LMFDB - Embedded newform 768.2.r.a.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(49,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(16))

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("768.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.r (of order $16$, degree $8$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	768.49
Dual form			768.2.r.a.721.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.980785 - 0.195090i) q^{3} +(-0.620781 - 0.929065i) q^{5} +(3.49586 + 1.44803i) q^{7} +(0.923880 - 0.382683i) q^{9} +O(q^{10})$	\(q+(0.980785 - 0.195090i) q^{3} +(-0.620781 - 0.929065i) q^{5} +(3.49586 + 1.44803i) q^{7} +(0.923880 - 0.382683i) q^{9} +(-0.138491 + 0.696240i) q^{11} +(3.26066 - 4.87993i) q^{13} +(-0.790105 - 0.790105i) q^{15} +(-1.76136 + 1.76136i) q^{17} +(-3.44626 - 2.30272i) q^{19} +(3.71118 + 0.738200i) q^{21} +(1.98584 + 4.79424i) q^{23} +(1.43563 - 3.46591i) q^{25} +(0.831470 - 0.555570i) q^{27} +(1.63206 + 8.20490i) q^{29} +2.85986i q^{31} +0.709881i q^{33} +(-0.824847 - 4.14679i) q^{35} +(9.21628 - 6.15812i) q^{37} +(2.24599 - 5.42229i) q^{39} +(-1.40714 - 3.39715i) q^{41} +(-2.84388 - 0.565682i) q^{43} +(-0.929065 - 0.620781i) q^{45} +(4.57246 - 4.57246i) q^{47} +(5.17447 + 5.17447i) q^{49} +(-1.38389 + 2.07114i) q^{51} +(1.62802 - 8.18462i) q^{53} +(0.732825 - 0.303546i) q^{55} +(-3.82928 - 1.58614i) q^{57} +(3.01734 + 4.51578i) q^{59} +(-4.52385 + 0.899849i) q^{61} +3.78389 q^{63} -6.55793 q^{65} +(2.79768 - 0.556492i) q^{67} +(2.88299 + 4.31470i) q^{69} +(-0.612866 - 0.253858i) q^{71} +(-7.40717 + 3.06815i) q^{73} +(0.731875 - 3.67939i) q^{75} +(-1.49232 + 2.23342i) q^{77} +(0.0773152 + 0.0773152i) q^{79} +(0.707107 - 0.707107i) q^{81} +(-13.2328 - 8.84185i) q^{83} +(2.72983 + 0.542997i) q^{85} +(3.20139 + 7.72885i) q^{87} +(-5.72963 + 13.8326i) q^{89} +(18.4651 - 12.3380i) q^{91} +(0.557931 + 2.80491i) q^{93} +4.63128i q^{95} +11.3093i q^{97} +(0.138491 + 0.696240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 32 q^{51} + 64 q^{55} + 128 q^{59} + 32 q^{63} + 32 q^{67} + 128 q^{71} + 64 q^{75} + 32 q^{79}+O(q^{100}) $ 128 * q + 32 * q^51 + 64 * q^55 + 128 * q^59 + 32 * q^63 + 32 * q^67 + 128 * q^71 + 64 * q^75 + 32 * q^79

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

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
$3$	0.980785	−	0.195090i	0.566257	−	0.112635i
$3$	0.980785	−	0.195090i	0.566257	−	0.112635i
$4$		0			0
$5$	−0.620781	−	0.929065i	−0.277622	−	0.415490i	0.666288	−	0.745695i	$-0.267882\pi$
$5$	−0.620781	−	0.929065i	−0.277622	−	0.415490i	−0.943909	+	0.330204i	$0.892882\pi$
$6$		0			0
$7$	3.49586	+	1.44803i	1.32131	+	0.547304i	0.928164	−	0.372172i	$-0.121387\pi$
$7$	3.49586	+	1.44803i	1.32131	+	0.547304i	0.393145	+	0.919476i	$0.371387\pi$
$8$		0			0
$9$	0.923880	−	0.382683i	0.307960	−	0.127561i
$10$		0			0
$11$	−0.138491	+	0.696240i	−0.0417566	+	0.209924i	−0.996031	−	0.0890077i	$-0.971630\pi$
$11$	−0.138491	+	0.696240i	−0.0417566	+	0.209924i	0.954274	+	0.298932i	$0.0966304\pi$
$12$		0			0
$13$	3.26066	−	4.87993i	0.904346	−	1.35345i	−0.0309272	−	0.999522i	$-0.509846\pi$
$13$	3.26066	−	4.87993i	0.904346	−	1.35345i	0.935273	−	0.353927i	$-0.115154\pi$
$14$		0			0
$15$	−0.790105	−	0.790105i	−0.204004	−	0.204004i
$16$		0			0
$17$	−1.76136	+	1.76136i	−0.427192	+	0.427192i	−0.887671	−	0.460479i	$-0.847678\pi$
$17$	−1.76136	+	1.76136i	−0.427192	+	0.427192i	0.460479	+	0.887671i	$0.347678\pi$
$18$		0			0
$19$	−3.44626	−	2.30272i	−0.790626	−	0.528279i	0.0934494	−	0.995624i	$-0.470211\pi$
$19$	−3.44626	−	2.30272i	−0.790626	−	0.528279i	−0.884075	+	0.467345i	$0.845211\pi$
$20$		0			0
$21$	3.71118	+	0.738200i	0.809846	+	0.161088i
$22$		0			0
$23$	1.98584	+	4.79424i	0.414076	+	0.999668i	0.984032	+	0.177992i	$0.0569603\pi$
$23$	1.98584	+	4.79424i	0.414076	+	0.999668i	−0.569956	+	0.821675i	$0.693040\pi$
$24$		0			0
$25$	1.43563	−	3.46591i	0.287125	−	0.693181i
$26$		0			0
$27$	0.831470	−	0.555570i	0.160016	−	0.106920i
$28$		0			0
$29$	1.63206	+	8.20490i	0.303065	+	1.52361i	0.769264	+	0.638932i	$0.220623\pi$
$29$	1.63206	+	8.20490i	0.303065	+	1.52361i	−0.466198	+	0.884680i	$0.654377\pi$
$30$		0			0
$31$			2.85986i			0.513646i	0.966458	+	0.256823i	$0.0826757\pi$
$31$			2.85986i			0.513646i	−0.966458	+	0.256823i	$0.917324\pi$
$32$		0			0
$33$			0.709881i			0.123574i
$34$		0			0
$35$	−0.824847	−	4.14679i	−0.139425	−	0.700935i
$36$		0			0
$37$	9.21628	−	6.15812i	1.51515	−	1.01239i	0.528608	−	0.848866i	$-0.322714\pi$
$37$	9.21628	−	6.15812i	1.51515	−	1.01239i	0.986540	−	0.163523i	$-0.0522857\pi$
$38$		0			0
$39$	2.24599	−	5.42229i	0.359645	−	0.868261i
$40$		0			0
$41$	−1.40714	−	3.39715i	−0.219759	−	0.530545i	0.775097	−	0.631842i	$-0.217701\pi$
$41$	−1.40714	−	3.39715i	−0.219759	−	0.530545i	−0.994856	+	0.101297i	$0.967701\pi$
$42$		0			0
$43$	−2.84388	−	0.565682i	−0.433687	−	0.0862657i	−0.0265812	−	0.999647i	$-0.508462\pi$
$43$	−2.84388	−	0.565682i	−0.433687	−	0.0862657i	−0.407106	+	0.913381i	$0.633462\pi$
$44$		0			0
$45$	−0.929065	−	0.620781i	−0.138497	−	0.0925406i
$46$		0			0
$47$	4.57246	−	4.57246i	0.666961	−	0.666961i	−0.290050	−	0.957011i	$-0.593672\pi$
$47$	4.57246	−	4.57246i	0.666961	−	0.666961i	0.957011	+	0.290050i	$0.0936719\pi$
$48$		0			0
$49$	5.17447	+	5.17447i	0.739209	+	0.739209i
$50$		0			0
$51$	−1.38389	+	2.07114i	−0.193783	+	0.290017i
$52$		0			0
$53$	1.62802	−	8.18462i	0.223626	−	1.12424i	−0.691903	−	0.721991i	$-0.743227\pi$
$53$	1.62802	−	8.18462i	0.223626	−	1.12424i	0.915529	−	0.402253i	$-0.131773\pi$
$54$		0			0
$55$	0.732825	−	0.303546i	0.0988141	−	0.0409301i
$56$		0			0
$57$	−3.82928	−	1.58614i	−0.507200	−	0.210089i
$58$		0			0
$59$	3.01734	+	4.51578i	0.392825	+	0.587904i	0.974187	−	0.225741i	$-0.0724802\pi$
$59$	3.01734	+	4.51578i	0.392825	+	0.587904i	−0.581363	+	0.813645i	$0.697480\pi$
$60$		0			0
$61$	−4.52385	+	0.899849i	−0.579219	+	0.115214i	−0.476001	−	0.879445i	$-0.657914\pi$
$61$	−4.52385	+	0.899849i	−0.579219	+	0.115214i	−0.103218	+	0.994659i	$0.532914\pi$
$62$		0			0
$63$	3.78389			0.476725
$64$		0			0
$65$	−6.55793			−0.813411
$66$		0			0
$67$	2.79768	−	0.556492i	0.341791	−	0.0679864i	−0.0212107	−	0.999775i	$-0.506752\pi$
$67$	2.79768	−	0.556492i	0.341791	−	0.0679864i	0.363001	+	0.931789i	$0.381752\pi$
$68$		0			0
$69$	2.88299	+	4.31470i	0.347071	+	0.519429i
$70$		0			0
$71$	−0.612866	−	0.253858i	−0.0727339	−	0.0301273i	0.346020	−	0.938227i	$-0.387533\pi$
$71$	−0.612866	−	0.253858i	−0.0727339	−	0.0301273i	−0.418754	+	0.908100i	$0.637533\pi$
$72$		0			0
$73$	−7.40717	+	3.06815i	−0.866944	+	0.359100i	−0.771419	−	0.636327i	$-0.780453\pi$
$73$	−7.40717	+	3.06815i	−0.866944	+	0.359100i	−0.0955247	+	0.995427i	$0.530453\pi$
$74$		0			0
