LMFDB - Embedded newform 1620.2.e.b.971.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.34
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.863299 + 1.12014i) q^{2} +(-0.509428 + 1.93403i) q^{4} +1.00000i q^{5} +1.02978i q^{7} +(-2.60618 + 1.09902i) q^{8} +O(q^{10})$	\(q+(0.863299 + 1.12014i) q^{2} +(-0.509428 + 1.93403i) q^{4} +1.00000i q^{5} +1.02978i q^{7} +(-2.60618 + 1.09902i) q^{8} +(-1.12014 + 0.863299i) q^{10} -3.69887 q^{11} -5.05195 q^{13} +(-1.15350 + 0.889012i) q^{14} +(-3.48097 - 1.97050i) q^{16} -2.05180i q^{17} -5.65622i q^{19} +(-1.93403 - 0.509428i) q^{20} +(-3.19323 - 4.14325i) q^{22} +0.311124 q^{23} -1.00000 q^{25} +(-4.36134 - 5.65889i) q^{26} +(-1.99164 - 0.524601i) q^{28} -0.993453i q^{29} -4.07754i q^{31} +(-0.797876 - 5.60030i) q^{32} +(2.29830 - 1.77132i) q^{34} -1.02978 q^{35} +8.38894 q^{37} +(6.33576 - 4.88301i) q^{38} +(-1.09902 - 2.60618i) q^{40} +9.77298i q^{41} +4.84241i q^{43} +(1.88431 - 7.15373i) q^{44} +(0.268593 + 0.348502i) q^{46} -10.5990 q^{47} +5.93954 q^{49} +(-0.863299 - 1.12014i) q^{50} +(2.57361 - 9.77063i) q^{52} +5.37471i q^{53} -3.69887i q^{55} +(-1.13175 - 2.68380i) q^{56} +(1.11281 - 0.857648i) q^{58} -8.13851 q^{59} -14.3485 q^{61} +(4.56742 - 3.52014i) q^{62} +(5.58432 - 5.72847i) q^{64} -5.05195i q^{65} +4.45736i q^{67} +(3.96824 + 1.04524i) q^{68} +(-0.889012 - 1.15350i) q^{70} +0.205268 q^{71} -5.22615 q^{73} +(7.24217 + 9.39679i) q^{74} +(10.9393 + 2.88144i) q^{76} -3.80903i q^{77} -13.5159i q^{79} +(1.97050 - 3.48097i) q^{80} +(-10.9471 + 8.43700i) q^{82} -0.215976 q^{83} +2.05180 q^{85} +(-5.42418 + 4.18045i) q^{86} +(9.63990 - 4.06512i) q^{88} +18.2569i q^{89} -5.20241i q^{91} +(-0.158495 + 0.601723i) q^{92} +(-9.15012 - 11.8724i) q^{94} +5.65622 q^{95} +9.67634 q^{97} +(5.12761 + 6.65312i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.863299	+	1.12014i	0.610445	+	0.792059i
$2$	0.863299	+	1.12014i	0.610445	+	0.792059i
$3$		0			0
$3$		0			0
$4$	−0.509428	+	1.93403i	−0.254714	+	0.967016i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			1.02978i			0.389222i	0.980881	+	0.194611i	$0.0623444\pi$
$7$			1.02978i			0.389222i	−0.980881	+	0.194611i	$0.937656\pi$
$8$	−2.60618	+	1.09902i	−0.921423	+	0.388562i
$9$		0			0
$10$	−1.12014	+	0.863299i	−0.354219	+	0.272999i
$11$	−3.69887			−1.11525			−0.557625	−	0.830093i	$-0.688287\pi$
$11$	−3.69887			−1.11525			−0.557625	+	0.830093i	$0.688287\pi$
$12$		0			0
$13$	−5.05195			−1.40116			−0.700579	−	0.713575i	$-0.747075\pi$
$13$	−5.05195			−1.40116			−0.700579	+	0.713575i	$0.747075\pi$
$14$	−1.15350	+	0.889012i	−0.308287	+	0.237598i
$15$		0			0
$16$	−3.48097	−	1.97050i	−0.870241	−	0.492626i
$17$		−	2.05180i		−	0.497634i	−0.968551	−	0.248817i	$-0.919958\pi$
$17$		−	2.05180i		−	0.497634i	0.968551	−	0.248817i	$-0.0800418\pi$
$18$		0			0
$19$		−	5.65622i		−	1.29763i	−0.760948	−	0.648813i	$-0.775266\pi$
$19$		−	5.65622i		−	1.29763i	0.760948	−	0.648813i	$-0.224734\pi$
$20$	−1.93403	−	0.509428i	−0.432463	−	0.113912i
$21$		0			0
$22$	−3.19323	−	4.14325i	−0.680798	−	0.883343i
$23$	0.311124			0.0648738			0.0324369	−	0.999474i	$-0.489673\pi$
$23$	0.311124			0.0648738			0.0324369	+	0.999474i	$0.489673\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−4.36134	−	5.65889i	−0.855330	−	1.10980i
$27$		0			0
$28$	−1.99164	−	0.524601i	−0.376384	−	0.0991403i
$29$		−	0.993453i		−	0.184480i	−0.995737	−	0.0922398i	$-0.970597\pi$
$29$		−	0.993453i		−	0.184480i	0.995737	−	0.0922398i	$-0.0294026\pi$
$30$		0			0
$31$		−	4.07754i		−	0.732349i	−0.930546	−	0.366174i	$-0.880667\pi$
$31$		−	4.07754i		−	0.732349i	0.930546	−	0.366174i	$-0.119333\pi$
$32$	−0.797876	−	5.60030i	−0.141046	−	0.990003i
$33$		0			0
$34$	2.29830	−	1.77132i	0.394155	−	0.303778i
$35$	−1.02978			−0.174065
$36$		0			0
$37$	8.38894			1.37913			0.689567	−	0.724222i	$-0.257801\pi$
$37$	8.38894			1.37913			0.689567	+	0.724222i	$0.257801\pi$
$38$	6.33576	−	4.88301i	1.02780	−	0.792129i
$39$		0			0
$40$	−1.09902	−	2.60618i	−0.173770	−	0.412073i
$41$			9.77298i			1.52628i	0.646232	+	0.763141i	$0.276344\pi$
$41$			9.77298i			1.52628i	−0.646232	+	0.763141i	$0.723656\pi$
$42$		0			0
$43$			4.84241i			0.738461i	0.929338	+	0.369230i	$0.120379\pi$
$43$			4.84241i			0.738461i	−0.929338	+	0.369230i	$0.879621\pi$
$44$	1.88431	−	7.15373i	0.284070	−	1.07846i
$45$		0			0
$46$	0.268593	+	0.348502i	0.0396018	+	0.0513838i
$47$	−10.5990			−1.54602			−0.773012	−	0.634391i	$-0.781251\pi$
$47$	−10.5990			−1.54602			−0.773012	+	0.634391i	$0.781251\pi$
$48$		0			0
$49$	5.93954			0.848506
$50$	−0.863299	−	1.12014i	−0.122089	−	0.158412i
$51$		0			0
$52$	2.57361	−	9.77063i	0.356895	−	1.35494i
$53$			5.37471i			0.738273i	0.929375	+	0.369136i	$0.120346\pi$
$53$			5.37471i			0.738273i	−0.929375	+	0.369136i	$0.879654\pi$
$54$		0			0
$55$		−	3.69887i		−	0.498755i
$56$	−1.13175	−	2.68380i	−0.151237	−	0.358638i
$57$		0			0
$58$	1.11281	−	0.857648i	0.146119	−	0.112615i
$59$	−8.13851			−1.05954			−0.529772	−	0.848140i	$-0.677722\pi$
$59$	−8.13851			−1.05954			−0.529772	+	0.848140i	$0.677722\pi$
$60$		0			0
$61$	−14.3485			−1.83714			−0.918571	−	0.395255i	$-0.870656\pi$
$61$	−14.3485			−1.83714			−0.918571	+	0.395255i	$0.870656\pi$
$62$	4.56742	−	3.52014i	0.580063	−	0.447058i
$63$		0			0
$64$	5.58432	−	5.72847i	0.698040	−	0.716059i
$65$		−	5.05195i		−	0.626617i
$66$		0			0
$67$			4.45736i			0.544554i	0.962219	+	0.272277i	$0.0877767\pi$
$67$			4.45736i			0.544554i	−0.962219	+	0.272277i	$0.912223\pi$
$68$	3.96824	+	1.04524i	0.481220	+	0.126754i
$69$		0			0
$70$	−0.889012	−	1.15350i	−0.106257	−	0.137870i
$71$	0.205268			0.0243609			0.0121804	−	0.999926i	$-0.496123\pi$
$71$	0.205268			0.0243609			0.0121804	+	0.999926i	$0.496123\pi$
$72$		0			0
$73$	−5.22615			−0.611675			−0.305837	−	0.952084i	$-0.598936\pi$
$73$	−5.22615			−0.611675			−0.305837	+	0.952084i	$0.598936\pi$
$74$	7.24217	+	9.39679i	0.841885	+	1.09235i
$75$		0			0
$76$	10.9393	+	2.88144i	1.25483	+	0.330524i
$77$		−	3.80903i		−	0.434080i
$78$		0			0
$79$		−	13.5159i		−	1.52066i	−0.649537	−	0.760330i	$-0.725037\pi$
$79$		−	13.5159i		−	1.52066i	0.649537	−	0.760330i	$-0.274963\pi$
$80$	1.97050	−	3.48097i	0.220309	−	0.389184i
$81$		0			0
$82$	−10.9471	+	8.43700i	−1.20891	+	0.931711i
$83$	−0.215976			−0.0237064			−0.0118532	−	0.999930i	$-0.503773\pi$
$83$	−0.215976			−0.0237064			−0.0118532	+	0.999930i	$0.503773\pi$
$84$		0			0
$85$	2.05180			0.222549
$86$	−5.42418	+	4.18045i	−0.584904	+	0.450790i
$87$		0			0
$88$	9.63990	−	4.06512i	1.02762	−	0.433343i
