LMFDB - Embedded newform 2548.2.bq.e.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(361,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2548.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,28,0,0,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$0.268953i$ of defining polynomial
Character	$\chi$	$=$	2548.361
Dual form			2548.2.bq.e.1941.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.268953 q^{3} +(1.17420 - 0.677925i) q^{5} -2.92766 q^{9} +2.80318i q^{11} +(0.303042 + 3.59279i) q^{13} +(-0.315805 + 0.182330i) q^{15} +(-2.90934 - 5.03912i) q^{17} -3.18458i q^{19} +(3.77674 - 6.54150i) q^{23} +(-1.58083 + 2.73809i) q^{25} +1.59426 q^{27} +(-3.60830 - 6.24977i) q^{29} +(6.96637 + 4.02203i) q^{31} -0.753925i q^{33} +(6.02532 + 3.47872i) q^{37} +(-0.0815041 - 0.966292i) q^{39} +(4.38164 - 2.52974i) q^{41} +(3.13427 - 5.42872i) q^{43} +(-3.43767 + 1.98474i) q^{45} +(-2.28903 + 1.32157i) q^{47} +(0.782475 + 1.35529i) q^{51} +(5.54434 - 9.60308i) q^{53} +(1.90035 + 3.29150i) q^{55} +0.856503i q^{57} +(5.45213 - 3.14779i) q^{59} +12.8081 q^{61} +(2.79148 + 4.01322i) q^{65} +4.96294i q^{67} +(-1.01576 + 1.75936i) q^{69} +(-14.2993 - 8.25572i) q^{71} +(13.3672 + 7.71755i) q^{73} +(0.425170 - 0.736416i) q^{75} +(-7.38303 - 12.7878i) q^{79} +8.35421 q^{81} +9.79310i q^{83} +(-6.83230 - 3.94463i) q^{85} +(0.970464 + 1.68089i) q^{87} +(7.24707 + 4.18410i) q^{89} +(-1.87363 - 1.08174i) q^{93} +(-2.15891 - 3.73934i) q^{95} +(-10.5685 - 6.10170i) q^{97} -8.20678i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{9} + 10 q^{13} + 6 q^{15} + 2 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} - 30 q^{31} - 12 q^{37} - 6 q^{39} + 36 q^{41} + 6 q^{43} + 30 q^{45} + 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 18 q^{59}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q + 28 * q^9 + 10 * q^13 + 6 * q^15 + 2 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 - 30 * q^31 - 12 * q^37 - 6 * q^39 + 36 * q^41 + 6 * q^43 + 30 * q^45 + 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 18 * q^59 - 8 * q^61 - 52 * q^69 + 36 * q^71 + 12 * q^73 - 10 * q^75 - 4 * q^79 + 42 * q^85 + 26 * q^87 + 36 * q^89 + 42 * q^93 - 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.268953			−0.155280			−0.0776400	−	0.996981i	$-0.524738\pi$
$3$	−0.268953			−0.155280			−0.0776400	+	0.996981i	$0.524738\pi$
$4$		0			0
$5$	1.17420	−	0.677925i	0.525119	−	0.303177i	−0.213908	−	0.976854i	$-0.568619\pi$
$5$	1.17420	−	0.677925i	0.525119	−	0.303177i	0.739026	+	0.673676i	$0.235286\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.92766			−0.975888
$10$		0			0
$11$			2.80318i			0.845192i	0.906318	+	0.422596i	$0.138881\pi$
$11$			2.80318i			0.845192i	−0.906318	+	0.422596i	$0.861119\pi$
$12$		0			0
$13$	0.303042	+	3.59279i	0.0840488	+	0.996462i
$13$	0.303042	+	3.59279i	0.0840488	+	0.996462i
$14$		0			0
$15$	−0.315805	+	0.182330i	−0.0815405	+	0.0470774i
$16$		0			0
$17$	−2.90934	−	5.03912i	−0.705618	−	1.22217i	−0.966468	−	0.256787i	$-0.917336\pi$
$17$	−2.90934	−	5.03912i	−0.705618	−	1.22217i	0.260850	−	0.965379i	$-0.415997\pi$
$18$		0			0
$19$		−	3.18458i		−	0.730594i	−0.930891	−	0.365297i	$-0.880968\pi$
$19$		−	3.18458i		−	0.730594i	0.930891	−	0.365297i	$-0.119032\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.77674	−	6.54150i	0.787504	−	1.36400i	−0.139988	−	0.990153i	$-0.544706\pi$
$23$	3.77674	−	6.54150i	0.787504	−	1.36400i	0.927492	−	0.373843i	$-0.121960\pi$
$24$		0			0
$25$	−1.58083	+	2.73809i	−0.316167	+	0.547617i
$26$		0			0
$27$	1.59426			0.306816
$28$		0			0
$29$	−3.60830	−	6.24977i	−0.670045	−	1.16055i	−0.977891	−	0.209116i	$-0.932941\pi$
$29$	−3.60830	−	6.24977i	−0.670045	−	1.16055i	0.307845	−	0.951436i	$-0.400392\pi$
$30$		0			0
$31$	6.96637	+	4.02203i	1.25120	+	0.722379i	0.971347	−	0.237665i	$-0.0763821\pi$
$31$	6.96637	+	4.02203i	1.25120	+	0.722379i	0.279849	+	0.960044i	$0.409715\pi$
$32$		0			0
$33$		−	0.753925i		−	0.131241i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.02532	+	3.47872i	0.990557	+	0.571898i	0.905441	−	0.424473i	$-0.139541\pi$
$37$	6.02532	+	3.47872i	0.990557	+	0.571898i	0.0851160	+	0.996371i	$0.472874\pi$
$38$		0			0
$39$	−0.0815041	−	0.966292i	−0.0130511	−	0.154731i
$40$		0			0
$41$	4.38164	−	2.52974i	0.684298	−	0.395079i	−0.117175	−	0.993111i	$-0.537384\pi$
$41$	4.38164	−	2.52974i	0.684298	−	0.395079i	0.801472	+	0.598032i	$0.204050\pi$
$42$		0			0
$43$	3.13427	−	5.42872i	0.477972	−	0.827872i	−0.521709	−	0.853123i	$-0.674705\pi$
$43$	3.13427	−	5.42872i	0.477972	−	0.827872i	0.999681	+	0.0252518i	$0.00803875\pi$
$44$		0			0
$45$	−3.43767	+	1.98474i	−0.512457	+	0.295867i
$46$		0			0
$47$	−2.28903	+	1.32157i	−0.333890	+	0.192771i	−0.657567	−	0.753396i	$-0.728414\pi$
$47$	−2.28903	+	1.32157i	−0.333890	+	0.192771i	0.323677	+	0.946168i	$0.395081\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.782475	+	1.35529i	0.109568	+	0.189778i
$52$		0			0
$53$	5.54434	−	9.60308i	0.761574	−	1.31908i	−0.180466	−	0.983581i	$-0.557760\pi$
$53$	5.54434	−	9.60308i	0.761574	−	1.31908i	0.942039	−	0.335503i	$-0.108906\pi$
$54$		0			0
$55$	1.90035	+	3.29150i	0.256243	+	0.443826i
$56$		0			0
$57$			0.856503i			0.113447i
$58$		0			0
$59$	5.45213	−	3.14779i	0.709807	−	0.409807i	−0.101183	−	0.994868i	$-0.532263\pi$
$59$	5.45213	−	3.14779i	0.709807	−	0.409807i	0.810989	+	0.585061i	$0.198929\pi$
$60$		0			0
$61$	12.8081			1.63991			0.819953	−	0.572431i	$-0.193999\pi$
$61$	12.8081			1.63991			0.819953	+	0.572431i	$0.193999\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.79148	+	4.01322i	0.346240	+	0.497779i
$66$		0			0
$67$			4.96294i			0.606319i	0.952940	+	0.303160i	$0.0980416\pi$
$67$			4.96294i			0.606319i	−0.952940	+	0.303160i	$0.901958\pi$
$68$		0			0
$69$	−1.01576	+	1.75936i	−0.122284	+	0.211801i
$70$		0			0
$71$	−14.2993	−	8.25572i	−1.69702	−	0.979773i	−0.948564	−	0.316586i	$-0.897464\pi$
$71$	−14.2993	−	8.25572i	−1.69702	−	0.979773i	−0.748453	−	0.663188i	$-0.769203\pi$
$72$		0			0
$73$	13.3672	+	7.71755i	1.56451	+	0.903271i	0.996791	+	0.0800494i	$0.0255078\pi$
$73$	13.3672	+	7.71755i	1.56451	+	0.903271i	0.567720	+	0.823222i	$0.307826\pi$
$74$		0			0
$75$	0.425170	−	0.736416i	0.0490944	−	0.0850340i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.38303	−	12.7878i	−0.830656	−	1.43874i	−0.897519	−	0.440976i	$-0.854632\pi$
