		0			0
$311$	−16.0876	−	9.28818i	−0.912244	−	0.526684i	−0.0310914	−	0.999517i	$-0.509898\pi$
$311$	−16.0876	−	9.28818i	−0.912244	−	0.526684i	−0.881152	+	0.472832i	$0.843232\pi$
$312$		0			0
$313$	3.33338	−	12.4403i	0.188414	−	0.703170i	−0.805460	−	0.592650i	$-0.798082\pi$
$313$	3.33338	−	12.4403i	0.188414	−	0.703170i	0.993874	−	0.110520i	$-0.0352516\pi$
$314$		0			0
$315$	0.366523	−	1.37920i	0.0206512	−	0.0777093i
$316$		0			0
$317$	1.01526	−	3.78899i	0.0570224	−	0.212811i	−0.931536	−	0.363649i	$-0.881531\pi$
$317$	1.01526	−	3.78899i	0.0570224	−	0.212811i	0.988558	+	0.150839i	$0.0481974\pi$
$318$		0			0
$319$	−2.38799	−	1.37871i	−0.133702	−	0.0771929i
$320$		0			0
$321$	−12.9768	−	1.74568i	−0.724296	−	0.0974345i
$322$		0			0
$323$	−4.05719	+	4.05719i	−0.225748	+	0.225748i
$324$		0			0
$325$	5.81796	−	5.99983i	0.322722	−	0.332811i
$326$		0			0
$327$	−12.8198	−	16.8050i	−0.708935	−	0.929318i
$328$		0			0
$329$	0.0563618	−	0.0976215i	0.00310733	−	0.00538205i
$330$		0			0
$331$	8.50779	+	14.7359i	0.467630	+	0.809960i	0.999316	−	0.0369823i	$-0.0117745\pi$
$331$	8.50779	+	14.7359i	0.467630	+	0.809960i	−0.531686	+	0.846942i	$0.678441\pi$
$332$		0			0
$333$	6.33562	+	11.1180i	0.347190	+	0.609262i
$334$		0			0
$335$	−5.34788	−	9.10037i	−0.292186	−	0.497206i
$336$		0			0
$337$	−1.78385	−	6.65742i	−0.0971725	−	0.362653i	0.900167	−	0.435544i	$-0.143444\pi$
$337$	−1.78385	−	6.65742i	−0.0971725	−	0.362653i	−0.997340	+	0.0728914i	$0.976777\pi$
$338$		0			0
$339$	−12.4464	−	9.60638i	−0.675998	−	0.521747i
$340$		0			0
$341$		−	8.90836i		−	0.482415i
$342$		0			0
$343$	−2.09917	−	2.09917i	−0.113344	−	0.113344i
$344$		0			0
$345$	−23.4052	−	9.56138i	−1.26009	−	0.514768i
$346$		0			0
$347$	−1.33571	+	0.357902i	−0.0717046	+	0.0192132i	−0.294493	−	0.955654i	$-0.595151\pi$
$347$	−1.33571	+	0.357902i	−0.0717046	+	0.0192132i	0.222788	+	0.974867i	$0.428484\pi$
$348$		0			0
$349$	20.5117	−	11.8424i	1.09796	−	0.633910i	0.162279	−	0.986745i	$-0.448116\pi$
$349$	20.5117	−	11.8424i	1.09796	−	0.633910i	0.935686	+	0.352835i	$0.114782\pi$
$350$		0			0
$351$	5.22878	+	6.93500i	0.279091	+	0.370163i
$352$		0			0
$353$	4.80349	+	1.28709i	0.255664	+	0.0685049i	0.384374	−	0.923177i	$-0.374417\pi$
$353$	4.80349	+	1.28709i	0.255664	+	0.0685049i	−0.128711	+	0.991682i	$0.541084\pi$
$354$		0			0
$355$	−9.35962	−	33.8855i	−0.496757	−	1.79846i
$356$		0			0
$357$	−1.65520	−	0.691081i	−0.0876023	−	0.0365759i
$358$		0			0
$359$	−0.999135			−0.0527323			−0.0263662	−	0.999652i	$-0.508394\pi$
$359$	−0.999135			−0.0527323			−0.0263662	+	0.999652i	$0.508394\pi$
$360$		0			0
$361$	17.6107			0.926879
$362$		0			0
$363$	−2.09556	−	16.2719i	−0.109989	−	0.854053i
$364$		0			0
$365$	−7.02458	−	3.98390i	−0.367683	−	0.208527i
$366$		0			0
$367$	−32.5779	−	8.72921i	−1.70055	−	0.455661i	−0.727472	−	0.686137i	$-0.759305\pi$
$367$	−32.5779	−	8.72921i	−1.70055	−	0.455661i	−0.973078	+	0.230476i	$0.925972\pi$
$368$		0			0
$369$	20.3053	−	20.0775i	1.05705	−	1.04519i
$370$		0			0
$371$	−1.43843	+	0.830477i	−0.0746795	+	0.0431162i
$372$		0			0
$373$	9.19030	−	2.46253i	0.475856	−	0.127505i	−0.0129165	−	0.999917i	$-0.504112\pi$
$373$	9.19030	−	2.46253i	0.475856	−	0.127505i	0.488772	+	0.872411i	$0.337445\pi$
$374$		0			0
$375$	−2.13812	+	19.2465i	−0.110412	+	0.993886i
$376$		0			0
$377$	−2.63665	−	2.63665i	−0.135794	−	0.135794i
$378$		0			0
$379$			32.6753i			1.67842i	0.543808	+	0.839209i	$0.316982\pi$
$379$			32.6753i			1.67842i	−0.543808	+	0.839209i	$0.683018\pi$
$380$		0			0
$381$	−3.16733	+	23.5449i	−0.162267	+	1.20624i
$382$		0			0
$383$	4.08266	+	15.2367i	0.208614	+	0.778559i	0.988317	+	0.152410i	$0.0487033\pi$
$383$	4.08266	+	15.2367i	0.208614	+	0.778559i	−0.779703	+	0.626149i	$0.784630\pi$
$384$		0			0
$385$	0.506929	−	0.297899i	0.0258355	−	0.0151824i
$386$		0			0
$387$	−11.9728	−	7.00283i	−0.608610	−	0.355974i
$388$		0			0
$389$	−2.57023	−	4.45176i	−0.130316	−	0.225713i	0.793483	−	0.608593i	$-0.208266\pi$
$389$	−2.57023	−	4.45176i	−0.130316	−	0.225713i	−0.923798	+	0.382880i	$0.874932\pi$
$390$		0			0
$391$	−15.8889	+	27.5204i	−0.803536	+	1.39177i
$392$		0			0
$393$	26.1641	−	3.36952i	1.31980	−	0.169970i
$394$		0			0
$395$	−5.93986	+	6.03198i	−0.298867	+	0.303502i
$396$		0			0
$397$	14.2664	−	14.2664i	0.716010	−	0.716010i	−0.251776	−	0.967786i	$-0.581014\pi$
$397$	14.2664	−	14.2664i	0.716010	−	0.716010i	0.967786	+	0.251776i	$0.0810145\pi$
$398$		0			0
$399$	−0.165070	−	0.401715i	−0.00826384	−	0.0201109i
