LMFDB - Embedded newform 1008.2.ca.e.257.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.9
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.e.353.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.859678 + 1.50365i) q^{3} +(1.29668 + 2.24592i) q^{5} +(-1.66807 + 2.05367i) q^{7} +(-1.52191 - 2.58530i) q^{9} +(-3.06832 - 1.77150i) q^{11} +(-2.74094 - 1.58248i) q^{13} +(-4.49180 + 0.0189845i) q^{15} +(0.487640 + 0.844616i) q^{17} +(-2.11191 - 1.21931i) q^{19} +(-1.65398 - 4.27368i) q^{21} +(-2.92435 + 1.68838i) q^{23} +(-0.862775 + 1.49437i) q^{25} +(5.19573 - 0.0658821i) q^{27} +(0.267645 - 0.154525i) q^{29} -5.03410i q^{31} +(5.30147 - 3.09076i) q^{33} +(-6.77533 - 1.08340i) q^{35} +(-3.47324 + 6.01583i) q^{37} +(4.73582 - 2.76098i) q^{39} +(6.08175 - 10.5339i) q^{41} +(5.47630 + 9.48523i) q^{43} +(3.83296 - 6.77040i) q^{45} +2.86688 q^{47} +(-1.43508 - 6.85132i) q^{49} +(-1.68922 + 0.00713944i) q^{51} +(-7.81416 + 4.51151i) q^{53} -9.18828i q^{55} +(3.64898 - 2.12736i) q^{57} +0.439455 q^{59} +3.94033i q^{61} +(7.84800 + 1.18698i) q^{63} -8.20791i q^{65} -3.65121 q^{67} +(-0.0247192 - 5.84865i) q^{69} -5.25055i q^{71} +(-14.0773 + 8.12752i) q^{73} +(-1.50530 - 2.58199i) q^{75} +(8.75624 - 3.34632i) q^{77} -6.99318 q^{79} +(-4.36760 + 7.86919i) q^{81} +(-7.23851 - 12.5375i) q^{83} +(-1.26463 + 2.19040i) q^{85} +(0.00226237 + 0.535285i) q^{87} +(-2.31101 + 4.00279i) q^{89} +(7.82197 - 2.98928i) q^{91} +(7.56950 + 4.32770i) q^{93} -6.32426i q^{95} +(-12.4805 + 7.20560i) q^{97} +(0.0898447 + 10.6286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.859678	+	1.50365i	−0.496335	+	0.868131i
$3$	−0.859678	+	1.50365i	−0.496335	+	0.868131i
$4$		0			0
$5$	1.29668	+	2.24592i	0.579894	+	1.00441i	0.995491	+	0.0948574i	$0.0302395\pi$
$5$	1.29668	+	2.24592i	0.579894	+	1.00441i	−0.415596	+	0.909549i	$0.636427\pi$
$6$		0			0
$7$	−1.66807	+	2.05367i	−0.630471	+	0.776213i
$7$	−1.66807	+	2.05367i	−0.630471	+	0.776213i
$8$		0			0
$9$	−1.52191	−	2.58530i	−0.507302	−	0.861768i
$10$		0			0
$11$	−3.06832	−	1.77150i	−0.925134	−	0.534126i	−0.0398645	−	0.999205i	$-0.512693\pi$
$11$	−3.06832	−	1.77150i	−0.925134	−	0.534126i	−0.885269	+	0.465079i	$0.846026\pi$
$12$		0			0
$13$	−2.74094	−	1.58248i	−0.760200	−	0.438902i	0.0691677	−	0.997605i	$-0.477966\pi$
$13$	−2.74094	−	1.58248i	−0.760200	−	0.438902i	−0.829367	+	0.558703i	$0.811299\pi$
$14$		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	$-0.128932\pi$
$17$	0.487640	+	0.844616i	0.118270	+	0.204850i	−0.800812	+	0.598916i	$0.795599\pi$
$18$		0			0
$19$	−2.11191	−	1.21931i	−0.484506	−	0.279730i	0.237786	−	0.971318i	$-0.423578\pi$
$19$	−2.11191	−	1.21931i	−0.484506	−	0.279730i	−0.722293	+	0.691588i	$0.756912\pi$
$20$		0			0
$21$	−1.65398	−	4.27368i	−0.360929	−	0.932593i
$22$		0			0
$23$	−2.92435	+	1.68838i	−0.609770	+	0.352051i	−0.772875	−	0.634558i	$-0.781182\pi$
$23$	−2.92435	+	1.68838i	−0.609770	+	0.352051i	0.163106	+	0.986609i	$0.447849\pi$
$24$		0			0
$25$	−0.862775	+	1.49437i	−0.172555	+	0.298874i
$26$		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
$31$		−	5.03410i		−	0.904150i	−0.891980	−	0.452075i	$-0.850684\pi$
$31$		−	5.03410i		−	0.904150i	0.891980	−	0.452075i	$-0.149316\pi$
$32$		0			0
$33$	5.30147	−	3.09076i	0.922868	−	0.538031i
$34$		0			0
$35$	−6.77533	−	1.08340i	−1.14524	−	0.183128i
$36$		0			0
$37$	−3.47324	+	6.01583i	−0.570997	+	0.988996i	0.425467	+	0.904974i	$0.360110\pi$
$37$	−3.47324	+	6.01583i	−0.570997	+	0.988996i	−0.996464	+	0.0840218i	$0.973223\pi$
$38$		0			0
$39$	4.73582	−	2.76098i	0.758338	−	0.442111i
$40$		0			0
$41$	6.08175	−	10.5339i	0.949810	−	1.64512i	0.203988	−	0.978973i	$-0.434610\pi$
$41$	6.08175	−	10.5339i	0.949810	−	1.64512i	0.745822	−	0.666146i	$-0.232057\pi$
$42$		0			0
$43$	5.47630	+	9.48523i	0.835128	+	1.44648i	0.893926	+	0.448214i	$0.147940\pi$
$43$	5.47630	+	9.48523i	0.835128	+	1.44648i	−0.0587983	+	0.998270i	$0.518727\pi$
$44$		0			0
$45$	3.83296	−	6.77040i	0.571384	−	1.00927i
$46$		0			0
$47$	2.86688			0.418177			0.209089	−	0.977897i	$-0.432950\pi$
$47$	2.86688			0.418177			0.209089	+	0.977897i	$0.432950\pi$
$48$		0			0
$49$	−1.43508	−	6.85132i	−0.205012	−	0.978760i
$50$		0			0
$51$	−1.68922	+	0.00713944i	−0.236538	+	0.000999722i
$52$		0			0
$53$	−7.81416	+	4.51151i	−1.07336	+	0.619703i	−0.929097	−	0.369836i	$-0.879414\pi$
$53$	−7.81416	+	4.51151i	−1.07336	+	0.619703i	−0.144261	+	0.989540i	$0.546080\pi$
$54$		0			0
$55$		−	9.18828i		−	1.23895i
$56$		0			0
$57$	3.64898	−	2.12736i	0.483320	−	0.281775i
$58$		0			0
$59$	0.439455			0.0572121			0.0286061	−	0.999591i	$-0.490893\pi$
$59$	0.439455			0.0572121			0.0286061	+	0.999591i	$0.490893\pi$
$60$		0			0
$61$			3.94033i			0.504507i	0.967661	+	0.252254i	$0.0811717\pi$
$61$			3.94033i			0.504507i	−0.967661	+	0.252254i	$0.918828\pi$
$62$		0			0
$63$	7.84800	+	1.18698i	0.988755	+	0.149546i
$64$		0			0
$65$		−	8.20791i		−	1.01807i
$66$		0			0
$67$	−3.65121			−0.446067			−0.223033	−	0.974811i	$-0.571596\pi$
$67$	−3.65121			−0.446067			−0.223033	+	0.974811i	$0.571596\pi$
$68$		0			0
$69$	−0.0247192	−	5.84865i	−0.00297584	−	0.704095i
$70$		0			0
$71$		−	5.25055i		−	0.623126i	−0.950226	−	0.311563i	$-0.899148\pi$
$71$		−	5.25055i		−	0.623126i	0.950226	−	0.311563i	$-0.100852\pi$
$72$		0			0
$73$	−14.0773	+	8.12752i	−1.64762	+	0.951254i	−0.669607	+	0.742716i	$0.733537\pi$
$73$	−14.0773	+	8.12752i	−1.64762	+	0.951254i	−0.978014	+	0.208539i	$0.933129\pi$
$74$		0			0
$75$	−1.50530	−	2.58199i	−0.173817	−	0.298142i
$76$		0			0