$79$	−7.38303	−	12.7878i	−0.830656	−	1.43874i	0.0668627	−	0.997762i	$-0.478701\pi$
$80$		0			0
$81$	8.35421			0.928246
$82$		0			0
$83$			9.79310i			1.07493i	0.843285	+	0.537466i	$0.180618\pi$
$83$			9.79310i			1.07493i	−0.843285	+	0.537466i	$0.819382\pi$
$84$		0			0
$85$	−6.83230	−	3.94463i	−0.741067	−	0.427855i
$86$		0			0
$87$	0.970464	+	1.68089i	0.104045	+	0.180211i
$88$		0			0
$89$	7.24707	+	4.18410i	0.768188	+	0.443513i	0.832228	−	0.554434i	$-0.187065\pi$
$89$	7.24707	+	4.18410i	0.768188	+	0.443513i	−0.0640399	+	0.997947i	$0.520398\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.87363	−	1.08174i	−0.194286	−	0.112171i
$94$		0			0
$95$	−2.15891	−	3.73934i	−0.221499	−	0.383648i
$96$		0			0
$97$	−10.5685	−	6.10170i	−1.07306	−	0.619534i	−0.144047	−	0.989571i	$-0.546012\pi$
$97$	−10.5685	−	6.10170i	−1.07306	−	0.619534i	−0.929017	+	0.370037i	$0.879345\pi$
$98$		0			0
$99$		−	8.20678i		−	0.824813i
$100$		0			0
$101$	2.42285			0.241083			0.120541	−	0.992708i	$-0.461537\pi$
$101$	2.42285			0.241083			0.120541	+	0.992708i	$0.461537\pi$
$102$		0			0
$103$	−7.24547	−	12.5495i	−0.713917	−	1.23654i	−0.963376	−	0.268155i	$-0.913586\pi$
$103$	−7.24547	−	12.5495i	−0.713917	−	1.23654i	0.249458	−	0.968386i	$-0.419747\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.24370	+	5.61826i	−0.313581	+	0.543138i	−0.979135	−	0.203212i	$-0.934862\pi$
$107$	−3.24370	+	5.61826i	−0.313581	+	0.543138i	0.665554	+	0.746350i	$0.268195\pi$
$108$		0			0
$109$	−2.54304	−	1.46822i	−0.243579	−	0.140630i	0.373242	−	0.927734i	$-0.378246\pi$
$109$	−2.54304	−	1.46822i	−0.243579	−	0.140630i	−0.616820	+	0.787104i	$0.711580\pi$
$110$		0			0
$111$	−1.62053	−	0.935612i	−0.153814	−	0.0888044i
$112$		0			0
$113$	1.66909	−	2.89095i	0.157015	−	0.271957i	−0.776776	−	0.629777i	$-0.783146\pi$
$113$	1.66909	−	2.89095i	0.157015	−	0.271957i	0.933791	+	0.357819i	$0.116480\pi$
$114$		0			0
$115$		−	10.2414i		−	0.955013i
$116$		0			0
$117$	−0.887206	−	10.5185i	−0.0820222	−	0.972435i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.14216			0.285651
$122$		0			0
$123$	−1.17846	+	0.680382i	−0.106258	+	0.0613480i
$124$		0			0
$125$			11.0660i			0.989773i
$126$		0			0
$127$	−6.27512	−	10.8688i	−0.556827	−	0.964452i	−0.997759	−	0.0669115i	$-0.978685\pi$
$127$	−6.27512	−	10.8688i	−0.556827	−	0.964452i	0.440932	−	0.897540i	$-0.354648\pi$
$128$		0			0
$129$	−0.842971	+	1.46007i	−0.0742195	+	0.128552i
$130$		0			0
$131$	−0.630004	−	1.09120i	−0.0550437	−	0.0953385i	0.837191	−	0.546911i	$-0.184196\pi$
$131$	−0.630004	−	1.09120i	−0.0550437	−	0.0953385i	−0.892234	+	0.451573i	$0.850863\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.87199	−	1.08079i	0.161115	−	0.0930197i
$136$		0			0
$137$	7.20794	−	4.16151i	0.615816	−	0.355542i	−0.159422	−	0.987211i	$-0.550963\pi$
$137$	7.20794	−	4.16151i	0.615816	−	0.355542i	0.775238	+	0.631669i	$0.217630\pi$
$138$		0			0
$139$	2.89438	−	5.01322i	0.245498	−	0.425216i	−0.716773	−	0.697306i	$-0.754382\pi$
$139$	2.89438	−	5.01322i	0.245498	−	0.425216i	0.962272	+	0.272091i	$0.0877151\pi$
$140$		0			0
$141$	0.615642	−	0.355441i	0.0518464	−	0.0299335i
$142$		0			0
$143$	−10.0713	+	0.849483i	−0.842201	+	0.0710374i
$144$		0			0
$145$	−8.47375	−	4.89232i	−0.703707	−	0.406285i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	14.2039i		−	1.16362i	−0.813323	−	0.581812i	$-0.802344\pi$
$149$		−	14.2039i		−	1.16362i	0.813323	−	0.581812i	$-0.197656\pi$
$150$		0			0
$151$	9.65700	+	5.57547i	0.785875	+	0.453725i	0.838508	−	0.544889i	$-0.183428\pi$
$151$	9.65700	+	5.57547i	0.785875	+	0.453725i	−0.0526332	+	0.998614i	$0.516761\pi$
$152$		0			0
$153$	8.51757	+	14.7529i	0.688605	+	1.19270i
$154$		0			0
$155$	10.9066			0.876036
$156$		0			0
$157$	−2.02375	+	3.50523i	−0.161513	+	0.279748i	−0.935411	−	0.353561i	$-0.884971\pi$
$157$	−2.02375	+	3.50523i	−0.161513	+	0.279748i	0.773899	+	0.633309i	$0.218304\pi$
$158$		0			0
$159$	−1.49117	+	2.58278i	−0.118257	+	0.204827i
$160$		0			0
$161$		0			0
$162$		0			0
$163$			5.27322i			0.413031i	0.978443	+	0.206515i	$0.0662124\pi$
$163$			5.27322i			0.413031i	−0.978443	+	0.206515i	$0.933788\pi$
$164$		0			0
$165$	−0.511105	−	0.885259i	−0.0397894	−	0.0689173i
$166$		0			0
$167$	−4.63307	+	2.67491i	−0.358518	+	0.206990i	−0.668430	−	0.743775i	$-0.733034\pi$
$167$	−4.63307	+	2.67491i	−0.358518	+	0.206990i	0.309912	+	0.950765i	$0.399700\pi$
$168$		0			0
$169$	−12.8163	+	2.17754i	−0.985872	+	0.167503i
$170$		0			0
$171$			9.32339i			0.712978i
$172$		0			0
$173$	9.74309			0.740754			0.370377	−	0.928882i	$-0.379229\pi$
$173$	9.74309			0.740754			0.370377	+	0.928882i	$0.379229\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.46637	+	0.846607i	−0.110219	+	0.0636349i
$178$		0			0
$179$	−11.4053			−0.852469			−0.426234	−	0.904613i	$-0.640160\pi$
$179$	−11.4053			−0.852469			−0.426234	+	0.904613i	$0.640160\pi$
$180$		0			0
$181$	25.4727			1.89337			0.946685	−	0.322160i	$-0.104409\pi$
$181$	25.4727			1.89337			0.946685	+	0.322160i	$0.104409\pi$
$182$		0			0
$183$	−3.44477			−0.254645
$184$		0			0
$185$	9.43325			0.693546
$186$		0			0
$187$	14.1256	−	8.15541i	1.03297	−	0.596383i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	16.3781			1.18508			0.592539	−	0.805542i	$-0.298126\pi$
$191$	16.3781			1.18508			0.592539	+	0.805542i	$0.298126\pi$
$192$		0			0
$193$			9.56245i			0.688320i	0.938911	+	0.344160i	$0.111836\pi$
$193$			9.56245i			0.688320i	−0.938911	+	0.344160i	$0.888164\pi$
$194$		0			0
$195$	−0.750776	−	1.07937i	−0.0537642	−	0.0772951i
$196$		0			0
$197$	2.60716	−	1.50525i	0.185753	−	0.107244i	−0.404240	−	0.914653i	$-0.632464\pi$
$197$	2.60716	−	1.50525i	0.185753	−	0.107244i	0.589993	+	0.807409i	$0.299131\pi$
$198$		0			0
$199$	−2.30985	−	4.00077i	−0.163741	−	0.283607i	0.772467	−	0.635055i	$-0.219023\pi$
$199$	−2.30985	−	4.00077i	−0.163741	−	0.283607i	−0.936207	+	0.351448i	$0.885689\pi$
$200$		0			0
$201$		−	1.33480i		−	0.0941493i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.42995	−	5.94085i	0.239558	−	0.414927i
$206$		0			0
$207$	−11.0570	+	19.1513i	−0.768516	+	1.33111i
$208$		0			0
$209$	8.92697			0.617492
$210$		0			0
$211$	−1.16932	−	2.02533i	−0.0804995	−	0.139429i	0.822965	−	0.568092i	$-0.192318\pi$
