LMFDB - Embedded newform 572.2.p.a.485.3

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			485.3
Character	$\chi$	$=$	572.485
Dual form			572.2.p.a.309.3

$q$-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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

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

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	0.367386	+	0.930069i	$0.380253\pi$
$3$	−1.07694	+	1.86531i	−0.621770	+	1.07694i	−0.989156	+	0.146869i	$0.953080\pi$
$4$		0			0
$5$		−	3.60411i		−	1.61181i	−0.592046	−	0.805905i	$-0.701679\pi$
$5$		−	3.60411i		−	1.61181i	0.592046	−	0.805905i	$-0.298321\pi$
$6$		0			0
$7$	−3.54414	+	2.04621i	−1.33956	+	0.773395i	−0.986742	−	0.162297i	$-0.948110\pi$
$7$	−3.54414	+	2.04621i	−1.33956	+	0.773395i	−0.352818	+	0.935692i	$0.614776\pi$
$8$		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	0.553884	−	0.832594i	$-0.313145\pi$
$17$	−1.83110	−	3.17155i	−0.444106	−	0.769214i	−0.997989	+	0.0633801i	$0.979812\pi$
$18$		0			0
$19$	5.54296	−	3.20023i	1.27164	−	0.734184i	0.296346	−	0.955081i	$-0.404232\pi$
$19$	5.54296	−	3.20023i	1.27164	−	0.734184i	0.975297	+	0.220897i	$0.0708985\pi$
$20$		0			0
$21$		−	8.81457i		−	1.92350i
$22$		0			0
$23$	4.23111	−	7.32850i	0.882248	−	1.52810i	0.0334119	−	0.999442i	$-0.489363\pi$
$23$	4.23111	−	7.32850i	0.882248	−	1.52810i	0.848836	−	0.528656i	$-0.177304\pi$
$24$		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	−0.156849	−	0.987623i	$-0.550134\pi$
$29$	4.18364	−	7.24627i	0.776882	−	1.34560i	0.933731	−	0.357976i	$-0.116533\pi$
$30$		0			0
$31$			6.40328i			1.15006i	0.818131	+	0.575032i	$0.195010\pi$
$31$			6.40328i			1.15006i	−0.818131	+	0.575032i	$0.804990\pi$
$32$		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	0.704591	−	0.709613i	$-0.251130\pi$
$37$	2.69067	+	1.55346i	0.442344	+	0.255387i	−0.262247	+	0.965001i	$0.584464\pi$
$38$		0			0
$39$	−1.10161	+	7.68738i	−0.176399	+	1.23097i
$40$		0			0
$41$	3.62129	+	2.09075i	0.565550	+	0.326521i	0.755370	−	0.655298i	$-0.227457\pi$
$41$	3.62129	+	2.09075i	0.565550	+	0.326521i	−0.189820	+	0.981819i	$0.560790\pi$
$42$		0			0
$43$	−1.72587	−	2.98929i	−0.263192	−	0.455863i	0.703896	−	0.710303i	$-0.251442\pi$
$43$	−1.72587	−	2.98929i	−0.263192	−	0.455863i	−0.967088	+	0.254440i	$0.918109\pi$
$44$		0			0
$45$	−5.11630	+	2.95390i	−0.762692	+	0.440341i
$46$		0			0
$47$		−	10.5233i		−	1.53498i	−0.641064	−	0.767488i	$-0.721507\pi$
$47$		−	10.5233i		−	1.53498i	0.641064	−	0.767488i	$-0.278493\pi$
$48$		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	−0.447518	−	0.894275i	$-0.647692\pi$
$59$	0.792595	−	0.457605i	0.103187	−	0.0595751i	0.550705	+	0.834700i	$0.314359\pi$
$60$		0			0
$61$	3.93267	+	6.81159i	0.503527	+	0.872134i	0.999992	+	0.00407750i	$0.00129791\pi$
$61$	3.93267	+	6.81159i	0.503527	+	0.872134i	−0.496465	+	0.868057i	$0.665369\pi$
$62$		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	−0.244194	−	0.969726i	$-0.578523\pi$
$67$	−9.87234	−	5.69980i	−1.20610	−	0.696341i	−0.961905	+	0.273385i	$0.911857\pi$
$68$		0			0
$69$	9.11329	+	15.7847i	1.09711	+	1.90025i
$70$		0			0
$71$	−8.21818	+	4.74477i	−0.975319	+	0.563101i	−0.900854	−	0.434123i	$-0.857058\pi$
$71$	−8.21818	+	4.74477i	−0.975319	+	0.563101i	−0.0744654	+	0.997224i	$0.523725\pi$
$72$		0			0
