LMFDB - Embedded newform 384.2.n.a.337.4

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			337.4
Character	$\chi$	$=$	384.337
Dual form			384.2.n.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{3} +(0.750897 + 1.81283i) q^{5} +(-0.638460 + 0.638460i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.923880 - 0.382683i) q^{3} +(0.750897 + 1.81283i) q^{5} +(-0.638460 + 0.638460i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.343096 - 0.142115i) q^{11} +(-1.56981 + 3.78987i) q^{13} -1.96219i q^{15} -1.52272i q^{17} +(-3.15404 + 7.61453i) q^{19} +(0.834188 - 0.345532i) q^{21} +(6.00496 + 6.00496i) q^{23} +(0.813044 - 0.813044i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(-0.647232 - 0.268092i) q^{29} +3.66460 q^{31} -0.371365 q^{33} +(-1.63683 - 0.677999i) q^{35} +(3.69013 + 8.90877i) q^{37} +(2.90064 - 2.90064i) q^{39} +(-8.19959 - 8.19959i) q^{41} +(1.86276 - 0.771580i) q^{43} +(-0.750897 + 1.81283i) q^{45} -3.21602i q^{47} +6.18474i q^{49} +(-0.582718 + 1.40681i) q^{51} +(7.71461 - 3.19550i) q^{53} +(0.515260 + 0.515260i) q^{55} +(5.82791 - 5.82791i) q^{57} +(-2.78703 - 6.72848i) q^{59} +(-10.4842 - 4.34269i) q^{61} -0.902919 q^{63} -8.04913 q^{65} +(-6.56831 - 2.72068i) q^{67} +(-3.24986 - 7.84586i) q^{69} +(-0.957148 + 0.957148i) q^{71} +(-2.14406 - 2.14406i) q^{73} +(-1.06229 + 0.440016i) q^{75} +(-0.128318 + 0.309788i) q^{77} -0.628155i q^{79} +1.00000i q^{81} +(4.17789 - 10.0863i) q^{83} +(2.76042 - 1.14340i) q^{85} +(0.495370 + 0.495370i) q^{87} +(8.70474 - 8.70474i) q^{89} +(-1.41741 - 3.42194i) q^{91} +(-3.38565 - 1.40238i) q^{93} -16.1722 q^{95} +10.2387 q^{97} +(0.343096 + 0.142115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.750897	+	1.81283i	0.335811	+	0.810720i	0.998108	+	0.0614789i	$0.0195817\pi$
$5$	0.750897	+	1.81283i	0.335811	+	0.810720i	−0.662297	+	0.749241i	$0.730418\pi$
$6$		0			0
$7$	−0.638460	+	0.638460i	−0.241315	+	0.241315i	−0.817394	−	0.576079i	$-0.804582\pi$
$7$	−0.638460	+	0.638460i	−0.241315	+	0.241315i	0.576079	+	0.817394i	$0.304582\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	0.343096	−	0.142115i	0.103447	−	0.0428493i	−0.330360	−	0.943855i	$-0.607170\pi$
$11$	0.343096	−	0.142115i	0.103447	−	0.0428493i	0.433807	+	0.901006i	$0.357170\pi$
$12$		0			0
$13$	−1.56981	+	3.78987i	−0.435388	+	1.05112i	0.542135	+	0.840291i	$0.317616\pi$
$13$	−1.56981	+	3.78987i	−0.435388	+	1.05112i	−0.977523	+	0.210828i	$0.932384\pi$
$14$		0			0
$15$		−	1.96219i		−	0.506635i
$16$		0			0
$17$		−	1.52272i		−	0.369313i	−0.982803	−	0.184656i	$-0.940883\pi$
$17$		−	1.52272i		−	0.369313i	0.982803	−	0.184656i	$-0.0591172\pi$
$18$		0			0
$19$	−3.15404	+	7.61453i	−0.723587	+	1.74689i	−0.0607223	+	0.998155i	$0.519340\pi$
$19$	−3.15404	+	7.61453i	−0.723587	+	1.74689i	−0.662865	+	0.748739i	$0.730660\pi$
$20$		0			0
$21$	0.834188	−	0.345532i	0.182035	−	0.0754013i
$22$		0			0
$23$	6.00496	+	6.00496i	1.25212	+	1.25212i	0.954767	+	0.297355i	$0.0961043\pi$
$23$	6.00496	+	6.00496i	1.25212	+	1.25212i	0.297355	+	0.954767i	$0.403896\pi$
$24$		0			0
$25$	0.813044	−	0.813044i	0.162609	−	0.162609i
$26$		0			0
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$		0			0
$29$	−0.647232	−	0.268092i	−0.120188	−	0.0497835i	0.321779	−	0.946815i	$-0.395719\pi$
$29$	−0.647232	−	0.268092i	−0.120188	−	0.0497835i	−0.441967	+	0.897031i	$0.645719\pi$
$30$		0			0
$31$	3.66460			0.658181			0.329091	−	0.944298i	$-0.393258\pi$
$31$	3.66460			0.658181			0.329091	+	0.944298i	$0.393258\pi$
$32$		0			0
$33$	−0.371365			−0.0646463
$34$		0			0
$35$	−1.63683	−	0.677999i	−0.276676	−	0.114603i
$36$		0			0
$37$	3.69013	+	8.90877i	0.606654	+	1.46459i	0.866617	+	0.498974i	$0.166290\pi$
$37$	3.69013	+	8.90877i	0.606654	+	1.46459i	−0.259963	+	0.965619i	$0.583710\pi$
$38$		0			0
$39$	2.90064	−	2.90064i	0.464474	−	0.464474i
$40$		0			0
$41$	−8.19959	−	8.19959i	−1.28056	−	1.28056i	−0.940349	−	0.340211i	$-0.889501\pi$
$41$	−8.19959	−	8.19959i	−1.28056	−	1.28056i	−0.340211	−	0.940349i	$-0.610499\pi$
$42$		0			0
$43$	1.86276	−	0.771580i	0.284068	−	0.117665i	−0.236100	−	0.971729i	$-0.575869\pi$
$43$	1.86276	−	0.771580i	0.284068	−	0.117665i	0.520168	+	0.854064i	$0.325869\pi$
$44$		0			0
$45$	−0.750897	+	1.81283i	−0.111937	+	0.270240i
$46$		0			0
$47$		−	3.21602i		−	0.469105i	−0.972103	−	0.234552i	$-0.924638\pi$
$47$		−	3.21602i		−	0.469105i	0.972103	−	0.234552i	$-0.0753624\pi$
$48$		0			0
$49$			6.18474i			0.883534i
$50$		0			0
$51$	−0.582718	+	1.40681i	−0.0815969	+	0.196992i
$52$		0			0
$53$	7.71461	−	3.19550i	1.05968	−	0.438935i	0.216344	−	0.976317i	$-0.430587\pi$
$53$	7.71461	−	3.19550i	1.05968	−	0.438935i	0.843339	+	0.537382i	$0.180587\pi$
$54$		0			0
$55$	0.515260	+	0.515260i	0.0694776	+	0.0694776i
$56$		0			0
$57$	5.82791	−	5.82791i	0.771926	−	0.771926i
$58$		0			0
$59$	−2.78703	−	6.72848i	−0.362840	−	0.875973i	−0.994882	−	0.101039i	$-0.967783\pi$
$59$	−2.78703	−	6.72848i	−0.362840	−	0.875973i	0.632042	−	0.774934i	$-0.282217\pi$
$60$		0			0
$61$	−10.4842	−	4.34269i	−1.34236	−	0.556024i	−0.408205	−	0.912890i	$-0.633845\pi$
$61$	−10.4842	−	4.34269i	−1.34236	−	0.556024i	−0.934155	+	0.356866i	$0.883845\pi$
$62$		0			0
$63$	−0.902919			−0.113757
$64$		0			0
$65$	−8.04913			−0.998372
$66$		0			0
$67$	−6.56831	−	2.72068i	−0.802447	−	0.332384i	−0.0565107	−	0.998402i	$-0.517997\pi$
$67$	−6.56831	−	2.72068i	−0.802447	−	0.332384i	−0.745936	+	0.666018i	$0.767997\pi$
$68$		0			0
$69$	−3.24986	−	7.84586i	−0.391238	−	0.944531i
$70$		0			0
$71$	−0.957148	+	0.957148i	−0.113593	+	0.113593i	−0.761618	−	0.648026i	$-0.775595\pi$
$71$	−0.957148	+	0.957148i	−0.113593	+	0.113593i	0.648026	+	0.761618i	$0.275595\pi$
$72$		0			0
$73$	−2.14406	−	2.14406i	−0.250944	−	0.250944i	0.570414	−	0.821357i	$-0.306783\pi$
$73$	−2.14406	−	2.14406i	−0.250944	−	0.250944i	−0.821357	+	0.570414i	$0.806783\pi$
$74$		0			0
$75$	−1.06229	+	0.440016i	−0.122663	+	0.0508087i
$76$		0			0
$77$	−0.128318	+	0.309788i	−0.0146232	+	0.0353036i
$78$		0			0
$79$		−	0.628155i		−	0.0706729i	−0.999375	−	0.0353365i	$-0.988750\pi$
$79$		−	0.628155i		−	0.0706729i	0.999375	−	0.0353365i	$-0.0112503\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	4.17789	−	10.0863i	0.458583	−	1.10712i	−0.510388	−	0.859944i	$-0.670498\pi$
$83$	4.17789	−	10.0863i	0.458583	−	1.10712i	0.968971	−	0.247174i	$-0.0795018\pi$
$84$		0			0
$85$	2.76042	−	1.14340i	0.299409	−	0.124019i
$86$		0			0
$87$	0.495370	+	0.495370i	0.0531092	+	0.0531092i