$77$	8.75624	−	3.34632i	0.997866	−	0.381349i
$78$		0			0
$79$	−6.99318			−0.786795			−0.393397	−	0.919369i	$-0.628700\pi$
$79$	−6.99318			−0.786795			−0.393397	+	0.919369i	$0.628700\pi$
$80$		0			0
$81$	−4.36760	+	7.86919i	−0.485288	+	0.874354i
$82$		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
$87$	0.00226237	+	0.535285i	0.000242552	+	0.0573886i
$88$		0			0
$89$	−2.31101	+	4.00279i	−0.244967	+	0.424295i	−0.962122	−	0.272619i	$-0.912110\pi$
$89$	−2.31101	+	4.00279i	−0.244967	+	0.424295i	0.717156	+	0.696913i	$0.245444\pi$
$90$		0			0
$91$	7.82197	−	2.98928i	0.819965	−	0.313362i
$92$		0			0
$93$	7.56950	+	4.32770i	0.784921	+	0.448762i
$94$		0			0
$95$		−	6.32426i		−	0.648855i
$96$		0			0
$97$	−12.4805	+	7.20560i	−1.26720	+	0.731617i	−0.974457	−	0.224574i	$-0.927901\pi$
$97$	−12.4805	+	7.20560i	−1.26720	+	0.731617i	−0.292742	+	0.956192i	$0.594568\pi$
$98$		0			0
$99$	0.0898447	+	10.6286i	0.00902973	+	1.06821i
$100$		0			0
$101$	−4.31460	+	7.47311i	−0.429319	+	0.743602i	−0.996813	−	0.0797753i	$-0.974580\pi$
$101$	−4.31460	+	7.47311i	−0.429319	+	0.743602i	0.567494	+	0.823378i	$0.307913\pi$
$102$		0			0
$103$	5.28044	−	3.04866i	0.520297	−	0.300394i	−0.216759	−	0.976225i	$-0.569549\pi$
$103$	5.28044	−	3.04866i	0.520297	−	0.300394i	0.737056	+	0.675832i	$0.236215\pi$
$104$		0			0
$105$	7.45365	−	9.25633i	0.727402	−	0.903325i
$106$		0			0
$107$	−13.8841	−	8.01599i	−1.34223	−	0.774935i	−0.355093	−	0.934831i	$-0.615551\pi$
$107$	−13.8841	−	8.01599i	−1.34223	−	0.774935i	−0.987134	+	0.159896i	$0.948884\pi$
$108$		0			0
$109$	2.78659	+	4.82652i	0.266907	+	0.462297i	0.968062	−	0.250713i	$-0.0806649\pi$
$109$	2.78659	+	4.82652i	0.266907	+	0.462297i	−0.701154	+	0.713010i	$0.747332\pi$
$110$		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
$115$	−7.58392	−	4.37858i	−0.707204	−	0.408305i
$116$		0			0
$117$	0.0802585	+	9.49455i	0.00741990	+	0.877772i
$118$		0			0
$119$	−2.54798	−	0.407431i	−0.233573	−	0.0373492i
$120$		0			0
$121$	0.776398	+	1.34476i	0.0705816	+	0.122251i
$122$		0			0
$123$	10.6109	+	18.2006i	0.956754	+	1.64109i
$124$		0			0
$125$	8.49185			0.759534
$126$		0			0
$127$	18.0255			1.59951			0.799754	−	0.600328i	$-0.204963\pi$
$127$	18.0255			1.59951			0.799754	+	0.600328i	$0.204963\pi$
$128$		0			0
$129$	−18.9703	+	0.0801775i	−1.67024	+	0.00705923i
$130$		0			0
$131$	−5.21967	−	9.04074i	−0.456045	−	0.789893i	0.542703	−	0.839925i	$-0.317401\pi$
$131$	−5.21967	−	9.04074i	−0.456045	−	0.789893i	−0.998748	+	0.0500320i	$0.984068\pi$
$132$		0			0
$133$	6.02688	−	2.30326i	0.522597	−	0.199718i
$134$		0			0
$135$	6.88519	+	11.5838i	0.592583	+	0.996973i
$136$		0			0
$137$	−3.33412	−	1.92496i	−0.284853	−	0.164460i	0.350765	−	0.936463i	$-0.385922\pi$
$137$	−3.33412	−	1.92496i	−0.284853	−	0.164460i	−0.635619	+	0.772003i	$0.719255\pi$
$138$		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
$147$	11.5357	+	3.73207i	0.951446	+	0.307816i
$148$		0			0
$149$	8.22975	−	4.75145i	0.674207	−	0.389254i	−0.123462	−	0.992349i	$-0.539400\pi$
$149$	8.22975	−	4.75145i	0.674207	−	0.389254i	0.797669	+	0.603096i	$0.206066\pi$
$150$		0			0
$151$	−10.6690	+	18.4793i	−0.868232	+	1.50382i	−0.00442944	+	0.999990i	$0.501410\pi$
$151$	−10.6690	+	18.4793i	−0.868232	+	1.50382i	−0.863802	+	0.503831i	$0.831923\pi$
$152$		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
$157$		−	2.43102i		−	0.194016i	−0.995284	−	0.0970082i	$-0.969073\pi$
$157$		−	2.43102i		−	0.194016i	0.995284	−	0.0970082i	$-0.0309273\pi$
$158$		0			0
$159$	−0.0660522	−	15.6282i	−0.00523828	−	1.23940i
$160$		0			0
$161$	1.41067	−	8.82197i	0.111176	−	0.695269i
$162$		0			0
$163$	−8.31072	+	14.3946i	−0.650946	+	1.12747i	0.331948	+	0.943298i	$0.392294\pi$
$163$	−8.31072	+	14.3946i	−0.650946	+	1.12747i	−0.982894	+	0.184174i	$0.941039\pi$
$164$		0			0
$165$	13.8159	+	7.89896i	1.07557	+	0.614933i
$166$		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
$171$	0.0618397	+	7.31562i	0.00472900	+	0.559440i
$172$		0			0
$173$	−10.1812			−0.774066			−0.387033	−	0.922066i	$-0.626500\pi$
$173$	−10.1812			−0.774066			−0.387033	+	0.922066i	$0.626500\pi$
$174$		0			0
$175$	−1.62977	−	4.26456i	−0.123199	−	0.322371i
$176$		0			0
$177$	−0.377789	+	0.660784i	−0.0283964	+	0.0496676i
$178$		0			0
$179$	−0.589482	+	0.340338i	−0.0440600	+	0.0254380i	−0.521868	−	0.853026i	$-0.674765\pi$
$179$	−0.589482	+	0.340338i	−0.0440600	+	0.0254380i	0.477808	+	0.878464i	$0.341431\pi$
$180$		0			0
$181$			19.1298i			1.42191i	0.703239	+	0.710954i	$0.251737\pi$
$181$			19.1298i			1.42191i	−0.703239	+	0.710954i	$0.748263\pi$
$182$		0			0
$183$	−5.92486	−	3.38741i	−0.437978	−	0.250405i
$184$		0			0
$185$	−18.0148			−1.32447
$186$		0			0
$187$		−	3.45541i		−	0.252684i
$188$		0			0
$189$	−8.53155	+	10.7802i	−0.620579	+	0.784144i
$190$		0			0
$191$			21.1511i			1.53044i	0.643768	+	0.765221i	$0.277370\pi$
$191$			21.1511i			1.53044i	−0.643768	+	0.765221i	$0.722630\pi$
$192$		0			0
$193$	12.8284			0.923410			0.461705	−	0.887033i	$-0.347238\pi$
$193$	12.8284			0.923410			0.461705	+	0.887033i	$0.347238\pi$
$194$		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	$-0.754493\pi$
$199$	−6.65637	+	3.84306i	−0.471858	+	0.272427i	0.245159	+	0.969483i	$0.421160\pi$
$200$		0			0
$201$	3.13887	−	5.49013i	0.221399	−	0.387244i
$202$		0			0
$203$	−0.129108	+	0.807412i	−0.00906162	+	0.0566692i
$204$		0			0
$205$	31.5444			2.20316
$206$		0			0
$207$	8.81556	+	4.99079i	0.612724	+	0.346884i
$208$		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	$0.361248\pi$
