LMFDB - Embedded newform 736.2.r.a.687.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [736,2,Mod(15,736)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("736.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(736, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 736 = 2^{5} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	736.r (of order $22$, degree $10$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.87698958877$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			687.22
Character	$\chi$	$=$	736.687
Dual form			736.2.r.a.15.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18656 - 2.59820i) q^{3} +(1.01624 - 1.17280i) q^{5} +(4.25438 - 2.73413i) q^{7} +(-3.37812 - 3.89856i) q^{9} +(-1.77318 - 0.254945i) q^{11} +(0.511843 - 0.796443i) q^{13} +(-1.84135 - 4.03199i) q^{15} +(-1.67446 + 5.70268i) q^{17} +(0.812847 + 2.76830i) q^{19} +(-2.05573 - 14.2979i) q^{21} +(3.08571 + 3.67130i) q^{23} +(0.368850 + 2.56541i) q^{25} +(-5.91571 + 1.73701i) q^{27} +(-1.87742 + 6.39390i) q^{29} +(2.15218 - 0.982870i) q^{31} +(-2.76637 + 4.30456i) q^{33} +(1.11688 - 7.76808i) q^{35} +(3.98474 + 4.59863i) q^{37} +(-1.46198 - 2.27489i) q^{39} +(-3.66827 + 4.23341i) q^{41} +(-5.98202 - 2.73190i) q^{43} -8.00523 q^{45} -4.26175i q^{47} +(7.71643 - 16.8966i) q^{49} +(12.8298 + 11.1171i) q^{51} +(-3.03402 + 1.94985i) q^{53} +(-2.10098 + 1.82051i) q^{55} +(8.15708 + 1.17281i) q^{57} +(-2.53954 - 1.63207i) q^{59} +(-2.27952 - 4.99144i) q^{61} +(-25.0310 - 7.34976i) q^{63} +(-0.413916 - 1.40967i) q^{65} +(-10.4452 + 1.50179i) q^{67} +(13.2001 - 3.66107i) q^{69} +(-2.06420 + 0.296788i) q^{71} +(-2.05582 + 0.603644i) q^{73} +(7.10309 + 2.08566i) q^{75} +(-8.24084 + 3.76346i) q^{77} +(-6.55104 - 4.21010i) q^{79} +(-0.303823 + 2.11314i) q^{81} +(-6.06755 + 5.25756i) q^{83} +(4.98647 + 7.75910i) q^{85} +(14.3849 + 12.4646i) q^{87} +(2.48788 + 1.13618i) q^{89} -4.78782i q^{91} -6.75803i q^{93} +(4.07272 + 1.85995i) q^{95} +(0.549986 + 0.476566i) q^{97} +(4.99610 + 7.77408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 18 q^{3} - 36 q^{9} + 22 q^{11} - 22 q^{17} + 22 q^{19} - 32 q^{25} + 18 q^{27} - 22 q^{33} - 2 q^{35} - 18 q^{41} + 22 q^{43} - 28 q^{49} + 22 q^{51} - 22 q^{57} + 6 q^{59} - 22 q^{65} + 22 q^{67}+ \cdots + 22 q^{99}+O(q^{100}) $ 220 * q + 18 * q^3 - 36 * q^9 + 22 * q^11 - 22 * q^17 + 22 * q^19 - 32 * q^25 + 18 * q^27 - 22 * q^33 - 2 * q^35 - 18 * q^41 + 22 * q^43 - 28 * q^49 + 22 * q^51 - 22 * q^57 + 6 * q^59 - 22 * q^65 + 22 * q^67 - 18 * q^73 - 14 * q^75 + 4 * q^81 + 22 * q^83 - 22 * q^89 - 22 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/736\mathbb{Z}\right)^\times$.

$n$	$97$	$415$	$645$
$\chi(n)$	$e\left(\frac{5}{22}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.18656	−	2.59820i	0.685058	−	1.50007i	−0.172135	−	0.985073i	$-0.555066\pi$
$3$	1.18656	−	2.59820i	0.685058	−	1.50007i	0.857193	−	0.514995i	$-0.172206\pi$
$4$		0			0
$5$	1.01624	−	1.17280i	0.454476	−	0.524494i	−0.481552	−	0.876417i	$-0.659927\pi$
$5$	1.01624	−	1.17280i	0.454476	−	0.524494i	0.936029	+	0.351924i	$0.114472\pi$
$6$		0			0
$7$	4.25438	−	2.73413i	1.60801	−	1.03340i	0.644905	−	0.764263i	$-0.276897\pi$
$7$	4.25438	−	2.73413i	1.60801	−	1.03340i	0.963101	−	0.269140i	$-0.0867394\pi$
$8$		0			0
$9$	−3.37812	−	3.89856i	−1.12604	−	1.29952i
$10$		0			0
$11$	−1.77318	−	0.254945i	−0.534634	−	0.0768687i	−0.130290	−	0.991476i	$-0.541591\pi$
$11$	−1.77318	−	0.254945i	−0.534634	−	0.0768687i	−0.404344	+	0.914607i	$0.632500\pi$
$12$		0			0
$13$	0.511843	−	0.796443i	0.141960	−	0.220894i	−0.762992	−	0.646408i	$-0.776270\pi$
$13$	0.511843	−	0.796443i	0.141960	−	0.220894i	0.904952	+	0.425514i	$0.139907\pi$
$14$		0			0
$15$	−1.84135	−	4.03199i	−0.475434	−	1.04105i
$16$		0			0
$17$	−1.67446	+	5.70268i	−0.406116	+	1.38310i	0.462061	+	0.886848i	$0.347110\pi$
$17$	−1.67446	+	5.70268i	−0.406116	+	1.38310i	−0.868177	+	0.496255i	$0.834708\pi$
$18$		0			0
$19$	0.812847	+	2.76830i	0.186480	+	0.635093i	0.998663	+	0.0516900i	$0.0164608\pi$
$19$	0.812847	+	2.76830i	0.186480	+	0.635093i	−0.812183	+	0.583403i	$0.801721\pi$
$20$		0			0
$21$	−2.05573	−	14.2979i	−0.448597	−	3.12006i
$22$		0			0
$23$	3.08571	+	3.67130i	0.643414	+	0.765518i
$23$	3.08571	+	3.67130i	0.643414	+	0.765518i
$24$		0			0
$25$	0.368850	+	2.56541i	0.0737700	+	0.513082i
$26$		0			0
$27$	−5.91571	+	1.73701i	−1.13848	+	0.334287i
$28$		0			0
$29$	−1.87742	+	6.39390i	−0.348628	+	1.18732i	0.579474	+	0.814991i	$0.303258\pi$
$29$	−1.87742	+	6.39390i	−0.348628	+	1.18732i	−0.928102	+	0.372326i	$0.878560\pi$
$30$		0			0
$31$	2.15218	−	0.982870i	0.386544	−	0.176529i	−0.212658	−	0.977127i	$-0.568212\pi$
$31$	2.15218	−	0.982870i	0.386544	−	0.176529i	0.599202	+	0.800598i	$0.295485\pi$
$32$		0			0
$33$	−2.76637	+	4.30456i	−0.481564	+	0.749328i
$34$		0			0
$35$	1.11688	−	7.76808i	0.188788	−	1.31305i
$36$		0			0
$37$	3.98474	+	4.59863i	0.655087	+	0.756010i	0.981966	−	0.189056i	$-0.0605426\pi$
$37$	3.98474	+	4.59863i	0.655087	+	0.756010i	−0.326880	+	0.945066i	$0.605997\pi$
$38$		0			0
$39$	−1.46198	−	2.27489i	−0.234105	−	0.364274i
$40$		0			0
$41$	−3.66827	+	4.23341i	−0.572888	+	0.661148i	−0.966060	−	0.258317i	$-0.916832\pi$
$41$	−3.66827	+	4.23341i	−0.572888	+	0.661148i	0.393172	+	0.919465i	$0.371378\pi$
$42$		0			0
$43$	−5.98202	−	2.73190i	−0.912250	−	0.416611i	−0.0967109	−	0.995313i	$-0.530832\pi$
$43$	−5.98202	−	2.73190i	−0.912250	−	0.416611i	−0.815539	+	0.578702i	$0.803559\pi$
$44$		0			0
$45$	−8.00523			−1.19335
$46$		0			0
$47$		−	4.26175i		−	0.621641i	−0.950469	−	0.310820i	$-0.899396\pi$
$47$		−	4.26175i		−	0.621641i	0.950469	−	0.310820i	$-0.100604\pi$
$48$		0			0
$49$	7.71643	−	16.8966i	1.10235	−	2.41380i
$50$		0			0
$51$	12.8298	+	11.1171i	1.79654	+	1.55671i
$52$		0			0
$53$	−3.03402	+	1.94985i	−0.416755	+	0.267832i	−0.732170	−	0.681122i	$-0.761492\pi$
$53$	−3.03402	+	1.94985i	−0.416755	+	0.267832i	0.315416	+	0.948954i	$0.397856\pi$
$54$		0			0
$55$	−2.10098	+	1.82051i	−0.283296	+	0.245477i
$56$		0			0
$57$	8.15708	+	1.17281i	1.08043	+	0.155343i
$58$		0			0
$59$	−2.53954	−	1.63207i	−0.330620	−	0.212477i	0.364790	−	0.931090i	$-0.381141\pi$
$59$	−2.53954	−	1.63207i	−0.330620	−	0.212477i	−0.695410	+	0.718613i	$0.744777\pi$
$60$		0			0
$61$	−2.27952	−	4.99144i	−0.291862	−	0.639089i	0.705727	−	0.708484i	$-0.250620\pi$
$61$	−2.27952	−	4.99144i	−0.291862	−	0.639089i	−0.997589	+	0.0693948i	$0.977893\pi$
$62$		0			0
$63$	−25.0310	−	7.34976i	−3.15361	−	0.925983i
$64$		0			0
$65$	−0.413916	−	1.40967i	−0.0513399	−	0.174848i
$66$		0			0
$67$	−10.4452	+	1.50179i	−1.27608	+	0.183472i	−0.746842	−	0.665002i	$-0.768431\pi$
$67$	−10.4452	+	1.50179i	−1.27608	+	0.183472i	−0.529237	+	0.848474i	$0.677522\pi$
$68$		0			0
$69$	13.2001	−	3.66107i	1.58911	−	0.440741i
$70$		0			0
$71$	−2.06420	+	0.296788i	−0.244976	+	0.0352222i	−0.263709	−	0.964602i	$-0.584946\pi$
