LMFDB - Embedded newform 384.2.n.a.337.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(49,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("384.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.n (of order $8$, degree $4$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			337.6
Character	$\chi$	$=$	384.337
Dual form			384.2.n.a.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 + 0.382683i) q^{3} +(0.184062 + 0.444366i) q^{5} +(0.134531 - 0.134531i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.923880 + 0.382683i) q^{3} +(0.184062 + 0.444366i) q^{5} +(0.134531 - 0.134531i) q^{7} +(0.707107 + 0.707107i) q^{9} +(4.83050 - 2.00086i) q^{11} +(-0.237510 + 0.573400i) q^{13} +0.480978i q^{15} +5.70425i q^{17} +(0.459376 - 1.10903i) q^{19} +(0.175774 - 0.0728078i) q^{21} +(4.07921 + 4.07921i) q^{23} +(3.37195 - 3.37195i) q^{25} +(0.382683 + 0.923880i) q^{27} +(-2.33405 - 0.966793i) q^{29} -10.2033 q^{31} +5.22850 q^{33} +(0.0845432 + 0.0350189i) q^{35} +(-3.05654 - 7.37913i) q^{37} +(-0.438862 + 0.438862i) q^{39} +(-0.877147 - 0.877147i) q^{41} +(2.15605 - 0.893063i) q^{43} +(-0.184062 + 0.444366i) q^{45} +4.94536i q^{47} +6.96380i q^{49} +(-2.18292 + 5.27004i) q^{51} +(9.74330 - 4.03581i) q^{53} +(1.77823 + 1.77823i) q^{55} +(0.848817 - 0.848817i) q^{57} +(-4.73462 - 11.4304i) q^{59} +(-9.46851 - 3.92198i) q^{61} +0.190256 q^{63} -0.298516 q^{65} +(-4.79416 - 1.98581i) q^{67} +(2.20765 + 5.32975i) q^{69} +(-4.32992 + 4.32992i) q^{71} +(-6.12055 - 6.12055i) q^{73} +(4.40567 - 1.82489i) q^{75} +(0.380675 - 0.919031i) q^{77} -11.9773i q^{79} +1.00000i q^{81} +(-1.59989 + 3.86247i) q^{83} +(-2.53477 + 1.04994i) q^{85} +(-1.78640 - 1.78640i) q^{87} +(-8.43934 + 8.43934i) q^{89} +(0.0451877 + 0.109093i) q^{91} +(-9.42658 - 3.90462i) q^{93} +0.577370 q^{95} -9.21817 q^{97} +(4.83050 + 2.00086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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			0
$2$		0			0
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$		0			0
$5$	0.184062	+	0.444366i	0.0823152	+	0.198726i	0.959678	−	0.281101i	$-0.0906994\pi$
$5$	0.184062	+	0.444366i	0.0823152	+	0.198726i	−0.877363	+	0.479827i	$0.840699\pi$
$6$		0			0
$7$	0.134531	−	0.134531i	0.0508480	−	0.0508480i	−0.681226	−	0.732074i	$-0.738553\pi$
$7$	0.134531	−	0.134531i	0.0508480	−	0.0508480i	0.732074	+	0.681226i	$0.238553\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	4.83050	−	2.00086i	1.45645	−	0.603282i	0.492727	−	0.870184i	$-0.336000\pi$
$11$	4.83050	−	2.00086i	1.45645	−	0.603282i	0.963724	+	0.266902i	$0.0860001\pi$
$12$		0			0
$13$	−0.237510	+	0.573400i	−0.0658735	+	0.159033i	−0.953388	−	0.301747i	$-0.902430\pi$
$13$	−0.237510	+	0.573400i	−0.0658735	+	0.159033i	0.887515	+	0.460780i	$0.152430\pi$
$14$		0			0
$15$			0.480978i			0.124188i
$16$		0			0
$17$			5.70425i			1.38348i	0.722145	+	0.691742i	$0.243157\pi$
$17$			5.70425i			1.38348i	−0.722145	+	0.691742i	$0.756843\pi$
$18$		0			0
$19$	0.459376	−	1.10903i	0.105388	−	0.254430i	−0.862385	−	0.506253i	$-0.831030\pi$
$19$	0.459376	−	1.10903i	0.105388	−	0.254430i	0.967773	+	0.251823i	$0.0810302\pi$
$20$		0			0
$21$	0.175774	−	0.0728078i	0.0383569	−	0.0158880i
$22$		0			0
$23$	4.07921	+	4.07921i	0.850575	+	0.850575i	0.990204	−	0.139629i	$-0.0445910\pi$
$23$	4.07921	+	4.07921i	0.850575	+	0.850575i	−0.139629	+	0.990204i	$0.544591\pi$
$24$		0			0
$25$	3.37195	−	3.37195i	0.674390	−	0.674390i
$26$		0			0
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$		0			0
$29$	−2.33405	−	0.966793i	−0.433421	−	0.179529i	0.155296	−	0.987868i	$-0.450367\pi$
$29$	−2.33405	−	0.966793i	−0.433421	−	0.179529i	−0.588717	+	0.808339i	$0.700367\pi$
$30$		0			0
$31$	−10.2033			−1.83256			−0.916280	−	0.400539i	$-0.868823\pi$
$31$	−10.2033			−1.83256			−0.916280	+	0.400539i	$0.868823\pi$
$32$		0			0
$33$	5.22850			0.910164
$34$		0			0
$35$	0.0845432	+	0.0350189i	0.0142904	+	0.00591928i
$36$		0			0
$37$	−3.05654	−	7.37913i	−0.502491	−	1.21312i	−0.948123	−	0.317905i	$-0.897021\pi$
$37$	−3.05654	−	7.37913i	−0.502491	−	1.21312i	0.445631	−	0.895217i	$-0.352979\pi$
$38$		0			0
$39$	−0.438862	+	0.438862i	−0.0702741	+	0.0702741i
$40$		0			0
$41$	−0.877147	−	0.877147i	−0.136987	−	0.136987i	0.635288	−	0.772275i	$-0.280881\pi$
$41$	−0.877147	−	0.877147i	−0.136987	−	0.136987i	−0.772275	+	0.635288i	$0.780881\pi$
$42$		0			0
$43$	2.15605	−	0.893063i	0.328794	−	0.136191i	−0.212179	−	0.977231i	$-0.568056\pi$
$43$	2.15605	−	0.893063i	0.328794	−	0.136191i	0.540973	+	0.841040i	$0.318056\pi$
$44$		0			0
$45$	−0.184062	+	0.444366i	−0.0274384	+	0.0662421i
$46$		0			0
$47$			4.94536i			0.721355i	0.932691	+	0.360677i	$0.117454\pi$
$47$			4.94536i			0.721355i	−0.932691	+	0.360677i	$0.882546\pi$
$48$		0			0
$49$			6.96380i			0.994829i
$50$		0			0
$51$	−2.18292	+	5.27004i	−0.305670	+	0.737953i
$52$		0			0
$53$	9.74330	−	4.03581i	1.33834	−	0.554361i	0.405321	−	0.914175i	$-0.367160\pi$
$53$	9.74330	−	4.03581i	1.33834	−	0.554361i	0.933024	+	0.359814i	$0.117160\pi$
$54$		0			0
$55$	1.77823	+	1.77823i	0.239776	+	0.239776i
$56$		0			0
$57$	0.848817	−	0.848817i	0.112429	−	0.112429i
$58$		0			0
$59$	−4.73462	−	11.4304i	−0.616395	−	1.48811i	−0.855861	−	0.517205i	$-0.826972\pi$
$59$	−4.73462	−	11.4304i	−0.616395	−	1.48811i	0.239466	−	0.970905i	$-0.423028\pi$
$60$		0			0
$61$	−9.46851	−	3.92198i	−1.21232	−	0.502159i	−0.317358	−	0.948306i	$-0.602796\pi$
$61$	−9.46851	−	3.92198i	−1.21232	−	0.502159i	−0.894960	+	0.446147i	$0.852796\pi$
$62$		0			0
$63$	0.190256			0.0239700
$64$		0			0
$65$	−0.298516			−0.0370264
$66$		0			0
$67$	−4.79416	−	1.98581i	−0.585700	−	0.242605i	0.0700997	−	0.997540i	$-0.477668\pi$
$67$	−4.79416	−	1.98581i	−0.585700	−	0.242605i	−0.655799	+	0.754935i	$0.727668\pi$
$68$		0			0
$69$	2.20765	+	5.32975i	0.265770	+	0.641626i
$70$		0			0
$71$	−4.32992	+	4.32992i	−0.513867	+	0.513867i	−0.915709	−	0.401842i	$-0.868370\pi$
$71$	−4.32992	+	4.32992i	−0.513867	+	0.513867i	0.401842	+	0.915709i	$0.368370\pi$
$72$		0			0
$73$	−6.12055	−	6.12055i	−0.716356	−	0.716356i	0.251501	−	0.967857i	$-0.419076\pi$
$73$	−6.12055	−	6.12055i	−0.716356	−	0.716356i	−0.967857	+	0.251501i	$0.919076\pi$
$74$		0			0
$75$	4.40567	−	1.82489i	0.508723	−	0.210720i
$76$		0			0
$77$	0.380675	−	0.919031i	0.0433820	−	0.104733i
$78$		0			0
$79$		−	11.9773i		−	1.34756i	−0.738934	−	0.673778i	$-0.764670\pi$
$79$		−	11.9773i		−	1.34756i	0.738934	−	0.673778i	$-0.235330\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	−1.59989	+	3.86247i	−0.175610	+	0.423961i	−0.987037	−	0.160493i	$-0.948691\pi$
