LMFDB - Embedded newform 280.2.bo.a.33.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.7
Character	$\chi$	$=$	280.33
Dual form			280.2.bo.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.120281 + 0.0322291i) q^{3} +(-2.04377 - 0.907205i) q^{5} +(-2.46167 - 0.969635i) q^{7} +(-2.58465 - 1.49225i) q^{9} +O(q^{10})$	\(q+(0.120281 + 0.0322291i) q^{3} +(-2.04377 - 0.907205i) q^{5} +(-2.46167 - 0.969635i) q^{7} +(-2.58465 - 1.49225i) q^{9} +(-1.40939 - 2.44113i) q^{11} +(3.28569 - 3.28569i) q^{13} +(-0.216587 - 0.174988i) q^{15} +(0.477081 - 1.78049i) q^{17} +(-4.01634 + 6.95650i) q^{19} +(-0.264840 - 0.195966i) q^{21} +(2.30451 - 0.617491i) q^{23} +(3.35396 + 3.70823i) q^{25} +(-0.526943 - 0.526943i) q^{27} -8.63838i q^{29} +(-2.81202 + 1.62352i) q^{31} +(-0.0908465 - 0.339044i) q^{33} +(4.15141 + 4.21495i) q^{35} +(-1.87374 - 6.99289i) q^{37} +(0.501099 - 0.289309i) q^{39} +9.45620i q^{41} +(1.04150 + 1.04150i) q^{43} +(3.92864 + 5.39461i) q^{45} +(-3.76695 + 1.00935i) q^{47} +(5.11961 + 4.77384i) q^{49} +(0.114767 - 0.198782i) q^{51} +(1.75344 - 6.54391i) q^{53} +(0.665850 + 6.26770i) q^{55} +(-0.707288 + 0.707288i) q^{57} +(-6.19733 - 10.7341i) q^{59} +(2.19428 + 1.26687i) q^{61} +(4.91561 + 6.17958i) q^{63} +(-9.69596 + 3.73438i) q^{65} +(13.8668 + 3.71560i) q^{67} +0.297088 q^{69} +2.72856 q^{71} +(3.90198 + 1.04553i) q^{73} +(0.283903 + 0.554123i) q^{75} +(1.10244 + 7.37584i) q^{77} +(-5.52096 - 3.18753i) q^{79} +(4.43034 + 7.67358i) q^{81} +(7.41399 - 7.41399i) q^{83} +(-2.59031 + 3.20609i) q^{85} +(0.278407 - 1.03903i) q^{87} +(-0.487628 + 0.844596i) q^{89} +(-11.2742 + 4.90235i) q^{91} +(-0.390556 + 0.104649i) q^{93} +(14.5194 - 10.5738i) q^{95} +(-5.12422 - 5.12422i) q^{97} +8.41261i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.120281	+	0.0322291i	0.0694440	+	0.0186075i	0.293374	−	0.955998i	$-0.405222\pi$
$3$	0.120281	+	0.0322291i	0.0694440	+	0.0186075i	−0.223930	+	0.974605i	$0.571889\pi$
$4$		0			0
$5$	−2.04377	−	0.907205i	−0.914000	−	0.405715i
$5$	−2.04377	−	0.907205i	−0.914000	−	0.405715i
$6$		0			0
$7$	−2.46167	−	0.969635i	−0.930423	−	0.366488i
$7$	−2.46167	−	0.969635i	−0.930423	−	0.366488i
$8$		0			0
$9$	−2.58465	−	1.49225i	−0.861549	−	0.497416i
$10$		0			0
$11$	−1.40939	−	2.44113i	−0.424946	−	0.736028i	0.571469	−	0.820623i	$-0.306374\pi$
$11$	−1.40939	−	2.44113i	−0.424946	−	0.736028i	−0.996415	+	0.0845951i	$0.973040\pi$
$12$		0			0
$13$	3.28569	−	3.28569i	0.911285	−	0.911285i	−0.0850882	−	0.996373i	$-0.527117\pi$
$13$	3.28569	−	3.28569i	0.911285	−	0.911285i	0.996373	+	0.0850882i	$0.0271172\pi$
$14$		0			0
$15$	−0.216587	−	0.174988i	−0.0559225	−	0.0451817i
$16$		0			0
$17$	0.477081	−	1.78049i	0.115709	−	0.431832i	−0.883630	−	0.468186i	$-0.844908\pi$
$17$	0.477081	−	1.78049i	0.115709	−	0.431832i	0.999339	+	0.0363538i	$0.0115743\pi$
$18$		0			0
$19$	−4.01634	+	6.95650i	−0.921411	+	1.59593i	−0.124176	+	0.992260i	$0.539629\pi$
$19$	−4.01634	+	6.95650i	−0.921411	+	1.59593i	−0.797235	+	0.603670i	$0.793705\pi$
$20$		0			0
$21$	−0.264840	−	0.195966i	−0.0577929	−	0.0427632i
$22$		0			0
$23$	2.30451	−	0.617491i	0.480523	−	0.128756i	−0.0104232	−	0.999946i	$-0.503318\pi$
$23$	2.30451	−	0.617491i	0.480523	−	0.128756i	0.490946	+	0.871190i	$0.336651\pi$
$24$		0			0
$25$	3.35396	+	3.70823i	0.670791	+	0.741646i
$26$		0			0
$27$	−0.526943	−	0.526943i	−0.101410	−	0.101410i
$28$		0			0
$29$		−	8.63838i		−	1.60411i	−0.597252	−	0.802053i	$-0.703741\pi$
$29$		−	8.63838i		−	1.60411i	0.597252	−	0.802053i	$-0.296259\pi$
$30$		0			0
$31$	−2.81202	+	1.62352i	−0.505054	+	0.291593i	−0.730798	−	0.682593i	$-0.760852\pi$
$31$	−2.81202	+	1.62352i	−0.505054	+	0.291593i	0.225744	+	0.974187i	$0.427519\pi$
$32$		0			0
$33$	−0.0908465	−	0.339044i	−0.0158143	−	0.0590199i
$34$		0			0
$35$	4.15141	+	4.21495i	0.701717	+	0.712456i
$36$		0			0
$37$	−1.87374	−	6.99289i	−0.308041	−	1.14962i	−0.930296	−	0.366809i	$-0.880450\pi$
$37$	−1.87374	−	6.99289i	−0.308041	−	1.14962i	0.622255	−	0.782814i	$-0.286217\pi$
$38$		0			0
$39$	0.501099	−	0.289309i	0.0802400	−	0.0463266i
$40$		0			0
$41$			9.45620i			1.47681i	0.674357	+	0.738405i	$0.264421\pi$
$41$			9.45620i			1.47681i	−0.674357	+	0.738405i	$0.735579\pi$
$42$		0			0
$43$	1.04150	+	1.04150i	0.158828	+	0.158828i	0.782047	−	0.623219i	$-0.214176\pi$
$43$	1.04150	+	1.04150i	0.158828	+	0.158828i	−0.623219	+	0.782047i	$0.714176\pi$
$44$		0			0
$45$	3.92864	+	5.39461i	0.585647	+	0.804181i
$46$		0			0
$47$	−3.76695	+	1.00935i	−0.549465	+	0.147229i	−0.522862	−	0.852417i	$-0.675136\pi$
$47$	−3.76695	+	1.00935i	−0.549465	+	0.147229i	−0.0266033	+	0.999646i	$0.508469\pi$
$48$		0			0
$49$	5.11961	+	4.77384i	0.731373	+	0.681977i
$50$		0			0
$51$	0.114767	−	0.198782i	0.0160706	−	0.0278351i
$52$		0			0
$53$	1.75344	−	6.54391i	0.240853	−	0.898875i	−0.734570	−	0.678533i	$-0.762616\pi$
$53$	1.75344	−	6.54391i	0.240853	−	0.898875i	0.975423	−	0.220342i	$-0.0707173\pi$
$54$		0			0
$55$	0.665850	+	6.26770i	0.0897832	+	0.845137i
$56$		0			0
$57$	−0.707288	+	0.707288i	−0.0936826	+	0.0936826i
$58$		0			0
$59$	−6.19733	−	10.7341i	−0.806823	−	1.39746i	−0.915053	−	0.403333i	$-0.867852\pi$
$59$	−6.19733	−	10.7341i	−0.806823	−	1.39746i	0.108230	−	0.994126i	$-0.465482\pi$
$60$		0			0
$61$	2.19428	+	1.26687i	0.280949	+	0.162206i	0.633853	−	0.773454i	$-0.281473\pi$
$61$	2.19428	+	1.26687i	0.280949	+	0.162206i	−0.352904	+	0.935659i	$0.614806\pi$
$62$		0			0
$63$	4.91561	+	6.17958i	0.619308	+	0.778554i
$64$		0			0
$65$	−9.69596	+	3.73438i	−1.20264	+	0.463193i
$66$		0			0
$67$	13.8668	+	3.71560i	1.69410	+	0.453932i	0.971442	−	0.237276i	$-0.0762545\pi$
$67$	13.8668	+	3.71560i	1.69410	+	0.453932i	0.722656	+	0.691208i	$0.242921\pi$
$68$		0			0
$69$	0.297088			0.0357652
$70$		0			0
$71$	2.72856			0.323820			0.161910	−	0.986805i	$-0.448235\pi$
$71$	2.72856			0.323820			0.161910	+	0.986805i	$0.448235\pi$
$72$		0			0
$73$	3.90198	+	1.04553i	0.456692	+	0.122370i	0.479829	−	0.877362i	$-0.340699\pi$
$73$	3.90198	+	1.04553i	0.456692	+	0.122370i	−0.0231369	+	0.999732i	$0.507365\pi$
$74$		0			0
$75$	0.283903	+	0.554123i	0.0327823	+	0.0639846i
$76$		0			0
$77$	1.10244	+	7.37584i	0.125634	+	0.840555i
$78$		0			0
$79$	−5.52096	−	3.18753i	−0.621156	−	0.358625i	0.156163	−	0.987731i	$-0.450088\pi$
$79$	−5.52096	−	3.18753i	−0.621156	−	0.358625i	−0.777319	+	0.629107i	$0.783421\pi$
$80$		0			0
$81$	4.43034	+	7.67358i	0.492260	+	0.852620i
$82$		0			0
$83$	7.41399	−	7.41399i	0.813791	−	0.813791i	−0.171409	−	0.985200i	$-0.554832\pi$
$83$	7.41399	−	7.41399i	0.813791	−	0.813791i	0.985200	+	0.171409i	$0.0548319\pi$
$84$		0			0
$85$	−2.59031	+	3.20609i	−0.280959	+	0.347750i
$86$		0			0
