LMFDB - Embedded newform 2548.2.bq.c.361.5

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			361.5
Root			$-0.268953i$ of defining polynomial
Character	$\chi$	$=$	2548.361
Dual form			2548.2.bq.c.1941.5

$q$-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	$-0.475262\pi$
$3$	0.268953			0.155280			0.0776400	+	0.996981i	$0.475262\pi$
$4$		0			0
$5$	−1.17420	+	0.677925i	−0.525119	+	0.303177i	−0.739026	−	0.673676i	$-0.764714\pi$
$5$	−1.17420	+	0.677925i	−0.525119	+	0.303177i	0.213908	+	0.976854i	$0.431381\pi$
$6$		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	$0.0826640\pi$
$17$	2.90934	+	5.03912i	0.705618	+	1.22217i	−0.260850	+	0.965379i	$0.584003\pi$
$18$		0			0
$19$			3.18458i			0.730594i	0.930891	+	0.365297i	$0.119032\pi$
$19$			3.18458i			0.730594i	−0.930891	+	0.365297i	$0.880968\pi$
$20$		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	−0.279849	−	0.960044i	$-0.590285\pi$
$31$	−6.96637	−	4.02203i	−1.25120	−	0.722379i	−0.971347	+	0.237665i	$0.923618\pi$
$32$		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	−0.801472	−	0.598032i	$-0.795950\pi$
$41$	−4.38164	+	2.52974i	−0.684298	+	0.395079i	0.117175	+	0.993111i	$0.462616\pi$
$42$		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	−0.323677	−	0.946168i	$-0.604919\pi$
$47$	2.28903	−	1.32157i	0.333890	−	0.192771i	0.657567	+	0.753396i	$0.271586\pi$
$48$		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	−0.810989	−	0.585061i	$-0.801071\pi$
$59$	−5.45213	+	3.14779i	−0.709807	+	0.409807i	0.101183	+	0.994868i	$0.467737\pi$
$60$		0			0
$61$	−12.8081			−1.63991			−0.819953	−	0.572431i	$-0.806001\pi$
$61$	−12.8081			−1.63991			−0.819953	+	0.572431i	$0.806001\pi$
$62$		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	$-0.974492\pi$
$73$	−13.3672	−	7.71755i	−1.56451	−	0.903271i	−0.567720	−	0.823222i	$-0.692174\pi$
$74$		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	$-0.819382\pi$
$83$		−	9.79310i		−	1.07493i	0.843285	−	0.537466i	$-0.180618\pi$
$84$		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	0.0640399	−	0.997947i	$-0.479602\pi$
$89$	−7.24707	−	4.18410i	−0.768188	−	0.443513i	−0.832228	+	0.554434i	$0.812935\pi$
$90$		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	0.929017	−	0.370037i	$-0.120655\pi$
$97$	10.5685	+	6.10170i	1.07306	+	0.619534i	0.144047	+	0.989571i	$0.453988\pi$
$98$		0			0
$99$		−	8.20678i		−	0.824813i
$100$		0			0
$101$	−2.42285			−0.241083			−0.120541	−	0.992708i	$-0.538463\pi$
$101$	−2.42285			−0.241083			−0.120541	+	0.992708i	$0.538463\pi$
$102$		0			0
$103$	7.24547	+	12.5495i	0.713917	+	1.23654i	0.963376	+	0.268155i	$0.0864141\pi$
$103$	7.24547	+	12.5495i	0.713917	+	1.23654i	−0.249458	+	0.968386i	$0.580253\pi$
$104$		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	0.892234	−	0.451573i	$-0.149137\pi$
$131$	0.630004	+	1.09120i	0.0550437	+	0.0953385i	−0.837191	+	0.546911i	$0.815804\pi$
$132$		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	−0.962272	−	0.272091i	$-0.912285\pi$
$139$	−2.89438	+	5.01322i	−0.245498	+	0.425216i	0.716773	+	0.697306i	$0.245618\pi$
$140$		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	−0.773899	−	0.633309i	$-0.781696\pi$
$157$	2.02375	−	3.50523i	0.161513	−	0.279748i	0.935411	+	0.353561i	$0.115029\pi$