$75$	0.731875	−	3.67939i	0.0845097	−	0.424859i
$76$		0			0
$77$	−1.49232	+	2.23342i	−0.170066	+	0.254521i
$78$		0			0
$79$	0.0773152	+	0.0773152i	0.00869864	+	0.00869864i	0.711443	−	0.702744i	$-0.248042\pi$
$79$	0.0773152	+	0.0773152i	0.00869864	+	0.00869864i	−0.702744	+	0.711443i	$0.748042\pi$
$80$		0			0
$81$	0.707107	−	0.707107i	0.0785674	−	0.0785674i
$82$		0			0
$83$	−13.2328	−	8.84185i	−1.45248	−	0.970519i	−0.996763	−	0.0803973i	$-0.974381\pi$
$83$	−13.2328	−	8.84185i	−1.45248	−	0.970519i	−0.455722	−	0.890122i	$-0.650619\pi$
$84$		0			0
$85$	2.72983	+	0.542997i	0.296092	+	0.0588963i
$86$		0			0
$87$	3.20139	+	7.72885i	0.343225	+	0.828619i
$88$		0			0
$89$	−5.72963	+	13.8326i	−0.607340	+	1.46625i	0.258542	+	0.966000i	$0.416758\pi$
$89$	−5.72963	+	13.8326i	−0.607340	+	1.46625i	−0.865882	+	0.500248i	$0.833242\pi$
$90$		0			0
$91$	18.4651	−	12.3380i	1.93567	−	1.29337i
$92$		0			0
$93$	0.557931	+	2.80491i	0.0578547	+	0.290855i
$94$		0			0
$95$			4.63128i			0.475159i
$96$		0			0
$97$			11.3093i			1.14828i	0.818757	+	0.574140i	$0.194664\pi$
$97$			11.3093i			1.14828i	−0.818757	+	0.574140i	$0.805336\pi$
$98$		0			0
$99$	0.138491	+	0.696240i	0.0139189	+	0.0699748i
$100$		0			0
$101$	−2.75095	+	1.83813i	−0.273730	+	0.182900i	−0.684857	−	0.728678i	$-0.740135\pi$
$101$	−2.75095	+	1.83813i	−0.273730	+	0.182900i	0.411127	+	0.911578i	$0.365135\pi$
$102$		0			0
$103$	−7.32914	+	17.6941i	−0.722162	+	1.74345i	−0.0550629	+	0.998483i	$0.517536\pi$
$103$	−7.32914	+	17.6941i	−0.722162	+	1.74345i	−0.667099	+	0.744969i	$0.732464\pi$
$104$		0			0
$105$	−1.61800	−	3.90619i	−0.157900	−	0.381205i
$106$		0			0
$107$	2.58430	+	0.514049i	0.249834	+	0.0496950i	0.318418	−	0.947950i	$-0.396848\pi$
$107$	2.58430	+	0.514049i	0.249834	+	0.0496950i	−0.0685846	+	0.997645i	$0.521848\pi$
$108$		0			0
$109$	−9.46703	−	6.32567i	−0.906777	−	0.605889i	0.0123185	−	0.999924i	$-0.496079\pi$
$109$	−9.46703	−	6.32567i	−0.906777	−	0.605889i	−0.919095	+	0.394035i	$0.871079\pi$
$110$		0			0
$111$	7.83780	−	7.83780i	0.743931	−	0.743931i
$112$		0			0
$113$	−5.39340	−	5.39340i	−0.507368	−	0.507368i	0.406349	−	0.913718i	$-0.366802\pi$
$113$	−5.39340	−	5.39340i	−0.507368	−	0.507368i	−0.913718	+	0.406349i	$0.866802\pi$
$114$		0			0
$115$	3.22139	−	4.82115i	0.300396	−	0.449574i
$116$		0			0
$117$	1.14499	−	5.75627i	0.105855	−	0.532167i
$118$		0			0
$119$	−8.70795	+	3.60695i	−0.798256	+	0.330649i
$120$		0			0
$121$	9.69710	+	4.01667i	0.881555	+	0.365152i
$122$		0			0
$123$	−2.04286	−	3.05735i	−0.184198	−	0.275672i
$124$		0			0
$125$	−9.59079	+	1.90773i	−0.857827	+	0.170632i
$126$		0			0
$127$	−9.49359			−0.842420			−0.421210	−	0.906963i	$-0.638394\pi$
$127$	−9.49359			−0.842420			−0.421210	+	0.906963i	$0.638394\pi$
$128$		0			0
$129$	−2.89959			−0.255295
$130$		0			0
$131$	−21.5523	+	4.28702i	−1.88303	+	0.374559i	−0.996167	−	0.0874690i	$-0.972122\pi$
$131$	−21.5523	+	4.28702i	−1.88303	+	0.374559i	−0.886866	+	0.462028i	$0.847122\pi$
$132$		0			0
$133$	−8.71322	−	13.0402i	−0.755532	−	1.13073i
$134$		0			0
$135$	−1.03232	−	0.427602i	−0.0888481	−	0.0368021i
$136$		0			0
$137$	3.41140	−	1.41305i	0.291456	−	0.120725i	−0.232165	−	0.972676i	$-0.574581\pi$
$137$	3.41140	−	1.41305i	0.291456	−	0.120725i	0.523621	+	0.851951i	$0.324581\pi$
$138$		0			0
$139$	−1.36309	+	6.85272i	−0.115616	+	0.581240i	0.878931	+	0.476949i	$0.158257\pi$
$139$	−1.36309	+	6.85272i	−0.115616	+	0.581240i	−0.994547	+	0.104291i	$0.966743\pi$
$140$		0			0
$141$	3.59256	−	5.37664i	0.302548	−	0.452795i
$142$		0			0
$143$	2.94603	+	2.94603i	0.246360	+	0.246360i
$144$		0			0
$145$	6.60974	−	6.60974i	0.548909	−	0.548909i
$146$		0			0
$147$	6.08453	+	4.06555i	0.501843	+	0.335321i
$148$		0			0
$149$	16.3709	+	3.25638i	1.34116	+	0.266773i	0.812947	−	0.582338i	$-0.197862\pi$
$149$	16.3709	+	3.25638i	1.34116	+	0.266773i	0.528213	+	0.849112i	$0.322862\pi$
$150$		0			0
$151$	3.38869	+	8.18102i	0.275768	+	0.665762i	0.999710	−	0.0240991i	$-0.00767172\pi$
$151$	3.38869	+	8.18102i	0.275768	+	0.665762i	−0.723942	+	0.689861i	$0.757672\pi$
$152$		0			0
$153$	−0.953239	+	2.30132i	−0.0770648	+	0.186051i
$154$		0			0
$155$	2.65699	−	1.77535i	0.213415	−	0.142599i
$156$		0			0
$157$	0.0499067	+	0.250898i	0.00398299	+	0.0200238i	0.982726	−	0.185068i	$-0.0592506\pi$
$157$	0.0499067	+	0.250898i	0.00398299	+	0.0200238i	−0.978743	+	0.205092i	$0.934251\pi$
$158$		0			0
$159$		−	8.34496i		−	0.661799i
$160$		0			0
$161$			19.6355i			1.54750i
$162$		0			0
$163$	0.0676192	+	0.339945i	0.00529635	+	0.0266265i	0.983343	−	0.181759i	$-0.0581791\pi$
$163$	0.0676192	+	0.339945i	0.00529635	+	0.0266265i	−0.978047	+	0.208386i	$0.933179\pi$
$164$		0			0
$165$	0.659525	−	0.440681i	0.0513440	−	0.0343069i
$166$		0			0
$167$	4.03890	−	9.75077i	0.312540	−	0.754538i	−0.687070	−	0.726591i	$-0.741103\pi$
$167$	4.03890	−	9.75077i	0.312540	−	0.754538i	0.999609	−	0.0279461i	$-0.00889667\pi$
$168$		0			0
$169$	−8.20690	−	19.8132i	−0.631300	−	1.52409i
$170$		0			0
$171$	−4.06514	−	0.808606i	−0.310869	−	0.0618357i
$172$		0			0
$173$	2.78323	+	1.85969i	0.211605	+	0.141390i	0.656857	−	0.754016i	$-0.271886\pi$
$173$	2.78323	+	1.85969i	0.211605	+	0.141390i	−0.445251	+	0.895406i	$0.646886\pi$
$174$		0			0
$175$	10.0375	−	10.0375i	0.758762	−	0.758762i
$176$		0			0
$177$	3.84035	+	3.84035i	0.288658	+	0.288658i
$178$		0			0
$179$	−5.11334	+	7.65265i	−0.382189	+	0.571986i	−0.971831	−	0.235679i	$-0.924269\pi$
$179$	−5.11334	+	7.65265i	−0.382189	+	0.571986i	0.589642	+	0.807664i	$0.299269\pi$
$180$		0			0
$181$	−2.58040	+	12.9725i	−0.191799	+	0.964241i	0.758208	+	0.652013i	$0.226075\pi$
$181$	−2.58040	+	12.9725i	−0.191799	+	0.964241i	−0.950007	+	0.312228i	$0.898925\pi$
$182$		0			0
$183$	−4.26137	+	1.76512i	−0.315010	+	0.130481i
$184$		0			0
$185$	−11.4426	−	4.73968i	−0.841276	−	0.348468i
$186$		0			0
$187$	−0.982396	−	1.47026i	−0.0718399	−	0.107516i
$188$		0			0
$189$	3.71118	−	0.738200i	0.269949	−	0.0536961i
$190$		0			0
$191$	−25.3777			−1.83627			−0.918133	−	0.396273i	$-0.870303\pi$
$191$	−25.3777			−1.83627			−0.918133	+	0.396273i	$0.870303\pi$
$192$		0			0
$193$	14.0067			1.00822			0.504112	−	0.863638i	$-0.331820\pi$
$193$	14.0067			1.00822			0.504112	+	0.863638i	$0.331820\pi$
$194$		0			0
$195$	−6.43192	+	1.27939i	−0.460600	+	0.0916189i
$196$		0			0
$197$	−5.00215	−	7.48625i	−0.356389	−	0.533373i	0.609346	−	0.792904i	$-0.291432\pi$
$197$	−5.00215	−	7.48625i	−0.356389	−	0.533373i	−0.965735	+	0.259531i	$0.916432\pi$
$198$		0			0
$199$	−9.18674	−	3.80527i	−0.651231	−	0.269749i	0.0325124	−	0.999471i	$-0.489649\pi$
$199$	−9.18674	−	3.80527i	−0.651231	−	0.269749i	−0.683743	+	0.729723i	$0.739649\pi$
$200$		0			0
$201$	2.63535	−	1.09160i	0.185884	−	0.0769955i
$202$		0			0
$203$	−6.17552	+	31.0464i	−0.433436	+	2.17903i