$71$	−2.06420	+	0.296788i	−0.244976	+	0.0352222i	0.0187330	+	0.999825i	$0.494037\pi$
$72$		0			0
$73$	−2.05582	+	0.603644i	−0.240616	+	0.0706512i	−0.399817	−	0.916595i	$-0.630926\pi$
$73$	−2.05582	+	0.603644i	−0.240616	+	0.0706512i	0.159201	+	0.987246i	$0.449108\pi$
$74$		0			0
$75$	7.10309	+	2.08566i	0.820194	+	0.240831i
$76$		0			0
$77$	−8.24084	+	3.76346i	−0.939131	+	0.428887i
$78$		0			0
$79$	−6.55104	−	4.21010i	−0.737050	−	0.473673i	0.117480	−	0.993075i	$-0.462518\pi$
$79$	−6.55104	−	4.21010i	−0.737050	−	0.473673i	−0.854530	+	0.519402i	$0.826155\pi$
$80$		0			0
$81$	−0.303823	+	2.11314i	−0.0337582	+	0.234793i
$82$		0			0
$83$	−6.06755	+	5.25756i	−0.666000	+	0.577092i	−0.920864	−	0.389885i	$-0.872515\pi$
$83$	−6.06755	+	5.25756i	−0.666000	+	0.577092i	0.254864	+	0.966977i	$0.417969\pi$
$84$		0			0
$85$	4.98647	+	7.75910i	0.540859	+	0.841593i
$86$		0			0
$87$	14.3849	+	12.4646i	1.54223	+	1.33635i
$88$		0			0
$89$	2.48788	+	1.13618i	0.263715	+	0.120435i	0.542885	−	0.839807i	$-0.317332\pi$
$89$	2.48788	+	1.13618i	0.263715	+	0.120435i	−0.279170	+	0.960242i	$0.590059\pi$
$90$		0			0
$91$		−	4.78782i		−	0.501900i
$92$		0			0
$93$		−	6.75803i		−	0.700775i
$94$		0			0
$95$	4.07272	+	1.85995i	0.417853	+	0.190827i
$96$		0			0
$97$	0.549986	+	0.476566i	0.0558426	+	0.0483879i	0.682335	−	0.731040i	$-0.260965\pi$
$97$	0.549986	+	0.476566i	0.0558426	+	0.0483879i	−0.626492	+	0.779428i	$0.715510\pi$
$98$		0			0
$99$	4.99610	+	7.77408i	0.502127	+	0.781325i
$100$		0			0
$101$	4.97284	−	4.30899i	0.494816	−	0.428760i	−0.371368	−	0.928486i	$-0.621111\pi$
$101$	4.97284	−	4.30899i	0.494816	−	0.428760i	0.866184	+	0.499725i	$0.166566\pi$
$102$		0			0
$103$	0.433456	−	3.01475i	0.0427097	−	0.297052i	−0.957260	−	0.289230i	$-0.906601\pi$
$103$	0.433456	−	3.01475i	0.0427097	−	0.297052i	0.999969	−	0.00782265i	$-0.00249005\pi$
$104$		0			0
$105$	−18.8578	−	12.1191i	−1.84033	−	1.18271i
$106$		0			0
$107$	4.86924	−	2.22371i	0.470727	−	0.214974i	−0.165905	−	0.986142i	$-0.553054\pi$
$107$	4.86924	−	2.22371i	0.470727	−	0.214974i	0.636632	+	0.771168i	$0.280327\pi$
$108$		0			0
$109$	11.1429	+	3.27186i	1.06730	+	0.313388i	0.767787	−	0.640705i	$-0.221358\pi$
$109$	11.1429	+	3.27186i	1.06730	+	0.313388i	0.299513	+	0.954092i	$0.403176\pi$
$110$		0			0
$111$	16.6763	−	4.89659i	1.58284	−	0.464764i
$112$		0			0
$113$	5.70500	−	0.820255i	0.536681	−	0.0771631i	0.131355	−	0.991335i	$-0.458067\pi$
$113$	5.70500	−	0.820255i	0.536681	−	0.0771631i	0.405326	+	0.914172i	$0.367158\pi$
$114$		0			0
$115$	7.44153	+	0.111989i	0.693926	+	0.0104430i
$116$		0			0
$117$	−4.83405	+	0.695031i	−0.446908	+	0.0642556i
$118$		0			0
$119$	8.46807	+	28.8396i	0.776266	+	2.64372i
$120$		0			0
$121$	−7.47525	−	2.19493i	−0.679568	−	0.199539i
$122$		0			0
$123$	6.64662	+	14.5541i	0.599306	+	1.31230i
$124$		0			0
$125$	9.91102	+	6.36943i	0.886468	+	0.569699i
$126$		0			0
$127$	−7.31678	−	1.05199i	−0.649259	−	0.0933494i	−0.190186	−	0.981748i	$-0.560909\pi$
$127$	−7.31678	−	1.05199i	−0.649259	−	0.0933494i	−0.459073	+	0.888399i	$0.651818\pi$
$128$		0			0
$129$	−14.1960	+	12.3009i	−1.24989	+	1.08304i
$130$		0			0
$131$	10.2101	−	6.56165i	0.892062	−	0.573294i	−0.0123639	−	0.999924i	$-0.503936\pi$
$131$	10.2101	−	6.56165i	0.892062	−	0.573294i	0.904426	+	0.426630i	$0.140299\pi$
$132$		0			0
$133$	11.0271	+	9.55500i	0.956167	+	0.828524i
$134$		0			0
$135$	−3.97461	+	8.70318i	−0.342080	+	0.749050i
$136$		0			0
$137$		−	7.56507i		−	0.646328i	−0.946343	−	0.323164i	$-0.895254\pi$
$137$		−	7.56507i		−	0.646328i	0.946343	−	0.323164i	$-0.104746\pi$
$138$		0			0
$139$	0.118762			0.0100732			0.00503662	−	0.999987i	$-0.498397\pi$
$139$	0.118762			0.0100732			0.00503662	+	0.999987i	$0.498397\pi$
$140$		0			0
$141$	−11.0729	−	5.05681i	−0.932504	−	0.425860i
$142$		0			0
$143$	−1.11064	+	1.28174i	−0.0928762	+	0.107185i
$144$		0			0
$145$	5.59088	+	8.69958i	0.464297	+	0.722460i
$146$		0			0
$147$	−34.7448	−	40.0976i	−2.86570	−	3.30719i
$148$		0			0
$149$	−0.0580693	+	0.403881i	−0.00475722	+	0.0330872i	−0.992062	−	0.125751i	$-0.959866\pi$
$149$	−0.0580693	+	0.403881i	−0.00475722	+	0.0330872i	0.987305	+	0.158839i	$0.0507749\pi$
$150$		0			0
$151$	10.8362	−	16.8615i	0.881841	−	1.37217i	−0.0459004	−	0.998946i	$-0.514616\pi$
$151$	10.8362	−	16.8615i	0.881841	−	1.37217i	0.927741	−	0.373225i	$-0.121748\pi$
$152$		0			0
$153$	27.8888	−	12.7364i	2.25467	−	1.02967i
$154$		0			0
$155$	1.03442	−	3.52292i	0.0830869	−	0.282968i
$156$		0			0
$157$	4.95710	−	1.45554i	0.395620	−	0.116164i	−0.0778705	−	0.996963i	$-0.524812\pi$
$157$	4.95710	−	1.45554i	0.395620	−	0.116164i	0.473490	+	0.880799i	$0.342994\pi$
$158$		0			0
$159$	1.46605	+	10.1966i	0.116265	+	0.808641i
$160$		0			0
$161$	23.1656	+	7.18239i	1.82570	+	0.566051i
$162$		0			0
$163$	2.18799	+	15.2178i	0.171377	+	1.19195i	0.875979	+	0.482349i	$0.160216\pi$
$163$	2.18799	+	15.2178i	0.171377	+	1.19195i	−0.704602	+	0.709602i	$0.748875\pi$
$164$		0			0
$165$	2.23710	+	7.61888i	0.174158	+	0.593129i
$166$		0			0
$167$	6.78687	−	23.1139i	0.525183	−	1.78861i	−0.0850357	−	0.996378i	$-0.527100\pi$
$167$	6.78687	−	23.1139i	0.525183	−	1.78861i	0.610219	−	0.792233i	$-0.291081\pi$
$168$		0			0
$169$	5.02806	+	11.0099i	0.386774	+	0.846916i
$170$		0			0
$171$	8.04650	−	12.5206i	0.615331	−	0.957474i
$172$		0			0
$173$	−23.6841	−	3.40525i	−1.80067	−	0.258897i	−0.841200	−	0.540724i	$-0.818150\pi$
$173$	−23.6841	−	3.40525i	−1.80067	−	0.258897i	−0.959465	+	0.281827i	$0.909060\pi$
$174$		0			0
$175$	8.58338	+	9.90575i	0.648843	+	0.748804i
$176$		0			0
$177$	−7.25374	+	4.66169i	−0.545224	+	0.350394i
$178$		0			0
$179$	0.730648	−	0.843213i	0.0546112	−	0.0630247i	−0.727787	−	0.685804i	$-0.759451\pi$
$179$	0.730648	−	0.843213i	0.0546112	−	0.0630247i	0.782398	+	0.622779i	$0.213996\pi$
$180$		0			0
$181$	2.00254	−	4.38495i	0.148847	−	0.325931i	−0.820491	−	0.571659i	$-0.806300\pi$
$181$	2.00254	−	4.38495i	0.148847	−	0.325931i	0.969339	+	0.245729i	$0.0790272\pi$
$182$		0			0
$183$	−15.6735			−1.15862
$184$		0			0
$185$	9.44274			0.694244
$186$		0			0
$187$	4.42299	−	9.68499i	0.323441	−	0.708236i
$188$		0			0
$189$	−20.4185	+	23.5642i	−1.48523	+	1.71404i
$190$		0			0
$191$	−16.9573	+	10.8978i	−1.22699	+	0.788538i	−0.983420	−	0.181345i	$-0.941955\pi$
$191$	−16.9573	+	10.8978i	−1.22699	+	0.788538i	−0.243570	+	0.969883i	$0.578319\pi$
$192$		0			0
$193$	−15.5292	−	17.9216i	−1.11781	−	1.29002i	−0.952755	−	0.303741i	$-0.901764\pi$
$193$	−15.5292	−	17.9216i	−1.11781	−	1.29002i	−0.165058	−	0.986284i	$-0.552781\pi$
$194$		0			0
$195$	−4.15373	−	0.597216i	−0.297455	−	0.0427675i
$196$		0			0
$197$	−7.43508	+	11.5692i	−0.529727	+	0.824272i	−0.998247	−	0.0591811i	$-0.981151\pi$
$197$	−7.43508	+	11.5692i	−0.529727	+	0.824272i	0.468520	+	0.883453i	$0.344787\pi$
$198$		0			0
$199$	4.70110	+	10.2940i	0.333252	+	0.729721i	0.999877	−	0.0156724i	$-0.00498888\pi$
