LMFDB - Embedded newform 768.2.r.a.721.10

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			721.10
Character	$\chi$	$=$	768.721
Dual form			768.2.r.a.49.10

$q$-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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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	−0.943909	−	0.330204i	$-0.892882\pi$
$5$	−0.620781	+	0.929065i	−0.277622	+	0.415490i	0.666288	+	0.745695i	$0.267882\pi$
$6$		0			0
$7$	3.49586	−	1.44803i	1.32131	−	0.547304i	0.393145	−	0.919476i	$-0.371387\pi$
$7$	3.49586	−	1.44803i	1.32131	−	0.547304i	0.928164	+	0.372172i	$0.121387\pi$
$8$		0			0
$9$	0.923880	+	0.382683i	0.307960	+	0.127561i
$10$		0			0
$11$	−0.138491	−	0.696240i	−0.0417566	−	0.209924i	0.954274	−	0.298932i	$-0.0966304\pi$
$11$	−0.138491	−	0.696240i	−0.0417566	−	0.209924i	−0.996031	+	0.0890077i	$0.971630\pi$
$12$		0			0
$13$	3.26066	+	4.87993i	0.904346	+	1.35345i	0.935273	+	0.353927i	$0.115154\pi$
$13$	3.26066	+	4.87993i	0.904346	+	1.35345i	−0.0309272	+	0.999522i	$0.509846\pi$
$14$		0			0
$15$	−0.790105	+	0.790105i	−0.204004	+	0.204004i
$16$		0			0
$17$	−1.76136	−	1.76136i	−0.427192	−	0.427192i	0.460479	−	0.887671i	$-0.347678\pi$
$17$	−1.76136	−	1.76136i	−0.427192	−	0.427192i	−0.887671	+	0.460479i	$0.847678\pi$
$18$		0			0
$19$	−3.44626	+	2.30272i	−0.790626	+	0.528279i	−0.884075	−	0.467345i	$-0.845211\pi$
$19$	−3.44626	+	2.30272i	−0.790626	+	0.528279i	0.0934494	+	0.995624i	$0.470211\pi$
$20$		0			0
$21$	3.71118	−	0.738200i	0.809846	−	0.161088i
$22$		0			0
$23$	1.98584	−	4.79424i	0.414076	−	0.999668i	−0.569956	−	0.821675i	$-0.693040\pi$
$23$	1.98584	−	4.79424i	0.414076	−	0.999668i	0.984032	−	0.177992i	$-0.0569603\pi$
$24$		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	−0.466198	−	0.884680i	$-0.654377\pi$
$29$	1.63206	−	8.20490i	0.303065	−	1.52361i	0.769264	−	0.638932i	$-0.220623\pi$
$30$		0			0
$31$		−	2.85986i		−	0.513646i	−0.966458	−	0.256823i	$-0.917324\pi$
$31$		−	2.85986i		−	0.513646i	0.966458	−	0.256823i	$-0.0826757\pi$
$32$		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	0.986540	+	0.163523i	$0.0522857\pi$
$37$	9.21628	+	6.15812i	1.51515	+	1.01239i	0.528608	+	0.848866i	$0.322714\pi$
$38$		0			0
$39$	2.24599	+	5.42229i	0.359645	+	0.868261i
$40$		0			0
$41$	−1.40714	+	3.39715i	−0.219759	+	0.530545i	−0.994856	−	0.101297i	$-0.967701\pi$
$41$	−1.40714	+	3.39715i	−0.219759	+	0.530545i	0.775097	+	0.631842i	$0.217701\pi$
$42$		0			0
$43$	−2.84388	+	0.565682i	−0.433687	+	0.0862657i	−0.407106	−	0.913381i	$-0.633462\pi$
$43$	−2.84388	+	0.565682i	−0.433687	+	0.0862657i	−0.0265812	+	0.999647i	$0.508462\pi$
$44$		0			0
$45$	−0.929065	+	0.620781i	−0.138497	+	0.0925406i
$46$		0			0
$47$	4.57246	+	4.57246i	0.666961	+	0.666961i	0.957011	−	0.290050i	$-0.0936719\pi$
$47$	4.57246	+	4.57246i	0.666961	+	0.666961i	−0.290050	+	0.957011i	$0.593672\pi$
$48$		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	0.915529	+	0.402253i	$0.131773\pi$
$53$	1.62802	+	8.18462i	0.223626	+	1.12424i	−0.691903	+	0.721991i	$0.743227\pi$
$54$		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	−0.581363	−	0.813645i	$-0.697480\pi$
$59$	3.01734	−	4.51578i	0.392825	−	0.587904i	0.974187	+	0.225741i	$0.0724802\pi$
$60$		0			0
$61$	−4.52385	−	0.899849i	−0.579219	−	0.115214i	−0.103218	−	0.994659i	$-0.532914\pi$
$61$	−4.52385	−	0.899849i	−0.579219	−	0.115214i	−0.476001	+	0.879445i	$0.657914\pi$
$62$		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	0.363001	−	0.931789i	$-0.381752\pi$
$67$	2.79768	+	0.556492i	0.341791	+	0.0679864i	−0.0212107	+	0.999775i	$0.506752\pi$
$68$		0			0
$69$	2.88299	−	4.31470i	0.347071	−	0.519429i
$70$		0			0
$71$	−0.612866	+	0.253858i	−0.0727339	+	0.0301273i	−0.418754	−	0.908100i	$-0.637533\pi$
$71$	−0.612866	+	0.253858i	−0.0727339	+	0.0301273i	0.346020	+	0.938227i	$0.387533\pi$
$72$		0			0
$73$	−7.40717	−	3.06815i	−0.866944	−	0.359100i	−0.0955247	−	0.995427i	$-0.530453\pi$
