LMFDB - Embedded newform 1152.2.p.g.959.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (of order $6$, degree $2$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			959.6
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.g.191.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0745691 - 1.73044i) q^{3} +(-2.11539 + 3.66397i) q^{5} +(3.25610 - 1.87991i) q^{7} +(-2.98888 + 0.258075i) q^{9} +O(q^{10})$	\(q+(-0.0745691 - 1.73044i) q^{3} +(-2.11539 + 3.66397i) q^{5} +(3.25610 - 1.87991i) q^{7} +(-2.98888 + 0.258075i) q^{9} +(0.424849 - 0.245287i) q^{11} +(1.78994 + 1.03342i) q^{13} +(6.49804 + 3.38735i) q^{15} +4.97653i q^{17} -6.32985 q^{19} +(-3.49588 - 5.49431i) q^{21} +(-0.0297041 + 0.0514489i) q^{23} +(-6.44977 - 11.1713i) q^{25} +(0.669463 + 5.15285i) q^{27} +(2.80785 + 4.86334i) q^{29} +(0.546572 + 0.315564i) q^{31} +(-0.456136 - 0.716887i) q^{33} +15.9070i q^{35} +6.74445i q^{37} +(1.65481 - 3.17446i) q^{39} +(4.44850 + 2.56834i) q^{41} +(4.35237 + 7.53853i) q^{43} +(5.37707 - 11.4971i) q^{45} +(4.58126 + 7.93498i) q^{47} +(3.56812 - 6.18016i) q^{49} +(8.61161 - 0.371095i) q^{51} -1.32172 q^{53} +2.07551i q^{55} +(0.472011 + 10.9535i) q^{57} +(-6.67923 - 3.85625i) q^{59} +(2.56940 - 1.48344i) q^{61} +(-9.24692 + 6.45914i) q^{63} +(-7.57287 + 4.37220i) q^{65} +(-2.07388 + 3.59207i) q^{67} +(0.0912445 + 0.0475647i) q^{69} -4.06938 q^{71} +8.03627 q^{73} +(-18.8504 + 11.9940i) q^{75} +(0.922234 - 1.59736i) q^{77} +(-0.601308 + 0.347165i) q^{79} +(8.86679 - 1.54271i) q^{81} +(8.46391 - 4.88664i) q^{83} +(-18.2338 - 10.5273i) q^{85} +(8.20637 - 5.22149i) q^{87} +6.19792i q^{89} +7.77098 q^{91} +(0.505308 - 0.969344i) q^{93} +(13.3901 - 23.1924i) q^{95} +(-0.864785 - 1.49785i) q^{97} +(-1.20652 + 0.842776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{7} - 4 q^{9}+O(q^{10}) $ 24 * q + 12 * q^7 - 4 * q^9	$ 24 q + 12 q^{7} - 4 q^{9} + 20 q^{15} - 12 q^{23} - 12 q^{25} - 36 q^{31} + 4 q^{33} + 20 q^{39} - 12 q^{41} + 12 q^{47} + 12 q^{49} + 4 q^{57} - 92 q^{63} - 48 q^{65} + 24 q^{73} + 84 q^{79} - 20 q^{81} + 68 q^{87} + 24 q^{95} - 12 q^{97}+O(q^{100}) $ 24 * q + 12 * q^7 - 4 * q^9 + 20 * q^15 - 12 * q^23 - 12 * q^25 - 36 * q^31 + 4 * q^33 + 20 * q^39 - 12 * q^41 + 12 * q^47 + 12 * q^49 + 4 * q^57 - 92 * q^63 - 48 * q^65 + 24 * q^73 + 84 * q^79 - 20 * q^81 + 68 * q^87 + 24 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−0.0745691	−	1.73044i	−0.0430525	−	0.999073i
$3$	−0.0745691	−	1.73044i	−0.0430525	−	0.999073i
$4$		0			0
$5$	−2.11539	+	3.66397i	−0.946032	+	1.63858i	−0.192361	+	0.981324i	$0.561614\pi$
$5$	−2.11539	+	3.66397i	−0.946032	+	1.63858i	−0.753671	+	0.657252i	$0.771719\pi$
$6$		0			0
$7$	3.25610	−	1.87991i	1.23069	−	0.710539i	0.263516	−	0.964655i	$-0.415118\pi$
$7$	3.25610	−	1.87991i	1.23069	−	0.710539i	0.967174	+	0.254116i	$0.0817846\pi$
$8$		0			0
$9$	−2.98888	+	0.258075i	−0.996293	+	0.0860251i
$10$		0			0
$11$	0.424849	−	0.245287i	0.128097	−	0.0739567i	−0.434582	−	0.900632i	$-0.643104\pi$
$11$	0.424849	−	0.245287i	0.128097	−	0.0739567i	0.562679	+	0.826675i	$0.309771\pi$
$12$		0			0
$13$	1.78994	+	1.03342i	0.496441	+	0.286620i	0.727243	−	0.686380i	$-0.240801\pi$
$13$	1.78994	+	1.03342i	0.496441	+	0.286620i	−0.230801	+	0.973001i	$0.574135\pi$
$14$		0			0
$15$	6.49804	+	3.38735i	1.67779	+	0.874610i
$16$		0			0
$17$			4.97653i			1.20699i	0.797368	+	0.603493i	$0.206225\pi$
$17$			4.97653i			1.20699i	−0.797368	+	0.603493i	$0.793775\pi$
$18$		0			0
$19$	−6.32985			−1.45217			−0.726083	−	0.687607i	$-0.758661\pi$
$19$	−6.32985			−1.45217			−0.726083	+	0.687607i	$0.758661\pi$
$20$		0			0
$21$	−3.49588	−	5.49431i	−0.762864	−	1.19896i
$22$		0			0
$23$	−0.0297041	+	0.0514489i	−0.00619372	+	0.0107278i	−0.869106	−	0.494626i	$-0.835305\pi$
$23$	−0.0297041	+	0.0514489i	−0.00619372	+	0.0107278i	0.862912	+	0.505354i	$0.168638\pi$
$24$		0			0
$25$	−6.44977	−	11.1713i	−1.28995	−	2.23427i
$26$		0			0
$27$	0.669463	+	5.15285i	0.128838	+	0.991666i
$28$		0			0
$29$	2.80785	+	4.86334i	0.521405	+	0.903100i	0.999690	+	0.0248955i	$0.00792529\pi$
$29$	2.80785	+	4.86334i	0.521405	+	0.903100i	−0.478285	+	0.878205i	$0.658741\pi$
$30$		0			0
$31$	0.546572	+	0.315564i	0.0981673	+	0.0566769i	0.548280	−	0.836295i	$-0.315283\pi$
$31$	0.546572	+	0.315564i	0.0981673	+	0.0566769i	−0.450113	+	0.892972i	$0.648616\pi$
$32$		0			0
$33$	−0.456136	−	0.716887i	−0.0794031	−	0.124794i
$34$		0			0
$35$			15.9070i			2.68877i
$36$		0			0
$37$			6.74445i			1.10878i	0.832257	+	0.554391i	$0.187049\pi$
$37$			6.74445i			1.10878i	−0.832257	+	0.554391i	$0.812951\pi$
$38$		0			0
$39$	1.65481	−	3.17446i	0.264982	−	0.508321i
$40$		0			0
$41$	4.44850	+	2.56834i	0.694739	+	0.401108i	0.805385	−	0.592752i	$-0.201959\pi$
$41$	4.44850	+	2.56834i	0.694739	+	0.401108i	−0.110646	+	0.993860i	$0.535292\pi$
$42$		0			0
$43$	4.35237	+	7.53853i	0.663731	+	1.14962i	0.979628	+	0.200822i	$0.0643612\pi$
$43$	4.35237	+	7.53853i	0.663731	+	1.14962i	−0.315897	+	0.948793i	$0.602305\pi$
$44$		0			0
$45$	5.37707	−	11.4971i	0.801567	−	1.71388i
$46$		0			0
$47$	4.58126	+	7.93498i	0.668246	+	1.15744i	0.978394	+	0.206748i	$0.0662879\pi$
$47$	4.58126	+	7.93498i	0.668246	+	1.15744i	−0.310149	+	0.950688i	$0.600379\pi$
$48$		0			0
$49$	3.56812	−	6.18016i	0.509731	−	0.882880i
$50$		0			0
$51$	8.61161	−	0.371095i	1.20587	−	0.0519637i
$52$		0			0
$53$	−1.32172			−0.181552			−0.0907759	−	0.995871i	$-0.528935\pi$
$53$	−1.32172			−0.181552			−0.0907759	+	0.995871i	$0.528935\pi$
$54$		0			0
$55$			2.07551i			0.279862i
$56$		0			0
$57$	0.472011	+	10.9535i	0.0625194	+	1.45082i
$58$		0			0
$59$	−6.67923	−	3.85625i	−0.869561	−	0.502041i	−0.00235881	−	0.999997i	$-0.500751\pi$
$59$	−6.67923	−	3.85625i	−0.869561	−	0.502041i	−0.867202	+	0.497956i	$0.834084\pi$
$60$		0			0
$61$	2.56940	−	1.48344i	0.328978	−	0.189935i	−0.326409	−	0.945229i	$-0.605839\pi$
$61$	2.56940	−	1.48344i	0.328978	−	0.189935i	0.655387	+	0.755293i	$0.272505\pi$
$62$		0			0
$63$	−9.24692	+	6.45914i	−1.16500	+	0.813775i
$64$		0			0
$65$	−7.57287	+	4.37220i	−0.939299	+	0.542304i
$66$		0			0
$67$	−2.07388	+	3.59207i	−0.253365	+	0.438842i	−0.964450	−	0.264265i	$-0.914871\pi$
$67$	−2.07388	+	3.59207i	−0.253365	+	0.438842i	0.711085	+	0.703106i	$0.248204\pi$
$68$		0			0
$69$	0.0912445	+	0.0475647i	0.0109846	+	0.00572612i
$70$		0			0
$71$	−4.06938			−0.482947			−0.241473	−	0.970407i	$-0.577631\pi$
$71$	−4.06938			−0.482947			−0.241473	+	0.970407i	$0.577631\pi$
$72$		0			0
$73$	8.03627			0.940574			0.470287	−	0.882514i	$-0.344150\pi$
$73$	8.03627			0.940574			0.470287	+	0.882514i	$0.344150\pi$
$74$		0			0
$75$	−18.8504	+	11.9940i	−2.17666	+	1.38495i