$83$	−1.59989	+	3.86247i	−0.175610	+	0.423961i	0.811426	+	0.584455i	$0.198691\pi$
$84$		0			0
$85$	−2.53477	+	1.04994i	−0.274935	+	0.113882i
$86$		0			0
$87$	−1.78640	−	1.78640i	−0.191522	−	0.191522i
$88$		0			0
$89$	−8.43934	+	8.43934i	−0.894569	+	0.894569i	−0.994949	−	0.100381i	$-0.967994\pi$
$89$	−8.43934	+	8.43934i	−0.894569	+	0.894569i	0.100381	+	0.994949i	$0.467994\pi$
$90$		0			0
$91$	0.0451877	+	0.109093i	0.00473696	+	0.0114360i
$92$		0			0
$93$	−9.42658	−	3.90462i	−0.977491	−	0.404890i
$94$		0			0
$95$	0.577370			0.0592369
$96$		0			0
$97$	−9.21817			−0.935964			−0.467982	−	0.883738i	$-0.655019\pi$
$97$	−9.21817			−0.935964			−0.467982	+	0.883738i	$0.655019\pi$
$98$		0			0
$99$	4.83050	+	2.00086i	0.485484	+	0.201094i
$100$		0			0
$101$	1.27818	+	3.08581i	0.127184	+	0.307050i	0.974626	−	0.223838i	$-0.0718586\pi$
$101$	1.27818	+	3.08581i	0.127184	+	0.307050i	−0.847442	+	0.530888i	$0.821859\pi$
$102$		0			0
$103$	7.17872	−	7.17872i	0.707340	−	0.707340i	−0.258635	−	0.965975i	$-0.583273\pi$
$103$	7.17872	−	7.17872i	0.707340	−	0.707340i	0.965975	+	0.258635i	$0.0832726\pi$
$104$		0			0
$105$	0.0647066	+	0.0647066i	0.00631471	+	0.00631471i
$106$		0			0
$107$	−1.52273	+	0.630735i	−0.147208	+	0.0609755i	−0.455071	−	0.890455i	$-0.650386\pi$
$107$	−1.52273	+	0.630735i	−0.147208	+	0.0609755i	0.307863	+	0.951431i	$0.400386\pi$
$108$		0			0
$109$	−5.64602	+	13.6307i	−0.540791	+	1.30558i	0.383375	+	0.923593i	$0.374762\pi$
$109$	−5.64602	+	13.6307i	−0.540791	+	1.30558i	−0.924166	+	0.381992i	$0.875238\pi$
$110$		0			0
$111$		−	7.98711i		−	0.758103i
$112$		0			0
$113$		−	4.48349i		−	0.421771i	−0.977511	−	0.210886i	$-0.932365\pi$
$113$		−	4.48349i		−	0.421771i	0.977511	−	0.210886i	$-0.0676348\pi$
$114$		0			0
$115$	−1.06183	+	2.56349i	−0.0990164	+	0.239047i
$116$		0			0
$117$	−0.573400	+	0.237510i	−0.0530109	+	0.0219578i
$118$		0			0
$119$	0.767400	+	0.767400i	0.0703474	+	0.0703474i
$120$		0			0
$121$	11.5521	−	11.5521i	1.05019	−	1.05019i
$122$		0			0
$123$	−0.474709	−	1.14605i	−0.0428030	−	0.103336i
$124$		0			0
$125$	4.34086	+	1.79804i	0.388258	+	0.160822i
$126$		0			0
$127$	−10.5535			−0.936470			−0.468235	−	0.883604i	$-0.655110\pi$
$127$	−10.5535			−0.936470			−0.468235	+	0.883604i	$0.655110\pi$
$128$		0			0
$129$	2.33369			0.205470
$130$		0			0
$131$	−6.23238	−	2.58153i	−0.544525	−	0.225550i	0.0934264	−	0.995626i	$-0.470218\pi$
$131$	−6.23238	−	2.58153i	−0.544525	−	0.225550i	−0.637952	+	0.770076i	$0.720218\pi$
$132$		0			0
$133$	−0.0873991	−	0.211000i	−0.00757846	−	0.0182960i
$134$		0			0
$135$	−0.340103	+	0.340103i	−0.0292714	+	0.0292714i
$136$		0			0
$137$	−10.4945	−	10.4945i	−0.896606	−	0.896606i	0.0985279	−	0.995134i	$-0.468587\pi$
$137$	−10.4945	−	10.4945i	−0.896606	−	0.896606i	−0.995134	+	0.0985279i	$0.968587\pi$
$138$		0			0
$139$	−9.16542	+	3.79644i	−0.777401	+	0.322010i	−0.735866	−	0.677127i	$-0.763225\pi$
$139$	−9.16542	+	3.79644i	−0.777401	+	0.322010i	−0.0415348	+	0.999137i	$0.513225\pi$
$140$		0			0
$141$	−1.89251	+	4.56891i	−0.159378	+	0.384772i
$142$		0			0
$143$			3.24504i			0.271364i
$144$		0			0
$145$		−	1.21512i		−	0.100910i
$146$		0			0
$147$	−2.66493	+	6.43371i	−0.219800	+	0.530644i
$148$		0			0
$149$	9.74535	−	4.03666i	0.798370	−	0.330696i	0.0540667	−	0.998537i	$-0.482782\pi$
$149$	9.74535	−	4.03666i	0.798370	−	0.330696i	0.744303	+	0.667842i	$0.232782\pi$
$150$		0			0
$151$	8.98745	+	8.98745i	0.731388	+	0.731388i	0.970895	−	0.239507i	$-0.0769857\pi$
$151$	8.98745	+	8.98745i	0.731388	+	0.731388i	−0.239507	+	0.970895i	$0.576986\pi$
$152$		0			0
$153$	−4.03352	+	4.03352i	−0.326090	+	0.326090i
$154$		0			0
$155$	−1.87804	−	4.53398i	−0.150847	−	0.364178i
$156$		0			0
$157$	20.8461	+	8.63473i	1.66370	+	0.689127i	0.998351	−	0.0574062i	$-0.0182830\pi$
$157$	20.8461	+	8.63473i	1.66370	+	0.689127i	0.665348	+	0.746533i	$0.268283\pi$
$158$		0			0
$159$	10.5461			0.836358
$160$		0			0
$161$	1.09756			0.0865001
$162$		0			0
$163$	7.04554	+	2.91836i	0.551849	+	0.228584i	0.641142	−	0.767422i	$-0.278461\pi$
$163$	7.04554	+	2.91836i	0.551849	+	0.228584i	−0.0892930	+	0.996005i	$0.528461\pi$
$164$		0			0
$165$	0.962369	+	2.32336i	0.0749203	+	0.180874i
$166$		0			0
$167$	0.832153	−	0.832153i	0.0643940	−	0.0643940i	−0.674176	−	0.738570i	$-0.735501\pi$
$167$	0.832153	−	0.832153i	0.0643940	−	0.0643940i	0.738570	+	0.674176i	$0.235501\pi$
$168$		0			0
$169$	8.92001	+	8.92001i	0.686155	+	0.686155i
$170$		0			0
$171$	1.10903	−	0.459376i	0.0848098	−	0.0351294i
$172$		0			0
$173$	4.67762	−	11.2928i	0.355633	−	0.858573i	−0.640271	−	0.768149i	$-0.721178\pi$
$173$	4.67762	−	11.2928i	0.355633	−	0.858573i	0.995903	−	0.0904237i	$-0.0288221\pi$
$174$		0			0
$175$		−	0.907266i		−	0.0685828i
$176$		0			0
$177$		−	12.3722i		−	0.929949i
$178$		0			0
$179$	−4.58465	+	11.0683i	−0.342673	+	0.827285i	0.654771	+	0.755828i	$0.272765\pi$
$179$	−4.58465	+	11.0683i	−0.342673	+	0.827285i	−0.997444	+	0.0714579i	$0.977235\pi$
$180$		0			0
$181$	4.59848	−	1.90475i	0.341802	−	0.141579i	−0.205178	−	0.978725i	$-0.565777\pi$
$181$	4.59848	−	1.90475i	0.341802	−	0.141579i	0.546980	+	0.837146i	$0.315777\pi$
$182$		0			0
$183$	−7.24688	−	7.24688i	−0.535705	−	0.535705i
$184$		0			0
$185$	2.71644	−	2.71644i	0.199717	−	0.199717i
$186$		0			0
$187$	11.4134	+	27.5544i	0.834631	+	2.01498i
$188$		0			0
$189$	0.175774	+	0.0728078i	0.0127856	+	0.00529599i
$190$		0			0
$191$	16.3142			1.18045			0.590227	−	0.807238i	$-0.299038\pi$
$191$	16.3142			1.18045			0.590227	+	0.807238i	$0.299038\pi$
$192$		0			0
$193$	3.22234			0.231949			0.115975	−	0.993252i	$-0.463001\pi$
$193$	3.22234			0.231949			0.115975	+	0.993252i	$0.463001\pi$
$194$		0			0
$195$	−0.275793	−	0.114237i	−0.0197499	−	0.00818070i
$196$		0			0
$197$	8.79059	+	21.2224i	0.626303	+	1.51203i	0.844183	+	0.536055i	$0.180086\pi$
$197$	8.79059	+	21.2224i	0.626303	+	1.51203i	−0.217880	+	0.975976i	$0.569914\pi$
$198$		0			0
$199$	7.10324	−	7.10324i	0.503535	−	0.503535i	−0.409000	−	0.912535i	$-0.634122\pi$
$199$	7.10324	−	7.10324i	0.503535	−	0.503535i	0.912535	+	0.409000i	$0.134122\pi$
$200$		0			0
$201$	−3.66929	−	3.66929i	−0.258812	−	0.258812i
$202$		0			0
$203$	−0.444066	+	0.183938i	−0.0311673	+	0.0129099i
$204$		0			0
$205$	0.228324	−	0.551224i	0.0159469	−	0.0384992i
$206$		0			0
$207$			5.76888i			0.400965i
$208$		0			0
$209$		−	6.27633i		−	0.434143i
$210$		0			0
$211$	4.72147	−	11.3986i	0.325040	−	0.784715i	−0.673906	−	0.738817i	$-0.735385\pi$