$400$		0			0
$401$	21.5919	+	12.4661i	1.07825	+	0.622525i	0.930423	−	0.366488i	$-0.119440\pi$
$401$	21.5919	+	12.4661i	1.07825	+	0.622525i	0.147823	+	0.989014i	$0.452773\pi$
$402$		0			0
$403$	3.11788	−	11.6361i	0.155312	−	0.579634i
$404$		0			0
$405$	−19.4201	−	5.27834i	−0.964991	−	0.262283i
$406$		0			0
$407$	−1.36459	+	5.09273i	−0.0676403	+	0.252437i
$408$		0			0
$409$	−22.7557	−	13.1380i	−1.12520	−	0.649632i	−0.182474	−	0.983211i	$-0.558411\pi$
$409$	−22.7557	−	13.1380i	−1.12520	−	0.649632i	−0.942722	+	0.333578i	$0.891744\pi$
$410$		0			0
$411$	−5.38347	−	13.1012i	−0.265547	−	0.646237i
$412$		0			0
$413$	−1.75622	+	1.75622i	−0.0864180	+	0.0864180i
$414$		0			0
$415$	−34.8503	+	0.268149i	−1.71073	+	0.0131629i
$416$		0			0
$417$	11.4210	−	1.47084i	0.559288	−	0.0720274i
$418$		0			0
$419$	2.32933	−	4.03451i	0.113795	−	0.197099i	−0.803502	−	0.595302i	$-0.797033\pi$
$419$	2.32933	−	4.03451i	0.113795	−	0.197099i	0.917297	+	0.398203i	$0.130366\pi$
$420$		0			0
$421$	−12.9588	−	22.4454i	−0.631575	−	1.09392i	−0.987230	−	0.159303i	$-0.949075\pi$
$421$	−12.9588	−	22.4454i	−0.631575	−	1.09392i	0.355655	−	0.934617i	$-0.384258\pi$
$422$		0			0
$423$	−1.37215	−	0.802568i	−0.0667164	−	0.0390222i
$424$		0			0
$425$	23.6044	+	5.93703i	1.14498	+	0.287988i
$426$		0			0
$427$	−0.727614	−	2.71549i	−0.0352117	−	0.131412i
$428$		0			0
$429$	−0.477093	+	3.54655i	−0.0230342	+	0.171229i
$430$		0			0
$431$			29.6916i			1.43019i	0.699026	+	0.715096i	$0.253617\pi$
$431$			29.6916i			1.43019i	−0.699026	+	0.715096i	$0.746383\pi$
$432$		0			0
$433$	−10.1017	−	10.1017i	−0.485459	−	0.485459i	0.421411	−	0.906870i	$-0.361535\pi$
$433$	−10.1017	−	10.1017i	−0.485459	−	0.485459i	−0.906870	+	0.421411i	$0.861535\pi$
$434$		0			0
$435$	8.57142	+	1.08598i	0.410968	+	0.0520686i
$436$		0			0
$437$	−7.43227	+	1.99147i	−0.355534	+	0.0952650i
$438$		0			0
$439$	14.5664	−	8.40990i	0.695215	−	0.401382i	−0.110348	−	0.993893i	$-0.535197\pi$
$439$	14.5664	−	8.40990i	0.695215	−	0.401382i	0.805563	+	0.592511i	$0.201863\pi$
$440$		0			0
$441$	−14.8362	+	14.6698i	−0.706487	+	0.698561i
$442$		0			0
$443$	−1.38032	−	0.369855i	−0.0655809	−	0.0175723i	0.225879	−	0.974155i	$-0.427474\pi$
$443$	−1.38032	−	0.369855i	−0.0655809	−	0.0175723i	−0.291460	+	0.956583i	$0.594141\pi$
$444$		0			0
$445$	22.4302	−	6.19552i	1.06329	−	0.293696i
$446$		0			0
$447$	0.369336	+	2.86786i	0.0174690	+	0.135645i
$448$		0			0
$449$	−3.25084			−0.153417			−0.0767084	−	0.997054i	$-0.524441\pi$
$449$	−3.25084			−0.153417			−0.0767084	+	0.997054i	$0.524441\pi$
$450$		0			0
$451$	11.7654			0.554009
$452$		0			0
$453$	−21.3971	−	8.93376i	−1.00532	−	0.419745i
$454$		0			0
$455$	0.766412	−	0.211693i	0.0359299	−	0.00992432i
$456$		0			0
$457$	23.4798	+	6.29140i	1.09834	+	0.294299i	0.762088	−	0.647473i	$-0.224174\pi$
$457$	23.4798	+	6.29140i	1.09834	+	0.294299i	0.336251	+	0.941772i	$0.390841\pi$
$458$		0			0
$459$	−9.87715	+	23.2863i	−0.461026	+	1.08691i
$460$		0			0
$461$	3.48630	−	2.01282i	0.162373	−	0.0937462i	−0.416612	−	0.909085i	$-0.636782\pi$
$461$	3.48630	−	2.01282i	0.162373	−	0.0937462i	0.578985	+	0.815338i	$0.303449\pi$
$462$		0			0
$463$	37.7866	−	10.1249i	1.75609	−	0.470543i	0.770182	−	0.637824i	$-0.220165\pi$
$463$	37.7866	−	10.1249i	1.75609	−	0.470543i	0.985909	+	0.167281i	$0.0534986\pi$
$464$		0			0
$465$	10.8074	+	25.7358i	0.501180	+	1.19347i
$466$		0			0
$467$	13.4512	+	13.4512i	0.622445	+	0.622445i	0.946156	−	0.323711i	$-0.104930\pi$
$467$	13.4512	+	13.4512i	0.622445	+	0.622445i	−0.323711	+	0.946156i	$0.604930\pi$
$468$		0			0
$469$		−	1.00422i		−	0.0463707i
$470$		0			0
$471$	−18.4732	−	14.2580i	−0.851201	−	0.656972i
$472$		0			0
$473$	−1.47911	−	5.52011i	−0.0680095	−	0.253815i
$474$		0			0
$475$	3.02490	+	5.05790i	0.138792	+	0.232072i
$476$		0			0
$477$	11.5968	+	20.3505i	0.530980	+	0.931784i
$478$		0			0
$479$	13.6187	+	23.5883i	0.622255	+	1.07778i	0.989065	+	0.147482i	$0.0471167\pi$
$479$	13.6187	+	23.5883i	0.622255	+	1.07778i	−0.366810	+	0.930296i	$0.619550\pi$
$480$		0			0
$481$	−3.56485	+	6.17451i	−0.162543	+	0.281533i
$482$		0			0
$483$	−1.45891	−	1.91243i	−0.0663826	−	0.0870185i
$484$		0			0
$485$	−32.1703	+	0.247528i	−1.46078	+	0.0112397i
$486$		0			0
$487$	9.62463	−	9.62463i	0.436134	−	0.436134i	−0.454575	−	0.890709i	$-0.650209\pi$
$487$	9.62463	−	9.62463i	0.436134	−	0.436134i	0.890709	+	0.454575i	$0.150209\pi$
$488$		0			0
$489$	30.8393	+	4.14860i	1.39460	+	0.187606i