$211$	−1.16932	−	2.02533i	−0.0804995	−	0.139429i	−0.903465	+	0.428663i	$0.858985\pi$
$212$		0			0
$213$	3.84584	+	2.22040i	0.263513	+	0.152139i
$214$		0			0
$215$		−	8.49921i		−	0.579641i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.59515	−	2.07566i	−0.242937	−	0.140260i
$220$		0			0
$221$	17.2229	−	11.9797i	1.15854	−	0.805843i
$222$		0			0
$223$	−4.21429	+	2.43312i	−0.282210	+	0.162934i	−0.634423	−	0.772986i	$-0.718762\pi$
$223$	−4.21429	+	2.43312i	−0.282210	+	0.162934i	0.352214	+	0.935920i	$0.385429\pi$
$224$		0			0
$225$	4.62815	−	8.01620i	0.308544	−	0.534413i
$226$		0			0
$227$	24.3177	−	14.0398i	1.61402	−	0.931855i	0.625594	−	0.780149i	$-0.284857\pi$
$227$	24.3177	−	14.0398i	1.61402	−	0.931855i	0.988426	−	0.151706i	$-0.0484766\pi$
$228$		0			0
$229$	0.155261	−	0.0896399i	0.0102599	−	0.00592357i	−0.494861	−	0.868972i	$-0.664781\pi$
$229$	0.155261	−	0.0896399i	0.0102599	−	0.00592357i	0.505121	+	0.863048i	$0.331448\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.56918	−	13.1102i	−0.495873	−	0.858878i	0.504115	−	0.863636i	$-0.331819\pi$
$233$	−7.56918	−	13.1102i	−0.495873	−	0.858878i	−0.999989	+	0.00475858i	$0.998485\pi$
$234$		0			0
$235$	−1.79186	+	3.10358i	−0.116888	+	0.202456i
$236$		0			0
$237$	1.98569	+	3.43931i	0.128984	+	0.223407i
$238$		0			0
$239$			12.8703i			0.832512i	0.909247	+	0.416256i	$0.136658\pi$
$239$			12.8703i			0.832512i	−0.909247	+	0.416256i	$0.863342\pi$
$240$		0			0
$241$	−8.51452	+	4.91586i	−0.548469	+	0.316659i	−0.748504	−	0.663130i	$-0.769228\pi$
$241$	−8.51452	+	4.91586i	−0.548469	+	0.316659i	0.200035	+	0.979789i	$0.435894\pi$
$242$		0			0
$243$	−7.02968			−0.450954
$244$		0			0
$245$		0			0
$246$		0			0
$247$	11.4416	−	0.965064i	0.728008	−	0.0614055i
$248$		0			0
$249$		−	2.63388i		−	0.166916i
$250$		0			0
$251$	−8.66099	+	15.0013i	−0.546677	+	0.946872i	0.451823	+	0.892108i	$0.350774\pi$
$251$	−8.66099	+	15.0013i	−0.546677	+	0.946872i	−0.998499	+	0.0547641i	$0.982559\pi$
$252$		0			0
$253$	18.3370	+	10.5869i	1.15284	+	0.665592i
$254$		0			0
$255$	1.83757	+	1.06092i	0.115073	+	0.0664374i
$256$		0			0
$257$	−5.35302	+	9.27170i	−0.333912	+	0.578353i	−0.983275	−	0.182126i	$-0.941702\pi$
$257$	−5.35302	+	9.27170i	−0.333912	+	0.578353i	0.649363	+	0.760478i	$0.275036\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	10.5639	+	18.2972i	0.653889	+	1.13257i
$262$		0			0
$263$	−14.0697			−0.867574			−0.433787	−	0.901015i	$-0.642823\pi$
$263$	−14.0697			−0.867574			−0.433787	+	0.901015i	$0.642823\pi$
$264$		0			0
$265$		−	15.0346i		−	0.923567i
$266$		0			0
$267$	−1.94912	−	1.12533i	−0.119284	−	0.0688688i
$268$		0			0
$269$	0.272011	+	0.471138i	0.0165848	+	0.0287258i	0.874199	−	0.485568i	$-0.161387\pi$
$269$	0.272011	+	0.471138i	0.0165848	+	0.0287258i	−0.857614	+	0.514294i	$0.828054\pi$
$270$		0			0
$271$	0.641910	+	0.370607i	0.0389933	+	0.0225128i	0.519370	−	0.854550i	$-0.326167\pi$
$271$	0.641910	+	0.370607i	0.0389933	+	0.0225128i	−0.480377	+	0.877062i	$0.659500\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.67536	−	4.43137i	−0.462842	−	0.267222i
$276$		0			0
$277$	−7.06675	−	12.2400i	−0.424600	−	0.735429i	0.571783	−	0.820405i	$-0.306252\pi$
$277$	−7.06675	−	12.2400i	−0.424600	−	0.735429i	−0.996383	+	0.0849763i	$0.972919\pi$
$278$		0			0
$279$	−20.3952	−	11.7752i	−1.22103	−	0.704961i
$280$		0			0
$281$		−	25.8051i		−	1.53940i	−0.638404	−	0.769702i	$-0.720405\pi$
$281$		−	25.8051i		−	1.53940i	0.638404	−	0.769702i	$-0.279595\pi$
$282$		0			0
$283$	−27.2817			−1.62173			−0.810865	−	0.585233i	$-0.801003\pi$
$283$	−27.2817			−1.62173			−0.810865	+	0.585233i	$0.801003\pi$
$284$		0			0
$285$	0.580645	+	1.00571i	0.0343944	+	0.0595729i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.42851	+	14.5986i	−0.495795	+	0.858742i
$290$		0			0
$291$	2.84242	+	1.64107i	0.166625	+	0.0962013i
$292$		0			0
$293$	−1.50010	−	0.866083i	−0.0876367	−	0.0505971i	0.455541	−	0.890215i	$-0.349446\pi$
$293$	−1.50010	−	0.866083i	−0.0876367	−	0.0505971i	−0.543178	+	0.839618i	$0.682779\pi$
$294$		0			0
$295$	4.26793	−	7.39227i	0.248489	−	0.430395i
$296$		0			0
$297$			4.46901i			0.259318i
$298$		0			0
$299$	24.6468	+	11.5867i	1.42536	+	0.670075i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.651633			−0.0374354
$304$		0			0
$305$	15.0393	−	8.68292i	0.861145	−	0.497182i
$306$		0			0
$307$		−	21.4365i		−	1.22345i	−0.791072	−	0.611723i	$-0.790477\pi$
$307$		−	21.4365i		−	1.22345i	0.791072	−	0.611723i	$-0.209523\pi$
$308$		0			0
$309$	1.94869	+	3.37523i	0.110857	+	0.192010i
$310$		0			0
$311$	13.6362	−	23.6186i	0.773237	−	1.33929i	−0.162543	−	0.986701i	$-0.551970\pi$
$311$	13.6362	−	23.6186i	0.773237	−	1.33929i	0.935780	−	0.352584i	$-0.114697\pi$
$312$		0			0
$313$	−3.64110	−	6.30658i	−0.205807	−	0.356469i	0.744582	−	0.667531i	$-0.232649\pi$
$313$	−3.64110	−	6.30658i	−0.205807	−	0.356469i	−0.950390	+	0.311062i	$0.899315\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.20695	−	1.27418i	0.123954	−	0.0715651i	−0.436741	−	0.899587i	$-0.643867\pi$
$317$	2.20695	−	1.27418i	0.123954	−	0.0715651i	0.560695	+	0.828022i	$0.310534\pi$
$318$		0			0
$319$	17.5192	−	10.1147i	0.980890	−	0.566317i
$320$		0			0
$321$	0.872404	−	1.51105i	0.0486928	−	0.0843384i
$322$		0			0
$323$	−16.0475	+	9.26503i	−0.892907	+	0.515520i
$324$		0			0
$325$	−10.3164	−	4.84986i	−0.572253	−	0.269022i
$326$		0			0
$327$	0.683957	+	0.394883i	0.0378229	+	0.0218371i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		−	0.195664i		−	0.0107547i	−0.999986	−	0.00537733i	$-0.998288\pi$
$331$		−	0.195664i		−	0.0107547i	0.999986	−	0.00537733i	$-0.00171167\pi$
$332$		0			0
$333$	−17.6401	−	10.1845i	−0.966672	−	0.558109i
$334$		0			0
$335$	3.36450	+	5.82749i	0.183822	+	0.318390i
$336$		0			0
$337$	2.00900			0.109437			0.0547185	−	0.998502i	$-0.482574\pi$
$337$	2.00900			0.109437			0.0547185	+	0.998502i	$0.482574\pi$
$338$		0			0
$339$	−0.448906	+	0.777529i	−0.0243813	+	0.0422296i
$340$		0			0
$341$	−11.2745	+	19.5280i	−0.610549	+	1.05750i
$342$		0			0
$343$		0			0
$344$		0			0
$345$			2.75445i			0.148295i
$346$		0			0
$347$	−2.27450	−	3.93956i	−0.122102	−	0.211486i	0.798495	−	0.602002i	$-0.205630\pi$
$347$	−2.27450	−	3.93956i	−0.122102	−	0.211486i	−0.920596	+	0.390516i	$0.872297\pi$
$348$		0			0
$349$	4.65700	−	2.68872i	0.249284	−	0.143924i	−0.370153	−	0.928971i	$-0.620695\pi$