$87$	0.278407	−	1.03903i	0.0298484	−	0.111396i
$88$		0			0
$89$	−0.487628	+	0.844596i	−0.0516885	+	0.0895270i	−0.890712	−	0.454568i	$-0.849794\pi$
$89$	−0.487628	+	0.844596i	−0.0516885	+	0.0895270i	0.839024	+	0.544095i	$0.183127\pi$
$90$		0			0
$91$	−11.2742	+	4.90235i	−1.18186	+	0.513906i
$92$		0			0
$93$	−0.390556	+	0.104649i	−0.0404988	+	0.0108516i
$94$		0			0
$95$	14.5194	−	10.5738i	1.48966	−	1.08485i
$96$		0			0
$97$	−5.12422	−	5.12422i	−0.520286	−	0.520286i	0.397372	−	0.917658i	$-0.369922\pi$
$97$	−5.12422	−	5.12422i	−0.520286	−	0.520286i	−0.917658	+	0.397372i	$0.869922\pi$
$98$		0			0
$99$			8.41261i			0.845499i
$100$		0			0
$101$	5.00307	−	2.88852i	0.497824	−	0.287419i	−0.229990	−	0.973193i	$-0.573869\pi$
$101$	5.00307	−	2.88852i	0.497824	−	0.287419i	0.727815	+	0.685774i	$0.240536\pi$
$102$		0			0
$103$	1.26130	+	4.70723i	0.124279	+	0.463817i	0.999813	−	0.0193403i	$-0.00615660\pi$
$103$	1.26130	+	4.70723i	0.124279	+	0.463817i	−0.875534	+	0.483157i	$0.839490\pi$
$104$		0			0
$105$	0.363490	+	0.640772i	0.0354730	+	0.0625329i
$106$		0			0
$107$	−4.35059	−	16.2366i	−0.420588	−	1.56965i	−0.773374	−	0.633950i	$-0.781432\pi$
$107$	−4.35059	−	16.2366i	−0.420588	−	1.56965i	0.352786	−	0.935704i	$-0.385234\pi$
$108$		0			0
$109$	−8.04799	+	4.64651i	−0.770858	+	0.445055i	−0.833181	−	0.553001i	$-0.813483\pi$
$109$	−8.04799	+	4.64651i	−0.770858	+	0.445055i	0.0623227	+	0.998056i	$0.480149\pi$
$110$		0			0
$111$		−	0.901497i		−	0.0855663i
$112$		0			0
$113$	−5.21788	−	5.21788i	−0.490857	−	0.490857i	0.417719	−	0.908576i	$-0.362830\pi$
$113$	−5.21788	−	5.21788i	−0.490857	−	0.490857i	−0.908576	+	0.417719i	$0.862830\pi$
$114$		0			0
$115$	−5.27006	−	0.828655i	−0.491436	−	0.0772725i
$116$		0			0
$117$	−13.3954	+	3.58928i	−1.23840	+	0.331829i
$118$		0			0
$119$	−2.90084	+	3.92038i	−0.265920	+	0.359381i
$120$		0			0
$121$	1.52726	−	2.64529i	0.138842	−	0.240481i
$122$		0			0
$123$	−0.304764	+	1.13740i	−0.0274797	+	0.102556i
$124$		0			0
$125$	−3.49057	−	10.6215i	−0.312206	−	0.950014i
$126$		0			0
$127$	7.88798	−	7.88798i	0.699945	−	0.699945i	−0.264453	−	0.964398i	$-0.585192\pi$
$127$	7.88798	−	7.88798i	0.699945	−	0.699945i	0.964398	+	0.264453i	$0.0851916\pi$
$128$		0			0
$129$	0.0917057	+	0.158839i	0.00807424	+	0.0139850i
$130$		0			0
$131$	−4.59922	−	2.65536i	−0.401836	−	0.232000i	0.285440	−	0.958397i	$-0.407860\pi$
$131$	−4.59922	−	2.65536i	−0.401836	−	0.232000i	−0.687276	+	0.726397i	$0.741194\pi$
$132$		0			0
$133$	16.6321	−	13.2302i	1.44219	−	1.14720i
$134$		0			0
$135$	0.598903	+	1.55499i	0.0515454	+	0.133833i
$136$		0			0
$137$	−6.16614	−	1.65221i	−0.526809	−	0.141158i	−0.0143944	−	0.999896i	$-0.504582\pi$
$137$	−6.16614	−	1.65221i	−0.526809	−	0.141158i	−0.512414	+	0.858738i	$0.671249\pi$
$138$		0			0
$139$	−0.995838			−0.0844659			−0.0422329	−	0.999108i	$-0.513447\pi$
$139$	−0.995838			−0.0844659			−0.0422329	+	0.999108i	$0.513447\pi$
$140$		0			0
$141$	−0.485621			−0.0408966
$142$		0			0
$143$	−12.6516	−	3.38998i	−1.05798	−	0.283485i
$144$		0			0
$145$	−7.83678	+	17.6548i	−0.650810	+	1.46615i
$146$		0			0
$147$	0.461933	+	0.739200i	0.0380996	+	0.0609682i
$148$		0			0
$149$	−2.96121	−	1.70965i	−0.242592	−	0.140060i	0.373776	−	0.927519i	$-0.378063\pi$
$149$	−2.96121	−	1.70965i	−0.242592	−	0.140060i	−0.616367	+	0.787459i	$0.711396\pi$
$150$		0			0
$151$	−9.79492	−	16.9653i	−0.797099	−	1.38062i	−0.921498	−	0.388383i	$-0.873034\pi$
$151$	−9.79492	−	16.9653i	−0.797099	−	1.38062i	0.124399	−	0.992232i	$-0.460300\pi$
$152$		0			0
$153$	−3.89002	+	3.89002i	−0.314489	+	0.314489i
$154$		0			0
$155$	7.21999	−	0.767017i	0.579923	−	0.0616083i
$156$		0			0
$157$	−1.22966	+	4.58914i	−0.0981373	+	0.366253i	−0.997476	−	0.0709984i	$-0.977381\pi$
$157$	−1.22966	+	4.58914i	−0.0981373	+	0.366253i	0.899339	+	0.437252i	$0.144048\pi$
$158$		0			0
$159$	0.421808	−	0.730593i	0.0334516	−	0.0579398i
$160$		0			0
$161$	−6.27167	−	0.714474i	−0.494277	−	0.0563085i
$162$		0			0
$163$	1.31013	−	0.351047i	0.102617	−	0.0274961i	−0.207145	−	0.978310i	$-0.566417\pi$
$163$	1.31013	−	0.351047i	0.102617	−	0.0274961i	0.309762	+	0.950814i	$0.399751\pi$
$164$		0			0
$165$	−0.121913	+	0.775342i	−0.00949094	+	0.0603603i
$166$		0			0
$167$	4.39184	+	4.39184i	0.339851	+	0.339851i	0.856311	−	0.516460i	$-0.172751\pi$
$167$	4.39184	+	4.39184i	0.339851	+	0.339851i	−0.516460	+	0.856311i	$0.672751\pi$
$168$		0			0
$169$		−	8.59146i		−	0.660881i
$170$		0			0
$171$	20.7616	−	11.9867i	1.58768	−	0.916648i
$172$		0			0
$173$	−2.46814	−	9.21122i	−0.187649	−	0.700316i	−0.994048	−	0.108944i	$-0.965253\pi$
$173$	−2.46814	−	9.21122i	−0.187649	−	0.700316i	0.806399	−	0.591372i	$-0.201414\pi$
$174$		0			0
$175$	−4.66069	−	12.3805i	−0.352315	−	0.935881i
$176$		0			0
$177$	−0.399468	−	1.49084i	−0.0300259	−	0.112058i
$178$		0			0
$179$	11.4852	−	6.63101i	0.858447	−	0.495625i	−0.00504471	−	0.999987i	$-0.501606\pi$
$179$	11.4852	−	6.63101i	0.858447	−	0.495625i	0.863492	+	0.504362i	$0.168272\pi$
$180$		0			0
$181$			10.8465i			0.806214i	0.915153	+	0.403107i	$0.132070\pi$
$181$			10.8465i			0.806214i	−0.915153	+	0.403107i	$0.867930\pi$
$182$		0			0
$183$	0.223099	+	0.223099i	0.0164920	+	0.0164920i
$184$		0			0
$185$	−2.51450	+	15.9917i	−0.184870	+	1.17573i
$186$		0			0
$187$	−5.01880	+	1.34478i	−0.367011	+	0.0983403i
$188$		0			0
$189$	0.786216	+	1.80810i	0.0571888	+	0.131520i
$190$		0			0
$191$	−1.52564	+	2.64249i	−0.110392	+	0.191204i	−0.915928	−	0.401342i	$-0.868544\pi$
$191$	−1.52564	+	2.64249i	−0.110392	+	0.191204i	0.805537	+	0.592546i	$0.201877\pi$
$192$		0			0
$193$	−6.09586	+	22.7501i	−0.438790	+	1.63759i	0.293042	+	0.956100i	$0.405333\pi$
$193$	−6.09586	+	22.7501i	−0.438790	+	1.63759i	−0.731831	+	0.681486i	$0.761334\pi$
$194$		0			0
$195$	−1.28659	+	0.136681i	−0.0921347	+	0.00978795i
$196$		0			0
$197$	1.84909	−	1.84909i	0.131743	−	0.131743i	−0.638161	−	0.769903i	$-0.720304\pi$
$197$	1.84909	−	1.84909i	0.131743	−	0.131743i	0.769903	+	0.638161i	$0.220304\pi$
$198$		0			0
$199$	0.310311	+	0.537475i	0.0219974	+	0.0381006i	0.876815	−	0.480829i	$-0.159664\pi$
$199$	0.310311	+	0.537475i	0.0219974	+	0.0381006i	−0.854817	+	0.518929i	$0.826331\pi$
$200$		0			0
$201$	1.54815	+	0.893828i	0.109198	+	0.0630457i
$202$		0			0
$203$	−8.37608	+	21.2648i	−0.587885	+	1.49250i
$204$		0			0
$205$	8.57871	−	19.3263i	0.599163	−	1.34980i
$206$		0			0
$207$	−6.87779	−	1.84290i	−0.478039	−	0.128090i
$208$		0			0
$209$	22.6423			1.56620
$210$		0			0
$211$	−13.7502			−0.946601			−0.473301	−	0.880901i	$-0.656938\pi$
$211$	−13.7502			−0.946601			−0.473301	+	0.880901i	$0.656938\pi$
$212$		0			0
$213$	0.328193	+	0.0879389i	0.0224874	+	0.00602548i
$214$		0			0
