LMFDB - Embedded newform 572.2.p.a.309.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(309,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("572.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.3
Character	$\chi$	$=$	572.309
Dual form			572.2.p.a.485.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07694 - 1.86531i) q^{3} +3.60411i q^{5} +(-3.54414 - 2.04621i) q^{7} +(-0.819590 + 1.41957i) q^{9} +O(q^{10})$	\(q+(-1.07694 - 1.86531i) q^{3} +3.60411i q^{5} +(-3.54414 - 2.04621i) q^{7} +(-0.819590 + 1.41957i) q^{9} +(0.866025 - 0.500000i) q^{11} +(3.34665 + 1.34161i) q^{13} +(6.72279 - 3.88141i) q^{15} +(-1.83110 + 3.17155i) q^{17} +(5.54296 + 3.20023i) q^{19} +8.81457i q^{21} +(4.23111 + 7.32850i) q^{23} -7.98964 q^{25} -2.93104 q^{27} +(4.18364 + 7.24627i) q^{29} -6.40328i q^{31} +(-1.86531 - 1.07694i) q^{33} +(7.37478 - 12.7735i) q^{35} +(2.69067 - 1.55346i) q^{37} +(-1.10161 - 7.68738i) q^{39} +(3.62129 - 2.09075i) q^{41} +(-1.72587 + 2.98929i) q^{43} +(-5.11630 - 2.95390i) q^{45} +10.5233i q^{47} +(4.87396 + 8.44195i) q^{49} +7.88790 q^{51} -0.556447 q^{53} +(1.80206 + 3.12125i) q^{55} -13.7858i q^{57} +(0.792595 + 0.457605i) q^{59} +(3.93267 - 6.81159i) q^{61} +(5.80948 - 3.35411i) q^{63} +(-4.83532 + 12.0617i) q^{65} +(-9.87234 + 5.69980i) q^{67} +(9.11329 - 15.7847i) q^{69} +(-8.21818 - 4.74477i) q^{71} -1.80157i q^{73} +(8.60435 + 14.9032i) q^{75} -4.09242 q^{77} +1.54855 q^{79} +(5.61531 + 9.72601i) q^{81} -4.44226i q^{83} +(-11.4306 - 6.59948i) q^{85} +(9.01103 - 15.6076i) q^{87} +(1.19067 - 0.687435i) q^{89} +(-9.11579 - 11.6028i) q^{91} +(-11.9441 + 6.89594i) q^{93} +(-11.5340 + 19.9775i) q^{95} +(-6.02664 - 3.47948i) q^{97} +1.63918i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.07694	−	1.86531i	−0.621770	−	1.07694i	−0.989156	−	0.146869i	$-0.953080\pi$
$3$	−1.07694	−	1.86531i	−0.621770	−	1.07694i	0.367386	−	0.930069i	$-0.380253\pi$
$4$		0			0
$5$			3.60411i			1.61181i	0.592046	+	0.805905i	$0.298321\pi$
$5$			3.60411i			1.61181i	−0.592046	+	0.805905i	$0.701679\pi$
$6$		0			0
$7$	−3.54414	−	2.04621i	−1.33956	−	0.773395i	−0.352818	−	0.935692i	$-0.614776\pi$
$7$	−3.54414	−	2.04621i	−1.33956	−	0.773395i	−0.986742	+	0.162297i	$0.948110\pi$
$8$		0			0
$9$	−0.819590	+	1.41957i	−0.273197	+	0.473190i
$10$		0			0
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$		0			0
$13$	3.34665	+	1.34161i	0.928194	+	0.372096i
$13$	3.34665	+	1.34161i	0.928194	+	0.372096i
$14$		0			0
$15$	6.72279	−	3.88141i	1.73582	−	1.00217i
$16$		0			0
$17$	−1.83110	+	3.17155i	−0.444106	+	0.769214i	−0.997989	−	0.0633801i	$-0.979812\pi$
$17$	−1.83110	+	3.17155i	−0.444106	+	0.769214i	0.553884	+	0.832594i	$0.313145\pi$
$18$		0			0
$19$	5.54296	+	3.20023i	1.27164	+	0.734184i	0.975297	−	0.220897i	$-0.0708985\pi$
$19$	5.54296	+	3.20023i	1.27164	+	0.734184i	0.296346	+	0.955081i	$0.404232\pi$
$20$		0			0
$21$			8.81457i			1.92350i
$22$		0			0
$23$	4.23111	+	7.32850i	0.882248	+	1.52810i	0.848836	+	0.528656i	$0.177304\pi$
$23$	4.23111	+	7.32850i	0.882248	+	1.52810i	0.0334119	+	0.999442i	$0.489363\pi$
$24$		0			0
$25$	−7.98964			−1.59793
$26$		0			0
$27$	−2.93104			−0.564079
$28$		0			0
$29$	4.18364	+	7.24627i	0.776882	+	1.34560i	0.933731	+	0.357976i	$0.116533\pi$
$29$	4.18364	+	7.24627i	0.776882	+	1.34560i	−0.156849	+	0.987623i	$0.550134\pi$
$30$		0			0
$31$		−	6.40328i		−	1.15006i	−0.818131	−	0.575032i	$-0.804990\pi$
$31$		−	6.40328i		−	1.15006i	0.818131	−	0.575032i	$-0.195010\pi$
$32$		0			0
$33$	−1.86531	−	1.07694i	−0.324709	−	0.187471i
$34$		0			0
$35$	7.37478	−	12.7735i	1.24657	−	2.15911i
$36$		0			0
$37$	2.69067	−	1.55346i	0.442344	−	0.255387i	−0.262247	−	0.965001i	$-0.584464\pi$
$37$	2.69067	−	1.55346i	0.442344	−	0.255387i	0.704591	+	0.709613i	$0.251130\pi$
$38$		0			0
$39$	−1.10161	−	7.68738i	−0.176399	−	1.23097i
$40$		0			0
$41$	3.62129	−	2.09075i	0.565550	−	0.326521i	−0.189820	−	0.981819i	$-0.560790\pi$
$41$	3.62129	−	2.09075i	0.565550	−	0.326521i	0.755370	+	0.655298i	$0.227457\pi$
$42$		0			0
$43$	−1.72587	+	2.98929i	−0.263192	+	0.455863i	−0.967088	−	0.254440i	$-0.918109\pi$
$43$	−1.72587	+	2.98929i	−0.263192	+	0.455863i	0.703896	+	0.710303i	$0.251442\pi$
$44$		0			0
$45$	−5.11630	−	2.95390i	−0.762692	−	0.440341i
$46$		0			0
$47$			10.5233i			1.53498i	0.641064	+	0.767488i	$0.278493\pi$
$47$			10.5233i			1.53498i	−0.641064	+	0.767488i	$0.721507\pi$
$48$		0			0
$49$	4.87396	+	8.44195i	0.696280	+	1.20599i
$50$		0			0
$51$	7.88790			1.10453
$52$		0			0
$53$	−0.556447			−0.0764338			−0.0382169	−	0.999269i	$-0.512168\pi$
$53$	−0.556447			−0.0764338			−0.0382169	+	0.999269i	$0.512168\pi$
$54$		0			0
$55$	1.80206	+	3.12125i	0.242989	+	0.420870i
$56$		0			0
$57$		−	13.7858i		−	1.82597i
$58$		0			0
$59$	0.792595	+	0.457605i	0.103187	+	0.0595751i	0.550705	−	0.834700i	$-0.314359\pi$
$59$	0.792595	+	0.457605i	0.103187	+	0.0595751i	−0.447518	+	0.894275i	$0.647692\pi$
$60$		0			0
$61$	3.93267	−	6.81159i	0.503527	−	0.872134i	−0.496465	−	0.868057i	$-0.665369\pi$
$61$	3.93267	−	6.81159i	0.503527	−	0.872134i	0.999992	−	0.00407750i	$-0.00129791\pi$
$62$		0			0
$63$	5.80948	−	3.35411i	0.731926	−	0.422578i
$64$		0			0
$65$	−4.83532	+	12.0617i	−0.599748	+	1.49607i
$66$		0			0
$67$	−9.87234	+	5.69980i	−1.20610	+	0.696341i	−0.961905	−	0.273385i	$-0.911857\pi$
$67$	−9.87234	+	5.69980i	−1.20610	+	0.696341i	−0.244194	+	0.969726i	$0.578523\pi$
$68$		0			0
$69$	9.11329	−	15.7847i	1.09711	−	1.90025i
$70$		0			0
$71$	−8.21818	−	4.74477i	−0.975319	−	0.563101i	−0.0744654	−	0.997224i	$-0.523725\pi$
$71$	−8.21818	−	4.74477i	−0.975319	−	0.563101i	−0.900854	+	0.434123i	$0.857058\pi$
$72$		0			0
$73$		−	1.80157i		−	0.210858i	−0.994427	−	0.105429i	$-0.966378\pi$
$73$		−	1.80157i		−	0.210858i	0.994427	−	0.105429i	$-0.0336215\pi$
$74$		0			0
$75$	8.60435	+	14.9032i	0.993544	+	1.72087i
$76$		0			0
$77$	−4.09242			−0.466375
$78$		0			0
$79$	1.54855			0.174226			0.0871130	−	0.996198i	$-0.472236\pi$
$79$	1.54855			0.174226			0.0871130	+	0.996198i	$0.472236\pi$
$80$		0			0
$81$	5.61531	+	9.72601i	0.623924	+	1.08067i
$82$		0			0
$83$		−	4.44226i		−	0.487602i	−0.969825	−	0.243801i	$-0.921606\pi$
$83$		−	4.44226i		−	0.487602i	0.969825	−	0.243801i	$-0.0783943\pi$
$84$		0			0
