LMFDB - Embedded newform 360.2.bs.a.113.8

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			113.8
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.699583 + 1.58448i) q^{3} +(-2.21911 - 0.274850i) q^{5} +(-1.41974 - 0.380419i) q^{7} +(-2.02117 - 2.21695i) q^{9} +O(q^{10})$	\(q+(-0.699583 + 1.58448i) q^{3} +(-2.21911 - 0.274850i) q^{5} +(-1.41974 - 0.380419i) q^{7} +(-2.02117 - 2.21695i) q^{9} +(3.66685 - 2.11705i) q^{11} +(-3.89991 + 1.04498i) q^{13} +(1.98795 - 3.32386i) q^{15} +(-5.51140 - 5.51140i) q^{17} +1.38947i q^{19} +(1.59599 - 1.98342i) q^{21} +(-1.58133 - 5.90160i) q^{23} +(4.84892 + 1.21984i) q^{25} +(4.92670 - 1.65156i) q^{27} +(-0.680413 - 1.17851i) q^{29} +(-2.78431 + 4.82257i) q^{31} +(0.789170 + 7.29111i) q^{33} +(3.04601 + 1.23441i) q^{35} +(-2.00935 + 2.00935i) q^{37} +(1.07257 - 6.91039i) q^{39} +(-5.03252 - 2.90553i) q^{41} +(1.37121 - 5.11743i) q^{43} +(3.87586 + 5.47519i) q^{45} +(-2.62590 + 9.79998i) q^{47} +(-4.19123 - 2.41981i) q^{49} +(12.5884 - 4.87703i) q^{51} +(-6.54423 + 6.54423i) q^{53} +(-8.71901 + 3.69015i) q^{55} +(-2.20160 - 0.972053i) q^{57} +(-0.427736 + 0.740861i) q^{59} +(3.25634 + 5.64014i) q^{61} +(2.02616 + 3.91639i) q^{63} +(8.94156 - 1.24704i) q^{65} +(2.39125 + 8.92428i) q^{67} +(10.4573 + 1.62308i) q^{69} -8.89725i q^{71} +(-3.74897 - 3.74897i) q^{73} +(-5.32504 + 6.82964i) q^{75} +(-6.01134 + 1.61073i) q^{77} +(-6.72630 + 3.88343i) q^{79} +(-0.829776 + 8.96167i) q^{81} +(-4.09593 - 1.09750i) q^{83} +(10.7156 + 13.7452i) q^{85} +(2.34333 - 0.253636i) q^{87} +3.77125 q^{89} +5.93440 q^{91} +(-5.69342 - 7.78548i) q^{93} +(0.381896 - 3.08340i) q^{95} +(5.66890 + 1.51898i) q^{97} +(-12.1047 - 3.85031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.699583	+	1.58448i	−0.403905	+	0.914801i
$3$	−0.699583	+	1.58448i	−0.403905	+	0.914801i
$4$		0			0
$5$	−2.21911	−	0.274850i	−0.992417	−	0.122916i
$5$	−2.21911	−	0.274850i	−0.992417	−	0.122916i
$6$		0			0
$7$	−1.41974	−	0.380419i	−0.536612	−	0.143785i	−0.0196720	−	0.999806i	$-0.506262\pi$
$7$	−1.41974	−	0.380419i	−0.536612	−	0.143785i	−0.516940	+	0.856022i	$0.672929\pi$
$8$		0			0
$9$	−2.02117	−	2.21695i	−0.673722	−	0.738985i
$10$		0			0
$11$	3.66685	−	2.11705i	1.10560	−	0.638316i	0.167911	−	0.985802i	$-0.446298\pi$
$11$	3.66685	−	2.11705i	1.10560	−	0.638316i	0.937685	+	0.347486i	$0.112965\pi$
$12$		0			0
$13$	−3.89991	+	1.04498i	−1.08164	+	0.289825i	−0.755268	−	0.655416i	$-0.772493\pi$
$13$	−3.89991	+	1.04498i	−1.08164	+	0.289825i	−0.326373	+	0.945241i	$0.605827\pi$
$14$		0			0
$15$	1.98795	−	3.32386i	0.513286	−	0.858218i
$16$		0			0
$17$	−5.51140	−	5.51140i	−1.33671	−	1.33671i	−0.899226	−	0.437485i	$-0.855869\pi$
$17$	−5.51140	−	5.51140i	−1.33671	−	1.33671i	−0.437485	−	0.899226i	$-0.644131\pi$
$18$		0			0
$19$			1.38947i			0.318767i	0.987217	+	0.159384i	$0.0509506\pi$
$19$			1.38947i			0.318767i	−0.987217	+	0.159384i	$0.949049\pi$
$20$		0			0
$21$	1.59599	−	1.98342i	0.348274	−	0.432818i
$22$		0			0
$23$	−1.58133	−	5.90160i	−0.329730	−	1.23057i	−0.909471	−	0.415768i	$-0.863513\pi$
$23$	−1.58133	−	5.90160i	−0.329730	−	1.23057i	0.579740	−	0.814801i	$-0.303154\pi$
$24$		0			0
$25$	4.84892	+	1.21984i	0.969783	+	0.243969i
$26$		0			0
$27$	4.92670	−	1.65156i	0.948144	−	0.317842i
$28$		0			0
$29$	−0.680413	−	1.17851i	−0.126350	−	0.218844i	0.795910	−	0.605415i	$-0.206993\pi$
$29$	−0.680413	−	1.17851i	−0.126350	−	0.218844i	−0.922260	+	0.386571i	$0.873659\pi$
$30$		0			0
$31$	−2.78431	+	4.82257i	−0.500077	+	0.866159i	0.499923	+	0.866070i	$0.333362\pi$
$31$	−2.78431	+	4.82257i	−0.500077	+	0.866159i	−1.00000		8.90578e-5i	$0.999972\pi$
$32$		0			0
$33$	0.789170	+	7.29111i	0.137377	+	1.26922i
$34$		0			0
$35$	3.04601	+	1.23441i	0.514869	+	0.208653i
$36$		0			0
$37$	−2.00935	+	2.00935i	−0.330335	+	0.330335i	−0.852714	−	0.522379i	$-0.825045\pi$
$37$	−2.00935	+	2.00935i	−0.330335	+	0.330335i	0.522379	+	0.852714i	$0.325045\pi$
$38$		0			0
$39$	1.07257	−	6.91039i	0.171748	−	1.10655i
$40$		0			0
$41$	−5.03252	−	2.90553i	−0.785948	−	0.453767i	0.0525864	−	0.998616i	$-0.483254\pi$
$41$	−5.03252	−	2.90553i	−0.785948	−	0.453767i	−0.838534	+	0.544849i	$0.816587\pi$
$42$		0			0
$43$	1.37121	−	5.11743i	0.209108	−	0.780401i	−0.779050	−	0.626961i	$-0.784298\pi$
$43$	1.37121	−	5.11743i	0.209108	−	0.780401i	0.988158	−	0.153439i	$-0.0490350\pi$
$44$		0			0
$45$	3.87586	+	5.47519i	0.577780	+	0.816193i
$46$		0			0
$47$	−2.62590	+	9.79998i	−0.383027	+	1.42947i	0.458228	+	0.888835i	$0.348484\pi$
$47$	−2.62590	+	9.79998i	−0.383027	+	1.42947i	−0.841254	+	0.540640i	$0.818182\pi$
$48$		0			0
$49$	−4.19123	−	2.41981i	−0.598747	−	0.345687i
$50$		0			0
$51$	12.5884	−	4.87703i	1.76273	−	0.682921i
$52$		0			0
$53$	−6.54423	+	6.54423i	−0.898919	+	0.898919i	−0.995341	−	0.0964211i	$-0.969260\pi$
$53$	−6.54423	+	6.54423i	−0.898919	+	0.898919i	0.0964211	+	0.995341i	$0.469260\pi$
$54$		0			0
$55$	−8.71901	+	3.69015i	−1.17567	+	0.497580i
$56$		0			0
$57$	−2.20160	−	0.972053i	−0.291608	−	0.128752i
$58$		0			0
$59$	−0.427736	+	0.740861i	−0.0556865	+	0.0964519i	−0.892525	−	0.450998i	$-0.851068\pi$
$59$	−0.427736	+	0.740861i	−0.0556865	+	0.0964519i	0.836838	+	0.547450i	$0.184401\pi$
$60$		0			0
$61$	3.25634	+	5.64014i	0.416931	+	0.722146i	0.995629	−	0.0933961i	$-0.0297723\pi$
$61$	3.25634	+	5.64014i	0.416931	+	0.722146i	−0.578698	+	0.815542i	$0.696439\pi$
$62$		0			0
$63$	2.02616	+	3.91639i	0.255272	+	0.493419i
$64$		0			0
$65$	8.94156	−	1.24704i	1.10906	−	0.154676i
$66$		0			0
$67$	2.39125	+	8.92428i	0.292138	+	1.09027i	0.943464	+	0.331476i	$0.107546\pi$
$67$	2.39125	+	8.92428i	0.292138	+	1.09027i	−0.651326	+	0.758798i	$0.725787\pi$
$68$		0			0
$69$	10.4573	+	1.62308i	1.25891	+	0.195395i
$70$		0			0
$71$		−	8.89725i		−	1.05591i	−0.849273	−	0.527955i	$-0.822959\pi$
$71$		−	8.89725i		−	1.05591i	0.849273	−	0.527955i	$-0.177041\pi$
$72$		0			0
$73$	−3.74897	−	3.74897i	−0.438784	−	0.438784i	0.452819	−	0.891603i	$-0.350418\pi$
$73$	−3.74897	−	3.74897i	−0.438784	−	0.438784i	−0.891603	+	0.452819i	$0.850418\pi$
$74$		0			0
$75$	−5.32504	+	6.82964i	−0.614883	+	0.788618i
$76$		0			0
$77$	−6.01134	+	1.61073i	−0.685056	+	0.183560i
$78$		0			0
$79$	−6.72630	+	3.88343i	−0.756768	+	0.436920i	−0.828134	−	0.560530i	$-0.810598\pi$
$79$	−6.72630	+	3.88343i	−0.756768	+	0.436920i	0.0713660	+	0.997450i	$0.477264\pi$
$80$		0			0
$81$	−0.829776	+	8.96167i	−0.0921974	+	0.995741i
$82$		0			0
$83$	−4.09593	−	1.09750i	−0.449586	−	0.120466i	0.0269196	−	0.999638i	$-0.491430\pi$
$83$	−4.09593	−	1.09750i	−0.449586	−	0.120466i	−0.476506	+	0.879171i	$0.658097\pi$
$84$		0			0
$85$	10.7156	+	13.7452i	1.16227	+	1.49088i
$86$		0			0
$87$	2.34333	−	0.253636i	0.251232	−	0.0271926i