$89$			18.2569i			1.93523i	0.252431	+	0.967615i	$0.418770\pi$
$89$			18.2569i			1.93523i	−0.252431	+	0.967615i	$0.581230\pi$
$90$		0			0
$91$		−	5.20241i		−	0.545361i
$92$	−0.158495	+	0.601723i	−0.0165243	+	0.0627340i
$93$		0			0
$94$	−9.15012	−	11.8724i	−0.943763	−	1.22454i
$95$	5.65622			0.580316
$96$		0			0
$97$	9.67634			0.982484			0.491242	−	0.871023i	$-0.336543\pi$
$97$	9.67634			0.982484			0.491242	+	0.871023i	$0.336543\pi$
$98$	5.12761	+	6.65312i	0.517966	+	0.672067i
$99$		0			0
$100$	0.509428	−	1.93403i	0.0509428	−	0.193403i
$101$			7.10060i			0.706536i	0.935522	+	0.353268i	$0.114930\pi$
$101$			7.10060i			0.706536i	−0.935522	+	0.353268i	$0.885070\pi$
$102$		0			0
$103$		−	3.73054i		−	0.367581i	−0.982965	−	0.183791i	$-0.941163\pi$
$103$		−	3.73054i		−	0.367581i	0.982965	−	0.183791i	$-0.0588368\pi$
$104$	13.1663	−	5.55218i	1.29106	−	0.544436i
$105$		0			0
$106$	−6.02042	+	4.63998i	−0.584755	+	0.450675i
$107$	−17.7410			−1.71509			−0.857544	−	0.514411i	$-0.828010\pi$
$107$	−17.7410			−1.71509			−0.857544	+	0.514411i	$0.828010\pi$
$108$		0			0
$109$	−9.54043			−0.913807			−0.456904	−	0.889516i	$-0.651042\pi$
$109$	−9.54043			−0.913807			−0.456904	+	0.889516i	$0.651042\pi$
$110$	4.14325	−	3.19323i	0.395043	−	0.304462i
$111$		0			0
$112$	2.02919	−	3.58464i	0.191741	−	0.338717i
$113$		−	1.10586i		−	0.104030i	−0.998646	−	0.0520151i	$-0.983436\pi$
$113$		−	1.10586i		−	0.104030i	0.998646	−	0.0520151i	$-0.0165644\pi$
$114$		0			0
$115$			0.311124i			0.0290124i
$116$	1.92137	+	0.506093i	0.178395	+	0.0469896i
$117$		0			0
$118$	−7.02597	−	9.11627i	−0.646793	−	0.839221i
$119$	2.11291			0.193690
$120$		0			0
$121$	2.68160			0.243782
$122$	−12.3871	−	16.0724i	−1.12147	−	1.45513i
$123$		0			0
$124$	7.88610	+	2.07722i	0.708193	+	0.186540i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	12.2087i		−	1.08335i	−0.840590	−	0.541673i	$-0.817791\pi$
$127$		−	12.2087i		−	1.08335i	0.840590	−	0.541673i	$-0.182209\pi$
$128$	11.2376	+	1.30983i	0.993276	+	0.115774i
$129$		0			0
$130$	5.65889	−	4.36134i	0.496317	−	0.382515i
$131$	−4.99703			−0.436592			−0.218296	−	0.975883i	$-0.570050\pi$
$131$	−4.99703			−0.436592			−0.218296	+	0.975883i	$0.570050\pi$
$132$		0			0
$133$	5.82469			0.505064
$134$	−4.99287	+	3.84804i	−0.431319	+	0.332420i
$135$		0			0
$136$	2.25496	+	5.34735i	0.193361	+	0.458531i
$137$			8.49386i			0.725679i	0.931852	+	0.362840i	$0.118193\pi$
$137$			8.49386i			0.725679i	−0.931852	+	0.362840i	$0.881807\pi$
$138$		0			0
$139$		−	14.3038i		−	1.21323i	−0.794995	−	0.606616i	$-0.792526\pi$
$139$		−	14.3038i		−	1.21323i	0.794995	−	0.606616i	$-0.207474\pi$
$140$	0.524601	−	1.99164i	0.0443369	−	0.168324i
$141$		0			0
$142$	0.177208	+	0.229929i	0.0148710	+	0.0192953i
$143$	18.6865			1.56264
$144$		0			0
$145$	0.993453			0.0825018
$146$	−4.51173	−	5.85402i	−0.373394	−	0.484482i
$147$		0			0
$148$	−4.27356	+	16.2245i	−0.351285	+	1.33364i
$149$		−	5.26864i		−	0.431624i	−0.976435	−	0.215812i	$-0.930760\pi$
$149$		−	5.26864i		−	0.431624i	0.976435	−	0.215812i	$-0.0692398\pi$
$150$		0			0
$151$		−	4.79361i		−	0.390098i	−0.980793	−	0.195049i	$-0.937513\pi$
$151$		−	4.79361i		−	0.390098i	0.980793	−	0.195049i	$-0.0624866\pi$
$152$	6.21629	+	14.7411i	0.504208	+	1.19566i
$153$		0			0
$154$	4.26665	−	3.28834i	0.343816	−	0.264982i
$155$	4.07754			0.327516
$156$		0			0
$157$	−14.6255			−1.16724			−0.583620	−	0.812027i	$-0.698364\pi$
$157$	−14.6255			−1.16724			−0.583620	+	0.812027i	$0.698364\pi$
$158$	15.1397	−	11.6683i	1.20445	−	0.928279i
$159$		0			0
$160$	5.60030	−	0.797876i	0.442743	−	0.0630777i
$161$			0.320390i			0.0252503i
$162$		0			0
$163$			17.5451i			1.37424i	0.726545	+	0.687119i	$0.241125\pi$
$163$			17.5451i			1.37424i	−0.726545	+	0.687119i	$0.758875\pi$
$164$	−18.9013	−	4.97863i	−1.47594	−	0.388766i
$165$		0			0
$166$	−0.186452	−	0.241923i	−0.0144715	−	0.0187769i
$167$	−4.09514			−0.316891			−0.158446	−	0.987368i	$-0.550648\pi$
$167$	−4.09514			−0.316891			−0.158446	+	0.987368i	$0.550648\pi$
$168$		0			0
$169$	12.5222			0.963244
$170$	1.77132	+	2.29830i	0.135854	+	0.176272i
$171$		0			0
$172$	−9.36538	−	2.46686i	−0.714104	−	0.188096i
$173$			12.2973i			0.934948i	0.884007	+	0.467474i	$0.154836\pi$
$173$			12.2973i			0.934948i	−0.884007	+	0.467474i	$0.845164\pi$
$174$		0			0
$175$		−	1.02978i		−	0.0778444i
$176$	12.8756	+	7.28862i	0.970537	+	0.549401i
$177$		0			0
$178$	−20.4503	+	15.7612i	−1.53282	+	1.18135i
$179$	2.27031			0.169691			0.0848456	−	0.996394i	$-0.472960\pi$
$179$	2.27031			0.169691			0.0848456	+	0.996394i	$0.472960\pi$
$180$		0			0
$181$	−12.0463			−0.895396			−0.447698	−	0.894185i	$-0.647756\pi$
$181$	−12.0463			−0.895396			−0.447698	+	0.894185i	$0.647756\pi$
$182$	5.82743	−	4.49124i	0.431958	−	0.332913i
$183$		0			0
$184$	−0.810843	+	0.341930i	−0.0597762	+	0.0252074i
$185$			8.38894i			0.616767i
$186$		0			0
$187$			7.58932i			0.554986i
$188$	5.39944	−	20.4988i	0.393794	−	1.49503i
$189$		0			0
$190$	4.88301	+	6.33576i	0.354251	+	0.459644i
$191$	−10.3730			−0.750561			−0.375281	−	0.926911i	$-0.622454\pi$
$191$	−10.3730			−0.750561			−0.375281	+	0.926911i	$0.622454\pi$
$192$		0			0
$193$	4.68332			0.337113			0.168557	−	0.985692i	$-0.446089\pi$
$193$	4.68332			0.337113			0.168557	+	0.985692i	$0.446089\pi$
$194$	8.35358	+	10.8389i	0.599752	+	0.778185i
$195$		0			0
$196$	−3.02577	+	11.4873i	−0.216127	+	0.820520i
$197$		−	2.61713i		−	0.186463i	−0.995644	−	0.0932314i	$-0.970280\pi$
$197$		−	2.61713i		−	0.186463i	0.995644	−	0.0932314i	$-0.0297197\pi$
$198$		0			0
$199$			25.6247i			1.81649i	0.418439	+	0.908245i	$0.362577\pi$
$199$			25.6247i			1.81649i	−0.418439	+	0.908245i	$0.637423\pi$
$200$	2.60618	−	1.09902i	0.184285	−	0.0777123i
$201$		0			0
$202$	−7.95366	+	6.12994i	−0.559618	+	0.431301i
$203$	1.02304			0.0718035
$204$		0			0
$205$	−9.77298			−0.682574
$206$	4.17873	−	3.22057i	0.291146	−	0.224388i
$207$		0			0
$208$	17.5857	+	9.95487i	1.21935	+	0.690246i
$209$			20.9216i			1.44718i
$210$		0			0
$211$		−	6.17549i		−	0.425139i	−0.977146	−	0.212569i	$-0.931817\pi$
$211$		−	6.17549i		−	0.425139i	0.977146	−	0.212569i	$-0.0681831\pi$
$212$	−10.3949	−	2.73803i	−0.713922	−	0.188048i
$213$		0			0
$214$	−15.3158	−	19.8724i	−1.04697	−	1.35845i
$215$	−4.84241			−0.330250
$216$		0			0
$217$	4.19899			0.285046
$218$	−8.23624	−	10.6866i	−0.557829	−	0.723789i
$219$		0			0
$220$	7.15373	+	1.88431i	0.482304	+	0.127040i
$221$			10.3656i			0.697264i
$222$		0			0
$223$		−	8.09589i		−	0.542141i	−0.962560	−	0.271070i	$-0.912622\pi$
