LMFDB - Embedded newform 504.2.cx.a.185.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(185,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.24
Character	$\chi$	$=$	504.185
Dual form			504.2.cx.a.425.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73204 - 0.00732041i) q^{3} +2.59337 q^{5} +(-2.61256 + 0.417759i) q^{7} +(2.99989 - 0.0253584i) q^{9} -3.54299i q^{11} +(2.74094 + 1.58248i) q^{13} +(4.49180 - 0.0189845i) q^{15} +(-0.487640 + 0.844616i) q^{17} +(2.11191 - 1.21931i) q^{19} +(-4.52199 + 0.742698i) q^{21} +3.37675i q^{23} +1.72555 q^{25} +(5.19573 - 0.0658821i) q^{27} +(0.267645 - 0.154525i) q^{29} +(-4.35965 + 2.51705i) q^{31} +(-0.0259361 - 6.13659i) q^{33} +(-6.77533 + 1.08340i) q^{35} +(-3.47324 - 6.01583i) q^{37} +(4.75899 + 2.72085i) q^{39} +(-6.08175 + 10.5339i) q^{41} +(-5.47630 - 9.48523i) q^{43} +(7.77982 - 0.0657636i) q^{45} +(-1.43344 + 2.48279i) q^{47} +(6.65096 - 2.18284i) q^{49} +(-0.838426 + 1.46648i) q^{51} +(7.81416 + 4.51151i) q^{53} -9.18828i q^{55} +(3.64898 - 2.12736i) q^{57} +(-0.219727 - 0.380579i) q^{59} +(3.41242 + 1.97016i) q^{61} +(-7.82681 + 1.31948i) q^{63} +(7.10826 + 4.10396i) q^{65} +(-1.82561 - 3.16204i) q^{67} +(0.0247192 + 5.84865i) q^{69} +5.25055i q^{71} +(-14.0773 - 8.12752i) q^{73} +(2.98871 - 0.0126317i) q^{75} +(1.48012 + 9.25629i) q^{77} +(-3.49659 + 6.05628i) q^{79} +(8.99871 - 0.152145i) q^{81} +(-7.23851 - 12.5375i) q^{83} +(-1.26463 + 2.19040i) q^{85} +(0.462439 - 0.269602i) q^{87} +(2.31101 + 4.00279i) q^{89} +(-7.82197 - 2.98928i) q^{91} +(-7.53265 + 4.39153i) q^{93} +(5.47697 - 3.16213i) q^{95} +(12.4805 - 7.20560i) q^{97} +(-0.0898447 - 10.6286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.73204	−	0.00732041i	0.999991	−	0.00422644i
$3$	1.73204	−	0.00732041i	0.999991	−	0.00422644i
$4$		0			0
$5$	2.59337			1.15979			0.579894	−	0.814692i	$-0.303094\pi$
$5$	2.59337			1.15979			0.579894	+	0.814692i	$0.303094\pi$
$6$		0			0
$7$	−2.61256	+	0.417759i	−0.987455	+	0.157898i
$7$	−2.61256	+	0.417759i	−0.987455	+	0.157898i
$8$		0			0
$9$	2.99989	−	0.0253584i	0.999964	−	0.00845280i
$10$		0			0
$11$		−	3.54299i		−	1.06825i	−0.845405	−	0.534126i	$-0.820641\pi$
$11$		−	3.54299i		−	1.06825i	0.845405	−	0.534126i	$-0.179359\pi$
$12$		0			0
$13$	2.74094	+	1.58248i	0.760200	+	0.438902i	0.829367	−	0.558703i	$-0.188701\pi$
$13$	2.74094	+	1.58248i	0.760200	+	0.438902i	−0.0691677	+	0.997605i	$0.522034\pi$
$14$		0			0
$15$	4.49180	−	0.0189845i	1.15978	−	0.00490178i
$16$		0			0
$17$	−0.487640	+	0.844616i	−0.118270	+	0.204850i	−0.919082	−	0.394066i	$-0.871068\pi$
$17$	−0.487640	+	0.844616i	−0.118270	+	0.204850i	0.800812	+	0.598916i	$0.204401\pi$
$18$		0			0
$19$	2.11191	−	1.21931i	0.484506	−	0.279730i	−0.237786	−	0.971318i	$-0.576422\pi$
$19$	2.11191	−	1.21931i	0.484506	−	0.279730i	0.722293	+	0.691588i	$0.243088\pi$
$20$		0			0
$21$	−4.52199	+	0.742698i	−0.986779	+	0.162070i
$22$		0			0
$23$			3.37675i			0.704102i	0.935981	+	0.352051i	$0.114516\pi$
$23$			3.37675i			0.704102i	−0.935981	+	0.352051i	$0.885484\pi$
$24$		0			0
$25$	1.72555			0.345110
$26$		0			0
$27$	5.19573	−	0.0658821i	0.999920	−	0.0126790i
$28$		0			0
$29$	0.267645	−	0.154525i	0.0497004	−	0.0286946i	−0.474944	−	0.880016i	$-0.657532\pi$
$29$	0.267645	−	0.154525i	0.0497004	−	0.0286946i	0.524644	+	0.851322i	$0.324198\pi$
$30$		0			0
$31$	−4.35965	+	2.51705i	−0.783017	+	0.452075i	−0.837498	−	0.546440i	$-0.815983\pi$
$31$	−4.35965	+	2.51705i	−0.783017	+	0.452075i	0.0544814	+	0.998515i	$0.482649\pi$
$32$		0			0
$33$	−0.0259361	−	6.13659i	−0.00451490	−	1.06824i
$34$		0			0
$35$	−6.77533	+	1.08340i	−1.14524	+	0.183128i
$36$		0			0
$37$	−3.47324	−	6.01583i	−0.570997	−	0.988996i	−0.996464	−	0.0840218i	$-0.973223\pi$
$37$	−3.47324	−	6.01583i	−0.570997	−	0.988996i	0.425467	−	0.904974i	$-0.360110\pi$
$38$		0			0
$39$	4.75899	+	2.72085i	0.762048	+	0.435685i
$40$		0			0
$41$	−6.08175	+	10.5339i	−0.949810	+	1.64512i	−0.203988	+	0.978973i	$0.565390\pi$
$41$	−6.08175	+	10.5339i	−0.949810	+	1.64512i	−0.745822	+	0.666146i	$0.767943\pi$
$42$		0			0
$43$	−5.47630	−	9.48523i	−0.835128	−	1.44648i	−0.893926	−	0.448214i	$-0.852060\pi$
$43$	−5.47630	−	9.48523i	−0.835128	−	1.44648i	0.0587983	−	0.998270i	$-0.481273\pi$
$44$		0			0
$45$	7.77982	−	0.0657636i	1.15975	−	0.00980347i
$46$		0			0
$47$	−1.43344	+	2.48279i	−0.209089	+	0.362152i	−0.951428	−	0.307872i	$-0.900383\pi$
$47$	−1.43344	+	2.48279i	−0.209089	+	0.362152i	0.742339	+	0.670024i	$0.233716\pi$
$48$		0			0
$49$	6.65096	−	2.18284i	0.950136	−	0.311834i
$50$		0			0
$51$	−0.838426	+	1.46648i	−0.117403	+	0.205348i
$52$		0			0
$53$	7.81416	+	4.51151i	1.07336	+	0.619703i	0.929097	−	0.369836i	$-0.120586\pi$
$53$	7.81416	+	4.51151i	1.07336	+	0.619703i	0.144261	+	0.989540i	$0.453920\pi$
$54$		0			0
$55$		−	9.18828i		−	1.23895i
$56$		0			0
$57$	3.64898	−	2.12736i	0.483320	−	0.281775i
$58$		0			0
$59$	−0.219727	−	0.380579i	−0.0286061	−	0.0495471i	0.851368	−	0.524569i	$-0.175773\pi$
$59$	−0.219727	−	0.380579i	−0.0286061	−	0.0495471i	−0.879974	+	0.475022i	$0.842440\pi$
$60$		0			0
$61$	3.41242	+	1.97016i	0.436916	+	0.252254i	0.702289	−	0.711892i	$-0.252162\pi$
$61$	3.41242	+	1.97016i	0.436916	+	0.252254i	−0.265373	+	0.964146i	$0.585495\pi$
$62$		0			0
$63$	−7.82681	+	1.31948i	−0.986085	+	0.166239i
$64$		0			0
$65$	7.10826	+	4.10396i	0.881671	+	0.509033i
$66$		0			0
$67$	−1.82561	−	3.16204i	−0.223033	−	0.386305i	0.732694	−	0.680558i	$-0.238263\pi$
$67$	−1.82561	−	3.16204i	−0.223033	−	0.386305i	−0.955728	+	0.294253i	$0.904929\pi$
$68$		0			0
$69$	0.0247192	+	5.84865i	0.00297584	+	0.704095i
$70$		0			0
$71$			5.25055i			0.623126i	0.950226	+	0.311563i	$0.100852\pi$
$71$			5.25055i			0.623126i	−0.950226	+	0.311563i	$0.899148\pi$
$72$		0			0
$73$	−14.0773	−	8.12752i	−1.64762	−	0.951254i	−0.978014	−	0.208539i	$-0.933129\pi$
$73$	−14.0773	−	8.12752i	−1.64762	−	0.951254i	−0.669607	−	0.742716i	$-0.733537\pi$
$74$		0			0
$75$	2.98871	−	0.0126317i	0.345107	−	0.00145859i
$76$		0			0
$77$	1.48012	+	9.25629i	0.168675	+	1.05485i
$78$		0			0
$79$	−3.49659	+	6.05628i	−0.393397	+	0.681384i	−0.992895	−	0.118992i	$-0.962034\pi$
$79$	−3.49659	+	6.05628i	−0.393397	+	0.681384i	0.599498	+	0.800376i	$0.295367\pi$
$80$		0			0
$81$	8.99871	−	0.152145i	0.999857	−	0.0169050i
$82$		0			0
$83$	−7.23851	−	12.5375i	−0.794529	−	1.37616i	−0.923138	−	0.384469i	$-0.874384\pi$
$83$	−7.23851	−	12.5375i	−0.794529	−	1.37616i	0.128609	−	0.991695i	$-0.458949\pi$
$84$		0			0
$85$	−1.26463	+	2.19040i	−0.137168	+	0.237582i