$204$		0			0
$205$	−2.28264	+	3.41621i	−0.159427	+	0.238599i
$206$		0			0
$207$	3.66935	+	3.66935i	0.255038	+	0.255038i
$208$		0			0
$209$	2.08052	−	2.08052i	0.143912	−	0.143912i
$210$		0			0
$211$	−15.8849	−	10.6139i	−1.09356	−	0.730694i	−0.128236	−	0.991744i	$-0.540931\pi$
$211$	−15.8849	−	10.6139i	−1.09356	−	0.730694i	−0.965325	+	0.261049i	$0.915931\pi$
$212$		0			0
$213$	−0.650615	−	0.129415i	−0.0445794	−	0.00886740i
$214$		0			0
$215$	1.23987	+	2.99331i	0.0845584	+	0.204142i
$216$		0			0
$217$	−4.14116	+	9.99766i	−0.281121	+	0.678685i
$218$		0			0
$219$	−6.66628	+	4.45427i	−0.450465	+	0.300991i
$220$		0			0
$221$	2.85210	+	14.3385i	0.191853	+	0.964511i
$222$		0			0
$223$		−	14.4176i		−	0.965471i	−0.875766	−	0.482736i	$-0.839643\pi$
$223$		−	14.4176i		−	0.965471i	0.875766	−	0.482736i	$-0.160357\pi$
$224$		0			0
$225$		−	3.75147i		−	0.250098i
$226$		0			0
$227$	2.46677	+	12.4013i	0.163725	+	0.823103i	0.972124	+	0.234468i	$0.0753347\pi$
$227$	2.46677	+	12.4013i	0.163725	+	0.823103i	−0.808399	+	0.588636i	$0.799665\pi$
$228$		0			0
$229$	−20.8026	+	13.8998i	−1.37467	+	0.918527i	−0.999963	−	0.00861437i	$-0.997258\pi$
$229$	−20.8026	+	13.8998i	−1.37467	+	0.918527i	−0.374711	+	0.927142i	$0.622258\pi$
$230$		0			0
$231$	−1.02793	+	2.48164i	−0.0676328	+	0.163280i
$232$		0			0
$233$	−7.55706	−	18.2444i	−0.495080	−	1.19523i	−0.952104	−	0.305774i	$-0.901085\pi$
$233$	−7.55706	−	18.2444i	−0.495080	−	1.19523i	0.457025	−	0.889454i	$-0.348915\pi$
$234$		0			0
$235$	−7.08661	−	1.40961i	−0.462279	−	0.0919530i
$236$		0			0
$237$	0.0909130	+	0.0607462i	0.00590544	+	0.00394589i
$238$		0			0
$239$	−4.39748	+	4.39748i	−0.284449	+	0.284449i	−0.834881	−	0.550431i	$-0.814463\pi$
$239$	−4.39748	+	4.39748i	−0.284449	+	0.284449i	0.550431	+	0.834881i	$0.314463\pi$
$240$		0			0
$241$	7.25045	+	7.25045i	0.467043	+	0.467043i	0.900955	−	0.433912i	$-0.142867\pi$
$241$	7.25045	+	7.25045i	0.467043	+	0.467043i	−0.433912	+	0.900955i	$0.642867\pi$
$242$		0			0
$243$	0.555570	−	0.831470i	0.0356398	−	0.0533388i
$244$		0			0
$245$	1.59520	−	8.01962i	0.101914	−	0.512355i
$246$		0			0
$247$	−22.4742	+	9.30911i	−1.43000	+	0.592325i
$248$		0			0
$249$	−14.7035	−	6.09037i	−0.931794	−	0.385962i
$250$		0			0
$251$	−8.08522	−	12.1004i	−0.510334	−	0.763769i	0.483417	−	0.875390i	$-0.339396\pi$
$251$	−8.08522	−	12.1004i	−0.510334	−	0.763769i	−0.993751	+	0.111621i	$0.964396\pi$
$252$		0			0
$253$	−3.61296	+	0.718663i	−0.227145	+	0.0451820i
$254$		0			0
$255$	2.78331			0.174298
$256$		0			0
$257$	−17.7578			−1.10770			−0.553852	−	0.832615i	$-0.686843\pi$
$257$	−17.7578			−1.10770			−0.553852	+	0.832615i	$0.686843\pi$
$258$		0			0
$259$	41.1359	−	8.18245i	2.55606	−	0.508432i
$260$		0			0
$261$	4.64770	+	6.95578i	0.287686	+	0.430552i
$262$		0			0
$263$	5.47839	+	2.26922i	0.337812	+	0.139926i	0.545140	−	0.838345i	$-0.316477\pi$
$263$	5.47839	+	2.26922i	0.337812	+	0.139926i	−0.207328	+	0.978272i	$0.566477\pi$
$264$		0			0
$265$	−8.61468	+	3.56832i	−0.529196	+	0.219200i
$266$		0			0
$267$	−2.92094	+	14.6846i	−0.178759	+	0.898681i
$268$		0			0
$269$	−1.48102	+	2.21650i	−0.0902994	+	0.135143i	−0.873869	−	0.486161i	$-0.838397\pi$
$269$	−1.48102	+	2.21650i	−0.0902994	+	0.135143i	0.783570	+	0.621304i	$0.213397\pi$
$270$		0			0
$271$	7.10092	+	7.10092i	0.431350	+	0.431350i	0.889088	−	0.457737i	$-0.151340\pi$
$271$	7.10092	+	7.10092i	0.431350	+	0.431350i	−0.457737	+	0.889088i	$0.651340\pi$
$272$		0			0
$273$	15.7033	−	15.7033i	0.950406	−	0.950406i
$274$		0			0
$275$	2.21428	+	1.47954i	0.133526	+	0.0892194i
$276$		0			0
$277$	15.4388	+	3.07097i	0.927627	+	0.184516i	0.635711	−	0.771927i	$-0.280707\pi$
$277$	15.4388	+	3.07097i	0.927627	+	0.184516i	0.291916	+	0.956444i	$0.405707\pi$
$278$		0			0
$279$	1.09442	+	2.64217i	0.0655213	+	0.158182i
$280$		0			0
$281$	11.9066	−	28.7451i	0.710289	−	1.71479i	0.0110096	−	0.999939i	$-0.496495\pi$
$281$	11.9066	−	28.7451i	0.710289	−	1.71479i	0.699279	−	0.714849i	$-0.253505\pi$
$282$		0			0
$283$	8.53764	−	5.70467i	0.507510	−	0.339107i	−0.275310	−	0.961355i	$-0.588781\pi$
$283$	8.53764	−	5.70467i	0.507510	−	0.339107i	0.782820	+	0.622248i	$0.213781\pi$
$284$		0			0
$285$	0.903518	+	4.54229i	0.0535198	+	0.269062i
$286$		0			0
$287$		−	13.9135i		−	0.821289i
$288$		0			0
$289$			10.7952i			0.635015i
$290$		0			0
$291$	2.20633	+	11.0919i	0.129337	+	0.650222i
$292$		0			0
$293$	0.803242	−	0.536709i	0.0469259	−	0.0313549i	−0.531886	−	0.846816i	$-0.678517\pi$
$293$	0.803242	−	0.536709i	0.0469259	−	0.0313549i	0.578812	+	0.815461i	$0.303517\pi$
$294$		0			0
$295$	2.32234	−	5.60662i	0.135212	−	0.326430i
$296$		0			0
$297$	0.271660	+	0.655844i	0.0157633	+	0.0380559i
$298$		0			0
$299$	29.8707	+	5.94165i	1.72747	+	0.343615i
$300$		0			0
$301$	−9.12266	−	6.09556i	−0.525821	−	0.351343i
$302$		0			0
$303$	−2.33949	+	2.33949i	−0.134400	+	0.134400i
$304$		0			0
$305$	3.64434	+	3.64434i	0.208674	+	0.208674i
$306$		0			0
$307$	−15.7591	+	23.5851i	−0.899419	+	1.34608i	0.0385138	+	0.999258i	$0.487738\pi$
$307$	−15.7591	+	23.5851i	−0.899419	+	1.34608i	−0.937933	+	0.346817i	$0.887262\pi$
$308$		0			0
$309$	−3.73636	+	18.7840i	−0.212554	+	1.06858i
$310$		0			0
$311$	31.7118	−	13.1355i	1.79821	−	0.744843i	0.811078	−	0.584938i	$-0.198881\pi$
$311$	31.7118	−	13.1355i	1.79821	−	0.744843i	0.987132	−	0.159905i	$-0.0511188\pi$
$312$		0			0
$313$	21.9508	+	9.09233i	1.24073	+	0.513929i	0.903944	−	0.427651i	$-0.140659\pi$
$313$	21.9508	+	9.09233i	1.24073	+	0.513929i	0.336790	+	0.941580i	$0.390659\pi$
$314$		0			0
$315$	−2.34897	−	3.51548i	−0.132349	−	0.198075i
$316$		0			0
$317$	−20.1343	+	4.00496i	−1.13086	+	0.224941i	−0.724835	−	0.688923i	$-0.758084\pi$
$317$	−20.1343	+	4.00496i	−1.13086	+	0.224941i	−0.406020	+	0.913864i	$0.633084\pi$
$318$		0			0
$319$	−5.93861			−0.332498
$320$		0			0
$321$	2.63493			0.147067
$322$		0			0
$323$	10.1260	−	2.01418i	0.563425	−	0.112072i
$324$		0			0
$325$	−12.2323	−	18.3069i	−0.678525	−	1.01548i
$326$		0			0
$327$	−10.5192	−	4.35719i	−0.581713	−	0.240953i
$328$		0			0
$329$	22.6057	−	9.36359i	1.24629	−	0.516232i
$330$		0			0
$331$	6.15597	−	30.9482i	0.338363	−	1.70106i	−0.319218	−	0.947681i	$-0.603420\pi$
$331$	6.15597	−	30.9482i	0.338363	−	1.70106i	0.657581	−	0.753384i	$-0.271580\pi$
$332$		0			0
$333$	6.15812	−	9.21628i	0.337463	−	0.505049i
$334$		0			0
$335$	−2.25376	−	2.25376i	−0.123136	−	0.123136i
$336$		0			0
$337$	1.21957	−	1.21957i	0.0664343	−	0.0664343i	−0.673109	−	0.739543i	$-0.735042\pi$
$337$	1.21957	−	1.21957i	0.0664343	−	0.0664343i	0.739543	+	0.673109i	$0.235042\pi$
$338$		0			0
$339$	−6.34197	−	4.23757i	−0.344448	−	0.230153i
$340$		0			0
$341$	−1.99115	−	0.396064i	−0.107827	−	0.0214481i
$342$		0			0
$343$	0.460183	+	1.11098i	0.0248475	+	0.0599873i