$88$		0			0
$89$	8.70474	−	8.70474i	0.922701	−	0.922701i	−0.0745189	−	0.997220i	$-0.523742\pi$
$89$	8.70474	−	8.70474i	0.922701	−	0.922701i	0.997220	+	0.0745189i	$0.0237421\pi$
$90$		0			0
$91$	−1.41741	−	3.42194i	−0.148585	−	0.358717i
$92$		0			0
$93$	−3.38565	−	1.40238i	−0.351075	−	0.145420i
$94$		0			0
$95$	−16.1722			−1.65923
$96$		0			0
$97$	10.2387			1.03959			0.519793	−	0.854292i	$-0.326009\pi$
$97$	10.2387			1.03959			0.519793	+	0.854292i	$0.326009\pi$
$98$		0			0
$99$	0.343096	+	0.142115i	0.0344825	+	0.0142831i
$100$		0			0
$101$	1.36634	+	3.29864i	0.135956	+	0.328227i	0.977165	−	0.212484i	$-0.0681553\pi$
$101$	1.36634	+	3.29864i	0.135956	+	0.328227i	−0.841208	+	0.540711i	$0.818155\pi$
$102$		0			0
$103$	2.02375	−	2.02375i	0.199406	−	0.199406i	−0.600340	−	0.799745i	$-0.704968\pi$
$103$	2.02375	−	2.02375i	0.199406	−	0.199406i	0.799745	+	0.600340i	$0.204968\pi$
$104$		0			0
$105$	1.25278	+	1.25278i	0.122259	+	0.122259i
$106$		0			0
$107$	8.80292	−	3.64629i	0.851010	−	0.352500i	0.0858251	−	0.996310i	$-0.472647\pi$
$107$	8.80292	−	3.64629i	0.851010	−	0.352500i	0.765185	+	0.643810i	$0.222647\pi$
$108$		0			0
$109$	3.58112	−	8.64559i	0.343009	−	0.828097i	−0.654399	−	0.756149i	$-0.727078\pi$
$109$	3.58112	−	8.64559i	0.343009	−	0.828097i	0.997408	−	0.0719480i	$-0.0229216\pi$
$110$		0			0
$111$		−	9.64278i		−	0.915253i
$112$		0			0
$113$			10.5067i			0.988391i	0.869351	+	0.494195i	$0.164537\pi$
$113$			10.5067i			0.988391i	−0.869351	+	0.494195i	$0.835463\pi$
$114$		0			0
$115$	−6.37684	+	15.3951i	−0.594644	+	1.43560i
$116$		0			0
$117$	−3.78987	+	1.56981i	−0.350373	+	0.145129i
$118$		0			0
$119$	0.972194	+	0.972194i	0.0891208	+	0.0891208i
$120$		0			0
$121$	−7.68066	+	7.68066i	−0.698241	+	0.698241i
$122$		0			0
$123$	4.43758	+	10.7133i	0.400124	+	0.965984i
$124$		0			0
$125$	11.1485	+	4.61788i	0.997156	+	0.413036i
$126$		0			0
$127$	−2.30939			−0.204925			−0.102462	−	0.994737i	$-0.532672\pi$
$127$	−2.30939			−0.204925			−0.102462	+	0.994737i	$0.532672\pi$
$128$		0			0
$129$	−2.01624			−0.177520
$130$		0			0
$131$	−4.80498	−	1.99029i	−0.419813	−	0.173892i	0.162769	−	0.986664i	$-0.447958\pi$
$131$	−4.80498	−	1.99029i	−0.419813	−	0.173892i	−0.582582	+	0.812772i	$0.697958\pi$
$132$		0			0
$133$	−2.84785	−	6.87531i	−0.246940	−	0.596165i
$134$		0			0
$135$	1.38748	−	1.38748i	0.119415	−	0.119415i
$136$		0			0
$137$	6.45738	+	6.45738i	0.551691	+	0.551691i	0.926929	−	0.375238i	$-0.122439\pi$
$137$	6.45738	+	6.45738i	0.551691	+	0.551691i	−0.375238	+	0.926929i	$0.622439\pi$
$138$		0			0
$139$	13.8089	−	5.71982i	1.17125	−	0.485149i	0.289646	−	0.957134i	$-0.406462\pi$
$139$	13.8089	−	5.71982i	1.17125	−	0.485149i	0.881607	+	0.471985i	$0.156462\pi$
$140$		0			0
$141$	−1.23072	+	2.97121i	−0.103645	+	0.250221i
$142$		0			0
$143$			1.52338i			0.127392i
$144$		0			0
$145$		−	1.37463i		−	0.114157i
$146$		0			0
$147$	2.36680	−	5.71395i	0.195210	−	0.471279i
$148$		0			0
$149$	6.65965	−	2.75852i	0.545580	−	0.225987i	−0.0928315	−	0.995682i	$-0.529592\pi$
$149$	6.65965	−	2.75852i	0.545580	−	0.225987i	0.638412	+	0.769695i	$0.279592\pi$
$150$		0			0
$151$	−4.80906	−	4.80906i	−0.391355	−	0.391355i	0.483815	−	0.875170i	$-0.339251\pi$
$151$	−4.80906	−	4.80906i	−0.391355	−	0.391355i	−0.875170	+	0.483815i	$0.839251\pi$
$152$		0			0
$153$	1.07672	−	1.07672i	0.0870479	−	0.0870479i
$154$		0			0
$155$	2.75174	+	6.64328i	0.221025	+	0.533601i
$156$		0			0
$157$	−8.75017	−	3.62444i	−0.698340	−	0.289262i	0.00513017	−	0.999987i	$-0.498367\pi$
$157$	−8.75017	−	3.62444i	−0.698340	−	0.289262i	−0.703470	+	0.710725i	$0.748367\pi$
$158$		0			0
$159$	−8.35023			−0.662217
$160$		0			0
$161$	−7.66786			−0.604312
$162$		0			0
$163$	15.2806	+	6.32945i	1.19687	+	0.495761i	0.889987	−	0.455986i	$-0.150713\pi$
$163$	15.2806	+	6.32945i	1.19687	+	0.495761i	0.306885	+	0.951747i	$0.400713\pi$
$164$		0			0
$165$	−0.278856	−	0.673219i	−0.0217089	−	0.0524100i
$166$		0			0
$167$	−7.16635	+	7.16635i	−0.554549	+	0.554549i	−0.927750	−	0.373201i	$-0.878260\pi$
$167$	−7.16635	+	7.16635i	−0.554549	+	0.554549i	0.373201	+	0.927750i	$0.378260\pi$
$168$		0			0
$169$	−2.70638	−	2.70638i	−0.208183	−	0.208183i
$170$		0			0
$171$	−7.61453	+	3.15404i	−0.582298	+	0.241196i
$172$		0			0
$173$	−4.47280	+	10.7983i	−0.340061	+	0.820979i	0.657648	+	0.753325i	$0.271551\pi$
$173$	−4.47280	+	10.7983i	−0.340061	+	0.820979i	−0.997709	+	0.0676539i	$0.978449\pi$
$174$		0			0
$175$			1.03819i			0.0784800i
$176$		0			0
$177$			7.28285i			0.547413i
$178$		0			0
$179$	1.44741	−	3.49435i	0.108184	−	0.261180i	−0.860511	−	0.509431i	$-0.829856\pi$
$179$	1.44741	−	3.49435i	0.108184	−	0.261180i	0.968696	+	0.248251i	$0.0798558\pi$
$180$		0			0
$181$	−10.1985	+	4.22436i	−0.758049	+	0.313994i	−0.728021	−	0.685555i	$-0.759560\pi$
$181$	−10.1985	+	4.22436i	−0.758049	+	0.313994i	−0.0300283	+	0.999549i	$0.509560\pi$
$182$		0			0
$183$	8.02424	+	8.02424i	0.593169	+	0.593169i
$184$		0			0
$185$	−13.3791	+	13.3791i	−0.983654	+	0.983654i
$186$		0			0
$187$	−0.216401	−	0.522438i	−0.0158248	−	0.0382044i
$188$		0			0
$189$	0.834188	+	0.345532i	0.0606783	+	0.0251338i
$190$		0			0
$191$	1.23454			0.0893282			0.0446641	−	0.999002i	$-0.485778\pi$
$191$	1.23454			0.0893282			0.0446641	+	0.999002i	$0.485778\pi$
$192$		0			0
$193$	11.6382			0.837739			0.418869	−	0.908047i	$-0.362427\pi$
$193$	11.6382			0.837739			0.418869	+	0.908047i	$0.362427\pi$
$194$		0			0
$195$	7.43643	+	3.08027i	0.532534	+	0.220583i
$196$		0			0
$197$	−7.96962	−	19.2404i	−0.567812	−	1.37082i	−0.903395	−	0.428809i	$-0.858933\pi$
$197$	−7.96962	−	19.2404i	−0.567812	−	1.37082i	0.335583	−	0.942011i	$-0.391067\pi$
$198$		0			0
$199$	−10.3810	+	10.3810i	−0.735892	+	0.735892i	−0.971780	−	0.235888i	$-0.924200\pi$
$199$	−10.3810	+	10.3810i	−0.735892	+	0.735892i	0.235888	+	0.971780i	$0.424200\pi$
$200$		0			0
$201$	5.02717	+	5.02717i	0.354589	+	0.354589i
$202$		0			0
$203$	0.584398	−	0.242066i	0.0410167	−	0.0169897i
$204$		0			0
$205$	8.70738	−	21.0215i	0.608149	−	1.46820i
$206$		0			0
$207$			8.49230i			0.590256i
$208$		0			0
$209$			3.06075i			0.211717i
$210$		0			0
$211$	0.213911	−	0.516427i	0.0147262	−	0.0355523i	−0.916345	−	0.400389i	$-0.868875\pi$
$211$	0.213911	−	0.516427i	0.0147262	−	0.0355523i	0.931072	+	0.364836i	$0.118875\pi$
$212$		0			0
$213$	1.25057	−	0.518005i	0.0856879	−	0.0354931i
$214$		0			0
$215$	2.79748	+	2.79748i	0.190787	+	0.190787i
$216$		0			0
$217$	−2.33970	+	2.33970i	−0.158829	+	0.158829i