$211$	4.72147	−	11.3986i	0.325040	−	0.784715i	0.998946	−	0.0458984i	$-0.0146151\pi$
$212$		0			0
$213$	−5.65732	+	2.34334i	−0.387633	+	0.160563i
$214$		0			0
$215$	0.793693	+	0.793693i	0.0541294	+	0.0541294i
$216$		0			0
$217$	−1.37266	+	1.37266i	−0.0931820	+	0.0931820i
$218$		0			0
$219$	−3.31242	−	7.99688i	−0.223832	−	0.540379i
$220$		0			0
$221$	−3.27082	−	1.35482i	−0.220019	−	0.0911349i
$222$		0			0
$223$	13.9899			0.936832			0.468416	−	0.883508i	$-0.344825\pi$
$223$	13.9899			0.936832			0.468416	+	0.883508i	$0.344825\pi$
$224$		0			0
$225$	4.76866			0.317911
$226$		0			0
$227$	−2.11043	−	0.874170i	−0.140074	−	0.0580207i	0.311545	−	0.950231i	$-0.399154\pi$
$227$	−2.11043	−	0.874170i	−0.140074	−	0.0580207i	−0.451619	+	0.892211i	$0.649154\pi$
$228$		0			0
$229$	−3.24245	−	7.82798i	−0.214267	−	0.517287i	0.779803	−	0.626025i	$-0.215319\pi$
$229$	−3.24245	−	7.82798i	−0.214267	−	0.517287i	−0.994070	+	0.108738i	$0.965319\pi$
$230$		0			0
$231$	0.703396	−	0.703396i	0.0462801	−	0.0462801i
$232$		0			0
$233$	7.83849	+	7.83849i	0.513516	+	0.513516i	0.915602	−	0.402086i	$-0.131715\pi$
$233$	7.83849	+	7.83849i	0.513516	+	0.513516i	−0.402086	+	0.915602i	$0.631715\pi$
$234$		0			0
$235$	−2.19755	+	0.910254i	−0.143352	+	0.0593784i
$236$		0			0
$237$	4.58353	−	11.0656i	0.297732	−	0.718789i
$238$		0			0
$239$		−	8.50653i		−	0.550242i	−0.961410	−	0.275121i	$-0.911282\pi$
$239$		−	8.50653i		−	0.550242i	0.961410	−	0.275121i	$-0.0887179\pi$
$240$		0			0
$241$			10.3310i			0.665475i	0.943019	+	0.332738i	$0.107972\pi$
$241$			10.3310i			0.665475i	−0.943019	+	0.332738i	$0.892028\pi$
$242$		0			0
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$		0			0
$245$	−3.09448	+	1.28177i	−0.197699	+	0.0818895i
$246$		0			0
$247$	0.526813	+	0.526813i	0.0335203	+	0.0335203i
$248$		0			0
$249$	−2.95621	+	2.95621i	−0.187342	+	0.187342i
$250$		0			0
$251$	0.371186	+	0.896122i	0.0234291	+	0.0565627i	0.935161	−	0.354223i	$-0.115255\pi$
$251$	0.371186	+	0.896122i	0.0234291	+	0.0565627i	−0.911732	+	0.410785i	$0.865255\pi$
$252$		0			0
$253$	27.8666	+	11.5427i	1.75196	+	0.725684i
$254$		0			0
$255$	−2.74362			−0.171812
$256$		0			0
$257$	−11.9183			−0.743442			−0.371721	−	0.928345i	$-0.621232\pi$
$257$	−11.9183			−0.743442			−0.371721	+	0.928345i	$0.621232\pi$
$258$		0			0
$259$	−1.40392	−	0.581524i	−0.0872355	−	0.0361341i
$260$		0			0
$261$	−0.966793	−	2.33405i	−0.0598430	−	0.144474i
$262$		0			0
$263$	−0.627327	+	0.627327i	−0.0386827	+	0.0386827i	−0.726184	−	0.687501i	$-0.758708\pi$
$263$	−0.627327	+	0.627327i	−0.0386827	+	0.0386827i	0.687501	+	0.726184i	$0.258708\pi$
$264$		0			0
$265$	3.58675	+	3.58675i	0.220332	+	0.220332i
$266$		0			0
$267$	−11.0265	+	4.56734i	−0.674813	+	0.279517i
$268$		0			0
$269$	−1.22418	+	2.95542i	−0.0746393	+	0.180195i	−0.956795	−	0.290762i	$-0.906091\pi$
$269$	−1.22418	+	2.95542i	−0.0746393	+	0.180195i	0.882156	+	0.470957i	$0.156091\pi$
$270$		0			0
$271$			26.7281i			1.62362i	0.583925	+	0.811808i	$0.301516\pi$
$271$			26.7281i			1.62362i	−0.583925	+	0.811808i	$0.698484\pi$
$272$		0			0
$273$			0.118081i			0.00714660i
$274$		0			0
$275$	9.54142	−	23.0350i	0.575369	−	1.38906i
$276$		0			0
$277$	−26.1483	+	10.8310i	−1.57110	+	0.650770i	−0.986972	−	0.160893i	$-0.948563\pi$
$277$	−26.1483	+	10.8310i	−1.57110	+	0.650770i	−0.584126	+	0.811663i	$0.698563\pi$
$278$		0			0
$279$	−7.21479	−	7.21479i	−0.431938	−	0.431938i
$280$		0			0
$281$	−13.5386	+	13.5386i	−0.807646	+	0.807646i	−0.984277	−	0.176631i	$-0.943480\pi$
$281$	−13.5386	+	13.5386i	−0.807646	+	0.807646i	0.176631	+	0.984277i	$0.443480\pi$
$282$		0			0
$283$	4.00203	+	9.66174i	0.237896	+	0.574331i	0.997065	−	0.0765624i	$-0.0243944\pi$
$283$	4.00203	+	9.66174i	0.237896	+	0.574331i	−0.759169	+	0.650893i	$0.774394\pi$
$284$		0			0
$285$	0.533420	+	0.220950i	0.0315971	+	0.0130879i
$286$		0			0
$287$	−0.236007			−0.0139311
$288$		0			0
$289$	−15.5385			−0.914029
$290$		0			0
$291$	−8.51648	−	3.52764i	−0.499245	−	0.206794i
$292$		0			0
$293$	−11.0520	−	26.6818i	−0.645663	−	1.55877i	−0.818930	−	0.573893i	$-0.805433\pi$
$293$	−11.0520	−	26.6818i	−0.645663	−	1.55877i	0.173268	−	0.984875i	$-0.444567\pi$
$294$		0			0
$295$	4.20781	−	4.20781i	0.244988	−	0.244988i
$296$		0			0
$297$	3.69711	+	3.69711i	0.214528	+	0.214528i
$298$		0			0
$299$	−3.30788	+	1.37017i	−0.191300	+	0.0792389i
$300$		0			0
$301$	0.169911	−	0.410200i	0.00979348	−	0.0236436i
$302$		0			0
$303$			3.34006i			0.191881i
$304$		0			0
$305$		−	4.92937i		−	0.282255i
$306$		0			0
$307$	9.87747	−	23.8463i	0.563737	−	1.36098i	−0.343020	−	0.939328i	$-0.611450\pi$
$307$	9.87747	−	23.8463i	0.563737	−	1.36098i	0.906757	−	0.421653i	$-0.138550\pi$
$308$		0			0
$309$	9.37945	−	3.88510i	0.533578	−	0.221015i
$310$		0			0
$311$	−18.0382	−	18.0382i	−1.02285	−	1.02285i	−0.999733	−	0.0231182i	$-0.992641\pi$
$311$	−18.0382	−	18.0382i	−1.02285	−	1.02285i	−0.0231182	−	0.999733i	$-0.507359\pi$
$312$		0			0
$313$	13.4949	−	13.4949i	0.762778	−	0.762778i	−0.214046	−	0.976824i	$-0.568664\pi$
$313$	13.4949	−	13.4949i	0.762778	−	0.762778i	0.976824	+	0.214046i	$0.0686643\pi$
$314$		0			0
$315$	0.0350189	+	0.0845432i	0.00197309	+	0.00476347i
$316$		0			0
$317$	−9.96898	−	4.12929i	−0.559914	−	0.231924i	0.0847339	−	0.996404i	$-0.472996\pi$
$317$	−9.96898	−	4.12929i	−0.559914	−	0.231924i	−0.644648	+	0.764480i	$0.722996\pi$
$318$		0			0
$319$	−13.2090			−0.739564
$320$		0			0
$321$	−1.64819			−0.0919930
$322$		0			0
$323$	6.32620	+	2.62040i	0.351999	+	0.145803i
$324$		0			0
$325$	1.13261	+	2.73435i	0.0628257	+	0.151675i
$326$		0			0
$327$	−10.4325	+	10.4325i	−0.576918	+	0.576918i
$328$		0			0
$329$	0.665305	+	0.665305i	0.0366795	+	0.0366795i
$330$		0			0
$331$	−11.3038	+	4.68220i	−0.621314	+	0.257357i	−0.671058	−	0.741405i	$-0.734160\pi$
$331$	−11.3038	+	4.68220i	−0.621314	+	0.257357i	0.0497433	+	0.998762i	$0.484160\pi$
$332$		0			0
$333$	3.05654	−	7.37913i	0.167497	−	0.404374i
$334$		0			0
$335$		−	2.49587i		−	0.136364i
$336$		0			0
$337$		−	1.45068i		−	0.0790237i	−0.999219	−	0.0395118i	$-0.987420\pi$
$337$		−	1.45068i		−	0.0790237i	0.999219	−	0.0395118i	$-0.0125803\pi$
$338$		0			0
$339$	1.71576	−	4.14221i	0.0931872	−	0.224974i
$340$		0			0
$341$	−49.2869	+	20.4153i	−2.66903	+	1.10555i
$342$		0			0
$343$	1.87857	+	1.87857i	0.101433	+	0.101433i
$344$		0			0
$345$	−1.96201	+	1.96201i	−0.105631	+	0.105631i
$346$		0			0
$347$	4.88124	+	11.7844i	0.262039	+	0.632618i	0.999064	−	0.0432472i	$-0.0137703\pi$