$73$	−7.40717	−	3.06815i	−0.866944	−	0.359100i	−0.771419	+	0.636327i	$0.780453\pi$
$74$		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	−0.702744	−	0.711443i	$-0.748042\pi$
$79$	0.0773152	−	0.0773152i	0.00869864	−	0.00869864i	0.711443	+	0.702744i	$0.248042\pi$
$80$		0			0
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$		0			0
$83$	−13.2328	+	8.84185i	−1.45248	+	0.970519i	−0.455722	+	0.890122i	$0.650619\pi$
$83$	−13.2328	+	8.84185i	−1.45248	+	0.970519i	−0.996763	+	0.0803973i	$0.974381\pi$
$84$		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	−0.865882	−	0.500248i	$-0.833242\pi$
$89$	−5.72963	−	13.8326i	−0.607340	−	1.46625i	0.258542	−	0.966000i	$-0.416758\pi$
$90$		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	$-0.805336\pi$
$97$		−	11.3093i		−	1.14828i	0.818757	−	0.574140i	$-0.194664\pi$
$98$		0			0
$99$	0.138491	−	0.696240i	0.0139189	−	0.0699748i
$100$		0			0
$101$	−2.75095	−	1.83813i	−0.273730	−	0.182900i	0.411127	−	0.911578i	$-0.365135\pi$
$101$	−2.75095	−	1.83813i	−0.273730	−	0.182900i	−0.684857	+	0.728678i	$0.740135\pi$
$102$		0			0
$103$	−7.32914	−	17.6941i	−0.722162	−	1.74345i	−0.667099	−	0.744969i	$-0.732464\pi$
$103$	−7.32914	−	17.6941i	−0.722162	−	1.74345i	−0.0550629	−	0.998483i	$-0.517536\pi$
$104$		0			0
$105$	−1.61800	+	3.90619i	−0.157900	+	0.381205i
$106$		0			0
$107$	2.58430	−	0.514049i	0.249834	−	0.0496950i	−0.0685846	−	0.997645i	$-0.521848\pi$
$107$	2.58430	−	0.514049i	0.249834	−	0.0496950i	0.318418	+	0.947950i	$0.396848\pi$
$108$		0			0
$109$	−9.46703	+	6.32567i	−0.906777	+	0.605889i	−0.919095	−	0.394035i	$-0.871079\pi$
$109$	−9.46703	+	6.32567i	−0.906777	+	0.605889i	0.0123185	+	0.999924i	$0.496079\pi$
$110$		0			0
$111$	7.83780	+	7.83780i	0.743931	+	0.743931i
$112$		0			0
$113$	−5.39340	+	5.39340i	−0.507368	+	0.507368i	−0.913718	−	0.406349i	$-0.866802\pi$
$113$	−5.39340	+	5.39340i	−0.507368	+	0.507368i	0.406349	+	0.913718i	$0.366802\pi$
$114$		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	−0.886866	−	0.462028i	$-0.847122\pi$
$131$	−21.5523	−	4.28702i	−1.88303	−	0.374559i	−0.996167	+	0.0874690i	$0.972122\pi$
$132$		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	0.523621	−	0.851951i	$-0.324581\pi$
$137$	3.41140	+	1.41305i	0.291456	+	0.120725i	−0.232165	+	0.972676i	$0.574581\pi$
$138$		0			0
$139$	−1.36309	−	6.85272i	−0.115616	−	0.581240i	−0.994547	−	0.104291i	$-0.966743\pi$
$139$	−1.36309	−	6.85272i	−0.115616	−	0.581240i	0.878931	−	0.476949i	$-0.158257\pi$
$140$		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	0.528213	−	0.849112i	$-0.322862\pi$
$149$	16.3709	−	3.25638i	1.34116	−	0.266773i	0.812947	+	0.582338i	$0.197862\pi$
$150$		0			0
$151$	3.38869	−	8.18102i	0.275768	−	0.665762i	−0.723942	−	0.689861i	$-0.757672\pi$
$151$	3.38869	−	8.18102i	0.275768	−	0.665762i	0.999710	+	0.0240991i	$0.00767172\pi$
$152$		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	−0.978743	−	0.205092i	$-0.934251\pi$
$157$	0.0499067	−	0.250898i	0.00398299	−	0.0200238i	0.982726	+	0.185068i	$0.0592506\pi$
$158$		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	−0.978047	−	0.208386i	$-0.933179\pi$
$163$	0.0676192	−	0.339945i	0.00529635	−	0.0266265i	0.983343	+	0.181759i	$0.0581791\pi$
$164$		0			0
$165$	0.659525	+	0.440681i	0.0513440	+	0.0343069i
$166$		0			0
$167$	4.03890	+	9.75077i	0.312540	+	0.754538i	0.999609	+	0.0279461i	$0.00889667\pi$
$167$	4.03890	+	9.75077i	0.312540	+	0.754538i	−0.687070	+	0.726591i	$0.741103\pi$
$168$		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	−0.445251	−	0.895406i	$-0.646886\pi$
$173$	2.78323	−	1.85969i	0.211605	−	0.141390i	0.656857	+	0.754016i	$0.271886\pi$
$174$		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	0.589642	−	0.807664i	$-0.299269\pi$
$179$	−5.11334	−	7.65265i	−0.382189	−	0.571986i	−0.971831	+	0.235679i	$0.924269\pi$
$180$		0			0