$73$			1.80157i			0.210858i	0.994427	+	0.105429i	$0.0336215\pi$
$73$			1.80157i			0.210858i	−0.994427	+	0.105429i	$0.966378\pi$
$74$		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	$0.0783943\pi$
$83$			4.44226i			0.487602i	−0.969825	+	0.243801i	$0.921606\pi$
$84$		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	0.561776	−	0.827289i	$-0.310118\pi$
$89$	1.19067	+	0.687435i	0.126211	+	0.0728680i	−0.435565	+	0.900157i	$0.643451\pi$
$90$		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	−0.773714	−	0.633536i	$-0.781603\pi$
$97$	−6.02664	+	3.47948i	−0.611912	+	0.353288i	0.161801	+	0.986823i	$0.448270\pi$
$98$		0			0
$99$		−	1.63918i		−	0.164744i
$100$		0			0
$101$	−2.13381	+	3.69586i	−0.212322	+	0.367752i	−0.952441	−	0.304724i	$-0.901436\pi$
$101$	−2.13381	+	3.69586i	−0.212322	+	0.367752i	0.740119	+	0.672476i	$0.234769\pi$
$102$		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	−0.956874	−	0.290502i	$-0.906178\pi$
$107$	−2.34661	+	4.06444i	−0.226855	+	0.392925i	0.730019	+	0.683427i	$0.239511\pi$
$108$		0			0
$109$		−	4.08873i		−	0.391630i	−0.980641	−	0.195815i	$-0.937265\pi$
$109$		−	4.08873i		−	0.391630i	0.980641	−	0.195815i	$-0.0627352\pi$
$110$		0			0
$111$	−5.79537	+	3.34596i	−0.550073	+	0.317585i
$112$		0			0
$113$	−7.74146	−	13.4086i	−0.728255	−	1.26137i	−0.957620	−	0.288034i	$-0.906998\pi$
$113$	−7.74146	−	13.4086i	−0.728255	−	1.26137i	0.229365	−	0.973340i	$-0.426335\pi$
$114$		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	0.249603	−	0.968348i	$-0.419700\pi$
$127$	10.8571	−	18.8051i	0.963416	−	1.66868i	0.713813	−	0.700337i	$-0.246967\pi$
$128$		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	−0.816724	−	0.577028i	$-0.804212\pi$
$137$	−8.49019	+	4.90181i	−0.725366	+	0.418790i	0.0913587	+	0.995818i	$0.470879\pi$
$138$		0			0
$139$	−8.69897	−	15.0671i	−0.737837	−	1.27797i	−0.953467	−	0.301496i	$-0.902514\pi$
$139$	−8.69897	−	15.0671i	−0.737837	−	1.27797i	0.215630	−	0.976475i	$-0.430819\pi$
$140$		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	−0.117315	−	0.993095i	$-0.537429\pi$
$149$	8.35018	−	4.82098i	0.684073	−	0.394950i	0.801388	+	0.598145i	$0.204095\pi$
$150$		0			0
$151$		−	2.71518i		−	0.220958i	−0.993878	−	0.110479i	$-0.964761\pi$
$151$		−	2.71518i		−	0.220958i	0.993878	−	0.110479i	$-0.0352385\pi$
$152$		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	−0.999505	−	0.0314662i	$-0.989982\pi$
$163$	−18.7933	+	10.8503i	−1.47201	+	0.849863i	−0.472502	+	0.881330i	$0.656649\pi$
$164$		0			0
$165$	3.88141	+	6.72279i	0.302167	+	0.523369i
$166$		0			0
$167$	12.1346	+	7.00592i	0.939005	+	0.542135i	0.889648	−	0.456647i	$-0.150950\pi$
$167$	12.1346	+	7.00592i	0.939005	+	0.542135i	0.0493564	+	0.998781i	$0.484283\pi$
$168$		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	0.785037	−	0.619449i	$-0.212644\pi$
$173$	−1.89323	−	3.27918i	−0.143940	−	0.249311i	−0.928977	+	0.370138i	$0.879311\pi$
$174$		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	0.413180	+	0.910649i	$0.364418\pi$
$179$	−7.78737	+	13.4881i	−0.582055	+	1.00815i	−0.995236	+	0.0975001i	$0.968915\pi$
$180$		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	0.960452	+	0.278447i	$0.0898196\pi$
$191$	9.96950	+	17.2677i	0.721368	+	1.24945i	−0.239084	+	0.970999i	$0.576847\pi$
$192$		0			0
