LMFDB - Embedded newform 1440.2.bv.b.241.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(241,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 0]))

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

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

chi := DirichletCharacter("1440.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.bv (of order $6$, degree $2$, not 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.19
Character	$\chi$	$=$	1440.241
Dual form			1440.2.bv.b.1201.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.443022 + 1.67443i) q^{3} +(0.866025 - 0.500000i) q^{5} +(-2.04026 + 3.53383i) q^{7} +(-2.60746 - 1.48362i) q^{9} +O(q^{10})$	\(q+(-0.443022 + 1.67443i) q^{3} +(0.866025 - 0.500000i) q^{5} +(-2.04026 + 3.53383i) q^{7} +(-2.60746 - 1.48362i) q^{9} +(0.320151 + 0.184839i) q^{11} +(-4.62646 + 2.67109i) q^{13} +(0.453549 + 1.67161i) q^{15} +2.60955 q^{17} +1.88128i q^{19} +(-5.01328 - 4.98184i) q^{21} +(-4.41270 - 7.64303i) q^{23} +(0.500000 - 0.866025i) q^{25} +(3.63939 - 3.70875i) q^{27} +(1.10689 + 0.639061i) q^{29} +(-2.07172 - 3.58832i) q^{31} +(-0.451336 + 0.454185i) q^{33} +4.08051i q^{35} +3.04014i q^{37} +(-2.42294 - 8.93006i) q^{39} +(-3.81584 - 6.60924i) q^{41} +(3.80708 + 2.19802i) q^{43} +(-2.99994 + 0.0188780i) q^{45} +(-0.882270 + 1.52814i) q^{47} +(-4.82528 - 8.35764i) q^{49} +(-1.15609 + 4.36953i) q^{51} +10.0632i q^{53} +0.369679 q^{55} +(-3.15008 - 0.833446i) q^{57} +(1.95366 - 1.12795i) q^{59} +(-12.1003 - 6.98612i) q^{61} +(10.5628 - 6.18736i) q^{63} +(-2.67109 + 4.62646i) q^{65} +(-1.47978 + 0.854350i) q^{67} +(14.7527 - 4.00276i) q^{69} -8.59323 q^{71} -11.9331 q^{73} +(1.22859 + 1.22089i) q^{75} +(-1.30638 + 0.754239i) q^{77} +(5.04431 - 8.73700i) q^{79} +(4.59773 + 7.73698i) q^{81} +(-1.36095 - 0.785746i) q^{83} +(2.25994 - 1.30478i) q^{85} +(-1.56044 + 1.57029i) q^{87} +12.9012 q^{89} -21.7988i q^{91} +(6.92622 - 1.87925i) q^{93} +(0.940639 + 1.62923i) q^{95} +(0.0450082 - 0.0779566i) q^{97} +(-0.560551 - 0.956946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 92 * q + 8 * q^7 + 6 * q^9	$ 92 q + 8 q^{7} + 6 q^{9} + 12 q^{17} - 28 q^{23} + 46 q^{25} - 8 q^{31} - 14 q^{33} + 24 q^{39} - 18 q^{41} + 36 q^{47} - 30 q^{49} - 20 q^{55} - 34 q^{57} + 32 q^{63} + 12 q^{65} + 8 q^{71} - 4 q^{73} - 20 q^{79} + 18 q^{81} + 48 q^{87} - 24 q^{89} + 18 q^{95} - 14 q^{97}+O(q^{100}) $ 92 * q + 8 * q^7 + 6 * q^9 + 12 * q^17 - 28 * q^23 + 46 * q^25 - 8 * q^31 - 14 * q^33 + 24 * q^39 - 18 * q^41 + 36 * q^47 - 30 * q^49 - 20 * q^55 - 34 * q^57 + 32 * q^63 + 12 * q^65 + 8 * q^71 - 4 * q^73 - 20 * q^79 + 18 * q^81 + 48 * q^87 - 24 * q^89 + 18 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	−0.443022	+	1.67443i	−0.255779	+	0.966735i
$3$	−0.443022	+	1.67443i	−0.255779	+	0.966735i
$4$		0			0
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$		0			0
$7$	−2.04026	+	3.53383i	−0.771144	+	1.33566i	0.165792	+	0.986161i	$0.446982\pi$
$7$	−2.04026	+	3.53383i	−0.771144	+	1.33566i	−0.936936	+	0.349500i	$0.886351\pi$
$8$		0			0
$9$	−2.60746	−	1.48362i	−0.869155	−	0.494541i
$10$		0			0
$11$	0.320151	+	0.184839i	0.0965293	+	0.0557312i	0.547488	−	0.836814i	$-0.315584\pi$
$11$	0.320151	+	0.184839i	0.0965293	+	0.0557312i	−0.450958	+	0.892545i	$0.648918\pi$
$12$		0			0
$13$	−4.62646	+	2.67109i	−1.28315	+	0.740827i	−0.977423	−	0.211292i	$-0.932233\pi$
$13$	−4.62646	+	2.67109i	−1.28315	+	0.740827i	−0.305727	+	0.952119i	$0.598900\pi$
$14$		0			0
$15$	0.453549	+	1.67161i	0.117106	+	0.431609i
$16$		0			0
$17$	2.60955			0.632910			0.316455	−	0.948608i	$-0.397507\pi$
$17$	2.60955			0.632910			0.316455	+	0.948608i	$0.397507\pi$
$18$		0			0
$19$			1.88128i			0.431595i	0.976438	+	0.215797i	$0.0692350\pi$
$19$			1.88128i			0.431595i	−0.976438	+	0.215797i	$0.930765\pi$
$20$		0			0
$21$	−5.01328	−	4.98184i	−1.09399	−	1.08713i
$22$		0			0
$23$	−4.41270	−	7.64303i	−0.920112	−	1.59368i	−0.799239	−	0.601013i	$-0.794764\pi$
$23$	−4.41270	−	7.64303i	−0.920112	−	1.59368i	−0.120873	−	0.992668i	$-0.538569\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	3.63939	−	3.70875i	0.700401	−	0.713750i
$28$		0			0
$29$	1.10689	+	0.639061i	0.205543	+	0.118671i	0.599239	−	0.800571i	$-0.295470\pi$
$29$	1.10689	+	0.639061i	0.205543	+	0.118671i	−0.393695	+	0.919241i	$0.628803\pi$
$30$		0			0
$31$	−2.07172	−	3.58832i	−0.372091	−	0.644481i	0.617796	−	0.786339i	$-0.288026\pi$
$31$	−2.07172	−	3.58832i	−0.372091	−	0.644481i	−0.989887	+	0.141858i	$0.954692\pi$
$32$		0			0
$33$	−0.451336	+	0.454185i	−0.0785674	+	0.0790634i
$34$		0			0
$35$			4.08051i			0.689732i
$36$		0			0
$37$			3.04014i			0.499795i	0.968272	+	0.249898i	$0.0803970\pi$
$37$			3.04014i			0.499795i	−0.968272	+	0.249898i	$0.919603\pi$
$38$		0			0
$39$	−2.42294	−	8.93006i	−0.387981	−	1.42995i
$40$		0			0
$41$	−3.81584	−	6.60924i	−0.595935	−	1.03219i	−0.993414	−	0.114578i	$-0.963448\pi$
$41$	−3.81584	−	6.60924i	−0.595935	−	1.03219i	0.397479	−	0.917611i	$-0.369885\pi$
$42$		0			0
$43$	3.80708	+	2.19802i	0.580575	+	0.335195i	0.761362	−	0.648327i	$-0.224531\pi$
$43$	3.80708	+	2.19802i	0.580575	+	0.335195i	−0.180787	+	0.983522i	$0.557864\pi$
$44$		0			0
$45$	−2.99994	+	0.0188780i	−0.447205	+	0.00281416i
$46$		0			0
$47$	−0.882270	+	1.52814i	−0.128692	+	0.222901i	−0.923170	−	0.384392i	$-0.874411\pi$
$47$	−0.882270	+	1.52814i	−0.128692	+	0.222901i	0.794478	+	0.607293i	$0.207745\pi$
$48$		0			0
$49$	−4.82528	−	8.35764i	−0.689326	−	1.19395i
$50$		0			0
$51$	−1.15609	+	4.36953i	−0.161885	+	0.611856i
$52$		0			0
$53$			10.0632i			1.38229i	0.722715	+	0.691146i	$0.242894\pi$
$53$			10.0632i			1.38229i	−0.722715	+	0.691146i	$0.757106\pi$
$54$		0			0
$55$	0.369679			0.0498475
$56$		0			0
$57$	−3.15008	−	0.833446i	−0.417238	−	0.110393i
$58$		0			0
$59$	1.95366	−	1.12795i	0.254345	−	0.146846i	−0.367407	−	0.930060i	$-0.619754\pi$
$59$	1.95366	−	1.12795i	0.254345	−	0.146846i	0.621752	+	0.783214i	$0.286421\pi$
$60$		0			0
$61$	−12.1003	−	6.98612i	−1.54929	−	0.894482i	−0.998196	−	0.0600366i	$-0.980878\pi$
$61$	−12.1003	−	6.98612i	−1.54929	−	0.894482i	−0.551091	−	0.834445i	$-0.685788\pi$
$62$		0			0
$63$	10.5628	−	6.18736i	1.33078	−	0.779534i
$64$		0			0
$65$	−2.67109	+	4.62646i	−0.331308	+	0.573842i
$66$		0			0
$67$	−1.47978	+	0.854350i	−0.180784	+	0.104375i	−0.587661	−	0.809107i	$-0.699951\pi$
$67$	−1.47978	+	0.854350i	−0.180784	+	0.104375i	0.406877	+	0.913483i	$0.366618\pi$
$68$		0			0
$69$	14.7527	−	4.00276i	1.77601	−	0.481876i
$70$		0			0
$71$	−8.59323			−1.01983			−0.509914	−	0.860225i	$-0.670323\pi$
$71$	−8.59323			−1.01983			−0.509914	+	0.860225i	$0.670323\pi$
$72$		0			0
$73$	−11.9331			−1.39666			−0.698329	−	0.715777i	$-0.746073\pi$