$211$	−8.33679	+	14.4397i	−0.573928	+	0.994073i	−0.996157	+	0.0875838i	$0.972085\pi$
$212$		0			0
$213$	7.89498	+	4.51378i	0.540955	+	0.309279i
$214$		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
$219$	−0.118994	−	28.1543i	−0.00804084	−	1.90249i
$220$		0			0
$221$		−	3.08672i		−	0.207635i
$222$		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
$227$	−5.99271	+	10.3797i	−0.397750	+	0.688924i	−0.993448	−	0.114285i	$-0.963542\pi$
$227$	−5.99271	+	10.3797i	−0.397750	+	0.688924i	0.595698	+	0.803209i	$0.296876\pi$
$228$		0			0
$229$	−2.25955	+	1.30455i	−0.149316	+	0.0862074i	−0.572796	−	0.819698i	$-0.694141\pi$
$229$	−2.25955	+	1.30455i	−0.149316	+	0.0862074i	0.423481	+	0.905905i	$0.360808\pi$
$230$		0			0
$231$	−2.49585	+	16.0430i	−0.164215	+	1.05556i
$232$		0			0
$233$	−3.13306	−	1.80887i	−0.205253	−	0.118503i	0.393850	−	0.919175i	$-0.371143\pi$
$233$	−3.13306	−	1.80887i	−0.205253	−	0.118503i	−0.599103	+	0.800672i	$0.704476\pi$
$234$		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	0.0248967	−	0.999690i	$-0.492074\pi$
$239$	−12.8069	−	7.39409i	−0.828412	−	0.478284i	−0.853309	+	0.521406i	$0.825408\pi$
$240$		0			0
$241$	−5.57890	−	3.22098i	−0.359368	−	0.207481i	0.309435	−	0.950921i	$-0.399860\pi$
$241$	−5.57890	−	3.22098i	−0.359368	−	0.207481i	−0.668804	+	0.743439i	$0.733193\pi$
$242$		0			0
$243$	−8.07775	−	13.3323i	−0.518188	−	0.855267i
$244$		0			0
$245$	13.5267	−	12.1071i	0.864187	−	0.773492i
$246$		0			0
$247$	3.85909	+	6.68413i	0.245548	+	0.425301i
$248$		0			0
$249$	25.0747	−	0.105978i	1.58904	−	0.00671606i
$250$		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
$255$	−2.20642	−	3.78459i	−0.138171	−	0.237000i
$256$		0			0
$257$	10.5883	+	18.3395i	0.660482	+	1.14399i	0.980489	+	0.196573i	$0.0629813\pi$
$257$	10.5883	+	18.3395i	0.660482	+	1.14399i	−0.320007	+	0.947415i	$0.603685\pi$
$258$		0			0
$259$	−6.56089	−	17.1677i	−0.407674	−	1.06675i
$260$		0			0
$261$	−0.806825	−	0.456771i	−0.0499412	−	0.0282734i
$262$		0			0
$263$	14.8592	+	8.57897i	0.916258	+	0.529002i	0.882439	−	0.470426i	$-0.155900\pi$
$263$	14.8592	+	8.57897i	0.916258	+	0.529002i	0.0338189	+	0.999428i	$0.489233\pi$
$264$		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	−0.980912	−	0.194453i	$-0.937707\pi$
$269$	−10.8061	−	18.7166i	−0.658857	−	1.14117i	0.322055	−	0.946721i	$-0.395627\pi$
$270$		0			0
$271$	−21.8475	−	12.6137i	−1.32714	−	0.766227i	−0.342287	−	0.939595i	$-0.611202\pi$
$271$	−21.8475	−	12.6137i	−1.32714	−	0.766227i	−0.984857	+	0.173368i	$0.944535\pi$
$272$		0			0
$273$	−2.22955	+	14.3313i	−0.134939	+	0.867370i
$274$		0			0
$275$	5.29454	−	3.05680i	0.319273	−	0.184332i
$276$		0			0
$277$	−11.2256	+	19.4434i	−0.674482	+	1.16824i	0.302137	+	0.953264i	$0.402300\pi$
$277$	−11.2256	+	19.4434i	−0.674482	+	1.16824i	−0.976620	+	0.214973i	$0.931033\pi$
$278$		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
$283$			21.7299i			1.29171i	0.763460	+	0.645855i	$0.223499\pi$
$283$			21.7299i			1.29171i	−0.763460	+	0.645855i	$0.776501\pi$
$284$		0			0
$285$	9.50945	+	5.43682i	0.563291	+	0.322050i
$286$		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
$291$	−0.105496	−	24.9607i	−0.00618427	−	1.46322i
$292$		0			0
$293$	5.38110	−	9.32035i	0.314367	−	0.544500i	−0.664935	−	0.746901i	$-0.731541\pi$
$293$	5.38110	−	9.32035i	0.314367	−	0.544500i	0.979303	+	0.202400i	$0.0648743\pi$
$294$		0			0
$295$	0.569833	+	0.986980i	0.0331770	+	0.0574642i
$296$		0			0
$297$	−16.0589	−	9.00208i	−0.931832	−	0.522353i
$298$		0			0
$299$	10.6873			0.618063
$300$		0			0
$301$	−28.6143	−	4.57554i	−1.64930	−	0.263730i
$302$		0			0
$303$	−7.52775	−	12.9121i	−0.432458	−	0.741781i
$304$		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
$311$	4.18531			0.237327			0.118664	−	0.992935i	$-0.462139\pi$
$311$	4.18531			0.237327			0.118664	+	0.992935i	$0.462139\pi$
$312$		0			0
$313$		−	22.0395i		−	1.24574i	−0.782324	−	0.622872i	$-0.785966\pi$
$313$		−	22.0395i		−	1.24574i	0.782324	−	0.622872i	$-0.214034\pi$
$314$		0			0
$315$	7.51050	+	19.1651i	0.423169	+	1.07983i
$316$		0			0
$317$		−	9.71612i		−	0.545711i	−0.962055	−	0.272856i	$-0.912032\pi$
$317$		−	9.71612i		−	0.545711i	0.962055	−	0.272856i	$-0.0879682\pi$
$318$		0			0
$319$	−1.09496			−0.0613061
$320$		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
$327$	−9.65296	+	0.0407980i	−0.533810	+	0.00225613i
$328$		0			0
$329$	−4.78215	+	5.88761i	−0.263649	+	0.324594i
$330$		0			0
$331$	−27.7176			−1.52350			−0.761749	−	0.647872i	$-0.775659\pi$
$331$	−27.7176			−1.52350			−0.761749	+	0.647872i	$0.775659\pi$
$332$		0			0
$333$	20.8387	−	0.176152i	1.14195	−	0.00965305i
$334$		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
$339$	24.5598	−	14.3183i	1.33390	−	0.777666i
$340$		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
$345$	13.1036	−	7.63937i	0.705472	−	0.411290i
$346$		0			0
$347$			16.7223i			0.897700i	0.893607	+	0.448850i	$0.148166\pi$
$347$			16.7223i			0.897700i	−0.893607	+	0.448850i	$0.851834\pi$
$348$		0			0
$349$	13.9900	−	8.07714i	0.748869	−	0.432359i	−0.0764164	−	0.997076i	$-0.524348\pi$
$349$	13.9900	−	8.07714i	0.748869	−	0.432359i	0.825285	+	0.564717i	$0.191015\pi$
$350$		0			0
$351$	−14.3455	−	8.04158i	−0.765704	−	0.429228i
$352$		0			0
$353$	7.82831	−	13.5590i	0.416659	−	0.721674i	−0.578942	−	0.815369i	$-0.696534\pi$
$353$	7.82831	−	13.5590i	0.416659	−	0.721674i	0.995601	+	0.0936943i	$0.0298676\pi$
$354$		0			0
$355$	11.7923	−	6.80830i	0.625872	−	0.361347i
$356$		0			0