$490$		0			0
$491$	25.8921	+	14.9488i	1.16849	+	0.674630i	0.953325	−	0.301946i	$-0.0976364\pi$
$491$	25.8921	+	14.9488i	1.16849	+	0.674630i	0.215169	+	0.976577i	$0.430970\pi$
$492$		0			0
$493$	2.81063	−	10.4894i	0.126585	−	0.472420i
$494$		0			0
$495$	−4.16059	−	7.17230i	−0.187004	−	0.322371i
$496$		0			0
$497$	0.865627	−	3.23056i	0.0388287	−	0.144911i
$498$		0			0
$499$	7.78788	+	4.49634i	0.348634	+	0.201284i	0.664083	−	0.747659i	$-0.268822\pi$
$499$	7.78788	+	4.49634i	0.348634	+	0.201284i	−0.315450	+	0.948942i	$0.602155\pi$
$500$		0			0
$501$	−10.4973	+	13.6007i	−0.468985	+	0.607636i
$502$		0			0
$503$	−12.1197	+	12.1197i	−0.540389	+	0.540389i	−0.923643	−	0.383254i	$-0.874803\pi$
$503$	−12.1197	+	12.1197i	−0.540389	+	0.540389i	0.383254	+	0.923643i	$0.374803\pi$
$504$		0			0
$505$	4.09015	−	4.15358i	0.182009	−	0.184832i
$506$		0			0
$507$	6.81094	−	16.3128i	0.302485	−	0.724476i
$508$		0			0
$509$	6.08023	−	10.5313i	0.269502	−	0.466791i	−0.699232	−	0.714895i	$-0.746474\pi$
$509$	6.08023	−	10.5313i	0.269502	−	0.466791i	0.968733	+	0.248105i	$0.0798077\pi$
$510$		0			0
$511$	−0.384152	−	0.665370i	−0.0169939	−	0.0294343i
$512$		0			0
$513$	−5.67804	+	2.29583i	−0.250692	+	0.101363i
$514$		0			0
$515$	23.9379	−	14.0672i	1.05483	−	0.619875i
$516$		0			0
$517$	−0.169515	−	0.632639i	−0.00745526	−	0.0278234i
$518$		0			0
$519$	41.9801	−	17.2502i	1.84272	−	0.757198i
$520$		0			0
$521$			20.5199i			0.898991i	0.893282	+	0.449496i	$0.148396\pi$
$521$			20.5199i			0.898991i	−0.893282	+	0.449496i	$0.851604\pi$
$522$		0			0
$523$	−16.5239	−	16.5239i	−0.722539	−	0.722539i	0.246583	−	0.969122i	$-0.420692\pi$
$523$	−16.5239	−	16.5239i	−0.722539	−	0.722539i	−0.969122	+	0.246583i	$0.920692\pi$
$524$		0			0
$525$	−1.10309	+	1.47561i	−0.0481428	+	0.0644009i
$526$		0			0
$527$	33.8881	−	9.08028i	1.47619	−	0.395543i
$528$		0			0
$529$	−16.9870	+	9.80746i	−0.738566	+	0.426411i
$530$		0			0
$531$	24.6262	+	24.9056i	1.06868	+	1.08081i
$532$		0			0
$533$	15.3679	+	4.11781i	0.665657	+	0.178362i
$534$		0			0
$535$	14.7038	+	8.33908i	0.635702	+	0.360530i
$536$		0			0
$537$	−6.52473	+	4.97743i	−0.281563	+	0.214792i
$538$		0			0
$539$	−8.59644			−0.370275
$540$		0			0
$541$	14.7507			0.634184			0.317092	−	0.948395i	$-0.397294\pi$
$541$	14.7507			0.634184			0.317092	+	0.948395i	$0.397294\pi$
$542$		0			0
$543$	−18.8194	+	14.3565i	−0.807616	+	0.616095i
$544$		0			0
$545$	7.26503	+	26.3023i	0.311200	+	1.12667i
$546$		0			0
$547$	−30.4544	−	8.16024i	−1.30214	−	0.348906i	−0.459879	−	0.887982i	$-0.652107\pi$
$547$	−30.4544	−	8.16024i	−1.30214	−	0.348906i	−0.842258	+	0.539075i	$0.818774\pi$
$548$		0			0
$549$	−38.3512	+	10.0446i	−1.63679	+	0.428695i
$550$		0			0
$551$	2.27716	−	1.31472i	0.0970101	−	0.0560088i
$552$		0			0
$553$	−0.777961	+	0.208454i	−0.0330823	+	0.00886436i
$554$		0			0
$555$	−2.23612	−	16.3681i	−0.0949178	−	0.694789i
$556$		0			0
$557$	5.45535	+	5.45535i	0.231151	+	0.231151i	0.813173	−	0.582022i	$-0.197738\pi$
$557$	5.45535	+	5.45535i	0.231151	+	0.231151i	−0.582022	+	0.813173i	$0.697738\pi$
$558$		0			0
$559$		−	7.72803i		−	0.326861i
$560$		0			0
$561$	−9.63966	+	3.96106i	−0.406987	+	0.167236i
$562$		0			0
$563$	5.15224	+	19.2284i	0.217141	+	0.810381i	0.985402	+	0.170244i	$0.0544557\pi$
$563$	5.15224	+	19.2284i	0.217141	+	0.810381i	−0.768261	+	0.640137i	$0.778878\pi$
$564$		0			0
$565$	10.2838	+	17.4997i	0.432641	+	0.736216i
$566$		0			0
$567$	−1.33848	−	1.36903i	−0.0562109	−	0.0574938i
$568$		0			0
$569$	1.17698	+	2.03860i	0.0493418	+	0.0854624i	0.889641	−	0.456660i	$-0.150954\pi$
$569$	1.17698	+	2.03860i	0.0493418	+	0.0854624i	−0.840300	+	0.542122i	$0.817621\pi$
$570$		0			0
$571$	5.62190	−	9.73742i	0.235269	−	0.407498i	−0.724082	−	0.689714i	$-0.757736\pi$
$571$	5.62190	−	9.73742i	0.235269	−	0.407498i	0.959351	+	0.282216i	$0.0910695\pi$
$572$		0			0
$573$	3.04519	−	7.29349i	0.127215	−	0.304690i
$574$		0			0
$575$	23.4324	+	22.7221i	0.977199	+	0.947578i
$576$		0			0
$577$	22.3795	−	22.3795i	0.931669	−	0.931669i	−0.0661412	−	0.997810i	$-0.521069\pi$
$577$	22.3795	−	22.3795i	0.931669	−	0.931669i	0.997810	+	0.0661412i	$0.0210688\pi$
$578$		0			0
$579$	16.7568	−	21.7108i	0.696390	−	0.902272i
$580$		0			0
$581$	−2.87148	−	1.65785i	−0.119129	−	0.0687791i
$582$		0			0
$583$	−2.49776	+	9.32178i	−0.103447	+	0.386069i
$584$		0			0
$585$	−2.92428	−	10.8246i	−0.120904	−	0.447543i
$586$		0			0
$587$	6.88139	−	25.6817i	0.284025	−	1.06000i	−0.665523	−	0.746377i	$-0.731792\pi$