$193$	8.87684	+	5.12505i	0.638969	+	0.368909i	0.784217	−	0.620486i	$-0.213065\pi$
$193$	8.87684	+	5.12505i	0.638969	+	0.368909i	−0.145248	+	0.989395i	$0.546398\pi$
$194$		0			0
$195$	27.7062	+	3.97034i	1.98408	+	0.284322i
$196$		0			0
$197$	20.5970	+	11.8917i	1.46747	+	0.847247i	0.999337	−	0.0364086i	$-0.0115918\pi$
$197$	20.5970	+	11.8917i	1.46747	+	0.847247i	0.468138	+	0.883656i	$0.344925\pi$
$198$		0			0
$199$	−1.72708	−	2.99140i	−0.122430	−	0.212054i	0.798296	−	0.602266i	$-0.205735\pi$
$199$	−1.72708	−	2.99140i	−0.122430	−	0.212054i	−0.920725	+	0.390211i	$0.872402\pi$
$200$		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	−0.317518	−	0.948252i	$-0.602849\pi$
$211$	9.62266	−	16.6669i	0.662451	−	1.14740i	0.979970	−	0.199147i	$-0.0638173\pi$
$212$		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	−0.00892754	−	0.999960i	$-0.502842\pi$
$223$	−13.1320	−	7.58175i	−0.879382	−	0.507712i	−0.870455	+	0.492249i	$0.836175\pi$
$224$		0			0
$225$	6.54823	+	11.3419i	0.436549	+	0.756124i
$226$		0			0
$227$	0.644934	−	0.372353i	0.0428057	−	0.0247139i	−0.478444	−	0.878118i	$-0.658799\pi$
$227$	0.644934	−	0.372353i	0.0428057	−	0.0247139i	0.521250	+	0.853404i	$0.325466\pi$
$228$		0			0
$229$			24.2605i			1.60318i	0.597875	+	0.801590i	$0.296012\pi$
$229$			24.2605i			1.60318i	−0.597875	+	0.801590i	$0.703988\pi$
$230$		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	$-0.865340\pi$
$239$		−	12.6936i		−	0.821080i	0.911843	−	0.410540i	$-0.134660\pi$
$240$		0			0
$241$	−4.68807	+	2.70666i	−0.301985	+	0.174351i	−0.643334	−	0.765585i	$-0.722449\pi$
$241$	−4.68807	+	2.70666i	−0.301985	+	0.174351i	0.341349	+	0.939937i	$0.389116\pi$
$242$		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	0.998996	−	0.0447979i	$-0.0142644\pi$
$251$	7.29889	+	12.6421i	0.460702	+	0.797959i	−0.538294	+	0.842757i	$0.680931\pi$
$252$		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	−0.423659	−	0.905822i	$-0.639254\pi$
$257$	9.18004	−	15.9003i	0.572635	−	0.991833i	0.996294	−	0.0860116i	$-0.0274122\pi$
$258$		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	−0.753184	−	0.657810i	$-0.771483\pi$
$263$	3.13137	−	5.42370i	0.193089	−	0.334440i	0.946272	+	0.323371i	$0.104816\pi$
$264$		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	0.985548	−	0.169396i	$-0.0541817\pi$
$269$	5.67601	+	9.83114i	0.346073	+	0.599415i	−0.639475	+	0.768812i	$0.720848\pi$
$270$		0			0
$271$	14.7506	+	8.51625i	0.896034	+	0.517325i	0.875911	−	0.482472i	$-0.160261\pi$
$271$	14.7506	+	8.51625i	0.896034	+	0.517325i	0.0201225	+	0.999798i	$0.493594\pi$
$272$		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	0.948456	−	0.316908i	$-0.102645\pi$
$277$	3.32496	+	5.75899i	0.199777	+	0.346024i	−0.748679	+	0.662933i	$0.769311\pi$
$278$		0			0
$279$	9.08992	−	5.24807i	0.544199	−	0.314194i
$280$		0			0
$281$		−	10.6183i		−	0.633433i	−0.948520	−	0.316717i	$-0.897420\pi$
$281$		−	10.6183i		−	0.633433i	0.948520	−	0.316717i	$-0.102580\pi$
$282$		0			0
$283$	−8.33389	+	14.4347i	−0.495398	+	0.858055i	−0.999986	−	0.00530527i	$-0.998311\pi$
$283$	−8.33389	+	14.4347i	−0.495398	+	0.858055i	0.504587	+	0.863361i	$0.331645\pi$
$284$		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	−0.787093	−	0.616835i	$-0.788415\pi$
$293$	−11.0653	+	6.38858i	−0.646445	+	0.373225i	0.140648	+	0.990060i	$0.455081\pi$