$85$	−11.4306	−	6.59948i	−1.23983	−	0.715814i
$86$		0			0
$87$	9.01103	−	15.6076i	0.966084	−	1.67331i
$88$		0			0
$89$	1.19067	−	0.687435i	0.126211	−	0.0728680i	−0.435565	−	0.900157i	$-0.643451\pi$
$89$	1.19067	−	0.687435i	0.126211	−	0.0728680i	0.561776	+	0.827289i	$0.310118\pi$
$90$		0			0
$91$	−9.11579	−	11.6028i	−0.955594	−	1.21631i
$92$		0			0
$93$	−11.9441	+	6.89594i	−1.23855	+	0.715076i
$94$		0			0
$95$	−11.5340	+	19.9775i	−1.18336	+	2.04965i
$96$		0			0
$97$	−6.02664	−	3.47948i	−0.611912	−	0.353288i	0.161801	−	0.986823i	$-0.448270\pi$
$97$	−6.02664	−	3.47948i	−0.611912	−	0.353288i	−0.773714	+	0.633536i	$0.781603\pi$
$98$		0			0
$99$			1.63918i			0.164744i
$100$		0			0
$101$	−2.13381	−	3.69586i	−0.212322	−	0.367752i	0.740119	−	0.672476i	$-0.234769\pi$
$101$	−2.13381	−	3.69586i	−0.212322	−	0.367752i	−0.952441	+	0.304724i	$0.901436\pi$
$102$		0			0
$103$	6.21626			0.612507			0.306253	−	0.951950i	$-0.400925\pi$
$103$	6.21626			0.612507			0.306253	+	0.951950i	$0.400925\pi$
$104$		0			0
$105$	−31.7687			−3.10031
$106$		0			0
$107$	−2.34661	−	4.06444i	−0.226855	−	0.392925i	0.730019	−	0.683427i	$-0.239511\pi$
$107$	−2.34661	−	4.06444i	−0.226855	−	0.392925i	−0.956874	+	0.290502i	$0.906178\pi$
$108$		0			0
$109$			4.08873i			0.391630i	0.980641	+	0.195815i	$0.0627352\pi$
$109$			4.08873i			0.391630i	−0.980641	+	0.195815i	$0.937265\pi$
$110$		0			0
$111$	−5.79537	−	3.34596i	−0.550073	−	0.317585i
$112$		0			0
$113$	−7.74146	+	13.4086i	−0.728255	+	1.26137i	0.229365	+	0.973340i	$0.426335\pi$
$113$	−7.74146	+	13.4086i	−0.728255	+	1.26137i	−0.957620	+	0.288034i	$0.906998\pi$
$114$		0			0
$115$	−26.4128	+	15.2494i	−2.46300	+	1.42202i
$116$		0			0
$117$	−4.64739	+	3.65124i	−0.429652	+	0.337557i
$118$		0			0
$119$	12.9793	−	7.49362i	1.18981	−	0.686939i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−7.79981	−	4.50322i	−0.703285	−	0.406042i
$124$		0			0
$125$		−	10.7750i		−	0.963746i
$126$		0			0
$127$	10.8571	+	18.8051i	0.963416	+	1.66868i	0.713813	+	0.700337i	$0.246967\pi$
$127$	10.8571	+	18.8051i	0.963416	+	1.66868i	0.249603	+	0.968348i	$0.419700\pi$
$128$		0			0
$129$	7.43461			0.654581
$130$		0			0
$131$	11.9431			1.04348			0.521738	−	0.853106i	$-0.325284\pi$
$131$	11.9431			1.04348			0.521738	+	0.853106i	$0.325284\pi$
$132$		0			0
$133$	−13.0967	−	22.6842i	−1.13563	−	1.96697i
$134$		0			0
$135$		−	10.5638i		−	0.909187i
$136$		0			0
$137$	−8.49019	−	4.90181i	−0.725366	−	0.418790i	0.0913587	−	0.995818i	$-0.470879\pi$
$137$	−8.49019	−	4.90181i	−0.725366	−	0.418790i	−0.816724	+	0.577028i	$0.804212\pi$
$138$		0			0
$139$	−8.69897	+	15.0671i	−0.737837	+	1.27797i	0.215630	+	0.976475i	$0.430819\pi$
$139$	−8.69897	+	15.0671i	−0.737837	+	1.27797i	−0.953467	+	0.301496i	$0.902514\pi$
$140$		0			0
$141$	19.6292	−	11.3329i	1.65307	−	0.954402i
$142$		0			0
$143$	3.56909	−	0.511457i	0.298462	−	0.0427701i
$144$		0			0
$145$	−26.1164	+	15.0783i	−2.16885	+	1.25219i
$146$		0			0
$147$	10.4979	−	18.1829i	0.865853	−	1.49970i
$148$		0			0
$149$	8.35018	+	4.82098i	0.684073	+	0.394950i	0.801388	−	0.598145i	$-0.204095\pi$
$149$	8.35018	+	4.82098i	0.684073	+	0.394950i	−0.117315	+	0.993095i	$0.537429\pi$
$150$		0			0
$151$			2.71518i			0.220958i	0.993878	+	0.110479i	$0.0352385\pi$
$151$			2.71518i			0.220958i	−0.993878	+	0.110479i	$0.964761\pi$
$152$		0			0
$153$	−3.00149	−	5.19874i	−0.242656	−	0.420293i
$154$		0			0
$155$	23.0782			1.85368
$156$		0			0
$157$	9.69948			0.774103			0.387051	−	0.922058i	$-0.373494\pi$
$157$	9.69948			0.774103			0.387051	+	0.922058i	$0.373494\pi$
$158$		0			0
$159$	0.599258	+	1.03795i	0.0475243	+	0.0823145i
$160$		0			0
$161$		−	34.6310i		−	2.72931i
$162$		0			0
$163$	−18.7933	−	10.8503i	−1.47201	−	0.849863i	−0.472502	−	0.881330i	$-0.656649\pi$
$163$	−18.7933	−	10.8503i	−1.47201	−	0.849863i	−0.999505	+	0.0314662i	$0.989982\pi$
$164$		0			0
$165$	3.88141	−	6.72279i	0.302167	−	0.523369i
$166$		0			0
$167$	12.1346	−	7.00592i	0.939005	−	0.542135i	0.0493564	−	0.998781i	$-0.484283\pi$
$167$	12.1346	−	7.00592i	0.939005	−	0.542135i	0.889648	+	0.456647i	$0.150950\pi$
$168$		0			0
$169$	9.40016	+	8.97981i	0.723089	+	0.690755i
$170$		0			0
$171$	−9.08591	+	5.24575i	−0.694817	+	0.401153i
$172$		0			0
$173$	−1.89323	+	3.27918i	−0.143940	+	0.249311i	−0.928977	−	0.370138i	$-0.879311\pi$
$173$	−1.89323	+	3.27918i	−0.143940	+	0.249311i	0.785037	+	0.619449i	$0.212644\pi$
$174$		0			0
$175$	28.3164	+	16.3485i	2.14052	+	1.23583i
$176$		0			0
$177$		−	1.97125i		−	0.148168i
$178$		0			0
$179$	−7.78737	−	13.4881i	−0.582055	−	1.00815i	−0.995236	−	0.0975001i	$-0.968915\pi$
$179$	−7.78737	−	13.4881i	−0.582055	−	1.00815i	0.413180	−	0.910649i	$-0.364418\pi$
$180$		0			0
$181$	−14.6042			−1.08552			−0.542761	−	0.839887i	$-0.682621\pi$
$181$	−14.6042			−1.08552			−0.542761	+	0.839887i	$0.682621\pi$
$182$		0			0
$183$	−16.9410			−1.25231
$184$		0			0
$185$	5.59885	+	9.69749i	0.411636	+	0.712974i
$186$		0			0
$187$			3.66219i			0.267806i
$188$		0			0
$189$	10.3880	+	5.99752i	0.755617	+	0.436256i
$190$		0			0
$191$	9.96950	−	17.2677i	0.721368	−	1.24945i	−0.239084	−	0.970999i	$-0.576847\pi$
$191$	9.96950	−	17.2677i	0.721368	−	1.24945i	0.960452	−	0.278447i	$-0.0898196\pi$
$192$		0			0
$193$	8.87684	−	5.12505i	0.638969	−	0.368909i	−0.145248	−	0.989395i	$-0.546398\pi$
$193$	8.87684	−	5.12505i	0.638969	−	0.368909i	0.784217	+	0.620486i	$0.213065\pi$
$194$		0			0
$195$	27.7062	−	3.97034i	1.98408	−	0.284322i
$196$		0			0
$197$	20.5970	−	11.8917i	1.46747	−	0.847247i	0.468138	−	0.883656i	$-0.344925\pi$
$197$	20.5970	−	11.8917i	1.46747	−	0.847247i	0.999337	+	0.0364086i	$0.0115918\pi$
$198$		0			0
$199$	−1.72708	+	2.99140i	−0.122430	+	0.212054i	−0.920725	−	0.390211i	$-0.872402\pi$
$199$	−1.72708	+	2.99140i	−0.122430	+	0.212054i	0.798296	+	0.602266i	$0.205735\pi$
$200$		0			0
$201$	21.2638	+	12.2767i	1.49983	+	0.865929i
$202$		0			0
$203$		−	34.2424i		−	2.40335i
$204$		0			0
$205$	7.53531	+	13.0515i	0.526289	+	0.911559i
$206$		0			0
$207$	−13.8711			−0.964108
$208$		0			0
$209$	6.40046			0.442729
$210$		0			0
$211$	9.62266	+	16.6669i	0.662451	+	1.14740i	0.979970	+	0.199147i	$0.0638173\pi$
$211$	9.62266	+	16.6669i	0.662451	+	1.14740i	−0.317518	+	0.948252i	$0.602849\pi$
$212$		0			0