$86$		0			0
$87$	0.462439	−	0.269602i	0.0495787	−	0.0289044i
$88$		0			0
$89$	2.31101	+	4.00279i	0.244967	+	0.424295i	0.962122	−	0.272619i	$-0.0878897\pi$
$89$	2.31101	+	4.00279i	0.244967	+	0.424295i	−0.717156	+	0.696913i	$0.754556\pi$
$90$		0			0
$91$	−7.82197	−	2.98928i	−0.819965	−	0.313362i
$92$		0			0
$93$	−7.53265	+	4.39153i	−0.781099	+	0.455380i
$94$		0			0
$95$	5.47697	−	3.16213i	0.561925	−	0.324428i
$96$		0			0
$97$	12.4805	−	7.20560i	1.26720	−	0.731617i	0.292742	−	0.956192i	$-0.405432\pi$
$97$	12.4805	−	7.20560i	1.26720	−	0.731617i	0.974457	+	0.224574i	$0.0720991\pi$
$98$		0			0
$99$	−0.0898447	−	10.6286i	−0.00902973	−	1.06821i
$100$		0			0
$101$	−8.62921			−0.858638			−0.429319	−	0.903153i	$-0.641246\pi$
$101$	−8.62921			−0.858638			−0.429319	+	0.903153i	$0.641246\pi$
$102$		0			0
$103$			6.09732i			0.600787i	0.953815	+	0.300394i	$0.0971180\pi$
$103$			6.09732i			0.600787i	−0.953815	+	0.300394i	$0.902882\pi$
$104$		0			0
$105$	−11.7272	+	1.92609i	−1.14446	+	0.187967i
$106$		0			0
$107$	−13.8841	+	8.01599i	−1.34223	+	0.774935i	−0.987134	−	0.159896i	$-0.948884\pi$
$107$	−13.8841	+	8.01599i	−1.34223	+	0.774935i	−0.355093	+	0.934831i	$0.615551\pi$
$108$		0			0
$109$	2.78659	−	4.82652i	0.266907	−	0.462297i	−0.701154	−	0.713010i	$-0.747332\pi$
$109$	2.78659	−	4.82652i	0.266907	−	0.462297i	0.968062	+	0.250713i	$0.0806649\pi$
$110$		0			0
$111$	−6.05981	−	10.3942i	−0.575172	−	0.986574i
$112$		0			0
$113$	−14.2144	−	8.20669i	−1.33718	−	0.772021i	−0.350791	−	0.936454i	$-0.614087\pi$
$113$	−14.2144	−	8.20669i	−1.33718	−	0.772021i	−0.986388	+	0.164433i	$0.947421\pi$
$114$		0			0
$115$			8.75716i			0.816609i
$116$		0			0
$117$	8.26265	+	4.67777i	0.763883	+	0.432460i
$118$		0			0
$119$	0.921142	−	2.41033i	0.0844410	−	0.220954i
$120$		0			0
$121$	−1.55280			−0.141163
$122$		0			0
$123$	−10.4567	+	18.2896i	−0.942848	+	1.64912i
$124$		0			0
$125$	−8.49185			−0.759534
$126$		0			0
$127$	−18.0255			−1.59951			−0.799754	−	0.600328i	$-0.795037\pi$
$127$	−18.0255			−1.59951			−0.799754	+	0.600328i	$0.795037\pi$
$128$		0			0
$129$	−9.55458	−	16.3887i	−0.841234	−	1.44294i
$130$		0			0
$131$	10.4393			0.912090			0.456045	−	0.889957i	$-0.349266\pi$
$131$	10.4393			0.912090			0.456045	+	0.889957i	$0.349266\pi$
$132$		0			0
$133$	−5.00813	+	4.06780i	−0.434260	+	0.352723i
$134$		0			0
$135$	13.4744	−	0.170856i	1.15970	−	0.0147050i
$136$		0			0
$137$			3.84991i			0.328920i	0.986384	+	0.164460i	$0.0525882\pi$
$137$			3.84991i			0.328920i	−0.986384	+	0.164460i	$0.947412\pi$
$138$		0			0
$139$	18.7634	+	10.8330i	1.59149	+	0.918847i	0.993052	+	0.117677i	$0.0375447\pi$
$139$	18.7634	+	10.8330i	1.59149	+	0.918847i	0.598437	+	0.801170i	$0.295789\pi$
$140$		0			0
$141$	−2.46459	+	4.31077i	−0.207556	+	0.363032i
$142$		0			0
$143$	5.60672	−	9.71113i	0.468858	−	0.812085i
$144$		0			0
$145$	0.694102	−	0.400740i	0.0576420	−	0.0332796i
$146$		0			0
$147$	11.5037	−	3.82944i	0.948810	−	0.315847i
$148$		0			0
$149$			9.50289i			0.778507i	0.921131	+	0.389254i	$0.127267\pi$
$149$			9.50289i			0.778507i	−0.921131	+	0.389254i	$0.872733\pi$
$150$		0			0
$151$	−21.3380			−1.73646			−0.868232	−	0.496159i	$-0.834743\pi$
$151$	−21.3380			−1.73646			−0.868232	+	0.496159i	$0.834743\pi$
$152$		0			0
$153$	−1.44145	+	2.54612i	−0.116534	+	0.205842i
$154$		0			0
$155$	−11.3062	+	6.52763i	−0.908134	+	0.524312i
$156$		0			0
$157$	2.10532	−	1.21551i	0.168023	−	0.0970082i	−0.413630	−	0.910445i	$-0.635739\pi$
$157$	2.10532	−	1.21551i	0.168023	−	0.0970082i	0.581653	+	0.813437i	$0.302406\pi$
$158$		0			0
$159$	13.5674	+	7.75689i	1.07597	+	0.615161i
$160$		0			0
$161$	−1.41067	−	8.82197i	−0.111176	−	0.695269i
$162$		0			0
$163$	8.31072	+	14.3946i	0.650946	+	1.12747i	0.982894	+	0.184174i	$0.0589609\pi$
$163$	8.31072	+	14.3946i	0.650946	+	1.12747i	−0.331948	+	0.943298i	$0.607706\pi$
$164$		0			0
$165$	−0.0672619	−	15.9144i	−0.00523633	−	1.23894i
$166$		0			0
$167$	10.6037	−	18.3661i	0.820535	−	1.42121i	−0.0847489	−	0.996402i	$-0.527009\pi$
$167$	10.6037	−	18.3661i	0.820535	−	1.42121i	0.905284	−	0.424806i	$-0.139658\pi$
$168$		0			0
$169$	−1.49150	−	2.58336i	−0.114731	−	0.198720i
$170$		0			0
$171$	6.30460	−	3.71137i	0.482124	−	0.283815i
$172$		0			0
$173$	−5.09062	+	8.81722i	−0.387033	+	0.670361i	−0.992049	−	0.125853i	$-0.959833\pi$
$173$	−5.09062	+	8.81722i	−0.387033	+	0.670361i	0.605016	+	0.796213i	$0.293167\pi$
$174$		0			0
$175$	−4.50810	+	0.720863i	−0.340781	+	0.0544922i
$176$		0			0
$177$	−0.383361	−	0.657567i	−0.0288152	−	0.0494258i
$178$		0			0
$179$	−0.589482	−	0.340338i	−0.0440600	−	0.0254380i	0.477808	−	0.878464i	$-0.341431\pi$
$179$	−0.589482	−	0.340338i	−0.0440600	−	0.0254380i	−0.521868	+	0.853026i	$0.674765\pi$
$180$		0			0
$181$		−	19.1298i		−	1.42191i	−0.703239	−	0.710954i	$-0.748263\pi$
$181$		−	19.1298i		−	1.42191i	0.703239	−	0.710954i	$-0.251737\pi$
$182$		0			0
$183$	5.92486	+	3.38741i	0.437978	+	0.250405i
$184$		0			0
$185$	−9.00738	−	15.6012i	−0.662236	−	1.14703i
$186$		0			0
$187$	2.99247	+	1.72770i	0.218831	+	0.126342i
$188$		0			0
$189$	−13.5467	+	2.34268i	−0.985374	+	0.170405i
$190$		0			0
$191$	18.3174	+	10.5756i	1.32540	+	0.765221i	0.984585	−	0.174909i	$-0.0559631\pi$
$191$	18.3174	+	10.5756i	1.32540	+	0.765221i	0.340817	+	0.940130i	$0.389296\pi$
$192$		0			0
$193$	−6.41421	−	11.1097i	−0.461705	−	0.799697i	0.537341	−	0.843365i	$-0.319429\pi$
$193$	−6.41421	−	11.1097i	−0.461705	−	0.799697i	−0.999046	+	0.0436683i	$0.986096\pi$
$194$		0			0
$195$	12.3418	+	7.05616i	0.883815	+	0.505302i
$196$		0			0
$197$			22.2854i			1.58777i	0.608069	+	0.793884i	$0.291944\pi$
$197$			22.2854i			1.58777i	−0.608069	+	0.793884i	$0.708056\pi$
$198$		0			0
$199$	6.65637	+	3.84306i	0.471858	+	0.272427i	0.717017	−	0.697056i	$-0.245507\pi$
$199$	6.65637	+	3.84306i	0.471858	+	0.272427i	−0.245159	+	0.969483i	$0.578840\pi$
$200$		0			0
$201$	−3.18516	−	5.46341i	−0.224664	−	0.385359i
$202$		0			0
$203$	−0.634685	+	0.515517i	−0.0445461	+	0.0361822i
$204$		0			0
$205$	−15.7722	+	27.3183i	−1.10158	+	1.90799i
$206$		0			0
$207$	0.0856291	+	10.1299i	0.00595163	+	0.704076i
$208$		0			0
$209$	−4.32002	−	7.48250i	−0.298822	−	0.517575i
$210$		0			0
$211$	8.33679	−	14.4397i	0.573928	−	0.994073i	−0.422229	−	0.906489i	$-0.638752\pi$
$211$	8.33679	−	14.4397i	0.573928	−	0.994073i	0.996157	−	0.0875838i	$-0.0279146\pi$
$212$		0			0
$213$	0.0384362	+	9.09414i	0.00263360	+	0.623120i
$214$		0			0
$215$	−14.2021	−	24.5987i	−0.968572	−	1.67762i
$216$		0			0
$217$	10.3383	−	8.39722i	0.701813	−	0.570041i
