LMFDB - Embedded newform 384.2.n.a.49.6

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			49.6
Character	$\chi$	$=$	384.49
Dual form			384.2.n.a.337.6

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

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	−0.877363	−	0.479827i	$-0.840699\pi$
$5$	0.184062	−	0.444366i	0.0823152	−	0.198726i	0.959678	+	0.281101i	$0.0906994\pi$
$6$		0			0
$7$	0.134531	+	0.134531i	0.0508480	+	0.0508480i	0.732074	−	0.681226i	$-0.238553\pi$
$7$	0.134531	+	0.134531i	0.0508480	+	0.0508480i	−0.681226	+	0.732074i	$0.738553\pi$
$8$		0			0
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$		0			0
$11$	4.83050	+	2.00086i	1.45645	+	0.603282i	0.963724	−	0.266902i	$-0.0860001\pi$
$11$	4.83050	+	2.00086i	1.45645	+	0.603282i	0.492727	+	0.870184i	$0.336000\pi$
$12$		0			0
$13$	−0.237510	−	0.573400i	−0.0658735	−	0.159033i	0.887515	−	0.460780i	$-0.152430\pi$
$13$	−0.237510	−	0.573400i	−0.0658735	−	0.159033i	−0.953388	+	0.301747i	$0.902430\pi$
$14$		0			0
$15$		−	0.480978i		−	0.124188i
$16$		0			0
$17$		−	5.70425i		−	1.38348i	−0.722145	−	0.691742i	$-0.756843\pi$
$17$		−	5.70425i		−	1.38348i	0.722145	−	0.691742i	$-0.243157\pi$
$18$		0			0
$19$	0.459376	+	1.10903i	0.105388	+	0.254430i	0.967773	−	0.251823i	$-0.0810302\pi$
$19$	0.459376	+	1.10903i	0.105388	+	0.254430i	−0.862385	+	0.506253i	$0.831030\pi$
$20$		0			0
$21$	0.175774	+	0.0728078i	0.0383569	+	0.0158880i
$22$		0			0
$23$	4.07921	−	4.07921i	0.850575	−	0.850575i	−0.139629	−	0.990204i	$-0.544591\pi$
$23$	4.07921	−	4.07921i	0.850575	−	0.850575i	0.990204	+	0.139629i	$0.0445910\pi$
$24$		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	−0.588717	−	0.808339i	$-0.700367\pi$
$29$	−2.33405	+	0.966793i	−0.433421	+	0.179529i	0.155296	+	0.987868i	$0.450367\pi$
$30$		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	0.445631	+	0.895217i	$0.352979\pi$
$37$	−3.05654	+	7.37913i	−0.502491	+	1.21312i	−0.948123	+	0.317905i	$0.897021\pi$
$38$		0			0
$39$	−0.438862	−	0.438862i	−0.0702741	−	0.0702741i
$40$		0			0
$41$	−0.877147	+	0.877147i	−0.136987	+	0.136987i	−0.772275	−	0.635288i	$-0.780881\pi$
$41$	−0.877147	+	0.877147i	−0.136987	+	0.136987i	0.635288	+	0.772275i	$0.280881\pi$
$42$		0			0
$43$	2.15605	+	0.893063i	0.328794	+	0.136191i	0.540973	−	0.841040i	$-0.318056\pi$
$43$	2.15605	+	0.893063i	0.328794	+	0.136191i	−0.212179	+	0.977231i	$0.568056\pi$
$44$		0			0
$45$	−0.184062	−	0.444366i	−0.0274384	−	0.0662421i
$46$		0			0
$47$		−	4.94536i		−	0.721355i	−0.932691	−	0.360677i	$-0.882546\pi$
$47$		−	4.94536i		−	0.721355i	0.932691	−	0.360677i	$-0.117454\pi$
$48$		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	0.933024	−	0.359814i	$-0.117160\pi$
$53$	9.74330	+	4.03581i	1.33834	+	0.554361i	0.405321	+	0.914175i	$0.367160\pi$
$54$		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	0.239466	+	0.970905i	$0.423028\pi$
$59$	−4.73462	+	11.4304i	−0.616395	+	1.48811i	−0.855861	+	0.517205i	$0.826972\pi$
$60$		0			0
$61$	−9.46851	+	3.92198i	−1.21232	+	0.502159i	−0.894960	−	0.446147i	$-0.852796\pi$
$61$	−9.46851	+	3.92198i	−1.21232	+	0.502159i	−0.317358	+	0.948306i	$0.602796\pi$
$62$		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	−0.655799	−	0.754935i	$-0.727668\pi$
$67$	−4.79416	+	1.98581i	−0.585700	+	0.242605i	0.0700997	+	0.997540i	$0.477668\pi$
$68$		0			0
$69$	2.20765	−	5.32975i	0.265770	−	0.641626i
$70$		0			0
$71$	−4.32992	−	4.32992i	−0.513867	−	0.513867i	0.401842	−	0.915709i	$-0.368370\pi$
$71$	−4.32992	−	4.32992i	−0.513867	−	0.513867i	−0.915709	+	0.401842i	$0.868370\pi$
$72$		0			0
$73$	−6.12055	+	6.12055i	−0.716356	+	0.716356i	−0.967857	−	0.251501i	$-0.919076\pi$