$344$		0			0
$345$	2.21893	−	5.35697i	0.119463	−	0.288410i
$346$		0			0
$347$	13.0931	−	8.74856i	0.702877	−	0.469647i	−0.152065	−	0.988370i	$-0.548592\pi$
$347$	13.0931	−	8.74856i	0.702877	−	0.469647i	0.854942	+	0.518723i	$0.173592\pi$
$348$		0			0
$349$	−2.51484	−	12.6430i	−0.134616	−	0.676763i	−0.987872	−	0.155270i	$-0.950375\pi$
$349$	−2.51484	−	12.6430i	−0.134616	−	0.676763i	0.853256	−	0.521493i	$-0.174625\pi$
$350$		0			0
$351$		−	5.86904i		−	0.313266i
$352$		0			0
$353$		−	17.2423i		−	0.917715i	−0.888510	−	0.458857i	$-0.848259\pi$
$353$		−	17.2423i		−	0.917715i	0.888510	−	0.458857i	$-0.151741\pi$
$354$		0			0
$355$	0.144606	+	0.726983i	0.00767488	+	0.0385842i
$356$		0			0
$357$	−7.83694	+	5.23648i	−0.414775	+	0.277144i
$358$		0			0
$359$	13.4499	−	32.4710i	0.709861	−	1.71375i	0.00951119	−	0.999955i	$-0.496972\pi$
$359$	13.4499	−	32.4710i	0.709861	−	1.71375i	0.700349	−	0.713800i	$-0.253028\pi$
$360$		0			0
$361$	−0.696794	−	1.68221i	−0.0366734	−	0.0885373i
$362$		0			0
$363$	10.2944	+	2.04768i	0.540315	+	0.107475i
$364$		0			0
$365$	7.44875	+	4.97709i	0.389885	+	0.260513i
$366$		0			0
$367$	13.2100	−	13.2100i	0.689554	−	0.689554i	−0.272579	−	0.962133i	$-0.587877\pi$
$367$	13.2100	−	13.2100i	0.689554	−	0.689554i	0.962133	+	0.272579i	$0.0878768\pi$
$368$		0			0
$369$	−2.60006	−	2.60006i	−0.135354	−	0.135354i
$370$		0			0
$371$	17.5429	−	26.2548i	0.910782	−	1.36308i
$372$		0			0
$373$	−1.25375	+	6.30303i	−0.0649167	+	0.326358i	−0.999574	−	0.0291920i	$-0.990707\pi$
$373$	−1.25375	+	6.30303i	−0.0649167	+	0.326358i	0.934657	+	0.355550i	$0.115707\pi$
$374$		0			0
$375$	−9.03433	+	3.74214i	−0.466531	+	0.193243i
$376$		0			0
$377$	45.3609	+	18.7891i	2.33621	+	0.967689i
$378$		0			0
$379$	11.6288	+	17.4038i	0.597332	+	0.893971i	0.999769	−	0.0214767i	$-0.00683676\pi$
$379$	11.6288	+	17.4038i	0.597332	+	0.893971i	−0.402437	+	0.915448i	$0.631837\pi$
$380$		0			0
$381$	−9.31117	+	1.85211i	−0.477026	+	0.0948864i
$382$		0			0
$383$	2.54816			0.130205			0.0651025	−	0.997879i	$-0.479263\pi$
$383$	2.54816			0.130205			0.0651025	+	0.997879i	$0.479263\pi$
$384$		0			0
$385$	3.00139			0.152965
$386$		0			0
$387$	−2.84388	+	0.565682i	−0.144562	+	0.0287552i
$388$		0			0
$389$	11.0546	+	16.5444i	0.560492	+	0.838836i	0.998181	−	0.0602905i	$-0.0192027\pi$
$389$	11.0546	+	16.5444i	0.560492	+	0.838836i	−0.437688	+	0.899127i	$0.644203\pi$
$390$		0			0
$391$	−11.9421	−	4.94659i	−0.603940	−	0.250160i
$392$		0			0
$393$	−20.3018	+	8.40929i	−1.02409	+	0.424192i
$394$		0			0
$395$	0.0238350	−	0.119827i	0.00119927	−	0.00602913i
$396$		0			0
$397$	−6.13387	+	9.17999i	−0.307850	+	0.460730i	−0.952845	−	0.303456i	$-0.901859\pi$
$397$	−6.13387	+	9.17999i	−0.307850	+	0.460730i	0.644995	+	0.764187i	$0.276859\pi$
$398$		0			0
$399$	−11.0898	−	11.0898i	−0.555185	−	0.555185i
$400$		0			0
$401$	13.1445	−	13.1445i	0.656407	−	0.656407i	−0.298121	−	0.954528i	$-0.596360\pi$
$401$	13.1445	−	13.1445i	0.656407	−	0.656407i	0.954528	+	0.298121i	$0.0963600\pi$
$402$		0			0
$403$	13.9559	+	9.32504i	0.695194	+	0.464514i
$404$		0			0
$405$	−1.09591	−	0.217989i	−0.0544560	−	0.0108320i
$406$		0			0
$407$	3.01116	+	7.26959i	0.149258	+	0.360340i
$408$		0			0
$409$	−10.2609	+	24.7721i	−0.507371	+	1.22490i	0.438021	+	0.898965i	$0.355680\pi$
$409$	−10.2609	+	24.7721i	−0.507371	+	1.22490i	−0.945392	+	0.325937i	$0.894320\pi$
$410$		0			0
$411$	3.07018	−	2.05143i	0.151441	−	0.101190i
$412$		0			0
$413$	4.00922	+	20.1557i	0.197281	+	0.991797i
$414$		0			0
$415$			17.7830i			0.872931i
$416$		0			0
$417$			6.98697i			0.342153i
$418$		0			0
$419$	3.41998	+	17.1934i	0.167077	+	0.839952i	0.969857	+	0.243676i	$0.0783534\pi$
$419$	3.41998	+	17.1934i	0.167077	+	0.839952i	−0.802780	+	0.596276i	$0.796647\pi$
$420$		0			0
$421$	2.88156	−	1.92540i	0.140439	−	0.0938382i	−0.483366	−	0.875418i	$-0.660586\pi$
$421$	2.88156	−	1.92540i	0.140439	−	0.0938382i	0.623805	+	0.781580i	$0.285586\pi$
$422$		0			0
$423$	2.47460	−	5.97420i	0.120319	−	0.290476i
$424$		0			0
$425$	3.57605	+	8.63334i	0.173464	+	0.418779i
$426$		0			0
$427$	−17.1177	−	3.40493i	−0.828385	−	0.164776i
$428$		0			0
$429$	3.46417	+	2.31468i	0.167252	+	0.111754i
$430$		0			0
$431$	3.75226	−	3.75226i	0.180740	−	0.180740i	−0.610938	−	0.791678i	$-0.709208\pi$
$431$	3.75226	−	3.75226i	0.180740	−	0.180740i	0.791678	+	0.610938i	$0.209208\pi$
$432$		0			0
$433$	13.0244	+	13.0244i	0.625913	+	0.625913i	0.947037	−	0.321124i	$-0.104061\pi$
$433$	13.0244	+	13.0244i	0.625913	+	0.625913i	−0.321124	+	0.947037i	$0.604061\pi$
$434$		0			0
$435$	5.19324	−	7.77223i	0.248997	−	0.372650i
$436$		0			0
$437$	4.19606	−	21.0950i	0.200725	−	1.00911i
$438$		0			0
$439$	11.1467	−	4.61710i	0.532001	−	0.220362i	−0.100478	−	0.994939i	$-0.532037\pi$
$439$	11.1467	−	4.61710i	0.532001	−	0.220362i	0.632480	+	0.774577i	$0.282037\pi$
$440$		0			0
$441$	6.76076	+	2.80040i	0.321941	+	0.133352i
$442$		0			0
$443$	10.1810	+	15.2369i	0.483713	+	0.723928i	0.990404	−	0.138200i	$-0.0441316\pi$
$443$	10.1810	+	15.2369i	0.483713	+	0.723928i	−0.506691	+	0.862128i	$0.669132\pi$
$444$		0			0
$445$	16.4082	−	3.26379i	0.777823	−	0.154719i
$446$		0			0
$447$	16.6917			0.789489
$448$		0			0
$449$	−30.0563			−1.41844			−0.709222	−	0.704985i	$-0.750954\pi$
$449$	−30.0563			−1.41844			−0.709222	+	0.704985i	$0.750954\pi$
$450$		0			0
$451$	2.56011	−	0.509237i	0.120551	−	0.0239790i
$452$		0			0
$453$	4.91961	+	7.36272i	0.231144	+	0.345931i
$454$		0			0
$455$	−22.9256	−	9.49609i	−1.07477	−	0.445183i
$456$		0			0
$457$	−0.408359	+	0.169148i	−0.0191022	+	0.00791240i	−0.392214	−	0.919874i	$-0.628291\pi$
$457$	−0.408359	+	0.169148i	−0.0191022	+	0.00791240i	0.373112	+	0.927786i	$0.378291\pi$
$458$		0			0
$459$	−0.485957	+	2.44307i	−0.0226825	+	0.114033i
$460$		0			0
$461$	7.21692	−	10.8009i	0.336126	−	0.503047i	−0.624451	−	0.781064i	$-0.714677\pi$
$461$	7.21692	−	10.8009i	0.336126	−	0.503047i	0.960576	+	0.278017i	$0.0896771\pi$
$462$		0			0
$463$	11.1030	+	11.1030i	0.516001	+	0.516001i	0.916359	−	0.400358i	$-0.131114\pi$
$463$	11.1030	+	11.1030i	0.516001	+	0.516001i	−0.400358	+	0.916359i	$0.631114\pi$
$464$		0			0
$465$	2.25959	−	2.25959i	0.104786	−	0.104786i
$466$		0			0
$467$	−17.5961	−	11.7573i	−0.814250	−	0.544065i	0.0772887	−	0.997009i	$-0.475374\pi$
$467$	−17.5961	−	11.7573i	−0.814250	−	0.544065i	−0.891539	+	0.452944i	$0.850374\pi$
$468$		0			0
$469$	10.5861	+	2.10570i	0.488820	+	0.0972324i
$470$		0			0
$471$	0.0978955	+	0.236341i	0.00451079	+	0.0108900i
$472$		0			0
$473$	0.787702	−	1.90168i	0.0362186	−	0.0874393i
$474$		0			0
$475$	−12.9285	+	8.63857i	−0.593202	+	0.396365i
$476$		0			0
$477$	−1.62802	−	8.18462i	−0.0745420	−	0.374748i
$478$		0			0
$479$			37.5114i			1.71394i	0.515365	+	0.856971i	$0.327656\pi$