$181$	−2.58040	−	12.9725i	−0.191799	−	0.964241i	−0.950007	−	0.312228i	$-0.898925\pi$
$181$	−2.58040	−	12.9725i	−0.191799	−	0.964241i	0.758208	−	0.652013i	$-0.226075\pi$
$182$		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	−0.965735	−	0.259531i	$-0.916432\pi$
$197$	−5.00215	+	7.48625i	−0.356389	+	0.533373i	0.609346	+	0.792904i	$0.291432\pi$
$198$		0			0
$199$	−9.18674	+	3.80527i	−0.651231	+	0.269749i	−0.683743	−	0.729723i	$-0.739649\pi$
$199$	−9.18674	+	3.80527i	−0.651231	+	0.269749i	0.0325124	+	0.999471i	$0.489649\pi$
$200$		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	−0.965325	−	0.261049i	$-0.915931\pi$
$211$	−15.8849	+	10.6139i	−1.09356	+	0.730694i	−0.128236	+	0.991744i	$0.540931\pi$
$212$		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	$0.160357\pi$
$223$			14.4176i			0.965471i	−0.875766	+	0.482736i	$0.839643\pi$
$224$		0			0
$225$			3.75147i			0.250098i
$226$		0			0
$227$	2.46677	−	12.4013i	0.163725	−	0.823103i	−0.808399	−	0.588636i	$-0.799665\pi$
$227$	2.46677	−	12.4013i	0.163725	−	0.823103i	0.972124	−	0.234468i	$-0.0753347\pi$
$228$		0			0
$229$	−20.8026	−	13.8998i	−1.37467	−	0.918527i	−0.374711	−	0.927142i	$-0.622258\pi$
$229$	−20.8026	−	13.8998i	−1.37467	−	0.918527i	−0.999963	+	0.00861437i	$0.997258\pi$
$230$		0			0
$231$	−1.02793	−	2.48164i	−0.0676328	−	0.163280i
$232$		0			0
$233$	−7.55706	+	18.2444i	−0.495080	+	1.19523i	0.457025	+	0.889454i	$0.348915\pi$
$233$	−7.55706	+	18.2444i	−0.495080	+	1.19523i	−0.952104	+	0.305774i	$0.901085\pi$
$234$		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	0.550431	−	0.834881i	$-0.314463\pi$
$239$	−4.39748	−	4.39748i	−0.284449	−	0.284449i	−0.834881	+	0.550431i	$0.814463\pi$
$240$		0			0
$241$	7.25045	−	7.25045i	0.467043	−	0.467043i	−0.433912	−	0.900955i	$-0.642867\pi$
$241$	7.25045	−	7.25045i	0.467043	−	0.467043i	0.900955	+	0.433912i	$0.142867\pi$
$242$		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	−0.993751	−	0.111621i	$-0.964396\pi$
$251$	−8.08522	+	12.1004i	−0.510334	+	0.763769i	0.483417	+	0.875390i	$0.339396\pi$
$252$		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	−0.207328	−	0.978272i	$-0.566477\pi$
$263$	5.47839	−	2.26922i	0.337812	−	0.139926i	0.545140	+	0.838345i	$0.316477\pi$
$264$		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	0.783570	−	0.621304i	$-0.213397\pi$
$269$	−1.48102	−	2.21650i	−0.0902994	−	0.135143i	−0.873869	+	0.486161i	$0.838397\pi$
$270$		0			0
$271$	7.10092	−	7.10092i	0.431350	−	0.431350i	−0.457737	−	0.889088i	$-0.651340\pi$
$271$	7.10092	−	7.10092i	0.431350	−	0.431350i	0.889088	+	0.457737i	$0.151340\pi$
$272$		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	0.291916	−	0.956444i	$-0.405707\pi$
$277$	15.4388	−	3.07097i	0.927627	−	0.184516i	0.635711	+	0.771927i	$0.280707\pi$
$278$		0			0
$279$	1.09442	−	2.64217i	0.0655213	−	0.158182i
$280$		0			0
$281$	11.9066	+	28.7451i	0.710289	+	1.71479i	0.699279	+	0.714849i	$0.253505\pi$
$281$	11.9066	+	28.7451i	0.710289	+	1.71479i	0.0110096	+	0.999939i	$0.496495\pi$
$282$		0			0
$283$	8.53764	+	5.70467i	0.507510	+	0.339107i	0.782820	−	0.622248i	$-0.213781\pi$
$283$	8.53764	+	5.70467i	0.507510	+	0.339107i	−0.275310	+	0.961355i	$0.588781\pi$
$284$		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	0.578812	−	0.815461i	$-0.303517\pi$
$293$	0.803242	+	0.536709i	0.0469259	+	0.0313549i	−0.531886	+	0.846816i	$0.678517\pi$
$294$		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	−0.937933	−	0.346817i	$-0.887262\pi$
$307$	−15.7591	−	23.5851i	−0.899419	−	1.34608i	0.0385138	−	0.999258i	$-0.487738\pi$
$308$		0			0
$309$	−3.73636	−	18.7840i	−0.212554	−	1.06858i
$310$		0			0
$311$	31.7118	+	13.1355i	1.79821	+	0.744843i	0.987132	+	0.159905i	$0.0511188\pi$
$311$	31.7118	+	13.1355i	1.79821	+	0.744843i	0.811078	+	0.584938i	$0.198881\pi$
$312$		0			0
$313$	21.9508	−	9.09233i	1.24073	−	0.513929i	0.336790	−	0.941580i	$-0.390659\pi$
$313$	21.9508	−	9.09233i	1.24073	−	0.513929i	0.903944	+	0.427651i	$0.140659\pi$