$223$		−	8.09589i		−	0.542141i	0.962560	−	0.271070i	$-0.0873776\pi$
$224$	5.76710	−	0.821640i	0.385331	−	0.0548981i
$225$		0			0
$226$	1.23871	−	0.954685i	0.0823980	−	0.0635047i
$227$	19.5180			1.29546			0.647728	−	0.761872i	$-0.275719\pi$
$227$	19.5180			1.29546			0.647728	+	0.761872i	$0.275719\pi$
$228$		0			0
$229$	2.32064			0.153352			0.0766760	−	0.997056i	$-0.475569\pi$
$229$	2.32064			0.153352			0.0766760	+	0.997056i	$0.475569\pi$
$230$	−0.348502	+	0.268593i	−0.0229795	+	0.0177105i
$231$		0			0
$232$	1.09182	+	2.58912i	0.0716817	+	0.169984i
$233$		−	3.61005i		−	0.236502i	−0.992984	−	0.118251i	$-0.962271\pi$
$233$		−	3.61005i		−	0.236502i	0.992984	−	0.118251i	$-0.0377287\pi$
$234$		0			0
$235$		−	10.5990i		−	0.691403i
$236$	4.14599	−	15.7401i	0.269881	−	1.02460i
$237$		0			0
$238$	1.82407	+	2.36675i	0.118237	+	0.153414i
$239$	−11.0195			−0.712791			−0.356395	−	0.934335i	$-0.615994\pi$
$239$	−11.0195			−0.712791			−0.356395	+	0.934335i	$0.615994\pi$
$240$		0			0
$241$	4.40567			0.283794			0.141897	−	0.989881i	$-0.454680\pi$
$241$	4.40567			0.283794			0.141897	+	0.989881i	$0.454680\pi$
$242$	2.31503	+	3.00377i	0.148816	+	0.193090i
$243$		0			0
$244$	7.30956	−	27.7506i	0.467946	−	1.77655i
$245$			5.93954i			0.379464i
$246$		0			0
$247$			28.5749i			1.81818i
$248$	4.48130	+	10.6268i	0.284563	+	0.674803i
$249$		0			0
$250$	1.12014	−	0.863299i	0.0708439	−	0.0545998i
$251$	−23.1609			−1.46190			−0.730952	−	0.682429i	$-0.760924\pi$
$251$	−23.1609			−1.46190			−0.730952	+	0.682429i	$0.760924\pi$
$252$		0			0
$253$	−1.15080			−0.0723504
$254$	13.6754	−	10.5397i	0.858073	−	0.661322i
$255$		0			0
$256$	8.23424	+	13.7185i	0.514640	+	0.857406i
$257$			28.8052i			1.79682i	0.439159	+	0.898410i	$0.355277\pi$
$257$			28.8052i			1.79682i	−0.439159	+	0.898410i	$0.644723\pi$
$258$		0			0
$259$			8.63880i			0.536789i
$260$	9.77063	+	2.57361i	0.605949	+	0.159608i
$261$		0			0
$262$	−4.31393	−	5.59737i	−0.266515	−	0.345807i
$263$	17.5153			1.08004			0.540021	−	0.841651i	$-0.318416\pi$
$263$	17.5153			1.08004			0.540021	+	0.841651i	$0.318416\pi$
$264$		0			0
$265$	−5.37471			−0.330166
$266$	5.02845	+	6.52446i	0.308314	+	0.400041i
$267$		0			0
$268$	−8.62069	−	2.27071i	−0.526592	−	0.138706i
$269$		−	4.31587i		−	0.263143i	−0.991307	−	0.131572i	$-0.957998\pi$
$269$		−	4.31587i		−	0.263143i	0.991307	−	0.131572i	$-0.0420023\pi$
$270$		0			0
$271$			15.3075i			0.929862i	0.885347	+	0.464931i	$0.153921\pi$
$271$			15.3075i			0.929862i	−0.885347	+	0.464931i	$0.846079\pi$
$272$	−4.04307	+	7.14223i	−0.245147	+	0.433062i
$273$		0			0
$274$	−9.51431	+	7.33274i	−0.574780	+	0.442987i
$275$	3.69887			0.223050
$276$		0			0
$277$	−7.99020			−0.480085			−0.240042	−	0.970762i	$-0.577161\pi$
$277$	−7.99020			−0.480085			−0.240042	+	0.970762i	$0.577161\pi$
$278$	16.0223	−	12.3485i	0.960952	−	0.740612i
$279$		0			0
$280$	2.68380	−	1.13175i	0.160388	−	0.0676351i
$281$		−	14.9592i		−	0.892393i	−0.894935	−	0.446196i	$-0.852778\pi$
$281$		−	14.9592i		−	0.892393i	0.894935	−	0.446196i	$-0.147222\pi$
$282$		0			0
$283$			16.8772i			1.00325i	0.865086	+	0.501623i	$0.167264\pi$
$283$			16.8772i			1.00325i	−0.865086	+	0.501623i	$0.832736\pi$
$284$	−0.104570	+	0.396996i	−0.00620506	+	0.0235574i
$285$		0			0
$286$	16.1320	+	20.9315i	0.953906	+	1.23770i
$287$	−10.0641			−0.594062
$288$		0			0
$289$	12.7901			0.752361
$290$	0.857648	+	1.11281i	0.0503628	+	0.0653463i
$291$		0			0
$292$	2.66235	−	10.1075i	0.155802	−	0.591500i
$293$		−	4.99558i		−	0.291845i	−0.989296	−	0.145923i	$-0.953385\pi$
$293$		−	4.99558i		−	0.291845i	0.989296	−	0.145923i	$-0.0466150\pi$
$294$		0			0
$295$		−	8.13851i		−	0.473842i
$296$	−21.8631	+	9.21960i	−1.27076	+	0.535878i
$297$		0			0
$298$	5.90162	−	4.54842i	0.341872	−	0.263483i
$299$	−1.57178			−0.0908984
$300$		0			0
$301$	−4.98664			−0.287425
$302$	5.36951	−	4.13832i	0.308981	−	0.238133i
$303$		0			0
$304$	−11.1456	+	19.6891i	−0.639244	+	1.12925i
$305$		−	14.3485i		−	0.821595i
$306$		0			0
$307$		−	3.45115i		−	0.196967i	−0.995139	−	0.0984837i	$-0.968601\pi$
$307$		−	3.45115i		−	0.196967i	0.995139	−	0.0984837i	$-0.0313992\pi$
$308$	7.36679	+	1.94043i	0.419762	+	0.110566i
$309$		0			0
$310$	3.52014	+	4.56742i	0.199931	+	0.259412i
$311$	−20.3625			−1.15465			−0.577327	−	0.816513i	$-0.695904\pi$
$311$	−20.3625			−1.15465			−0.577327	+	0.816513i	$0.695904\pi$
$312$		0			0
$313$	−13.1995			−0.746081			−0.373041	−	0.927815i	$-0.621685\pi$
$313$	−13.1995			−0.746081			−0.373041	+	0.927815i	$0.621685\pi$
$314$	−12.6262	−	16.3826i	−0.712536	−	0.924523i
$315$		0			0
$316$	26.1402	+	6.88540i	1.47050	+	0.387334i
$317$		−	1.81430i		−	0.101901i	−0.998701	−	0.0509507i	$-0.983775\pi$
$317$		−	1.81430i		−	0.101901i	0.998701	−	0.0509507i	$-0.0162251\pi$
$318$		0			0
$319$			3.67465i			0.205741i
$320$	5.72847	+	5.58432i	0.320231	+	0.312173i
$321$		0			0
$322$	−0.358882	+	0.276593i	−0.0199997	+	0.0154139i
$323$	−11.6054			−0.645743
$324$		0			0
$325$	5.05195			0.280232
$326$	−19.6530	+	15.1467i	−1.08848	+	0.838896i
$327$		0			0
$328$	−10.7407	−	25.4701i	−0.593055	−	1.40635i
$329$		−	10.9147i		−	0.601747i
$330$		0			0
$331$			0.500351i			0.0275018i	0.999905	+	0.0137509i	$0.00437718\pi$
$331$			0.500351i			0.0275018i	−0.999905	+	0.0137509i	$0.995623\pi$
$332$	0.110024	−	0.417704i	0.00603836	−	0.0229245i
$333$		0			0
$334$	−3.53533	−	4.58713i	−0.193445	−	0.250996i
$335$	−4.45736			−0.243532
$336$		0			0
$337$	10.1572			0.553298			0.276649	−	0.960971i	$-0.410776\pi$
$337$	10.1572			0.553298			0.276649	+	0.960971i	$0.410776\pi$
$338$	10.8104	+	14.0266i	0.588007	+	0.762946i
$339$		0			0
$340$	−1.04524	+	3.96824i	−0.0566863	+	0.215208i
$341$			15.0823i			0.816752i
$342$		0			0
$343$			13.3249i			0.719479i
$344$	−5.32190	−	12.6202i	−0.286938	−	0.680435i
$345$		0			0
$346$	−13.7747	+	10.6163i	−0.740534	+	0.570734i
$347$	34.1158			1.83143			0.915715	−	0.401828i	$-0.131625\pi$
$347$	34.1158			1.83143			0.915715	+	0.401828i	$0.131625\pi$
$348$		0			0
$349$	25.8722			1.38491			0.692453	−	0.721463i	$-0.256530\pi$
$349$	25.8722			1.38491			0.692453	+	0.721463i	$0.256530\pi$
$350$	1.15350	−	0.889012i	0.0616573	−	0.0475197i
$351$		0			0
$352$	2.95124	+	20.7148i	0.157301	+	1.10410i
$353$		−	7.14762i		−	0.380429i	−0.981743	−	0.190215i	$-0.939082\pi$
$353$		−	7.14762i		−	0.380429i	0.981743	−	0.190215i	$-0.0609184\pi$
$354$		0			0
$355$			0.205268i			0.0108945i
$356$	−35.3095	−	9.30060i	−1.87140	−	0.492931i
$357$		0			0
$358$	1.95996	+	2.54307i	0.103587	+	0.134405i
$359$	26.7259			1.41054			0.705269	−	0.708940i	$-0.250826\pi$
