LMFDB - Embedded newform 2646.2.m.c.1763.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1763.19
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.c.881.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.712984 - 1.23492i) q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.712984 - 1.23492i) q^{5} +1.00000i q^{8} -1.42597i q^{10} +(2.12170 + 1.22496i) q^{11} +(-1.61819 + 0.934264i) q^{13} +(-0.500000 + 0.866025i) q^{16} -1.98625 q^{17} +5.90920i q^{19} +(0.712984 - 1.23492i) q^{20} +(1.22496 + 2.12170i) q^{22} +(5.65337 - 3.26397i) q^{23} +(1.48331 - 2.56917i) q^{25} -1.86853 q^{26} +(5.51198 + 3.18234i) q^{29} +(-4.15157 + 2.39691i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.72014 - 0.993125i) q^{34} -1.83032 q^{37} +(-2.95460 + 5.11752i) q^{38} +(1.23492 - 0.712984i) q^{40} +(2.32289 + 4.02337i) q^{41} +(-5.07994 + 8.79872i) q^{43} +2.44993i q^{44} +6.52794 q^{46} +(6.47952 - 11.2229i) q^{47} +(2.56917 - 1.48331i) q^{50} +(-1.61819 - 0.934264i) q^{52} +11.8930i q^{53} -3.49352i q^{55} +(3.18234 + 5.51198i) q^{58} +(-2.88911 - 5.00408i) q^{59} +(8.38524 + 4.84122i) q^{61} -4.79382 q^{62} -1.00000 q^{64} +(2.30749 + 1.33223i) q^{65} +(7.60449 + 13.1714i) q^{67} +(-0.993125 - 1.72014i) q^{68} +0.594087i q^{71} +13.5874i q^{73} +(-1.58511 - 0.915162i) q^{74} +(-5.11752 + 2.95460i) q^{76} +(4.87348 - 8.44111i) q^{79} +1.42597 q^{80} +4.64578i q^{82} +(1.60586 - 2.78143i) q^{83} +(1.41616 + 2.45287i) q^{85} +(-8.79872 + 5.07994i) q^{86} +(-1.22496 + 2.12170i) q^{88} +0.144657 q^{89} +(5.65337 + 3.26397i) q^{92} +(11.2229 - 6.47952i) q^{94} +(7.29742 - 4.21317i) q^{95} +(-2.32972 - 1.34506i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 48 * q^11 - 24 * q^16 - 48 * q^23 - 24 * q^25 + 48 * q^50 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 96 * q^86 - 48 * q^92 + 192 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.712984	−	1.23492i	−0.318856	−	0.552275i	0.661394	−	0.750039i	$-0.269965\pi$
$5$	−0.712984	−	1.23492i	−0.318856	−	0.552275i	−0.980250	+	0.197764i	$0.936632\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$		−	1.42597i		−	0.450931i
$11$	2.12170	+	1.22496i	0.639717	+	0.369341i	0.784505	−	0.620122i	$-0.212917\pi$
$11$	2.12170	+	1.22496i	0.639717	+	0.369341i	−0.144789	+	0.989463i	$0.546250\pi$
$12$		0			0
$13$	−1.61819	+	0.934264i	−0.448806	+	0.259118i	−0.707326	−	0.706888i	$-0.750099\pi$
$13$	−1.61819	+	0.934264i	−0.448806	+	0.259118i	0.258520	+	0.966006i	$0.416765\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.98625			−0.481737			−0.240868	−	0.970558i	$-0.577432\pi$
$17$	−1.98625			−0.481737			−0.240868	+	0.970558i	$0.577432\pi$
$18$		0			0
$19$			5.90920i			1.35566i	0.735217	+	0.677832i	$0.237080\pi$
$19$			5.90920i			1.35566i	−0.735217	+	0.677832i	$0.762920\pi$
$20$	0.712984	−	1.23492i	0.159428	−	0.276137i
$21$		0			0
$22$	1.22496	+	2.12170i	0.261163	+	0.452348i
$23$	5.65337	−	3.26397i	1.17881	−	0.680585i	0.223070	−	0.974802i	$-0.428392\pi$
$23$	5.65337	−	3.26397i	1.17881	−	0.680585i	0.955739	+	0.294217i	$0.0950589\pi$
$24$		0			0
$25$	1.48331	−	2.56917i	0.296662	−	0.513833i
$26$	−1.86853			−0.366448
$27$		0			0
$28$		0			0
$29$	5.51198	+	3.18234i	1.02355	+	0.590946i	0.915130	−	0.403159i	$-0.132088\pi$
$29$	5.51198	+	3.18234i	1.02355	+	0.590946i	0.108419	+	0.994105i	$0.465421\pi$
$30$		0			0
$31$	−4.15157	+	2.39691i	−0.745644	+	0.430498i	−0.824118	−	0.566419i	$-0.808329\pi$
$31$	−4.15157	+	2.39691i	−0.745644	+	0.430498i	0.0784741	+	0.996916i	$0.474995\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−1.72014	−	0.993125i	−0.295002	−	0.170320i
$35$		0			0
$36$		0			0
$37$	−1.83032			−0.300903			−0.150452	−	0.988617i	$-0.548073\pi$
$37$	−1.83032			−0.300903			−0.150452	+	0.988617i	$0.548073\pi$
$38$	−2.95460	+	5.11752i	−0.479300	+	0.830171i
$39$		0			0
$40$	1.23492	−	0.712984i	0.195259	−	0.112733i
$41$	2.32289	+	4.02337i	0.362775	+	0.628344i	0.988416	−	0.151766i	$-0.0484961\pi$
$41$	2.32289	+	4.02337i	0.362775	+	0.628344i	−0.625642	+	0.780111i	$0.715163\pi$
$42$		0			0
$43$	−5.07994	+	8.79872i	−0.774684	+	1.34179i	0.160288	+	0.987070i	$0.448758\pi$
$43$	−5.07994	+	8.79872i	−0.774684	+	1.34179i	−0.934972	+	0.354722i	$0.884575\pi$
$44$			2.44993i			0.369341i
$45$		0			0
$46$	6.52794			0.962493
$47$	6.47952	−	11.2229i	0.945135	−	1.63702i	0.189654	−	0.981851i	$-0.439263\pi$
$47$	6.47952	−	11.2229i	0.945135	−	1.63702i	0.755481	−	0.655170i	$-0.227403\pi$
$48$		0			0
$49$		0			0
$50$	2.56917	−	1.48331i	0.363335	−	0.209771i
$51$		0			0
$52$	−1.61819	−	0.934264i	−0.224403	−	0.129559i
$53$			11.8930i			1.63363i	0.576897	+	0.816817i	$0.304264\pi$
$53$			11.8930i			1.63363i	−0.576897	+	0.816817i	$0.695736\pi$
$54$		0			0
$55$		−	3.49352i		−	0.471066i
$56$		0			0
$57$		0			0
$58$	3.18234	+	5.51198i	0.417862	+	0.723759i
$59$	−2.88911	−	5.00408i	−0.376130	−	0.651475i	0.614366	−	0.789021i	$-0.289412\pi$
$59$	−2.88911	−	5.00408i	−0.376130	−	0.651475i	−0.990495	+	0.137546i	$0.956079\pi$
$60$		0			0
$61$	8.38524	+	4.84122i	1.07362	+	0.619855i	0.929168	−	0.369657i	$-0.120525\pi$
$61$	8.38524	+	4.84122i	1.07362	+	0.619855i	0.144452	+	0.989512i	$0.453858\pi$
$62$	−4.79382			−0.608815
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.30749	+	1.33223i	0.286209	+	0.165243i
$66$		0			0
$67$	7.60449	+	13.1714i	0.929036	+	1.60914i	0.784938	+	0.619574i	$0.212695\pi$
$67$	7.60449	+	13.1714i	0.929036	+	1.60914i	0.144098	+	0.989563i	$0.453972\pi$
$68$	−0.993125	−	1.72014i	−0.120434	−	0.208598i
$69$		0			0
$70$		0			0
$71$			0.594087i			0.0705051i	0.999378	+	0.0352526i	$0.0112236\pi$
$71$			0.594087i			0.0705051i	−0.999378	+	0.0352526i	$0.988776\pi$
$72$		0			0
$73$			13.5874i			1.59029i	0.606422	+	0.795143i	$0.292604\pi$
$73$			13.5874i			1.59029i	−0.606422	+	0.795143i	$0.707396\pi$
$74$	−1.58511	−	0.915162i	−0.184265	−	0.106385i
$75$		0			0
$76$	−5.11752	+	2.95460i	−0.587020	+	0.338916i
$77$		0			0
$78$		0			0
$79$	4.87348	−	8.44111i	0.548309	−	0.949699i	−0.450081	−	0.892988i	$-0.648605\pi$
$79$	4.87348	−	8.44111i	0.548309	−	0.949699i	0.998391	−	0.0567119i	$-0.0180616\pi$
$80$	1.42597			0.159428
$81$		0			0
$82$			4.64578i			0.513041i
$83$	1.60586	−	2.78143i	0.176266	−	0.305302i	−0.764333	−	0.644822i	$-0.776931\pi$
$83$	1.60586	−	2.78143i	0.176266	−	0.305302i	0.940599	+	0.339520i	$0.110265\pi$
$84$		0			0
$85$	1.41616	+	2.45287i	0.153605	+	0.266051i
$86$	−8.79872	+	5.07994i	−0.948791	+	0.547784i
$87$		0			0
$88$	−1.22496	+	2.12170i	−0.130582	+	0.226174i
$89$	0.144657			0.0153336			0.00766680	−	0.999971i	$-0.497560\pi$
$89$	0.144657			0.0153336			0.00766680	+	0.999971i	$0.497560\pi$
$90$		0			0
$91$		0			0