$76$		0			0
$77$	0.922234	−	1.59736i	0.105098	−	0.182036i
$78$		0			0
$79$	−0.601308	+	0.347165i	−0.0676524	+	0.0390591i	−0.533445	−	0.845835i	$-0.679103\pi$
$79$	−0.601308	+	0.347165i	−0.0676524	+	0.0390591i	0.465792	+	0.884894i	$0.345769\pi$
$80$		0			0
$81$	8.86679	−	1.54271i	0.985199	−	0.171412i
$82$		0			0
$83$	8.46391	−	4.88664i	0.929035	−	0.536378i	0.0425285	−	0.999095i	$-0.486459\pi$
$83$	8.46391	−	4.88664i	0.929035	−	0.536378i	0.886506	+	0.462717i	$0.153125\pi$
$84$		0			0
$85$	−18.2338	−	10.5273i	−1.97774	−	1.14185i
$86$		0			0
$87$	8.20637	−	5.22149i	0.879815	−	0.559802i
$88$		0			0
$89$			6.19792i			0.656978i	0.944508	+	0.328489i	$0.106539\pi$
$89$			6.19792i			0.656978i	−0.944508	+	0.328489i	$0.893461\pi$
$90$		0			0
$91$	7.77098			0.814620
$92$		0			0
$93$	0.505308	−	0.969344i	0.0523980	−	0.100516i
$94$		0			0
$95$	13.3901	−	23.1924i	1.37380	−	2.37949i
$96$		0			0
$97$	−0.864785	−	1.49785i	−0.0878057	−	0.152084i	0.818778	−	0.574111i	$-0.194652\pi$
$97$	−0.864785	−	1.49785i	−0.0878057	−	0.152084i	−0.906583	+	0.422027i	$0.861319\pi$
$98$		0			0
$99$	−1.20652	+	0.842776i	−0.121260	+	0.0847021i
$100$		0			0
$101$	5.24408	+	9.08302i	0.521806	+	0.903794i	0.999678	+	0.0253649i	$0.00807476\pi$
$101$	5.24408	+	9.08302i	0.521806	+	0.903794i	−0.477873	+	0.878429i	$0.658592\pi$
$102$		0			0
$103$	11.4545	+	6.61326i	1.12865	+	0.651624i	0.943594	−	0.331105i	$-0.107421\pi$
$103$	11.4545	+	6.61326i	1.12865	+	0.651624i	0.185052	+	0.982729i	$0.440755\pi$
$104$		0			0
$105$	27.5262	−	1.18617i	2.68628	−	0.115758i
$106$		0			0
$107$		−	8.31329i		−	0.803676i	−0.915711	−	0.401838i	$-0.868372\pi$
$107$		−	8.31329i		−	0.803676i	0.915711	−	0.401838i	$-0.131628\pi$
$108$		0			0
$109$			3.88212i			0.371840i	0.982565	+	0.185920i	$0.0595265\pi$
$109$			3.88212i			0.371840i	−0.982565	+	0.185920i	$0.940473\pi$
$110$		0			0
$111$	11.6709	−	0.502928i	1.10775	−	0.0477358i
$112$		0			0
$113$	−9.53325	−	5.50402i	−0.896813	−	0.517775i	−0.0206478	−	0.999787i	$-0.506573\pi$
$113$	−9.53325	−	5.50402i	−0.896813	−	0.517775i	−0.876165	+	0.482012i	$0.839906\pi$
$114$		0			0
$115$	−0.125671	−	0.217669i	−0.0117189	−	0.0202978i
$116$		0			0
$117$	−5.61663	−	2.62684i	−0.519257	−	0.242852i
$118$		0			0
$119$	9.35542	+	16.2041i	0.857610	+	1.48542i
$120$		0			0
$121$	−5.37967	+	9.31786i	−0.489061	+	0.847078i
$122$		0			0
$123$	4.11266	−	7.88941i	0.370826	−	0.711364i
$124$		0			0
$125$	33.4212			2.98929
$126$		0			0
$127$			10.4394i			0.926348i	0.886267	+	0.463174i	$0.153289\pi$
$127$			10.4394i			0.926348i	−0.886267	+	0.463174i	$0.846711\pi$
$128$		0			0
$129$	12.7205	−	8.09368i	1.11997	−	0.712609i
$130$		0			0
$131$	−11.9280	−	6.88664i	−1.04216	−	0.601689i	−0.121712	−	0.992565i	$-0.538838\pi$
$131$	−11.9280	−	6.88664i	−1.04216	−	0.601689i	−0.920443	+	0.390877i	$0.872172\pi$
$132$		0			0
$133$	−20.6106	+	11.8995i	−1.78717	+	1.03182i
$134$		0			0
$135$	−20.2960	−	8.44740i	−1.74680	−	0.727036i
$136$		0			0
$137$	−13.8978	+	8.02389i	−1.18737	+	0.685527i	−0.957707	−	0.287744i	$-0.907095\pi$
$137$	−13.8978	+	8.02389i	−1.18737	+	0.685527i	−0.229660	+	0.973271i	$0.573762\pi$
$138$		0			0
$139$	5.07456	−	8.78940i	0.430419	−	0.745507i	−0.566490	−	0.824068i	$-0.691699\pi$
$139$	5.07456	−	8.78940i	0.430419	−	0.745507i	0.996909	+	0.0785609i	$0.0250325\pi$
$140$		0			0
$141$	13.3894	−	8.51933i	1.12759	−	0.717457i
$142$		0			0
$143$	1.01394			0.0847901
$144$		0			0
$145$	−23.7588			−1.97306
$146$		0			0
$147$	−10.9605	−	5.71358i	−0.904006	−	0.471248i
$148$		0			0
$149$	4.26774	−	7.39194i	0.349627	−	0.605571i	−0.636556	−	0.771230i	$-0.719642\pi$
$149$	4.26774	−	7.39194i	0.349627	−	0.605571i	0.986183	+	0.165659i	$0.0529750\pi$
$150$		0			0
$151$	10.8930	−	6.28906i	0.886458	−	0.511797i	0.0136755	−	0.999906i	$-0.495647\pi$
$151$	10.8930	−	6.28906i	0.886458	−	0.511797i	0.872782	+	0.488110i	$0.162313\pi$
$152$		0			0
$153$	−1.28432	−	14.8742i	−0.103831	−	1.20251i
$154$		0			0
$155$	−2.31243	+	1.33508i	−0.185739	+	0.107236i
$156$		0			0
$157$	−18.1433	−	10.4750i	−1.44799	−	0.835999i	−0.449630	−	0.893215i	$-0.648444\pi$
$157$	−18.1433	−	10.4750i	−1.44799	−	0.835999i	−0.998362	+	0.0572162i	$0.981778\pi$
$158$		0			0
$159$	0.0985592	+	2.28716i	0.00781626	+	0.181384i
$160$		0			0
$161$			0.223364i			0.0176035i
$162$		0			0
$163$	−6.19418			−0.485165			−0.242583	−	0.970131i	$-0.577995\pi$
$163$	−6.19418			−0.485165			−0.242583	+	0.970131i	$0.577995\pi$
$164$		0			0
$165$	3.59156	−	0.154769i	0.279602	−	0.0120487i
$166$		0			0
$167$	−5.25143	+	9.09574i	−0.406367	+	0.703849i	−0.994480	−	0.104930i	$-0.966538\pi$
$167$	−5.25143	+	9.09574i	−0.406367	+	0.703849i	0.588112	+	0.808779i	$0.299871\pi$
$168$		0			0
$169$	−4.36407	−	7.55878i	−0.335697	−	0.581445i
$170$		0			0
$171$	18.9191	−	1.63358i	1.44678	−	0.124923i
$172$		0			0
$173$	−1.14186	−	1.97775i	−0.0868138	−	0.150366i	0.819349	−	0.573295i	$-0.194335\pi$
$173$	−1.14186	−	1.97775i	−0.0868138	−	0.150366i	−0.906163	+	0.422929i	$0.861002\pi$
$174$		0			0
$175$	−42.0022	−	24.2500i	−3.17506	−	1.83312i
$176$		0			0
$177$	−6.17497	+	11.8456i	−0.464139	+	0.890369i
$178$		0			0
$179$		−	2.13370i		−	0.159480i	−0.996816	−	0.0797401i	$-0.974591\pi$
$179$		−	2.13370i		−	0.159480i	0.996816	−	0.0797401i	$-0.0254090\pi$
$180$		0			0
$181$			2.74445i			0.203994i	0.994785	+	0.101997i	$0.0325232\pi$
$181$			2.74445i			0.203994i	−0.994785	+	0.101997i	$0.967477\pi$
$182$		0			0
$183$	−2.75861	−	4.33558i	−0.203923	−	0.320496i
$184$		0			0
$185$	−24.7115	−	14.2672i	−1.81682	−	1.04894i
$186$		0			0
$187$	1.22068	+	2.11427i	0.0892647	+	0.154611i
$188$		0			0
$189$	11.8667	+	15.5196i	0.863177	+	1.12889i
$190$		0			0
$191$	−9.96140	−	17.2537i	−0.720782	−	1.24843i	−0.960687	−	0.277634i	$-0.910450\pi$
$191$	−9.96140	−	17.2537i	−0.720782	−	1.24843i	0.239905	−	0.970796i	$-0.422884\pi$
$192$		0			0
$193$	7.90105	−	13.6850i	0.568730	−	0.985070i	−0.427962	−	0.903797i	$-0.640768\pi$
$193$	7.90105	−	13.6850i	0.568730	−	0.985070i	0.996692	−	0.0812727i	$-0.0258985\pi$
$194$		0			0
$195$	8.13055	+	12.7784i	0.582241	+	0.915080i
$196$		0			0
$197$	−8.90082			−0.634157			−0.317078	−	0.948399i	$-0.602702\pi$
$197$	−8.90082			−0.634157			−0.317078	+	0.948399i	$0.602702\pi$
$198$		0			0
$199$			21.4330i			1.51935i	0.650305	+	0.759673i	$0.274641\pi$
$199$			21.4330i			1.51935i	−0.650305	+	0.759673i	$0.725359\pi$
$200$		0			0
$201$	6.37053	+	3.32089i	0.449343	+	0.234237i
$202$		0			0
$203$	18.2853	+	10.5570i	1.28338	+	0.740957i
$204$		0			0
$205$	−18.8207	+	10.8661i	−1.31449	+	0.758922i
$206$		0			0
$207$	0.0755041	−	0.161441i	0.00524790	−	0.0112209i
$208$		0			0
$209$	−2.68923	+	1.55263i	−0.186018	+	0.107398i