$213$			20.4393i			1.40048i
$214$		0			0
$215$	−10.7738	−	6.22023i	−0.734764	−	0.424216i
$216$		0			0
$217$	−13.1025	+	22.6942i	−0.889454	+	1.54058i
$218$		0			0
$219$	−3.36049	+	1.94018i	−0.227081	+	0.131105i
$220$		0			0
$221$	−10.3830	+	8.15746i	−0.698438	+	0.548730i
$222$		0			0
$223$	−13.1320	+	7.58175i	−0.879382	+	0.507712i	−0.870455	−	0.492249i	$-0.836175\pi$
$223$	−13.1320	+	7.58175i	−0.879382	+	0.507712i	−0.00892754	+	0.999960i	$0.502842\pi$
$224$		0			0
$225$	6.54823	−	11.3419i	0.436549	−	0.756124i
$226$		0			0
$227$	0.644934	+	0.372353i	0.0428057	+	0.0247139i	0.521250	−	0.853404i	$-0.325466\pi$
$227$	0.644934	+	0.372353i	0.0428057	+	0.0247139i	−0.478444	+	0.878118i	$0.658799\pi$
$228$		0			0
$229$		−	24.2605i		−	1.60318i	−0.597875	−	0.801590i	$-0.703988\pi$
$229$		−	24.2605i		−	1.60318i	0.597875	−	0.801590i	$-0.296012\pi$
$230$		0			0
$231$	4.40728	+	7.63364i	0.289978	+	0.502257i
$232$		0			0
$233$	−17.0078			−1.11422			−0.557110	−	0.830439i	$-0.688090\pi$
$233$	−17.0078			−1.11422			−0.557110	+	0.830439i	$0.688090\pi$
$234$		0			0
$235$	−37.9270			−2.47409
$236$		0			0
$237$	−1.66770	−	2.88853i	−0.108328	−	0.187630i
$238$		0			0
$239$			12.6936i			0.821080i	0.911843	+	0.410540i	$0.134660\pi$
$239$			12.6936i			0.821080i	−0.911843	+	0.410540i	$0.865340\pi$
$240$		0			0
$241$	−4.68807	−	2.70666i	−0.301985	−	0.174351i	0.341349	−	0.939937i	$-0.389116\pi$
$241$	−4.68807	−	2.70666i	−0.301985	−	0.174351i	−0.643334	+	0.765585i	$0.722449\pi$
$242$		0			0
$243$	7.69813	−	13.3336i	0.493835	−	0.855348i
$244$		0			0
$245$	−30.4258	+	17.5663i	−1.94383	+	1.12227i
$246$		0			0
$247$	14.2569	+	18.1466i	0.907145	+	1.15464i
$248$		0			0
$249$	−8.28620	+	4.78404i	−0.525116	+	0.303176i
$250$		0			0
$251$	7.29889	−	12.6421i	0.460702	−	0.797959i	−0.538294	−	0.842757i	$-0.680931\pi$
$251$	7.29889	−	12.6421i	0.460702	−	0.797959i	0.998996	+	0.0447979i	$0.0142644\pi$
$252$		0			0
$253$	7.32850	+	4.23111i	0.460739	+	0.266008i
$254$		0			0
$255$			28.4289i			1.78029i
$256$		0			0
$257$	9.18004	+	15.9003i	0.572635	+	0.991833i	0.996294	+	0.0860116i	$0.0274122\pi$
$257$	9.18004	+	15.9003i	0.572635	+	0.991833i	−0.423659	+	0.905822i	$0.639254\pi$
$258$		0			0
$259$	−12.7148			−0.790061
$260$		0			0
$261$	−13.7155			−0.848966
$262$		0			0
$263$	3.13137	+	5.42370i	0.193089	+	0.334440i	0.946272	−	0.323371i	$-0.104816\pi$
$263$	3.13137	+	5.42370i	0.193089	+	0.334440i	−0.753184	+	0.657810i	$0.771483\pi$
$264$		0			0
$265$		−	2.00550i		−	0.123197i
$266$		0			0
$267$	−2.56456	−	1.48065i	−0.156949	−	0.0906143i
$268$		0			0
$269$	5.67601	−	9.83114i	0.346073	−	0.599415i	−0.639475	−	0.768812i	$-0.720848\pi$
$269$	5.67601	−	9.83114i	0.346073	−	0.599415i	0.985548	+	0.169396i	$0.0541817\pi$
$270$		0			0
$271$	14.7506	−	8.51625i	0.896034	−	0.517325i	0.0201225	−	0.999798i	$-0.493594\pi$
$271$	14.7506	−	8.51625i	0.896034	−	0.517325i	0.875911	+	0.482472i	$0.160261\pi$
$272$		0			0
$273$	−11.8257	+	29.4993i	−0.715725	+	1.78538i
$274$		0			0
$275$	−6.91923	+	3.99482i	−0.417245	+	0.240897i
$276$		0			0
$277$	3.32496	−	5.75899i	0.199777	−	0.346024i	−0.748679	−	0.662933i	$-0.769311\pi$
$277$	3.32496	−	5.75899i	0.199777	−	0.346024i	0.948456	+	0.316908i	$0.102645\pi$
$278$		0			0
$279$	9.08992	+	5.24807i	0.544199	+	0.314194i
$280$		0			0
$281$			10.6183i			0.633433i	0.948520	+	0.316717i	$0.102580\pi$
$281$			10.6183i			0.633433i	−0.948520	+	0.316717i	$0.897420\pi$
$282$		0			0
$283$	−8.33389	−	14.4347i	−0.495398	−	0.858055i	0.504587	−	0.863361i	$-0.331645\pi$
$283$	−8.33389	−	14.4347i	−0.495398	−	0.858055i	−0.999986	+	0.00530527i	$0.998311\pi$
$284$		0			0
$285$	49.6856			2.94312
$286$		0			0
$287$	−17.1125			−1.01012
$288$		0			0
$289$	1.79418	+	3.10761i	0.105540	+	0.182800i
$290$		0			0
$291$			14.9887i			0.878655i
$292$		0			0
$293$	−11.0653	−	6.38858i	−0.646445	−	0.373225i	0.140648	−	0.990060i	$-0.455081\pi$
$293$	−11.0653	−	6.38858i	−0.646445	−	0.373225i	−0.787093	+	0.616835i	$0.788415\pi$
$294$		0			0
$295$	−1.64926	+	2.85660i	−0.0960237	+	0.166318i
$296$		0			0
$297$	−2.53835	+	1.46552i	−0.147290	+	0.0850380i
$298$		0			0
$299$	4.32806	+	30.2024i	0.250298	+	1.74665i
$300$		0			0
$301$	12.2334	−	7.06298i	0.705124	−	0.407104i
$302$		0			0
$303$	−4.59595	+	7.96043i	−0.264031	+	0.457315i
$304$		0			0
$305$	24.5497	+	14.1738i	1.40571	+	0.811589i
$306$		0			0
$307$		−	20.1110i		−	1.14779i	−0.818928	−	0.573897i	$-0.805431\pi$
$307$		−	20.1110i		−	1.14779i	0.818928	−	0.573897i	$-0.194569\pi$
$308$		0			0
$309$	−6.69453	−	11.5953i	−0.380838	−	0.659632i
$310$		0			0
$311$	10.4971			0.595237			0.297619	−	0.954685i	$-0.403808\pi$
$311$	10.4971			0.595237			0.297619	+	0.954685i	$0.403808\pi$
$312$		0			0
$313$	13.2265			0.747603			0.373802	−	0.927509i	$-0.378054\pi$
$313$	13.2265			0.747603			0.373802	+	0.927509i	$0.378054\pi$
$314$		0			0
$315$	12.0886	+	20.9380i	0.681115	+	1.17973i
$316$		0			0
$317$		−	19.6640i		−	1.10444i	−0.833698	−	0.552221i	$-0.813781\pi$
$317$		−	19.6640i		−	1.10444i	0.833698	−	0.552221i	$-0.186219\pi$
$318$		0			0
$319$	7.24627	+	4.18364i	0.405713	+	0.234239i
$320$		0			0
$321$	−5.05430	+	8.75431i	−0.282104	+	0.488618i
$322$		0			0
$323$	−20.2994	+	11.7199i	−1.12949	+	0.652111i
$324$		0			0
$325$	−26.7385	−	10.7190i	−1.48319	−	0.594583i
$326$		0			0
$327$	7.62676	−	4.40331i	0.421761	−	0.243504i
$328$		0			0
$329$	21.5328	−	37.2959i	1.18714	−	2.05619i
$330$		0			0
$331$	4.76448	+	2.75077i	0.261880	+	0.151196i	0.625192	−	0.780471i	$-0.285021\pi$
$331$	4.76448	+	2.75077i	0.261880	+	0.151196i	−0.363312	+	0.931667i	$0.618354\pi$
$332$		0			0
$333$			5.09280i			0.279084i
$334$		0			0
$335$	−20.5427	−	35.5810i	−1.12237	−	1.94400i
$336$		0			0
$337$	22.7738			1.24057			0.620284	−	0.784377i	$-0.287017\pi$
$337$	22.7738			1.24057			0.620284	+	0.784377i	$0.287017\pi$
$338$		0			0
$339$	33.3483			1.81123
$340$		0			0
$341$	−3.20164	−	5.54541i	−0.173379	−	0.300301i
$342$		0			0
$343$		−	11.2457i		−	0.607209i
$344$		0			0
$345$	56.8898	+	32.8453i	3.06284	+	1.76833i
$346$		0			0
$347$	8.78830	−	15.2218i	0.471781	−	0.817148i	−0.527698	−	0.849432i	$-0.676945\pi$
$347$	8.78830	−	15.2218i	0.471781	−	0.817148i	0.999479	+	0.0322841i	$0.0102781\pi$
$348$		0			0