$357$	2.80307	−	3.48100i	0.148354	−	0.184234i
$358$		0			0
$359$	19.1396	+	11.0502i	1.01015	+	0.583209i	0.911235	−	0.411887i	$-0.135130\pi$
$359$	19.1396	+	11.0502i	1.01015	+	0.583209i	0.0989127	+	0.995096i	$0.468464\pi$
$360$		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
$367$	11.3893	+	6.57564i	0.594519	+	0.343246i	0.766882	−	0.641788i	$-0.221807\pi$
$367$	11.3893	+	6.57564i	0.594519	+	0.343246i	−0.172363	+	0.985033i	$0.555140\pi$
$368$		0			0
$369$	−36.4892	+	0.308447i	−1.89955	+	0.0160571i
$370$		0			0
$371$	3.76944	−	23.5732i	0.195700	−	1.22386i
$372$		0			0
$373$	2.21915	+	3.84367i	0.114903	+	0.199018i	0.917741	−	0.397179i	$-0.130011\pi$
$373$	2.21915	+	3.84367i	0.114903	+	0.199018i	−0.802838	+	0.596197i	$0.796678\pi$
$374$		0			0
$375$	−7.30026	+	12.7687i	−0.376984	+	0.659375i
$376$		0			0
$377$	−0.978132			−0.0503763
$378$		0			0
$379$	−14.8875			−0.764718			−0.382359	−	0.924014i	$-0.624888\pi$
$379$	−14.8875			−0.764718			−0.382359	+	0.924014i	$0.624888\pi$
$380$		0			0
$381$	−15.4962	+	27.1040i	−0.793892	+	1.38858i
$382$		0			0
$383$	−2.81901	−	4.88267i	−0.144045	−	0.249493i	0.784971	−	0.619532i	$-0.212678\pi$
$383$	−2.81901	−	4.88267i	−0.144045	−	0.249493i	−0.929016	+	0.370039i	$0.879344\pi$
$384$		0			0
$385$	18.8696	+	15.3267i	0.961686	+	0.781121i
$386$		0			0
$387$	16.1878	−	28.5935i	0.822871	−	1.45349i
$388$		0			0
$389$	33.3523	+	19.2560i	1.69103	+	0.976317i	0.953688	+	0.300797i	$0.0972528\pi$
$389$	33.3523	+	19.2560i	1.69103	+	0.976317i	0.737342	+	0.675519i	$0.236081\pi$
$390$		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	0.561609	−	0.827402i	$-0.310182\pi$
$397$	2.50780	+	1.44788i	0.125863	+	0.0726669i	−0.435747	+	0.900069i	$0.643516\pi$
$398$		0			0
$399$	−1.71789	+	11.0424i	−0.0860019	+	0.552810i
$400$		0			0
$401$	−22.2857	+	12.8666i	−1.11289	+	0.642530i	−0.939577	−	0.342337i	$-0.888782\pi$
$401$	−22.2857	+	12.8666i	−1.11289	+	0.642530i	−0.173316	+	0.984866i	$0.555448\pi$
$402$		0			0
$403$	−7.96637	+	13.7981i	−0.396833	+	0.687335i
$404$		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
$409$			28.8575i			1.42691i	0.700699	+	0.713457i	$0.252871\pi$
$409$			28.8575i			1.42691i	−0.700699	+	0.713457i	$0.747129\pi$
$410$		0			0
$411$	5.76073	−	3.35850i	0.284156	−	0.165663i
$412$		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
$417$	−32.4195	+	18.9006i	−1.58759	+	0.925565i
$418$		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
$423$	−4.36312	−	7.41175i	−0.212142	−	0.360372i
$424$		0			0
$425$	−1.68289			−0.0816323
$426$		0			0
$427$	−8.09211	−	6.57274i	−0.391605	−	0.318077i
$428$		0			0
$429$	−19.4221	+	0.0820870i	−0.937707	+	0.00396320i
$430$		0			0
$431$	13.9975	−	8.08147i	0.674236	−	0.389271i	−0.123444	−	0.992352i	$-0.539394\pi$
$431$	13.9975	−	8.08147i	0.674236	−	0.389271i	0.797680	+	0.603081i	$0.206060\pi$
$432$		0			0
$433$		−	5.27197i		−	0.253355i	−0.991944	−	0.126677i	$-0.959569\pi$
$433$		−	5.27197i		−	0.253355i	0.991944	−	0.126677i	$-0.0404313\pi$
$434$		0			0
$435$	−1.19927	+	0.699176i	−0.0575008	+	0.0335229i
$436$		0			0
$437$	8.23464			0.393916
$438$		0			0
$439$		−	10.5108i		−	0.501654i	−0.968032	−	0.250827i	$-0.919298\pi$
$439$		−	10.5108i		−	0.501654i	0.968032	−	0.250827i	$-0.0807025\pi$
$440$		0			0
$441$	−15.5287	+	14.1372i	−0.739461	+	0.673200i
$442$		0			0
$443$			5.95601i			0.282978i	0.989940	+	0.141489i	$0.0451891\pi$
$443$			5.95601i			0.282978i	−0.989940	+	0.141489i	$0.954811\pi$
$444$		0			0
$445$	−11.9866			−0.568219
$446$		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
$453$	−18.6144	−	31.9286i	−0.874580	−	1.50014i
$454$		0			0
$455$	16.8563	+	13.6914i	0.790236	+	0.641862i
$456$		0			0
$457$	29.7493			1.39162			0.695808	−	0.718228i	$-0.255047\pi$
$457$	29.7493			1.39162			0.695808	+	0.718228i	$0.255047\pi$
$458$		0			0
$459$	2.58929	+	4.35628i	0.120858	+	0.203334i
$460$		0			0
$461$	14.9738	+	25.9353i	0.697398	+	1.20793i	0.969366	+	0.245622i	$0.0789921\pi$
$461$	14.9738	+	25.9353i	0.697398	+	1.20793i	−0.271968	+	0.962306i	$0.587675\pi$
$462$		0			0
$463$	−7.57406	+	13.1187i	−0.351997	+	0.609676i	−0.986599	−	0.163163i	$-0.947830\pi$
$463$	−7.57406	+	13.1187i	−0.351997	+	0.609676i	0.634603	+	0.772839i	$0.281164\pi$
$464$		0			0
$465$	0.0955698	+	22.6122i	0.00443194	+	1.04861i
$466$		0			0
$467$	5.85158	−	10.1352i	0.270779	−	0.469002i	−0.698283	−	0.715822i	$-0.746052\pi$
$467$	5.85158	−	10.1352i	0.270779	−	0.469002i	0.969061	+	0.246820i	$0.0793855\pi$
$468$		0			0
$469$	6.09048	−	7.49837i	0.281232	−	0.346243i
$470$		0			0
$471$	3.65539	+	2.08989i	0.168432	+	0.0962972i
$472$		0			0
$473$		−	38.8050i		−	1.78425i
$474$		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
$479$	−6.07088	+	10.5151i	−0.277385	+	0.480446i	−0.970734	−	0.240156i	$-0.922801\pi$
$479$	−6.07088	+	10.5151i	−0.277385	+	0.480446i	0.693349	+	0.720602i	$0.256135\pi$
$480$		0			0
$481$	19.0399	−	10.9927i	0.868144	−	0.501223i
$482$		0			0
$483$	12.0524	+	9.70520i	0.548404	+	0.441602i
$484$		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	$-0.0906426\pi$
$487$	5.22070	+	9.04251i	0.236572	+	0.409755i	−0.723156	+	0.690685i	$0.757309\pi$
$488$		0			0
$489$	−14.4998	−	24.8711i	−0.655705	−	1.12471i
$490$		0			0
$491$	−20.9972	−	12.1227i	−0.947589	−	0.547091i	−0.0552576	−	0.998472i	$-0.517598\pi$
$491$	−20.9972	−	12.1227i	−0.947589	−	0.547091i	−0.892331	+	0.451382i	$0.850931\pi$
$492$		0			0
$493$	0.261029	+	0.150705i	0.0117561	+	0.00678741i
$494$		0			0
$495$	−23.7545	+	13.9837i	−1.06769	+	0.628521i