$158$		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	−0.309912	−	0.950765i	$-0.600300\pi$
$167$	4.63307	−	2.67491i	0.358518	−	0.206990i	0.668430	+	0.743775i	$0.266966\pi$
$168$		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	$-0.620771\pi$
$173$	−9.74309			−0.740754			−0.370377	+	0.928882i	$0.620771\pi$
$174$		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	$-0.895591\pi$
$181$	−25.4727			−1.89337			−0.946685	+	0.322160i	$0.895591\pi$
$182$		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	0.936207	−	0.351448i	$-0.114311\pi$
$199$	2.30985	+	4.00077i	0.163741	+	0.283607i	−0.772467	+	0.635055i	$0.780977\pi$
$200$		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	−0.352214	−	0.935920i	$-0.614571\pi$
$223$	4.21429	−	2.43312i	0.282210	−	0.162934i	0.634423	+	0.772986i	$0.281238\pi$
$224$		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	$0.715143\pi$
$227$	−24.3177	+	14.0398i	−1.61402	+	0.931855i	−0.988426	+	0.151706i	$0.951523\pi$
$228$		0			0
$229$	−0.155261	+	0.0896399i	−0.0102599	+	0.00592357i	−0.505121	−	0.863048i	$-0.668552\pi$
$229$	−0.155261	+	0.0896399i	−0.0102599	+	0.00592357i	0.494861	+	0.868972i	$0.335219\pi$
$230$		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	−0.200035	−	0.979789i	$-0.564106\pi$
$241$	8.51452	−	4.91586i	0.548469	−	0.316659i	0.748504	+	0.663130i	$0.230772\pi$
$242$		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	$-0.649226\pi$
$251$	8.66099	−	15.0013i	0.546677	−	0.946872i	0.998499	−	0.0547641i	$-0.0174407\pi$
$252$		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	−0.649363	−	0.760478i	$-0.724964\pi$
$257$	5.35302	−	9.27170i	0.333912	−	0.578353i	0.983275	+	0.182126i	$0.0582978\pi$
$258$		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	0.857614	−	0.514294i	$-0.171946\pi$
$269$	−0.272011	−	0.471138i	−0.0165848	−	0.0287258i	−0.874199	+	0.485568i	$0.838613\pi$
$270$		0			0
$271$	−0.641910	−	0.370607i	−0.0389933	−	0.0225128i	0.480377	−	0.877062i	$-0.340500\pi$
$271$	−0.641910	−	0.370607i	−0.0389933	−	0.0225128i	−0.519370	+	0.854550i	$0.673833\pi$
$272$		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	$-0.198997\pi$
$283$	27.2817			1.62173			0.810865	+	0.585233i	$0.198997\pi$
$284$		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	0.543178	−	0.839618i	$-0.317221\pi$
$293$	1.50010	+	0.866083i	0.0876367	+	0.0505971i	−0.455541	+	0.890215i	$0.650554\pi$
$294$		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	$0.209523\pi$
$307$			21.4365i			1.22345i	−0.791072	+	0.611723i	$0.790477\pi$
$308$		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	$0.448030\pi$
$311$	−13.6362	+	23.6186i	−0.773237	+	1.33929i	−0.935780	+	0.352584i	$0.885303\pi$
$312$		0			0
$313$	3.64110	+	6.30658i	0.205807	+	0.356469i	0.950390	−	0.311062i	$-0.100685\pi$
$313$	3.64110	+	6.30658i	0.205807	+	0.356469i	−0.744582	+	0.667531i	$0.767351\pi$
$314$		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	−0.619436	−	0.785047i	$-0.712639\pi$
$349$	−4.65700	+	2.68872i	−0.249284	+	0.143924i	0.370153	+	0.928971i	$0.379305\pi$
$350$		0			0
$351$	0.483129	+	5.72786i	0.0257875	+	0.305730i
$352$		0			0
$353$		−	8.20095i		−	0.436492i	−0.975894	−	0.218246i	$-0.929966\pi$
$353$		−	8.20095i		−	0.436492i	0.975894	−	0.218246i	$-0.0700336\pi$