$347$	4.88124	+	11.7844i	0.262039	+	0.632618i	−0.737026	+	0.675865i	$0.763770\pi$
$348$		0			0
$349$	−7.72369	−	3.19926i	−0.413440	−	0.171252i	0.166261	−	0.986082i	$-0.446831\pi$
$349$	−7.72369	−	3.19926i	−0.413440	−	0.171252i	−0.579701	+	0.814829i	$0.696831\pi$
$350$		0			0
$351$	−0.620644			−0.0331275
$352$		0			0
$353$	17.4309			0.927751			0.463875	−	0.885900i	$-0.346459\pi$
$353$	17.4309			0.927751			0.463875	+	0.885900i	$0.346459\pi$
$354$		0			0
$355$	−2.72104	−	1.12709i	−0.144418	−	0.0598199i
$356$		0			0
$357$	0.415314	+	1.00266i	0.0219807	+	0.0530662i
$358$		0			0
$359$	−4.53639	+	4.53639i	−0.239422	+	0.239422i	−0.816611	−	0.577189i	$-0.804150\pi$
$359$	−4.53639	+	4.53639i	−0.239422	+	0.239422i	0.577189	+	0.816611i	$0.304150\pi$
$360$		0			0
$361$	12.4161	+	12.4161i	0.653479	+	0.653479i
$362$		0			0
$363$	15.0936	−	6.25197i	0.792208	−	0.328143i
$364$		0			0
$365$	1.59320	−	3.84632i	0.0833919	−	0.201326i
$366$		0			0
$367$		−	7.18068i		−	0.374828i	−0.982281	−	0.187414i	$-0.939989\pi$
$367$		−	7.18068i		−	0.374828i	0.982281	−	0.187414i	$-0.0600106\pi$
$368$		0			0
$369$		−	1.24047i		−	0.0645765i
$370$		0			0
$371$	0.767836	−	1.85372i	0.0398640	−	0.0962403i
$372$		0			0
$373$	14.3497	−	5.94383i	0.742998	−	0.307760i	0.0211168	−	0.999777i	$-0.493278\pi$
$373$	14.3497	−	5.94383i	0.742998	−	0.307760i	0.721881	+	0.692017i	$0.243278\pi$
$374$		0			0
$375$	3.32235	+	3.32235i	0.171565	+	0.171565i
$376$		0			0
$377$	1.10872	−	1.10872i	0.0571020	−	0.0571020i
$378$		0			0
$379$	−3.45126	−	8.33209i	−0.177280	−	0.427991i	0.810115	−	0.586272i	$-0.199405\pi$
$379$	−3.45126	−	8.33209i	−0.177280	−	0.427991i	−0.987394	+	0.158281i	$0.949405\pi$
$380$		0			0
$381$	−9.75014	−	4.03864i	−0.499515	−	0.206906i
$382$		0			0
$383$	4.45958			0.227874			0.113937	−	0.993488i	$-0.463654\pi$
$383$	4.45958			0.227874			0.113937	+	0.993488i	$0.463654\pi$
$384$		0			0
$385$	0.478454			0.0243843
$386$		0			0
$387$	2.15605	+	0.893063i	0.109598	+	0.0453969i
$388$		0			0
$389$	2.19268	+	5.29359i	0.111173	+	0.268396i	0.969668	−	0.244427i	$-0.0785998\pi$
$389$	2.19268	+	5.29359i	0.111173	+	0.268396i	−0.858495	+	0.512823i	$0.828600\pi$
$390$		0			0
$391$	−23.2689	+	23.2689i	−1.17676	+	1.17676i
$392$		0			0
$393$	−4.77005	−	4.77005i	−0.240617	−	0.240617i
$394$		0			0
$395$	5.32232	−	2.20458i	0.267795	−	0.110924i
$396$		0			0
$397$	5.25839	−	12.6949i	0.263911	−	0.637137i	−0.735263	−	0.677782i	$-0.762941\pi$
$397$	5.25839	−	12.6949i	0.263911	−	0.637137i	0.999174	+	0.0406449i	$0.0129412\pi$
$398$		0			0
$399$		−	0.228385i		−	0.0114335i
$400$		0			0
$401$		−	22.6945i		−	1.13331i	−0.823955	−	0.566655i	$-0.808237\pi$
$401$		−	22.6945i		−	1.13331i	0.823955	−	0.566655i	$-0.191763\pi$
$402$		0			0
$403$	2.42338	−	5.85055i	0.120717	−	0.291437i
$404$		0			0
$405$	−0.444366	+	0.184062i	−0.0220807	+	0.00914613i
$406$		0			0
$407$	−29.5292	−	29.5292i	−1.46371	−	1.46371i
$408$		0			0
$409$	−18.9178	+	18.9178i	−0.935424	+	0.935424i	−0.998038	−	0.0626139i	$-0.980056\pi$
$409$	−18.9178	+	18.9178i	−0.935424	+	0.935424i	0.0626139	+	0.998038i	$0.480056\pi$
$410$		0			0
$411$	−5.67959	−	13.7117i	−0.280153	−	0.676350i
$412$		0			0
$413$	−2.17470	−	0.900790i	−0.107010	−	0.0443250i
$414$		0			0
$415$	−2.01083			−0.0987077
$416$		0			0
$417$	−9.92058			−0.485813
$418$		0			0
$419$	20.8524	+	8.63734i	1.01871	+	0.421962i	0.828623	−	0.559807i	$-0.189125\pi$
$419$	20.8524	+	8.63734i	1.01871	+	0.421962i	0.190082	+	0.981768i	$0.439125\pi$
$420$		0			0
$421$	−14.3106	−	34.5489i	−0.697456	−	1.68381i	−0.729189	−	0.684312i	$-0.760103\pi$
$421$	−14.3106	−	34.5489i	−0.697456	−	1.68381i	0.0317327	−	0.999496i	$-0.489897\pi$
$422$		0			0
$423$	−3.49690	+	3.49690i	−0.170025	+	0.170025i
$424$		0			0
$425$	19.2345	+	19.2345i	0.933008	+	0.933008i
$426$		0			0
$427$	−1.80144	+	0.746181i	−0.0871777	+	0.0361102i
$428$		0			0
$429$	−1.24182	+	2.99802i	−0.0599557	+	0.144746i
$430$		0			0
$431$			38.4560i			1.85236i	0.377080	+	0.926181i	$0.376928\pi$
$431$			38.4560i			1.85236i	−0.377080	+	0.926181i	$0.623072\pi$
$432$		0			0
$433$		−	8.55433i		−	0.411095i	−0.978647	−	0.205547i	$-0.934102\pi$
$433$		−	8.55433i		−	0.411095i	0.978647	−	0.205547i	$-0.0658975\pi$
$434$		0			0
$435$	0.465006	−	1.12262i	0.0222954	−	0.0538257i
$436$		0			0
$437$	6.39787	−	2.65009i	0.306052	−	0.126771i
$438$		0			0
$439$	−5.13653	−	5.13653i	−0.245153	−	0.245153i	0.573825	−	0.818978i	$-0.305459\pi$
$439$	−5.13653	−	5.13653i	−0.245153	−	0.245153i	−0.818978	+	0.573825i	$0.805459\pi$
$440$		0			0
$441$	−4.92415	+	4.92415i	−0.234483	+	0.234483i
$442$		0			0
$443$	−2.45339	−	5.92301i	−0.116564	−	0.281411i	0.854820	−	0.518925i	$-0.173667\pi$
$443$	−2.45339	−	5.92301i	−0.116564	−	0.281411i	−0.971384	+	0.237514i	$0.923667\pi$
$444$		0			0
$445$	−5.30352	−	2.19679i	−0.251411	−	0.104138i
$446$		0			0
$447$	10.5483			0.498917
$448$		0			0
$449$	23.7582			1.12122			0.560610	−	0.828080i	$-0.310567\pi$
$449$	23.7582			1.12122			0.560610	+	0.828080i	$0.310567\pi$
$450$		0			0
$451$	−5.99211	−	2.48201i	−0.282157	−	0.116873i
$452$		0			0
$453$	4.86397	+	11.7427i	0.228529	+	0.551718i
$454$		0			0
$455$	−0.0401598	+	0.0401598i	−0.00188272	+	0.00188272i
$456$		0			0
$457$	−1.16506	−	1.16506i	−0.0544992	−	0.0544992i	0.679332	−	0.733831i	$-0.262270\pi$
$457$	−1.16506	−	1.16506i	−0.0544992	−	0.0544992i	−0.733831	+	0.679332i	$0.762270\pi$
$458$		0			0
$459$	−5.27004	+	2.18292i	−0.245984	+	0.101890i
$460$		0			0
$461$	1.61683	−	3.90337i	0.0753032	−	0.181798i	−0.881745	−	0.471726i	$-0.843631\pi$
$461$	1.61683	−	3.90337i	0.0753032	−	0.181798i	0.957049	+	0.289928i	$0.0936313\pi$
$462$		0			0
$463$			3.11687i			0.144853i	0.997374	+	0.0724267i	$0.0230743\pi$
$463$			3.11687i			0.144853i	−0.997374	+	0.0724267i	$0.976926\pi$
$464$		0			0
$465$		−	4.90754i		−	0.227582i
$466$		0			0
$467$	−7.59921	+	18.3461i	−0.351649	+	0.848957i	0.644767	+	0.764379i	$0.276954\pi$
$467$	−7.59921	+	18.3461i	−0.351649	+	0.848957i	−0.996417	+	0.0845781i	$0.973046\pi$
$468$		0			0
$469$	−0.912117	+	0.377811i	−0.0421176	+	0.0174457i
$470$		0			0
$471$	15.9549	+	15.9549i	0.735163	+	0.735163i
$472$		0			0
$473$	8.62788	−	8.62788i	0.396711	−	0.396711i
$474$		0			0
$475$	−2.19061	−	5.28860i	−0.100512	−	0.242658i
$476$		0			0
$477$	9.74330	+	4.03581i	0.446115	+	0.184787i
$478$		0			0
$479$	−14.5634			−0.665418			−0.332709	−	0.943030i	$-0.607963\pi$
$479$	−14.5634			−0.665418			−0.332709	+	0.943030i	$0.607963\pi$
$480$		0			0
$481$	4.95716			0.226027
$482$		0			0
$483$	1.01402	+	0.420019i	0.0461393	+	0.0191115i
