LMFDB - Embedded newform 1008.2.ca.e.257.4

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			257.4
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.e.353.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38355 - 1.04201i) q^{3} +(-0.537427 - 0.930850i) q^{5} +(1.37797 + 2.25858i) q^{7} +(0.828420 + 2.88335i) q^{9} +(-3.55011 - 2.04966i) q^{11} +(3.69867 + 2.13543i) q^{13} +(-0.226401 + 1.84788i) q^{15} +(-0.717607 - 1.24293i) q^{17} +(-6.41973 - 3.70644i) q^{19} +(0.446987 - 4.56072i) q^{21} +(-5.43530 + 3.13807i) q^{23} +(1.92235 - 3.32960i) q^{25} +(1.85833 - 4.85249i) q^{27} +(-8.09846 + 4.67565i) q^{29} +6.88527i q^{31} +(2.77598 + 6.53506i) q^{33} +(1.36185 - 2.49651i) q^{35} +(-0.453413 + 0.785334i) q^{37} +(-2.89215 - 6.80854i) q^{39} +(-3.88978 + 6.73730i) q^{41} +(6.32181 + 10.9497i) q^{43} +(2.23875 - 2.32073i) q^{45} +8.43528 q^{47} +(-3.20241 + 6.22451i) q^{49} +(-0.302305 + 2.46741i) q^{51} +(-1.50593 + 0.869452i) q^{53} +4.40616i q^{55} +(5.01987 + 11.8175i) q^{57} +6.10146 q^{59} -2.72573i q^{61} +(-5.37076 + 5.84422i) q^{63} -4.59055i q^{65} -12.0391 q^{67} +(10.7899 + 1.32197i) q^{69} +0.783113i q^{71} +(-1.95868 + 1.13085i) q^{73} +(-6.12914 + 2.60356i) q^{75} +(-0.262612 - 10.8426i) q^{77} -1.63543 q^{79} +(-7.62744 + 4.77725i) q^{81} +(4.48646 + 7.77077i) q^{83} +(-0.771322 + 1.33597i) q^{85} +(16.0767 + 1.96971i) q^{87} +(-1.71834 + 2.97625i) q^{89} +(0.273602 + 11.2963i) q^{91} +(7.17454 - 9.52611i) q^{93} +7.96775i q^{95} +(-5.05015 + 2.91570i) q^{97} +(2.96890 - 11.9342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.38355	−	1.04201i	−0.798793	−	0.601606i
$3$	−1.38355	−	1.04201i	−0.798793	−	0.601606i
$4$		0			0
$5$	−0.537427	−	0.930850i	−0.240345	−	0.416289i	0.720468	−	0.693488i	$-0.243927\pi$
$5$	−0.537427	−	0.930850i	−0.240345	−	0.416289i	−0.960812	+	0.277199i	$0.910594\pi$
$6$		0			0
$7$	1.37797	+	2.25858i	0.520823	+	0.853665i
$7$	1.37797	+	2.25858i	0.520823	+	0.853665i
$8$		0			0
$9$	0.828420	+	2.88335i	0.276140	+	0.961117i
$10$		0			0
$11$	−3.55011	−	2.04966i	−1.07040	−	0.617994i	−0.142108	−	0.989851i	$-0.545388\pi$
$11$	−3.55011	−	2.04966i	−1.07040	−	0.617994i	−0.928290	+	0.371857i	$0.878721\pi$
$12$		0			0
$13$	3.69867	+	2.13543i	1.02583	+	0.592262i	0.915787	−	0.401665i	$-0.131568\pi$
$13$	3.69867	+	2.13543i	1.02583	+	0.592262i	0.110041	+	0.993927i	$0.464902\pi$
$14$		0			0
$15$	−0.226401	+	1.84788i	−0.0584565	+	0.477121i
$16$		0			0
$17$	−0.717607	−	1.24293i	−0.174045	−	0.301455i	0.765785	−	0.643096i	$-0.222351\pi$
$17$	−0.717607	−	1.24293i	−0.174045	−	0.301455i	−0.939830	+	0.341641i	$0.889017\pi$
$18$		0			0
$19$	−6.41973	−	3.70644i	−1.47279	−	0.850315i	−0.473257	−	0.880925i	$-0.656922\pi$
$19$	−6.41973	−	3.70644i	−1.47279	−	0.850315i	−0.999531	+	0.0306101i	$0.990255\pi$
$20$		0			0
$21$	0.446987	−	4.56072i	0.0975406	−	0.995232i
$22$		0			0
$23$	−5.43530	+	3.13807i	−1.13334	+	0.654334i	−0.944773	−	0.327727i	$-0.893717\pi$
$23$	−5.43530	+	3.13807i	−1.13334	+	0.654334i	−0.188567	+	0.982060i	$0.560384\pi$
$24$		0			0
$25$	1.92235	−	3.32960i	0.384469	−	0.665920i
$26$		0			0
$27$	1.85833	−	4.85249i	0.357636	−	0.933861i
$28$		0			0
$29$	−8.09846	+	4.67565i	−1.50385	+	0.868246i	−0.503856	+	0.863788i	$0.668086\pi$
$29$	−8.09846	+	4.67565i	−1.50385	+	0.868246i	−0.999990	+	0.00445828i	$0.998581\pi$
$30$		0			0
$31$			6.88527i			1.23663i	0.785930	+	0.618316i	$0.212185\pi$
$31$			6.88527i			1.23663i	−0.785930	+	0.618316i	$0.787815\pi$
$32$		0			0
$33$	2.77598	+	6.53506i	0.483237	+	1.13761i
$34$		0			0
$35$	1.36185	−	2.49651i	0.230194	−	0.421986i
$36$		0			0
$37$	−0.453413	+	0.785334i	−0.0745406	+	0.129108i	−0.900886	−	0.434055i	$-0.857082\pi$
$37$	−0.453413	+	0.785334i	−0.0745406	+	0.129108i	0.826346	+	0.563163i	$0.190416\pi$
$38$		0			0
$39$	−2.89215	−	6.80854i	−0.463115	−	1.09024i
$40$		0			0
$41$	−3.88978	+	6.73730i	−0.607482	+	1.05219i	0.384172	+	0.923262i	$0.374487\pi$
$41$	−3.88978	+	6.73730i	−0.607482	+	1.05219i	−0.991654	+	0.128928i	$0.958846\pi$
$42$		0			0
$43$	6.32181	+	10.9497i	0.964067	+	1.66981i	0.712102	+	0.702076i	$0.247743\pi$
$43$	6.32181	+	10.9497i	0.964067	+	1.66981i	0.251965	+	0.967736i	$0.418923\pi$
$44$		0			0
$45$	2.23875	−	2.32073i	0.333734	−	0.345953i
$46$		0			0
$47$	8.43528			1.23041			0.615206	−	0.788366i	$-0.289073\pi$
$47$	8.43528			1.23041			0.615206	+	0.788366i	$0.289073\pi$
$48$		0			0
$49$	−3.20241	+	6.22451i	−0.457487	+	0.889216i
$50$		0			0
$51$	−0.302305	+	2.46741i	−0.0423312	+	0.345507i
$52$		0			0
$53$	−1.50593	+	0.869452i	−0.206856	+	0.119428i	−0.599849	−	0.800113i	$-0.704773\pi$
$53$	−1.50593	+	0.869452i	−0.206856	+	0.119428i	0.392993	+	0.919541i	$0.371440\pi$
$54$		0			0
$55$			4.40616i			0.594126i
$56$		0			0
$57$	5.01987	+	11.8175i	0.664898	+	1.56526i
$58$		0			0
$59$	6.10146			0.794342			0.397171	−	0.917745i	$-0.369992\pi$
$59$	6.10146			0.794342			0.397171	+	0.917745i	$0.369992\pi$
$60$		0			0
$61$		−	2.72573i		−	0.348994i	−0.984658	−	0.174497i	$-0.944170\pi$
$61$		−	2.72573i		−	0.348994i	0.984658	−	0.174497i	$-0.0558299\pi$
$62$		0			0
$63$	−5.37076	+	5.84422i	−0.676652	+	0.736303i
$64$		0			0
$65$		−	4.59055i		−	0.569388i
$66$		0			0
$67$	−12.0391			−1.47081			−0.735403	−	0.677630i	$-0.763007\pi$
$67$	−12.0391			−1.47081			−0.735403	+	0.677630i	$0.763007\pi$
$68$		0			0
$69$	10.7899	+	1.32197i	1.29895	+	0.159147i
$70$		0			0
$71$			0.783113i			0.0929385i	0.998920	+	0.0464692i	$0.0147969\pi$
$71$			0.783113i			0.0929385i	−0.998920	+	0.0464692i	$0.985203\pi$
$72$		0			0
$73$	−1.95868	+	1.13085i	−0.229247	+	0.132356i	−0.610224	−	0.792229i	$-0.708921\pi$
$73$	−1.95868	+	1.13085i	−0.229247	+	0.132356i	0.380978	+	0.924584i	$0.375587\pi$
$74$		0			0
$75$	−6.12914	+	2.60356i	−0.707733	+	0.300633i
$76$		0			0
$77$	−0.262612	−	10.8426i	−0.0299274	−	1.23563i
$78$		0			0
$79$	−1.63543			−0.184000			−0.0919999	−	0.995759i	$-0.529326\pi$
$79$	−1.63543			−0.184000			−0.0919999	+	0.995759i	$0.529326\pi$
$80$		0			0
$81$	−7.62744	+	4.77725i	−0.847494	+	0.530806i
$82$		0			0
$83$	4.48646	+	7.77077i	0.492452	+	0.852953i	0.999962	−	0.00869330i	$-0.00276720\pi$
$83$	4.48646	+	7.77077i	0.492452	+	0.852953i	−0.507510	+	0.861646i	$0.669434\pi$
$84$		0			0
$85$	−0.771322	+	1.33597i	−0.0836616	+	0.144906i
$86$		0			0
$87$	16.0767	+	1.96971i	1.72360	+	0.211175i
$88$		0			0
$89$	−1.71834	+	2.97625i	−0.182144	+	0.315482i	−0.942610	−	0.333895i	$-0.891637\pi$
$89$	−1.71834	+	2.97625i	−0.182144	+	0.315482i	0.760467	+	0.649377i	$0.224970\pi$