$218$		0			0
$219$	−24.4418	−	13.9741i	−1.65163	−	0.944282i
$220$		0			0
$221$	−2.67318	+	1.54336i	−0.179818	+	0.103818i
$222$		0			0
$223$	−4.45390	+	2.57146i	−0.298255	+	0.172198i	−0.641659	−	0.766990i	$-0.721753\pi$
$223$	−4.45390	+	2.57146i	−0.298255	+	0.172198i	0.343404	+	0.939188i	$0.388420\pi$
$224$		0			0
$225$	5.17646	−	0.0437572i	0.345098	−	0.00291715i
$226$		0			0
$227$	11.9854			0.795500			0.397750	−	0.917494i	$-0.369791\pi$
$227$	11.9854			0.795500			0.397750	+	0.917494i	$0.369791\pi$
$228$		0			0
$229$			2.60911i			0.172415i	0.996277	+	0.0862074i	$0.0274748\pi$
$229$			2.60911i			0.172415i	−0.996277	+	0.0862074i	$0.972525\pi$
$230$		0			0
$231$	2.63137	+	16.0214i	0.173132	+	1.05413i
$232$		0			0
$233$	3.13306	−	1.80887i	0.205253	−	0.118503i	−0.393850	−	0.919175i	$-0.628857\pi$
$233$	3.13306	−	1.80887i	0.205253	−	0.118503i	0.599103	+	0.800672i	$0.295524\pi$
$234$		0			0
$235$	−3.71743	+	6.43878i	−0.242499	+	0.420020i
$236$		0			0
$237$	−6.01189	+	10.5153i	−0.390514	+	0.683041i
$238$		0			0
$239$	12.8069	+	7.39409i	0.828412	+	0.478284i	0.853309	−	0.521406i	$-0.174592\pi$
$239$	12.8069	+	7.39409i	0.828412	+	0.478284i	−0.0248967	+	0.999690i	$0.507926\pi$
$240$		0			0
$241$		−	6.44196i		−	0.414963i	−0.978239	−	0.207481i	$-0.933473\pi$
$241$		−	6.44196i		−	0.414963i	0.978239	−	0.207481i	$-0.0665267\pi$
$242$		0			0
$243$	15.5850	−	0.329395i	0.999777	−	0.0211307i
$244$		0			0
$245$	17.2484	−	5.66091i	1.10196	−	0.361662i
$246$		0			0
$247$	7.71817			0.491095
$248$		0			0
$249$	−12.6291	−	21.6623i	−0.800338	−	1.37279i
$250$		0			0
$251$	6.21012			0.391979			0.195990	−	0.980606i	$-0.437208\pi$
$251$	6.21012			0.391979			0.195990	+	0.980606i	$0.437208\pi$
$252$		0			0
$253$	11.9638			0.752158
$254$		0			0
$255$	−2.17435	+	3.80311i	−0.136163	+	0.238160i
$256$		0			0
$257$	21.1767			1.32096			0.660482	−	0.750842i	$-0.270352\pi$
$257$	21.1767			1.32096			0.660482	+	0.750842i	$0.270352\pi$
$258$		0			0
$259$	11.5872	+	14.2657i	0.719995	+	0.886430i
$260$		0			0
$261$	0.798988	−	0.470345i	0.0494561	−	0.0291136i
$262$		0			0
$263$			17.1579i			1.05800i	0.848621	+	0.529002i	$0.177434\pi$
$263$			17.1579i			1.05800i	−0.848621	+	0.529002i	$0.822566\pi$
$264$		0			0
$265$	20.2650	+	11.7000i	1.24487	+	0.718725i
$266$		0			0
$267$	4.03205	+	6.91605i	0.246758	+	0.423255i
$268$		0			0
$269$	10.8061	−	18.7166i	0.658857	−	1.14117i	−0.322055	−	0.946721i	$-0.604373\pi$
$269$	10.8061	−	18.7166i	0.658857	−	1.14117i	0.980912	−	0.194453i	$-0.0622932\pi$
$270$		0			0
$271$	21.8475	−	12.6137i	1.32714	−	0.766227i	0.342287	−	0.939595i	$-0.388798\pi$
$271$	21.8475	−	12.6137i	1.32714	−	0.766227i	0.984857	+	0.173368i	$0.0554652\pi$
$272$		0			0
$273$	−13.5698	−	5.12028i	−0.821282	−	0.309893i
$274$		0			0
$275$		−	6.11361i		−	0.368665i
$276$		0			0
$277$	22.4512			1.34896			0.674482	−	0.738291i	$-0.264367\pi$
$277$	22.4512			1.34896			0.674482	+	0.738291i	$0.264367\pi$
$278$		0			0
$279$	−13.0147	+	7.66143i	−0.779168	+	0.458678i
$280$		0			0
$281$	10.3691	−	5.98662i	0.618571	−	0.357132i	−0.157742	−	0.987480i	$-0.550421\pi$
$281$	10.3691	−	5.98662i	0.618571	−	0.357132i	0.776312	+	0.630349i	$0.217088\pi$
$282$		0			0
$283$	18.8187	−	10.8650i	1.11865	−	0.645855i	0.177596	−	0.984103i	$-0.443168\pi$
$283$	18.8187	−	10.8650i	1.11865	−	0.645855i	0.941057	+	0.338249i	$0.109835\pi$
$284$		0			0
$285$	9.46315	−	5.51701i	0.560549	−	0.326800i
$286$		0			0
$287$	11.4883	−	30.0612i	0.678134	−	1.77445i
$288$		0			0
$289$	8.02442	+	13.8987i	0.472024	+	0.817570i
$290$		0			0
$291$	21.5638	−	12.5717i	1.26410	−	0.736967i
$292$		0			0
$293$	−5.38110	+	9.32035i	−0.314367	+	0.544500i	−0.979303	−	0.202400i	$-0.935126\pi$
$293$	−5.38110	+	9.32035i	−0.314367	+	0.544500i	0.664935	+	0.746901i	$0.268459\pi$
$294$		0			0
$295$	−0.569833	−	0.986980i	−0.0331770	−	0.0574642i
$296$		0			0
$297$	−0.233420	−	18.4084i	−0.0135444	−	1.06817i
$298$		0			0
$299$	−5.34365	+	9.25547i	−0.309031	+	0.535258i
$300$		0			0
$301$	18.2697	+	22.4930i	1.05305	+	1.29647i
$302$		0			0
$303$	−14.9461	+	0.0631693i	−0.858630	+	0.00362898i
$304$		0			0
$305$	8.84966	+	5.10935i	0.506730	+	0.292561i
$306$		0			0
$307$		−	4.22117i		−	0.240915i	−0.992719	−	0.120457i	$-0.961564\pi$
$307$		−	4.22117i		−	0.240915i	0.992719	−	0.120457i	$-0.0384361\pi$
$308$		0			0
$309$	0.0446349	+	10.5608i	0.00253919	+	0.600782i
$310$		0			0
$311$	−2.09266	−	3.62459i	−0.118664	−	0.205532i	0.800575	−	0.599233i	$-0.204528\pi$
$311$	−2.09266	−	3.62459i	−0.118664	−	0.205532i	−0.919238	+	0.393702i	$0.871194\pi$
$312$		0			0
$313$	−19.0867	−	11.0197i	−1.07885	−	0.622872i	−0.148261	−	0.988948i	$-0.547368\pi$
$313$	−19.0867	−	11.0197i	−1.07885	−	0.622872i	−0.930585	+	0.366076i	$0.880701\pi$
$314$		0			0
$315$	−20.2978	+	3.42190i	−1.14365	+	0.192802i
$316$		0			0
$317$	8.41440	+	4.85806i	0.472600	+	0.272856i	0.717327	−	0.696736i	$-0.245365\pi$
$317$	8.41440	+	4.85806i	0.472600	+	0.272856i	−0.244727	+	0.969592i	$0.578698\pi$
$318$		0			0
$319$	−0.547481	−	0.948264i	−0.0306530	−	0.0530926i
$320$		0			0
$321$	−23.9891	+	13.9856i	−1.33894	+	0.780601i
$322$		0			0
$323$			2.37834i			0.132335i
$324$		0			0
$325$	4.72963	+	2.73065i	0.262353	+	0.151469i
$326$		0			0
$327$	4.79115	−	8.38011i	0.264951	−	0.463421i
$328$		0			0
$329$	2.70774	−	7.08527i	0.149283	−	0.390624i
$330$		0			0
$331$	−13.8588	+	24.0042i	−0.761749	+	1.31939i	0.180200	+	0.983630i	$0.442326\pi$
$331$	−13.8588	+	24.0042i	−0.761749	+	1.31939i	−0.941948	+	0.335758i	$0.891008\pi$
$332$		0			0
$333$	−10.5719	−	17.9588i	−0.579336	−	0.984134i
$334$		0			0
$335$	−4.73447	−	8.20034i	−0.258672	−	0.448032i
$336$		0			0
$337$	6.29141	−	10.8970i	0.342715	−	0.593600i	−0.642221	−	0.766520i	$-0.721987\pi$
$337$	6.29141	−	10.8970i	0.342715	−	0.593600i	0.984936	+	0.172920i	$0.0553201\pi$
$338$		0			0
$339$	−24.6799	−	14.1102i	−1.34043	−	0.766362i
$340$		0			0
$341$	8.91788	+	15.4462i	0.482930	+	0.836460i
$342$		0			0
$343$	−16.4641	+	8.48130i	−0.888979	+	0.457947i
$344$		0			0
$345$	0.0641060	+	15.1677i	0.00345135	+	0.816602i
$346$		0			0
$347$	−14.4819	+	8.36115i	−0.777431	+	0.448850i	−0.835519	−	0.549462i	$-0.814833\pi$
$347$	−14.4819	+	8.36115i	−0.777431	+	0.448850i	0.0580881	+	0.998311i	$0.481500\pi$
$348$		0			0
$349$	−13.9900	+	8.07714i	−0.748869	+	0.432359i	−0.825285	−	0.564717i	$-0.808985\pi$
$349$	−13.9900	+	8.07714i	−0.748869	+	0.432359i	0.0764164	+	0.997076i	$0.475652\pi$
$350$		0			0
$351$	14.3455	+	8.04158i	0.765704	+	0.429228i
$352$		0			0