$215$	−1.18373	−	3.07344i	−0.0807297	−	0.209607i
$216$		0			0
$217$	8.49649	−	1.26994i	0.576780	−	0.0862088i
$218$		0			0
$219$	0.435636	+	0.251514i	0.0294375	+	0.0169958i
$220$		0			0
$221$	−4.28259	−	7.41767i	−0.288078	−	0.498966i
$222$		0			0
$223$	0.443239	−	0.443239i	0.0296815	−	0.0296815i	−0.692110	−	0.721792i	$-0.743319\pi$
$223$	0.443239	−	0.443239i	0.0296815	−	0.0296815i	0.721792	+	0.692110i	$0.243319\pi$
$224$		0			0
$225$	−3.13520	−	14.5894i	−0.209013	−	0.972627i
$226$		0			0
$227$	−5.54585	+	20.6974i	−0.368091	+	1.37373i	0.495092	+	0.868841i	$0.335135\pi$
$227$	−5.54585	+	20.6974i	−0.368091	+	1.37373i	−0.863182	+	0.504892i	$0.831532\pi$
$228$		0			0
$229$	3.71101	−	6.42766i	0.245230	−	0.424752i	−0.716966	−	0.697108i	$-0.754470\pi$
$229$	3.71101	−	6.42766i	0.245230	−	0.424752i	0.962196	+	0.272357i	$0.0878030\pi$
$230$		0			0
$231$	−0.105115	+	0.922701i	−0.00691605	+	0.0607092i
$232$		0			0
$233$	−5.25237	+	1.40737i	−0.344094	+	0.0921997i	−0.426727	−	0.904380i	$-0.640334\pi$
$233$	−5.25237	+	1.40737i	−0.344094	+	0.0921997i	0.0826334	+	0.996580i	$0.473667\pi$
$234$		0			0
$235$	8.61444	+	1.35452i	0.561944	+	0.0883591i
$236$		0			0
$237$	−0.561333	−	0.561333i	−0.0364625	−	0.0364625i
$238$		0			0
$239$			10.0507i			0.650124i	0.945693	+	0.325062i	$0.105385\pi$
$239$			10.0507i			0.650124i	−0.945693	+	0.325062i	$0.894615\pi$
$240$		0			0
$241$	17.9706	−	10.3753i	1.15759	−	0.668333i	0.206862	−	0.978370i	$-0.433675\pi$
$241$	17.9706	−	10.3753i	1.15759	−	0.668333i	0.950725	+	0.310037i	$0.100341\pi$
$242$		0			0
$243$	0.864196	+	3.22522i	0.0554382	+	0.206898i
$244$		0			0
$245$	−6.13244	−	14.4012i	−0.391787	−	0.920056i
$246$		0			0
$247$	9.66045	+	36.0533i	0.614679	+	2.29401i
$248$		0			0
$249$	1.13070	−	0.652813i	0.0716555	−	0.0413703i
$250$		0			0
$251$			0.0396287i			0.00250134i	0.999999	+	0.00125067i	$0.000398101\pi$
$251$			0.0396287i			0.00250134i	−0.999999	+	0.00125067i	$0.999602\pi$
$252$		0			0
$253$	−4.75532	−	4.75532i	−0.298964	−	0.298964i
$254$		0			0
$255$	−0.414894	+	0.302147i	−0.0259816	+	0.0189212i
$256$		0			0
$257$	16.4339	−	4.40345i	1.02512	−	0.274679i	0.293184	−	0.956056i	$-0.405285\pi$
$257$	16.4339	−	4.40345i	1.02512	−	0.274679i	0.731933	+	0.681376i	$0.238618\pi$
$258$		0			0
$259$	−2.16803	+	19.0310i	−0.134715	+	1.18253i
$260$		0			0
$261$	−12.8906	+	22.3272i	−0.797908	+	1.38202i
$262$		0			0
$263$	−1.89339	+	7.06624i	−0.116752	+	0.435723i	−0.999412	−	0.0342884i	$-0.989084\pi$
$263$	−1.89339	+	7.06624i	−0.116752	+	0.435723i	0.882660	+	0.470011i	$0.155750\pi$
$264$		0			0
$265$	−9.52028	+	11.7835i	−0.584826	+	0.723854i
$266$		0			0
$267$	−0.0858727	+	0.0858727i	−0.00525532	+	0.00525532i
$268$		0			0
$269$	−3.24863	−	5.62679i	−0.198072	−	0.343071i	0.749831	−	0.661629i	$-0.230135\pi$
$269$	−3.24863	−	5.62679i	−0.198072	−	0.343071i	−0.947903	+	0.318558i	$0.896801\pi$
$270$		0			0
$271$	18.0071	+	10.3964i	1.09385	+	0.631537i	0.934600	−	0.355701i	$-0.115758\pi$
$271$	18.0071	+	10.3964i	1.09385	+	0.631537i	0.159254	+	0.987238i	$0.449091\pi$
$272$		0			0
$273$	−1.51406	+	0.226301i	−0.0916352	+	0.0136963i
$274$		0			0
$275$	4.32525	−	13.4138i	0.260822	−	0.808881i
$276$		0			0
$277$	26.6010	+	7.12770i	1.59830	+	0.428262i	0.944528	−	0.328432i	$-0.106520\pi$
$277$	26.6010	+	7.12770i	1.59830	+	0.428262i	0.653769	+	0.756694i	$0.273187\pi$
$278$		0			0
$279$	9.69079			0.580172
$280$		0			0
$281$	23.0686			1.37616			0.688080	−	0.725635i	$-0.258454\pi$
$281$	23.0686			1.37616			0.688080	+	0.725635i	$0.258454\pi$
$282$		0			0
$283$	−26.9506	−	7.22139i	−1.60205	−	0.429267i	−0.656387	−	0.754424i	$-0.727916\pi$
$283$	−26.9506	−	7.22139i	−1.60205	−	0.429267i	−0.945660	+	0.325157i	$0.894583\pi$
$284$		0			0
$285$	2.08719	−	0.803876i	0.123634	−	0.0476175i
$286$		0			0
$287$	9.16906	−	23.2780i	0.541233	−	1.37406i
$288$		0			0
$289$	11.7799	+	6.80112i	0.692935	+	0.400066i
$290$		0			0
$291$	−0.451195	−	0.781492i	−0.0264495	−	0.0458119i
$292$		0			0
$293$	−7.37797	+	7.37797i	−0.431025	+	0.431025i	−0.888977	−	0.457952i	$-0.848583\pi$
$293$	−7.37797	+	7.37797i	−0.431025	+	0.431025i	0.457952	+	0.888977i	$0.348583\pi$
$294$		0			0
$295$	2.92786	+	27.5602i	0.170467	+	1.60462i
$296$		0			0
$297$	−0.543670	+	2.02900i	−0.0315469	+	0.117735i
$298$		0			0
$299$	5.54300	−	9.60076i	0.320560	−	0.555227i
$300$		0			0
$301$	−1.55395	−	3.57371i	−0.0895684	−	0.205985i
$302$		0			0
$303$	0.694867	−	0.186189i	0.0399190	−	0.0106963i
$304$		0			0
$305$	−3.33528	−	4.57984i	−0.190978	−	0.262241i
$306$		0			0
$307$	4.95205	+	4.95205i	0.282628	+	0.282628i	0.834156	−	0.551528i	$-0.185955\pi$
$307$	4.95205	+	4.95205i	0.282628	+	0.282628i	−0.551528	+	0.834156i	$0.685955\pi$
$308$		0			0
$309$			0.606838i			0.0345218i
$310$		0			0
$311$	−8.08514	+	4.66796i	−0.458466	+	0.264696i	−0.711399	−	0.702788i	$-0.751938\pi$
$311$	−8.08514	+	4.66796i	−0.458466	+	0.264696i	0.252933	+	0.967484i	$0.418605\pi$
$312$		0			0
$313$	−5.12415	−	19.1236i	−0.289634	−	1.08093i	−0.945386	−	0.325953i	$-0.894315\pi$
$313$	−5.12415	−	19.1236i	−0.289634	−	1.08093i	0.655752	−	0.754976i	$-0.272352\pi$
$314$		0			0
$315$	−4.44020	−	17.0891i	−0.250177	−	0.962861i
$316$		0			0
$317$	4.37369	+	16.3228i	0.245651	+	0.916782i	0.973055	+	0.230573i	$0.0740600\pi$
$317$	4.37369	+	16.3228i	0.245651	+	0.916782i	−0.727404	+	0.686209i	$0.759273\pi$
$318$		0			0
$319$	−21.0874	+	12.1748i	−1.18067	+	0.681659i
$320$		0			0
$321$		−	2.09317i		−	0.116829i
$322$		0			0
$323$	10.4699	+	10.4699i	0.582559	+	0.582559i
$324$		0			0
$325$	23.2041	+	1.16403i	1.28713	+	0.0645690i
$326$		0			0
$327$	−1.11777	+	0.299505i	−0.0618128	+	0.0165627i
$328$		0			0
$329$	10.2517	+	1.16788i	0.565193	+	0.0643873i
$330$		0			0
$331$	4.97088	−	8.60981i	0.273224	−	0.473238i	−0.696461	−	0.717594i	$-0.745243\pi$
$331$	4.97088	−	8.60981i	0.273224	−	0.473238i	0.969686	+	0.244356i	$0.0785766\pi$
$332$		0			0
$333$	−5.59216	+	20.8702i	−0.306449	+	1.14368i
$334$		0			0
$335$	−24.9697	−	20.1738i	−1.36424	−	1.10221i
$336$		0			0
$337$	−17.4904	+	17.4904i	−0.952762	+	0.952762i	−0.998934	−	0.0461714i	$-0.985298\pi$
$337$	−17.4904	+	17.4904i	−0.952762	+	0.952762i	0.0461714	+	0.998934i	$0.485298\pi$
$338$		0			0
$339$	−0.459442	−	0.795777i	−0.0249535	−	0.0432207i
$340$		0			0
$341$	7.92646	+	4.57634i	0.429242	+	0.247823i
$342$		0			0
$343$	−7.97390	−	16.7158i	−0.430550	−	0.902567i
$344$		0			0
$345$	−0.607179	−	0.269520i	−0.0326894	−	0.0145105i
$346$		0			0
$347$	−3.55893	−	0.953611i	−0.191053	−	0.0511925i	0.162024	−	0.986787i	$-0.448198\pi$
$347$	−3.55893	−	0.953611i	−0.191053	−	0.0511925i	−0.353077	+	0.935594i	$0.614865\pi$
$348$		0			0
$349$	1.25235			0.0670367			0.0335183	−	0.999438i	$-0.489329\pi$