$210$		0			0
$211$	13.4490	−	23.2944i	0.925870	−	1.60365i	0.135713	−	0.990748i	$-0.456667\pi$
$211$	13.4490	−	23.2944i	0.925870	−	1.60365i	0.790156	−	0.612905i	$-0.209999\pi$
$212$		0			0
$213$	0.303450	+	7.04184i	0.0207920	+	0.482499i
$214$		0			0
$215$	−36.8279			−2.51164
$216$		0			0
$217$	2.37292			0.161085
$218$		0			0
$219$	−0.599257	−	13.9063i	−0.0404940	−	0.939702i
$220$		0			0
$221$	−5.14287	+	8.90771i	−0.345947	+	0.599197i
$222$		0			0
$223$	0.284057	−	0.164001i	0.0190219	−	0.0109823i	−0.490459	−	0.871464i	$-0.663171\pi$
$223$	0.284057	−	0.164001i	0.0190219	−	0.0109823i	0.509481	+	0.860482i	$0.329837\pi$
$224$		0			0
$225$	22.1606	+	31.7252i	1.47737	+	2.11501i
$226$		0			0
$227$	8.35119	−	4.82156i	0.554288	−	0.320018i	−0.196562	−	0.980491i	$-0.562978\pi$
$227$	8.35119	−	4.82156i	0.554288	−	0.320018i	0.750850	+	0.660473i	$0.229644\pi$
$228$		0			0
$229$	7.63081	+	4.40565i	0.504258	+	0.291134i	0.730470	−	0.682944i	$-0.239301\pi$
$229$	7.63081	+	4.40565i	0.504258	+	0.291134i	−0.226212	+	0.974078i	$0.572634\pi$
$230$		0			0
$231$	−2.83291	−	1.47676i	−0.186392	−	0.0971638i
$232$		0			0
$233$			3.03994i			0.199153i	0.995030	+	0.0995766i	$0.0317488\pi$
$233$			3.03994i			0.199153i	−0.995030	+	0.0995766i	$0.968251\pi$
$234$		0			0
$235$	−38.7647			−2.52873
$236$		0			0
$237$	0.645589	+	1.01464i	0.0419355	+	0.0659081i
$238$		0			0
$239$	−8.04459	+	13.9336i	−0.520361	+	0.901292i	0.479359	+	0.877619i	$0.340869\pi$
$239$	−8.04459	+	13.9336i	−0.520361	+	0.901292i	−0.999720	+	0.0236728i	$0.992464\pi$
$240$		0			0
$241$	0.931165	+	1.61283i	0.0599816	+	0.103891i	0.894457	−	0.447154i	$-0.147562\pi$
$241$	0.931165	+	1.61283i	0.0599816	+	0.103891i	−0.834475	+	0.551045i	$0.814229\pi$
$242$		0			0
$243$	−3.33077	−	15.2285i	−0.213669	−	0.976906i
$244$		0			0
$245$	15.0959	+	26.1469i	0.964443	+	1.67046i
$246$		0			0
$247$	−11.3301	−	6.54142i	−0.720915	−	0.416221i
$248$		0			0
$249$	−9.08721	−	14.2819i	−0.575878	−	0.905081i
$250$		0			0
$251$			11.5470i			0.728837i	0.931235	+	0.364419i	$0.118732\pi$
$251$			11.5470i			0.728837i	−0.931235	+	0.364419i	$0.881268\pi$
$252$		0			0
$253$			0.0291440i			0.00183227i
$254$		0			0
$255$	−16.8572	+	32.3377i	−1.05564	+	2.02506i
$256$		0			0
$257$	20.7249	+	11.9655i	1.29279	+	0.746390i	0.979147	−	0.203152i	$-0.0651185\pi$
$257$	20.7249	+	11.9655i	1.29279	+	0.746390i	0.313639	+	0.949542i	$0.398452\pi$
$258$		0			0
$259$	12.6790	+	21.9606i	0.787832	+	1.36457i
$260$		0			0
$261$	−9.64744	−	13.8113i	−0.597162	−	0.854898i
$262$		0			0
$263$	−7.57540	−	13.1210i	−0.467119	−	0.809074i	0.532175	−	0.846634i	$-0.321375\pi$
$263$	−7.57540	−	13.1210i	−0.467119	−	0.809074i	−0.999294	+	0.0375603i	$0.988041\pi$
$264$		0			0
$265$	2.79595	−	4.84273i	0.171754	−	0.297486i
$266$		0			0
$267$	10.7252	−	0.462173i	0.656369	−	0.0282845i
$268$		0			0
$269$	−0.882470			−0.0538051			−0.0269026	−	0.999638i	$-0.508564\pi$
$269$	−0.882470			−0.0538051			−0.0269026	+	0.999638i	$0.508564\pi$
$270$		0			0
$271$		−	21.5768i		−	1.31070i	−0.755325	−	0.655350i	$-0.772521\pi$
$271$		−	21.5768i		−	1.31070i	0.755325	−	0.655350i	$-0.227479\pi$
$272$		0			0
$273$	−0.579475	−	13.4473i	−0.0350714	−	0.813865i
$274$		0			0
$275$	−5.48036	−	3.16409i	−0.330478	−	0.190802i
$276$		0			0
$277$	−6.73557	+	3.88878i	−0.404701	+	0.233654i	−0.688510	−	0.725226i	$-0.741735\pi$
$277$	−6.73557	+	3.88878i	−0.404701	+	0.233654i	0.283809	+	0.958881i	$0.408402\pi$
$278$		0			0
$279$	−1.71508	−	0.802125i	−0.102679	−	0.0480219i
$280$		0			0
$281$	−18.1985	+	10.5069i	−1.08563	+	0.626790i	−0.932410	−	0.361402i	$-0.882298\pi$
$281$	−18.1985	+	10.5069i	−1.08563	+	0.626790i	−0.153222	+	0.988192i	$0.548965\pi$
$282$		0			0
$283$	3.05872	−	5.29786i	0.181822	−	0.314925i	−0.760679	−	0.649128i	$-0.775134\pi$
$283$	3.05872	−	5.29786i	0.181822	−	0.314925i	0.942501	+	0.334203i	$0.108467\pi$
$284$		0			0
$285$	−41.1316	−	21.4414i	−2.43642	−	1.27008i
$286$		0			0
$287$	19.3130			1.14001
$288$		0			0
$289$	−7.76584			−0.456814
$290$		0			0
$291$	−2.52746	+	1.60816i	−0.148163	+	0.0942718i
$292$		0			0
$293$	4.27055	−	7.39681i	0.249488	−	0.432126i	−0.713896	−	0.700252i	$-0.753071\pi$
$293$	4.27055	−	7.39681i	0.249488	−	0.432126i	0.963384	+	0.268126i	$0.0864043\pi$
$294$		0			0
$295$	28.2584	−	16.3150i	1.64527	−	0.949895i
$296$		0			0
$297$	1.54835	+	2.02497i	0.0898441	+	0.117501i
$298$		0			0
$299$	−0.106337	+	0.0613938i	−0.00614964	+	0.00355050i
$300$		0			0
$301$	28.3435	+	16.3641i	1.63369	+	0.943213i
$302$		0			0
$303$	15.3266	−	9.75191i	0.880491	−	0.560233i
$304$		0			0
$305$			12.5523i			0.718740i
$306$		0			0
$307$	13.8026			0.787757			0.393878	−	0.919163i	$-0.371133\pi$
$307$	13.8026			0.787757			0.393878	+	0.919163i	$0.371133\pi$
$308$		0			0
$309$	10.5897	−	20.3145i	0.602429	−	1.15565i
$310$		0			0
$311$	−12.4010	+	21.4791i	−0.703194	+	1.21797i	0.264145	+	0.964483i	$0.414910\pi$
$311$	−12.4010	+	21.4791i	−0.703194	+	1.21797i	−0.967339	+	0.253485i	$0.918423\pi$
$312$		0			0
$313$	−9.78878	−	16.9547i	−0.553295	−	0.958335i	−0.998034	−	0.0626745i	$-0.980037\pi$
$313$	−9.78878	−	16.9547i	−0.553295	−	0.958335i	0.444739	−	0.895660i	$-0.353296\pi$
$314$		0			0
$315$	−4.10520	−	47.5440i	−0.231302	−	2.67880i
$316$		0			0
$317$	−1.19851	−	2.07588i	−0.0673151	−	0.116593i	0.830403	−	0.557163i	$-0.188110\pi$
$317$	−1.19851	−	2.07588i	−0.0673151	−	0.116593i	−0.897719	+	0.440569i	$0.854777\pi$
$318$		0			0
$319$	2.38583	+	1.37746i	0.133581	+	0.0771229i
$320$		0			0
$321$	−14.3857	+	0.619914i	−0.802931	+	0.0346002i
$322$		0			0
$323$		−	31.5007i		−	1.75274i
$324$		0			0
$325$		−	26.6614i		−	1.47891i
$326$		0			0
$327$	6.71780	−	0.289486i	0.371495	−	0.0160086i
$328$		0			0
$329$	29.8341	+	17.2247i	1.64481	+	0.949629i
$330$		0			0
$331$	−16.1385	−	27.9527i	−0.887051	−	1.53642i	−0.843345	−	0.537373i	$-0.819417\pi$
$331$	−16.1385	−	27.9527i	−0.887051	−	1.53642i	−0.0437062	−	0.999044i	$-0.513917\pi$
$332$		0			0
$333$	−1.74058	−	20.1584i	−0.0953830	−	1.10467i
$334$		0			0
$335$	−8.77416	−	15.1973i	−0.479383	−	0.830317i
$336$		0			0
$337$	15.4664	−	26.7886i	0.842508	−	1.45927i	−0.0452603	−	0.998975i	$-0.514412\pi$
$337$	15.4664	−	26.7886i	0.842508	−	1.45927i	0.887768	−	0.460291i	$-0.152255\pi$
$338$		0			0
$339$	−8.81352	+	16.9072i	−0.478685	+	0.918273i
$340$		0			0
$341$	0.309614			0.0167666
$342$		0			0
$343$		−	0.512201i		−	0.0276562i
$344$		0			0
$345$	−0.367294	+	0.233699i	−0.0197744	+	0.0125819i
$346$		0			0
$347$	−0.296173	−	0.170995i	−0.0158994	−	0.00917951i	0.492029	−	0.870579i	$-0.336255\pi$
$347$	−0.296173	−	0.170995i	−0.0158994	−	0.00917951i	−0.507929	+	0.861399i	$0.669589\pi$
$348$		0			0