$496$		0			0
$497$	10.7829	+	8.75829i	0.483678	+	0.392863i
$498$		0			0
$499$	−0.174119	−	0.301584i	−0.00779466	−	0.0135007i	0.862102	−	0.506735i	$-0.169148\pi$
$499$	−0.174119	−	0.301584i	−0.00779466	−	0.0135007i	−0.869896	+	0.493234i	$0.835814\pi$
$500$		0			0
$501$	18.5003	+	31.7331i	0.826535	+	1.41773i
$502$		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
$507$	5.16667	−	0.0218368i	0.229460	−	0.000969806i
$508$		0			0
$509$	−6.85232	−	11.8686i	−0.303724	−	0.526065i	0.673253	−	0.739413i	$-0.264897\pi$
$509$	−6.85232	−	11.8686i	−0.303724	−	0.526065i	−0.976976	+	0.213347i	$0.931563\pi$
$510$		0			0
$511$	6.79069	−	42.4673i	0.300402	−	1.87864i
$512$		0			0
$513$	−11.0533	−	6.19610i	−0.488014	−	0.273564i
$514$		0			0
$515$	13.6941	+	7.90630i	0.603434	+	0.348393i
$516$		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	$-0.0416629\pi$
$521$	8.73516	+	15.1297i	0.382694	+	0.662846i	−0.608752	+	0.793361i	$0.708330\pi$
$522$		0			0
$523$	23.3238	+	13.4660i	1.01988	+	0.588827i	0.914069	−	0.405559i	$-0.132923\pi$
$523$	23.3238	+	13.4660i	1.01988	+	0.588827i	0.105810	+	0.994386i	$0.466257\pi$
$524$		0			0
$525$	7.81347	+	1.21556i	0.341008	+	0.0530514i
$526$		0			0
$527$	4.25188	−	2.45482i	0.185215	−	0.106934i
$528$		0			0
$529$	−5.79877	+	10.0438i	−0.252120	+	0.436685i
$530$		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
$535$		−	41.5768i		−	1.79752i
$536$		0			0
$537$	−0.00498282	−	1.17895i	−0.000215025	−	0.0508756i
$538$		0			0
$539$	−7.73379	+	23.5643i	−0.333118	+	1.01499i
$540$		0			0
$541$	−7.43375	+	12.8756i	−0.319602	+	0.553567i	−0.980405	−	0.196993i	$-0.936882\pi$
$541$	−7.43375	+	12.8756i	−0.319602	+	0.553567i	0.660803	+	0.750559i	$0.270216\pi$
$542$		0			0
$543$	−28.7645	−	16.4455i	−1.23440	−	0.705743i
$544$		0			0
$545$	−7.22666	+	12.5169i	−0.309556	+	0.536167i
$546$		0			0
$547$	4.17953	+	7.23915i	0.178704	+	0.309524i	0.941437	−	0.337190i	$-0.109476\pi$
$547$	4.17953	+	7.23915i	0.178704	+	0.309524i	−0.762733	+	0.646713i	$0.776143\pi$
$548$		0			0
$549$	10.1869	−	5.99681i	0.434768	−	0.255938i
$550$		0			0
$551$	−0.753658			−0.0321069
$552$		0			0
$553$	11.6651	−	14.3617i	0.496052	−	0.610720i
$554$		0			0
$555$	15.4869	−	27.0878i	0.657382	−	1.14981i
$556$		0			0
$557$	0.617917	−	0.356754i	0.0261820	−	0.0151162i	−0.486852	−	0.873485i	$-0.661855\pi$
$557$	0.617917	−	0.356754i	0.0261820	−	0.0151162i	0.513034	+	0.858368i	$0.328522\pi$
$558$		0			0
$559$		−	34.6646i		−	1.46616i
$560$		0			0
$561$	5.19571	+	2.97054i	0.219363	+	0.125416i
$562$		0			0
$563$	−27.1877			−1.14582			−0.572912	−	0.819617i	$-0.694187\pi$
$563$	−27.1877			−1.14582			−0.572912	+	0.819617i	$0.694187\pi$
$564$		0			0
$565$		−	42.5659i		−	1.79076i
$566$		0			0
$567$	−8.87522	−	22.0959i	−0.372724	−	0.927942i
$568$		0			0
$569$		−	1.75321i		−	0.0734985i	−0.999325	−	0.0367492i	$-0.988300\pi$
$569$		−	1.75321i		−	0.0734985i	0.999325	−	0.0367492i	$-0.0117003\pi$
$570$		0			0
$571$	−0.457634			−0.0191514			−0.00957570	−	0.999954i	$-0.503048\pi$
$571$	−0.457634			−0.0191514			−0.00957570	+	0.999954i	$0.503048\pi$
$572$		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	−0.0254193	−	0.999677i	$-0.508092\pi$
$577$	19.8800	−	11.4777i	0.827617	−	0.477825i	0.853036	+	0.521852i	$0.174759\pi$
$578$		0			0
$579$	−11.0283	+	19.2894i	−0.458321	+	0.801641i
$580$		0			0
$581$	37.8221	+	6.04790i	1.56912	+	0.250909i
$582$		0			0
$583$	31.9685			1.32400
$584$		0			0
$585$	−21.2199	+	12.4917i	−0.877337	+	0.516467i
$586$		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
$591$	−33.5094	−	19.1583i	−1.37839	−	0.788066i
$592$		0			0
$593$	−1.35121	+	2.34037i	−0.0554876	+	0.0961074i	−0.892435	−	0.451176i	$-0.851005\pi$
$593$	−1.35121	+	2.34037i	−0.0554876	+	0.0961074i	0.836947	+	0.547283i	$0.184338\pi$
$594$		0			0
$595$	−2.38886	−	6.25086i	−0.0979337	−	0.256260i
$596$		0			0
$597$	−0.0562655	−	13.3126i	−0.00230279	−	0.544850i
$598$		0			0
$599$		−	11.9966i		−	0.490168i	−0.969502	−	0.245084i	$-0.921184\pi$
$599$		−	11.9966i		−	0.490168i	0.969502	−	0.245084i	$-0.0788156\pi$
$600$		0			0
$601$	−26.7530	+	15.4459i	−1.09128	+	0.630050i	−0.933917	−	0.357491i	$-0.883632\pi$
$601$	−26.7530	+	15.4459i	−1.09128	+	0.630050i	−0.157363	+	0.987541i	$0.550299\pi$
$602$		0			0
$603$	5.55681	+	9.43950i	0.226291	+	0.384406i
$604$		0			0
$605$	−2.01348	+	3.48746i	−0.0818598	+	0.141785i
$606$		0			0
$607$	−5.95361	+	3.43732i	−0.241649	+	0.139516i	−0.615935	−	0.787797i	$-0.711221\pi$
$607$	−5.95361	+	3.43732i	−0.241649	+	0.139516i	0.374285	+	0.927314i	$0.377888\pi$
$608$		0			0
$609$	−1.10307	−	0.888247i	−0.0446987	−	0.0359936i
$610$		0			0
$611$	−7.85794	−	4.53678i	−0.317898	−	0.183539i
$612$		0			0
$613$	−16.6455	−	28.8308i	−0.672304	−	1.16447i	−0.977249	−	0.212095i	$-0.931971\pi$
$613$	−16.6455	−	28.8308i	−0.672304	−	1.16447i	0.304945	−	0.952370i	$-0.401362\pi$
$614$		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
$619$	16.7876	+	9.69230i	0.674749	+	0.389567i	0.797874	−	0.602825i	$-0.205958\pi$
$619$	16.7876	+	9.69230i	0.674749	+	0.389567i	−0.123125	+	0.992391i	$0.539291\pi$
$620$		0			0
$621$	−15.0829	+	8.96502i	−0.605257	+	0.359754i
$622$		0			0
$623$	−4.36546	−	11.4230i	−0.174898	−	0.457652i
$624$		0			0
$625$	15.3251	+	26.5439i	0.613005	+	1.06175i
$626$		0			0
$627$	−14.9649	+	0.0632486i	−0.597639	+	0.00252591i
$628$		0			0
$629$	−6.77476			−0.270127
$630$		0			0
$631$	27.3629			1.08930			0.544649	−	0.838664i	$-0.316663\pi$
$631$	27.3629			1.08930			0.544649	+	0.838664i	$0.316663\pi$