$73$	−6.12055	+	6.12055i	−0.716356	+	0.716356i	0.251501	+	0.967857i	$0.419076\pi$
$74$		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	$0.235330\pi$
$79$			11.9773i			1.34756i	−0.738934	+	0.673778i	$0.764670\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−1.59989	−	3.86247i	−0.175610	−	0.423961i	0.811426	−	0.584455i	$-0.198691\pi$
$83$	−1.59989	−	3.86247i	−0.175610	−	0.423961i	−0.987037	+	0.160493i	$0.948691\pi$
$84$		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	0.100381	−	0.994949i	$-0.467994\pi$
$89$	−8.43934	−	8.43934i	−0.894569	−	0.894569i	−0.994949	+	0.100381i	$0.967994\pi$
$90$		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	−0.847442	−	0.530888i	$-0.821859\pi$
$101$	1.27818	−	3.08581i	0.127184	−	0.307050i	0.974626	+	0.223838i	$0.0718586\pi$
$102$		0			0
$103$	7.17872	+	7.17872i	0.707340	+	0.707340i	0.965975	−	0.258635i	$-0.0832726\pi$
$103$	7.17872	+	7.17872i	0.707340	+	0.707340i	−0.258635	+	0.965975i	$0.583273\pi$
$104$		0			0
$105$	0.0647066	−	0.0647066i	0.00631471	−	0.00631471i
$106$		0			0
$107$	−1.52273	−	0.630735i	−0.147208	−	0.0609755i	0.307863	−	0.951431i	$-0.400386\pi$
$107$	−1.52273	−	0.630735i	−0.147208	−	0.0609755i	−0.455071	+	0.890455i	$0.650386\pi$
$108$		0			0
$109$	−5.64602	−	13.6307i	−0.540791	−	1.30558i	−0.924166	−	0.381992i	$-0.875238\pi$
$109$	−5.64602	−	13.6307i	−0.540791	−	1.30558i	0.383375	−	0.923593i	$-0.374762\pi$
$110$		0			0
$111$			7.98711i			0.758103i
$112$		0			0
$113$			4.48349i			0.421771i	0.977511	+	0.210886i	$0.0676348\pi$
$113$			4.48349i			0.421771i	−0.977511	+	0.210886i	$0.932365\pi$
$114$		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	−0.637952	−	0.770076i	$-0.720218\pi$
$131$	−6.23238	+	2.58153i	−0.544525	+	0.225550i	0.0934264	+	0.995626i	$0.470218\pi$
$132$		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	−0.995134	−	0.0985279i	$-0.968587\pi$
$137$	−10.4945	+	10.4945i	−0.896606	+	0.896606i	0.0985279	+	0.995134i	$0.468587\pi$
$138$		0			0
$139$	−9.16542	−	3.79644i	−0.777401	−	0.322010i	−0.0415348	−	0.999137i	$-0.513225\pi$
$139$	−9.16542	−	3.79644i	−0.777401	−	0.322010i	−0.735866	+	0.677127i	$0.763225\pi$
$140$		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	0.744303	−	0.667842i	$-0.232782\pi$
$149$	9.74535	+	4.03666i	0.798370	+	0.330696i	0.0540667	+	0.998537i	$0.482782\pi$
$150$		0			0
$151$	8.98745	−	8.98745i	0.731388	−	0.731388i	−0.239507	−	0.970895i	$-0.576986\pi$
$151$	8.98745	−	8.98745i	0.731388	−	0.731388i	0.970895	+	0.239507i	$0.0769857\pi$
$152$		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	0.665348	−	0.746533i	$-0.268283\pi$
$157$	20.8461	−	8.63473i	1.66370	−	0.689127i	0.998351	+	0.0574062i	$0.0182830\pi$
$158$		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	−0.0892930	−	0.996005i	$-0.528461\pi$
$163$	7.04554	−	2.91836i	0.551849	−	0.228584i	0.641142	+	0.767422i	$0.278461\pi$
$164$		0			0
$165$	0.962369	−	2.32336i	0.0749203	−	0.180874i
$166$		0			0
$167$	0.832153	+	0.832153i	0.0643940	+	0.0643940i	0.738570	−	0.674176i	$-0.235501\pi$
$167$	0.832153	+	0.832153i	0.0643940	+	0.0643940i	−0.674176	+	0.738570i	$0.735501\pi$
$168$		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	0.995903	+	0.0904237i	$0.0288221\pi$
$173$	4.67762	+	11.2928i	0.355633	+	0.858573i	−0.640271	+	0.768149i	$0.721178\pi$
$174$		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	−0.997444	−	0.0714579i	$-0.977235\pi$
$179$	−4.58465	−	11.0683i	−0.342673	−	0.827285i	0.654771	−	0.755828i	$-0.272765\pi$
$180$		0			0
$181$	4.59848	+	1.90475i	0.341802	+	0.141579i	0.546980	−	0.837146i	$-0.315777\pi$
