LMFDB - Embedded newform 2548.2.y.f.961.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(753,2548)] 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("2548.753"); 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, 3])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-8,0,0,0,4] 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:	16.0.11348687176217973595570176.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{14} + 176x^{12} - 1016x^{10} + 4224x^{8} - 8512x^{6} + 12304x^{4} - 8448x^{2} + 4096 $ x^16 - 16x^14 + 176x^12 - 1016x^10 + 4224x^8 - 8512x^6 + 12304x^4 - 8448*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
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			961.6
Root			$1.12031 + 0.646813i$ of defining polynomial
Character	$\chi$	$=$	2548.961
Dual form			2548.2.y.f.753.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.646813 + 1.12031i) q^{3} +(2.42353 + 1.39923i) q^{5} +(0.663266 - 1.14881i) q^{9} +(0.894522 - 0.516453i) q^{11} +(-1.79846 - 3.12499i) q^{13} +3.62016i q^{15} +(3.47818 + 6.02438i) q^{17} +(2.19774 + 1.26887i) q^{19} +(1.91568 - 3.31806i) q^{23} +(1.41568 + 2.45203i) q^{25} +5.59691 q^{27} -5.10175 q^{29} +(-3.28119 + 1.89440i) q^{31} +(1.15718 + 0.668097i) q^{33} +(5.37577 + 3.10370i) q^{37} +(2.33770 - 4.03612i) q^{39} +0.990338i q^{41} +0.560979 q^{43} +(3.21489 - 1.85612i) q^{45} +(6.22741 + 3.59540i) q^{47} +(-4.49946 + 7.79329i) q^{51} +(-0.589150 - 1.02044i) q^{53} +2.89054 q^{55} +3.28288i q^{57} +(10.3260 - 5.96172i) q^{59} +(-6.92345 + 11.9918i) q^{61} +(0.0139493 - 10.0900i) q^{65} +(11.9348 - 6.89054i) q^{67} +4.95635 q^{69} +3.80432i q^{71} +(2.76331 - 1.59540i) q^{73} +(-1.83136 + 3.17201i) q^{75} +(-3.66620 + 6.35004i) q^{79} +(1.63036 + 2.82387i) q^{81} -16.6260i q^{83} +19.4670i q^{85} +(-3.29988 - 5.71555i) q^{87} +(10.3026 + 5.94820i) q^{89} +(-4.24464 - 2.45064i) q^{93} +(3.55087 + 6.15029i) q^{95} -8.60355i q^{97} -1.37018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9} + 4 q^{13} - 4 q^{17} + 6 q^{23} - 2 q^{25} + 24 q^{27} - 4 q^{29} - 12 q^{43} + 8 q^{51} - 22 q^{53} - 40 q^{55} - 8 q^{61} + 6 q^{65} - 40 q^{69} + 20 q^{75} + 26 q^{79} + 24 q^{81} + 32 q^{87}+ \cdots + 18 q^{95}+O(q^{100}) $ 16 * q - 8 * q^9 + 4 * q^13 - 4 * q^17 + 6 * q^23 - 2 * q^25 + 24 * q^27 - 4 * q^29 - 12 * q^43 + 8 * q^51 - 22 * q^53 - 40 * q^55 - 8 * q^61 + 6 * q^65 - 40 * q^69 + 20 * q^75 + 26 * q^79 + 24 * q^81 + 32 * q^87 + 18 * q^95

Character values

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

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

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
$3$	0.646813	+	1.12031i	0.373438	+	0.646813i	0.990092	−	0.140421i	$-0.0448456\pi$
$3$	0.646813	+	1.12031i	0.373438	+	0.646813i	−0.616654	+	0.787234i	$0.711512\pi$
$4$		0			0
$5$	2.42353	+	1.39923i	1.08384	+	0.625754i	0.931929	−	0.362641i	$-0.118125\pi$
$5$	2.42353	+	1.39923i	1.08384	+	0.625754i	0.151909	+	0.988395i	$0.451458\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.663266	−	1.14881i	0.221089	−	0.382937i
$10$		0			0
$11$	0.894522	−	0.516453i	0.269709	−	0.155716i	−0.359047	−	0.933320i	$-0.616898\pi$
$11$	0.894522	−	0.516453i	0.269709	−	0.155716i	0.628755	+	0.777603i	$0.283565\pi$
$12$		0			0
$13$	−1.79846	−	3.12499i	−0.498802	−	0.866716i
$13$	−1.79846	−	3.12499i	−0.498802	−	0.866716i
$14$		0			0
$15$			3.62016i			0.934721i
$16$		0			0
$17$	3.47818	+	6.02438i	0.843581	+	1.46113i	0.886847	+	0.462062i	$0.152890\pi$
$17$	3.47818	+	6.02438i	0.843581	+	1.46113i	−0.0432661	+	0.999064i	$0.513776\pi$
$18$		0			0
$19$	2.19774	+	1.26887i	0.504197	+	0.291098i	0.730445	−	0.682971i	$-0.239313\pi$
$19$	2.19774	+	1.26887i	0.504197	+	0.291098i	−0.226248	+	0.974070i	$0.572646\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.91568	−	3.31806i	0.399447	−	0.691863i	−0.594211	−	0.804309i	$-0.702535\pi$
$23$	1.91568	−	3.31806i	0.399447	−	0.691863i	0.993658	+	0.112447i	$0.0358688\pi$
$24$		0			0
$25$	1.41568	+	2.45203i	0.283136	+	0.490406i
$26$		0			0
$27$	5.59691			1.07713
$28$		0			0
$29$	−5.10175			−0.947370			−0.473685	−	0.880694i	$-0.657077\pi$
$29$	−5.10175			−0.947370			−0.473685	+	0.880694i	$0.657077\pi$
$30$		0			0
$31$	−3.28119	+	1.89440i	−0.589320	+	0.340244i	−0.764828	−	0.644234i	$-0.777176\pi$
$31$	−3.28119	+	1.89440i	−0.589320	+	0.340244i	0.175509	+	0.984478i	$0.443843\pi$
$32$		0			0
$33$	1.15718	+	0.668097i	0.201439	+	0.116301i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.37577	+	3.10370i	0.883772	+	0.510246i	0.871900	−	0.489684i	$-0.162888\pi$
$37$	5.37577	+	3.10370i	0.883772	+	0.510246i	0.0118717	+	0.999930i	$0.496221\pi$
$38$		0			0
$39$	2.33770	−	4.03612i	0.374332	−	0.646296i
$40$		0			0
$41$			0.990338i			0.154665i	0.997005	+	0.0773324i	$0.0246403\pi$
$41$			0.990338i			0.154665i	−0.997005	+	0.0773324i	$0.975360\pi$
$42$		0			0
$43$	0.560979			0.0855485			0.0427743	−	0.999085i	$-0.486380\pi$
$43$	0.560979			0.0855485			0.0427743	+	0.999085i	$0.486380\pi$
$44$		0			0
$45$	3.21489	−	1.85612i	0.479248	−	0.276694i