$359$	26.7259			1.41054			0.705269	+	0.708940i	$0.250826\pi$
$360$		0			0
$361$	−12.9928			−0.683833
$362$	−10.3996	−	13.4936i	−0.546590	−	0.709206i
$363$		0			0
$364$	10.0616	+	2.65026i	0.527373	+	0.138911i
$365$		−	5.22615i		−	0.273549i
$366$		0			0
$367$			12.1993i			0.636801i	0.947956	+	0.318400i	$0.103146\pi$
$367$			12.1993i			0.636801i	−0.947956	+	0.318400i	$0.896854\pi$
$368$	−1.08301	−	0.613070i	−0.0564558	−	0.0319585i
$369$		0			0
$370$	−9.39679	+	7.24217i	−0.488516	+	0.376502i
$371$	−5.53479			−0.287352
$372$		0			0
$373$	15.9608			0.826418			0.413209	−	0.910636i	$-0.364408\pi$
$373$	15.9608			0.826418			0.413209	+	0.910636i	$0.364408\pi$
$374$	−8.50110	+	6.55186i	−0.439582	+	0.338788i
$375$		0			0
$376$	27.6229	−	11.6485i	1.42454	−	0.600726i
$377$			5.01887i			0.258485i
$378$		0			0
$379$			10.4566i			0.537122i	0.963263	+	0.268561i	$0.0865480\pi$
$379$			10.4566i			0.537122i	−0.963263	+	0.268561i	$0.913452\pi$
$380$	−2.88144	+	10.9393i	−0.147815	+	0.561175i
$381$		0			0
$382$	−8.95497	−	11.6192i	−0.458176	−	0.594488i
$383$	5.87433			0.300164			0.150082	−	0.988674i	$-0.452046\pi$
$383$	5.87433			0.300164			0.150082	+	0.988674i	$0.452046\pi$
$384$		0			0
$385$	3.80903			0.194126
$386$	4.04311	+	5.24598i	0.205789	+	0.267013i
$387$		0			0
$388$	−4.92940	+	18.7144i	−0.250253	+	0.950078i
$389$		−	12.0401i		−	0.610458i	−0.952279	−	0.305229i	$-0.901267\pi$
$389$		−	12.0401i		−	0.610458i	0.952279	−	0.305229i	$-0.0987330\pi$
$390$		0			0
$391$		−	0.638362i		−	0.0322834i
$392$	−15.4795	+	6.52767i	−0.781833	+	0.329697i
$393$		0			0
$394$	2.93155	−	2.25937i	0.147690	−	0.113825i
$395$	13.5159			0.680060
$396$		0			0
$397$	23.9335			1.20119			0.600593	−	0.799555i	$-0.294931\pi$
$397$	23.9335			1.20119			0.600593	+	0.799555i	$0.294931\pi$
$398$	−28.7033	+	22.1218i	−1.43877	+	1.10887i
$399$		0			0
$400$	3.48097	+	1.97050i	0.174048	+	0.0985251i
$401$		−	32.6712i		−	1.63152i	−0.578391	−	0.815760i	$-0.696319\pi$
$401$		−	32.6712i		−	1.63152i	0.578391	−	0.815760i	$-0.303681\pi$
$402$		0			0
$403$			20.5995i			1.02614i
$404$	−13.7328	−	3.61725i	−0.683232	−	0.179965i
$405$		0			0
$406$	0.883192	+	1.14595i	0.0438321	+	0.0568726i
$407$	−31.0296			−1.53808
$408$		0			0
$409$	25.5411			1.26292			0.631462	−	0.775406i	$-0.282455\pi$
$409$	25.5411			1.26292			0.631462	+	0.775406i	$0.282455\pi$
$410$	−8.43700	−	10.9471i	−0.416674	−	0.540639i
$411$		0			0
$412$	7.21499	+	1.90044i	0.355457	+	0.0936281i
$413$		−	8.38091i		−	0.412398i
$414$		0			0
$415$		−	0.215976i		−	0.0106018i
$416$	4.03083	+	28.2924i	0.197628	+	1.38715i
$417$		0			0
$418$	−23.4351	+	18.0616i	−1.14625	+	0.883422i
$419$	−13.4542			−0.657282			−0.328641	−	0.944455i	$-0.606591\pi$
$419$	−13.4542			−0.657282			−0.328641	+	0.944455i	$0.606591\pi$
$420$		0			0
$421$	−0.788136			−0.0384114			−0.0192057	−	0.999816i	$-0.506114\pi$
$421$	−0.788136			−0.0384114			−0.0192057	+	0.999816i	$0.506114\pi$
$422$	6.91742	−	5.33130i	0.336735	−	0.259524i
$423$		0			0
$424$	−5.90690	−	14.0074i	−0.286864	−	0.680261i
$425$			2.05180i			0.0995268i
$426$		0			0
$427$		−	14.7759i		−	0.715056i
$428$	9.03777	−	34.3117i	0.436857	−	1.65852i
$429$		0			0
$430$	−4.18045	−	5.42418i	−0.201599	−	0.261577i
$431$	−22.1893			−1.06882			−0.534411	−	0.845225i	$-0.679467\pi$
$431$	−22.1893			−1.06882			−0.534411	+	0.845225i	$0.679467\pi$
$432$		0			0
$433$	9.40036			0.451753			0.225876	−	0.974156i	$-0.427475\pi$
$433$	9.40036			0.451753			0.225876	+	0.974156i	$0.427475\pi$
$434$	3.62499	+	4.70346i	0.174005	+	0.225773i
$435$		0			0
$436$	4.86016	−	18.4515i	0.232760	−	0.883667i
$437$		−	1.75978i		−	0.0841819i
$438$		0			0
$439$		−	8.67990i		−	0.414269i	−0.978312	−	0.207134i	$-0.933586\pi$
$439$		−	8.67990i		−	0.414269i	0.978312	−	0.207134i	$-0.0664138\pi$
$440$	4.06512	+	9.63990i	0.193797	+	0.459564i
$441$		0			0
$442$	−11.6109	+	8.94859i	−0.552274	+	0.425641i
$443$	22.3328			1.06106			0.530532	−	0.847665i	$-0.321992\pi$
$443$	22.3328			1.06106			0.530532	+	0.847665i	$0.321992\pi$
$444$		0			0
$445$	−18.2569			−0.865461
$446$	9.06853	−	6.98917i	0.429407	−	0.330947i
$447$		0			0
$448$	5.89909	+	5.75064i	0.278706	+	0.271692i
$449$		−	11.9137i		−	0.562242i	−0.959672	−	0.281121i	$-0.909294\pi$
$449$		−	11.9137i		−	0.562242i	0.959672	−	0.281121i	$-0.0907063\pi$
$450$		0			0
$451$		−	36.1489i		−	1.70219i
$452$	2.13876	+	0.563354i	0.100599	+	0.0264980i
$453$		0			0
$454$	16.8499	+	21.8629i	0.790804	+	1.02608i
$455$	5.20241			0.243893
$456$		0			0
$457$	21.5663			1.00883			0.504414	−	0.863462i	$-0.331709\pi$
$457$	21.5663			1.00883			0.504414	+	0.863462i	$0.331709\pi$
$458$	2.00341	+	2.59944i	0.0936130	+	0.121464i
$459$		0			0
$460$	−0.601723	−	0.158495i	−0.0280555	−	0.00738988i
$461$			3.24691i			0.151224i	0.997137	+	0.0756118i	$0.0240910\pi$
$461$			3.24691i			0.151224i	−0.997137	+	0.0756118i	$0.975909\pi$
$462$		0			0
$463$			11.3775i			0.528759i	0.964419	+	0.264379i	$0.0851671\pi$
$463$			11.3775i			0.528759i	−0.964419	+	0.264379i	$0.914833\pi$
$464$	−1.95760	+	3.45818i	−0.0908794	+	0.160542i
$465$		0			0
$466$	4.04376	−	3.11655i	0.187324	−	0.144371i
$467$	−7.65660			−0.354305			−0.177153	−	0.984183i	$-0.556689\pi$
$467$	−7.65660			−0.354305			−0.177153	+	0.984183i	$0.556689\pi$
$468$		0			0
$469$	−4.59012			−0.211952
$470$	11.8724	−	9.15012i	0.547632	−	0.422064i
$471$		0			0
$472$	21.2104	−	8.94437i	0.976288	−	0.411698i
$473$		−	17.9114i		−	0.823568i
$474$		0			0
$475$			5.65622i			0.259525i
$476$	−1.07638	+	4.08643i	−0.0493356	+	0.187301i
$477$		0			0
$478$	−9.51311	−	12.3434i	−0.435120	−	0.564572i
$479$	−27.0504			−1.23596			−0.617982	−	0.786192i	$-0.712050\pi$
$479$	−27.0504			−1.23596			−0.617982	+	0.786192i	$0.712050\pi$
$480$		0			0
$481$	−42.3805			−1.93238
$482$	3.80341	+	4.93496i	0.173241	+	0.224781i
$483$		0			0
$484$	−1.36608	+	5.18631i	−0.0620948	+	0.235741i
$485$			9.67634i			0.439380i
$486$		0			0
$487$			24.1705i			1.09527i	0.836718	+	0.547634i	$0.184471\pi$
$487$			24.1705i			1.09527i	−0.836718	+	0.547634i	$0.815529\pi$
$488$	37.3949	−	15.7693i	1.69279	−	0.713843i
$489$		0			0
$490$	−6.65312	+	5.12761i	−0.300557	+	0.231642i
$491$	−27.3771			−1.23551			−0.617755	−	0.786371i	$-0.711958\pi$
$491$	−27.3771			−1.23551			−0.617755	+	0.786371i	$0.711958\pi$
$492$		0			0
$493$	−2.03836			−0.0918033
$494$	−32.0079	+	24.6687i	−1.44010	+	1.10990i
$495$		0			0
$496$	−8.03481	+	14.1938i	−0.360774	+	0.637320i
$497$			0.211382i			0.00948179i
$498$		0			0
$499$		−	5.38175i		−	0.240920i	−0.992718	−	0.120460i	$-0.961563\pi$