$349$	4.65700	−	2.68872i	0.249284	−	0.143924i	0.619436	+	0.785047i	$0.287361\pi$
$350$		0			0
$351$	0.483129	+	5.72786i	0.0257875	+	0.305730i
$352$		0			0
$353$			8.20095i			0.436492i	0.975894	+	0.218246i	$0.0700336\pi$
$353$			8.20095i			0.436492i	−0.975894	+	0.218246i	$0.929966\pi$
$354$		0			0
$355$	−22.3870			−1.18818
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−27.5105	+	15.8832i	−1.45195	+	0.838284i	−0.998592	−	0.0530438i	$-0.983108\pi$
$359$	−27.5105	+	15.8832i	−1.45195	+	0.838284i	−0.453359	+	0.891328i	$0.649774\pi$
$360$		0			0
$361$	8.85843			0.466233
$362$		0			0
$363$	−0.845093			−0.0443559
$364$		0			0
$365$	20.9277			1.09541
$366$		0			0
$367$	17.3374			0.905005			0.452502	−	0.891763i	$-0.350531\pi$
$367$	17.3374			0.905005			0.452502	+	0.891763i	$0.350531\pi$
$368$		0			0
$369$	−12.8280	+	7.40624i	−0.667798	+	0.385553i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	16.0963			0.833434			0.416717	−	0.909036i	$-0.363181\pi$
$373$	16.0963			0.833434			0.416717	+	0.909036i	$0.363181\pi$
$374$		0			0
$375$		−	2.97623i		−	0.153692i
$376$		0			0
$377$	21.3607	−	14.8578i	1.10013	−	0.765218i
$378$		0			0
$379$	−15.2907	+	8.82811i	−0.785432	+	0.453470i	−0.838352	−	0.545129i	$-0.816481\pi$
$379$	−15.2907	+	8.82811i	−0.785432	+	0.453470i	0.0529197	+	0.998599i	$0.483147\pi$
$380$		0			0
$381$	1.68771	+	2.92320i	0.0864641	+	0.149760i
$382$		0			0
$383$		−	8.22450i		−	0.420252i	−0.977674	−	0.210126i	$-0.932613\pi$
$383$		−	8.22450i		−	0.420252i	0.977674	−	0.210126i	$-0.0673874\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.17609	+	15.8935i	−0.466447	+	0.807910i
$388$		0			0
$389$	−7.58442	+	13.1366i	−0.384545	+	0.666052i	−0.991706	−	0.128527i	$-0.958975\pi$
$389$	−7.58442	+	13.1366i	−0.384545	+	0.666052i	0.607161	+	0.794579i	$0.292308\pi$
$390$		0			0
$391$	−43.9512			−2.22271
$392$		0			0
$393$	0.169441	+	0.293481i	0.00854719	+	0.0148042i
$394$		0			0
$395$	−17.3383	−	10.0103i	−0.872386	−	0.503672i
$396$		0			0
$397$			28.3063i			1.42065i	0.703874	+	0.710325i	$0.251452\pi$
$397$			28.3063i			1.42065i	−0.703874	+	0.710325i	$0.748548\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.8257	−	8.55962i	−0.740360	−	0.427447i	0.0818403	−	0.996645i	$-0.473920\pi$
$401$	−14.8257	−	8.55962i	−0.740360	−	0.427447i	−0.822200	+	0.569198i	$0.807254\pi$
$402$		0			0
$403$	−12.3392	+	26.2476i	−0.614661	+	1.30748i
$404$		0			0
$405$	9.80952	−	5.66353i	0.487439	−	0.281423i
$406$		0			0
$407$	−9.75149	+	16.8901i	−0.483364	+	0.837210i
$408$		0			0
$409$	−9.82072	+	5.66999i	−0.485603	+	0.280363i	−0.722749	−	0.691111i	$-0.757122\pi$
$409$	−9.82072	+	5.66999i	−0.485603	+	0.280363i	0.237145	+	0.971474i	$0.423788\pi$
$410$		0			0
$411$	−1.93860	+	1.11925i	−0.0956240	+	0.0552085i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.63899	+	11.4991i	0.325895	+	0.564467i
$416$		0			0
$417$	−0.778453	+	1.34832i	−0.0381210	+	0.0660275i
$418$		0			0
$419$	−0.0694276	−	0.120252i	−0.00339176	−	0.00587470i	0.864325	−	0.502934i	$-0.167746\pi$
$419$	−0.0694276	−	0.120252i	−0.00339176	−	0.00587470i	−0.867716	+	0.497060i	$0.834413\pi$
$420$		0			0
$421$			24.3258i			1.18557i	0.805362	+	0.592783i	$0.201971\pi$
$421$			24.3258i			1.18557i	−0.805362	+	0.592783i	$0.798029\pi$
$422$		0			0
$423$	6.70152	−	3.86912i	0.325839	−	0.188123i
$424$		0			0
$425$	18.3967			0.892373
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2.70870	−	0.228471i	0.130777	−	0.0110307i
$430$		0			0
$431$			28.7924i			1.38688i	0.720514	+	0.693440i	$0.243906\pi$
$431$			28.7924i			1.38688i	−0.720514	+	0.693440i	$0.756094\pi$
$432$		0			0
$433$	−12.6367	+	21.8873i	−0.607279	+	1.05184i	0.384408	+	0.923163i	$0.374406\pi$
$433$	−12.6367	+	21.8873i	−0.607279	+	1.05184i	−0.991687	+	0.128675i	$0.958928\pi$
$434$		0			0
$435$	2.27904	+	1.31580i	0.109272	+	0.0630880i
$436$		0			0
$437$	−20.8319	−	12.0273i	−0.996527	−	0.575345i
$438$		0			0
$439$	3.01512	−	5.22234i	0.143904	−	0.249248i	−0.785060	−	0.619420i	$-0.787368\pi$
$439$	3.01512	−	5.22234i	0.143904	−	0.249248i	0.928963	+	0.370172i	$0.120701\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.7494	−	20.3505i	−0.558230	−	0.966883i	−0.997644	−	0.0685983i	$-0.978147\pi$
$443$	−11.7494	−	20.3505i	−0.558230	−	0.966883i	0.439414	−	0.898285i	$-0.355186\pi$
$444$		0			0
$445$	11.3460			0.537853
$446$		0			0
$447$			3.82017i			0.180688i
$448$		0			0
$449$	20.2543	+	11.6938i	0.955859	+	0.551865i	0.894896	−	0.446275i	$-0.147250\pi$
$449$	20.2543	+	11.6938i	0.955859	+	0.551865i	0.0609627	+	0.998140i	$0.480583\pi$
$450$		0			0
$451$	7.09133	+	12.2826i	0.333918	+	0.578363i
$452$		0			0
$453$	−2.59728	−	1.49954i	−0.122031	−	0.0704545i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	22.6616	+	13.0837i	1.06007	+	0.612030i	0.925451	−	0.378868i	$-0.123687\pi$
$457$	22.6616	+	13.0837i	1.06007	+	0.612030i	0.134616	+	0.990898i	$0.457020\pi$
$458$		0			0
$459$	−4.63825	−	8.03369i	−0.216495	−	0.374980i
$460$		0			0
$461$	−21.8524	−	12.6165i	−1.01777	−	0.587609i	−0.104312	−	0.994545i	$-0.533264\pi$
$461$	−21.8524	−	12.6165i	−1.01777	−	0.587609i	−0.913457	+	0.406936i	$0.866597\pi$
$462$		0			0
$463$			18.1600i			0.843968i	0.906603	+	0.421984i	$0.138666\pi$
$463$			18.1600i			0.843968i	−0.906603	+	0.421984i	$0.861334\pi$
$464$		0			0
$465$	−2.93335			−0.136031
$466$		0			0
$467$	6.31641	+	10.9403i	0.292289	+	0.506259i	0.974351	−	0.225036i	$-0.0722499\pi$
$467$	6.31641	+	10.9403i	0.292289	+	0.506259i	−0.682062	+	0.731294i	$0.738917\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.544293	−	0.942743i	0.0250797	−	0.0434393i
$472$		0			0
$473$	15.2177	+	8.78594i	0.699710	+	0.403978i
$474$		0			0
$475$	8.71966	+	5.03430i	0.400086	+	0.230990i
$476$		0			0
$477$	−16.2320	+	28.1146i	−0.743211	+	1.28728i
$478$		0			0
$479$			12.3074i			0.562338i	0.959658	+	0.281169i	$0.0907221\pi$
$479$			12.3074i			0.562338i	−0.959658	+	0.281169i	$0.909278\pi$
$480$		0			0
$481$	−10.6724	+	22.7019i	−0.486619	+	1.03512i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.5460			−0.751315
$486$		0			0
$487$	−13.5393	+	7.81693i	−0.613525	+	0.354219i	−0.774344	−	0.632765i	$-0.781920\pi$
$487$	−13.5393	+	7.81693i	−0.613525	+	0.354219i	0.160819	+	0.986984i	$0.448587\pi$
$488$		0			0
$489$		−	1.41825i		−	0.0641355i