$92$	5.65337	+	3.26397i	0.589404	+	0.340293i
$93$		0			0
$94$	11.2229	−	6.47952i	1.15755	−	0.668311i
$95$	7.29742	−	4.21317i	0.748699	−	0.432262i
$96$		0			0
$97$	−2.32972	−	1.34506i	−0.236547	−	0.136571i	0.377042	−	0.926196i	$-0.376941\pi$
$97$	−2.32972	−	1.34506i	−0.236547	−	0.136571i	−0.613589	+	0.789626i	$0.710275\pi$
$98$		0			0
$99$		0			0
$100$	2.96662			0.296662
$101$	−1.84869	+	3.20202i	−0.183951	+	0.318613i	−0.943223	−	0.332161i	$-0.892222\pi$
$101$	−1.84869	+	3.20202i	−0.183951	+	0.318613i	0.759271	+	0.650774i	$0.225556\pi$
$102$		0			0
$103$	13.9648	−	8.06260i	1.37600	−	0.794431i	0.384321	−	0.923200i	$-0.374436\pi$
$103$	13.9648	−	8.06260i	1.37600	−	0.794431i	0.991675	+	0.128768i	$0.0411024\pi$
$104$	−0.934264	−	1.61819i	−0.0916121	−	0.158677i
$105$		0			0
$106$	−5.94652	+	10.2997i	−0.577577	+	1.00039i
$107$		−	0.545248i		−	0.0527111i	−0.999653	−	0.0263556i	$-0.991610\pi$
$107$		−	0.545248i		−	0.0527111i	0.999653	−	0.0263556i	$-0.00839020\pi$
$108$		0			0
$109$	−6.33018			−0.606321			−0.303161	−	0.952939i	$-0.598042\pi$
$109$	−6.33018			−0.606321			−0.303161	+	0.952939i	$0.598042\pi$
$110$	1.74676	−	3.02547i	0.166547	−	0.288468i
$111$		0			0
$112$		0			0
$113$	9.21222	−	5.31868i	0.866612	−	0.500339i	0.000391395	−	1.00000i	$-0.499875\pi$
$113$	9.21222	−	5.31868i	0.866612	−	0.500339i	0.866221	+	0.499661i	$0.166542\pi$
$114$		0			0
$115$	−8.06152	−	4.65432i	−0.751740	−	0.434017i
$116$			6.36469i			0.590946i
$117$		0			0
$118$		−	5.77821i		−	0.531927i
$119$		0			0
$120$		0			0
$121$	−2.49893	−	4.32827i	−0.227175	−	0.393479i
$122$	4.84122	+	8.38524i	0.438304	+	0.759164i
$123$		0			0
$124$	−4.15157	−	2.39691i	−0.372822	−	0.215249i
$125$	−11.3601			−1.01608
$126$		0			0
$127$	5.92432			0.525698			0.262849	−	0.964837i	$-0.415338\pi$
$127$	5.92432			0.525698			0.262849	+	0.964837i	$0.415338\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.33223	+	2.30749i	0.116844	+	0.202380i
$131$	6.81751	+	11.8083i	0.595649	+	1.03169i	0.993455	+	0.114224i	$0.0364383\pi$
$131$	6.81751	+	11.8083i	0.595649	+	1.03169i	−0.397806	+	0.917469i	$0.630228\pi$
$132$		0			0
$133$		0			0
$134$			15.2090i			1.31386i
$135$		0			0
$136$		−	1.98625i		−	0.170320i
$137$	15.5598	+	8.98348i	1.32937	+	0.767510i	0.985202	−	0.171399i	$-0.0548288\pi$
$137$	15.5598	+	8.98348i	1.32937	+	0.767510i	0.344165	+	0.938909i	$0.388162\pi$
$138$		0			0
$139$	−8.22479	+	4.74858i	−0.697617	+	0.402769i	−0.806459	−	0.591290i	$-0.798619\pi$
$139$	−8.22479	+	4.74858i	−0.697617	+	0.402769i	0.108842	+	0.994059i	$0.465286\pi$
$140$		0			0
$141$		0			0
$142$	−0.297043	+	0.514494i	−0.0249273	+	0.0431754i
$143$	−4.57776			−0.382811
$144$		0			0
$145$		−	9.07584i		−	0.753707i
$146$	−6.79371	+	11.7670i	−0.562251	+	0.973847i
$147$		0			0
$148$	−0.915162	−	1.58511i	−0.0752258	−	0.130295i
$149$	−4.61041	+	2.66182i	−0.377699	+	0.218065i	−0.676817	−	0.736151i	$-0.736641\pi$
$149$	−4.61041	+	2.66182i	−0.377699	+	0.218065i	0.299117	+	0.954216i	$0.403308\pi$
$150$		0			0
$151$	−6.97282	+	12.0773i	−0.567440	+	0.982834i	0.429378	+	0.903125i	$0.358733\pi$
$151$	−6.97282	+	12.0773i	−0.567440	+	0.982834i	−0.996818	+	0.0797096i	$0.974601\pi$
$152$	−5.90920			−0.479300
$153$		0			0
$154$		0			0
$155$	5.92000	+	3.41791i	0.475506	+	0.274533i
$156$		0			0
$157$	−4.55518	+	2.62993i	−0.363543	+	0.209891i	−0.670634	−	0.741789i	$-0.733978\pi$
$157$	−4.55518	+	2.62993i	−0.363543	+	0.209891i	0.307091	+	0.951680i	$0.400644\pi$
$158$	8.44111	−	4.87348i	0.671539	−	0.387713i
$159$		0			0
$160$	1.23492	+	0.712984i	0.0976293	+	0.0563663i
$161$		0			0
$162$		0			0
$163$	−9.87851			−0.773745			−0.386872	−	0.922133i	$-0.626445\pi$
$163$	−9.87851			−0.773745			−0.386872	+	0.922133i	$0.626445\pi$
$164$	−2.32289	+	4.02337i	−0.181387	+	0.314172i
$165$		0			0
$166$	2.78143	−	1.60586i	0.215881	−	0.124639i
$167$	8.86749	+	15.3589i	0.686187	+	1.18851i	0.973062	+	0.230542i	$0.0740500\pi$
$167$	8.86749	+	15.3589i	0.686187	+	1.18851i	−0.286876	+	0.957968i	$0.592617\pi$
$168$		0			0
$169$	−4.75430	+	8.23469i	−0.365716	+	0.633438i
$170$			2.83233i			0.217230i
$171$		0			0
$172$	−10.1599			−0.774684
$173$	4.20045	−	7.27539i	0.319354	−	0.553137i	−0.660999	−	0.750386i	$-0.729867\pi$
$173$	4.20045	−	7.27539i	0.319354	−	0.553137i	0.980353	+	0.197249i	$0.0632007\pi$
$174$		0			0
$175$		0			0
$176$	−2.12170	+	1.22496i	−0.159929	+	0.0923351i
$177$		0			0
$178$	0.125277	+	0.0723285i	0.00938988	+	0.00542125i
$179$		−	3.02300i		−	0.225950i	−0.993598	−	0.112975i	$-0.963962\pi$
$179$		−	3.02300i		−	0.225950i	0.993598	−	0.112975i	$-0.0360380\pi$
$180$		0			0
$181$		−	4.94729i		−	0.367729i	−0.982952	−	0.183865i	$-0.941139\pi$
$181$		−	4.94729i		−	0.367729i	0.982952	−	0.183865i	$-0.0588608\pi$
$182$		0			0
$183$		0			0
$184$	3.26397	+	5.65337i	0.240623	+	0.416772i
$185$	1.30499	+	2.26031i	0.0959449	+	0.166181i
$186$		0			0
$187$	−4.21423	−	2.43309i	−0.308175	−	0.177925i
$188$	12.9590			0.945135
$189$		0			0
$190$	8.42633			0.611310
$191$	−4.42179	−	2.55292i	−0.319949	−	0.184723i	0.331421	−	0.943483i	$-0.392472\pi$
$191$	−4.42179	−	2.55292i	−0.319949	−	0.184723i	−0.651370	+	0.758760i	$0.725805\pi$
$192$		0			0
$193$	−0.527061	−	0.912897i	−0.0379387	−	0.0657118i	0.846433	−	0.532496i	$-0.178746\pi$
$193$	−0.527061	−	0.912897i	−0.0379387	−	0.0657118i	−0.884371	+	0.466784i	$0.845413\pi$
$194$	−1.34506	−	2.32972i	−0.0965700	−	0.167264i
$195$		0			0
$196$		0			0
$197$		−	4.97775i		−	0.354650i	−0.984152	−	0.177325i	$-0.943256\pi$
$197$		−	4.97775i		−	0.354650i	0.984152	−	0.177325i	$-0.0567444\pi$
$198$		0			0
$199$			1.15120i			0.0816064i	0.999167	+	0.0408032i	$0.0129917\pi$
$199$			1.15120i			0.0816064i	−0.999167	+	0.0408032i	$0.987008\pi$
$200$	2.56917	+	1.48331i	0.181667	+	0.104886i
$201$		0			0
$202$	−3.20202	+	1.84869i	−0.225294	+	0.130073i
$203$		0			0
$204$		0			0
$205$	3.31237	−	5.73719i	0.231346	−	0.400703i
$206$	16.1252			1.12350
$207$		0			0
$208$		−	1.86853i		−	0.129559i
$209$	−7.23856	+	12.5376i	−0.500702	+	0.867241i
$210$		0			0
$211$	−7.03245	−	12.1806i	−0.484134	−	0.838545i	0.515700	−	0.856769i	$-0.327532\pi$
$211$	−7.03245	−	12.1806i	−0.484134	−	0.838545i	−0.999834	+	0.0182244i	$0.994199\pi$
$212$	−10.2997	+	5.94652i	−0.707384	+	0.408409i
$213$		0			0
$214$	0.272624	−	0.472199i	0.0186362	−	0.0322788i
$215$	14.4877			0.988051
$216$		0			0
$217$		0			0
$218$	−5.48210	−	3.16509i	−0.371294	−	0.214367i
$219$		0			0
$220$	3.02547	−	1.74676i	0.203977	−	0.117766i
$221$	3.21414	−	1.85568i	0.216206	−	0.124827i
$222$		0			0
$223$	−17.3777	−	10.0330i	−1.16370	−	0.671860i	−0.211509	−	0.977376i	$-0.567838\pi$
$223$	−17.3777	−	10.0330i	−1.16370	−	0.671860i	−0.952187	+	0.305516i	$0.901171\pi$
$224$		0			0