$181$	4.59848	+	1.90475i	0.341802	+	0.141579i	−0.205178	+	0.978725i	$0.565777\pi$
$182$		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	−0.217880	−	0.975976i	$-0.569914\pi$
$197$	8.79059	−	21.2224i	0.626303	−	1.51203i	0.844183	−	0.536055i	$-0.180086\pi$
$198$		0			0
$199$	7.10324	+	7.10324i	0.503535	+	0.503535i	0.912535	−	0.409000i	$-0.134122\pi$
$199$	7.10324	+	7.10324i	0.503535	+	0.503535i	−0.409000	+	0.912535i	$0.634122\pi$
$200$		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	0.998946	+	0.0458984i	$0.0146151\pi$
$211$	4.72147	+	11.3986i	0.325040	+	0.784715i	−0.673906	+	0.738817i	$0.735385\pi$
$212$		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	−0.451619	−	0.892211i	$-0.649154\pi$
$227$	−2.11043	+	0.874170i	−0.140074	+	0.0580207i	0.311545	+	0.950231i	$0.399154\pi$
$228$		0			0
$229$	−3.24245	+	7.82798i	−0.214267	+	0.517287i	−0.994070	−	0.108738i	$-0.965319\pi$
$229$	−3.24245	+	7.82798i	−0.214267	+	0.517287i	0.779803	+	0.626025i	$0.215319\pi$
$230$		0			0
$231$	0.703396	+	0.703396i	0.0462801	+	0.0462801i
$232$		0			0
$233$	7.83849	−	7.83849i	0.513516	−	0.513516i	−0.402086	−	0.915602i	$-0.631715\pi$
$233$	7.83849	−	7.83849i	0.513516	−	0.513516i	0.915602	+	0.402086i	$0.131715\pi$
$234$		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	$0.0887179\pi$
$239$			8.50653i			0.550242i	−0.961410	+	0.275121i	$0.911282\pi$
$240$		0			0
$241$		−	10.3310i		−	0.665475i	−0.943019	−	0.332738i	$-0.892028\pi$
$241$		−	10.3310i		−	0.665475i	0.943019	−	0.332738i	$-0.107972\pi$
$242$		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	−0.911732	−	0.410785i	$-0.865255\pi$
$251$	0.371186	−	0.896122i	0.0234291	−	0.0565627i	0.935161	+	0.354223i	$0.115255\pi$
$252$		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	0.687501	−	0.726184i	$-0.258708\pi$
$263$	−0.627327	−	0.627327i	−0.0386827	−	0.0386827i	−0.726184	+	0.687501i	$0.758708\pi$
$264$		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	0.882156	−	0.470957i	$-0.156091\pi$
$269$	−1.22418	−	2.95542i	−0.0746393	−	0.180195i	−0.956795	+	0.290762i	$0.906091\pi$
$270$		0			0
$271$		−	26.7281i		−	1.62362i	−0.583925	−	0.811808i	$-0.698484\pi$
$271$		−	26.7281i		−	1.62362i	0.583925	−	0.811808i	$-0.301516\pi$
$272$		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	−0.584126	−	0.811663i	$-0.698563\pi$
$277$	−26.1483	−	10.8310i	−1.57110	−	0.650770i	−0.986972	+	0.160893i	$0.948563\pi$
$278$		0			0
$279$	−7.21479	+	7.21479i	−0.431938	+	0.431938i
$280$		0			0
$281$	−13.5386	−	13.5386i	−0.807646	−	0.807646i	0.176631	−	0.984277i	$-0.443480\pi$
$281$	−13.5386	−	13.5386i	−0.807646	−	0.807646i	−0.984277	+	0.176631i	$0.943480\pi$
$282$		0			0
$283$	4.00203	−	9.66174i	0.237896	−	0.574331i	−0.759169	−	0.650893i	$-0.774394\pi$
$283$	4.00203	−	9.66174i	0.237896	−	0.574331i	0.997065	+	0.0765624i	$0.0243944\pi$
$284$		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	0.173268	+	0.984875i	$0.444567\pi$
$293$	−11.0520	+	26.6818i	−0.645663	+	1.55877i	−0.818930	+	0.573893i	$0.805433\pi$
$294$		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	0.906757	+	0.421653i	$0.138550\pi$
$307$	9.87747	+	23.8463i	0.563737	+	1.36098i	−0.343020	+	0.939328i	$0.611450\pi$
$308$		0			0
$309$	9.37945	+	3.88510i	0.533578	+	0.221015i
$310$		0			0
$311$	−18.0382	+	18.0382i	−1.02285	+	1.02285i	−0.0231182	+	0.999733i	$0.507359\pi$
$311$	−18.0382	+	18.0382i	−1.02285	+	1.02285i	−0.999733	+	0.0231182i	$0.992641\pi$
$312$		0			0
$313$	13.4949	+	13.4949i	0.762778	+	0.762778i	0.976824	−	0.214046i	$-0.0686643\pi$
$313$	13.4949	+	13.4949i	0.762778	+	0.762778i	−0.214046	+	0.976824i	$0.568664\pi$
$314$		0			0