$349$	14.7950	−	8.54188i	0.791957	−	0.457236i	−0.0486942	−	0.998814i	$-0.515506\pi$
$349$	14.7950	−	8.54188i	0.791957	−	0.457236i	0.840651	+	0.541577i	$0.182173\pi$
$350$		0			0
$351$	−4.12678	+	9.91515i	−0.220271	+	0.529231i
$352$		0			0
$353$	6.90382	−	3.98592i	0.367453	−	0.212149i	−0.304892	−	0.952387i	$-0.598620\pi$
$353$	6.90382	−	3.98592i	0.367453	−	0.212149i	0.672345	+	0.740238i	$0.265287\pi$
$354$		0			0
$355$	8.60834	−	14.9101i	0.456883	−	0.791345i
$356$		0			0
$357$	27.3426	−	17.3974i	1.44712	−	0.920766i
$358$		0			0
$359$	17.3701			0.916758			0.458379	−	0.888757i	$-0.348430\pi$
$359$	17.3701			0.916758			0.458379	+	0.888757i	$0.348430\pi$
$360$		0			0
$361$	21.0670			1.10879
$362$		0			0
$363$	16.5252	+	8.61440i	0.867348	+	0.452139i
$364$		0			0
$365$	−16.9999	+	29.4446i	−0.889813	+	1.54120i
$366$		0			0
$367$	−28.7169	+	16.5797i	−1.49901	+	0.865454i	−0.999999	−	0.00114176i	$-0.999637\pi$
$367$	−28.7169	+	16.5797i	−1.49901	+	0.865454i	−0.499011	+	0.866596i	$0.666303\pi$
$368$		0			0
$369$	−13.9589	−	6.52842i	−0.726669	−	0.339856i
$370$		0			0
$371$	−4.30364	+	2.48471i	−0.223434	+	0.129000i
$372$		0			0
$373$	27.6294	+	15.9518i	1.43059	+	0.825954i	0.997166	−	0.0752346i	$-0.0239706\pi$
$373$	27.6294	+	15.9518i	1.43059	+	0.825954i	0.433428	+	0.901188i	$0.357304\pi$
$374$		0			0
$375$	−2.49219	−	57.8336i	−0.128696	−	2.98651i
$376$		0			0
$377$			11.6068i			0.597782i
$378$		0			0
$379$	−12.9807			−0.666774			−0.333387	−	0.942790i	$-0.608192\pi$
$379$	−12.9807			−0.666774			−0.333387	+	0.942790i	$0.608192\pi$
$380$		0			0
$381$	18.0648	−	0.778457i	0.925489	−	0.0398816i
$382$		0			0
$383$	13.4445	−	23.2866i	0.686984	−	1.18989i	−0.285825	−	0.958282i	$-0.592268\pi$
$383$	13.4445	−	23.2866i	0.686984	−	1.18989i	0.972809	−	0.231609i	$-0.0743989\pi$
$384$		0			0
$385$	3.90177	+	6.75807i	0.198853	+	0.344423i
$386$		0			0
$387$	−14.9542	−	21.4085i	−0.760166	−	1.08826i
$388$		0			0
$389$	−8.06209	−	13.9639i	−0.408764	−	0.708000i	0.585988	−	0.810320i	$-0.300707\pi$
$389$	−8.06209	−	13.9639i	−0.408764	−	0.708000i	−0.994752	+	0.102320i	$0.967373\pi$
$390$		0			0
$391$	−0.256037	−	0.147823i	−0.0129484	−	0.00747573i
$392$		0			0
$393$	−11.0275	+	21.1543i	−0.556263	+	1.06709i
$394$		0			0
$395$		−	2.93756i		−	0.147805i
$396$		0			0
$397$		−	13.0546i		−	0.655193i	−0.944818	−	0.327596i	$-0.893761\pi$
$397$		−	13.0546i		−	0.655193i	0.944818	−	0.327596i	$-0.106239\pi$
$398$		0			0
$399$	22.1284	+	34.7782i	1.10781	+	1.74109i
$400$		0			0
$401$	−8.18134	−	4.72350i	−0.408557	−	0.235880i	0.281613	−	0.959528i	$-0.409131\pi$
$401$	−8.18134	−	4.72350i	−0.408557	−	0.235880i	−0.690169	+	0.723648i	$0.742464\pi$
$402$		0			0
$403$	0.652222	+	1.12968i	0.0324895	+	0.0562735i
$404$		0			0
$405$	−13.1043	+	35.7511i	−0.651158	+	1.77649i
$406$		0			0
$407$	1.65433	+	2.86538i	0.0820019	+	0.142031i
$408$		0			0
$409$	3.65255	−	6.32641i	0.180607	−	0.312821i	−0.761480	−	0.648188i	$-0.775527\pi$
$409$	3.65255	−	6.32641i	0.180607	−	0.312821i	0.942087	+	0.335367i	$0.108860\pi$
$410$		0			0
$411$	14.9212	+	23.4510i	0.736011	+	1.15675i
$412$		0			0
$413$	−28.9976			−1.42688
$414$		0			0
$415$			41.3486i			2.02972i
$416$		0			0
$417$	−15.5880	−	8.12584i	−0.763347	−	0.397924i
$418$		0			0
$419$	7.41857	+	4.28311i	0.362421	+	0.209244i	0.670142	−	0.742233i	$-0.266233\pi$
$419$	7.41857	+	4.28311i	0.362421	+	0.209244i	−0.307721	+	0.951477i	$0.599566\pi$
$420$		0			0
$421$	22.4005	−	12.9330i	1.09174	−	0.630314i	0.157698	−	0.987487i	$-0.449593\pi$
$421$	22.4005	−	12.9330i	1.09174	−	0.630314i	0.934038	+	0.357173i	$0.116259\pi$
$422$		0			0
$423$	−15.7407	−	22.5344i	−0.765337	−	1.09566i
$424$		0			0
$425$	55.5944	−	32.0975i	2.69673	−	1.55696i
$426$		0			0
$427$	5.57748	−	9.66047i	0.269913	−	0.467503i
$428$		0			0
$429$	−0.0756087	−	1.75457i	−0.00365042	−	0.0847115i
$430$		0			0
$431$	29.9904			1.44459			0.722294	−	0.691586i	$-0.243088\pi$
$431$	29.9904			1.44459			0.722294	+	0.691586i	$0.243088\pi$
$432$		0			0
$433$	−6.07397			−0.291896			−0.145948	−	0.989292i	$-0.546623\pi$
$433$	−6.07397			−0.291896			−0.145948	+	0.989292i	$0.546623\pi$
$434$		0			0
$435$	1.77167	+	41.1134i	0.0849453	+	1.97123i
$436$		0			0
$437$	0.188022	−	0.325664i	0.00899432	−	0.0155786i
$438$		0			0
$439$	8.98592	−	5.18802i	0.428875	−	0.247611i	−0.269992	−	0.962862i	$-0.587021\pi$
$439$	8.98592	−	5.18802i	0.428875	−	0.247611i	0.698867	+	0.715252i	$0.253688\pi$
$440$		0			0
$441$	−9.06972	+	19.3926i	−0.431891	+	0.923456i
$442$		0			0
$443$	−18.5840	+	10.7295i	−0.882954	+	0.509774i	−0.871631	−	0.490162i	$-0.836938\pi$
$443$	−18.5840	+	10.7295i	−0.882954	+	0.509774i	−0.0113228	+	0.999936i	$0.503604\pi$
$444$		0			0
$445$	−22.7090	−	13.1110i	−1.07651	−	0.621522i
$446$		0			0
$447$	−13.1096	−	6.83388i	−0.620062	−	0.323231i
$448$		0			0
$449$		−	9.67036i		−	0.456373i	−0.973617	−	0.228186i	$-0.926720\pi$
$449$		−	9.67036i		−	0.456373i	0.973617	−	0.228186i	$-0.0732795\pi$
$450$		0			0
$451$	2.51992			0.118659
$452$		0			0
$453$	−11.6952	−	18.3807i	−0.549486	−	0.863602i
$454$		0			0
$455$	−16.4387	+	28.4726i	−0.770657	+	1.33482i
$456$		0			0
$457$	12.5847	+	21.7974i	0.588689	+	1.01964i	0.994404	+	0.105640i	$0.0336891\pi$
$457$	12.5847	+	21.7974i	0.588689	+	1.01964i	−0.405715	+	0.913999i	$0.632978\pi$
$458$		0			0
$459$	−25.6433	+	3.33160i	−1.19693	+	0.155506i
$460$		0			0
$461$	−9.94291	−	17.2216i	−0.463087	−	0.802091i	0.536026	−	0.844202i	$-0.319925\pi$
$461$	−9.94291	−	17.2216i	−0.463087	−	0.802091i	−0.999113	+	0.0421109i	$0.986592\pi$
$462$		0			0
$463$	−13.7287	−	7.92626i	−0.638026	−	0.368365i	0.145827	−	0.989310i	$-0.453416\pi$
$463$	−13.7287	−	7.92626i	−0.638026	−	0.368365i	−0.783854	+	0.620945i	$0.786749\pi$
$464$		0			0
$465$	2.48272	+	3.90197i	0.115133	+	0.180950i
$466$		0			0
$467$		−	24.9598i		−	1.15500i	−0.816390	−	0.577501i	$-0.804028\pi$
$467$		−	24.9598i		−	1.15500i	0.816390	−	0.577501i	$-0.195972\pi$
$468$		0			0
$469$			15.5949i			0.720104i
$470$		0			0
$471$	−16.7735	+	32.1771i	−0.772884	+	1.48264i
$472$		0			0
$473$	3.69820	+	2.13516i	0.170044	+	0.0981747i
$474$		0			0
$475$	40.8261	+	70.7128i	1.87323	+	3.24453i
$476$		0			0
$477$	3.95045	−	0.341103i	0.180879	−	0.0156180i
$478$		0			0
$479$	3.56542	+	6.17550i	0.162908	+	0.282166i	0.935911	−	0.352238i	$-0.114579\pi$
$479$	3.56542	+	6.17550i	0.162908	+	0.282166i	−0.773002	+	0.634403i	$0.781246\pi$
$480$		0			0
$481$	−6.96989	+	12.0722i	−0.317799	+	0.550445i
$482$		0			0
$483$	0.386519	−	0.0166560i	0.0175872	−	0.000757875i
$484$		0			0
$485$	7.31744			0.332268
$486$		0			0
$487$			8.51518i			0.385860i	0.981213	+	0.192930i	$0.0617990\pi$