$46$		0			0
$47$	6.22741	+	3.59540i	0.908362	+	0.524443i	0.879904	−	0.475152i	$-0.157607\pi$
$47$	6.22741	+	3.59540i	0.908362	+	0.524443i	0.0284580	+	0.999595i	$0.490940\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.49946	+	7.79329i	−0.630050	+	1.09128i
$52$		0			0
$53$	−0.589150	−	1.02044i	−0.0809260	−	0.140168i	0.822722	−	0.568444i	$-0.192454\pi$
$53$	−0.589150	−	1.02044i	−0.0809260	−	0.140168i	−0.903648	+	0.428276i	$0.859121\pi$
$54$		0			0
$55$	2.89054			0.389760
$56$		0			0
$57$			3.28288i			0.434828i
$58$		0			0
$59$	10.3260	−	5.96172i	1.34433	−	0.776150i	0.356892	−	0.934146i	$-0.383837\pi$
$59$	10.3260	−	5.96172i	1.34433	−	0.776150i	0.987440	+	0.157996i	$0.0505032\pi$
$60$		0			0
$61$	−6.92345	+	11.9918i	−0.886456	+	1.53539i	−0.0424210	+	0.999100i	$0.513507\pi$
$61$	−6.92345	+	11.9918i	−0.886456	+	1.53539i	−0.844035	+	0.536288i	$0.819826\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0139493	−	10.0900i	0.00173020	−	1.25151i
$66$		0			0
$67$	11.9348	−	6.89054i	1.45806	−	0.841813i	0.459148	−	0.888360i	$-0.348155\pi$
$67$	11.9348	−	6.89054i	1.45806	−	0.841813i	0.998916	+	0.0465465i	$0.0148216\pi$
$68$		0			0
$69$	4.95635			0.596674
$70$		0			0
$71$			3.80432i			0.451490i	0.974186	+	0.225745i	$0.0724816\pi$
$71$			3.80432i			0.451490i	−0.974186	+	0.225745i	$0.927518\pi$
$72$		0			0
$73$	2.76331	−	1.59540i	0.323421	−	0.186727i	−0.329495	−	0.944157i	$-0.606879\pi$
$73$	2.76331	−	1.59540i	0.323421	−	0.186727i	0.652917	+	0.757430i	$0.273545\pi$
$74$		0			0
$75$	−1.83136	+	3.17201i	−0.211467	+	0.366272i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.66620	+	6.35004i	−0.412480	+	0.714436i	−0.995160	−	0.0982656i	$-0.968671\pi$
$79$	−3.66620	+	6.35004i	−0.412480	+	0.714436i	0.582681	+	0.812701i	$0.302004\pi$
$80$		0			0
$81$	1.63036	+	2.82387i	0.181151	+	0.313763i
$82$		0			0
$83$		−	16.6260i		−	1.82494i	−0.409140	−	0.912472i	$-0.634171\pi$
$83$		−	16.6260i		−	1.82494i	0.409140	−	0.912472i	$-0.365829\pi$
$84$		0			0
$85$			19.4670i			2.11150i
$86$		0			0
$87$	−3.29988	−	5.71555i	−0.353784	−	0.612772i
$88$		0			0
$89$	10.3026	+	5.94820i	1.09207	+	0.630508i	0.934127	−	0.356940i	$-0.116180\pi$
$89$	10.3026	+	5.94820i	1.09207	+	0.630508i	0.157945	+	0.987448i	$0.449513\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.24464	−	2.45064i	−0.440148	−	0.254120i
$94$		0			0
$95$	3.55087	+	6.15029i	0.364312	+	0.631007i
$96$		0			0
$97$		−	8.60355i		−	0.873558i	−0.899569	−	0.436779i	$-0.856119\pi$
$97$		−	8.60355i		−	0.873558i	0.899569	−	0.436779i	$-0.143881\pi$
$98$		0			0
$99$		−	1.37018i		−	0.137708i
$100$		0			0
$101$	−4.18455	−	7.24785i	−0.416378	−	0.721188i	0.579194	−	0.815190i	$-0.303367\pi$
$101$	−4.18455	−	7.24785i	−0.416378	−	0.721188i	−0.995572	+	0.0940017i	$0.970034\pi$
$102$		0			0
$103$	−0.260721	+	0.451582i	−0.0256896	+	0.0444957i	−0.878584	−	0.477587i	$-0.841511\pi$
$103$	−0.260721	+	0.451582i	−0.0256896	+	0.0444957i	0.852895	+	0.522083i	$0.174845\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.71761	+	8.17115i	−0.456069	+	0.789934i	−0.998749	−	0.0500050i	$-0.984076\pi$
$107$	−4.71761	+	8.17115i	−0.456069	+	0.789934i	0.542680	+	0.839939i	$0.317410\pi$
$108$		0			0
$109$	−11.8524	+	6.84298i	−1.13525	+	0.655439i	−0.945251	−	0.326345i	$-0.894183\pi$
$109$	−11.8524	+	6.84298i	−1.13525	+	0.655439i	−0.190003	+	0.981784i	$0.560850\pi$
$110$		0			0
$111$			8.03007i			0.762180i
$112$		0			0
$113$	−12.2655			−1.15384			−0.576921	−	0.816800i	$-0.695746\pi$
$113$	−12.2655			−1.15384			−0.576921	+	0.816800i	$0.695746\pi$
$114$		0			0
$115$	9.28544	−	5.36095i	0.865872	−	0.499911i
$116$		0			0
$117$	−4.78287	−	0.00661227i	−0.442177	−	0.000611305i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.96655	+	8.60232i	−0.451505	+	0.782029i
$122$		0			0
$123$	−1.10949	+	0.640564i	−0.100039	+	0.0577577i
$124$		0			0
$125$		−	6.06884i		−	0.542814i
$126$		0			0
$127$	−10.9331			−0.970156			−0.485078	−	0.874471i	$-0.661209\pi$
$127$	−10.9331			−0.970156			−0.485078	+	0.874471i	$0.661209\pi$
$128$		0			0
$129$	0.362849	+	0.628472i	0.0319470	+	0.0553339i
$130$		0			0
$131$	3.29363	−	5.70473i	0.287765	−	0.498424i	−0.685511	−	0.728063i	$-0.740421\pi$
$131$	3.29363	−	5.70473i	0.287765	−	0.498424i	0.973276	+	0.229638i	$0.0737543\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	13.5643	+	7.83136i	1.16743	+	0.674016i
$136$		0			0
$137$	−11.1140	+	6.41665i	−0.949531	+	0.548212i	−0.892935	−	0.450185i	$-0.851358\pi$
$137$	−11.1140	+	6.41665i	−0.949531	+	0.548212i	−0.0565956	+	0.998397i	$0.518025\pi$
$138$		0			0
$139$	−18.5998			−1.57761			−0.788805	−	0.614643i	$-0.789300\pi$
$139$	−18.5998			−1.57761			−0.788805	+	0.614643i	$0.789300\pi$
$140$		0			0
$141$			9.30221i			0.783387i
$142$		0			0
$143$	−3.22267	−	1.86655i	−0.269493	−	0.156089i
$144$		0			0
$145$	−12.3643	−	7.13851i	−1.02680	−	0.592821i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.64012	+	4.98838i	0.707827	+	0.408664i	0.810256	−	0.586076i	$-0.199328\pi$
$149$	8.64012	+	4.98838i	0.707827	+	0.408664i	−0.102429	+	0.994740i	$0.532662\pi$