$315$	0.0350189	−	0.0845432i	0.00197309	−	0.00476347i
$316$		0			0
$317$	−9.96898	+	4.12929i	−0.559914	+	0.231924i	−0.644648	−	0.764480i	$-0.722996\pi$
$317$	−9.96898	+	4.12929i	−0.559914	+	0.231924i	0.0847339	+	0.996404i	$0.472996\pi$
$318$		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	0.0497433	−	0.998762i	$-0.484160\pi$
$331$	−11.3038	−	4.68220i	−0.621314	−	0.257357i	−0.671058	+	0.741405i	$0.734160\pi$
$332$		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	$0.0125803\pi$
$337$			1.45068i			0.0790237i	−0.999219	+	0.0395118i	$0.987420\pi$
$338$		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	−0.737026	−	0.675865i	$-0.763770\pi$
$347$	4.88124	−	11.7844i	0.262039	−	0.632618i	0.999064	+	0.0432472i	$0.0137703\pi$
$348$		0			0
$349$	−7.72369	+	3.19926i	−0.413440	+	0.171252i	−0.579701	−	0.814829i	$-0.696831\pi$
$349$	−7.72369	+	3.19926i	−0.413440	+	0.171252i	0.166261	+	0.986082i	$0.446831\pi$
$350$		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	0.577189	−	0.816611i	$-0.304150\pi$
$359$	−4.53639	−	4.53639i	−0.239422	−	0.239422i	−0.816611	+	0.577189i	$0.804150\pi$
$360$		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	$0.0600106\pi$
$367$			7.18068i			0.374828i	−0.982281	+	0.187414i	$0.939989\pi$
$368$		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	0.721881	−	0.692017i	$-0.243278\pi$
$373$	14.3497	+	5.94383i	0.742998	+	0.307760i	0.0211168	+	0.999777i	$0.493278\pi$
$374$		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	−0.987394	−	0.158281i	$-0.949405\pi$
$379$	−3.45126	+	8.33209i	−0.177280	+	0.427991i	0.810115	+	0.586272i	$0.199405\pi$
$380$		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	−0.858495	−	0.512823i	$-0.828600\pi$
$389$	2.19268	−	5.29359i	0.111173	−	0.268396i	0.969668	+	0.244427i	$0.0785998\pi$
$390$		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	0.999174	−	0.0406449i	$-0.0129412\pi$
$397$	5.25839	+	12.6949i	0.263911	+	0.637137i	−0.735263	+	0.677782i	$0.762941\pi$
$398$		0			0
$399$			0.228385i			0.0114335i
$400$		0			0
$401$			22.6945i			1.13331i	0.823955	+	0.566655i	$0.191763\pi$
$401$			22.6945i			1.13331i	−0.823955	+	0.566655i	$0.808237\pi$
$402$		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	0.0626139	−	0.998038i	$-0.480056\pi$
$409$	−18.9178	−	18.9178i	−0.935424	−	0.935424i	−0.998038	+	0.0626139i	$0.980056\pi$
$410$		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	0.190082	−	0.981768i	$-0.439125\pi$
$419$	20.8524	−	8.63734i	1.01871	−	0.421962i	0.828623	+	0.559807i	$0.189125\pi$
$420$		0			0
$421$	−14.3106	+	34.5489i	−0.697456	+	1.68381i	0.0317327	+	0.999496i	$0.489897\pi$
$421$	−14.3106	+	34.5489i	−0.697456	+	1.68381i	−0.729189	+	0.684312i	$0.760103\pi$
$422$		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	$-0.623072\pi$
$431$		−	38.4560i		−	1.85236i	0.377080	−	0.926181i	$-0.376928\pi$
$432$		0			0
$433$			8.55433i			0.411095i	0.978647	+	0.205547i	$0.0658975\pi$
$433$			8.55433i			0.411095i	−0.978647	+	0.205547i	$0.934102\pi$
$434$		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	−0.818978	−	0.573825i	$-0.805459\pi$
$439$	−5.13653	+	5.13653i	−0.245153	+	0.245153i	0.573825	+	0.818978i	$0.305459\pi$
$440$		0			0
$441$	−4.92415	−	4.92415i	−0.234483	−	0.234483i
$442$		0			0
$443$	−2.45339	+	5.92301i	−0.116564	+	0.281411i	−0.971384	−	0.237514i	$-0.923667\pi$
$443$	−2.45339	+	5.92301i	−0.116564	+	0.281411i	0.854820	+	0.518925i	$0.173667\pi$
$444$		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	−0.733831	−	0.679332i	$-0.762270\pi$
$457$	−1.16506	+	1.16506i	−0.0544992	+	0.0544992i	0.679332	+	0.733831i	$0.262270\pi$
$458$		0			0