$225$		0			0
$226$	10.6374			0.707586
$227$	3.01495	−	5.22205i	0.200109	−	0.346600i	−0.748454	−	0.663187i	$-0.769204\pi$
$227$	3.01495	−	5.22205i	0.200109	−	0.346600i	0.948563	+	0.316587i	$0.102537\pi$
$228$		0			0
$229$	19.8379	−	11.4534i	1.31092	−	0.756862i	0.328674	−	0.944443i	$-0.393398\pi$
$229$	19.8379	−	11.4534i	1.31092	−	0.756862i	0.982249	+	0.187581i	$0.0600648\pi$
$230$	−4.65432	−	8.06152i	−0.306897	−	0.531561i
$231$		0			0
$232$	−3.18234	+	5.51198i	−0.208931	+	0.361879i
$233$		−	29.7780i		−	1.95082i	−0.220395	−	0.975411i	$-0.570735\pi$
$233$		−	29.7780i		−	1.95082i	0.220395	−	0.975411i	$-0.429265\pi$
$234$		0			0
$235$	−18.4792			−1.20545
$236$	2.88911	−	5.00408i	0.188065	−	0.325738i
$237$		0			0
$238$		0			0
$239$	−10.5976	+	6.11850i	−0.685499	+	0.395773i	−0.801924	−	0.597427i	$-0.796190\pi$
$239$	−10.5976	+	6.11850i	−0.685499	+	0.395773i	0.116425	+	0.993200i	$0.462857\pi$
$240$		0			0
$241$	−21.0423	−	12.1488i	−1.35545	−	0.782571i	−0.366445	−	0.930440i	$-0.619425\pi$
$241$	−21.0423	−	12.1488i	−1.35545	−	0.782571i	−0.989007	+	0.147869i	$0.952759\pi$
$242$		−	4.99785i		−	0.321274i
$243$		0			0
$244$			9.68245i			0.619855i
$245$		0			0
$246$		0			0
$247$	−5.52075	−	9.56223i	−0.351277	−	0.608430i
$248$	−2.39691	−	4.15157i	−0.152204	−	0.263625i
$249$		0			0
$250$	−9.83817	−	5.68007i	−0.622220	−	0.359239i
$251$	−13.0834			−0.825815			−0.412908	−	0.910773i	$-0.635487\pi$
$251$	−13.0834			−0.825815			−0.412908	+	0.910773i	$0.635487\pi$
$252$		0			0
$253$	15.9930			1.00547
$254$	5.13061	+	2.96216i	0.321923	+	0.185862i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.24569	+	5.62170i	0.202461	+	0.350672i	0.949321	−	0.314309i	$-0.101773\pi$
$257$	3.24569	+	5.62170i	0.202461	+	0.350672i	−0.746860	+	0.664981i	$0.768439\pi$
$258$		0			0
$259$		0			0
$260$			2.66446i			0.165243i
$261$		0			0
$262$			13.6350i			0.842375i
$263$	−23.2937	−	13.4486i	−1.43635	−	0.829276i	−0.438755	−	0.898607i	$-0.644580\pi$
$263$	−23.2937	−	13.4486i	−1.43635	−	0.829276i	−0.997594	+	0.0693309i	$0.977914\pi$
$264$		0			0
$265$	14.6870	−	8.47954i	0.902215	−	0.520894i
$266$		0			0
$267$		0			0
$268$	−7.60449	+	13.1714i	−0.464518	+	0.804569i
$269$	−15.3040			−0.933099			−0.466550	−	0.884495i	$-0.654503\pi$
$269$	−15.3040			−0.933099			−0.466550	+	0.884495i	$0.654503\pi$
$270$		0			0
$271$			9.36077i			0.568626i	0.958731	+	0.284313i	$0.0917656\pi$
$271$			9.36077i			0.568626i	−0.958731	+	0.284313i	$0.908234\pi$
$272$	0.993125	−	1.72014i	0.0602171	−	0.104299i
$273$		0			0
$274$	8.98348	+	15.5598i	0.542712	+	0.940004i
$275$	6.29427	−	3.63400i	0.379559	−	0.219138i
$276$		0			0
$277$	13.5195	−	23.4164i	0.812307	−	1.40696i	−0.0989390	−	0.995093i	$-0.531545\pi$
$277$	13.5195	−	23.4164i	0.812307	−	1.40696i	0.911246	−	0.411863i	$-0.135122\pi$
$278$	−9.49716			−0.569602
$279$		0			0
$280$		0			0
$281$	16.4502	+	9.49754i	0.981338	+	0.566576i	0.902674	−	0.430325i	$-0.141601\pi$
$281$	16.4502	+	9.49754i	0.981338	+	0.566576i	0.0786642	+	0.996901i	$0.474935\pi$
$282$		0			0
$283$	15.6354	−	9.02710i	0.929428	−	0.536606i	0.0427975	−	0.999084i	$-0.486373\pi$
$283$	15.6354	−	9.02710i	0.929428	−	0.536606i	0.886631	+	0.462478i	$0.153040\pi$
$284$	−0.514494	+	0.297043i	−0.0305296	+	0.0176263i
$285$		0			0
$286$	−3.96445	−	2.28888i	−0.234423	−	0.135344i
$287$		0			0
$288$		0			0
$289$	−13.0548			−0.767930
$290$	4.53792	−	7.85991i	0.266476	−	0.461550i
$291$		0			0
$292$	−11.7670	+	6.79371i	−0.688614	+	0.397572i
$293$	9.99970	+	17.3200i	0.584189	+	1.01184i	0.994976	+	0.100113i	$0.0319205\pi$
$293$	9.99970	+	17.3200i	0.584189	+	1.01184i	−0.410788	+	0.911731i	$0.634746\pi$
$294$		0			0
$295$	−4.11977	+	7.13565i	−0.239862	+	0.415454i
$296$		−	1.83032i		−	0.106385i
$297$		0			0
$298$	−5.32364			−0.308390
$299$	−6.09882	+	10.5635i	−0.352704	+	0.610901i
$300$		0			0
$301$		0			0
$302$	−12.0773	+	6.97282i	−0.694969	+	0.401240i
$303$		0			0
$304$	−5.11752	−	2.95460i	−0.293510	−	0.169458i
$305$		−	13.8069i		−	0.790578i
$306$		0			0
$307$			2.13374i			0.121779i	0.998145	+	0.0608896i	$0.0193937\pi$
$307$			2.13374i			0.121779i	−0.998145	+	0.0608896i	$0.980606\pi$
$308$		0			0
$309$		0			0
$310$	3.41791	+	5.92000i	0.194124	+	0.336233i
$311$	−4.56419	−	7.90541i	−0.258812	−	0.448275i	0.707112	−	0.707101i	$-0.249998\pi$
$311$	−4.56419	−	7.90541i	−0.258812	−	0.448275i	−0.965924	+	0.258827i	$0.916664\pi$
$312$		0			0
$313$	−12.9579	−	7.48122i	−0.732421	−	0.422864i	0.0868859	−	0.996218i	$-0.472308\pi$
$313$	−12.9579	−	7.48122i	−0.732421	−	0.422864i	−0.819307	+	0.573355i	$0.805642\pi$
$314$	−5.25986			−0.296831
$315$		0			0
$316$	9.74696			0.548309
$317$	−1.83555	−	1.05976i	−0.103095	−	0.0595219i	0.447566	−	0.894251i	$-0.352291\pi$
$317$	−1.83555	−	1.05976i	−0.103095	−	0.0595219i	−0.550661	+	0.834729i	$0.685624\pi$
$318$		0			0
$319$	7.79651	+	13.5040i	0.436521	+	0.756076i
$320$	0.712984	+	1.23492i	0.0398570	+	0.0690344i
$321$		0			0
$322$		0			0
$323$		−	11.7372i		−	0.653073i
$324$		0			0
$325$			5.54321i			0.307482i
$326$	−8.55504	−	4.93926i	−0.473820	−	0.273560i
$327$		0			0
$328$	−4.02337	+	2.32289i	−0.222153	+	0.128260i
$329$		0			0
$330$		0			0
$331$	6.21840	−	10.7706i	0.341794	−	0.592005i	−0.642972	−	0.765890i	$-0.722299\pi$
$331$	6.21840	−	10.7706i	0.341794	−	0.592005i	0.984766	+	0.173885i	$0.0556322\pi$
$332$	3.21172			0.176266
$333$		0			0
$334$			17.7350i			0.970414i
$335$	10.8438	−	18.7819i	0.592457	−	1.02617i
$336$		0			0
$337$	−9.57144	−	16.5782i	−0.521389	−	0.903073i	−0.999691	−	0.0248771i	$-0.992081\pi$
$337$	−9.57144	−	16.5782i	−0.521389	−	0.903073i	0.478301	−	0.878196i	$-0.341253\pi$
$338$	−8.23469	+	4.75430i	−0.447908	+	0.258600i
$339$		0			0
$340$	−1.41616	+	2.45287i	−0.0768023	+	0.133025i
$341$	−11.7445			−0.636001
$342$		0			0
$343$		0			0
$344$	−8.79872	−	5.07994i	−0.474395	−	0.273892i
$345$		0			0
$346$	7.27539	−	4.20045i	0.391127	−	0.225817i
$347$	−3.85149	+	2.22366i	−0.206759	+	0.119372i	−0.599804	−	0.800147i	$-0.704755\pi$
$347$	−3.85149	+	2.22366i	−0.206759	+	0.119372i	0.393045	+	0.919519i	$0.371422\pi$
$348$		0			0
$349$	25.0865	+	14.4837i	1.34285	+	0.775294i	0.987225	−	0.159335i	$-0.0509349\pi$
$349$	25.0865	+	14.4837i	1.34285	+	0.775294i	0.355624	+	0.934629i	$0.384268\pi$
$350$		0			0
$351$		0			0
$352$	−2.44993			−0.130582
$353$	10.7060	−	18.5433i	0.569822	−	0.986961i	−0.426761	−	0.904365i	$-0.640345\pi$
$353$	10.7060	−	18.5433i	0.569822	−	0.986961i	0.996583	−	0.0825966i	$-0.0263213\pi$
$354$		0			0
$355$	0.733652	−	0.423574i	0.0389382	−	0.0224810i
$356$	0.0723285	+	0.125277i	0.00383340	+	0.00663965i
$357$		0			0
$358$	1.51150	−	2.61800i	0.0798853	−	0.138365i