$199$	4.70110	+	10.2940i	0.333252	+	0.729721i	−0.666625	+	0.745394i	$0.732262\pi$
$200$		0			0
$201$	−8.49183	+	28.9205i	−0.598967	+	2.03990i
$202$		0			0
$203$	9.49447	+	32.3352i	0.666381	+	2.26949i
$204$		0			0
$205$	1.23712	+	8.60433i	0.0864039	+	0.600952i
$206$		0			0
$207$	3.88887	−	24.4319i	0.270295	−	1.69813i
$208$		0			0
$209$	−0.735560	−	5.11593i	−0.0508797	−	0.353876i
$210$		0			0
$211$	−19.8313	+	5.82299i	−1.36524	+	0.400871i	−0.880608	−	0.473846i	$-0.842866\pi$
$211$	−19.8313	+	5.82299i	−1.36524	+	0.400871i	−0.484634	+	0.874717i	$0.661047\pi$
$212$		0			0
$213$	−1.67818	+	5.71536i	−0.114987	+	0.391610i
$214$		0			0
$215$	−9.28315	+	4.23947i	−0.633106	+	0.289130i
$216$		0			0
$217$	6.46893	−	10.0659i	0.439140	−	0.683315i
$218$		0			0
$219$	−0.870964	+	6.05769i	−0.0588543	+	0.409340i
$220$		0			0
$221$	3.68480	+	4.25249i	0.247867	+	0.286053i
$222$		0			0
$223$	9.09188	+	14.1472i	0.608838	+	0.947370i	0.999638	+	0.0268945i	$0.00856182\pi$
$223$	9.09188	+	14.1472i	0.608838	+	0.947370i	−0.390801	+	0.920475i	$0.627802\pi$
$224$		0			0
$225$	8.75538	−	10.1042i	0.583692	−	0.673616i
$226$		0			0
$227$	8.26371	+	3.77391i	0.548482	+	0.250483i	0.670327	−	0.742066i	$-0.266154\pi$
$227$	8.26371	+	3.77391i	0.548482	+	0.250483i	−0.121845	+	0.992549i	$0.538881\pi$
$228$		0			0
$229$	5.97598			0.394904			0.197452	−	0.980313i	$-0.436733\pi$
$229$	5.97598			0.394904			0.197452	+	0.980313i	$0.436733\pi$
$230$		0			0
$231$			25.8769i			1.70257i
$232$		0			0
$233$	−5.31970	+	11.6485i	−0.348505	+	0.763120i	0.651485	+	0.758662i	$0.274146\pi$
$233$	−5.31970	+	11.6485i	−0.348505	+	0.763120i	−0.999990	+	0.00445810i	$0.998581\pi$
$234$		0			0
$235$	−4.99820	−	4.33096i	−0.326047	−	0.282521i
$236$		0			0
$237$	−18.7118	+	12.0254i	−1.21546	+	0.781131i
$238$		0			0
$239$	−11.2879	+	9.78101i	−0.730153	+	0.632681i	−0.938462	−	0.345382i	$-0.887749\pi$
$239$	−11.2879	+	9.78101i	−0.730153	+	0.632681i	0.208309	+	0.978063i	$0.433204\pi$
$240$		0			0
$241$	5.50463	+	0.791446i	0.354584	+	0.0509815i	0.317306	−	0.948323i	$-0.397222\pi$
$241$	5.50463	+	0.791446i	0.354584	+	0.0509815i	0.0372789	+	0.999305i	$0.488131\pi$
$242$		0			0
$243$	−10.4303	−	6.70313i	−0.669103	−	0.430006i
$244$		0			0
$245$	−11.9747	−	26.2209i	−0.765034	−	1.67519i
$246$		0			0
$247$	2.62085	+	0.769550i	0.166760	+	0.0489653i
$248$		0			0
$249$	6.46069	+	22.0031i	0.409429	+	1.39439i
$250$		0			0
$251$	29.2090	−	4.19961i	1.84365	−	0.265077i	0.869990	−	0.493069i	$-0.164125\pi$
$251$	29.2090	−	4.19961i	1.84365	−	0.265077i	0.973663	+	0.227992i	$0.0732159\pi$
$252$		0			0
$253$	−4.53554	−	7.29655i	−0.285147	−	0.458730i
$254$		0			0
$255$	26.0764	−	3.74922i	1.63297	−	0.234785i
$256$		0			0
$257$	−17.9623	+	5.27421i	−1.12046	+	0.328996i	−0.788951	−	0.614457i	$-0.789375\pi$
$257$	−17.9623	+	5.27421i	−1.12046	+	0.328996i	−0.331507	+	0.943453i	$0.607557\pi$
$258$		0			0
$259$	29.5258	+	8.66957i	1.83465	+	0.538701i
$260$		0			0
$261$	31.2691	−	14.2801i	1.93551	−	0.883918i
$262$		0			0
$263$	−5.04812	−	3.24423i	−0.311280	−	0.200048i	0.375667	−	0.926755i	$-0.377414\pi$
$263$	−5.04812	−	3.24423i	−0.311280	−	0.200048i	−0.686948	+	0.726707i	$0.741050\pi$
$264$		0			0
$265$	−0.796506	+	5.53982i	−0.0489290	+	0.340308i
$266$		0			0
$267$	5.90402	−	5.11587i	0.361320	−	0.313086i
$268$		0			0
$269$	7.79282	+	12.1259i	0.475137	+	0.739327i	0.993251	−	0.115984i	$-0.0370022\pi$
$269$	7.79282	+	12.1259i	0.475137	+	0.739327i	−0.518114	+	0.855311i	$0.673366\pi$
$270$		0			0
$271$	−14.9068	−	12.9168i	−0.905521	−	0.784638i	0.0715755	−	0.997435i	$-0.477197\pi$
$271$	−14.9068	−	12.9168i	−0.905521	−	0.784638i	−0.977096	+	0.212797i	$0.931743\pi$
$272$		0			0
$273$	−12.4397	−	5.68101i	−0.752884	−	0.343831i
$274$		0			0
$275$		−	4.64297i		−	0.279981i
$276$		0			0
$277$		−	25.9987i		−	1.56211i	−0.624462	−	0.781055i	$-0.714682\pi$
$277$		−	25.9987i		−	1.56211i	0.624462	−	0.781055i	$-0.285318\pi$
$278$		0			0
$279$	−11.1021	−	5.07017i	−0.664666	−	0.303543i
$280$		0			0
$281$	−7.23906	−	6.27268i	−0.431846	−	0.374197i	0.411641	−	0.911346i	$-0.364956\pi$
$281$	−7.23906	−	6.27268i	−0.431846	−	0.374197i	−0.843487	+	0.537149i	$0.819501\pi$
$282$		0			0
$283$	−12.4318	−	19.3442i	−0.738992	−	1.14989i	−0.983616	−	0.180276i	$-0.942301\pi$
$283$	−12.4318	−	19.3442i	−0.738992	−	1.14989i	0.244624	−	0.969618i	$-0.421336\pi$
$284$		0			0
$285$	9.66503	−	8.37480i	0.572507	−	0.496080i
$286$		0			0
$287$	−4.03156	+	28.0401i	−0.237975	+	1.65515i
$288$		0			0
$289$	−15.4155	−	9.90692i	−0.906792	−	0.582760i
$290$		0			0
$291$	1.89080	−	0.863499i	0.110841	−	0.0506192i
$292$		0			0
$293$	4.91323	+	1.44266i	0.287034	+	0.0842808i	0.422080	−	0.906559i	$-0.361300\pi$
$293$	4.91323	+	1.44266i	0.287034	+	0.0842808i	−0.135046	+	0.990839i	$0.543118\pi$
$294$		0			0
$295$	−4.49488	+	1.31982i	−0.261702	+	0.0768426i
$296$		0			0
$297$	10.9325	−	1.57185i	0.634365	−	0.0912080i
$298$		0			0
$299$	4.50337	−	0.578464i	0.260437	−	0.0334534i
$300$		0			0
$301$	−32.9192	+	4.73306i	−1.89743	+	0.272809i
$302$		0			0
$303$	−5.29504	−	18.0333i	−0.304192	−	1.03598i
$304$		0			0
$305$	−8.17052	−	2.39908i	−0.467843	−	0.137371i
$306$		0			0
$307$	5.47087	+	11.9795i	0.312239	+	0.683708i	0.999070	−	0.0431085i	$-0.0137261\pi$
$307$	5.47087	+	11.9795i	0.312239	+	0.683708i	−0.686831	+	0.726817i	$0.740999\pi$
$308$		0			0
$309$	−7.31860	−	4.70338i	−0.416340	−	0.267566i
$310$		0			0
$311$	−11.6388	−	1.67340i	−0.659974	−	0.0948900i	−0.195814	−	0.980641i	$-0.562735\pi$
$311$	−11.6388	−	1.67340i	−0.659974	−	0.0948900i	−0.464160	+	0.885751i	$0.653644\pi$
$312$		0			0
$313$	−4.12965	+	3.57836i	−0.233422	+	0.202261i	−0.763716	−	0.645553i	$-0.776627\pi$
$313$	−4.12965	+	3.57836i	−0.233422	+	0.202261i	0.530294	+	0.847814i	$0.322082\pi$
$314$		0			0
$315$	−34.0573	+	21.8873i	−1.91891	+	1.23321i
$316$		0			0
$317$	−0.757874	−	0.656701i	−0.0425664	−	0.0368840i	0.633318	−	0.773892i	$-0.281693\pi$
$317$	−0.757874	−	0.656701i	−0.0425664	−	0.0368840i	−0.675884	+	0.737008i	$0.736238\pi$
$318$		0			0
$319$	4.95909	−	10.8589i	0.277656	−	0.607981i
$320$		0			0
$321$		−	15.2898i		−	0.853393i
$322$		0			0
$323$	−17.1478			−0.954131
$324$		0			0
$325$	2.23199	+	1.01932i	0.123809	+	0.0565416i
$326$		0			0
$327$	21.7227	−	25.0693i	1.20127	−	1.38633i
$328$		0			0
$329$	−11.6522	−	18.1311i	−0.642405	−	0.999602i
$330$		0			0
$331$	0.0677879	+	0.0782314i	0.00372596	+	0.00429998i	0.757609	−	0.652708i	$-0.226367\pi$
$331$	0.0677879	+	0.0782314i	0.00372596	+	0.00429998i	−0.753884	+	0.657008i	$0.771822\pi$
$332$		0			0
$333$	4.46712	−	31.0695i	0.244796	−	1.70260i
$334$		0			0
$335$	−8.85349	+	13.7763i	−0.483718	+	0.752679i
$336$		0			0
$337$	3.26885	−	1.49283i	0.178066	−	0.0813199i	−0.324388	−	0.945924i	$-0.605158\pi$
$337$	3.26885	−	1.49283i	0.178066	−	0.0813199i	0.502453	+	0.864604i	$0.332431\pi$
$338$		0			0