$218$		0			0
$219$	1.16036	+	2.80135i	0.0784098	+	0.189298i
$220$		0			0
$221$	5.77089	+	2.39038i	0.388192	+	0.160794i
$222$		0			0
$223$	23.4290			1.56892			0.784460	−	0.620179i	$-0.212940\pi$
$223$	23.4290			1.56892			0.784460	+	0.620179i	$0.212940\pi$
$224$		0			0
$225$	1.14982			0.0766545
$226$		0			0
$227$	11.5345	+	4.77773i	0.765568	+	0.317109i	0.731076	−	0.682296i	$-0.239019\pi$
$227$	11.5345	+	4.77773i	0.765568	+	0.317109i	0.0344925	+	0.999405i	$0.489019\pi$
$228$		0			0
$229$	7.39995	+	17.8651i	0.489002	+	1.18056i	0.955223	+	0.295888i	$0.0956154\pi$
$229$	7.39995	+	17.8651i	0.489002	+	1.18056i	−0.466220	+	0.884669i	$0.654385\pi$
$230$		0			0
$231$	0.237101	−	0.237101i	0.0156001	−	0.0156001i
$232$		0			0
$233$	7.86004	+	7.86004i	0.514928	+	0.514928i	0.916033	−	0.401104i	$-0.131373\pi$
$233$	7.86004	+	7.86004i	0.514928	+	0.514928i	−0.401104	+	0.916033i	$0.631373\pi$
$234$		0			0
$235$	5.83008	−	2.41490i	0.380313	−	0.157531i
$236$		0			0
$237$	−0.240384	+	0.580339i	−0.0156146	+	0.0376971i
$238$		0			0
$239$			26.1171i			1.68937i	0.535262	+	0.844686i	$0.320213\pi$
$239$			26.1171i			1.68937i	−0.535262	+	0.844686i	$0.679787\pi$
$240$		0			0
$241$		−	12.8873i		−	0.830144i	−0.909788	−	0.415072i	$-0.863756\pi$
$241$		−	12.8873i		−	0.830144i	0.909788	−	0.415072i	$-0.136244\pi$
$242$		0			0
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$		0			0
$245$	−11.2118	+	4.64410i	−0.716299	+	0.296701i
$246$		0			0
$247$	−23.9068	−	23.9068i	−1.52115	−	1.52115i
$248$		0			0
$249$	−7.71974	+	7.71974i	−0.489218	+	0.489218i
$250$		0			0
$251$	−0.265442	−	0.640835i	−0.0167546	−	0.0404491i	0.915281	−	0.402816i	$-0.131969\pi$
$251$	−0.265442	−	0.640835i	−0.0167546	−	0.0404491i	−0.932035	+	0.362367i	$0.881969\pi$
$252$		0			0
$253$	2.91368	+	1.20688i	0.183181	+	0.0758761i
$254$		0			0
$255$	−2.98786			−0.187107
$256$		0			0
$257$	−10.6839			−0.666442			−0.333221	−	0.942849i	$-0.608136\pi$
$257$	−10.6839			−0.666442			−0.333221	+	0.942849i	$0.608136\pi$
$258$		0			0
$259$	−8.04390	−	3.33189i	−0.499824	−	0.207034i
$260$		0			0
$261$	−0.268092	−	0.647232i	−0.0165945	−	0.0400627i
$262$		0			0
$263$	−0.733161	+	0.733161i	−0.0452086	+	0.0452086i	−0.729350	−	0.684141i	$-0.760177\pi$
$263$	−0.733161	+	0.733161i	−0.0452086	+	0.0452086i	0.684141	+	0.729350i	$0.260177\pi$
$264$		0			0
$265$	11.5858	+	11.5858i	0.711707	+	0.711707i
$266$		0			0
$267$	−11.3733	+	4.71097i	−0.696034	+	0.288307i
$268$		0			0
$269$	0.757304	−	1.82829i	0.0461736	−	0.111473i	−0.899110	−	0.437723i	$-0.855785\pi$
$269$	0.757304	−	1.82829i	0.0461736	−	0.111473i	0.945284	+	0.326250i	$0.105785\pi$
$270$		0			0
$271$		−	4.80909i		−	0.292131i	−0.989275	−	0.146066i	$-0.953339\pi$
$271$		−	4.80909i		−	0.292131i	0.989275	−	0.146066i	$-0.0466611\pi$
$272$		0			0
$273$			3.70388i			0.224169i
$274$		0			0
$275$	0.163406	−	0.394498i	0.00985378	−	0.0237891i
$276$		0			0
$277$	8.34968	−	3.45855i	0.501684	−	0.207804i	−0.117466	−	0.993077i	$-0.537477\pi$
$277$	8.34968	−	3.45855i	0.501684	−	0.207804i	0.619150	+	0.785273i	$0.287477\pi$
$278$		0			0
$279$	2.59126	+	2.59126i	0.155135	+	0.155135i
$280$		0			0
$281$	8.76860	−	8.76860i	0.523091	−	0.523091i	−0.395413	−	0.918504i	$-0.629398\pi$
$281$	8.76860	−	8.76860i	0.523091	−	0.523091i	0.918504	+	0.395413i	$0.129398\pi$
$282$		0			0
$283$	−7.62757	−	18.4146i	−0.453412	−	1.09463i	−0.971016	−	0.239013i	$-0.923176\pi$
$283$	−7.62757	−	18.4146i	−0.453412	−	1.09463i	0.517605	−	0.855620i	$-0.326824\pi$
$284$		0			0
$285$	14.9411	+	6.18883i	0.885037	+	0.366594i
$286$		0			0
$287$	10.4702			0.618038
$288$		0			0
$289$	14.6813			0.863608
$290$		0			0
$291$	−9.45936	−	3.91819i	−0.554517	−	0.229689i
$292$		0			0
$293$	3.54788	+	8.56535i	0.207270	+	0.500393i	0.992991	−	0.118187i	$-0.0377082\pi$
$293$	3.54788	+	8.56535i	0.207270	+	0.500393i	−0.785722	+	0.618580i	$0.787708\pi$
$294$		0			0
$295$	10.1048	−	10.1048i	0.588323	−	0.588323i
$296$		0			0
$297$	−0.262594	−	0.262594i	−0.0152373	−	0.0152373i
$298$		0			0
$299$	−32.1847	+	13.3313i	−1.86129	+	0.770971i
$300$		0			0
$301$	−0.696674	+	1.68192i	−0.0401556	+	0.0969443i
$302$		0			0
$303$		−	3.57042i		−	0.205116i
$304$		0			0
$305$		−	22.2669i		−	1.27500i
$306$		0			0
$307$	10.9217	−	26.3674i	0.623336	−	1.50487i	−0.224427	−	0.974491i	$-0.572051\pi$
$307$	10.9217	−	26.3674i	0.623336	−	1.50487i	0.847763	−	0.530375i	$-0.177949\pi$
$308$		0			0
$309$	−2.64415	+	1.09524i	−0.150420	+	0.0623062i
$310$		0			0
$311$	−10.0285	−	10.0285i	−0.568665	−	0.568665i	0.363089	−	0.931754i	$-0.381722\pi$
$311$	−10.0285	−	10.0285i	−0.568665	−	0.568665i	−0.931754	+	0.363089i	$0.881722\pi$
$312$		0			0
$313$	−13.6930	+	13.6930i	−0.773973	+	0.773973i	−0.978799	−	0.204826i	$-0.934337\pi$
$313$	−13.6930	+	13.6930i	−0.773973	+	0.773973i	0.204826	+	0.978799i	$0.434337\pi$
$314$		0			0
$315$	−0.677999	−	1.63683i	−0.0382009	−	0.0922252i
$316$		0			0
$317$	−3.88745	−	1.61024i	−0.218341	−	0.0904398i	0.270832	−	0.962627i	$-0.412701\pi$
$317$	−3.88745	−	1.61024i	−0.218341	−	0.0904398i	−0.489173	+	0.872187i	$0.662701\pi$
$318$		0			0
$319$	−0.260163			−0.0145663
$320$		0			0
$321$	−9.52821			−0.531813
$322$		0			0
$323$	11.5948	+	4.80271i	0.645150	+	0.267230i
$324$		0			0
$325$	1.80500	+	4.35765i	0.100123	+	0.241719i
$326$		0			0
$327$	−6.61705	+	6.61705i	−0.365924	+	0.365924i
$328$		0			0
$329$	2.05330	+	2.05330i	0.113202	+	0.113202i
$330$		0			0
$331$	−24.2486	+	10.0441i	−1.33283	+	0.552074i	−0.931460	−	0.363844i	$-0.881464\pi$
$331$	−24.2486	+	10.0441i	−1.33283	+	0.552074i	−0.401365	+	0.915918i	$0.631464\pi$
$332$		0			0
$333$	−3.69013	+	8.90877i	−0.202218	+	0.488198i
$334$		0			0
$335$		−	13.9501i		−	0.762178i
$336$		0			0
$337$		−	28.8246i		−	1.57018i	−0.619383	−	0.785089i	$-0.712617\pi$
$337$		−	28.8246i		−	1.57018i	0.619383	−	0.785089i	$-0.287383\pi$
$338$		0			0
$339$	4.02075	−	9.70696i	0.218377	−	0.527210i
$340$		0			0
$341$	1.25731	−	0.520795i	0.0680871	−	0.0282026i
$342$		0			0
$343$	−8.41793	−	8.41793i	−0.454525	−	0.454525i
$344$		0			0
$345$	11.7829	−	11.7829i	0.634368	−	0.634368i
$346$		0			0
$347$	9.62155	+	23.2285i	0.516512	+	1.24697i	0.940033	+	0.341084i	$0.110794\pi$
$347$	9.62155	+	23.2285i	0.516512	+	1.24697i	−0.423521	+	0.905886i	$0.639206\pi$
$348$		0			0
$349$	−0.998904	−	0.413760i	−0.0534701	−	0.0221480i	0.355788	−	0.934567i	$-0.384212\pi$
$349$	−0.998904	−	0.413760i	−0.0534701	−	0.0221480i	−0.409258	+	0.912419i	$0.634212\pi$
$350$		0			0