$90$		0			0
$91$	0.273602	+	11.2963i	0.0286813	+	1.18418i
$92$		0			0
$93$	7.17454	−	9.52611i	0.743965	−	0.987812i
$94$		0			0
$95$			7.96775i			0.817474i
$96$		0			0
$97$	−5.05015	+	2.91570i	−0.512765	+	0.296045i	−0.733969	−	0.679182i	$-0.762334\pi$
$97$	−5.05015	+	2.91570i	−0.512765	+	0.296045i	0.221205	+	0.975227i	$0.429001\pi$
$98$		0			0
$99$	2.96890	−	11.9342i	0.298386	−	1.19943i
$100$		0			0
$101$	−2.31220	+	4.00485i	−0.230073	+	0.398497i	−0.957829	−	0.287338i	$-0.907230\pi$
$101$	−2.31220	+	4.00485i	−0.230073	+	0.398497i	0.727757	+	0.685835i	$0.240563\pi$
$102$		0			0
$103$	3.68450	−	2.12724i	0.363044	−	0.209604i	−0.307371	−	0.951590i	$-0.599449\pi$
$103$	3.68450	−	2.12724i	0.363044	−	0.209604i	0.670415	+	0.741986i	$0.266116\pi$
$104$		0			0
$105$	−4.48557	+	2.03498i	−0.437747	+	0.198593i
$106$		0			0
$107$	−8.73964	−	5.04583i	−0.844893	−	0.487799i	0.0140314	−	0.999902i	$-0.495534\pi$
$107$	−8.73964	−	5.04583i	−0.844893	−	0.487799i	−0.858924	+	0.512102i	$0.828867\pi$
$108$		0			0
$109$	0.548395	+	0.949848i	0.0525267	+	0.0909790i	0.891093	−	0.453820i	$-0.149939\pi$
$109$	0.548395	+	0.949848i	0.0525267	+	0.0909790i	−0.838567	+	0.544799i	$0.816606\pi$
$110$		0			0
$111$	1.44565	−	0.614086i	0.137215	−	0.0582865i
$112$		0			0
$113$	−8.51839	−	4.91809i	−0.801343	−	0.462655i	0.0425979	−	0.999092i	$-0.486437\pi$
$113$	−8.51839	−	4.91809i	−0.801343	−	0.462655i	−0.843940	+	0.536437i	$0.819770\pi$
$114$		0			0
$115$	5.84215	+	3.37297i	0.544784	+	0.314531i
$116$		0			0
$117$	−3.09315	+	12.4336i	−0.285961	+	1.14949i
$118$		0			0
$119$	1.81843	−	3.33350i	0.166695	−	0.305581i
$120$		0			0
$121$	2.90217	+	5.02671i	0.263834	+	0.456974i
$122$		0			0
$123$	12.4021	−	5.26819i	1.11826	−	0.475017i
$124$		0			0
$125$	−9.50674			−0.850309
$126$		0			0
$127$	−15.2201			−1.35056			−0.675282	−	0.737559i	$-0.735978\pi$
$127$	−15.2201			−1.35056			−0.675282	+	0.737559i	$0.735978\pi$
$128$		0			0
$129$	2.66318	−	21.7368i	0.234480	−	1.91382i
$130$		0			0
$131$	−4.45441	−	7.71526i	−0.389184	−	0.674086i	0.603156	−	0.797623i	$-0.293910\pi$
$131$	−4.45441	−	7.71526i	−0.389184	−	0.674086i	−0.992340	+	0.123537i	$0.960576\pi$
$132$		0			0
$133$	−0.474887	−	19.6069i	−0.0411779	−	1.70013i
$134$		0			0
$135$	−5.51565	+	0.878028i	−0.474712	+	0.0755686i
$136$		0			0
$137$	−9.76339	−	5.63689i	−0.834143	−	0.481592i	0.0211264	−	0.999777i	$-0.493275\pi$
$137$	−9.76339	−	5.63689i	−0.834143	−	0.481592i	−0.855269	+	0.518184i	$0.826608\pi$
$138$		0			0
$139$	12.0468	+	6.95522i	1.02180	+	0.589934i	0.914624	−	0.404306i	$-0.132487\pi$
$139$	12.0468	+	6.95522i	1.02180	+	0.589934i	0.107172	+	0.994240i	$0.465820\pi$
$140$		0			0
$141$	−11.6706	−	8.78967i	−0.982845	−	0.740224i
$142$		0			0
$143$	−8.75380	−	15.1620i	−0.732029	−	1.26791i
$144$		0			0
$145$	8.70466	+	5.02564i	0.722882	+	0.417356i
$146$		0			0
$147$	10.9167	−	5.27497i	0.900396	−	0.435072i
$148$		0			0
$149$	3.09504	−	1.78692i	0.253555	−	0.146390i	−0.367836	−	0.929891i	$-0.619901\pi$
$149$	3.09504	−	1.78692i	0.253555	−	0.146390i	0.621391	+	0.783501i	$0.286568\pi$
$150$		0			0
$151$	3.30180	−	5.71888i	0.268696	−	0.465396i	−0.699829	−	0.714310i	$-0.746741\pi$
$151$	3.30180	−	5.71888i	0.268696	−	0.465396i	0.968525	+	0.248915i	$0.0800739\pi$
$152$		0			0
$153$	2.98933	−	3.09878i	0.241673	−	0.250522i
$154$		0			0
$155$	6.40916	−	3.70033i	0.514796	−	0.297217i
$156$		0			0
$157$			9.19553i			0.733883i	0.930244	+	0.366942i	$0.119595\pi$
$157$			9.19553i			0.733883i	−0.930244	+	0.366942i	$0.880405\pi$
$158$		0			0
$159$	2.98951	+	0.366273i	0.237084	+	0.0290473i
$160$		0			0
$161$	−14.5773	−	7.95193i	−1.14885	−	0.626700i
$162$		0			0
$163$	−3.64872	+	6.31976i	−0.285790	+	0.495002i	−0.972800	−	0.231645i	$-0.925589\pi$
$163$	−3.64872	+	6.31976i	−0.285790	+	0.495002i	0.687011	+	0.726647i	$0.258923\pi$
$164$		0			0
$165$	4.59127	−	6.09614i	0.357430	−	0.474584i
$166$		0			0
$167$	7.07118	−	12.2476i	0.547184	−	0.947751i	−0.451282	−	0.892382i	$-0.649033\pi$
$167$	7.07118	−	12.2476i	0.547184	−	0.947751i	0.998466	−	0.0553694i	$-0.0176336\pi$
$168$		0			0
$169$	2.62013	+	4.53820i	0.201549	+	0.349092i
$170$		0			0
$171$	5.36872	−	21.5808i	0.410557	−	1.65033i
$172$		0			0
$173$	13.4985			1.02627			0.513134	−	0.858308i	$-0.328484\pi$
$173$	13.4985			1.02627			0.513134	+	0.858308i	$0.328484\pi$
$174$		0			0
$175$	10.1691	−	0.246300i	0.768713	−	0.0186186i
$176$		0			0
$177$	−8.44167	−	6.35780i	−0.634515	−	0.477881i
$178$		0			0
$179$	−3.97036	+	2.29229i	−0.296759	+	0.171334i	−0.640986	−	0.767553i	$-0.721474\pi$
$179$	−3.97036	+	2.29229i	−0.296759	+	0.171334i	0.344227	+	0.938886i	$0.388141\pi$
$180$		0			0
$181$		−	2.22901i		−	0.165681i	−0.996563	−	0.0828405i	$-0.973601\pi$
$181$		−	2.22901i		−	0.165681i	0.996563	−	0.0828405i	$-0.0263992\pi$
$182$		0			0
$183$	−2.84024	+	3.77118i	−0.209957	+	0.278774i
$184$		0			0
$185$	0.974704			0.0716617
$186$		0			0
$187$			5.88339i			0.430236i
$188$		0			0
$189$	13.5205	−	2.48937i	0.983469	−	0.181075i
$190$		0			0
$191$			21.0351i			1.52204i	0.648726	+	0.761022i	$0.275302\pi$
$191$			21.0351i			1.52204i	−0.648726	+	0.761022i	$0.724698\pi$
$192$		0			0
$193$	−11.2043			−0.806500			−0.403250	−	0.915090i	$-0.632119\pi$
$193$	−11.2043			−0.806500			−0.403250	+	0.915090i	$0.632119\pi$
$194$		0			0
$195$	−4.78341	+	6.35125i	−0.342547	+	0.454823i
$196$		0			0
$197$		−	20.8945i		−	1.48867i	−0.667805	−	0.744336i	$-0.732766\pi$
$197$		−	20.8945i		−	1.48867i	0.667805	−	0.744336i	$-0.267234\pi$
$198$		0			0
$199$	15.8521	−	9.15222i	1.12373	−	0.648784i	0.181377	−	0.983414i	$-0.441945\pi$
$199$	15.8521	−	9.15222i	1.12373	−	0.648784i	0.942350	+	0.334630i	$0.108611\pi$
$200$		0			0
$201$	16.6566	+	12.5449i	1.17487	+	0.884846i
$202$		0			0
$203$	−21.7198	−	11.8482i	−1.52443	−	0.831578i
$204$		0			0
$205$	8.36189			0.584020
$206$		0			0
$207$	−13.5509	−	13.0723i	−0.941852	−	0.908584i
$208$		0			0
$209$	15.1938	+	26.3165i	1.05098	+	1.82035i
$210$		0			0
$211$	−5.93845	+	10.2857i	−0.408820	+	0.708096i	−0.994758	−	0.102260i	$-0.967393\pi$
$211$	−5.93845	+	10.2857i	−0.408820	+	0.708096i	0.585938	+	0.810356i	$0.300726\pi$
$212$		0			0
$213$	0.816014	−	1.08348i	0.0559124	−	0.0742386i
$214$		0			0
$215$	6.79502	−	11.7693i	0.463416	−	0.802660i
$216$		0			0
$217$	−15.5510	+	9.48768i	−1.05567	+	0.644066i
$218$		0			0
$219$	3.88829	+	0.476391i	0.262747	+	0.0321915i
$220$		0			0
$221$		−	6.12960i		−	0.412321i
$222$		0			0
$223$	4.19957	−	2.42462i	0.281224	−	0.162365i	−0.352754	−	0.935716i	$-0.614755\pi$