$499$		−	5.38175i		−	0.240920i	0.992718	−	0.120460i	$-0.0384370\pi$
$500$	1.93403	+	0.509428i	0.0864926	+	0.0227823i
$501$		0			0
$502$	−19.9948	−	25.9435i	−0.892412	−	1.15791i
$503$	38.2209			1.70419			0.852093	−	0.523391i	$-0.175333\pi$
$503$	38.2209			1.70419			0.852093	+	0.523391i	$0.175333\pi$
$504$		0			0
$505$	−7.10060			−0.315972
$506$	−0.993489	−	1.28906i	−0.0441660	−	0.0573058i
$507$		0			0
$508$	23.6120	+	6.21945i	1.04761	+	0.275943i
$509$			8.67779i			0.384636i	0.981333	+	0.192318i	$0.0616006\pi$
$509$			8.67779i			0.384636i	−0.981333	+	0.192318i	$0.938399\pi$
$510$		0			0
$511$		−	5.38181i		−	0.238077i
$512$	−8.25803	+	21.0667i	−0.364957	+	0.931024i
$513$		0			0
$514$	−32.2659	+	24.8675i	−1.42319	+	1.09686i
$515$	3.73054			0.164387
$516$		0			0
$517$	39.2043			1.72420
$518$	−9.67666	+	7.45787i	−0.425168	+	0.327680i
$519$		0			0
$520$	5.55218	+	13.1663i	0.243479	+	0.577379i
$521$			4.73534i			0.207459i	0.994606	+	0.103729i	$0.0330776\pi$
$521$			4.73534i			0.207459i	−0.994606	+	0.103729i	$0.966922\pi$
$522$		0			0
$523$		−	16.8917i		−	0.738622i	−0.929306	−	0.369311i	$-0.879594\pi$
$523$		−	16.8917i		−	0.738622i	0.929306	−	0.369311i	$-0.120406\pi$
$524$	2.54563	−	9.66441i	0.111206	−	0.422192i
$525$		0			0
$526$	15.1210	+	19.6196i	0.659306	+	0.855457i
$527$	−8.36629			−0.364442
$528$		0			0
$529$	−22.9032			−0.995791
$530$	−4.63998	−	6.02042i	−0.201548	−	0.261510i
$531$		0			0
$532$	−2.96726	+	11.2651i	−0.128647	+	0.488405i
$533$		−	49.3726i		−	2.13856i
$534$		0			0
$535$		−	17.7410i		−	0.767010i
$536$	−4.89872	−	11.6167i	−0.211593	−	0.501764i
$537$		0			0
$538$	4.83438	−	3.72589i	0.208425	−	0.160635i
$539$	−21.9696			−0.946297
$540$		0			0
$541$	−28.3850			−1.22037			−0.610184	−	0.792260i	$-0.708905\pi$
$541$	−28.3850			−1.22037			−0.610184	+	0.792260i	$0.708905\pi$
$542$	−17.1465	+	13.2149i	−0.736505	+	0.567629i
$543$		0			0
$544$	−11.4907	+	1.63708i	−0.492659	+	0.0701892i
$545$		−	9.54043i		−	0.408667i
$546$		0			0
$547$			38.2984i			1.63752i	0.574135	+	0.818761i	$0.305338\pi$
$547$			38.2984i			1.63752i	−0.574135	+	0.818761i	$0.694662\pi$
$548$	−16.4274	−	4.32701i	−0.701744	−	0.184841i
$549$		0			0
$550$	3.19323	+	4.14325i	0.136160	+	0.176669i
$551$	−5.61919			−0.239386
$552$		0			0
$553$	13.9185			0.591874
$554$	−6.89794	−	8.95015i	−0.293065	−	0.380255i
$555$		0			0
$556$	27.6640	+	7.28676i	1.17322	+	0.309028i
$557$		−	9.14064i		−	0.387301i	−0.981071	−	0.193651i	$-0.937967\pi$
$557$		−	9.14064i		−	0.387301i	0.981071	−	0.193651i	$-0.0620329\pi$
$558$		0			0
$559$		−	24.4636i		−	1.03470i
$560$	3.58464	+	2.02919i	0.151479	+	0.0857490i
$561$		0			0
$562$	16.7564	−	12.9143i	0.706827	−	0.544756i
$563$	20.6124			0.868709			0.434354	−	0.900742i	$-0.356977\pi$
$563$	20.6124			0.868709			0.434354	+	0.900742i	$0.356977\pi$
$564$		0			0
$565$	1.10586			0.0465237
$566$	−18.9048	+	14.5701i	−0.794630	+	0.612426i
$567$		0			0
$568$	−0.534966	+	0.225594i	−0.0224467	+	0.00946570i
$569$		−	18.0502i		−	0.756705i	−0.925662	−	0.378352i	$-0.876491\pi$
$569$		−	18.0502i		−	0.756705i	0.925662	−	0.378352i	$-0.123509\pi$
$570$		0			0
$571$			9.52272i			0.398513i	0.979947	+	0.199257i	$0.0638528\pi$
$571$			9.52272i			0.398513i	−0.979947	+	0.199257i	$0.936147\pi$
$572$	−9.51942	+	36.1402i	−0.398027	+	1.51110i
$573$		0			0
$574$	−8.68829	−	11.2732i	−0.362642	−	0.470532i
$575$	−0.311124			−0.0129748
$576$		0			0
$577$	27.7792			1.15646			0.578232	−	0.815872i	$-0.303743\pi$
$577$	27.7792			1.15646			0.578232	+	0.815872i	$0.303743\pi$
$578$	11.0417	+	14.3267i	0.459275	+	0.595914i
$579$		0			0
$580$	−0.506093	+	1.92137i	−0.0210144	+	0.0797806i
$581$		−	0.222408i		−	0.00922705i
$582$		0			0
$583$		−	19.8803i		−	0.823358i
$584$	13.6203	−	5.74363i	0.563611	−	0.237673i
$585$		0			0
$586$	5.59576	−	4.31268i	0.231159	−	0.178155i
$587$	−8.56854			−0.353662			−0.176831	−	0.984241i	$-0.556585\pi$
$587$	−8.56854			−0.353662			−0.176831	+	0.984241i	$0.556585\pi$
$588$		0			0
$589$	−23.0635			−0.950315
$590$	9.11627	−	7.02597i	0.375311	−	0.289255i
$591$		0			0
$592$	−29.2016	−	16.5304i	−1.20018	−	0.679396i
$593$			18.7375i			0.769457i	0.923030	+	0.384728i	$0.125705\pi$
$593$			18.7375i			0.769457i	−0.923030	+	0.384728i	$0.874295\pi$
$594$		0			0
$595$			2.11291i			0.0866208i
$596$	10.1897	+	2.68400i	0.417388	+	0.109941i
$597$		0			0
$598$	−1.35692	−	1.76061i	−0.0554885	−	0.0719969i
$599$	7.32641			0.299349			0.149674	−	0.988735i	$-0.452177\pi$
$599$	7.32641			0.299349			0.149674	+	0.988735i	$0.452177\pi$
$600$		0			0
$601$	−33.0583			−1.34848			−0.674239	−	0.738513i	$-0.735528\pi$
$601$	−33.0583			−1.34848			−0.674239	+	0.738513i	$0.735528\pi$
$602$	−4.30496	−	5.58574i	−0.175457	−	0.227658i
$603$		0			0
$604$	9.27099	+	2.44200i	0.377231	+	0.0993636i
$605$			2.68160i			0.109023i
$606$		0			0
$607$			33.4276i			1.35678i	0.734701	+	0.678392i	$0.237323\pi$
$607$			33.4276i			1.35678i	−0.734701	+	0.678392i	$0.762677\pi$
$608$	−31.6765	+	4.51296i	−1.28465	+	0.183025i
$609$		0			0
$610$	16.0724	−	12.3871i	0.650752	−	0.501539i
$611$	53.5457			2.16623
$612$		0			0
$613$	−41.1231			−1.66095			−0.830474	−	0.557058i	$-0.811930\pi$
$613$	−41.1231			−1.66095			−0.830474	+	0.557058i	$0.811930\pi$
$614$	3.86577	−	2.97937i	0.156010	−	0.120238i
$615$		0			0
$616$	4.18619	+	9.92701i	0.168667	+	0.399971i
$617$			32.6494i			1.31442i	0.753709	+	0.657208i	$0.228263\pi$
$617$			32.6494i			1.31442i	−0.753709	+	0.657208i	$0.771737\pi$
$618$		0			0
$619$			38.8452i			1.56132i	0.624955	+	0.780661i	$0.285117\pi$
$619$			38.8452i			1.56132i	−0.624955	+	0.780661i	$0.714883\pi$
$620$	−2.07722	+	7.88610i	−0.0834230	+	0.316714i
$621$		0			0
$622$	−17.5790	−	22.8089i	−0.704852	−	0.914554i
$623$	−18.8007			−0.753234
$624$		0			0
$625$	1.00000			0.0400000
$626$	−11.3951	−	14.7853i	−0.455441	−	0.590940i
$627$		0			0
$628$	7.45064	−	28.2862i	0.297313	−	1.12874i
$629$		−	17.2124i		−	0.686303i
$630$		0			0
$631$			8.19354i			0.326180i	0.986611	+	0.163090i	$0.0521460\pi$
$631$			8.19354i			0.326180i	−0.986611	+	0.163090i	$0.947854\pi$
$632$	14.8542	+	35.2249i	0.590870	+	1.40117i
$633$		0			0
$634$	2.03227	−	1.56629i	0.0807118	−	0.0622051i
$635$	12.2087			0.484487
$636$		0			0
$637$	−30.0063			−1.18889
$638$	−4.11612	+	3.17232i	−0.162959	+	0.125593i
$639$		0			0
$640$	−1.30983	+	11.2376i	−0.0517758	+	0.444206i
$641$			32.8414i			1.29716i	0.761147	+	0.648580i	$0.224637\pi$
$641$			32.8414i			1.29716i	−0.761147	+	0.648580i	$0.775363\pi$
$642$		0			0
$643$		−	34.9708i		−	1.37911i	−0.724232	−	0.689557i	$-0.757805\pi$