$351$	4.10212			0.218955
$352$		0			0
$353$	0.259074			0.0137891			0.00689456	−	0.999976i	$-0.497805\pi$
$353$	0.259074			0.0137891			0.00689456	+	0.999976i	$0.497805\pi$
$354$		0			0
$355$	−2.45386	−	1.01642i	−0.130237	−	0.0539461i
$356$		0			0
$357$	−0.526147	−	1.27023i	−0.0278467	−	0.0672278i
$358$		0			0
$359$	19.4929	−	19.4929i	1.02879	−	1.02879i	0.0292206	−	0.999573i	$-0.490697\pi$
$359$	19.4929	−	19.4929i	1.02879	−	1.02879i	0.999573	−	0.0292206i	$-0.00930254\pi$
$360$		0			0
$361$	−34.5981	−	34.5981i	−1.82095	−	1.82095i
$362$		0			0
$363$	10.0353	−	4.15674i	0.526715	−	0.218172i
$364$		0			0
$365$	2.27684	−	5.49678i	0.119175	−	0.287715i
$366$		0			0
$367$			20.4476i			1.06735i	0.845689	+	0.533677i	$0.179190\pi$
$367$			20.4476i			1.06735i	−0.845689	+	0.533677i	$0.820810\pi$
$368$		0			0
$369$		−	11.5960i		−	0.603662i
$370$		0			0
$371$	−2.88527	+	6.96567i	−0.149796	+	0.361640i
$372$		0			0
$373$	−9.59680	+	3.97512i	−0.496903	+	0.205824i	−0.617038	−	0.786934i	$-0.711667\pi$
$373$	−9.59680	+	3.97512i	−0.496903	+	0.205824i	0.120134	+	0.992758i	$0.461667\pi$
$374$		0			0
$375$	−8.53273	−	8.53273i	−0.440628	−	0.440628i
$376$		0			0
$377$	2.03207	−	2.03207i	0.104657	−	0.104657i
$378$		0			0
$379$	−2.18850	−	5.28351i	−0.112416	−	0.271396i	0.857652	−	0.514231i	$-0.171923\pi$
$379$	−2.18850	−	5.28351i	−0.112416	−	0.271396i	−0.970068	+	0.242835i	$0.921923\pi$
$380$		0			0
$381$	2.13360	+	0.883764i	0.109307	+	0.0452766i
$382$		0			0
$383$	25.5047			1.30323			0.651614	−	0.758550i	$-0.274092\pi$
$383$	25.5047			1.30323			0.651614	+	0.758550i	$0.274092\pi$
$384$		0			0
$385$	−0.657945			−0.0335320
$386$		0			0
$387$	1.86276	+	0.771580i	0.0946893	+	0.0392216i
$388$		0			0
$389$	−10.0662	−	24.3021i	−0.510379	−	1.23216i	−0.943664	−	0.330907i	$-0.892646\pi$
$389$	−10.0662	−	24.3021i	−0.510379	−	1.23216i	0.433285	−	0.901257i	$-0.357354\pi$
$390$		0			0
$391$	9.14386	−	9.14386i	0.462425	−	0.462425i
$392$		0			0
$393$	3.67758	+	3.67758i	0.185509	+	0.185509i
$394$		0			0
$395$	1.13873	−	0.471679i	0.0572960	−	0.0237328i
$396$		0			0
$397$	0.0155261	−	0.0374832i	0.000779230	−	0.00188123i	−0.923489	−	0.383624i	$-0.874676\pi$
$397$	0.0155261	−	0.0374832i	0.000779230	−	0.00188123i	0.924269	+	0.381743i	$0.124676\pi$
$398$		0			0
$399$			7.44178i			0.372555i
$400$		0			0
$401$		−	7.24998i		−	0.362047i	−0.983479	−	0.181023i	$-0.942059\pi$
$401$		−	7.24998i		−	0.362047i	0.983479	−	0.181023i	$-0.0579410\pi$
$402$		0			0
$403$	−5.75274	+	13.8883i	−0.286564	+	0.691827i
$404$		0			0
$405$	−1.81283	+	0.750897i	−0.0900800	+	0.0373124i
$406$		0			0
$407$	2.53214	+	2.53214i	0.125514	+	0.125514i
$408$		0			0
$409$	4.79664	−	4.79664i	0.237179	−	0.237179i	−0.578502	−	0.815681i	$-0.696363\pi$
$409$	4.79664	−	4.79664i	0.237179	−	0.237179i	0.815681	+	0.578502i	$0.196363\pi$
$410$		0			0
$411$	−3.49471	−	8.43697i	−0.172381	−	0.416165i
$412$		0			0
$413$	6.07527	+	2.51646i	0.298945	+	0.123827i
$414$		0			0
$415$	21.4219			1.05156
$416$		0			0
$417$	−14.9466			−0.731939
$418$		0			0
$419$	−25.2331	−	10.4519i	−1.23272	−	0.510608i	−0.331285	−	0.943531i	$-0.607482\pi$
$419$	−25.2331	−	10.4519i	−1.23272	−	0.510608i	−0.901431	+	0.432923i	$0.857482\pi$
$420$		0			0
$421$	−4.02613	−	9.71993i	−0.196222	−	0.473721i	0.794890	−	0.606753i	$-0.207528\pi$
$421$	−4.02613	−	9.71993i	−0.196222	−	0.473721i	−0.991112	+	0.133033i	$0.957528\pi$
$422$		0			0
$423$	2.27407	−	2.27407i	0.110569	−	0.110569i
$424$		0			0
$425$	−1.23804	−	1.23804i	−0.0600535	−	0.0600535i
$426$		0			0
$427$	9.46636	−	3.92109i	0.458109	−	0.189755i
$428$		0			0
$429$	0.582973	−	1.40742i	0.0281462	−	0.0679510i
$430$		0			0
$431$		−	32.0275i		−	1.54271i	−0.636404	−	0.771356i	$-0.719579\pi$
$431$		−	32.0275i		−	1.54271i	0.636404	−	0.771356i	$-0.280421\pi$
$432$		0			0
$433$		−	15.7159i		−	0.755258i	−0.925957	−	0.377629i	$-0.876739\pi$
$433$		−	15.7159i		−	0.755258i	0.925957	−	0.377629i	$-0.123261\pi$
$434$		0			0
$435$	−0.526048	+	1.26999i	−0.0252221	+	0.0608914i
$436$		0			0
$437$	−64.6649	+	26.7851i	−3.09334	+	1.28130i
$438$		0			0
$439$	15.0452	+	15.0452i	0.718067	+	0.718067i	0.968209	−	0.250143i	$-0.0804775\pi$
$439$	15.0452	+	15.0452i	0.718067	+	0.718067i	−0.250143	+	0.968209i	$0.580477\pi$
$440$		0			0
$441$	−4.37327	+	4.37327i	−0.208251	+	0.208251i
$442$		0			0
$443$	−0.935563	−	2.25865i	−0.0444499	−	0.107312i	0.900095	−	0.435693i	$-0.143497\pi$
$443$	−0.935563	−	2.25865i	−0.0444499	−	0.107312i	−0.944545	+	0.328382i	$0.893497\pi$
$444$		0			0
$445$	22.3165	+	9.24381i	1.05791	+	0.438199i
$446$		0			0
$447$	−7.20836			−0.340944
$448$		0			0
$449$	39.2374			1.85173			0.925865	−	0.377855i	$-0.123338\pi$
$449$	39.2374			1.85173			0.925865	+	0.377855i	$0.123338\pi$
$450$		0			0
$451$	−3.97853	−	1.64796i	−0.187342	−	0.0775995i
$452$		0			0
$453$	2.60264	+	6.28333i	0.122283	+	0.295217i
$454$		0			0
$455$	5.13905	−	5.13905i	0.240922	−	0.240922i
$456$		0			0
$457$	25.5724	+	25.5724i	1.19623	+	1.19623i	0.975287	+	0.220940i	$0.0709125\pi$
$457$	25.5724	+	25.5724i	1.19623	+	1.19623i	0.220940	+	0.975287i	$0.429088\pi$
$458$		0			0
$459$	−1.40681	+	0.582718i	−0.0656641	+	0.0271990i
$460$		0			0
$461$	−6.04846	+	14.6023i	−0.281705	+	0.680096i	−0.999876	−	0.0157709i	$-0.994980\pi$
$461$	−6.04846	+	14.6023i	−0.281705	+	0.680096i	0.718171	+	0.695867i	$0.244980\pi$
$462$		0			0
$463$			18.8446i			0.875785i	0.899027	+	0.437892i	$0.144275\pi$
$463$			18.8446i			0.875785i	−0.899027	+	0.437892i	$0.855725\pi$
$464$		0			0
$465$		−	7.19063i		−	0.333458i
$466$		0			0
$467$	8.99695	−	21.7206i	0.416329	−	1.00511i	−0.567073	−	0.823668i	$-0.691924\pi$
$467$	8.99695	−	21.7206i	0.416329	−	1.00511i	0.983402	−	0.181440i	$-0.0580758\pi$
$468$		0			0
$469$	5.93065	−	2.45656i	0.273852	−	0.113433i
$470$		0			0
$471$	6.69709	+	6.69709i	0.308586	+	0.308586i
$472$		0			0
$473$	0.529452	−	0.529452i	0.0243442	−	0.0243442i
$474$		0			0
$475$	3.62657	+	8.75533i	0.166399	+	0.401722i
$476$		0			0
$477$	7.71461	+	3.19550i	0.353228	+	0.146312i
$478$		0			0
$479$	−37.2438			−1.70171			−0.850857	−	0.525397i	$-0.823917\pi$
$479$	−37.2438			−1.70171			−0.850857	+	0.525397i	$0.823917\pi$
$480$		0			0
$481$	−39.5559			−1.80359
$482$		0			0
$483$	7.08418	+	2.93436i	0.322341	+	0.133518i
$484$		0			0
$485$	7.68823	+	18.5610i	0.349105	+	0.842813i
$486$		0			0
$487$	−27.2623	+	27.2623i	−1.23537	+	1.23537i	−0.273503	+	0.961871i	$0.588182\pi$
$487$	−27.2623	+	27.2623i	−1.23537	+	1.23537i	−0.961871	+	0.273503i	$0.911818\pi$