$459$	−5.27004	−	2.18292i	−0.245984	−	0.101890i
$460$		0			0
$461$	1.61683	+	3.90337i	0.0753032	+	0.181798i	0.957049	−	0.289928i	$-0.0936313\pi$
$461$	1.61683	+	3.90337i	0.0753032	+	0.181798i	−0.881745	+	0.471726i	$0.843631\pi$
$462$		0			0
$463$		−	3.11687i		−	0.144853i	−0.997374	−	0.0724267i	$-0.976926\pi$
$463$		−	3.11687i		−	0.144853i	0.997374	−	0.0724267i	$-0.0230743\pi$
$464$		0			0
$465$			4.90754i			0.227582i
$466$		0			0
$467$	−7.59921	−	18.3461i	−0.351649	−	0.848957i	−0.996417	−	0.0845781i	$-0.973046\pi$
$467$	−7.59921	−	18.3461i	−0.351649	−	0.848957i	0.644767	−	0.764379i	$-0.276954\pi$
$468$		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	0.377964	−	0.925820i	$-0.376624\pi$
$487$	−12.0901	−	12.0901i	−0.547856	−	0.547856i	−0.925820	+	0.377964i	$0.876624\pi$
$488$		0			0
$489$	5.39242	−	5.39242i	0.243854	−	0.243854i
$490$		0			0
$491$	−20.2368	−	8.38236i	−0.913274	−	0.378290i	−0.123965	−	0.992287i	$-0.539561\pi$
$491$	−20.2368	−	8.38236i	−0.913274	−	0.378290i	−0.789309	+	0.613996i	$0.789561\pi$
$492$		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	0.979921	−	0.199385i	$-0.0638945\pi$
$499$	3.26197	+	7.87508i	0.146026	+	0.352537i	−0.833896	+	0.551922i	$0.813894\pi$
$500$		0			0
$501$	1.08726	+	0.450358i	0.0485752	+	0.0201205i
$502$		0			0
$503$	12.2760	−	12.2760i	0.547362	−	0.547362i	−0.378315	−	0.925677i	$-0.623496\pi$
$503$	12.2760	−	12.2760i	0.547362	−	0.547362i	0.925677	+	0.378315i	$0.123496\pi$
$504$		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	−0.401287	−	0.915952i	$-0.631437\pi$
$509$	−0.842977	+	0.349172i	−0.0373643	+	0.0154768i	0.363923	+	0.931429i	$0.381437\pi$
$510$		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	−0.592142	−	0.805834i	$-0.701717\pi$
$521$	4.87761	−	4.87761i	0.213692	−	0.213692i	0.805834	+	0.592142i	$0.201717\pi$
$522$		0			0
$523$	20.5648	+	8.51821i	0.899235	+	0.372475i	0.783926	−	0.620854i	$-0.213214\pi$
$523$	20.5648	+	8.51821i	0.899235	+	0.372475i	0.115309	+	0.993330i	$0.463214\pi$
$524$		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	−0.562191	−	0.827008i	$-0.690041\pi$
$541$	−8.72081	+	3.61228i	−0.374937	+	0.155304i	0.187254	+	0.982312i	$0.440041\pi$
$542$		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	−0.456451	−	0.889748i	$-0.650880\pi$
$547$	−3.50970	+	1.45377i	−0.150064	+	0.0621586i	0.306387	+	0.951907i	$0.400880\pi$
$548$		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	−0.965153	−	0.261687i	$-0.915721\pi$
$557$	−11.0388	−	26.6499i	−0.467727	−	1.12919i	0.497425	−	0.867507i	$-0.334279\pi$
$558$		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	0.934053	−	0.357134i	$-0.116246\pi$
$563$	0.499373	+	1.20559i	0.0210461	+	0.0508097i	−0.913007	+	0.407944i	$0.866246\pi$
$564$		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	0.999340	+	0.0363184i	$0.0115631\pi$
$569$	24.7043	+	24.7043i	1.03566	+	1.03566i	0.0363184	+	0.999340i	$0.488437\pi$
$570$		0			0
$571$	−12.4201	+	29.9848i	−0.519765	+	1.25482i	0.418282	+	0.908317i	$0.362632\pi$
$571$	−12.4201	+	29.9848i	−0.519765	+	1.25482i	−0.938047	+	0.346507i	$0.887368\pi$
$572$		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	0.931856	−	0.362828i	$-0.118189\pi$
$587$	32.3256	+	13.3897i	1.33422	+	0.552652i	0.402363	+	0.915480i	$0.368189\pi$
$588$		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	$-0.821862\pi$
$593$		−	25.8554i		−	1.06176i	0.847448	−	0.530878i	$-0.178138\pi$
$594$		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	0.129914	−	0.991525i	$-0.458530\pi$
$599$	27.4466	−	27.4466i	1.12144	−	1.12144i	0.991525	−	0.129914i	$-0.0414701\pi$
$600$		0			0