$484$		0			0
$485$	−1.69672	−	4.09624i	−0.0770440	−	0.186001i
$486$		0			0
$487$	−12.0901	+	12.0901i	−0.547856	+	0.547856i	−0.925820	−	0.377964i	$-0.876624\pi$
$487$	−12.0901	+	12.0901i	−0.547856	+	0.547856i	0.377964	+	0.925820i	$0.376624\pi$
$488$		0			0
$489$	5.39242	+	5.39242i	0.243854	+	0.243854i
$490$		0			0
$491$	−20.2368	+	8.38236i	−0.913274	+	0.378290i	−0.789309	−	0.613996i	$-0.789561\pi$
$491$	−20.2368	+	8.38236i	−0.913274	+	0.378290i	−0.123965	+	0.992287i	$0.539561\pi$
$492$		0			0
$493$	5.51483	−	13.3140i	0.248376	−	0.599632i
$494$		0			0
$495$			2.51479i			0.113031i
$496$		0			0
$497$			1.16502i			0.0522583i
$498$		0			0
$499$	3.26197	−	7.87508i	0.146026	−	0.352537i	−0.833896	−	0.551922i	$-0.813894\pi$
$499$	3.26197	−	7.87508i	0.146026	−	0.352537i	0.979921	+	0.199385i	$0.0638945\pi$
$500$		0			0
$501$	1.08726	−	0.450358i	0.0485752	−	0.0201205i
$502$		0			0
$503$	12.2760	+	12.2760i	0.547362	+	0.547362i	0.925677	−	0.378315i	$-0.123496\pi$
$503$	12.2760	+	12.2760i	0.547362	+	0.547362i	−0.378315	+	0.925677i	$0.623496\pi$
$504$		0			0
$505$	−1.13596	+	1.13596i	−0.0505497	+	0.0505497i
$506$		0			0
$507$	4.82748	+	11.6546i	0.214396	+	0.517597i
$508$		0			0
$509$	−0.842977	−	0.349172i	−0.0373643	−	0.0154768i	0.363923	−	0.931429i	$-0.381437\pi$
$509$	−0.842977	−	0.349172i	−0.0373643	−	0.0154768i	−0.401287	+	0.915952i	$0.631437\pi$
$510$		0			0
$511$	−1.64681			−0.0728506
$512$		0			0
$513$	1.20041			0.0529993
$514$		0			0
$515$	4.51131	+	1.86865i	0.198792	+	0.0823424i
$516$		0			0
$517$	9.89496	+	23.8886i	0.435180	+	1.05062i
$518$		0			0
$519$	8.64311	−	8.64311i	0.379390	−	0.379390i
$520$		0			0
$521$	4.87761	+	4.87761i	0.213692	+	0.213692i	0.805834	−	0.592142i	$-0.201717\pi$
$521$	4.87761	+	4.87761i	0.213692	+	0.213692i	−0.592142	+	0.805834i	$0.701717\pi$
$522$		0			0
$523$	20.5648	−	8.51821i	0.899235	−	0.372475i	0.115309	−	0.993330i	$-0.463214\pi$
$523$	20.5648	−	8.51821i	0.899235	−	0.372475i	0.783926	+	0.620854i	$0.213214\pi$
$524$		0			0
$525$	0.347196	−	0.838204i	0.0151529	−	0.0365822i
$526$		0			0
$527$		−	58.2020i		−	2.53532i
$528$		0			0
$529$			10.2800i			0.446955i
$530$		0			0
$531$	4.73462	−	11.4304i	0.205465	−	0.496037i
$532$		0			0
$533$	0.711288	−	0.294625i	0.0308093	−	0.0127616i
$534$		0			0
$535$	−0.560554	−	0.560554i	−0.0242349	−	0.0242349i
$536$		0			0
$537$	−8.47133	+	8.47133i	−0.365565	+	0.365565i
$538$		0			0
$539$	13.9336	+	33.6387i	0.600162	+	1.44892i
$540$		0			0
$541$	−8.72081	−	3.61228i	−0.374937	−	0.155304i	0.187254	−	0.982312i	$-0.440041\pi$
$541$	−8.72081	−	3.61228i	−0.374937	−	0.155304i	−0.562191	+	0.827008i	$0.690041\pi$
$542$		0			0
$543$	4.97735			0.213599
$544$		0			0
$545$	−7.09624			−0.303969
$546$		0			0
$547$	−3.50970	−	1.45377i	−0.150064	−	0.0621586i	0.306387	−	0.951907i	$-0.400880\pi$
$547$	−3.50970	−	1.45377i	−0.150064	−	0.0621586i	−0.456451	+	0.889748i	$0.650880\pi$
$548$		0			0
$549$	−3.92198	−	9.46851i	−0.167386	−	0.404106i
$550$		0			0
$551$	−2.14441	+	2.14441i	−0.0913550	+	0.0913550i
$552$		0			0
$553$	−1.61133	−	1.61133i	−0.0685206	−	0.0685206i
$554$		0			0
$555$	3.54920	−	1.47013i	0.150655	−	0.0624034i
$556$		0			0
$557$	−11.0388	+	26.6499i	−0.467727	+	1.12919i	0.497425	+	0.867507i	$0.334279\pi$
$557$	−11.0388	+	26.6499i	−0.467727	+	1.12919i	−0.965153	+	0.261687i	$0.915721\pi$
$558$		0			0
$559$			1.44839i			0.0612603i
$560$		0			0
$561$			29.8247i			1.25920i
$562$		0			0
$563$	0.499373	−	1.20559i	0.0210461	−	0.0508097i	−0.913007	−	0.407944i	$-0.866246\pi$
$563$	0.499373	−	1.20559i	0.0210461	−	0.0508097i	0.934053	+	0.357134i	$0.116246\pi$
$564$		0			0
$565$	1.99231	−	0.825242i	0.0838171	−	0.0347182i
$566$		0			0
$567$	0.134531	+	0.134531i	0.00564978	+	0.00564978i
$568$		0			0
$569$	24.7043	−	24.7043i	1.03566	−	1.03566i	0.0363184	−	0.999340i	$-0.488437\pi$
$569$	24.7043	−	24.7043i	1.03566	−	1.03566i	0.999340	−	0.0363184i	$-0.0115631\pi$
$570$		0			0
$571$	−12.4201	−	29.9848i	−0.519765	−	1.25482i	−0.938047	−	0.346507i	$-0.887368\pi$
$571$	−12.4201	−	29.9848i	−0.519765	−	1.25482i	0.418282	−	0.908317i	$-0.362632\pi$
$572$		0			0
$573$	15.0723	+	6.24317i	0.629656	+	0.260812i
$574$		0			0
$575$	27.5098			1.14724
$576$		0			0
$577$	−38.7977			−1.61517			−0.807585	−	0.589752i	$-0.799226\pi$
$577$	−38.7977			−1.61517			−0.807585	+	0.589752i	$0.799226\pi$
$578$		0			0
$579$	2.97705	+	1.23314i	0.123722	+	0.0512474i
$580$		0			0
$581$	0.304388	+	0.734858i	0.0126281	+	0.0304870i
$582$		0			0
$583$	38.9899	−	38.9899i	1.61480	−	1.61480i
$584$		0			0
$585$	−0.211083	−	0.211083i	−0.00872720	−	0.00872720i
$586$		0			0
$587$	32.3256	−	13.3897i	1.33422	−	0.552652i	0.402363	−	0.915480i	$-0.368189\pi$
$587$	32.3256	−	13.3897i	1.33422	−	0.552652i	0.931856	+	0.362828i	$0.118189\pi$
$588$		0			0
$589$	−4.68714	+	11.3157i	−0.193130	+	0.466257i
$590$		0			0
$591$			22.9709i			0.944897i
$592$		0			0
$593$			25.8554i			1.06176i	0.847448	+	0.530878i	$0.178138\pi$
$593$			25.8554i			1.06176i	−0.847448	+	0.530878i	$0.821862\pi$
$594$		0			0
$595$	−0.199757	+	0.482256i	−0.00818923	+	0.0197706i
$596$		0			0
$597$	9.28082	−	3.84424i	0.379839	−	0.157334i
$598$		0			0
$599$	27.4466	+	27.4466i	1.12144	+	1.12144i	0.991525	+	0.129914i	$0.0414701\pi$
$599$	27.4466	+	27.4466i	1.12144	+	1.12144i	0.129914	+	0.991525i	$0.458530\pi$
$600$		0			0
$601$	−17.2120	+	17.2120i	−0.702091	+	0.702091i	−0.964859	−	0.262768i	$-0.915365\pi$
$601$	−17.2120	+	17.2120i	−0.702091	+	0.702091i	0.262768	+	0.964859i	$0.415365\pi$
$602$		0			0
$603$	−1.98581	−	4.79416i	−0.0808682	−	0.195233i
$604$		0			0
$605$	7.25968	+	3.00706i	0.295148	+	0.122254i
$606$		0			0
$607$	35.6136			1.44551			0.722756	−	0.691103i	$-0.242875\pi$
$607$	35.6136			1.44551			0.722756	+	0.691103i	$0.242875\pi$
$608$		0			0
$609$	−0.480654			−0.0194771
$610$		0			0
$611$	−2.83567	−	1.17457i	−0.114719	−	0.0475181i
$612$		0			0
$613$	7.20887	+	17.4038i	0.291164	+	0.702931i	0.999997	−	0.00244484i	$-0.000778219\pi$
$613$	7.20887	+	17.4038i	0.291164	+	0.702931i	−0.708833	+	0.705376i	$0.750778\pi$
$614$		0			0
$615$	0.421889	−	0.421889i	0.0170122	−	0.0170122i
$616$		0			0
$617$	12.8299	+	12.8299i	0.516511	+	0.516511i	0.916514	−	0.400003i	$-0.130991\pi$
$617$	12.8299	+	12.8299i	0.516511	+	0.516511i	−0.400003	+	0.916514i	$0.630991\pi$
$618$		0			0
$619$	−12.1156	+	5.01844i	−0.486966	+	0.201708i	−0.612638	−	0.790364i	$-0.709892\pi$
$619$	−12.1156	+	5.01844i	−0.486966	+	0.201708i	0.125671	+	0.992072i	$0.459892\pi$
$620$		0			0