$353$	15.6566			0.833318			0.416659	−	0.909063i	$-0.363201\pi$
$353$	15.6566			0.833318			0.416659	+	0.909063i	$0.363201\pi$
$354$		0			0
$355$			13.6166i			0.722694i
$356$		0			0
$357$	1.57781	−	4.18152i	0.0835064	−	0.221309i
$358$		0			0
$359$	19.1396	−	11.0502i	1.01015	−	0.583209i	0.0989127	−	0.995096i	$-0.468464\pi$
$359$	19.1396	−	11.0502i	1.01015	−	0.583209i	0.911235	+	0.411887i	$0.135130\pi$
$360$		0			0
$361$	−6.52655	+	11.3043i	−0.343502	+	0.594964i
$362$		0			0
$363$	−2.68950	+	0.0113671i	−0.141162	+	0.000596618i
$364$		0			0
$365$	−36.5075	−	21.0776i	−1.91089	−	1.10325i
$366$		0			0
$367$		−	13.1513i		−	0.686492i	−0.939246	−	0.343246i	$-0.888474\pi$
$367$		−	13.1513i		−	0.686492i	0.939246	−	0.343246i	$-0.111526\pi$
$368$		0			0
$369$	−17.9775	+	31.7548i	−0.935870	+	1.65309i
$370$		0			0
$371$	−22.2997	−	8.52216i	−1.15774	−	0.442448i
$372$		0			0
$373$	−4.43829			−0.229806			−0.114903	−	0.993377i	$-0.536656\pi$
$373$	−4.43829			−0.229806			−0.114903	+	0.993377i	$0.536656\pi$
$374$		0			0
$375$	−14.7082	+	0.0621638i	−0.759527	+	0.00321012i
$376$		0			0
$377$	0.978132			0.0503763
$378$		0			0
$379$	14.8875			0.764718			0.382359	−	0.924014i	$-0.375112\pi$
$379$	14.8875			0.764718			0.382359	+	0.924014i	$0.375112\pi$
$380$		0			0
$381$	−31.2209	+	0.131954i	−1.59949	+	0.00676022i
$382$		0			0
$383$	5.63802			0.288089			0.144045	−	0.989571i	$-0.453989\pi$
$383$	5.63802			0.288089			0.144045	+	0.989571i	$0.453989\pi$
$384$		0			0
$385$	3.83848	+	24.0049i	0.195627	+	1.22341i
$386$		0			0
$387$	−16.6688	−	28.3158i	−0.847325	−	1.43937i
$388$		0			0
$389$		−	38.5120i		−	1.95263i	−0.216346	−	0.976317i	$-0.569414\pi$
$389$		−	38.5120i		−	1.95263i	0.216346	−	0.976317i	$-0.430586\pi$
$390$		0			0
$391$	−2.85206	−	1.64664i	−0.144235	−	0.0832741i
$392$		0			0
$393$	18.0813	−	0.0764202i	0.912082	−	0.00385489i
$394$		0			0
$395$	−9.06795	+	15.7061i	−0.456258	+	0.790262i
$396$		0			0
$397$	2.50780	−	1.44788i	0.125863	−	0.0726669i	−0.435747	−	0.900069i	$-0.643516\pi$
$397$	2.50780	−	1.44788i	0.125863	−	0.0726669i	0.561609	+	0.827402i	$0.310182\pi$
$398$		0			0
$399$	−8.64447	+	7.08224i	−0.432765	+	0.354556i
$400$		0			0
$401$		−	25.7333i		−	1.28506i	−0.766261	−	0.642530i	$-0.777885\pi$
$401$		−	25.7333i		−	1.28506i	0.766261	−	0.642530i	$-0.222115\pi$
$402$		0			0
$403$	−15.9327			−0.793666
$404$		0			0
$405$	23.3370	−	0.394568i	1.15962	−	0.0196062i
$406$		0			0
$407$	−21.3140	+	12.3057i	−1.05650	+	0.609969i
$408$		0			0
$409$	−24.9914	+	14.4288i	−1.23574	+	0.713457i	−0.968221	−	0.250095i	$-0.919538\pi$
$409$	−24.9914	+	14.4288i	−1.23574	+	0.713457i	−0.267522	+	0.963552i	$0.586205\pi$
$410$		0			0
$411$	0.0281829	+	6.66818i	0.00139016	+	0.328917i
$412$		0			0
$413$	0.733041	+	0.902492i	0.0360706	+	0.0444088i
$414$		0			0
$415$	−18.7721	−	32.5142i	−0.921486	−	1.59606i
$416$		0			0
$417$	32.5781	+	18.6259i	1.59536	+	0.912112i
$418$		0			0
$419$	6.07870	−	10.5286i	0.296964	−	0.514357i	−0.678476	−	0.734623i	$-0.737359\pi$
$419$	6.07870	−	10.5286i	0.296964	−	0.514357i	0.975440	+	0.220266i	$0.0706925\pi$
$420$		0			0
$421$	−13.9914	−	24.2338i	−0.681898	−	1.18108i	−0.974401	−	0.224817i	$-0.927821\pi$
$421$	−13.9914	−	24.2338i	−0.681898	−	1.18108i	0.292503	−	0.956265i	$-0.405512\pi$
$422$		0			0
$423$	−4.23720	+	7.48445i	−0.206020	+	0.363906i
$424$		0			0
$425$	−0.841446	+	1.45743i	−0.0408161	+	0.0706956i
$426$		0			0
$427$	−9.73822	−	3.72160i	−0.471265	−	0.180101i
$428$		0			0
$429$	9.63995	−	16.8611i	0.465421	−	0.814060i
$430$		0			0
$431$	13.9975	+	8.08147i	0.674236	+	0.389271i	0.797680	−	0.603081i	$-0.206060\pi$
$431$	13.9975	+	8.08147i	0.674236	+	0.389271i	−0.123444	+	0.992352i	$0.539394\pi$
$432$		0			0
$433$			5.27197i			0.253355i	0.991944	+	0.126677i	$0.0404313\pi$
$433$			5.27197i			0.253355i	−0.991944	+	0.126677i	$0.959569\pi$
$434$		0			0
$435$	1.19927	−	0.699176i	0.0575008	−	0.0335229i
$436$		0			0
$437$	4.11732	+	7.13141i	0.196958	+	0.341142i
$438$		0			0
$439$	9.10263	+	5.25541i	0.434445	+	0.250827i	0.701238	−	0.712927i	$-0.252631\pi$
$439$	9.10263	+	5.25541i	0.434445	+	0.250827i	−0.266794	+	0.963754i	$0.585964\pi$
$440$		0			0
$441$	19.8968	−	6.71695i	0.947467	−	0.319855i
$442$		0			0
$443$	5.15805	+	2.97800i	0.245066	+	0.141489i	0.617503	−	0.786568i	$-0.288144\pi$
$443$	5.15805	+	2.97800i	0.245066	+	0.141489i	−0.372437	+	0.928058i	$0.621478\pi$
$444$		0			0
$445$	5.99330	+	10.3807i	0.284109	+	0.492092i
$446$		0			0
$447$	0.0695651	+	16.4593i	0.00329031	+	0.778500i
$448$		0			0
$449$			1.85897i			0.0877304i	0.999037	+	0.0438652i	$0.0139672\pi$
$449$			1.85897i			0.0877304i	−0.999037	+	0.0438652i	$0.986033\pi$
$450$		0			0
$451$	37.3215	+	21.5476i	1.75740	+	1.01464i
$452$		0			0
$453$	−36.9582	+	0.156203i	−1.73645	+	0.00733906i
$454$		0			0
$455$	−20.2852	−	7.75230i	−0.950986	−	0.363433i
$456$		0			0
$457$	−14.8747	+	25.7637i	−0.695808	+	1.20517i	0.274100	+	0.961701i	$0.411620\pi$
$457$	−14.8747	+	25.7637i	−0.695808	+	1.20517i	−0.969908	+	0.243473i	$0.921713\pi$
$458$		0			0
$459$	−2.47800	+	4.42053i	−0.115663	+	0.206333i
$460$		0			0
$461$	−14.9738	−	25.9353i	−0.697398	−	1.20793i	−0.969366	−	0.245622i	$-0.921008\pi$
$461$	−14.9738	−	25.9353i	−0.697398	−	1.20793i	0.271968	−	0.962306i	$-0.412325\pi$
$462$		0			0
$463$	7.57406	−	13.1187i	0.351997	−	0.609676i	−0.634603	−	0.772839i	$-0.718836\pi$
$463$	7.57406	−	13.1187i	0.351997	−	0.609676i	0.986599	+	0.163163i	$0.0521695\pi$
$464$		0			0
$465$	−19.5349	+	11.3888i	−0.905910	+	0.528145i
$466$		0			0
$467$	5.85158	+	10.1352i	0.270779	+	0.469002i	0.969061	−	0.246820i	$-0.0793855\pi$
$467$	5.85158	+	10.1352i	0.270779	+	0.469002i	−0.698283	+	0.715822i	$0.746052\pi$
$468$		0			0
$469$	6.09048	+	7.49837i	0.281232	+	0.346243i
$470$		0			0
$471$	3.63760	−	2.12072i	0.167612	−	0.0977175i
$472$		0			0
$473$	−33.6061	+	19.4025i	−1.54521	+	0.892127i
$474$		0			0
$475$	3.64421	−	2.10399i	0.167208	−	0.0965375i
$476$		0			0
$477$	23.5561	+	13.3359i	1.07856	+	0.610608i
$478$		0			0
$479$	12.1418			0.554771			0.277385	−	0.960759i	$-0.410532\pi$
$479$	12.1418			0.554771			0.277385	+	0.960759i	$0.410532\pi$
$480$		0			0
$481$		−	21.9854i		−	1.00245i
$482$		0			0
$483$	−2.50791	−	15.2696i	−0.114114	−	0.694793i
$484$		0			0
$485$	32.3664	−	18.6868i	1.46968	−	0.848522i
$486$		0			0
$487$	−5.22070	+	9.04251i	−0.236572	+	0.409755i	−0.959728	−	0.280929i	$-0.909357\pi$
$487$	−5.22070	+	9.04251i	−0.236572	+	0.409755i	0.723156	+	0.690685i	$0.242691\pi$
$488$		0			0
$489$	14.4998	+	24.8711i	0.655705	+	1.12471i