$479$			37.5114i			1.71394i	−0.515365	+	0.856971i	$0.672344\pi$
$480$		0			0
$481$		−	65.0544i		−	2.96622i
$482$		0			0
$483$	3.83070	+	19.2582i	0.174303	+	0.876280i
$484$		0			0
$485$	10.5070	−	7.02057i	0.477100	−	0.318788i
$486$		0			0
$487$	2.35376	−	5.68247i	0.106659	−	0.257497i	−0.861535	−	0.507698i	$-0.830497\pi$
$487$	2.35376	−	5.68247i	0.106659	−	0.257497i	0.968194	+	0.250201i	$0.0804966\pi$
$488$		0			0
$489$	0.132640	+	0.320221i	0.00599818	+	0.0144809i
$490$		0			0
$491$	−21.0860	−	4.19426i	−0.951596	−	0.189284i	−0.305202	−	0.952288i	$-0.598724\pi$
$491$	−21.0860	−	4.19426i	−0.951596	−	0.189284i	−0.646394	+	0.763004i	$0.723724\pi$
$492$		0			0
$493$	−17.3264	−	11.5771i	−0.780341	−	0.521407i
$494$		0			0
$495$	0.560880	−	0.560880i	0.0252097	−	0.0252097i
$496$		0			0
$497$	−1.77490	−	1.77490i	−0.0796151	−	0.0796151i
$498$		0			0
$499$	−1.69766	+	2.54073i	−0.0759977	+	0.113739i	−0.867521	−	0.497400i	$-0.834288\pi$
$499$	−1.69766	+	2.54073i	−0.0759977	+	0.113739i	0.791524	+	0.611139i	$0.209288\pi$
$500$		0			0
$501$	2.05901	−	10.3514i	0.0919900	−	0.462465i
$502$		0			0
$503$	−2.40213	+	0.994994i	−0.107106	+	0.0443646i	−0.435593	−	0.900144i	$-0.643461\pi$
$503$	−2.40213	+	0.994994i	−0.107106	+	0.0443646i	0.328487	+	0.944508i	$0.393461\pi$
$504$		0			0
$505$	3.41548	+	1.41474i	0.151987	+	0.0629550i
$506$		0			0
$507$	−11.9146	−	17.8314i	−0.529144	−	0.791921i
$508$		0			0
$509$	20.0993	−	3.99799i	0.890885	−	0.177208i	0.271633	−	0.962401i	$-0.412436\pi$
$509$	20.0993	−	3.99799i	0.890885	−	0.177208i	0.619251	+	0.785193i	$0.287436\pi$
$510$		0			0
$511$	−30.3372			−1.34204
$512$		0			0
$513$	−4.14478			−0.182996
$514$		0			0
$515$	20.9888	−	4.17493i	0.924876	−	0.183969i
$516$		0			0
$517$	2.55029	+	3.81677i	0.112161	+	0.167861i
$518$		0			0
$519$	3.09256	+	1.28098i	0.135748	+	0.0562288i
$520$		0			0
$521$	3.86702	−	1.60177i	0.169417	−	0.0701749i	−0.296363	−	0.955075i	$-0.595774\pi$
$521$	3.86702	−	1.60177i	0.169417	−	0.0701749i	0.465780	+	0.884900i	$0.345774\pi$
$522$		0			0
$523$	−1.56719	+	7.87877i	−0.0685282	+	0.344515i	−0.999804	−	0.0198005i	$-0.993697\pi$
$523$	−1.56719	+	7.87877i	−0.0685282	+	0.344515i	0.931276	+	0.364315i	$0.118697\pi$
$524$		0			0
$525$	7.88639	−	11.8028i	0.344190	−	0.515117i
$526$		0			0
$527$	−5.03723	−	5.03723i	−0.219425	−	0.219425i
$528$		0			0
$529$	−2.77771	+	2.77771i	−0.120770	+	0.120770i
$530$		0			0
$531$	4.51578	+	3.01734i	0.195968	+	0.130942i
$532$		0			0
$533$	−21.1661	−	4.21019i	−0.916804	−	0.182364i
$534$		0			0
$535$	−1.12670	−	2.72010i	−0.0487115	−	0.117600i
$536$		0			0
$537$	−3.52213	+	8.50317i	−0.151991	+	0.366939i
$538$		0			0
$539$	−4.31929	+	2.88606i	−0.186045	+	0.124311i
$540$		0			0
$541$	3.64447	+	18.3220i	0.156688	+	0.787725i	0.976571	+	0.215194i	$0.0690383\pi$
$541$	3.64447	+	18.3220i	0.156688	+	0.787725i	−0.819883	+	0.572531i	$0.805962\pi$
$542$		0			0
$543$			13.2267i			0.567611i
$544$		0			0
$545$			12.7223i			0.544965i
$546$		0			0
$547$	1.88616	+	9.48238i	0.0806465	+	0.405437i	0.999930	+	0.0118410i	$0.00376918\pi$
$547$	1.88616	+	9.48238i	0.0806465	+	0.405437i	−0.919283	+	0.393596i	$0.871231\pi$
$548$		0			0
$549$	−3.83513	+	2.56255i	−0.163679	+	0.109367i
$550$		0			0
$551$	13.2691	−	32.0344i	0.565281	−	1.36471i
$552$		0			0
$553$	0.158328	+	0.382238i	0.00673279	+	0.0162544i
$554$		0			0
$555$	−12.1474	−	2.41627i	−0.515628	−	0.102565i
$556$		0			0
$557$	18.3390	+	12.2537i	0.777049	+	0.519208i	0.879711	−	0.475509i	$-0.157736\pi$
$557$	18.3390	+	12.2537i	0.777049	+	0.519208i	−0.102662	+	0.994716i	$0.532736\pi$
$558$		0			0
$559$	−12.0334	+	12.0334i	−0.508959	+	0.508959i
$560$		0			0
$561$	−1.25035	−	1.25035i	−0.0527899	−	0.0527899i
$562$		0			0
$563$	4.64630	−	6.95368i	0.195818	−	0.293063i	−0.720547	−	0.693406i	$-0.756109\pi$
$563$	4.64630	−	6.95368i	0.195818	−	0.293063i	0.916365	+	0.400344i	$0.131109\pi$
$564$		0			0
$565$	−1.66270	+	8.35894i	−0.0699502	+	0.351663i
$566$		0			0
$567$	3.49586	−	1.44803i	0.146812	−	0.0608116i
$568$		0			0
$569$	7.83040	+	3.24346i	0.328268	+	0.135973i	0.540730	−	0.841196i	$-0.318148\pi$
$569$	7.83040	+	3.24346i	0.328268	+	0.135973i	−0.212462	+	0.977169i	$0.568148\pi$
$570$		0			0
$571$	3.24847	+	4.86168i	0.135944	+	0.203455i	0.893195	−	0.449669i	$-0.148458\pi$
$571$	3.24847	+	4.86168i	0.135944	+	0.203455i	−0.757251	+	0.653124i	$0.773458\pi$
$572$		0			0
$573$	−24.8901	+	4.95094i	−1.03980	+	0.206829i
$574$		0			0
$575$	19.4673			0.811842
$576$		0			0
$577$	−30.1719			−1.25607			−0.628037	−	0.778183i	$-0.716141\pi$
$577$	−30.1719			−1.25607			−0.628037	+	0.778183i	$0.716141\pi$
$578$		0			0
$579$	13.7376	−	2.73257i	0.570914	−	0.113562i
$580$		0			0
$581$	−33.4566	−	50.0713i	−1.38801	−	2.07731i
$582$		0			0
$583$	5.47299	+	2.26699i	0.226668	+	0.0938891i
$584$		0			0
$585$	−6.05874	+	2.50961i	−0.250498	+	0.103760i
$586$		0			0
$587$	0.302143	−	1.51898i	0.0124708	−	0.0626948i	−0.974049	−	0.226338i	$-0.927325\pi$
$587$	0.302143	−	1.51898i	0.0124708	−	0.0626948i	0.986520	+	0.163643i	$0.0523246\pi$
$588$		0			0
$589$	6.58544	−	9.85581i	0.271348	−	0.406102i
$590$		0			0
$591$	−6.36653	−	6.36653i	−0.261884	−	0.261884i
$592$		0			0
$593$	6.82959	−	6.82959i	0.280458	−	0.280458i	−0.552834	−	0.833292i	$-0.686454\pi$
$593$	6.82959	−	6.82959i	0.280458	−	0.280458i	0.833292	+	0.552834i	$0.186454\pi$
$594$		0			0
$595$	8.75682	+	5.85112i	0.358995	+	0.239873i
$596$		0			0
$597$	−9.75259	−	1.93991i	−0.399147	−	0.0793953i
$598$		0			0
$599$	1.44858	+	3.49717i	0.0591872	+	0.142891i	0.950707	−	0.310092i	$-0.100360\pi$
$599$	1.44858	+	3.49717i	0.0591872	+	0.142891i	−0.891519	+	0.452983i	$0.850360\pi$
$600$		0			0
$601$	13.2637	−	32.0214i	0.541037	−	1.30618i	−0.382955	−	0.923767i	$-0.625093\pi$
$601$	13.2637	−	32.0214i	0.541037	−	1.30618i	0.923992	−	0.382412i	$-0.124907\pi$
$602$		0			0
$603$	2.37176	−	1.58476i	0.0965853	−	0.0645363i
$604$		0			0
$605$	−2.28803	−	11.5027i	−0.0930217	−	0.467652i
$606$		0			0
$607$		−	15.6455i		−	0.635031i	−0.948253	−	0.317516i	$-0.897151\pi$
$607$		−	15.6455i		−	0.635031i	0.948253	−	0.317516i	$-0.102849\pi$
$608$		0			0
$609$			31.6547i			1.28271i
$610$		0			0
$611$	−7.40402	−	37.2225i	−0.299535	−	1.50586i
$612$		0			0
$613$	−29.3870	+	19.6358i	−1.18693	+	0.793082i	−0.982584	−	0.185817i	$-0.940507\pi$
$613$	−29.3870	+	19.6358i	−1.18693	+	0.793082i	−0.204346	+	0.978899i	$0.565507\pi$
$614$		0			0
$615$	−1.57231	+	3.79589i	−0.0634017	+	0.153065i
$616$		0			0
$617$	17.2764	+	41.7089i	0.695521	+	1.67914i	0.733349	+	0.679852i	$0.237956\pi$
$617$	17.2764	+	41.7089i	0.695521	+	1.67914i	−0.0378285	+	0.999284i	$0.512044\pi$
$618$		0			0
$619$	−21.7653	−	4.32939i	−0.874822	−	0.174013i	−0.262797	−	0.964851i	$-0.584645\pi$