$487$			8.51518i			0.385860i	−0.981213	+	0.192930i	$0.938201\pi$
$488$		0			0
$489$	0.461894	+	10.7187i	0.0208876	+	0.484716i
$490$		0			0
$491$	18.7051	+	10.7994i	0.844148	+	0.487369i	0.858672	−	0.512526i	$-0.171290\pi$
$491$	18.7051	+	10.7994i	0.844148	+	0.487369i	−0.0145241	+	0.999895i	$0.504623\pi$
$492$		0			0
$493$	−24.2026	+	13.9734i	−1.09003	+	0.629328i
$494$		0			0
$495$	−0.535638	−	6.20345i	−0.0240751	−	0.278824i
$496$		0			0
$497$	−13.2503	+	7.65006i	−0.594357	+	0.343152i
$498$		0			0
$499$	−13.6695	+	23.6762i	−0.611930	+	1.05989i	0.378984	+	0.925403i	$0.376273\pi$
$499$	−13.6695	+	23.6762i	−0.611930	+	1.05989i	−0.990915	+	0.134491i	$0.957060\pi$
$500$		0			0
$501$	16.1313	+	8.40904i	0.720692	+	0.375688i
$502$		0			0
$503$	19.4082			0.865370			0.432685	−	0.901545i	$-0.357566\pi$
$503$	19.4082			0.865370			0.432685	+	0.901545i	$0.357566\pi$
$504$		0			0
$505$	−44.3732			−1.97458
$506$		0			0
$507$	−12.7546	+	8.11543i	−0.566453	+	0.360419i
$508$		0			0
$509$	1.37957	−	2.38948i	0.0611482	−	0.105912i	−0.833831	−	0.552020i	$-0.813857\pi$
$509$	1.37957	−	2.38948i	0.0611482	−	0.105912i	0.894979	+	0.446108i	$0.147190\pi$
$510$		0			0
$511$	26.1669	−	15.1074i	1.15755	−	0.668314i
$512$		0			0
$513$	−4.23760	−	32.6167i	−0.187095	−	1.44006i
$514$		0			0
$515$	−48.4615	+	27.9793i	−2.13547	+	1.23291i
$516$		0			0
$517$	3.89269	+	2.24745i	0.171200	+	0.0988426i
$518$		0			0
$519$	−3.33725	+	2.12340i	−0.146489	+	0.0932069i
$520$		0			0
$521$			6.57146i			0.287901i	0.989585	+	0.143951i	$0.0459806\pi$
$521$			6.57146i			0.287901i	−0.989585	+	0.143951i	$0.954019\pi$
$522$		0			0
$523$	16.5664			0.724398			0.362199	−	0.932101i	$-0.382026\pi$
$523$	16.5664			0.724398			0.362199	+	0.932101i	$0.382026\pi$
$524$		0			0
$525$	−38.8311	+	74.4907i	−1.69473	+	3.25104i
$526$		0			0
$527$	−1.57041	+	2.72003i	−0.0684082	+	0.118486i
$528$		0			0
$529$	11.4982	+	19.9155i	0.499923	+	0.865893i
$530$		0			0
$531$	20.9586	+	9.80213i	0.909526	+	0.425376i
$532$		0			0
$533$	5.30838	+	9.19439i	0.229932	+	0.398253i
$534$		0			0
$535$	30.4596	+	17.5859i	1.31688	+	0.760303i
$536$		0			0
$537$	−3.69225	+	0.159108i	−0.159332	+	0.00686602i
$538$		0			0
$539$		−	3.50085i		−	0.150792i
$540$		0			0
$541$			38.7716i			1.66692i	0.552577	+	0.833462i	$0.313644\pi$
$541$			38.7716i			1.66692i	−0.552577	+	0.833462i	$0.686356\pi$
$542$		0			0
$543$	4.74913	−	0.204651i	0.203805	−	0.00878243i
$544$		0			0
$545$	−14.2240	−	8.21221i	−0.609288	−	0.351773i
$546$		0			0
$547$	13.6876	+	23.7076i	0.585239	+	1.01366i	0.994846	+	0.101401i	$0.0323325\pi$
$547$	13.6876	+	23.7076i	0.585239	+	1.01366i	−0.409607	+	0.912262i	$0.634334\pi$
$548$		0			0
$549$	−7.29678	+	5.09693i	−0.311419	+	0.217532i
$550$		0			0
$551$	−17.7733	−	30.7842i	−0.757167	−	1.31145i
$552$		0			0
$553$	−1.30528	+	2.26081i	−0.0555061	+	0.0961393i
$554$		0			0
$555$	−22.8458	+	43.8257i	−0.969752	+	1.86030i
$556$		0			0
$557$	16.6931			0.707307			0.353654	−	0.935376i	$-0.384939\pi$
$557$	16.6931			0.707307			0.353654	+	0.935376i	$0.384939\pi$
$558$		0			0
$559$			17.9914i			0.760955i
$560$		0			0
$561$	3.56761	−	2.26997i	0.150625	−	0.0958383i
$562$		0			0
$563$	39.9269	+	23.0518i	1.68272	+	0.971518i	0.959843	+	0.280539i	$0.0905133\pi$
$563$	39.9269	+	23.0518i	1.68272	+	0.971518i	0.722875	+	0.690978i	$0.242820\pi$
$564$		0			0
$565$	40.3331	−	23.2863i	1.69683	−	0.979664i
$566$		0			0
$567$	25.9710	−	21.6920i	1.09068	−	0.910978i
$568$		0			0
$569$	−10.3238	+	5.96045i	−0.432796	+	0.249875i	−0.700537	−	0.713616i	$-0.747056\pi$
$569$	−10.3238	+	5.96045i	−0.432796	+	0.249875i	0.267741	+	0.963491i	$0.413723\pi$
$570$		0			0
$571$	4.99834	−	8.65737i	0.209174	−	0.362300i	−0.742281	−	0.670089i	$-0.766256\pi$
$571$	4.99834	−	8.65737i	0.209174	−	0.362300i	0.951455	+	0.307789i	$0.0995892\pi$
$572$		0			0
$573$	−29.1137	+	18.5242i	−1.21624	+	0.773861i
$574$		0			0
$575$	0.766337			0.0319585
$576$		0			0
$577$	38.3282			1.59562			0.797812	−	0.602906i	$-0.205991\pi$
$577$	38.3282			1.59562			0.797812	+	0.602906i	$0.205991\pi$
$578$		0			0
$579$	−24.2704	−	12.6519i	−1.00864	−	0.525793i
$580$		0			0
$581$	18.3729	−	31.8228i	0.762235	−	1.32023i
$582$		0			0
$583$	−0.561531	+	0.324200i	−0.0232562	+	0.0134270i
$584$		0			0
$585$	21.5060	−	15.0223i	0.889165	−	0.621097i
$586$		0			0
$587$	22.9858	−	13.2709i	0.948726	−	0.547747i	0.0560413	−	0.998428i	$-0.482152\pi$
$587$	22.9858	−	13.2709i	0.948726	−	0.547747i	0.892685	+	0.450681i	$0.148819\pi$
$588$		0			0
$589$	−3.45972	−	1.99747i	−0.142555	−	0.0823043i
$590$		0			0
$591$	0.663726	+	15.4024i	0.0273020	+	0.633569i
$592$		0			0
$593$		−	31.4637i		−	1.29206i	−0.763312	−	0.646030i	$-0.776428\pi$
$593$		−	31.4637i		−	1.29206i	0.763312	−	0.646030i	$-0.223572\pi$
$594$		0			0
$595$	−79.1615			−3.24531
$596$		0			0
$597$	37.0886	−	1.59824i	1.51794	−	0.0654116i
$598$		0			0
$599$	8.10378	−	14.0362i	0.331112	−	0.573502i	−0.651618	−	0.758547i	$-0.725910\pi$
$599$	8.10378	−	14.0362i	0.331112	−	0.573502i	0.982730	+	0.185045i	$0.0592430\pi$
$600$		0			0
$601$	7.06787	+	12.2419i	0.288304	+	0.499358i	0.973405	−	0.229091i	$-0.0735752\pi$
$601$	7.06787	+	12.2419i	0.288304	+	0.499358i	−0.685101	+	0.728448i	$0.740242\pi$
$602$		0			0
$603$	5.27156	−	11.2715i	0.214675	−	0.459011i
$604$		0			0
$605$	−22.7602	−	39.4219i	−0.925334	−	1.60273i
$606$		0			0
$607$	−36.3473	−	20.9851i	−1.47529	−	0.851760i	−0.475680	−	0.879619i	$-0.657798\pi$
$607$	−36.3473	−	20.9851i	−1.47529	−	0.851760i	−0.999612	+	0.0278586i	$0.991131\pi$
$608$		0			0
$609$	16.9048	−	32.4289i	0.685018	−	1.31409i
$610$		0			0
$611$			18.9376i			0.766132i
$612$		0			0
$613$		−	0.434288i		−	0.0175407i	−0.999962	−	0.00877037i	$-0.997208\pi$
$613$		−	0.434288i		−	0.0175407i	0.999962	−	0.00877037i	$-0.00279173\pi$
$614$		0			0
$615$	20.2066	+	31.7578i	0.814811	+	1.28060i
$616$		0			0
$617$	−36.4955	−	21.0707i	−1.46925	−	0.848273i	−0.469846	−	0.882748i	$-0.655691\pi$
$617$	−36.4955	−	21.0707i	−1.46925	−	0.848273i	−0.999406	+	0.0344751i	$0.989024\pi$
$618$		0			0
$619$	−8.67117	−	15.0189i	−0.348524	−	0.603661i	0.637464	−	0.770481i	$-0.279984\pi$
$619$	−8.67117	−	15.0189i	−0.348524	−	0.603661i	−0.985987	+	0.166819i	$0.946650\pi$
$620$		0			0
$621$	−0.284994	−	0.118617i	−0.0114364	−	0.00475995i
$622$		0			0
$623$	11.6515	+	20.1810i	0.466808	+	0.808536i
$624$		0			0
$625$	−38.4502	+	66.5977i	−1.53801	+	2.66391i
$626$		0			0
$627$	2.88727	+	4.53779i	0.115306	+	0.181222i
$628$		0			0
$629$	−33.5640			−1.33828
$630$		0			0
$631$			36.5529i			1.45515i	0.686029	+	0.727574i	$0.259352\pi$
$631$			36.5529i			1.45515i	−0.686029	+	0.727574i	$0.740648\pi$
$632$		0			0
$633$	−41.3126	−	21.5358i	−1.64203	−	0.855970i