$601$	−17.2120	−	17.2120i	−0.702091	−	0.702091i	0.262768	−	0.964859i	$-0.415365\pi$
$601$	−17.2120	−	17.2120i	−0.702091	−	0.702091i	−0.964859	+	0.262768i	$0.915365\pi$
$602$		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	−0.708833	−	0.705376i	$-0.750778\pi$
$613$	7.20887	−	17.4038i	0.291164	−	0.702931i	0.999997	+	0.00244484i	$0.000778219\pi$
$614$		0			0
$615$	0.421889	+	0.421889i	0.0170122	+	0.0170122i
$616$		0			0
$617$	12.8299	−	12.8299i	0.516511	−	0.516511i	−0.400003	−	0.916514i	$-0.630991\pi$
$617$	12.8299	−	12.8299i	0.516511	−	0.516511i	0.916514	+	0.400003i	$0.130991\pi$
$618$		0			0
$619$	−12.1156	−	5.01844i	−0.486966	−	0.201708i	0.125671	−	0.992072i	$-0.459892\pi$
$619$	−12.1156	−	5.01844i	−0.486966	−	0.201708i	−0.612638	+	0.790364i	$0.709892\pi$
$620$		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	−0.479489	−	0.877548i	$-0.659178\pi$
$631$	9.99914	−	9.99914i	0.398059	−	0.398059i	0.877548	+	0.479489i	$0.159178\pi$
$632$		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	−0.266077	−	0.963952i	$-0.585728\pi$
$643$	5.76614	−	2.38841i	0.227394	−	0.0941898i	0.493472	+	0.869762i	$0.335728\pi$
$644$		0			0
$645$	0.429544	−	1.03701i	0.0169133	−	0.0408322i
$646$		0			0
$647$	0.783090	+	0.783090i	0.0307864	+	0.0307864i	0.722332	−	0.691546i	$-0.243070\pi$
$647$	0.783090	+	0.783090i	0.0307864	+	0.0307864i	−0.691546	+	0.722332i	$0.743070\pi$
$648$		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	0.839300	−	0.543669i	$-0.182965\pi$
$653$	−3.54194	−	8.55101i	−0.138607	−	0.334627i	−0.977907	+	0.209042i	$0.932965\pi$
$654$		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	−0.745673	−	0.666313i	$-0.767872\pi$
$659$	−17.7016	−	42.7355i	−0.689557	−	1.66474i	0.0561160	−	0.998424i	$-0.482128\pi$
$660$		0			0
$661$	−0.187232	−	0.0775542i	−0.00728249	−	0.00301651i	0.379039	−	0.925381i	$-0.376255\pi$
$661$	−0.187232	−	0.0775542i	−0.00728249	−	0.00301651i	−0.386322	+	0.922364i	$0.626255\pi$
$662$		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	−0.563661	−	0.826006i	$-0.690607\pi$
$677$	10.9016	−	26.3188i	0.418982	−	1.01151i	0.982643	−	0.185506i	$-0.0593925\pi$
$678$		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	0.0379356	−	0.999280i	$-0.487922\pi$
$683$	−16.7740	−	6.94800i	−0.641838	−	0.265858i	−0.679773	+	0.733422i	$0.737922\pi$
$684$		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	−0.788407	−	0.615154i	$-0.789094\pi$
$691$	−17.5044	−	42.2593i	−0.665898	−	1.60762i	0.122509	−	0.992467i	$-0.460906\pi$
$692$		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	−0.559414	−	0.828888i	$-0.688974\pi$
$701$	−9.76630	+	4.04533i	−0.368868	+	0.152790i	0.190547	+	0.981678i	$0.438974\pi$
$702$		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	−0.960229	−	0.279213i	$-0.909926\pi$
$709$	−2.23164	+	5.38765i	−0.0838109	+	0.202337i	0.876418	+	0.481551i	$0.159926\pi$
$710$		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	$0.0768293\pi$
$719$			12.8188i			0.478059i	−0.971012	+	0.239030i	$0.923171\pi$
$720$		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	−0.986235	−	0.165347i	$-0.947126\pi$
$727$	−22.1336	+	22.1336i	−0.820889	+	0.820889i	0.165347	+	0.986235i	$0.447126\pi$
$728$		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	−0.685535	−	0.728040i	$-0.740432\pi$
$733$	−17.7464	+	7.35081i	−0.655479	+	0.271508i	0.0300555	+	0.999548i	$0.490432\pi$
$734$		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	−0.725324	−	0.688408i	$-0.758310\pi$
$739$	−20.4272	+	8.46123i	−0.751428	+	0.311251i	−0.0261037	+	0.999659i	$0.508310\pi$
$740$		0			0
$741$	0.285109	−	0.688315i	0.0104738	−	0.0252859i
$742$		0			0