$619$	−21.7653	−	4.32939i	−0.874822	−	0.174013i	−0.612025	+	0.790838i	$0.709645\pi$
$620$		0			0
$621$	4.31470	+	2.88299i	0.173143	+	0.115690i
$622$		0			0
$623$	−40.0599	+	40.0599i	−1.60497	+	1.60497i
$624$		0			0
$625$	−5.53726	−	5.53726i	−0.221490	−	0.221490i
$626$		0			0
$627$	1.63465	−	2.44643i	0.0652818	−	0.0977010i
$628$		0			0
$629$	−5.38651	+	27.0798i	−0.214774	+	1.07974i
$630$		0			0
$631$	−9.39685	+	3.89230i	−0.374083	+	0.154950i	−0.561800	−	0.827273i	$-0.689891\pi$
$631$	−9.39685	+	3.89230i	−0.374083	+	0.154950i	0.187718	+	0.982223i	$0.439891\pi$
$632$		0			0
$633$	−17.6504	−	7.31102i	−0.701539	−	0.290587i
$634$		0			0
$635$	5.89344	+	8.82016i	0.233874	+	0.350017i
$636$		0			0
$637$	42.1232	−	8.37883i	1.66898	−	0.331981i
$638$		0			0
$639$	−0.663362			−0.0262422
$640$		0			0
$641$	25.7419			1.01675			0.508373	−	0.861137i	$-0.330247\pi$
$641$	25.7419			1.01675			0.508373	+	0.861137i	$0.330247\pi$
$642$		0			0
$643$	−6.09343	+	1.21206i	−0.240301	+	0.0477989i	−0.313772	−	0.949499i	$-0.601593\pi$
$643$	−6.09343	+	1.21206i	−0.240301	+	0.0477989i	0.0734703	+	0.997297i	$0.476593\pi$
$644$		0			0
$645$	1.80001	+	2.69391i	0.0708754	+	0.106073i
$646$		0			0
$647$	25.6309	+	10.6167i	1.00766	+	0.417385i	0.824599	−	0.565717i	$-0.191401\pi$
$647$	25.6309	+	10.6167i	1.00766	+	0.417385i	0.183057	+	0.983102i	$0.441401\pi$
$648$		0			0
$649$	−3.56194	+	1.47540i	−0.139818	+	0.0579147i
$650$		0			0
$651$	−2.11115	+	10.6135i	−0.0827424	+	0.415974i
$652$		0			0
$653$	17.0614	−	25.5342i	0.667665	−	0.999231i	−0.330792	−	0.943704i	$-0.607316\pi$
$653$	17.0614	−	25.5342i	0.667665	−	0.999231i	0.998457	−	0.0555278i	$-0.0176841\pi$
$654$		0			0
$655$	17.3622	+	17.3622i	0.678396	+	0.678396i
$656$		0			0
$657$	−5.66920	+	5.66920i	−0.221177	+	0.221177i
$658$		0			0
$659$	−37.3402	−	24.9499i	−1.45457	−	0.971911i	−0.996552	−	0.0829675i	$-0.973560\pi$
$659$	−37.3402	−	24.9499i	−1.45457	−	0.971911i	−0.458016	−	0.888944i	$-0.651440\pi$
$660$		0			0
$661$	−4.50510	−	0.896119i	−0.175228	−	0.0348550i	0.106696	−	0.994292i	$-0.465973\pi$
$661$	−4.50510	−	0.896119i	−0.175228	−	0.0348550i	−0.281924	+	0.959437i	$0.590973\pi$
$662$		0			0
$663$	5.59460	+	13.5066i	0.217276	+	0.524551i
$664$		0			0
$665$	−6.70623	+	16.1903i	−0.260057	+	0.627832i
$666$		0			0
$667$	−36.0953	+	24.1181i	−1.39761	+	0.933856i
$668$		0			0
$669$	−2.81273	−	14.1405i	−0.108746	−	0.546704i
$670$		0			0
$671$		−	3.27431i		−	0.126403i
$672$		0			0
$673$		−	23.1854i		−	0.893730i	−0.894601	−	0.446865i	$-0.852540\pi$
$673$		−	23.1854i		−	0.893730i	0.894601	−	0.446865i	$-0.147460\pi$
$674$		0			0
$675$	−0.731875	−	3.67939i	−0.0281699	−	0.141620i
$676$		0			0
$677$	−20.0645	+	13.4067i	−0.771140	+	0.515260i	−0.877795	−	0.479037i	$-0.840986\pi$
$677$	−20.0645	+	13.4067i	−0.771140	+	0.515260i	0.106655	+	0.994296i	$0.465986\pi$
$678$		0			0
$679$	−16.3761	+	39.5355i	−0.628459	+	1.51723i
$680$		0			0
$681$	4.83875	+	11.6818i	0.185421	+	0.447646i
$682$		0			0
$683$	31.2265	+	6.21134i	1.19485	+	0.237670i	0.752145	−	0.658997i	$-0.229019\pi$
$683$	31.2265	+	6.21134i	1.19485	+	0.237670i	0.442704	+	0.896668i	$0.354019\pi$
$684$		0			0
$685$	−3.43055	−	2.29222i	−0.131075	−	0.0875812i
$686$		0			0
$687$	−17.6911	+	17.6911i	−0.674959	+	0.674959i
$688$		0			0
$689$	−34.6319	−	34.6319i	−1.31937	−	1.31937i
$690$		0			0
$691$	−1.26704	+	1.89625i	−0.0482004	+	0.0721369i	−0.854787	−	0.518979i	$-0.826312\pi$
$691$	−1.26704	+	1.89625i	−0.0482004	+	0.0721369i	0.806587	+	0.591116i	$0.201312\pi$
$692$		0			0
$693$	−0.524034	+	2.63449i	−0.0199064	+	0.100076i
$694$		0			0
$695$	7.21280	−	2.98764i	0.273597	−	0.113328i
$696$		0			0
$697$	8.46207	+	3.50510i	0.320524	+	0.132765i
$698$		0			0
$699$	−10.9712	−	16.4195i	−0.414967	−	0.621042i
$700$		0			0
$701$	5.27607	−	1.04947i	0.199274	−	0.0396381i	−0.0944439	−	0.995530i	$-0.530107\pi$
$701$	5.27607	−	1.04947i	0.199274	−	0.0396381i	0.293718	+	0.955892i	$0.405107\pi$
$702$		0			0
$703$	−45.9421			−1.73274
$704$		0			0
$705$	−7.22544			−0.272126
$706$		0			0
$707$	−12.2786	+	2.44236i	−0.461784	+	0.0918545i
$708$		0			0
$709$	−2.12834	−	3.18528i	−0.0799314	−	0.119626i	0.789350	−	0.613944i	$-0.210418\pi$
$709$	−2.12834	−	3.18528i	−0.0799314	−	0.119626i	−0.869281	+	0.494318i	$0.835418\pi$
$710$		0			0
$711$	0.101017	+	0.0418427i	0.00378844	+	0.00156922i
$712$		0			0
$713$	−13.7108	+	5.67922i	−0.513475	+	0.212688i
$714$		0			0
$715$	0.908213	−	4.56590i	0.0339652	−	0.170755i
$716$		0			0
$717$	−3.45508	+	5.17089i	−0.129032	+	0.193110i
$718$		0			0
$719$	2.46881	+	2.46881i	0.0920713	+	0.0920713i	0.751642	−	0.659571i	$-0.229262\pi$
$719$	2.46881	+	2.46881i	0.0920713	+	0.0920713i	−0.659571	+	0.751642i	$0.729262\pi$
$720$		0			0
$721$	−51.2432	+	51.2432i	−1.90840	+	1.90840i
$722$		0			0
$723$	8.52563	+	5.69664i	0.317071	+	0.211860i
$724$		0			0
$725$	30.7804	+	6.12261i	1.14316	+	0.227388i
$726$		0			0
$727$	−10.6814	−	25.7872i	−0.396152	−	0.956394i	−0.988570	−	0.150764i	$-0.951827\pi$
$727$	−10.6814	−	25.7872i	−0.396152	−	0.956394i	0.592418	−	0.805631i	$-0.298173\pi$
$728$		0			0
$729$	0.382683	−	0.923880i	0.0141735	−	0.0342178i
$730$		0			0
$731$	6.00545	−	4.01271i	0.222120	−	0.148416i
$732$		0			0
$733$	−0.0750289	−	0.377196i	−0.00277125	−	0.0139320i	0.979375	−	0.202051i	$-0.0647608\pi$
$733$	−0.0750289	−	0.377196i	−0.00277125	−	0.0139320i	−0.982146	+	0.188119i	$0.939761\pi$
$734$		0			0
$735$		−	8.17674i		−	0.301604i
$736$		0			0
$737$			2.02492i			0.0745890i
$738$		0			0
$739$	−0.178539	−	0.897576i	−0.00656766	−	0.0330179i	0.977362	−	0.211572i	$-0.0678582\pi$
$739$	−0.178539	−	0.897576i	−0.00656766	−	0.0330179i	−0.983930	+	0.178554i	$0.942858\pi$
$740$		0			0
$741$	−20.2262	+	13.5147i	−0.743029	+	0.496476i
$742$		0			0
$743$	−9.08935	+	21.9436i	−0.333456	+	0.805034i	0.664857	+	0.746971i	$0.268493\pi$
$743$	−9.08935	+	21.9436i	−0.333456	+	0.805034i	−0.998313	+	0.0580634i	$0.981507\pi$
$744$		0			0
$745$	−7.13738	−	17.2312i	−0.261494	−	0.631301i
$746$		0			0
$747$	−15.6091	−	3.10485i	−0.571108	−	0.113600i
$748$		0			0
$749$	8.28998	+	5.53919i	0.302909	+	0.202398i
$750$		0			0
$751$	30.3650	−	30.3650i	1.10804	−	1.10804i	0.114628	−	0.993409i	$-0.463433\pi$
$751$	30.3650	−	30.3650i	1.10804	−	1.10804i	0.993409	−	0.114628i	$-0.0365675\pi$
$752$		0			0
$753$	−10.2905	−	10.2905i	−0.375008	−	0.375008i
$754$		0			0
$755$	5.49706	−	8.22693i	0.200059	−	0.299409i
$756$		0			0
$757$	−2.66007	+	13.3731i	−0.0966818	+	0.486052i	0.901858	+	0.432032i	$0.142203\pi$
$757$	−2.66007	+	13.3731i	−0.0966818	+	0.486052i	−0.998540	+	0.0540198i	$0.982797\pi$
$758$		0			0
$759$	−3.40334	+	1.40971i	−0.123533	+	0.0511692i
$760$		0			0
$761$	−35.9341	−	14.8844i	−1.30261	−	0.539559i	−0.379891	−	0.925031i	$-0.624039\pi$