$354$		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	$-0.649469\pi$
$367$	−17.3374			−0.905005			−0.452502	+	0.891763i	$0.649469\pi$
$368$		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	$0.0673874\pi$
$383$			8.22450i			0.420252i	−0.977674	+	0.210126i	$0.932613\pi$
$384$		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	$-0.748548\pi$
$397$		−	28.3063i		−	1.42065i	0.703874	−	0.710325i	$-0.251452\pi$
$398$		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	−0.237145	−	0.971474i	$-0.576212\pi$
$409$	9.82072	−	5.66999i	0.485603	−	0.280363i	0.722749	+	0.691111i	$0.242878\pi$
$410$		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	0.867716	−	0.497060i	$-0.165587\pi$
$419$	0.0694276	+	0.120252i	0.00339176	+	0.00587470i	−0.864325	+	0.502934i	$0.832254\pi$
$420$		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	$-0.625594\pi$
$433$	12.6367	−	21.8873i	0.607279	−	1.05184i	0.991687	−	0.128675i	$-0.0410723\pi$
$434$		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	−0.928963	−	0.370172i	$-0.879299\pi$
$439$	−3.01512	+	5.22234i	−0.143904	+	0.249248i	0.785060	+	0.619420i	$0.212632\pi$
$440$		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	0.913457	−	0.406936i	$-0.133403\pi$
$461$	21.8524	+	12.6165i	1.01777	+	0.587609i	0.104312	+	0.994545i	$0.466736\pi$
$462$		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	0.682062	−	0.731294i	$-0.261083\pi$
$467$	−6.31641	−	10.9403i	−0.292289	−	0.506259i	−0.974351	+	0.225036i	$0.927750\pi$
$468$		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	$-0.909278\pi$
$479$		−	12.3074i		−	0.562338i	0.959658	−	0.281169i	$-0.0907221\pi$
$480$		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	$0.455484\pi$
$503$	−17.6701	+	30.6056i	−0.787873	+	1.36464i	−0.927268	+	0.374399i	$0.877849\pi$
$504$		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	0.786876	−	0.617111i	$-0.211697\pi$
$509$	14.5717	+	8.41300i	0.645881	+	0.372900i	−0.140995	+	0.990010i	$0.545030\pi$
$510$		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	−0.809090	−	0.587685i	$-0.800039\pi$
$521$	2.38310	−	4.12764i	0.104405	−	0.180835i	0.913495	+	0.406850i	$0.133373\pi$
$522$		0			0
$523$	−0.319080	+	0.552662i	−0.0139524	+	0.0241662i	−0.872917	−	0.487868i	$-0.837775\pi$
$523$	−0.319080	+	0.552662i	−0.0139524	+	0.0241662i	0.858965	+	0.512034i	$0.171108\pi$
$524$		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	0.959457	−	0.281856i	$-0.0909500\pi$
$563$	5.59103	+	9.68395i	0.235634	+	0.408130i	−0.723823	+	0.689986i	$0.757617\pi$
$564$		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	0.644856	−	0.764304i	$-0.276917\pi$
$577$	7.33543	+	4.23511i	0.305378	+	0.176310i	−0.339478	+	0.940614i	$0.610251\pi$
$578$		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	−0.826808	−	0.562484i	$-0.809846\pi$
$587$	−18.2459	+	10.5342i	−0.753087	+	0.434795i	0.0737213	+	0.997279i	$0.476512\pi$
$588$		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	−0.244993	−	0.969525i	$-0.578786\pi$
$593$	11.4975	−	6.63806i	0.472144	−	0.272593i	0.717137	+	0.696932i	$0.245452\pi$
$594$		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	0.501519	−	0.865147i	$-0.332775\pi$
$601$	−12.2204	−	21.1663i	−0.498480	−	0.863392i	−0.999998	+	0.00175467i	$0.999441\pi$