$488$		0			0
$489$	−11.6953	−	11.6953i	−0.528879	−	0.528879i
$490$		0			0
$491$	−26.3108	+	10.8983i	−1.18739	+	0.491832i	−0.886904	−	0.461955i	$-0.847148\pi$
$491$	−26.3108	+	10.8983i	−1.18739	+	0.491832i	−0.300484	+	0.953787i	$0.597148\pi$
$492$		0			0
$493$	−0.408229	+	0.985551i	−0.0183857	+	0.0443870i
$494$		0			0
$495$			0.728687i			0.0327520i
$496$		0			0
$497$		−	1.22220i		−	0.0548232i
$498$		0			0
$499$	−2.00327	+	4.83631i	−0.0896785	+	0.216503i	−0.962355	−	0.271796i	$-0.912382\pi$
$499$	−2.00327	+	4.83631i	−0.0896785	+	0.216503i	0.872676	+	0.488299i	$0.162382\pi$
$500$		0			0
$501$	9.36329	−	3.87840i	0.418321	−	0.173274i
$502$		0			0
$503$	9.33046	+	9.33046i	0.416024	+	0.416024i	0.883831	−	0.467806i	$-0.154956\pi$
$503$	9.33046	+	9.33046i	0.416024	+	0.416024i	−0.467806	+	0.883831i	$0.654956\pi$
$504$		0			0
$505$	−4.95388	+	4.95388i	−0.220445	+	0.220445i
$506$		0			0
$507$	1.46468	+	3.53605i	0.0650488	+	0.157042i
$508$		0			0
$509$	−4.91588	−	2.03622i	−0.217893	−	0.0902541i	0.271067	−	0.962560i	$-0.412623\pi$
$509$	−4.91588	−	2.03622i	−0.217893	−	0.0902541i	−0.488960	+	0.872306i	$0.662623\pi$
$510$		0			0
$511$	2.73780			0.121113
$512$		0			0
$513$	8.24191			0.363889
$514$		0			0
$515$	5.18832	+	2.14907i	0.228625	+	0.0946995i
$516$		0			0
$517$	−0.457045	−	1.10340i	−0.0201008	−	0.0485276i
$518$		0			0
$519$	8.26466	−	8.26466i	0.362778	−	0.362778i
$520$		0			0
$521$	10.3057	+	10.3057i	0.451502	+	0.451502i	0.895853	−	0.444351i	$-0.146566\pi$
$521$	10.3057	+	10.3057i	0.451502	+	0.451502i	−0.444351	+	0.895853i	$0.646566\pi$
$522$		0			0
$523$	1.09031	−	0.451621i	0.0476759	−	0.0197480i	−0.358718	−	0.933446i	$-0.616786\pi$
$523$	1.09031	−	0.451621i	0.0476759	−	0.0197480i	0.406394	+	0.913698i	$0.366786\pi$
$524$		0			0
$525$	0.397299	−	0.959165i	0.0173396	−	0.0418614i
$526$		0			0
$527$		−	5.58014i		−	0.243075i
$528$		0			0
$529$			49.1192i			2.13562i
$530$		0			0
$531$	2.78703	−	6.72848i	0.120947	−	0.291991i
$532$		0			0
$533$	43.9472	−	18.2035i	1.90356	−	0.788481i
$534$		0			0
$535$	13.2202	+	13.2202i	0.571558	+	0.571558i
$536$		0			0
$537$	−2.67446	+	2.67446i	−0.115412	+	0.115412i
$538$		0			0
$539$	0.878944	+	2.12196i	0.0378588	+	0.0913993i
$540$		0			0
$541$	29.9414	+	12.4021i	1.28728	+	0.533209i	0.918174	−	0.396177i	$-0.129663\pi$
$541$	29.9414	+	12.4021i	1.28728	+	0.533209i	0.369107	+	0.929387i	$0.379663\pi$
$542$		0			0
$543$	11.0388			0.473720
$544$		0			0
$545$	18.3620			0.786541
$546$		0			0
$547$	−7.78227	−	3.22352i	−0.332746	−	0.137828i	0.210054	−	0.977690i	$-0.432636\pi$
$547$	−7.78227	−	3.22352i	−0.332746	−	0.137828i	−0.542800	+	0.839862i	$0.682636\pi$
$548$		0			0
$549$	−4.34269	−	10.4842i	−0.185341	−	0.447454i
$550$		0			0
$551$	4.08280	−	4.08280i	0.173933	−	0.173933i
$552$		0			0
$553$	0.401052	+	0.401052i	0.0170545	+	0.0170545i
$554$		0			0
$555$	17.4807	−	7.24074i	0.742014	−	0.307352i
$556$		0			0
$557$	5.41814	−	13.0806i	0.229574	−	0.554241i	−0.766551	−	0.642183i	$-0.778029\pi$
$557$	5.41814	−	13.0806i	0.229574	−	0.554241i	0.996126	+	0.0879419i	$0.0280290\pi$
$558$		0			0
$559$			8.27084i			0.349819i
$560$		0			0
$561$			0.565483i			0.0238747i
$562$		0			0
$563$	−10.5280	+	25.4168i	−0.443702	+	1.07119i	0.530938	+	0.847411i	$0.321840\pi$
$563$	−10.5280	+	25.4168i	−0.443702	+	1.07119i	−0.974640	+	0.223780i	$0.928160\pi$
$564$		0			0
$565$	−19.0469	+	7.88947i	−0.801308	+	0.331913i
$566$		0			0
$567$	−0.638460	−	0.638460i	−0.0268128	−	0.0268128i
$568$		0			0
$569$	−0.593219	+	0.593219i	−0.0248690	+	0.0248690i	−0.719432	−	0.694563i	$-0.755598\pi$
$569$	−0.593219	+	0.593219i	−0.0248690	+	0.0248690i	0.694563	+	0.719432i	$0.255598\pi$
$570$		0			0
$571$	8.10194	+	19.5598i	0.339056	+	0.818553i	0.997807	+	0.0661921i	$0.0210850\pi$
$571$	8.10194	+	19.5598i	0.339056	+	0.818553i	−0.658751	+	0.752361i	$0.728915\pi$
$572$		0			0
$573$	−1.14057	−	0.472438i	−0.0476479	−	0.0197364i
$574$		0			0
$575$	9.76460			0.407212
$576$		0			0
$577$	−11.2774			−0.469484			−0.234742	−	0.972058i	$-0.575424\pi$
$577$	−11.2774			−0.469484			−0.234742	+	0.972058i	$0.575424\pi$
$578$		0			0
$579$	−10.7523	−	4.45376i	−0.446852	−	0.185092i
$580$		0			0
$581$	3.77230	+	9.10713i	0.156501	+	0.377828i
$582$		0			0
$583$	2.19272	−	2.19272i	0.0908134	−	0.0908134i
$584$		0			0
$585$	−5.69160	−	5.69160i	−0.235319	−	0.235319i
$586$		0			0
$587$	6.13139	−	2.53970i	0.253070	−	0.104825i	−0.252542	−	0.967586i	$-0.581267\pi$
$587$	6.13139	−	2.53970i	0.253070	−	0.104825i	0.505612	+	0.862761i	$0.331267\pi$
$588$		0			0
$589$	−11.5583	+	27.9042i	−0.476251	+	1.14977i
$590$		0			0
$591$			20.8256i			0.856652i
$592$		0			0
$593$			26.2096i			1.07630i	0.842849	+	0.538149i	$0.180876\pi$
$593$			26.2096i			1.07630i	−0.842849	+	0.538149i	$0.819124\pi$
$594$		0			0
$595$	−1.03240	+	2.49243i	−0.0423243	+	0.102180i
$596$		0			0
$597$	13.5635	−	5.61818i	0.555116	−	0.229937i
$598$		0			0
$599$	−30.3211	−	30.3211i	−1.23888	−	1.23888i	−0.960457	−	0.278428i	$-0.910187\pi$
$599$	−30.3211	−	30.3211i	−1.23888	−	1.23888i	−0.278428	−	0.960457i	$-0.589813\pi$
$600$		0			0
$601$	9.96259	−	9.96259i	0.406383	−	0.406383i	−0.474092	−	0.880475i	$-0.657224\pi$
$601$	9.96259	−	9.96259i	0.406383	−	0.406383i	0.880475	+	0.474092i	$0.157224\pi$
$602$		0			0
$603$	−2.72068	−	6.56831i	−0.110795	−	0.267482i
$604$		0			0
$605$	−19.6911	−	8.15631i	−0.800556	−	0.331601i
$606$		0			0
$607$	−17.4543			−0.708447			−0.354223	−	0.935161i	$-0.615255\pi$
$607$	−17.4543			−0.708447			−0.354223	+	0.935161i	$0.615255\pi$
$608$		0			0
$609$	−0.632548			−0.0256321
$610$		0			0
$611$	12.1883	+	5.04855i	0.493085	+	0.204243i
$612$		0			0
$613$	12.6691	+	30.5860i	0.511701	+	1.23536i	0.942893	+	0.333095i	$0.108093\pi$
$613$	12.6691	+	30.5860i	0.511701	+	1.23536i	−0.431192	+	0.902260i	$0.641907\pi$
$614$		0			0
$615$	−16.0891	+	16.0891i	−0.648776	+	0.648776i
$616$		0			0
$617$	−5.81018	−	5.81018i	−0.233909	−	0.233909i	0.580413	−	0.814322i	$-0.302891\pi$
$617$	−5.81018	−	5.81018i	−0.233909	−	0.233909i	−0.814322	+	0.580413i	$0.802891\pi$
$618$		0			0
$619$	9.00884	−	3.73158i	0.362096	−	0.149985i	−0.194216	−	0.980959i	$-0.562216\pi$
$619$	9.00884	−	3.73158i	0.362096	−	0.149985i	0.556312	+	0.830974i	$0.312216\pi$
$620$		0			0
$621$	3.24986	−	7.84586i	0.130413	−	0.314844i
$622$		0			0
$623$			11.1153i			0.445324i
$624$		0			0
$625$			17.9288i			0.717153i
$626$		0			0
$627$	1.17130	−	2.82777i	0.0467772	−	0.112930i
$628$		0			0