$314$		0			0
$315$	−2.34897	+	3.51548i	−0.132349	+	0.198075i
$316$		0			0
$317$	−20.1343	−	4.00496i	−1.13086	−	0.224941i	−0.406020	−	0.913864i	$-0.633084\pi$
$317$	−20.1343	−	4.00496i	−1.13086	−	0.224941i	−0.724835	+	0.688923i	$0.758084\pi$
$318$		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	0.657581	+	0.753384i	$0.271580\pi$
$331$	6.15597	+	30.9482i	0.338363	+	1.70106i	−0.319218	+	0.947681i	$0.603420\pi$
$332$		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	0.739543	−	0.673109i	$-0.235042\pi$
$337$	1.21957	+	1.21957i	0.0664343	+	0.0664343i	−0.673109	+	0.739543i	$0.735042\pi$
$338$		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	0.854942	−	0.518723i	$-0.173592\pi$
$347$	13.0931	+	8.74856i	0.702877	+	0.469647i	−0.152065	+	0.988370i	$0.548592\pi$
$348$		0			0
$349$	−2.51484	+	12.6430i	−0.134616	+	0.676763i	0.853256	+	0.521493i	$0.174625\pi$
$349$	−2.51484	+	12.6430i	−0.134616	+	0.676763i	−0.987872	+	0.155270i	$0.950375\pi$
$350$		0			0
$351$			5.86904i			0.313266i
$352$		0			0
$353$			17.2423i			0.917715i	0.888510	+	0.458857i	$0.151741\pi$
$353$			17.2423i			0.917715i	−0.888510	+	0.458857i	$0.848259\pi$
$354$		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	0.700349	+	0.713800i	$0.253028\pi$
$359$	13.4499	+	32.4710i	0.709861	+	1.71375i	0.00951119	+	0.999955i	$0.496972\pi$
$360$		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	0.962133	−	0.272579i	$-0.0878768\pi$
$367$	13.2100	+	13.2100i	0.689554	+	0.689554i	−0.272579	+	0.962133i	$0.587877\pi$
$368$		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	0.934657	−	0.355550i	$-0.115707\pi$
$373$	−1.25375	−	6.30303i	−0.0649167	−	0.326358i	−0.999574	+	0.0291920i	$0.990707\pi$
$374$		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	−0.402437	−	0.915448i	$-0.631837\pi$
$379$	11.6288	−	17.4038i	0.597332	−	0.893971i	0.999769	+	0.0214767i	$0.00683676\pi$
$380$		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	−0.437688	−	0.899127i	$-0.644203\pi$
$389$	11.0546	−	16.5444i	0.560492	−	0.838836i	0.998181	+	0.0602905i	$0.0192027\pi$
$390$		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	0.644995	−	0.764187i	$-0.276859\pi$
$397$	−6.13387	−	9.17999i	−0.307850	−	0.460730i	−0.952845	+	0.303456i	$0.901859\pi$
$398$		0			0
$399$	−11.0898	+	11.0898i	−0.555185	+	0.555185i
$400$		0			0
$401$	13.1445	+	13.1445i	0.656407	+	0.656407i	0.954528	−	0.298121i	$-0.0963600\pi$
$401$	13.1445	+	13.1445i	0.656407	+	0.656407i	−0.298121	+	0.954528i	$0.596360\pi$
$402$		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	−0.945392	−	0.325937i	$-0.894320\pi$
$409$	−10.2609	−	24.7721i	−0.507371	−	1.22490i	0.438021	−	0.898965i	$-0.355680\pi$
$410$		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	−0.802780	−	0.596276i	$-0.796647\pi$
$419$	3.41998	−	17.1934i	0.167077	−	0.839952i	0.969857	−	0.243676i	$-0.0783534\pi$
$420$		0			0
$421$	2.88156	+	1.92540i	0.140439	+	0.0938382i	0.623805	−	0.781580i	$-0.285586\pi$
$421$	2.88156	+	1.92540i	0.140439	+	0.0938382i	−0.483366	+	0.875418i	$0.660586\pi$
$422$		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	0.791678	−	0.610938i	$-0.209208\pi$
$431$	3.75226	+	3.75226i	0.180740	+	0.180740i	−0.610938	+	0.791678i	$0.709208\pi$
$432$		0			0
$433$	13.0244	−	13.0244i	0.625913	−	0.625913i	−0.321124	−	0.947037i	$-0.604061\pi$
$433$	13.0244	−	13.0244i	0.625913	−	0.625913i	0.947037	+	0.321124i	$0.104061\pi$
$434$		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	0.632480	−	0.774577i	$-0.282037\pi$
$439$	11.1467	+	4.61710i	0.532001	+	0.220362i	−0.100478	+	0.994939i	$0.532037\pi$
$440$		0			0
$441$	6.76076	−	2.80040i	0.321941	−	0.133352i
$442$		0			0
$443$	10.1810	−	15.2369i	0.483713	−	0.723928i	−0.506691	−	0.862128i	$-0.669132\pi$
$443$	10.1810	−	15.2369i	0.483713	−	0.723928i	0.990404	+	0.138200i	$0.0441316\pi$
$444$		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	0.373112	−	0.927786i	$-0.378291\pi$