$223$	4.19957	−	2.42462i	0.281224	−	0.162365i	0.633977	+	0.773352i	$0.281421\pi$
$224$		0			0
$225$	11.1929	+	2.78449i	0.746194	+	0.185633i
$226$		0			0
$227$	−1.43645	+	2.48801i	−0.0953408	+	0.165135i	−0.909751	−	0.415155i	$-0.863727\pi$
$227$	−1.43645	+	2.48801i	−0.0953408	+	0.165135i	0.814410	+	0.580290i	$0.197061\pi$
$228$		0			0
$229$	3.74833	−	2.16410i	0.247697	−	0.143008i	−0.371013	−	0.928628i	$-0.620989\pi$
$229$	3.74833	−	2.16410i	0.247697	−	0.143008i	0.618709	+	0.785620i	$0.287656\pi$
$230$		0			0
$231$	−10.9348	+	15.2749i	−0.719455	+	1.00501i
$232$		0			0
$233$	11.9136	+	6.87834i	0.780488	+	0.450615i	0.836603	−	0.547809i	$-0.184538\pi$
$233$	11.9136	+	6.87834i	0.780488	+	0.450615i	−0.0561154	+	0.998424i	$0.517871\pi$
$234$		0			0
$235$	−4.53335	−	7.85198i	−0.295723	−	0.512207i
$236$		0			0
$237$	2.26269	+	1.70413i	0.146978	+	0.110695i
$238$		0			0
$239$	15.6571	+	9.03963i	1.01277	+	0.584725i	0.912003	−	0.410184i	$-0.134536\pi$
$239$	15.6571	+	9.03963i	1.01277	+	0.584725i	0.100771	+	0.994910i	$0.467869\pi$
$240$		0			0
$241$	−5.17659	−	2.98871i	−0.333454	−	0.192520i	0.323920	−	0.946085i	$-0.394999\pi$
$241$	−5.17659	−	2.98871i	−0.333454	−	0.192520i	−0.657373	+	0.753565i	$0.728333\pi$
$242$		0			0
$243$	15.5309	+	1.33833i	0.996308	+	0.0858536i
$244$		0			0
$245$	7.51515	−	0.364254i	0.480125	−	0.0232713i
$246$		0			0
$247$	−15.8297	−	27.4178i	−1.00722	−	1.74455i
$248$		0			0
$249$	1.89000	−	15.4262i	0.119774	−	0.977595i
$250$		0			0
$251$	−11.0004			−0.694337			−0.347169	−	0.937803i	$-0.612857\pi$
$251$	−11.0004			−0.694337			−0.347169	+	0.937803i	$0.612857\pi$
$252$		0			0
$253$	25.7279			1.61750
$254$		0			0
$255$	2.45926	−	1.04465i	0.154005	−	0.0654187i
$256$		0			0
$257$	4.74280	+	8.21477i	0.295848	+	0.512423i	0.975182	−	0.221406i	$-0.0710646\pi$
$257$	4.74280	+	8.21477i	0.295848	+	0.512423i	−0.679334	+	0.733829i	$0.737731\pi$
$258$		0			0
$259$	−2.39853	+	0.0580935i	−0.149037	+	0.00360975i
$260$		0			0
$261$	−20.1905	−	19.4773i	−1.24976	−	1.20562i
$262$		0			0
$263$	−16.3241	−	9.42470i	−1.00658	−	0.581152i	−0.0963945	−	0.995343i	$-0.530731\pi$
$263$	−16.3241	−	9.42470i	−1.00658	−	0.581152i	−0.910190	+	0.414192i	$0.864064\pi$
$264$		0			0
$265$	1.61866	+	0.934533i	0.0994334	+	0.0574079i
$266$		0			0
$267$	5.47870	−	2.32726i	0.335291	−	0.142426i
$268$		0			0
$269$	−10.0233	−	17.3609i	−0.611133	−	1.05851i	−0.991050	−	0.133493i	$-0.957381\pi$
$269$	−10.0233	−	17.3609i	−0.611133	−	1.05851i	0.379916	−	0.925021i	$-0.375953\pi$
$270$		0			0
$271$	−17.3369	−	10.0095i	−1.05314	−	0.608032i	−0.129615	−	0.991564i	$-0.541374\pi$
$271$	−17.3369	−	10.0095i	−1.05314	−	0.608032i	−0.923528	+	0.383532i	$0.874708\pi$
$272$		0			0
$273$	11.3924	−	15.9141i	0.689498	−	0.963167i
$274$		0			0
$275$	−13.6491	+	7.88029i	−0.823069	+	0.475199i
$276$		0			0
$277$	1.70372	−	2.95093i	0.102367	−	0.177304i	−0.810293	−	0.586026i	$-0.800692\pi$
$277$	1.70372	−	2.95093i	0.102367	−	0.177304i	0.912659	+	0.408721i	$0.134025\pi$
$278$		0			0
$279$	−19.8527	+	5.70389i	−1.18855	+	0.341483i
$280$		0			0
$281$	16.0313	−	9.25568i	0.956347	−	0.552147i	0.0613004	−	0.998119i	$-0.480475\pi$
$281$	16.0313	−	9.25568i	0.956347	−	0.552147i	0.895047	+	0.445972i	$0.147142\pi$
$282$		0			0
$283$		−	25.1116i		−	1.49273i	−0.665535	−	0.746366i	$-0.731797\pi$
$283$		−	25.1116i		−	1.49273i	0.665535	−	0.746366i	$-0.268203\pi$
$284$		0			0
$285$	8.30249	−	11.0238i	0.491797	−	0.652992i
$286$		0			0
$287$	−20.5768	+	0.498378i	−1.21461	+	0.0294183i
$288$		0			0
$289$	7.47008	−	12.9386i	0.439417	−	0.761092i
$290$		0			0
$291$	10.0253	+	1.22830i	0.587695	+	0.0720040i
$292$		0			0
$293$	−1.11299	+	1.92775i	−0.0650214	+	0.112620i	−0.896703	−	0.442632i	$-0.854045\pi$
$293$	−1.11299	+	1.92775i	−0.0650214	+	0.112620i	0.831682	+	0.555252i	$0.187378\pi$
$294$		0			0
$295$	−3.27909	−	5.67955i	−0.190916	−	0.330676i
$296$		0			0
$297$	−16.5432	+	13.4179i	−0.959933	+	0.778586i
$298$		0			0
$299$	−26.8046			−1.55015
$300$		0			0
$301$	−16.0196	+	29.3667i	−0.923352	+	1.69267i
$302$		0			0
$303$	7.37215	−	3.13156i	0.423519	−	0.179904i
$304$		0			0
$305$	−2.53725	+	1.46488i	−0.145282	+	0.0838788i
$306$		0			0
$307$			24.2535i			1.38422i	0.721791	+	0.692111i	$0.243319\pi$
$307$			24.2535i			1.38422i	−0.721791	+	0.692111i	$0.756681\pi$
$308$		0			0
$309$	−7.31430	−	0.896142i	−0.416096	−	0.0509798i
$310$		0			0
$311$	19.6300			1.11312			0.556559	−	0.830808i	$-0.312121\pi$
$311$	19.6300			1.11312			0.556559	+	0.830808i	$0.312121\pi$
$312$		0			0
$313$			17.1547i			0.969643i	0.874613	+	0.484822i	$0.161115\pi$
$313$			17.1547i			0.969643i	−0.874613	+	0.484822i	$0.838885\pi$
$314$		0			0
$315$	8.32649	+	1.85853i	0.469144	+	0.104716i
$316$		0			0
$317$			12.4507i			0.699300i	0.936880	+	0.349650i	$0.113699\pi$
$317$			12.4507i			0.699300i	−0.936880	+	0.349650i	$0.886301\pi$
$318$		0			0
$319$	38.3339			2.14628
$320$		0			0
$321$	6.83391	+	16.0880i	0.381431	+	0.897943i
$322$		0			0
$323$			10.6391i			0.591973i
$324$		0			0
$325$	14.2203	−	8.21007i	0.788798	−	0.455413i
$326$		0			0
$327$	0.231022	−	1.88560i	0.0127755	−	0.104274i
$328$		0			0
$329$	11.6235	+	19.0518i	0.640827	+	1.05036i
$330$		0			0
$331$	30.9175			1.69938			0.849691	−	0.527281i	$-0.176789\pi$
$331$	30.9175			1.69938			0.849691	+	0.527281i	$0.176789\pi$
$332$		0			0
$333$	−2.64001	−	0.656762i	−0.144672	−	0.0359904i
$334$		0			0
$335$	6.47011	+	11.2066i	0.353500	+	0.612280i
$336$		0			0
$337$	−1.06492	+	1.84450i	−0.0580099	+	0.100476i	−0.893572	−	0.448920i	$-0.851809\pi$
$337$	−1.06492	+	1.84450i	−0.0580099	+	0.100476i	0.835562	+	0.549396i	$0.185142\pi$
$338$		0			0
$339$	6.66090	+	15.6807i	0.361770	+	0.851658i
$340$		0			0
$341$	14.1124	−	24.4434i	0.764231	−	1.32369i
$342$		0			0
$343$	−18.4714	+	1.34426i	−0.997362	+	0.0725832i
$344$		0			0
$345$	−4.56823	−	10.7543i	−0.245945	−	0.578990i
$346$		0			0
$347$		−	23.0026i		−	1.23485i	−0.786631	−	0.617423i	$-0.788177\pi$
$347$		−	23.0026i		−	1.23485i	0.786631	−	0.617423i	$-0.211823\pi$
$348$		0			0
$349$	−21.3306	+	12.3152i	−1.14180	+	0.659219i	−0.946876	−	0.321599i	$-0.895780\pi$
$349$	−21.3306	+	12.3152i	−1.14180	+	0.659219i	−0.194925	+	0.980818i	$0.562446\pi$
$350$		0			0
$351$	17.2355	−	13.9794i	0.919963	−	0.746167i
$352$		0			0
$353$	1.62190	−	2.80921i	0.0863248	−	0.149519i	−0.819630	−	0.572893i	$-0.805821\pi$
$353$	1.62190	−	2.80921i	0.0863248	−	0.149519i	0.905955	+	0.423374i	$0.139154\pi$
$354$		0			0