$73$	−11.9331			−1.39666			−0.698329	+	0.715777i	$0.746073\pi$
$74$		0			0
$75$	1.22859	+	1.22089i	0.141866	+	0.140976i
$76$		0			0
$77$	−1.30638	+	0.754239i	−0.148876	+	0.0859535i
$78$		0			0
$79$	5.04431	−	8.73700i	0.567529	−	0.982990i	−0.429280	−	0.903171i	$-0.641233\pi$
$79$	5.04431	−	8.73700i	0.567529	−	0.982990i	0.996809	−	0.0798182i	$-0.0254340\pi$
$80$		0			0
$81$	4.59773	+	7.73698i	0.510859	+	0.859664i
$82$		0			0
$83$	−1.36095	−	0.785746i	−0.149384	−	0.0862468i	0.423445	−	0.905922i	$-0.360821\pi$
$83$	−1.36095	−	0.785746i	−0.149384	−	0.0862468i	−0.572829	+	0.819675i	$0.694154\pi$
$84$		0			0
$85$	2.25994	−	1.30478i	0.245125	−	0.141523i
$86$		0			0
$87$	−1.56044	+	1.57029i	−0.167297	+	0.168353i
$88$		0			0
$89$	12.9012			1.36752			0.683762	−	0.729706i	$-0.260343\pi$
$89$	12.9012			1.36752			0.683762	+	0.729706i	$0.260343\pi$
$90$		0			0
$91$		−	21.7988i		−	2.28514i
$92$		0			0
$93$	6.92622	−	1.87925i	0.718216	−	0.194869i
$94$		0			0
$95$	0.940639	+	1.62923i	0.0965075	+	0.167156i
$96$		0			0
$97$	0.0450082	−	0.0779566i	0.00456989	−	0.00791529i	−0.863731	−	0.503952i	$-0.831879\pi$
$97$	0.0450082	−	0.0779566i	0.00456989	−	0.00791529i	0.868301	+	0.496037i	$0.165212\pi$
$98$		0			0
$99$	−0.560551	−	0.956946i	−0.0563375	−	0.0961766i
$100$		0			0
$101$	4.70263	+	2.71507i	0.467929	+	0.270159i	0.715372	−	0.698743i	$-0.246257\pi$
$101$	4.70263	+	2.71507i	0.467929	+	0.270159i	−0.247443	+	0.968902i	$0.579590\pi$
$102$		0			0
$103$	8.21543	+	14.2295i	0.809490	+	1.40208i	0.913218	+	0.407472i	$0.133590\pi$
$103$	8.21543	+	14.2295i	0.809490	+	1.40208i	−0.103728	+	0.994606i	$0.533077\pi$
$104$		0			0
$105$	−6.83255	−	1.80775i	−0.666789	−	0.176419i
$106$		0			0
$107$			4.93967i			0.477536i	0.971077	+	0.238768i	$0.0767435\pi$
$107$			4.93967i			0.477536i	−0.971077	+	0.238768i	$0.923257\pi$
$108$		0			0
$109$		−	9.83808i		−	0.942318i	−0.882048	−	0.471159i	$-0.843836\pi$
$109$		−	9.83808i		−	0.942318i	0.882048	−	0.471159i	$-0.156164\pi$
$110$		0			0
$111$	−5.09051	−	1.34685i	−0.483170	−	0.127837i
$112$		0			0
$113$	−8.10981	−	14.0466i	−0.762907	−	1.32139i	−0.941346	−	0.337442i	$-0.890438\pi$
$113$	−8.10981	−	14.0466i	−0.762907	−	1.32139i	0.178439	−	0.983951i	$-0.442895\pi$
$114$		0			0
$115$	−7.64303	−	4.41270i	−0.712716	−	0.411487i
$116$		0			0
$117$	16.0262	−	0.100849i	1.48162	−	0.00932353i
$118$		0			0
$119$	−5.32416	+	9.22171i	−0.488065	+	0.845353i
$120$		0			0
$121$	−5.43167	−	9.40793i	−0.493788	−	0.855266i
$122$		0			0
$123$	12.7572	−	3.46135i	1.15028	−	0.312099i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−9.08563			−0.806219			−0.403110	−	0.915152i	$-0.632071\pi$
$127$	−9.08563			−0.806219			−0.403110	+	0.915152i	$0.632071\pi$
$128$		0			0
$129$	−5.36706	+	5.40094i	−0.472544	+	0.475527i
$130$		0			0
$131$	−15.9462	+	9.20657i	−1.39323	+	0.804382i	−0.993671	−	0.112326i	$-0.964170\pi$
$131$	−15.9462	+	9.20657i	−1.39323	+	0.804382i	−0.399559	+	0.916708i	$0.630837\pi$
$132$		0			0
$133$	−6.64811	−	3.83829i	−0.576464	−	0.332822i
$134$		0			0
$135$	1.29743	−	5.03157i	0.111665	−	0.433048i
$136$		0			0
$137$	−5.53509	+	9.58706i	−0.472895	+	0.819078i	−0.999519	−	0.0310207i	$-0.990124\pi$
$137$	−5.53509	+	9.58706i	−0.472895	+	0.819078i	0.526624	+	0.850098i	$0.323458\pi$
$138$		0			0
$139$	−12.4794	+	7.20500i	−1.05849	+	0.611120i	−0.925014	−	0.379932i	$-0.875947\pi$
$139$	−12.4794	+	7.20500i	−1.05849	+	0.611120i	−0.133476	+	0.991052i	$0.542614\pi$
$140$		0			0
$141$	−2.16790	−	2.15430i	−0.182570	−	0.181425i
$142$		0			0
$143$	−1.97489			−0.165149
$144$		0			0
$145$	1.27812			0.106142
$146$		0			0
$147$	16.1320	−	4.37701i	1.33055	−	0.361010i
$148$		0			0
$149$	−10.9375	+	6.31478i	−0.896037	+	0.517327i	−0.875912	−	0.482470i	$-0.839740\pi$
$149$	−10.9375	+	6.31478i	−0.896037	+	0.517327i	−0.0201244	+	0.999797i	$0.506406\pi$
$150$		0			0
$151$	−6.18106	+	10.7059i	−0.503008	+	0.871235i	0.496986	+	0.867758i	$0.334440\pi$
$151$	−6.18106	+	10.7059i	−0.503008	+	0.871235i	−0.999994	+	0.00347665i	$0.998893\pi$
$152$		0			0
$153$	−6.80432	−	3.87159i	−0.550096	−	0.312999i
$154$		0			0
$155$	−3.58832	−	2.07172i	−0.288221	−	0.166404i
$156$		0			0
$157$	11.2378	−	6.48813i	0.896872	−	0.517809i	0.0206880	−	0.999786i	$-0.493414\pi$
$157$	11.2378	−	6.48813i	0.896872	−	0.517809i	0.876184	+	0.481977i	$0.160081\pi$
$158$		0			0
$159$	−16.8502	−	4.45823i	−1.33631	−	0.353561i
$160$		0			0
$161$	36.0122			2.83816
$162$		0			0
$163$		−	19.8572i		−	1.55533i	−0.628677	−	0.777666i	$-0.716403\pi$
$163$		−	19.8572i		−	1.55533i	0.628677	−	0.777666i	$-0.283597\pi$
$164$		0			0
$165$	−0.163776	+	0.619003i	−0.0127499	+	0.0481893i
$166$		0			0
$167$	−6.75667	−	11.7029i	−0.522847	−	0.905597i	−0.999647	−	0.0265854i	$-0.991537\pi$
$167$	−6.75667	−	11.7029i	−0.522847	−	0.905597i	0.476800	−	0.879012i	$-0.341797\pi$
$168$		0			0
$169$	7.76945	−	13.4571i	0.597650	−	1.03516i
$170$		0			0
$171$	2.79110	−	4.90536i	0.213441	−	0.375122i
$172$		0			0
$173$	4.48715	+	2.59066i	0.341152	+	0.196964i	0.660781	−	0.750579i	$-0.270225\pi$
$173$	4.48715	+	2.59066i	0.341152	+	0.196964i	−0.319630	+	0.947543i	$0.603558\pi$
$174$		0			0
$175$	2.04026	+	3.53383i	0.154229	+	0.267132i
$176$		0			0
$177$	1.02316	+	3.77098i	0.0769053	+	0.283444i
$178$		0			0
$179$			17.7907i			1.32974i	0.746961	+	0.664868i	$0.231512\pi$
$179$			17.7907i			1.32974i	−0.746961	+	0.664868i	$0.768488\pi$
$180$		0			0
$181$			9.23958i			0.686772i	0.939194	+	0.343386i	$0.111574\pi$
$181$			9.23958i			0.686772i	−0.939194	+	0.343386i	$0.888426\pi$
$182$		0			0
$183$	17.0585	−	17.1662i	1.26100	−	1.26896i
$184$		0			0
$185$	1.52007	+	2.63284i	0.111758	+	0.193570i
$186$		0			0
$187$	0.835452	+	0.482348i	0.0610943	+	0.0352728i
$188$		0			0
$189$	5.68080	+	20.4278i	0.413217	+	1.48590i
$190$		0			0
$191$	5.17948	−	8.97112i	0.374774	−	0.649127i	−0.615519	−	0.788122i	$-0.711054\pi$
$191$	5.17948	−	8.97112i	0.374774	−	0.649127i	0.990293	+	0.138994i	$0.0443870\pi$
$192$		0			0
$193$	6.84990	+	11.8644i	0.493067	+	0.854017i	0.999968	−	0.00798751i	$-0.00254253\pi$
$193$	6.84990	+	11.8644i	0.493067	+	0.854017i	−0.506901	+	0.862004i	$0.669209\pi$
$194$		0			0
$195$	−6.56336	−	6.52219i	−0.470012	−	0.467064i
$196$		0			0
$197$			14.1112i			1.00538i	0.864467	+	0.502689i	$0.167656\pi$
$197$			14.1112i			1.00538i	−0.864467	+	0.502689i	$0.832344\pi$
$198$		0			0
$199$	18.1566			1.28709			0.643543	−	0.765410i	$-0.277464\pi$
$199$	18.1566			1.28709			0.643543	+	0.765410i	$0.277464\pi$
$200$		0			0
$201$	−0.774980	−	2.85629i	−0.0546629	−	0.201467i
$202$		0			0
$203$	−4.51666	+	2.60769i	−0.317007	+	0.183024i
$204$		0			0
$205$	−6.60924	−	3.81584i	−0.461609	−	0.266510i
$206$		0			0