$294$		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	$0.194569\pi$
$307$			20.1110i			1.14779i	−0.818928	+	0.573897i	$0.805431\pi$
$308$		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	$0.186219\pi$
$317$			19.6640i			1.10444i	−0.833698	+	0.552221i	$0.813781\pi$
$318$		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	−0.363312	−	0.931667i	$-0.618354\pi$
$331$	4.76448	−	2.75077i	0.261880	−	0.151196i	0.625192	+	0.780471i	$0.285021\pi$
$332$		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	0.999479	−	0.0322841i	$-0.0102781\pi$
$347$	8.78830	+	15.2218i	0.471781	+	0.817148i	−0.527698	+	0.849432i	$0.676945\pi$
$348$		0			0
$349$	8.13600	+	4.69732i	0.435510	+	0.251442i	0.701691	−	0.712481i	$-0.252429\pi$
$349$	8.13600	+	4.69732i	0.435510	+	0.251442i	−0.266181	+	0.963923i	$0.585762\pi$
$350$		0			0
$351$	−9.80916	+	3.93231i	−0.523574	+	0.209891i
$352$		0			0
$353$	−10.8862	−	6.28512i	−0.579412	−	0.334523i	0.181488	−	0.983393i	$-0.441909\pi$
$353$	−10.8862	−	6.28512i	−0.579412	−	0.334523i	−0.760899	+	0.648870i	$0.775242\pi$
$354$		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	$-0.907902\pi$
$359$		−	10.8119i		−	0.570631i	0.958434	−	0.285316i	$-0.0920984\pi$
$360$		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	−0.986000	−	0.166746i	$-0.946674\pi$
$367$	−6.67809	+	11.5668i	−0.348594	+	0.603782i	0.637406	+	0.770528i	$0.280007\pi$
$368$		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	−0.991272	−	0.131832i	$-0.957914\pi$
$373$	−11.7773	−	20.3989i	−0.609806	−	1.05621i	0.381466	−	0.924383i	$-0.375419\pi$
$374$		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	0.473526	−	0.880780i	$-0.342981\pi$
$379$	−1.02186	−	0.589972i	−0.0524895	−	0.0303048i	−0.526015	+	0.850475i	$0.676314\pi$
$380$		0			0
$381$	23.3849	+	40.5039i	1.19805	+	2.07508i
$382$		0			0
$383$	24.4859	−	14.1369i	1.25117	−	0.722364i	0.279829	−	0.960050i	$-0.409722\pi$
$383$	24.4859	−	14.1369i	1.25117	−	0.722364i	0.971342	+	0.237686i	$0.0763888\pi$
$384$		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	−0.588871	−	0.808227i	$-0.700427\pi$
$397$	−3.65345	+	2.10932i	−0.183361	+	0.105864i	0.405510	+	0.914091i	$0.367094\pi$
$398$		0			0
$399$	−28.2087	−	48.8588i	−1.41220	−	2.44600i
$400$		0			0
$401$	−3.47645	−	2.00713i	−0.173606	−	0.100231i	0.410679	−	0.911780i	$-0.365292\pi$
$401$	−3.47645	−	2.00713i	−0.173606	−	0.100231i	−0.584285	+	0.811549i	$0.698625\pi$
$402$		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	−0.968163	−	0.250319i	$-0.919464\pi$
$409$	−24.9857	+	14.4255i	−1.23546	+	0.713295i	−0.267299	+	0.963614i	$0.586131\pi$
$410$		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	−0.996890	−	0.0788044i	$-0.974890\pi$
$419$	−8.80594	+	15.2523i	−0.430198	+	0.745125i	0.566692	+	0.823930i	$0.308223\pi$
$420$		0			0
$421$		−	27.6167i		−	1.34595i	−0.739663	−	0.672977i	$-0.765015\pi$
$421$		−	27.6167i		−	1.34595i	0.739663	−	0.672977i	$-0.234985\pi$
$422$		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	0.474872	−	0.880055i	$-0.342494\pi$
$431$	−1.03475	−	0.597412i	−0.0498420	−	0.0287763i	−0.524714	+	0.851279i	$0.675828\pi$
$432$		0			0
$433$	6.05655	+	10.4902i	0.291059	+	0.504129i	0.974060	−	0.226288i	$-0.0726590\pi$
$433$	6.05655	+	10.4902i	0.291059	+	0.504129i	−0.683001	+	0.730417i	$0.739326\pi$