$150$		0			0
$151$	12.1714	−	7.02715i	0.990493	−	0.571861i	0.0850714	−	0.996375i	$-0.472888\pi$
$151$	12.1714	−	7.02715i	0.990493	−	0.571861i	0.905422	+	0.424513i	$0.139555\pi$
$152$		0			0
$153$	9.22782			0.746025
$154$		0			0
$155$	−10.6028			−0.851636
$156$		0			0
$157$	3.88429	+	6.72779i	0.310000	+	0.536936i	0.978362	−	0.206900i	$-0.0663376\pi$
$157$	3.88429	+	6.72779i	0.310000	+	0.536936i	−0.668362	+	0.743836i	$0.733004\pi$
$158$		0			0
$159$	0.762140	−	1.32006i	0.0604416	−	0.104688i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.40289	−	3.69671i	−0.501513	−	0.289549i	0.227825	−	0.973702i	$-0.426839\pi$
$163$	−6.40289	−	3.69671i	−0.501513	−	0.289549i	−0.729338	+	0.684153i	$0.760172\pi$
$164$		0			0
$165$	1.86964	+	3.23831i	0.145551	+	0.252102i
$166$		0			0
$167$			15.7122i			1.21585i	0.793995	+	0.607925i	$0.207998\pi$
$167$			15.7122i			1.21585i	−0.793995	+	0.607925i	$0.792002\pi$
$168$		0			0
$169$	−6.53110	+	11.2403i	−0.502393	+	0.864640i
$170$		0			0
$171$	2.91538	−	1.68319i	0.222944	−	0.128717i
$172$		0			0
$173$	0.207792	−	0.359907i	0.0157982	−	0.0273632i	−0.858018	−	0.513619i	$-0.828304\pi$
$173$	0.207792	−	0.359907i	0.0157982	−	0.0273632i	0.873816	+	0.486256i	$0.161638\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	13.3580	+	7.71224i	1.00405	+	0.579688i
$178$		0			0
$179$	−1.95396	−	3.38436i	−0.146046	−	0.252959i	0.783717	−	0.621118i	$-0.213321\pi$
$179$	−1.95396	−	3.38436i	−0.146046	−	0.252959i	−0.929763	+	0.368160i	$0.879988\pi$
$180$		0			0
$181$	4.79151			0.356150			0.178075	−	0.984017i	$-0.443013\pi$
$181$	4.79151			0.356150			0.178075	+	0.984017i	$0.443013\pi$
$182$		0			0
$183$	−17.9127			−1.32414
$184$		0			0
$185$	8.68559	+	15.0439i	0.638577	+	1.10605i
$186$		0			0
$187$	6.22261	+	3.59262i	0.455042	+	0.262719i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.31453	−	7.47298i	0.312188	−	0.540726i	−0.666648	−	0.745373i	$-0.732271\pi$
$191$	4.31453	−	7.47298i	0.312188	−	0.540726i	0.978836	+	0.204647i	$0.0656047\pi$
$192$		0			0
$193$	−21.1773	+	12.2267i	−1.52438	+	0.880100i	−0.524794	+	0.851229i	$0.675858\pi$
$193$	−21.1773	+	12.2267i	−1.52438	+	0.880100i	−0.999583	+	0.0288702i	$0.990809\pi$
$194$		0			0
$195$	11.3129	−	6.51070i	0.810137	−	0.466241i
$196$		0			0
$197$			7.14128i			0.508795i	0.967100	+	0.254398i	$0.0818772\pi$
$197$			7.14128i			0.508795i	−0.967100	+	0.254398i	$0.918123\pi$
$198$		0			0
$199$	0.501418	+	0.868482i	0.0355446	+	0.0615651i	0.883250	−	0.468902i	$-0.155350\pi$
$199$	0.501418	+	0.868482i	0.0355446	+	0.0615651i	−0.847706	+	0.530467i	$0.822017\pi$
$200$		0			0
$201$	15.4391	+	8.91378i	1.08899	+	0.628730i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.38571	+	2.40012i	−0.0967822	+	0.167632i
$206$		0			0
$207$	−2.54121	−	4.40151i	−0.176626	−	0.305926i
$208$		0			0
$209$	2.62124			0.181315
$210$		0			0
$211$	26.2655			1.80819			0.904096	−	0.427329i	$-0.140546\pi$
$211$	26.2655			1.80819			0.904096	+	0.427329i	$0.140546\pi$
$212$		0			0
$213$	−4.26203	+	2.46069i	−0.292030	+	0.168603i
$214$		0			0
$215$	1.35955	+	0.784938i	0.0927207	+	0.0535323i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.57469	+	2.06385i	0.241555	+	0.139462i
$220$		0			0
$221$	12.5708	−	21.7038i	0.845601	−	1.45996i
$222$		0			0
$223$		−	17.7540i		−	1.18890i	−0.804133	−	0.594449i	$-0.797370\pi$
$223$		−	17.7540i		−	1.18890i	0.804133	−	0.594449i	$-0.202630\pi$
$224$		0			0
$225$	3.75589			0.250393
$226$		0			0
$227$	−15.4391	+	8.91378i	−1.02473	+	0.591629i	−0.915471	−	0.402385i	$-0.868181\pi$
$227$	−15.4391	+	8.91378i	−1.02473	+	0.591629i	−0.109260	+	0.994013i	$0.534848\pi$
$228$		0			0
$229$	−3.64963	−	2.10712i	−0.241175	−	0.139242i	0.374542	−	0.927210i	$-0.377800\pi$
$229$	−3.64963	−	2.10712i	−0.241175	−	0.139242i	−0.615716	+	0.787968i	$0.711133\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.1440	−	24.4981i	0.926604	−	1.60492i	0.137642	−	0.990482i	$-0.456048\pi$
$233$	14.1440	−	24.4981i	0.926604	−	1.60492i	0.788961	−	0.614443i	$-0.210619\pi$
$234$		0			0
$235$	10.0616	+	17.4272i	0.656344	+	1.13682i
$236$		0			0
$237$	−9.48538			−0.616142
$238$		0			0
$239$		−	8.94385i		−	0.578530i	−0.957249	−	0.289265i	$-0.906589\pi$
$239$		−	8.94385i		−	0.578530i	0.957249	−	0.289265i	$-0.0934108\pi$
$240$		0			0
$241$	14.7241	−	8.50097i	0.948464	−	0.547596i	0.0558604	−	0.998439i	$-0.482210\pi$
$241$	14.7241	−	8.50097i	0.948464	−	0.547596i	0.892603	+	0.450843i	$0.148876\pi$
$242$		0			0
$243$	6.28629	−	10.8882i	0.403266	−	0.698477i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.0126497	−	9.14993i	0.000804880	−	0.582196i
$248$		0			0
$249$	18.6264	−	10.7539i	1.18040	−	0.681503i
$250$		0			0
$251$	−6.70637			−0.423303			−0.211651	−	0.977345i	$-0.567884\pi$
$251$	−6.70637			−0.423303			−0.211651	+	0.977345i	$0.567884\pi$
$252$		0			0
$253$		−	3.95743i		−	0.248802i
$254$		0			0
$255$	−21.8092	+	12.5915i	−1.36574	+	0.788513i
$256$		0			0
$257$	7.33278	−	12.7007i	0.457406	−	0.792251i	−0.541417	−	0.840754i	$-0.682112\pi$