$355$	0.728961	−	0.420866i	0.0386892	−	0.0223372i
$356$		0			0
$357$	−5.98943	+	2.71723i	−0.316994	+	0.143811i
$358$		0			0
$359$	−4.88399	−	2.81977i	−0.257767	−	0.148822i	0.365548	−	0.930792i	$-0.380881\pi$
$359$	−4.88399	−	2.81977i	−0.257767	−	0.148822i	−0.623316	+	0.781970i	$0.714215\pi$
$360$		0			0
$361$	17.9753	+	31.1342i	0.946070	+	1.63864i
$362$		0			0
$363$	1.22260	−	9.97881i	0.0641697	−	0.523752i
$364$		0			0
$365$	2.10530	+	1.21549i	0.110196	+	0.0636219i
$366$		0			0
$367$	−10.8668	−	6.27396i	−0.567243	−	0.327498i	0.188804	−	0.982015i	$-0.439539\pi$
$367$	−10.8668	−	6.27396i	−0.567243	−	0.327498i	−0.756048	+	0.654517i	$0.772872\pi$
$368$		0			0
$369$	−22.6484	−	5.63430i	−1.17903	−	0.293310i
$370$		0			0
$371$	−4.03886	−	2.20320i	−0.209687	−	0.114385i
$372$		0			0
$373$	6.58770	+	11.4102i	0.341098	+	0.590799i	0.984637	−	0.174614i	$-0.0558678\pi$
$373$	6.58770	+	11.4102i	0.341098	+	0.590799i	−0.643539	+	0.765414i	$0.722534\pi$
$374$		0			0
$375$	13.1531	+	9.90615i	0.679221	+	0.511551i
$376$		0			0
$377$	−39.9381			−2.05692
$378$		0			0
$379$	6.80285			0.349439			0.174720	−	0.984618i	$-0.444098\pi$
$379$	6.80285			0.349439			0.174720	+	0.984618i	$0.444098\pi$
$380$		0			0
$381$	21.0578	+	15.8595i	1.07882	+	0.812508i
$382$		0			0
$383$	9.82982	+	17.0257i	0.502280	+	0.869975i	0.999997	+	0.00263511i	$0.000838781\pi$
$383$	9.82982	+	17.0257i	0.502280	+	0.869975i	−0.497716	+	0.867340i	$0.665828\pi$
$384$		0			0
$385$	−9.95168	+	6.07154i	−0.507185	+	0.309434i
$386$		0			0
$387$	−26.3347	+	27.2989i	−1.33867	+	1.38768i
$388$		0			0
$389$	−15.8135	−	9.12995i	−0.801778	−	0.462907i	0.0423145	−	0.999104i	$-0.486527\pi$
$389$	−15.8135	−	9.12995i	−0.801778	−	0.462907i	−0.844092	+	0.536198i	$0.819860\pi$
$390$		0			0
$391$	7.80082	+	4.50381i	0.394504	+	0.227767i
$392$		0			0
$393$	−1.87650	+	15.3160i	−0.0946572	+	0.772590i
$394$		0			0
$395$	0.878921	+	1.52234i	0.0442233	+	0.0765970i
$396$		0			0
$397$	−31.8395	−	18.3825i	−1.59798	−	0.922593i	−0.991876	−	0.127206i	$-0.959399\pi$
$397$	−31.8395	−	18.3825i	−1.59798	−	0.922593i	−0.606101	−	0.795387i	$-0.707267\pi$
$398$		0			0
$399$	−19.7736	+	27.6219i	−0.989916	+	1.38282i
$400$		0			0
$401$	13.8175	−	7.97753i	0.690012	−	0.398379i	−0.113604	−	0.993526i	$-0.536240\pi$
$401$	13.8175	−	7.97753i	0.690012	−	0.398379i	0.803617	+	0.595147i	$0.202906\pi$
$402$		0			0
$403$	−14.7030	+	25.4664i	−0.732410	+	1.26857i
$404$		0			0
$405$	8.54610	+	4.53258i	0.424659	+	0.225226i
$406$		0			0
$407$	3.21933	−	1.85868i	0.159576	−	0.0921313i
$408$		0			0
$409$		−	9.84803i		−	0.486954i	−0.969907	−	0.243477i	$-0.921712\pi$
$409$		−	9.84803i		−	0.486954i	0.969907	−	0.243477i	$-0.0782880\pi$
$410$		0			0
$411$	7.63442	+	17.9725i	0.376578	+	0.886518i
$412$		0			0
$413$	8.40761	+	13.7807i	0.413712	+	0.678102i
$414$		0			0
$415$	4.82228	−	8.35244i	0.236716	−	0.410005i
$416$		0			0
$417$	−9.41992	−	22.1758i	−0.461295	−	1.08595i
$418$		0			0
$419$	19.4482	−	33.6853i	0.950106	−	1.64563i	0.204917	−	0.978779i	$-0.434308\pi$
$419$	19.4482	−	33.6853i	0.950106	−	1.64563i	0.745189	−	0.666853i	$-0.232359\pi$
$420$		0			0
$421$	−8.99598	−	15.5815i	−0.438437	−	0.759396i	0.559132	−	0.829079i	$-0.311135\pi$
$421$	−8.99598	−	15.5815i	−0.438437	−	0.759396i	−0.997569	+	0.0696829i	$0.977801\pi$
$422$		0			0
$423$	6.98795	+	24.3219i	0.339766	+	1.18257i
$424$		0			0
$425$	−5.51795			−0.267660
$426$		0			0
$427$	6.15629	−	3.75597i	0.297924	−	0.181764i
$428$		0			0
$429$	−3.68770	+	30.0990i	−0.178044	+	1.45319i
$430$		0			0
$431$	−6.23236	+	3.59826i	−0.300202	+	0.173322i	−0.642534	−	0.766257i	$-0.722117\pi$
$431$	−6.23236	+	3.59826i	−0.300202	+	0.173322i	0.342331	+	0.939579i	$0.388783\pi$
$432$		0			0
$433$		−	26.5567i		−	1.27623i	−0.769939	−	0.638117i	$-0.779714\pi$
$433$		−	26.5567i		−	1.27623i	0.769939	−	0.638117i	$-0.220286\pi$
$434$		0			0
$435$	−6.80655	−	16.0236i	−0.326349	−	0.768272i
$436$		0			0
$437$	46.5243			2.22556
$438$		0			0
$439$		−	26.6825i		−	1.27349i	−0.771076	−	0.636744i	$-0.780281\pi$
$439$		−	26.6825i		−	1.27349i	0.771076	−	0.636744i	$-0.219719\pi$
$440$		0			0
$441$	−20.6004	−	4.07717i	−0.980972	−	0.194151i
$442$		0			0
$443$			38.1169i			1.81099i	0.424359	+	0.905494i	$0.360499\pi$
$443$			38.1169i			1.81099i	−0.424359	+	0.905494i	$0.639501\pi$
$444$		0			0
$445$	3.69392			0.175109
$446$		0			0
$447$	−6.14413	−	0.752774i	−0.290607	−	0.0356050i
$448$		0			0
$449$			21.5864i			1.01872i	0.860552	+	0.509362i	$0.170119\pi$
$449$			21.5864i			1.01872i	−0.860552	+	0.509362i	$0.829881\pi$
$450$		0			0
$451$	27.6183	−	15.9454i	1.30049	−	0.750841i
$452$		0			0
$453$	−10.5273	+	4.47184i	−0.494618	+	0.210105i
$454$		0			0
$455$	10.3681	−	6.32563i	0.486066	−	0.296550i
$456$		0			0
$457$	2.85522			0.133562			0.0667809	−	0.997768i	$-0.478727\pi$
$457$	2.85522			0.133562			0.0667809	+	0.997768i	$0.478727\pi$
$458$		0			0
$459$	−7.36486	+	1.17240i	−0.343762	+	0.0547229i
$460$		0			0
$461$	13.3315	+	23.0909i	0.620911	+	1.07545i	0.989316	+	0.145784i	$0.0465706\pi$
$461$	13.3315	+	23.0909i	0.620911	+	1.07545i	−0.368405	+	0.929665i	$0.620096\pi$
$462$		0			0
$463$	3.63687	−	6.29925i	0.169020	−	0.292751i	−0.769056	−	0.639182i	$-0.779273\pi$
$463$	3.63687	−	6.29925i	0.169020	−	0.292751i	0.938076	+	0.346431i	$0.112606\pi$
$464$		0			0
$465$	−12.7232	−	1.55883i	−0.590023	−	0.0722892i
$466$		0			0
$467$	−2.37755	+	4.11804i	−0.110020	+	0.190560i	−0.915778	−	0.401685i	$-0.868425\pi$
$467$	−2.37755	+	4.11804i	−0.110020	+	0.190560i	0.805758	+	0.592245i	$0.201758\pi$
$468$		0			0
$469$	−16.5894	−	27.1912i	−0.766029	−	1.25557i
$470$		0			0
$471$	9.58186	−	12.7225i	0.441509	−	0.586221i
$472$		0			0
$473$		−	51.8301i		−	2.38315i
$474$		0			0
$475$	−24.6819	+	14.2501i	−1.13248	+	0.653839i
$476$		0			0
$477$	−3.75448	−	3.62187i	−0.171906	−	0.165834i
$478$		0			0
$479$	−9.90097	+	17.1490i	−0.452387	+	0.783557i	−0.998534	−	0.0541324i	$-0.982761\pi$
$479$	−9.90097	+	17.1490i	−0.452387	+	0.783557i	0.546147	+	0.837689i	$0.316094\pi$
$480$		0			0
$481$	−3.35405	+	1.93646i	−0.152932	+	0.0882951i
$482$		0			0
$483$	11.8824	+	26.1916i	0.540667	+	1.19176i
$484$		0			0
$485$	5.42817	+	3.13395i	0.246480	+	0.142306i
$486$		0			0
$487$	−17.0806	−	29.5845i	−0.773996	−	1.34060i	−0.935357	−	0.353704i	$-0.884922\pi$
$487$	−17.0806	−	29.5845i	−0.773996	−	1.34060i	0.161362	−	0.986895i	$-0.448411\pi$
$488$		0			0
$489$	11.6335	−	4.94170i	0.526083	−	0.223471i
$490$		0			0
$491$	9.91208	+	5.72274i	0.447326	+	0.258264i	0.706700	−	0.707513i	$-0.250183\pi$