$359$			11.4103i			0.602214i	0.953590	+	0.301107i	$0.0973561\pi$
$359$			11.4103i			0.602214i	−0.953590	+	0.301107i	$0.902644\pi$
$360$		0			0
$361$	−15.9187			−0.837825
$362$	2.47364	−	4.28448i	0.130012	−	0.225187i
$363$		0			0
$364$		0			0
$365$	16.7794	−	9.68760i	0.878275	−	0.507072i
$366$		0			0
$367$	−13.4460	−	7.76303i	−0.701873	−	0.405227i	0.106171	−	0.994348i	$-0.466141\pi$
$367$	−13.4460	−	7.76303i	−0.701873	−	0.405227i	−0.808045	+	0.589121i	$0.799474\pi$
$368$			6.52794i			0.340293i
$369$		0			0
$370$			2.60998i			0.135687i
$371$		0			0
$372$		0			0
$373$	9.04807	+	15.6717i	0.468491	+	0.811451i	0.999351	−	0.0360087i	$-0.0114644\pi$
$373$	9.04807	+	15.6717i	0.468491	+	0.811451i	−0.530860	+	0.847459i	$0.678131\pi$
$374$	−2.43309	−	4.21423i	−0.125812	−	0.217913i
$375$		0			0
$376$	11.2229	+	6.47952i	0.578774	+	0.334156i
$377$	−11.8926			−0.612500
$378$		0			0
$379$	−24.2482			−1.24555			−0.622774	−	0.782402i	$-0.713994\pi$
$379$	−24.2482			−1.24555			−0.622774	+	0.782402i	$0.713994\pi$
$380$	7.29742	+	4.21317i	0.374350	+	0.216131i
$381$		0			0
$382$	−2.55292	−	4.42179i	−0.130619	−	0.226238i
$383$	3.05053	+	5.28368i	0.155875	+	0.269983i	0.933377	−	0.358897i	$-0.116847\pi$
$383$	3.05053	+	5.28368i	0.155875	+	0.269983i	−0.777502	+	0.628880i	$0.783514\pi$
$384$		0			0
$385$		0			0
$386$		−	1.05412i		−	0.0536534i
$387$		0			0
$388$		−	2.69013i		−	0.136571i
$389$	−8.39221	−	4.84524i	−0.425502	−	0.245664i	0.271927	−	0.962318i	$-0.412339\pi$
$389$	−8.39221	−	4.84524i	−0.425502	−	0.245664i	−0.697429	+	0.716654i	$0.745673\pi$
$390$		0			0
$391$	−11.2290	+	6.48307i	−0.567875	+	0.327863i
$392$		0			0
$393$		0			0
$394$	2.48888	−	4.31086i	0.125388	−	0.217178i
$395$	−13.8988			−0.699327
$396$		0			0
$397$			14.4928i			0.727373i	0.931521	+	0.363687i	$0.118482\pi$
$397$			14.4928i			0.727373i	−0.931521	+	0.363687i	$0.881518\pi$
$398$	−0.575600	+	0.996968i	−0.0288522	+	0.0499735i
$399$		0			0
$400$	1.48331	+	2.56917i	0.0741654	+	0.128458i
$401$	21.6413	−	12.4946i	1.08072	−	0.623952i	0.149627	−	0.988742i	$-0.452193\pi$
$401$	21.6413	−	12.4946i	1.08072	−	0.623952i	0.931090	+	0.364790i	$0.118859\pi$
$402$		0			0
$403$	4.47869	−	7.75732i	0.223099	−	0.386420i
$404$	−3.69738			−0.183951
$405$		0			0
$406$		0			0
$407$	−3.88340	−	2.24208i	−0.192493	−	0.111136i
$408$		0			0
$409$	32.2174	−	18.6007i	1.59305	−	0.919746i	0.600266	−	0.799801i	$-0.295061\pi$
$409$	32.2174	−	18.6007i	1.59305	−	0.919746i	0.992781	−	0.119945i	$-0.0382718\pi$
$410$	5.73719	−	3.31237i	0.283340	−	0.163586i
$411$		0			0
$412$	13.9648	+	8.06260i	0.687998	+	0.397216i
$413$		0			0
$414$		0			0
$415$	−4.57981			−0.224814
$416$	0.934264	−	1.61819i	0.0458061	−	0.0793384i
$417$		0			0
$418$	−12.5376	+	7.23856i	−0.613232	+	0.354050i
$419$	−17.7624	−	30.7654i	−0.867750	−	1.50299i	−0.864290	−	0.502993i	$-0.832232\pi$
$419$	−17.7624	−	30.7654i	−0.867750	−	1.50299i	−0.00345977	−	0.999994i	$-0.501101\pi$
$420$		0			0
$421$	16.8698	−	29.2193i	0.822181	−	1.42406i	−0.0818731	−	0.996643i	$-0.526090\pi$
$421$	16.8698	−	29.2193i	0.822181	−	1.42406i	0.904055	−	0.427417i	$-0.140576\pi$
$422$		−	14.0649i		−	0.684669i
$423$		0			0
$424$	−11.8930			−0.577577
$425$	−2.94622	+	5.10301i	−0.142913	+	0.247532i
$426$		0			0
$427$		0			0
$428$	0.472199	−	0.272624i	0.0228246	−	0.0131778i
$429$		0			0
$430$	12.5467	+	7.24384i	0.605055	+	0.349329i
$431$			3.13857i			0.151180i	0.997139	+	0.0755899i	$0.0240840\pi$
$431$			3.13857i			0.151180i	−0.997139	+	0.0755899i	$0.975916\pi$
$432$		0			0
$433$			36.1258i			1.73609i	0.496482	+	0.868047i	$0.334625\pi$
$433$			36.1258i			1.73609i	−0.496482	+	0.868047i	$0.665375\pi$
$434$		0			0
$435$		0			0
$436$	−3.16509	−	5.48210i	−0.151580	−	0.262545i
$437$	19.2875	+	33.4069i	0.922645	+	1.59807i
$438$		0			0
$439$	−12.5331	−	7.23602i	−0.598175	−	0.345356i	0.170149	−	0.985418i	$-0.445575\pi$
$439$	−12.5331	−	7.23602i	−0.598175	−	0.345356i	−0.768323	+	0.640062i	$0.778909\pi$
$440$	3.49352			0.166547
$441$		0			0
$442$	3.71136			0.176532
$443$	9.50209	+	5.48604i	0.451458	+	0.260649i	0.708446	−	0.705765i	$-0.249397\pi$
$443$	9.50209	+	5.48604i	0.451458	+	0.260649i	−0.256988	+	0.966415i	$0.582730\pi$
$444$		0			0
$445$	−0.103138	−	0.178640i	−0.00488921	−	0.00846837i
$446$	−10.0330	−	17.3777i	−0.475077	−	0.822857i
$447$		0			0
$448$		0			0
$449$		−	29.7298i		−	1.40304i	−0.712652	−	0.701518i	$-0.752506\pi$
$449$		−	29.7298i		−	1.40304i	0.712652	−	0.701518i	$-0.247494\pi$
$450$		0			0
$451$			11.3818i			0.535949i
$452$	9.21222	+	5.31868i	0.433306	+	0.250169i
$453$		0			0
$454$	5.22205	−	3.01495i	0.245083	−	0.141499i
$455$		0			0
$456$		0			0
$457$	−5.07662	+	8.79296i	−0.237474	+	0.411317i	−0.959989	−	0.280038i	$-0.909653\pi$
$457$	−5.07662	+	8.79296i	−0.237474	+	0.411317i	0.722515	+	0.691356i	$0.242986\pi$
$458$	22.9068			1.07036
$459$		0			0
$460$		−	9.30864i		−	0.434017i
$461$	13.9677	−	24.1927i	0.650539	−	1.12677i	−0.332454	−	0.943120i	$-0.607876\pi$
$461$	13.9677	−	24.1927i	0.650539	−	1.12677i	0.982992	−	0.183647i	$-0.0587902\pi$
$462$		0			0
$463$	−11.4477	−	19.8280i	−0.532019	−	0.921485i	−0.999301	−	0.0373763i	$-0.988100\pi$
$463$	−11.4477	−	19.8280i	−0.532019	−	0.921485i	0.467282	−	0.884108i	$-0.345233\pi$
$464$	−5.51198	+	3.18234i	−0.255887	+	0.147737i
$465$		0			0
$466$	14.8890	−	25.7885i	0.689719	−	1.19463i
$467$	14.8691			0.688059			0.344029	−	0.938959i	$-0.388208\pi$
$467$	14.8691			0.688059			0.344029	+	0.938959i	$0.388208\pi$
$468$		0			0
$469$		0			0
$470$	−16.0034	−	9.23958i	−0.738183	−	0.426190i
$471$		0			0
$472$	5.00408	−	2.88911i	0.230331	−	0.132982i
$473$	−21.5562	+	12.4455i	−0.991157	+	0.572245i
$474$		0			0
$475$	15.1817	+	8.76517i	0.696585	+	0.402174i
$476$		0			0
$477$		0			0
$478$	−12.2370			−0.559707
$479$	−3.82550	+	6.62595i	−0.174791	+	0.302748i	−0.940089	−	0.340929i	$-0.889258\pi$
$479$	−3.82550	+	6.62595i	−0.174791	+	0.302748i	0.765298	+	0.643677i	$0.222592\pi$
$480$		0			0
$481$	2.96182	−	1.71001i	0.135047	−	0.0779695i
$482$	−12.1488	−	21.0423i	−0.553361	−	0.958449i
$483$		0			0
$484$	2.49893	−	4.32827i	0.113588	−	0.196739i
$485$			3.83604i			0.174186i
$486$		0			0
$487$	22.0497			0.999168			0.499584	−	0.866265i	$-0.333486\pi$
$487$	22.0497			0.999168			0.499584	+	0.866265i	$0.333486\pi$
$488$	−4.84122	+	8.38524i	−0.219152	+	0.379582i
$489$		0			0
$490$		0			0
$491$	−26.3385	+	15.2065i	−1.18864	+	0.686261i	−0.957997	−	0.286778i	$-0.907416\pi$
$491$	−26.3385	+	15.2065i	−1.18864	+	0.686261i	−0.230641	+	0.973039i	$0.574082\pi$
$492$		0			0
$493$	−10.9482	−	6.32093i	−0.493081	−	0.284681i
$494$		−	11.0415i		−	0.496781i
$495$		0			0
$496$		−	4.79382i		−	0.215249i
$497$		0			0
$498$		0			0