$587$	6.88139	−	25.6817i	0.284025	−	1.06000i	0.949549	−	0.313620i	$-0.101542\pi$
$588$		0			0
$589$	7.35678	+	4.24744i	0.303131	+	0.175013i
$590$		0			0
$591$	1.30966	+	0.176179i	0.0538722	+	0.00724705i
$592$		0			0
$593$	−9.51652	+	9.51652i	−0.390797	+	0.390797i	−0.874971	−	0.484175i	$-0.839120\pi$
$593$	−9.51652	+	9.51652i	−0.390797	+	0.390797i	0.484175	+	0.874971i	$0.339120\pi$
$594$		0			0
$595$	1.64994	+	1.62475i	0.0676411	+	0.0666081i
$596$		0			0
$597$	−0.691470	−	0.906423i	−0.0283000	−	0.0370974i
$598$		0			0
$599$	14.6078	−	25.3015i	0.596860	−	1.03379i	−0.396421	−	0.918069i	$-0.629748\pi$
$599$	14.6078	−	25.3015i	0.596860	−	1.03379i	0.993281	−	0.115723i	$-0.0369186\pi$
$600$		0			0
$601$	−16.8452	−	29.1767i	−0.687130	−	1.19014i	−0.972762	−	0.231805i	$-0.925537\pi$
$601$	−16.8452	−	29.1767i	−0.687130	−	1.19014i	0.285632	−	0.958339i	$-0.407796\pi$
$602$		0			0
$603$	−14.1613	−	0.0798853i	−0.576694	−	0.00325318i
$604$		0			0
$605$	−5.32432	+	20.5003i	−0.216464	+	0.833455i
$606$		0			0
$607$	0.289444	+	1.08022i	0.0117482	+	0.0438448i	0.971551	−	0.236830i	$-0.0761084\pi$
$607$	0.289444	+	1.08022i	0.0117482	+	0.0438448i	−0.959803	+	0.280675i	$0.909442\pi$
$608$		0			0
$609$	0.650714	+	0.502232i	0.0263682	+	0.0203515i
$610$		0			0
$611$		−	0.885680i		−	0.0358308i
$612$		0			0
$613$	11.9586	+	11.9586i	0.483002	+	0.483002i	0.906089	−	0.423087i	$-0.139053\pi$
$613$	11.9586	+	11.9586i	0.483002	+	0.483002i	−0.423087	+	0.906089i	$0.639053\pi$
$614$		0			0
$615$	−33.9896	+	14.2734i	−1.37059	+	0.575560i
$616$		0			0
$617$	5.45293	−	1.46111i	0.219527	−	0.0588220i	−0.147379	−	0.989080i	$-0.547084\pi$
$617$	5.45293	−	1.46111i	0.219527	−	0.0588220i	0.366906	+	0.930258i	$0.380417\pi$
$618$		0			0
$619$	40.1278	−	23.1678i	1.61287	−	0.931191i	0.624170	−	0.781288i	$-0.285437\pi$
$619$	40.1278	−	23.1678i	1.61287	−	0.931191i	0.988701	−	0.149903i	$-0.0478961\pi$
$620$		0			0
$621$	−27.0847	+	20.4211i	−1.08687	+	0.819469i
$622$		0			0
$623$	2.13844	+	0.572995i	0.0856750	+	0.0229565i
$624$		0			0
$625$	11.8279	−	22.0250i	0.473114	−	0.881001i
$626$		0			0
$627$	−2.32863	−	0.972256i	−0.0929967	−	0.0388281i
$628$		0			0
$629$	−20.7641			−0.827917
$630$		0			0
$631$	−13.2008			−0.525517			−0.262758	−	0.964862i	$-0.584632\pi$
$631$	−13.2008			−0.525517			−0.262758	+	0.964862i	$0.584632\pi$
$632$		0			0
$633$	−3.76842	−	29.2615i	−0.149781	−	1.16304i
$634$		0			0
$635$	15.1303	−	26.6783i	0.600426	−	1.05870i
$636$		0			0
$637$	−11.2286	−	3.00871i	−0.444895	−	0.119209i
$638$		0			0
$639$	−45.4879	−	12.4639i	−1.79947	−	0.493063i
$640$		0			0
$641$	−3.33311	+	1.92437i	−0.131650	+	0.0760082i	−0.564379	−	0.825516i	$-0.690884\pi$
$641$	−3.33311	+	1.92437i	−0.131650	+	0.0760082i	0.432729	+	0.901524i	$0.357551\pi$
$642$		0			0
$643$	1.53569	−	0.411487i	0.0605617	−	0.0162275i	−0.228411	−	0.973565i	$-0.573353\pi$
$643$	1.53569	−	0.411487i	0.0605617	−	0.0162275i	0.288973	+	0.957337i	$0.406686\pi$
$644$		0			0
$645$	10.9699	+	14.1529i	0.431941	+	0.557271i
$646$		0			0
$647$	−14.0232	−	14.0232i	−0.551310	−	0.551310i	0.375509	−	0.926819i	$-0.377468\pi$
$647$	−14.0232	−	14.0232i	−0.551310	−	0.551310i	−0.926819	+	0.375509i	$0.877468\pi$
$648$		0			0
$649$			14.4308i			0.566460i
$650$		0			0
$651$	−0.354049	+	2.63188i	−0.0138763	+	0.103152i
$652$		0			0
$653$	−8.57591	−	32.0057i	−0.335601	−	1.25248i	−0.903216	−	0.429186i	$-0.858800\pi$
$653$	−8.57591	−	32.0057i	−0.335601	−	1.25248i	0.567615	−	0.823294i	$-0.307866\pi$
$654$		0			0
$655$	−32.9631	−	8.56115i	−1.28797	−	0.334512i
$656$		0			0
$657$	−9.41347	+	5.36430i	−0.367255	+	0.209281i
$658$		0			0
$659$	17.6445	+	30.5612i	0.687333	+	1.19050i	0.972698	+	0.232076i	$0.0745519\pi$
$659$	17.6445	+	30.5612i	0.687333	+	1.19050i	−0.285365	+	0.958419i	$0.592115\pi$
$660$		0			0
$661$	13.1607	−	22.7950i	0.511892	−	0.886623i	−0.488013	−	0.872837i	$-0.662278\pi$
$661$	13.1607	−	22.7950i	0.511892	−	0.886623i	0.999905	−	0.0137868i	$-0.00438863\pi$
$662$		0			0
$663$	−13.9777	+	1.80010i	−0.542847	+	0.0699101i
$664$		0			0
$665$	0.00431400	+	0.560673i	0.000167290	+	0.0217420i
$666$		0			0
$667$	10.2975	−	10.2975i	0.398720	−	0.398720i
$668$		0			0
$669$	5.02161	+	12.2206i	0.194147	+	0.472476i
$670$		0			0
$671$	−14.1460	−	8.16718i	−0.546099	−	0.315291i
$672$		0			0
$673$	−7.45639	+	27.8276i	−0.287423	+	1.07268i	0.659628	+	0.751592i	$0.270714\pi$
$673$	−7.45639	+	27.8276i	−0.287423	+	1.07268i	−0.947051	+	0.321084i	$0.895953\pi$