$339$	4.63812	−	15.7960i	0.251908	−	0.857920i
$340$		0			0
$341$	−4.06679	+	1.19412i	−0.220229	+	0.0646650i
$342$		0			0
$343$	−8.33086	−	57.9424i	−0.449824	−	3.12859i
$344$		0			0
$345$	9.12076	−	19.2017i	0.491045	−	1.03378i
$346$		0			0
$347$	−1.43435	−	9.97614i	−0.0770000	−	0.535547i	−0.991413	−	0.130765i	$-0.958257\pi$
$347$	−1.43435	−	9.97614i	−0.0770000	−	0.535547i	0.914413	−	0.404782i	$-0.132653\pi$
$348$		0			0
$349$	3.47686	+	11.8411i	0.186112	+	0.633839i	0.998699	+	0.0509990i	$0.0162405\pi$
$349$	3.47686	+	11.8411i	0.186112	+	0.633839i	−0.812587	+	0.582840i	$0.801941\pi$
$350$		0			0
$351$	−1.64448	+	5.60060i	−0.0877761	+	0.298938i
$352$		0			0
$353$	5.28114	+	11.5641i	0.281087	+	0.615494i	0.996535	−	0.0831712i	$-0.0265048\pi$
$353$	5.28114	+	11.5641i	0.281087	+	0.615494i	−0.715448	+	0.698666i	$0.753778\pi$
$354$		0			0
$355$	−1.74965	+	2.72251i	−0.0928619	+	0.144496i
$356$		0			0
$357$	84.9787	+	12.2181i	4.49755	+	0.646650i
$358$		0			0
$359$	−12.0759	−	13.9363i	−0.637342	−	0.735532i	0.341561	−	0.939860i	$-0.389044\pi$
$359$	−12.0759	−	13.9363i	−0.637342	−	0.735532i	−0.978902	+	0.204328i	$0.934499\pi$
$360$		0			0
$361$	8.98103	−	5.77176i	0.472686	−	0.303777i
$362$		0			0
$363$	−14.5727	+	16.8178i	−0.764867	+	0.882703i
$364$		0			0
$365$	−1.38125	+	3.02452i	−0.0722981	+	0.158311i
$366$		0			0
$367$	32.2136			1.68154			0.840768	−	0.541396i	$-0.182104\pi$
$367$	32.2136			1.68154			0.840768	+	0.541396i	$0.182104\pi$
$368$		0			0
$369$	28.8961			1.50427
$370$		0			0
$371$	−7.57676	+	16.5908i	−0.393366	+	0.861351i
$372$		0			0
$373$	19.2000	−	22.1580i	0.994137	−	1.14730i	0.00504651	−	0.999987i	$-0.498394\pi$
$373$	19.2000	−	22.1580i	0.994137	−	1.14730i	0.989091	−	0.147308i	$-0.0470609\pi$
$374$		0			0
$375$	28.3090	−	18.1931i	1.46187	−	0.939487i
$376$		0			0
$377$	4.13143	+	4.76793i	0.212780	+	0.245561i
$378$		0			0
$379$	−6.85191	−	0.985157i	−0.351959	−	0.0506041i	−0.0359320	−	0.999354i	$-0.511440\pi$
$379$	−6.85191	−	0.985157i	−0.351959	−	0.0506041i	−0.316027	+	0.948750i	$0.602349\pi$
$380$		0			0
$381$	−11.4151	+	17.7622i	−0.584811	+	0.909984i
$382$		0			0
$383$	−2.51646	−	5.51028i	−0.128585	−	0.281562i	0.834379	−	0.551191i	$-0.185826\pi$
$383$	−2.51646	−	5.51028i	−0.128585	−	0.281562i	−0.962964	+	0.269629i	$0.913099\pi$
$384$		0			0
$385$	−3.96086	+	13.4895i	−0.201864	+	0.687487i
$386$		0			0
$387$	9.55753	+	32.5500i	0.485837	+	1.65461i
$388$		0			0
$389$	−1.30274	−	9.06078i	−0.0660517	−	0.459400i	−0.995826	−	0.0912700i	$-0.970907\pi$
$389$	−1.30274	−	9.06078i	−0.0660517	−	0.459400i	0.929774	−	0.368130i	$-0.120002\pi$
$390$		0			0
$391$	−26.1031	+	11.4494i	−1.32009	+	0.579020i
$392$		0			0
$393$	−4.93356	−	34.3136i	−0.248865	−	1.73089i
$394$		0			0
$395$	−11.5950	+	3.40461i	−0.583410	+	0.171305i
$396$		0			0
$397$	5.55659	−	18.9240i	0.278877	−	0.949769i	−0.694295	−	0.719691i	$-0.744284\pi$
$397$	5.55659	−	18.9240i	0.278877	−	0.949769i	0.973172	−	0.230078i	$-0.0738983\pi$
$398$		0			0
$399$	37.9100	−	17.3129i	1.89787	−	0.866730i
$400$		0			0
$401$	0.0268091	−	0.0417158i	0.00133878	−	0.00208319i	−0.840583	−	0.541682i	$-0.817788\pi$
$401$	0.0268091	−	0.0417158i	0.00133878	−	0.00208319i	0.841922	+	0.539599i	$0.181424\pi$
$402$		0			0
$403$	0.318781	−	2.21717i	0.0158796	−	0.110445i
$404$		0			0
$405$	2.16954	+	2.50378i	0.107805	+	0.124414i
$406$		0			0
$407$	−5.89326	−	9.17009i	−0.292118	−	0.454544i
$408$		0			0
$409$	9.98127	−	11.5190i	0.493542	−	0.569578i	−0.453267	−	0.891375i	$-0.649741\pi$
$409$	9.98127	−	11.5190i	0.493542	−	0.569578i	0.946809	+	0.321797i	$0.104287\pi$
$410$		0			0
$411$	−19.6555	−	8.97638i	−0.969536	−	0.442772i
$412$		0			0
$413$	−15.2665			−0.751214
$414$		0			0
$415$			12.4590i			0.611588i
$416$		0			0
$417$	0.140917	−	0.308566i	0.00690075	−	0.0151105i
$418$		0			0
$419$	−21.4069	−	18.5492i	−1.04579	−	0.906186i	−0.0500876	−	0.998745i	$-0.515950\pi$
$419$	−21.4069	−	18.5492i	−1.04579	−	0.906186i	−0.995707	+	0.0925585i	$0.970495\pi$
$420$		0			0
$421$	29.3409	−	18.8562i	1.42999	−	0.918996i	0.430117	−	0.902773i	$-0.358472\pi$
$421$	29.3409	−	18.8562i	1.42999	−	0.918996i	0.999868	−	0.0162229i	$-0.00516414\pi$
$422$		0			0
$423$	−16.6147	+	14.3967i	−0.807834	+	0.699992i
$424$		0			0
$425$	−15.2473	−	2.19224i	−0.739604	−	0.106339i
$426$		0			0
$427$	−23.3452	−	15.0030i	−1.12975	−	0.726048i
$428$		0			0
$429$	2.01239	+	4.40652i	0.0971590	+	0.212749i
$430$		0			0
$431$	8.68040	+	2.54879i	0.418120	+	0.122771i	0.484024	−	0.875055i	$-0.339175\pi$
$431$	8.68040	+	2.54879i	0.418120	+	0.122771i	−0.0659037	+	0.997826i	$0.520993\pi$
$432$		0			0
$433$	8.64141	+	29.4300i	0.415280	+	1.41431i	0.856143	+	0.516739i	$0.172854\pi$
$433$	8.64141	+	29.4300i	0.415280	+	1.41431i	−0.440863	+	0.897574i	$0.645328\pi$
$434$		0			0
$435$	29.2371	−	4.20366i	1.40181	−	0.201550i
$436$		0			0
$437$	−7.65505	+	11.5264i	−0.366191	+	0.551382i
$438$		0			0
$439$	−15.5033	+	2.22904i	−0.739934	+	0.106386i	−0.501967	−	0.864887i	$-0.667390\pi$
$439$	−15.5033	+	2.22904i	−0.739934	+	0.106386i	−0.237967	+	0.971273i	$0.576481\pi$
$440$		0			0
$441$	−91.9395	+	26.9959i	−4.37807	+	1.28552i
$442$		0			0
$443$	−1.84283	−	0.541103i	−0.0875553	−	0.0257086i	0.237662	−	0.971348i	$-0.423619\pi$
$443$	−1.84283	−	0.541103i	−0.0875553	−	0.0257086i	−0.325217	+	0.945639i	$0.605437\pi$
$444$		0			0
$445$	3.86080	−	1.76317i	0.183019	−	0.0835822i
$446$		0			0
$447$	0.980458	+	0.630102i	0.0463741	+	0.0298028i
$448$		0			0
$449$	−0.675575	+	4.69872i	−0.0318823	+	0.221747i	−0.999533	−	0.0305459i	$-0.990275\pi$
$449$	−0.675575	+	4.69872i	−0.0318823	+	0.221747i	0.967651	+	0.252292i	$0.0811845\pi$
$450$		0			0
$451$	7.58379	−	6.57139i	0.357107	−	0.309435i
$452$		0			0
$453$	−30.9517	−	48.1618i	−1.45424	−	2.26284i
$454$		0			0
$455$	−5.61517	−	4.86557i	−0.263243	−	0.228101i
$456$		0			0
$457$	34.4422	+	15.7292i	1.61114	+	0.735783i	0.998509	−	0.0545870i	$-0.0173842\pi$
$457$	34.4422	+	15.7292i	1.61114	+	0.735783i	0.612630	+	0.790370i	$0.290112\pi$
$458$		0			0
$459$		−	36.6439i		−	1.71039i
$460$		0			0
$461$			26.0410i			1.21285i	0.795140	+	0.606426i	$0.207397\pi$
$461$			26.0410i			1.21285i	−0.795140	+	0.606426i	$0.792603\pi$
$462$		0			0
$463$	18.5165	+	8.45622i	0.860536	+	0.392994i	0.796272	−	0.604939i	$-0.206803\pi$
$463$	18.5165	+	8.45622i	0.860536	+	0.392994i	0.0642646	+	0.997933i	$0.479530\pi$
$464$		0			0
$465$	−7.92584	−	6.86778i	−0.367552	−	0.318485i
$466$		0			0
$467$	19.9073	+	30.9763i	0.921199	+	1.43341i	0.901098	+	0.433616i	$0.142763\pi$
$467$	19.9073	+	30.9763i	0.921199	+	1.43341i	0.0201018	+	0.999798i	$0.493601\pi$
$468$		0			0
$469$	−40.3316	+	34.9476i	−1.86234	+	1.61373i
$470$		0			0
$471$	2.10011	−	14.6066i	0.0967680	−	0.673036i
$472$		0			0
$473$	9.91072	+	6.36923i	0.455695	+	0.292858i
$474$		0			0
$475$	−6.80201	+	3.10637i	−0.312098	+	0.142530i
$476$		0			0