$434$		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	−0.843089	−	0.537774i	$-0.819265\pi$
$439$	0.925707	−	1.60337i	0.0441816	−	0.0765248i	0.887271	+	0.461249i	$0.152599\pi$
$440$		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	−0.861506	−	0.507747i	$-0.830478\pi$
$449$	−18.0649	+	10.4298i	−0.852537	+	0.492212i	0.00896915	+	0.999960i	$0.497145\pi$
$450$		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	0.863171	−	0.504912i	$-0.168475\pi$
$457$	18.3310	+	10.5834i	0.857490	+	0.495072i	−0.00568090	+	0.999984i	$0.501808\pi$
$458$		0			0
$459$	5.36701	+	9.29594i	0.250511	+	0.433897i
$460$		0			0
$461$	−21.7115	+	12.5351i	−1.01120	+	0.583819i	−0.911544	−	0.411202i	$-0.865109\pi$
$461$	−21.7115	+	12.5351i	−1.01120	+	0.583819i	−0.0996603	+	0.995022i	$0.531776\pi$
$462$		0			0
$463$			6.06858i			0.282031i	0.990007	+	0.141015i	$0.0450367\pi$
$463$			6.06858i			0.282031i	−0.990007	+	0.141015i	$0.954963\pi$
$464$		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	0.304994	−	0.952354i	$-0.401345\pi$
$479$	−8.03813	−	4.64081i	−0.367271	−	0.212044i	−0.672266	+	0.740310i	$0.734679\pi$
$480$		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	−0.943967	−	0.330041i	$-0.892938\pi$
$487$	−24.9397	+	14.3990i	−1.13013	+	0.652479i	−0.186160	+	0.982519i	$0.559604\pi$
$488$		0			0
$489$		−	46.7405i		−	2.11368i
$490$		0			0
$491$	1.96203	−	3.39834i	0.0885452	−	0.153365i	−0.818351	−	0.574719i	$-0.805112\pi$
$491$	1.96203	−	3.39834i	0.0885452	−	0.153365i	0.906896	+	0.421354i	$0.138445\pi$
$492$		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	$-0.946898\pi$
$499$		−	7.41866i		−	0.332105i	0.986117	−	0.166052i	$-0.0531021\pi$
$500$		0			0
$501$	−26.1364	+	15.0899i	−1.16769	+	0.674166i
$502$		0			0
$503$	2.76733	+	4.79315i	0.123389	+	0.213716i	0.921102	−	0.389321i	$-0.127290\pi$
$503$	2.76733	+	4.79315i	0.123389	+	0.213716i	−0.797713	+	0.603037i	$0.793957\pi$
$504$		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	0.839835	−	0.542841i	$-0.182651\pi$
$509$	17.8151	+	10.2855i	0.789639	+	0.455898i	−0.0501964	+	0.998739i	$0.515985\pi$
$510$		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	−0.950220	−	0.311581i	$-0.899142\pi$
$523$	−4.69443	+	8.13099i	−0.205273	+	0.355544i	0.744947	+	0.667124i	$0.232475\pi$
$524$		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	$-0.996926\pi$
$541$		−	0.449242i		−	0.0193144i	0.999953	−	0.00965721i	$-0.00307403\pi$
$542$		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	0.546160	−	0.837681i	$-0.316089\pi$
$557$	2.21347	+	1.27795i	0.0937876	+	0.0541483i	−0.452373	+	0.891829i	$0.649422\pi$
$558$		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	0.782472	−	0.622685i	$-0.213958\pi$
$563$	−3.51228	−	6.08345i	−0.148025	−	0.256387i	−0.930497	+	0.366298i	$0.880625\pi$
$564$		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	−0.392791	−	0.919628i	$-0.628490\pi$
$569$	14.3128	−	24.7906i	0.600025	−	1.03927i	0.992817	−	0.119647i	$-0.0381762\pi$
$570$		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	$0.340435\pi$
$577$			42.1308i			1.75393i	−0.480557	+	0.876964i	$0.659565\pi$
$578$		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	0.724685	−	0.689080i	$-0.241985\pi$
$587$	11.8782	+	6.85789i	0.490266	+	0.283055i	−0.234419	+	0.972136i	$0.575319\pi$
$588$		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	$-0.937654\pi$