$621$	−2.20765	+	5.32975i	−0.0885901	+	0.213875i
$622$		0			0
$623$			2.27071i			0.0909741i
$624$		0			0
$625$		−	21.5834i		−	0.863337i
$626$		0			0
$627$	2.40185	−	5.79857i	0.0959205	−	0.231573i
$628$		0			0
$629$	42.0924	−	17.4352i	1.67833	−	0.695189i
$630$		0			0
$631$	9.99914	+	9.99914i	0.398059	+	0.398059i	0.877548	−	0.479489i	$-0.159178\pi$
$631$	9.99914	+	9.99914i	0.398059	+	0.398059i	−0.479489	+	0.877548i	$0.659178\pi$
$632$		0			0
$633$	8.72415	−	8.72415i	0.346754	−	0.346754i
$634$		0			0
$635$	−1.94250	−	4.68960i	−0.0770857	−	0.186101i
$636$		0			0
$637$	−3.99305	−	1.65397i	−0.158210	−	0.0655329i
$638$		0			0
$639$	−6.12343			−0.242239
$640$		0			0
$641$	28.5513			1.12771			0.563854	−	0.825875i	$-0.309318\pi$
$641$	28.5513			1.12771			0.563854	+	0.825875i	$0.309318\pi$
$642$		0			0
$643$	5.76614	+	2.38841i	0.227394	+	0.0941898i	0.493472	−	0.869762i	$-0.335728\pi$
$643$	5.76614	+	2.38841i	0.227394	+	0.0941898i	−0.266077	+	0.963952i	$0.585728\pi$
$644$		0			0
$645$	0.429544	+	1.03701i	0.0169133	+	0.0408322i
$646$		0			0
$647$	0.783090	−	0.783090i	0.0307864	−	0.0307864i	−0.691546	−	0.722332i	$-0.743070\pi$
$647$	0.783090	−	0.783090i	0.0307864	−	0.0307864i	0.722332	+	0.691546i	$0.243070\pi$
$648$		0			0
$649$	−45.7412	−	45.7412i	−1.79550	−	1.79550i
$650$		0			0
$651$	−1.79346	+	0.742877i	−0.0702914	+	0.0291156i
$652$		0			0
$653$	−3.54194	+	8.55101i	−0.138607	+	0.334627i	−0.977907	−	0.209042i	$-0.932965\pi$
$653$	−3.54194	+	8.55101i	−0.138607	+	0.334627i	0.839300	+	0.543669i	$0.182965\pi$
$654$		0			0
$655$		−	3.24462i		−	0.126778i
$656$		0			0
$657$		−	8.65576i		−	0.337694i
$658$		0			0
$659$	−17.7016	+	42.7355i	−0.689557	+	1.66474i	0.0561160	+	0.998424i	$0.482128\pi$
$659$	−17.7016	+	42.7355i	−0.689557	+	1.66474i	−0.745673	+	0.666313i	$0.767872\pi$
$660$		0			0
$661$	−0.187232	+	0.0775542i	−0.00728249	+	0.00301651i	−0.386322	−	0.922364i	$-0.626255\pi$
$661$	−0.187232	+	0.0775542i	−0.00728249	+	0.00301651i	0.379039	+	0.925381i	$0.376255\pi$
$662$		0			0
$663$	−2.50338	−	2.50338i	−0.0972231	−	0.0972231i
$664$		0			0
$665$	0.0776743	−	0.0776743i	0.00301208	−	0.00301208i
$666$		0			0
$667$	−5.57731	−	13.4648i	−0.215954	−	0.521360i
$668$		0			0
$669$	12.9250	+	5.35370i	0.499708	+	0.206986i
$670$		0			0
$671$	−53.5850			−2.06862
$672$		0			0
$673$	48.7073			1.87753			0.938765	−	0.344558i	$-0.111971\pi$
$673$	48.7073			1.87753			0.938765	+	0.344558i	$0.111971\pi$
$674$		0			0
$675$	4.40567	+	1.82489i	0.169574	+	0.0702399i
$676$		0			0
$677$	10.9016	+	26.3188i	0.418982	+	1.01151i	0.982643	+	0.185506i	$0.0593925\pi$
$677$	10.9016	+	26.3188i	0.418982	+	1.01151i	−0.563661	+	0.826006i	$0.690607\pi$
$678$		0			0
$679$	−1.24013	+	1.24013i	−0.0475919	+	0.0475919i
$680$		0			0
$681$	−1.61526	−	1.61526i	−0.0618967	−	0.0618967i
$682$		0			0
$683$	−16.7740	+	6.94800i	−0.641838	+	0.265858i	−0.679773	−	0.733422i	$-0.737922\pi$
$683$	−16.7740	+	6.94800i	−0.641838	+	0.265858i	0.0379356	+	0.999280i	$0.487922\pi$
$684$		0			0
$685$	2.73176	−	6.59504i	0.104375	−	0.251984i
$686$		0			0
$687$		−	8.47294i		−	0.323263i
$688$		0			0
$689$			6.54536i			0.249358i
$690$		0			0
$691$	−17.5044	+	42.2593i	−0.665898	+	1.60762i	0.122509	+	0.992467i	$0.460906\pi$
$691$	−17.5044	+	42.2593i	−0.665898	+	1.60762i	−0.788407	+	0.615154i	$0.789094\pi$
$692$		0			0
$693$	0.919031	−	0.380675i	0.0349111	−	0.0144607i
$694$		0			0
$695$	−3.37402	−	3.37402i	−0.127984	−	0.127984i
$696$		0			0
$697$	5.00347	−	5.00347i	0.189520	−	0.189520i
$698$		0			0
$699$	4.24216	+	10.2415i	0.160453	+	0.387368i
$700$		0			0
$701$	−9.76630	−	4.04533i	−0.368868	−	0.152790i	0.190547	−	0.981678i	$-0.438974\pi$
$701$	−9.76630	−	4.04533i	−0.368868	−	0.152790i	−0.559414	+	0.828888i	$0.688974\pi$
$702$		0			0
$703$	−9.58780			−0.361611
$704$		0			0
$705$	−2.37861			−0.0895836
$706$		0			0
$707$	0.587094	+	0.243182i	0.0220799	+	0.00914581i
$708$		0			0
$709$	−2.23164	−	5.38765i	−0.0838109	−	0.202337i	0.876418	−	0.481551i	$-0.159926\pi$
$709$	−2.23164	−	5.38765i	−0.0838109	−	0.202337i	−0.960229	+	0.279213i	$0.909926\pi$
$710$		0			0
$711$	8.46926	−	8.46926i	0.317622	−	0.317622i
$712$		0			0
$713$	−41.6213	−	41.6213i	−1.55873	−	1.55873i
$714$		0			0
$715$	−1.44198	+	0.597289i	−0.0539271	+	0.0223373i
$716$		0			0
$717$	3.25531	−	7.85901i	0.121572	−	0.293500i
$718$		0			0
$719$		−	12.8188i		−	0.478059i	−0.971012	−	0.239030i	$-0.923171\pi$
$719$		−	12.8188i		−	0.478059i	0.971012	−	0.239030i	$-0.0768293\pi$
$720$		0			0
$721$		−	1.93152i		−	0.0719337i
$722$		0			0
$723$	−3.95349	+	9.54456i	−0.147032	+	0.354966i
$724$		0			0
$725$	−11.1303	+	4.61031i	−0.413368	+	0.171223i
$726$		0			0
$727$	−22.1336	−	22.1336i	−0.820889	−	0.820889i	0.165347	−	0.986235i	$-0.447126\pi$
$727$	−22.1336	−	22.1336i	−0.820889	−	0.820889i	−0.986235	+	0.165347i	$0.947126\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	5.09426	+	12.2986i	0.188418	+	0.454881i
$732$		0			0
$733$	−17.7464	−	7.35081i	−0.655479	−	0.271508i	0.0300555	−	0.999548i	$-0.490432\pi$
$733$	−17.7464	−	7.35081i	−0.655479	−	0.271508i	−0.685535	+	0.728040i	$0.740432\pi$
$734$		0			0
$735$	−3.34944			−0.123546
$736$		0			0
$737$	−27.1315			−0.999402
$738$		0			0
$739$	−20.4272	−	8.46123i	−0.751428	−	0.311251i	−0.0261037	−	0.999659i	$-0.508310\pi$
$739$	−20.4272	−	8.46123i	−0.751428	−	0.311251i	−0.725324	+	0.688408i	$0.758310\pi$
$740$		0			0
$741$	0.285109	+	0.688315i	0.0104738	+	0.0252859i
$742$		0			0
$743$	26.6427	−	26.6427i	0.977427	−	0.977427i	−0.0223237	−	0.999751i	$-0.507106\pi$
$743$	26.6427	−	26.6427i	0.977427	−	0.977427i	0.999751	+	0.0223237i	$0.00710644\pi$
$744$		0			0
$745$	3.58750	+	3.58750i	0.131436	+	0.131436i
$746$		0			0
$747$	−3.86247	+	1.59989i	−0.141320	+	0.0585368i
$748$		0			0
$749$	−0.120001	+	0.289708i	−0.00438474	+	0.0105857i
$750$		0			0
$751$		−	23.4989i		−	0.857486i	−0.903427	−	0.428743i	$-0.858957\pi$
$751$		−	23.4989i		−	0.857486i	0.903427	−	0.428743i	$-0.141043\pi$
$752$		0			0
$753$			0.969956i			0.0353472i
$754$		0			0
$755$	−2.33946	+	5.64796i	−0.0851418	+	0.205550i
$756$		0			0
$757$	39.9311	−	16.5400i	1.45132	−	0.601157i	0.488809	−	0.872391i	$-0.337432\pi$
$757$	39.9311	−	16.5400i	1.45132	−	0.601157i	0.962513	+	0.271234i	$0.0874317\pi$
$758$		0			0
$759$	21.3282	+	21.3282i	0.774163	+	0.774163i
$760$		0			0
$761$	33.7925	−	33.7925i	1.22498	−	1.22498i	0.259134	−	0.965841i	$-0.416563\pi$
$761$	33.7925	−	33.7925i	1.22498	−	1.22498i	0.965841	−	0.259134i	$-0.0834372\pi$
$762$		0			0
$763$	1.07419	+	2.59332i	0.0388883	+	0.0938845i