$257$	7.33278	−	12.7007i	0.457406	−	0.792251i	0.998823	+	0.0485035i	$0.0154452\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.38381	+	5.86093i	−0.209453	+	0.362783i
$262$		0			0
$263$	3.01314	+	5.21891i	0.185798	+	0.321812i	0.943845	−	0.330388i	$-0.107180\pi$
$263$	3.01314	+	5.21891i	0.185798	+	0.321812i	−0.758047	+	0.652200i	$0.773846\pi$
$264$		0			0
$265$		−	3.29742i		−	0.202559i
$266$		0			0
$267$			15.3895i			0.941822i
$268$		0			0
$269$	0.412748	+	0.714900i	0.0251657	+	0.0435882i	0.878334	−	0.478048i	$-0.158655\pi$
$269$	0.412748	+	0.714900i	0.0251657	+	0.0435882i	−0.853168	+	0.521636i	$0.825322\pi$
$270$		0			0
$271$	−8.51092	−	4.91378i	−0.517002	−	0.298491i	0.218705	−	0.975791i	$-0.429817\pi$
$271$	−8.51092	−	4.91378i	−0.517002	−	0.298491i	−0.735707	+	0.677300i	$0.763150\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.53272	+	1.46226i	0.152729	+	0.0881778i
$276$		0			0
$277$	−13.9258	−	24.1203i	−0.836722	−	1.44925i	−0.892620	−	0.450809i	$-0.851135\pi$
$277$	−13.9258	−	24.1203i	−0.836722	−	1.44925i	0.0558978	−	0.998436i	$-0.482198\pi$
$278$		0			0
$279$			5.02596i			0.300896i
$280$		0			0
$281$		−	4.04257i		−	0.241159i	−0.992704	−	0.120580i	$-0.961525\pi$
$281$		−	4.04257i		−	0.241159i	0.992704	−	0.120580i	$-0.0384753\pi$
$282$		0			0
$283$	14.8798	+	25.7726i	0.884512	+	1.53202i	0.846272	+	0.532751i	$0.178842\pi$
$283$	14.8798	+	25.7726i	0.884512	+	1.53202i	0.0382402	+	0.999269i	$0.487825\pi$
$284$		0			0
$285$	−4.59350	+	7.95618i	−0.272096	+	0.471283i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−15.6954	+	27.1852i	−0.923259	+	1.59913i
$290$		0			0
$291$	9.63867	−	5.56489i	0.565029	−	0.326219i
$292$		0			0
$293$			29.8091i			1.74147i	0.491755	+	0.870733i	$0.336355\pi$
$293$			29.8091i			1.74147i	−0.491755	+	0.870733i	$0.663645\pi$
$294$		0			0
$295$	33.3673			1.94272
$296$		0			0
$297$	5.00656	−	2.89054i	0.290510	−	0.167726i
$298$		0			0
$299$	−13.8142	−	0.0190979i	−0.798893	−	0.00110446i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	5.41324	−	9.37601i	0.310983	−	0.538638i
$304$		0			0
$305$	−33.5584	+	19.3750i	−1.92155	+	1.10941i
$306$		0			0
$307$		−	18.5928i		−	1.06115i	−0.847639	−	0.530574i	$-0.821977\pi$
$307$		−	18.5928i		−	1.06115i	0.847639	−	0.530574i	$-0.178023\pi$
$308$		0			0
$309$	−0.674552			−0.0383739
$310$		0			0
$311$	−7.95597	−	13.7801i	−0.451142	−	0.781400i	0.547316	−	0.836926i	$-0.315650\pi$
$311$	−7.95597	−	13.7801i	−0.451142	−	0.781400i	−0.998457	+	0.0555262i	$0.982316\pi$
$312$		0			0
$313$	0.897873	−	1.55516i	0.0507508	−	0.0879029i	−0.839534	−	0.543307i	$-0.817172\pi$
$313$	0.897873	−	1.55516i	0.0507508	−	0.0879029i	0.890285	+	0.455404i	$0.150505\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.8833	−	8.01553i	−0.779764	−	0.450197i	0.0565827	−	0.998398i	$-0.481980\pi$
$317$	−13.8833	−	8.01553i	−0.779764	−	0.450197i	−0.836347	+	0.548201i	$0.815313\pi$
$318$		0			0
$319$	−4.56362	+	2.63481i	−0.255514	+	0.147521i
$320$		0			0
$321$	−12.2057			−0.681253
$322$		0			0
$323$			17.6534i			0.982260i
$324$		0			0
$325$	5.11653	−	8.83386i	0.283814	−	0.490014i
$326$		0			0
$327$	−15.3326	−	8.85226i	−0.847893	−	0.489531i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	5.90448	+	3.40895i	0.324540	+	0.187373i	0.653414	−	0.757001i	$-0.273336\pi$
$331$	5.90448	+	3.40895i	0.324540	+	0.187373i	−0.328875	+	0.944374i	$0.606669\pi$
$332$		0			0
$333$	7.13113	−	4.11716i	0.390784	−	0.225619i
$334$		0			0
$335$	38.5658			2.10707
$336$		0			0
$337$	0.418615			0.0228034			0.0114017	−	0.999935i	$-0.496371\pi$
$337$	0.418615			0.0228034			0.0114017	+	0.999935i	$0.496371\pi$
$338$		0			0
$339$	−7.93349	−	13.7412i	−0.430888	−	0.746320i
$340$		0			0
$341$	−1.95673	+	3.38916i	−0.105963	+	0.183533i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	12.0119	+	6.93507i	0.646698	+	0.373371i
$346$		0			0
$347$	5.03291	+	8.71725i	0.270180	+	0.467966i	0.968908	−	0.247422i	$-0.0795833\pi$
$347$	5.03291	+	8.71725i	0.270180	+	0.467966i	−0.698727	+	0.715388i	$0.746250\pi$
$348$		0			0
$349$			8.27233i			0.442808i	0.975182	+	0.221404i	$0.0710639\pi$
$349$			8.27233i			0.442808i	−0.975182	+	0.221404i	$0.928936\pi$
$350$		0			0
$351$	−10.0658	−	17.4903i	−0.537273	−	0.933563i
$352$		0			0
$353$	−14.1949	+	8.19541i	−0.755516	+	0.436197i	−0.827684	−	0.561195i	$-0.810342\pi$
$353$	−14.1949	+	8.19541i	−0.755516	+	0.436197i	0.0721674	+	0.997393i	$0.477008\pi$
$354$		0			0
$355$	−5.32312	+	9.21991i	−0.282522	+	0.489342i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−27.8437	−	16.0756i	−1.46954	−	0.848437i	−0.470120	−	0.882603i	$-0.655789\pi$
$359$	−27.8437	−	16.0756i	−1.46954	−	0.848437i	−0.999416	+	0.0341658i	$0.989123\pi$
$360$		0			0
$361$	−6.27995	−	10.8772i	−0.330524	−	0.572484i
$362$		0			0
$363$	−12.8497			−0.674436
$364$		0			0
$365$	8.92931			0.467382
$366$		0			0
$367$	3.89787	+	6.75131i	0.203467	+	0.352416i	0.949643	−	0.313333i	$-0.101446\pi$
$367$	3.89787	+	6.75131i	0.203467	+	0.352416i	−0.746176	+	0.665749i	$0.768112\pi$
$368$		0			0
$369$	1.13771	+	0.656857i	0.0592268	+	0.0341946i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−15.8686	+	27.4851i	−0.821643	+	1.42313i	0.0828156	+	0.996565i	$0.473609\pi$