$491$	9.91208	+	5.72274i	0.447326	+	0.258264i	−0.259374	+	0.965777i	$0.583516\pi$
$492$		0			0
$493$	11.6230	+	6.71055i	0.523474	+	0.302228i
$494$		0			0
$495$	−12.7045	+	3.65015i	−0.571025	+	0.164062i
$496$		0			0
$497$	−1.76873	+	1.07910i	−0.0793383	+	0.0484045i
$498$		0			0
$499$	3.88151	+	6.72298i	0.173760	+	0.300962i	0.939732	−	0.341913i	$-0.111075\pi$
$499$	3.88151	+	6.72298i	0.173760	+	0.300962i	−0.765971	+	0.642875i	$0.777742\pi$
$500$		0			0
$501$	−22.5455	+	9.57696i	−1.00726	+	0.427867i
$502$		0			0
$503$	−2.92995			−0.130640			−0.0653200	−	0.997864i	$-0.520807\pi$
$503$	−2.92995			−0.130640			−0.0653200	+	0.997864i	$0.520807\pi$
$504$		0			0
$505$	4.97055			0.221187
$506$		0			0
$507$	1.10378	−	9.00903i	0.0490206	−	0.400105i
$508$		0			0
$509$	5.81338	+	10.0691i	0.257673	+	0.446303i	0.965618	−	0.259964i	$-0.0837108\pi$
$509$	5.81338	+	10.0691i	0.257673	+	0.446303i	−0.707945	+	0.706268i	$0.750377\pi$
$510$		0			0
$511$	−5.25312	−	2.86558i	−0.232384	−	0.126766i
$512$		0			0
$513$	−29.9154	+	24.2639i	−1.32080	+	1.07128i
$514$		0			0
$515$	−3.96029	−	2.28648i	−0.174511	−	0.100754i
$516$		0			0
$517$	−29.9462	−	17.2894i	−1.31703	−	0.760388i
$518$		0			0
$519$	−18.6758	−	14.0656i	−0.819776	−	0.617410i
$520$		0			0
$521$	12.7515	+	22.0863i	0.558655	+	0.967619i	0.997609	+	0.0691093i	$0.0220157\pi$
$521$	12.7515	+	22.0863i	0.558655	+	0.967619i	−0.438954	+	0.898509i	$0.644651\pi$
$522$		0			0
$523$	−0.781452	−	0.451172i	−0.0341705	−	0.0197284i	0.482817	−	0.875721i	$-0.339613\pi$
$523$	−0.781452	−	0.451172i	−0.0341705	−	0.0197284i	−0.516988	+	0.855993i	$0.672947\pi$
$524$		0			0
$525$	−14.3261	−	10.2556i	−0.625243	−	0.447590i
$526$		0			0
$527$	8.55792	−	4.94092i	0.372789	−	0.215230i
$528$		0			0
$529$	8.19501	−	14.1942i	0.356305	−	0.617138i
$530$		0			0
$531$	5.05457	+	17.5927i	0.219350	+	0.763456i
$532$		0			0
$533$	−28.7741	+	16.6127i	−1.24634	+	0.719577i
$534$		0			0
$535$			10.8471i			0.468959i
$536$		0			0
$537$	7.88178	+	0.965670i	0.340124	+	0.0416717i
$538$		0			0
$539$	24.1270	−	15.5339i	1.03922	−	0.669090i
$540$		0			0
$541$	−17.2460	+	29.8710i	−0.741464	+	1.28425i	0.210365	+	0.977623i	$0.432535\pi$
$541$	−17.2460	+	29.8710i	−0.741464	+	1.28425i	−0.951829	+	0.306630i	$0.900799\pi$
$542$		0			0
$543$	−2.32266	+	3.08395i	−0.0996747	+	0.132345i
$544$		0			0
$545$	0.589444	−	1.02095i	0.0252490	−	0.0437326i
$546$		0			0
$547$	−3.68664	−	6.38545i	−0.157629	−	0.273022i	0.776384	−	0.630260i	$-0.217052\pi$
$547$	−3.68664	−	6.38545i	−0.157629	−	0.273022i	−0.934013	+	0.357238i	$0.883718\pi$
$548$		0			0
$549$	7.85924	−	2.25805i	0.335424	−	0.0963711i
$550$		0			0
$551$	69.3199			2.95313
$552$		0			0
$553$	−2.25356	−	3.69375i	−0.0958312	−	0.157074i
$554$		0			0
$555$	−1.34855	−	1.01565i	−0.0572428	−	0.0431121i
$556$		0			0
$557$	−18.6335	+	10.7581i	−0.789528	+	0.455834i	−0.839796	−	0.542902i	$-0.817326\pi$
$557$	−18.6335	+	10.7581i	−0.789528	+	0.455834i	0.0502687	+	0.998736i	$0.483992\pi$
$558$		0			0
$559$			53.9991i			2.28392i
$560$		0			0
$561$	6.13056	−	8.13996i	0.258833	−	0.343669i
$562$		0			0
$563$	−31.5550			−1.32988			−0.664942	−	0.746895i	$-0.731544\pi$
$563$	−31.5550			−1.32988			−0.664942	+	0.746895i	$0.731544\pi$
$564$		0			0
$565$			10.5725i			0.444787i
$566$		0			0
$567$	−21.3002	−	10.6443i	−0.894524	−	0.447020i
$568$		0			0
$569$			23.5719i			0.988184i	0.869410	+	0.494092i	$0.164499\pi$
$569$			23.5719i			0.988184i	−0.869410	+	0.494092i	$0.835501\pi$
$570$		0			0
$571$	−15.6689			−0.655723			−0.327861	−	0.944726i	$-0.606328\pi$
$571$	−15.6689			−0.655723			−0.327861	+	0.944726i	$0.606328\pi$
$572$		0			0
$573$	21.9188	−	29.1031i	0.915671	−	1.21580i
$574$		0			0
$575$			24.1298i			1.00628i
$576$		0			0
$577$	0.137448	−	0.0793554i	0.00572202	−	0.00330361i	−0.497136	−	0.867672i	$-0.665615\pi$
$577$	0.137448	−	0.0793554i	0.00572202	−	0.00330361i	0.502858	+	0.864369i	$0.332282\pi$
$578$		0			0
$579$	15.5016	+	11.6750i	0.644226	+	0.485195i
$580$		0			0
$581$	−11.3688	+	20.8409i	−0.471655	+	0.864627i
$582$		0			0
$583$	7.12831			0.295224
$584$		0			0
$585$	13.2362	−	3.80290i	0.547248	−	0.157231i
$586$		0			0
$587$	−15.9041	−	27.5467i	−0.656432	−	1.13697i	−0.981533	−	0.191294i	$-0.938732\pi$
$587$	−15.9041	−	27.5467i	−0.656432	−	1.13697i	0.325101	−	0.945679i	$-0.394602\pi$
$588$		0			0
$589$	25.5198	−	44.2016i	1.05153	−	1.82130i
$590$		0			0
$591$	−21.7723	+	28.9086i	−0.895595	+	1.18914i
$592$		0			0
$593$	15.8934	−	27.5283i	0.652666	−	1.13045i	−0.329808	−	0.944048i	$-0.606984\pi$
$593$	15.8934	−	27.5283i	0.652666	−	1.13045i	0.982474	−	0.186402i	$-0.0596827\pi$
$594$		0			0
$595$	−4.08026	+	0.0988256i	−0.167274	+	0.00405145i
$596$		0			0
$597$	−31.4689	−	3.85555i	−1.28794	−	0.157797i
$598$		0			0
$599$			12.1844i			0.497842i	0.968524	+	0.248921i	$0.0800760\pi$
$599$			12.1844i			0.497842i	−0.968524	+	0.248921i	$0.919924\pi$
$600$		0			0
$601$	13.6048	−	7.85473i	0.554951	−	0.320401i	−0.196165	−	0.980571i	$-0.562849\pi$
$601$	13.6048	−	7.85473i	0.554951	−	0.320401i	0.751117	+	0.660170i	$0.229516\pi$
$602$		0			0
$603$	−9.97339	−	34.7129i	−0.406148	−	1.41362i
$604$		0			0
$605$	3.11941	−	5.40298i	0.126822	−	0.219662i
$606$		0			0
$607$	−10.9361	+	6.31398i	−0.443884	+	0.256277i	−0.705244	−	0.708965i	$-0.749162\pi$
$607$	−10.9361	+	6.31398i	−0.443884	+	0.256277i	0.261360	+	0.965241i	$0.415829\pi$
$608$		0			0
$609$	17.7044	+	39.0248i	0.717420	+	1.58136i
$610$		0			0
$611$	31.1994	+	18.0130i	1.26219	+	0.728727i
$612$		0			0
$613$	11.3476	+	19.6546i	0.458325	+	0.793842i	0.998873	−	0.0474711i	$-0.0151162\pi$
$613$	11.3476	+	19.6546i	0.458325	+	0.793842i	−0.540547	+	0.841314i	$0.681783\pi$
$614$		0			0
$615$	−11.5691	−	8.71320i	−0.466511	−	0.351350i
$616$		0			0
$617$	−32.6259	−	18.8366i	−1.31347	−	0.758333i	−0.330801	−	0.943700i	$-0.607319\pi$
$617$	−32.6259	−	18.8366i	−1.31347	−	0.758333i	−0.982669	+	0.185368i	$0.940652\pi$
$618$		0			0
$619$	−4.50897	−	2.60326i	−0.181231	−	0.104634i	0.406640	−	0.913588i	$-0.366700\pi$
$619$	−4.50897	−	2.60326i	−0.181231	−	0.104634i	−0.587871	+	0.808955i	$0.700034\pi$
$620$		0			0
$621$	5.12687	+	32.2063i	0.205734	+	1.29239i
$622$		0			0
$623$	−9.08993	+	0.220162i	−0.364180	+	0.00882061i
$624$		0			0
$625$	−4.50255	−	7.79864i	−0.180102	−	0.311946i
$626$		0			0
$627$	6.40069	−	52.2423i	0.255619	−	2.08636i
$628$		0			0
$629$	1.30149			0.0518937
$630$		0			0
$631$	5.73635			0.228361			0.114180	−	0.993460i	$-0.463576\pi$