$349$	8.13600	−	4.69732i	0.435510	−	0.251442i	−0.266181	−	0.963923i	$-0.585762\pi$
$349$	8.13600	−	4.69732i	0.435510	−	0.251442i	0.701691	+	0.712481i	$0.252429\pi$
$350$		0			0
$351$	−9.80916	−	3.93231i	−0.523574	−	0.209891i
$352$		0			0
$353$	−10.8862	+	6.28512i	−0.579412	+	0.334523i	−0.760899	−	0.648870i	$-0.775242\pi$
$353$	−10.8862	+	6.28512i	−0.579412	+	0.334523i	0.181488	+	0.983393i	$0.441909\pi$
$354$		0			0
$355$	17.1007	−	29.6193i	0.907611	−	1.57203i
$356$		0			0
$357$	−27.9559	−	16.1403i	−1.47958	−	0.854236i
$358$		0			0
$359$			10.8119i			0.570631i	0.958434	+	0.285316i	$0.0920984\pi$
$359$			10.8119i			0.570631i	−0.958434	+	0.285316i	$0.907902\pi$
$360$		0			0
$361$	10.9830	+	19.0231i	0.578051	+	1.00121i
$362$		0			0
$363$	−2.15388			−0.113049
$364$		0			0
$365$	6.49306			0.339862
$366$		0			0
$367$	−6.67809	−	11.5668i	−0.348594	−	0.603782i	0.637406	−	0.770528i	$-0.280007\pi$
$367$	−6.67809	−	11.5668i	−0.348594	−	0.603782i	−0.986000	+	0.166746i	$0.946674\pi$
$368$		0			0
$369$			6.85424i			0.356817i
$370$		0			0
$371$	1.97213	+	1.13861i	0.102388	+	0.0591136i
$372$		0			0
$373$	−11.7773	+	20.3989i	−0.609806	+	1.05621i	0.381466	+	0.924383i	$0.375419\pi$
$373$	−11.7773	+	20.3989i	−0.609806	+	1.05621i	−0.991272	+	0.131832i	$0.957914\pi$
$374$		0			0
$375$	−20.0987	+	11.6040i	−1.03789	+	0.599229i
$376$		0			0
$377$	4.27950	+	29.8636i	0.220405	+	1.53805i
$378$		0			0
$379$	−1.02186	+	0.589972i	−0.0524895	+	0.0303048i	−0.526015	−	0.850475i	$-0.676314\pi$
$379$	−1.02186	+	0.589972i	−0.0524895	+	0.0303048i	0.473526	+	0.880780i	$0.342981\pi$
$380$		0			0
$381$	23.3849	−	40.5039i	1.19805	−	2.07508i
$382$		0			0
$383$	24.4859	+	14.1369i	1.25117	+	0.722364i	0.971342	−	0.237686i	$-0.0763888\pi$
$383$	24.4859	+	14.1369i	1.25117	+	0.722364i	0.279829	+	0.960050i	$0.409722\pi$
$384$		0			0
$385$		−	14.7496i		−	0.751707i
$386$		0			0
$387$	−2.82901	−	4.89999i	−0.143807	−	0.249080i
$388$		0			0
$389$	7.95924			0.403550			0.201775	−	0.979432i	$-0.435329\pi$
$389$	7.95924			0.403550			0.201775	+	0.979432i	$0.435329\pi$
$390$		0			0
$391$	−30.9903			−1.56725
$392$		0			0
$393$	−12.8620	−	22.2777i	−0.648803	−	1.12376i
$394$		0			0
$395$			5.58117i			0.280819i
$396$		0			0
$397$	−3.65345	−	2.10932i	−0.183361	−	0.105864i	0.405510	−	0.914091i	$-0.367094\pi$
$397$	−3.65345	−	2.10932i	−0.183361	−	0.105864i	−0.588871	+	0.808227i	$0.700427\pi$
$398$		0			0
$399$	−28.2087	+	48.8588i	−1.41220	+	2.44600i
$400$		0			0
$401$	−3.47645	+	2.00713i	−0.173606	+	0.100231i	−0.584285	−	0.811549i	$-0.698625\pi$
$401$	−3.47645	+	2.00713i	−0.173606	+	0.100231i	0.410679	+	0.911780i	$0.365292\pi$
$402$		0			0
$403$	8.59072	−	21.4296i	0.427934	−	1.06748i
$404$		0			0
$405$	−35.0537	+	20.2382i	−1.74183	+	1.00565i
$406$		0			0
$407$	1.55346	−	2.69067i	0.0770022	−	0.133372i
$408$		0			0
$409$	−24.9857	−	14.4255i	−1.23546	−	0.713295i	−0.267299	−	0.963614i	$-0.586131\pi$
$409$	−24.9857	−	14.4255i	−1.23546	−	0.713295i	−0.968163	+	0.250319i	$0.919464\pi$
$410$		0			0
$411$			21.1158i			1.04156i
$412$		0			0
$413$	−1.87271	−	3.24364i	−0.0921502	−	0.159609i
$414$		0			0
$415$	16.0104			0.785921
$416$		0			0
$417$	37.4730			1.83506
$418$		0			0
$419$	−8.80594	−	15.2523i	−0.430198	−	0.745125i	0.566692	−	0.823930i	$-0.308223\pi$
$419$	−8.80594	−	15.2523i	−0.430198	−	0.745125i	−0.996890	+	0.0788044i	$0.974890\pi$
$420$		0			0
$421$			27.6167i			1.34595i	0.739663	+	0.672977i	$0.234985\pi$
$421$			27.6167i			1.34595i	−0.739663	+	0.672977i	$0.765015\pi$
$422$		0			0
$423$	−14.9385	−	8.62476i	−0.726336	−	0.419350i
$424$		0			0
$425$	14.6298	−	25.3396i	0.709649	−	1.22915i
$426$		0			0
$427$	−27.8759	+	16.0942i	−1.34901	+	0.778851i
$428$		0			0
$429$	−4.79771	−	6.10666i	−0.231636	−	0.294832i
$430$		0			0
$431$	−1.03475	+	0.597412i	−0.0498420	+	0.0287763i	−0.524714	−	0.851279i	$-0.675828\pi$
$431$	−1.03475	+	0.597412i	−0.0498420	+	0.0287763i	0.474872	+	0.880055i	$0.342494\pi$
$432$		0			0
$433$	6.05655	−	10.4902i	0.291059	−	0.504129i	−0.683001	−	0.730417i	$-0.739326\pi$
$433$	6.05655	−	10.4902i	0.291059	−	0.504129i	0.974060	+	0.226288i	$0.0726590\pi$
$434$		0			0
$435$	56.2515	+	32.4768i	2.69705	+	1.55714i
$436$		0			0
$437$			54.1622i			2.59093i
$438$		0			0
$439$	0.925707	+	1.60337i	0.0441816	+	0.0765248i	0.887271	−	0.461249i	$-0.152599\pi$
$439$	0.925707	+	1.60337i	0.0441816	+	0.0765248i	−0.843089	+	0.537774i	$0.819265\pi$
$440$		0			0
$441$	−15.9786			−0.760886
$442$		0			0
$443$	−15.6654			−0.744285			−0.372143	−	0.928176i	$-0.621377\pi$
$443$	−15.6654			−0.744285			−0.372143	+	0.928176i	$0.621377\pi$
$444$		0			0
$445$	2.47760	+	4.29132i	0.117449	+	0.203428i
$446$		0			0
$447$		−	20.7676i		−	0.982272i
$448$		0			0
$449$	−18.0649	−	10.4298i	−0.852537	−	0.492212i	0.00896915	−	0.999960i	$-0.497145\pi$
$449$	−18.0649	−	10.4298i	−0.852537	−	0.492212i	−0.861506	+	0.507747i	$0.830478\pi$
$450$		0			0
$451$	2.09075	−	3.62129i	0.0984497	−	0.170520i
$452$		0			0
$453$	5.06466	−	2.92408i	0.237958	−	0.137385i
$454$		0			0
$455$	41.8179	−	32.8544i	1.96045	−	1.54024i
$456$		0			0
$457$	18.3310	−	10.5834i	0.857490	−	0.495072i	−0.00568090	−	0.999984i	$-0.501808\pi$
$457$	18.3310	−	10.5834i	0.857490	−	0.495072i	0.863171	+	0.504912i	$0.168475\pi$
$458$		0			0
$459$	5.36701	−	9.29594i	0.250511	−	0.433897i
$460$		0			0
$461$	−21.7115	−	12.5351i	−1.01120	−	0.583819i	−0.0996603	−	0.995022i	$-0.531776\pi$
$461$	−21.7115	−	12.5351i	−1.01120	−	0.583819i	−0.911544	+	0.411202i	$0.865109\pi$
$462$		0			0
$463$		−	6.06858i		−	0.282031i	−0.990007	−	0.141015i	$-0.954963\pi$
$463$		−	6.06858i		−	0.282031i	0.990007	−	0.141015i	$-0.0450367\pi$
$464$		0			0
$465$	−24.8538	−	43.0480i	−1.15257	−	1.99630i
$466$		0			0
$467$	10.9386			0.506179			0.253090	−	0.967443i	$-0.418553\pi$
$467$	10.9386			0.506179			0.253090	+	0.967443i	$0.418553\pi$
$468$		0			0
$469$	46.6520			2.15419
$470$		0			0
$471$	−10.4457	−	18.0925i	−0.481314	−	0.833660i
$472$		0			0
$473$			3.45174i			0.158711i
$474$		0			0
$475$	−44.2863	−	25.5687i	−2.03199	−	1.17317i
$476$		0			0
$477$	0.456058	−	0.789916i	0.0208815	−	0.0361678i
$478$		0			0
$479$	−8.03813	+	4.64081i	−0.367271	+	0.212044i	−0.672266	−	0.740310i	$-0.734679\pi$
$479$	−8.03813	+	4.64081i	−0.367271	+	0.212044i	0.304994	+	0.952354i	$0.401345\pi$