$674$		0			0
$675$	20.7210	+	15.6729i	0.797551	+	0.603251i
$676$		0			0
$677$	2.81949	−	10.5225i	0.108362	−	0.404412i	−0.890343	−	0.455291i	$-0.849535\pi$
$677$	2.81949	−	10.5225i	0.108362	−	0.404412i	0.998705	+	0.0508782i	$0.0162020\pi$
$678$		0			0
$679$	−2.65066	−	1.53036i	−0.101723	−	0.0587297i
$680$		0			0
$681$	−8.75323	−	21.3019i	−0.335425	−	0.816291i
$682$		0			0
$683$	4.24595	−	4.24595i	0.162467	−	0.162467i	−0.621192	−	0.783659i	$-0.713351\pi$
$683$	4.24595	−	4.24595i	0.162467	−	0.162467i	0.783659	+	0.621192i	$0.213351\pi$
$684$		0			0
$685$	0.140693	+	18.2853i	0.00537562	+	0.698647i
$686$		0			0
$687$	21.8801	−	2.81781i	0.834776	−	0.107506i
$688$		0			0
$689$	−6.52514	+	11.3019i	−0.248588	+	0.430567i
$690$		0			0
$691$	−5.63644	−	9.76260i	−0.214420	−	0.371387i	0.738673	−	0.674064i	$-0.235453\pi$
$691$	−5.63644	−	9.76260i	−0.214420	−	0.371387i	−0.953093	+	0.302677i	$0.902120\pi$
$692$		0			0
$693$	0.00444994	−	0.788846i	0.000169039	−	0.0299658i
$694$		0			0
$695$	−14.3888	−	3.73705i	−0.545799	−	0.141755i
$696$		0			0
$697$	11.9924	+	44.7563i	0.454246	+	1.69527i
$698$		0			0
$699$	−0.636974	+	4.73506i	−0.0240926	+	0.179096i
$700$		0			0
$701$		−	0.171730i		−	0.00648615i	−0.999995	−	0.00324308i	$-0.998968\pi$
$701$		−	0.171730i		−	0.00648615i	0.999995	−	0.00324308i	$-0.00103231\pi$
$702$		0			0
$703$	−3.55510	−	3.55510i	−0.134083	−	0.134083i
$704$		0			0
$705$	1.25722	+	1.62201i	0.0473497	+	0.0610886i
$706$		0			0
$707$	0.535699	−	0.143540i	0.0201470	−	0.00539838i
$708$		0			0
$709$	6.67248	−	3.85236i	0.250590	−	0.144678i	−0.369444	−	0.929253i	$-0.620452\pi$
$709$	6.67248	−	3.85236i	0.250590	−	0.144678i	0.620034	+	0.784575i	$0.287119\pi$
$710$		0			0
$711$	2.87769	+	10.9872i	0.107922	+	0.412053i
$712$		0			0
$713$	45.4449	+	12.1769i	1.70192	+	0.456029i
$714$		0			0
$715$	2.27906	−	4.01854i	0.0852319	−	0.150285i
$716$		0			0
$717$	−0.272715	−	2.11761i	−0.0101847	−	0.0790837i
$718$		0			0
$719$	−24.6989			−0.921112			−0.460556	−	0.887631i	$-0.652350\pi$
$719$	−24.6989			−0.921112			−0.460556	+	0.887631i	$0.652350\pi$
$720$		0			0
$721$	2.64154			0.0983759
$722$		0			0
$723$	−22.8196	−	9.52770i	−0.848672	−	0.354339i
$724$		0			0
$725$	−9.74442	−	5.42776i	−0.361899	−	0.201582i
$726$		0			0
$727$	−0.140535	−	0.0376563i	−0.00521216	−	0.00139659i	0.256212	−	0.966621i	$-0.417525\pi$
$727$	−0.140535	−	0.0376563i	−0.00521216	−	0.00139659i	−0.261424	+	0.965224i	$0.584192\pi$
$728$		0			0
$729$	−19.4122	+	18.7661i	−0.718971	+	0.695040i
$730$		0			0
$731$	19.4913	−	11.2533i	0.720911	−	0.416218i
$732$		0			0
$733$	3.60410	−	0.965714i	0.133120	−	0.0356695i	−0.191644	−	0.981465i	$-0.561382\pi$
$733$	3.60410	−	0.965714i	0.133120	−	0.0356695i	0.324764	+	0.945795i	$0.394715\pi$
$734$		0			0
$735$	24.8347	−	10.4290i	0.916043	−	0.384678i
$736$		0			0
$737$	−4.12584	−	4.12584i	−0.151977	−	0.151977i
$738$		0			0
$739$			36.5511i			1.34455i	0.740300	+	0.672276i	$0.234683\pi$
$739$			36.5511i			1.34455i	−0.740300	+	0.672276i	$0.765317\pi$
$740$		0			0
$741$	−2.70137	−	2.08497i	−0.0992373	−	0.0765932i
$742$		0			0
$743$	7.89387	+	29.4603i	0.289598	+	1.08079i	0.945414	+	0.325873i	$0.105658\pi$
$743$	7.89387	+	29.4603i	0.289598	+	1.08079i	−0.655816	+	0.754921i	$0.727675\pi$
$744$		0			0
$745$	0.938393	−	3.61310i	0.0343801	−	0.132374i
$746$		0			0
$747$	−23.6070	+	40.3611i	−0.863736	+	1.47673i
$748$		0			0
$749$	0.804105	+	1.39275i	0.0293814	+	0.0508900i
$750$		0			0
$751$	−12.6674	+	21.9405i	−0.462238	+	0.800620i	−0.999072	−	0.0430677i	$-0.986287\pi$
$751$	−12.6674	+	21.9405i	−0.462238	+	0.800620i	0.536834	+	0.843688i	$0.319620\pi$
$752$		0			0
$753$	7.77991	+	10.1984i	0.283516	+	0.371651i
$754$		0			0
$755$	21.3292	+	21.0035i	0.776249	+	0.764394i
$756$		0			0
$757$	−24.8342	+	24.8342i	−0.902613	+	0.902613i	−0.995662	−	0.0930486i	$-0.970339\pi$
$757$	−24.8342	+	24.8342i	−0.902613	+	0.902613i	0.0930486	+	0.995662i	$0.470339\pi$
$758$		0			0
$759$	−13.8511	−	1.86329i	−0.502763	−	0.0676332i
$760$		0			0
$761$	−29.9233	−	17.2762i	−1.08472	−	0.626263i	−0.152554	−	0.988295i	$-0.548750\pi$
$761$	−29.9233	−	17.2762i	−1.08472	−	0.626263i	−0.932166	+	0.362032i	$0.882083\pi$
$762$		0			0
$763$	−0.671909	+	2.50760i	−0.0243247	+	0.0907811i
$764$		0			0
$765$	23.0431	−	23.1379i	0.833125	−	0.836553i
$766$		0			0
$767$	−5.05072	+	18.8495i	−0.182371	+	0.680617i
$768$		0			0
$769$	−32.0392	−	18.4979i	−1.15536	−	0.667050i	−0.205175	−	0.978725i	$-0.565777\pi$