$593$		−	9.47847i		−	0.389234i	0.980879	−	0.194617i	$-0.0623464\pi$
$594$		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	−0.880207	−	0.474591i	$-0.842596\pi$
$601$	−0.713292	+	1.23546i	−0.0290958	+	0.0503954i	0.851111	+	0.524986i	$0.175929\pi$
$602$		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	0.999606	−	0.0280845i	$-0.00894074\pi$
$607$	11.7146	+	20.2903i	0.475481	+	0.823557i	−0.524125	+	0.851642i	$0.675607\pi$
$608$		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	0.956093	−	0.293064i	$-0.0946750\pi$
$613$	29.2238	+	16.8724i	1.18034	+	0.681468i	0.224245	+	0.974533i	$0.428008\pi$
$614$		0			0
$615$	16.2301	+	28.1114i	0.654462	+	1.13356i
$616$		0			0
$617$	19.6606	−	11.3511i	0.791507	−	0.456977i	−0.0489859	−	0.998799i	$-0.515599\pi$
$617$	19.6606	−	11.3511i	0.791507	−	0.456977i	0.840493	+	0.541823i	$0.182266\pi$
$618$		0			0
$619$			23.4282i			0.941660i	0.882224	+	0.470830i	$0.156045\pi$
$619$			23.4282i			0.941660i	−0.882224	+	0.470830i	$0.843955\pi$
$620$		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	−0.992574	−	0.121644i	$-0.961183\pi$
$631$	−34.7535	+	20.0649i	−1.38351	+	0.798772i	−0.390940	+	0.920416i	$0.627850\pi$
$632$		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	0.962170	−	0.272450i	$-0.0878341\pi$
$641$	6.20634	+	10.7497i	0.245136	+	0.424588i	−0.717034	+	0.697038i	$0.754501\pi$
$642$		0			0
$643$	20.4887	−	11.8292i	0.807997	−	0.466497i	−0.0382628	−	0.999268i	$-0.512182\pi$
$643$	20.4887	−	11.8292i	0.807997	−	0.466497i	0.846260	+	0.532770i	$0.178849\pi$
$644$		0			0
$645$		−	26.7952i		−	1.05506i
$646$		0			0
$647$	−19.0844	+	33.0551i	−0.750283	+	1.29953i	0.197402	+	0.980323i	$0.436750\pi$
$647$	−19.0844	+	33.0551i	−0.750283	+	1.29953i	−0.947685	+	0.319206i	$0.896584\pi$
$648$		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	−0.960339	−	0.278835i	$-0.910052\pi$
$653$	−6.09948	+	10.5646i	−0.238691	+	0.413425i	0.721648	+	0.692260i	$0.243385\pi$
$654$		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	−0.999009	−	0.0445045i	$-0.985829\pi$
$659$	−13.8122	−	23.9234i	−0.538047	−	0.931924i	0.460963	−	0.887420i	$-0.347504\pi$
$660$		0			0
$661$	−14.5613	−	8.40699i	−0.566370	−	0.326994i	0.189328	−	0.981914i	$-0.439369\pi$
$661$	−14.5613	−	8.40699i	−0.566370	−	0.326994i	−0.755698	+	0.654920i	$0.772702\pi$
$662$		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	−0.972205	−	0.234132i	$-0.924775\pi$
$673$	−7.35043	+	12.7313i	−0.283338	+	0.490756i	0.688867	+	0.724888i	$0.258109\pi$
$674$		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	−0.528043	−	0.849217i	$-0.677074\pi$
$683$	−1.47976	+	0.854339i	−0.0566214	+	0.0326904i	0.471422	+	0.881908i	$0.343741\pi$
$684$		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	−0.0761985	−	0.997093i	$-0.524278\pi$
$691$	−25.7035	−	14.8399i	−0.977805	−	0.564536i	−0.901607	+	0.432556i	$0.857612\pi$
$692$		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	0.382028	−	0.924151i	$-0.375226\pi$
$709$	36.5690	−	21.1132i	1.37338	−	0.792921i	0.991352	+	0.131230i	$0.0418926\pi$
$710$		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	0.767583	−	0.640950i	$-0.221459\pi$
$719$	−4.59294	−	7.95520i	−0.171288	−	0.296679i	−0.938870	+	0.344271i	$0.888126\pi$
$720$		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	$0.127359\pi$