$349$	1.25235			0.0670367			0.0335183	+	0.999438i	$0.489329\pi$
$350$		0			0
$351$	−3.46274			−0.184827
$352$		0			0
$353$	−22.5220	−	6.03475i	−1.19872	−	0.321197i	−0.396396	−	0.918080i	$-0.629739\pi$
$353$	−22.5220	−	6.03475i	−1.19872	−	0.321197i	−0.802329	+	0.596882i	$0.796406\pi$
$354$		0			0
$355$	−5.57654	−	2.47536i	−0.295972	−	0.131379i
$356$		0			0
$357$	−0.475265	+	0.378054i	−0.0251537	+	0.0200087i
$358$		0			0
$359$	24.7688	+	14.3003i	1.30725	+	0.754741i	0.981636	−	0.190762i	$-0.0610958\pi$
$359$	24.7688	+	14.3003i	1.30725	+	0.754741i	0.325614	+	0.945503i	$0.394429\pi$
$360$		0			0
$361$	−22.7619	−	39.4248i	−1.19799	−	2.07499i
$362$		0			0
$363$	0.268954	−	0.268954i	0.0141164	−	0.0141164i
$364$		0			0
$365$	−7.02622	−	5.67672i	−0.367769	−	0.297133i
$366$		0			0
$367$	3.76258	−	14.0422i	0.196405	−	0.732995i	−0.795493	−	0.605962i	$-0.792788\pi$
$367$	3.76258	−	14.0422i	0.196405	−	0.732995i	0.991899	−	0.127032i	$-0.0405452\pi$
$368$		0			0
$369$	14.1110	−	24.4409i	0.734588	−	1.27234i
$370$		0			0
$371$	−10.6616	+	14.4087i	−0.553522	+	0.748064i
$372$		0			0
$373$	−1.58716	+	0.425279i	−0.0821802	+	0.0220201i	−0.299675	−	0.954041i	$-0.596878\pi$
$373$	−1.58716	+	0.425279i	−0.0821802	+	0.0220201i	0.217495	+	0.976062i	$0.430212\pi$
$374$		0			0
$375$	−0.0775275	−	1.39006i	−0.00400350	−	0.0717822i
$376$		0			0
$377$	−28.3830	−	28.3830i	−1.46180	−	1.46180i
$378$		0			0
$379$		−	11.7601i		−	0.604077i	−0.953296	−	0.302038i	$-0.902333\pi$
$379$		−	11.7601i		−	0.604077i	0.953296	−	0.302038i	$-0.0976671\pi$
$380$		0			0
$381$	1.20299	−	0.694548i	0.0616312	−	0.0355828i
$382$		0			0
$383$	3.70668	+	13.8335i	0.189402	+	0.706859i	0.993645	+	0.112558i	$0.0359045\pi$
$383$	3.70668	+	13.8335i	0.189402	+	0.706859i	−0.804243	+	0.594301i	$0.797429\pi$
$384$		0			0
$385$	4.43828	−	16.0746i	0.226196	−	0.819239i
$386$		0			0
$387$	−1.13774	−	4.24609i	−0.0578344	−	0.215841i
$388$		0			0
$389$	−28.7560	+	16.6023i	−1.45799	+	0.841768i	−0.998912	−	0.0466300i	$-0.985152\pi$
$389$	−28.7560	+	16.6023i	−1.45799	+	0.841768i	−0.459073	+	0.888398i	$0.651818\pi$
$390$		0			0
$391$		−	4.39774i		−	0.222404i
$392$		0			0
$393$	−0.467617	−	0.467617i	−0.0235881	−	0.0235881i
$394$		0			0
$395$	8.39180	+	11.5232i	0.422237	+	0.579795i
$396$		0			0
$397$	31.4212	−	8.41928i	1.57698	−	0.422552i	0.638993	−	0.769212i	$-0.279351\pi$
$397$	31.4212	−	8.41928i	1.57698	−	0.422552i	0.937991	+	0.346661i	$0.112684\pi$
$398$		0			0
$399$	2.42692	−	1.05530i	0.121498	−	0.0528309i
$400$		0			0
$401$	5.03475	−	8.72044i	0.251423	−	0.435478i	−0.712495	−	0.701678i	$-0.752435\pi$
$401$	5.03475	−	8.72044i	0.251423	−	0.435478i	0.963918	+	0.266200i	$0.0857680\pi$
$402$		0			0
$403$	−3.90504	+	14.5738i	−0.194524	+	0.725973i
$404$		0			0
$405$	−2.09307	−	19.7022i	−0.104005	−	0.979012i
$406$		0			0
$407$	−14.4297	+	14.4297i	−0.715255	+	0.715255i
$408$		0			0
$409$	11.4380	+	19.8113i	0.565575	+	0.979605i	0.996996	+	0.0774540i	$0.0246791\pi$
$409$	11.4380	+	19.8113i	0.565575	+	0.979605i	−0.431421	+	0.902151i	$0.641988\pi$
$410$		0			0
$411$	−0.688417	−	0.397458i	−0.0339571	−	0.0196051i
$412$		0			0
$413$	4.84761	+	32.4329i	0.238535	+	1.59592i
$414$		0			0
$415$	−21.8785	+	8.42645i	−1.07397	+	0.413638i
$416$		0			0
$417$	−0.119780	−	0.0320949i	−0.00586565	−	0.00157170i
$418$		0			0
$419$	−3.51110			−0.171529			−0.0857643	−	0.996315i	$-0.527333\pi$
$419$	−3.51110			−0.171529			−0.0857643	+	0.996315i	$0.527333\pi$
$420$		0			0
$421$	−0.852753			−0.0415606			−0.0207803	−	0.999784i	$-0.506615\pi$
$421$	−0.852753			−0.0415606			−0.0207803	+	0.999784i	$0.506615\pi$
$422$		0			0
$423$	11.2424	+	3.01240i	0.546625	+	0.146468i
$424$		0			0
$425$	8.20258	−	4.20256i	0.397883	−	0.203854i
$426$		0			0
$427$	−4.17318	−	5.24626i	−0.201955	−	0.253884i
$428$		0			0
$429$	−1.41248	−	0.815498i	−0.0681953	−	0.0393726i
$430$		0			0
$431$	−14.4142	−	24.9661i	−0.694306	−	1.20257i	−0.970414	−	0.241447i	$-0.922378\pi$
$431$	−14.4142	−	24.9661i	−0.694306	−	1.20257i	0.276108	−	0.961127i	$-0.410955\pi$
$432$		0			0
$433$	12.3865	−	12.3865i	0.595257	−	0.595257i	−0.343789	−	0.939047i	$-0.611711\pi$
$433$	12.3865	−	12.3865i	0.595257	−	0.595257i	0.939047	+	0.343789i	$0.111711\pi$
$434$		0			0
$435$	−1.51161	+	1.87096i	−0.0724762	+	0.0897056i
$436$		0			0
$437$	−4.96010	+	18.5113i	−0.237274	+	0.885518i
$438$		0			0
$439$	17.7310	−	30.7110i	0.846256	−	1.46576i	−0.0382703	−	0.999267i	$-0.512185\pi$
$439$	17.7310	−	30.7110i	0.846256	−	1.46576i	0.884526	−	0.466491i	$-0.154482\pi$
$440$		0			0
$441$	−6.10865	−	19.9784i	−0.290888	−	0.951353i
$442$		0			0
$443$	24.3705	−	6.53005i	1.15788	−	0.310252i	0.371759	−	0.928329i	$-0.378755\pi$
$443$	24.3705	−	6.53005i	1.15788	−	0.310252i	0.786118	+	0.618077i	$0.212088\pi$
$444$		0			0
$445$	1.76282	−	1.28378i	0.0835657	−	0.0608569i
$446$		0			0
$447$	−0.301075	−	0.301075i	−0.0142404	−	0.0142404i
$448$		0			0
$449$			26.2571i			1.23915i	0.784937	+	0.619575i	$0.212695\pi$
$449$			26.2571i			1.23915i	−0.784937	+	0.619575i	$0.787305\pi$
$450$		0			0
$451$	23.0838	−	13.3274i	1.08697	−	0.627565i
$452$		0			0
$453$	−0.631362	−	2.35627i	−0.0296640	−	0.110707i
$454$		0			0
$455$	27.4892	+	0.208749i	1.28871	+	0.00978629i
$456$		0			0
$457$	−2.69818	−	10.0697i	−0.126215	−	0.471042i	0.873665	−	0.486528i	$-0.161737\pi$
$457$	−2.69818	−	10.0697i	−0.126215	−	0.471042i	−0.999880	+	0.0154864i	$0.995070\pi$
$458$		0			0
$459$	−1.18961	+	0.686823i	−0.0555263	+	0.0320582i
$460$		0			0
$461$			29.1465i			1.35749i	0.734374	+	0.678745i	$0.237476\pi$
$461$			29.1465i			1.35749i	−0.734374	+	0.678745i	$0.762524\pi$
$462$		0			0
$463$	−23.7580	−	23.7580i	−1.10413	−	1.10413i	−0.993907	−	0.110219i	$-0.964845\pi$
$463$	−23.7580	−	23.7580i	−1.10413	−	1.10413i	−0.110219	−	0.993907i	$-0.535155\pi$
$464$		0			0
$465$	0.893144	+	0.140436i	0.0414186	+	0.00651258i
$466$		0			0
$467$	−26.3185	+	7.05201i	−1.21787	+	0.326328i	−0.809846	−	0.586642i	$-0.800450\pi$
$467$	−26.3185	+	7.05201i	−1.21787	+	0.326328i	−0.408026	+	0.912970i	$0.633783\pi$
$468$		0			0
$469$	−30.5327	−	22.5923i	−1.40987	−	1.04322i
$470$		0			0
$471$	−0.295808	+	0.512354i	−0.0136301	+	0.0236080i
$472$		0			0
$473$	1.07456	−	4.01032i	0.0494084	−	0.184395i
$474$		0			0
$475$	−39.2669	+	8.43829i	−1.80169	+	0.387175i
$476$		0			0
$477$	−14.2971	+	14.2971i	−0.654621	+	0.654621i
$478$		0			0
$479$	−15.5080	−	26.8607i	−0.708580	−	1.22730i	−0.965384	−	0.260834i	$-0.916003\pi$
$479$	−15.5080	−	26.8607i	−0.708580	−	1.22730i	0.256803	−	0.966464i	$-0.417331\pi$
$480$		0			0
$481$	−29.1330	−	16.8199i	−1.32835	−	0.766922i
$482$		0			0
$483$	−0.731333	−	0.288067i	−0.0332768	−	0.0131075i