$457$	−0.408359	−	0.169148i	−0.0191022	−	0.00791240i	−0.392214	+	0.919874i	$0.628291\pi$
$458$		0			0
$459$	−0.485957	−	2.44307i	−0.0226825	−	0.114033i
$460$		0			0
$461$	7.21692	+	10.8009i	0.336126	+	0.503047i	0.960576	−	0.278017i	$-0.0896771\pi$
$461$	7.21692	+	10.8009i	0.336126	+	0.503047i	−0.624451	+	0.781064i	$0.714677\pi$
$462$		0			0
$463$	11.1030	−	11.1030i	0.516001	−	0.516001i	−0.400358	−	0.916359i	$-0.631114\pi$
$463$	11.1030	−	11.1030i	0.516001	−	0.516001i	0.916359	+	0.400358i	$0.131114\pi$
$464$		0			0
$465$	2.25959	+	2.25959i	0.104786	+	0.104786i
$466$		0			0
$467$	−17.5961	+	11.7573i	−0.814250	+	0.544065i	−0.891539	−	0.452944i	$-0.850374\pi$
$467$	−17.5961	+	11.7573i	−0.814250	+	0.544065i	0.0772887	+	0.997009i	$0.475374\pi$
$468$		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	$-0.672344\pi$
$479$		−	37.5114i		−	1.71394i	0.515365	−	0.856971i	$-0.327656\pi$
$480$		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	0.968194	−	0.250201i	$-0.0804966\pi$
$487$	2.35376	+	5.68247i	0.106659	+	0.257497i	−0.861535	+	0.507698i	$0.830497\pi$
$488$		0			0
$489$	0.132640	−	0.320221i	0.00599818	−	0.0144809i
$490$		0			0
$491$	−21.0860	+	4.19426i	−0.951596	+	0.189284i	−0.646394	−	0.763004i	$-0.723724\pi$
$491$	−21.0860	+	4.19426i	−0.951596	+	0.189284i	−0.305202	+	0.952288i	$0.598724\pi$
$492$		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	0.791524	−	0.611139i	$-0.209288\pi$
$499$	−1.69766	−	2.54073i	−0.0759977	−	0.113739i	−0.867521	+	0.497400i	$0.834288\pi$
$500$		0			0
$501$	2.05901	+	10.3514i	0.0919900	+	0.462465i
$502$		0			0
$503$	−2.40213	−	0.994994i	−0.107106	−	0.0443646i	0.328487	−	0.944508i	$-0.393461\pi$
$503$	−2.40213	−	0.994994i	−0.107106	−	0.0443646i	−0.435593	+	0.900144i	$0.643461\pi$
$504$		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	0.619251	−	0.785193i	$-0.287436\pi$
$509$	20.0993	+	3.99799i	0.890885	+	0.177208i	0.271633	+	0.962401i	$0.412436\pi$
$510$		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	0.465780	−	0.884900i	$-0.345774\pi$
$521$	3.86702	+	1.60177i	0.169417	+	0.0701749i	−0.296363	+	0.955075i	$0.595774\pi$
$522$		0			0
$523$	−1.56719	−	7.87877i	−0.0685282	−	0.344515i	0.931276	−	0.364315i	$-0.118697\pi$
$523$	−1.56719	−	7.87877i	−0.0685282	−	0.344515i	−0.999804	+	0.0198005i	$0.993697\pi$
$524$		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	−0.819883	−	0.572531i	$-0.805962\pi$
$541$	3.64447	−	18.3220i	0.156688	−	0.787725i	0.976571	−	0.215194i	$-0.0690383\pi$
$542$		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	−0.919283	−	0.393596i	$-0.871231\pi$
$547$	1.88616	−	9.48238i	0.0806465	−	0.405437i	0.999930	−	0.0118410i	$-0.00376918\pi$
$548$		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	−0.102662	−	0.994716i	$-0.532736\pi$
$557$	18.3390	−	12.2537i	0.777049	−	0.519208i	0.879711	+	0.475509i	$0.157736\pi$
$558$		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	0.916365	−	0.400344i	$-0.131109\pi$
$563$	4.64630	+	6.95368i	0.195818	+	0.293063i	−0.720547	+	0.693406i	$0.756109\pi$
$564$		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	−0.212462	−	0.977169i	$-0.568148\pi$
$569$	7.83040	−	3.24346i	0.328268	−	0.135973i	0.540730	+	0.841196i	$0.318148\pi$
$570$		0			0
$571$	3.24847	−	4.86168i	0.135944	−	0.203455i	−0.757251	−	0.653124i	$-0.773458\pi$
$571$	3.24847	−	4.86168i	0.135944	−	0.203455i	0.893195	+	0.449669i	$0.148458\pi$
$572$		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	0.986520	−	0.163643i	$-0.0523246\pi$
$587$	0.302143	+	1.51898i	0.0124708	+	0.0626948i	−0.974049	+	0.226338i	$0.927325\pi$
$588$		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	0.833292	−	0.552834i	$-0.186454\pi$
$593$	6.82959	+	6.82959i	0.280458	+	0.280458i	−0.552834	+	0.833292i	$0.686454\pi$
$594$		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	−0.891519	−	0.452983i	$-0.850360\pi$