$88$		0			0
$89$	3.77125			0.399752			0.199876	−	0.979821i	$-0.435946\pi$
$89$	3.77125			0.399752			0.199876	+	0.979821i	$0.435946\pi$
$90$		0			0
$91$	5.93440			0.622094
$92$		0			0
$93$	−5.69342	−	7.78548i	−0.590380	−	0.807317i
$94$		0			0
$95$	0.381896	−	3.08340i	0.0391817	−	0.316350i
$96$		0			0
$97$	5.66890	+	1.51898i	0.575590	+	0.154229i	0.534859	−	0.844941i	$-0.320365\pi$
$97$	5.66890	+	1.51898i	0.575590	+	0.154229i	0.0407310	+	0.999170i	$0.487031\pi$
$98$		0			0
$99$	−12.1047	−	3.85031i	−1.21657	−	0.386971i
$100$		0			0
$101$	12.8384	−	7.41228i	1.27747	−	0.737549i	0.301089	−	0.953596i	$-0.402650\pi$
$101$	12.8384	−	7.41228i	1.27747	−	0.737549i	0.976383	+	0.216047i	$0.0693164\pi$
$102$		0			0
$103$	3.91640	−	1.04940i	0.385895	−	0.103400i	−0.0606556	−	0.998159i	$-0.519319\pi$
$103$	3.91640	−	1.04940i	0.385895	−	0.103400i	0.446550	+	0.894759i	$0.352652\pi$
$104$		0			0
$105$	−4.08683	+	3.96277i	−0.398834	+	0.386727i
$106$		0			0
$107$	13.1703	+	13.1703i	1.27322	+	1.27322i	0.944390	+	0.328826i	$0.106653\pi$
$107$	13.1703	+	13.1703i	1.27322	+	1.27322i	0.328826	+	0.944390i	$0.393347\pi$
$108$		0			0
$109$		−	10.5545i		−	1.01094i	−0.862844	−	0.505470i	$-0.831319\pi$
$109$		−	10.5545i		−	1.01094i	0.862844	−	0.505470i	$-0.168681\pi$
$110$		0			0
$111$	−1.77807	−	4.58948i	−0.168767	−	0.435614i
$112$		0			0
$113$	−5.32410	−	19.8698i	−0.500849	−	1.86919i	−0.494437	−	0.869214i	$-0.664626\pi$
$113$	−5.32410	−	19.8698i	−0.500849	−	1.86919i	−0.00641180	−	0.999979i	$-0.502041\pi$
$114$		0			0
$115$	1.88710	+	13.5309i	0.175973	+	1.26177i
$116$		0			0
$117$	10.1990	+	6.53386i	0.942902	+	0.604055i
$118$		0			0
$119$	5.72812	+	9.92140i	0.525096	+	0.909493i
$120$		0			0
$121$	3.46384	−	5.99954i	0.314894	−	0.545413i
$122$		0			0
$123$	8.12442	−	5.94128i	0.732555	−	0.535707i
$124$		0			0
$125$	−10.4250	−	4.03969i	−0.932441	−	0.361321i
$126$		0			0
$127$	0.953694	−	0.953694i	0.0846266	−	0.0846266i	−0.663526	−	0.748153i	$-0.730941\pi$
$127$	0.953694	−	0.953694i	0.0846266	−	0.0846266i	0.748153	+	0.663526i	$0.230941\pi$
$128$		0			0
$129$	7.14920	+	5.75273i	0.629452	+	0.506499i
$130$		0			0
$131$	−0.419530	−	0.242216i	−0.0366545	−	0.0211625i	0.481561	−	0.876413i	$-0.340070\pi$
$131$	−0.419530	−	0.242216i	−0.0366545	−	0.0211625i	−0.518215	+	0.855250i	$0.673403\pi$
$132$		0			0
$133$	0.528581	−	1.97269i	0.0458338	−	0.171054i
$134$		0			0
$135$	−11.3868	+	2.31089i	−0.980022	+	0.198889i
$136$		0			0
$137$	−0.373949	+	1.39560i	−0.0319486	+	0.119234i	−0.980059	−	0.198709i	$-0.936325\pi$
$137$	−0.373949	+	1.39560i	−0.0319486	+	0.119234i	0.948110	+	0.317942i	$0.102992\pi$
$138$		0			0
$139$	−9.65741	−	5.57571i	−0.819131	−	0.472926i	0.0309856	−	0.999520i	$-0.490135\pi$
$139$	−9.65741	−	5.57571i	−0.819131	−	0.472926i	−0.850117	+	0.526594i	$0.823469\pi$
$140$		0			0
$141$	−13.6909	−	11.0166i	−1.15298	−	0.927765i
$142$		0			0
$143$	−12.0881	+	12.0881i	−1.01086	+	1.01086i
$144$		0			0
$145$	1.18600	+	2.80226i	0.0984919	+	0.232715i
$146$		0			0
$147$	6.76626	−	4.94807i	0.558072	−	0.408110i
$148$		0			0
$149$	−3.00804	+	5.21007i	−0.246428	+	0.426826i	−0.962532	−	0.271168i	$-0.912590\pi$
$149$	−3.00804	+	5.21007i	−0.246428	+	0.426826i	0.716104	+	0.697993i	$0.245924\pi$
$150$		0			0
$151$	−8.40595	−	14.5595i	−0.684066	−	1.18484i	−0.973729	−	0.227709i	$-0.926877\pi$
$151$	−8.40595	−	14.5595i	−0.684066	−	1.18484i	0.289663	−	0.957129i	$-0.406457\pi$
$152$		0			0
$153$	−1.07907	+	23.3580i	−0.0872377	+	1.88838i
$154$		0			0
$155$	7.50418	−	9.93655i	0.602750	−	0.798123i
$156$		0			0
$157$	−5.57799	−	20.8173i	−0.445172	−	1.66140i	−0.715482	−	0.698631i	$-0.753793\pi$
$157$	−5.57799	−	20.8173i	−0.445172	−	1.66140i	0.270310	−	0.962773i	$-0.412874\pi$
$158$		0			0
$159$	−5.79098	−	14.9475i	−0.459255	−	1.18541i
$160$		0			0
$161$			8.98032i			0.707748i
$162$		0			0
$163$	7.48680	+	7.48680i	0.586412	+	0.586412i	0.936658	−	0.350246i	$-0.113902\pi$
$163$	7.48680	+	7.48680i	0.586412	+	0.586412i	−0.350246	+	0.936658i	$0.613902\pi$
$164$		0			0
$165$	0.252701	−	16.3967i	0.0196728	−	1.27648i
$166$		0			0
$167$	3.58882	−	0.961620i	0.277711	−	0.0744124i	−0.117275	−	0.993099i	$-0.537416\pi$
$167$	3.58882	−	0.961620i	0.277711	−	0.0744124i	0.394986	+	0.918687i	$0.370749\pi$
$168$		0			0
$169$	2.85902	−	1.65066i	0.219925	−	0.126974i
$170$		0			0
$171$	3.08040	−	2.80836i	0.235564	−	0.214760i
$172$		0			0
$173$	−8.23187	−	2.20572i	−0.625857	−	0.167698i	−0.0680682	−	0.997681i	$-0.521684\pi$
$173$	−8.23187	−	2.20572i	−0.625857	−	0.167698i	−0.557789	+	0.829983i	$0.688350\pi$
$174$		0			0
$175$	−6.42015	−	3.57648i	−0.485318	−	0.270356i
$176$		0			0
$177$	−0.874644	−	1.19603i	−0.0657423	−	0.0898995i
$178$		0			0
$179$	−15.5813			−1.16460			−0.582300	−	0.812974i	$-0.697847\pi$
$179$	−15.5813			−1.16460			−0.582300	+	0.812974i	$0.697847\pi$
$180$		0			0
$181$	0.984247			0.0731585			0.0365793	−	0.999331i	$-0.488354\pi$
$181$	0.984247			0.0731585			0.0365793	+	0.999331i	$0.488354\pi$
$182$		0			0
$183$	−11.2148	+	1.21386i	−0.829020	+	0.0897309i
$184$		0			0
$185$	5.01124	−	3.90670i	0.368434	−	0.287226i
$186$		0			0
$187$	−31.8774	−	8.54152i	−2.33111	−	0.624618i
$188$		0			0
$189$	−7.62292	+	0.470575i	−0.554486	+	0.0342293i
$190$		0			0
$191$	8.08702	−	4.66904i	0.585156	−	0.337840i	−0.178024	−	0.984026i	$-0.556970\pi$
$191$	8.08702	−	4.66904i	0.585156	−	0.337840i	0.763180	+	0.646186i	$0.223637\pi$
$192$		0			0
$193$	26.0179	−	6.97148i	1.87281	−	0.501818i	0.872909	−	0.487884i	$-0.162231\pi$
$193$	26.0179	−	6.97148i	1.87281	−	0.501818i	0.999903	−	0.0139345i	$-0.00443563\pi$
$194$		0			0
$195$	−4.27946	+	15.0401i	−0.306459	+	1.07705i
$196$		0			0
$197$	4.89080	+	4.89080i	0.348455	+	0.348455i	0.859534	−	0.511079i	$-0.170754\pi$
$197$	4.89080	+	4.89080i	0.348455	+	0.348455i	−0.511079	+	0.859534i	$0.670754\pi$
$198$		0			0
$199$			7.72017i			0.547268i	0.961834	+	0.273634i	$0.0882258\pi$
$199$			7.72017i			0.547268i	−0.961834	+	0.273634i	$0.911774\pi$
$200$		0			0
$201$	−15.8132	−	2.45438i	−1.11538	−	0.173119i
$202$		0			0
$203$	0.517684	+	1.93202i	0.0363343	+	0.135601i
$204$		0			0
$205$	10.3691	+	7.83088i	0.724212	+	0.546932i
$206$		0			0
$207$	−9.88746	+	15.4339i	−0.687226	+	1.07273i
$208$		0			0
$209$	2.94159	+	5.09498i	0.203474	+	0.352427i
$210$		0			0
$211$	−3.93870	+	6.82204i	−0.271152	+	0.469648i	−0.969157	−	0.246444i	$-0.920738\pi$
$211$	−3.93870	+	6.82204i	−0.271152	+	0.469648i	0.698005	+	0.716093i	$0.254071\pi$
$212$		0			0
$213$	14.0975	+	6.22437i	0.965947	+	0.426487i
$214$		0			0
$215$	−4.44939	+	10.9793i	−0.303446	+	0.748780i
$216$		0			0
$217$	5.78760	−	5.78760i	0.392888	−	0.392888i
$218$		0			0
$219$	8.56290	−	3.31746i	0.578627	−	0.224173i