$631$	5.73635			0.228361			0.114180	+	0.993460i	$0.463576\pi$
$632$		0			0
$633$	18.9340	−	8.04283i	0.752557	−	0.319674i
$634$		0			0
$635$	8.17968	+	14.1676i	0.324601	+	0.562225i
$636$		0			0
$637$	−25.1367	+	16.1839i	−0.995952	+	0.641230i
$638$		0			0
$639$	−2.25799	+	0.648746i	−0.0893248	+	0.0256640i
$640$		0			0
$641$	23.0328	+	13.2980i	0.909743	+	0.525240i	0.880348	−	0.474328i	$-0.157309\pi$
$641$	23.0328	+	13.2980i	0.909743	+	0.525240i	0.0293943	+	0.999568i	$0.490642\pi$
$642$		0			0
$643$	−22.7885	−	13.1569i	−0.898689	−	0.518858i	−0.0219144	−	0.999760i	$-0.506976\pi$
$643$	−22.7885	−	13.1569i	−0.898689	−	0.518858i	−0.876775	+	0.480901i	$0.840309\pi$
$644$		0			0
$645$	−21.6650	+	9.20294i	−0.853059	+	0.362365i
$646$		0			0
$647$	23.8420	+	41.2955i	0.937324	+	1.62349i	0.770436	+	0.637517i	$0.220039\pi$
$647$	23.8420	+	41.2955i	0.937324	+	1.62349i	0.166888	+	0.985976i	$0.446628\pi$
$648$		0			0
$649$	−21.6608	−	12.5059i	−0.850262	−	0.490899i
$650$		0			0
$651$	31.4018	+	3.07763i	1.23073	+	0.120622i
$652$		0			0
$653$	28.3370	−	16.3604i	1.10891	−	0.640231i	0.170366	−	0.985381i	$-0.445505\pi$
$653$	28.3370	−	16.3604i	1.10891	−	0.640231i	0.938548	+	0.345149i	$0.112172\pi$
$654$		0			0
$655$	−4.78784	+	8.29278i	−0.187076	+	0.324026i
$656$		0			0
$657$	−4.88324	−	4.71076i	−0.190513	−	0.183784i
$658$		0			0
$659$	−26.5499	+	15.3286i	−1.03424	+	0.597118i	−0.918196	−	0.396126i	$-0.870354\pi$
$659$	−26.5499	+	15.3286i	−1.03424	+	0.597118i	−0.116043	+	0.993244i	$0.537021\pi$
$660$		0			0
$661$		−	10.8025i		−	0.420167i	−0.977683	−	0.210084i	$-0.932626\pi$
$661$		−	10.8025i		−	0.420167i	0.977683	−	0.210084i	$-0.0673736\pi$
$662$		0			0
$663$	−6.38712	+	8.48061i	−0.248055	+	0.329359i
$664$		0			0
$665$	−17.9958	+	10.9793i	−0.697849	+	0.425759i
$666$		0			0
$667$	29.3451	−	50.8271i	1.13624	−	1.96803i
$668$		0			0
$669$	−8.33679	−	1.02142i	−0.322319	−	0.0394903i
$670$		0			0
$671$	−5.58681	+	9.67663i	−0.215676	+	0.373562i
$672$		0			0
$673$	19.4199	+	33.6363i	0.748583	+	1.29658i	0.948502	+	0.316771i	$0.102599\pi$
$673$	19.4199	+	33.6363i	0.748583	+	1.29658i	−0.199919	+	0.979812i	$0.564068\pi$
$674$		0			0
$675$	−12.5845	−	15.5156i	−0.484377	−	0.597197i
$676$		0			0
$677$	−18.8638			−0.724996			−0.362498	−	0.931984i	$-0.618076\pi$
$677$	−18.8638			−0.724996			−0.362498	+	0.931984i	$0.618076\pi$
$678$		0			0
$679$	−13.5443	−	7.38844i	−0.519783	−	0.283542i
$680$		0			0
$681$	4.57995	−	1.94548i	0.175504	−	0.0745511i
$682$		0			0
$683$	−29.7510	+	17.1768i	−1.13839	+	0.657251i	−0.946032	−	0.324074i	$-0.894947\pi$
$683$	−29.7510	+	17.1768i	−1.13839	+	0.657251i	−0.192360	+	0.981325i	$0.561614\pi$
$684$		0			0
$685$			12.1177i			0.462992i
$686$		0			0
$687$	−7.44102	−	0.911668i	−0.283892	−	0.0347823i
$688$		0			0
$689$	−7.42662			−0.282932
$690$		0			0
$691$			25.5640i			0.972502i	0.873819	+	0.486251i	$0.161636\pi$
$691$			25.5640i			0.972502i	−0.873819	+	0.486251i	$0.838364\pi$
$692$		0			0
$693$	31.0454	−	9.73941i	1.17932	−	0.369969i
$694$		0			0
$695$		−	14.9517i		−	0.567150i
$696$		0			0
$697$	11.1653			0.422917
$698$		0			0
$699$	−9.31578	−	21.9307i	−0.352355	−	0.829494i
$700$		0			0
$701$			32.3485i			1.22178i	0.791714	+	0.610892i	$0.209189\pi$
$701$			32.3485i			1.22178i	−0.791714	+	0.610892i	$0.790811\pi$
$702$		0			0
$703$	5.82158	−	3.36109i	0.219565	−	0.126766i
$704$		0			0
$705$	−1.90976	+	15.5874i	−0.0719256	+	0.587056i
$706$		0			0
$707$	−12.2314	+	0.296250i	−0.460010	+	0.0111416i
$708$		0			0
$709$	2.60238			0.0977344			0.0488672	−	0.998805i	$-0.484439\pi$
$709$	2.60238			0.0977344			0.0488672	+	0.998805i	$0.484439\pi$
$710$		0			0
$711$	−1.35482	−	4.71551i	−0.0508097	−	0.176845i
$712$		0			0
$713$	−21.6065	−	37.4235i	−0.809169	−	1.40152i
$714$		0			0
$715$	−9.40905	+	16.2969i	−0.351878	+	0.609471i
$716$		0			0
$717$	−12.2430	−	28.8217i	−0.457222	−	1.07637i
$718$		0			0
$719$	8.42868	−	14.5989i	0.314337	−	0.544447i	−0.664960	−	0.746879i	$-0.731551\pi$
$719$	8.42868	−	14.5989i	0.314337	−	0.544447i	0.979296	+	0.202432i	$0.0648846\pi$
$720$		0			0
$721$	9.88168	+	5.39047i	0.368013	+	0.200752i
$722$		0			0
$723$	4.04780	+	9.52910i	0.150539	+	0.354391i
$724$		0			0
$725$			35.9528i			1.33525i
$726$		0			0
$727$	36.1005	−	20.8426i	1.33889	−	0.773009i	0.352249	−	0.935906i	$-0.385417\pi$
$727$	36.1005	−	20.8426i	1.33889	−	0.773009i	0.986643	+	0.162897i	$0.0520838\pi$
$728$		0			0
$729$	−20.0932	−	18.0350i	−0.744193	−	0.667964i
$730$		0			0
$731$	9.07314	−	15.7151i	0.335582	−	0.581246i
$732$		0			0
$733$	31.2134	−	18.0211i	1.15289	−	0.665623i	0.203303	−	0.979116i	$-0.434832\pi$
$733$	31.2134	−	18.0211i	1.15289	−	0.665623i	0.949591	+	0.313492i	$0.101499\pi$
$734$		0			0
$735$	−10.7771	−	7.32692i	−0.397521	−	0.270257i
$736$		0			0
$737$	42.7400	+	24.6759i	1.57435	+	0.908949i
$738$		0			0
$739$	14.1322	+	24.4777i	0.519861	+	0.900426i	0.999733	+	0.0230879i	$0.00734977\pi$
$739$	14.1322	+	24.4777i	0.519861	+	0.900426i	−0.479872	+	0.877339i	$0.659317\pi$
$740$		0			0
$741$	−6.66855	+	54.4286i	−0.244975	+	1.99948i
$742$		0			0
$743$	28.7161	+	16.5793i	1.05349	+	0.608234i	0.923625	−	0.383298i	$-0.125212\pi$
$743$	28.7161	+	16.5793i	1.05349	+	0.608234i	0.129867	+	0.991531i	$0.458545\pi$
$744$		0			0
$745$	−3.32671	−	1.92068i	−0.121881	−	0.0703682i
$746$		0			0
$747$	−18.6892	+	19.3735i	−0.683802	+	0.708839i
$748$		0			0
$749$	−0.646497	−	26.6922i	−0.0236225	−	0.975312i
$750$		0			0
$751$	−21.6155	−	37.4391i	−0.788761	−	1.36617i	−0.926726	−	0.375737i	$-0.877390\pi$
$751$	−21.6155	−	37.4391i	−0.788761	−	1.36617i	0.137965	−	0.990437i	$-0.455944\pi$
$752$		0			0
$753$	15.2196	+	11.4625i	0.554632	+	0.417718i
$754$		0			0
$755$	−7.09789			−0.258319
$756$		0			0
$757$	33.2085			1.20698			0.603492	−	0.797369i	$-0.293776\pi$
$757$	33.2085			1.20698			0.603492	+	0.797369i	$0.293776\pi$
$758$		0			0
$759$	−35.5958	−	26.8088i	−1.29205	−	0.973097i
$760$		0			0
$761$	−2.15969	−	3.74069i	−0.0782887	−	0.135600i	0.824223	−	0.566265i	$-0.191612\pi$
$761$	−2.15969	−	3.74069i	−0.0782887	−	0.135600i	−0.902512	+	0.430665i	$0.858279\pi$
$762$		0			0
$763$	−1.38964	+	2.54746i	−0.0503084	+	0.0922241i
$764$		0			0
$765$	−4.49105	−	1.11725i	−0.162374	−	0.0403943i
$766$		0			0
$767$	22.5673	+	13.0292i	0.814859	+	0.470459i
$768$		0			0
$769$	16.1845	+	9.34412i	0.583628	+	0.336958i	0.762574	−	0.646901i	$-0.223935\pi$
$769$	16.1845	+	9.34412i	0.583628	+	0.336958i	−0.178946	+	0.983859i	$0.557269\pi$
$770$		0			0
$771$	1.99799	−	16.3076i	0.0719560	−	0.587303i