$634$		0			0
$635$	−38.2496	−	22.0834i	−1.51789	−	0.876355i
$636$		0			0
$637$	12.7735	−	7.37476i	0.506103	−	0.292199i
$638$		0			0
$639$	12.1629	−	1.05021i	0.481156	−	0.0415455i
$640$		0			0
$641$	−6.07674	+	3.50841i	−0.240017	+	0.138574i	−0.615184	−	0.788383i	$-0.710918\pi$
$641$	−6.07674	+	3.50841i	−0.240017	+	0.138574i	0.375168	+	0.926957i	$0.377585\pi$
$642$		0			0
$643$	18.6887	−	32.3698i	0.737011	−	1.27654i	−0.216824	−	0.976211i	$-0.569570\pi$
$643$	18.6887	−	32.3698i	0.737011	−	1.27654i	0.953835	−	0.300330i	$-0.0970968\pi$
$644$		0			0
$645$	2.74622	+	63.7287i	0.108132	+	2.50931i
$646$		0			0
$647$	19.8140			0.778967			0.389484	−	0.921033i	$-0.372654\pi$
$647$	19.8140			0.778967			0.389484	+	0.921033i	$0.372654\pi$
$648$		0			0
$649$	−3.78355			−0.148517
$650$		0			0
$651$	−0.176947	−	4.10621i	−0.00693509	−	0.160935i
$652$		0			0
$653$	1.18500	−	2.05247i	0.0463725	−	0.0803195i	−0.841907	−	0.539622i	$-0.818567\pi$
$653$	1.18500	−	2.05247i	0.0463725	−	0.0803195i	0.888280	+	0.459302i	$0.151901\pi$
$654$		0			0
$655$	50.4648	−	29.1359i	1.97182	−	1.13843i
$656$		0			0
$657$	−24.0194	+	2.07396i	−0.937087	+	0.0809130i
$658$		0			0
$659$	−5.84785	+	3.37626i	−0.227800	+	0.131520i	−0.609557	−	0.792742i	$-0.708653\pi$
$659$	−5.84785	+	3.37626i	−0.227800	+	0.131520i	0.381757	+	0.924263i	$0.375319\pi$
$660$		0			0
$661$	−23.6719	−	13.6670i	−0.920730	−	0.531584i	−0.0368621	−	0.999320i	$-0.511736\pi$
$661$	−23.6719	−	13.6670i	−0.920730	−	0.531584i	−0.883868	+	0.467737i	$0.845070\pi$
$662$		0			0
$663$	15.7978	+	8.23521i	0.613536	+	0.319829i
$664$		0			0
$665$		−	100.689i		−	3.90454i
$666$		0			0
$667$	−0.333618			−0.0129178
$668$		0			0
$669$	−0.304976	−	0.479316i	−0.0117910	−	0.0185314i
$670$		0			0
$671$	0.727738	−	1.26048i	0.0280940	−	0.0486603i
$672$		0			0
$673$	6.86454	+	11.8897i	0.264608	+	0.458315i	0.967461	−	0.253020i	$-0.0814240\pi$
$673$	6.86454	+	11.8897i	0.264608	+	0.458315i	−0.702853	+	0.711336i	$0.748091\pi$
$674$		0			0
$675$	53.2462	−	40.7135i	2.04945	−	1.56706i
$676$		0			0
$677$	7.08375	+	12.2694i	0.272251	+	0.471552i	0.969438	−	0.245337i	$-0.0788986\pi$
$677$	7.08375	+	12.2694i	0.272251	+	0.471552i	−0.697187	+	0.716889i	$0.745565\pi$
$678$		0			0
$679$	−5.63165	−	3.25144i	−0.216123	−	0.124779i
$680$		0			0
$681$	−8.96619	−	14.0917i	−0.343585	−	0.539997i
$682$		0			0
$683$		−	8.86446i		−	0.339189i	−0.985514	−	0.169594i	$-0.945754\pi$
$683$		−	8.86446i		−	0.339189i	0.985514	−	0.169594i	$-0.0542458\pi$
$684$		0			0
$685$		−	67.8947i		−	2.59412i
$686$		0			0
$687$	7.05472	−	13.5332i	0.269154	−	0.516325i
$688$		0			0
$689$	−2.36580	−	1.36590i	−0.0901298	−	0.0520365i
$690$		0			0
$691$	−3.12192	−	5.40733i	−0.118764	−	0.205705i	0.800514	−	0.599314i	$-0.204560\pi$
$691$	−3.12192	−	5.40733i	−0.118764	−	0.205705i	−0.919278	+	0.393609i	$0.871226\pi$
$692$		0			0
$693$	−2.34421	+	5.01231i	−0.0890490	+	0.190402i
$694$		0			0
$695$	21.4694	+	37.1861i	0.814380	+	1.41055i
$696$		0			0
$697$	−12.7814	+	22.1381i	−0.484132	+	0.838540i
$698$		0			0
$699$	5.26045	−	0.226686i	0.198968	−	0.00857403i
$700$		0			0
$701$	1.69776			0.0641236			0.0320618	−	0.999486i	$-0.489793\pi$
$701$	1.69776			0.0641236			0.0320618	+	0.999486i	$0.489793\pi$
$702$		0			0
$703$		−	42.6914i		−	1.61014i
$704$		0			0
$705$	2.89065	+	67.0801i	0.108868	+	2.52638i
$706$		0			0
$707$	34.1505	+	19.7168i	1.28436	+	0.741526i
$708$		0			0
$709$	3.73097	−	2.15408i	0.140119	−	0.0808980i	−0.428301	−	0.903636i	$-0.640888\pi$
$709$	3.73097	−	2.15408i	0.140119	−	0.0808980i	0.568421	+	0.822738i	$0.307555\pi$
$710$		0			0
$711$	1.70764	−	1.19282i	0.0640415	−	0.0447341i
$712$		0			0
$713$	−0.0324708	+	0.0187470i	−0.00121604	+	0.000702082i
$714$		0			0
$715$	−2.14488	+	3.71505i	−0.0802141	+	0.138935i
$716$		0			0
$717$	24.7113	+	12.8817i	0.922859	+	0.481076i
$718$		0			0
$719$	0.552165			0.0205923			0.0102961	−	0.999947i	$-0.496723\pi$
$719$	0.552165			0.0205923			0.0102961	+	0.999947i	$0.496723\pi$
$720$		0			0
$721$	49.7293			1.85202
$722$		0			0
$723$	2.72147	−	1.73160i	0.101213	−	0.0643988i
$724$		0			0
$725$	36.2200	−	62.7349i	1.34518	−	2.32991i
$726$		0			0
$727$	43.5871	−	25.1650i	1.61656	−	0.933320i	0.628756	−	0.777603i	$-0.283565\pi$
$727$	43.5871	−	25.1650i	1.61656	−	0.933320i	0.987802	−	0.155717i	$-0.0497688\pi$
$728$		0			0
$729$	−26.1036	+	6.89928i	−0.966801	+	0.255529i
$730$		0			0
$731$	−37.5157	+	21.6597i	−1.38757	+	0.801113i
$732$		0			0
$733$	4.44881	+	2.56852i	0.164321	+	0.0948706i	0.579905	−	0.814684i	$-0.303090\pi$
$733$	4.44881	+	2.56852i	0.164321	+	0.0948706i	−0.415584	+	0.909555i	$0.636423\pi$
$734$		0			0
$735$	44.1201	−	28.0724i	1.62739	−	1.03547i
$736$		0			0
$737$			2.03479i			0.0749523i
$738$		0			0
$739$	−6.89660			−0.253695			−0.126848	−	0.991922i	$-0.540486\pi$
$739$	−6.89660			−0.253695			−0.126848	+	0.991922i	$0.540486\pi$
$740$		0			0
$741$	−10.4747	+	20.0939i	−0.384798	+	0.738166i
$742$		0			0
$743$	−8.74944	+	15.1545i	−0.320986	+	0.555964i	−0.980692	−	0.195560i	$-0.937348\pi$
$743$	−8.74944	+	15.1545i	−0.320986	+	0.555964i	0.659706	+	0.751524i	$0.270681\pi$
$744$		0			0
$745$	18.0559	+	31.2737i	0.661516	+	1.14578i
$746$		0			0
$747$	−24.0365	+	16.7899i	−0.879449	+	0.614310i
$748$		0			0
$749$	−15.6282	−	27.0689i	−0.571043	−	0.989075i
$750$		0			0
$751$	21.8956	+	12.6414i	0.798980	+	0.461292i	0.843115	−	0.537734i	$-0.180720\pi$
$751$	21.8956	+	12.6414i	0.798980	+	0.461292i	−0.0441341	+	0.999026i	$0.514053\pi$
$752$		0			0
$753$	19.9814	−	0.861045i	0.728161	−	0.0313782i
$754$		0			0
$755$			53.2153i			1.93670i
$756$		0			0
$757$			5.80007i			0.210807i	0.994430	+	0.105404i	$0.0336135\pi$
$757$			5.80007i			0.210807i	−0.994430	+	0.105404i	$0.966387\pi$
$758$		0			0
$759$	0.0504322	−	0.00217324i	0.00183057	−	7.88838e-5i
$760$		0			0
$761$	34.2084	+	19.7503i	1.24006	+	0.715946i	0.969105	−	0.246647i	$-0.0793289\pi$
$761$	34.2084	+	19.7503i	1.24006	+	0.715946i	0.270950	+	0.962593i	$0.412662\pi$
$762$		0			0
$763$	7.29804	+	12.6406i	0.264207	+	0.457619i
$764$		0			0
$765$	57.2156	+	26.7592i	2.06863	+	0.967479i
$766$		0			0
$767$	−7.97030	−	13.8050i	−0.287791	−	0.498468i
$768$		0			0
$769$	−23.8518	+	41.3126i	−0.860119	+	1.48977i	0.0116939	+	0.999932i	$0.496278\pi$
$769$	−23.8518	+	41.3126i	−0.860119	+	1.48977i	−0.871813	+	0.489839i	$0.837056\pi$
$770$		0			0
$771$	19.1603	−	36.7556i	0.690041	−	1.32372i
$772$		0			0
$773$	−26.5971			−0.956632			−0.478316	−	0.878188i	$-0.658753\pi$
$773$	−26.5971			−0.956632			−0.478316	+	0.878188i	$0.658753\pi$
$774$		0			0
$775$		−	8.14125i		−	0.292442i
$776$		0			0
$777$	37.0562	−	23.5778i	1.32938	−	0.845850i