$743$	26.6427	+	26.6427i	0.977427	+	0.977427i	0.999751	−	0.0223237i	$-0.00710644\pi$
$743$	26.6427	+	26.6427i	0.977427	+	0.977427i	−0.0223237	+	0.999751i	$0.507106\pi$
$744$		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	$0.141043\pi$
$751$			23.4989i			0.857486i	−0.903427	+	0.428743i	$0.858957\pi$
$752$		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	0.962513	−	0.271234i	$-0.0874317\pi$
$757$	39.9311	+	16.5400i	1.45132	+	0.601157i	0.488809	+	0.872391i	$0.337432\pi$
$758$		0			0
$759$	21.3282	−	21.3282i	0.774163	−	0.774163i
$760$		0			0
$761$	33.7925	+	33.7925i	1.22498	+	1.22498i	0.965841	+	0.259134i	$0.0834372\pi$
$761$	33.7925	+	33.7925i	1.22498	+	1.22498i	0.259134	+	0.965841i	$0.416563\pi$
$762$		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	−0.820380	−	0.571818i	$-0.806238\pi$
$773$	4.56113	−	11.0116i	0.164053	−	0.396058i	0.984433	+	0.175760i	$0.0562383\pi$
$774$		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	−0.941456	−	0.337135i	$-0.890542\pi$
$787$	−14.4233	−	34.8210i	−0.514137	−	1.24124i	0.427320	−	0.904101i	$-0.359458\pi$
$788$		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	−0.283684	−	0.958918i	$-0.591557\pi$
$797$	5.47061	−	2.26600i	0.193779	−	0.0802659i	0.477463	+	0.878652i	$0.341557\pi$
$798$		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	−0.970405	−	0.241485i	$-0.922366\pi$
$809$	−20.7326	+	20.7326i	−0.728920	+	0.728920i	0.241485	+	0.970405i	$0.422366\pi$
$810$		0			0
$811$	37.2071	+	15.4117i	1.30652	+	0.541177i	0.923866	−	0.382716i	$-0.125011\pi$
$811$	37.2071	+	15.4117i	1.30652	+	0.541177i	0.382651	+	0.923893i	$0.375011\pi$
$812$		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	−0.190067	−	0.981771i	$-0.560870\pi$
$821$	−29.1884	−	12.0902i	−1.01868	−	0.421952i	−0.828615	+	0.559820i	$0.810870\pi$
$822$		0			0
$823$	3.31937	−	3.31937i	0.115706	−	0.115706i	−0.646883	−	0.762589i	$-0.723928\pi$
$823$	3.31937	−	3.31937i	0.115706	−	0.115706i	0.762589	+	0.646883i	$0.223928\pi$
$824$		0			0
$825$	17.6302	+	17.6302i	0.613806	+	0.613806i
$826$		0			0
$827$	−2.47114	+	5.96586i	−0.0859300	+	0.207453i	−0.961003	−	0.276537i	$-0.910813\pi$
$827$	−2.47114	+	5.96586i	−0.0859300	+	0.207453i	0.875073	+	0.483991i	$0.160813\pi$
$828$		0			0
$829$	−0.339967	+	0.140819i	−0.0118075	+	0.00489085i	−0.388579	−	0.921415i	$-0.627034\pi$
$829$	−0.339967	+	0.140819i	−0.0118075	+	0.00489085i	0.376772	+	0.926306i	$0.377034\pi$
$830$		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	0.988969	+	0.148122i	$0.0473227\pi$
$839$	32.9364	+	32.9364i	1.13709	+	1.13709i	0.148122	+	0.988969i	$0.452677\pi$
$840$		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	0.424033	−	0.905647i	$-0.360614\pi$
$853$	2.43815	+	1.00992i	0.0834808	+	0.0345789i	−0.340552	+	0.940226i	$0.610614\pi$
$854$		0			0
$855$	0.408262	−	0.408262i	0.0139623	−	0.0139623i
$856$		0			0
$857$	−31.8225	−	31.8225i	−1.08704	−	1.08704i	−0.995832	−	0.0912053i	$-0.970928\pi$
$857$	−31.8225	−	31.8225i	−1.08704	−	1.08704i	−0.0912053	−	0.995832i	$-0.529072\pi$
$858$		0			0
$859$	−11.6288	+	28.0745i	−0.396771	+	0.957890i	0.591656	+	0.806191i	$0.298474\pi$
$859$	−11.6288	+	28.0745i	−0.396771	+	0.957890i	−0.988427	+	0.151699i	$0.951526\pi$
$860$		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	0.922983	+	0.384842i	$0.125744\pi$
$877$	16.0645	+	38.7831i	0.542459	+	1.30961i	−0.380523	+	0.924771i	$0.624256\pi$
$878$		0			0
$879$			28.8802i			0.974104i
$880$		0			0
$881$		−	21.4254i		−	0.721841i	−0.932597	−	0.360921i	$-0.882463\pi$
$881$		−	21.4254i		−	0.721841i	0.932597	−	0.360921i	$-0.117537\pi$
$882$		0			0
$883$	−2.94264	−	7.10415i	−0.0990276	−	0.239074i	0.866600	−	0.499004i	$-0.166301\pi$