$373$	−15.8686	+	27.4851i	−0.821643	+	1.42313i	−0.904458	+	0.426562i	$0.859725\pi$
$374$		0			0
$375$	6.79900	−	3.92541i	0.351099	−	0.202707i
$376$		0			0
$377$	9.17527	+	15.9429i	0.472550	+	0.821101i
$378$		0			0
$379$		−	30.3236i		−	1.55762i	−0.627261	−	0.778809i	$-0.715824\pi$
$379$		−	30.3236i		−	1.55762i	0.627261	−	0.778809i	$-0.284176\pi$
$380$		0			0
$381$	−7.07168	−	12.2485i	−0.362293	−	0.627510i
$382$		0			0
$383$	12.1411	+	7.00966i	0.620381	+	0.358177i	0.777017	−	0.629479i	$-0.216732\pi$
$383$	12.1411	+	7.00966i	0.620381	+	0.358177i	−0.156636	+	0.987656i	$0.550065\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.372078	−	0.644458i	0.0189138	−	0.0327597i
$388$		0			0
$389$	−9.94435	−	17.2241i	−0.504198	−	0.873297i	−0.999988	−	0.00485467i	$-0.998455\pi$
$389$	−9.94435	−	17.2241i	−0.504198	−	0.873297i	0.495790	−	0.868443i	$-0.334879\pi$
$390$		0			0
$391$	26.6523			1.34786
$392$		0			0
$393$	8.52144			0.429850
$394$		0			0
$395$	−17.7703	+	10.2597i	−0.894122	+	0.516222i
$396$		0			0
$397$	12.7495	+	7.36095i	0.639881	+	0.369436i	0.784569	−	0.620042i	$-0.212884\pi$
$397$	12.7495	+	7.36095i	0.639881	+	0.369436i	−0.144688	+	0.989477i	$0.546218\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.0098	−	9.82062i	−0.849429	−	0.490418i	0.0110289	−	0.999939i	$-0.496489\pi$
$401$	−17.0098	−	9.82062i	−0.849429	−	0.490418i	−0.860458	+	0.509521i	$0.829823\pi$
$402$		0			0
$403$	11.8211	+	6.84670i	0.588849	+	0.341058i
$404$		0			0
$405$			9.12499i			0.453424i
$406$		0			0
$407$	6.41166			0.317814
$408$		0			0
$409$	20.8826	−	12.0566i	1.03258	−	0.596160i	0.114856	−	0.993382i	$-0.463359\pi$
$409$	20.8826	−	12.0566i	1.03258	−	0.596160i	0.917722	+	0.397223i	$0.130026\pi$
$410$		0			0
$411$	−14.3773	−	8.30075i	−0.709181	−	0.409446i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	23.2636	−	40.2938i	1.14197	−	1.97794i
$416$		0			0
$417$	−12.0306	−	20.8375i	−0.589139	−	1.02042i
$418$		0			0
$419$	−19.7818			−0.966406			−0.483203	−	0.875508i	$-0.660527\pi$
$419$	−19.7818			−0.966406			−0.483203	+	0.875508i	$0.660527\pi$
$420$		0			0
$421$		−	19.1237i		−	0.932033i	−0.884776	−	0.466016i	$-0.845689\pi$
$421$		−	19.1237i		−	0.932033i	0.884776	−	0.466016i	$-0.154311\pi$
$422$		0			0
$423$	8.26086	−	4.76941i	0.401657	−	0.231897i
$424$		0			0
$425$	−9.84797	+	17.0572i	−0.477697	+	0.827395i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.00666043	−	4.81771i	0.000321569	−	0.232601i
$430$		0			0
$431$	7.68673	−	4.43794i	0.370257	−	0.213768i	−0.303314	−	0.952891i	$-0.598093\pi$
$431$	7.68673	−	4.43794i	0.370257	−	0.213768i	0.673571	+	0.739123i	$0.264760\pi$
$432$		0			0
$433$	−36.9341			−1.77494			−0.887470	−	0.460866i	$-0.847539\pi$
$433$	−36.9341			−1.77494			−0.887470	+	0.460866i	$0.847539\pi$
$434$		0			0
$435$		−	18.4691i		−	0.885527i
$436$		0			0
$437$	8.42035	−	4.86149i	0.402800	−	0.232557i
$438$		0			0
$439$	10.3296	−	17.8913i	0.493003	−	0.853906i	−0.506964	−	0.861967i	$-0.669232\pi$
$439$	10.3296	−	17.8913i	0.493003	−	0.853906i	0.999968	+	0.00806061i	$0.00256580\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.42746	+	2.47244i	−0.0678207	+	0.117469i	−0.897942	−	0.440114i	$-0.854938\pi$
$443$	−1.42746	+	2.47244i	−0.0678207	+	0.117469i	0.830121	+	0.557583i	$0.188271\pi$
$444$		0			0
$445$	16.6458	+	28.8314i	0.789086	+	1.36674i
$446$		0			0
$447$			12.9062i			0.610442i
$448$		0			0
$449$		−	30.0443i		−	1.41788i	−0.705269	−	0.708940i	$-0.749174\pi$
$449$		−	30.0443i		−	1.41788i	0.705269	−	0.708940i	$-0.250826\pi$
$450$		0			0
$451$	0.511463	+	0.885879i	0.0240838	+	0.0417144i
$452$		0			0
$453$	15.7452	+	9.09051i	0.739775	+	0.427109i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−24.8109	−	14.3246i	−1.16060	−	0.670075i	−0.209156	−	0.977882i	$-0.567071\pi$
$457$	−24.8109	−	14.3246i	−1.16060	−	0.670075i	−0.951449	+	0.307807i	$0.900405\pi$
$458$		0			0
$459$	19.4670	+	33.7179i	0.908644	+	1.57382i
$460$		0			0
$461$			0.922363i			0.0429587i	0.999769	+	0.0214794i	$0.00683762\pi$
$461$			0.922363i			0.0429587i	−0.999769	+	0.0214794i	$0.993162\pi$
$462$		0			0
$463$		−	26.0929i		−	1.21264i	−0.795220	−	0.606321i	$-0.792645\pi$
$463$		−	26.0929i		−	1.21264i	0.795220	−	0.606321i	$-0.207355\pi$
$464$		0			0
$465$	−6.85802	−	11.8784i	−0.318033	−	0.550849i
$466$		0			0
$467$	−14.7777	+	25.5957i	−0.683829	+	1.18443i	0.289974	+	0.957034i	$0.406353\pi$
$467$	−14.7777	+	25.5957i	−0.683829	+	1.18443i	−0.973803	+	0.227392i	$0.926980\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−5.02482	+	8.70324i	−0.231532	+	0.401024i
$472$		0			0
$473$	0.501808	−	0.289719i	0.0230732	−	0.0133213i
$474$		0			0
$475$			7.18525i			0.329682i
$476$		0			0
$477$	−1.56305			−0.0715672
$478$		0			0
$479$	13.7658	−	7.94771i	0.628977	−	0.363140i	−0.151379	−	0.988476i	$-0.548371\pi$
$479$	13.7658	−	7.94771i	0.628977	−	0.363140i	0.780356	+	0.625336i	$0.215038\pi$
$480$		0			0
$481$	0.0309417	−	22.3811i	0.00141082	−	1.02049i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	12.0383	−	20.8510i	0.546632	−	0.946795i