$477$	17.8509	+	5.24149i	0.817336	+	0.239991i
$478$		0			0
$479$	−8.41142	+	2.46982i	−0.384328	+	0.112849i	−0.468188	−	0.883629i	$-0.655093\pi$
$479$	−8.41142	+	2.46982i	−0.384328	+	0.112849i	0.0838606	+	0.996477i	$0.473275\pi$
$480$		0			0
$481$	5.70211	−	0.819839i	0.259994	−	0.0373815i
$482$		0			0
$483$	46.1485	−	51.6664i	2.09983	−	2.35090i
$484$		0			0
$485$	1.11784	−	0.160720i	0.0507583	−	0.00729794i
$486$		0			0
$487$	−4.41486	−	15.0356i	−0.200056	−	0.681330i	−0.997009	−	0.0772876i	$-0.975374\pi$
$487$	−4.41486	−	15.0356i	−0.200056	−	0.681330i	0.796952	−	0.604042i	$-0.206444\pi$
$488$		0			0
$489$	42.1350	+	12.3720i	1.90541	+	0.559480i
$490$		0			0
$491$	10.6783	+	23.3822i	0.481905	+	1.05522i	0.981935	+	0.189217i	$0.0605948\pi$
$491$	10.6783	+	23.3822i	0.481905	+	1.05522i	−0.500031	+	0.866008i	$0.666678\pi$
$492$		0			0
$493$	−33.3187	−	21.4126i	−1.50060	−	0.964377i
$494$		0			0
$495$	14.1947	+	2.04089i	0.638004	+	0.0917312i
$496$		0			0
$497$	−7.97046	+	6.90645i	−0.357524	+	0.309796i
$498$		0			0
$499$	5.08585	−	3.26848i	0.227674	−	0.146317i	−0.421831	−	0.906674i	$-0.638612\pi$
$499$	5.08585	−	3.26848i	0.227674	−	0.146317i	0.649505	+	0.760357i	$0.274976\pi$
$500$		0			0
$501$	−52.0015	−	45.0596i	−2.32326	−	2.01311i
$502$		0			0
$503$	2.18735	−	4.78963i	0.0975291	−	0.213559i	−0.854578	−	0.519322i	$-0.826184\pi$
$503$	2.18735	−	4.78963i	0.0975291	−	0.213559i	0.952108	+	0.305763i	$0.0989117\pi$
$504$		0			0
$505$		−	10.2111i		−	0.454389i
$506$		0			0
$507$	34.5720			1.53539
$508$		0			0
$509$	−16.0937	−	7.34974i	−0.713340	−	0.325771i	0.0254791	−	0.999675i	$-0.491889\pi$
$509$	−16.0937	−	7.34974i	−0.713340	−	0.325771i	−0.738819	+	0.673904i	$0.764616\pi$
$510$		0			0
$511$	−7.09582	+	8.18901i	−0.313901	+	0.362261i
$512$		0			0
$513$	−9.61714	−	14.9646i	−0.424607	−	0.660701i
$514$		0			0
$515$	−3.09522	−	3.57207i	−0.136392	−	0.157404i
$516$		0			0
$517$	−1.08651	+	7.55685i	−0.0477847	+	0.332350i
$518$		0			0
$519$	−36.9500	+	57.4953i	−1.62192	+	2.52376i
$520$		0			0
$521$	4.77483	−	2.18059i	0.209189	−	0.0955335i	−0.308065	−	0.951365i	$-0.599681\pi$
$521$	4.77483	−	2.18059i	0.209189	−	0.0955335i	0.517254	+	0.855832i	$0.326954\pi$
$522$		0			0
$523$	−4.60996	+	15.7001i	−0.201580	+	0.686517i	0.795201	+	0.606345i	$0.207365\pi$
$523$	−4.60996	+	15.7001i	−0.201580	+	0.686517i	−0.996781	+	0.0801719i	$0.974453\pi$
$524$		0			0
$525$	35.9217	−	10.5476i	1.56775	−	0.460334i
$526$		0			0
$527$	2.00125	+	13.9190i	0.0871758	+	0.606321i
$528$		0			0
$529$	−3.95682	+	22.6571i	−0.172036	+	0.985091i
$530$		0			0
$531$	2.21618	+	15.4139i	0.0961741	+	0.668905i
$532$		0			0
$533$	1.49409	+	5.08841i	0.0647163	+	0.220404i
$534$		0			0
$535$	2.34034	−	7.97048i	0.101182	−	0.344594i
$536$		0			0
$537$	−1.32388	−	2.89889i	−0.0571295	−	0.125096i
$538$		0			0
$539$	−17.9903	+	27.9935i	−0.774898	+	1.20576i
$540$		0			0
$541$	−23.8290	−	3.42610i	−1.02449	−	0.147299i	−0.390470	−	0.920616i	$-0.627687\pi$
$541$	−23.8290	−	3.42610i	−1.02449	−	0.147299i	−0.634021	+	0.773316i	$0.718597\pi$
$542$		0			0
$543$	−9.01683	−	10.4060i	−0.386949	−	0.446563i
$544$		0			0
$545$	15.1612	−	9.74348i	0.649433	−	0.417365i
$546$		0			0
$547$	−4.35607	+	5.02717i	−0.186252	+	0.214946i	−0.841195	−	0.540732i	$-0.818147\pi$
$547$	−4.35607	+	5.02717i	−0.186252	+	0.214946i	0.654943	+	0.755678i	$0.272693\pi$
$548$		0			0
$549$	−11.7590	+	25.7485i	−0.501860	+	1.09892i
$550$		0			0
$551$	−19.2263			−0.819068
$552$		0			0
$553$	−39.3816			−1.67468
$554$		0			0
$555$	11.2043	−	24.5341i	0.475598	−	1.04141i
$556$		0			0
$557$	10.3521	−	11.9470i	0.438635	−	0.506211i	−0.492789	−	0.870149i	$-0.664022\pi$
$557$	10.3521	−	11.9470i	0.438635	−	0.506211i	0.931423	+	0.363938i	$0.118568\pi$
$558$		0			0
$559$	−5.23766	+	3.36604i	−0.221529	+	0.142368i
$560$		0			0
$561$	−19.9154	−	22.9836i	−0.840827	−	0.970367i
$562$		0			0
$563$	−16.8778	−	2.42666i	−0.711313	−	0.102271i	−0.222846	−	0.974854i	$-0.571535\pi$
$563$	−16.8778	−	2.42666i	−0.711313	−	0.102271i	−0.488467	+	0.872582i	$0.662444\pi$
$564$		0			0
$565$	4.83565	−	7.52442i	0.203437	−	0.316555i
$566$		0			0
$567$	4.48501	+	9.82079i	0.188353	+	0.412435i
$568$		0			0
$569$	6.28352	−	21.3997i	0.263419	−	0.897122i	−0.716477	−	0.697611i	$-0.754246\pi$
$569$	6.28352	−	21.3997i	0.263419	−	0.897122i	0.979896	−	0.199511i	$-0.0639354\pi$
$570$		0			0
$571$	−9.12923	−	31.0913i	−0.382046	−	1.30113i	−0.896283	−	0.443482i	$-0.853743\pi$
$571$	−9.12923	−	31.0913i	−0.382046	−	1.30113i	0.514237	−	0.857648i	$-0.328075\pi$
$572$		0			0
$573$	8.19383	+	56.9893i	0.342302	+	2.38076i
$574$		0			0
$575$	−8.28021	+	9.27026i	−0.345309	+	0.386596i
$576$		0			0
$577$	−2.92744	−	20.3608i	−0.121871	−	0.847632i	−0.955433	−	0.295206i	$-0.904612\pi$
$577$	−2.92744	−	20.3608i	−0.121871	−	0.847632i	0.833562	−	0.552425i	$-0.186298\pi$
$578$		0			0
$579$	−64.9900	+	19.0828i	−2.70089	+	0.793054i
$580$		0			0
$581$	−11.4388	+	38.9571i	−0.474563	+	1.61621i
$582$		0			0
$583$	5.87697	−	2.68392i	0.243399	−	0.111157i
$584$		0			0
$585$	−4.09742	+	6.37571i	−0.169407	+	0.263603i
$586$		0			0
$587$	0.369212	−	2.56793i	0.0152390	−	0.105990i	−0.980782	−	0.195106i	$-0.937495\pi$
$587$	0.369212	−	2.56793i	0.0152390	−	0.105990i	0.996021	+	0.0891159i	$0.0284042\pi$
$588$		0			0
$589$	4.47028	+	5.15898i	0.184195	+	0.212572i
$590$		0			0
$591$	21.2369	+	33.0453i	0.873570	+	1.35930i
$592$		0			0
$593$	−23.6073	+	27.2443i	−0.969437	+	1.11879i	0.0234490	+	0.999725i	$0.492535\pi$
$593$	−23.6073	+	27.2443i	−0.969437	+	1.11879i	−0.992886	+	0.119065i	$0.962010\pi$
$594$		0			0
$595$	42.4287	+	19.3766i	1.73941	+	0.794362i
$596$		0			0
$597$	32.3239			1.32293
$598$		0			0
$599$		−	26.2291i		−	1.07169i	−0.844316	−	0.535846i	$-0.819993\pi$
$599$		−	26.2291i		−	1.07169i	0.844316	−	0.535846i	$-0.180007\pi$
$600$		0			0
$601$	−6.19230	+	13.5592i	−0.252589	+	0.553093i	−0.992870	−	0.119205i	$-0.961965\pi$
$601$	−6.19230	+	13.5592i	−0.252589	+	0.553093i	0.740280	+	0.672298i	$0.234693\pi$
$602$		0			0
$603$	41.1398	+	35.6479i	1.67534	+	1.45169i
$604$		0			0
$605$	−10.1709	+	6.53642i	−0.413505	+	0.265743i
$606$		0			0
$607$	−10.7092	+	9.27954i	−0.434671	+	0.376645i	−0.844534	−	0.535502i	$-0.820122\pi$
$607$	−10.7092	+	9.27954i	−0.434671	+	0.376645i	0.409862	+	0.912147i	$0.365577\pi$
$608$		0			0
$609$	95.2789	+	13.6990i	3.86089	+	0.555113i
$610$		0			0
$611$	−3.39424	−	2.18135i	−0.137316	−	0.0882479i
$612$		0			0
$613$	15.0550	+	32.9658i	0.608065	+	1.33148i	0.923890	+	0.382659i	$0.124992\pi$
$613$	15.0550	+	32.9658i	0.608065	+	1.33148i	−0.315825	+	0.948818i	$0.602281\pi$
$614$		0			0
$615$	23.8236	+	6.99525i	0.960661	+	0.282076i
$616$		0			0
$617$	2.83232	+	9.64601i	0.114025	+	0.388334i	0.996654	−	0.0817367i	$-0.0260467\pi$
$617$	2.83232	+	9.64601i	0.114025	+	0.388334i	−0.882629	+	0.470070i	$0.844228\pi$
$618$		0			0
$619$	33.9420	−	4.88013i	1.36425	−	0.196149i	0.578997	−	0.815330i	$-0.303444\pi$