$499$	−12.6832	−	21.9680i	−0.567778	−	0.983421i	−0.996785	−	0.0801195i	$-0.974470\pi$
$499$	−12.6832	−	21.9680i	−0.567778	−	0.983421i	0.429007	−	0.903301i	$-0.358864\pi$
$500$	−5.68007	−	9.83817i	−0.254020	−	0.439976i
$501$		0			0
$502$	−11.3305	−	6.54169i	−0.505706	−	0.291970i
$503$	29.1075			1.29784			0.648919	−	0.760858i	$-0.275222\pi$
$503$	29.1075			1.29784			0.648919	+	0.760858i	$0.275222\pi$
$504$		0			0
$505$	5.27234			0.234616
$506$	13.8503	+	7.99650i	0.615723	+	0.355488i
$507$		0			0
$508$	2.96216	+	5.13061i	0.131425	+	0.227634i
$509$	−5.80749	−	10.0589i	−0.257412	−	0.445851i	0.708136	−	0.706076i	$-0.249537\pi$
$509$	−5.80749	−	10.0589i	−0.257412	−	0.445851i	−0.965548	+	0.260225i	$0.916203\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			6.49138i			0.286323i
$515$	−19.9134	−	11.4970i	−0.877489	−	0.506618i
$516$		0			0
$517$	27.4952	−	15.8744i	1.20924	−	0.698153i
$518$		0			0
$519$		0			0
$520$	−1.33223	+	2.30749i	−0.0584221	+	0.101190i
$521$	−1.41619			−0.0620443			−0.0310221	−	0.999519i	$-0.509876\pi$
$521$	−1.41619			−0.0620443			−0.0310221	+	0.999519i	$0.509876\pi$
$522$		0			0
$523$			8.91703i			0.389915i	0.980812	+	0.194957i	$0.0624568\pi$
$523$			8.91703i			0.389915i	−0.980812	+	0.194957i	$0.937543\pi$
$524$	−6.81751	+	11.8083i	−0.297824	+	0.515847i
$525$		0			0
$526$	−13.4486	−	23.2937i	−0.586387	−	1.01565i
$527$	8.24605	−	4.76086i	0.359204	−	0.207386i
$528$		0			0
$529$	9.80703	−	16.9863i	0.426393	−	0.738534i
$530$	16.9591			0.736656
$531$		0			0
$532$		0			0
$533$	−7.51777	−	4.34039i	−0.325631	−	0.188003i
$534$		0			0
$535$	−0.673340	+	0.388753i	−0.0291110	+	0.0168073i
$536$	−13.1714	+	7.60449i	−0.568916	+	0.328464i
$537$		0			0
$538$	−13.2536	−	7.65198i	−0.571404	−	0.329900i
$539$		0			0
$540$		0			0
$541$	8.74127			0.375817			0.187908	−	0.982187i	$-0.439829\pi$
$541$	8.74127			0.375817			0.187908	+	0.982187i	$0.439829\pi$
$542$	−4.68039	+	8.10667i	−0.201040	+	0.348211i
$543$		0			0
$544$	1.72014	−	0.993125i	0.0737505	−	0.0425799i
$545$	4.51332	+	7.81729i	0.193329	+	0.334856i
$546$		0			0
$547$	−12.4767	+	21.6103i	−0.533466	+	0.923990i	0.465770	+	0.884906i	$0.345777\pi$
$547$	−12.4767	+	21.6103i	−0.533466	+	0.923990i	−0.999236	+	0.0390840i	$0.987556\pi$
$548$			17.9670i			0.767510i
$549$		0			0
$550$	7.26800			0.309908
$551$	−18.8051	+	32.5714i	−0.801125	+	1.38759i
$552$		0			0
$553$		0			0
$554$	23.4164	−	13.5195i	0.994869	−	0.574388i
$555$		0			0
$556$	−8.22479	−	4.74858i	−0.348809	−	0.201385i
$557$			0.0493284i			0.00209011i	0.999999	+	0.00104506i	$0.000332652\pi$
$557$			0.0493284i			0.00209011i	−0.999999	+	0.00104506i	$0.999667\pi$
$558$		0			0
$559$		−	18.9840i		−	0.802939i
$560$		0			0
$561$		0			0
$562$	9.49754	+	16.4502i	0.400630	+	0.693911i
$563$	−3.24507	−	5.62062i	−0.136763	−	0.236881i	0.789506	−	0.613742i	$-0.210337\pi$
$563$	−3.24507	−	5.62062i	−0.136763	−	0.236881i	−0.926270	+	0.376861i	$0.877003\pi$
$564$		0			0
$565$	−13.1363	−	7.58426i	−0.552649	−	0.319072i
$566$	18.0542			0.758875
$567$		0			0
$568$	−0.594087			−0.0249273
$569$	−33.5802	−	19.3876i	−1.40776	−	0.812768i	−0.412585	−	0.910919i	$-0.635374\pi$
$569$	−33.5802	−	19.3876i	−1.40776	−	0.812768i	−0.995172	+	0.0981509i	$0.968707\pi$
$570$		0			0
$571$	−0.128832	−	0.223143i	−0.00539143	−	0.00933824i	0.863317	−	0.504662i	$-0.168383\pi$
$571$	−0.128832	−	0.223143i	−0.00539143	−	0.00933824i	−0.868709	+	0.495324i	$0.835049\pi$
$572$	−2.28888	−	3.96445i	−0.0957028	−	0.165762i
$573$		0			0
$574$		0			0
$575$		−	19.3659i		−	0.807614i
$576$		0			0
$577$			33.5074i			1.39493i	0.716618	+	0.697465i	$0.245689\pi$
$577$			33.5074i			1.39493i	−0.716618	+	0.697465i	$0.754311\pi$
$578$	−11.3058	−	6.52740i	−0.470259	−	0.271504i
$579$		0			0
$580$	7.85991	−	4.53792i	0.326365	−	0.188427i
$581$		0			0
$582$		0			0
$583$	−14.5685	+	25.2335i	−0.603367	+	1.04506i
$584$	−13.5874			−0.562251
$585$		0			0
$586$			19.9994i			0.826167i
$587$	22.4541	−	38.8916i	0.926779	−	1.60523i	0.138104	−	0.990418i	$-0.455899\pi$
$587$	22.4541	−	38.8916i	0.926779	−	1.60523i	0.788675	−	0.614811i	$-0.210768\pi$
$588$		0			0
$589$	−14.1638	−	24.5325i	−0.583610	−	1.01084i
$590$	−7.13565	+	4.11977i	−0.293770	+	0.169608i
$591$		0			0
$592$	0.915162	−	1.58511i	0.0376129	−	0.0651475i
$593$	−21.2653			−0.873260			−0.436630	−	0.899641i	$-0.643828\pi$
$593$	−21.2653			−0.873260			−0.436630	+	0.899641i	$0.643828\pi$
$594$		0			0
$595$		0			0
$596$	−4.61041	−	2.66182i	−0.188850	−	0.109032i
$597$		0			0
$598$	−10.5635	+	6.09882i	−0.431972	+	0.249399i
$599$	−22.1002	+	12.7596i	−0.902990	+	0.521341i	−0.878169	−	0.478351i	$-0.841235\pi$
$599$	−22.1002	+	12.7596i	−0.902990	+	0.521341i	−0.0248208	+	0.999692i	$0.507902\pi$
$600$		0			0
$601$	14.4139	+	8.32184i	0.587953	+	0.339455i	0.764288	−	0.644875i	$-0.223091\pi$
$601$	14.4139	+	8.32184i	0.587953	+	0.339455i	−0.176335	+	0.984330i	$0.556424\pi$
$602$		0			0
$603$		0			0
$604$	−13.9456			−0.567440
$605$	−3.56339	+	6.17197i	−0.144872	+	0.250926i
$606$		0			0
$607$	−4.89357	+	2.82531i	−0.198624	+	0.114676i	−0.596014	−	0.802974i	$-0.703250\pi$
$607$	−4.89357	+	2.82531i	−0.198624	+	0.114676i	0.397389	+	0.917650i	$0.369916\pi$
$608$	−2.95460	−	5.11752i	−0.119825	−	0.207543i
$609$		0			0
$610$	6.90343	−	11.9571i	0.279512	−	0.484128i
$611$			24.2143i			0.979606i
$612$		0			0
$613$	39.8457			1.60935			0.804676	−	0.593714i	$-0.202339\pi$
$613$	39.8457			1.60935			0.804676	+	0.593714i	$0.202339\pi$
$614$	−1.06687	+	1.84788i	−0.0430554	+	0.0745742i
$615$		0			0
$616$		0			0
$617$	−13.6398	+	7.87493i	−0.549117	+	0.317033i	−0.748766	−	0.662835i	$-0.769353\pi$
$617$	−13.6398	+	7.87493i	−0.549117	+	0.317033i	0.199649	+	0.979868i	$0.436020\pi$
$618$		0			0
$619$	23.3655	+	13.4901i	0.939140	+	0.542213i	0.889691	−	0.456564i	$-0.150920\pi$
$619$	23.3655	+	13.4901i	0.939140	+	0.542213i	0.0494494	+	0.998777i	$0.484253\pi$
$620$			6.83583i			0.274533i
$621$		0			0
$622$		−	9.12838i		−	0.366015i
$623$		0			0
$624$		0			0
$625$	0.683051	+	1.18308i	0.0273220	+	0.0473232i
$626$	−7.48122	−	12.9579i	−0.299010	−	0.517900i
$627$		0			0
$628$	−4.55518	−	2.62993i	−0.181771	−	0.104946i
$629$	3.63548			0.144956
$630$		0			0
$631$	22.1618			0.882246			0.441123	−	0.897447i	$-0.354580\pi$
$631$	22.1618			0.882246			0.441123	+	0.897447i	$0.354580\pi$
$632$	8.44111	+	4.87348i	0.335769	+	0.193857i
$633$		0			0
$634$	−1.05976	−	1.83555i	−0.0420883	−	0.0728992i
$635$	−4.22394	−	7.31609i	−0.167622	−	0.290330i
$636$		0			0
$637$		0			0
$638$			15.5930i			0.617334i
$639$		0			0
$640$			1.42597i			0.0563663i
$641$	21.1748	+	12.2253i	0.836356	+	0.482870i	0.856024	−	0.516936i	$-0.172928\pi$
$641$	21.1748	+	12.2253i	0.836356	+	0.482870i	−0.0196680	+	0.999807i	$0.506261\pi$