$480$		0			0
$481$	11.0889	−	1.58906i	0.505610	−	0.0724547i
$482$		0			0
$483$	−64.5976	+	37.2954i	−2.93929	+	1.69700i
$484$		0			0
$485$	12.5404	−	21.7207i	0.569432	−	0.986286i
$486$		0			0
$487$	−24.9397	−	14.3990i	−1.13013	−	0.652479i	−0.186160	−	0.982519i	$-0.559604\pi$
$487$	−24.9397	−	14.3990i	−1.13013	−	0.652479i	−0.943967	+	0.330041i	$0.892938\pi$
$488$		0			0
$489$			46.7405i			2.11368i
$490$		0			0
$491$	1.96203	+	3.39834i	0.0885452	+	0.153365i	0.906896	−	0.421354i	$-0.138445\pi$
$491$	1.96203	+	3.39834i	0.0885452	+	0.153365i	−0.818351	+	0.574719i	$0.805112\pi$
$492$		0			0
$493$	−30.6426			−1.38007
$494$		0			0
$495$	−5.90779			−0.265535
$496$		0			0
$497$	19.4176	+	33.6323i	0.870999	+	1.50861i
$498$		0			0
$499$			7.41866i			0.332105i	0.986117	+	0.166052i	$0.0531021\pi$
$499$			7.41866i			0.332105i	−0.986117	+	0.166052i	$0.946898\pi$
$500$		0			0
$501$	−26.1364	−	15.0899i	−1.16769	−	0.674166i
$502$		0			0
$503$	2.76733	−	4.79315i	0.123389	−	0.213716i	−0.797713	−	0.603037i	$-0.793957\pi$
$503$	2.76733	−	4.79315i	0.123389	−	0.213716i	0.921102	+	0.389321i	$0.127290\pi$
$504$		0			0
$505$	13.3203	−	7.69049i	0.592746	−	0.342222i
$506$		0			0
$507$	6.62676	−	27.2049i	0.294305	−	1.20821i
$508$		0			0
$509$	17.8151	−	10.2855i	0.789639	−	0.455898i	−0.0501964	−	0.998739i	$-0.515985\pi$
$509$	17.8151	−	10.2855i	0.789639	−	0.455898i	0.839835	+	0.542841i	$0.182651\pi$
$510$		0			0
$511$	−3.68639	+	6.38502i	−0.163076	+	0.282456i
$512$		0			0
$513$	−16.2466	−	9.38000i	−0.717307	−	0.414137i
$514$		0			0
$515$			22.4041i			0.987244i
$516$		0			0
$517$	5.26163	+	9.11341i	0.231406	+	0.400807i
$518$		0			0
$519$	8.15558			0.357990
$520$		0			0
$521$	−5.83479			−0.255627			−0.127813	−	0.991798i	$-0.540796\pi$
$521$	−5.83479			−0.255627			−0.127813	+	0.991798i	$0.540796\pi$
$522$		0			0
$523$	−4.69443	−	8.13099i	−0.205273	−	0.355544i	0.744947	−	0.667124i	$-0.232475\pi$
$523$	−4.69443	−	8.13099i	−0.205273	−	0.355544i	−0.950220	+	0.311581i	$0.899142\pi$
$524$		0			0
$525$		−	70.4253i		−	3.07361i
$526$		0			0
$527$	20.3083	+	11.7250i	0.884645	+	0.510750i
$528$		0			0
$529$	−24.3046	+	42.0968i	−1.05672	+	1.83030i
$530$		0			0
$531$	−1.29921	+	0.750097i	−0.0563807	+	0.0325514i
$532$		0			0
$533$	14.9242	−	2.13866i	0.646438	−	0.0926356i
$534$		0			0
$535$	14.6487	−	8.45744i	0.633319	−	0.365647i
$536$		0			0
$537$	−16.7730	+	29.0517i	−0.723809	+	1.25367i
$538$		0			0
$539$	8.44195	+	4.87396i	0.363621	+	0.209936i
$540$		0			0
$541$			0.449242i			0.0193144i	0.999953	+	0.00965721i	$0.00307403\pi$
$541$			0.449242i			0.0193144i	−0.999953	+	0.00965721i	$0.996926\pi$
$542$		0			0
$543$	15.7278	+	27.2414i	0.674946	+	1.16904i
$544$		0			0
$545$	−14.7363			−0.631232
$546$		0			0
$547$	17.9360			0.766890			0.383445	−	0.923564i	$-0.374738\pi$
$547$	17.9360			0.766890			0.383445	+	0.923564i	$0.374738\pi$
$548$		0			0
$549$	6.44635	+	11.1654i	0.275124	+	0.476528i
$550$		0			0
$551$			53.5544i			2.28150i
$552$		0			0
$553$	−5.48830	−	3.16867i	−0.233386	−	0.134745i
$554$		0			0
$555$	12.0592	−	20.8872i	0.511886	−	0.886612i
$556$		0			0
$557$	2.21347	−	1.27795i	0.0937876	−	0.0541483i	−0.452373	−	0.891829i	$-0.649422\pi$
$557$	2.21347	−	1.27795i	0.0937876	−	0.0541483i	0.546160	+	0.837681i	$0.316089\pi$
$558$		0			0
$559$	−9.78635	+	7.68868i	−0.413918	+	0.325196i
$560$		0			0
$561$	6.83113	−	3.94395i	0.288410	−	0.166514i
$562$		0			0
$563$	−3.51228	+	6.08345i	−0.148025	+	0.256387i	−0.930497	−	0.366298i	$-0.880625\pi$
$563$	−3.51228	+	6.08345i	−0.148025	+	0.256387i	0.782472	+	0.622685i	$0.213958\pi$
$564$		0			0
$565$	−48.3261	−	27.9011i	−2.03310	−	1.17381i
$566$		0			0
$567$		−	45.9605i		−	1.93016i
$568$		0			0
$569$	14.3128	+	24.7906i	0.600025	+	1.03927i	0.992817	+	0.119647i	$0.0381762\pi$
$569$	14.3128	+	24.7906i	0.600025	+	1.03927i	−0.392791	+	0.919628i	$0.628490\pi$
$570$		0			0
$571$	−6.10740			−0.255587			−0.127793	−	0.991801i	$-0.540789\pi$
$571$	−6.10740			−0.255587			−0.127793	+	0.991801i	$0.540789\pi$
$572$		0			0
$573$	−42.9461			−1.79410
$574$		0			0
$575$	−33.8051	−	58.5521i	−1.40977	−	2.44179i
$576$		0			0
$577$		−	42.1308i		−	1.75393i	−0.480557	−	0.876964i	$-0.659565\pi$
$577$		−	42.1308i		−	1.75393i	0.480557	−	0.876964i	$-0.340435\pi$
$578$		0			0
$579$	−19.1196	−	11.0387i	−0.794584	−	0.458753i
$580$		0			0
$581$	−9.08981	+	15.7440i	−0.377109	+	0.653171i
$582$		0			0
$583$	−0.481897	+	0.278223i	−0.0199581	+	0.0115228i
$584$		0			0
$585$	−13.1595	−	16.7497i	−0.544078	−	0.692517i
$586$		0			0
$587$	11.8782	−	6.85789i	0.490266	−	0.283055i	−0.234419	−	0.972136i	$-0.575319\pi$
$587$	11.8782	−	6.85789i	0.490266	−	0.283055i	0.724685	+	0.689080i	$0.241985\pi$
$588$		0			0
$589$	20.4920	−	35.4932i	0.844358	−	1.46247i
$590$		0			0
$591$	−44.3633	−	25.6132i	−1.82486	−	1.05359i
$592$		0			0
$593$			9.47847i			0.389234i	0.980879	+	0.194617i	$0.0623464\pi$
$593$			9.47847i			0.389234i	−0.980879	+	0.194617i	$0.937654\pi$
$594$		0			0
$595$	27.0079	+	46.7790i	1.10721	+	1.91775i
$596$		0			0
$597$	7.43985			0.304493
$598$		0			0
$599$	−43.7796			−1.78879			−0.894394	−	0.447280i	$-0.852393\pi$
$599$	−43.7796			−1.78879			−0.894394	+	0.447280i	$0.852393\pi$
$600$		0			0
$601$	−0.713292	−	1.23546i	−0.0290958	−	0.0503954i	0.851111	−	0.524986i	$-0.175929\pi$
$601$	−0.713292	−	1.23546i	−0.0290958	−	0.0503954i	−0.880207	+	0.474591i	$0.842596\pi$
$602$		0			0
$603$		−	18.6860i		−	0.760952i
$604$		0			0
$605$	3.12125	+	1.80206i	0.126897	+	0.0732640i
$606$		0			0
$607$	11.7146	−	20.2903i	0.475481	−	0.823557i	−0.524125	−	0.851642i	$-0.675607\pi$
$607$	11.7146	−	20.2903i	0.475481	−	0.823557i	0.999606	+	0.0280845i	$0.00894074\pi$
$608$		0			0
$609$	−63.8728	+	36.8770i	−2.58825	+	1.49433i
$610$		0			0
$611$	−14.1181	+	35.2177i	−0.571158	+	1.42476i
$612$		0			0
$613$	29.2238	−	16.8724i	1.18034	−	0.681468i	0.224245	−	0.974533i	$-0.428008\pi$
$613$	29.2238	−	16.8724i	1.18034	−	0.681468i	0.956093	+	0.293064i	$0.0946750\pi$
$614$		0			0
$615$	16.2301	−	28.1114i	0.654462	−	1.13356i
$616$		0			0
$617$	19.6606	+	11.3511i	0.791507	+	0.456977i	0.840493	−	0.541823i	$-0.182266\pi$
$617$	19.6606	+	11.3511i	0.791507	+	0.456977i	−0.0489859	+	0.998799i	$0.515599\pi$