$207$	0.166606	+	26.4757i	0.0115799	+	1.84019i
$208$		0			0
$209$	−0.347734	+	0.602293i	−0.0240533	+	0.0416615i
$210$		0			0
$211$	−22.5320	+	13.0088i	−1.55117	+	0.895566i	−0.553118	+	0.833103i	$0.686562\pi$
$211$	−22.5320	+	13.0088i	−1.55117	+	0.895566i	−0.998047	+	0.0624631i	$0.980104\pi$
$212$		0			0
$213$	3.80699	−	14.3888i	0.260850	−	0.985905i
$214$		0			0
$215$	4.39604			0.299808
$216$		0			0
$217$	16.9073			1.14774
$218$		0			0
$219$	5.28660	−	19.9811i	0.357235	−	1.35020i
$220$		0			0
$221$	−12.0730	+	6.97035i	−0.812118	+	0.468877i
$222$		0			0
$223$	0.952729	−	1.65017i	0.0637994	−	0.110504i	−0.832361	−	0.554233i	$-0.813012\pi$
$223$	0.952729	−	1.65017i	0.0637994	−	0.110504i	0.896161	+	0.443729i	$0.146345\pi$
$224$		0			0
$225$	−2.58859	+	1.51632i	−0.172572	+	0.101088i
$226$		0			0
$227$	15.9311	+	9.19784i	1.05739	+	0.610482i	0.924708	−	0.380677i	$-0.124309\pi$
$227$	15.9311	+	9.19784i	1.05739	+	0.610482i	0.132678	+	0.991159i	$0.457642\pi$
$228$		0			0
$229$	9.54790	−	5.51249i	0.630943	−	0.364275i	−0.150174	−	0.988660i	$-0.547983\pi$
$229$	9.54790	−	5.51249i	0.630943	−	0.364275i	0.781117	+	0.624384i	$0.214650\pi$
$230$		0			0
$231$	−0.684170	−	2.52159i	−0.0450151	−	0.165909i
$232$		0			0
$233$	−16.8788			−1.10577			−0.552885	−	0.833258i	$-0.686473\pi$
$233$	−16.8788			−1.10577			−0.552885	+	0.833258i	$0.686473\pi$
$234$		0			0
$235$			1.76454i			0.115106i
$236$		0			0
$237$	12.3948	+	12.3170i	0.805129	+	0.800078i
$238$		0			0
$239$	5.15400	+	8.92699i	0.333385	+	0.577439i	0.983173	−	0.182676i	$-0.0584759\pi$
$239$	5.15400	+	8.92699i	0.333385	+	0.577439i	−0.649789	+	0.760115i	$0.725143\pi$
$240$		0			0
$241$	−2.50577	+	4.34011i	−0.161411	+	0.279571i	−0.935375	−	0.353658i	$-0.884938\pi$
$241$	−2.50577	+	4.34011i	−0.161411	+	0.279571i	0.773964	+	0.633229i	$0.218271\pi$
$242$		0			0
$243$	−14.9920	+	4.27096i	−0.961735	+	0.273982i
$244$		0			0
$245$	−8.35764	−	4.82528i	−0.533950	−	0.308276i
$246$		0			0
$247$	−5.02506	−	8.70366i	−0.319737	−	0.553801i
$248$		0			0
$249$	1.91861	−	1.93072i	0.121587	−	0.122355i
$250$		0			0
$251$		−	1.21512i		−	0.0766977i	−0.999264	−	0.0383488i	$-0.987790\pi$
$251$		−	1.21512i		−	0.0766977i	0.999264	−	0.0383488i	$-0.0122098\pi$
$252$		0			0
$253$		−	3.26257i		−	0.205116i
$254$		0			0
$255$	1.18356	+	4.36217i	0.0741175	+	0.273169i
$256$		0			0
$257$	8.44091	+	14.6201i	0.526530	+	0.911976i	0.999522	+	0.0309097i	$0.00984044\pi$
$257$	8.44091	+	14.6201i	0.526530	+	0.911976i	−0.472992	+	0.881066i	$0.656826\pi$
$258$		0			0
$259$	−10.7433	−	6.20265i	−0.667557	−	0.385414i
$260$		0			0
$261$	−1.93804	−	3.30853i	−0.119962	−	0.204793i
$262$		0			0
$263$	−6.72703	+	11.6516i	−0.414806	+	0.718466i	−0.995408	−	0.0957219i	$-0.969484\pi$
$263$	−6.72703	+	11.6516i	−0.414806	+	0.718466i	0.580602	+	0.814188i	$0.302817\pi$
$264$		0			0
$265$	5.03162	+	8.71502i	0.309090	+	0.535359i
$266$		0			0
$267$	−5.71550	+	21.6022i	−0.349783	+	1.32203i
$268$		0			0
$269$		−	8.72380i		−	0.531900i	−0.963987	−	0.265950i	$-0.914314\pi$
$269$		−	8.72380i		−	0.531900i	0.963987	−	0.265950i	$-0.0856855\pi$
$270$		0			0
$271$	−8.15697			−0.495501			−0.247750	−	0.968824i	$-0.579691\pi$
$271$	−8.15697			−0.495501			−0.247750	+	0.968824i	$0.579691\pi$
$272$		0			0
$273$	36.5007	+	9.65735i	2.20912	+	0.584489i
$274$		0			0
$275$	0.320151	−	0.184839i	0.0193059	−	0.0111462i
$276$		0			0
$277$	−18.4491	−	10.6516i	−1.10850	−	0.639991i	−0.170057	−	0.985434i	$-0.554395\pi$
$277$	−18.4491	−	10.6516i	−1.10850	−	0.639991i	−0.938440	+	0.345443i	$0.887729\pi$
$278$		0			0
$279$	0.0782195	+	12.4301i	0.00468288	+	0.744168i
$280$		0			0
$281$	−8.58557	+	14.8707i	−0.512172	+	0.887109i	0.487728	+	0.872996i	$0.337826\pi$
$281$	−8.58557	+	14.8707i	−0.512172	+	0.887109i	−0.999900	+	0.0141130i	$0.995508\pi$
$282$		0			0
$283$	−7.07353	+	4.08390i	−0.420478	+	0.242763i	−0.695282	−	0.718737i	$-0.744720\pi$
$283$	−7.07353	+	4.08390i	−0.420478	+	0.242763i	0.274804	+	0.961500i	$0.411387\pi$
$284$		0			0
$285$	−3.14477	+	0.853252i	−0.186280	+	0.0505423i
$286$		0			0
$287$	31.1412			1.83821
$288$		0			0
$289$	−10.1902			−0.599425
$290$		0			0
$291$	0.110594	+	0.109900i	0.00648311	+	0.00644244i
$292$		0			0
$293$	7.81917	−	4.51440i	0.456801	−	0.263734i	−0.253897	−	0.967231i	$-0.581713\pi$
$293$	7.81917	−	4.51440i	0.456801	−	0.263734i	0.710698	+	0.703497i	$0.248379\pi$
$294$		0			0
$295$	1.12795	−	1.95366i	0.0656716	−	0.113747i
$296$		0			0
$297$	1.85068	−	0.514659i	0.107387	−	0.0298635i
$298$		0			0
$299$	40.8304	+	23.5735i	2.36128	+	1.36329i
$300$		0			0
$301$	−15.5348	+	8.96905i	−0.895414	+	0.516967i
$302$		0			0
$303$	−6.62957	+	6.67142i	−0.380859	+	0.383263i
$304$		0			0
$305$	−13.9722			−0.800049
$306$		0			0
$307$			24.7416i			1.41208i	0.708174	+	0.706038i	$0.249519\pi$
$307$			24.7416i			1.41208i	−0.708174	+	0.706038i	$0.750481\pi$
$308$		0			0
$309$	−27.4660	+	7.45220i	−1.56249	+	0.423941i
$310$		0			0
$311$	11.4925	+	19.9056i	0.651681	+	1.12874i	0.982715	+	0.185125i	$0.0592691\pi$
$311$	11.4925	+	19.9056i	0.651681	+	1.12874i	−0.331034	+	0.943619i	$0.607398\pi$
$312$		0			0
$313$	−14.0443	+	24.3254i	−0.793830	+	1.37495i	0.129749	+	0.991547i	$0.458583\pi$
$313$	−14.0443	+	24.3254i	−0.793830	+	1.37495i	−0.923579	+	0.383407i	$0.874751\pi$
$314$		0			0
$315$	6.05393	−	10.6398i	0.341101	−	0.599484i
$316$		0			0
$317$	23.3386	+	13.4745i	1.31082	+	0.756805i	0.982233	−	0.187667i	$-0.0600925\pi$
$317$	23.3386	+	13.4745i	1.31082	+	0.756805i	0.328592	+	0.944472i	$0.393426\pi$
$318$		0			0
$319$	0.236247	+	0.409192i	0.0132273	+	0.0229104i
$320$		0			0
$321$	−8.27115	−	2.18838i	−0.461651	−	0.122143i
$322$		0			0
$323$			4.90929i			0.273160i
$324$		0			0
$325$			5.34218i			0.296331i
$326$		0			0
$327$	16.4732	+	4.35848i	0.910972	+	0.241025i
$328$		0			0
$329$	−3.60011	−	6.23557i	−0.198481	−	0.343778i
$330$		0			0
$331$	0.187126	+	0.108037i	0.0102854	+	0.00593828i	0.505134	−	0.863041i	$-0.331443\pi$
$331$	0.187126	+	0.108037i	0.0102854	+	0.00593828i	−0.494848	+	0.868979i	$0.664776\pi$
$332$		0			0
$333$	4.51041	−	7.92705i	0.247169	−	0.434399i
$334$		0			0
$335$	−0.854350	+	1.47978i	−0.0466781	+	0.0808489i
$336$		0			0
$337$	0.992756	+	1.71950i	0.0540789	+	0.0936674i	0.891798	−	0.452435i	$-0.149444\pi$
$337$	0.992756	+	1.71950i	0.0540789	+	0.0936674i	−0.837719	+	0.546102i	$0.816111\pi$
$338$		0			0
$339$	27.1129	−	7.35640i	1.47257	−	0.399545i
$340$		0			0
$341$		−	1.53174i		−	0.0829484i
$342$		0			0
$343$	10.8157			0.583991
$344$		0			0
$345$	10.7748	−	10.8428i	0.580096	−	0.583758i
$346$		0			0
$347$	10.5340	−	6.08183i	0.565497	−	0.326490i	−0.189852	−	0.981813i	$-0.560801\pi$
$347$	10.5340	−	6.08183i	0.565497	−	0.326490i	0.755349	+	0.655323i	$0.227467\pi$