$632$		0			0
$633$	−14.5453	−	24.9491i	−0.578125	−	0.991639i
$634$		0			0
$635$	23.3734	+	40.4839i	0.927546	+	1.60656i
$636$		0			0
$637$	−6.90861	+	21.0500i	−0.273729	+	0.834033i
$638$		0			0
$639$	−13.5743	+	7.99085i	−0.536990	+	0.316113i
$640$		0			0
$641$	−30.0686	−	17.3601i	−1.18764	−	0.685683i	−0.229868	−	0.973222i	$-0.573830\pi$
$641$	−30.0686	−	17.3601i	−1.18764	−	0.685683i	−0.957769	+	0.287539i	$0.907163\pi$
$642$		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	0.708360	−	0.705851i	$-0.249435\pi$
$647$	−6.53976	−	11.3272i	−0.257105	−	0.445318i	−0.965465	+	0.260533i	$0.916102\pi$
$648$		0			0
$649$	−1.34839	−	0.778492i	−0.0529288	−	0.0305585i
$650$		0			0
$651$	−21.5141	+	8.32631i	−0.843204	+	0.326334i
$652$		0			0
$653$	−5.40555	+	3.12090i	−0.211535	+	0.122130i	−0.602025	−	0.798477i	$-0.705639\pi$
$653$	−5.40555	+	3.12090i	−0.211535	+	0.122130i	0.390489	+	0.920607i	$0.372306\pi$
$654$		0			0
$655$	13.5365	−	23.4459i	0.528916	−	0.916109i
$656$		0			0
$657$	42.4364	+	24.0247i	1.65560	+	0.937293i
$658$		0			0
$659$	−1.79139	+	1.03426i	−0.0697827	+	0.0402891i	−0.534485	−	0.845178i	$-0.679495\pi$
$659$	−1.79139	+	1.03426i	−0.0697827	+	0.0402891i	0.464703	+	0.885467i	$0.346161\pi$
$660$		0			0
$661$		−	15.6238i		−	0.607695i	−0.952721	−	0.303848i	$-0.901729\pi$
$661$		−	15.6238i		−	0.607695i	0.952721	−	0.303848i	$-0.0982714\pi$
$662$		0			0
$663$	4.64134	+	2.65359i	0.180255	+	0.103057i
$664$		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
$669$	−0.0376483	−	8.90772i	−0.00145557	−	0.344392i
$670$		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
$675$	−4.38430	+	7.82119i	−0.168752	+	0.301038i
$676$		0			0
$677$	28.6876			1.10256			0.551278	−	0.834322i	$-0.314141\pi$
$677$	28.6876			1.10256			0.551278	+	0.834322i	$0.314141\pi$
$678$		0			0
$679$	6.02040	−	37.6501i	0.231042	−	1.44488i
$680$		0			0
$681$	−10.4556	−	17.9341i	−0.400658	−	0.687236i
$682$		0			0
$683$	7.48345	−	4.32057i	0.286346	−	0.165322i	−0.349947	−	0.936770i	$-0.613800\pi$
$683$	7.48345	−	4.32057i	0.286346	−	0.165322i	0.636293	+	0.771448i	$0.280467\pi$
$684$		0			0
$685$		−	9.98423i		−	0.381478i
$686$		0			0
$687$	−0.0190997	−	4.51907i	−0.000728701	−	0.172413i
$688$		0			0
$689$	28.5575			1.08796
$690$		0			0
$691$		−	12.2390i		−	0.465594i	−0.972525	−	0.232797i	$-0.925212\pi$
$691$		−	12.2390i		−	0.465594i	0.972525	−	0.232797i	$-0.0747878\pi$
$692$		0			0
$693$	−21.9774	−	17.5447i	−0.834854	−	0.666469i
$694$		0			0
$695$			56.1881i			2.13134i
$696$		0			0
$697$	11.8628			0.449336
$698$		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
$705$	−12.8774	+	0.0544262i	−0.484993	+	0.00204981i
$706$		0			0
$707$	−8.15021	−	21.3264i	−0.306520	−	0.802063i
$708$		0			0
$709$	−12.0820			−0.453750			−0.226875	−	0.973924i	$-0.572851\pi$
$709$	−12.0820			−0.453750			−0.226875	+	0.973924i	$0.572851\pi$
$710$		0			0
$711$	10.6430	+	18.0795i	0.399143	+	0.678035i
$712$		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
$717$	22.1279	−	12.9006i	0.826383	−	0.481781i
$718$		0			0
$719$	−6.27436	+	10.8675i	−0.233994	+	0.405290i	−0.958980	−	0.283474i	$-0.908513\pi$
$719$	−6.27436	+	10.8675i	−0.233994	+	0.405290i	0.724986	+	0.688764i	$0.241846\pi$
$720$		0			0
$721$	−2.54721	+	15.9296i	−0.0948630	+	0.593250i
$722$		0			0
$723$	9.63927	−	5.61969i	0.358488	−	0.208998i
$724$		0			0
$725$			0.533281i			0.0198056i
$726$		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
$731$	−5.34092	+	9.25075i	−0.197541	+	0.342151i
$732$		0			0
$733$	30.6628	−	17.7032i	1.13256	−	0.653882i	0.187981	−	0.982173i	$-0.439806\pi$
$733$	30.6628	−	17.7032i	1.13256	−	0.653882i	0.944577	+	0.328290i	$0.106472\pi$
$734$		0			0
$735$	6.57617	+	30.7475i	0.242566	+	1.13414i
$736$		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	$-0.301028\pi$
$739$	−11.1371	−	19.2900i	−0.409684	−	0.709593i	−0.994854	+	0.101317i	$0.967694\pi$
$740$		0			0
$741$	−13.3681	+	0.0565002i	−0.491091	+	0.00207559i
$742$		0			0
$743$	8.68932	+	5.01678i	0.318780	+	0.184048i	0.650849	−	0.759207i	$-0.274413\pi$
$743$	8.68932	+	5.01678i	0.318780	+	0.184048i	−0.332069	+	0.943255i	$0.607747\pi$
$744$		0			0
$745$	21.3428	+	12.3222i	0.781938	+	0.451452i
$746$		0			0
$747$	−21.3968	+	37.7946i	−0.782868	+	1.38283i
$748$		0			0
$749$	39.6218	−	15.1421i	1.44775	−	0.553279i
$750$		0			0
$751$	16.7771	+	29.0587i	0.612203	+	1.06037i	0.990868	+	0.134833i	$0.0430499\pi$
$751$	16.7771	+	29.0587i	0.612203	+	1.06037i	−0.378665	+	0.925534i	$0.623617\pi$
$752$		0			0
$753$	−5.33870	+	9.33783i	−0.194553	+	0.340289i
$754$		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
$759$	−10.2850	+	17.9893i	−0.373323	+	0.652972i
$760$		0			0
$761$	11.4846	+	19.8919i	0.416315	+	0.721079i	0.995566	−	0.0940705i	$-0.0299879\pi$
$761$	11.4846	+	19.8919i	0.416315	+	0.721079i	−0.579250	+	0.815150i	$0.696655\pi$
$762$		0			0
$763$	−14.5603	−	2.32825i	−0.527118	−	0.0842882i
$764$		0			0
$765$	7.58750	−	0.0641379i	0.274327	−	0.00231891i
$766$		0			0
$767$	−1.20452	−	0.695429i	−0.0434926	−	0.0251105i
$768$		0			0
$769$	−14.3775	−	8.30086i	−0.518466	−	0.299337i	0.217841	−	0.975984i	$-0.430099\pi$
$769$	−14.3775	−	8.30086i	−0.518466	−	0.299337i	−0.736307	+	0.676648i	$0.763432\pi$
$770$		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	$-0.157470\pi$
$773$	0.803138	+	1.39107i	0.0288868	+	0.0500335i	−0.851221	+	0.524808i	$0.824137\pi$
$774$		0			0
$775$	7.52280	+	4.34329i	0.270227	+	0.156016i
$776$		0			0
$777$	31.4544	+	4.89343i	1.12842	+	0.175551i
$778$		0			0