$619$	33.9420	−	4.88013i	1.36425	−	0.196149i	0.785248	+	0.619181i	$0.212535\pi$
$620$		0			0
$621$	−24.6312	−	16.3584i	−0.988417	−	0.656440i
$622$		0			0
$623$	13.6909	−	1.96845i	0.548513	−	0.0788642i
$624$		0			0
$625$	5.10804	−	1.49986i	0.204322	−	0.0599942i
$626$		0			0
$627$	−14.1650	−	4.15921i	−0.565695	−	0.166103i
$628$		0			0
$629$	−32.8968	+	15.0235i	−1.31168	+	0.599025i
$630$		0			0
$631$	22.0076	+	14.1434i	0.876109	+	0.563041i	0.899616	−	0.436683i	$-0.143847\pi$
$631$	22.0076	+	14.1434i	0.876109	+	0.563041i	−0.0235068	+	0.999724i	$0.507483\pi$
$632$		0			0
$633$	−8.40167	+	58.4349i	−0.333936	+	2.32258i
$634$		0			0
$635$	−8.66939	+	7.51207i	−0.344034	+	0.298107i
$636$		0			0
$637$	−9.50760	−	14.7941i	−0.376705	−	0.586164i
$638$		0			0
$639$	8.13018	+	7.04484i	0.321625	+	0.278690i
$640$		0			0
$641$	−13.6583	−	6.23754i	−0.539471	−	0.246368i	0.126995	−	0.991903i	$-0.459467\pi$
$641$	−13.6583	−	6.23754i	−0.539471	−	0.246368i	−0.666466	+	0.745535i	$0.732194\pi$
$642$		0			0
$643$		−	35.7644i		−	1.41041i	−0.709003	−	0.705205i	$-0.750855\pi$
$643$		−	35.7644i		−	1.41041i	0.709003	−	0.705205i	$-0.249145\pi$
$644$		0			0
$645$			29.1498i			1.14777i
$646$		0			0
$647$	−1.09000	−	0.497786i	−0.0428523	−	0.0195700i	0.393874	−	0.919165i	$-0.371135\pi$
$647$	−1.09000	−	0.497786i	−0.0428523	−	0.0195700i	−0.436726	+	0.899595i	$0.643862\pi$
$648$		0			0
$649$	4.08698	+	3.54139i	0.160428	+	0.139012i
$650$		0			0
$651$	−18.4773	−	28.7512i	−0.724182	−	1.12685i
$652$		0			0
$653$	10.6665	−	9.24256i	0.417412	−	0.361689i	−0.420689	−	0.907205i	$-0.638212\pi$
$653$	10.6665	−	9.24256i	0.417412	−	0.361689i	0.838101	+	0.545516i	$0.183666\pi$
$654$		0			0
$655$	2.68041	−	18.6427i	0.104732	−	0.728429i
$656$		0			0
$657$	9.29816	+	5.97556i	0.362756	+	0.233129i
$658$		0			0
$659$	11.2336	−	5.13020i	0.437598	−	0.199844i	−0.184420	−	0.982848i	$-0.559041\pi$
$659$	11.2336	−	5.13020i	0.437598	−	0.199844i	0.622017	+	0.783003i	$0.286313\pi$
$660$		0			0
$661$	19.0983	+	5.60776i	0.742836	+	0.218116i	0.631186	−	0.775631i	$-0.282568\pi$
$661$	19.0983	+	5.60776i	0.742836	+	0.218116i	0.111650	+	0.993748i	$0.464386\pi$
$662$		0			0
$663$	15.4210	−	4.52802i	0.598903	−	0.175854i
$664$		0			0
$665$	22.4123	−	3.22240i	0.869111	−	0.124959i
$666$		0			0
$667$	−29.2670	+	12.8371i	−1.13322	+	0.497056i
$668$		0			0
$669$	47.5453	−	6.83599i	1.83821	−	0.264295i
$670$		0			0
$671$	2.76945	+	9.43188i	0.106913	+	0.364114i
$672$		0			0
$673$	−12.3190	−	3.61717i	−0.474861	−	0.139432i	0.0355402	−	0.999368i	$-0.488685\pi$
$673$	−12.3190	−	3.61717i	−0.474861	−	0.139432i	−0.510401	+	0.859937i	$0.670503\pi$
$674$		0			0
$675$	−6.63814	−	14.5355i	−0.255502	−	0.559472i
$676$		0			0
$677$	10.7903	+	6.93450i	0.414704	+	0.266514i	0.731313	−	0.682042i	$-0.238908\pi$
$677$	10.7903	+	6.93450i	0.414704	+	0.266514i	−0.316609	+	0.948556i	$0.602544\pi$
$678$		0			0
$679$	3.64284	+	0.523762i	0.139799	+	0.0201001i
$680$		0			0
$681$	19.6107	−	16.9928i	0.751484	−	0.651165i
$682$		0			0
$683$	−40.3338	+	25.9210i	−1.54333	+	0.991838i	−0.556359	+	0.830942i	$0.687802\pi$
$683$	−40.3338	+	25.9210i	−1.54333	+	0.991838i	−0.986971	+	0.160897i	$0.948561\pi$
$684$		0			0
$685$	−8.87234	−	7.68793i	−0.338995	−	0.293741i
$686$		0			0
$687$	7.09084	−	15.5268i	0.270532	−	0.592383i
$688$		0			0
$689$			3.41444i			0.130080i
$690$		0			0
$691$	−16.9423			−0.644515			−0.322258	−	0.946652i	$-0.604442\pi$
$691$	−16.9423			−0.644515			−0.322258	+	0.946652i	$0.604442\pi$
$692$		0			0
$693$	42.5106	+	19.4140i	1.61485	+	0.737475i
$694$		0			0
$695$	0.120690	−	0.139284i	0.00457804	−	0.00528335i
$696$		0			0
$697$	−17.9994	−	28.0077i	−0.681777	−	1.06087i
$698$		0			0
$699$	23.9530	+	27.6432i	0.905986	+	1.04556i
$700$		0			0
$701$	6.72785	−	46.7932i	0.254107	−	1.76735i	−0.318885	−	0.947793i	$-0.603308\pi$
$701$	6.72785	−	46.7932i	0.254107	−	1.76735i	0.572992	−	0.819561i	$-0.305783\pi$
$702$		0			0
$703$	−9.49143	+	14.7690i	−0.357976	+	0.557022i
$704$		0			0
$705$	−17.1833	+	7.84736i	−0.647162	+	0.295549i
$706$		0			0
$707$	9.37504	−	31.9285i	0.352585	−	1.20079i
$708$		0			0
$709$	−21.7974	+	6.40031i	−0.818620	+	0.240369i	−0.664122	−	0.747625i	$-0.731194\pi$
$709$	−21.7974	+	6.40031i	−0.818620	+	0.240369i	−0.154498	+	0.987993i	$0.549376\pi$
$710$		0			0
$711$	5.71689	+	39.7618i	0.214400	+	1.49119i
$712$		0			0
$713$	10.2494	+	4.86846i	0.383844	+	0.182325i
$714$		0			0
$715$	0.374560	+	2.60512i	0.0140077	+	0.0974260i
$716$		0			0
$717$	12.0193	+	40.9339i	0.448868	+	1.52870i
$718$		0			0
$719$	11.8548	−	40.3738i	0.442110	−	1.50569i	−0.373800	−	0.927509i	$-0.621945\pi$
$719$	11.8548	−	40.3738i	0.442110	−	1.50569i	0.815910	−	0.578179i	$-0.196236\pi$
$720$		0			0
$721$	−6.39863	−	14.0110i	−0.238297	−	0.521798i
$722$		0			0
$723$	8.58788	−	13.3630i	0.319387	−	0.496976i
$724$		0			0
$725$	−17.0954	−	2.45795i	−0.634909	−	0.0912861i
$726$		0			0
$727$	5.67584	+	6.55027i	0.210505	+	0.242936i	0.851177	−	0.524879i	$-0.175889\pi$
$727$	5.67584	+	6.55027i	0.210505	+	0.242936i	−0.640672	+	0.767815i	$0.721344\pi$
$728$		0			0
$729$	−35.1801	+	22.6089i	−1.30297	+	0.837365i
$730$		0			0
$731$	25.5958	−	29.5391i	0.946695	−	1.09254i
$732$		0			0
$733$	−5.47637	+	11.9916i	−0.202274	+	0.442919i	−0.983399	−	0.181456i	$-0.941919\pi$
$733$	−5.47637	+	11.9916i	−0.202274	+	0.442919i	0.781125	+	0.624375i	$0.214646\pi$
$734$		0			0
$735$	−82.3356			−3.03699
$736$		0			0
$737$	18.9040			0.696338
$738$		0			0
$739$	−12.4623	+	27.2886i	−0.458432	+	1.00383i	0.529410	+	0.848366i	$0.322413\pi$
$739$	−12.4623	+	27.2886i	−0.458432	+	1.00383i	−0.987842	+	0.155461i	$0.950314\pi$
$740$		0			0
$741$	5.10922	−	5.89636i	0.187692	−	0.216608i
$742$		0			0
$743$	−13.1475	+	8.44939i	−0.482335	+	0.309978i	−0.759116	−	0.650955i	$-0.774369\pi$
$743$	−13.1475	+	8.44939i	−0.482335	+	0.309978i	0.276781	+	0.960933i	$0.410732\pi$
$744$		0			0
$745$	0.414660	+	0.478544i	0.0151920	+	0.0175325i
$746$		0			0
$747$	40.9938	+	5.89402i	1.49989	+	0.215651i
$748$		0			0
$749$	14.6357	−	22.7736i	0.534778	−	0.832130i
$750$		0			0
$751$	16.9947	+	37.2132i	0.620145	+	1.35793i	0.915414	+	0.402513i	$0.131863\pi$
$751$	16.9947	+	37.2132i	0.620145	+	1.35793i	−0.295270	+	0.955414i	$0.595409\pi$
$752$		0			0
$753$	23.7467	−	80.8737i	0.865376	−	2.94720i
$754$		0			0
$755$	−8.76303	−	29.8441i	−0.318919	−	1.08614i
$756$		0			0
$757$	−2.54318	−	17.6882i	−0.0924336	−	0.642890i	−0.982390	−	0.186844i	$-0.940174\pi$
$757$	−2.54318	−	17.6882i	−0.0924336	−	0.642890i	0.889956	−	0.456046i	$-0.150735\pi$
$758$		0			0
$759$	−24.3395	+	3.12644i	−0.883469	+	0.113483i
$760$		0			0
$761$	−3.72667	−	25.9195i	−0.135092	−	0.939583i	−0.938776	−	0.344527i	$-0.888039\pi$
$761$	−3.72667	−	25.9195i	−0.135092	−	0.939583i	0.803685	−	0.595055i	$-0.202870\pi$
$762$		0			0
$763$	56.3520	−	16.5465i	2.04008	−	0.599022i