$618$		0			0
$619$		−	23.4282i		−	0.941660i	−0.882224	−	0.470830i	$-0.843955\pi$
$619$		−	23.4282i		−	0.941660i	0.882224	−	0.470830i	$-0.156045\pi$
$620$		0			0
$621$	−12.4016	−	21.4801i	−0.497657	−	0.861967i
$622$		0			0
$623$	−5.62655			−0.225423
$624$		0			0
$625$	−1.11383			−0.0445534
$626$		0			0
$627$	−6.89290	−	11.9389i	−0.275276	−	0.476792i
$628$		0			0
$629$			11.3781i			0.453676i
$630$		0			0
$631$	−34.7535	−	20.0649i	−1.38351	−	0.798772i	−0.390940	−	0.920416i	$-0.627850\pi$
$631$	−34.7535	−	20.0649i	−1.38351	−	0.798772i	−0.992574	+	0.121644i	$0.961183\pi$
$632$		0			0
$633$	20.7260	−	35.8985i	0.823785	−	1.42684i
$634$		0			0
$635$	−67.7758	+	39.1304i	−2.68960	+	1.55284i
$636$		0			0
$637$	4.98564	+	34.7912i	0.197538	+	1.37848i
$638$		0			0
$639$	13.4711	−	7.77753i	0.532908	−	0.307674i
$640$		0			0
$641$	6.20634	−	10.7497i	0.245136	−	0.424588i	−0.717034	−	0.697038i	$-0.754501\pi$
$641$	6.20634	−	10.7497i	0.245136	−	0.424588i	0.962170	+	0.272450i	$0.0878341\pi$
$642$		0			0
$643$	20.4887	+	11.8292i	0.807997	+	0.466497i	0.846260	−	0.532770i	$-0.178849\pi$
$643$	20.4887	+	11.8292i	0.807997	+	0.466497i	−0.0382628	+	0.999268i	$0.512182\pi$
$644$		0			0
$645$			26.7952i			1.05506i
$646$		0			0
$647$	−19.0844	−	33.0551i	−0.750283	−	1.29953i	−0.947685	−	0.319206i	$-0.896584\pi$
$647$	−19.0844	−	33.0551i	−0.750283	−	1.29953i	0.197402	−	0.980323i	$-0.436750\pi$
$648$		0			0
$649$	0.915210			0.0359251
$650$		0			0
$651$	56.4422			2.21214
$652$		0			0
$653$	−6.09948	−	10.5646i	−0.238691	−	0.413425i	0.721648	−	0.692260i	$-0.243385\pi$
$653$	−6.09948	−	10.5646i	−0.238691	−	0.413425i	−0.960339	+	0.278835i	$0.910052\pi$
$654$		0			0
$655$			43.0444i			1.68188i
$656$		0			0
$657$	2.55745	+	1.47655i	0.0997758	+	0.0576056i
$658$		0			0
$659$	−13.8122	+	23.9234i	−0.538047	+	0.931924i	0.460963	+	0.887420i	$0.347504\pi$
$659$	−13.8122	+	23.9234i	−0.538047	+	0.931924i	−0.999009	+	0.0445045i	$0.985829\pi$
$660$		0			0
$661$	−14.5613	+	8.40699i	−0.566370	+	0.326994i	−0.755698	−	0.654920i	$-0.772702\pi$
$661$	−14.5613	+	8.40699i	−0.566370	+	0.326994i	0.189328	+	0.981914i	$0.439369\pi$
$662$		0			0
$663$	26.3981	+	10.5825i	1.02522	+	0.410990i
$664$		0			0
$665$	81.7563	−	47.2020i	3.17037	−	1.83042i
$666$		0			0
$667$	−35.4029	+	61.3196i	−1.37080	+	2.37430i
$668$		0			0
$669$	28.2846	+	16.3301i	1.09355	+	0.631360i
$670$		0			0
$671$		−	7.86534i		−	0.303638i
$672$		0			0
$673$	−7.35043	−	12.7313i	−0.283338	−	0.490756i	0.688867	−	0.724888i	$-0.258109\pi$
$673$	−7.35043	−	12.7313i	−0.283338	−	0.490756i	−0.972205	+	0.234132i	$0.924775\pi$
$674$		0			0
$675$	23.4179			0.901357
$676$		0			0
$677$	−21.2148			−0.815353			−0.407676	−	0.913127i	$-0.633661\pi$
$677$	−21.2148			−0.815353			−0.407676	+	0.913127i	$0.633661\pi$
$678$		0			0
$679$	14.2395	+	24.6636i	0.546462	+	0.946500i
$680$		0			0
$681$		−	1.60400i		−	0.0614655i
$682$		0			0
$683$	−1.47976	−	0.854339i	−0.0566214	−	0.0326904i	0.471422	−	0.881908i	$-0.343741\pi$
$683$	−1.47976	−	0.854339i	−0.0566214	−	0.0326904i	−0.528043	+	0.849217i	$0.677074\pi$
$684$		0			0
$685$	17.6667	−	30.5996i	0.675010	−	1.16915i
$686$		0			0
$687$	−45.2534	+	26.1271i	−1.72652	+	0.996809i
$688$		0			0
$689$	−1.86223	−	0.746535i	−0.0709454	−	0.0284407i
$690$		0			0
$691$	−25.7035	+	14.8399i	−0.977805	+	0.564536i	−0.901607	−	0.432556i	$-0.857612\pi$
$691$	−25.7035	+	14.8399i	−0.977805	+	0.564536i	−0.0761985	+	0.997093i	$0.524278\pi$
$692$		0			0
$693$	3.35411	−	5.80948i	0.127412	−	0.220684i
$694$		0			0
$695$	−54.3034	−	31.3521i	−2.05985	−	1.18925i
$696$		0			0
$697$			15.3135i			0.580039i
$698$		0			0
$699$	18.3164	+	31.7249i	0.692789	+	1.19995i
$700$		0			0
$701$	41.0316			1.54974			0.774871	−	0.632119i	$-0.217815\pi$
$701$	41.0316			1.54974			0.774871	+	0.632119i	$0.217815\pi$
$702$		0			0
$703$	19.8857			0.750005
$704$		0			0
$705$	40.8451	+	70.7457i	1.53831	+	2.66444i
$706$		0			0
$707$			17.4649i			0.656835i
$708$		0			0
$709$	36.5690	+	21.1132i	1.37338	+	0.792921i	0.991352	−	0.131230i	$-0.0418926\pi$
$709$	36.5690	+	21.1132i	1.37338	+	0.792921i	0.382028	+	0.924151i	$0.375226\pi$
$710$		0			0
$711$	−1.26918	+	2.19828i	−0.0475979	+	0.0824420i
$712$		0			0
$713$	46.9265	−	27.0930i	1.75741	−	1.01464i
$714$		0			0
$715$	1.84335	+	12.8634i	0.0689373	+	0.481064i
$716$		0			0
$717$	23.6775	−	13.6702i	0.884252	−	0.510523i
$718$		0			0
$719$	−4.59294	+	7.95520i	−0.171288	+	0.296679i	−0.938870	−	0.344271i	$-0.888126\pi$
$719$	−4.59294	+	7.95520i	−0.171288	+	0.296679i	0.767583	+	0.640950i	$0.221459\pi$
$720$		0			0
$721$	−22.0313	−	12.7198i	−0.820489	−	0.473710i
$722$		0			0
$723$			11.6596i			0.433625i
$724$		0			0
$725$	−33.4258	−	57.8951i	−1.24140	−	2.15017i
$726$		0			0
$727$	−35.7307			−1.32518			−0.662590	−	0.748983i	$-0.730543\pi$
$727$	−35.7307			−1.32518			−0.662590	+	0.748983i	$0.730543\pi$
$728$		0			0
$729$	0.530257			0.0196391
$730$		0			0
$731$	−6.32046	−	10.9474i	−0.233771	−	0.404903i
$732$		0			0
$733$		−	21.0917i		−	0.779039i	−0.921018	−	0.389519i	$-0.872641\pi$
$733$		−	21.0917i		−	0.779039i	0.921018	−	0.389519i	$-0.127359\pi$
$734$		0			0
$735$	65.5333	+	37.8357i	2.41723	+	1.39559i
$736$		0			0
$737$	−5.69980	+	9.87234i	−0.209955	+	0.363652i
$738$		0			0
$739$	30.3280	−	17.5099i	1.11563	−	0.644111i	0.175350	−	0.984506i	$-0.443894\pi$
$739$	30.3280	−	17.5099i	1.11563	−	0.644111i	0.940283	+	0.340395i	$0.110561\pi$
$740$		0			0
$741$	18.4952	−	46.1363i	0.679438	−	1.69486i
$742$		0			0
$743$	−6.62745	+	3.82636i	−0.243138	+	0.140376i	−0.616618	−	0.787263i	$-0.711498\pi$
$743$	−6.62745	+	3.82636i	−0.243138	+	0.140376i	0.373480	+	0.927638i	$0.378164\pi$
$744$		0			0
$745$	−17.3753	+	30.0950i	−0.636584	+	1.10260i
$746$		0			0
$747$	6.30611	+	3.64083i	0.230728	+	0.133211i
$748$		0			0
$749$			19.2066i			0.701795i
$750$		0			0
$751$	−13.5680	−	23.5005i	−0.495103	−	0.857544i	0.504881	−	0.863189i	$-0.331536\pi$
$751$	−13.5680	−	23.5005i	−0.495103	−	0.857544i	−0.999984	+	0.00564504i	$0.998203\pi$
$752$		0			0
$753$	−31.4418			−1.14580
$754$		0			0
$755$	−9.78582			−0.356143
$756$		0			0
$757$	9.70753	+	16.8139i	0.352826	+	0.611113i	0.986743	−	0.162288i	$-0.0518874\pi$
$757$	9.70753	+	16.8139i	0.352826	+	0.611113i	−0.633917	+	0.773401i	$0.718554\pi$