$490$		0			0
$491$	20.9972	+	12.1227i	0.947589	+	0.547091i	0.892331	−	0.451382i	$-0.149069\pi$
$491$	20.9972	+	12.1227i	0.947589	+	0.547091i	0.0552576	+	0.998472i	$0.482402\pi$
$492$		0			0
$493$			0.301410i			0.0135748i
$494$		0			0
$495$	−0.233000	−	27.5638i	−0.0104726	−	1.23890i
$496$		0			0
$497$	−2.19346	−	13.7174i	−0.0983903	−	0.615309i
$498$		0			0
$499$	−0.348239			−0.0155893			−0.00779466	−	0.999970i	$-0.502481\pi$
$499$	−0.348239			−0.0155893			−0.00779466	+	0.999970i	$0.502481\pi$
$500$		0			0
$501$	18.2315	−	31.8883i	0.814521	−	1.42466i
$502$		0			0
$503$	−32.3099			−1.44063			−0.720314	−	0.693648i	$-0.756002\pi$
$503$	−32.3099			−1.44063			−0.720314	+	0.693648i	$0.756002\pi$
$504$		0			0
$505$	−22.3787			−0.995839
$506$		0			0
$507$	−2.60224	−	4.46354i	−0.115570	−	0.198233i
$508$		0			0
$509$	−13.7046			−0.607448			−0.303724	−	0.952760i	$-0.598230\pi$
$509$	−13.7046			−0.607448			−0.303724	+	0.952760i	$0.598230\pi$
$510$		0			0
$511$	40.1731	+	15.3527i	1.77715	+	0.679165i
$512$		0			0
$513$	10.8926	−	6.47437i	0.480921	−	0.285850i
$514$		0			0
$515$			15.8126i			0.696786i
$516$		0			0
$517$	8.79650	+	5.07866i	0.386870	+	0.223359i
$518$		0			0
$519$	−8.75259	+	15.3090i	−0.384196	+	0.671990i
$520$		0			0
$521$	−8.73516	+	15.1297i	−0.382694	+	0.662846i	−0.991446	−	0.130514i	$-0.958337\pi$
$521$	−8.73516	+	15.1297i	−0.382694	+	0.662846i	0.608752	+	0.793361i	$0.291670\pi$
$522$		0			0
$523$	−23.3238	+	13.4660i	−1.01988	+	0.588827i	−0.914069	−	0.405559i	$-0.867077\pi$
$523$	−23.3238	+	13.4660i	−1.01988	+	0.588827i	−0.105810	+	0.994386i	$0.533743\pi$
$524$		0			0
$525$	−7.80292	+	1.28156i	−0.340547	+	0.0559320i
$526$		0			0
$527$		−	4.90965i		−	0.213868i
$528$		0			0
$529$	11.5975			0.504241
$530$		0			0
$531$	−0.668809	−	1.13612i	−0.0290238	−	0.0493036i
$532$		0			0
$533$	−33.3394	+	19.2485i	−1.44409	+	0.833746i
$534$		0			0
$535$	−36.0066	+	20.7884i	−1.55670	+	0.898761i
$536$		0			0
$537$	−1.02350	−	0.585162i	−0.0441671	−	0.0252516i
$538$		0			0
$539$	−7.73379	−	23.5643i	−0.333118	−	1.01499i
$540$		0			0
$541$	−7.43375	−	12.8756i	−0.319602	−	0.553567i	0.660803	−	0.750559i	$-0.270216\pi$
$541$	−7.43375	−	12.8756i	−0.319602	−	0.553567i	−0.980405	+	0.196993i	$0.936882\pi$
$542$		0			0
$543$	−0.140038	−	33.1335i	−0.00600961	−	1.42190i
$544$		0			0
$545$	7.22666	−	12.5169i	0.309556	−	0.536167i
$546$		0			0
$547$	−4.17953	−	7.23915i	−0.178704	−	0.309524i	0.762733	−	0.646713i	$-0.223857\pi$
$547$	−4.17953	−	7.23915i	−0.178704	−	0.309524i	−0.941437	+	0.337190i	$0.890524\pi$
$548$		0			0
$549$	10.2869	+	5.82374i	0.439033	+	0.248551i
$550$		0			0
$551$	0.376829	−	0.652687i	0.0160534	−	0.0278054i
$552$		0			0
$553$	6.60500	−	17.2831i	0.280873	−	0.734953i
$554$		0			0
$555$	−15.7153	−	26.9560i	−0.667078	−	1.14422i
$556$		0			0
$557$	−0.617917	−	0.356754i	−0.0261820	−	0.0151162i	0.486852	−	0.873485i	$-0.338145\pi$
$557$	−0.617917	−	0.356754i	−0.0261820	−	0.0151162i	−0.513034	+	0.858368i	$0.671478\pi$
$558$		0			0
$559$		−	34.6646i		−	1.46616i
$560$		0			0
$561$	5.19571	+	2.97054i	0.219363	+	0.125416i
$562$		0			0
$563$	13.5939	+	23.5452i	0.572912	+	0.992314i	0.996265	+	0.0863485i	$0.0275199\pi$
$563$	13.5939	+	23.5452i	0.572912	+	0.992314i	−0.423352	+	0.905965i	$0.639147\pi$
$564$		0			0
$565$	−36.8632	−	21.2830i	−1.55085	−	0.895381i
$566$		0			0
$567$	−23.4461	+	4.15678i	−0.984645	+	0.174568i
$568$		0			0
$569$	1.51833	+	0.876606i	0.0636515	+	0.0367492i	0.531488	−	0.847066i	$-0.321633\pi$
$569$	1.51833	+	0.876606i	0.0636515	+	0.0367492i	−0.467836	+	0.883815i	$0.654966\pi$
$570$		0			0
$571$	−0.228817	−	0.396323i	−0.00957570	−	0.0165856i	0.861198	−	0.508270i	$-0.169715\pi$
$571$	−0.228817	−	0.396323i	−0.00957570	−	0.0165856i	−0.870774	+	0.491684i	$0.836381\pi$
$572$		0			0
$573$	31.8038	+	18.1832i	1.32862	+	0.759612i
$574$		0			0
$575$			5.82675i			0.242992i
$576$		0			0
$577$	19.8800	+	11.4777i	0.827617	+	0.477825i	0.853036	−	0.521852i	$-0.174759\pi$
$577$	19.8800	+	11.4777i	0.827617	+	0.477825i	−0.0254193	+	0.999677i	$0.508092\pi$
$578$		0			0
$579$	−11.1910	−	19.1955i	−0.465081	−	0.797738i
$580$		0			0
$581$	24.1487	+	29.7309i	1.00186	+	1.23345i
$582$		0			0
$583$	15.9842	−	27.6855i	0.662000	−	1.14662i
$584$		0			0
$585$	21.4281	+	12.1312i	0.885942	+	0.501562i
$586$		0			0
$587$	2.81513	+	4.87594i	0.116193	+	0.201252i	0.918256	−	0.395987i	$-0.129598\pi$
$587$	2.81513	+	4.87594i	0.116193	+	0.201252i	−0.802063	+	0.597239i	$0.796264\pi$
$588$		0			0
$589$	−6.13814	+	10.6316i	−0.252918	+	0.438066i
$590$		0			0
$591$	0.163138	+	38.5991i	0.00671061	+	1.58775i
$592$		0			0
$593$	1.35121	+	2.34037i	0.0554876	+	0.0961074i	0.892435	−	0.451176i	$-0.148995\pi$
$593$	1.35121	+	2.34037i	0.0554876	+	0.0961074i	−0.836947	+	0.547283i	$0.815662\pi$
$594$		0			0
$595$	2.38886	−	6.25086i	0.0979337	−	0.256260i
$596$		0			0
$597$	11.5572	+	6.60759i	0.473005	+	0.270430i
$598$		0			0
$599$	10.3894	−	5.99831i	0.424498	−	0.245084i	−0.272502	−	0.962155i	$-0.587851\pi$
$599$	10.3894	−	5.99831i	0.424498	−	0.245084i	0.697000	+	0.717071i	$0.254518\pi$
$600$		0			0
$601$	26.7530	−	15.4459i	1.09128	−	0.630050i	0.157363	−	0.987541i	$-0.449701\pi$
$601$	26.7530	−	15.4459i	1.09128	−	0.630050i	0.933917	+	0.357491i	$0.116368\pi$
$602$		0			0
$603$	−5.55681	−	9.43950i	−0.226291	−	0.384406i
$604$		0			0
$605$	−4.02697			−0.163720
$606$		0			0
$607$		−	6.87463i		−	0.279033i	−0.990220	−	0.139516i	$-0.955445\pi$
$607$		−	6.87463i		−	0.279033i	0.990220	−	0.139516i	$-0.0445548\pi$
$608$		0			0
$609$	−1.09552	+	0.897540i	−0.0443928	+	0.0363701i
$610$		0			0
$611$	−7.85794	+	4.53678i	−0.317898	+	0.183539i
$612$		0			0
$613$	−16.6455	+	28.8308i	−0.672304	+	1.16447i	0.304945	+	0.952370i	$0.401362\pi$
$613$	−16.6455	+	28.8308i	−0.672304	+	1.16447i	−0.977249	+	0.212095i	$0.931971\pi$
$614$		0			0
$615$	−27.1180	+	47.4317i	−1.09351	+	1.91263i
$616$		0			0
$617$	18.0757	+	10.4360i	0.727702	+	0.420139i	0.817581	−	0.575814i	$-0.195315\pi$
$617$	18.0757	+	10.4360i	0.727702	+	0.420139i	−0.0898790	+	0.995953i	$0.528648\pi$
$618$		0			0
$619$		−	19.3846i		−	0.779133i	−0.920998	−	0.389567i	$-0.872625\pi$
$619$		−	19.3846i		−	0.779133i	0.920998	−	0.389567i	$-0.127375\pi$
$620$		0			0
$621$	0.222468	+	17.5447i	0.00892731	+	0.704045i
$622$		0			0
$623$	−7.70985	−	9.49208i	−0.308889	−	0.380292i
$624$		0			0
$625$	−30.6502			−1.22601
$626$		0			0
$627$	−7.53720	−	12.9283i	−0.301007	−	0.516307i
$628$		0			0
$629$	6.77476			0.270127
$630$		0			0