$220$		0			0
$221$	27.2533	+	15.7347i	1.83325	+	1.05843i
$222$		0			0
$223$	5.18775	−	19.3610i	0.347398	−	1.29651i	−0.542388	−	0.840128i	$-0.682480\pi$
$223$	5.18775	−	19.3610i	0.347398	−	1.29651i	0.889786	−	0.456378i	$-0.150854\pi$
$224$		0			0
$225$	−7.09612	−	13.2153i	−0.473075	−	0.881022i
$226$		0			0
$227$	0.729963	−	2.72426i	0.0484494	−	0.180815i	−0.937461	−	0.348091i	$-0.886830\pi$
$227$	0.729963	−	2.72426i	0.0484494	−	0.180815i	0.985910	+	0.167275i	$0.0534968\pi$
$228$		0			0
$229$	−17.5948	−	10.1584i	−1.16270	−	0.671285i	−0.210750	−	0.977540i	$-0.567591\pi$
$229$	−17.5948	−	10.1584i	−1.16270	−	0.671285i	−0.951950	+	0.306255i	$0.900924\pi$
$230$		0			0
$231$	1.65326	−	10.6517i	0.108776	−	0.700830i
$232$		0			0
$233$	−4.63086	+	4.63086i	−0.303378	+	0.303378i	−0.842334	−	0.538956i	$-0.818819\pi$
$233$	−4.63086	+	4.63086i	−0.303378	+	0.303378i	0.538956	+	0.842334i	$0.318819\pi$
$234$		0			0
$235$	8.52068	−	21.0255i	0.555828	−	1.37155i
$236$		0			0
$237$	−1.44762	−	13.3745i	−0.0940330	−	0.868767i
$238$		0			0
$239$	6.10021	−	10.5659i	0.394590	−	0.683449i	−0.598459	−	0.801153i	$-0.704220\pi$
$239$	6.10021	−	10.5659i	0.394590	−	0.683449i	0.993049	+	0.117704i	$0.0375535\pi$
$240$		0			0
$241$	1.71860	+	2.97671i	0.110705	+	0.191746i	0.916055	−	0.401053i	$-0.131356\pi$
$241$	1.71860	+	2.97671i	0.110705	+	0.191746i	−0.805350	+	0.592800i	$0.798022\pi$
$242$		0			0
$243$	−13.6191	−	7.58420i	−0.873666	−	0.486527i
$244$		0			0
$245$	8.63573	+	6.52178i	0.551716	+	0.416661i
$246$		0			0
$247$	−1.45197	−	5.41883i	−0.0923867	−	0.344792i
$248$		0			0
$249$	4.60441	−	5.72213i	0.291793	−	0.362625i
$250$		0			0
$251$			15.1025i			0.953261i	0.879104	+	0.476630i	$0.158142\pi$
$251$			15.1025i			0.953261i	−0.879104	+	0.476630i	$0.841858\pi$
$252$		0			0
$253$	−18.2925	−	18.2925i	−1.15004	−	1.15004i
$254$		0			0
$255$	−29.2755	+	7.36276i	−1.83330	+	0.461074i
$256$		0			0
$257$	−9.45175	+	2.53259i	−0.589584	+	0.157979i	−0.541263	−	0.840853i	$-0.682054\pi$
$257$	−9.45175	+	2.53259i	−0.589584	+	0.157979i	−0.0483210	+	0.998832i	$0.515387\pi$
$258$		0			0
$259$	3.61715	−	2.08836i	0.224759	−	0.129764i
$260$		0			0
$261$	−1.23748	+	3.89041i	−0.0765978	+	0.240810i
$262$		0			0
$263$	0.684379	+	0.183379i	0.0422006	+	0.0113076i	0.279858	−	0.960042i	$-0.409713\pi$
$263$	0.684379	+	0.183379i	0.0422006	+	0.0113076i	−0.237657	+	0.971349i	$0.576379\pi$
$264$		0			0
$265$	16.3211	−	12.7237i	1.00259	−	0.781611i
$266$		0			0
$267$	−2.63831	+	5.97548i	−0.161462	+	0.365693i
$268$		0			0
$269$	9.71691			0.592451			0.296225	−	0.955118i	$-0.404272\pi$
$269$	9.71691			0.592451			0.296225	+	0.955118i	$0.404272\pi$
$270$		0			0
$271$	10.1023			0.613669			0.306835	−	0.951763i	$-0.400730\pi$
$271$	10.1023			0.613669			0.306835	+	0.951763i	$0.400730\pi$
$272$		0			0
$273$	−4.15161	+	9.40295i	−0.251267	+	0.569092i
$274$		0			0
$275$	20.3627	−	5.79244i	1.22792	−	0.349297i
$276$		0			0
$277$	−9.30161	−	2.49236i	−0.558879	−	0.149751i	−0.0316879	−	0.999498i	$-0.510088\pi$
$277$	−9.30161	−	2.49236i	−0.558879	−	0.149751i	−0.527191	+	0.849747i	$0.676755\pi$
$278$		0			0
$279$	16.3190	−	3.57452i	0.976991	−	0.214001i
$280$		0			0
$281$	−16.4109	+	9.47482i	−0.978991	+	0.565221i	−0.901965	−	0.431808i	$-0.857876\pi$
$281$	−16.4109	+	9.47482i	−0.978991	+	0.565221i	−0.0770255	+	0.997029i	$0.524542\pi$
$282$		0			0
$283$	30.8401	−	8.26357i	1.83325	−	0.491218i	0.834996	−	0.550256i	$-0.185470\pi$
$283$	30.8401	−	8.26357i	1.83325	−	0.491218i	0.998256	+	0.0590375i	$0.0188031\pi$
$284$		0			0
$285$	4.61842	+	2.76220i	0.273571	+	0.163619i
$286$		0			0
$287$	6.03956	+	6.03956i	0.356504	+	0.356504i
$288$		0			0
$289$			43.7511i			2.57359i
$290$		0			0
$291$	−6.37267	+	7.91962i	−0.373572	+	0.464257i
$292$		0			0
$293$	0.290808	+	1.08531i	0.0169892	+	0.0634045i	0.973900	−	0.226977i	$-0.0728843\pi$
$293$	0.290808	+	1.08531i	0.0169892	+	0.0634045i	−0.956911	+	0.290382i	$0.906218\pi$
$294$		0			0
$295$	1.15282	−	1.52649i	0.0671198	−	0.0888757i
$296$		0			0
$297$	14.5690	−	16.4861i	0.845380	−	0.956620i
$298$		0			0
$299$	12.3341	+	21.3633i	0.713300	+	1.23547i
$300$		0			0
$301$	−3.89353	+	6.74379i	−0.224419	+	0.388706i
$302$		0			0
$303$	2.76306	+	25.5278i	0.158734	+	1.46653i
$304$		0			0
$305$	−5.67598	−	13.4111i	−0.325006	−	0.767917i
$306$		0			0
$307$	14.1839	−	14.1839i	0.809516	−	0.809516i	−0.175044	−	0.984561i	$-0.556007\pi$
$307$	14.1839	−	14.1839i	0.809516	−	0.809516i	0.984561	+	0.175044i	$0.0560068\pi$
$308$		0			0
$309$	−1.07710	+	6.93961i	−0.0612741	+	0.394781i
$310$		0			0
$311$	−26.8900	−	15.5250i	−1.52479	−	0.880340i	−0.999568	−	0.0293766i	$-0.990648\pi$
$311$	−26.8900	−	15.5250i	−1.52479	−	0.880340i	−0.525225	−	0.850963i	$-0.676019\pi$
$312$		0			0
$313$	−4.69031	+	17.5045i	−0.265112	+	0.989411i	0.697070	+	0.717003i	$0.254487\pi$
$313$	−4.69031	+	17.5045i	−0.265112	+	0.989411i	−0.962182	+	0.272408i	$0.912180\pi$
$314$		0			0
$315$	−3.41986	−	9.24780i	−0.192687	−	0.521055i
$316$		0			0
$317$	1.59044	−	5.93561i	0.0893281	−	0.333377i	−0.906770	−	0.421625i	$-0.861460\pi$
$317$	1.59044	−	5.93561i	0.0893281	−	0.333377i	0.996099	+	0.0882477i	$0.0281267\pi$
$318$		0			0
$319$	−4.98994	−	2.88094i	−0.279383	−	0.161302i
$320$		0			0
$321$	−30.0817	+	11.6543i	−1.67900	+	0.650482i
$322$		0			0
$323$	7.65794	−	7.65794i	0.426099	−	0.426099i
$324$		0			0
$325$	−20.1851	+	0.309728i	−1.11967	+	0.0171806i
$326$		0			0
$327$	16.7235	+	7.38377i	0.924810	+	0.408324i
$328$		0			0
$329$	7.45619	−	12.9145i	0.411073	−	0.711999i
$330$		0			0
$331$	9.15242	+	15.8525i	0.503062	+	0.871330i	0.999994	+	0.00353980i	$0.00112676\pi$
$331$	9.15242	+	15.8525i	0.503062	+	0.871330i	−0.496931	+	0.867790i	$0.665540\pi$
$332$		0			0
$333$	8.51586	+	0.393408i	0.466666	+	0.0215586i
$334$		0			0
$335$	−2.85362	−	20.4612i	−0.155910	−	1.11792i
$336$		0			0
$337$	0.712608	+	2.65949i	0.0388182	+	0.144872i	0.982615	−	0.185654i	$-0.0594405\pi$
$337$	0.712608	+	2.65949i	0.0388182	+	0.144872i	−0.943797	+	0.330526i	$0.892774\pi$
$338$		0			0
$339$	35.2080	+	5.46465i	1.91223	+	0.296799i
$340$		0			0
$341$			23.5782i			1.27683i
$342$		0			0
$343$	12.3052	+	12.3052i	0.664417	+	0.664417i
$344$		0			0
$345$	−22.7597	−	6.47596i	−1.22534	−	0.348654i
$346$		0			0
$347$	−14.1066	+	3.77986i	−0.757284	+	0.202914i	−0.616746	−	0.787162i	$-0.711550\pi$
$347$	−14.1066	+	3.77986i	−0.757284	+	0.202914i	−0.140537	+	0.990075i	$0.544883\pi$
$348$		0			0
$349$	0.590521	−	0.340938i	0.0316099	−	0.0182500i	−0.484112	−	0.875006i	$-0.660857\pi$
$349$	0.590521	−	0.340938i	0.0316099	−	0.0182500i	0.515722	+	0.856756i	$0.327524\pi$
$350$		0			0
$351$	−17.4879	+	11.5892i	−0.933433	+	0.618587i
$352$		0			0