$484$		0			0
$485$	5.82398	+	15.1214i	0.264453	+	0.686628i
$486$		0			0
$487$	−1.63160	−	0.437185i	−0.0739347	−	0.0198107i	0.221662	−	0.975124i	$-0.428852\pi$
$487$	−1.63160	−	0.437185i	−0.0739347	−	0.0198107i	−0.295597	+	0.955313i	$0.595518\pi$
$488$		0			0
$489$	0.168897			0.00763777
$490$		0			0
$491$	21.4431			0.967712			0.483856	−	0.875148i	$-0.339236\pi$
$491$	21.4431			0.967712			0.483856	+	0.875148i	$0.339236\pi$
$492$		0			0
$493$	−15.3806	−	4.12121i	−0.692705	−	0.185610i
$494$		0			0
$495$	7.63197	−	17.1934i	0.343032	−	0.772786i
$496$		0			0
$497$	−6.71681	−	2.64571i	−0.301290	−	0.118676i
$498$		0			0
$499$	21.1074	+	12.1864i	0.944898	+	0.545537i	0.891492	−	0.453036i	$-0.149659\pi$
$499$	21.1074	+	12.1864i	0.944898	+	0.545537i	0.0534054	+	0.998573i	$0.482992\pi$
$500$		0			0
$501$	0.386708	+	0.669798i	0.0172768	+	0.0299244i
$502$		0			0
$503$	11.7774	−	11.7774i	0.525127	−	0.525127i	−0.393989	−	0.919115i	$-0.628905\pi$
$503$	11.7774	−	11.7774i	0.525127	−	0.525127i	0.919115	+	0.393989i	$0.128905\pi$
$504$		0			0
$505$	−12.8456	+	1.36465i	−0.571621	+	0.0607263i
$506$		0			0
$507$	0.276895	−	1.03339i	0.0122973	−	0.0458942i
$508$		0			0
$509$	−14.7893	+	25.6158i	−0.655523	+	1.13540i	0.326240	+	0.945287i	$0.394218\pi$
$509$	−14.7893	+	25.6158i	−0.655523	+	1.13540i	−0.981763	+	0.190111i	$0.939115\pi$
$510$		0			0
$511$	−8.59159	−	6.35725i	−0.380070	−	0.281228i
$512$		0			0
$513$	5.78206	−	1.54930i	0.255284	−	0.0684032i
$514$		0			0
$515$	1.69263	−	10.7647i	0.0745860	−	0.474351i
$516$		0			0
$517$	7.77304	+	7.77304i	0.341858	+	0.341858i
$518$		0			0
$519$		−	1.18748i		−	0.0521244i
$520$		0			0
$521$	2.80920	−	1.62189i	0.123073	−	0.0710564i	−0.437200	−	0.899365i	$-0.644030\pi$
$521$	2.80920	−	1.62189i	0.123073	−	0.0710564i	0.560273	+	0.828308i	$0.310696\pi$
$522$		0			0
$523$	−9.09811	−	33.9546i	−0.397833	−	1.48473i	−0.816901	−	0.576777i	$-0.804310\pi$
$523$	−9.09811	−	33.9546i	−0.397833	−	1.48473i	0.419069	−	0.907955i	$-0.362357\pi$
$524$		0			0
$525$	−0.161577	−	1.63935i	−0.00705181	−	0.0715470i
$526$		0			0
$527$	1.54910	+	5.78133i	0.0674800	+	0.251839i
$528$		0			0
$529$	−14.9891	+	8.65398i	−0.651701	+	0.376260i
$530$		0			0
$531$			36.9918i			1.60531i
$532$		0			0
$533$	31.0701	+	31.0701i	1.34580	+	1.34580i
$534$		0			0
$535$	−5.83837	+	37.1307i	−0.252415	+	1.60530i
$536$		0			0
$537$	1.59516	−	0.427422i	0.0688363	−	0.0184446i
$538$		0			0
$539$	4.43805	−	19.2258i	0.191160	−	0.828115i
$540$		0			0
$541$	−6.68424	+	11.5774i	−0.287378	+	0.497753i	−0.973183	−	0.230032i	$-0.926117\pi$
$541$	−6.68424	+	11.5774i	−0.287378	+	0.497753i	0.685805	+	0.727785i	$0.259450\pi$
$542$		0			0
$543$	−0.349573	+	1.30462i	−0.0150016	+	0.0559867i
$544$		0			0
$545$	20.6635	−	2.19520i	0.885129	−	0.0940319i
$546$		0			0
$547$	27.7636	−	27.7636i	1.18708	−	1.18708i	0.209215	−	0.977870i	$-0.432909\pi$
$547$	27.7636	−	27.7636i	1.18708	−	1.18708i	0.977870	−	0.209215i	$-0.0670910\pi$
$548$		0			0
$549$	−3.78096	−	6.54881i	−0.161367	−	0.279496i
$550$		0			0
$551$	60.0929	+	34.6946i	2.56004	+	1.47804i
$552$		0			0
$553$	10.5000	+	13.1999i	0.446506	+	0.561319i
$554$		0			0
$555$	−0.817843	+	1.84245i	−0.0347155	+	0.0782076i
$556$		0			0
$557$	−5.47809	−	1.46785i	−0.232114	−	0.0621948i	0.140887	−	0.990026i	$-0.455005\pi$
$557$	−5.47809	−	1.46785i	−0.232114	−	0.0621948i	−0.373001	+	0.927831i	$0.621671\pi$
$558$		0			0
$559$	6.84409			0.289474
$560$		0			0
$561$	−0.647005			−0.0273166
$562$		0			0
$563$	8.17372	+	2.19014i	0.344481	+	0.0923034i	0.426912	−	0.904293i	$-0.359602\pi$
$563$	8.17372	+	2.19014i	0.344481	+	0.0923034i	−0.0824304	+	0.996597i	$0.526268\pi$
$564$		0			0
$565$	5.93044	+	15.3978i	0.249495	+	0.647791i
$566$		0			0
$567$	−3.46546	−	23.1856i	−0.145536	−	0.973704i
$568$		0			0
$569$	33.6387	+	19.4213i	1.41021	+	0.814183i	0.995407	−	0.0957306i	$-0.0305187\pi$
$569$	33.6387	+	19.4213i	1.41021	+	0.814183i	0.414798	+	0.909913i	$0.363852\pi$
$570$		0			0
$571$	15.7235	+	27.2339i	0.658007	+	1.13970i	0.981131	+	0.193345i	$0.0619337\pi$
$571$	15.7235	+	27.2339i	0.658007	+	1.13970i	−0.323124	+	0.946357i	$0.604733\pi$
$572$		0			0
$573$	−0.268670	+	0.268670i	−0.0112238	+	0.0112238i
$574$		0			0
$575$	10.0190	+	6.47461i	0.417822	+	0.270010i
$576$		0			0
$577$	2.15216	−	8.03197i	0.0895956	−	0.334375i	−0.906549	−	0.422100i	$-0.861293\pi$
$577$	2.15216	−	8.03197i	0.0895956	−	0.334375i	0.996145	+	0.0877249i	$0.0279597\pi$
$578$		0			0
$579$	−1.46643	+	2.53993i	−0.0609426	+	0.105556i
$580$		0			0
$581$	−25.4396	+	11.0619i	−1.05541	+	0.458925i
$582$		0			0
$583$	−18.4458	+	4.94254i	−0.763947	+	0.204699i
$584$		0			0
$585$	30.6333	+	4.81672i	1.26653	+	0.199147i
$586$		0			0
$587$	18.1577	+	18.1577i	0.749448	+	0.749448i	0.974376	−	0.224927i	$-0.0722145\pi$
$587$	18.1577	+	18.1577i	0.749448	+	0.749448i	−0.224927	+	0.974376i	$0.572214\pi$
$588$		0			0
$589$		−	26.0824i		−	1.07471i
$590$		0			0
$591$	0.282005	−	0.162815i	0.0116001	−	0.00669733i
$592$		0			0
$593$	3.50935	+	13.0971i	0.144112	+	0.537833i	0.999793	+	0.0203298i	$0.00647163\pi$
$593$	3.50935	+	13.0971i	0.144112	+	0.537833i	−0.855682	+	0.517503i	$0.826862\pi$
$594$		0			0
$595$	9.48523	−	5.38068i	0.388857	−	0.220586i
$596$		0			0
$597$	0.0200021	+	0.0746488i	0.000818631	+	0.00305517i
$598$		0			0
$599$	−19.0934	+	11.0236i	−0.780136	+	0.450412i	−0.836478	−	0.548000i	$-0.815389\pi$
$599$	−19.0934	+	11.0236i	−0.780136	+	0.450412i	0.0563425	+	0.998411i	$0.482056\pi$
$600$		0			0
$601$			8.82954i			0.360165i	0.983652	+	0.180082i	$0.0576364\pi$
$601$			8.82954i			0.360165i	−0.983652	+	0.180082i	$0.942364\pi$
$602$		0			0
$603$	−30.2962	−	30.2962i	−1.23376	−	1.23376i
$604$		0			0
$605$	−5.52117	+	4.02081i	−0.224468	+	0.163469i
$606$		0			0
$607$	30.4048	−	8.14693i	1.23409	−	0.330674i	0.417920	−	0.908484i	$-0.362759\pi$
$607$	30.4048	−	8.14693i	1.23409	−	0.330674i	0.816171	+	0.577810i	$0.196092\pi$
$608$		0			0
$609$	−1.69282	+	2.28779i	−0.0685967	+	0.0927059i
$610$		0			0
$611$	−9.06059	+	15.6934i	−0.366552	+	0.634887i
$612$		0			0
$613$	0.273366	−	1.02021i	0.0110411	−	0.0412061i	−0.960186	−	0.279363i	$-0.909877\pi$
$613$	0.273366	−	1.02021i	0.0110411	−	0.0412061i	0.971227	+	0.238157i	$0.0765433\pi$
$614$		0			0
$615$	1.65472	−	2.04809i	0.0667247	−	0.0825869i
$616$		0			0
$617$	8.65940	−	8.65940i	0.348614	−	0.348614i	−0.510979	−	0.859593i	$-0.670717\pi$
$617$	8.65940	−	8.65940i	0.348614	−	0.348614i	0.859593	+	0.510979i	$0.170717\pi$
$618$		0			0
$619$	−3.65777	−	6.33544i	−0.147018	−	0.254643i	0.783106	−	0.621888i	$-0.213634\pi$
$619$	−3.65777	−	6.33544i	−0.147018	−	0.254643i	−0.930124	+	0.367245i	$0.880301\pi$
$620$		0			0