$883$	−2.94264	−	7.10415i	−0.0990276	−	0.239074i	−0.965627	+	0.259930i	$0.916301\pi$
$884$		0			0
$885$	5.49777	+	2.27725i	0.184805	+	0.0765489i
$886$		0			0
$887$	30.7269	−	30.7269i	1.03171	−	1.03171i	0.0322295	−	0.999480i	$-0.489739\pi$
$887$	30.7269	−	30.7269i	1.03171	−	1.03171i	0.999480	−	0.0322295i	$-0.0102607\pi$
$888$		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	−0.236142	−	0.971718i	$-0.575883\pi$
$907$	−32.8338	−	13.6002i	−1.09023	−	0.451588i	−0.854087	+	0.520131i	$0.825883\pi$
$908$		0			0
$909$	−1.27818	−	3.08581i	−0.0423947	−	0.102350i
$910$		0			0
$911$		−	15.3896i		−	0.509879i	−0.966957	−	0.254940i	$-0.917944\pi$
$911$		−	15.3896i		−	0.509879i	0.966957	−	0.254940i	$-0.0820556\pi$
$912$		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	−0.733109	−	0.680111i	$-0.761932\pi$
$919$	−1.60663	+	1.60663i	−0.0529979	+	0.0529979i	0.680111	+	0.733109i	$0.261932\pi$
$920$		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	−0.517549	−	0.855654i	$-0.673155\pi$
$937$	10.3496	−	10.3496i	0.338105	−	0.338105i	0.855654	+	0.517549i	$0.173155\pi$
$938$		0			0
$939$	17.6320	+	7.30339i	0.575397	+	0.238337i
$940$		0			0
$941$	−19.5970	−	47.3114i	−0.638844	−	1.54231i	−0.828221	−	0.560402i	$-0.810647\pi$
$941$	−19.5970	−	47.3114i	−0.638844	−	1.54231i	0.189376	−	0.981905i	$-0.439353\pi$
$942$		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	0.999727	+	0.0233749i	$0.00744115\pi$
$947$	9.51949	+	22.9821i	0.309342	+	0.746817i	−0.690385	+	0.723442i	$0.742559\pi$
$948$		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	0.131244	−	0.991350i	$-0.458103\pi$
$953$	−26.5521	−	26.5521i	−0.860106	−	0.860106i	−0.991350	+	0.131244i	$0.958103\pi$
$954$		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	0.930442	−	0.366440i	$-0.119424\pi$
$967$	17.5385	+	17.5385i	0.564001	+	0.564001i	−0.366440	+	0.930442i	$0.619424\pi$
$968$		0			0
$969$	4.84186	−	4.84186i	0.155543	−	0.155543i
$970$		0			0
$971$	26.0783	+	10.8020i	0.836894	+	0.346653i	0.759628	−	0.650358i	$-0.225381\pi$
$971$	26.0783	+	10.8020i	0.836894	+	0.346653i	0.0772656	+	0.997011i	$0.475381\pi$
$972$		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	$0.0965948\pi$
$977$			18.6808i			0.597651i	−0.954308	+	0.298825i	$0.903405\pi$
$978$		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	−0.658807	−	0.752312i	$-0.728939\pi$
$983$	2.93163	−	2.93163i	0.0935046	−	0.0935046i	0.752312	+	0.658807i	$0.228939\pi$
$984$		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	−0.849924	−	0.526906i	$-0.823352\pi$
$997$	3.90402	−	9.42514i	0.123642	−	0.298497i	0.973565	+	0.228408i	$0.0733522\pi$
$998$		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.49.6		32
3.2	odd	2		1152.2.v.c.433.4		32
4.3	odd	2		96.2.n.a.85.8	yes	32
8.3	odd	2		768.2.n.a.97.7		32
8.5	even	2		768.2.n.b.97.3		32
12.11	even	2		288.2.v.d.181.1		32
32.3	odd	8		96.2.n.a.61.8	✓	32
32.13	even	8		768.2.n.b.673.3		32
32.19	odd	8		768.2.n.a.673.7		32
32.29	even	8	inner	384.2.n.a.337.6		32
96.29	odd	8		1152.2.v.c.721.4		32
96.35	even	8		288.2.v.d.253.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.8	✓	32	32.3	odd	8
96.2.n.a.85.8	yes	32	4.3	odd	2
288.2.v.d.181.1		32	12.11	even	2
288.2.v.d.253.1		32	96.35	even	8
384.2.n.a.49.6		32	1.1	even	1	trivial
384.2.n.a.337.6		32	32.29	even	8	inner
768.2.n.a.97.7		32	8.3	odd	2
768.2.n.a.673.7		32	32.19	odd	8
768.2.n.b.97.3		32	8.5	even	2
768.2.n.b.673.3		32	32.13	even	8
1152.2.v.c.433.4		32	3.2	odd	2
1152.2.v.c.721.4		32	96.29	odd	8

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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