$599$	1.44858	−	3.49717i	0.0591872	−	0.142891i	0.950707	+	0.310092i	$0.100360\pi$
$600$		0			0
$601$	13.2637	+	32.0214i	0.541037	+	1.30618i	0.923992	+	0.382412i	$0.124907\pi$
$601$	13.2637	+	32.0214i	0.541037	+	1.30618i	−0.382955	+	0.923767i	$0.625093\pi$
$602$		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	$0.102849\pi$
$607$			15.6455i			0.635031i	−0.948253	+	0.317516i	$0.897151\pi$
$608$		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	−0.204346	−	0.978899i	$-0.565507\pi$
$613$	−29.3870	−	19.6358i	−1.18693	−	0.793082i	−0.982584	+	0.185817i	$0.940507\pi$
$614$		0			0
$615$	−1.57231	−	3.79589i	−0.0634017	−	0.153065i
$616$		0			0
$617$	17.2764	−	41.7089i	0.695521	−	1.67914i	−0.0378285	−	0.999284i	$-0.512044\pi$
$617$	17.2764	−	41.7089i	0.695521	−	1.67914i	0.733349	−	0.679852i	$-0.237956\pi$
$618$		0			0
$619$	−21.7653	+	4.32939i	−0.874822	+	0.174013i	−0.612025	−	0.790838i	$-0.709645\pi$
$619$	−21.7653	+	4.32939i	−0.874822	+	0.174013i	−0.262797	+	0.964851i	$0.584645\pi$
$620$		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	0.187718	−	0.982223i	$-0.439891\pi$
$631$	−9.39685	−	3.89230i	−0.374083	−	0.154950i	−0.561800	+	0.827273i	$0.689891\pi$
$632$		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	0.0734703	−	0.997297i	$-0.476593\pi$
$643$	−6.09343	−	1.21206i	−0.240301	−	0.0477989i	−0.313772	+	0.949499i	$0.601593\pi$
$644$		0			0
$645$	1.80001	−	2.69391i	0.0708754	−	0.106073i
$646$		0			0
$647$	25.6309	−	10.6167i	1.00766	−	0.417385i	0.183057	−	0.983102i	$-0.441401\pi$
$647$	25.6309	−	10.6167i	1.00766	−	0.417385i	0.824599	+	0.565717i	$0.191401\pi$
$648$		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	0.998457	+	0.0555278i	$0.0176841\pi$
$653$	17.0614	+	25.5342i	0.667665	+	0.999231i	−0.330792	+	0.943704i	$0.607316\pi$
$654$		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	−0.458016	+	0.888944i	$0.651440\pi$
$659$	−37.3402	+	24.9499i	−1.45457	+	0.971911i	−0.996552	+	0.0829675i	$0.973560\pi$
$660$		0			0
$661$	−4.50510	+	0.896119i	−0.175228	+	0.0348550i	−0.281924	−	0.959437i	$-0.590973\pi$
$661$	−4.50510	+	0.896119i	−0.175228	+	0.0348550i	0.106696	+	0.994292i	$0.465973\pi$
$662$		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	$0.147460\pi$
$673$			23.1854i			0.893730i	−0.894601	+	0.446865i	$0.852540\pi$
$674$		0			0
$675$	−0.731875	+	3.67939i	−0.0281699	+	0.141620i
$676$		0			0
$677$	−20.0645	−	13.4067i	−0.771140	−	0.515260i	0.106655	−	0.994296i	$-0.465986\pi$
$677$	−20.0645	−	13.4067i	−0.771140	−	0.515260i	−0.877795	+	0.479037i	$0.840986\pi$
$678$		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	0.442704	−	0.896668i	$-0.354019\pi$
$683$	31.2265	−	6.21134i	1.19485	−	0.237670i	0.752145	+	0.658997i	$0.229019\pi$
$684$		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	0.806587	−	0.591116i	$-0.201312\pi$
$691$	−1.26704	−	1.89625i	−0.0482004	−	0.0721369i	−0.854787	+	0.518979i	$0.826312\pi$
$692$		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	0.293718	−	0.955892i	$-0.405107\pi$
$701$	5.27607	+	1.04947i	0.199274	+	0.0396381i	−0.0944439	+	0.995530i	$0.530107\pi$
$702$		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	−0.869281	−	0.494318i	$-0.835418\pi$
$709$	−2.12834	+	3.18528i	−0.0799314	+	0.119626i	0.789350	+	0.613944i	$0.210418\pi$
$710$		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	−0.659571	−	0.751642i	$-0.729262\pi$
$719$	2.46881	−	2.46881i	0.0920713	−	0.0920713i	0.751642	+	0.659571i	$0.229262\pi$
$720$		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	0.592418	+	0.805631i	$0.298173\pi$
$727$	−10.6814	+	25.7872i	−0.396152	+	0.956394i	−0.988570	+	0.150764i	$0.951827\pi$
$728$		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	−0.982146	−	0.188119i	$-0.939761\pi$
$733$	−0.0750289	+	0.377196i	−0.00277125	+	0.0139320i	0.979375	+	0.202051i	$0.0647608\pi$
$734$		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	−0.983930	−	0.178554i	$-0.942858\pi$