$631$	−27.3629			−1.08930			−0.544649	−	0.838664i	$-0.683337\pi$
$631$	−27.3629			−1.08930			−0.544649	+	0.838664i	$0.683337\pi$
$632$		0			0
$633$	14.3339	−	25.0712i	0.569722	−	0.996490i
$634$		0			0
$635$	−46.7468			−1.85509
$636$		0			0
$637$	21.6842	+	4.54198i	0.859158	+	0.179960i
$638$		0			0
$639$	0.133146	+	15.7511i	0.00526716	+	0.623104i
$640$		0			0
$641$			34.7202i			1.37137i	0.727900	+	0.685683i	$0.240496\pi$
$641$			34.7202i			1.37137i	−0.727900	+	0.685683i	$0.759504\pi$
$642$		0			0
$643$	3.52980	+	2.03793i	0.139202	+	0.0803681i	0.567983	−	0.823040i	$-0.307724\pi$
$643$	3.52980	+	2.03793i	0.139202	+	0.0803681i	−0.428782	+	0.903408i	$0.641057\pi$
$644$		0			0
$645$	−24.7785	−	42.5018i	−0.975654	−	1.67351i
$646$		0			0
$647$	−6.53976	+	11.3272i	−0.257105	+	0.445318i	−0.965465	−	0.260533i	$-0.916102\pi$
$647$	−6.53976	+	11.3272i	−0.257105	+	0.445318i	0.708360	+	0.705851i	$0.249435\pi$
$648$		0			0
$649$	−1.34839	+	0.778492i	−0.0529288	+	0.0305585i
$650$		0			0
$651$	17.8449	−	14.6200i	0.699397	−	0.573002i
$652$		0			0
$653$		−	6.24179i		−	0.244260i	−0.992514	−	0.122130i	$-0.961027\pi$
$653$		−	6.24179i		−	0.244260i	0.992514	−	0.122130i	$-0.0389725\pi$
$654$		0			0
$655$	27.0730			1.05783
$656$		0			0
$657$	−42.4364	−	24.0247i	−1.65560	−	0.937293i
$658$		0			0
$659$	1.79139	−	1.03426i	0.0697827	−	0.0402891i	−0.464703	−	0.885467i	$-0.653839\pi$
$659$	1.79139	−	1.03426i	0.0697827	−	0.0402891i	0.534485	+	0.845178i	$0.320505\pi$
$660$		0			0
$661$	13.5306	−	7.81190i	0.526280	−	0.303848i	−0.213220	−	0.977004i	$-0.568395\pi$
$661$	13.5306	−	7.81190i	0.526280	−	0.303848i	0.739500	+	0.673156i	$0.235062\pi$
$662$		0			0
$663$	−4.61875	+	2.69273i	−0.179377	+	0.104577i
$664$		0			0
$665$	−12.9879	+	10.5493i	−0.503649	+	0.409085i
$666$		0			0
$667$	0.521792	+	0.903771i	0.0202039	+	0.0349941i
$668$		0			0
$669$	−7.69549	+	4.48646i	−0.297525	+	0.173457i
$670$		0			0
$671$	6.98027	−	12.0902i	0.269470	−	0.466736i
$672$		0			0
$673$	−15.1108	−	26.1727i	−0.582478	−	1.00888i	−0.995185	−	0.0980180i	$-0.968750\pi$
$673$	−15.1108	−	26.1727i	−0.582478	−	1.00888i	0.412706	−	0.910864i	$-0.364584\pi$
$674$		0			0
$675$	8.96550	−	0.113683i	0.345082	−	0.00437565i
$676$		0			0
$677$	14.3438	−	24.8442i	0.551278	−	0.954841i	−0.446905	−	0.894581i	$-0.647474\pi$
$677$	14.3438	−	24.8442i	0.551278	−	0.954841i	0.998183	−	0.0602595i	$-0.0191928\pi$
$678$		0			0
$679$	−29.5958	+	24.0389i	−1.13578	+	0.922528i
$680$		0			0
$681$	20.7592	−	0.0877382i	0.795493	−	0.00336213i
$682$		0			0
$683$	7.48345	+	4.32057i	0.286346	+	0.165322i	0.636293	−	0.771448i	$-0.280467\pi$
$683$	7.48345	+	4.32057i	0.286346	+	0.165322i	−0.349947	+	0.936770i	$0.613800\pi$
$684$		0			0
$685$			9.98423i			0.381478i
$686$		0			0
$687$	0.0190997	+	4.51907i	0.000728701	+	0.172413i
$688$		0			0
$689$	14.2788	+	24.7315i	0.543978	+	0.942197i
$690$		0			0
$691$	10.5993	+	6.11951i	0.403216	+	0.232797i	0.687871	−	0.725833i	$-0.258546\pi$
$691$	10.5993	+	6.11951i	0.403216	+	0.232797i	−0.284655	+	0.958630i	$0.591879\pi$
$692$		0			0
$693$	4.67491	+	27.7303i	0.177585	+	1.05339i
$694$		0			0
$695$	48.6603	+	28.0940i	1.84579	+	1.06567i
$696$		0			0
$697$	−5.93140	−	10.2735i	−0.224668	−	0.389136i
$698$		0			0
$699$	5.41332	−	3.15596i	0.204751	−	0.119369i
$700$		0			0
$701$			3.05683i			0.115455i	0.998332	+	0.0577274i	$0.0183854\pi$
$701$			3.05683i			0.115455i	−0.998332	+	0.0577274i	$0.981615\pi$
$702$		0			0
$703$	−14.6704	−	8.46994i	−0.553303	−	0.319450i
$704$		0			0
$705$	−6.39159	+	11.1794i	−0.240721	+	0.421041i
$706$		0			0
$707$	22.5443	−	3.60493i	0.847867	−	0.135577i
$708$		0			0
$709$	6.04101	−	10.4633i	0.226875	−	0.392959i	−0.730005	−	0.683441i	$-0.760482\pi$
$709$	6.04101	−	10.4633i	0.226875	−	0.392959i	0.956880	+	0.290482i	$0.0938158\pi$
$710$		0			0
$711$	−10.3358	+	18.2568i	−0.387624	+	0.684685i
$712$		0			0
$713$	−8.49945	−	14.7215i	−0.318307	−	0.551324i
$714$		0			0
$715$	14.5403	−	25.1845i	0.543776	−	0.941847i
$716$		0			0
$717$	22.2362	+	12.7131i	0.830426	+	0.474778i
$718$		0			0
$719$	−6.27436	−	10.8675i	−0.233994	−	0.405290i	0.724986	−	0.688764i	$-0.241846\pi$
$719$	−6.27436	−	10.8675i	−0.233994	−	0.405290i	−0.958980	+	0.283474i	$0.908513\pi$
$720$		0			0
$721$	−2.54721	−	15.9296i	−0.0948630	−	0.593250i
$722$		0			0
$723$	−0.0471578	−	11.1577i	−0.00175382	−	0.414959i
$724$		0			0
$725$	0.461835	−	0.266640i	0.0171521	−	0.00990278i
$726$		0			0
$727$	16.2736	−	9.39555i	0.603553	−	0.348462i	−0.166885	−	0.985976i	$-0.553371\pi$
$727$	16.2736	−	9.39555i	0.603553	−	0.348462i	0.770438	+	0.637515i	$0.220038\pi$
$728$		0			0
$729$	26.9913	−	0.684612i	0.999678	−	0.0253560i
$730$		0			0
$731$	10.6818			0.395082
$732$		0			0
$733$		−	35.4064i		−	1.30776i	−0.756596	−	0.653882i	$-0.773139\pi$
$733$		−	35.4064i		−	1.30776i	0.756596	−	0.653882i	$-0.226861\pi$
$734$		0			0
$735$	29.8333	−	9.93115i	1.10042	−	0.366316i
$736$		0			0
$737$	−11.2031	+	6.46811i	−0.412671	+	0.238256i
$738$		0			0
$739$	11.1371	−	19.2900i	0.409684	−	0.709593i	−0.585170	−	0.810910i	$-0.698972\pi$
$739$	11.1371	−	19.2900i	0.409684	−	0.709593i	0.994854	+	0.101317i	$0.0323057\pi$
$740$		0			0
$741$	13.3681	−	0.0565002i	0.491091	−	0.00207559i
$742$		0			0
$743$	−8.68932	−	5.01678i	−0.318780	−	0.184048i	0.332069	−	0.943255i	$-0.392253\pi$
$743$	−8.68932	−	5.01678i	−0.318780	−	0.184048i	−0.650849	+	0.759207i	$0.725587\pi$
$744$		0			0
$745$			24.6445i			0.902904i
$746$		0			0
$747$	−22.0327	−	37.4275i	−0.806133	−	1.36940i
$748$		0			0
$749$	32.9243	−	26.7425i	1.20303	−	0.977148i
$750$		0			0
$751$	33.5541			1.22441			0.612203	−	0.790700i	$-0.290283\pi$
$751$	33.5541			1.22441			0.612203	+	0.790700i	$0.290283\pi$
$752$		0			0
$753$	10.7561	−	0.0454606i	0.391976	−	0.00165668i
$754$		0			0
$755$	−55.3373			−2.01393
$756$		0			0
$757$	0.0340541			0.00123772			0.000618859	−	1.00000i	$-0.499803\pi$
$757$	0.0340541			0.00123772			0.000618859		1.00000i	$0.499803\pi$
$758$		0			0
$759$	20.7217	−	0.0875800i	0.752151	−	0.00317895i
$760$		0			0
$761$	22.9691			0.832631			0.416315	−	0.909220i	$-0.363321\pi$
$761$	22.9691			0.832631			0.416315	+	0.909220i	$0.363321\pi$
$762$		0			0
$763$	−5.26383	+	13.7737i	−0.190563	+	0.498642i
$764$		0			0
$765$	−3.73820	+	6.60303i	−0.135155	+	0.238733i
$766$		0			0
$767$		−	1.39086i		−	0.0502210i
$768$		0			0
$769$	14.3775	+	8.30086i	0.518466	+	0.299337i	0.736307	−	0.676648i	$-0.236568\pi$
$769$	14.3775	+	8.30086i	0.518466	+	0.299337i	−0.217841	+	0.975984i	$0.569901\pi$
$770$		0			0
$771$	36.6787	−	0.155022i	1.32095	−	0.00558297i