$761$	−35.9341	−	14.8844i	−1.30261	−	0.539559i	−0.922719	+	0.385472i	$0.874039\pi$
$762$		0			0
$763$	−23.9356	−	35.8222i	−0.866527	−	1.29685i
$764$		0			0
$765$	2.72983	−	0.542997i	0.0986973	−	0.0196321i
$766$		0			0
$767$	31.8752			1.15095
$768$		0			0
$769$	7.61350			0.274550			0.137275	−	0.990533i	$-0.456166\pi$
$769$	7.61350			0.274550			0.137275	+	0.990533i	$0.456166\pi$
$770$		0			0
$771$	−17.4166	+	3.46438i	−0.627245	+	0.124767i
$772$		0			0
$773$	21.7666	+	32.5760i	0.782890	+	1.17168i	0.981474	+	0.191594i	$0.0613656\pi$
$773$	21.7666	+	32.5760i	0.782890	+	1.17168i	−0.198585	+	0.980084i	$0.563634\pi$
$774$		0			0
$775$	9.91200	+	4.10569i	0.356050	+	0.147481i
$776$		0			0
$777$	38.7492	−	16.0504i	1.39012	−	0.575807i
$778$		0			0
$779$	−2.97328	+	14.9477i	−0.106529	+	0.535557i
$780$		0			0
$781$	0.261622	−	0.391545i	0.00936158	−	0.0140106i
$782$		0			0
$783$	5.91540	+	5.91540i	0.211399	+	0.211399i
$784$		0			0
$785$	0.202119	−	0.202119i	0.00721395	−	0.00721395i
$786$		0			0
$787$	22.4613	+	15.0082i	0.800659	+	0.534983i	0.887265	−	0.461260i	$-0.152602\pi$
$787$	22.4613	+	15.0082i	0.800659	+	0.534983i	−0.0866065	+	0.996243i	$0.527602\pi$
$788$		0			0
$789$	5.81582	+	1.15684i	0.207049	+	0.0411846i
$790$		0			0
$791$	−11.0447	−	26.6644i	−0.392706	−	0.948075i
$792$		0			0
$793$	−10.3595	+	25.0102i	−0.367878	+	0.888137i
$794$		0			0
$795$	−7.75301	+	5.18040i	−0.274971	+	0.183730i
$796$		0			0
$797$	0.567187	+	2.85144i	0.0200908	+	0.101003i	0.989530	−	0.144330i	$-0.0461027\pi$
$797$	0.567187	+	2.85144i	0.0200908	+	0.101003i	−0.969439	+	0.245333i	$0.921103\pi$
$798$		0			0
$799$			16.1075i			0.569841i
$800$		0			0
$801$			14.9722i			0.529018i
$802$		0			0
$803$	−1.11035	−	5.58208i	−0.0391832	−	0.196987i
$804$		0			0
$805$	18.2427	−	12.1894i	0.642970	−	0.429619i
$806$		0			0
$807$	−1.02014	+	2.46285i	−0.0359108	+	0.0866963i
$808$		0			0
$809$	8.26668	+	19.9575i	0.290641	+	0.701669i	0.999995	−	0.00318309i	$-0.00101321\pi$
$809$	8.26668	+	19.9575i	0.290641	+	0.701669i	−0.709354	+	0.704852i	$0.751013\pi$
$810$		0			0
$811$	−18.8077	−	3.74108i	−0.660428	−	0.131367i	−0.146513	−	0.989209i	$-0.546805\pi$
$811$	−18.8077	−	3.74108i	−0.660428	−	0.131367i	−0.513914	+	0.857842i	$0.671805\pi$
$812$		0			0
$813$	8.34980	+	5.57916i	0.292840	+	0.195670i
$814$		0			0
$815$	0.273854	−	0.273854i	0.00959269	−	0.00959269i
$816$		0			0
$817$	8.49813	+	8.49813i	0.297312	+	0.297312i
$818$		0			0
$819$	12.3380	−	18.4651i	0.431124	−	0.645223i
$820$		0			0
$821$	8.86425	−	44.5636i	0.309364	−	1.55528i	−0.442993	−	0.896525i	$-0.646083\pi$
$821$	8.86425	−	44.5636i	0.309364	−	1.55528i	0.752358	−	0.658755i	$-0.228917\pi$
$822$		0			0
$823$	51.6937	−	21.4122i	1.80193	−	0.746383i	0.816262	−	0.577682i	$-0.196043\pi$
$823$	51.6937	−	21.4122i	1.80193	−	0.746383i	0.985667	−	0.168701i	$-0.0539572\pi$
$824$		0			0
$825$	2.46038	+	1.01912i	0.0856594	+	0.0354813i
$826$		0			0
$827$	−21.2106	−	31.7440i	−0.737566	−	1.10385i	−0.990654	−	0.136402i	$-0.956446\pi$
$827$	−21.2106	−	31.7440i	−0.737566	−	1.10385i	0.253088	−	0.967443i	$-0.418554\pi$
$828$		0			0
$829$	30.0252	−	5.97239i	1.04282	−	0.207430i	0.356172	−	0.934420i	$-0.384082\pi$
$829$	30.0252	−	5.97239i	1.04282	−	0.207430i	0.686647	+	0.726991i	$0.259082\pi$
$830$		0			0
$831$	15.7413			0.546058
$832$		0			0
$833$	−18.2282			−0.631568
$834$		0			0
$835$	−11.5664	+	2.30070i	−0.400271	+	0.0796188i
$836$		0			0
$837$	1.58885	+	2.37789i	0.0549188	+	0.0821918i
$838$		0			0
$839$	−8.31645	−	3.44478i	−0.287116	−	0.118927i	0.234478	−	0.972122i	$-0.424662\pi$
$839$	−8.31645	−	3.44478i	−0.287116	−	0.118927i	−0.521593	+	0.853194i	$0.674662\pi$
$840$		0			0
$841$	−37.8643	+	15.6839i	−1.30567	+	0.540824i
$842$		0			0
$843$	6.06994	−	30.5156i	0.209060	−	1.05101i
$844$		0			0
$845$	−13.3131	+	19.9244i	−0.457983	+	0.685420i
$846$		0			0
$847$	28.0834	+	28.0834i	0.964957	+	0.964957i
$848$		0			0
$849$	7.26067	−	7.26067i	0.249185	−	0.249185i
$850$		0			0
$851$	47.8255	+	31.9560i	1.63944	+	1.09544i
$852$		0			0
$853$	29.1995	+	5.80814i	0.999771	+	0.198867i	0.667734	−	0.744400i	$-0.267264\pi$
$853$	29.1995	+	5.80814i	0.999771	+	0.198867i	0.332037	+	0.943266i	$0.392264\pi$
$854$		0			0
$855$	1.77231	+	4.27874i	0.0606119	+	0.146330i
$856$		0			0
$857$	−11.6403	+	28.1022i	−0.397626	+	0.959954i	0.590602	+	0.806963i	$0.298890\pi$
$857$	−11.6403	+	28.1022i	−0.397626	+	0.959954i	−0.988228	+	0.152991i	$0.951110\pi$
$858$		0			0
$859$	−11.2509	+	7.51760i	−0.383875	+	0.256497i	−0.732503	−	0.680764i	$-0.761648\pi$
$859$	−11.2509	+	7.51760i	−0.383875	+	0.256497i	0.348627	+	0.937261i	$0.386648\pi$
$860$		0			0
$861$	−2.71439	−	13.6462i	−0.0925063	−	0.465060i
$862$		0			0
$863$			5.22703i			0.177930i	0.996035	+	0.0889651i	$0.0283560\pi$
$863$			5.22703i			0.177930i	−0.996035	+	0.0889651i	$0.971644\pi$
$864$		0			0
$865$		−	3.74027i		−	0.127173i
$866$		0			0
$867$	2.10605	+	10.5878i	0.0715251	+	0.359581i
$868$		0			0
$869$	−0.0645374	+	0.0431225i	−0.00218928	+	0.00146283i
$870$		0			0
$871$	6.40664	−	15.4670i	0.217081	−	0.524079i
$872$		0			0
$873$	4.32786	+	10.4484i	0.146476	+	0.353624i
$874$		0			0
$875$	−36.2905	−	7.21862i	−1.22684	−	0.244034i
$876$		0			0
$877$	−4.15505	−	2.77631i	−0.140306	−	0.0937494i	0.483436	−	0.875380i	$-0.339388\pi$
$877$	−4.15505	−	2.77631i	−0.140306	−	0.0937494i	−0.623742	+	0.781630i	$0.714388\pi$
$878$		0			0
$879$	0.683101	−	0.683101i	0.0230404	−	0.0230404i
$880$		0			0
$881$	−23.5280	−	23.5280i	−0.792679	−	0.792679i	0.189250	−	0.981929i	$-0.439394\pi$
$881$	−23.5280	−	23.5280i	−0.792679	−	0.792679i	−0.981929	+	0.189250i	$0.939394\pi$
$882$		0			0
$883$	−15.4198	+	23.0774i	−0.518919	+	0.776617i	−0.994686	−	0.102954i	$-0.967171\pi$
$883$	−15.4198	+	23.0774i	−0.518919	+	0.776617i	0.475767	+	0.879571i	$0.342171\pi$
$884$		0			0
$885$	1.18392	−	5.95195i	0.0397969	−	0.200073i
$886$		0			0
$887$	12.6038	−	5.22068i	0.423196	−	0.175293i	−0.160913	−	0.986969i	$-0.551444\pi$
$887$	12.6038	−	5.22068i	0.423196	−	0.175293i	0.584109	+	0.811675i	$0.301444\pi$
$888$		0			0
$889$	−33.1882	−	13.7470i	−1.11310	−	0.461060i
$890$		0			0
$891$	0.394389	+	0.590244i	0.0132125	+	0.0197739i
$892$		0			0
$893$	−26.2869	+	5.22880i	−0.879659	+	0.174975i
$894$		0			0
$895$	10.2841			0.343759
$896$		0			0
$897$	30.4559			1.01689
$898$		0			0
$899$	−23.4649	+	4.66745i	−0.782597	+	0.155668i
$900$		0			0
$901$	11.5485	+	17.2836i	0.384736	+	0.575799i
$902$		0			0
$903$	−10.1366	−	4.19870i	−0.337323	−	0.139724i
$904$		0			0
$905$	13.6542	−	5.65575i	0.453880	−	0.188003i
$906$		0			0
$907$	2.78335	−	13.9929i	0.0924197	−	0.464625i	−0.906665	−	0.421851i	$-0.861380\pi$
$907$	2.78335	−	13.9929i	0.0924197	−	0.464625i	0.999085	−	0.0427741i	$-0.0136196\pi$
$908$		0			0
$909$	−1.83813	+	2.75095i	−0.0609668	+	0.0912433i