$629$	13.5655	−	5.61903i	0.540893	−	0.224045i
$630$		0			0
$631$	8.01798	+	8.01798i	0.319191	+	0.319191i	0.848456	−	0.529266i	$-0.177532\pi$
$631$	8.01798	+	8.01798i	0.319191	+	0.319191i	−0.529266	+	0.848456i	$0.677532\pi$
$632$		0			0
$633$	−0.395256	+	0.395256i	−0.0157100	+	0.0157100i
$634$		0			0
$635$	−1.73411	−	4.18652i	−0.0688161	−	0.166137i
$636$		0			0
$637$	−23.4393	−	9.70889i	−0.928700	−	0.384680i
$638$		0			0
$639$	−1.35361			−0.0535481
$640$		0			0
$641$	−7.70306			−0.304253			−0.152126	−	0.988361i	$-0.548612\pi$
$641$	−7.70306			−0.304253			−0.152126	+	0.988361i	$0.548612\pi$
$642$		0			0
$643$	15.6982	+	6.50239i	0.619075	+	0.256429i	0.670103	−	0.742268i	$-0.266250\pi$
$643$	15.6982	+	6.50239i	0.619075	+	0.256429i	−0.0510280	+	0.998697i	$0.516250\pi$
$644$		0			0
$645$	−1.51398	−	3.65508i	−0.0596131	−	0.143919i
$646$		0			0
$647$	4.89235	−	4.89235i	0.192338	−	0.192338i	−0.604367	−	0.796706i	$-0.706574\pi$
$647$	4.89235	−	4.89235i	0.192338	−	0.192338i	0.796706	+	0.604367i	$0.206574\pi$
$648$		0			0
$649$	−1.91244	−	1.91244i	−0.0750697	−	0.0750697i
$650$		0			0
$651$	3.05697	−	1.26624i	0.119812	−	0.0496277i
$652$		0			0
$653$	8.81462	−	21.2804i	0.344943	−	0.832766i	−0.652258	−	0.757997i	$-0.726178\pi$
$653$	8.81462	−	21.2804i	0.344943	−	0.832766i	0.997201	−	0.0747688i	$-0.0238219\pi$
$654$		0			0
$655$		−	10.2051i		−	0.398746i
$656$		0			0
$657$		−	3.03216i		−	0.118296i
$658$		0			0
$659$	−6.42799	+	15.5185i	−0.250399	+	0.604516i	−0.998236	−	0.0593655i	$-0.981092\pi$
$659$	−6.42799	+	15.5185i	−0.250399	+	0.604516i	0.747837	+	0.663882i	$0.231092\pi$
$660$		0			0
$661$	34.2088	−	14.1697i	1.33057	−	0.551139i	0.399750	−	0.916624i	$-0.369097\pi$
$661$	34.2088	−	14.1697i	1.33057	−	0.551139i	0.930817	+	0.365486i	$0.119097\pi$
$662$		0			0
$663$	−4.41685	−	4.41685i	−0.171536	−	0.171536i
$664$		0			0
$665$	10.3253	−	10.3253i	0.400398	−	0.400398i
$666$		0			0
$667$	−2.27672	−	5.49649i	−0.0881550	−	0.212825i
$668$		0			0
$669$	−21.6455	−	8.96588i	−0.836865	−	0.346641i
$670$		0			0
$671$	−4.21424			−0.162689
$672$		0			0
$673$	8.37057			0.322662			0.161331	−	0.986900i	$-0.448421\pi$
$673$	8.37057			0.322662			0.161331	+	0.986900i	$0.448421\pi$
$674$		0			0
$675$	−1.06229	−	0.440016i	−0.0408877	−	0.0169362i
$676$		0			0
$677$	−3.93149	−	9.49145i	−0.151099	−	0.364786i	0.830147	−	0.557545i	$-0.188257\pi$
$677$	−3.93149	−	9.49145i	−0.151099	−	0.364786i	−0.981246	+	0.192759i	$0.938257\pi$
$678$		0			0
$679$	−6.53702	+	6.53702i	−0.250868	+	0.250868i
$680$		0			0
$681$	−8.82809	−	8.82809i	−0.338293	−	0.338293i
$682$		0			0
$683$	8.70888	−	3.60734i	0.333236	−	0.138031i	−0.209791	−	0.977746i	$-0.567278\pi$
$683$	8.70888	−	3.60734i	0.333236	−	0.138031i	0.543027	+	0.839715i	$0.317278\pi$
$684$		0			0
$685$	−6.85727	+	16.5549i	−0.262003	+	0.632531i
$686$		0			0
$687$		−	19.3370i		−	0.737753i
$688$		0			0
$689$			34.2537i			1.30496i
$690$		0			0
$691$	−0.128590	+	0.310443i	−0.00489178	+	0.0118098i	−0.926307	−	0.376771i	$-0.877034\pi$
$691$	−0.128590	+	0.310443i	−0.00489178	+	0.0118098i	0.921415	+	0.388581i	$0.127034\pi$
$692$		0			0
$693$	−0.309788	+	0.128318i	−0.0117679	+	0.00487441i
$694$		0			0
$695$	20.7381	+	20.7381i	0.786640	+	0.786640i
$696$		0			0
$697$	−12.4856	+	12.4856i	−0.472927	+	0.472927i
$698$		0			0
$699$	−4.25382	−	10.2696i	−0.160894	−	0.388433i
$700$		0			0
$701$	−29.8219	−	12.3527i	−1.12636	−	0.466553i	−0.259817	−	0.965658i	$-0.583662\pi$
$701$	−29.8219	−	12.3527i	−1.12636	−	0.466553i	−0.866542	+	0.499104i	$0.833662\pi$
$702$		0			0
$703$	−79.4750			−2.99746
$704$		0			0
$705$	−6.31044			−0.237665
$706$		0			0
$707$	−2.97841	−	1.23370i	−0.112015	−	0.0463979i
$708$		0			0
$709$	−11.8266	−	28.5520i	−0.444158	−	1.07229i	−0.974476	−	0.224494i	$-0.927927\pi$
$709$	−11.8266	−	28.5520i	−0.444158	−	1.07229i	0.530317	−	0.847799i	$-0.322073\pi$
$710$		0			0
$711$	0.444172	−	0.444172i	0.0166578	−	0.0166578i
$712$		0			0
$713$	22.0058	+	22.0058i	0.824123	+	0.824123i
$714$		0			0
$715$	−2.76163	+	1.14390i	−0.103279	+	0.0427795i
$716$		0			0
$717$	9.99457	−	24.1290i	0.373254	−	0.901115i
$718$		0			0
$719$		−	34.8049i		−	1.29801i	−0.760786	−	0.649003i	$-0.775186\pi$
$719$		−	34.8049i		−	1.29801i	0.760786	−	0.649003i	$-0.224814\pi$
$720$		0			0
$721$			2.58416i			0.0962392i
$722$		0			0
$723$	−4.93176	+	11.9063i	−0.183414	+	0.442801i
$724$		0			0
$725$	−0.744199	+	0.308257i	−0.0276389	+	0.0114484i
$726$		0			0
$727$	4.11603	+	4.11603i	0.152655	+	0.152655i	0.779303	−	0.626648i	$-0.215573\pi$
$727$	4.11603	+	4.11603i	0.152655	+	0.152655i	−0.626648	+	0.779303i	$0.715573\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	−1.17490	−	2.83645i	−0.0434551	−	0.104910i
$732$		0			0
$733$	−30.7463	−	12.7356i	−1.13564	−	0.470398i	−0.265947	−	0.963988i	$-0.585685\pi$
$733$	−30.7463	−	12.7356i	−1.13564	−	0.470398i	−0.869695	+	0.493589i	$0.835685\pi$
$734$		0			0
$735$	12.1356			0.447629
$736$		0			0
$737$	−2.64021			−0.0972534
$738$		0			0
$739$	34.5685	+	14.3188i	1.27162	+	0.526724i	0.913458	−	0.406934i	$-0.133402\pi$
$739$	34.5685	+	14.3188i	1.27162	+	0.526724i	0.358166	+	0.933658i	$0.383402\pi$
$740$		0			0
$741$	12.9383	+	31.2357i	0.475299	+	1.14747i
$742$		0			0
$743$	−10.7639	+	10.7639i	−0.394888	+	0.394888i	−0.876425	−	0.481538i	$-0.840078\pi$
$743$	−10.7639	+	10.7639i	−0.394888	+	0.394888i	0.481538	+	0.876425i	$0.340078\pi$
$744$		0			0
$745$	10.0014	+	10.0014i	0.366424	+	0.366424i
$746$		0			0
$747$	10.0863	−	4.17789i	0.369039	−	0.152861i
$748$		0			0
$749$	−3.29230	+	7.94832i	−0.120298	+	0.290425i
$750$		0			0
$751$		−	19.3932i		−	0.707669i	−0.935308	−	0.353835i	$-0.884878\pi$
$751$		−	19.3932i		−	0.707669i	0.935308	−	0.353835i	$-0.115122\pi$
$752$		0			0
$753$			0.693634i			0.0252774i
$754$		0			0
$755$	5.10687	−	12.3291i	0.185858	−	0.448701i
$756$		0			0
$757$	−5.99265	+	2.48224i	−0.217807	+	0.0902184i	−0.488919	−	0.872329i	$-0.662609\pi$
$757$	−5.99265	+	2.48224i	−0.217807	+	0.0902184i	0.271112	+	0.962548i	$0.412609\pi$
$758$		0			0
$759$	−2.23003	−	2.23003i	−0.0809450	−	0.0809450i
$760$		0			0
$761$	−11.8001	+	11.8001i	−0.427755	+	0.427755i	−0.887863	−	0.460108i	$-0.847811\pi$
$761$	−11.8001	+	11.8001i	−0.427755	+	0.427755i	0.460108	+	0.887863i	$0.347811\pi$
$762$		0			0
$763$	3.23346	+	7.80627i	0.117059	+	0.282606i
$764$		0			0
$765$	2.76042	+	1.14340i	0.0998031	+	0.0413398i
$766$		0			0
$767$	29.8751			1.07873
$768$		0			0
$769$	8.82366			0.318189			0.159095	−	0.987263i	$-0.449142\pi$