$348$		0			0
$349$	23.6671	+	13.6642i	1.26687	+	0.731428i	0.974395	−	0.224845i	$-0.0721875\pi$
$349$	23.6671	+	13.6642i	1.26687	+	0.731428i	0.292476	+	0.956273i	$0.405521\pi$
$350$		0			0
$351$	−6.93110	+	26.8795i	−0.369955	+	1.43472i
$352$		0			0
$353$	−3.43602	+	5.95137i	−0.182881	+	0.316759i	−0.942860	−	0.333188i	$-0.891876\pi$
$353$	−3.43602	+	5.95137i	−0.182881	+	0.316759i	0.759979	+	0.649947i	$0.225209\pi$
$354$		0			0
$355$	−7.44196	+	4.29662i	−0.394978	+	0.228041i
$356$		0			0
$357$	−13.0824	−	13.0004i	−0.692396	−	0.688052i
$358$		0			0
$359$	0.510693			0.0269533			0.0134767	−	0.999909i	$-0.495710\pi$
$359$	0.510693			0.0269533			0.0134767	+	0.999909i	$0.495710\pi$
$360$		0			0
$361$	15.4608			0.813726
$362$		0			0
$363$	18.1593	−	4.92706i	0.953116	−	0.258604i
$364$		0			0
$365$	−10.3343	+	5.96653i	−0.540924	+	0.312302i
$366$		0			0
$367$	−1.14997	+	1.99180i	−0.0600277	+	0.103971i	−0.894478	−	0.447113i	$-0.852452\pi$
$367$	−1.14997	+	1.99180i	−0.0600277	+	0.103971i	0.834450	+	0.551084i	$0.185786\pi$
$368$		0			0
$369$	0.144071	+	22.8946i	0.00750002	+	1.19185i
$370$		0			0
$371$	−35.5617	−	20.5316i	−1.84627	−	1.06595i
$372$		0			0
$373$	−11.0670	+	6.38951i	−0.573025	+	0.330836i	−0.758357	−	0.651840i	$-0.773997\pi$
$373$	−11.0670	+	6.38951i	−0.573025	+	0.330836i	0.185331	+	0.982676i	$0.440664\pi$
$374$		0			0
$375$	1.67443	+	0.443022i	0.0864674	+	0.0228775i
$376$		0			0
$377$	−6.82795			−0.351658
$378$		0			0
$379$		−	8.23995i		−	0.423258i	−0.977350	−	0.211629i	$-0.932123\pi$
$379$		−	8.23995i		−	0.423258i	0.977350	−	0.211629i	$-0.0678768\pi$
$380$		0			0
$381$	4.02513	−	15.2133i	0.206214	−	0.779401i
$382$		0			0
$383$	−2.55256	−	4.42116i	−0.130430	−	0.225911i	0.793413	−	0.608684i	$-0.208302\pi$
$383$	−2.55256	−	4.42116i	−0.130430	−	0.225911i	−0.923842	+	0.382773i	$0.874969\pi$
$384$		0			0
$385$	−0.754239	+	1.30638i	−0.0384396	+	0.0665793i
$386$		0			0
$387$	−6.66580	−	11.3795i	−0.338842	−	0.578454i
$388$		0			0
$389$	−14.1799	−	8.18674i	−0.718947	−	0.415084i	0.0954178	−	0.995437i	$-0.469581\pi$
$389$	−14.1799	−	8.18674i	−0.718947	−	0.415084i	−0.814365	+	0.580353i	$0.802915\pi$
$390$		0			0
$391$	−11.5152	−	19.9449i	−0.582348	−	1.00866i
$392$		0			0
$393$	−8.35127	−	30.7797i	−0.421266	−	1.55263i
$394$		0			0
$395$		−	10.0886i		−	0.507614i
$396$		0			0
$397$		−	0.186817i		−	0.00937606i	−0.999989	−	0.00468803i	$-0.998508\pi$
$397$		−	0.186817i		−	0.00937606i	0.999989	−	0.00468803i	$-0.00149225\pi$
$398$		0			0
$399$	9.37221	−	9.43138i	0.469198	−	0.472159i
$400$		0			0
$401$	−4.70535	−	8.14990i	−0.234974	−	0.406987i	0.724291	−	0.689494i	$-0.242167\pi$
$401$	−4.70535	−	8.14990i	−0.234974	−	0.406987i	−0.959265	+	0.282507i	$0.908834\pi$
$402$		0			0
$403$	19.1694	+	11.0675i	0.954898	+	0.551311i
$404$		0			0
$405$	7.85024	+	4.40155i	0.390082	+	0.218715i
$406$		0			0
$407$	−0.561937	+	0.973304i	−0.0278542	+	0.0482449i
$408$		0			0
$409$	9.14059	+	15.8320i	0.451973	+	0.782841i	0.998509	−	0.0545955i	$-0.0173869\pi$
$409$	9.14059	+	15.8320i	0.451973	+	0.782841i	−0.546535	+	0.837436i	$0.684054\pi$
$410$		0			0
$411$	−13.6007	−	13.5154i	−0.670875	−	0.666667i
$412$		0			0
$413$			9.20519i			0.452958i
$414$		0			0
$415$	−1.57149			−0.0771415
$416$		0			0
$417$	−6.53564	−	24.0879i	−0.320052	−	1.17959i
$418$		0			0
$419$	6.84038	−	3.94929i	0.334174	−	0.192936i	−0.323518	−	0.946222i	$-0.604866\pi$
$419$	6.84038	−	3.94929i	0.334174	−	0.192936i	0.657693	+	0.753286i	$0.271532\pi$
$420$		0			0
$421$	−26.7251	−	15.4298i	−1.30250	−	0.752000i	−0.321670	−	0.946852i	$-0.604244\pi$
$421$	−26.7251	−	15.4298i	−1.30250	−	0.752000i	−0.980833	+	0.194852i	$0.937577\pi$
$422$		0			0
$423$	4.56766	−	2.67560i	0.222087	−	0.130092i
$424$		0			0
$425$	1.30478	−	2.25994i	0.0632910	−	0.109623i
$426$		0			0
$427$	49.3755	−	28.5070i	2.38945	−	1.37955i
$428$		0			0
$429$	0.874920	−	3.30683i	0.0422415	−	0.159655i
$430$		0			0
$431$	26.2550			1.26466			0.632329	−	0.774700i	$-0.282099\pi$
$431$	26.2550			1.26466			0.632329	+	0.774700i	$0.282099\pi$
$432$		0			0
$433$	9.71829			0.467031			0.233516	−	0.972353i	$-0.424977\pi$
$433$	9.71829			0.467031			0.233516	+	0.972353i	$0.424977\pi$
$434$		0			0
$435$	−0.566235	+	2.14013i	−0.0271489	+	0.102611i
$436$		0			0
$437$	14.3787	−	8.30152i	0.687824	−	0.397116i
$438$		0			0
$439$	−9.66765	+	16.7449i	−0.461412	+	0.799189i	−0.999032	−	0.0439987i	$-0.985990\pi$
$439$	−9.66765	+	16.7449i	−0.461412	+	0.799189i	0.537620	+	0.843187i	$0.319324\pi$
$440$		0			0
$441$	0.182183	+	28.9511i	0.00867538	+	1.37863i
$442$		0			0
$443$	−14.5245	−	8.38573i	−0.690080	−	0.398418i	0.113562	−	0.993531i	$-0.463774\pi$
$443$	−14.5245	−	8.38573i	−0.690080	−	0.398418i	−0.803642	+	0.595113i	$0.797107\pi$
$444$		0			0
$445$	11.1728	−	6.45059i	0.529639	−	0.305787i
$446$		0			0
$447$	−5.72813	−	21.1118i	−0.270931	−	0.998552i
$448$		0			0
$449$	11.0309			0.520582			0.260291	−	0.965530i	$-0.416181\pi$
$449$	11.0309			0.520582			0.260291	+	0.965530i	$0.416181\pi$
$450$		0			0
$451$		−	2.82127i		−	0.132849i
$452$		0			0
$453$	−15.1880	−	15.0927i	−0.713595	−	0.709119i
$454$		0			0
$455$	−10.8994	−	18.8783i	−0.510972	−	0.885030i
$456$		0			0
$457$	9.61496	−	16.6536i	0.449769	−	0.779022i	−0.548602	−	0.836084i	$-0.684840\pi$
$457$	9.61496	−	16.6536i	0.449769	−	0.779022i	0.998371	+	0.0570614i	$0.0181731\pi$
$458$		0			0
$459$	9.49718	−	9.67819i	0.443291	−	0.451739i
$460$		0			0
$461$	−27.0061	−	15.5920i	−1.25780	−	0.726191i	−0.285154	−	0.958482i	$-0.592045\pi$
$461$	−27.0061	−	15.5920i	−1.25780	−	0.726191i	−0.972646	+	0.232291i	$0.925378\pi$
$462$		0			0
$463$	14.5978	+	25.2841i	0.678416	+	1.17505i	0.975458	+	0.220186i	$0.0706666\pi$
$463$	14.5978	+	25.2841i	0.678416	+	1.17505i	−0.297042	+	0.954864i	$0.596000\pi$
$464$		0			0
$465$	5.05866	−	5.09059i	0.234590	−	0.236070i
$466$		0			0
$467$			7.90238i			0.365679i	0.983143	+	0.182839i	$0.0585288\pi$
$467$			7.90238i			0.365679i	−0.983143	+	0.182839i	$0.941471\pi$
$468$		0			0
$469$		−	6.97237i		−	0.321954i
$470$		0			0
$471$	5.88538	+	21.6913i	0.271184	+	0.999483i
$472$		0			0
$473$	0.812562	+	1.40740i	0.0373616	+	0.0647123i
$474$		0			0
$475$	1.62923	+	0.940639i	0.0747544	+	0.0431595i
$476$		0			0
$477$	14.9300	−	26.2395i	0.683599	−	1.20143i
$478$		0			0
$479$	6.75925	−	11.7074i	0.308838	−	0.534923i	−0.669271	−	0.743019i	$-0.733393\pi$
$479$	6.75925	−	11.7074i	0.308838	−	0.534923i	0.978108	+	0.208096i	$0.0667266\pi$
$480$		0			0
$481$	−8.12048	−	14.0651i	−0.370262	−	0.641313i
$482$		0			0
$483$	−15.9542	+	60.3000i	−0.725940	+	2.74375i
$484$		0			0
$485$		−	0.0900165i		−	0.00408744i
$486$		0			0
$487$	−10.4175			−0.472061			−0.236031	−	0.971746i	$-0.575847\pi$