$758$		0			0
$759$		−	18.2266i		−	0.661583i
$760$		0			0
$761$	−30.6121	−	17.6739i	−1.10969	−	0.640678i	−0.170938	−	0.985282i	$-0.554680\pi$
$761$	−30.6121	−	17.6739i	−1.10969	−	0.640678i	−0.938748	+	0.344604i	$0.888013\pi$
$762$		0			0
$763$	8.36641	−	14.4911i	0.302885	−	0.524611i
$764$		0			0
$765$	18.7369	−	10.8177i	0.677432	−	0.391116i
$766$		0			0
$767$	2.03861	+	2.59480i	0.0736100	+	0.0936928i
$768$		0			0
$769$	8.35334	−	4.82280i	0.301229	−	0.173915i	−0.341766	−	0.939785i	$-0.611025\pi$
$769$	8.35334	−	4.82280i	0.301229	−	0.173915i	0.642995	+	0.765870i	$0.277692\pi$
$770$		0			0
$771$	19.7727	−	34.2473i	0.712095	−	1.23339i
$772$		0			0
$773$	31.9321	+	18.4360i	1.14852	+	0.663097i	0.948526	−	0.316701i	$-0.102575\pi$
$773$	31.9321	+	18.4360i	1.14852	+	0.663097i	0.199992	+	0.979798i	$0.435908\pi$
$774$		0			0
$775$			51.1600i			1.83772i
$776$		0			0
$777$	13.6931	+	23.7171i	0.491237	+	0.850847i
$778$		0			0
$779$	26.7636			0.958905
$780$		0			0
$781$	−9.48954			−0.339563
$782$		0			0
$783$	−12.2624	−	21.2391i	−0.438222	−	0.759023i
$784$		0			0
$785$			34.9580i			1.24771i
$786$		0			0
$787$	9.67170	+	5.58396i	0.344759	+	0.199047i	0.662374	−	0.749173i	$-0.269549\pi$
$787$	9.67170	+	5.58396i	0.344759	+	0.199047i	−0.317616	+	0.948220i	$0.602882\pi$
$788$		0			0
$789$	6.74459	−	11.6820i	0.240114	−	0.415889i
$790$		0			0
$791$	54.8737	−	31.6813i	1.95108	−	1.12646i
$792$		0			0
$793$	22.2998	−	17.5199i	0.791889	−	0.622150i
$794$		0			0
$795$	−3.74088	+	2.15980i	−0.132675	+	0.0766001i
$796$		0			0
$797$	−12.7819	+	22.1389i	−0.452759	+	0.784201i	−0.998556	−	0.0537160i	$-0.982893\pi$
$797$	−12.7819	+	22.1389i	−0.452759	+	0.784201i	0.545798	+	0.837917i	$0.316227\pi$
$798$		0			0
$799$	−33.3751	−	19.2691i	−1.18072	−	0.681692i
$800$		0			0
$801$			2.25366i			0.0796291i
$802$		0			0
$803$	−0.900784	−	1.56020i	−0.0317880	−	0.0550584i
$804$		0			0
$805$	124.814			4.39912
$806$		0			0
$807$	−24.4509			−0.860711
$808$		0			0
$809$	5.51603	+	9.55404i	0.193933	+	0.335902i	0.946550	−	0.322556i	$-0.104542\pi$
$809$	5.51603	+	9.55404i	0.193933	+	0.335902i	−0.752617	+	0.658458i	$0.771209\pi$
$810$		0			0
$811$		−	4.83609i		−	0.169818i	−0.996389	−	0.0849091i	$-0.972940\pi$
$811$		−	4.83609i		−	0.169818i	0.996389	−	0.0849091i	$-0.0270600\pi$
$812$		0			0
$813$	−31.7709	−	18.3429i	−1.11425	−	0.643315i
$814$		0			0
$815$	39.1058	−	67.7333i	1.36982	−	2.37259i
$816$		0			0
$817$	−19.1329	+	11.0464i	−0.669374	+	0.386463i
$818$		0			0
$819$	23.9422	−	3.43096i	0.836609	−	0.119887i
$820$		0			0
$821$	−14.6156	+	8.43833i	−0.510089	+	0.294500i	−0.732870	−	0.680369i	$-0.761820\pi$
$821$	−14.6156	+	8.43833i	−0.510089	+	0.294500i	0.222782	+	0.974868i	$0.428486\pi$
$822$		0			0
$823$	−0.180223	+	0.312156i	−0.00628219	+	0.0108811i	−0.869149	−	0.494550i	$-0.835333\pi$
$823$	−0.180223	+	0.312156i	−0.00628219	+	0.0108811i	0.862867	+	0.505431i	$0.168666\pi$
$824$		0			0
$825$	14.9032	+	8.60435i	0.518862	+	0.299565i
$826$		0			0
$827$			7.75357i			0.269618i	0.990872	+	0.134809i	$0.0430421\pi$
$827$			7.75357i			0.269618i	−0.990872	+	0.134809i	$0.956958\pi$
$828$		0			0
$829$	14.6951	+	25.4526i	0.510381	+	0.884006i	0.999928	+	0.0120291i	$0.00382906\pi$
$829$	14.6951	+	25.4526i	0.510381	+	0.884006i	−0.489546	+	0.871977i	$0.662838\pi$
$830$		0			0
$831$	−14.3231			−0.496862
$832$		0			0
$833$	−35.6988			−1.23689
$834$		0			0
$835$	25.2501	+	43.7345i	0.873817	+	1.51350i
$836$		0			0
$837$			18.7683i			0.648726i
$838$		0			0
$839$	40.4848	+	23.3739i	1.39769	+	0.806958i	0.994150	−	0.108004i	$-0.0344460\pi$
$839$	40.4848	+	23.3739i	1.39769	+	0.806958i	0.403541	+	0.914962i	$0.367779\pi$
$840$		0			0
$841$	−20.5056	+	35.5168i	−0.707091	+	1.22472i
$842$		0			0
$843$	19.8064	−	11.4352i	0.682168	−	0.393850i
$844$		0			0
$845$	−32.3643	+	33.8792i	−1.11336	+	1.16548i
$846$		0			0
$847$	−3.54414	+	2.04621i	−0.121778	+	0.0703087i
$848$		0			0
$849$	−17.9502	+	31.0906i	−0.616048	+	1.06703i
$850$		0			0
$851$	22.7691	+	13.1457i	0.780514	+	0.450630i
$852$		0			0
$853$		−	44.9860i		−	1.54029i	−0.637867	−	0.770146i	$-0.720183\pi$
$853$		−	44.9860i		−	1.54029i	0.637867	−	0.770146i	$-0.279817\pi$
$854$		0			0
$855$	−18.9063	−	32.7467i	−0.646582	−	1.11991i
$856$		0			0
$857$	−24.1745			−0.825787			−0.412893	−	0.910779i	$-0.635482\pi$
$857$	−24.1745			−0.825787			−0.412893	+	0.910779i	$0.635482\pi$
$858$		0			0
$859$	−31.4578			−1.07332			−0.536662	−	0.843797i	$-0.680315\pi$
$859$	−31.4578			−1.07332			−0.536662	+	0.843797i	$0.680315\pi$
$860$		0			0
$861$	18.4291	+	31.9201i	0.628062	+	1.08783i
$862$		0			0
$863$			41.8309i			1.42394i	0.702209	+	0.711971i	$0.252197\pi$
$863$			41.8309i			1.42394i	−0.702209	+	0.711971i	$0.747803\pi$
$864$		0			0
$865$	−11.8185	−	6.82343i	−0.401842	−	0.232004i
$866$		0			0
$867$	3.86443	−	6.69340i	0.131243	−	0.227320i
$868$		0			0
$869$	1.34109	−	0.774277i	0.0454933	−	0.0262655i
$870$		0			0
$871$	−40.6862	+	5.83040i	−1.37860	+	0.197556i
$872$		0			0
$873$	9.87874	−	5.70349i	0.334345	−	0.193034i
$874$		0			0
$875$	−22.0480	+	38.1882i	−0.745357	+	1.29100i
$876$		0			0
$877$	−50.3552	−	29.0726i	−1.70037	−	0.981712i	−0.945374	−	0.325987i	$-0.894304\pi$
$877$	−50.3552	−	29.0726i	−1.70037	−	0.981712i	−0.755000	−	0.655725i	$-0.772363\pi$
$878$		0			0
$879$			27.5204i			0.928241i
$880$		0			0
$881$	−20.1202	−	34.8493i	−0.677868	−	1.17410i	−0.975622	−	0.219460i	$-0.929571\pi$
$881$	−20.1202	−	34.8493i	−0.677868	−	1.17410i	0.297753	−	0.954643i	$-0.403763\pi$
$882$		0			0
$883$	48.8280			1.64319			0.821597	−	0.570068i	$-0.193083\pi$
$883$	48.8280			1.64319			0.821597	+	0.570068i	$0.193083\pi$
$884$		0			0
$885$	7.10461			0.238819
$886$		0			0
$887$	−15.1211	−	26.1905i	−0.507716	−	0.879390i	−0.999960	−	0.00893297i	$-0.997157\pi$
$887$	−15.1211	−	26.1905i	−0.507716	−	0.879390i	0.492244	−	0.870457i	$-0.336177\pi$
$888$		0			0
$889$		−	88.8640i		−	2.98040i
$890$		0			0
$891$	9.72601	+	5.61531i	0.325834	+	0.188120i
$892$		0			0
$893$	−33.6769	+	58.3301i	−1.12695	+	1.95194i
$894$		0			0
$895$	48.6127	−	28.0666i	1.62494	−	0.938162i
$896$		0			0
$897$	51.6759	−	40.5993i	1.72541	−	1.35557i
$898$		0			0
$899$	46.3999	−	26.7890i	1.54752	−	0.893464i