$769$	8.82366			0.318189			0.159095	+	0.987263i	$0.449142\pi$
$770$		0			0
$771$	9.87062	+	4.08855i	0.355482	+	0.147245i
$772$		0			0
$773$	−7.48121	−	18.0612i	−0.269080	−	0.649617i	0.730360	−	0.683062i	$-0.239352\pi$
$773$	−7.48121	−	18.0612i	−0.269080	−	0.649617i	−0.999441	+	0.0334448i	$0.989352\pi$
$774$		0			0
$775$	2.97948	−	2.97948i	0.107026	−	0.107026i
$776$		0			0
$777$	6.15653	+	6.15653i	0.220864	+	0.220864i
$778$		0			0
$779$	88.2979	−	36.5742i	3.16360	−	1.31041i
$780$		0			0
$781$	−0.192369	+	0.464419i	−0.00688349	+	0.0166182i
$782$		0			0
$783$			0.700559i			0.0250359i
$784$		0			0
$785$		−	18.5841i		−	0.663296i
$786$		0			0
$787$	5.49189	−	13.2586i	0.195765	−	0.472618i	−0.795265	−	0.606263i	$-0.792668\pi$
$787$	5.49189	−	13.2586i	0.195765	−	0.472618i	0.991029	+	0.133645i	$0.0426681\pi$
$788$		0			0
$789$	0.957921	−	0.396784i	0.0341029	−	0.0141259i
$790$		0			0
$791$	−6.70813	−	6.70813i	−0.238514	−	0.238514i
$792$		0			0
$793$	32.9164	−	32.9164i	1.16890	−	1.16890i
$794$		0			0
$795$	−6.27017	−	15.1375i	−0.222380	−	0.536872i
$796$		0			0
$797$	−32.2565	−	13.3611i	−1.14258	−	0.473274i	−0.270544	−	0.962708i	$-0.587203\pi$
$797$	−32.2565	−	13.3611i	−1.14258	−	0.473274i	−0.872040	+	0.489434i	$0.837203\pi$
$798$		0			0
$799$	−4.89708			−0.173246
$800$		0			0
$801$	12.3104			0.434965
$802$		0			0
$803$	−1.04032	−	0.430916i	−0.0367122	−	0.0152067i
$804$		0			0
$805$	−5.75777	−	13.9005i	−0.202935	−	0.489928i
$806$		0			0
$807$	−1.39931	+	1.39931i	−0.0492582	+	0.0492582i
$808$		0			0
$809$	−37.6487	−	37.6487i	−1.32366	−	1.32366i	−0.910791	−	0.412867i	$-0.864527\pi$
$809$	−37.6487	−	37.6487i	−1.32366	−	1.32366i	−0.412867	−	0.910791i	$-0.635473\pi$
$810$		0			0
$811$	18.2939	−	7.57757i	0.642384	−	0.266084i	−0.0376202	−	0.999292i	$-0.511978\pi$
$811$	18.2939	−	7.57757i	0.642384	−	0.266084i	0.680005	+	0.733208i	$0.261978\pi$
$812$		0			0
$813$	−1.84036	+	4.44302i	−0.0645442	+	0.155824i
$814$		0			0
$815$			32.4539i			1.13681i
$816$		0			0
$817$			16.6176i			0.581377i
$818$		0			0
$819$	1.41741	−	3.42194i	0.0495285	−	0.119572i
$820$		0			0
$821$	17.7744	−	7.36238i	0.620330	−	0.256949i	−0.0503084	−	0.998734i	$-0.516020\pi$
$821$	17.7744	−	7.36238i	0.620330	−	0.256949i	0.670638	+	0.741785i	$0.266020\pi$
$822$		0			0
$823$	21.0095	+	21.0095i	0.732346	+	0.732346i	0.971084	−	0.238738i	$-0.0767338\pi$
$823$	21.0095	+	21.0095i	0.732346	+	0.732346i	−0.238738	+	0.971084i	$0.576734\pi$
$824$		0			0
$825$	−0.301936	+	0.301936i	−0.0105121	+	0.0105121i
$826$		0			0
$827$	−9.54821	−	23.0514i	−0.332024	−	0.801577i	−0.998431	−	0.0559889i	$-0.982169\pi$
$827$	−9.54821	−	23.0514i	−0.332024	−	0.801577i	0.666408	−	0.745588i	$-0.267831\pi$
$828$		0			0
$829$	−2.96213	−	1.22696i	−0.102879	−	0.0426140i	0.330650	−	0.943753i	$-0.392732\pi$
$829$	−2.96213	−	1.22696i	−0.102879	−	0.0426140i	−0.433529	+	0.901139i	$0.642732\pi$
$830$		0			0
$831$	−9.03763			−0.313512
$832$		0			0
$833$	9.41760			0.326300
$834$		0			0
$835$	−18.3725	−	7.61016i	−0.635808	−	0.263360i
$836$		0			0
$837$	−1.40238	−	3.38565i	−0.0484734	−	0.117025i
$838$		0			0
$839$	−28.5404	+	28.5404i	−0.985326	+	0.985326i	−0.999894	−	0.0145682i	$-0.995363\pi$
$839$	−28.5404	+	28.5404i	−0.985326	+	0.985326i	0.0145682	+	0.999894i	$0.495363\pi$
$840$		0			0
$841$	−20.1591	−	20.1591i	−0.695140	−	0.695140i
$842$		0			0
$843$	−11.4567	+	4.74553i	−0.394591	+	0.163445i
$844$		0			0
$845$	2.87398	−	6.93840i	0.0988679	−	0.238688i
$846$		0			0
$847$		−	9.80759i		−	0.336993i
$848$		0			0
$849$			19.9318i			0.684057i
$850$		0			0
$851$	−31.3377	+	75.6560i	−1.07424	+	2.59345i
$852$		0			0
$853$	21.0190	−	8.70635i	0.719677	−	0.298100i	0.00737458	−	0.999973i	$-0.497653\pi$
$853$	21.0190	−	8.70635i	0.719677	−	0.298100i	0.712302	+	0.701873i	$0.247653\pi$
$854$		0			0
$855$	−11.4355	−	11.4355i	−0.391084	−	0.391084i
$856$		0			0
$857$	11.4073	−	11.4073i	0.389665	−	0.389665i	−0.484903	−	0.874568i	$-0.661145\pi$
$857$	11.4073	−	11.4073i	0.389665	−	0.389665i	0.874568	+	0.484903i	$0.161145\pi$
$858$		0			0
$859$	2.82922	+	6.83034i	0.0965317	+	0.233048i	0.964768	−	0.263103i	$-0.0847461\pi$
$859$	2.82922	+	6.83034i	0.0965317	+	0.233048i	−0.868236	+	0.496151i	$0.834746\pi$
$860$		0			0
$861$	−9.67322	−	4.00678i	−0.329663	−	0.136551i
$862$		0			0
$863$	−19.4563			−0.662299			−0.331150	−	0.943578i	$-0.607436\pi$
$863$	−19.4563			−0.662299			−0.331150	+	0.943578i	$0.607436\pi$
$864$		0			0
$865$	−22.9340			−0.779781
$866$		0			0
$867$	−13.5638	−	5.61830i	−0.460650	−	0.190808i
$868$		0			0
$869$	−0.0892702	−	0.215517i	−0.00302829	−	0.00731093i
$870$		0			0
$871$	20.6220	−	20.6220i	0.698751	−	0.698751i
$872$		0			0
$873$	7.23988	+	7.23988i	0.245033	+	0.245033i
$874$		0			0
$875$	−10.0662	+	4.16957i	−0.340301	+	0.140957i
$876$		0			0
$877$	12.6782	−	30.6079i	0.428112	−	1.03355i	−0.551773	−	0.833994i	$-0.686049\pi$
$877$	12.6782	−	30.6079i	0.428112	−	1.03355i	0.979885	−	0.199561i	$-0.0639515\pi$
$878$		0			0
$879$		−	9.27107i		−	0.312705i
$880$		0			0
$881$		−	19.3726i		−	0.652680i	−0.945252	−	0.326340i	$-0.894185\pi$
$881$		−	19.3726i		−	0.652680i	0.945252	−	0.326340i	$-0.105815\pi$
$882$		0			0
$883$	12.1472	−	29.3260i	0.408787	−	0.986899i	−0.576670	−	0.816977i	$-0.695648\pi$
$883$	12.1472	−	29.3260i	0.408787	−	0.986899i	0.985457	−	0.169922i	$-0.0543517\pi$
$884$		0			0
$885$	−13.2025	+	5.46867i	−0.443799	+	0.183827i
$886$		0			0
$887$	−25.5426	−	25.5426i	−0.857636	−	0.857636i	0.133423	−	0.991059i	$-0.457403\pi$
$887$	−25.5426	−	25.5426i	−0.857636	−	0.857636i	−0.991059	+	0.133423i	$0.957403\pi$
$888$		0			0
$889$	1.47445	−	1.47445i	0.0494515	−	0.0494515i
$890$		0			0
$891$	0.142115	+	0.343096i	0.00476103	+	0.0114942i
$892$		0			0
$893$	24.4885	+	10.1435i	0.819476	+	0.339438i
$894$		0			0
$895$	7.42150			0.248074
$896$		0			0
$897$	34.8365			1.16316
$898$		0			0
$899$	−2.37185	−	0.982451i	−0.0791055	−	0.0327666i
$900$		0			0
$901$	−4.86583	−	11.7472i	−0.162104	−	0.391355i
$902$		0			0
$903$	1.28729	−	1.28729i	0.0428382	−	0.0428382i
$904$		0			0
$905$	−15.3161	−	15.3161i	−0.509123	−	0.509123i
$906$		0			0
$907$	−36.9589	+	15.3089i	−1.22720	+	0.508323i	−0.899692	−	0.436525i	$-0.856209\pi$
$907$	−36.9589	+	15.3089i	−1.22720	+	0.508323i	−0.327509	+	0.944848i	$0.606209\pi$
$908$		0			0
$909$	−1.36634	+	3.29864i	−0.0453187	+	0.109409i
$910$		0			0
$911$		−	33.2235i		−	1.10074i	−0.834920	−	0.550372i	$-0.814486\pi$