$642$		0			0
$643$	5.38012	−	3.10621i	0.212171	−	0.122497i	−0.390149	−	0.920752i	$-0.627576\pi$
$643$	5.38012	−	3.10621i	0.212171	−	0.122497i	0.602320	+	0.798255i	$0.294243\pi$
$644$		0			0
$645$		0			0
$646$	5.86858	−	10.1647i	0.230896	−	0.399924i
$647$	34.2800			1.34769			0.673844	−	0.738874i	$-0.264642\pi$
$647$	34.2800			1.34769			0.673844	+	0.738874i	$0.264642\pi$
$648$		0			0
$649$		−	14.1562i		−	0.555679i
$650$	−2.77160	+	4.80056i	−0.108711	+	0.188293i
$651$		0			0
$652$	−4.93926	−	8.55504i	−0.193436	−	0.335041i
$653$	7.85846	−	4.53709i	0.307525	−	0.177550i	−0.338293	−	0.941041i	$-0.609850\pi$
$653$	7.85846	−	4.53709i	0.307525	−	0.177550i	0.645819	+	0.763491i	$0.276516\pi$
$654$		0			0
$655$	9.72155	−	16.8382i	0.379852	−	0.657924i
$656$	−4.64578			−0.181387
$657$		0			0
$658$		0			0
$659$	−42.1898	−	24.3583i	−1.64348	−	0.948865i	−0.979582	−	0.201043i	$-0.935567\pi$
$659$	−42.1898	−	24.3583i	−1.64348	−	0.948865i	−0.663900	−	0.747821i	$-0.731100\pi$
$660$		0			0
$661$	9.43876	−	5.44947i	0.367125	−	0.211960i	−0.305077	−	0.952328i	$-0.598682\pi$
$661$	9.43876	−	5.44947i	0.367125	−	0.211960i	0.672202	+	0.740368i	$0.265349\pi$
$662$	10.7706	−	6.21840i	0.418610	−	0.241685i
$663$		0			0
$664$	2.78143	+	1.60586i	0.107941	+	0.0623195i
$665$		0			0
$666$		0			0
$667$	41.5483			1.60876
$668$	−8.86749	+	15.3589i	−0.343093	+	0.594255i
$669$		0			0
$670$	18.7819	−	10.8438i	0.725609	−	0.418931i
$671$	11.8606	+	20.5432i	0.457875	+	0.793063i
$672$		0			0
$673$	23.6565	−	40.9743i	0.911893	−	1.57944i	0.100505	−	0.994937i	$-0.467954\pi$
$673$	23.6565	−	40.9743i	0.911893	−	1.57944i	0.811388	−	0.584508i	$-0.198712\pi$
$674$		−	19.1429i		−	0.737356i
$675$		0			0
$676$	−9.50860			−0.365716
$677$	2.46212	−	4.26452i	0.0946270	−	0.163899i	−0.814826	−	0.579706i	$-0.803167\pi$
$677$	2.46212	−	4.26452i	0.0946270	−	0.163899i	0.909453	+	0.415807i	$0.136501\pi$
$678$		0			0
$679$		0			0
$680$	−2.45287	+	1.41616i	−0.0940632	+	0.0543074i
$681$		0			0
$682$	−10.1710	−	5.87225i	−0.389469	−	0.224860i
$683$		−	11.2280i		−	0.429629i	−0.976655	−	0.214814i	$-0.931085\pi$
$683$		−	11.2280i		−	0.429629i	0.976655	−	0.214814i	$-0.0689147\pi$
$684$		0			0
$685$		−	25.6203i		−	0.978901i
$686$		0			0
$687$		0			0
$688$	−5.07994	−	8.79872i	−0.193671	−	0.335448i
$689$	−11.1112	−	19.2452i	−0.423304	−	0.733185i
$690$		0			0
$691$	12.0725	+	6.97005i	0.459259	+	0.265153i	0.711732	−	0.702451i	$-0.247911\pi$
$691$	12.0725	+	6.97005i	0.459259	+	0.265153i	−0.252474	+	0.967604i	$0.581244\pi$
$692$	8.40089			0.319354
$693$		0			0
$694$	−4.44732			−0.168818
$695$	11.7283	+	6.77132i	0.444879	+	0.256851i
$696$		0			0
$697$	−4.61384	−	7.99141i	−0.174762	−	0.302696i
$698$	14.4837	+	25.0865i	0.548216	+	0.949538i
$699$		0			0
$700$		0			0
$701$			33.1186i			1.25087i	0.780276	+	0.625435i	$0.215079\pi$
$701$			33.1186i			1.25087i	−0.780276	+	0.625435i	$0.784921\pi$
$702$		0			0
$703$		−	10.8158i		−	0.407924i
$704$	−2.12170	−	1.22496i	−0.0799646	−	0.0461676i
$705$		0			0
$706$	18.5433	−	10.7060i	0.697887	−	0.402925i
$707$		0			0
$708$		0			0
$709$	9.06989	−	15.7095i	0.340627	−	0.589983i	−0.643922	−	0.765091i	$-0.722694\pi$
$709$	9.06989	−	15.7095i	0.340627	−	0.589983i	0.984549	+	0.175108i	$0.0560274\pi$
$710$	0.847148			0.0317929
$711$		0			0
$712$			0.144657i			0.00542125i
$713$	−15.6469	+	27.1012i	−0.585981	+	1.01495i
$714$		0			0
$715$	3.26387	+	5.65318i	0.122062	+	0.211417i
$716$	2.61800	−	1.51150i	0.0978391	−	0.0564874i
$717$		0			0
$718$	−5.70516	+	9.88163i	−0.212915	+	0.368779i
$719$	−25.0164			−0.932953			−0.466476	−	0.884534i	$-0.654477\pi$
$719$	−25.0164			−0.932953			−0.466476	+	0.884534i	$0.654477\pi$
$720$		0			0
$721$		0			0
$722$	−13.7860	−	7.95934i	−0.513061	−	0.296216i
$723$		0			0
$724$	4.28448	−	2.47364i	0.159231	−	0.0919323i
$725$	16.3519	−	9.44080i	0.607296	−	0.350622i
$726$		0			0
$727$	−32.3382	−	18.6705i	−1.19936	−	0.692450i	−0.238946	−	0.971033i	$-0.576802\pi$
$727$	−32.3382	−	18.6705i	−1.19936	−	0.692450i	−0.960412	+	0.278583i	$0.910135\pi$
$728$		0			0
$729$		0			0
$730$	19.3752			0.717109
$731$	10.0900	−	17.4765i	0.373194	−	0.646390i
$732$		0			0
$733$	−34.3841	+	19.8516i	−1.27000	+	0.733237i	−0.974989	−	0.222255i	$-0.928658\pi$
$733$	−34.3841	+	19.8516i	−1.27000	+	0.733237i	−0.295016	+	0.955492i	$0.595325\pi$
$734$	−7.76303	−	13.4460i	−0.286539	−	0.496299i
$735$		0			0
$736$	−3.26397	+	5.65337i	−0.120312	+	0.208386i
$737$			37.2609i			1.37252i
$738$		0			0
$739$	−39.8006			−1.46409			−0.732044	−	0.681257i	$-0.761433\pi$
$739$	−39.8006			−1.46409			−0.732044	+	0.681257i	$0.761433\pi$
$740$	−1.30499	+	2.26031i	−0.0479724	+	0.0830907i
$741$		0			0
$742$		0			0
$743$	−34.6622	+	20.0123i	−1.27163	+	0.734178i	−0.975295	−	0.220905i	$-0.929099\pi$
$743$	−34.6622	+	20.0123i	−1.27163	+	0.734178i	−0.296339	+	0.955083i	$0.595766\pi$
$744$		0			0
$745$	6.57429	+	3.79567i	0.240863	+	0.139063i
$746$			18.0961i			0.662547i
$747$		0			0
$748$		−	4.86617i		−	0.177925i
$749$		0			0
$750$		0			0
$751$	5.98284	+	10.3626i	0.218317	+	0.378136i	0.954294	−	0.298871i	$-0.0966100\pi$
$751$	5.98284	+	10.3626i	0.218317	+	0.378136i	−0.735977	+	0.677007i	$0.763277\pi$
$752$	6.47952	+	11.2229i	0.236284	+	0.409255i
$753$		0			0
$754$	−10.2993	−	5.94630i	−0.375078	−	0.216551i
$755$	19.8860			0.723726
$756$		0			0
$757$	−0.372779			−0.0135489			−0.00677443	−	0.999977i	$-0.502156\pi$
$757$	−0.372779			−0.0135489			−0.00677443	+	0.999977i	$0.502156\pi$
$758$	−20.9996	−	12.1241i	−0.762739	−	0.440368i
$759$		0			0
$760$	4.21317	+	7.29742i	0.152828	+	0.264705i
$761$	3.82232	+	6.62046i	0.138559	+	0.239991i	0.926951	−	0.375181i	$-0.122420\pi$
$761$	3.82232	+	6.62046i	0.138559	+	0.239991i	−0.788392	+	0.615173i	$0.789086\pi$
$762$		0			0
$763$		0			0
$764$		−	5.10584i		−	0.184723i
$765$		0			0
$766$			6.10106i			0.220440i
$767$	9.35026	+	5.39837i	0.337618	+	0.194924i
$768$		0			0
$769$	−7.18496	+	4.14824i	−0.259096	+	0.149589i	−0.623922	−	0.781486i	$-0.714462\pi$
$769$	−7.18496	+	4.14824i	−0.259096	+	0.149589i	0.364826	+	0.931076i	$0.381128\pi$
$770$		0			0
$771$		0			0
$772$	0.527061	−	0.912897i	0.0189694	−	0.0328559i
$773$	−16.8724			−0.606856			−0.303428	−	0.952854i	$-0.598131\pi$
$773$	−16.8724			−0.606856			−0.303428	+	0.952854i	$0.598131\pi$
$774$		0			0
$775$			14.2214i			0.510848i
$776$	1.34506	−	2.32972i	0.0482850	−	0.0836321i
$777$		0			0
$778$	−4.84524	−	8.39221i	−0.173710	−	0.300875i
$779$	−23.7749	+	13.7264i	−0.851823	+	0.491801i
$780$		0			0
$781$	−0.727735	+	1.26047i	−0.0260404	+	0.0451033i
$782$	−12.9661			−0.463668
$783$		0			0
$784$		0			0
$785$	6.49553	+	3.75020i	0.231835	+	0.133850i