$353$	−7.58681	−	2.03288i	−0.403805	−	0.108199i	0.0511993	−	0.998688i	$-0.483696\pi$
$353$	−7.58681	−	2.03288i	−0.403805	−	0.108199i	−0.455004	+	0.890489i	$0.650362\pi$
$354$		0			0
$355$	−2.44540	+	19.7440i	−0.129789	+	1.04790i
$356$		0			0
$357$	−19.7276	+	2.13526i	−1.04409	+	0.113010i
$358$		0			0
$359$	1.02248			0.0539645			0.0269822	−	0.999636i	$-0.491410\pi$
$359$	1.02248			0.0539645			0.0269822	+	0.999636i	$0.491410\pi$
$360$		0			0
$361$	17.0694			0.898388
$362$		0			0
$363$	7.08293	+	9.68557i	0.371757	+	0.508361i
$364$		0			0
$365$	7.28898	+	9.34979i	0.381523	+	0.489390i
$366$		0			0
$367$	14.9082	+	3.99465i	0.778203	+	0.208519i	0.625993	−	0.779829i	$-0.284694\pi$
$367$	14.9082	+	3.99465i	0.778203	+	0.208519i	0.152211	+	0.988348i	$0.451361\pi$
$368$		0			0
$369$	3.73014	+	17.0294i	0.194183	+	0.886516i
$370$		0			0
$371$	11.7807	−	6.80157i	0.611622	−	0.353120i
$372$		0			0
$373$	−9.17054	+	2.45724i	−0.474833	+	0.127231i	−0.488296	−	0.872678i	$-0.662381\pi$
$373$	−9.17054	+	2.45724i	−0.474833	+	0.127231i	0.0134628	+	0.999909i	$0.495715\pi$
$374$		0			0
$375$	13.6940	−	13.6921i	0.707154	−	0.707059i
$376$		0			0
$377$	3.88507	+	3.88507i	0.200091	+	0.200091i
$378$		0			0
$379$			3.54042i			0.181859i	0.995857	+	0.0909297i	$0.0289839\pi$
$379$			3.54042i			0.181859i	−0.995857	+	0.0909297i	$0.971016\pi$
$380$		0			0
$381$	0.843922	+	2.17830i	0.0432354	+	0.111598i
$382$		0			0
$383$	7.35407	+	27.4457i	0.375775	+	1.40241i	0.852209	+	0.523202i	$0.175263\pi$
$383$	7.35407	+	27.4457i	0.375775	+	1.40241i	−0.476434	+	0.879210i	$0.658071\pi$
$384$		0			0
$385$	13.7825	−	1.92218i	0.702423	−	0.0979636i
$386$		0			0
$387$	−14.1166	+	7.30326i	−0.717585	+	0.371246i
$388$		0			0
$389$	16.8816	+	29.2398i	0.855931	+	1.48252i	0.875778	+	0.482713i	$0.160349\pi$
$389$	16.8816	+	29.2398i	0.855931	+	1.48252i	−0.0198472	+	0.999803i	$0.506318\pi$
$390$		0			0
$391$	−23.8108	+	41.2414i	−1.20416	+	2.08567i
$392$		0			0
$393$	0.677284	−	0.495288i	0.0341644	−	0.0249840i
$394$		0			0
$395$	15.9938	−	6.76905i	0.804734	−	0.340588i
$396$		0			0
$397$	−15.2741	+	15.2741i	−0.766586	+	0.766586i	−0.977504	−	0.210918i	$-0.932355\pi$
$397$	−15.2741	+	15.2741i	−0.766586	+	0.766586i	0.210918	+	0.977504i	$0.432355\pi$
$398$		0			0
$399$	2.75591	+	2.21759i	0.137968	+	0.111018i
$400$		0			0
$401$	1.73121	+	0.999512i	0.0864523	+	0.0499133i	0.542603	−	0.839989i	$-0.317439\pi$
$401$	1.73121	+	0.999512i	0.0864523	+	0.0499133i	−0.456151	+	0.889903i	$0.650772\pi$
$402$		0			0
$403$	5.81909	−	21.7172i	0.289870	−	1.08181i
$404$		0			0
$405$	4.30448	−	19.6589i	0.213891	−	0.976857i
$406$		0			0
$407$	−3.11407	+	11.6219i	−0.154359	+	0.576075i
$408$		0			0
$409$	−23.9729	−	13.8408i	−1.18538	−	0.684381i	−0.228130	−	0.973631i	$-0.573261\pi$
$409$	−23.9729	−	13.8408i	−1.18538	−	0.684381i	−0.957254	+	0.289249i	$0.906594\pi$
$410$		0			0
$411$	−1.94969	−	1.56885i	−0.0961710	−	0.0773857i
$412$		0			0
$413$	0.889112	−	0.889112i	0.0437504	−	0.0437504i
$414$		0			0
$415$	8.78767	+	3.56124i	0.431370	+	0.174814i
$416$		0			0
$417$	15.5908	−	11.4013i	0.763484	−	0.558325i
$418$		0			0
$419$	−10.3486	+	17.9243i	−0.505563	+	0.875660i	0.494417	+	0.869225i	$0.335382\pi$
$419$	−10.3486	+	17.9243i	−0.505563	+	0.875660i	−0.999979	+	0.00643524i	$0.997952\pi$
$420$		0			0
$421$	−15.3928	−	26.6610i	−0.750197	−	1.29938i	−0.947727	−	0.319083i	$-0.896625\pi$
$421$	−15.3928	−	26.6610i	−0.750197	−	1.29938i	0.197529	−	0.980297i	$-0.436708\pi$
$422$		0			0
$423$	27.0335	−	13.9859i	1.31441	−	0.680018i
$424$		0			0
$425$	−20.0013	−	33.4474i	−0.970204	−	1.62244i
$426$		0			0
$427$	−2.47754	−	9.24631i	−0.119897	−	0.447460i
$428$		0			0
$429$	−10.6967	−	27.6100i	−0.516444	−	1.33302i
$430$		0			0
$431$		−	23.4464i		−	1.12937i	−0.825306	−	0.564686i	$-0.808997\pi$
$431$		−	23.4464i		−	1.12937i	0.825306	−	0.564686i	$-0.191003\pi$
$432$		0			0
$433$	9.64077	+	9.64077i	0.463306	+	0.463306i	0.899738	−	0.436431i	$-0.143758\pi$
$433$	9.64077	+	9.64077i	0.463306	+	0.463306i	−0.436431	+	0.899738i	$0.643758\pi$
$434$		0			0
$435$	−5.26983	−	0.0812173i	−0.252669	−	0.00389407i
$436$		0			0
$437$	8.20012	−	2.19722i	0.392265	−	0.105107i
$438$		0			0
$439$	32.3152	−	18.6572i	1.54232	−	0.890460i	0.543630	−	0.839325i	$-0.317049\pi$
$439$	32.3152	−	18.6572i	1.54232	−	0.890460i	0.998692	−	0.0511349i	$-0.0162838\pi$
$440$		0			0
$441$	3.10657	+	14.1826i	0.147932	+	0.675362i
$442$		0			0
$443$	−31.1371	−	8.34317i	−1.47937	−	0.396396i	−0.573238	−	0.819389i	$-0.694313\pi$
$443$	−31.1371	−	8.34317i	−1.47937	−	0.396396i	−0.906133	+	0.422993i	$0.860979\pi$
$444$		0			0
$445$	−8.36883	−	1.03653i	−0.396721	−	0.0491361i
$446$		0			0
$447$	−6.15089	−	8.41106i	−0.290927	−	0.397830i
$448$		0			0
$449$	31.1038			1.46788			0.733940	−	0.679215i	$-0.237679\pi$
$449$	31.1038			1.46788			0.733940	+	0.679215i	$0.237679\pi$
$450$		0			0
$451$	−24.6046			−1.15859
$452$		0			0
$453$	28.9500	−	3.13347i	1.36019	−	0.147223i
$454$		0			0
$455$	−13.1691	−	1.63107i	−0.617377	−	0.0764656i
$456$		0			0
$457$	−31.1011	−	8.33352i	−1.45485	−	0.389826i	−0.557141	−	0.830418i	$-0.688102\pi$
$457$	−31.1011	−	8.33352i	−1.45485	−	0.389826i	−0.897707	+	0.440592i	$0.854769\pi$
$458$		0			0
$459$	−36.2554	−	18.0506i	−1.69226	−	0.842531i
$460$		0			0
$461$	−3.90772	+	2.25612i	−0.182000	+	0.105078i	−0.588232	−	0.808692i	$-0.700176\pi$
$461$	−3.90772	+	2.25612i	−0.182000	+	0.105078i	0.406232	+	0.913770i	$0.366843\pi$
$462$		0			0
$463$	9.60797	−	2.57445i	0.446520	−	0.119645i	−0.0285505	−	0.999592i	$-0.509089\pi$
$463$	9.60797	−	2.57445i	0.446520	−	0.119645i	0.475071	+	0.879948i	$0.342422\pi$
$464$		0			0
$465$	10.4945	+	18.8417i	0.486670	+	0.873762i
$466$		0			0
$467$	−26.4448	−	26.4448i	−1.22372	−	1.22372i	−0.966300	−	0.257419i	$-0.917128\pi$
$467$	−26.4448	−	26.4448i	−1.22372	−	1.22372i	−0.257419	−	0.966300i	$-0.582872\pi$
$468$		0			0
$469$		−	13.5798i		−	0.627059i
$470$		0			0
$471$	36.8870	+	5.72524i	1.69966	+	0.263805i
$472$		0			0
$473$	−5.80586	−	21.6678i	−0.266954	−	0.996284i
$474$		0			0
$475$	−1.69494	+	6.73744i	−0.0777692	+	0.309135i
$476$		0			0
$477$	27.7352	+	1.28129i	1.26991	+	0.0586661i
$478$		0			0
$479$	−7.47701	−	12.9506i	−0.341633	−	0.591726i	0.643103	−	0.765780i	$-0.277647\pi$
$479$	−7.47701	−	12.9506i	−0.341633	−	0.591726i	−0.984736	+	0.174053i	$0.944313\pi$
$480$		0			0
$481$	5.73656	−	9.93601i	0.261565	−	0.453043i
$482$		0			0
$483$	−14.2292	−	6.28248i	−0.647449	−	0.285863i
$484$		0			0
$485$	−12.1624	−	4.92888i	−0.552268	−	0.223809i
$486$		0			0
$487$	24.3357	−	24.3357i	1.10275	−	1.10275i	0.108678	−	0.994077i	$-0.465338\pi$
$487$	24.3357	−	24.3357i	1.10275	−	1.10275i	0.994077	−	0.108678i	$-0.0346616\pi$