$900$		0			0
$901$	1.01891	−	1.76480i	0.0339447	−	0.0587940i
$902$		0			0
$903$	−26.3493	−	15.2128i	−0.876851	−	0.506250i
$904$		0			0
$905$		−	52.6353i		−	1.74966i
$906$		0			0
$907$	21.9656	+	38.0455i	0.729355	+	1.26328i	0.957156	+	0.289572i	$0.0935130\pi$
$907$	21.9656	+	38.0455i	0.729355	+	1.26328i	−0.227801	+	0.973708i	$0.573154\pi$
$908$		0			0
$909$	6.99539			0.232022
$910$		0			0
$911$	24.4533			0.810175			0.405087	−	0.914278i	$-0.367241\pi$
$911$	24.4533			0.810175			0.405087	+	0.914278i	$0.367241\pi$
$912$		0			0
$913$	−2.22113	−	3.84711i	−0.0735087	−	0.127321i
$914$		0			0
$915$		−	61.0572i		−	2.01849i
$916$		0			0
$917$	−42.3282	−	24.4382i	−1.39780	−	0.807020i
$918$		0			0
$919$	−4.29549	+	7.44000i	−0.141695	+	0.245423i	−0.928135	−	0.372244i	$-0.878589\pi$
$919$	−4.29549	+	7.44000i	−0.141695	+	0.245423i	0.786440	+	0.617667i	$0.211922\pi$
$920$		0			0
$921$	−37.5132	+	21.6583i	−1.23610	+	0.713664i
$922$		0			0
$923$	−21.1378	−	26.9047i	−0.695758	−	0.885579i
$924$		0			0
$925$	−21.4975	+	12.4116i	−0.706834	+	0.408091i
$926$		0			0
$927$	−5.09479	+	8.82443i	−0.167335	+	0.289832i
$928$		0			0
$929$	10.5934	+	6.11613i	0.347560	+	0.200664i	0.663610	−	0.748079i	$-0.269023\pi$
$929$	10.5934	+	6.11613i	0.347560	+	0.200664i	−0.316050	+	0.948742i	$0.602357\pi$
$930$		0			0
$931$			62.3913i			2.04479i
$932$		0			0
$933$	−11.3048	−	19.5804i	−0.370101	−	0.641034i
$934$		0			0
$935$	−13.1990			−0.431652
$936$		0			0
$937$	−38.6595			−1.26295			−0.631475	−	0.775397i	$-0.717550\pi$
$937$	−38.6595			−1.26295			−0.631475	+	0.775397i	$0.717550\pi$
$938$		0			0
$939$	−14.2441	−	24.6714i	−0.464838	−	0.805122i
$940$		0			0
$941$			38.7667i			1.26376i	0.775067	+	0.631879i	$0.217716\pi$
$941$			38.7667i			1.26376i	−0.775067	+	0.631879i	$0.782284\pi$
$942$		0			0
$943$	30.6442	+	17.6924i	0.997911	+	0.576144i
$944$		0			0
$945$	−21.6158	+	37.4396i	−0.703161	+	1.21791i
$946$		0			0
$947$	40.6855	−	23.4898i	1.32210	−	0.763316i	0.338039	−	0.941132i	$-0.390237\pi$
$947$	40.6855	−	23.4898i	1.32210	−	0.763316i	0.984064	+	0.177816i	$0.0569032\pi$
$948$		0			0
$949$	2.41700	−	6.02922i	0.0784593	−	0.195717i
$950$		0			0
$951$	−36.6795	+	21.1769i	−1.18941	+	0.686709i
$952$		0			0
$953$	−21.7425	+	37.6591i	−0.704309	+	1.21990i	0.262632	+	0.964896i	$0.415409\pi$
$953$	−21.7425	+	37.6591i	−0.704309	+	1.21990i	−0.966941	+	0.255002i	$0.917924\pi$
$954$		0			0
$955$	62.2347	+	35.9312i	2.01387	+	1.16271i
$956$		0			0
$957$		−	18.0221i		−	0.582571i
$958$		0			0
$959$	20.0603	+	34.7454i	0.647781	+	1.12199i
$960$		0			0
$961$	−10.0021			−0.322647
$962$		0			0
$963$	7.69302			0.247904
$964$		0			0
$965$	18.4713	+	31.9932i	0.594611	+	1.02990i
$966$		0			0
$967$			39.5537i			1.27196i	0.771705	+	0.635981i	$0.219404\pi$
$967$			39.5537i			1.27196i	−0.771705	+	0.635981i	$0.780596\pi$
$968$		0			0
$969$	43.7224	+	25.2431i	1.40457	+	0.810926i
$970$		0			0
$971$	−7.83343	+	13.5679i	−0.251387	+	0.435414i	−0.963908	−	0.266236i	$-0.914220\pi$
$971$	−7.83343	+	13.5679i	−0.251387	+	0.435414i	0.712521	+	0.701651i	$0.247553\pi$
$972$		0			0
$973$	61.6608	−	35.5999i	1.97675	−	1.14128i
$974$		0			0
$975$	8.80150	+	61.4194i	0.281874	+	1.96699i
$976$		0			0
$977$	−7.98584	+	4.61063i	−0.255490	+	0.147507i	−0.622275	−	0.782798i	$-0.713792\pi$
$977$	−7.98584	+	4.61063i	−0.255490	+	0.147507i	0.366786	+	0.930305i	$0.380458\pi$
$978$		0			0
$979$	0.687435	−	1.19067i	0.0219705	−	0.0380541i
$980$		0			0
$981$	−5.80425	−	3.35108i	−0.185315	−	0.106992i
$982$		0			0
$983$			3.09979i			0.0988678i	0.998777	+	0.0494339i	$0.0157417\pi$
$983$			3.09979i			0.0988678i	−0.998777	+	0.0494339i	$0.984258\pi$
$984$		0			0
$985$	42.8590	+	74.2339i	1.36560	+	2.36529i
$986$		0			0
$987$	−92.7580			−2.95252
$988$		0			0
$989$	−29.2094			−0.928804
$990$		0			0
$991$	−10.9371	−	18.9437i	−0.347430	−	0.601766i	0.638362	−	0.769736i	$-0.279612\pi$
$991$	−10.9371	−	18.9437i	−0.347430	−	0.601766i	−0.985792	+	0.167970i	$0.946279\pi$
$992$		0			0
$993$		−	11.8496i		−	0.376037i
$994$		0			0
$995$	−10.7813	−	6.22461i	−0.341791	−	0.197333i
$996$		0			0
$997$	17.6809	−	30.6243i	0.559961	−	0.969881i	−0.437538	−	0.899200i	$-0.644149\pi$
$997$	17.6809	−	30.6243i	0.559961	−	0.969881i	0.997499	−	0.0706812i	$-0.0225173\pi$
$998$		0			0
$999$	−7.88646	+	4.55325i	−0.249517	+	0.144059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.p.a.309.3	✓	24
13.2	odd	12		7436.2.a.u.1.10		12
13.4	even	6	inner	572.2.p.a.485.3	yes	24
13.11	odd	12		7436.2.a.v.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.3	✓	24	1.1	even	1	trivial
572.2.p.a.485.3	yes	24	13.4	even	6	inner
7436.2.a.u.1.10		12	13.2	odd	12
7436.2.a.v.1.10		12	13.11	odd	12

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07694 - 1.86531i) q^{3} +3.60411i q^{5} +(-3.54414 - 2.04621i) q^{7} +(-0.819590 + 1.41957i) q^{9} +O(q^{10})\)	\(q+(-1.07694 - 1.86531i) q^{3} +3.60411i q^{5} +(-3.54414 - 2.04621i) q^{7} +(-0.819590 + 1.41957i) q^{9} +(0.866025 - 0.500000i) q^{11} +(3.34665 + 1.34161i) q^{13} +(6.72279 - 3.88141i) q^{15} +(-1.83110 + 3.17155i) q^{17} +(5.54296 + 3.20023i) q^{19} +8.81457i q^{21} +(4.23111 + 7.32850i) q^{23} -7.98964 q^{25} -2.93104 q^{27} +(4.18364 + 7.24627i) q^{29} -6.40328i q^{31} +(-1.86531 - 1.07694i) q^{33} +(7.37478 - 12.7735i) q^{35} +(2.69067 - 1.55346i) q^{37} +(-1.10161 - 7.68738i) q^{39} +(3.62129 - 2.09075i) q^{41} +(-1.72587 + 2.98929i) q^{43} +(-5.11630 - 2.95390i) q^{45} +10.5233i q^{47} +(4.87396 + 8.44195i) q^{49} +7.88790 q^{51} -0.556447 q^{53} +(1.80206 + 3.12125i) q^{55} -13.7858i q^{57} +(0.792595 + 0.457605i) q^{59} +(3.93267 - 6.81159i) q^{61} +(5.80948 - 3.35411i) q^{63} +(-4.83532 + 12.0617i) q^{65} +(-9.87234 + 5.69980i) q^{67} +(9.11329 - 15.7847i) q^{69} +(-8.21818 - 4.74477i) q^{71} -1.80157i q^{73} +(8.60435 + 14.9032i) q^{75} -4.09242 q^{77} +1.54855 q^{79} +(5.61531 + 9.72601i) q^{81} -4.44226i q^{83} +(-11.4306 - 6.59948i) q^{85} +(9.01103 - 15.6076i) q^{87} +(1.19067 - 0.687435i) q^{89} +(-9.11579 - 11.6028i) q^{91} +(-11.9441 + 6.89594i) q^{93} +(-11.5340 + 19.9775i) q^{95} +(-6.02664 - 3.47948i) q^{97} +1.63918i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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