$602$		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	$-0.324149\pi$
$607$	25.8582			1.04955			0.524776	+	0.851240i	$0.324149\pi$
$608$		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	0.694518	−	0.719476i	$-0.255618\pi$
$619$	10.4169	+	6.01422i	0.418692	+	0.241732i	−0.275825	+	0.961208i	$0.588951\pi$
$620$		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	0.999568	−	0.0293964i	$-0.00935852\pi$
$643$	37.3742	+	21.5780i	1.47389	+	0.850953i	0.474326	+	0.880349i	$0.342692\pi$
$644$		0			0
$645$			2.28589i			0.0900067i
$646$		0			0
$647$	−10.7995			−0.424571			−0.212286	−	0.977208i	$-0.568091\pi$
$647$	−10.7995			−0.424571			−0.212286	+	0.977208i	$0.568091\pi$
$648$		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	$0.177609\pi$
$661$			27.2252i			1.05894i	−0.848329	+	0.529469i	$0.822391\pi$
$662$		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	$-0.979717\pi$
$677$	−14.4181	−	24.9728i	−0.554131	−	0.959783i	0.443840	−	0.896106i	$-0.353616\pi$
$678$		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	−0.398534	−	0.917154i	$-0.630481\pi$
$691$	−36.5934	−	21.1272i	−1.39208	−	0.803717i	−0.993545	+	0.113436i	$0.963814\pi$
$692$		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	$-0.541846\pi$
$719$	−7.02982			−0.262168			−0.131084	+	0.991371i	$0.541846\pi$
$720$		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	$-0.374716\pi$
$727$	20.6810			0.767015			0.383507	+	0.923538i	$0.374716\pi$
$728$		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	−0.970634	−	0.240560i	$-0.922669\pi$
$733$	−33.7780	+	19.5018i	−1.24762	+	0.720314i	−0.276986	+	0.960874i	$0.589336\pi$
$734$		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	$-0.878135\pi$
$761$		−	20.6105i		−	0.747130i	0.927604	−	0.373565i	$-0.121865\pi$
$762$		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	−0.636474	−	0.771298i	$-0.719608\pi$
$769$	−7.95173	+	4.59093i	−0.286747	+	0.165553i	0.349727	+	0.936852i	$0.386274\pi$
$770$		0			0
$771$	1.43971	−	2.49365i	0.0518499	−	0.0898066i
$772$		0			0
$773$	−7.35736	+	4.24777i	−0.264626	+	0.152782i	−0.626443	−	0.779467i	$-0.715490\pi$
$773$	−7.35736	+	4.24777i	−0.264626	+	0.152782i	0.361817	+	0.932249i	$0.382157\pi$
$774$		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	−0.469310	−	0.883033i	$-0.655497\pi$
$787$	1.70464	−	0.984173i	0.0607638	−	0.0350820i	0.530074	+	0.847951i	$0.322164\pi$
$788$		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	$-0.594579\pi$
$797$	19.2449	−	33.3332i	0.681690	−	1.18072i	0.974465	−	0.224540i	$-0.0720879\pi$
$798$		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	$0.340144\pi$
$811$			49.9235i			1.75305i	−0.481357	+	0.876525i	$0.659856\pi$
$812$		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	$-0.907262\pi$
$829$	−55.1580			−1.91572			−0.957858	+	0.287242i	$0.907262\pi$
$830$		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	0.601263	−	0.799051i	$-0.294664\pi$
$839$	6.07974	+	3.51014i	0.209896	+	0.121184i	−0.391367	+	0.920235i	$0.627998\pi$
$840$		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	$-0.551454\pi$
$853$		−	57.6508i		−	1.97393i	0.160945	−	0.986963i	$-0.448546\pi$
$854$		0			0
$855$	6.32056	+	10.9475i	0.216159	+	0.374398i
$856$		0			0