$490$		0			0
$491$	5.10543	+	8.84286i	0.230405	+	0.399073i	0.957927	−	0.287011i	$-0.0926617\pi$
$491$	5.10543	+	8.84286i	0.230405	+	0.399073i	−0.727523	+	0.686084i	$0.759328\pi$
$492$		0			0
$493$	−20.9956	+	36.3654i	−0.945593	+	1.63781i
$494$		0			0
$495$	−5.56358	−	9.63641i	−0.250065	−	0.433124i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.589766	−	0.340502i	0.0264016	−	0.0152430i	−0.486741	−	0.873546i	$-0.661814\pi$
$499$	0.589766	−	0.340502i	0.0264016	−	0.0152430i	0.513143	+	0.858303i	$0.328481\pi$
$500$		0			0
$501$	1.24608	−	0.719424i	0.0556707	−	0.0321415i
$502$		0			0
$503$	17.6701	−	30.6056i	0.787873	−	1.36464i	−0.139395	−	0.990237i	$-0.544516\pi$
$503$	17.6701	−	30.6056i	0.787873	−	1.36464i	0.927268	−	0.374399i	$-0.122151\pi$
$504$		0			0
$505$	2.84492	−	1.64251i	0.126597	−	0.0730909i
$506$		0			0
$507$	3.44699	−	0.585655i	0.153086	−	0.0260099i
$508$		0			0
$509$	−14.5717	−	8.41300i	−0.645881	−	0.372900i	0.140995	−	0.990010i	$-0.454970\pi$
$509$	−14.5717	−	8.41300i	−0.645881	−	0.372900i	−0.786876	+	0.617111i	$0.788303\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		−	5.07706i		−	0.224158i
$514$		0			0
$515$	−17.0153	−	9.82377i	−0.749783	−	0.432887i
$516$		0			0
$517$	−3.70461	−	6.41658i	−0.162929	−	0.282201i
$518$		0			0
$519$	−2.62043			−0.115024
$520$		0			0
$521$	−2.38310	+	4.12764i	−0.104405	+	0.180835i	−0.913495	−	0.406850i	$-0.866627\pi$
$521$	−2.38310	+	4.12764i	−0.104405	+	0.180835i	0.809090	+	0.587685i	$0.199961\pi$
$522$		0			0
$523$	0.319080	−	0.552662i	0.0139524	−	0.0241662i	−0.858965	−	0.512034i	$-0.828892\pi$
$523$	0.319080	−	0.552662i	0.0139524	−	0.0241662i	0.872917	+	0.487868i	$0.162225\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	46.8058i		−	2.03889i
$528$		0			0
$529$	−17.0275	−	29.4924i	−0.740325	−	1.28228i
$530$		0			0
$531$	−15.9620	+	9.21567i	−0.692692	+	0.399926i
$532$		0			0
$533$	10.4167	+	14.9757i	0.451196	+	0.648670i
$534$		0			0
$535$			8.79595i			0.380282i
$536$		0			0
$537$	3.06748			0.132371
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.2301	+	11.1025i	−0.826767	+	0.477334i	−0.852744	−	0.522328i	$-0.825063\pi$
$541$	−19.2301	+	11.1025i	−0.826767	+	0.477334i	0.0259776	+	0.999663i	$0.491730\pi$
$542$		0			0
$543$	−6.85096			−0.294003
$544$		0			0
$545$	−3.98138			−0.170544
$546$		0			0
$547$	16.2608			0.695263			0.347631	−	0.937631i	$-0.386986\pi$
$547$	16.2608			0.695263			0.347631	+	0.937631i	$0.386986\pi$
$548$		0			0
$549$	−37.4977			−1.60036
$550$		0			0
$551$	−19.9029	+	11.4909i	−0.847892	+	0.489531i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.53710			−0.107694
$556$		0			0
$557$		−	21.4676i		−	0.909612i	−0.890591	−	0.454806i	$-0.849709\pi$
$557$		−	21.4676i		−	0.909612i	0.890591	−	0.454806i	$-0.150291\pi$
$558$		0			0
$559$	20.4541	+	9.61566i	0.865115	+	0.406699i
$560$		0			0
$561$	−3.79912	+	2.19342i	−0.160399	+	0.0926064i
$562$		0			0
$563$	−5.59103	−	9.68395i	−0.235634	−	0.408130i	0.723823	−	0.689986i	$-0.242383\pi$
$563$	−5.59103	−	9.68395i	−0.235634	−	0.408130i	−0.959457	+	0.281856i	$0.909050\pi$
$564$		0			0
$565$		−	4.52607i		−	0.190413i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.58165	+	11.3998i	−0.275917	+	0.477903i	−0.970366	−	0.241639i	$-0.922315\pi$
$569$	−6.58165	+	11.3998i	−0.275917	+	0.477903i	0.694449	+	0.719542i	$0.255648\pi$
$570$		0			0
$571$	8.70996	−	15.0861i	0.364501	−	0.631334i	−0.624195	−	0.781268i	$-0.714573\pi$
$571$	8.70996	−	15.0861i	0.364501	−	0.631334i	0.988696	+	0.149935i	$0.0479064\pi$
$572$		0			0
$573$	−4.40494			−0.184019
$574$		0			0
$575$	11.9408	+	20.6821i	0.497965	+	0.862501i
$576$		0			0
$577$	−7.33543	−	4.23511i	−0.305378	−	0.176310i	0.339478	−	0.940614i	$-0.389749\pi$
$577$	−7.33543	−	4.23511i	−0.305378	−	0.176310i	−0.644856	+	0.764304i	$0.723083\pi$
$578$		0			0
$579$		−	2.57185i		−	0.106882i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	26.9192	+	15.5418i	1.11488	+	0.643676i
$584$		0			0
$585$	−8.17251	−	11.7494i	−0.337892	−	0.485776i
$586$		0			0
$587$	18.2459	−	10.5342i	0.753087	−	0.434795i	−0.0737213	−	0.997279i	$-0.523488\pi$
$587$	18.2459	−	10.5342i	0.753087	−	0.434795i	0.826808	+	0.562484i	$0.190154\pi$
$588$		0			0
$589$	12.8085	−	22.1850i	0.527765	−	0.914116i
$590$		0			0
$591$	−0.701205	+	0.404841i	−0.0288437	+	0.0166529i
$592$		0			0
$593$	−11.4975	+	6.63806i	−0.472144	+	0.272593i	−0.717137	−	0.696932i	$-0.754548\pi$
$593$	−11.4975	+	6.63806i	−0.472144	+	0.272593i	0.244993	+	0.969525i	$0.421214\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.621240	+	1.07602i	0.0254257	+	0.0440385i
$598$		0			0
$599$	−2.69542	+	4.66860i	−0.110132	+	0.190754i	−0.915823	−	0.401582i	$-0.868461\pi$
$599$	−2.69542	+	4.66860i	−0.110132	+	0.190754i	0.805691	+	0.592335i	$0.201794\pi$
$600$		0			0
$601$	12.2204	+	21.1663i	0.498480	+	0.863392i	0.999998	−	0.00175467i	$-0.000558528\pi$
$601$	12.2204	+	21.1663i	0.498480	+	0.863392i	−0.501519	+	0.865147i	$0.667225\pi$
$602$		0			0
$603$		−	14.5298i		−	0.591700i
$604$		0			0
$605$	3.68953	−	2.13015i	0.150001	−	0.0866029i
$606$		0			0
$607$	−25.8582			−1.04955			−0.524776	−	0.851240i	$-0.675851\pi$
$607$	−25.8582			−1.04955			−0.524776	+	0.851240i	$0.675851\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.44181	−	7.82352i	−0.220152	−	0.316506i
$612$		0			0
$613$			14.1688i			0.572273i	0.958189	+	0.286136i	$0.0923711\pi$
$613$			14.1688i			0.572273i	−0.958189	+	0.286136i	$0.907629\pi$
$614$		0			0
$615$	−0.922496	+	1.59781i	−0.0371986	+	0.0644299i
$616$		0			0
$617$	39.8763	+	23.0226i	1.60536	+	0.926855i	0.990390	+	0.138305i	$0.0441654\pi$
$617$	39.8763	+	23.0226i	1.60536	+	0.926855i	0.614970	+	0.788550i	$0.289168\pi$
$618$		0			0
$619$	−10.4169	−	6.01422i	−0.418692	−	0.241732i	0.275825	−	0.961208i	$-0.411049\pi$
$619$	−10.4169	−	6.01422i	−0.418692	−	0.241732i	−0.694518	+	0.719476i	$0.744382\pi$
$620$		0			0
$621$	6.02111	−	10.4289i	0.241619	−	0.418496i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.402250	−	0.696717i	−0.0160900	−	0.0278687i
$626$		0			0
$627$	−2.40094			−0.0958841
$628$		0			0
$629$		−	40.4831i		−	1.61417i
$630$		0			0
$631$	21.0476	+	12.1518i	0.837890	+	0.483756i	0.856546	−	0.516070i	$-0.172606\pi$
$631$	21.0476	+	12.1518i	0.837890	+	0.483756i	−0.0186564	+	0.999826i	$0.505939\pi$
$632$		0			0