$778$		0			0
$779$	−28.1583	−	16.2572i	−1.00888	−	0.582476i
$780$		0			0
$781$	−1.72887	+	0.998165i	−0.0618639	+	0.0357172i
$782$		0			0
$783$	−23.1803	+	17.7243i	−0.828397	+	0.633413i
$784$		0			0
$785$	76.7603	−	44.3176i	2.73969	−	1.58176i
$786$		0			0
$787$	−12.4660	+	21.5917i	−0.444364	+	0.769660i	−0.998008	−	0.0630931i	$-0.979903\pi$
$787$	−12.4660	+	21.5917i	−0.444364	+	0.769660i	0.553644	+	0.832753i	$0.313237\pi$
$788$		0			0
$789$	−22.1402	+	14.0872i	−0.788213	+	0.501519i
$790$		0			0
$791$	−41.3883			−1.47160
$792$		0			0
$793$	6.13211			0.217758
$794$		0			0
$795$	−8.58857	−	4.47712i	−0.304605	−	0.158787i
$796$		0			0
$797$	−26.4737	+	45.8537i	−0.937745	+	1.62422i	−0.168082	+	0.985773i	$0.553757\pi$
$797$	−26.4737	+	45.8537i	−0.937745	+	1.62422i	−0.769664	+	0.638450i	$0.779576\pi$
$798$		0			0
$799$	−39.4887	+	22.7988i	−1.39701	+	0.806563i
$800$		0			0
$801$	−1.59953	−	18.5248i	−0.0565166	−	0.654543i
$802$		0			0
$803$	3.41420	−	1.97119i	0.120485	−	0.0695618i
$804$		0			0
$805$	−0.818397	−	0.472502i	−0.0288447	−	0.0166535i
$806$		0			0
$807$	0.0658050	+	1.52707i	0.00231644	+	0.0537553i
$808$		0			0
$809$			42.9267i			1.50922i	0.656172	+	0.754612i	$0.272175\pi$
$809$			42.9267i			1.50922i	−0.656172	+	0.754612i	$0.727825\pi$
$810$		0			0
$811$	−21.8439			−0.767044			−0.383522	−	0.923532i	$-0.625289\pi$
$811$	−21.8439			−0.767044			−0.383522	+	0.923532i	$0.625289\pi$
$812$		0			0
$813$	−37.3375	+	1.60897i	−1.30948	+	0.0564289i
$814$		0			0
$815$	13.1031	−	22.6953i	0.458982	−	0.794980i
$816$		0			0
$817$	−27.5499	−	47.7177i	−0.963847	−	1.66943i
$818$		0			0
$819$	−23.2265	+	2.00550i	−0.811600	+	0.0700778i
$820$		0			0
$821$	−15.8837	−	27.5114i	−0.554346	−	0.960155i	−0.997954	−	0.0639346i	$-0.979635\pi$
$821$	−15.8837	−	27.5114i	−0.554346	−	0.960155i	0.443608	−	0.896221i	$-0.353698\pi$
$822$		0			0
$823$	−41.7348	−	24.0956i	−1.45478	−	0.839920i	−0.456037	−	0.889961i	$-0.650732\pi$
$823$	−41.7348	−	24.0956i	−1.45478	−	0.839920i	−0.998747	+	0.0500406i	$0.984065\pi$
$824$		0			0
$825$	−5.06661	+	9.71940i	−0.176397	+	0.338386i
$826$		0			0
$827$			25.0818i			0.872178i	0.899904	+	0.436089i	$0.143637\pi$
$827$			25.0818i			0.872178i	−0.899904	+	0.436089i	$0.856363\pi$
$828$		0			0
$829$			50.2271i			1.74446i	0.489096	+	0.872230i	$0.337327\pi$
$829$			50.2271i			1.74446i	−0.489096	+	0.872230i	$0.662673\pi$
$830$		0			0
$831$	7.23159	+	11.3656i	0.250861	+	0.394267i
$832$		0			0
$833$	30.7557	+	17.7568i	1.06562	+	0.615238i
$834$		0			0
$835$	−22.2176	−	38.4821i	−0.768873	−	1.33173i
$836$		0			0
$837$	−1.26014	+	3.02766i	−0.0435568	+	0.104651i
$838$		0			0
$839$	18.1864	+	31.4997i	0.627863	+	1.08749i	0.987980	+	0.154583i	$0.0494035\pi$
$839$	18.1864	+	31.4997i	0.627863	+	1.08749i	−0.360117	+	0.932907i	$0.617263\pi$
$840$		0			0
$841$	−1.26807	+	2.19637i	−0.0437266	+	0.0757367i
$842$		0			0
$843$	19.5387	+	30.7080i	0.672948	+	1.05764i
$844$		0			0
$845$	36.9268			1.27032
$846$		0			0
$847$			40.4531i			1.38999i
$848$		0			0
$849$	−9.39574	−	4.89789i	−0.322461	−	0.168095i
$850$		0			0
$851$	−0.346995	−	0.200338i	−0.0118948	−	0.00686749i
$852$		0			0
$853$	10.0120	−	5.78041i	0.342803	−	0.197917i	−0.318708	−	0.947853i	$-0.603249\pi$
$853$	10.0120	−	5.78041i	0.342803	−	0.197917i	0.661511	+	0.749936i	$0.269916\pi$
$854$		0			0
$855$	−34.0360	+	72.7748i	−1.16401	+	2.48885i
$856$		0			0
$857$	9.35374	−	5.40038i	0.319518	−	0.184474i	−0.331660	−	0.943399i	$-0.607609\pi$
$857$	9.35374	−	5.40038i	0.319518	−	0.184474i	0.651178	+	0.758925i	$0.274275\pi$
$858$		0			0
$859$	−2.13803	+	3.70317i	−0.0729485	+	0.126351i	−0.900192	−	0.435493i	$-0.856574\pi$
$859$	−2.13803	+	3.70317i	−0.0729485	+	0.126351i	0.827244	+	0.561843i	$0.189908\pi$
$860$		0			0
$861$	−1.44015	−	33.4201i	−0.0490803	−	1.13895i
$862$		0			0
$863$	−50.5426			−1.72049			−0.860245	−	0.509881i	$-0.829689\pi$
$863$	−50.5426			−1.72049			−0.860245	+	0.509881i	$0.829689\pi$
$864$		0			0
$865$	9.66190			0.328515
$866$		0			0
$867$	0.579091	+	13.4384i	0.0196670	+	0.456390i
$868$		0			0
$869$	−0.170310	+	0.294986i	−0.00577737	+	0.0100067i
$870$		0			0
$871$	−7.42428	+	4.28641i	−0.251562	+	0.145239i
$872$		0			0
$873$	2.97130	+	4.25372i	0.100563	+	0.143967i
$874$		0			0
$875$	108.823	−	62.8289i	3.67888	−	2.12400i
$876$		0			0
$877$	32.5446	+	18.7896i	1.09895	+	0.634481i	0.935946	−	0.352144i	$-0.114547\pi$
$877$	32.5446	+	18.7896i	1.09895	+	0.634481i	0.163007	+	0.986625i	$0.447881\pi$
$878$		0			0
$879$	−13.1182	−	6.83838i	−0.442466	−	0.230653i
$880$		0			0
$881$			25.6381i			0.863769i	0.901929	+	0.431885i	$0.142151\pi$
$881$			25.6381i			0.863769i	−0.901929	+	0.431885i	$0.857849\pi$
$882$		0			0
$883$	26.8456			0.903426			0.451713	−	0.892163i	$-0.350813\pi$
$883$	26.8456			0.903426			0.451713	+	0.892163i	$0.350813\pi$
$884$		0			0
$885$	−30.3394	−	47.6830i	−1.01985	−	1.60284i
$886$		0			0
$887$	10.0655	−	17.4339i	0.337965	−	0.585373i	−0.646084	−	0.763266i	$-0.723595\pi$
$887$	10.0655	−	17.4339i	0.337965	−	0.585373i	0.984050	+	0.177893i	$0.0569280\pi$
$888$		0			0
$889$	19.6251	+	33.9917i	0.658206	+	1.14005i
$890$		0			0
$891$	3.38864	−	2.83033i	0.113524	−	0.0948195i
$892$		0			0
$893$	−28.9987	−	50.2272i	−0.970404	−	1.68079i
$894$		0			0
$895$	7.81780	+	4.51361i	0.261320	+	0.150873i
$896$		0			0
$897$	0.114168	+	0.179433i	0.00381196	+	0.00599108i
$898$		0			0
$899$			3.54422i			0.118206i
$900$		0			0
$901$		−	6.57757i		−	0.219130i
$902$		0			0
$903$	26.2037	−	50.2671i	0.872004	−	1.67279i
$904$		0			0
$905$	−10.0556	−	5.80560i	−0.334259	−	0.192985i
$906$		0			0
$907$	8.21720	+	14.2326i	0.272848	+	0.472586i	0.969590	−	0.244736i	$-0.0787012\pi$
$907$	8.21720	+	14.2326i	0.272848	+	0.472586i	−0.696742	+	0.717322i	$0.745368\pi$
$908$		0			0
$909$	−18.0180	−	25.7947i	−0.597620	−	0.855555i
$910$		0			0
$911$	−28.7160	−	49.7376i	−0.951405	−	1.64788i	−0.742389	−	0.669969i	$-0.766307\pi$
$911$	−28.7160	−	49.7376i	−0.951405	−	1.64788i	−0.209016	−	0.977912i	$-0.567026\pi$
$912$		0			0
$913$	2.39726	−	4.15217i	0.0793376	−	0.137417i
$914$		0			0
$915$	21.7210	−	0.936010i	0.718074	−	0.0309435i
$916$		0			0
$917$	−51.7850			−1.71009
$918$		0			0
$919$		−	9.87518i		−	0.325752i	−0.986647	−	0.162876i	$-0.947923\pi$
$919$		−	9.87518i		−	0.325752i	0.986647	−	0.162876i	$-0.0520771\pi$
$920$		0			0
$921$	−1.02925	−	23.8847i	−0.0339149	−	0.787026i
$922$		0			0
$923$	−7.28396	−	4.20540i	−0.239755	−	0.138422i
$924$		0			0
$925$	75.3445	−	43.5002i	2.47731	−	1.43028i
$926$		0			0
$927$	−35.9428	−	16.8101i	−1.18052	−	0.552117i
$928$		0			0
$929$	18.4476	−	10.6507i	0.605247	−	0.349440i	−0.165856	−	0.986150i	$-0.553039\pi$