$764$		0			0
$765$	13.4044	−	45.6513i	0.484638	−	1.65052i
$766$		0			0
$767$	−2.59969	+	1.18724i	−0.0938695	+	0.0428688i
$768$		0			0
$769$	−25.1988	+	39.2101i	−0.908692	+	1.41395i	0.00160673	+	0.999999i	$0.499489\pi$
$769$	−25.1988	+	39.2101i	−0.908692	+	1.41395i	−0.910298	+	0.413953i	$0.864148\pi$
$770$		0			0
$771$	−7.60986	+	52.9277i	−0.274062	+	1.90615i
$772$		0			0
$773$	−8.58697	−	9.90989i	−0.308852	−	0.356434i	0.580010	−	0.814609i	$-0.303049\pi$
$773$	−8.58697	−	9.90989i	−0.308852	−	0.356434i	−0.888862	+	0.458175i	$0.848503\pi$
$774$		0			0
$775$	3.31530	+	5.15870i	0.119089	+	0.185306i
$776$		0			0
$777$	57.5593	−	66.4270i	2.06493	−	2.38305i
$778$		0			0
$779$	−14.7011	−	6.71378i	−0.526722	−	0.240546i
$780$		0			0
$781$	3.73587			0.133680
$782$		0			0
$783$		−	41.0855i		−	1.46828i
$784$		0			0
$785$	3.33055	−	7.29288i	0.118872	−	0.260294i
$786$		0			0
$787$	14.4910	+	12.5565i	0.516547	+	0.447591i	0.873707	−	0.486453i	$-0.161709\pi$
$787$	14.4910	+	12.5565i	0.516547	+	0.447591i	−0.357160	+	0.934043i	$0.616255\pi$
$788$		0			0
$789$	−14.4190	+	9.26654i	−0.513331	+	0.329898i
$790$		0			0
$791$	22.0286	−	19.0879i	0.783246	−	0.678687i
$792$		0			0
$793$	−5.14215	−	0.739330i	−0.182603	−	0.0262544i
$794$		0			0
$795$	13.4484	+	8.64279i	0.476967	+	0.306528i
$796$		0			0
$797$	17.1629	+	37.5815i	0.607941	+	1.33120i	0.923974	+	0.382456i	$0.124922\pi$
$797$	17.1629	+	37.5815i	0.607941	+	1.33120i	−0.316033	+	0.948748i	$0.602351\pi$
$798$		0			0
$799$	24.3034	+	7.13613i	0.859793	+	0.252458i
$800$		0			0
$801$	−3.97491	−	13.5373i	−0.140447	−	0.478317i
$802$		0			0
$803$	3.79924	−	0.546248i	0.134072	−	0.0192767i
$804$		0			0
$805$	31.9653	−	19.8696i	1.12663	−	0.700313i
$806$		0			0
$807$	40.7520	−	5.85925i	1.43454	−	0.206255i
$808$		0			0
$809$	33.4662	−	9.82656i	1.17661	−	0.345483i	0.365743	−	0.930716i	$-0.380815\pi$
$809$	33.4662	−	9.82656i	1.17661	−	0.345483i	0.810866	+	0.585233i	$0.198997\pi$
$810$		0			0
$811$	−14.0562	−	4.12727i	−0.493579	−	0.144928i	0.0254643	−	0.999676i	$-0.491894\pi$
$811$	−14.0562	−	4.12727i	−0.493579	−	0.144928i	−0.519044	+	0.854748i	$0.673712\pi$
$812$		0			0
$813$	−51.2480	+	23.4042i	−1.79735	+	0.820821i
$814$		0			0
$815$	20.0710	+	12.8989i	0.703058	+	0.451828i
$816$		0			0
$817$	2.70025	−	18.7807i	0.0944699	−	0.657053i
$818$		0			0
$819$	−18.6656	+	16.1738i	−0.652229	+	0.565159i
$820$		0			0
$821$	19.8827	+	30.9380i	0.693910	+	1.07975i	0.992126	+	0.125247i	$0.0399722\pi$
$821$	19.8827	+	30.9380i	0.693910	+	1.07975i	−0.298216	+	0.954499i	$0.596391\pi$
$822$		0			0
$823$	20.5637	+	17.8186i	0.716806	+	0.621116i	0.934941	−	0.354802i	$-0.115452\pi$
$823$	20.5637	+	17.8186i	0.716806	+	0.621116i	−0.218135	+	0.975919i	$0.569997\pi$
$824$		0			0
$825$	−12.0633	−	5.50914i	−0.419991	−	0.191804i
$826$		0			0
$827$		−	51.2196i		−	1.78108i	−0.454903	−	0.890541i	$-0.650326\pi$
$827$		−	51.2196i		−	1.78108i	0.454903	−	0.890541i	$-0.349674\pi$
$828$		0			0
$829$		−	28.0969i		−	0.975846i	−0.872887	−	0.487923i	$-0.837755\pi$
$829$		−	28.0969i		−	0.975846i	0.872887	−	0.487923i	$-0.162245\pi$
$830$		0			0
$831$	−67.5497	−	30.8489i	−2.34327	−	1.07014i
$832$		0			0
$833$	83.4353	+	72.2971i	2.89086	+	2.50494i
$834$		0			0
$835$	−20.2110	−	31.4490i	−0.699431	−	1.08834i
$836$		0			0
$837$	−11.0244	+	9.55273i	−0.381060	+	0.330191i
$838$		0			0
$839$	−1.77813	+	12.3672i	−0.0613878	+	0.426962i	0.935832	+	0.352446i	$0.114650\pi$
$839$	−1.77813	+	12.3672i	−0.0613878	+	0.426962i	−0.997220	+	0.0745153i	$0.976259\pi$
$840$		0			0
$841$	−12.9609	−	8.32945i	−0.446927	−	0.287222i
$842$		0			0
$843$	−24.8872	+	11.3656i	−0.857161	+	0.391452i
$844$		0			0
$845$	18.0222	+	5.29179i	0.619981	+	0.182043i
$846$		0			0
$847$	−37.8038	+	11.1002i	−1.29895	+	0.381408i
$848$		0			0
$849$	−65.0110	+	9.34718i	−2.23117	+	0.320794i
$850$		0			0
$851$	−4.58720	+	28.8192i	−0.157247	+	0.987909i
$852$		0			0
$853$	−44.0942	+	6.33980i	−1.50976	+	0.217070i	−0.846931	−	0.531702i	$-0.821553\pi$
$853$	−44.0942	+	6.33980i	−1.50976	+	0.217070i	−0.662827	+	0.748773i	$0.730643\pi$
$854$		0			0
$855$	−6.50703	−	22.1609i	−0.222536	−	0.757887i
$856$		0			0
$857$	−27.7333	−	8.14322i	−0.947350	−	0.278167i	−0.228667	−	0.973505i	$-0.573437\pi$
$857$	−27.7333	−	8.14322i	−0.947350	−	0.278167i	−0.718683	+	0.695338i	$0.755255\pi$
$858$		0			0
$859$	10.7736	+	23.5909i	0.367591	+	0.804911i	0.999553	+	0.0299119i	$0.00952267\pi$
$859$	10.7736	+	23.5909i	0.367591	+	0.804911i	−0.631962	+	0.775000i	$0.717750\pi$
$860$		0			0
$861$	68.0700	+	43.7459i	2.31982	+	1.49086i
$862$		0			0
$863$	18.7725	+	2.69908i	0.639023	+	0.0918776i	0.454208	−	0.890896i	$-0.349922\pi$
$863$	18.7725	+	2.69908i	0.639023	+	0.0918776i	0.184815	+	0.982773i	$0.440831\pi$
$864$		0			0
$865$	−28.0624	+	24.3162i	−0.954149	+	0.826775i
$866$		0			0
$867$	−44.0314	+	28.2973i	−1.49539	+	0.961026i
$868$		0			0
$869$	10.5428	+	9.13541i	0.357641	+	0.309898i
$870$		0			0
$871$	−4.15019	+	9.08765i	−0.140624	+	0.307923i
$872$		0			0
$873$		−	3.75405i		−	0.127055i
$874$		0			0
$875$	59.5801			2.01417
$876$		0			0
$877$	13.4336	+	6.13494i	0.453622	+	0.207162i	0.629105	−	0.777320i	$-0.283422\pi$
$877$	13.4336	+	6.13494i	0.453622	+	0.207162i	−0.175483	+	0.984482i	$0.556149\pi$
$878$		0			0
$879$	9.57812	−	11.0537i	0.323062	−	0.372834i
$880$		0			0
$881$	5.64865	+	8.78948i	0.190308	+	0.296125i	0.923275	−	0.384139i	$-0.125502\pi$
$881$	5.64865	+	8.78948i	0.190308	+	0.296125i	−0.732967	+	0.680264i	$0.761865\pi$
$882$		0			0
$883$	−19.5356	−	22.5453i	−0.657427	−	0.758711i	0.324928	−	0.945739i	$-0.394660\pi$
$883$	−19.5356	−	22.5453i	−0.657427	−	0.758711i	−0.982355	+	0.187028i	$0.940115\pi$
$884$		0			0
$885$	−1.90429	+	13.2446i	−0.0640119	+	0.445213i
$886$		0			0
$887$	2.24655	−	3.49570i	0.0754317	−	0.117374i	−0.801488	−	0.598011i	$-0.795958\pi$
$887$	2.24655	−	3.49570i	0.0754317	−	0.117374i	0.876920	+	0.480637i	$0.159594\pi$
$888$		0			0
$889$	−34.0047	+	15.5294i	−1.14048	+	0.520840i
$890$		0			0
$891$	1.07747	−	3.66952i	0.0360965	−	0.122933i
$892$		0			0
$893$	11.7978	−	3.46416i	0.394799	−	0.115924i
$894$		0			0
$895$	−0.246409	−	1.71381i	−0.00823655	−	0.0572865i
$896$		0			0
$897$	3.84054	−	12.3870i	0.128232	−	0.413591i
$898$		0			0
$899$	2.24382	+	15.6061i	0.0748356	+	0.520493i
$900$		0			0
$901$	−6.03901	−	20.5670i	−0.201189	−	0.685186i
$902$		0			0
$903$	−26.7630	+	91.1465i	−0.890618	+	3.03317i
$904$		0			0
$905$	−3.10762	−	6.80474i	−0.103301	−	0.226197i
$906$		0			0
$907$	−18.8527	+	29.3354i	−0.625994	+	0.974066i	0.372938	+	0.927856i	$0.378350\pi$
$907$	−18.8527	+	29.3354i	−0.625994	+	0.974066i	−0.998932	+	0.0462092i	$0.985286\pi$
$908$		0			0
$909$	−33.5977	−	4.83062i	−1.11437	−	0.160222i
$910$		0			0
$911$	−3.03578	−	3.50347i	−0.100580	−	0.116075i	0.703228	−	0.710964i	$-0.251741\pi$
$911$	−3.03578	−	3.50347i	−0.100580	−	0.116075i	−0.803808	+	0.594889i	$0.797196\pi$