$786$		0			0
$787$	−28.6503	+	16.5413i	−1.02127	+	0.589633i	−0.914473	−	0.404647i	$-0.867394\pi$
$787$	−28.6503	+	16.5413i	−1.02127	+	0.589633i	−0.106802	+	0.994280i	$0.534061\pi$
$788$	4.31086	−	2.48888i	0.153568	−	0.0886625i
$789$		0			0
$790$	−12.0368	−	6.94942i	−0.428248	−	0.247249i
$791$		0			0
$792$		0			0
$793$	−18.0919			−0.642463
$794$	−7.24641	+	12.5511i	−0.257165	+	0.445423i
$795$		0			0
$796$	−0.996968	+	0.575600i	−0.0353366	+	0.0204016i
$797$	−8.51205	−	14.7433i	−0.301512	−	0.522234i	0.674967	−	0.737848i	$-0.264158\pi$
$797$	−8.51205	−	14.7433i	−0.301512	−	0.522234i	−0.976479	+	0.215614i	$0.930825\pi$
$798$		0			0
$799$	−12.8699	+	22.2914i	−0.455306	+	0.788613i
$800$			2.96662i			0.104886i
$801$		0			0
$802$	24.9893			0.882402
$803$	−16.6441	+	28.8284i	−0.587357	+	1.01733i
$804$		0			0
$805$		0			0
$806$	7.75732	−	4.47869i	0.273240	−	0.157755i
$807$		0			0
$808$	−3.20202	−	1.84869i	−0.112647	−	0.0650366i
$809$		−	31.2639i		−	1.09918i	−0.835435	−	0.549590i	$-0.814784\pi$
$809$		−	31.2639i		−	1.09918i	0.835435	−	0.549590i	$-0.185216\pi$
$810$		0			0
$811$		−	14.9333i		−	0.524380i	−0.965016	−	0.262190i	$-0.915555\pi$
$811$		−	14.9333i		−	0.524380i	0.965016	−	0.262190i	$-0.0844448\pi$
$812$		0			0
$813$		0			0
$814$	−2.24208	−	3.88340i	−0.0785849	−	0.136113i
$815$	7.04322	+	12.1992i	0.246713	+	0.427320i
$816$		0			0
$817$	−51.9934	−	30.0184i	−1.81902	−	1.05021i
$818$	37.2014			1.30072
$819$		0			0
$820$	6.62473			0.231346
$821$	6.23049	+	3.59718i	0.217446	+	0.125542i	0.604767	−	0.796402i	$-0.293266\pi$
$821$	6.23049	+	3.59718i	0.217446	+	0.125542i	−0.387321	+	0.921945i	$0.626600\pi$
$822$		0			0
$823$	−13.6761	−	23.6877i	−0.476719	−	0.825701i	0.522925	−	0.852379i	$-0.324841\pi$
$823$	−13.6761	−	23.6877i	−0.476719	−	0.825701i	−0.999644	+	0.0266772i	$0.991507\pi$
$824$	8.06260	+	13.9648i	0.280874	+	0.486488i
$825$		0			0
$826$		0			0
$827$		−	18.1171i		−	0.629994i	−0.949093	−	0.314997i	$-0.897996\pi$
$827$		−	18.1171i		−	0.629994i	0.949093	−	0.314997i	$-0.102004\pi$
$828$		0			0
$829$			22.3227i			0.775301i	0.921807	+	0.387650i	$0.126713\pi$
$829$			22.3227i			0.775301i	−0.921807	+	0.387650i	$0.873287\pi$
$830$	−3.96623	−	2.28991i	−0.137670	−	0.0794838i
$831$		0			0
$832$	1.61819	−	0.934264i	0.0561007	−	0.0323898i
$833$		0			0
$834$		0			0
$835$	12.6447	−	21.9013i	0.437589	−	0.757927i
$836$	−14.4771			−0.500702
$837$		0			0
$838$		−	35.5248i		−	1.22718i
$839$	5.47947	−	9.49072i	0.189172	−	0.327656i	−0.755802	−	0.654800i	$-0.772753\pi$
$839$	5.47947	−	9.49072i	0.189172	−	0.327656i	0.944975	+	0.327144i	$0.106086\pi$
$840$		0			0
$841$	5.75463	+	9.96731i	0.198435	+	0.343700i
$842$	29.2193	−	16.8698i	1.00696	−	0.581370i
$843$		0			0
$844$	7.03245	−	12.1806i	0.242067	−	0.419272i
$845$	13.5590			0.466442
$846$		0			0
$847$		0			0
$848$	−10.2997	−	5.94652i	−0.353692	−	0.204204i
$849$		0			0
$850$	−5.10301	+	2.94622i	−0.175032	+	0.101055i
$851$	−10.3475	+	5.97413i	−0.354707	+	0.204790i
$852$		0			0
$853$	23.6890	+	13.6768i	0.811095	+	0.468286i	0.847336	−	0.531057i	$-0.178205\pi$
$853$	23.6890	+	13.6768i	0.811095	+	0.468286i	−0.0362411	+	0.999343i	$0.511538\pi$
$854$		0			0
$855$		0			0
$856$	0.545248			0.0186362
$857$	4.14390	−	7.17745i	0.141553	−	0.245177i	−0.786529	−	0.617554i	$-0.788124\pi$
$857$	4.14390	−	7.17745i	0.141553	−	0.245177i	0.928082	+	0.372377i	$0.121457\pi$
$858$		0			0
$859$	−9.29234	+	5.36494i	−0.317051	+	0.183049i	−0.650077	−	0.759868i	$-0.725263\pi$
$859$	−9.29234	+	5.36494i	−0.317051	+	0.183049i	0.333027	+	0.942917i	$0.391930\pi$
$860$	7.24384	+	12.5467i	0.247013	+	0.427839i
$861$		0			0
$862$	−1.56929	+	2.71808i	−0.0534501	+	0.0925783i
$863$		−	5.16864i		−	0.175942i	−0.996123	−	0.0879712i	$-0.971962\pi$
$863$		−	5.16864i		−	0.175942i	0.996123	−	0.0879712i	$-0.0280384\pi$
$864$		0			0
$865$	−11.9794			−0.407312
$866$	−18.0629	+	31.2858i	−0.613802	+	1.06314i
$867$		0			0
$868$		0			0
$869$	20.6801	−	11.9397i	0.701525	−	0.405026i
$870$		0			0
$871$	−24.6110	−	14.2092i	−0.833914	−	0.481460i
$872$		−	6.33018i		−	0.214367i
$873$		0			0
$874$			38.5749i			1.30482i
$875$		0			0
$876$		0			0
$877$	26.7198	+	46.2800i	0.902263	+	1.56276i	0.824550	+	0.565789i	$0.191428\pi$
$877$	26.7198	+	46.2800i	0.902263	+	1.56276i	0.0777127	+	0.996976i	$0.475238\pi$
$878$	−7.23602	−	12.5331i	−0.244204	−	0.422973i
$879$		0			0
$880$	3.02547	+	1.74676i	0.101989	+	0.0588832i
$881$	−21.7352			−0.732277			−0.366139	−	0.930560i	$-0.619320\pi$
$881$	−21.7352			−0.732277			−0.366139	+	0.930560i	$0.619320\pi$
$882$		0			0
$883$	20.2657			0.681996			0.340998	−	0.940064i	$-0.389235\pi$
$883$	20.2657			0.681996			0.340998	+	0.940064i	$0.389235\pi$
$884$	3.21414	+	1.85568i	0.108103	+	0.0624133i
$885$		0			0
$886$	5.48604	+	9.50209i	0.184307	+	0.319229i
$887$	4.61858	+	7.99962i	0.155077	+	0.268601i	0.933087	−	0.359651i	$-0.117104\pi$
$887$	4.61858	+	7.99962i	0.155077	+	0.268601i	−0.778010	+	0.628252i	$0.783771\pi$
$888$		0			0
$889$		0			0
$890$		−	0.206276i		−	0.00691439i
$891$		0			0
$892$		−	20.0660i		−	0.671860i
$893$	66.3181	+	38.2888i	2.21925	+	1.28129i
$894$		0			0
$895$	−3.73318	+	2.15535i	−0.124786	+	0.0720454i
$896$		0			0
$897$		0			0
$898$	14.8649	−	25.7468i	0.496048	−	0.859181i
$899$	−30.5112			−1.01760
$900$		0			0
$901$		−	23.6226i		−	0.786981i
$902$	−5.69092	+	9.85695i	−0.189487	+	0.328201i
$903$		0			0
$904$	5.31868	+	9.21222i	0.176897	+	0.306394i
$905$	−6.10953	+	3.52734i	−0.203088	+	0.117253i
$906$		0			0
$907$	−19.0122	+	32.9300i	−0.631289	+	1.09342i	0.356000	+	0.934486i	$0.384140\pi$
$907$	−19.0122	+	32.9300i	−0.631289	+	1.09342i	−0.987289	+	0.158938i	$0.949193\pi$
$908$	6.02990			0.200109
$909$		0			0
$910$		0			0
$911$	7.06404	+	4.07842i	0.234042	+	0.135124i	0.612435	−	0.790521i	$-0.290190\pi$
$911$	7.06404	+	4.07842i	0.234042	+	0.135124i	−0.378393	+	0.925645i	$0.623523\pi$
$912$		0			0
$913$	6.81431	−	3.93424i	0.225521	−	0.130204i
$914$	−8.79296	+	5.07662i	−0.290845	+	0.167920i
$915$		0			0
$916$	19.8379	+	11.4534i	0.655462	+	0.378431i
$917$		0			0
$918$		0			0
$919$	−9.50580			−0.313567			−0.156784	−	0.987633i	$-0.550113\pi$
$919$	−9.50580			−0.313567			−0.156784	+	0.987633i	$0.550113\pi$
$920$	4.65432	−	8.06152i	0.153448	−	0.265780i
$921$		0			0
$922$	24.1927	−	13.9677i	0.796744	−	0.460000i
$923$	−0.555034	−	0.961346i	−0.0182692	−	0.0316431i
$924$		0			0
$925$	−2.71493	+	4.70240i	−0.0892665	+	0.154614i
$926$		−	22.8954i		−	0.752389i
$927$		0			0
$928$	−6.36469			−0.208931
$929$	15.0501	−	26.0675i	0.493776	−	0.855246i	−0.506198	−	0.862417i	$-0.668949\pi$
$929$	15.0501	−	26.0675i	0.493776	−	0.855246i	0.999974	+	0.00717155i	$0.00228280\pi$
$930$		0			0