$487$	−10.4175			−0.472061			−0.236031	+	0.971746i	$0.575847\pi$
$488$		0			0
$489$	33.2495	+	8.79715i	1.50360	+	0.397821i
$490$		0			0
$491$	11.9665	−	6.90884i	0.540038	−	0.311791i	−0.205056	−	0.978750i	$-0.565738\pi$
$491$	11.9665	−	6.90884i	0.540038	−	0.311791i	0.745095	+	0.666959i	$0.232404\pi$
$492$		0			0
$493$	2.88848	+	1.66766i	0.130090	+	0.0751078i
$494$		0			0
$495$	−0.963924	−	0.548464i	−0.0433252	−	0.0246516i
$496$		0			0
$497$	17.5324	−	30.3670i	0.786435	−	1.36215i
$498$		0			0
$499$	0.591237	−	0.341351i	0.0264674	−	0.0152810i	−0.486708	−	0.873565i	$-0.661802\pi$
$499$	0.591237	−	0.341351i	0.0264674	−	0.0152810i	0.513175	+	0.858284i	$0.328469\pi$
$500$		0			0
$501$	22.5891	−	6.12897i	1.00921	−	0.273822i
$502$		0			0
$503$	−4.46146			−0.198927			−0.0994633	−	0.995041i	$-0.531713\pi$
$503$	−4.46146			−0.198927			−0.0994633	+	0.995041i	$0.531713\pi$
$504$		0			0
$505$	5.43013			0.241638
$506$		0			0
$507$	19.0910	+	18.9712i	0.847860	+	0.842541i
$508$		0			0
$509$	9.56309	−	5.52125i	0.423876	−	0.244725i	−0.272858	−	0.962054i	$-0.587969\pi$
$509$	9.56309	−	5.52125i	0.423876	−	0.244725i	0.696734	+	0.717329i	$0.254636\pi$
$510$		0			0
$511$	24.3465	−	42.1693i	1.07702	−	1.86546i
$512$		0			0
$513$	6.97719	+	6.84670i	0.308050	+	0.302289i
$514$		0			0
$515$	14.2295	+	8.21543i	0.627028	+	0.362015i
$516$		0			0
$517$	−0.564919	+	0.326156i	−0.0248451	+	0.0143443i
$518$		0			0
$519$	−6.32579	+	6.36572i	−0.277671	+	0.279424i
$520$		0			0
$521$	−1.96137			−0.0859292			−0.0429646	−	0.999077i	$-0.513680\pi$
$521$	−1.96137			−0.0859292			−0.0429646	+	0.999077i	$0.513680\pi$
$522$		0			0
$523$		−	16.4134i		−	0.717709i	−0.933394	−	0.358854i	$-0.883167\pi$
$523$		−	16.4134i		−	0.717709i	0.933394	−	0.358854i	$-0.116833\pi$
$524$		0			0
$525$	−6.82104	+	1.85071i	−0.297695	+	0.0807718i
$526$		0			0
$527$	−5.40626	−	9.36391i	−0.235500	−	0.407898i
$528$		0			0
$529$	−27.4439	+	47.5342i	−1.19321	+	2.06671i
$530$		0			0
$531$	−6.76754	+	0.0425866i	−0.293686	+	0.00184810i
$532$		0			0
$533$	35.3077	+	20.3849i	1.52935	+	0.882969i
$534$		0			0
$535$	2.46983	+	4.27788i	0.106780	+	0.184949i
$536$		0			0
$537$	−29.7893	−	7.88164i	−1.28550	−	0.340118i
$538$		0			0
$539$		−	3.56761i		−	0.153668i
$540$		0			0
$541$		−	11.3797i		−	0.489250i	−0.969618	−	0.244625i	$-0.921335\pi$
$541$		−	11.3797i		−	0.489250i	0.969618	−	0.244625i	$-0.0786649\pi$
$542$		0			0
$543$	−15.4711	−	4.09333i	−0.663927	−	0.175662i
$544$		0			0
$545$	−4.91904	−	8.52003i	−0.210709	−	0.364958i
$546$		0			0
$547$	−27.2507	−	15.7332i	−1.16516	−	0.672704i	−0.212623	−	0.977134i	$-0.568201\pi$
$547$	−27.2507	−	15.7332i	−1.16516	−	0.672704i	−0.952535	+	0.304430i	$0.901534\pi$
$548$		0			0
$549$	21.1864	+	36.1684i	0.904213	+	1.54363i
$550$		0			0
$551$	−1.20225	+	2.08236i	−0.0512176	+	0.0887114i
$552$		0			0
$553$	20.5834	+	35.6514i	0.875294	+	1.51605i
$554$		0			0
$555$	−5.08193	+	1.37885i	−0.215716	+	0.0585290i
$556$		0			0
$557$			9.00129i			0.381397i	0.981649	+	0.190699i	$0.0610753\pi$
$557$			9.00129i			0.381397i	−0.981649	+	0.190699i	$0.938925\pi$
$558$		0			0
$559$	−23.4845			−0.993287
$560$		0			0
$561$	−1.17778	+	1.18522i	−0.0497261	+	0.0500400i
$562$		0			0
$563$	−20.7439	+	11.9765i	−0.874251	+	0.504749i	−0.868759	−	0.495236i	$-0.835082\pi$
$563$	−20.7439	+	11.9765i	−0.874251	+	0.504749i	−0.00549239	+	0.999985i	$0.501748\pi$
$564$		0			0
$565$	−14.0466	−	8.10981i	−0.590945	−	0.341182i
$566$		0			0
$567$	−36.7217	+	0.462181i	−1.54217	+	0.0194098i
$568$		0			0
$569$	−13.4946	+	23.3734i	−0.565724	+	0.979863i	0.431258	+	0.902229i	$0.358070\pi$
$569$	−13.4946	+	23.3734i	−0.565724	+	0.979863i	−0.996982	+	0.0776341i	$0.975263\pi$
$570$		0			0
$571$	−5.95950	+	3.44072i	−0.249397	+	0.143990i	−0.619488	−	0.785006i	$-0.712660\pi$
$571$	−5.95950	+	3.44072i	−0.249397	+	0.143990i	0.370091	+	0.928996i	$0.379327\pi$
$572$		0			0
$573$	12.7269	+	12.6471i	0.531675	+	0.528340i
$574$		0			0
$575$	−8.82541			−0.368045
$576$		0			0
$577$	−22.2291			−0.925410			−0.462705	−	0.886512i	$-0.653121\pi$
$577$	−22.2291			−0.925410			−0.462705	+	0.886512i	$0.653121\pi$
$578$		0			0
$579$	−22.9008	+	6.21354i	−0.951724	+	0.258226i
$580$		0			0
$581$	5.55338	−	3.20625i	0.230393	−	0.133017i
$582$		0			0
$583$	−1.86008	+	3.22176i	−0.0770368	+	0.133432i
$584$		0			0
$585$	13.8287	−	8.10045i	0.571746	−	0.334912i
$586$		0			0
$587$	−25.9524	−	14.9836i	−1.07117	−	0.618440i	−0.142668	−	0.989771i	$-0.545568\pi$
$587$	−25.9524	−	14.9836i	−1.07117	−	0.618440i	−0.928501	+	0.371331i	$0.878902\pi$
$588$		0			0
$589$	6.75062	−	3.89747i	0.278155	−	0.160593i
$590$		0			0
$591$	−23.6282	−	6.25155i	−0.971935	−	0.257154i
$592$		0			0
$593$	−13.8975			−0.570700			−0.285350	−	0.958423i	$-0.592110\pi$
$593$	−13.8975			−0.570700			−0.285350	+	0.958423i	$0.592110\pi$
$594$		0			0
$595$			10.6483i			0.436538i
$596$		0			0
$597$	−8.04375	+	30.4020i	−0.329209	+	1.24427i
$598$		0			0
$599$	0.252190	+	0.436806i	0.0103042	+	0.0178474i	0.871132	−	0.491050i	$-0.163387\pi$
$599$	0.252190	+	0.436806i	0.0103042	+	0.0178474i	−0.860827	+	0.508897i	$0.830053\pi$
$600$		0			0
$601$	11.0731	−	19.1791i	0.451680	−	0.782333i	−0.546811	−	0.837256i	$-0.684158\pi$
$601$	11.0731	−	19.1791i	0.451680	−	0.782333i	0.998491	+	0.0549238i	$0.0174916\pi$
$602$		0			0
$603$	5.12600	−	0.0322568i	0.208747	−	0.00131360i
$604$		0			0
$605$	−9.40793	−	5.43167i	−0.382487	−	0.220829i
$606$		0			0
$607$	−22.0621	−	38.2126i	−0.895471	−	1.55100i	−0.833220	−	0.552941i	$-0.813506\pi$
$607$	−22.0621	−	38.2126i	−0.895471	−	1.55100i	−0.0622507	−	0.998061i	$-0.519828\pi$
$608$		0			0
$609$	−2.36544	−	8.71811i	−0.0958523	−	0.353276i
$610$		0			0
$611$		−	9.42649i		−	0.381355i
$612$		0			0
$613$			17.3208i			0.699579i	0.936828	+	0.349789i	$0.113747\pi$
$613$			17.3208i			0.699579i	−0.936828	+	0.349789i	$0.886253\pi$
$614$		0			0
$615$	9.31742	−	9.37623i	0.375715	−	0.378086i
$616$		0			0
$617$	−6.92480	−	11.9941i	−0.278782	−	0.482864i	0.692300	−	0.721609i	$-0.256597\pi$
$617$	−6.92480	−	11.9941i	−0.278782	−	0.482864i	−0.971082	+	0.238745i	$0.923264\pi$
$618$		0			0
$619$	2.47292	+	1.42774i	0.0993952	+	0.0573858i	0.548874	−	0.835905i	$-0.315057\pi$
$619$	2.47292	+	1.42774i	0.0993952	+	0.0573858i	−0.449478	+	0.893291i	$0.648390\pi$
$620$		0			0
$621$	−44.4056	−	11.4503i	−1.78194	−	0.459486i
$622$		0			0
$623$	−26.3217	+	45.5905i	−1.05456	+	1.82655i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.854447	−	0.849087i	−0.0341233	−	0.0339093i
$628$		0			0
$629$			7.93340i			0.316325i
$630$		0			0
$631$	2.51505			0.100122			0.0500612	−	0.998746i	$-0.484058\pi$
$631$	2.51505			0.100122			0.0500612	+	0.998746i	$0.484058\pi$
$632$		0			0