$733$			21.0917i			0.779039i	−0.921018	+	0.389519i	$0.872641\pi$
$734$		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	0.940283	−	0.340395i	$-0.110561\pi$
$739$	30.3280	+	17.5099i	1.11563	+	0.644111i	0.175350	+	0.984506i	$0.443894\pi$
$740$		0			0
$741$	18.4952	+	46.1363i	0.679438	+	1.69486i
$742$		0			0
$743$	−6.62745	−	3.82636i	−0.243138	−	0.140376i	0.373480	−	0.927638i	$-0.378164\pi$
$743$	−6.62745	−	3.82636i	−0.243138	−	0.140376i	−0.616618	+	0.787263i	$0.711498\pi$
$744$		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	−0.999984	−	0.00564504i	$-0.998203\pi$
$751$	−13.5680	+	23.5005i	−0.495103	+	0.857544i	0.504881	+	0.863189i	$0.331536\pi$
$752$		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	−0.633917	−	0.773401i	$-0.718554\pi$
$757$	9.70753	−	16.8139i	0.352826	−	0.611113i	0.986743	+	0.162288i	$0.0518874\pi$
$758$		0			0
$759$			18.2266i			0.661583i
$760$		0			0
$761$	−30.6121	+	17.6739i	−1.10969	+	0.640678i	−0.938748	−	0.344604i	$-0.888013\pi$
$761$	−30.6121	+	17.6739i	−1.10969	+	0.640678i	−0.170938	+	0.985282i	$0.554680\pi$
$762$		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	0.642995	−	0.765870i	$-0.277692\pi$
$769$	8.35334	+	4.82280i	0.301229	+	0.173915i	−0.341766	+	0.939785i	$0.611025\pi$
$770$		0			0
$771$	19.7727	+	34.2473i	0.712095	+	1.23339i
$772$		0			0
$773$	31.9321	−	18.4360i	1.14852	−	0.663097i	0.199992	−	0.979798i	$-0.435908\pi$
$773$	31.9321	−	18.4360i	1.14852	−	0.663097i	0.948526	+	0.316701i	$0.102575\pi$
$774$		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	−0.317616	−	0.948220i	$-0.602882\pi$
$787$	9.67170	−	5.58396i	0.344759	−	0.199047i	0.662374	+	0.749173i	$0.269549\pi$
$788$		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	0.545798	−	0.837917i	$-0.316227\pi$
$797$	−12.7819	−	22.1389i	−0.452759	−	0.784201i	−0.998556	+	0.0537160i	$0.982893\pi$
$798$		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	−0.752617	−	0.658458i	$-0.771209\pi$
$809$	5.51603	−	9.55404i	0.193933	−	0.335902i	0.946550	+	0.322556i	$0.104542\pi$
$810$		0			0
$811$			4.83609i			0.169818i	0.996389	+	0.0849091i	$0.0270600\pi$
$811$			4.83609i			0.169818i	−0.996389	+	0.0849091i	$0.972940\pi$
$812$		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	0.222782	−	0.974868i	$-0.428486\pi$
$821$	−14.6156	−	8.43833i	−0.510089	−	0.294500i	−0.732870	+	0.680369i	$0.761820\pi$
$822$		0			0
$823$	−0.180223	−	0.312156i	−0.00628219	−	0.0108811i	0.862867	−	0.505431i	$-0.168666\pi$
$823$	−0.180223	−	0.312156i	−0.00628219	−	0.0108811i	−0.869149	+	0.494550i	$0.835333\pi$
$824$		0			0
$825$	14.9032	−	8.60435i	0.518862	−	0.299565i
$826$		0			0
$827$		−	7.75357i		−	0.269618i	−0.990872	−	0.134809i	$-0.956958\pi$
$827$		−	7.75357i		−	0.269618i	0.990872	−	0.134809i	$-0.0430421\pi$
$828$		0			0
$829$	14.6951	−	25.4526i	0.510381	−	0.884006i	−0.489546	−	0.871977i	$-0.662838\pi$
$829$	14.6951	−	25.4526i	0.510381	−	0.884006i	0.999928	−	0.0120291i	$-0.00382906\pi$
$830$		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	0.403541	−	0.914962i	$-0.367779\pi$
$839$	40.4848	−	23.3739i	1.39769	−	0.806958i	0.994150	+	0.108004i	$0.0344460\pi$
$840$		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	$0.279817\pi$
$853$			44.9860i			1.54029i	−0.637867	+	0.770146i	$0.720183\pi$