$779$	−25.6883	+	14.8311i	−0.920378	+	0.531380i
$780$		0			0
$781$	−9.30133	+	16.1104i	−0.332828	+	0.576475i
$782$		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
$787$		−	15.9080i		−	0.567060i	−0.958963	−	0.283530i	$-0.908494\pi$
$787$		−	15.9080i		−	0.567060i	0.958963	−	0.283530i	$-0.0915055\pi$
$788$		0			0
$789$	−25.6739	+	14.9679i	−0.914014	+	0.532870i
$790$		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
$795$	35.0140	−	20.4132i	1.24182	−	0.723980i
$796$		0			0
$797$	10.1844	−	17.6399i	0.360749	−	0.624836i	−0.627335	−	0.778749i	$-0.715854\pi$
$797$	10.1844	−	17.6399i	0.360749	−	0.624836i	0.988084	+	0.153914i	$0.0491878\pi$
$798$		0			0
$799$	1.39800	+	2.42141i	0.0494578	+	0.0856634i
$800$		0			0
$801$	13.8656	−	0.117207i	0.489916	−	0.00414131i
$802$		0			0
$803$	57.5915			2.03236
$804$		0			0
$805$	21.6426	−	8.27106i	0.762803	−	0.291516i
$806$		0			0
$807$	37.4330	−	0.158210i	1.31770	−	0.00556924i
$808$		0			0
$809$	35.7396	−	20.6343i	1.25654	−	0.725462i	0.284137	−	0.958784i	$-0.408293\pi$
$809$	35.7396	−	20.6343i	1.25654	−	0.725462i	0.972400	+	0.233322i	$0.0749595\pi$
$810$		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
$815$	−43.1055			−1.50992
$816$		0			0
$817$		−	26.7093i		−	0.934441i
$818$		0			0
$819$	−19.6325	−	15.6728i	−0.686015	−	0.547651i
$820$		0			0
$821$			32.4939i			1.13404i	0.823703	+	0.567022i	$0.191905\pi$
$821$			32.4939i			1.13404i	−0.823703	+	0.567022i	$0.808095\pi$
$822$		0			0
$823$	−55.7913			−1.94476			−0.972381	−	0.233397i	$-0.925016\pi$
$823$	−55.7913			−1.94476			−0.972381	+	0.233397i	$0.925016\pi$
$824$		0			0
$825$	0.0447541	+	10.5890i	0.00155814	+	0.368661i
$826$		0			0
$827$		−	18.2989i		−	0.636314i	−0.948038	−	0.318157i	$-0.896936\pi$
$827$		−	18.2989i		−	0.636314i	0.948038	−	0.318157i	$-0.103064\pi$
$828$		0			0
$829$	12.6483	−	7.30247i	0.439292	−	0.253625i	−0.264005	−	0.964521i	$-0.585044\pi$
$829$	12.6483	−	7.30247i	0.439292	−	0.253625i	0.703297	+	0.710896i	$0.251710\pi$
$830$		0			0
$831$	−19.5855	−	33.5944i	−0.679414	−	1.16538i
$832$		0			0
$833$	5.08693	−	4.55307i	0.176252	−	0.157754i
$834$		0			0
$835$	54.9983			1.90330
$836$		0			0
$837$	−0.331657	−	26.1558i	−0.0114637	−	0.904077i
$838$		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
$843$	0.0876490	+	20.7381i	0.00301879	+	0.714257i
$844$		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
$849$	−32.6741	−	18.6807i	−1.12137	−	0.641121i
$850$		0			0
$851$		−	23.4565i		−	0.804080i
$852$		0			0
$853$	21.2554	−	12.2718i	0.727771	−	0.420179i	−0.0898353	−	0.995957i	$-0.528634\pi$
$853$	21.2554	−	12.2718i	0.727771	−	0.420179i	0.817606	+	0.575778i	$0.195301\pi$
$854$		0			0
$855$	−16.3501	+	9.62493i	−0.559163	+	0.329166i
$856$		0			0
$857$	−5.86511	+	10.1587i	−0.200348	+	0.347014i	−0.948641	−	0.316355i	$-0.897541\pi$
$857$	−5.86511	+	10.1587i	−0.200348	+	0.347014i	0.748292	+	0.663369i	$0.230874\pi$
$858$		0			0
$859$	29.5421	−	17.0561i	1.00796	−	0.581948i	0.0973688	−	0.995248i	$-0.468957\pi$
$859$	29.5421	−	17.0561i	1.00796	−	0.581948i	0.910595	+	0.413300i	$0.135624\pi$
$860$		0			0
$861$	−55.0776	−	8.56855i	−1.87704	−	0.292015i
$862$		0			0
$863$	−20.8863	−	12.0587i	−0.710978	−	0.410483i	0.100445	−	0.994943i	$-0.467973\pi$
$863$	−20.8863	−	12.0587i	−0.710978	−	0.410483i	−0.811423	+	0.584459i	$0.801307\pi$
$864$		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
$871$	10.0078	+	5.77798i	0.339100	+	0.195779i
$872$		0			0
$873$	37.6228	+	21.2995i	1.27334	+	0.720880i
$874$		0			0
$875$	−14.1650	+	17.4394i	−0.478865	+	0.589560i
$876$		0			0
$877$	25.8753	+	44.8173i	0.873747	+	1.51337i	0.858092	+	0.513496i	$0.171650\pi$
$877$	25.8753	+	44.8173i	0.873747	+	1.51337i	0.0156551	+	0.999877i	$0.495017\pi$
$878$		0			0
$879$	9.38849	+	16.1038i	0.316666	+	0.543167i
$880$		0			0
$881$	30.3925			1.02395			0.511975	−	0.859000i	$-0.328914\pi$
$881$	30.3925			1.02395			0.511975	+	0.859000i	$0.328914\pi$
$882$		0			0
$883$	−35.4897			−1.19432			−0.597162	−	0.802121i	$-0.703705\pi$
$883$	−35.4897			−1.19432			−0.597162	+	0.802121i	$0.703705\pi$
$884$		0			0
$885$	−1.97394	+	0.00834282i	−0.0663534	+	0.000280441i
$886$		0			0
$887$	23.2756	+	40.3145i	0.781517	+	1.35363i	0.931058	+	0.364872i	$0.118887\pi$
$887$	23.2756	+	40.3145i	0.781517	+	1.35363i	−0.149540	+	0.988756i	$0.547779\pi$
$888$		0			0
$889$	−30.0679	+	37.0184i	−1.00844	+	1.24156i
$890$		0			0
$891$	27.3414	−	16.4080i	0.915972	−	0.549689i
$892$		0			0
$893$	−6.05460	−	3.49562i	−0.202609	−	0.116977i
$894$		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
$903$	31.4791	−	39.0924i	1.04756	−	1.30091i
$904$		0			0
$905$	−42.9641	+	24.8053i	−1.42817	+	0.824556i
$906$		0			0
$907$	−7.31653	+	12.6726i	−0.242941	+	0.420787i	−0.961551	−	0.274627i	$-0.911446\pi$
$907$	−7.31653	+	12.6726i	−0.242941	+	0.420787i	0.718610	+	0.695414i	$0.244779\pi$
$908$		0			0
$909$	25.8867	−	0.218823i	0.858607	−	0.00725790i
$910$		0			0
$911$	6.67661	−	3.85474i	0.221206	−	0.127713i	−0.385303	−	0.922790i	$-0.625903\pi$
$911$	6.67661	−	3.85474i	0.221206	−	0.127713i	0.606508	+	0.795077i	$0.292570\pi$
$912$		0			0
$913$			51.2919i			1.69752i
$914$		0			0
$915$	−0.0748051	−	17.6992i	−0.00247298	−	0.585116i
$916$		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	$-0.979938\pi$
$919$	−13.4738	+	23.3373i	−0.444460	+	0.769827i	0.553555	+	0.832813i	$0.313271\pi$
$920$		0			0
$921$	6.34714	+	3.62884i	0.209145	+	0.119574i
$922$		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
$927$	−15.9181	−	9.01175i	−0.522817	−	0.295985i