$486$		0			0
$487$	−0.0737279	+	0.0425668i	−0.00334093	+	0.00192889i	−0.501670	−	0.865059i	$-0.667281\pi$
$487$	−0.0737279	+	0.0425668i	−0.00334093	+	0.00192889i	0.498329	+	0.866988i	$0.333947\pi$
$488$		0			0
$489$		−	9.56433i		−	0.432514i
$490$		0			0
$491$	2.56324			0.115678			0.0578388	−	0.998326i	$-0.481579\pi$
$491$	2.56324			0.115678			0.0578388	+	0.998326i	$0.481579\pi$
$492$		0			0
$493$	−17.7448	−	30.7348i	−0.799184	−	1.38423i
$494$		0			0
$495$	1.91720	−	3.32068i	0.0861716	−	0.149254i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	24.8498	+	14.3470i	1.11243	+	0.642262i	0.939458	−	0.342664i	$-0.111329\pi$
$499$	24.8498	+	14.3470i	1.11243	+	0.642262i	0.172973	+	0.984927i	$0.444663\pi$
$500$		0			0
$501$	−17.6026	+	10.1629i	−0.786428	+	0.454044i
$502$		0			0
$503$	−32.7056			−1.45827			−0.729136	−	0.684369i	$-0.760078\pi$
$503$	−32.7056			−1.45827			−0.729136	+	0.684369i	$0.760078\pi$
$504$		0			0
$505$		−	23.4206i		−	1.04220i
$506$		0			0
$507$	−16.8171	−	0.0464990i	−0.746873	−	0.00206509i
$508$		0			0
$509$	22.5979	+	13.0469i	1.00164	+	0.578295i	0.908732	−	0.417381i	$-0.137052\pi$
$509$	22.5979	+	13.0469i	1.00164	+	0.578295i	0.0929037	+	0.995675i	$0.470385\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	12.3006	+	7.10175i	0.543084	+	0.313550i
$514$		0			0
$515$	−1.26373	+	0.729617i	−0.0556868	+	0.0321508i
$516$		0			0
$517$	7.42741			0.326657
$518$		0			0
$519$	0.537611			0.0235985
$520$		0			0
$521$	0.877849	+	1.52048i	0.0384592	+	0.0666134i	0.884614	−	0.466323i	$-0.154422\pi$
$521$	0.877849	+	1.52048i	0.0384592	+	0.0666134i	−0.846155	+	0.532937i	$0.821088\pi$
$522$		0			0
$523$	16.1890	−	28.0401i	0.707893	−	1.22611i	−0.257744	−	0.966213i	$-0.582979\pi$
$523$	16.1890	−	28.0401i	0.707893	−	1.22611i	0.965637	−	0.259894i	$-0.0836876\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−22.8251	−	13.1781i	−0.994278	−	0.574047i
$528$		0			0
$529$	4.16033	+	7.20591i	0.180884	+	0.313300i
$530$		0			0
$531$		−	15.8168i		−	0.686392i
$532$		0			0
$533$	3.09480	−	1.78108i	0.134050	−	0.0771472i
$534$		0			0
$535$	−22.8666	+	13.2020i	−0.988609	+	0.570774i
$536$		0			0
$537$	2.52769	−	4.37809i	0.109078	−	0.188929i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−7.38318	−	4.26268i	−0.317428	−	0.183267i	0.332818	−	0.942991i	$-0.392001\pi$
$541$	−7.38318	−	4.26268i	−0.317428	−	0.183267i	−0.650245	+	0.759724i	$0.725334\pi$
$542$		0			0
$543$	3.09921	+	5.36799i	0.133000	+	0.230362i
$544$		0			0
$545$	−38.2996			−1.64057
$546$		0			0
$547$	1.14355			0.0488945			0.0244473	−	0.999701i	$-0.492217\pi$
$547$	1.14355			0.0488945			0.0244473	+	0.999701i	$0.492217\pi$
$548$		0			0
$549$	9.18417	+	15.9074i	0.391971	+	0.678913i
$550$		0			0
$551$	−11.2123	−	6.47344i	−0.477661	−	0.275778i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−11.2359	+	19.4612i	−0.476937	+	0.826080i
$556$		0			0
$557$	−37.0897	+	21.4137i	−1.57154	+	0.907329i	−0.575560	+	0.817760i	$0.695216\pi$
$557$	−37.0897	+	21.4137i	−1.57154	+	0.907329i	−0.995981	+	0.0895693i	$0.971451\pi$
$558$		0			0
$559$	−1.00890	−	1.75305i	−0.0426718	−	0.0741463i
$560$		0			0
$561$			9.29503i			0.392436i
$562$		0			0
$563$	−6.78771	−	11.7567i	−0.286068	−	0.495484i	0.686800	−	0.726847i	$-0.259015\pi$
$563$	−6.78771	−	11.7567i	−0.286068	−	0.495484i	−0.972868	+	0.231363i	$0.925682\pi$
$564$		0			0
$565$	−29.7259	−	17.1622i	−1.25058	−	0.722021i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.43555	−	7.68259i	0.185948	−	0.322071i	−0.757948	−	0.652315i	$-0.773798\pi$
$569$	4.43555	−	7.68259i	0.185948	−	0.322071i	0.943895	+	0.330244i	$0.107131\pi$
$570$		0			0
$571$	−3.14047	−	5.43945i	−0.131424	−	0.227634i	0.792801	−	0.609480i	$-0.208622\pi$
$571$	−3.14047	−	5.43945i	−0.131424	−	0.227634i	−0.924226	+	0.381846i	$0.875288\pi$
$572$		0			0
$573$	11.1628			0.466331
$574$		0			0
$575$	10.8480			0.452392
$576$		0			0
$577$	21.7376	−	12.5502i	0.904950	−	0.522473i	0.0261471	−	0.999658i	$-0.491676\pi$
$577$	21.7376	−	12.5502i	0.904950	−	0.522473i	0.878803	+	0.477185i	$0.158343\pi$
$578$		0			0
$579$	−27.3955	−	15.8168i	−1.13852	−	0.657325i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.05401	−	0.608536i	−0.0436528	−	0.0252030i
$584$		0			0
$585$	−11.5822	−	6.70836i	−0.478865	−	0.277356i
$586$		0			0
$587$		−	28.2963i		−	1.16791i	−0.811784	−	0.583957i	$-0.801503\pi$
$587$		−	28.2963i		−	1.16791i	0.811784	−	0.583957i	$-0.198497\pi$
$588$		0			0
$589$	−9.61496			−0.396178
$590$		0			0
$591$	−8.00047	+	4.61907i	−0.329095	+	0.190003i
$592$		0			0
$593$	−11.1408	−	6.43213i	−0.457497	−	0.264136i	0.253494	−	0.967337i	$-0.418420\pi$
$593$	−11.1408	−	6.43213i	−0.457497	−	0.264136i	−0.710991	+	0.703201i	$0.751753\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.648648	+	1.12349i	−0.0265474	+	0.0459814i
$598$		0			0
$599$	−12.7842	−	22.1429i	−0.522350	−	0.904736i	−0.999662	−	0.0260025i	$-0.991722\pi$
$599$	−12.7842	−	22.1429i	−0.522350	−	0.904736i	0.477312	−	0.878734i	$-0.341611\pi$
$600$		0			0