$764$		0			0
$765$	−2.53477	−	1.04994i	−0.0916449	−	0.0379606i
$766$		0			0
$767$	7.67871			0.277262
$768$		0			0
$769$	−22.1545			−0.798913			−0.399457	−	0.916752i	$-0.630801\pi$
$769$	−22.1545			−0.798913			−0.399457	+	0.916752i	$0.630801\pi$
$770$		0			0
$771$	−11.0111	−	4.56093i	−0.396553	−	0.164258i
$772$		0			0
$773$	4.56113	+	11.0116i	0.164053	+	0.396058i	0.984433	−	0.175760i	$-0.0562383\pi$
$773$	4.56113	+	11.0116i	0.164053	+	0.396058i	−0.820380	+	0.571818i	$0.806238\pi$
$774$		0			0
$775$	−34.4049	+	34.4049i	−1.23586	+	1.23586i
$776$		0			0
$777$	−1.07452	−	1.07452i	−0.0385481	−	0.0385481i
$778$		0			0
$779$	−1.37573	+	0.569844i	−0.0492905	+	0.0204168i
$780$		0			0
$781$	−12.2521	+	29.5793i	−0.438416	+	1.05843i
$782$		0			0
$783$		−	2.52635i		−	0.0902845i
$784$		0			0
$785$			10.8526i			0.387347i
$786$		0			0
$787$	−14.4233	+	34.8210i	−0.514137	+	1.24124i	0.427320	+	0.904101i	$0.359458\pi$
$787$	−14.4233	+	34.8210i	−0.514137	+	1.24124i	−0.941456	+	0.337135i	$0.890542\pi$
$788$		0			0
$789$	−0.819643	+	0.339507i	−0.0291801	+	0.0120868i
$790$		0			0
$791$	−0.603170	−	0.603170i	−0.0214462	−	0.0214462i
$792$		0			0
$793$	4.49773	−	4.49773i	0.159719	−	0.159719i
$794$		0			0
$795$	1.94113	+	4.68631i	0.0688449	+	0.166206i
$796$		0			0
$797$	5.47061	+	2.26600i	0.193779	+	0.0802659i	0.477463	−	0.878652i	$-0.341557\pi$
$797$	5.47061	+	2.26600i	0.193779	+	0.0802659i	−0.283684	+	0.958918i	$0.591557\pi$
$798$		0			0
$799$	−28.2096			−0.997983
$800$		0			0
$801$	−11.9350			−0.421704
$802$		0			0
$803$	−41.8117	−	17.3190i	−1.47550	−	0.611173i
$804$		0			0
$805$	0.202020	+	0.487719i	0.00712027	+	0.0171899i
$806$		0			0
$807$	−2.26198	+	2.26198i	−0.0796255	+	0.0796255i
$808$		0			0
$809$	−20.7326	−	20.7326i	−0.728920	−	0.728920i	0.241485	−	0.970405i	$-0.422366\pi$
$809$	−20.7326	−	20.7326i	−0.728920	−	0.728920i	−0.970405	+	0.241485i	$0.922366\pi$
$810$		0			0
$811$	37.2071	−	15.4117i	1.30652	−	0.541177i	0.382651	−	0.923893i	$-0.375011\pi$
$811$	37.2071	−	15.4117i	1.30652	−	0.541177i	0.923866	+	0.382716i	$0.125011\pi$
$812$		0			0
$813$	−10.2284	+	24.6935i	−0.358726	+	0.866040i
$814$		0			0
$815$			3.66796i			0.128483i
$816$		0			0
$817$		−	2.80138i		−	0.0980077i
$818$		0			0
$819$	−0.0451877	+	0.109093i	−0.00157899	+	0.00381201i
$820$		0			0
$821$	−29.1884	+	12.0902i	−1.01868	+	0.421952i	−0.828615	−	0.559820i	$-0.810870\pi$
$821$	−29.1884	+	12.0902i	−1.01868	+	0.421952i	−0.190067	+	0.981771i	$0.560870\pi$
$822$		0			0
$823$	3.31937	+	3.31937i	0.115706	+	0.115706i	0.762589	−	0.646883i	$-0.223928\pi$
$823$	3.31937	+	3.31937i	0.115706	+	0.115706i	−0.646883	+	0.762589i	$0.723928\pi$
$824$		0			0
$825$	17.6302	−	17.6302i	0.613806	−	0.613806i
$826$		0			0
$827$	−2.47114	−	5.96586i	−0.0859300	−	0.207453i	0.875073	−	0.483991i	$-0.160813\pi$
$827$	−2.47114	−	5.96586i	−0.0859300	−	0.207453i	−0.961003	+	0.276537i	$0.910813\pi$
$828$		0			0
$829$	−0.339967	−	0.140819i	−0.0118075	−	0.00489085i	0.376772	−	0.926306i	$-0.377034\pi$
$829$	−0.339967	−	0.140819i	−0.0118075	−	0.00489085i	−0.388579	+	0.921415i	$0.627034\pi$
$830$		0			0
$831$	−28.3027			−0.981810
$832$		0			0
$833$	−39.7233			−1.37633
$834$		0			0
$835$	0.522948	+	0.216612i	0.0180974	+	0.00749618i
$836$		0			0
$837$	−3.90462	−	9.42658i	−0.134963	−	0.325830i
$838$		0			0
$839$	32.9364	−	32.9364i	1.13709	−	1.13709i	0.148122	−	0.988969i	$-0.452677\pi$
$839$	32.9364	−	32.9364i	1.13709	−	1.13709i	0.988969	−	0.148122i	$-0.0473227\pi$
$840$		0			0
$841$	−15.9930	−	15.9930i	−0.551483	−	0.551483i
$842$		0			0
$843$	−17.6890	+	7.32704i	−0.609243	+	0.252357i
$844$		0			0
$845$	−2.32191	+	5.60559i	−0.0798761	+	0.192838i
$846$		0			0
$847$		−	3.10824i		−	0.106801i
$848$		0			0
$849$			10.4578i			0.358911i
$850$		0			0
$851$	17.6328	−	42.5693i	0.604444	−	1.45926i
$852$		0			0
$853$	2.43815	−	1.00992i	0.0834808	−	0.0345789i	−0.340552	−	0.940226i	$-0.610614\pi$
$853$	2.43815	−	1.00992i	0.0834808	−	0.0345789i	0.424033	+	0.905647i	$0.360614\pi$
$854$		0			0
$855$	0.408262	+	0.408262i	0.0139623	+	0.0139623i
$856$		0			0
$857$	−31.8225	+	31.8225i	−1.08704	+	1.08704i	−0.0912053	+	0.995832i	$0.529072\pi$
$857$	−31.8225	+	31.8225i	−1.08704	+	1.08704i	−0.995832	+	0.0912053i	$0.970928\pi$
$858$		0			0
$859$	−11.6288	−	28.0745i	−0.396771	−	0.957890i	−0.988427	−	0.151699i	$-0.951526\pi$
$859$	−11.6288	−	28.0745i	−0.396771	−	0.957890i	0.591656	−	0.806191i	$-0.298474\pi$
$860$		0			0
$861$	−0.218042	−	0.0903161i	−0.00743087	−	0.00307797i
$862$		0			0
$863$	−18.9524			−0.645148			−0.322574	−	0.946544i	$-0.604548\pi$
$863$	−18.9524			−0.645148			−0.322574	+	0.946544i	$0.604548\pi$
$864$		0			0
$865$	5.87909			0.199895
$866$		0			0
$867$	−14.3557	−	5.94632i	−0.487545	−	0.201948i
$868$		0			0
$869$	−23.9650	−	57.8566i	−0.812956	−	1.96265i
$870$		0			0
$871$	2.27732	−	2.27732i	0.0771642	−	0.0771642i
$872$		0			0
$873$	−6.51823	−	6.51823i	−0.220609	−	0.220609i
$874$		0			0
$875$	0.825874	−	0.342088i	0.0279196	−	0.0115647i
$876$		0			0
$877$	16.0645	−	38.7831i	0.542459	−	1.30961i	−0.380523	−	0.924771i	$-0.624256\pi$
$877$	16.0645	−	38.7831i	0.542459	−	1.30961i	0.922983	−	0.384842i	$-0.125744\pi$
$878$		0			0
$879$		−	28.8802i		−	0.974104i
$880$		0			0
$881$			21.4254i			0.721841i	0.932597	+	0.360921i	$0.117537\pi$
$881$			21.4254i			0.721841i	−0.932597	+	0.360921i	$0.882463\pi$
$882$		0			0
$883$	−2.94264	+	7.10415i	−0.0990276	+	0.239074i	−0.965627	−	0.259930i	$-0.916301\pi$
$883$	−2.94264	+	7.10415i	−0.0990276	+	0.239074i	0.866600	+	0.499004i	$0.166301\pi$
$884$		0			0
$885$	5.49777	−	2.27725i	0.184805	−	0.0765489i
$886$		0			0
$887$	30.7269	+	30.7269i	1.03171	+	1.03171i	0.999480	+	0.0322295i	$0.0102607\pi$
$887$	30.7269	+	30.7269i	1.03171	+	1.03171i	0.0322295	+	0.999480i	$0.489739\pi$
$888$		0			0
$889$	−1.41977	+	1.41977i	−0.0476176	+	0.0476176i
$890$		0			0
$891$	2.00086	+	4.83050i	0.0670313	+	0.161828i
$892$		0			0
$893$	5.48456	+	2.27178i	0.183534	+	0.0760222i
$894$		0			0
$895$	−5.76225			−0.192611
$896$		0			0
$897$	−3.58042			−0.119547
$898$		0			0
$899$	23.8149	+	9.86444i	0.794271	+	0.328998i
$900$		0			0
$901$	23.0213	+	55.5782i	0.766949	+	1.85158i
$902$		0			0
$903$	0.313954	−	0.313954i	0.0104477	−	0.0104477i
$904$		0			0
$905$	1.69281	+	1.69281i	0.0562710	+	0.0562710i
$906$		0			0
$907$	−32.8338	+	13.6002i	−1.09023	+	0.451588i	−0.854087	−	0.520131i	$-0.825883\pi$
$907$	−32.8338	+	13.6002i	−1.09023	+	0.451588i	−0.236142	+	0.971718i	$0.575883\pi$
$908$		0			0