$621$	−1.53973	−	0.888962i	−0.0617871	−	0.0356728i
$622$		0			0
$623$	2.01933	−	1.60629i	0.0809027	−	0.0643548i
$624$		0			0
$625$	−2.50195	+	24.8745i	−0.100078	+	0.994980i
$626$		0			0
$627$	2.72343	+	0.729740i	0.108763	+	0.0291430i
$628$		0			0
$629$	−13.3447			−0.532088
$630$		0			0
$631$	−23.3631			−0.930071			−0.465035	−	0.885292i	$-0.653958\pi$
$631$	−23.3631			−0.930071			−0.465035	+	0.885292i	$0.653958\pi$
$632$		0			0
$633$	−1.65388	−	0.443155i	−0.0657358	−	0.0176138i
$634$		0			0
$635$	−23.2772	+	8.96516i	−0.923727	+	0.355772i
$636$		0			0
$637$	32.5068	−	1.13611i	1.28797	−	0.0450141i
$638$		0			0
$639$	−7.05236	−	4.07168i	−0.278987	−	0.161073i
$640$		0			0
$641$	−13.9662	−	24.1903i	−0.551634	−	0.955457i	−0.998157	−	0.0606855i	$-0.980671\pi$
$641$	−13.9662	−	24.1903i	−0.551634	−	0.955457i	0.446523	−	0.894772i	$-0.352662\pi$
$642$		0			0
$643$	30.5610	−	30.5610i	1.20521	−	1.20521i	0.232647	−	0.972561i	$-0.425261\pi$
$643$	30.5610	−	30.5610i	1.20521	−	1.20521i	0.972561	−	0.232647i	$-0.0747387\pi$
$644$		0			0
$645$	−0.0433254	−	0.407826i	−0.00170594	−	0.0160581i
$646$		0			0
$647$	−10.9104	+	40.7181i	−0.428932	+	1.60079i	0.326253	+	0.945282i	$0.394214\pi$
$647$	−10.9104	+	40.7181i	−0.428932	+	1.60079i	−0.755185	+	0.655512i	$0.772453\pi$
$648$		0			0
$649$	−17.4689	+	30.2570i	−0.685713	+	1.18769i
$650$		0			0
$651$	1.06289	+	0.121086i	0.0416580	+	0.00474572i
$652$		0			0
$653$	20.6017	−	5.52020i	0.806205	−	0.216022i	0.167898	−	0.985804i	$-0.446302\pi$
$653$	20.6017	−	5.52020i	0.806205	−	0.216022i	0.638306	+	0.769782i	$0.279635\pi$
$654$		0			0
$655$	6.99077	+	9.59937i	0.273152	+	0.375078i
$656$		0			0
$657$	−8.52505	−	8.52505i	−0.332594	−	0.332594i
$658$		0			0
$659$			5.48161i			0.213533i	0.994284	+	0.106767i	$0.0340498\pi$
$659$			5.48161i			0.213533i	−0.994284	+	0.106767i	$0.965950\pi$
$660$		0			0
$661$	−4.01484	+	2.31797i	−0.156159	+	0.0901585i	−0.576043	−	0.817419i	$-0.695404\pi$
$661$	−4.01484	+	2.31797i	−0.156159	+	0.0901585i	0.419884	+	0.907578i	$0.362071\pi$
$662$		0			0
$663$	−0.276048	−	1.03023i	−0.0107208	−	0.0400106i
$664$		0			0
$665$	−45.9947	+	11.9507i	−1.78360	+	0.463427i
$666$		0			0
$667$	−5.33412	−	19.9072i	−0.206538	−	0.770810i
$668$		0			0
$669$	0.0675982	−	0.0390278i	0.00261350	−	0.00150890i
$670$		0			0
$671$		−	7.14202i		−	0.275715i
$672$		0			0
$673$	17.1639	+	17.1639i	0.661620	+	0.661620i	0.955762	−	0.294142i	$-0.0950339\pi$
$673$	17.1639	+	17.1639i	0.661620	+	0.661620i	−0.294142	+	0.955762i	$0.595034\pi$
$674$		0			0
$675$	0.186683	−	3.72137i	0.00718542	−	0.143236i
$676$		0			0
$677$	8.72528	−	2.33793i	0.335340	−	0.0898540i	−0.0872200	−	0.996189i	$-0.527798\pi$
$677$	8.72528	−	2.33793i	0.335340	−	0.0898540i	0.422560	+	0.906335i	$0.361132\pi$
$678$		0			0
$679$	7.64550	+	17.5827i	0.293407	+	0.674764i
$680$		0			0
$681$	−1.33411	+	2.31075i	−0.0511234	+	0.0885483i
$682$		0			0
$683$	−6.53495	+	24.3888i	−0.250053	+	0.933211i	0.720723	+	0.693223i	$0.243810\pi$
$683$	−6.53495	+	24.3888i	−0.250053	+	0.933211i	−0.970776	+	0.239987i	$0.922857\pi$
$684$		0			0
$685$	11.1032	+	8.97069i	0.424233	+	0.342752i
$686$		0			0
$687$	0.653520	−	0.653520i	0.0249333	−	0.0249333i
$688$		0			0
$689$	−15.7400	−	27.2625i	−0.599646	−	1.03862i
$690$		0			0
$691$	−19.9794	−	11.5351i	−0.760051	−	0.438815i	0.0692633	−	0.997598i	$-0.477935\pi$
$691$	−19.9794	−	11.5351i	−0.760051	−	0.438815i	−0.829314	+	0.558783i	$0.811268\pi$
$692$		0			0
$693$	8.15717	−	20.7091i	0.309865	−	0.786672i
$694$		0			0
$695$	2.03526	+	0.903430i	0.0772018	+	0.0342690i
$696$		0			0
$697$	16.8367	+	4.51137i	0.637734	+	0.170880i
$698$		0			0
$699$	−0.677116			−0.0256109
$700$		0			0
$701$	24.4288			0.922662			0.461331	−	0.887228i	$-0.347372\pi$
$701$	24.4288			0.922662			0.461331	+	0.887228i	$0.347372\pi$
$702$		0			0
$703$	56.1716	+	15.0511i	2.11855	+	0.567664i
$704$		0			0
$705$	0.992495	+	0.440558i	0.0373795	+	0.0165924i
$706$		0			0
$707$	−15.1167	+	2.25943i	−0.568523	+	0.0849747i
$708$		0			0
$709$	−24.1321	−	13.9327i	−0.906298	−	0.523252i	−0.0270602	−	0.999634i	$-0.508615\pi$
$709$	−24.1321	−	13.9327i	−0.906298	−	0.523252i	−0.879238	+	0.476382i	$0.841948\pi$
$710$		0			0
$711$	9.51315	+	16.4773i	0.356771	+	0.617946i
$712$		0			0
$713$	−5.47782	+	5.47782i	−0.205146	+	0.205146i
$714$		0			0
$715$	22.7815	+	18.4059i	0.851979	+	0.688342i
$716$		0			0
$717$	−0.323924	+	1.20890i	−0.0120972	+	0.0451472i
$718$		0			0
$719$	16.7674	−	29.0420i	0.625318	−	1.08308i	−0.363161	−	0.931726i	$-0.618303\pi$
$719$	16.7674	−	29.0420i	0.625318	−	1.08308i	0.988479	−	0.151356i	$-0.0483641\pi$
$720$		0			0
$721$	1.45940	−	12.8106i	0.0543509	−	0.477093i
$722$		0			0
$723$	2.49590	−	0.668774i	0.0928234	−	0.0248720i
$724$		0			0
$725$	32.0331	−	28.9727i	1.18968	−	1.07602i
$726$		0			0
$727$	−27.1571	−	27.1571i	−1.00720	−	1.00720i	−0.999974	−	0.00722682i	$-0.997700\pi$
$727$	−27.1571	−	27.1571i	−1.00720	−	1.00720i	−0.00722682	−	0.999974i	$-0.502300\pi$
$728$		0			0
$729$		−	26.1663i		−	0.969121i
$730$		0			0
$731$	2.35126	−	1.35750i	0.0869647	−	0.0502091i
$732$		0			0
$733$	−7.67522	−	28.6443i	−0.283491	−	1.05800i	−0.949935	−	0.312447i	$-0.898851\pi$
$733$	−7.67522	−	28.6443i	−0.283491	−	1.05800i	0.666445	−	0.745555i	$-0.267815\pi$
$734$		0			0
$735$	−0.273477	−	1.92982i	−0.0100874	−	0.0711825i
$736$		0			0
$737$	−10.4734	−	39.0873i	−0.385794	−	1.43980i
$738$		0			0
$739$	−3.47223	+	2.00470i	−0.127728	+	0.0737439i	−0.562503	−	0.826795i	$-0.690161\pi$
$739$	−3.47223	+	2.00470i	−0.127728	+	0.0737439i	0.434775	+	0.900539i	$0.356828\pi$
$740$		0			0
$741$			4.64785i			0.170743i
$742$		0			0
$743$	0.177216	+	0.177216i	0.00650141	+	0.00650141i	0.710350	−	0.703849i	$-0.248537\pi$
$743$	0.177216	+	0.177216i	0.00650141	+	0.00650141i	−0.703849	+	0.710350i	$0.748537\pi$
$744$		0			0
$745$	4.50101	+	6.18056i	0.164904	+	0.226438i
$746$		0			0
$747$	−30.2261	+	8.09905i	−1.10591	+	0.296329i
$748$		0			0
$749$	−5.03390	+	44.1877i	−0.183935	+	1.61458i
$750$		0			0
$751$	−19.7200	+	34.1561i	−0.719594	+	1.24637i	0.241567	+	0.970384i	$0.422339\pi$
$751$	−19.7200	+	34.1561i	−0.719594	+	1.24637i	−0.961161	+	0.275989i	$0.910995\pi$
$752$		0			0
$753$	−0.00127720	+	0.00476656i	−4.65436e−5	+	0.000173703i
$754$		0			0
$755$	4.62751	+	43.5591i	0.168412	+	1.58528i
$756$		0			0
$757$	−24.2463	+	24.2463i	−0.881247	+	0.881247i	−0.993661	−	0.112414i	$-0.964142\pi$
$757$	−24.2463	+	24.2463i	−0.881247	+	0.881247i	0.112414	+	0.993661i	$0.464142\pi$
$758$		0			0
$759$	−0.418713	−	0.725231i	−0.0151983	−	0.0263242i
$760$		0			0
$761$	17.9497	+	10.3633i	0.650678	+	0.375669i	0.788716	−	0.614758i	$-0.210746\pi$