$931$		0			0
$932$	25.7885	−	14.8890i	0.844730	−	0.487705i
$933$		0			0
$934$	12.8770	+	7.43454i	0.421348	+	0.243265i
$935$			6.93900i			0.226930i
$936$		0			0
$937$		−	17.4421i		−	0.569807i	−0.958556	−	0.284904i	$-0.908038\pi$
$937$		−	17.4421i		−	0.569807i	0.958556	−	0.284904i	$-0.0919616\pi$
$938$		0			0
$939$		0			0
$940$	−9.23958	−	16.0034i	−0.301362	−	0.521974i
$941$	3.40279	+	5.89380i	0.110928	+	0.192132i	0.916145	−	0.400848i	$-0.131284\pi$
$941$	3.40279	+	5.89380i	0.110928	+	0.192132i	−0.805217	+	0.592980i	$0.797951\pi$
$942$		0			0
$943$	26.2643	+	15.1637i	0.855284	+	0.493798i
$944$	5.77821			0.188065
$945$		0			0
$946$	−24.8910			−0.809276
$947$	−47.8503	−	27.6264i	−1.55493	−	0.897736i	−0.997729	−	0.0673554i	$-0.978544\pi$
$947$	−47.8503	−	27.6264i	−1.55493	−	0.897736i	−0.557196	−	0.830381i	$-0.688123\pi$
$948$		0			0
$949$	−12.6942	−	21.9870i	−0.412072	−	0.713730i
$950$	8.76517	+	15.1817i	0.284380	+	0.492560i
$951$		0			0
$952$		0			0
$953$			17.8094i			0.576904i	0.957494	+	0.288452i	$0.0931405\pi$
$953$			17.8094i			0.576904i	−0.957494	+	0.288452i	$0.906859\pi$
$954$		0			0
$955$			7.28076i			0.235600i
$956$	−10.5976	−	6.11850i	−0.342749	−	0.197886i
$957$		0			0
$958$	−6.62595	+	3.82550i	−0.214075	+	0.123596i
$959$		0			0
$960$		0			0
$961$	−4.00966	+	6.94493i	−0.129344	+	0.224030i
$962$	3.42001			0.110266
$963$		0			0
$964$		−	24.2975i		−	0.782571i
$965$	−0.751573	+	1.30176i	−0.0241940	+	0.0419052i
$966$		0			0
$967$	19.4677	+	33.7190i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$967$	19.4677	+	33.7190i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$968$	4.32827	−	2.49893i	0.139116	−	0.0803185i
$969$		0			0
$970$	−1.91802	+	3.32211i	−0.0615839	+	0.106666i
$971$	50.4684			1.61961			0.809804	−	0.586700i	$-0.199573\pi$
$971$	50.4684			1.61961			0.809804	+	0.586700i	$0.199573\pi$
$972$		0			0
$973$		0			0
$974$	19.0956	+	11.0249i	0.611863	+	0.353259i
$975$		0			0
$976$	−8.38524	+	4.84122i	−0.268405	+	0.154964i
$977$	30.3086	−	17.4987i	0.969658	−	0.559832i	0.0705259	−	0.997510i	$-0.477532\pi$
$977$	30.3086	−	17.4987i	0.969658	−	0.559832i	0.899132	+	0.437678i	$0.144199\pi$
$978$		0			0
$979$	0.306919	+	0.177200i	0.00980916	+	0.00566332i
$980$		0			0
$981$		0			0
$982$	−30.4130			−0.970519
$983$	−3.48888	+	6.04291i	−0.111278	+	0.192739i	−0.916286	−	0.400525i	$-0.868828\pi$
$983$	−3.48888	+	6.04291i	−0.111278	+	0.192739i	0.805008	+	0.593264i	$0.202161\pi$
$984$		0			0
$985$	−6.14714	+	3.54906i	−0.195864	+	0.113082i
$986$	−6.32093	−	10.9482i	−0.201300	−	0.348661i
$987$		0			0
$988$	5.52075	−	9.56223i	0.175639	−	0.304215i
$989$			66.3232i			2.10895i
$990$		0			0
$991$	−31.3465			−0.995754			−0.497877	−	0.867248i	$-0.665887\pi$
$991$	−31.3465			−0.995754			−0.497877	+	0.867248i	$0.665887\pi$
$992$	2.39691	−	4.15157i	0.0761019	−	0.131812i
$993$		0			0
$994$		0			0
$995$	1.42164	−	0.820786i	0.0450691	−	0.0260207i
$996$		0			0
$997$	43.1945	+	24.9384i	1.36798	+	0.789806i	0.990670	−	0.136280i	$-0.0435148\pi$
$997$	43.1945	+	24.9384i	1.36798	+	0.789806i	0.377313	+	0.926086i	$0.376848\pi$
$998$		−	25.3664i		−	0.802960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.c.1763.19		48
3.2	odd	2		882.2.m.c.587.5	yes	48
7.2	even	3		2646.2.l.c.521.11		48
7.3	odd	6		2646.2.t.c.1979.3		48
7.4	even	3		2646.2.t.c.1979.4		48
7.5	odd	6		2646.2.l.c.521.12		48
7.6	odd	2	inner	2646.2.m.c.1763.20		48
9.4	even	3		882.2.m.c.293.8	yes	48
9.5	odd	6	inner	2646.2.m.c.881.20		48
21.2	odd	6		882.2.l.c.227.23		48
21.5	even	6		882.2.l.c.227.14		48
21.11	odd	6		882.2.t.c.803.15		48
21.17	even	6		882.2.t.c.803.22		48
21.20	even	2		882.2.m.c.587.8	yes	48
63.4	even	3		882.2.l.c.509.2		48
63.5	even	6		2646.2.t.c.2285.4		48
63.13	odd	6		882.2.m.c.293.5	✓	48
63.23	odd	6		2646.2.t.c.2285.3		48
63.31	odd	6		882.2.l.c.509.11		48
63.32	odd	6		2646.2.l.c.1097.12		48
63.40	odd	6		882.2.t.c.815.15		48
63.41	even	6	inner	2646.2.m.c.881.19		48
63.58	even	3		882.2.t.c.815.22		48
63.59	even	6		2646.2.l.c.1097.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.14		48	21.5	even	6
882.2.l.c.227.23		48	21.2	odd	6
882.2.l.c.509.2		48	63.4	even	3
882.2.l.c.509.11		48	63.31	odd	6
882.2.m.c.293.5	✓	48	63.13	odd	6
882.2.m.c.293.8	yes	48	9.4	even	3
882.2.m.c.587.5	yes	48	3.2	odd	2
882.2.m.c.587.8	yes	48	21.20	even	2
882.2.t.c.803.15		48	21.11	odd	6
882.2.t.c.803.22		48	21.17	even	6
882.2.t.c.815.15		48	63.40	odd	6
882.2.t.c.815.22		48	63.58	even	3
2646.2.l.c.521.11		48	7.2	even	3
2646.2.l.c.521.12		48	7.5	odd	6
2646.2.l.c.1097.11		48	63.59	even	6
2646.2.l.c.1097.12		48	63.32	odd	6
2646.2.m.c.881.19		48	63.41	even	6	inner
2646.2.m.c.881.20		48	9.5	odd	6	inner
2646.2.m.c.1763.19		48	1.1	even	1	trivial
2646.2.m.c.1763.20		48	7.6	odd	2	inner
2646.2.t.c.1979.3		48	7.3	odd	6
2646.2.t.c.1979.4		48	7.4	even	3
2646.2.t.c.2285.3		48	63.23	odd	6
2646.2.t.c.2285.4		48	63.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.712984 - 1.23492i) q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.712984 - 1.23492i) q^{5} +1.00000i q^{8} -1.42597i q^{10} +(2.12170 + 1.22496i) q^{11} +(-1.61819 + 0.934264i) q^{13} +(-0.500000 + 0.866025i) q^{16} -1.98625 q^{17} +5.90920i q^{19} +(0.712984 - 1.23492i) q^{20} +(1.22496 + 2.12170i) q^{22} +(5.65337 - 3.26397i) q^{23} +(1.48331 - 2.56917i) q^{25} -1.86853 q^{26} +(5.51198 + 3.18234i) q^{29} +(-4.15157 + 2.39691i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.72014 - 0.993125i) q^{34} -1.83032 q^{37} +(-2.95460 + 5.11752i) q^{38} +(1.23492 - 0.712984i) q^{40} +(2.32289 + 4.02337i) q^{41} +(-5.07994 + 8.79872i) q^{43} +2.44993i q^{44} +6.52794 q^{46} +(6.47952 - 11.2229i) q^{47} +(2.56917 - 1.48331i) q^{50} +(-1.61819 - 0.934264i) q^{52} +11.8930i q^{53} -3.49352i q^{55} +(3.18234 + 5.51198i) q^{58} +(-2.88911 - 5.00408i) q^{59} +(8.38524 + 4.84122i) q^{61} -4.79382 q^{62} -1.00000 q^{64} +(2.30749 + 1.33223i) q^{65} +(7.60449 + 13.1714i) q^{67} +(-0.993125 - 1.72014i) q^{68} +0.594087i q^{71} +13.5874i q^{73} +(-1.58511 - 0.915162i) q^{74} +(-5.11752 + 2.95460i) q^{76} +(4.87348 - 8.44111i) q^{79} +1.42597 q^{80} +4.64578i q^{82} +(1.60586 - 2.78143i) q^{83} +(1.41616 + 2.45287i) q^{85} +(-8.79872 + 5.07994i) q^{86} +(-1.22496 + 2.12170i) q^{88} +0.144657 q^{89} +(5.65337 + 3.26397i) q^{92} +(11.2229 - 6.47952i) q^{94} +(7.29742 - 4.21317i) q^{95} +(-2.32972 - 1.34506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 48 * q^11 - 24 * q^16 - 48 * q^23 - 24 * q^25 + 48 * q^50 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 96 * q^86 - 48 * q^92 + 192 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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