$643$		−	34.9708i		−	1.37911i	0.724232	−	0.689557i	$-0.242195\pi$
$644$	−0.619645	−	0.163216i	−0.0244174	−	0.00643160i
$645$		0			0
$646$	−10.0189	−	12.9997i	−0.394190	−	0.511466i
$647$	38.1802			1.50102			0.750510	−	0.660860i	$-0.229808\pi$
$647$	38.1802			1.50102			0.750510	+	0.660860i	$0.229808\pi$
$648$		0			0
$649$	30.1033			1.18166
$650$	4.36134	+	5.65889i	0.171066	+	0.221960i
$651$		0			0
$652$	−33.9328	−	8.93797i	−1.32891	−	0.350038i
$653$			15.1554i			0.593075i	0.955021	+	0.296537i	$0.0958319\pi$
$653$			15.1554i			0.593075i	−0.955021	+	0.296537i	$0.904168\pi$
$654$		0			0
$655$		−	4.99703i		−	0.195250i
$656$	19.2577	−	34.0194i	0.751886	−	1.32823i
$657$		0			0
$658$	12.2260	−	9.42265i	0.476619	−	0.367333i
$659$	33.0192			1.28625			0.643123	−	0.765763i	$-0.277638\pi$
$659$	33.0192			1.28625			0.643123	+	0.765763i	$0.277638\pi$
$660$		0			0
$661$	−33.5642			−1.30550			−0.652748	−	0.757575i	$-0.726384\pi$
$661$	−33.5642			−1.30550			−0.652748	+	0.757575i	$0.726384\pi$
$662$	−0.560463	+	0.431952i	−0.0217830	+	0.0167883i
$663$		0			0
$664$	0.562871	−	0.237361i	0.0218436	−	0.00921140i
$665$			5.82469i			0.225872i
$666$		0			0
$667$		−	0.309087i		−	0.0119679i
$668$	2.08618	−	7.92013i	0.0807167	−	0.306439i
$669$		0			0
$670$	−3.84804	−	4.99287i	−0.148663	−	0.192892i
$671$	53.0733			2.04887
$672$		0			0
$673$	29.6008			1.14103			0.570513	−	0.821289i	$-0.306744\pi$
$673$	29.6008			1.14103			0.570513	+	0.821289i	$0.306744\pi$
$674$	8.76871	+	11.3775i	0.337758	+	0.438245i
$675$		0			0
$676$	−6.37915	+	24.2183i	−0.245352	+	0.931473i
$677$		−	26.9399i		−	1.03538i	−0.855567	−	0.517692i	$-0.826791\pi$
$677$		−	26.9399i		−	1.03538i	0.855567	−	0.517692i	$-0.173209\pi$
$678$		0			0
$679$			9.96454i			0.382404i
$680$	−5.34735	+	2.25496i	−0.205061	+	0.0864738i
$681$		0			0
$682$	−16.8943	+	13.0205i	−0.646915	+	0.498582i
$683$	7.55463			0.289070			0.144535	−	0.989500i	$-0.453831\pi$
$683$	7.55463			0.289070			0.144535	+	0.989500i	$0.453831\pi$
$684$		0			0
$685$	−8.49386			−0.324534
$686$	−14.9258	+	11.5034i	−0.569870	+	0.439202i
$687$		0			0
$688$	9.54199	−	16.8563i	0.363785	−	0.642639i
$689$		−	27.1527i		−	1.03444i
$690$		0			0
$691$		−	44.2394i		−	1.68295i	−0.540299	−	0.841473i	$-0.681689\pi$
$691$		−	44.2394i		−	1.68295i	0.540299	−	0.841473i	$-0.318311\pi$
$692$	−23.7834	−	6.26460i	−0.904110	−	0.238144i
$693$		0			0
$694$	29.4521	+	38.2144i	1.11799	+	1.45060i
$695$	14.3038			0.542574
$696$		0			0
$697$	20.0522			0.759530
$698$	22.3354	+	28.9805i	0.845409	+	1.09693i
$699$		0			0
$700$	1.99164	+	0.524601i	0.0752768	+	0.0198281i
$701$		−	17.8740i		−	0.675090i	−0.941309	−	0.337545i	$-0.890403\pi$
$701$		−	17.8740i		−	0.675090i	0.941309	−	0.337545i	$-0.109597\pi$
$702$		0			0
$703$		−	47.4497i		−	1.78960i
$704$	−20.6556	+	21.1888i	−0.778489	+	0.798585i
$705$		0			0
$706$	8.00633	−	6.17053i	0.301322	−	0.232231i
$707$	−7.31208			−0.274999
$708$		0			0
$709$	−32.4489			−1.21864			−0.609322	−	0.792923i	$-0.708558\pi$
$709$	−32.4489			−1.21864			−0.609322	+	0.792923i	$0.708558\pi$
$710$	−0.229929	+	0.177208i	−0.00862910	+	0.00665050i
$711$		0			0
$712$	−20.0647	−	47.5808i	−0.751956	−	1.78316i
$713$		−	1.26862i		−	0.0475102i
$714$		0			0
$715$			18.6865i			0.698834i
$716$	−1.15656	+	4.39086i	−0.0432227	+	0.164094i
$717$		0			0
$718$	23.0724	+	29.9367i	0.861056	+	1.11723i
$719$	−2.86842			−0.106974			−0.0534869	−	0.998569i	$-0.517034\pi$
$719$	−2.86842			−0.106974			−0.0534869	+	0.998569i	$0.517034\pi$
$720$		0			0
$721$	3.84165			0.143071
$722$	−11.2167	−	14.5538i	−0.417443	−	0.541636i
$723$		0			0
$724$	6.13674	−	23.2980i	0.228070	−	0.865863i
$725$			0.993453i			0.0368959i
$726$		0			0
$727$		−	17.1383i		−	0.635624i	−0.948154	−	0.317812i	$-0.897052\pi$
$727$		−	17.1383i		−	0.635624i	0.948154	−	0.317812i	$-0.102948\pi$
$728$	5.71755	+	13.5584i	0.211906	+	0.502508i
$729$		0			0
$730$	5.85402	−	4.51173i	0.216667	−	0.166987i
$731$	9.93565			0.367483
$732$		0			0
$733$	−30.1942			−1.11525			−0.557625	−	0.830093i	$-0.688287\pi$
$733$	−30.1942			−1.11525			−0.557625	+	0.830093i	$0.688287\pi$
$734$	−13.6650	+	10.5317i	−0.504384	+	0.388732i
$735$		0			0
$736$	−0.248238	−	1.74239i	−0.00915018	−	0.0642252i
$737$		−	16.4872i		−	0.607313i
$738$		0			0
$739$			35.4967i			1.30577i	0.757458	+	0.652884i	$0.226441\pi$
$739$			35.4967i			1.30577i	−0.757458	+	0.652884i	$0.773559\pi$
$740$	−16.2245	−	4.27356i	−0.596424	−	0.157099i
$741$		0			0
$742$	−4.77818	−	6.19974i	−0.175412	−	0.227599i
$743$	12.4402			0.456386			0.228193	−	0.973616i	$-0.426718\pi$
$743$	12.4402			0.456386			0.228193	+	0.973616i	$0.426718\pi$
$744$		0			0
$745$	5.26864			0.193028
$746$	13.7789	+	17.8783i	0.504482	+	0.654571i
$747$		0			0
$748$	−14.6780	−	3.86622i	−0.536681	−	0.141363i
$749$		−	18.2694i		−	0.667549i
$750$		0			0
$751$		−	36.7108i		−	1.33960i	−0.742543	−	0.669798i	$-0.766381\pi$
$751$		−	36.7108i		−	1.33960i	0.742543	−	0.669798i	$-0.233619\pi$
$752$	36.8948	+	20.8854i	1.34541	+	0.761611i
$753$		0			0
$754$	−5.62184	+	4.33279i	−0.204735	+	0.157791i
$755$	4.79361			0.174457
$756$		0			0
$757$	5.38791			0.195827			0.0979134	−	0.995195i	$-0.468783\pi$
$757$	5.38791			0.195827			0.0979134	+	0.995195i	$0.468783\pi$
$758$	−11.7129	+	9.02721i	−0.425432	+	0.327883i
$759$		0			0
$760$	−14.7411	+	6.21629i	−0.534716	+	0.225488i
$761$		−	15.4529i		−	0.560166i	−0.959976	−	0.280083i	$-0.909638\pi$
$761$		−	15.4529i		−	0.560166i	0.959976	−	0.280083i	$-0.0903620\pi$
$762$		0			0
$763$		−	9.82458i		−	0.355674i
$764$	5.28428	−	20.0616i	0.191179	−	0.725805i
$765$		0			0
$766$	5.07130	+	6.58007i	0.183234	+	0.237748i
$767$	41.1153			1.48459
$768$		0			0
$769$	−6.55401			−0.236344			−0.118172	−	0.992993i	$-0.537703\pi$
$769$	−6.55401			−0.236344			−0.118172	+	0.992993i	$0.537703\pi$
$770$	3.28834	+	4.26665i	0.118503	+	0.153759i
$771$		0			0
$772$	−2.38582	+	9.05770i	−0.0858675	+	0.325994i
$773$		−	16.6815i		−	0.599990i	−0.953941	−	0.299995i	$-0.903015\pi$
$773$		−	16.6815i		−	0.599990i	0.953941	−	0.299995i	$-0.0969850\pi$
$774$		0			0
$775$			4.07754i			0.146470i
$776$	−25.2183	+	10.6345i	−0.905283	+	0.381755i
$777$		0			0
$778$	13.4866	−	10.3942i	0.483519	−	0.372651i
$779$	55.2781			1.98054
$780$		0			0
$781$	−0.759260			−0.0271685
$782$	0.715056	−	0.551098i	0.0255703	−	0.0197072i
$783$		0			0
$784$	−20.6754	−	11.7039i	−0.738405	−	0.417996i
$785$		−	14.6255i		−	0.522006i
$786$		0			0
$787$		−	9.17023i		−	0.326884i	−0.986553	−	0.163442i	$-0.947740\pi$