$761$	17.9497	+	10.3633i	0.650678	+	0.375669i	−0.138038	+	0.990427i	$0.544080\pi$
$762$		0			0
$763$	24.3169	−	3.63455i	0.880331	−	0.131579i
$764$		0			0
$765$	11.4793	−	4.42124i	0.415036	−	0.159850i
$766$		0			0
$767$	−55.6313	−	14.9064i	−2.00873	−	0.538237i
$768$		0			0
$769$	17.6819			0.637626			0.318813	−	0.947818i	$-0.396716\pi$
$769$	17.6819			0.637626			0.318813	+	0.947818i	$0.396716\pi$
$770$		0			0
$771$	2.11860			0.0762993
$772$		0			0
$773$	−25.5524	−	6.84675i	−0.919057	−	0.246261i	−0.231875	−	0.972746i	$-0.574486\pi$
$773$	−25.5524	−	6.84675i	−0.919057	−	0.246261i	−0.687182	+	0.726485i	$0.741153\pi$
$774$		0			0
$775$	−15.4518	−	4.98241i	−0.555045	−	0.178973i
$776$		0			0
$777$	−0.874124	+	2.21919i	−0.0313590	+	0.0796129i
$778$		0			0
$779$	−65.7820	−	37.9793i	−2.35689	−	1.36075i
$780$		0			0
$781$	−3.84560	−	6.66077i	−0.137606	−	0.238341i
$782$		0			0
$783$	−4.55194	+	4.55194i	−0.162673	+	0.162673i
$784$		0			0
$785$	6.67643	−	8.26358i	0.238292	−	0.294940i
$786$		0			0
$787$	−4.60079	+	17.1704i	−0.164001	+	0.612059i	0.834165	+	0.551515i	$0.185950\pi$
$787$	−4.60079	+	17.1704i	−0.164001	+	0.612059i	−0.998166	+	0.0605435i	$0.980717\pi$
$788$		0			0
$789$	−0.455477	+	0.788909i	−0.0162154	+	0.0280859i
$790$		0			0
$791$	7.78525	+	17.9041i	0.276811	+	0.636598i
$792$		0			0
$793$	11.3722	−	3.04718i	0.403840	−	0.108209i
$794$		0			0
$795$	−1.52488	+	1.11049i	−0.0540818	+	0.0393852i
$796$		0			0
$797$	−21.2435	−	21.2435i	−0.752485	−	0.752485i	0.222457	−	0.974942i	$-0.428592\pi$
$797$	−21.2435	−	21.2435i	−0.752485	−	0.752485i	−0.974942	+	0.222457i	$0.928592\pi$
$798$		0			0
$799$			7.18855i			0.254313i
$800$		0			0
$801$	2.52069	−	1.45532i	0.0890643	−	0.0514213i
$802$		0			0
$803$	−2.94712	−	10.9988i	−0.104002	−	0.388139i
$804$		0			0
$805$	12.1696	+	7.14991i	0.428924	+	0.252001i
$806$		0			0
$807$	−0.209400	−	0.781493i	−0.00737125	−	0.0275099i
$808$		0			0
$809$	36.5682	−	21.1126i	1.28567	−	0.742281i	0.307790	−	0.951454i	$-0.400411\pi$
$809$	36.5682	−	21.1126i	1.28567	−	0.742281i	0.977879	+	0.209173i	$0.0670773\pi$
$810$		0			0
$811$		−	30.9818i		−	1.08792i	−0.839112	−	0.543959i	$-0.816925\pi$
$811$		−	30.9818i		−	1.08792i	0.839112	−	0.543959i	$-0.183075\pi$
$812$		0			0
$813$	1.83084	+	1.83084i	0.0642103	+	0.0642103i
$814$		0			0
$815$	−2.99606	−	0.471095i	−0.104947	−	0.0165017i
$816$		0			0
$817$	−11.4282	+	3.06218i	−0.399823	+	0.107132i
$818$		0			0
$819$	36.4553	+	4.15302i	1.27385	+	0.145118i
$820$		0			0
$821$	18.4155	−	31.8965i	0.642704	−	1.11320i	−0.342122	−	0.939655i	$-0.611146\pi$
$821$	18.4155	−	31.8965i	0.642704	−	1.11320i	0.984827	−	0.173541i	$-0.0555209\pi$
$822$		0			0
$823$	9.31758	−	34.7737i	0.324791	−	1.21213i	−0.589732	−	0.807599i	$-0.700767\pi$
$823$	9.31758	−	34.7737i	0.324791	−	1.21213i	0.914522	−	0.404535i	$-0.132567\pi$
$824$		0			0
$825$	0.952557	−	1.47402i	0.0331638	−	0.0513187i
$826$		0			0
$827$	15.1281	−	15.1281i	0.526056	−	0.526056i	−0.393338	−	0.919394i	$-0.628680\pi$
$827$	15.1281	−	15.1281i	0.526056	−	0.526056i	0.919394	+	0.393338i	$0.128680\pi$
$828$		0			0
$829$	−24.7248	−	42.8245i	−0.858726	−	1.48736i	−0.873144	−	0.487462i	$-0.837923\pi$
$829$	−24.7248	−	42.8245i	−0.858726	−	1.48736i	0.0144178	−	0.999896i	$-0.495411\pi$
$830$		0			0
$831$	2.96986	+	1.71465i	0.103023	+	0.0594805i
$832$		0			0
$833$	10.9422	−	6.83792i	0.379126	−	0.236920i
$834$		0			0
$835$	−4.99159	−	12.9602i	−0.172741	−	0.448506i
$836$		0			0
$837$	2.33728	+	0.626273i	0.0807883	+	0.0216472i
$838$		0			0
$839$	−20.4290			−0.705286			−0.352643	−	0.935758i	$-0.614717\pi$
$839$	−20.4290			−0.705286			−0.352643	+	0.935758i	$0.614717\pi$
$840$		0			0
$841$	−45.6216			−1.57316
$842$		0			0
$843$	2.77471	+	0.743481i	0.0955660	+	0.0256068i
$844$		0			0
$845$	−7.79422	+	17.5589i	−0.268129	+	0.604045i
$846$		0			0
$847$	−6.32456	+	5.03093i	−0.217315	+	0.172865i
$848$		0			0
$849$	−3.00889	−	1.73719i	−0.103265	−	0.0596201i
$850$		0			0
$851$	−8.63609	−	14.9581i	−0.296041	−	0.512759i
$852$		0			0
$853$	2.07657	−	2.07657i	0.0711005	−	0.0711005i	−0.670662	−	0.741763i	$-0.733990\pi$
$853$	2.07657	−	2.07657i	0.0711005	−	0.0711005i	0.741763	+	0.670662i	$0.233990\pi$
$854$		0			0
$855$	−53.3063	+	5.66301i	−1.82304	+	0.193671i
$856$		0			0
$857$	10.3110	−	38.4814i	0.352219	−	1.31450i	−0.531730	−	0.846914i	$-0.678458\pi$
$857$	10.3110	−	38.4814i	0.352219	−	1.31450i	0.883949	−	0.467584i	$-0.154876\pi$
$858$		0			0
$859$	−23.1562	+	40.1078i	−0.790081	+	1.36846i	0.135836	+	0.990731i	$0.456628\pi$
$859$	−23.1562	+	40.1078i	−0.790081	+	1.36846i	−0.925916	+	0.377728i	$0.876705\pi$
$860$		0			0
$861$	1.85309	−	2.50438i	0.0631531	−	0.0853491i
$862$		0			0
$863$	25.7695	−	6.90492i	0.877204	−	0.235046i	0.208004	−	0.978128i	$-0.433303\pi$
$863$	25.7695	−	6.90492i	0.877204	−	0.235046i	0.669201	+	0.743082i	$0.266637\pi$
$864$		0			0
$865$	−3.31217	+	21.0647i	−0.112617	+	0.716220i
$866$		0			0
$867$	1.19770	+	1.19770i	0.0406759	+	0.0406759i
$868$		0			0
$869$			17.9698i			0.609585i
$870$		0			0
$871$	57.7702	−	33.3536i	1.95747	−	1.13014i
$872$		0			0
$873$	5.59770	+	20.8909i	0.189453	+	0.707050i
$874$		0			0
$875$	−1.70633	+	29.5311i	−0.0576846	+	0.998335i
$876$		0			0
$877$	3.21228	+	11.9884i	0.108471	+	0.404819i	0.998716	−	0.0506634i	$-0.0161336\pi$
$877$	3.21228	+	11.9884i	0.108471	+	0.404819i	−0.890245	+	0.455482i	$0.849467\pi$
$878$		0			0
$879$	−1.12521	+	0.649641i	−0.0379524	+	0.0219118i
$880$		0			0
$881$			4.12556i			0.138994i	0.997582	+	0.0694968i	$0.0221394\pi$
$881$			4.12556i			0.138994i	−0.997582	+	0.0694968i	$0.977861\pi$
$882$		0			0
$883$	8.53349	+	8.53349i	0.287175	+	0.287175i	0.835962	−	0.548787i	$-0.184910\pi$
$883$	8.53349	+	8.53349i	0.287175	+	0.287175i	−0.548787	+	0.835962i	$0.684910\pi$
$884$		0			0
$885$	−0.536075	+	3.40932i	−0.0180200	+	0.114603i
$886$		0			0
$887$	−28.2358	+	7.56575i	−0.948064	+	0.254033i	−0.699541	−	0.714593i	$-0.746612\pi$
$887$	−28.2358	+	7.56575i	−0.948064	+	0.254033i	−0.248524	+	0.968626i	$0.579945\pi$
$888$		0			0
$889$	−27.0660	+	11.7691i	−0.907766	+	0.394724i
$890$		0			0
$891$	12.4881	−	21.6301i	0.418368	−	0.724635i
$892$		0			0
$893$	8.10778	−	30.2586i	0.271316	−	1.01257i
$894$		0			0
$895$	−29.4888	+	3.13275i	−0.985703	+	0.104716i
$896$		0			0
$897$	0.976139	−	0.976139i	0.0325923	−	0.0325923i
$898$		0			0
$899$	14.0246	+	24.2913i	0.467747	+	0.810161i
$900$		0			0
$901$	−10.8148	−	6.24395i	−0.360294	−	0.208016i
$902$		0			0
$903$	−0.0717331	−	0.479930i	−0.00238713	−	0.0159711i
$904$		0			0
$905$	9.84000	−	22.1677i	0.327093	−	0.736879i
$906$		0			0
$907$	32.6219	+	8.74101i	1.08319	+	0.290240i	0.755903	−	0.654684i	$-0.227198\pi$