$909$	−1.27818	+	3.08581i	−0.0423947	+	0.102350i
$910$		0			0
$911$			15.3896i			0.509879i	0.966957	+	0.254940i	$0.0820556\pi$
$911$			15.3896i			0.509879i	−0.966957	+	0.254940i	$0.917944\pi$
$912$		0			0
$913$			21.8588i			0.723421i
$914$		0			0
$915$	1.88639	−	4.55414i	0.0623621	−	0.150555i
$916$		0			0
$917$	−1.18575	+	0.491152i	−0.0391568	+	0.0162193i
$918$		0			0
$919$	−1.60663	−	1.60663i	−0.0529979	−	0.0529979i	0.680111	−	0.733109i	$-0.261932\pi$
$919$	−1.60663	−	1.60663i	−0.0529979	−	0.0529979i	−0.733109	+	0.680111i	$0.761932\pi$
$920$		0			0
$921$	18.2512	−	18.2512i	0.601397	−	0.601397i
$922$		0			0
$923$	−1.45438	−	3.51118i	−0.0478715	−	0.115572i
$924$		0			0
$925$	−35.1886	−	14.5756i	−1.15699	−	0.479242i
$926$		0			0
$927$	10.1522			0.333443
$928$		0			0
$929$	8.22205			0.269757			0.134878	−	0.990862i	$-0.456936\pi$
$929$	8.22205			0.269757			0.134878	+	0.990862i	$0.456936\pi$
$930$		0			0
$931$	7.72308	+	3.19901i	0.253114	+	0.104843i
$932$		0			0
$933$	−9.76219	−	23.5680i	−0.319600	−	0.771582i
$934$		0			0
$935$	−10.1435	+	10.1435i	−0.331726	+	0.331726i
$936$		0			0
$937$	10.3496	+	10.3496i	0.338105	+	0.338105i	0.855654	−	0.517549i	$-0.173155\pi$
$937$	10.3496	+	10.3496i	0.338105	+	0.338105i	−0.517549	+	0.855654i	$0.673155\pi$
$938$		0			0
$939$	17.6320	−	7.30339i	0.575397	−	0.238337i
$940$		0			0
$941$	−19.5970	+	47.3114i	−0.638844	+	1.54231i	0.189376	+	0.981905i	$0.439353\pi$
$941$	−19.5970	+	47.3114i	−0.638844	+	1.54231i	−0.828221	+	0.560402i	$0.810647\pi$
$942$		0			0
$943$		−	7.15614i		−	0.233036i
$944$		0			0
$945$			0.0915089i			0.00297678i
$946$		0			0
$947$	9.51949	−	22.9821i	0.309342	−	0.746817i	−0.690385	−	0.723442i	$-0.742559\pi$
$947$	9.51949	−	22.9821i	0.309342	−	0.746817i	0.999727	−	0.0233749i	$-0.00744115\pi$
$948$		0			0
$949$	4.96322	−	2.05583i	0.161113	−	0.0667352i
$950$		0			0
$951$	−7.62993	−	7.62993i	−0.247417	−	0.247417i
$952$		0			0
$953$	−26.5521	+	26.5521i	−0.860106	+	0.860106i	−0.991350	−	0.131244i	$-0.958103\pi$
$953$	−26.5521	+	26.5521i	−0.860106	+	0.860106i	0.131244	+	0.991350i	$0.458103\pi$
$954$		0			0
$955$	3.00283	+	7.24947i	0.0971692	+	0.234587i
$956$		0			0
$957$	−12.2036	−	5.05488i	−0.394485	−	0.163401i
$958$		0			0
$959$	−2.82368			−0.0911813
$960$		0			0
$961$	73.1065			2.35827
$962$		0			0
$963$	−1.52273	−	0.630735i	−0.0490693	−	0.0203252i
$964$		0			0
$965$	0.593112	+	1.43190i	0.0190929	+	0.0460944i
$966$		0			0
$967$	17.5385	−	17.5385i	0.564001	−	0.564001i	−0.366440	−	0.930442i	$-0.619424\pi$
$967$	17.5385	−	17.5385i	0.564001	−	0.564001i	0.930442	+	0.366440i	$0.119424\pi$
$968$		0			0
$969$	4.84186	+	4.84186i	0.155543	+	0.155543i
$970$		0			0
$971$	26.0783	−	10.8020i	0.836894	−	0.346653i	0.0772656	−	0.997011i	$-0.475381\pi$
$971$	26.0783	−	10.8020i	0.836894	−	0.346653i	0.759628	+	0.650358i	$0.225381\pi$
$972$		0			0
$973$	−0.722295	+	1.74378i	−0.0231557	+	0.0559029i
$974$		0			0
$975$			2.95964i			0.0947844i
$976$		0			0
$977$		−	18.6808i		−	0.597651i	−0.954308	−	0.298825i	$-0.903405\pi$
$977$		−	18.6808i		−	0.597651i	0.954308	−	0.298825i	$-0.0965948\pi$
$978$		0			0
$979$	−23.8803	+	57.6522i	−0.763218	+	1.84257i
$980$		0			0
$981$	−13.6307	+	5.64602i	−0.435195	+	0.180264i
$982$		0			0
$983$	2.93163	+	2.93163i	0.0935046	+	0.0935046i	0.752312	−	0.658807i	$-0.228939\pi$
$983$	2.93163	+	2.93163i	0.0935046	+	0.0935046i	−0.658807	+	0.752312i	$0.728939\pi$
$984$		0			0
$985$	−7.81247	+	7.81247i	−0.248926	+	0.248926i
$986$		0			0
$987$	0.360061	+	0.869263i	0.0114609	+	0.0276689i
$988$		0			0
$989$	12.4380	+	5.15197i	0.395504	+	0.163823i
$990$		0			0
$991$	56.5710			1.79704			0.898519	−	0.438935i	$-0.144644\pi$
$991$	56.5710			1.79704			0.898519	+	0.438935i	$0.144644\pi$
$992$		0			0
$993$	−12.2352			−0.388271
$994$		0			0
$995$	4.46387	+	1.84900i	0.141514	+	0.0586171i
$996$		0			0
$997$	3.90402	+	9.42514i	0.123642	+	0.298497i	0.973565	−	0.228408i	$-0.0733522\pi$
$997$	3.90402	+	9.42514i	0.123642	+	0.298497i	−0.849924	+	0.526906i	$0.823352\pi$
$998$		0			0
$999$	5.64774	−	5.64774i	0.178687	−	0.178687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.n.a.337.6		32
3.2	odd	2		1152.2.v.c.721.4		32
4.3	odd	2		96.2.n.a.61.8	✓	32
8.3	odd	2		768.2.n.a.673.7		32
8.5	even	2		768.2.n.b.673.3		32
12.11	even	2		288.2.v.d.253.1		32
32.5	even	8		768.2.n.b.97.3		32
32.11	odd	8		96.2.n.a.85.8	yes	32
32.21	even	8	inner	384.2.n.a.49.6		32
32.27	odd	8		768.2.n.a.97.7		32
96.11	even	8		288.2.v.d.181.1		32
96.53	odd	8		1152.2.v.c.433.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.8	✓	32	4.3	odd	2
96.2.n.a.85.8	yes	32	32.11	odd	8
288.2.v.d.181.1		32	96.11	even	8
288.2.v.d.253.1		32	12.11	even	2
384.2.n.a.49.6		32	32.21	even	8	inner
384.2.n.a.337.6		32	1.1	even	1	trivial
768.2.n.a.97.7		32	32.27	odd	8
768.2.n.a.673.7		32	8.3	odd	2
768.2.n.b.97.3		32	32.5	even	8
768.2.n.b.673.3		32	8.5	even	2
1152.2.v.c.433.4		32	96.53	odd	8
1152.2.v.c.721.4		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{3} +(0.184062 + 0.444366i) q^{5} +(0.134531 - 0.134531i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.923880 + 0.382683i) q^{3} +(0.184062 + 0.444366i) q^{5} +(0.134531 - 0.134531i) q^{7} +(0.707107 + 0.707107i) q^{9} +(4.83050 - 2.00086i) q^{11} +(-0.237510 + 0.573400i) q^{13} +0.480978i q^{15} +5.70425i q^{17} +(0.459376 - 1.10903i) q^{19} +(0.175774 - 0.0728078i) q^{21} +(4.07921 + 4.07921i) q^{23} +(3.37195 - 3.37195i) q^{25} +(0.382683 + 0.923880i) q^{27} +(-2.33405 - 0.966793i) q^{29} -10.2033 q^{31} +5.22850 q^{33} +(0.0845432 + 0.0350189i) q^{35} +(-3.05654 - 7.37913i) q^{37} +(-0.438862 + 0.438862i) q^{39} +(-0.877147 - 0.877147i) q^{41} +(2.15605 - 0.893063i) q^{43} +(-0.184062 + 0.444366i) q^{45} +4.94536i q^{47} +6.96380i q^{49} +(-2.18292 + 5.27004i) q^{51} +(9.74330 - 4.03581i) q^{53} +(1.77823 + 1.77823i) q^{55} +(0.848817 - 0.848817i) q^{57} +(-4.73462 - 11.4304i) q^{59} +(-9.46851 - 3.92198i) q^{61} +0.190256 q^{63} -0.298516 q^{65} +(-4.79416 - 1.98581i) q^{67} +(2.20765 + 5.32975i) q^{69} +(-4.32992 + 4.32992i) q^{71} +(-6.12055 - 6.12055i) q^{73} +(4.40567 - 1.82489i) q^{75} +(0.380675 - 0.919031i) q^{77} -11.9773i q^{79} +1.00000i q^{81} +(-1.59989 + 3.86247i) q^{83} +(-2.53477 + 1.04994i) q^{85} +(-1.78640 - 1.78640i) q^{87} +(-8.43934 + 8.43934i) q^{89} +(0.0451877 + 0.109093i) q^{91} +(-9.42658 - 3.90462i) q^{93} +0.577370 q^{95} -9.21817 q^{97} +(4.83050 + 2.00086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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