$787$		−	9.17023i		−	0.326884i	0.986553	−	0.163442i	$-0.0522596\pi$
$788$	5.06162	+	1.33324i	0.180313	+	0.0474947i
$789$		0			0
$790$	11.6683	+	15.1397i	0.415139	+	0.538648i
$791$	1.13879			0.0404908
$792$		0			0
$793$	72.4881			2.57413
$794$	20.6617	+	26.8088i	0.733258	+	0.951410i
$795$		0			0
$796$	−49.5591	−	13.0540i	−1.75657	−	0.462686i
$797$		−	41.4597i		−	1.46858i	−0.678838	−	0.734288i	$-0.737516\pi$
$797$		−	41.4597i		−	1.46858i	0.678838	−	0.734288i	$-0.262484\pi$
$798$		0			0
$799$			21.7470i			0.769354i
$800$	0.797876	+	5.60030i	0.0282092	+	0.198001i
$801$		0			0
$802$	36.5963	−	28.2050i	1.29226	−	0.995953i
$803$	19.3308			0.682170
$804$		0			0
$805$	−0.320390			−0.0112923
$806$	−23.0744	+	17.7836i	−0.812760	+	0.626400i
$807$		0			0
$808$	−7.80368	−	18.5054i	−0.274533	−	0.651018i
$809$			4.83449i			0.169972i	0.996382	+	0.0849858i	$0.0270845\pi$
$809$			4.83449i			0.169972i	−0.996382	+	0.0849858i	$0.972915\pi$
$810$		0			0
$811$		−	47.3558i		−	1.66289i	−0.555610	−	0.831443i	$-0.687515\pi$
$811$		−	47.3558i		−	1.66289i	0.555610	−	0.831443i	$-0.312485\pi$
$812$	−0.521167	+	1.97860i	−0.0182894	+	0.0694352i
$813$		0			0
$814$	−26.7878	−	34.7575i	−0.938912	−	1.21825i
$815$	−17.5451			−0.614578
$816$		0			0
$817$	27.3898			0.958246
$818$	22.0496	+	28.6096i	0.770946	+	1.00031i
$819$		0			0
$820$	4.97863	−	18.9013i	0.173861	−	0.660060i
$821$		−	7.87867i		−	0.274968i	−0.990504	−	0.137484i	$-0.956099\pi$
$821$		−	7.87867i		−	0.274968i	0.990504	−	0.137484i	$-0.0439015\pi$
$822$		0			0
$823$		−	31.8584i		−	1.11052i	−0.831678	−	0.555258i	$-0.812620\pi$
$823$		−	31.8584i		−	1.11052i	0.831678	−	0.555258i	$-0.187380\pi$
$824$	4.09993	+	9.72245i	0.142828	+	0.338698i
$825$		0			0
$826$	9.38779	−	7.23523i	0.326643	−	0.251746i
$827$	−22.1483			−0.770171			−0.385085	−	0.922881i	$-0.625828\pi$
$827$	−22.1483			−0.770171			−0.385085	+	0.922881i	$0.625828\pi$
$828$		0			0
$829$	−40.7965			−1.41692			−0.708460	−	0.705751i	$-0.750610\pi$
$829$	−40.7965			−1.41692			−0.708460	+	0.705751i	$0.750610\pi$
$830$	0.241923	−	0.186452i	0.00839727	−	0.00647183i
$831$		0			0
$832$	−28.2117	+	28.9399i	−0.978064	+	1.00331i
$833$		−	12.1867i		−	0.422246i
$834$		0			0
$835$		−	4.09514i		−	0.141718i
$836$	−40.4631	−	10.6581i	−1.39944	−	0.368617i
$837$		0			0
$838$	−11.6150	−	15.0706i	−0.401234	−	0.520606i
$839$	−7.62437			−0.263223			−0.131611	−	0.991301i	$-0.542015\pi$
$839$	−7.62437			−0.263223			−0.131611	+	0.991301i	$0.542015\pi$
$840$		0			0
$841$	28.0131			0.965967
$842$	−0.680397	−	0.882823i	−0.0234480	−	0.0304241i
$843$		0			0
$844$	11.9436	+	3.14597i	0.411116	+	0.108289i
$845$			12.5222i			0.430776i
$846$		0			0
$847$			2.76147i			0.0948853i
$848$	10.5909	−	18.7092i	0.363692	−	0.642475i
$849$		0			0
$850$	−2.29830	+	1.77132i	−0.0788311	+	0.0607556i
$851$	2.61000			0.0894695
$852$		0			0
$853$	6.38552			0.218636			0.109318	−	0.994007i	$-0.465133\pi$
$853$	6.38552			0.218636			0.109318	+	0.994007i	$0.465133\pi$
$854$	16.5511	−	12.7560i	0.566366	−	0.436502i
$855$		0			0
$856$	46.2362	−	19.4977i	1.58032	−	0.666417i
$857$		−	20.4279i		−	0.697803i	−0.937159	−	0.348902i	$-0.886555\pi$
$857$		−	20.4279i		−	0.697803i	0.937159	−	0.348902i	$-0.113445\pi$
$858$		0			0
$859$			33.5312i			1.14407i	0.820229	+	0.572035i	$0.193846\pi$
$859$			33.5312i			1.14407i	−0.820229	+	0.572035i	$0.806154\pi$
$860$	2.46686	−	9.36538i	0.0841193	−	0.319357i
$861$		0			0
$862$	−19.1560	−	24.8551i	−0.652457	−	0.846570i
$863$	−35.9028			−1.22215			−0.611073	−	0.791574i	$-0.709262\pi$
$863$	−35.9028			−1.22215			−0.611073	+	0.791574i	$0.709262\pi$
$864$		0			0
$865$	−12.2973			−0.418121
$866$	8.11533	+	10.5297i	0.275770	+	0.357815i
$867$		0			0
$868$	−2.13908	+	8.12098i	−0.0726053	+	0.275644i
$869$			49.9936i			1.69592i
$870$		0			0
$871$		−	22.5184i		−	0.763006i
$872$	24.8640	−	10.4851i	0.842003	−	0.355070i
$873$		0			0
$874$	1.97120	−	1.51922i	0.0666770	−	0.0513884i
$875$	1.02978			0.0348131
$876$		0			0
$877$	16.4227			0.554555			0.277277	−	0.960790i	$-0.410568\pi$
$877$	16.4227			0.554555			0.277277	+	0.960790i	$0.410568\pi$
$878$	9.72270	−	7.49335i	0.328125	−	0.252888i
$879$		0			0
$880$	−7.28862	+	12.8756i	−0.245699	+	0.434037i
$881$		−	9.53250i		−	0.321158i	−0.987023	−	0.160579i	$-0.948664\pi$
$881$		−	9.53250i		−	0.321158i	0.987023	−	0.160579i	$-0.0513362\pi$
$882$		0			0
$883$			0.503628i			0.0169484i	0.999964	+	0.00847421i	$0.00269746\pi$
$883$			0.503628i			0.0169484i	−0.999964	+	0.00847421i	$0.997303\pi$
$884$	−20.0474	−	5.28052i	−0.674265	−	0.177603i
$885$		0			0
$886$	19.2799	+	25.0159i	0.647722	+	0.840426i
$887$	−27.2152			−0.913796			−0.456898	−	0.889519i	$-0.651040\pi$
$887$	−27.2152			−0.913796			−0.456898	+	0.889519i	$0.651040\pi$
$888$		0			0
$889$	12.5723			0.421661
$890$	−15.7612	−	20.4503i	−0.528316	−	0.685496i
$891$		0			0
$892$	15.6577	+	4.12427i	0.524259	+	0.138091i
$893$			59.9504i			2.00616i
$894$		0			0
$895$			2.27031i			0.0758882i
$896$	−1.34885	+	11.5723i	−0.0450618	+	0.386604i
$897$		0			0
$898$	13.3450	−	10.2851i	0.445329	−	0.343218i
$899$	−4.05085			−0.135103
$900$		0			0
$901$	11.0278			0.367389
$902$	40.4919	−	31.2073i	1.34823	−	1.03909i
$903$		0			0
$904$	1.21536	+	2.88206i	0.0404221	+	0.0958558i
$905$		−	12.0463i		−	0.400433i
$906$		0			0
$907$		−	27.3092i		−	0.906789i	−0.891310	−	0.453394i	$-0.850213\pi$
$907$		−	27.3092i		−	0.906789i	0.891310	−	0.453394i	$-0.149787\pi$
$908$	−9.94303	+	37.7485i	−0.329971	+	1.25273i
$909$		0			0
$910$	4.49124	+	5.82743i	0.148883	+	0.193178i
$911$	26.2854			0.870874			0.435437	−	0.900219i	$-0.356594\pi$
$911$	26.2854			0.870874			0.435437	+	0.900219i	$0.356594\pi$
$912$		0			0
$913$	0.798865			0.0264386
$914$	18.6181	+	24.1572i	0.615833	+	0.799051i
$915$		0			0
$916$	−1.18220	+	4.48819i	−0.0390609	+	0.148294i
$917$		−	5.14586i		−	0.169931i
$918$		0			0
$919$		−	18.2667i		−	0.602563i	−0.953535	−	0.301281i	$-0.902586\pi$
$919$		−	18.2667i		−	0.602563i	0.953535	−	0.301281i	$-0.0974143\pi$
$920$	−0.341930	−	0.810843i	−0.0112731	−	0.0267327i
$921$		0			0
$922$	−3.63699	+	2.80306i	−0.119778	+	0.0923137i
$923$	−1.03701			−0.0341335
$924$		0			0
$925$	−8.38894			−0.275827
$926$	−12.7444	+	9.82222i	−0.418808	+	0.322778i
$927$		0			0
$928$	−5.56364	+	0.792653i	−0.182635	+	0.0260201i
$929$		−	4.31123i		−	0.141447i	−0.997496	−	0.0707234i	$-0.977469\pi$
$929$		−	4.31123i		−	0.141447i	0.997496	−	0.0707234i	$-0.0225308\pi$
$930$		0			0
$931$		−	33.5954i		−	1.10104i
$932$	6.98195	+	1.83906i	0.228701	+	0.0602404i
$933$		0			0
$934$	−6.60994	−	8.57646i	−0.216284	−	0.280630i