$907$	32.6219	+	8.74101i	1.08319	+	0.290240i	0.327289	+	0.944924i	$0.393865\pi$
$908$		0			0
$909$	−17.2416			−0.571867
$910$		0			0
$911$	−48.6206			−1.61087			−0.805437	−	0.592682i	$-0.798069\pi$
$911$	−48.6206			−1.61087			−0.805437	+	0.592682i	$0.798069\pi$
$912$		0			0
$913$	−28.5477	−	7.64933i	−0.944791	−	0.253156i
$914$		0			0
$915$	−0.253565	−	0.658359i	−0.00838261	−	0.0217647i
$916$		0			0
$917$	8.74701	+	10.9962i	0.288852	+	0.363126i
$918$		0			0
$919$	−11.1514	−	6.43824i	−0.367849	−	0.212378i	0.304669	−	0.952458i	$-0.401454\pi$
$919$	−11.1514	−	6.43824i	−0.367849	−	0.212378i	−0.672518	+	0.740080i	$0.734787\pi$
$920$		0			0
$921$	0.436035	+	0.755234i	0.0143678	+	0.0248858i
$922$		0			0
$923$	8.96519	−	8.96519i	0.295093	−	0.295093i
$924$		0			0
$925$	19.6468	−	30.4021i	0.645983	−	0.999615i
$926$		0			0
$927$	3.76434	−	14.0487i	0.123637	−	0.461420i
$928$		0			0
$929$	2.45072	−	4.24477i	0.0804056	−	0.139267i	−0.823019	−	0.568014i	$-0.807712\pi$
$929$	2.45072	−	4.24477i	0.0804056	−	0.139267i	0.903424	+	0.428748i	$0.141045\pi$
$930$		0			0
$931$	−53.7713	+	16.4412i	−1.76228	+	0.538840i
$932$		0			0
$933$	−1.12293	+	0.300888i	−0.0367630	+	0.00985063i
$934$		0			0
$935$	11.4772	+	1.80466i	0.375346	+	0.0590187i
$936$		0			0
$937$	2.98269	+	2.98269i	0.0974401	+	0.0974401i	0.754146	−	0.656706i	$-0.228051\pi$
$937$	2.98269	+	2.98269i	0.0974401	+	0.0974401i	−0.656706	+	0.754146i	$0.728051\pi$
$938$		0			0
$939$		−	2.46534i		−	0.0804534i
$940$		0			0
$941$	−26.7673	+	15.4541i	−0.872589	+	0.503789i	−0.868208	−	0.496201i	$-0.834728\pi$
$941$	−26.7673	+	15.4541i	−0.872589	+	0.503789i	−0.00438099	+	0.999990i	$0.501395\pi$
$942$		0			0
$943$	5.83911	+	21.7919i	0.190148	+	0.709641i
$944$		0			0
$945$	0.0334782	−	4.40860i	0.00108905	−	0.143412i
$946$		0			0
$947$	−9.86991	−	36.8350i	−0.320729	−	1.19698i	−0.918536	−	0.395337i	$-0.870628\pi$
$947$	−9.86991	−	36.8350i	−0.320729	−	1.19698i	0.597808	−	0.801640i	$-0.296039\pi$
$948$		0			0
$949$	16.2560	−	9.38539i	0.527691	−	0.304663i
$950$		0			0
$951$			2.10428i			0.0682360i
$952$		0			0
$953$	1.90574	+	1.90574i	0.0617328	+	0.0617328i	0.737299	−	0.675566i	$-0.236101\pi$
$953$	1.90574	+	1.90574i	0.0617328	+	0.0617328i	−0.675566	+	0.737299i	$0.736101\pi$
$954$		0			0
$955$	5.51533	−	4.01656i	0.178472	−	0.129973i
$956$		0			0
$957$	−2.92879	+	0.784766i	−0.0946742	+	0.0253679i
$958$		0			0
$959$	13.5769	+	10.0461i	0.438422	+	0.324405i
$960$		0			0
$961$	−10.2283	+	17.7160i	−0.329947	+	0.571484i
$962$		0			0
$963$	−12.9843	+	48.4581i	−0.418414	+	1.56154i
$964$		0			0
$965$	33.0975	−	40.9656i	1.06545	−	1.31873i
$966$		0			0
$967$	29.7649	−	29.7649i	0.957175	−	0.957175i	−0.0419452	−	0.999120i	$-0.513356\pi$
$967$	29.7649	−	29.7649i	0.957175	−	0.957175i	0.999120	+	0.0419452i	$0.0133555\pi$
$968$		0			0
$969$	0.921886	+	1.59675i	0.0296153	+	0.0512951i
$970$		0			0
$971$	−2.90731	−	1.67854i	−0.0933001	−	0.0538669i	0.452624	−	0.891701i	$-0.350488\pi$
$971$	−2.90731	−	1.67854i	−0.0933001	−	0.0538669i	−0.545924	+	0.837835i	$0.683821\pi$
$972$		0			0
$973$	2.45142	+	0.965600i	0.0785890	+	0.0309557i
$974$		0			0
$975$	2.75349	+	0.887858i	0.0881822	+	0.0284342i
$976$		0			0
$977$	35.1564	+	9.42013i	1.12475	+	0.301377i	0.772805	−	0.634643i	$-0.218853\pi$
$977$	35.1564	+	9.42013i	1.12475	+	0.301377i	0.351948	+	0.936020i	$0.385519\pi$
$978$		0			0
$979$	2.74903			0.0878592
$980$		0			0
$981$	27.7350			0.885509
$982$		0			0
$983$	−47.8111	−	12.8109i	−1.52494	−	0.408605i	−0.603573	−	0.797308i	$-0.706257\pi$
$983$	−47.8111	−	12.8109i	−1.52494	−	0.408605i	−0.921363	+	0.388702i	$0.872923\pi$
$984$		0			0
$985$	−5.45662	+	2.10161i	−0.173863	+	0.0669628i
$986$		0			0
$987$	1.19544	+	0.470875i	0.0380512	+	0.0149881i
$988$		0			0
$989$	3.04326	+	1.75703i	0.0967702	+	0.0558703i
$990$		0			0
$991$	21.8876	+	37.9104i	0.695282	+	1.20426i	0.970086	+	0.242763i	$0.0780537\pi$
$991$	21.8876	+	37.9104i	0.695282	+	1.20426i	−0.274804	+	0.961500i	$0.588613\pi$
$992$		0			0
$993$	0.875386	−	0.875386i	0.0277795	−	0.0277795i
$994$		0			0
$995$	−0.146603	−	1.37999i	−0.00464764	−	0.0437486i
$996$		0			0
$997$	12.0722	−	45.0542i	0.382332	−	1.42688i	−0.459998	−	0.887920i	$-0.652150\pi$
$997$	12.0722	−	45.0542i	0.382332	−	1.42688i	0.842330	−	0.538962i	$-0.181183\pi$
$998$		0			0
$999$	−2.69750	+	4.67221i	−0.0853452	+	0.147822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.33.7	yes	48
4.3	odd	2		560.2.ci.e.33.6		48
5.2	odd	4	inner	280.2.bo.a.257.7	yes	48
7.3	odd	6	inner	280.2.bo.a.73.7	yes	48
20.7	even	4		560.2.ci.e.257.6		48
28.3	even	6		560.2.ci.e.353.6		48
35.17	even	12	inner	280.2.bo.a.17.7	✓	48
140.87	odd	12		560.2.ci.e.17.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.7	✓	48	35.17	even	12	inner
280.2.bo.a.33.7	yes	48	1.1	even	1	trivial
280.2.bo.a.73.7	yes	48	7.3	odd	6	inner
280.2.bo.a.257.7	yes	48	5.2	odd	4	inner
560.2.ci.e.17.6		48	140.87	odd	12
560.2.ci.e.33.6		48	4.3	odd	2
560.2.ci.e.257.6		48	20.7	even	4
560.2.ci.e.353.6		48	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.120281 + 0.0322291i) q^{3} +(-2.04377 - 0.907205i) q^{5} +(-2.46167 - 0.969635i) q^{7} +(-2.58465 - 1.49225i) q^{9} +O(q^{10})\)	\(q+(0.120281 + 0.0322291i) q^{3} +(-2.04377 - 0.907205i) q^{5} +(-2.46167 - 0.969635i) q^{7} +(-2.58465 - 1.49225i) q^{9} +(-1.40939 - 2.44113i) q^{11} +(3.28569 - 3.28569i) q^{13} +(-0.216587 - 0.174988i) q^{15} +(0.477081 - 1.78049i) q^{17} +(-4.01634 + 6.95650i) q^{19} +(-0.264840 - 0.195966i) q^{21} +(2.30451 - 0.617491i) q^{23} +(3.35396 + 3.70823i) q^{25} +(-0.526943 - 0.526943i) q^{27} -8.63838i q^{29} +(-2.81202 + 1.62352i) q^{31} +(-0.0908465 - 0.339044i) q^{33} +(4.15141 + 4.21495i) q^{35} +(-1.87374 - 6.99289i) q^{37} +(0.501099 - 0.289309i) q^{39} +9.45620i q^{41} +(1.04150 + 1.04150i) q^{43} +(3.92864 + 5.39461i) q^{45} +(-3.76695 + 1.00935i) q^{47} +(5.11961 + 4.77384i) q^{49} +(0.114767 - 0.198782i) q^{51} +(1.75344 - 6.54391i) q^{53} +(0.665850 + 6.26770i) q^{55} +(-0.707288 + 0.707288i) q^{57} +(-6.19733 - 10.7341i) q^{59} +(2.19428 + 1.26687i) q^{61} +(4.91561 + 6.17958i) q^{63} +(-9.69596 + 3.73438i) q^{65} +(13.8668 + 3.71560i) q^{67} +0.297088 q^{69} +2.72856 q^{71} +(3.90198 + 1.04553i) q^{73} +(0.283903 + 0.554123i) q^{75} +(1.10244 + 7.37584i) q^{77} +(-5.52096 - 3.18753i) q^{79} +(4.43034 + 7.67358i) q^{81} +(7.41399 - 7.41399i) q^{83} +(-2.59031 + 3.20609i) q^{85} +(0.278407 - 1.03903i) q^{87} +(-0.487628 + 0.844596i) q^{89} +(-11.2742 + 4.90235i) q^{91} +(-0.390556 + 0.104649i) q^{93} +(14.5194 - 10.5738i) q^{95} +(-5.12422 - 5.12422i) q^{97} +8.41261i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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