$601$	6.63763			0.270755			0.135377	−	0.990794i	$-0.456775\pi$
$601$	6.63763			0.270755			0.135377	+	0.990794i	$0.456775\pi$
$602$		0			0
$603$		−	18.2810i		−	0.744461i
$604$		0			0
$605$	−24.0732	+	13.8987i	−0.978716	+	0.565062i
$606$		0			0
$607$	−11.1613	+	19.3319i	−0.453023	+	0.784660i	−0.998572	−	0.0534195i	$-0.982988\pi$
$607$	−11.1613	+	19.3319i	−0.453023	+	0.784660i	0.545549	+	0.838079i	$0.316321\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0358435	−	25.9268i	0.00145007	−	1.04888i
$612$		0			0
$613$	−3.66910	+	2.11836i	−0.148194	+	0.0855596i	−0.572263	−	0.820070i	$-0.693934\pi$
$613$	−3.66910	+	2.11836i	−0.148194	+	0.0855596i	0.424070	+	0.905630i	$0.360601\pi$
$614$		0			0
$615$	−3.58518			−0.144568
$616$		0			0
$617$		−	14.0193i		−	0.564397i	−0.959356	−	0.282198i	$-0.908936\pi$
$617$		−	14.0193i		−	0.564397i	0.959356	−	0.282198i	$-0.0910636\pi$
$618$		0			0
$619$	−20.6520	+	11.9234i	−0.830074	+	0.479244i	−0.853878	−	0.520473i	$-0.825756\pi$
$619$	−20.6520	+	11.9234i	−0.830074	+	0.479244i	0.0238037	+	0.999717i	$0.492422\pi$
$620$		0			0
$621$	10.7219	−	18.5709i	0.430255	−	0.745224i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.5701	−	26.9682i	0.622804	−	1.07873i
$626$		0			0
$627$	1.69545	+	2.93661i	0.0677099	+	0.117277i
$628$		0			0
$629$			43.1809i			1.72174i
$630$		0			0
$631$		−	7.18624i		−	0.286080i	−0.989717	−	0.143040i	$-0.954312\pi$
$631$		−	7.18624i		−	0.286080i	0.989717	−	0.143040i	$-0.0456877\pi$
$632$		0			0
$633$	16.9889	+	29.4256i	0.675247	+	1.16956i
$634$		0			0
$635$	−26.4968	−	15.2979i	−1.05149	−	0.607079i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.37044	+	2.52328i	0.172892	+	0.0998193i
$640$		0			0
$641$	4.02943	+	6.97918i	0.159153	+	0.275661i	0.934563	−	0.355796i	$-0.115790\pi$
$641$	4.02943	+	6.97918i	0.159153	+	0.275661i	−0.775411	+	0.631457i	$0.782457\pi$
$642$		0			0
$643$			28.4148i			1.12057i	0.828300	+	0.560286i	$0.189309\pi$
$643$			28.4148i			1.12057i	−0.828300	+	0.560286i	$0.810691\pi$
$644$		0			0
$645$			2.03083i			0.0799640i
$646$		0			0
$647$	−18.8396	−	32.6311i	−0.740659	−	1.28286i	−0.952195	−	0.305490i	$-0.901180\pi$
$647$	−18.8396	−	32.6311i	−0.740659	−	1.28286i	0.211536	−	0.977370i	$-0.432153\pi$
$648$		0			0
$649$	6.15789	−	10.6658i	0.241718	−	0.418669i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.5243	+	32.0850i	−0.724911	+	1.25558i	0.234100	+	0.972213i	$0.424786\pi$
$653$	−18.5243	+	32.0850i	−0.724911	+	1.25558i	−0.959011	+	0.283370i	$0.908547\pi$
$654$		0			0
$655$	15.9644	−	9.21707i	0.623782	−	0.360141i
$656$		0			0
$657$		−	4.23269i		−	0.165133i
$658$		0			0
$659$	44.4553			1.73173			0.865867	−	0.500274i	$-0.166767\pi$
$659$	44.4553			1.73173			0.865867	+	0.500274i	$0.166767\pi$
$660$		0			0
$661$	−34.9366	+	20.1706i	−1.35888	+	0.784547i	−0.989472	−	0.144722i	$-0.953771\pi$
$661$	−34.9366	+	20.1706i	−1.35888	+	0.784547i	−0.369403	+	0.929269i	$0.620438\pi$
$662$		0			0
$663$	32.4460	+	0.0448563i	1.26010	+	0.00174207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−9.77332	+	16.9279i	−0.378424	+	0.655450i
$668$		0			0
$669$	19.8901	−	11.4835i	0.768995	−	0.443980i
$670$		0			0
$671$			14.3025i			0.552143i
$672$		0			0
$673$	−16.8024			−0.647684			−0.323842	−	0.946111i	$-0.604975\pi$
$673$	−16.8024			−0.647684			−0.323842	+	0.946111i	$0.604975\pi$
$674$		0			0
$675$	7.92345	+	13.7238i	0.304974	+	0.528230i
$676$		0			0
$677$	23.2825	−	40.3265i	0.894819	−	1.54987i	0.0607909	−	0.998151i	$-0.480638\pi$
$677$	23.2825	−	40.3265i	0.894819	−	1.54987i	0.834028	−	0.551722i	$-0.186029\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−19.9725	−	11.5311i	−0.765346	−	0.441873i
$682$		0			0
$683$	5.01860	−	2.89749i	0.192031	−	0.110869i	−0.400902	−	0.916121i	$-0.631303\pi$
$683$	5.01860	−	2.89749i	0.192031	−	0.110869i	0.592933	+	0.805252i	$0.297970\pi$
$684$		0			0
$685$	−35.9135			−1.37218
$686$		0			0
$687$		−	5.45164i		−	0.207993i
$688$		0			0
$689$	−2.12929	+	3.67630i	−0.0811197	+	0.140056i
$690$		0			0
$691$	−23.4877	−	13.5606i	−0.893515	−	0.515871i	−0.0184246	−	0.999830i	$-0.505865\pi$
$691$	−23.4877	−	13.5606i	−0.893515	−	0.515871i	−0.875091	+	0.483959i	$0.839198\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−45.0771	−	26.0253i	−1.70987	−	0.987196i
$696$		0			0
$697$	−5.96617	+	3.44457i	−0.225985	+	0.130472i
$698$		0			0
$699$	36.5941			1.38412
$700$		0			0
$701$	11.0283			0.416535			0.208267	−	0.978072i	$-0.433218\pi$
$701$	11.0283			0.416535			0.208267	+	0.978072i	$0.433218\pi$
$702$		0			0
$703$	7.87638	+	13.6423i	0.297063	+	0.514529i
$704$		0			0
$705$	−13.0159	+	22.5442i	−0.490208	+	0.849064i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	43.0844	+	24.8748i	1.61807	+	0.934193i	0.987419	+	0.158126i	$0.0505453\pi$
$709$	43.0844	+	24.8748i	1.61807	+	0.934193i	0.630651	+	0.776067i	$0.282788\pi$
$710$		0			0
$711$	4.86333	+	8.42353i	0.182389	+	0.315907i
$712$		0			0
$713$			14.5162i			0.543638i
$714$		0			0
$715$	−5.19851	−	9.03291i	−0.194413	−	0.337811i
$716$		0			0
$717$	10.0199	−	5.78500i	0.374201	−	0.216045i
$718$		0			0