$772$		0			0
$773$	−0.803138	+	1.39107i	−0.0288868	+	0.0500335i	−0.880107	−	0.474775i	$-0.842530\pi$
$773$	−0.803138	+	1.39107i	−0.0288868	+	0.0500335i	0.851221	+	0.524808i	$0.175863\pi$
$774$		0			0
$775$	−7.52280	+	4.34329i	−0.270227	+	0.156016i
$776$		0			0
$777$	20.1739	+	24.6239i	0.723735	+	0.883379i
$778$		0			0
$779$			29.6623i			1.06276i
$780$		0			0
$781$	18.6027			0.665656
$782$		0			0
$783$	1.38043	−	0.820503i	0.0493326	−	0.0293224i
$784$		0			0
$785$	5.45988	−	3.15226i	0.194871	−	0.112509i
$786$		0			0
$787$	−13.7768	+	7.95401i	−0.491088	+	0.283530i	−0.725026	−	0.688722i	$-0.758172\pi$
$787$	−13.7768	+	7.95401i	−0.491088	+	0.283530i	0.233938	+	0.972252i	$0.424839\pi$
$788$		0			0
$789$	0.125603	+	29.7182i	0.00447159	+	1.05799i
$790$		0			0
$791$	40.5644	+	15.5023i	1.44231	+	0.551198i
$792$		0			0
$793$	6.23549	+	10.8002i	0.221429	+	0.383526i
$794$		0			0
$795$	35.1853	+	20.1165i	1.24789	+	0.713457i
$796$		0			0
$797$	−10.1844	+	17.6399i	−0.360749	+	0.624836i	−0.988084	−	0.153914i	$-0.950812\pi$
$797$	−10.1844	+	17.6399i	−0.360749	+	0.624836i	0.627335	+	0.778749i	$0.284146\pi$
$798$		0			0
$799$	−1.39800	−	2.42141i	−0.0494578	−	0.0856634i
$800$		0			0
$801$	7.03429	+	11.9493i	0.248544	+	0.422209i
$802$		0			0
$803$	−28.7957	+	49.8757i	−1.01618	+	1.76008i
$804$		0			0
$805$	−3.65838	−	22.8786i	−0.128941	−	0.806365i
$806$		0			0
$807$	18.5795	−	32.4970i	0.654028	−	1.14395i
$808$		0			0
$809$	−35.7396	−	20.6343i	−1.25654	−	0.725462i	−0.284137	−	0.958784i	$-0.591707\pi$
$809$	−35.7396	−	20.6343i	−1.25654	−	0.725462i	−0.972400	+	0.233322i	$0.925040\pi$
$810$		0			0
$811$		−	19.3660i		−	0.680032i	−0.940420	−	0.340016i	$-0.889568\pi$
$811$		−	19.3660i		−	0.680032i	0.940420	−	0.340016i	$-0.110432\pi$
$812$		0			0
$813$	37.7484	−	22.0073i	1.32389	−	0.771829i
$814$		0			0
$815$	21.5527	+	37.3305i	0.754960	+	1.30763i
$816$		0			0
$817$	−23.1309	−	13.3547i	−0.809249	−	0.467220i
$818$		0			0
$819$	−23.5409	−	8.76917i	−0.822585	−	0.306420i
$820$		0			0
$821$	−28.1405	−	16.2469i	−0.982111	−	0.567022i	−0.0792043	−	0.996858i	$-0.525238\pi$
$821$	−28.1405	−	16.2469i	−0.982111	−	0.567022i	−0.902907	+	0.429836i	$0.858571\pi$
$822$		0			0
$823$	−27.8957	−	48.3167i	−0.972381	−	1.68421i	−0.688319	−	0.725408i	$-0.741651\pi$
$823$	−27.8957	−	48.3167i	−0.972381	−	1.68421i	−0.284063	−	0.958806i	$-0.591682\pi$
$824$		0			0
$825$	−0.0447541	−	10.5890i	−0.00155814	−	0.368661i
$826$		0			0
$827$			18.2989i			0.636314i	0.948038	+	0.318157i	$0.103064\pi$
$827$			18.2989i			0.636314i	−0.948038	+	0.318157i	$0.896936\pi$
$828$		0			0
$829$	12.6483	+	7.30247i	0.439292	+	0.253625i	0.703297	−	0.710896i	$-0.251710\pi$
$829$	12.6483	+	7.30247i	0.439292	+	0.253625i	−0.264005	+	0.964521i	$0.585044\pi$
$830$		0			0
$831$	38.8864	−	0.164352i	1.34895	−	0.00570132i
$832$		0			0
$833$	−1.39961	+	6.68195i	−0.0484935	+	0.231516i
$834$		0			0
$835$	27.4992	−	47.6299i	0.951648	−	1.64830i
$836$		0			0
$837$	−22.4858	+	13.3651i	−0.777222	+	0.461967i
$838$		0			0
$839$	15.7379	+	27.2588i	0.543332	+	0.941079i	0.998710	+	0.0507803i	$0.0161708\pi$
$839$	15.7379	+	27.2588i	0.543332	+	0.941079i	−0.455378	+	0.890298i	$0.650496\pi$
$840$		0			0
$841$	−14.4522	+	25.0320i	−0.498353	+	0.863173i
$842$		0			0
$843$	17.9159	−	10.4449i	0.617056	−	0.359743i
$844$		0			0
$845$	−3.86801	−	6.69959i	−0.133064	−	0.230473i
$846$		0			0
$847$	4.05677	−	0.648694i	0.139392	−	0.0222894i
$848$		0			0
$849$	32.5150	−	18.9562i	1.11591	−	0.650577i
$850$		0			0
$851$	20.3140	−	11.7283i	0.696354	−	0.402040i
$852$		0			0
$853$	−21.2554	+	12.2718i	−0.727771	+	0.420179i	−0.817606	−	0.575778i	$-0.804699\pi$
$853$	−21.2554	+	12.2718i	−0.727771	+	0.420179i	0.0898353	+	0.995957i	$0.471366\pi$
$854$		0			0
$855$	16.3501	−	9.62493i	0.559163	−	0.329166i
$856$		0			0
$857$	−11.7302			−0.400697			−0.200348	−	0.979725i	$-0.564207\pi$
$857$	−11.7302			−0.400697			−0.200348	+	0.979725i	$0.564207\pi$
$858$		0			0
$859$			34.1123i			1.16390i	0.813226	+	0.581948i	$0.197709\pi$
$859$			34.1123i			1.16390i	−0.813226	+	0.581948i	$0.802291\pi$
$860$		0			0
$861$	19.6781	−	52.1511i	0.670628	−	1.77731i
$862$		0			0
$863$	−20.8863	+	12.0587i	−0.710978	+	0.410483i	−0.811423	−	0.584459i	$-0.801307\pi$
$863$	−20.8863	+	12.0587i	−0.710978	+	0.410483i	0.100445	+	0.994943i	$0.467973\pi$
$864$		0			0
$865$	−13.2018	+	22.8663i	−0.448876	+	0.777477i
$866$		0			0
$867$	14.0003	+	24.0143i	0.475476	+	0.815568i
$868$		0			0
$869$	21.4573	+	12.3884i	0.727890	+	0.420248i
$870$		0			0
$871$		−	11.5560i		−	0.391559i
$872$		0			0
$873$	37.2573	−	21.9325i	1.26097	−	0.742303i
$874$		0			0
$875$	22.1855	−	3.54754i	0.750006	−	0.119929i
$876$		0			0
$877$	−51.7506			−1.74749			−0.873747	−	0.486381i	$-0.838317\pi$
$877$	−51.7506			−1.74749			−0.873747	+	0.486381i	$0.838317\pi$
$878$		0			0
$879$	−9.25203	+	16.1826i	−0.312063	+	0.545824i
$880$		0			0
$881$	−30.3925			−1.02395			−0.511975	−	0.859000i	$-0.671086\pi$
$881$	−30.3925			−1.02395			−0.511975	+	0.859000i	$0.671086\pi$
$882$		0			0
$883$	35.4897			1.19432			0.597162	−	0.802121i	$-0.296295\pi$
$883$	35.4897			1.19432			0.597162	+	0.802121i	$0.296295\pi$
$884$		0			0
$885$	−0.994197	−	1.70531i	−0.0334195	−	0.0573235i
$886$		0			0
$887$	−46.5511			−1.56303			−0.781517	−	0.623884i	$-0.785554\pi$
$887$	−46.5511			−1.56303			−0.781517	+	0.623884i	$0.785554\pi$
$888$		0			0
$889$	47.0928	−	7.53033i	1.57944	−	0.252559i
$890$		0			0
$891$	−0.539049	−	31.8824i	−0.0180588	−	1.06810i
$892$		0			0
$893$			6.99125i			0.233953i
$894$		0			0
$895$	−1.52874	−	0.882620i	−0.0511003	−	0.0295027i
$896$		0			0
$897$	−9.18764	+	16.0699i	−0.306766	+	0.536559i
$898$		0			0
$899$	−0.777893	+	1.34735i	−0.0259442	+	0.0449366i
$900$		0			0
$901$	−7.62099	+	4.39998i	−0.253892	+	0.146585i
$902$		0			0
$903$	31.8084	+	38.8249i	1.05852	+	1.29201i
$904$		0			0
$905$		−	49.6106i		−	1.64911i
$906$		0			0
$907$	−14.6331			−0.485883			−0.242941	−	0.970041i	$-0.578112\pi$
$907$	−14.6331			−0.485883			−0.242941	+	0.970041i	$0.578112\pi$
$908$		0			0
$909$	−25.8867	+	0.218823i	−0.858607	+	0.00725790i
$910$		0			0
$911$	−6.67661	+	3.85474i	−0.221206	+	0.127713i	−0.606508	−	0.795077i	$-0.707430\pi$
$911$	−6.67661	+	3.85474i	−0.221206	+	0.127713i	0.385303	+	0.922790i	$0.374097\pi$
$912$		0			0
$913$	−44.4201	+	25.6460i	−1.47009	+	0.848758i
$914$		0			0
$915$	15.3653	+	8.78480i	0.507962	+	0.290417i
$916$		0			0
$917$	−27.2734	+	4.36113i	−0.900648	+	0.144017i
$918$		0			0