$488$		0			0
$489$	−17.1003	+	6.62506i	−0.773304	+	0.299596i
$490$		0			0
$491$	−20.8229	−	12.0221i	−0.939723	−	0.542549i	−0.0498495	−	0.998757i	$-0.515874\pi$
$491$	−20.8229	−	12.0221i	−0.939723	−	0.542549i	−0.889873	+	0.456207i	$0.849208\pi$
$492$		0			0
$493$	−2.74521	+	10.2453i	−0.123638	+	0.461424i
$494$		0			0
$495$	25.8035	+	11.8713i	1.15978	+	0.533573i
$496$		0			0
$497$	−3.38468	+	12.6318i	−0.151824	+	0.566613i
$498$		0			0
$499$	20.3829	+	11.7681i	0.912464	+	0.526812i	0.881223	−	0.472700i	$-0.156721\pi$
$499$	20.3829	+	11.7681i	0.912464	+	0.526812i	0.0312411	+	0.999512i	$0.490054\pi$
$500$		0			0
$501$	−0.987006	+	6.35915i	−0.0440962	+	0.284106i
$502$		0			0
$503$	−3.05962	+	3.05962i	−0.136422	+	0.136422i	−0.772020	−	0.635598i	$-0.780753\pi$
$503$	−3.05962	+	3.05962i	−0.136422	+	0.136422i	0.635598	+	0.772020i	$0.280753\pi$
$504$		0			0
$505$	−30.5272	+	12.9200i	−1.35844	+	0.574934i
$506$		0			0
$507$	0.615312	+	5.68484i	0.0273270	+	0.252473i
$508$		0			0
$509$	−14.0151	+	24.2749i	−0.621208	+	1.07596i	0.368053	+	0.929805i	$0.380025\pi$
$509$	−14.0151	+	24.2749i	−0.621208	+	1.07596i	−0.989261	+	0.146159i	$0.953309\pi$
$510$		0			0
$511$	3.89639	+	6.74875i	0.172366	+	0.298547i
$512$		0			0
$513$	2.29479	+	6.84552i	0.101318	+	0.302237i
$514$		0			0
$515$	−8.97936	+	1.25231i	−0.395678	+	0.0551833i
$516$		0			0
$517$	11.1183	+	41.4942i	0.488984	+	1.82491i
$518$		0			0
$519$	9.25381	−	11.5002i	0.406197	−	0.504801i
$520$		0			0
$521$		−	21.4824i		−	0.941162i	−0.882357	−	0.470581i	$-0.844044\pi$
$521$		−	21.4824i		−	0.941162i	0.882357	−	0.470581i	$-0.155956\pi$
$522$		0			0
$523$	−24.7925	−	24.7925i	−1.08410	−	1.08410i	−0.996123	−	0.0879761i	$-0.971960\pi$
$523$	−24.7925	−	24.7925i	−1.08410	−	1.08410i	−0.0879761	−	0.996123i	$-0.528040\pi$
$524$		0			0
$525$	10.1583	−	7.67057i	0.443345	−	0.334771i
$526$		0			0
$527$	41.9246	−	11.2337i	1.82626	−	0.489346i
$528$		0			0
$529$	−12.4097	+	7.16477i	−0.539554	+	0.311512i
$530$		0			0
$531$	2.50698	−	0.549131i	0.108794	−	0.0238303i
$532$		0			0
$533$	22.6626	+	6.07243i	0.981627	+	0.263026i
$534$		0			0
$535$	−25.6064	−	32.8461i	−1.10706	−	1.42006i
$536$		0			0
$537$	10.9004	−	24.6883i	0.470388	−	1.06538i
$538$		0			0
$539$	−20.4915			−0.882630
$540$		0			0
$541$	−29.0872			−1.25056			−0.625279	−	0.780401i	$-0.715015\pi$
$541$	−29.0872			−1.25056			−0.625279	+	0.780401i	$0.715015\pi$
$542$		0			0
$543$	−0.688563	+	1.55952i	−0.0295491	+	0.0669255i
$544$		0			0
$545$	−2.90091	+	23.4217i	−0.124261	+	1.00327i
$546$		0			0
$547$	−5.62309	−	1.50670i	−0.240426	−	0.0644219i	0.136594	−	0.990627i	$-0.456384\pi$
$547$	−5.62309	−	1.50670i	−0.240426	−	0.0644219i	−0.377020	+	0.926205i	$0.623051\pi$
$548$		0			0
$549$	5.92234	−	18.6188i	0.252759	−	0.794631i
$550$		0			0
$551$	1.63751	−	0.945416i	0.0697602	−	0.0402761i
$552$		0			0
$553$	11.0269	−	2.95466i	0.468913	−	0.125645i
$554$		0			0
$555$	2.68432	+	10.6733i	0.113943	+	0.453055i
$556$		0			0
$557$	−8.02544	−	8.02544i	−0.340049	−	0.340049i	0.516337	−	0.856386i	$-0.327295\pi$
$557$	−8.02544	−	8.02544i	−0.340049	−	0.340049i	−0.856386	+	0.516337i	$0.827295\pi$
$558$		0			0
$559$			21.3904i			0.904719i
$560$		0			0
$561$	35.8348	−	44.5336i	1.51295	−	1.88021i
$562$		0			0
$563$	−0.932408	−	3.47979i	−0.0392963	−	0.146656i	0.943490	−	0.331400i	$-0.107521\pi$
$563$	−0.932408	−	3.47979i	−0.0392963	−	0.146656i	−0.982787	+	0.184744i	$0.940854\pi$
$564$		0			0
$565$	6.35356	+	45.5566i	0.267296	+	1.91658i
$566$		0			0
$567$	4.58725	−	12.4076i	0.192646	−	0.521070i
$568$		0			0
$569$	−18.7722	−	32.5143i	−0.786970	−	1.36307i	−0.927815	−	0.373040i	$-0.878315\pi$
$569$	−18.7722	−	32.5143i	−0.786970	−	1.36307i	0.140845	−	0.990032i	$-0.455018\pi$
$570$		0			0
$571$	−13.6613	+	23.6620i	−0.571706	+	0.990224i	0.424685	+	0.905341i	$0.360385\pi$
$571$	−13.6613	+	23.6620i	−0.571706	+	0.990224i	−0.996391	+	0.0848825i	$0.972948\pi$
$572$		0			0
$573$	1.74047	+	16.0801i	0.0727091	+	0.671756i
$574$		0			0
$575$	−0.468701	−	30.5454i	−0.0195462	−	1.27383i
$576$		0			0
$577$	18.9975	−	18.9975i	0.790875	−	0.790875i	−0.190762	−	0.981636i	$-0.561096\pi$
$577$	18.9975	−	18.9975i	0.790875	−	0.790875i	0.981636	+	0.190762i	$0.0610957\pi$
$578$		0			0
$579$	−7.15552	+	46.1021i	−0.297373	+	1.91594i
$580$		0			0
$581$	5.39764	+	3.11633i	0.223932	+	0.129287i
$582$		0			0
$583$	−10.1422	+	37.8512i	−0.420047	+	1.56764i
$584$		0			0
$585$	−20.8370	−	17.3026i	−0.861504	−	0.715373i
$586$		0			0
$587$	0.612912	−	2.28742i	0.0252976	−	0.0944118i	−0.952123	−	0.305716i	$-0.901104\pi$
$587$	0.612912	−	2.28742i	0.0252976	−	0.0944118i	0.977420	+	0.211304i	$0.0677710\pi$
$588$		0			0
$589$	−6.70083	−	3.86873i	−0.276103	−	0.159408i
$590$		0			0
$591$	−11.1709	+	4.32786i	−0.459510	+	0.178024i
$592$		0			0
$593$	24.7852	−	24.7852i	1.01781	−	1.01781i	0.0179674	−	0.999839i	$-0.494280\pi$
$593$	24.7852	−	24.7852i	1.01781	−	1.01781i	0.999839	−	0.0179674i	$-0.00571951\pi$
$594$		0			0
$595$	−9.98446	−	23.5911i	−0.409323	−	0.967140i
$596$		0			0
$597$	−12.2325	−	5.40090i	−0.500642	−	0.221044i
$598$		0			0
$599$	−14.7612	+	25.5672i	−0.603127	+	1.04465i	0.389217	+	0.921146i	$0.372746\pi$
$599$	−14.7612	+	25.5672i	−0.603127	+	1.04465i	−0.992344	+	0.123501i	$0.960588\pi$
$600$		0			0
$601$	8.94195	+	15.4879i	0.364750	+	0.631765i	0.988736	−	0.149670i	$-0.0478211\pi$
$601$	8.94195	+	15.4879i	0.364750	+	0.631765i	−0.623986	+	0.781435i	$0.714488\pi$
$602$		0			0
$603$	14.9516	−	23.3387i	0.608876	−	0.950427i
$604$		0			0
$605$	−9.33562	+	12.3616i	−0.379547	+	0.502572i
$606$		0			0
$607$	2.84301	+	10.6102i	0.115394	+	0.430656i	0.999316	−	0.0369779i	$-0.0117731\pi$
$607$	2.84301	+	10.6102i	0.115394	+	0.430656i	−0.883922	+	0.467634i	$0.845106\pi$
$608$		0			0
$609$	−3.42342	−	0.531350i	−0.138724	−	0.0215314i
$610$		0			0
$611$		−	40.9631i		−	1.65719i
$612$		0			0
$613$	2.33799	+	2.33799i	0.0944306	+	0.0944306i	0.752744	−	0.658313i	$-0.228730\pi$
$613$	2.33799	+	2.33799i	0.0944306	+	0.0944306i	−0.658313	+	0.752744i	$0.728730\pi$
$614$		0			0
$615$	−19.6620	+	10.9514i	−0.792847	+	0.441602i
$616$		0			0
$617$	−38.6286	+	10.3505i	−1.55513	+	0.416696i	−0.931118	−	0.364719i	$-0.881165\pi$
$617$	−38.6286	+	10.3505i	−1.55513	+	0.416696i	−0.624012	+	0.781415i	$0.714498\pi$
$618$		0			0
$619$	−28.5874	+	16.5049i	−1.14902	+	0.663389i	−0.948649	−	0.316331i	$-0.897549\pi$
$619$	−28.5874	+	16.5049i	−1.14902	+	0.663389i	−0.200374	+	0.979719i	$0.564216\pi$
$620$		0			0
$621$	−17.5376	−	26.4638i	−0.703758	−	1.06195i
$622$		0			0
$623$	−5.35420	−	1.43465i	−0.214512	−	0.0574782i
$624$		0			0
$625$	22.0240	+	11.8298i	0.880958	+	0.473194i
$626$		0			0
$627$	−10.1308	+	1.09653i	−0.404585	+	0.0437912i