$739$	−0.178539	+	0.897576i	−0.00656766	+	0.0330179i	0.977362	+	0.211572i	$0.0678582\pi$
$740$		0			0
$741$	−20.2262	−	13.5147i	−0.743029	−	0.496476i
$742$		0			0
$743$	−9.08935	−	21.9436i	−0.333456	−	0.805034i	−0.998313	−	0.0580634i	$-0.981507\pi$
$743$	−9.08935	−	21.9436i	−0.333456	−	0.805034i	0.664857	−	0.746971i	$-0.268493\pi$
$744$		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	0.993409	+	0.114628i	$0.0365675\pi$
$751$	30.3650	+	30.3650i	1.10804	+	1.10804i	0.114628	+	0.993409i	$0.463433\pi$
$752$		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	−0.998540	−	0.0540198i	$-0.982797\pi$
$757$	−2.66007	−	13.3731i	−0.0966818	−	0.486052i	0.901858	−	0.432032i	$-0.142203\pi$
$758$		0			0
$759$	−3.40334	−	1.40971i	−0.123533	−	0.0511692i
$760$		0			0
$761$	−35.9341	+	14.8844i	−1.30261	+	0.539559i	−0.922719	−	0.385472i	$-0.874039\pi$
$761$	−35.9341	+	14.8844i	−1.30261	+	0.539559i	−0.379891	+	0.925031i	$0.624039\pi$
$762$		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	−0.198585	−	0.980084i	$-0.563634\pi$
$773$	21.7666	−	32.5760i	0.782890	−	1.17168i	0.981474	−	0.191594i	$-0.0613656\pi$
$774$		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	−0.0866065	−	0.996243i	$-0.527602\pi$
$787$	22.4613	−	15.0082i	0.800659	−	0.534983i	0.887265	+	0.461260i	$0.152602\pi$
$788$		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	−0.969439	−	0.245333i	$-0.921103\pi$
$797$	0.567187	−	2.85144i	0.0200908	−	0.101003i	0.989530	+	0.144330i	$0.0461027\pi$
$798$		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	−0.709354	−	0.704852i	$-0.751013\pi$
$809$	8.26668	−	19.9575i	0.290641	−	0.701669i	0.999995	+	0.00318309i	$0.00101321\pi$
$810$		0			0
$811$	−18.8077	+	3.74108i	−0.660428	+	0.131367i	−0.513914	−	0.857842i	$-0.671805\pi$
$811$	−18.8077	+	3.74108i	−0.660428	+	0.131367i	−0.146513	+	0.989209i	$0.546805\pi$
$812$		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	0.752358	+	0.658755i	$0.228917\pi$
$821$	8.86425	+	44.5636i	0.309364	+	1.55528i	−0.442993	+	0.896525i	$0.646083\pi$
$822$		0			0
$823$	51.6937	+	21.4122i	1.80193	+	0.746383i	0.985667	+	0.168701i	$0.0539572\pi$
$823$	51.6937	+	21.4122i	1.80193	+	0.746383i	0.816262	+	0.577682i	$0.196043\pi$
$824$		0			0
$825$	2.46038	−	1.01912i	0.0856594	−	0.0354813i
$826$		0			0
$827$	−21.2106	+	31.7440i	−0.737566	+	1.10385i	0.253088	+	0.967443i	$0.418554\pi$
$827$	−21.2106	+	31.7440i	−0.737566	+	1.10385i	−0.990654	+	0.136402i	$0.956446\pi$
$828$		0			0
$829$	30.0252	+	5.97239i	1.04282	+	0.207430i	0.686647	−	0.726991i	$-0.259082\pi$
$829$	30.0252	+	5.97239i	1.04282	+	0.207430i	0.356172	+	0.934420i	$0.384082\pi$
$830$		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	−0.521593	−	0.853194i	$-0.674662\pi$
$839$	−8.31645	+	3.44478i	−0.287116	+	0.118927i	0.234478	+	0.972122i	$0.424662\pi$
$840$		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	0.332037	−	0.943266i	$-0.392264\pi$
$853$	29.1995	−	5.80814i	0.999771	−	0.198867i	0.667734	+	0.744400i	$0.267264\pi$
$854$		0			0
$855$	1.77231	−	4.27874i	0.0606119	−	0.146330i
$856$		0			0
$857$	−11.6403	−	28.1022i	−0.397626	−	0.959954i	−0.988228	−	0.152991i	$-0.951110\pi$
$857$	−11.6403	−	28.1022i	−0.397626	−	0.959954i	0.590602	−	0.806963i	$-0.298890\pi$
$858$		0			0
$859$	−11.2509	−	7.51760i	−0.383875	−	0.256497i	0.348627	−	0.937261i	$-0.386648\pi$
$859$	−11.2509	−	7.51760i	−0.383875	−	0.256497i	−0.732503	+	0.680764i	$0.761648\pi$
$860$		0			0
$861$	−2.71439	+	13.6462i	−0.0925063	+	0.465060i
$862$		0			0
$863$		−	5.22703i		−	0.177930i	−0.996035	−	0.0889651i	$-0.971644\pi$
$863$		−	5.22703i		−	0.177930i	0.996035	−	0.0889651i	$-0.0283560\pi$
$864$		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	−0.623742	−	0.781630i	$-0.714388\pi$
$877$	−4.15505	+	2.77631i	−0.140306	+	0.0937494i	0.483436	+	0.875380i	$0.339388\pi$
$878$		0			0
$879$	0.683101	+	0.683101i	0.0230404	+	0.0230404i