$911$		−	33.2235i		−	1.10074i	0.834920	−	0.550372i	$-0.185514\pi$
$912$		0			0
$913$		−	4.05432i		−	0.134178i
$914$		0			0
$915$	−8.52117	+	20.5719i	−0.281701	+	0.680087i
$916$		0			0
$917$	4.33851	−	1.79707i	0.143270	−	0.0593445i
$918$		0			0
$919$	20.6698	+	20.6698i	0.681834	+	0.681834i	0.960413	−	0.278579i	$-0.0898634\pi$
$919$	20.6698	+	20.6698i	0.681834	+	0.681834i	−0.278579	+	0.960413i	$0.589863\pi$
$920$		0			0
$921$	−20.1807	+	20.1807i	−0.664978	+	0.664978i
$922$		0			0
$923$	−2.12492	−	5.13001i	−0.0699425	−	0.168856i
$924$		0			0
$925$	10.2435	+	4.24298i	0.336803	+	0.139508i
$926$		0			0
$927$	2.86201			0.0940007
$928$		0			0
$929$	−40.8116			−1.33899			−0.669493	−	0.742819i	$-0.733488\pi$
$929$	−40.8116			−1.33899			−0.669493	+	0.742819i	$0.733488\pi$
$930$		0			0
$931$	−47.0939	−	19.5069i	−1.54344	−	0.639314i
$932$		0			0
$933$	5.42740	+	13.1029i	0.177685	+	0.428969i
$934$		0			0
$935$	0.784594	−	0.784594i	0.0256590	−	0.0256590i
$936$		0			0
$937$	17.9669	+	17.9669i	0.586953	+	0.586953i	0.936805	−	0.349852i	$-0.113768\pi$
$937$	17.9669	+	17.9669i	0.586953	+	0.586953i	−0.349852	+	0.936805i	$0.613768\pi$
$938$		0			0
$939$	17.8907	−	7.41059i	0.583842	−	0.241835i
$940$		0			0
$941$	−4.59141	+	11.0846i	−0.149676	+	0.361349i	−0.980879	−	0.194620i	$-0.937653\pi$
$941$	−4.59141	+	11.0846i	−0.149676	+	0.361349i	0.831203	+	0.555969i	$0.187653\pi$
$942$		0			0
$943$		−	98.4765i		−	3.20683i
$944$		0			0
$945$			1.77170i			0.0576333i
$946$		0			0
$947$	12.6675	−	30.5820i	0.411638	−	0.993781i	−0.573061	−	0.819513i	$-0.694244\pi$
$947$	12.6675	−	30.5820i	0.411638	−	0.993781i	0.984698	−	0.174268i	$-0.0557560\pi$
$948$		0			0
$949$	11.4915	−	4.75993i	0.373030	−	0.154514i
$950$		0			0
$951$	2.97533	+	2.97533i	0.0964816	+	0.0964816i
$952$		0			0
$953$	−12.1459	+	12.1459i	−0.393443	+	0.393443i	−0.875913	−	0.482469i	$-0.839740\pi$
$953$	−12.1459	+	12.1459i	−0.393443	+	0.393443i	0.482469	+	0.875913i	$0.339740\pi$
$954$		0			0
$955$	0.927013	+	2.23801i	0.0299974	+	0.0724202i
$956$		0			0
$957$	0.240359	+	0.0995600i	0.00776971	+	0.00321832i
$958$		0			0
$959$	−8.24555			−0.266263
$960$		0			0
$961$	−17.5707			−0.566798
$962$		0			0
$963$	8.80292	+	3.64629i	0.283670	+	0.117500i
$964$		0			0
$965$	8.73912	+	21.0981i	0.281322	+	0.679172i
$966$		0			0
$967$	−17.1419	+	17.1419i	−0.551247	+	0.551247i	−0.926801	−	0.375554i	$-0.877453\pi$
$967$	−17.1419	+	17.1419i	−0.551247	+	0.551247i	0.375554	+	0.926801i	$0.377453\pi$
$968$		0			0
$969$	−8.87426	−	8.87426i	−0.285082	−	0.285082i
$970$		0			0
$971$	6.66860	−	2.76223i	0.214006	−	0.0886440i	−0.273105	−	0.961984i	$-0.588051\pi$
$971$	6.66860	−	2.76223i	0.214006	−	0.0886440i	0.487111	+	0.873340i	$0.338051\pi$
$972$		0			0
$973$	−5.16453	+	12.4683i	−0.165567	+	0.399715i
$974$		0			0
$975$		−	4.71669i		−	0.151055i
$976$		0			0
$977$			10.1771i			0.325595i	0.986659	+	0.162798i	$0.0520518\pi$
$977$			10.1771i			0.325595i	−0.986659	+	0.162798i	$0.947948\pi$
$978$		0			0
$979$	1.74949	−	4.22364i	0.0559139	−	0.134988i
$980$		0			0
$981$	8.64559	−	3.58112i	0.276032	−	0.114336i
$982$		0			0
$983$	27.2758	+	27.2758i	0.869964	+	0.869964i	0.992468	−	0.122504i	$-0.0390924\pi$
$983$	27.2758	+	27.2758i	0.869964	+	0.869964i	−0.122504	+	0.992468i	$0.539092\pi$
$984$		0			0
$985$	28.8951	−	28.8951i	0.920674	−	0.920674i
$986$		0			0
$987$	−1.11124	−	2.68277i	−0.0353711	−	0.0853934i
$988$		0			0
$989$	15.8191	+	6.55249i	0.503018	+	0.208357i
$990$		0			0
$991$	−23.2742			−0.739330			−0.369665	−	0.929165i	$-0.620528\pi$
$991$	−23.2742			−0.739330			−0.369665	+	0.929165i	$0.620528\pi$
$992$		0			0
$993$	26.2465			0.832908
$994$		0			0
$995$	−26.6141	−	11.0239i	−0.843724	−	0.349482i
$996$		0			0
$997$	−4.77878	−	11.5370i	−0.151346	−	0.365381i	0.829964	−	0.557817i	$-0.188361\pi$
$997$	−4.77878	−	11.5370i	−0.151346	−	0.365381i	−0.981309	+	0.192437i	$0.938361\pi$
$998$		0			0
$999$	6.81848	−	6.81848i	0.215727	−	0.215727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.n.a.337.4		32
3.2	odd	2		1152.2.v.c.721.2		32
4.3	odd	2		96.2.n.a.61.2	✓	32
8.3	odd	2		768.2.n.a.673.1		32
8.5	even	2		768.2.n.b.673.5		32
12.11	even	2		288.2.v.d.253.7		32
32.5	even	8		768.2.n.b.97.5		32
32.11	odd	8		96.2.n.a.85.2	yes	32
32.21	even	8	inner	384.2.n.a.49.4		32
32.27	odd	8		768.2.n.a.97.1		32
96.11	even	8		288.2.v.d.181.7		32
96.53	odd	8		1152.2.v.c.433.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.2	✓	32	4.3	odd	2
96.2.n.a.85.2	yes	32	32.11	odd	8
288.2.v.d.181.7		32	96.11	even	8
288.2.v.d.253.7		32	12.11	even	2
384.2.n.a.49.4		32	32.21	even	8	inner
384.2.n.a.337.4		32	1.1	even	1	trivial
768.2.n.a.97.1		32	32.27	odd	8
768.2.n.a.673.1		32	8.3	odd	2
768.2.n.b.97.5		32	32.5	even	8
768.2.n.b.673.5		32	8.5	even	2
1152.2.v.c.433.2		32	96.53	odd	8
1152.2.v.c.721.2		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)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{3} +(0.750897 + 1.81283i) q^{5} +(-0.638460 + 0.638460i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.923880 - 0.382683i) q^{3} +(0.750897 + 1.81283i) q^{5} +(-0.638460 + 0.638460i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.343096 - 0.142115i) q^{11} +(-1.56981 + 3.78987i) q^{13} -1.96219i q^{15} -1.52272i q^{17} +(-3.15404 + 7.61453i) q^{19} +(0.834188 - 0.345532i) q^{21} +(6.00496 + 6.00496i) q^{23} +(0.813044 - 0.813044i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(-0.647232 - 0.268092i) q^{29} +3.66460 q^{31} -0.371365 q^{33} +(-1.63683 - 0.677999i) q^{35} +(3.69013 + 8.90877i) q^{37} +(2.90064 - 2.90064i) q^{39} +(-8.19959 - 8.19959i) q^{41} +(1.86276 - 0.771580i) q^{43} +(-0.750897 + 1.81283i) q^{45} -3.21602i q^{47} +6.18474i q^{49} +(-0.582718 + 1.40681i) q^{51} +(7.71461 - 3.19550i) q^{53} +(0.515260 + 0.515260i) q^{55} +(5.82791 - 5.82791i) q^{57} +(-2.78703 - 6.72848i) q^{59} +(-10.4842 - 4.34269i) q^{61} -0.902919 q^{63} -8.04913 q^{65} +(-6.56831 - 2.72068i) q^{67} +(-3.24986 - 7.84586i) q^{69} +(-0.957148 + 0.957148i) q^{71} +(-2.14406 - 2.14406i) q^{73} +(-1.06229 + 0.440016i) q^{75} +(-0.128318 + 0.309788i) q^{77} -0.628155i q^{79} +1.00000i q^{81} +(4.17789 - 10.0863i) q^{83} +(2.76042 - 1.14340i) q^{85} +(0.495370 + 0.495370i) q^{87} +(8.70474 - 8.70474i) q^{89} +(-1.41741 - 3.42194i) q^{91} +(-3.38565 - 1.40238i) q^{93} -16.1722 q^{95} +10.2387 q^{97} +(0.343096 + 0.142115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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