$628$		0			0
$629$	22.1486			0.883124
$630$		0			0
$631$	18.0672			0.719246			0.359623	−	0.933098i	$-0.382905\pi$
$631$	18.0672			0.719246			0.359623	+	0.933098i	$0.382905\pi$
$632$		0			0
$633$	−8.05394	−	11.0134i	−0.320115	−	0.437743i
$634$		0			0
$635$	−2.37848	+	1.85423i	−0.0943869	+	0.0735829i
$636$		0			0
$637$	18.8741	+	5.05730i	0.747819	+	0.200377i
$638$		0			0
$639$	−19.7248	+	17.9828i	−0.780301	+	0.711389i
$640$		0			0
$641$	−22.1761	+	12.8034i	−0.875902	+	0.505702i	−0.869305	−	0.494276i	$-0.835433\pi$
$641$	−22.1761	+	12.8034i	−0.875902	+	0.505702i	−0.00659683	+	0.999978i	$0.502100\pi$
$642$		0			0
$643$	2.24397	−	0.601270i	0.0884935	−	0.0237118i	−0.214301	−	0.976768i	$-0.568747\pi$
$643$	2.24397	−	0.601270i	0.0884935	−	0.0237118i	0.302794	+	0.953056i	$0.402081\pi$
$644$		0			0
$645$	−14.2837	−	14.7309i	−0.562422	−	0.580029i
$646$		0			0
$647$	−17.1979	−	17.1979i	−0.676118	−	0.676118i	0.283001	−	0.959120i	$-0.408670\pi$
$647$	−17.1979	−	17.1979i	−0.676118	−	0.676118i	−0.959120	+	0.283001i	$0.908670\pi$
$648$		0			0
$649$			3.62216i			0.142182i
$650$		0			0
$651$	5.12144	+	13.2192i	0.200725	+	0.518103i
$652$		0			0
$653$	−8.91788	−	33.2820i	−0.348984	−	1.30243i	−0.887889	−	0.460059i	$-0.847828\pi$
$653$	−8.91788	−	33.2820i	−0.348984	−	1.30243i	0.538905	−	0.842367i	$-0.318838\pi$
$654$		0			0
$655$	0.864412	+	0.652812i	0.0337754	+	0.0255075i
$656$		0			0
$657$	−0.734007	+	15.8886i	−0.0286363	+	0.619873i
$658$		0			0
$659$	−12.4974	−	21.6461i	−0.486828	−	0.843211i	0.513057	−	0.858354i	$-0.328513\pi$
$659$	−12.4974	−	21.6461i	−0.486828	−	0.843211i	−0.999885	+	0.0151432i	$0.995180\pi$
$660$		0			0
$661$	8.88614	−	15.3912i	0.345631	−	0.598650i	−0.639837	−	0.768510i	$-0.720998\pi$
$661$	8.88614	−	15.3912i	0.345631	−	0.598650i	0.985468	+	0.169860i	$0.0543317\pi$
$662$		0			0
$663$	−43.9973	+	32.1746i	−1.70871	+	1.24956i
$664$		0			0
$665$	−1.71517	+	4.23235i	−0.0665116	+	0.164123i
$666$		0			0
$667$	−5.87914	+	5.87914i	−0.227641	+	0.227641i
$668$		0			0
$669$	27.0478	+	21.7645i	1.04573	+	0.841465i
$670$		0			0
$671$	23.8810	+	13.7877i	0.921914	+	0.532267i
$672$		0			0
$673$	4.90203	−	18.2946i	0.188960	−	0.705206i	−0.804789	−	0.593561i	$-0.797721\pi$
$673$	4.90203	−	18.2946i	0.188960	−	0.705206i	0.993748	−	0.111645i	$-0.0356120\pi$
$674$		0			0
$675$	25.9038	−	1.99845i	0.997037	−	0.0769205i
$676$		0			0
$677$	0.713666	−	2.66344i	0.0274284	−	0.102364i	−0.950855	−	0.309638i	$-0.899792\pi$
$677$	0.713666	−	2.66344i	0.0274284	−	0.102364i	0.978283	+	0.207273i	$0.0664590\pi$
$678$		0			0
$679$	−7.47053	−	4.31311i	−0.286693	−	0.165522i
$680$		0			0
$681$	3.80587	+	3.06246i	0.145841	+	0.117354i
$682$		0			0
$683$	16.3284	−	16.3284i	0.624788	−	0.624788i	−0.321964	−	0.946752i	$-0.604343\pi$
$683$	16.3284	−	16.3284i	0.624788	−	0.624788i	0.946752	+	0.321964i	$0.104343\pi$
$684$		0			0
$685$	1.21341	−	2.99420i	0.0463621	−	0.114403i
$686$		0			0
$687$	28.4048	−	20.7721i	1.08371	−	0.792504i
$688$		0			0
$689$	18.6834	−	32.3605i	0.711779	−	1.23284i
$690$		0			0
$691$	4.99219	+	8.64672i	0.189912	+	0.328937i	0.945221	−	0.326432i	$-0.105846\pi$
$691$	4.99219	+	8.64672i	0.189912	+	0.328937i	−0.755309	+	0.655369i	$0.772513\pi$
$692$		0			0
$693$	15.7208	+	10.0713i	0.597185	+	0.382577i
$694$		0			0
$695$	19.8984	+	15.0275i	0.754789	+	0.570024i
$696$		0			0
$697$	11.7227	+	43.7498i	0.444029	+	1.65714i
$698$		0			0
$699$	−4.09784	−	10.5772i	−0.154995	−	0.400066i
$700$		0			0
$701$		−	0.395928i		−	0.0149540i	−0.999972	−	0.00747701i	$-0.997620\pi$
$701$		−	0.395928i		−	0.0149540i	0.999972	−	0.00747701i	$-0.00238003\pi$
$702$		0			0
$703$	−2.79194	−	2.79194i	−0.105300	−	0.105300i
$704$		0			0
$705$	27.3536	+	28.2100i	1.03020	+	1.06245i
$706$		0			0
$707$	−21.0470	+	5.63953i	−0.791555	+	0.212097i
$708$		0			0
$709$	28.7017	−	16.5709i	1.07792	−	0.622335i	0.147582	−	0.989050i	$-0.452851\pi$
$709$	28.7017	−	16.5709i	1.07792	−	0.622335i	0.930333	+	0.366715i	$0.119518\pi$
$710$		0			0
$711$	22.2044	+	7.06285i	0.832729	+	0.264877i
$712$		0			0
$713$	32.8638	+	8.80583i	1.23076	+	0.329781i
$714$		0			0
$715$	30.1473	−	23.5025i	1.12744	−	0.878942i
$716$		0			0
$717$	12.4738	+	17.0574i	0.465843	+	0.637019i
$718$		0			0
$719$	3.37521			0.125874			0.0629371	−	0.998017i	$-0.479953\pi$
$719$	3.37521			0.125874			0.0629371	+	0.998017i	$0.479953\pi$
$720$		0			0
$721$	−5.95949			−0.221943
$722$		0			0
$723$	−5.91884	+	0.640640i	−0.220124	+	0.0238256i
$724$		0			0
$725$	−1.86167	−	6.54449i	−0.0691406	−	0.243056i
$726$		0			0
$727$	−21.8809	−	5.86298i	−0.811519	−	0.217446i	−0.170884	−	0.985291i	$-0.554662\pi$
$727$	−21.8809	−	5.86298i	−0.811519	−	0.217446i	−0.640635	+	0.767845i	$0.721329\pi$
$728$		0			0
$729$	21.5447	−	16.2734i	0.797953	−	0.602720i
$730$		0			0
$731$	−35.7615	+	20.6469i	−1.32269	+	0.763654i
$732$		0			0
$733$	−35.7595	+	9.58172i	−1.32081	+	0.353909i	−0.849280	−	0.527943i	$-0.822963\pi$
$733$	−35.7595	+	9.58172i	−1.32081	+	0.353909i	−0.471526	+	0.881852i	$0.656297\pi$
$734$		0			0
$735$	−16.3751	+	9.12062i	−0.604003	+	0.336419i
$736$		0			0
$737$	27.6615	+	27.6615i	1.01893	+	1.01893i
$738$		0			0
$739$			9.68253i			0.356178i	0.984014	+	0.178089i	$0.0569914\pi$
$739$			9.68253i			0.356178i	−0.984014	+	0.178089i	$0.943009\pi$
$740$		0			0
$741$	9.60181	+	1.49030i	0.352731	+	0.0547476i
$742$		0			0
$743$	11.9689	+	44.6685i	0.439096	+	1.63873i	0.731071	+	0.682301i	$0.239021\pi$
$743$	11.9689	+	44.6685i	0.439096	+	1.63873i	−0.291976	+	0.956426i	$0.594313\pi$
$744$		0			0
$745$	8.10716	−	10.7350i	0.297023	−	0.393299i
$746$		0			0
$747$	5.84544	+	11.2987i	0.213873	+	0.413398i
$748$		0			0
$749$	−13.6881	−	23.7086i	−0.500154	−	0.866292i
$750$		0			0
$751$	−1.63780	+	2.83675i	−0.0597640	+	0.103514i	−0.894359	−	0.447349i	$-0.852368\pi$
$751$	−1.63780	+	2.83675i	−0.0597640	+	0.103514i	0.834595	+	0.550863i	$0.185701\pi$
$752$		0			0
$753$	−23.9296	−	10.5655i	−0.872044	−	0.385027i
$754$		0			0
$755$	14.6521	+	34.6196i	0.533243	+	1.25994i
$756$		0			0
$757$	−9.29455	+	9.29455i	−0.337816	+	0.337816i	−0.855545	−	0.517729i	$-0.826778\pi$
$757$	−9.29455	+	9.29455i	−0.337816	+	0.337816i	0.517729	+	0.855545i	$0.326778\pi$
$758$		0			0
$759$	41.7813	−	16.1870i	1.51656	−	0.587551i
$760$		0			0
$761$	13.5353	+	7.81461i	0.490654	+	0.283279i	0.724846	−	0.688911i	$-0.241911\pi$
$761$	13.5353	+	7.81461i	0.490654	+	0.283279i	−0.234192	+	0.972190i	$0.575244\pi$
$762$		0			0
$763$	−4.01514	+	14.9847i	−0.145358	+	0.542483i
$764$		0			0
$765$	8.81451	−	51.5374i	0.318689	−	1.86334i
$766$		0			0
$767$	0.893951	−	3.33627i	0.0322787	−	0.120466i
$768$		0			0
$769$	−3.80386	−	2.19616i	−0.137171	−	0.0791955i	0.429844	−	0.902903i	$-0.358568\pi$