$928$		0			0
$929$	27.6274			0.906427			0.453213	−	0.891402i	$-0.350278\pi$
$929$	27.6274			0.906427			0.453213	+	0.891402i	$0.350278\pi$
$930$		0			0
$931$	−5.32314	+	16.2192i	−0.174459	+	0.531563i
$932$		0			0
$933$	−3.59802	+	6.29323i	−0.117794	+	0.206031i
$934$		0			0
$935$	7.76057	−	4.48057i	0.253798	−	0.146530i
$936$		0			0
$937$		−	7.60743i		−	0.248524i	−0.992249	−	0.124262i	$-0.960344\pi$
$937$		−	7.60743i		−	0.248524i	0.992249	−	0.124262i	$-0.0396563\pi$
$938$		0			0
$939$	33.1396	+	18.9468i	1.08147	+	0.618307i
$940$		0			0
$941$	−41.2996			−1.34633			−0.673165	−	0.739493i	$-0.735066\pi$
$941$	−41.2996			−1.34633			−0.673165	+	0.739493i	$0.735066\pi$
$942$		0			0
$943$			41.0731i			1.33753i
$944$		0			0
$945$	−35.2742	−	5.18269i	−1.14747	−	0.168593i
$946$		0			0
$947$		−	41.6059i		−	1.35201i	−0.736897	−	0.676005i	$-0.763710\pi$
$947$		−	41.6059i		−	1.35201i	0.736897	−	0.676005i	$-0.236290\pi$
$948$		0			0
$949$	51.4466			1.67003
$950$		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
$957$	0.941314	−	1.64643i	0.0304284	−	0.0532217i
$958$		0			0
$959$	9.51477	−	3.63621i	0.307248	−	0.117419i
$960$		0			0
$961$	5.65789			0.182512
$962$		0			0
$963$	0.406545	+	48.0942i	0.0131007	+	1.54981i
$964$		0			0
$965$	16.6344	+	28.8116i	0.535480	+	0.927479i
$966$		0			0
$967$	2.60192	−	4.50665i	0.0836720	−	0.144924i	−0.821153	−	0.570709i	$-0.806669\pi$
$967$	2.60192	−	4.50665i	0.0836720	−	0.144924i	0.904825	+	0.425785i	$0.140002\pi$
$968$		0			0
$969$	3.57619	+	2.04461i	0.114884	+	0.0656823i
$970$		0			0
$971$	8.67233	−	15.0209i	0.278308	−	0.482044i	−0.692656	−	0.721268i	$-0.743560\pi$
$971$	8.67233	−	15.0209i	0.278308	−	0.482044i	0.970964	+	0.239224i	$0.0768929\pi$
$972$		0			0
$973$	−53.5461	+	20.4634i	−1.71661	+	0.656027i
$974$		0			0
$975$	0.0399790	+	9.45917i	0.00128035	+	0.302936i
$976$		0			0
$977$			26.9670i			0.862751i	0.902172	+	0.431376i	$0.141972\pi$
$977$			26.9670i			0.862751i	−0.902172	+	0.431376i	$0.858028\pi$
$978$		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
$983$	8.55646	−	14.8202i	0.272909	−	0.472692i	−0.696697	−	0.717366i	$-0.745348\pi$
$983$	8.55646	−	14.8202i	0.272909	−	0.472692i	0.969605	+	0.244674i	$0.0786810\pi$
$984$		0			0
$985$	−50.0512	+	28.8971i	−1.59476	+	0.920738i
$986$		0			0
$987$	−4.74177	−	12.2521i	−0.150932	−	0.389989i
$988$		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	$-0.107232\pi$
$991$	5.84386	+	10.1219i	0.185636	+	0.321531i	−0.758155	+	0.652075i	$0.773899\pi$
$992$		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
$997$	−25.0296	−	14.4508i	−0.792695	−	0.457663i	0.0482154	−	0.998837i	$-0.484647\pi$
$997$	−25.0296	−	14.4508i	−0.792695	−	0.457663i	−0.840910	+	0.541174i	$0.817980\pi$
$998$		0			0
$999$	−17.6497	+	31.4855i	−0.558412	+	0.996156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.e.257.9		48
3.2	odd	2		3024.2.ca.e.2609.5		48
4.3	odd	2		504.2.bs.a.257.16	✓	48
7.3	odd	6		1008.2.df.e.689.1		48
9.2	odd	6		1008.2.df.e.929.1		48
9.7	even	3		3024.2.df.e.1601.5		48
12.11	even	2		1512.2.bs.a.1097.5		48
21.17	even	6		3024.2.df.e.17.5		48
28.3	even	6		504.2.cx.a.185.24	yes	48
36.7	odd	6		1512.2.cx.a.89.5		48
36.11	even	6		504.2.cx.a.425.24	yes	48
63.38	even	6	inner	1008.2.ca.e.353.9		48
63.52	odd	6		3024.2.ca.e.2033.5		48
84.59	odd	6		1512.2.cx.a.17.5		48
252.115	even	6		1512.2.bs.a.521.5		48
252.227	odd	6		504.2.bs.a.353.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.16	✓	48	4.3	odd	2
504.2.bs.a.353.16	yes	48	252.227	odd	6
504.2.cx.a.185.24	yes	48	28.3	even	6
504.2.cx.a.425.24	yes	48	36.11	even	6
1008.2.ca.e.257.9		48	1.1	even	1	trivial
1008.2.ca.e.353.9		48	63.38	even	6	inner
1008.2.df.e.689.1		48	7.3	odd	6
1008.2.df.e.929.1		48	9.2	odd	6
1512.2.bs.a.521.5		48	252.115	even	6
1512.2.bs.a.1097.5		48	12.11	even	2
1512.2.cx.a.17.5		48	84.59	odd	6
1512.2.cx.a.89.5		48	36.7	odd	6
3024.2.ca.e.2033.5		48	63.52	odd	6
3024.2.ca.e.2609.5		48	3.2	odd	2
3024.2.df.e.17.5		48	21.17	even	6
3024.2.df.e.1601.5		48	9.7	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.859678 + 1.50365i) q^{3} +(1.29668 + 2.24592i) q^{5} +(-1.66807 + 2.05367i) q^{7} +(-1.52191 - 2.58530i) q^{9} +(-3.06832 - 1.77150i) q^{11} +(-2.74094 - 1.58248i) q^{13} +(-4.49180 + 0.0189845i) q^{15} +(0.487640 + 0.844616i) q^{17} +(-2.11191 - 1.21931i) q^{19} +(-1.65398 - 4.27368i) q^{21} +(-2.92435 + 1.68838i) q^{23} +(-0.862775 + 1.49437i) q^{25} +(5.19573 - 0.0658821i) q^{27} +(0.267645 - 0.154525i) q^{29} -5.03410i q^{31} +(5.30147 - 3.09076i) q^{33} +(-6.77533 - 1.08340i) q^{35} +(-3.47324 + 6.01583i) q^{37} +(4.73582 - 2.76098i) q^{39} +(6.08175 - 10.5339i) q^{41} +(5.47630 + 9.48523i) q^{43} +(3.83296 - 6.77040i) q^{45} +2.86688 q^{47} +(-1.43508 - 6.85132i) q^{49} +(-1.68922 + 0.00713944i) q^{51} +(-7.81416 + 4.51151i) q^{53} -9.18828i q^{55} +(3.64898 - 2.12736i) q^{57} +0.439455 q^{59} +3.94033i q^{61} +(7.84800 + 1.18698i) q^{63} -8.20791i q^{65} -3.65121 q^{67} +(-0.0247192 - 5.84865i) q^{69} -5.25055i q^{71} +(-14.0773 + 8.12752i) q^{73} +(-1.50530 - 2.58199i) q^{75} +(8.75624 - 3.34632i) q^{77} -6.99318 q^{79} +(-4.36760 + 7.86919i) q^{81} +(-7.23851 - 12.5375i) q^{83} +(-1.26463 + 2.19040i) q^{85} +(0.00226237 + 0.535285i) q^{87} +(-2.31101 + 4.00279i) q^{89} +(7.82197 - 2.98928i) q^{91} +(7.56950 + 4.32770i) q^{93} -6.32426i q^{95} +(-12.4805 + 7.20560i) q^{97} +(0.0898447 + 10.6286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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