$912$		0			0
$913$	12.0992	−	7.77571i	0.400427	−	0.257339i
$914$		0			0
$915$	−15.9281	+	18.3820i	−0.526565	+	0.607689i
$916$		0			0
$917$	25.4974	−	55.8315i	0.841998	−	1.84372i
$918$		0			0
$919$	9.64342			0.318107			0.159054	−	0.987270i	$-0.449156\pi$
$919$	9.64342			0.318107			0.159054	+	0.987270i	$0.449156\pi$
$920$		0			0
$921$	37.6167			1.23951
$922$		0			0
$923$	−0.820174	+	1.79593i	−0.0269963	+	0.0591137i
$924$		0			0
$925$	−10.3276	+	11.9187i	−0.339569	+	0.391884i
$926$		0			0
$927$	−13.2175	+	8.49434i	−0.434118	+	0.278991i
$928$		0			0
$929$	−20.5715	−	23.7408i	−0.674930	−	0.778910i	0.310210	−	0.950668i	$-0.399601\pi$
$929$	−20.5715	−	23.7408i	−0.674930	−	0.778910i	−0.985139	+	0.171758i	$0.945055\pi$
$930$		0			0
$931$	53.0473	+	7.62705i	1.73855	+	0.249966i
$932$		0			0
$933$	−18.1579	+	28.2542i	−0.594462	+	0.925001i
$934$		0			0
$935$	−6.86377	−	15.0296i	−0.224469	−	0.491519i
$936$		0			0
$937$	−3.56682	+	12.1475i	−0.116523	+	0.396840i	−0.997014	−	0.0772224i	$-0.975395\pi$
$937$	−3.56682	+	12.1475i	−0.116523	+	0.396840i	0.880491	+	0.474063i	$0.157213\pi$
$938$		0			0
$939$	4.39723	+	14.9756i	0.143498	+	0.488709i
$940$		0			0
$941$	4.53269	+	31.5255i	0.147761	+	1.02770i	0.919873	+	0.392216i	$0.128292\pi$
$941$	4.53269	+	31.5255i	0.147761	+	1.02770i	−0.772112	+	0.635487i	$0.780799\pi$
$942$		0			0
$943$	−26.8613	−	0.404241i	−0.874725	−	0.0131639i
$944$		0			0
$945$	6.88608	+	47.8937i	0.224004	+	1.55798i
$946$		0			0
$947$	14.9139	−	4.37912i	0.484637	−	0.142302i	−0.0302813	−	0.999541i	$-0.509640\pi$
$947$	14.9139	−	4.37912i	0.484637	−	0.142302i	0.514919	+	0.857239i	$0.327822\pi$
$948$		0			0
$949$	−0.571490	+	1.94632i	−0.0185513	+	0.0631801i
$950$		0			0
$951$	−2.60550	+	1.18989i	−0.0844891	+	0.0385849i
$952$		0			0
$953$	−10.5180	+	16.3663i	−0.340712	+	0.530158i	−0.968755	−	0.248021i	$-0.920220\pi$
$953$	−10.5180	+	16.3663i	−0.340712	+	0.530158i	0.628043	+	0.778179i	$0.283856\pi$
$954$		0			0
$955$	−4.45172	+	30.9624i	−0.144054	+	1.00192i
$956$		0			0
$957$	−22.3293	−	25.7694i	−0.721803	−	0.833005i
$958$		0			0
$959$	−20.6839	−	32.1847i	−0.667917	−	1.03930i
$960$		0			0
$961$	−16.6348	+	19.1976i	−0.536607	+	0.619277i
$962$		0			0
$963$	−25.1181	−	11.4711i	−0.809421	−	0.369650i
$964$		0			0
$965$	−36.7999			−1.18463
$966$		0			0
$967$		−	52.0426i		−	1.67358i	−0.547527	−	0.836788i	$-0.684431\pi$
$967$		−	52.0426i		−	1.67358i	0.547527	−	0.836788i	$-0.315569\pi$
$968$		0			0
$969$	−20.3469	+	44.5534i	−0.653636	+	1.43126i
$970$		0			0
$971$	14.6900	+	12.7290i	0.471426	+	0.408493i	0.857907	−	0.513804i	$-0.171764\pi$
$971$	14.6900	+	12.7290i	0.471426	+	0.408493i	−0.386482	+	0.922297i	$0.626310\pi$
$972$		0			0
$973$	0.505258	−	0.324709i	0.0161978	−	0.0104097i
$974$		0			0
$975$	5.29677	−	4.58968i	0.169632	−	0.146987i
$976$		0			0
$977$	14.2751	+	2.05245i	0.456700	+	0.0656636i	0.366826	−	0.930290i	$-0.380444\pi$
$977$	14.2751	+	2.05245i	0.456700	+	0.0656636i	0.0898742	+	0.995953i	$0.471354\pi$
$978$		0			0
$979$	−4.12180	−	2.64892i	−0.131733	−	0.0846599i
$980$		0			0
$981$	−24.8867	−	54.4942i	−0.794570	−	1.73987i
$982$		0			0
$983$	−13.5418	−	3.97623i	−0.431916	−	0.126822i	0.0585456	−	0.998285i	$-0.481354\pi$
$983$	−13.5418	−	3.97623i	−0.431916	−	0.126822i	−0.490462	+	0.871463i	$0.663172\pi$
$984$		0			0
$985$	6.01258	+	20.4770i	0.191577	+	0.652451i
$986$		0			0
$987$	−60.9342	+	8.76101i	−1.93956	+	0.278866i
$988$		0			0
$989$	−8.42917	−	30.3916i	−0.268032	−	0.966397i
$990$		0			0
$991$	−48.2699	+	6.94017i	−1.53334	+	0.220462i	−0.856687	−	0.515836i	$-0.827481\pi$
$991$	−48.2699	+	6.94017i	−1.53334	+	0.220462i	−0.676657	+	0.736298i	$0.736572\pi$
$992$		0			0
$993$	0.283694	−	0.0833002i	0.00900277	−	0.00264345i
$994$		0			0
$995$	16.8503	+	4.94769i	0.534189	+	0.156852i
$996$		0			0
$997$	43.6622	−	19.9399i	1.38280	−	0.631502i	0.421452	−	0.906851i	$-0.361521\pi$
$997$	43.6622	−	19.9399i	1.38280	−	0.631502i	0.961344	+	0.275349i	$0.0887933\pi$
$998$		0			0
$999$	−31.5604	−	20.2826i	−0.998527	−	0.641714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	736.2.r.a.687.22		220
4.3	odd	2		184.2.j.a.43.10	✓	220
8.3	odd	2	inner	736.2.r.a.687.21		220
8.5	even	2		184.2.j.a.43.15	yes	220
23.15	odd	22	inner	736.2.r.a.15.21		220
92.15	even	22		184.2.j.a.107.15	yes	220
184.61	odd	22		184.2.j.a.107.10	yes	220
184.107	even	22	inner	736.2.r.a.15.22		220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.j.a.43.10	✓	220	4.3	odd	2
184.2.j.a.43.15	yes	220	8.5	even	2
184.2.j.a.107.10	yes	220	184.61	odd	22
184.2.j.a.107.15	yes	220	92.15	even	22
736.2.r.a.15.21		220	23.15	odd	22	inner
736.2.r.a.15.22		220	184.107	even	22	inner
736.2.r.a.687.21		220	8.3	odd	2	inner
736.2.r.a.687.22		220	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.r (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18656 - 2.59820i) q^{3} +(1.01624 - 1.17280i) q^{5} +(4.25438 - 2.73413i) q^{7} +(-3.37812 - 3.89856i) q^{9} +(-1.77318 - 0.254945i) q^{11} +(0.511843 - 0.796443i) q^{13} +(-1.84135 - 4.03199i) q^{15} +(-1.67446 + 5.70268i) q^{17} +(0.812847 + 2.76830i) q^{19} +(-2.05573 - 14.2979i) q^{21} +(3.08571 + 3.67130i) q^{23} +(0.368850 + 2.56541i) q^{25} +(-5.91571 + 1.73701i) q^{27} +(-1.87742 + 6.39390i) q^{29} +(2.15218 - 0.982870i) q^{31} +(-2.76637 + 4.30456i) q^{33} +(1.11688 - 7.76808i) q^{35} +(3.98474 + 4.59863i) q^{37} +(-1.46198 - 2.27489i) q^{39} +(-3.66827 + 4.23341i) q^{41} +(-5.98202 - 2.73190i) q^{43} -8.00523 q^{45} -4.26175i q^{47} +(7.71643 - 16.8966i) q^{49} +(12.8298 + 11.1171i) q^{51} +(-3.03402 + 1.94985i) q^{53} +(-2.10098 + 1.82051i) q^{55} +(8.15708 + 1.17281i) q^{57} +(-2.53954 - 1.63207i) q^{59} +(-2.27952 - 4.99144i) q^{61} +(-25.0310 - 7.34976i) q^{63} +(-0.413916 - 1.40967i) q^{65} +(-10.4452 + 1.50179i) q^{67} +(13.2001 - 3.66107i) q^{69} +(-2.06420 + 0.296788i) q^{71} +(-2.05582 + 0.603644i) q^{73} +(7.10309 + 2.08566i) q^{75} +(-8.24084 + 3.76346i) q^{77} +(-6.55104 - 4.21010i) q^{79} +(-0.303823 + 2.11314i) q^{81} +(-6.06755 + 5.25756i) q^{83} +(4.98647 + 7.75910i) q^{85} +(14.3849 + 12.4646i) q^{87} +(2.48788 + 1.13618i) q^{89} -4.78782i q^{91} -6.75803i q^{93} +(4.07272 + 1.85995i) q^{95} +(0.549986 + 0.476566i) q^{97} +(4.99610 + 7.77408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 18 q^{3} - 36 q^{9} + 22 q^{11} - 22 q^{17} + 22 q^{19} - 32 q^{25} + 18 q^{27} - 22 q^{33} - 2 q^{35} - 18 q^{41} + 22 q^{43} - 28 q^{49} + 22 q^{51} - 22 q^{57} + 6 q^{59} - 22 q^{65} + 22 q^{67}+ \cdots + 22 q^{99}+O(q^{100}) \) 220 * q + 18 * q^3 - 36 * q^9 + 22 * q^11 - 22 * q^17 + 22 * q^19 - 32 * q^25 + 18 * q^27 - 22 * q^33 - 2 * q^35 - 18 * q^41 + 22 * q^43 - 28 * q^49 + 22 * q^51 - 22 * q^57 + 6 * q^59 - 22 * q^65 + 22 * q^67 - 18 * q^73 - 14 * q^75 + 4 * q^81 + 22 * q^83 - 22 * q^89 - 22 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more