$769$	−3.80386	−	2.19616i	−0.137171	−	0.0791955i	−0.567015	+	0.823708i	$0.691902\pi$
$770$		0			0
$771$	2.59945	−	16.7479i	0.0936168	−	0.603160i
$772$		0			0
$773$	−2.77515	+	2.77515i	−0.0998153	+	0.0998153i	−0.755251	−	0.655436i	$-0.772485\pi$
$773$	−2.77515	+	2.77515i	−0.0998153	+	0.0998153i	0.655436	+	0.755251i	$0.272485\pi$
$774$		0			0
$775$	−19.3837	+	19.9878i	−0.696282	+	0.717983i
$776$		0			0
$777$	0.778474	+	7.19229i	0.0279276	+	0.258022i
$778$		0			0
$779$	4.03715	−	6.99255i	0.144646	−	0.250534i
$780$		0			0
$781$	−18.8360	−	32.6248i	−0.674004	−	1.16741i
$782$		0			0
$783$	−5.29857	−	4.68242i	−0.189355	−	0.167336i
$784$		0			0
$785$	6.65655	+	47.7291i	0.237582	+	1.70353i
$786$		0			0
$787$	8.92857	+	33.3219i	0.318269	+	1.18780i	0.920907	+	0.389782i	$0.127450\pi$
$787$	8.92857	+	33.3219i	0.318269	+	1.18780i	−0.602638	+	0.798015i	$0.705884\pi$
$788$		0			0
$789$	−0.769340	+	0.956097i	−0.0273892	+	0.0340379i
$790$		0			0
$791$			30.2354i			1.07505i
$792$		0			0
$793$	−18.5933	−	18.5933i	−0.660266	−	0.660266i
$794$		0			0
$795$	8.74253	+	34.7617i	0.310066	+	1.23287i
$796$		0			0
$797$	23.9335	−	6.41295i	0.847767	−	0.227158i	0.191317	−	0.981528i	$-0.438724\pi$
$797$	23.9335	−	6.41295i	0.847767	−	0.227158i	0.656450	+	0.754370i	$0.272057\pi$
$798$		0			0
$799$	68.4840	−	39.5393i	2.42279	−	1.39880i
$800$		0			0
$801$	−7.62233	−	8.36070i	−0.269322	−	0.295411i
$802$		0			0
$803$	−21.6837	−	5.81012i	−0.765200	−	0.205035i
$804$		0			0
$805$	2.46824	−	19.9283i	0.0869939	−	0.702381i
$806$		0			0
$807$	−6.79779	+	15.3963i	−0.239294	+	0.541974i
$808$		0			0
$809$	−15.1911			−0.534090			−0.267045	−	0.963684i	$-0.586047\pi$
$809$	−15.1911			−0.534090			−0.267045	+	0.963684i	$0.586047\pi$
$810$		0			0
$811$	32.4942			1.14103			0.570513	−	0.821289i	$-0.306744\pi$
$811$	32.4942			1.14103			0.570513	+	0.821289i	$0.306744\pi$
$812$		0			0
$813$	−7.06738	+	16.0069i	−0.247864	+	0.561385i
$814$		0			0
$815$	−14.5563	−	18.6718i	−0.509885	−	0.654044i
$816$		0			0
$817$	7.11053	+	1.90526i	0.248766	+	0.0666567i
$818$		0			0
$819$	−11.9944	−	13.1563i	−0.419118	−	0.459718i
$820$		0			0
$821$	12.1088	−	6.99103i	0.422601	−	0.243989i	−0.273589	−	0.961847i	$-0.588211\pi$
$821$	12.1088	−	6.99103i	0.422601	−	0.243989i	0.696189	+	0.717858i	$0.254877\pi$
$822$		0			0
$823$	−28.5432	+	7.64813i	−0.994953	+	0.266597i	−0.719330	−	0.694669i	$-0.755551\pi$
$823$	−28.5432	+	7.64813i	−0.994953	+	0.266597i	−0.275623	+	0.961266i	$0.588884\pi$
$824$		0			0
$825$	−5.06739	+	36.3166i	−0.176424	+	1.26438i
$826$		0			0
$827$	8.87270	+	8.87270i	0.308534	+	0.308534i	0.844341	−	0.535807i	$-0.179992\pi$
$827$	8.87270	+	8.87270i	0.308534	+	0.308534i	−0.535807	+	0.844341i	$0.679992\pi$
$828$		0			0
$829$			13.6786i			0.475078i	0.971378	+	0.237539i	$0.0763408\pi$
$829$			13.6786i			0.475078i	−0.971378	+	0.237539i	$0.923659\pi$
$830$		0			0
$831$	10.4563	−	12.9946i	0.362727	−	0.450778i
$832$		0			0
$833$	9.76302	+	36.4361i	0.338269	+	1.26244i
$834$		0			0
$835$	−8.22828	+	1.14756i	−0.284752	+	0.0397129i
$836$		0			0
$837$	−5.75272	+	28.3578i	−0.198843	+	0.980189i
$838$		0			0
$839$	−4.72348	−	8.18131i	−0.163073	−	0.282450i	0.772896	−	0.634532i	$-0.218807\pi$
$839$	−4.72348	−	8.18131i	−0.163073	−	0.282450i	−0.935969	+	0.352082i	$0.885474\pi$
$840$		0			0
$841$	13.5741	−	23.5110i	0.468072	−	0.810724i
$842$		0			0
$843$	−3.53191	−	32.6312i	−0.121645	−	1.12388i
$844$		0			0
$845$	−6.79817	+	2.87719i	−0.233864	+	0.0989784i
$846$		0			0
$847$	−7.20009	+	7.20009i	−0.247398	+	0.247398i
$848$		0			0
$849$	−8.48172	+	54.6466i	−0.291092	+	1.87547i
$850$		0			0
$851$	15.0358	+	8.68094i	0.515421	+	0.297579i
$852$		0			0
$853$	−2.07430	+	7.74141i	−0.0710228	+	0.265061i	−0.992302	−	0.123841i	$-0.960479\pi$
$853$	−2.07430	+	7.74141i	−0.0710228	+	0.265061i	0.921279	+	0.388902i	$0.127145\pi$
$854$		0			0
$855$	−7.60763	+	5.38541i	−0.260175	+	0.184177i
$856$		0			0
$857$	−1.32705	+	4.95263i	−0.0453312	+	0.169178i	−0.984880	−	0.173235i	$-0.944578\pi$
$857$	−1.32705	+	4.95263i	−0.0453312	+	0.169178i	0.939549	+	0.342414i	$0.111245\pi$
$858$		0			0
$859$	−18.8910	−	10.9067i	−0.644551	−	0.372132i	0.141814	−	0.989893i	$-0.454706\pi$
$859$	−18.8910	−	10.9067i	−0.644551	−	0.372132i	−0.786366	+	0.617762i	$0.788040\pi$
$860$		0			0
$861$	−13.7948	+	5.34440i	−0.470124	+	0.182137i
$862$		0			0
$863$	5.51048	−	5.51048i	0.187579	−	0.187579i	−0.607070	−	0.794649i	$-0.707655\pi$
$863$	5.51048	−	5.51048i	0.187579	−	0.187579i	0.794649	+	0.607070i	$0.207655\pi$
$864$		0			0
$865$	17.6612	+	7.15727i	0.600499	+	0.243354i
$866$		0			0
$867$	−69.3228	−	30.6075i	−2.35432	−	1.03949i
$868$		0			0
$869$	−16.4429	+	28.4799i	−0.557786	+	0.966114i
$870$		0			0
$871$	−18.6514	−	32.3051i	−0.631977	−	1.09462i
$872$		0			0
$873$	−8.09029	−	15.6378i	−0.273815	−	0.529260i
$874$		0			0
$875$	13.2640	+	9.70119i	0.448407	+	0.327960i
$876$		0			0
$877$	−4.93781	−	18.4281i	−0.166738	−	0.622274i	−0.997812	−	0.0661128i	$-0.978940\pi$
$877$	−4.93781	−	18.4281i	−0.166738	−	0.622274i	0.831074	−	0.556161i	$-0.187726\pi$
$878$		0			0
$879$	−1.92310	−	0.298485i	−0.0648645	−	0.0100676i
$880$		0			0
$881$		−	33.4235i		−	1.12607i	−0.826434	−	0.563033i	$-0.809634\pi$
$881$		−	33.4235i		−	1.12607i	0.826434	−	0.563033i	$-0.190366\pi$
$882$		0			0
$883$	−4.76726	−	4.76726i	−0.160431	−	0.160431i	0.622327	−	0.782758i	$-0.286188\pi$
$883$	−4.76726	−	4.76726i	−0.160431	−	0.160431i	−0.782758	+	0.622327i	$0.786188\pi$
$884$		0			0
$885$	1.61220	+	2.89453i	0.0541936	+	0.0972986i
$886$		0			0
$887$	30.9801	−	8.30109i	1.04021	−	0.278723i	0.302009	−	0.953305i	$-0.402343\pi$
$887$	30.9801	−	8.30109i	1.04021	−	0.278723i	0.738200	+	0.674582i	$0.235676\pi$
$888$		0			0
$889$	−1.71680	+	0.991196i	−0.0575797	+	0.0332436i
$890$		0			0
$891$	15.9297	+	34.6177i	0.533664	+	1.15974i
$892$		0			0
$893$	−13.6168	−	3.64861i	−0.455669	−	0.122096i
$894$		0			0
$895$	34.5766	+	4.28251i	1.15577	+	0.143149i
$896$		0			0
$897$	−42.4785	+	4.59776i	−1.41832	+	0.153515i
$898$		0			0
$899$	7.57793			0.252738
$900$		0			0
$901$	72.1358			2.40319
$902$		0			0
$903$	−7.96157	−	10.8871i	−0.264944	−	0.362299i
$904$		0			0
$905$	−2.18416	−	0.270520i	−0.0726038	−	0.00899239i
$906$		0			0
$907$	−24.4511	−	6.55167i	−0.811887	−	0.217544i	−0.171091	−	0.985255i	$-0.554729\pi$
$907$	−24.4511	−	6.55167i	−0.811887	−	0.217544i	−0.640796	+	0.767711i	$0.721396\pi$
$908$		0			0
$909$	−42.3813	−	13.4808i	−1.40570	−	0.447130i
$910$		0			0
$911$	−21.7794	+	12.5743i	−0.721584	+	0.416607i	−0.815335	−	0.578989i	$-0.803447\pi$
$911$	−21.7794	+	12.5743i	−0.721584	+	0.416607i	0.0937515	+	0.995596i	$0.470114\pi$
$912$		0			0
$913$	−17.3426	+	4.64693i	−0.573956	+	0.153791i