$633$	−11.8003	−	43.4915i	−0.469020	−	1.72863i
$634$		0			0
$635$	−7.86839	+	4.54281i	−0.312247	+	0.180276i
$636$		0			0
$637$	44.6480	+	25.7775i	1.76902	+	1.02134i
$638$		0			0
$639$	22.4065	+	12.7491i	0.886389	+	0.504347i
$640$		0			0
$641$	3.00957	−	5.21272i	0.118871	−	0.205890i	−0.800450	−	0.599400i	$-0.795406\pi$
$641$	3.00957	−	5.21272i	0.118871	−	0.205890i	0.919320	+	0.393510i	$0.128739\pi$
$642$		0			0
$643$	14.8943	−	8.59924i	0.587374	−	0.339121i	−0.176684	−	0.984268i	$-0.556537\pi$
$643$	14.8943	−	8.59924i	0.587374	−	0.339121i	0.764059	+	0.645147i	$0.223204\pi$
$644$		0			0
$645$	−1.94754	+	7.36089i	−0.0766844	+	0.289835i
$646$		0			0
$647$	42.0612			1.65359			0.826797	−	0.562500i	$-0.190160\pi$
$647$	42.0612			1.65359			0.826797	+	0.562500i	$0.190160\pi$
$648$		0			0
$649$	0.833956			0.0327356
$650$		0			0
$651$	−7.49031	+	28.3102i	−0.293568	+	1.10956i
$652$		0			0
$653$	−6.29892	+	3.63668i	−0.246496	+	0.142314i	−0.618159	−	0.786053i	$-0.712121\pi$
$653$	−6.29892	+	3.63668i	−0.246496	+	0.142314i	0.371663	+	0.928368i	$0.378788\pi$
$654$		0			0
$655$	−9.20657	+	15.9462i	−0.359730	+	0.623071i
$656$		0			0
$657$	31.1150	+	17.7041i	1.21391	+	0.690704i
$658$		0			0
$659$	−29.9779	−	17.3077i	−1.16777	−	0.674214i	−0.214619	−	0.976698i	$-0.568851\pi$
$659$	−29.9779	−	17.3077i	−1.16777	−	0.674214i	−0.953155	+	0.302484i	$0.902184\pi$
$660$		0			0
$661$	24.1531	−	13.9448i	0.939445	−	0.542389i	0.0496585	−	0.998766i	$-0.484187\pi$
$661$	24.1531	−	13.9448i	0.939445	−	0.542389i	0.889786	+	0.456378i	$0.150853\pi$
$662$		0			0
$663$	−6.32280	−	23.3035i	−0.245557	−	0.905032i
$664$		0			0
$665$	−7.67657			−0.297685
$666$		0			0
$667$		−	11.2799i		−	0.436761i
$668$		0			0
$669$	2.34103	+	2.32634i	0.0905094	+	0.0899417i
$670$		0			0
$671$	−2.58262	−	4.47323i	−0.0997010	−	0.172687i
$672$		0			0
$673$	22.2270	−	38.4983i	0.856789	−	1.48400i	−0.0181861	−	0.999835i	$-0.505789\pi$
$673$	22.2270	−	38.4983i	0.856789	−	1.48400i	0.874975	−	0.484168i	$-0.160878\pi$
$674$		0			0
$675$	−1.39218	−	5.00618i	−0.0535850	−	0.192688i
$676$		0			0
$677$	−9.50348	−	5.48684i	−0.365248	−	0.210876i	0.306132	−	0.951989i	$-0.400965\pi$
$677$	−9.50348	−	5.48684i	−0.365248	−	0.210876i	−0.671381	+	0.741113i	$0.734298\pi$
$678$		0			0
$679$	0.183657	+	0.318103i	0.00704809	+	0.0122077i
$680$		0			0
$681$	−22.4590	+	22.6008i	−0.860632	+	0.866064i
$682$		0			0
$683$		−	28.5694i		−	1.09318i	−0.837401	−	0.546589i	$-0.815926\pi$
$683$		−	28.5694i		−	1.09318i	0.837401	−	0.546589i	$-0.184074\pi$
$684$		0			0
$685$			11.0702i			0.422970i
$686$		0			0
$687$	5.00037	+	18.4295i	0.190776	+	0.703129i
$688$		0			0
$689$	−26.8798	−	46.5572i	−1.02404	−	1.77369i
$690$		0			0
$691$	23.0851	+	13.3282i	0.878197	+	0.507027i	0.870063	−	0.492940i	$-0.164078\pi$
$691$	23.0851	+	13.3282i	0.878197	+	0.507027i	0.00813334	+	0.999967i	$0.497411\pi$
$692$		0			0
$693$	4.52535	−	0.0284770i	0.171904	−	0.00108175i
$694$		0			0
$695$	−7.20500	+	12.4794i	−0.273301	+	0.473371i
$696$		0			0
$697$	−9.95765	−	17.2472i	−0.377173	−	0.653283i
$698$		0			0
$699$	7.47769	−	28.2625i	0.282832	−	1.06899i
$700$		0			0
$701$			6.86083i			0.259130i	0.991571	+	0.129565i	$0.0413581\pi$
$701$			6.86083i			0.259130i	−0.991571	+	0.129565i	$0.958642\pi$
$702$		0			0
$703$	−5.71934			−0.215709
$704$		0			0
$705$	−2.95461	−	0.781729i	−0.111277	−	0.0294416i
$706$		0			0
$707$	−19.1891	+	11.0789i	−0.721682	+	0.416663i
$708$		0			0
$709$	−5.70057	−	3.29122i	−0.214089	−	0.123605i	0.389121	−	0.921187i	$-0.372779\pi$
$709$	−5.70057	−	3.29122i	−0.214089	−	0.123605i	−0.603210	+	0.797582i	$0.706112\pi$
$710$		0			0
$711$	−26.1153	+	15.2976i	−0.979399	+	0.573704i
$712$		0			0
$713$	−18.2837	+	31.6684i	−0.684732	+	1.18599i
$714$		0			0
$715$	−1.71031	+	0.987446i	−0.0639618	+	0.0369284i
$716$		0			0
$717$	−17.2310	+	4.67519i	−0.643503	+	0.174598i
$718$		0			0
$719$	−6.63542			−0.247460			−0.123730	−	0.992316i	$-0.539486\pi$
$719$	−6.63542			−0.247460			−0.123730	+	0.992316i	$0.539486\pi$
$720$		0			0
$721$	−67.0463			−2.49693
$722$		0			0
$723$	−6.15713	−	6.11850i	−0.228986	−	0.227550i
$724$		0			0
$725$	1.10689	−	0.639061i	0.0411087	−	0.0237341i
$726$		0			0
$727$	18.9981	−	32.9056i	0.704600	−	1.22040i	−0.262236	−	0.965004i	$-0.584460\pi$
$727$	18.9981	−	32.9056i	0.704600	−	1.22040i	0.966836	−	0.255399i	$-0.0822067\pi$
$728$		0			0
$729$	−0.509678	−	26.9952i	−0.0188770	−	0.999822i
$730$		0			0
$731$	9.93479	+	5.73585i	0.367452	+	0.212148i
$732$		0			0
$733$	−23.1471	+	13.3640i	−0.854957	+	0.493609i	−0.862320	−	0.506363i	$-0.830989\pi$
$733$	−23.1471	+	13.3640i	−0.854957	+	0.493609i	0.00736353	+	0.999973i	$0.497656\pi$
$734$		0			0
$735$	11.7822	−	11.8566i	0.434594	−	0.437338i
$736$		0			0
$737$	−0.631671			−0.0232679
$738$		0			0
$739$			34.7551i			1.27849i	0.769004	+	0.639243i	$0.220752\pi$
$739$			34.7551i			1.27849i	−0.769004	+	0.639243i	$0.779248\pi$
$740$		0			0
$741$	16.7999	−	4.55823i	0.617161	−	0.167451i
$742$		0			0
$743$	−22.2636	−	38.5617i	−0.816773	−	1.41469i	−0.908048	−	0.418867i	$-0.862427\pi$
$743$	−22.2636	−	38.5617i	−0.816773	−	1.41469i	0.0912747	−	0.995826i	$-0.470906\pi$
$744$		0			0
$745$	−6.31478	+	10.9375i	−0.231356	+	0.400720i
$746$		0			0
$747$	2.38288	+	4.06794i	0.0871852	+	0.148838i
$748$		0			0
$749$	−17.4559	−	10.0782i	−0.637826	−	0.368249i
$750$		0			0
$751$	−6.94636	−	12.0314i	−0.253476	−	0.439034i	0.711004	−	0.703188i	$-0.248241\pi$
$751$	−6.94636	−	12.0314i	−0.253476	−	0.439034i	−0.964481	+	0.264154i	$0.914907\pi$
$752$		0			0
$753$	2.03464	+	0.538324i	0.0741464	+	0.0196176i
$754$		0			0
$755$			12.3621i			0.449904i
$756$		0			0
$757$			44.0570i			1.60128i	0.599145	+	0.800640i	$0.295507\pi$
$757$			44.0570i			1.60128i	−0.599145	+	0.800640i	$0.704493\pi$
$758$		0			0
$759$	5.46296	+	1.44539i	0.198293	+	0.0524642i
$760$		0			0
$761$	15.2569	+	26.4257i	0.553062	+	0.957932i	0.998051	+	0.0623957i	$0.0198741\pi$
$761$	15.2569	+	26.4257i	0.553062	+	0.957932i	−0.444989	+	0.895536i	$0.646793\pi$
$762$		0			0
$763$	34.7661	+	20.0722i	1.25862	+	0.726663i
$764$		0			0
$765$	−7.82851	+	0.0492630i	−0.283040	+	0.00178111i
$766$		0			0
$767$	−6.02569	+	10.4368i	−0.217575	+	0.376851i
$768$		0			0
$769$	−16.8187	−	29.1308i	−0.606498	−	1.05049i	−0.991813	−	0.127700i	$-0.959241\pi$
$769$	−16.8187	−	29.1308i	−0.606498	−	1.05049i	0.385315	−	0.922785i	$-0.374093\pi$
$770$		0			0
$771$	−28.2199	+	7.65674i	−1.01631	+	0.275751i
$772$		0			0
$773$		−	31.3456i		−	1.12742i	−0.825972	−	0.563712i	$-0.809373\pi$
$773$		−	31.3456i		−	1.12742i	0.825972	−	0.563712i	$-0.190627\pi$
$774$		0			0
$775$	−4.14343			−0.148837
$776$		0			0
$777$	15.1455	−	15.2411i	0.543340	−	0.546770i
$778$		0			0