$769$	−32.0392	−	18.4979i	−1.15536	−	0.667050i	−0.950189	+	0.311675i	$0.899110\pi$
$770$		0			0
$771$	28.2744	−	36.6335i	1.01828	−	1.31932i
$772$		0			0
$773$	−11.2090	+	11.2090i	−0.403160	+	0.403160i	−0.879345	−	0.476185i	$-0.842019\pi$
$773$	−11.2090	+	11.2090i	−0.403160	+	0.403160i	0.476185	+	0.879345i	$0.342019\pi$
$774$		0			0
$775$	−0.554504	−	36.0312i	−0.0199184	−	1.29428i
$776$		0			0
$777$	0.605557	−	1.45036i	0.0217242	−	0.0520314i
$778$		0			0
$779$	−5.60964	+	9.71618i	−0.200986	+	0.348118i
$780$		0			0
$781$	−9.71632	−	16.8292i	−0.347677	−	0.602195i
$782$		0			0
$783$	7.13414	−	9.13627i	0.254953	−	0.326504i
$784$		0			0
$785$	15.2633	+	25.9733i	0.544772	+	0.927027i
$786$		0			0
$787$	−5.89222	−	21.9901i	−0.210035	−	0.783862i	−0.987856	−	0.155375i	$-0.950341\pi$
$787$	−5.89222	−	21.9901i	−0.210035	−	0.783862i	0.777820	−	0.628487i	$-0.216325\pi$
$788$		0			0
$789$	2.70559	−	1.11176i	0.0963217	−	0.0395798i
$790$		0			0
$791$			1.93108i			0.0686613i
$792$		0			0
$793$	−15.6190	−	15.6190i	−0.554646	−	0.554646i
$794$		0			0
$795$	−4.09301	−	29.9604i	−0.145164	−	1.06259i
$796$		0			0
$797$	10.4917	−	2.81124i	0.371635	−	0.0995793i	−0.0681674	−	0.997674i	$-0.521715\pi$
$797$	10.4917	−	2.81124i	0.371635	−	0.0995793i	0.439802	+	0.898095i	$0.355049\pi$
$798$		0			0
$799$	2.23382	−	1.28970i	0.0790269	−	0.0456262i
$800$		0			0
$801$	8.25036	−	30.1103i	0.291512	−	1.06390i
$802$		0			0
$803$	−4.31195	−	1.15538i	−0.152166	−	0.0407726i
$804$		0			0
$805$	0.826770	+	2.99323i	0.0291398	+	0.105498i
$806$		0			0
$807$	−37.5559	+	28.6497i	−1.32203	+	1.00852i
$808$		0			0
$809$	−23.3629			−0.821396			−0.410698	−	0.911771i	$-0.634715\pi$
$809$	−23.3629			−0.821396			−0.410698	+	0.911771i	$0.634715\pi$
$810$		0			0
$811$	16.6186			0.583558			0.291779	−	0.956486i	$-0.405753\pi$
$811$	16.6186			0.583558			0.291779	+	0.956486i	$0.405753\pi$
$812$		0			0
$813$	11.8244	−	9.02033i	0.414701	−	0.316357i
$814$		0			0
$815$	−34.9435	−	19.8177i	−1.22402	−	0.694185i
$816$		0			0
$817$	5.26390	+	1.41046i	0.184160	+	0.0493456i
$818$		0			0
$819$	0.281904	−	1.02883i	0.00985053	−	0.0359502i
$820$		0			0
$821$	18.8616	−	10.8897i	0.658274	−	0.380054i	−0.133345	−	0.991070i	$-0.542572\pi$
$821$	18.8616	−	10.8897i	0.658274	−	0.380054i	0.791619	+	0.611015i	$0.209239\pi$
$822$		0			0
$823$	−23.2053	+	6.21783i	−0.808885	+	0.216740i	−0.639481	−	0.768807i	$-0.720851\pi$
$823$	−23.2053	+	6.21783i	−0.808885	+	0.216740i	−0.169404	+	0.985547i	$0.554184\pi$
$824$		0			0
$825$	1.53049	+	10.5946i	0.0532849	+	0.368855i
$826$		0			0
$827$	−32.6039	−	32.6039i	−1.13375	−	1.13375i	−0.989549	−	0.144199i	$-0.953939\pi$
$827$	−32.6039	−	32.6039i	−1.13375	−	1.13375i	−0.144199	−	0.989549i	$-0.546061\pi$
$828$		0			0
$829$		−	14.5321i		−	0.504721i	−0.967633	−	0.252361i	$-0.918793\pi$
$829$		−	14.5321i		−	0.504721i	0.967633	−	0.252361i	$-0.0812069\pi$
$830$		0			0
$831$	31.1546	−	12.8018i	1.08074	−	0.444091i
$832$		0			0
$833$	−8.76235	−	32.7015i	−0.303597	−	1.13304i
$834$		0			0
$835$	19.1226	−	11.2375i	0.661765	−	0.388890i
$836$		0			0
$837$	37.0861	+	5.20208i	1.28188	+	0.179810i
$838$		0			0
$839$	−27.8760	−	48.2826i	−0.962386	−	1.66690i	−0.716481	−	0.697607i	$-0.754248\pi$
$839$	−27.8760	−	48.2826i	−0.962386	−	1.66690i	−0.245904	−	0.969294i	$-0.579085\pi$
$840$		0			0
$841$	12.0117	−	20.8049i	0.414197	−	0.717410i
$842$		0			0
$843$	−3.72925	+	8.93188i	−0.128442	+	0.307630i
$844$		0			0
$845$	−16.0127	+	16.2610i	−0.550853	+	0.559396i
$846$		0			0
$847$	−1.42487	+	1.42487i	−0.0489590	+	0.0489590i
$848$		0			0
$849$	−18.4478	+	23.9017i	−0.633127	+	0.820306i
$850$		0			0
$851$	−24.1146	−	13.9226i	−0.826639	−	0.477260i
$852$		0			0
$853$	−8.56880	+	31.9792i	−0.293390	+	1.09495i	0.649098	+	0.760705i	$0.275147\pi$
$853$	−8.56880	+	31.9792i	−0.293390	+	1.09495i	−0.942488	+	0.334241i	$0.891520\pi$
$854$		0			0
$855$	7.90683	−	0.0162339i	0.270408	−	0.000555187i
$856$		0			0
$857$	−11.4637	+	42.7830i	−0.391592	+	1.46144i	0.435917	+	0.899987i	$0.356424\pi$
$857$	−11.4637	+	42.7830i	−0.391592	+	1.46144i	−0.827509	+	0.561453i	$0.810243\pi$
$858$		0			0
$859$	−17.8431	−	10.3017i	−0.608798	−	0.351490i	0.163697	−	0.986511i	$-0.447658\pi$
$859$	−17.8431	−	10.3017i	−0.608798	−	0.351490i	−0.772495	+	0.635021i	$0.780991\pi$
$860$		0			0
$861$	−3.47595	−	0.467596i	−0.118460	−	0.0159356i
$862$		0			0
$863$	9.78220	−	9.78220i	0.332990	−	0.332990i	−0.520731	−	0.853721i	$-0.674341\pi$