$633$	0.314493	+	0.544718i	0.0125000	+	0.0216506i
$634$		0			0
$635$	−14.7365	−	8.50812i	−0.584800	−	0.337634i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	41.8636	+	24.1700i	1.65610	+	0.956149i
$640$		0			0
$641$	−8.88276	−	15.3854i	−0.350848	−	0.607687i	0.635550	−	0.772060i	$-0.280773\pi$
$641$	−8.88276	−	15.3854i	−0.350848	−	0.607687i	−0.986398	+	0.164373i	$0.947440\pi$
$642$		0			0
$643$	−37.3742	−	21.5780i	−1.47389	−	0.850953i	−0.474326	−	0.880349i	$-0.657308\pi$
$643$	−37.3742	−	21.5780i	−1.47389	−	0.850953i	−0.999568	+	0.0293964i	$0.990641\pi$
$644$		0			0
$645$			2.28589i			0.0900067i
$646$		0			0
$647$	10.7995			0.424571			0.212286	−	0.977208i	$-0.431909\pi$
$647$	10.7995			0.424571			0.212286	+	0.977208i	$0.431909\pi$
$648$		0			0
$649$	8.82383	+	15.2833i	0.346366	+	0.599923i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.53280	−	2.65489i	0.0599831	−	0.103894i	−0.834475	−	0.551047i	$-0.814229\pi$
$653$	1.53280	−	2.65489i	0.0599831	−	0.103894i	0.894458	+	0.447153i	$0.147562\pi$
$654$		0			0
$655$	−1.47950	−	0.854191i	−0.0578089	−	0.0333760i
$656$		0			0
$657$	−39.1346	−	22.5944i	−1.52679	−	0.881491i
$658$		0			0
$659$	1.82436	−	3.15988i	0.0710670	−	0.123092i	−0.828302	−	0.560282i	$-0.810693\pi$
$659$	1.82436	−	3.15988i	0.0710670	−	0.123092i	0.899369	+	0.437190i	$0.144026\pi$
$660$		0			0
$661$		−	27.2252i		−	1.05894i	−0.848329	−	0.529469i	$-0.822391\pi$
$661$		−	27.2252i		−	1.05894i	0.848329	−	0.529469i	$-0.177609\pi$
$662$		0			0
$663$	−4.63214	+	3.22198i	−0.179898	+	0.125131i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−54.5105			−2.11065
$668$		0			0
$669$	1.13345	−	0.654396i	0.0438216	−	0.0253004i
$670$		0			0
$671$			35.9034i			1.38604i
$672$		0			0
$673$	14.1485	+	24.5059i	0.545384	+	0.944633i	0.998583	+	0.0532233i	$0.0169495\pi$
$673$	14.1485	+	24.5059i	0.545384	+	0.944633i	−0.453199	+	0.891410i	$0.649717\pi$
$674$		0			0
$675$	−2.52027	+	4.36523i	−0.0970051	+	0.168018i
$676$		0			0
$677$	14.4181	+	24.9728i	0.554131	+	0.959783i	0.997971	+	0.0636769i	$0.0202827\pi$
$677$	14.4181	+	24.9728i	0.554131	+	0.959783i	−0.443840	+	0.896106i	$0.646384\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−6.54031	+	3.77605i	−0.250625	+	0.144698i
$682$		0			0
$683$	−35.4243	+	20.4522i	−1.35547	+	0.782583i	−0.989010	−	0.147849i	$-0.952765\pi$
$683$	−35.4243	+	20.4522i	−1.35547	+	0.782583i	−0.366464	+	0.930432i	$0.619432\pi$
$684$		0			0
$685$	5.64238	−	9.77290i	0.215584	−	0.373403i
$686$		0			0
$687$	−0.0417579	+	0.0241089i	−0.00159316	+	0.000919813i
$688$		0			0
$689$	36.1820	+	17.0095i	1.37843	+	0.648011i
$690$		0			0
$691$	36.5934	+	21.1272i	1.39208	+	0.803717i	0.993545	−	0.113436i	$-0.0361858\pi$
$691$	36.5934	+	21.1272i	1.39208	+	0.803717i	0.398534	+	0.917154i	$0.369519\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	7.84870i		−	0.297718i
$696$		0			0
$697$	−25.4954	−	14.7198i	−0.965706	−	0.557551i
$698$		0			0
$699$	2.03575	+	3.52603i	0.0769992	+	0.133367i
$700$		0			0
$701$	−30.3734			−1.14719			−0.573594	−	0.819140i	$-0.694451\pi$
$701$	−30.3734			−1.14719			−0.573594	+	0.819140i	$0.694451\pi$
$702$		0			0
$703$	11.0783	−	19.1881i	0.417825	−	0.723694i
$704$		0			0
$705$	0.481925	−	0.834718i	0.0181503	−	0.0314373i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			23.4297i			0.879920i	0.898017	+	0.439960i	$0.145007\pi$
$709$			23.4297i			0.879920i	−0.898017	+	0.439960i	$0.854993\pi$
$710$		0			0
$711$	21.6150	+	37.4383i	0.810627	+	1.40405i
$712$		0			0
$713$	52.6203	−	30.3803i	1.97064	−	1.13775i
$714$		0			0
$715$	−11.2498	+	7.82503i	−0.420719	+	0.292639i
$716$		0			0
$717$		−	3.46151i		−	0.129273i
$718$		0			0
$719$	7.02982			0.262168			0.131084	−	0.991371i	$-0.458154\pi$
$719$	7.02982			0.262168			0.131084	+	0.991371i	$0.458154\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.29001	−	1.32214i	0.0851662	−	0.0491708i
$724$		0			0
$725$	22.8165			0.847385
$726$		0			0
$727$	−20.6810			−0.767015			−0.383507	−	0.923538i	$-0.625284\pi$
$727$	−20.6810			−0.767015			−0.383507	+	0.923538i	$0.625284\pi$
$728$		0			0
$729$	−23.1720			−0.858222
$730$		0			0
$731$	−36.4746			−1.34906
$732$		0			0
$733$	33.7780	−	19.5018i	1.24762	−	0.720314i	0.276986	−	0.960874i	$-0.410664\pi$
$733$	33.7780	−	19.5018i	1.24762	−	0.720314i	0.970634	+	0.240560i	$0.0773311\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.9120			−0.512456
$738$		0			0
$739$			28.7416i			1.05728i	0.848847	+	0.528639i	$0.177297\pi$
$739$			28.7416i			1.05728i	−0.848847	+	0.528639i	$0.822703\pi$
$740$		0			0
$741$	−3.07724	+	0.259557i	−0.113045	+	0.00953505i
$742$		0			0
$743$	−5.48059	+	3.16422i	−0.201063	+	0.116084i	−0.597151	−	0.802129i	$-0.703701\pi$
$743$	−5.48059	+	3.16422i	−0.201063	+	0.116084i	0.396088	+	0.918213i	$0.370367\pi$
$744$		0			0
$745$	−9.62915	−	16.6782i	−0.352785	−	0.611041i
$746$		0			0
$747$		−	28.6709i		−	1.04901i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−15.7203	+	27.2283i	−0.573641	+	0.993575i	0.422547	+	0.906341i	$0.361136\pi$
$751$	−15.7203	+	27.2283i	−0.573641	+	0.993575i	−0.996188	+	0.0872339i	$0.972197\pi$
$752$		0			0
$753$	2.32940	−	4.03464i	0.0848880	−	0.147030i
$754$		0			0
$755$	15.1190			0.550237
$756$		0			0
$757$	−12.7212	−	22.0337i	−0.462358	−	0.800828i	0.536720	−	0.843760i	$-0.319663\pi$
$757$	−12.7212	−	22.0337i	−0.462358	−	0.800828i	−0.999078	+	0.0429328i	$0.986330\pi$
$758$		0			0
$759$	−4.93180	−	2.84737i	−0.179013	−	0.103353i
$760$		0			0
$761$			20.6105i			0.747130i	0.927604	+	0.373565i	$0.121865\pi$
$761$			20.6105i			0.747130i	−0.927604	+	0.373565i	$0.878135\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	20.0027	+	11.5485i	0.723198	+	0.417539i
$766$		0			0
$767$	12.9616	+	18.6345i	0.468016	+	0.672851i
$768$		0			0
$769$	7.95173	−	4.59093i	0.286747	−	0.165553i	−0.349727	−	0.936852i	$-0.613726\pi$
$769$	7.95173	−	4.59093i	0.286747	−	0.165553i	0.636474	+	0.771298i	$0.280392\pi$
$770$		0			0
$771$	1.43971	−	2.49365i	0.0518499	−	0.0898066i
$772$		0			0
$773$	7.35736	−	4.24777i	0.264626	−	0.152782i	−0.361817	−	0.932249i	$-0.617843\pi$
$773$	7.35736	−	4.24777i	0.264626	−	0.152782i	0.626443	+	0.779467i	$0.284510\pi$
$774$		0			0
$775$	−22.0254	+	12.7163i	−0.791174	+	0.456785i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.05618	−	13.9537i	−0.288642	−	0.499943i