$919$	13.4738	+	23.3373i	0.444460	+	0.769827i	0.998014	−	0.0629860i	$-0.0200623\pi$
$919$	13.4738	+	23.3373i	0.444460	+	0.769827i	−0.553555	+	0.832813i	$0.686729\pi$
$920$		0			0
$921$	−0.0309006	−	7.31121i	−0.00101821	−	0.240912i
$922$		0			0
$923$	−8.30890	+	14.3914i	−0.273491	+	0.473700i
$924$		0			0
$925$	−5.99325	−	10.3806i	−0.197057	−	0.341312i
$926$		0			0
$927$	0.154618	+	18.2913i	0.00507833	+	0.600766i
$928$		0			0
$929$	13.8137	−	23.9261i	0.453213	−	0.784989i	−0.545370	−	0.838195i	$-0.683611\pi$
$929$	13.8137	−	23.9261i	0.453213	−	0.784989i	0.998584	+	0.0532068i	$0.0169442\pi$
$930$		0			0
$931$	11.3847	−	12.7196i	0.373118	−	0.416867i
$932$		0			0
$933$	−3.65109	−	6.26259i	−0.119531	−	0.205028i
$934$		0			0
$935$	7.76057	+	4.48057i	0.253798	+	0.146530i
$936$		0			0
$937$			7.60743i			0.248524i	0.992249	+	0.124262i	$0.0396563\pi$
$937$			7.60743i			0.248524i	−0.992249	+	0.124262i	$0.960344\pi$
$938$		0			0
$939$	−33.1396	−	18.9468i	−1.08147	−	0.618307i
$940$		0			0
$941$	−20.6498	−	35.7665i	−0.673165	−	1.16596i	−0.977002	−	0.213231i	$-0.931601\pi$
$941$	−20.6498	−	35.7665i	−0.673165	−	1.16596i	0.303837	−	0.952724i	$-0.401732\pi$
$942$		0			0
$943$	−35.5704	−	20.5366i	−1.15833	−	0.668763i
$944$		0			0
$945$	−35.1314	+	6.07544i	−1.14283	+	0.197634i
$946$		0			0
$947$	−36.0318	−	20.8030i	−1.17088	−	0.676005i	−0.216989	−	0.976174i	$-0.569624\pi$
$947$	−36.0318	−	20.8030i	−1.17088	−	0.676005i	−0.953886	+	0.300169i	$0.902957\pi$
$948$		0			0
$949$	−25.7233	−	44.5541i	−0.835014	−	1.44629i
$950$		0			0
$951$	14.6096	+	8.35273i	0.473749	+	0.270856i
$952$		0			0
$953$			47.2656i			1.53108i	0.643386	+	0.765542i	$0.277529\pi$
$953$			47.2656i			1.53108i	−0.643386	+	0.765542i	$0.722471\pi$
$954$		0			0
$955$	47.5038	+	27.4263i	1.53719	+	0.887494i
$956$		0			0
$957$	−0.955197	−	1.63842i	−0.0308771	−	0.0529626i
$958$		0			0
$959$	−1.60833	−	10.0581i	−0.0519358	−	0.324794i
$960$		0			0
$961$	−2.82894	+	4.89987i	−0.0912562	+	0.158060i
$962$		0			0
$963$	−41.4475	+	24.3992i	−1.33563	+	0.786253i
$964$		0			0
$965$	−16.6344	−	28.8116i	−0.535480	−	0.927479i
$966$		0			0
$967$	−2.60192	+	4.50665i	−0.0836720	+	0.144924i	−0.904825	−	0.425785i	$-0.859998\pi$
$967$	−2.60192	+	4.50665i	−0.0836720	+	0.144924i	0.821153	+	0.570709i	$0.193331\pi$
$968$		0			0
$969$	0.0174104	+	4.11937i	0.000559304	+	0.132333i
$970$		0			0
$971$	8.67233	+	15.0209i	0.278308	+	0.482044i	0.970964	−	0.239224i	$-0.0768929\pi$
$971$	8.67233	+	15.0209i	0.278308	+	0.482044i	−0.692656	+	0.721268i	$0.743560\pi$
$972$		0			0
$973$	−53.5461	−	20.4634i	−1.71661	−	0.656027i
$974$		0			0
$975$	8.21187	+	4.69496i	0.262990	+	0.150359i
$976$		0			0
$977$	23.3541	−	13.4835i	0.747165	−	0.431376i	−0.0775039	−	0.996992i	$-0.524695\pi$
$977$	23.3541	−	13.4835i	0.747165	−	0.431376i	0.824668	+	0.565616i	$0.191362\pi$
$978$		0			0
$979$	14.1818	−	8.18789i	0.453254	−	0.261686i
$980$		0			0
$981$	8.23709	−	14.5497i	0.262990	−	0.464537i
$982$		0			0
$983$	−17.1129			−0.545817			−0.272909	−	0.962040i	$-0.587986\pi$
$983$	−17.1129			−0.545817			−0.272909	+	0.962040i	$0.587986\pi$
$984$		0			0
$985$			57.7942i			1.84148i
$986$		0			0
$987$	4.63804	−	12.2918i	0.147630	−	0.391251i
$988$		0			0
$989$	32.0293	−	18.4921i	1.01847	−	0.588015i
$990$		0			0
$991$	−5.84386	+	10.1219i	−0.185636	+	0.321531i	−0.943791	−	0.330544i	$-0.892768\pi$
$991$	−5.84386	+	10.1219i	−0.185636	+	0.321531i	0.758155	+	0.652075i	$0.226101\pi$
$992$		0			0
$993$	−23.8282	+	41.6775i	−0.756166	+	1.32260i
$994$		0			0
$995$	17.2624	+	9.96646i	0.547255	+	0.315958i
$996$		0			0
$997$		−	28.9017i		−	0.915325i	−0.889126	−	0.457663i	$-0.848687\pi$
$997$		−	28.9017i		−	0.915325i	0.889126	−	0.457663i	$-0.151313\pi$
$998$		0			0
$999$	−18.4424	−	31.0278i	−0.583491	−	0.981677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.185.24	yes	48
3.2	odd	2		1512.2.cx.a.17.5		48
4.3	odd	2		1008.2.df.e.689.1		48
7.5	odd	6		504.2.bs.a.257.16	✓	48
9.2	odd	6		504.2.bs.a.353.16	yes	48
9.7	even	3		1512.2.bs.a.521.5		48
12.11	even	2		3024.2.df.e.17.5		48
21.5	even	6		1512.2.bs.a.1097.5		48
28.19	even	6		1008.2.ca.e.257.9		48
36.7	odd	6		3024.2.ca.e.2033.5		48
36.11	even	6		1008.2.ca.e.353.9		48
63.47	even	6	inner	504.2.cx.a.425.24	yes	48
63.61	odd	6		1512.2.cx.a.89.5		48
84.47	odd	6		3024.2.ca.e.2609.5		48
252.47	odd	6		1008.2.df.e.929.1		48
252.187	even	6		3024.2.df.e.1601.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.16	✓	48	7.5	odd	6
504.2.bs.a.353.16	yes	48	9.2	odd	6
504.2.cx.a.185.24	yes	48	1.1	even	1	trivial
504.2.cx.a.425.24	yes	48	63.47	even	6	inner
1008.2.ca.e.257.9		48	28.19	even	6
1008.2.ca.e.353.9		48	36.11	even	6
1008.2.df.e.689.1		48	4.3	odd	2
1008.2.df.e.929.1		48	252.47	odd	6
1512.2.bs.a.521.5		48	9.7	even	3
1512.2.bs.a.1097.5		48	21.5	even	6
1512.2.cx.a.17.5		48	3.2	odd	2
1512.2.cx.a.89.5		48	63.61	odd	6
3024.2.ca.e.2033.5		48	36.7	odd	6
3024.2.ca.e.2609.5		48	84.47	odd	6
3024.2.df.e.17.5		48	12.11	even	2
3024.2.df.e.1601.5		48	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73204 - 0.00732041i) q^{3} +2.59337 q^{5} +(-2.61256 + 0.417759i) q^{7} +(2.99989 - 0.0253584i) q^{9} -3.54299i q^{11} +(2.74094 + 1.58248i) q^{13} +(4.49180 - 0.0189845i) q^{15} +(-0.487640 + 0.844616i) q^{17} +(2.11191 - 1.21931i) q^{19} +(-4.52199 + 0.742698i) q^{21} +3.37675i q^{23} +1.72555 q^{25} +(5.19573 - 0.0658821i) q^{27} +(0.267645 - 0.154525i) q^{29} +(-4.35965 + 2.51705i) q^{31} +(-0.0259361 - 6.13659i) q^{33} +(-6.77533 + 1.08340i) q^{35} +(-3.47324 - 6.01583i) q^{37} +(4.75899 + 2.72085i) q^{39} +(-6.08175 + 10.5339i) q^{41} +(-5.47630 - 9.48523i) q^{43} +(7.77982 - 0.0657636i) q^{45} +(-1.43344 + 2.48279i) q^{47} +(6.65096 - 2.18284i) q^{49} +(-0.838426 + 1.46648i) q^{51} +(7.81416 + 4.51151i) q^{53} -9.18828i q^{55} +(3.64898 - 2.12736i) q^{57} +(-0.219727 - 0.380579i) q^{59} +(3.41242 + 1.97016i) q^{61} +(-7.82681 + 1.31948i) q^{63} +(7.10826 + 4.10396i) q^{65} +(-1.82561 - 3.16204i) q^{67} +(0.0247192 + 5.84865i) q^{69} +5.25055i q^{71} +(-14.0773 - 8.12752i) q^{73} +(2.98871 - 0.0126317i) q^{75} +(1.48012 + 9.25629i) q^{77} +(-3.49659 + 6.05628i) q^{79} +(8.99871 - 0.152145i) q^{81} +(-7.23851 - 12.5375i) q^{83} +(-1.26463 + 2.19040i) q^{85} +(0.462439 - 0.269602i) q^{87} +(2.31101 + 4.00279i) q^{89} +(-7.82197 - 2.98928i) q^{91} +(-7.53265 + 4.39153i) q^{93} +(5.47697 - 3.16213i) q^{95} +(12.4805 - 7.20560i) q^{97} +(-0.0898447 - 10.6286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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