$857$	−1.25327	+	2.17073i	−0.0428109	+	0.0741506i	−0.886637	−	0.462466i	$-0.846965\pi$
$857$	−1.25327	+	2.17073i	−0.0428109	+	0.0741506i	0.843826	+	0.536617i	$0.180298\pi$
$858$		0			0
$859$	8.56526	+	14.8355i	0.292243	+	0.506180i	0.974340	−	0.225082i	$-0.0722650\pi$
$859$	8.56526	+	14.8355i	0.292243	+	0.506180i	−0.682097	+	0.731262i	$0.738932\pi$
$860$		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	$-0.840103\pi$
$881$	−25.3837	−	43.9658i	−0.855197	−	1.48124i	0.0212650	−	0.999774i	$-0.493231\pi$
$882$		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	−0.939177	−	0.343435i	$-0.888410\pi$
$887$	−5.12752	+	8.88113i	−0.172165	+	0.298199i	0.767011	+	0.641634i	$0.221743\pi$
$888$		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	$0.183739\pi$
$929$			33.2658i			1.09142i	−0.837976	+	0.545708i	$0.816261\pi$
$930$		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	$-0.184535\pi$
$937$	51.2179			1.67322			0.836608	+	0.547802i	$0.184535\pi$
$938$		0			0
$939$	0.979286	+	1.69617i	0.0319578	+	0.0553525i
$940$		0			0
$941$	−8.91293	−	5.14588i	−0.290553	−	0.167751i	0.347638	−	0.937629i	$-0.386984\pi$
$941$	−8.91293	−	5.14588i	−0.290553	−	0.167751i	−0.638191	+	0.769878i	$0.720317\pi$
$942$		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	$-0.454712\pi$
$971$	8.83702			0.283593			0.141797	+	0.989896i	$0.454712\pi$
$972$		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	0.192066	−	0.981382i	$-0.438481\pi$
$983$	−17.6141	−	10.1695i	−0.561803	−	0.324357i	−0.753869	+	0.657025i	$0.771815\pi$
$984$		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	0.801527	−	0.597959i	$-0.204021\pi$
$997$	−3.69697	−	6.40334i	−0.117084	−	0.202796i	−0.918611	+	0.395163i	$0.870688\pi$
$998$		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.c.361.5		16
7.2	even	3		2548.2.bb.c.569.4		16
7.3	odd	6		364.2.u.a.309.5	yes	16
7.4	even	3		2548.2.u.c.1765.4		16
7.5	odd	6		2548.2.bb.d.569.5		16
7.6	odd	2		2548.2.bq.e.361.4		16
13.4	even	6		2548.2.bb.c.1733.4		16
21.17	even	6		3276.2.cf.c.1765.4		16
28.3	even	6		1456.2.cc.f.673.4		16
91.3	odd	6		4732.2.g.k.337.8		16
91.4	even	6		2548.2.u.c.589.4		16
91.10	odd	6		4732.2.g.k.337.7		16
91.17	odd	6		364.2.u.a.225.5	✓	16
91.24	even	12		4732.2.a.s.1.4		8
91.30	even	6	inner	2548.2.bq.c.1941.5		16
91.69	odd	6		2548.2.bb.d.1733.5		16
91.80	even	12		4732.2.a.t.1.4		8
91.82	odd	6		2548.2.bq.e.1941.4		16
273.17	even	6		3276.2.cf.c.2773.5		16
364.199	even	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	91.17	odd	6
364.2.u.a.309.5	yes	16	7.3	odd	6
1456.2.cc.f.225.4		16	364.199	even	6
1456.2.cc.f.673.4		16	28.3	even	6
2548.2.u.c.589.4		16	91.4	even	6
2548.2.u.c.1765.4		16	7.4	even	3
2548.2.bb.c.569.4		16	7.2	even	3
2548.2.bb.c.1733.4		16	13.4	even	6
2548.2.bb.d.569.5		16	7.5	odd	6
2548.2.bb.d.1733.5		16	91.69	odd	6
2548.2.bq.c.361.5		16	1.1	even	1	trivial
2548.2.bq.c.1941.5		16	91.30	even	6	inner
2548.2.bq.e.361.4		16	7.6	odd	2
2548.2.bq.e.1941.4		16	91.82	odd	6
3276.2.cf.c.1765.4		16	21.17	even	6
3276.2.cf.c.2773.5		16	273.17	even	6
4732.2.a.s.1.4		8	91.24	even	12
4732.2.a.t.1.4		8	91.80	even	12
4732.2.g.k.337.7		16	91.10	odd	6
4732.2.g.k.337.8		16	91.3	odd	6

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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