$935$	−7.58932			−0.248197
$936$		0			0
$937$	−35.7428			−1.16767			−0.583833	−	0.811874i	$-0.698448\pi$
$937$	−35.7428			−1.16767			−0.583833	+	0.811874i	$0.698448\pi$
$938$	−3.96265	−	5.14158i	−0.129385	−	0.167879i
$939$		0			0
$940$	20.4988	+	5.39944i	0.668598	+	0.176110i
$941$		−	4.06873i		−	0.132637i	−0.997799	−	0.0663184i	$-0.978875\pi$
$941$		−	4.06873i		−	0.132637i	0.997799	−	0.0663184i	$-0.0211253\pi$
$942$		0			0
$943$			3.04060i			0.0990157i
$944$	28.3299	+	16.0370i	0.922059	+	0.521958i
$945$		0			0
$946$	20.0633	−	15.4629i	0.652315	−	0.502743i
$947$	−8.58362			−0.278930			−0.139465	−	0.990227i	$-0.544538\pi$
$947$	−8.58362			−0.278930			−0.139465	+	0.990227i	$0.544538\pi$
$948$		0			0
$949$	26.4022			0.857053
$950$	−6.33576	+	4.88301i	−0.205559	+	0.158426i
$951$		0			0
$952$	−5.50661	+	2.32212i	−0.178470	+	0.0752605i
$953$		−	37.2045i		−	1.20517i	−0.798053	−	0.602587i	$-0.794137\pi$
$953$		−	37.2045i		−	1.20517i	0.798053	−	0.602587i	$-0.205863\pi$
$954$		0			0
$955$		−	10.3730i		−	0.335661i
$956$	5.61364	−	21.3120i	0.181558	−	0.689281i
$957$		0			0
$958$	−23.3526	−	30.3002i	−0.754488	−	0.978956i
$959$	−8.74684			−0.282450
$960$		0			0
$961$	14.3736			0.463665
$962$	−36.5870	−	47.4721i	−1.17961	−	1.53056i
$963$		0			0
$964$	−2.24437	+	8.52070i	−0.0722863	+	0.274433i
$965$			4.68332i			0.150762i
$966$		0			0
$967$		−	36.9125i		−	1.18703i	−0.804824	−	0.593513i	$-0.797740\pi$
$967$		−	36.9125i		−	1.18703i	0.804824	−	0.593513i	$-0.202260\pi$
$968$	−6.98873	+	2.94713i	−0.224626	+	0.0947244i
$969$		0			0
$970$	−10.8389	+	8.35358i	−0.348015	+	0.268217i
$971$	−7.44613			−0.238958			−0.119479	−	0.992837i	$-0.538122\pi$
$971$	−7.44613			−0.238958			−0.119479	+	0.992837i	$0.538122\pi$
$972$		0			0
$973$	14.7298			0.472217
$974$	−27.0743	+	20.8663i	−0.867517	+	0.668601i
$975$		0			0
$976$	49.9468	+	28.2738i	1.59876	+	0.905024i
$977$		−	21.6043i		−	0.691183i	−0.938385	−	0.345592i	$-0.887678\pi$
$977$		−	21.6043i		−	0.691183i	0.938385	−	0.345592i	$-0.112322\pi$
$978$		0			0
$979$		−	67.5299i		−	2.15826i
$980$	−11.4873	−	3.02577i	−0.366948	−	0.0966548i
$981$		0			0
$982$	−23.6346	−	30.6661i	−0.754210	−	0.978596i
$983$	4.71758			0.150468			0.0752338	−	0.997166i	$-0.476030\pi$
$983$	4.71758			0.150468			0.0752338	+	0.997166i	$0.476030\pi$
$984$		0			0
$985$	2.61713			0.0833887
$986$	−1.75972	−	2.28325i	−0.0560409	−	0.0727136i
$987$		0			0
$988$	−55.2649	−	14.5569i	−1.75821	−	0.463116i
$989$			1.50659i			0.0479067i
$990$		0			0
$991$			10.1931i			0.323794i	0.986808	+	0.161897i	$0.0517612\pi$
$991$			10.1931i			0.323794i	−0.986808	+	0.161897i	$0.948239\pi$
$992$	−22.8355	+	3.25338i	−0.725027	+	0.103295i
$993$		0			0
$994$	−0.236778	+	0.182486i	−0.00751013	+	0.00578811i
$995$	−25.6247			−0.812359
$996$		0			0
$997$	15.2402			0.482661			0.241331	−	0.970443i	$-0.422416\pi$
$997$	15.2402			0.482661			0.241331	+	0.970443i	$0.422416\pi$
$998$	6.02832	−	4.64606i	0.190823	−	0.147069i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.34		48
3.2	odd	2	inner	1620.2.e.b.971.15		48
4.3	odd	2	inner	1620.2.e.b.971.16		48
9.2	odd	6		540.2.q.a.71.9		48
9.4	even	3		540.2.q.a.251.1		48
9.5	odd	6		180.2.q.a.11.24	yes	48
9.7	even	3		180.2.q.a.131.16	yes	48
12.11	even	2	inner	1620.2.e.b.971.33		48
36.7	odd	6		180.2.q.a.131.24	yes	48
36.11	even	6		540.2.q.a.71.1		48
36.23	even	6		180.2.q.a.11.16	✓	48
36.31	odd	6		540.2.q.a.251.9		48
45.7	odd	12		900.2.o.b.599.22		48
45.14	odd	6		900.2.r.f.551.1		48
45.23	even	12		900.2.o.b.299.12		48
45.32	even	12		900.2.o.c.299.13		48
45.34	even	6		900.2.r.f.851.9		48
45.43	odd	12		900.2.o.c.599.3		48
180.7	even	12		900.2.o.b.599.12		48
180.23	odd	12		900.2.o.b.299.22		48
180.43	even	12		900.2.o.c.599.13		48
180.59	even	6		900.2.r.f.551.9		48
180.79	odd	6		900.2.r.f.851.1		48
180.167	odd	12		900.2.o.c.299.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.16	✓	48	36.23	even	6
180.2.q.a.11.24	yes	48	9.5	odd	6
180.2.q.a.131.16	yes	48	9.7	even	3
180.2.q.a.131.24	yes	48	36.7	odd	6
540.2.q.a.71.1		48	36.11	even	6
540.2.q.a.71.9		48	9.2	odd	6
540.2.q.a.251.1		48	9.4	even	3
540.2.q.a.251.9		48	36.31	odd	6
900.2.o.b.299.12		48	45.23	even	12
900.2.o.b.299.22		48	180.23	odd	12
900.2.o.b.599.12		48	180.7	even	12
900.2.o.b.599.22		48	45.7	odd	12
900.2.o.c.299.3		48	180.167	odd	12
900.2.o.c.299.13		48	45.32	even	12
900.2.o.c.599.3		48	45.43	odd	12
900.2.o.c.599.13		48	180.43	even	12
900.2.r.f.551.1		48	45.14	odd	6
900.2.r.f.551.9		48	180.59	even	6
900.2.r.f.851.1		48	180.79	odd	6
900.2.r.f.851.9		48	45.34	even	6
1620.2.e.b.971.15		48	3.2	odd	2	inner
1620.2.e.b.971.16		48	4.3	odd	2	inner
1620.2.e.b.971.33		48	12.11	even	2	inner
1620.2.e.b.971.34		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.863299 + 1.12014i) q^{2} +(-0.509428 + 1.93403i) q^{4} +1.00000i q^{5} +1.02978i q^{7} +(-2.60618 + 1.09902i) q^{8} +O(q^{10})\)	\(q+(0.863299 + 1.12014i) q^{2} +(-0.509428 + 1.93403i) q^{4} +1.00000i q^{5} +1.02978i q^{7} +(-2.60618 + 1.09902i) q^{8} +(-1.12014 + 0.863299i) q^{10} -3.69887 q^{11} -5.05195 q^{13} +(-1.15350 + 0.889012i) q^{14} +(-3.48097 - 1.97050i) q^{16} -2.05180i q^{17} -5.65622i q^{19} +(-1.93403 - 0.509428i) q^{20} +(-3.19323 - 4.14325i) q^{22} +0.311124 q^{23} -1.00000 q^{25} +(-4.36134 - 5.65889i) q^{26} +(-1.99164 - 0.524601i) q^{28} -0.993453i q^{29} -4.07754i q^{31} +(-0.797876 - 5.60030i) q^{32} +(2.29830 - 1.77132i) q^{34} -1.02978 q^{35} +8.38894 q^{37} +(6.33576 - 4.88301i) q^{38} +(-1.09902 - 2.60618i) q^{40} +9.77298i q^{41} +4.84241i q^{43} +(1.88431 - 7.15373i) q^{44} +(0.268593 + 0.348502i) q^{46} -10.5990 q^{47} +5.93954 q^{49} +(-0.863299 - 1.12014i) q^{50} +(2.57361 - 9.77063i) q^{52} +5.37471i q^{53} -3.69887i q^{55} +(-1.13175 - 2.68380i) q^{56} +(1.11281 - 0.857648i) q^{58} -8.13851 q^{59} -14.3485 q^{61} +(4.56742 - 3.52014i) q^{62} +(5.58432 - 5.72847i) q^{64} -5.05195i q^{65} +4.45736i q^{67} +(3.96824 + 1.04524i) q^{68} +(-0.889012 - 1.15350i) q^{70} +0.205268 q^{71} -5.22615 q^{73} +(7.24217 + 9.39679i) q^{74} +(10.9393 + 2.88144i) q^{76} -3.80903i q^{77} -13.5159i q^{79} +(1.97050 - 3.48097i) q^{80} +(-10.9471 + 8.43700i) q^{82} -0.215976 q^{83} +2.05180 q^{85} +(-5.42418 + 4.18045i) q^{86} +(9.63990 - 4.06512i) q^{88} +18.2569i q^{89} -5.20241i q^{91} +(-0.158495 + 0.601723i) q^{92} +(-9.15012 - 11.8724i) q^{94} +5.65622 q^{95} +9.67634 q^{97} +(5.12761 + 6.65312i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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