$779$	12.4338	−	7.17866i	0.445487	−	0.257202i
$780$		0			0
$781$	−2.75113	−	1.58837i	−0.0984433	−	0.0568363i
$782$		0			0
$783$	6.39850	−	1.77937i	0.228664	−	0.0635896i
$784$		0			0
$785$	6.48813	−	11.2378i	0.231571	−	0.401093i
$786$		0			0
$787$	−22.3487	+	12.9030i	−0.796646	+	0.459944i	−0.842297	−	0.539014i	$-0.818797\pi$
$787$	−22.3487	+	12.9030i	−0.796646	+	0.459944i	0.0456513	+	0.998957i	$0.485464\pi$
$788$		0			0
$789$	−16.5296	−	16.4259i	−0.588468	−	0.584776i
$790$		0			0
$791$	66.1843			2.35324
$792$		0			0
$793$	74.6423			2.65062
$794$		0			0
$795$	−16.8218	+	4.56418i	−0.596610	+	0.161875i
$796$		0			0
$797$	18.8953	−	10.9092i	0.669307	−	0.386424i	−0.126507	−	0.991966i	$-0.540377\pi$
$797$	18.8953	−	10.9092i	0.669307	−	0.386424i	0.795814	+	0.605541i	$0.207043\pi$
$798$		0			0
$799$	−2.30233	+	3.98775i	−0.0814506	+	0.141077i
$800$		0			0
$801$	−33.6394	−	19.1405i	−1.18859	−	0.676296i
$802$		0			0
$803$	−3.82038	−	2.20570i	−0.134818	−	0.0778374i
$804$		0			0
$805$	31.1875	−	18.0061i	1.09921	−	0.634631i
$806$		0			0
$807$	14.6074	+	3.86483i	0.514206	+	0.136049i
$808$		0			0
$809$	0.650891			0.0228841			0.0114421	−	0.999935i	$-0.496358\pi$
$809$	0.650891			0.0228841			0.0114421	+	0.999935i	$0.496358\pi$
$810$		0			0
$811$		−	8.64169i		−	0.303451i	−0.988423	−	0.151725i	$-0.951517\pi$
$811$		−	8.64169i		−	0.303451i	0.988423	−	0.151725i	$-0.0484829\pi$
$812$		0			0
$813$	3.61372	−	13.6583i	0.126739	−	0.479018i
$814$		0			0
$815$	−9.92858	−	17.1968i	−0.347783	−	0.602378i
$816$		0			0
$817$	−4.13509	+	7.16218i	−0.144668	+	0.250573i
$818$		0			0
$819$	−32.3412	+	56.8396i	−1.13009	+	1.98614i
$820$		0			0
$821$	30.1278	+	17.3943i	1.05147	+	0.607065i	0.923060	−	0.384657i	$-0.125680\pi$
$821$	30.1278	+	17.3943i	1.05147	+	0.607065i	0.128407	+	0.991722i	$0.459014\pi$
$822$		0			0
$823$	−16.6190	−	28.7850i	−0.579304	−	1.00338i	−0.995559	−	0.0941356i	$-0.969991\pi$
$823$	−16.6190	−	28.7850i	−0.579304	−	1.00338i	0.416256	−	0.909248i	$-0.363342\pi$
$824$		0			0
$825$	0.167668	+	0.617960i	0.00583744	+	0.0215146i
$826$		0			0
$827$		−	31.7824i		−	1.10518i	−0.833452	−	0.552592i	$-0.813639\pi$
$827$		−	31.7824i		−	1.10518i	0.833452	−	0.552592i	$-0.186361\pi$
$828$		0			0
$829$			34.9590i			1.21418i	0.794635	+	0.607088i	$0.207662\pi$
$829$			34.9590i			1.21418i	−0.794635	+	0.607088i	$0.792338\pi$
$830$		0			0
$831$	26.0087	−	26.1729i	0.902232	−	0.907927i
$832$		0			0
$833$	−12.5918	−	21.8097i	−0.436281	−	0.755661i
$834$		0			0
$835$	−11.7029	−	6.75667i	−0.404995	−	0.233824i
$836$		0			0
$837$	−20.8480	−	5.37581i	−0.720611	−	0.185815i
$838$		0			0
$839$	10.4075	−	18.0263i	0.359305	−	0.622335i	−0.628539	−	0.777778i	$-0.716347\pi$
$839$	10.4075	−	18.0263i	0.359305	−	0.622335i	0.987845	+	0.155442i	$0.0496803\pi$
$840$		0			0
$841$	−13.6832	−	23.7000i	−0.471835	−	0.817241i
$842$		0			0
$843$	−21.0963	−	20.9640i	−0.726597	−	0.722039i
$844$		0			0
$845$		−	15.5389i		−	0.534554i
$846$		0			0
$847$	44.3280			1.52313
$848$		0			0
$849$	−3.70450	−	13.6534i	−0.127138	−	0.468584i
$850$		0			0
$851$	23.2358	−	13.4152i	0.796515	−	0.459868i
$852$		0			0
$853$	21.0687	+	12.1640i	0.721378	+	0.416488i	0.815260	−	0.579096i	$-0.196594\pi$
$853$	21.0687	+	12.1640i	0.721378	+	0.416488i	−0.0938817	+	0.995583i	$0.529928\pi$
$854$		0			0
$855$	−0.0355147	−	5.64372i	−0.00121458	−	0.193011i
$856$		0			0
$857$	−15.9593	+	27.6423i	−0.545159	+	0.944243i	0.453438	+	0.891288i	$0.350197\pi$
$857$	−15.9593	+	27.6423i	−0.545159	+	0.944243i	−0.998597	+	0.0529552i	$0.983136\pi$
$858$		0			0
$859$	−25.3361	+	14.6278i	−0.864458	+	0.499095i	−0.865502	−	0.500905i	$-0.833001\pi$
$859$	−25.3361	+	14.6278i	−0.864458	+	0.499095i	0.00104493	+	0.999999i	$0.499667\pi$
$860$		0			0
$861$	−13.7962	+	52.1439i	−0.470174	+	1.77706i
$862$		0			0
$863$	−56.1769			−1.91228			−0.956142	−	0.292904i	$-0.905378\pi$
$863$	−56.1769			−1.91228			−0.956142	+	0.292904i	$0.905378\pi$
$864$		0			0
$865$	5.18131			0.176170
$866$		0			0
$867$	4.51449	−	17.0629i	0.153320	−	0.579486i
$868$		0			0
$869$	3.22989	−	1.86478i	0.109566	−	0.0632582i
$870$		0			0
$871$	4.56409	−	7.90524i	0.154648	−	0.267859i
$872$		0			0
$873$	−0.233015	+	0.136494i	−0.00788638	+	0.00461961i
$874$		0			0
$875$	3.53383	+	2.04026i	0.119465	+	0.0689732i
$876$		0			0
$877$	−12.8329	+	7.40909i	−0.433337	+	0.250187i	−0.700767	−	0.713390i	$-0.747159\pi$
$877$	−12.8329	+	7.40909i	−0.433337	+	0.250187i	0.267430	+	0.963577i	$0.413825\pi$
$878$		0			0
$879$	4.09501	+	15.0927i	0.138121	+	0.509063i
$880$		0			0
$881$	46.2780			1.55915			0.779573	−	0.626311i	$-0.215436\pi$
$881$	46.2780			1.55915			0.779573	+	0.626311i	$0.215436\pi$
$882$		0			0
$883$			7.99121i			0.268926i	0.990919	+	0.134463i	$0.0429309\pi$
$883$			7.99121i			0.268926i	−0.990919	+	0.134463i	$0.957069\pi$
$884$		0			0
$885$	2.77157	+	2.75419i	0.0931654	+	0.0925810i
$886$		0			0
$887$	−5.27185	−	9.13111i	−0.177011	−	0.306593i	0.763844	−	0.645401i	$-0.223310\pi$
$887$	−5.27185	−	9.13111i	−0.177011	−	0.306593i	−0.940855	+	0.338808i	$0.889976\pi$
$888$		0			0
$889$	18.5370	−	32.1070i	0.621711	−	1.07684i
$890$		0			0
$891$	0.0418719	+	3.32685i	0.00140276	+	0.111454i
$892$		0			0
$893$	−2.87485	−	1.65979i	−0.0962031	−	0.0555429i
$894$		0			0
$895$	8.89533	+	15.4072i	0.297338	+	0.515004i
$896$		0			0
$897$	−57.5610	+	57.9243i	−1.92191	+	1.93404i
$898$		0			0
$899$		−	5.29581i		−	0.176625i
$900$		0			0
$901$			26.2606i			0.874866i
$902$		0			0
$903$	−8.13581	−	29.9856i	−0.270743	−	0.997857i
$904$		0			0
$905$	4.61979	+	8.00171i	0.153567	+	0.265986i
$906$		0			0
$907$	24.4462	+	14.1140i	0.811721	+	0.468648i	0.847553	−	0.530710i	$-0.178075\pi$
$907$	24.4462	+	14.1140i	0.811721	+	0.468648i	−0.0358320	+	0.999358i	$0.511408\pi$
$908$		0			0
$909$	−8.23381	−	14.0564i	−0.273098	−	0.466220i
$910$		0			0
$911$	−1.38749	+	2.40320i	−0.0459695	+	0.0796215i	−0.888095	−	0.459661i	$-0.847971\pi$
$911$	−1.38749	+	2.40320i	−0.0459695	+	0.0796215i	0.842125	+	0.539282i	$0.181304\pi$
$912$		0			0
$913$	−0.290474	−	0.503115i	−0.00961328	−	0.0166507i
$914$		0			0
$915$	6.19001	−	23.3956i	0.204635	−	0.773435i
$916$		0			0
$917$		−	75.1350i		−	2.48118i
$918$		0			0
$919$	−35.7713			−1.17999			−0.589994	−	0.807408i	$-0.700870\pi$
$919$	−35.7713			−1.17999			−0.589994	+	0.807408i	$0.700870\pi$
$920$		0			0
$921$	−41.4282	−	10.9611i	−1.36510	−	0.361179i
$922$		0			0
$923$	39.7563	−	22.9533i	1.30859	−	0.755517i
$924$		0			0
$925$	2.63284	+	1.52007i	0.0865671	+	0.0499795i
$926$		0			0
$927$	−0.310181	−	49.2916i	−0.0101877	−	1.61895i
$928$		0			0
$929$	−5.98498	+	10.3663i	−0.196361	+	0.340107i	−0.947346	−	0.320213i	$-0.896246\pi$
$929$	−5.98498	+	10.3663i	−0.196361	+	0.340107i	0.750985	+	0.660319i	$0.229579\pi$