$880$		0			0
$881$	−23.5280	+	23.5280i	−0.792679	+	0.792679i	−0.981929	−	0.189250i	$-0.939394\pi$
$881$	−23.5280	+	23.5280i	−0.792679	+	0.792679i	0.189250	+	0.981929i	$0.439394\pi$
$882$		0			0
$883$	−15.4198	−	23.0774i	−0.518919	−	0.776617i	0.475767	−	0.879571i	$-0.342171\pi$
$883$	−15.4198	−	23.0774i	−0.518919	−	0.776617i	−0.994686	+	0.102954i	$0.967171\pi$
$884$		0			0
$885$	1.18392	+	5.95195i	0.0397969	+	0.200073i
$886$		0			0
$887$	12.6038	+	5.22068i	0.423196	+	0.175293i	0.584109	−	0.811675i	$-0.301444\pi$
$887$	12.6038	+	5.22068i	0.423196	+	0.175293i	−0.160913	+	0.986969i	$0.551444\pi$
$888$		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	0.999085	+	0.0427741i	$0.0136196\pi$
$907$	2.78335	+	13.9929i	0.0924197	+	0.464625i	−0.906665	+	0.421851i	$0.861380\pi$
$908$		0			0
$909$	−1.83813	−	2.75095i	−0.0609668	−	0.0912433i
$910$		0			0
$911$	3.11574	−	3.11574i	0.103229	−	0.103229i	−0.653606	−	0.756835i	$-0.726745\pi$
$911$	3.11574	−	3.11574i	0.103229	−	0.103229i	0.756835	+	0.653606i	$0.226745\pi$
$912$		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	0.204268	+	0.978915i	$0.434518\pi$
$919$	−19.1703	+	46.2811i	−0.632369	+	1.52667i	−0.836637	+	0.547758i	$0.815482\pi$
$920$		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	$-0.872935\pi$
$929$		−	23.6929i		−	0.777338i	0.921377	−	0.388669i	$-0.127065\pi$
$930$		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	−0.989056	−	0.147541i	$-0.952864\pi$
$937$	−5.67396	+	13.6982i	−0.185360	+	0.447499i	0.803696	+	0.595041i	$0.202864\pi$
$938$		0			0
$939$	23.3029	−	4.63523i	0.760461	−	0.151265i
$940$		0			0
$941$	−4.05896	+	2.71211i	−0.132318	+	0.0884122i	−0.619968	−	0.784627i	$-0.712854\pi$
$941$	−4.05896	+	2.71211i	−0.132318	+	0.0884122i	0.487650	+	0.873039i	$0.337854\pi$
$942$		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	0.839956	−	0.542654i	$-0.182581\pi$
$947$	0.528434	+	0.790858i	0.0171718	+	0.0256994i	−0.822784	+	0.568354i	$0.807581\pi$
$948$		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	−0.566978	−	0.823733i	$-0.691888\pi$
$953$	−11.8983	+	4.92846i	−0.385425	+	0.159648i	0.181553	+	0.983381i	$0.441888\pi$
$954$		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	0.151680	−	0.988430i	$-0.451532\pi$
$967$	29.7862	−	12.3378i	0.957859	−	0.396758i	0.806179	+	0.591672i	$0.201532\pi$
$968$		0			0
$969$	9.53848	+	3.95097i	0.306420	+	0.126923i
$970$		0			0
$971$	1.46360	+	7.35802i	0.0469692	+	0.236130i	0.997138	−	0.0756067i	$-0.0240893\pi$
$971$	1.46360	+	7.35802i	0.0469692	+	0.236130i	−0.950169	+	0.311737i	$0.899089\pi$
$972$		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	−0.999468	−	0.0326286i	$-0.989612\pi$
$977$	−32.2602	−	32.2602i	−1.03210	−	1.03210i	−0.0326286	−	0.999468i	$-0.510388\pi$
$978$		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	−0.514518	−	0.857479i	$-0.672029\pi$
$983$	14.2853	−	34.4878i	0.455631	−	1.09999i	0.970149	−	0.242510i	$-0.0779708\pi$
$984$		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	$-0.861079\pi$
$991$		−	26.6140i		−	0.845420i	0.906265	−	0.422710i	$-0.138921\pi$
$992$		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	0.921663	−	0.387991i	$-0.126831\pi$
$997$	28.9202	+	19.3239i	0.915912	+	0.611993i	−0.00575155	+	0.999983i	$0.501831\pi$
$998$		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.721.10		128
4.3	odd	2		192.2.r.a.157.10	✓	128
12.11	even	2		576.2.bd.b.541.7		128
64.11	odd	16		192.2.r.a.181.10	yes	128
64.53	even	16	inner	768.2.r.a.49.10		128
192.11	even	16		576.2.bd.b.181.7		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.10	✓	128	4.3	odd	2
192.2.r.a.181.10	yes	128	64.11	odd	16
576.2.bd.b.181.7		128	192.11	even	16
576.2.bd.b.541.7		128	12.11	even	2
768.2.r.a.49.10		128	64.53	even	16	inner
768.2.r.a.721.10		128	1.1	even	1	trivial

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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