$863$	9.78220	−	9.78220i	0.332990	−	0.332990i	0.853721	+	0.520731i	$0.174341\pi$
$864$		0			0
$865$	−58.5914	+	0.450821i	−1.99217	+	0.0153284i
$866$		0			0
$867$	−7.03495	−	9.22187i	−0.238920	−	0.313191i
$868$		0			0
$869$	−2.33981	+	4.05268i	−0.0793728	+	0.137478i
$870$		0			0
$871$	−3.94514	−	6.83318i	−0.133676	−	0.231533i
$872$		0			0
$873$	−21.7916	+	37.2572i	−0.737535	+	1.26097i
$874$		0			0
$875$	2.03181	−	1.23645i	0.0686876	−	0.0417997i
$876$		0			0
$877$	4.37985	+	16.3458i	0.147897	+	0.551959i	0.999609	+	0.0279495i	$0.00889775\pi$
$877$	4.37985	+	16.3458i	0.147897	+	0.551959i	−0.851712	+	0.524010i	$0.824436\pi$
$878$		0			0
$879$	41.1508	+	31.7609i	1.38798	+	1.07127i
$880$		0			0
$881$		−	6.69363i		−	0.225514i	−0.993623	−	0.112757i	$-0.964032\pi$
$881$		−	6.69363i		−	0.225514i	0.993623	−	0.112757i	$-0.0359682\pi$
$882$		0			0
$883$	28.0058	+	28.0058i	0.942471	+	0.942471i	0.998433	−	0.0559622i	$-0.0178226\pi$
$883$	28.0058	+	28.0058i	0.942471	+	0.942471i	−0.0559622	+	0.998433i	$0.517823\pi$
$884$		0			0
$885$	−17.5071	−	41.6900i	−0.588495	−	1.40140i
$886$		0			0
$887$	−12.7040	+	3.40403i	−0.426559	+	0.114296i	−0.465711	−	0.884937i	$-0.654201\pi$
$887$	−12.7040	+	3.40403i	−0.426559	+	0.114296i	0.0391513	+	0.999233i	$0.487535\pi$
$888$		0			0
$889$	2.52698	−	1.45895i	0.0847522	−	0.0489317i
$890$		0			0
$891$	−11.1238	−	0.125504i	−0.372661	−	0.00420455i
$892$		0			0
$893$	0.603275	+	0.161647i	0.0201878	+	0.00540931i
$894$		0			0
$895$	10.2122	−	2.82073i	0.341355	−	0.0942867i
$896$		0			0
$897$	−17.4401	−	7.28164i	−0.582309	−	0.243127i
$898$		0			0
$899$	−16.0778			−0.536223
$900$		0			0
$901$	−38.0067			−1.26619
$902$		0			0
$903$	0.217599	+	1.68964i	0.00724126	+	0.0562279i
$904$		0			0
$905$	29.4551	−	8.13588i	0.979120	−	0.270446i
$906$		0			0
$907$	29.4545	+	7.89231i	0.978021	+	0.262060i	0.712211	−	0.701966i	$-0.247694\pi$
$907$	29.4545	+	7.89231i	0.978021	+	0.262060i	0.265810	+	0.964025i	$0.414361\pi$
$908$		0			0
$909$	−1.98156	−	7.56573i	−0.0657241	−	0.250939i
$910$		0			0
$911$	−16.9646	+	9.79453i	−0.562063	+	0.324507i	−0.753973	−	0.656905i	$-0.771865\pi$
$911$	−16.9646	+	9.79453i	−0.562063	+	0.324507i	0.191910	+	0.981413i	$0.438532\pi$
$912$		0			0
$913$	−18.6087	+	4.98618i	−0.615858	+	0.165019i
$914$		0			0
$915$	50.7753	+	6.43310i	1.67858	+	0.212672i
$916$		0			0
$917$	−2.29109	−	2.29109i	−0.0756585	−	0.0756585i
$918$		0			0
$919$		−	32.6937i		−	1.07846i	−0.842157	−	0.539232i	$-0.818714\pi$
$919$		−	32.6937i		−	1.07846i	0.842157	−	0.539232i	$-0.181286\pi$
$920$		0			0
$921$	6.90658	−	51.3413i	0.227580	−	1.69175i
$922$		0			0
$923$	−6.80132	−	25.3829i	−0.223868	−	0.835487i
$924$		0			0
$925$	−5.20230	+	20.6832i	−0.171051	+	0.680061i
$926$		0			0
$927$	0.210133	−	37.2504i	0.00690166	−	1.22346i
$928$		0			0
$929$	−28.0625	−	48.6057i	−0.920702	−	1.59470i	−0.798331	−	0.602218i	$-0.794284\pi$
$929$	−28.0625	−	48.6057i	−0.920702	−	1.59470i	−0.122371	−	0.992484i	$-0.539050\pi$
$930$		0			0
$931$	4.09872	−	7.09919i	0.134330	−	0.232667i
$932$		0			0
$933$	31.9116	−	4.10971i	1.04474	−	0.134546i
$934$		0			0
$935$	13.4540	−	0.103520i	0.439994	−	0.00338546i
$936$		0			0
$937$	30.8671	−	30.8671i	1.00838	−	1.00838i	0.00842027	−	0.999965i	$-0.497320\pi$
$937$	30.8671	−	30.8671i	1.00838	−	1.00838i	0.999965	−	0.00842027i	$-0.00268029\pi$
$938$		0			0
$939$	8.47852	+	20.6334i	0.276686	+	0.673344i
$940$		0			0
$941$	29.0014	+	16.7440i	0.945418	+	0.545837i	0.891655	−	0.452716i	$-0.149545\pi$
$941$	29.0014	+	16.7440i	0.945418	+	0.545837i	0.0537635	+	0.998554i	$0.482878\pi$
$942$		0			0
$943$	−16.0822	+	60.0195i	−0.523708	+	1.95450i
$944$		0			0
$945$	0.944150	+	2.28434i	0.0307132	+	0.0743095i
$946$		0			0
$947$	−10.3487	+	38.6219i	−0.336288	+	1.25504i	0.566178	+	0.824283i	$0.308421\pi$
$947$	−10.3487	+	38.6219i	−0.336288	+	1.25504i	−0.902466	+	0.430761i	$0.858245\pi$
$948$		0			0
$949$	−5.22788	−	3.01832i	−0.169704	−	0.0979788i
$950$		0			0
$951$	2.58232	+	6.28435i	0.0837375	+	0.203784i
$952$		0			0
$953$	1.84992	−	1.84992i	0.0599248	−	0.0599248i	−0.676509	−	0.736434i	$-0.736508\pi$
$953$	1.84992	−	1.84992i	0.0599248	−	0.0599248i	0.736434	+	0.676509i	$0.236508\pi$
$954$		0			0
$955$	−7.15931	+	7.27034i	−0.231670	+	0.235263i
$956$		0			0
$957$	4.73687	−	0.610034i	0.153121	−	0.0197196i
$958$		0			0
$959$	−0.869844	+	1.50661i	−0.0280887	+	0.0486511i
$960$		0			0
$961$	−10.4711	−	18.1365i	−0.337777	−	0.585047i