$914$		0			0
$915$	25.2205	+	0.388691i	0.833763	+	0.0128497i
$916$		0			0
$917$	0.503481	+	0.503481i	0.0166264	+	0.0166264i
$918$		0			0
$919$			9.41136i			0.310452i	0.987879	+	0.155226i	$0.0496106\pi$
$919$			9.41136i			0.310452i	−0.987879	+	0.155226i	$0.950389\pi$
$920$		0			0
$921$	12.5513	+	32.3969i	0.413579	+	1.06751i
$922$		0			0
$923$	9.29744	+	34.6985i	0.306029	+	1.14212i
$924$		0			0
$925$	−12.1943	+	7.29207i	−0.400945	+	0.239762i
$926$		0			0
$927$	−10.2422	−	6.56148i	−0.336397	−	0.215507i
$928$		0			0
$929$	−18.9072	−	32.7483i	−0.620326	−	1.07444i	−0.989425	−	0.145046i	$-0.953667\pi$
$929$	−18.9072	−	32.7483i	−0.620326	−	1.07444i	0.369099	−	0.929390i	$-0.379666\pi$
$930$		0			0
$931$	3.36226	−	5.82360i	0.110194	−	0.190861i
$932$		0			0
$933$	43.4108	−	31.7458i	1.42121	−	1.03931i
$934$		0			0
$935$	68.3919	+	27.7161i	2.23665	+	0.906413i
$936$		0			0
$937$	4.19484	−	4.19484i	0.137039	−	0.137039i	−0.635259	−	0.772299i	$-0.719107\pi$
$937$	4.19484	−	4.19484i	0.137039	−	0.137039i	0.772299	+	0.635259i	$0.219107\pi$
$938$		0			0
$939$	−24.4543	−	19.6776i	−0.798035	−	0.642153i
$940$		0			0
$941$	38.2869	+	22.1050i	1.24812	+	0.720602i	0.970734	−	0.240157i	$-0.0771990\pi$
$941$	38.2869	+	22.1050i	1.24812	+	0.720602i	0.277385	+	0.960759i	$0.410532\pi$
$942$		0			0
$943$	−9.18919	+	34.2945i	−0.299241	+	1.11678i
$944$		0			0
$945$	17.0455	+	1.05090i	0.554489	+	0.0341857i
$946$		0			0
$947$	4.05833	−	15.1459i	0.131878	−	0.492175i	−0.868113	−	0.496366i	$-0.834667\pi$
$947$	4.05833	−	15.1459i	0.131878	−	0.492175i	0.999991	+	0.00419101i	$0.00133404\pi$
$948$		0			0
$949$	18.5383	+	10.7031i	0.601778	+	0.347436i
$950$		0			0
$951$	8.29222	+	6.67248i	0.268894	+	0.216370i
$952$		0			0
$953$	−12.7239	+	12.7239i	−0.412169	+	0.412169i	−0.882494	−	0.470324i	$-0.844137\pi$
$953$	−12.7239	+	12.7239i	−0.412169	+	0.412169i	0.470324	+	0.882494i	$0.344137\pi$
$954$		0			0
$955$	−19.2293	+	8.13841i	−0.622245	+	0.263353i
$956$		0			0
$957$	8.05568	−	5.89101i	0.260403	−	0.190429i
$958$		0			0
$959$	1.06182	−	1.83913i	0.0342880	−	0.0593885i
$960$		0			0
$961$	−0.00478208	−	0.00828280i	−0.000154261	−	0.000267187i
$962$		0			0
$963$	2.57859	−	55.8171i	0.0830938	−	1.79868i
$964$		0			0
$965$	−59.6528	+	8.31949i	−1.92029	+	0.267814i
$966$		0			0
$967$	−13.9689	−	52.1327i	−0.449210	−	1.67647i	−0.704576	−	0.709629i	$-0.748863\pi$
$967$	−13.9689	−	52.1327i	−0.449210	−	1.67647i	0.255366	−	0.966844i	$-0.417804\pi$
$968$		0			0
$969$	6.77650	+	17.4912i	0.217693	+	0.561900i
$970$		0			0
$971$			10.2855i			0.330078i	0.986287	+	0.165039i	$0.0527749\pi$
$971$			10.2855i			0.330078i	−0.986287	+	0.165039i	$0.947225\pi$
$972$		0			0
$973$	11.5899	+	11.5899i	0.371556	+	0.371556i
$974$		0			0
$975$	13.6304	−	32.1996i	0.436522	−	1.03121i
$976$		0			0
$977$	−0.244837	+	0.0656039i	−0.00783303	+	0.00209886i	−0.262733	−	0.964868i	$-0.584624\pi$
$977$	−0.244837	+	0.0656039i	−0.00783303	+	0.00209886i	0.254900	+	0.966967i	$0.417957\pi$
$978$		0			0
$979$	13.8286	−	7.98395i	0.441964	−	0.255168i
$980$		0			0
$981$	−23.3989	+	21.3325i	−0.747070	+	0.681093i
$982$		0			0
$983$	−27.5363	−	7.37832i	−0.878270	−	0.235332i	−0.208609	−	0.977999i	$-0.566894\pi$
$983$	−27.5363	−	7.37832i	−0.878270	−	0.235332i	−0.669661	+	0.742667i	$0.733560\pi$
$984$		0			0
$985$	−9.50900	−	12.1975i	−0.302982	−	0.388644i
$986$		0			0
$987$	15.2466	+	20.8490i	0.485304	+	0.663630i
$988$		0			0
$989$	−32.3694			−1.02929
$990$		0			0
$991$	−26.4358			−0.839762			−0.419881	−	0.907579i	$-0.637928\pi$
$991$	−26.4358			−0.839762			−0.419881	+	0.907579i	$0.637928\pi$
$992$		0			0
$993$	−31.5208	+	3.41173i	−1.00028	+	0.108268i
$994$		0			0
$995$	2.12189	−	17.1319i	0.0672683	−	0.543119i
$996$		0			0
$997$	−32.1788	−	8.62229i	−1.01911	−	0.273071i	−0.289681	−	0.957123i	$-0.593549\pi$
$997$	−32.1788	−	8.62229i	−1.01911	−	0.273071i	−0.729433	+	0.684053i	$0.760216\pi$
$998$		0			0
$999$	−6.58090	+	13.2180i	−0.208211	+	0.418199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.8	✓	72
3.2	odd	2		1080.2.bt.a.233.17		72
4.3	odd	2		720.2.cu.e.113.11		72
5.2	odd	4	inner	360.2.bs.a.257.17	yes	72
9.2	odd	6	inner	360.2.bs.a.353.17	yes	72
9.7	even	3		1080.2.bt.a.953.13		72
15.2	even	4		1080.2.bt.a.17.13		72
20.7	even	4		720.2.cu.e.257.2		72
36.11	even	6		720.2.cu.e.353.2		72
45.2	even	12	inner	360.2.bs.a.137.8	yes	72
45.7	odd	12		1080.2.bt.a.737.17		72
180.47	odd	12		720.2.cu.e.497.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.8	✓	72	1.1	even	1	trivial
360.2.bs.a.137.8	yes	72	45.2	even	12	inner
360.2.bs.a.257.17	yes	72	5.2	odd	4	inner
360.2.bs.a.353.17	yes	72	9.2	odd	6	inner
720.2.cu.e.113.11		72	4.3	odd	2
720.2.cu.e.257.2		72	20.7	even	4
720.2.cu.e.353.2		72	36.11	even	6
720.2.cu.e.497.11		72	180.47	odd	12
1080.2.bt.a.17.13		72	15.2	even	4
1080.2.bt.a.233.17		72	3.2	odd	2
1080.2.bt.a.737.17		72	45.7	odd	12
1080.2.bt.a.953.13		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)

\(f(q)\)	\(=\)	\(q+(-0.699583 + 1.58448i) q^{3} +(-2.21911 - 0.274850i) q^{5} +(-1.41974 - 0.380419i) q^{7} +(-2.02117 - 2.21695i) q^{9} +O(q^{10})\)	\(q+(-0.699583 + 1.58448i) q^{3} +(-2.21911 - 0.274850i) q^{5} +(-1.41974 - 0.380419i) q^{7} +(-2.02117 - 2.21695i) q^{9} +(3.66685 - 2.11705i) q^{11} +(-3.89991 + 1.04498i) q^{13} +(1.98795 - 3.32386i) q^{15} +(-5.51140 - 5.51140i) q^{17} +1.38947i q^{19} +(1.59599 - 1.98342i) q^{21} +(-1.58133 - 5.90160i) q^{23} +(4.84892 + 1.21984i) q^{25} +(4.92670 - 1.65156i) q^{27} +(-0.680413 - 1.17851i) q^{29} +(-2.78431 + 4.82257i) q^{31} +(0.789170 + 7.29111i) q^{33} +(3.04601 + 1.23441i) q^{35} +(-2.00935 + 2.00935i) q^{37} +(1.07257 - 6.91039i) q^{39} +(-5.03252 - 2.90553i) q^{41} +(1.37121 - 5.11743i) q^{43} +(3.87586 + 5.47519i) q^{45} +(-2.62590 + 9.79998i) q^{47} +(-4.19123 - 2.41981i) q^{49} +(12.5884 - 4.87703i) q^{51} +(-6.54423 + 6.54423i) q^{53} +(-8.71901 + 3.69015i) q^{55} +(-2.20160 - 0.972053i) q^{57} +(-0.427736 + 0.740861i) q^{59} +(3.25634 + 5.64014i) q^{61} +(2.02616 + 3.91639i) q^{63} +(8.94156 - 1.24704i) q^{65} +(2.39125 + 8.92428i) q^{67} +(10.4573 + 1.62308i) q^{69} -8.89725i q^{71} +(-3.74897 - 3.74897i) q^{73} +(-5.32504 + 6.82964i) q^{75} +(-6.01134 + 1.61073i) q^{77} +(-6.72630 + 3.88343i) q^{79} +(-0.829776 + 8.96167i) q^{81} +(-4.09593 - 1.09750i) q^{83} +(10.7156 + 13.7452i) q^{85} +(2.34333 - 0.253636i) q^{87} +3.77125 q^{89} +5.93440 q^{91} +(-5.69342 - 7.78548i) q^{93} +(0.381896 - 3.08340i) q^{95} +(5.66890 + 1.51898i) q^{97} +(-12.1047 - 3.85031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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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