$930$		0			0
$931$	15.7230	−	9.07770i	0.515302	−	0.297509i
$932$		0			0
$933$	−38.4221	+	10.4248i	−1.25788	+	0.341294i
$934$		0			0
$935$	0.964697			0.0315490
$936$		0			0
$937$	−9.78732			−0.319738			−0.159869	−	0.987138i	$-0.551107\pi$
$937$	−9.78732			−0.319738			−0.159869	+	0.987138i	$0.551107\pi$
$938$		0			0
$939$	−34.5094	−	34.2929i	−1.12617	−	1.11911i
$940$		0			0
$941$	8.66132	−	5.00061i	0.282351	−	0.163015i	−0.352136	−	0.935949i	$-0.614545\pi$
$941$	8.66132	−	5.00061i	0.282351	−	0.163015i	0.634487	+	0.772933i	$0.281211\pi$
$942$		0			0
$943$	−33.6764	+	58.3292i	−1.09665	+	1.89946i
$944$		0			0
$945$	15.1336	+	14.8506i	0.492296	+	0.483089i
$946$		0			0
$947$	26.4968	+	15.2979i	0.861031	+	0.497116i	0.864357	−	0.502878i	$-0.167726\pi$
$947$	26.4968	+	15.2979i	0.861031	+	0.497116i	−0.00332652	+	0.999994i	$0.501059\pi$
$948$		0			0
$949$	55.2079	−	31.8743i	1.79212	−	1.03468i
$950$		0			0
$951$	−32.9017	+	33.1094i	−1.06691	+	1.07365i
$952$		0			0
$953$	23.8769			0.773448			0.386724	−	0.922196i	$-0.373607\pi$
$953$	23.8769			0.773448			0.386724	+	0.922196i	$0.373607\pi$
$954$		0			0
$955$		−	10.3590i		−	0.335208i
$956$		0			0
$957$	−0.789828	+	0.214300i	−0.0255315	+	0.00692732i
$958$		0			0
$959$	−22.5860	−	39.1201i	−0.729340	−	1.26325i
$960$		0			0
$961$	6.91598	−	11.9788i	0.223096	−	0.386414i
$962$		0			0
$963$	7.32860	−	12.8800i	0.236161	−	0.415052i
$964$		0			0
$965$	11.8644	+	6.84990i	0.381928	+	0.220506i
$966$		0			0
$967$	21.6620	+	37.5196i	0.696601	+	1.20655i	0.969638	+	0.244545i	$0.0786387\pi$
$967$	21.6620	+	37.5196i	0.696601	+	1.20655i	−0.273036	+	0.962004i	$0.588028\pi$
$968$		0			0
$969$	−8.22029	−	2.17492i	−0.264074	−	0.0698686i
$970$		0			0
$971$		−	13.1135i		−	0.420831i	−0.977612	−	0.210416i	$-0.932518\pi$
$971$		−	13.1135i		−	0.420831i	0.977612	−	0.210416i	$-0.0674817\pi$
$972$		0			0
$973$		−	58.8001i		−	1.88505i
$974$		0			0
$975$	−8.94513	−	2.36670i	−0.286474	−	0.0757951i
$976$		0			0
$977$	2.21853	+	3.84260i	0.0709770	+	0.122936i	0.899330	−	0.437271i	$-0.144055\pi$
$977$	2.21853	+	3.84260i	0.0709770	+	0.122936i	−0.828353	+	0.560207i	$0.810722\pi$
$978$		0			0
$979$	4.13033	+	2.38465i	0.132006	+	0.0762137i
$980$		0			0
$981$	−14.5960	+	25.6524i	−0.466014	+	0.819020i
$982$		0			0
$983$	4.89137	−	8.47211i	0.156011	−	0.270218i	−0.777416	−	0.628987i	$-0.783470\pi$
$983$	4.89137	−	8.47211i	0.156011	−	0.270218i	0.933427	+	0.358769i	$0.116803\pi$
$984$		0			0
$985$	7.05558	+	12.2206i	0.224809	+	0.389381i
$986$		0			0
$987$	12.0360	−	3.26566i	0.383110	−	0.103947i
$988$		0			0
$989$		−	38.7969i		−	1.23367i
$990$		0			0
$991$	−7.98599			−0.253683			−0.126842	−	0.991923i	$-0.540484\pi$
$991$	−7.98599			−0.253683			−0.126842	+	0.991923i	$0.540484\pi$
$992$		0			0
$993$	−0.263803	+	0.265468i	−0.00837153	+	0.00842437i
$994$		0			0
$995$	15.7241	−	9.07828i	0.498486	−	0.287801i
$996$		0			0
$997$	3.22357	+	1.86113i	0.102091	+	0.0589425i	0.550176	−	0.835048i	$-0.314560\pi$
$997$	3.22357	+	1.86113i	0.102091	+	0.0589425i	−0.448085	+	0.893991i	$0.647894\pi$
$998$		0			0
$999$	11.2751	+	11.0642i	0.356729	+	0.350057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.bv.b.241.19		92
3.2	odd	2		4320.2.bv.b.721.16		92
4.3	odd	2		360.2.bf.b.61.37	yes	92
8.3	odd	2		360.2.bf.b.61.7	✓	92
8.5	even	2	inner	1440.2.bv.b.241.28		92
9.4	even	3	inner	1440.2.bv.b.1201.28		92
9.5	odd	6		4320.2.bv.b.3601.41		92
12.11	even	2		1080.2.bf.b.181.10		92
24.5	odd	2		4320.2.bv.b.721.41		92
24.11	even	2		1080.2.bf.b.181.40		92
36.23	even	6		1080.2.bf.b.901.40		92
36.31	odd	6		360.2.bf.b.301.7	yes	92
72.5	odd	6		4320.2.bv.b.3601.16		92
72.13	even	6	inner	1440.2.bv.b.1201.19		92
72.59	even	6		1080.2.bf.b.901.10		92
72.67	odd	6		360.2.bf.b.301.37	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bf.b.61.7	✓	92	8.3	odd	2
360.2.bf.b.61.37	yes	92	4.3	odd	2
360.2.bf.b.301.7	yes	92	36.31	odd	6
360.2.bf.b.301.37	yes	92	72.67	odd	6
1080.2.bf.b.181.10		92	12.11	even	2
1080.2.bf.b.181.40		92	24.11	even	2
1080.2.bf.b.901.10		92	72.59	even	6
1080.2.bf.b.901.40		92	36.23	even	6
1440.2.bv.b.241.19		92	1.1	even	1	trivial
1440.2.bv.b.241.28		92	8.5	even	2	inner
1440.2.bv.b.1201.19		92	72.13	even	6	inner
1440.2.bv.b.1201.28		92	9.4	even	3	inner
4320.2.bv.b.721.16		92	3.2	odd	2
4320.2.bv.b.721.41		92	24.5	odd	2
4320.2.bv.b.3601.16		92	72.5	odd	6
4320.2.bv.b.3601.41		92	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.443022 + 1.67443i) q^{3} +(0.866025 - 0.500000i) q^{5} +(-2.04026 + 3.53383i) q^{7} +(-2.60746 - 1.48362i) q^{9} +O(q^{10})\)	\(q+(-0.443022 + 1.67443i) q^{3} +(0.866025 - 0.500000i) q^{5} +(-2.04026 + 3.53383i) q^{7} +(-2.60746 - 1.48362i) q^{9} +(0.320151 + 0.184839i) q^{11} +(-4.62646 + 2.67109i) q^{13} +(0.453549 + 1.67161i) q^{15} +2.60955 q^{17} +1.88128i q^{19} +(-5.01328 - 4.98184i) q^{21} +(-4.41270 - 7.64303i) q^{23} +(0.500000 - 0.866025i) q^{25} +(3.63939 - 3.70875i) q^{27} +(1.10689 + 0.639061i) q^{29} +(-2.07172 - 3.58832i) q^{31} +(-0.451336 + 0.454185i) q^{33} +4.08051i q^{35} +3.04014i q^{37} +(-2.42294 - 8.93006i) q^{39} +(-3.81584 - 6.60924i) q^{41} +(3.80708 + 2.19802i) q^{43} +(-2.99994 + 0.0188780i) q^{45} +(-0.882270 + 1.52814i) q^{47} +(-4.82528 - 8.35764i) q^{49} +(-1.15609 + 4.36953i) q^{51} +10.0632i q^{53} +0.369679 q^{55} +(-3.15008 - 0.833446i) q^{57} +(1.95366 - 1.12795i) q^{59} +(-12.1003 - 6.98612i) q^{61} +(10.5628 - 6.18736i) q^{63} +(-2.67109 + 4.62646i) q^{65} +(-1.47978 + 0.854350i) q^{67} +(14.7527 - 4.00276i) q^{69} -8.59323 q^{71} -11.9331 q^{73} +(1.22859 + 1.22089i) q^{75} +(-1.30638 + 0.754239i) q^{77} +(5.04431 - 8.73700i) q^{79} +(4.59773 + 7.73698i) q^{81} +(-1.36095 - 0.785746i) q^{83} +(2.25994 - 1.30478i) q^{85} +(-1.56044 + 1.57029i) q^{87} +12.9012 q^{89} -21.7988i q^{91} +(6.92622 - 1.87925i) q^{93} +(0.940639 + 1.62923i) q^{95} +(0.0450082 - 0.0779566i) q^{97} +(-0.560551 - 0.956946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 92 * q + 8 * q^7 + 6 * q^9	\( 92 q + 8 q^{7} + 6 q^{9} + 12 q^{17} - 28 q^{23} + 46 q^{25} - 8 q^{31} - 14 q^{33} + 24 q^{39} - 18 q^{41} + 36 q^{47} - 30 q^{49} - 20 q^{55} - 34 q^{57} + 32 q^{63} + 12 q^{65} + 8 q^{71} - 4 q^{73} - 20 q^{79} + 18 q^{81} + 48 q^{87} - 24 q^{89} + 18 q^{95} - 14 q^{97}+O(q^{100}) \) 92 * q + 8 * q^7 + 6 * q^9 + 12 * q^17 - 28 * q^23 + 46 * q^25 - 8 * q^31 - 14 * q^33 + 24 * q^39 - 18 * q^41 + 36 * q^47 - 30 * q^49 - 20 * q^55 - 34 * q^57 + 32 * q^63 + 12 * q^65 + 8 * q^71 - 4 * q^73 - 20 * q^79 + 18 * q^81 + 48 * q^87 - 24 * q^89 + 18 * q^95 - 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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