$962$		0			0
$963$	19.7042	−	11.2285i	0.634960	−	0.361834i
$964$		0			0
$965$	−30.5254	+	17.9384i	−0.982647	+	0.577458i
$966$		0			0
$967$	13.8024	+	51.5112i	0.443854	+	1.65649i	0.718943	+	0.695069i	$0.244626\pi$
$967$	13.8024	+	51.5112i	0.443854	+	1.65649i	−0.275089	+	0.961419i	$0.588707\pi$
$968$		0			0
$969$	1.32496	−	9.84932i	0.0425638	−	0.316406i
$970$		0			0
$971$		−	25.7021i		−	0.824821i	−0.910998	−	0.412411i	$-0.864687\pi$
$971$		−	25.7021i		−	0.824821i	0.910998	−	0.412411i	$-0.135313\pi$
$972$		0			0
$973$	−1.00009	−	1.00009i	−0.0320615	−	0.0320615i
$974$		0			0
$975$	−1.70892	+	14.3743i	−0.0547291	+	0.460345i
$976$		0			0
$977$	0.0690472	−	0.0185011i	0.00220901	−	0.000591904i	−0.257714	−	0.966221i	$-0.582969\pi$
$977$	0.0690472	−	0.0185011i	0.00220901	−	0.000591904i	0.259923	+	0.965629i	$0.416303\pi$
$978$		0			0
$979$	11.1399	−	6.43164i	0.356034	−	0.205556i
$980$		0			0
$981$	35.3082	+	9.67459i	1.12730	+	0.308886i
$982$		0			0
$983$	54.4616	+	14.5929i	1.73706	+	0.465443i	0.981789	−	0.189976i	$-0.0608409\pi$
$983$	54.4616	+	14.5929i	1.73706	+	0.465443i	0.755266	+	0.655418i	$0.227508\pi$
$984$		0			0
$985$	−1.48395	−	0.841603i	−0.0472826	−	0.0268157i
$986$		0			0
$987$	0.0249382	+	0.193644i	0.000793793	+	0.00616375i
$988$		0			0
$989$	30.1820			0.959730
$990$		0			0
$991$	51.1676			1.62539			0.812697	−	0.582687i	$-0.197998\pi$
$991$	51.1676			1.62539			0.812697	+	0.582687i	$0.197998\pi$
$992$		0			0
$993$	−27.1965	−	11.3551i	−0.863055	−	0.360344i
$994$		0			0
$995$	0.391859	+	1.41869i	0.0124228	+	0.0449754i
$996$		0			0
$997$	48.4100	+	12.9714i	1.53316	+	0.410809i	0.924049	−	0.382275i	$-0.124859\pi$
$997$	48.4100	+	12.9714i	1.53316	+	0.410809i	0.609112	+	0.793084i	$0.291526\pi$
$998$		0			0
$999$	−20.4045	−	8.65481i	−0.645570	−	0.273826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.4	✓	72
3.2	odd	2		1080.2.bt.a.233.2		72
4.3	odd	2		720.2.cu.e.113.15		72
5.2	odd	4	inner	360.2.bs.a.257.13	yes	72
9.2	odd	6	inner	360.2.bs.a.353.13	yes	72
9.7	even	3		1080.2.bt.a.953.8		72
15.2	even	4		1080.2.bt.a.17.8		72
20.7	even	4		720.2.cu.e.257.6		72
36.11	even	6		720.2.cu.e.353.6		72
45.2	even	12	inner	360.2.bs.a.137.4	yes	72
45.7	odd	12		1080.2.bt.a.737.2		72
180.47	odd	12		720.2.cu.e.497.15		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.4	✓	72	1.1	even	1	trivial
360.2.bs.a.137.4	yes	72	45.2	even	12	inner
360.2.bs.a.257.13	yes	72	5.2	odd	4	inner
360.2.bs.a.353.13	yes	72	9.2	odd	6	inner
720.2.cu.e.113.15		72	4.3	odd	2
720.2.cu.e.257.6		72	20.7	even	4
720.2.cu.e.353.6		72	36.11	even	6
720.2.cu.e.497.15		72	180.47	odd	12
1080.2.bt.a.17.8		72	15.2	even	4
1080.2.bt.a.233.2		72	3.2	odd	2
1080.2.bt.a.737.2		72	45.7	odd	12
1080.2.bt.a.953.8		72	9.7	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37710 + 1.05053i) q^{3} +(2.15536 - 0.595338i) q^{5} +(0.205487 + 0.0550600i) q^{7} +(0.792791 - 2.89335i) q^{9} +O(q^{10})\)	\(q+(-1.37710 + 1.05053i) q^{3} +(2.15536 - 0.595338i) q^{5} +(0.205487 + 0.0550600i) q^{7} +(0.792791 - 2.89335i) q^{9} +(1.07045 - 0.618027i) q^{11} +(1.61453 - 0.432612i) q^{13} +(-2.34272 + 3.08410i) q^{15} +(3.44214 + 3.44214i) q^{17} +1.17868i q^{19} +(-0.340817 + 0.140046i) q^{21} +(1.68957 + 6.30557i) q^{23} +(4.29115 - 2.56633i) q^{25} +(1.94779 + 4.81727i) q^{27} +(-1.11541 - 1.93195i) q^{29} +(3.60355 - 6.24153i) q^{31} +(-0.824866 + 1.97562i) q^{33} +(0.475677 - 0.00366001i) q^{35} +(-3.01616 + 3.01616i) q^{37} +(-1.76889 + 2.29185i) q^{39} +(8.24325 + 4.75924i) q^{41} +(1.19664 - 4.46591i) q^{43} +(-0.0137729 - 6.70819i) q^{45} +(0.137142 - 0.511821i) q^{47} +(-6.02298 - 3.47737i) q^{49} +(-8.35621 - 1.12410i) q^{51} +(-5.52081 + 5.52081i) q^{53} +(1.93928 - 1.96935i) q^{55} +(-1.23824 - 1.62316i) q^{57} +(-5.83746 + 10.1108i) q^{59} +(-6.60746 - 11.4445i) q^{61} +(0.322216 - 0.550894i) q^{63} +(3.22234 - 1.89363i) q^{65} +(-1.22176 - 4.55967i) q^{67} +(-8.95087 - 6.90844i) q^{69} -15.7215i q^{71} +(-2.55375 - 2.55375i) q^{73} +(-3.21332 + 8.04205i) q^{75} +(0.253993 - 0.0680572i) q^{77} +(-3.27872 + 1.89297i) q^{79} +(-7.74296 - 4.58765i) q^{81} +(-15.0549 - 4.03395i) q^{83} +(9.46827 + 5.36980i) q^{85} +(3.56559 + 1.48871i) q^{87} +10.4067 q^{89} +0.355584 q^{91} +(1.59445 + 12.3808i) q^{93} +(0.701715 + 2.54049i) q^{95} +(-13.8972 - 3.72373i) q^{97} +(-0.939523 - 3.58717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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