$780$		0			0
$781$	23.1423	−	40.0836i	0.828096	−	1.43430i
$782$		0			0
$783$	−5.75259	−	9.96377i	−0.205581	−	0.356076i
$784$		0			0
$785$			5.48780i			0.195868i
$786$		0			0
$787$	−1.70464	+	0.984173i	−0.0607638	+	0.0350820i	−0.530074	−	0.847951i	$-0.677836\pi$
$787$	−1.70464	+	0.984173i	−0.0607638	+	0.0350820i	0.469310	+	0.883033i	$0.344503\pi$
$788$		0			0
$789$	3.78408			0.134717
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.88139	+	46.0168i	0.137832	+	1.63410i
$794$		0			0
$795$			4.04360i			0.143412i
$796$		0			0
$797$	−19.2449	+	33.3332i	−0.681690	+	1.18072i	0.292775	+	0.956181i	$0.405421\pi$
$797$	−19.2449	+	33.3332i	−0.681690	+	1.18072i	−0.974465	+	0.224540i	$0.927912\pi$
$798$		0			0
$799$	13.3191	+	7.68981i	0.471197	+	0.272046i
$800$		0			0
$801$	−21.2170	−	12.2496i	−0.749665	−	0.432820i
$802$		0			0
$803$	−21.6337	+	37.4707i	−0.763437	+	1.32231i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.0731583	−	0.126714i	−0.00257529	−	0.00446054i
$808$		0			0
$809$	1.79976			0.0632760			0.0316380	−	0.999499i	$-0.489928\pi$
$809$	1.79976			0.0632760			0.0316380	+	0.999499i	$0.489928\pi$
$810$		0			0
$811$		−	49.9235i		−	1.75305i	−0.481357	−	0.876525i	$-0.659856\pi$
$811$		−	49.9235i		−	1.75305i	0.481357	−	0.876525i	$-0.340144\pi$
$812$		0			0
$813$	−0.172644	−	0.0996759i	−0.00605488	−	0.00349579i
$814$		0			0
$815$	3.57485	+	6.19183i	0.125222	+	0.216890i
$816$		0			0
$817$	−17.2882	−	9.98135i	−0.604838	−	0.349203i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.65310	−	2.10912i	−0.127494	−	0.0736087i	0.434897	−	0.900480i	$-0.356785\pi$
$821$	−3.65310	−	2.10912i	−0.127494	−	0.0736087i	−0.562391	+	0.826872i	$0.690118\pi$
$822$		0			0
$823$	7.24912	+	12.5558i	0.252688	+	0.437669i	0.964265	−	0.264939i	$-0.0853519\pi$
$823$	7.24912	+	12.5558i	0.252688	+	0.437669i	−0.711577	+	0.702608i	$0.752019\pi$
$824$		0			0
$825$	2.06431	+	1.19183i	0.0718701	+	0.0414942i
$826$		0			0
$827$		−	26.2618i		−	0.913213i	−0.889669	−	0.456607i	$-0.849065\pi$
$827$		−	26.2618i		−	0.913213i	0.889669	−	0.456607i	$-0.150935\pi$
$828$		0			0
$829$	55.1580			1.91572			0.957858	−	0.287242i	$-0.0927383\pi$
$829$	55.1580			1.91572			0.957858	+	0.287242i	$0.0927383\pi$
$830$		0			0
$831$	1.90062	+	3.29198i	0.0659319	+	0.114197i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.62677	+	6.28175i	−0.125510	+	0.217389i
$836$		0			0
$837$	11.1062	+	6.41218i	0.383887	+	0.221637i
$838$		0			0
$839$	−6.07974	−	3.51014i	−0.209896	−	0.121184i	0.391367	−	0.920235i	$-0.372002\pi$
$839$	−6.07974	−	3.51014i	−0.209896	−	0.121184i	−0.601263	+	0.799051i	$0.705336\pi$
$840$		0			0
$841$	−11.5397	+	19.9874i	−0.397922	+	0.689221i
$842$		0			0
$843$			6.94036i			0.239039i
$844$		0			0
$845$	−13.5727	+	11.2454i	−0.466916	+	0.386853i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	7.33750			0.251822
$850$		0			0
$851$	45.5121	−	26.2764i	1.56013	−	0.900744i
$852$		0			0
$853$			57.6508i			1.97393i	0.160945	+	0.986963i	$0.448546\pi$
$853$			57.6508i			1.97393i	−0.160945	+	0.986963i	$0.551454\pi$
$854$		0			0
$855$	6.32056	+	10.9475i	0.216159	+	0.374398i
$856$		0			0
$857$	1.25327	−	2.17073i	0.0428109	−	0.0741506i	−0.843826	−	0.536617i	$-0.819702\pi$
$857$	1.25327	−	2.17073i	0.0428109	−	0.0741506i	0.886637	+	0.462466i	$0.153035\pi$
$858$		0			0
$859$	−8.56526	−	14.8355i	−0.292243	−	0.506180i	0.682097	−	0.731262i	$-0.261068\pi$
$859$	−8.56526	−	14.8355i	−0.292243	−	0.506180i	−0.974340	+	0.225082i	$0.927735\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	48.1881	−	27.8214i	1.64034	−	0.947053i	0.659632	−	0.751589i	$-0.270712\pi$
$863$	48.1881	−	27.8214i	1.64034	−	0.947053i	0.980711	−	0.195464i	$-0.0626213\pi$
$864$		0			0
$865$	11.4403	−	6.60509i	0.388984	−	0.224580i
$866$		0			0
$867$	2.26687	−	3.92634i	0.0769870	−	0.133345i
$868$		0			0
$869$	35.8465	−	20.6960i	1.21601	−	0.702064i
$870$		0			0
$871$	−17.8308	+	1.50398i	−0.604174	+	0.0509604i
$872$		0			0
$873$	30.9409	+	17.8637i	1.04719	+	0.604596i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	40.1549i		−	1.35593i	−0.735093	−	0.677967i	$-0.762861\pi$
$877$		−	40.1549i		−	1.35593i	0.735093	−	0.677967i	$-0.237139\pi$
$878$		0			0
$879$	0.403456	+	0.232936i	0.0136082	+	0.00785672i
$880$		0			0
$881$	25.3837	+	43.9658i	0.855197	+	1.48124i	0.876462	+	0.481471i	$0.159897\pi$
$881$	25.3837	+	43.9658i	0.855197	+	1.48124i	−0.0212650	+	0.999774i	$0.506769\pi$
$882$		0			0
$883$	−46.3312			−1.55917			−0.779585	−	0.626297i	$-0.784570\pi$
$883$	−46.3312			−1.55917			−0.779585	+	0.626297i	$0.784570\pi$
$884$		0			0
$885$	−1.14787	+	1.98817i	−0.0385853	+	0.0668317i
$886$		0			0
$887$	5.12752	−	8.88113i	0.172165	−	0.298199i	−0.767011	−	0.641634i	$-0.778257\pi$
$887$	5.12752	−	8.88113i	0.172165	−	0.298199i	0.939177	+	0.343435i	$0.111590\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			23.4184i			0.784546i
$892$		0			0
$893$	4.20866	+	7.28961i	0.140837	+	0.243938i
$894$		0			0
$895$	−13.3921	+	7.73191i	−0.447647	+	0.258449i
$896$		0			0
$897$	−6.62882	−	3.11627i	−0.221330	−	0.104049i
$898$		0			0
$899$		−	58.0509i		−	1.93611i
$900$		0			0
$901$	−64.5214			−2.14952
$902$		0			0
$903$		0			0
$904$		0			0
$905$	29.9101	−	17.2686i	0.994244	−	0.574027i
$906$		0			0
$907$	−52.2945			−1.73641			−0.868205	−	0.496206i	$-0.834726\pi$
$907$	−52.2945			−1.73641			−0.868205	+	0.496206i	$0.834726\pi$
$908$		0			0
$909$	−7.09330			−0.235270
$910$		0			0
$911$	50.9172			1.68696			0.843481	−	0.537159i	$-0.180502\pi$
$911$	50.9172			1.68696			0.843481	+	0.537159i	$0.180502\pi$
$912$		0			0
$913$	−27.4519			−0.908524
$914$		0			0
$915$	−4.04485	+	2.33530i	−0.133719	+	0.0772025i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	22.8646			0.754234			0.377117	−	0.926166i	$-0.376915\pi$
$919$	22.8646			0.754234			0.377117	+	0.926166i	$0.376915\pi$
$920$		0			0
$921$			5.76541i			0.189977i
$922$		0			0
$923$	25.3278	−	53.8763i	0.833674	−	1.77336i
$924$		0			0
$925$	−19.0501	+	10.9986i	−0.626363	+	0.361631i
$926$		0			0
$927$	21.2123	+	36.7408i	0.696703	+	1.20673i
$928$		0			0
$929$		−	33.2658i		−	1.09142i	−0.837976	−	0.545708i	$-0.816261\pi$
$929$		−	33.2658i		−	1.09142i	0.837976	−	0.545708i	$-0.183739\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−3.66749	+	6.35228i	−0.120068	+	0.207964i