$910$		0			0
$911$	3.11574	+	3.11574i	0.103229	+	0.103229i	0.756835	−	0.653606i	$-0.226745\pi$
$911$	3.11574	+	3.11574i	0.103229	+	0.103229i	−0.653606	+	0.756835i	$0.726745\pi$
$912$		0			0
$913$	7.98867	−	7.98867i	0.264386	−	0.264386i
$914$		0			0
$915$	4.28529	+	2.86334i	0.141667	+	0.0946590i
$916$		0			0
$917$	−81.5514	−	16.2216i	−2.69307	−	0.535684i
$918$		0			0
$919$	−19.1703	−	46.2811i	−0.632369	−	1.52667i	−0.836637	−	0.547758i	$-0.815482\pi$
$919$	−19.1703	−	46.2811i	−0.632369	−	1.52667i	0.204268	−	0.978915i	$-0.434518\pi$
$920$		0			0
$921$	−10.8551	+	26.2064i	−0.357686	+	0.863531i
$922$		0			0
$923$	−3.23716	+	2.16300i	−0.106552	+	0.0711960i
$924$		0			0
$925$	−8.11235	−	40.7835i	−0.266732	−	1.34095i
$926$		0			0
$927$			19.1520i			0.629033i
$928$		0			0
$929$			23.6929i			0.777338i	0.921377	+	0.388669i	$0.127065\pi$
$929$			23.6929i			0.777338i	−0.921377	+	0.388669i	$0.872935\pi$
$930$		0			0
$931$	−5.91722	−	29.7479i	−0.193929	−	0.974947i
$932$		0			0
$933$	28.5399	−	19.0697i	0.934353	−	0.624315i
$934$		0			0
$935$	−0.756113	+	1.82542i	−0.0247275	+	0.0596976i
$936$		0			0
$937$	−5.67396	−	13.6982i	−0.185360	−	0.447499i	0.803696	−	0.595041i	$-0.202864\pi$
$937$	−5.67396	−	13.6982i	−0.185360	−	0.447499i	−0.989056	+	0.147541i	$0.952864\pi$
$938$		0			0
$939$	23.3029	+	4.63523i	0.760461	+	0.151265i
$940$		0			0
$941$	−4.05896	−	2.71211i	−0.132318	−	0.0884122i	0.487650	−	0.873039i	$-0.337854\pi$
$941$	−4.05896	−	2.71211i	−0.132318	−	0.0884122i	−0.619968	+	0.784627i	$0.712854\pi$
$942$		0			0
$943$	13.4924	−	13.4924i	0.439372	−	0.439372i
$944$		0			0
$945$	−2.98967	−	2.98967i	−0.0972539	−	0.0972539i
$946$		0			0
$947$	0.528434	−	0.790858i	0.0171718	−	0.0256994i	−0.822784	−	0.568354i	$-0.807581\pi$
$947$	0.528434	−	0.790858i	0.0171718	−	0.0256994i	0.839956	+	0.542654i	$0.182581\pi$
$948$		0			0
$949$	−9.17995	+	46.1507i	−0.297994	+	1.49812i
$950$		0			0
$951$	−18.9661	+	7.85601i	−0.615018	+	0.254749i
$952$		0			0
$953$	−11.8983	−	4.92846i	−0.385425	−	0.159648i	0.181553	−	0.983381i	$-0.441888\pi$
$953$	−11.8983	−	4.92846i	−0.385425	−	0.159648i	−0.566978	+	0.823733i	$0.691888\pi$
$954$		0			0
$955$	15.7540	+	23.5775i	0.509787	+	0.762951i
$956$		0			0
$957$	−5.82450	+	1.15857i	−0.188279	+	0.0374511i
$958$		0			0
$959$	13.9719			0.451177
$960$		0			0
$961$	22.8212			0.736168
$962$		0			0
$963$	2.58430	−	0.514049i	0.0832779	−	0.0165650i
$964$		0			0
$965$	−8.69510	−	13.0131i	−0.279905	−	0.418908i
$966$		0			0
$967$	29.7862	+	12.3378i	0.957859	+	0.396758i	0.806179	−	0.591672i	$-0.201532\pi$
$967$	29.7862	+	12.3378i	0.957859	+	0.396758i	0.151680	+	0.988430i	$0.451532\pi$
$968$		0			0
$969$	9.53848	−	3.95097i	0.306420	−	0.126923i
$970$		0			0
$971$	1.46360	−	7.35802i	0.0469692	−	0.236130i	−0.950169	−	0.311737i	$-0.899089\pi$
$971$	1.46360	−	7.35802i	0.0469692	−	0.236130i	0.997138	+	0.0756067i	$0.0240893\pi$
$972$		0			0
$973$	−14.6881	+	21.9823i	−0.470879	+	0.704720i
$974$		0			0
$975$	−15.5687	−	15.5687i	−0.498599	−	0.498599i
$976$		0			0
$977$	−32.2602	+	32.2602i	−1.03210	+	1.03210i	−0.0326286	+	0.999468i	$0.510388\pi$
$977$	−32.2602	+	32.2602i	−1.03210	+	1.03210i	−0.999468	+	0.0326286i	$0.989612\pi$
$978$		0			0
$979$	−8.83728	−	5.90488i	−0.282441	−	0.188721i
$980$		0			0
$981$	−11.1671	−	2.22128i	−0.356539	−	0.0709200i
$982$		0			0
$983$	14.2853	+	34.4878i	0.455631	+	1.09999i	0.970149	+	0.242510i	$0.0779708\pi$
$983$	14.2853	+	34.4878i	0.455631	+	1.09999i	−0.514518	+	0.857479i	$0.672029\pi$
$984$		0			0
$985$	−3.84997	+	9.29465i	−0.122670	+	0.296152i
$986$		0			0
$987$	20.3446	−	13.5938i	0.647576	−	0.432696i
$988$		0			0
$989$	−2.93546	−	14.7576i	−0.0933423	−	0.469264i
$990$		0			0
$991$			26.6140i			0.845420i	0.906265	+	0.422710i	$0.138921\pi$
$991$			26.6140i			0.845420i	−0.906265	+	0.422710i	$0.861079\pi$
$992$		0			0
$993$		−	31.5545i		−	1.00135i
$994$		0			0
$995$	2.16761	+	10.8973i	0.0687179	+	0.345468i
$996$		0			0
$997$	28.9202	−	19.3239i	0.915912	−	0.611993i	−0.00575155	−	0.999983i	$-0.501831\pi$
$997$	28.9202	−	19.3239i	0.915912	−	0.611993i	0.921663	+	0.387991i	$0.126831\pi$
$998$		0			0
$999$	4.24179	−	10.2406i	0.134204	−	0.323998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.r.a.49.10		128
4.3	odd	2		192.2.r.a.181.10	yes	128
12.11	even	2		576.2.bd.b.181.7		128
64.29	even	16	inner	768.2.r.a.721.10		128
64.35	odd	16		192.2.r.a.157.10	✓	128
192.35	even	16		576.2.bd.b.541.7		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.10	✓	128	64.35	odd	16
192.2.r.a.181.10	yes	128	4.3	odd	2
576.2.bd.b.181.7		128	12.11	even	2
576.2.bd.b.541.7		128	192.35	even	16
768.2.r.a.49.10		128	1.1	even	1	trivial
768.2.r.a.721.10		128	64.29	even	16	inner

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.r (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.980785 - 0.195090i) q^{3} +(-0.620781 - 0.929065i) q^{5} +(3.49586 + 1.44803i) q^{7} +(0.923880 - 0.382683i) q^{9} +O(q^{10})\)	\(q+(0.980785 - 0.195090i) q^{3} +(-0.620781 - 0.929065i) q^{5} +(3.49586 + 1.44803i) q^{7} +(0.923880 - 0.382683i) q^{9} +(-0.138491 + 0.696240i) q^{11} +(3.26066 - 4.87993i) q^{13} +(-0.790105 - 0.790105i) q^{15} +(-1.76136 + 1.76136i) q^{17} +(-3.44626 - 2.30272i) q^{19} +(3.71118 + 0.738200i) q^{21} +(1.98584 + 4.79424i) q^{23} +(1.43563 - 3.46591i) q^{25} +(0.831470 - 0.555570i) q^{27} +(1.63206 + 8.20490i) q^{29} +2.85986i q^{31} +0.709881i q^{33} +(-0.824847 - 4.14679i) q^{35} +(9.21628 - 6.15812i) q^{37} +(2.24599 - 5.42229i) q^{39} +(-1.40714 - 3.39715i) q^{41} +(-2.84388 - 0.565682i) q^{43} +(-0.929065 - 0.620781i) q^{45} +(4.57246 - 4.57246i) q^{47} +(5.17447 + 5.17447i) q^{49} +(-1.38389 + 2.07114i) q^{51} +(1.62802 - 8.18462i) q^{53} +(0.732825 - 0.303546i) q^{55} +(-3.82928 - 1.58614i) q^{57} +(3.01734 + 4.51578i) q^{59} +(-4.52385 + 0.899849i) q^{61} +3.78389 q^{63} -6.55793 q^{65} +(2.79768 - 0.556492i) q^{67} +(2.88299 + 4.31470i) q^{69} +(-0.612866 - 0.253858i) q^{71} +(-7.40717 + 3.06815i) q^{73} +(0.731875 - 3.67939i) q^{75} +(-1.49232 + 2.23342i) q^{77} +(0.0773152 + 0.0773152i) q^{79} +(0.707107 - 0.707107i) q^{81} +(-13.2328 - 8.84185i) q^{83} +(2.72983 + 0.542997i) q^{85} +(3.20139 + 7.72885i) q^{87} +(-5.72963 + 13.8326i) q^{89} +(18.4651 - 12.3380i) q^{91} +(0.557931 + 2.80491i) q^{93} +4.63128i q^{95} +11.3093i q^{97} +(0.138491 + 0.696240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 32 q^{51} + 64 q^{55} + 128 q^{59} + 32 q^{63} + 32 q^{67} + 128 q^{71} + 64 q^{75} + 32 q^{79}+O(q^{100}) \) 128 * q + 32 * q^51 + 64 * q^55 + 128 * q^59 + 32 * q^63 + 32 * q^67 + 128 * q^71 + 64 * q^75 + 32 * q^79

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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