$929$	18.4476	−	10.6507i	0.605247	−	0.349440i	0.771103	+	0.636710i	$0.219705\pi$
$930$		0			0
$931$	−22.5856	+	39.1195i	−0.740214	+	1.28209i
$932$		0			0
$933$	38.0931	+	19.8575i	1.24711	+	0.650106i
$934$		0			0
$935$	−10.3288			−0.337789
$936$		0			0
$937$	35.6286			1.16394			0.581968	−	0.813212i	$-0.302283\pi$
$937$	35.6286			1.16394			0.581968	+	0.813212i	$0.302283\pi$
$938$		0			0
$939$	−28.6092	+	18.2032i	−0.933625	+	0.594040i
$940$		0			0
$941$	0.794731	−	1.37651i	0.0259075	−	0.0448731i	−0.852781	−	0.522269i	$-0.825086\pi$
$941$	0.794731	−	1.37651i	0.0259075	−	0.0448731i	0.878688	+	0.477396i	$0.158419\pi$
$942$		0			0
$943$	−0.264277	+	0.152580i	−0.00860605	+	0.00496870i
$944$		0			0
$945$	−81.9662	+	10.6491i	−2.66636	+	0.346416i
$946$		0			0
$947$	17.0690	−	9.85480i	0.554668	−	0.320238i	−0.196334	−	0.980537i	$-0.562904\pi$
$947$	17.0690	−	9.85480i	0.554668	−	0.320238i	0.751003	+	0.660299i	$0.229570\pi$
$948$		0			0
$949$	14.3845	+	8.30488i	0.466940	+	0.269588i
$950$		0			0
$951$	−3.50283	+	2.22876i	−0.113587	+	0.0722724i
$952$		0			0
$953$			28.4142i			0.920425i	0.887809	+	0.460213i	$0.152227\pi$
$953$			28.4142i			0.920425i	−0.887809	+	0.460213i	$0.847773\pi$
$954$		0			0
$955$	84.2891			2.72753
$956$		0			0
$957$	2.20571	−	4.23126i	0.0713004	−	0.136777i
$958$		0			0
$959$	−30.1684	+	52.2531i	−0.974187	+	1.68734i
$960$		0			0
$961$	−15.3008	−	26.5018i	−0.493575	−	0.854898i
$962$		0			0
$963$	2.14545	+	24.8474i	0.0691363	+	0.800697i
$964$		0			0
$965$	33.4276	+	57.8984i	1.07607	+	1.86382i
$966$		0			0
$967$	−23.2411	−	13.4182i	−0.747383	−	0.431502i	0.0773646	−	0.997003i	$-0.475349\pi$
$967$	−23.2411	−	13.4182i	−0.747383	−	0.431502i	−0.824748	+	0.565501i	$0.808683\pi$
$968$		0			0
$969$	−54.5102	+	2.34898i	−1.75112	+	0.0754600i
$970$		0			0
$971$		−	8.16592i		−	0.262057i	−0.991379	−	0.131028i	$-0.958172\pi$
$971$		−	8.16592i		−	0.262057i	0.991379	−	0.131028i	$-0.0418279\pi$
$972$		0			0
$973$		−	38.1589i		−	1.22332i
$974$		0			0
$975$	−46.1361	+	1.98812i	−1.47754	+	0.0636707i
$976$		0			0
$977$	−21.8440	−	12.6117i	−0.698852	−	0.403483i	0.108068	−	0.994144i	$-0.465534\pi$
$977$	−21.8440	−	12.6117i	−0.698852	−	0.403483i	−0.806920	+	0.590661i	$0.798867\pi$
$978$		0			0
$979$	1.52027	+	2.63318i	0.0485880	+	0.0841568i
$980$		0			0
$981$	−1.00188	−	11.6032i	−0.0319876	−	0.370462i
$982$		0			0
$983$	−26.1298	−	45.2581i	−0.833411	−	1.44351i	−0.895318	−	0.445428i	$-0.853052\pi$
$983$	−26.1298	−	45.2581i	−0.833411	−	1.44351i	0.0619068	−	0.998082i	$-0.480282\pi$
$984$		0			0
$985$	18.8287	−	32.6123i	0.599933	−	1.03911i
$986$		0			0
$987$	27.5817	−	52.9107i	0.877936	−	1.68416i
$988$		0			0
$989$	−0.517132			−0.0164439
$990$		0			0
$991$		−	34.3144i		−	1.09003i	−0.838425	−	0.545017i	$-0.816523\pi$
$991$		−	34.3144i		−	1.09003i	0.838425	−	0.545017i	$-0.183477\pi$
$992$		0			0
$993$	−47.1671	+	30.0111i	−1.49680	+	0.952375i
$994$		0			0
$995$	−78.5298	−	45.3392i	−2.48956	−	1.43735i
$996$		0			0
$997$	11.5746	−	6.68258i	0.366570	−	0.211639i	−0.305389	−	0.952228i	$-0.598786\pi$
$997$	11.5746	−	6.68258i	0.366570	−	0.211639i	0.671959	+	0.740588i	$0.265453\pi$
$998$		0			0
$999$	−34.7531	+	4.51516i	−1.09954	+	0.142853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.g.959.6	yes	24
3.2	odd	2		3456.2.p.g.2879.12		24
4.3	odd	2		1152.2.p.f.959.7	yes	24
8.3	odd	2		1152.2.p.f.959.6	yes	24
8.5	even	2	inner	1152.2.p.g.959.7	yes	24
9.2	odd	6		1152.2.p.f.191.6	✓	24
9.7	even	3		3456.2.p.f.575.1		24
12.11	even	2		3456.2.p.f.2879.12		24
24.5	odd	2		3456.2.p.g.2879.1		24
24.11	even	2		3456.2.p.f.2879.1		24
36.7	odd	6		3456.2.p.g.575.1		24
36.11	even	6	inner	1152.2.p.g.191.7	yes	24
72.11	even	6	inner	1152.2.p.g.191.6	yes	24
72.29	odd	6		1152.2.p.f.191.7	yes	24
72.43	odd	6		3456.2.p.g.575.12		24
72.61	even	6		3456.2.p.f.575.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.f.191.6	✓	24	9.2	odd	6
1152.2.p.f.191.7	yes	24	72.29	odd	6
1152.2.p.f.959.6	yes	24	8.3	odd	2
1152.2.p.f.959.7	yes	24	4.3	odd	2
1152.2.p.g.191.6	yes	24	72.11	even	6	inner
1152.2.p.g.191.7	yes	24	36.11	even	6	inner
1152.2.p.g.959.6	yes	24	1.1	even	1	trivial
1152.2.p.g.959.7	yes	24	8.5	even	2	inner
3456.2.p.f.575.1		24	9.7	even	3
3456.2.p.f.575.12		24	72.61	even	6
3456.2.p.f.2879.1		24	24.11	even	2
3456.2.p.f.2879.12		24	12.11	even	2
3456.2.p.g.575.1		24	36.7	odd	6
3456.2.p.g.575.12		24	72.43	odd	6
3456.2.p.g.2879.1		24	24.5	odd	2
3456.2.p.g.2879.12		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0745691 - 1.73044i) q^{3} +(-2.11539 + 3.66397i) q^{5} +(3.25610 - 1.87991i) q^{7} +(-2.98888 + 0.258075i) q^{9} +O(q^{10})\)	\(q+(-0.0745691 - 1.73044i) q^{3} +(-2.11539 + 3.66397i) q^{5} +(3.25610 - 1.87991i) q^{7} +(-2.98888 + 0.258075i) q^{9} +(0.424849 - 0.245287i) q^{11} +(1.78994 + 1.03342i) q^{13} +(6.49804 + 3.38735i) q^{15} +4.97653i q^{17} -6.32985 q^{19} +(-3.49588 - 5.49431i) q^{21} +(-0.0297041 + 0.0514489i) q^{23} +(-6.44977 - 11.1713i) q^{25} +(0.669463 + 5.15285i) q^{27} +(2.80785 + 4.86334i) q^{29} +(0.546572 + 0.315564i) q^{31} +(-0.456136 - 0.716887i) q^{33} +15.9070i q^{35} +6.74445i q^{37} +(1.65481 - 3.17446i) q^{39} +(4.44850 + 2.56834i) q^{41} +(4.35237 + 7.53853i) q^{43} +(5.37707 - 11.4971i) q^{45} +(4.58126 + 7.93498i) q^{47} +(3.56812 - 6.18016i) q^{49} +(8.61161 - 0.371095i) q^{51} -1.32172 q^{53} +2.07551i q^{55} +(0.472011 + 10.9535i) q^{57} +(-6.67923 - 3.85625i) q^{59} +(2.56940 - 1.48344i) q^{61} +(-9.24692 + 6.45914i) q^{63} +(-7.57287 + 4.37220i) q^{65} +(-2.07388 + 3.59207i) q^{67} +(0.0912445 + 0.0475647i) q^{69} -4.06938 q^{71} +8.03627 q^{73} +(-18.8504 + 11.9940i) q^{75} +(0.922234 - 1.59736i) q^{77} +(-0.601308 + 0.347165i) q^{79} +(8.86679 - 1.54271i) q^{81} +(8.46391 - 4.88664i) q^{83} +(-18.2338 - 10.5273i) q^{85} +(8.20637 - 5.22149i) q^{87} +6.19792i q^{89} +7.77098 q^{91} +(0.505308 - 0.969344i) q^{93} +(13.3901 - 23.1924i) q^{95} +(-0.864785 - 1.49785i) q^{97} +(-1.20652 + 0.842776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{7} - 4 q^{9}+O(q^{10}) \) 24 * q + 12 * q^7 - 4 * q^9	\( 24 q + 12 q^{7} - 4 q^{9} + 20 q^{15} - 12 q^{23} - 12 q^{25} - 36 q^{31} + 4 q^{33} + 20 q^{39} - 12 q^{41} + 12 q^{47} + 12 q^{49} + 4 q^{57} - 92 q^{63} - 48 q^{65} + 24 q^{73} + 84 q^{79} - 20 q^{81} + 68 q^{87} + 24 q^{95} - 12 q^{97}+O(q^{100}) \) 24 * q + 12 * q^7 - 4 * q^9 + 20 * q^15 - 12 * q^23 - 12 * q^25 - 36 * q^31 + 4 * q^33 + 20 * q^39 - 12 * q^41 + 12 * q^47 + 12 * q^49 + 4 * q^57 - 92 * q^63 - 48 * q^65 + 24 * q^73 + 84 * q^79 - 20 * q^81 + 68 * q^87 + 24 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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