$934$		0			0
$935$	11.0575	−	19.1522i	0.361620	−	0.626344i
$936$		0			0
$937$	−51.2179			−1.67322			−0.836608	−	0.547802i	$-0.815465\pi$
$937$	−51.2179			−1.67322			−0.836608	+	0.547802i	$0.815465\pi$
$938$		0			0
$939$	0.979286	+	1.69617i	0.0319578	+	0.0553525i
$940$		0			0
$941$	8.91293	+	5.14588i	0.290553	+	0.167751i	0.638191	−	0.769878i	$-0.279683\pi$
$941$	8.91293	+	5.14588i	0.290553	+	0.167751i	−0.347638	+	0.937629i	$0.613016\pi$
$942$		0			0
$943$		−	38.2167i		−	1.24451i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.7341	−	17.7444i	−0.998725	−	0.576614i	−0.0908539	−	0.995864i	$-0.528960\pi$
$947$	−30.7341	−	17.7444i	−0.998725	−	0.576614i	−0.907871	+	0.419250i	$0.862293\pi$
$948$		0			0
$949$	−23.6767	+	50.3643i	−0.768580	+	1.63489i
$950$		0			0
$951$	−0.593565	+	0.342695i	−0.0192477	+	0.0111126i
$952$		0			0
$953$	16.6676	−	28.8691i	0.539916	−	0.935163i	−0.458992	−	0.888441i	$-0.651789\pi$
$953$	16.6676	−	28.8691i	0.539916	−	0.935163i	0.998908	−	0.0467220i	$-0.0148775\pi$
$954$		0			0
$955$	19.2312	−	11.1031i	0.622306	−	0.359289i
$956$		0			0
$957$	−4.71185	+	2.72039i	−0.152313	+	0.0879377i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	16.8535	+	29.1912i	0.543662	+	0.941650i
$962$		0			0
$963$	9.49647	−	16.4484i	0.306020	−	0.530041i
$964$		0			0
$965$	6.48263	+	11.2282i	0.208683	+	0.361450i
$966$		0			0
$967$		−	29.7131i		−	0.955509i	−0.878494	−	0.477754i	$-0.841451\pi$
$967$		−	29.7131i		−	0.955509i	0.878494	−	0.477754i	$-0.158549\pi$
$968$		0			0
$969$	4.31602	−	2.49186i	0.138651	−	0.0800500i
$970$		0			0
$971$	−8.83702			−0.283593			−0.141797	−	0.989896i	$-0.545288\pi$
$971$	−8.83702			−0.283593			−0.141797	+	0.989896i	$0.545288\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.77464	+	1.30438i	0.0888595	+	0.0417737i
$976$		0			0
$977$		−	14.8307i		−	0.474475i	−0.971452	−	0.237237i	$-0.923758\pi$
$977$		−	14.8307i		−	0.474475i	0.971452	−	0.237237i	$-0.0762419\pi$
$978$		0			0
$979$	−11.7288	+	20.3149i	−0.374854	+	0.649266i
$980$		0			0
$981$	7.44516	+	4.29846i	0.237706	+	0.137239i
$982$		0			0
$983$	17.6141	+	10.1695i	0.561803	+	0.324357i	0.753869	−	0.657025i	$-0.228185\pi$
$983$	17.6141	+	10.1695i	0.561803	+	0.324357i	−0.192066	+	0.981382i	$0.561519\pi$
$984$		0			0
$985$	2.04089	−	3.53493i	0.0650282	−	0.112632i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.6746	−	41.0057i	−0.752809	−	1.30390i
$990$		0			0
$991$	−50.8906			−1.61659			−0.808297	−	0.588775i	$-0.799611\pi$
$991$	−50.8906			−1.61659			−0.808297	+	0.588775i	$0.799611\pi$
$992$		0			0
$993$			0.0526244i			0.00166999i
$994$		0			0
$995$	−5.42445	−	3.13181i	−0.171967	−	0.0992849i
$996$		0			0
$997$	3.69697	+	6.40334i	0.117084	+	0.202796i	0.918611	−	0.395163i	$-0.129312\pi$
$997$	3.69697	+	6.40334i	0.117084	+	0.202796i	−0.801527	+	0.597959i	$0.795979\pi$
$998$		0			0
$999$	9.60595	+	5.54600i	0.303919	+	0.175468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bq.e.361.4		16
7.2	even	3		2548.2.bb.d.569.5		16
7.3	odd	6		2548.2.u.c.1765.4		16
7.4	even	3		364.2.u.a.309.5	yes	16
7.5	odd	6		2548.2.bb.c.569.4		16
7.6	odd	2		2548.2.bq.c.361.5		16
13.4	even	6		2548.2.bb.d.1733.5		16
21.11	odd	6		3276.2.cf.c.1765.4		16
28.11	odd	6		1456.2.cc.f.673.4		16
91.4	even	6		364.2.u.a.225.5	✓	16
91.11	odd	12		4732.2.a.s.1.4		8
91.17	odd	6		2548.2.u.c.589.4		16
91.30	even	6	inner	2548.2.bq.e.1941.4		16
91.67	odd	12		4732.2.a.t.1.4		8
91.69	odd	6		2548.2.bb.c.1733.4		16
91.81	even	3		4732.2.g.k.337.8		16
91.82	odd	6		2548.2.bq.c.1941.5		16
91.88	even	6		4732.2.g.k.337.7		16
273.95	odd	6		3276.2.cf.c.2773.5		16
364.95	odd	6		1456.2.cc.f.225.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.5	✓	16	91.4	even	6
364.2.u.a.309.5	yes	16	7.4	even	3
1456.2.cc.f.225.4		16	364.95	odd	6
1456.2.cc.f.673.4		16	28.11	odd	6
2548.2.u.c.589.4		16	91.17	odd	6
2548.2.u.c.1765.4		16	7.3	odd	6
2548.2.bb.c.569.4		16	7.5	odd	6
2548.2.bb.c.1733.4		16	91.69	odd	6
2548.2.bb.d.569.5		16	7.2	even	3
2548.2.bb.d.1733.5		16	13.4	even	6
2548.2.bq.c.361.5		16	7.6	odd	2
2548.2.bq.c.1941.5		16	91.82	odd	6
2548.2.bq.e.361.4		16	1.1	even	1	trivial
2548.2.bq.e.1941.4		16	91.30	even	6	inner
3276.2.cf.c.1765.4		16	21.11	odd	6
3276.2.cf.c.2773.5		16	273.95	odd	6
4732.2.a.s.1.4		8	91.11	odd	12
4732.2.a.t.1.4		8	91.67	odd	12
4732.2.g.k.337.7		16	91.88	even	6
4732.2.g.k.337.8		16	91.81	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.268953 q^{3} +(1.17420 - 0.677925i) q^{5} -2.92766 q^{9} +2.80318i q^{11} +(0.303042 + 3.59279i) q^{13} +(-0.315805 + 0.182330i) q^{15} +(-2.90934 - 5.03912i) q^{17} -3.18458i q^{19} +(3.77674 - 6.54150i) q^{23} +(-1.58083 + 2.73809i) q^{25} +1.59426 q^{27} +(-3.60830 - 6.24977i) q^{29} +(6.96637 + 4.02203i) q^{31} -0.753925i q^{33} +(6.02532 + 3.47872i) q^{37} +(-0.0815041 - 0.966292i) q^{39} +(4.38164 - 2.52974i) q^{41} +(3.13427 - 5.42872i) q^{43} +(-3.43767 + 1.98474i) q^{45} +(-2.28903 + 1.32157i) q^{47} +(0.782475 + 1.35529i) q^{51} +(5.54434 - 9.60308i) q^{53} +(1.90035 + 3.29150i) q^{55} +0.856503i q^{57} +(5.45213 - 3.14779i) q^{59} +12.8081 q^{61} +(2.79148 + 4.01322i) q^{65} +4.96294i q^{67} +(-1.01576 + 1.75936i) q^{69} +(-14.2993 - 8.25572i) q^{71} +(13.3672 + 7.71755i) q^{73} +(0.425170 - 0.736416i) q^{75} +(-7.38303 - 12.7878i) q^{79} +8.35421 q^{81} +9.79310i q^{83} +(-6.83230 - 3.94463i) q^{85} +(0.970464 + 1.68089i) q^{87} +(7.24707 + 4.18410i) q^{89} +(-1.87363 - 1.08174i) q^{93} +(-2.15891 - 3.73934i) q^{95} +(-10.5685 - 6.10170i) q^{97} -8.20678i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{9} + 10 q^{13} + 6 q^{15} + 2 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} - 30 q^{31} - 12 q^{37} - 6 q^{39} + 36 q^{41} + 6 q^{43} + 30 q^{45} + 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 18 q^{59}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q + 28 * q^9 + 10 * q^13 + 6 * q^15 + 2 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 - 30 * q^31 - 12 * q^37 - 6 * q^39 + 36 * q^41 + 6 * q^43 + 30 * q^45 + 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 18 * q^59 - 8 * q^61 - 52 * q^69 + 36 * q^71 + 12 * q^73 - 10 * q^75 - 4 * q^79 + 42 * q^85 + 26 * q^87 + 36 * q^89 + 42 * q^93 - 30 * q^95 - 42 * q^97

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