$772$		0			0
$773$	4.91482	+	8.51272i	0.176774	+	0.306181i	0.940774	−	0.339035i	$-0.110101\pi$
$773$	4.91482	+	8.51272i	0.176774	+	0.306181i	−0.764000	+	0.645216i	$0.776767\pi$
$774$		0			0
$775$	22.9252	+	13.2359i	0.823497	+	0.475446i
$776$		0			0
$777$	3.37902	+	2.41892i	0.121222	+	0.0867784i
$778$		0			0
$779$	49.9427	−	28.8345i	1.78938	−	1.03310i
$780$		0			0
$781$	1.60511	−	2.78014i	0.0574354	−	0.0994811i
$782$		0			0
$783$	7.63890	+	47.9865i	0.272992	+	1.71490i
$784$		0			0
$785$	8.55966	−	4.94192i	0.305507	−	0.176385i
$786$		0			0
$787$			45.4273i			1.61931i	0.586908	+	0.809654i	$0.300345\pi$
$787$			45.4273i			1.61931i	−0.586908	+	0.809654i	$0.699655\pi$
$788$		0			0
$789$	12.7645	+	30.0494i	0.454428	+	1.06979i
$790$		0			0
$791$	−0.630130	−	26.0165i	−0.0224049	−	0.925039i
$792$		0			0
$793$	5.82061	−	10.0816i	0.206696	−	0.358008i
$794$		0			0
$795$	−1.26570	−	2.97964i	−0.0448897	−	0.105677i
$796$		0			0
$797$	7.67140	−	13.2872i	0.271735	−	0.470658i	−0.697571	−	0.716515i	$-0.745736\pi$
$797$	7.67140	−	13.2872i	0.271735	−	0.470658i	0.969306	+	0.245857i	$0.0790693\pi$
$798$		0			0
$799$	−6.05322	−	10.4845i	−0.214147	−	0.370914i
$800$		0			0
$801$	−10.0051	−	2.48899i	−0.353512	−	0.0879442i
$802$		0			0
$803$	9.27139			0.327180
$804$		0			0
$805$	0.432161	+	17.8428i	0.0152317	+	0.628878i
$806$		0			0
$807$	−4.22252	+	34.4641i	−0.148640	+	1.21319i
$808$		0			0
$809$	0.785783	−	0.453672i	0.0276267	−	0.0159503i	−0.486123	−	0.873890i	$-0.661589\pi$
$809$	0.785783	−	0.453672i	0.0276267	−	0.0159503i	0.513750	+	0.857940i	$0.328256\pi$
$810$		0			0
$811$		−	7.95121i		−	0.279205i	−0.990208	−	0.139602i	$-0.955418\pi$
$811$		−	7.95121i		−	0.279205i	0.990208	−	0.139602i	$-0.0445824\pi$
$812$		0			0
$813$	13.5565	+	31.9139i	0.475447	+	1.11927i
$814$		0			0
$815$	7.84367			0.274752
$816$		0			0
$817$		−	93.7255i		−	3.27904i
$818$		0			0
$819$	−32.3446	+	10.1470i	−1.13021	+	0.354564i
$820$		0			0
$821$			46.8699i			1.63577i	0.575380	+	0.817886i	$0.304854\pi$
$821$			46.8699i			1.63577i	−0.575380	+	0.817886i	$0.695146\pi$
$822$		0			0
$823$	−20.9899			−0.731661			−0.365831	−	0.930681i	$-0.619215\pi$
$823$	−20.9899			−0.731661			−0.365831	+	0.930681i	$0.619215\pi$
$824$		0			0
$825$	27.0955	+	3.31972i	0.943345	+	0.115578i
$826$		0			0
$827$		−	12.6370i		−	0.439430i	−0.975564	−	0.219715i	$-0.929487\pi$
$827$		−	12.6370i		−	0.439430i	0.975564	−	0.219715i	$-0.0705127\pi$
$828$		0			0
$829$	3.12273	−	1.80291i	0.108457	−	0.0626177i	−0.444790	−	0.895635i	$-0.646722\pi$
$829$	3.12273	−	1.80291i	0.108457	−	0.0626177i	0.553247	+	0.833017i	$0.313388\pi$
$830$		0			0
$831$	−5.43209	+	2.30746i	−0.188437	+	0.0800450i
$832$		0			0
$833$	10.0347	−	0.486376i	0.347682	−	0.0168519i
$834$		0			0
$835$	−15.2010			−0.526051
$836$		0			0
$837$	33.4107	+	12.7951i	1.15484	+	0.442263i
$838$		0			0
$839$	0.287256	+	0.497541i	0.00991716	+	0.0171770i	0.870941	−	0.491387i	$-0.163510\pi$
$839$	0.287256	+	0.497541i	0.00991716	+	0.0171770i	−0.861024	+	0.508564i	$0.830177\pi$
$840$		0			0
$841$	29.2234	−	50.6163i	1.00770	−	1.74539i
$842$		0			0
$843$	−31.8246	−	3.89913i	−1.09610	−	0.134293i
$844$		0			0
$845$	2.81626	−	4.87790i	0.0968822	−	0.167805i
$846$		0			0
$847$	−7.35416	+	13.4815i	−0.252692	+	0.463228i
$848$		0			0
$849$	−26.1667	+	34.7432i	−0.898037	+	1.19238i
$850$		0			0
$851$		−	5.69137i		−	0.195098i
$852$		0			0
$853$	5.62283	−	3.24634i	0.192522	−	0.111153i	−0.400641	−	0.916235i	$-0.631212\pi$
$853$	5.62283	−	3.24634i	0.192522	−	0.111153i	0.593163	+	0.805083i	$0.297879\pi$
$854$		0			0
$855$	−22.9738	+	6.60064i	−0.785688	+	0.225737i
$856$		0			0
$857$	−1.15768	+	2.00517i	−0.0395457	+	0.0684952i	−0.885121	−	0.465361i	$-0.845924\pi$
$857$	−1.15768	+	2.00517i	−0.0395457	+	0.0684952i	0.845575	+	0.533857i	$0.179258\pi$
$858$		0			0
$859$	−48.1991	+	27.8278i	−1.64453	+	0.949471i	−0.665338	+	0.746542i	$0.731713\pi$
$859$	−48.1991	+	27.8278i	−1.64453	+	0.949471i	−0.979194	+	0.202929i	$0.934954\pi$
$860$		0			0
$861$	28.9883	+	20.7517i	0.987918	+	0.707217i
$862$		0			0
$863$	−7.50527	−	4.33317i	−0.255482	−	0.147503i	0.366790	−	0.930304i	$-0.380457\pi$
$863$	−7.50527	−	4.33317i	−0.255482	−	0.147503i	−0.622272	+	0.782801i	$0.713790\pi$
$864$		0			0
$865$	−7.25443	−	12.5650i	−0.246658	−	0.427224i
$866$		0			0
$867$	−23.8174	+	10.1172i	−0.808880	+	0.343599i
$868$		0			0
$869$	5.80593	+	3.35206i	0.196953	+	0.113711i
$870$		0			0
$871$	−44.5286	−	25.7086i	−1.50879	−	0.871102i
$872$		0			0
$873$	−12.5906	−	12.1459i	−0.426129	−	0.411077i
$874$		0			0
$875$	−13.1000	−	21.4718i	−0.442860	−	0.725879i
$876$		0			0
$877$	−17.8315	−	30.8850i	−0.602126	−	1.04291i	−0.992499	−	0.122255i	$-0.960987\pi$
$877$	−17.8315	−	30.8850i	−0.602126	−	1.04291i	0.390373	−	0.920657i	$-0.372346\pi$
$878$		0			0
$879$	3.54861	−	1.50739i	0.119692	−	0.0508431i
$880$		0			0
$881$	−7.57740			−0.255289			−0.127644	−	0.991820i	$-0.540742\pi$
$881$	−7.57740			−0.255289			−0.127644	+	0.991820i	$0.540742\pi$
$882$		0			0
$883$	5.35854			0.180329			0.0901646	−	0.995927i	$-0.471261\pi$
$883$	5.35854			0.180329			0.0901646	+	0.995927i	$0.471261\pi$
$884$		0			0
$885$	−1.38138	+	11.2748i	−0.0464345	+	0.378998i
$886$		0			0
$887$	11.7952	+	20.4299i	0.396045	+	0.685970i	0.993234	−	0.116131i	$-0.0370492\pi$
$887$	11.7952	+	20.4299i	0.396045	+	0.685970i	−0.597189	+	0.802100i	$0.703716\pi$
$888$		0			0
$889$	−20.9728	−	34.3759i	−0.703405	−	1.15293i
$890$		0			0
$891$	36.8700	−	1.32613i	1.23519	−	0.0444269i
$892$		0			0
$893$	−54.1523	−	31.2648i	−1.81214	−	1.04624i
$894$		0			0
$895$	4.26755	+	2.46387i	0.142649	+	0.0823582i
$896$		0			0
$897$	37.0854	+	27.9307i	1.23825	+	0.932579i
$898$		0			0
$899$	−32.1931	−	55.7601i	−1.07370	−	1.85970i
$900$		0			0
$901$	2.16134	+	1.24785i	0.0720046	+	0.0415719i
$902$		0			0
$903$	52.7643	−	23.9376i	1.75589	−	0.796595i
$904$		0			0
$905$	−2.07487	+	1.19793i	−0.0689711	+	0.0398205i
$906$		0			0
$907$	−7.13516	+	12.3585i	−0.236919	+	0.410356i	−0.959829	−	0.280587i	$-0.909471\pi$
$907$	−7.13516	+	12.3585i	−0.236919	+	0.410356i	0.722910	+	0.690943i	$0.242804\pi$
$908$		0			0
$909$	−13.4629	−	3.34919i	−0.446535	−	0.111086i
$910$		0			0
$911$	40.0156	−	23.1030i	1.32578	−	0.765437i	0.341133	−	0.940015i	$-0.389189\pi$
$911$	40.0156	−	23.1030i	1.32578	−	0.765437i	0.984643	+	0.174578i	$0.0558560\pi$
$912$		0			0
$913$		−	36.7828i		−	1.21733i
$914$		0			0
$915$	5.03683	+	0.617108i	0.166512	+	0.0204010i
$916$		0			0