$854$		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	$-0.747803\pi$
$863$		−	41.8309i		−	1.42394i	0.702209	−	0.711971i	$-0.252197\pi$
$864$		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	−0.755000	+	0.655725i	$0.772363\pi$
$877$	−50.3552	+	29.0726i	−1.70037	+	0.981712i	−0.945374	+	0.325987i	$0.894304\pi$
$878$		0			0
$879$		−	27.5204i		−	0.928241i
$880$		0			0
$881$	−20.1202	+	34.8493i	−0.677868	+	1.17410i	0.297753	+	0.954643i	$0.403763\pi$
$881$	−20.1202	+	34.8493i	−0.677868	+	1.17410i	−0.975622	+	0.219460i	$0.929571\pi$
$882$		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	0.492244	+	0.870457i	$0.336177\pi$
$887$	−15.1211	+	26.1905i	−0.507716	+	0.879390i	−0.999960	+	0.00893297i	$0.997157\pi$
$888$		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	−0.227801	−	0.973708i	$-0.573154\pi$
$907$	21.9656	−	38.0455i	0.729355	−	1.26328i	0.957156	−	0.289572i	$-0.0935130\pi$
$908$		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	0.786440	−	0.617667i	$-0.211922\pi$
$919$	−4.29549	−	7.44000i	−0.141695	−	0.245423i	−0.928135	+	0.372244i	$0.878589\pi$
$920$		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	−0.316050	−	0.948742i	$-0.602357\pi$
$929$	10.5934	−	6.11613i	0.347560	−	0.200664i	0.663610	+	0.748079i	$0.269023\pi$
$930$		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	$-0.782284\pi$
$941$		−	38.7667i		−	1.26376i	0.775067	−	0.631879i	$-0.217716\pi$
$942$		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	0.984064	−	0.177816i	$-0.0569032\pi$
$947$	40.6855	+	23.4898i	1.32210	+	0.763316i	0.338039	+	0.941132i	$0.390237\pi$
$948$		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	−0.966941	−	0.255002i	$-0.917924\pi$
$953$	−21.7425	−	37.6591i	−0.704309	−	1.21990i	0.262632	−	0.964896i	$-0.415409\pi$
$954$		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	$-0.780596\pi$
$967$		−	39.5537i		−	1.27196i	0.771705	−	0.635981i	$-0.219404\pi$
$968$		0			0
$969$	43.7224	−	25.2431i	1.40457	−	0.810926i
$970$		0			0
$971$	−7.83343	−	13.5679i	−0.251387	−	0.435414i	0.712521	−	0.701651i	$-0.247553\pi$
$971$	−7.83343	−	13.5679i	−0.251387	−	0.435414i	−0.963908	+	0.266236i	$0.914220\pi$
$972$		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	0.366786	−	0.930305i	$-0.380458\pi$
$977$	−7.98584	−	4.61063i	−0.255490	−	0.147507i	−0.622275	+	0.782798i	$0.713792\pi$
$978$		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	$-0.984258\pi$
$983$		−	3.09979i		−	0.0988678i	0.998777	−	0.0494339i	$-0.0157417\pi$
$984$		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	−0.985792	−	0.167970i	$-0.946279\pi$
$991$	−10.9371	+	18.9437i	−0.347430	+	0.601766i	0.638362	+	0.769736i	$0.279612\pi$
$992$		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	0.997499	+	0.0706812i	$0.0225173\pi$
$997$	17.6809	+	30.6243i	0.559961	+	0.969881i	−0.437538	+	0.899200i	$0.644149\pi$
$998$		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.485.3	yes	24
13.6	odd	12		7436.2.a.v.1.10		12
13.7	odd	12		7436.2.a.u.1.10		12
13.10	even	6	inner	572.2.p.a.309.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.3	✓	24	13.10	even	6	inner
572.2.p.a.485.3	yes	24	1.1	even	1	trivial
7436.2.a.u.1.10		12	13.7	odd	12
7436.2.a.v.1.10		12	13.6	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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