$917$	11.2875	−	20.6920i	0.372748	−	0.683312i
$918$		0			0
$919$	16.8957	−	29.2643i	0.557339	−	0.965339i	−0.440379	−	0.897812i	$-0.645156\pi$
$919$	16.8957	−	29.2643i	0.557339	−	0.965339i	0.997717	−	0.0675269i	$-0.0215109\pi$
$920$		0			0
$921$	25.2725	−	33.5560i	0.832757	−	1.10571i
$922$		0			0
$923$	−1.67228	+	2.89648i	−0.0550439	+	0.0953389i
$924$		0			0
$925$	1.74323	+	3.01936i	0.0573171	+	0.0992761i
$926$		0			0
$927$	9.18591	+	8.86145i	0.301705	+	0.291048i
$928$		0			0
$929$	34.9369			1.14624			0.573121	−	0.819471i	$-0.305733\pi$
$929$	34.9369			1.14624			0.573121	+	0.819471i	$0.305733\pi$
$930$		0			0
$931$	43.6294	−	28.0902i	1.42990	−	0.920619i
$932$		0			0
$933$	−27.1591	−	20.4548i	−0.889151	−	0.669659i
$934$		0			0
$935$	5.47655	−	3.16189i	0.179102	−	0.103405i
$936$		0			0
$937$		−	11.6175i		−	0.379528i	−0.981830	−	0.189764i	$-0.939228\pi$
$937$		−	11.6175i		−	0.379528i	0.981830	−	0.189764i	$-0.0607723\pi$
$938$		0			0
$939$	17.8755	−	23.7344i	0.583343	−	0.774544i
$940$		0			0
$941$	−9.55030			−0.311331			−0.155665	−	0.987810i	$-0.549752\pi$
$941$	−9.55030			−0.311331			−0.155665	+	0.987810i	$0.549752\pi$
$942$		0			0
$943$		−	48.8257i		−	1.58998i
$944$		0			0
$945$	−9.58349	−	11.2477i	−0.311751	−	0.365887i
$946$		0			0
$947$			36.6873i			1.19218i	0.802919	+	0.596088i	$0.203279\pi$
$947$			36.6873i			1.19218i	−0.802919	+	0.596088i	$0.796721\pi$
$948$		0			0
$949$	−9.65938			−0.313557
$950$		0			0
$951$	12.9738	−	17.2261i	0.420703	−	0.558596i
$952$		0			0
$953$		−	17.1813i		−	0.556556i	−0.960501	−	0.278278i	$-0.910236\pi$
$953$		−	17.1813i		−	0.556556i	0.960501	−	0.278278i	$-0.0897636\pi$
$954$		0			0
$955$	19.5805	−	11.3048i	0.633610	−	0.365815i
$956$		0			0
$957$	−53.0368	−	39.9444i	−1.71444	−	1.29122i
$958$		0			0
$959$	−0.722227	−	29.8189i	−0.0233219	−	0.962902i
$960$		0			0
$961$	−16.4069			−0.529256
$962$		0			0
$963$	7.30883	−	29.3795i	0.235524	−	0.946742i
$964$		0			0
$965$	6.02146	+	10.4295i	0.193838	+	0.335737i
$966$		0			0
$967$	2.43550	−	4.21841i	0.0783204	−	0.135655i	−0.824205	−	0.566292i	$-0.808378\pi$
$967$	2.43550	−	4.21841i	0.0783204	−	0.135655i	0.902525	+	0.430637i	$0.141711\pi$
$968$		0			0
$969$	11.0860	−	14.7197i	0.356134	−	0.472864i
$970$		0			0
$971$	14.0544	−	24.3429i	0.451026	−	0.781200i	−0.547424	−	0.836855i	$-0.684392\pi$
$971$	14.0544	−	24.3429i	0.451026	−	0.781200i	0.998450	+	0.0556556i	$0.0177249\pi$
$972$		0			0
$973$	0.891137	+	36.7928i	0.0285686	+	1.17952i
$974$		0			0
$975$	−28.2294	−	3.45865i	−0.904065	−	0.110765i
$976$		0			0
$977$		−	30.5582i		−	0.977643i	−0.872384	−	0.488822i	$-0.837427\pi$
$977$		−	30.5582i		−	0.977643i	0.872384	−	0.488822i	$-0.162573\pi$
$978$		0			0
$979$	12.2006	−	7.04401i	0.389932	−	0.225127i
$980$		0			0
$981$	−2.28445	+	2.36809i	−0.0729367	+	0.0756073i
$982$		0			0
$983$	−5.98556	+	10.3673i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$983$	−5.98556	+	10.3673i	−0.190910	+	0.330665i	0.754642	+	0.656137i	$0.227810\pi$
$984$		0			0
$985$	−19.4497	+	11.2293i	−0.619718	+	0.357794i
$986$		0			0
$987$	3.77046	−	38.4710i	0.120015	−	1.22455i
$988$		0			0
$989$	−68.7219	−	39.6766i	−2.18523	−	1.26164i
$990$		0			0
$991$	3.32513	+	5.75929i	0.105626	+	0.182950i	0.913994	−	0.405728i	$-0.132982\pi$
$991$	3.32513	+	5.75929i	0.105626	+	0.182950i	−0.808368	+	0.588678i	$0.799649\pi$
$992$		0			0
$993$	−42.7759	−	32.2165i	−1.35745	−	1.02236i
$994$		0			0
$995$	−17.0387	−	9.83730i	−0.540163	−	0.311863i
$996$		0			0
$997$	47.6751	+	27.5252i	1.50989	+	0.871733i	0.999934	+	0.0115298i	$0.00367014\pi$
$997$	47.6751	+	27.5252i	1.50989	+	0.871733i	0.509952	+	0.860203i	$0.329663\pi$
$998$		0			0
$999$	2.96823	+	3.65959i	0.0939106	+	0.115784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.e.257.4		48
3.2	odd	2		3024.2.ca.e.2609.16		48
4.3	odd	2		504.2.bs.a.257.21	✓	48
7.3	odd	6		1008.2.df.e.689.13		48
9.2	odd	6		1008.2.df.e.929.13		48
9.7	even	3		3024.2.df.e.1601.16		48
12.11	even	2		1512.2.bs.a.1097.16		48
21.17	even	6		3024.2.df.e.17.16		48
28.3	even	6		504.2.cx.a.185.12	yes	48
36.7	odd	6		1512.2.cx.a.89.16		48
36.11	even	6		504.2.cx.a.425.12	yes	48
63.38	even	6	inner	1008.2.ca.e.353.4		48
63.52	odd	6		3024.2.ca.e.2033.16		48
84.59	odd	6		1512.2.cx.a.17.16		48
252.115	even	6		1512.2.bs.a.521.16		48
252.227	odd	6		504.2.bs.a.353.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.21	✓	48	4.3	odd	2
504.2.bs.a.353.21	yes	48	252.227	odd	6
504.2.cx.a.185.12	yes	48	28.3	even	6
504.2.cx.a.425.12	yes	48	36.11	even	6
1008.2.ca.e.257.4		48	1.1	even	1	trivial
1008.2.ca.e.353.4		48	63.38	even	6	inner
1008.2.df.e.689.13		48	7.3	odd	6
1008.2.df.e.929.13		48	9.2	odd	6
1512.2.bs.a.521.16		48	252.115	even	6
1512.2.bs.a.1097.16		48	12.11	even	2
1512.2.cx.a.17.16		48	84.59	odd	6
1512.2.cx.a.89.16		48	36.7	odd	6
3024.2.ca.e.2033.16		48	63.52	odd	6
3024.2.ca.e.2609.16		48	3.2	odd	2
3024.2.df.e.17.16		48	21.17	even	6
3024.2.df.e.1601.16		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)

\(f(q)\)	\(=\)	\(q+(-1.38355 - 1.04201i) q^{3} +(-0.537427 - 0.930850i) q^{5} +(1.37797 + 2.25858i) q^{7} +(0.828420 + 2.88335i) q^{9} +(-3.55011 - 2.04966i) q^{11} +(3.69867 + 2.13543i) q^{13} +(-0.226401 + 1.84788i) q^{15} +(-0.717607 - 1.24293i) q^{17} +(-6.41973 - 3.70644i) q^{19} +(0.446987 - 4.56072i) q^{21} +(-5.43530 + 3.13807i) q^{23} +(1.92235 - 3.32960i) q^{25} +(1.85833 - 4.85249i) q^{27} +(-8.09846 + 4.67565i) q^{29} +6.88527i q^{31} +(2.77598 + 6.53506i) q^{33} +(1.36185 - 2.49651i) q^{35} +(-0.453413 + 0.785334i) q^{37} +(-2.89215 - 6.80854i) q^{39} +(-3.88978 + 6.73730i) q^{41} +(6.32181 + 10.9497i) q^{43} +(2.23875 - 2.32073i) q^{45} +8.43528 q^{47} +(-3.20241 + 6.22451i) q^{49} +(-0.302305 + 2.46741i) q^{51} +(-1.50593 + 0.869452i) q^{53} +4.40616i q^{55} +(5.01987 + 11.8175i) q^{57} +6.10146 q^{59} -2.72573i q^{61} +(-5.37076 + 5.84422i) q^{63} -4.59055i q^{65} -12.0391 q^{67} +(10.7899 + 1.32197i) q^{69} +0.783113i q^{71} +(-1.95868 + 1.13085i) q^{73} +(-6.12914 + 2.60356i) q^{75} +(-0.262612 - 10.8426i) q^{77} -1.63543 q^{79} +(-7.62744 + 4.77725i) q^{81} +(4.48646 + 7.77077i) q^{83} +(-0.771322 + 1.33597i) q^{85} +(16.0767 + 1.96971i) q^{87} +(-1.71834 + 2.97625i) q^{89} +(0.273602 + 11.2963i) q^{91} +(7.17454 - 9.52611i) q^{93} +7.96775i q^{95} +(-5.05015 + 2.91570i) q^{97} +(2.96890 - 11.9342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) \) 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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