$719$	−14.2825	+	24.7380i	−0.532647	+	0.922572i	0.466626	+	0.884455i	$0.345469\pi$
$719$	−14.2825	+	24.7380i	−0.532647	+	0.922572i	−0.999273	+	0.0381175i	$0.987864\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	19.0475	+	10.9971i	0.708384	+	0.408986i
$724$		0			0
$725$	−7.22244	−	12.5096i	−0.268235	−	0.464596i
$726$		0			0
$727$	36.5250			1.35464			0.677318	−	0.735691i	$-0.263142\pi$
$727$	36.5250			1.35464			0.677318	+	0.735691i	$0.263142\pi$
$728$		0			0
$729$	26.0464			0.964681
$730$		0			0
$731$	1.95118	+	3.37955i	0.0721671	+	0.124997i
$732$		0			0
$733$	16.2331	+	9.37219i	0.599584	+	0.346170i	0.768878	−	0.639396i	$-0.220815\pi$
$733$	16.2331	+	9.37219i	0.599584	+	0.346170i	−0.169294	+	0.985566i	$0.554149\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.11727	−	12.3275i	0.262168	−	0.454089i
$738$		0			0
$739$	9.68550	−	5.59192i	0.356287	−	0.205702i	−0.311164	−	0.950356i	$-0.600719\pi$
$739$	9.68550	−	5.59192i	0.356287	−	0.205702i	0.667451	+	0.744654i	$0.267385\pi$
$740$		0			0
$741$	10.2590	−	5.90412i	0.376873	−	0.216893i
$742$		0			0
$743$		−	32.7986i		−	1.20326i	−0.798774	−	0.601632i	$-0.794518\pi$
$743$		−	32.7986i		−	1.20326i	0.798774	−	0.601632i	$-0.205482\pi$
$744$		0			0
$745$	13.9598	+	24.1790i	0.511446	+	0.885851i
$746$		0			0
$747$	−19.1001	−	11.0275i	−0.698838	−	0.403474i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	14.3726	−	24.8940i	0.524463	−	0.908396i	−0.475132	−	0.879915i	$-0.657600\pi$
$751$	14.3726	−	24.8940i	0.524463	−	0.908396i	0.999594	−	0.0284812i	$-0.00906708\pi$
$752$		0			0
$753$	−4.33777	−	7.51324i	−0.158077	−	0.273798i
$754$		0			0
$755$	39.3304			1.43138
$756$		0			0
$757$	12.4952			0.454145			0.227072	−	0.973878i	$-0.427085\pi$
$757$	12.4952			0.454145			0.227072	+	0.973878i	$0.427085\pi$
$758$		0			0
$759$	4.43356	−	2.55972i	0.160928	−	0.0929119i
$760$		0			0
$761$	25.6888	+	14.8314i	0.931218	+	0.537639i	0.887196	−	0.461392i	$-0.152650\pi$
$761$	25.6888	+	14.8314i	0.931218	+	0.537639i	0.0440211	+	0.999031i	$0.485983\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	22.3639	+	12.9118i	0.808570	+	0.466828i
$766$		0			0
$767$	−37.2012	−	21.5467i	−1.34326	−	0.778008i
$768$		0			0
$769$			40.8488i			1.47305i	0.676412	+	0.736523i	$0.263534\pi$
$769$			40.8488i			1.47305i	−0.676412	+	0.736523i	$0.736466\pi$
$770$		0			0
$771$	18.9718			0.683251
$772$		0			0
$773$	−16.8048	+	9.70226i	−0.604427	+	0.348966i	−0.770781	−	0.637100i	$-0.780134\pi$
$773$	−16.8048	+	9.70226i	−0.604427	+	0.348966i	0.166354	+	0.986066i	$0.446800\pi$
$774$		0			0
$775$	−9.29025	−	5.36373i	−0.333715	−	0.192671i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.25661	+	2.17651i	−0.0450227	+	0.0779816i
$780$		0			0
$781$	1.96475	+	3.40305i	0.0703044	+	0.121771i
$782$		0			0
$783$	−28.5540			−1.02044
$784$		0			0
$785$			21.7400i			0.775935i
$786$		0			0
$787$	8.73934	−	5.04566i	0.311524	−	0.179858i	−0.336084	−	0.941832i	$-0.609103\pi$
$787$	8.73934	−	5.04566i	0.311524	−	0.179858i	0.647608	+	0.761974i	$0.275769\pi$
$788$		0			0
$789$	−3.89787	+	6.75131i	−0.138768	+	0.240353i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	49.9256	+	0.0690217i	1.77291	+	0.00245103i
$794$		0			0
$795$	3.69414	−	2.13282i	0.131018	−	0.0756432i
$796$		0			0
$797$	−11.2735			−0.399329			−0.199665	−	0.979864i	$-0.563985\pi$
$797$	−11.2735			−0.399329			−0.199665	+	0.979864i	$0.563985\pi$
$798$		0			0
$799$			50.0217i			1.76964i
$800$		0			0
$801$	13.6667	−	7.89048i	0.482889	−	0.278796i
$802$		0			0
$803$	1.64790	−	2.85424i	0.0581530	−	0.100724i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.533941	+	0.924813i	−0.0187956	+	0.0325550i
$808$		0			0
$809$	−8.71180	−	15.0893i	−0.306290	−	0.530511i	0.671257	−	0.741224i	$-0.265755\pi$
$809$	−8.71180	−	15.0893i	−0.306290	−	0.530511i	−0.977548	+	0.210714i	$0.932421\pi$
$810$		0			0
$811$		−	35.9555i		−	1.26257i	−0.775552	−	0.631284i	$-0.782528\pi$
$811$		−	35.9555i		−	1.26257i	0.775552	−	0.631284i	$-0.217472\pi$
$812$		0			0
$813$		−	12.7132i		−	0.445871i
$814$		0			0
$815$	−10.3451	−	17.9182i	−0.362373	−	0.627648i
$816$		0			0
$817$	1.23289	+	0.711808i	0.0431333	+	0.0249030i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.0928	−	7.55913i	−0.456942	−	0.263816i	0.253816	−	0.967253i	$-0.418314\pi$
$821$	−13.0928	−	7.55913i	−0.456942	−	0.263816i	−0.710758	+	0.703437i	$0.751648\pi$
$822$		0			0
$823$	−21.6167	−	37.4413i	−0.753512	−	1.30512i	−0.946111	−	0.323843i	$-0.895025\pi$
$823$	−21.6167	−	37.4413i	−0.753512	−	1.30512i	0.192599	−	0.981278i	$-0.438308\pi$
$824$		0			0
$825$			3.78325i			0.131716i
$826$		0			0
$827$			50.4513i			1.75436i	0.480158	+	0.877182i	$0.340579\pi$
$827$			50.4513i			1.75436i	−0.480158	+	0.877182i	$0.659421\pi$
$828$		0			0
$829$	−0.898637	−	1.55649i	−0.0312110	−	0.0540590i	0.849998	−	0.526786i	$-0.176603\pi$
$829$	−0.898637	−	1.55649i	−0.0312110	−	0.0540590i	−0.881209	+	0.472727i	$0.843270\pi$
$830$		0			0
$831$	18.0148	−	31.2026i	0.624927	−	1.08241i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−21.9850	+	38.0792i	−0.760823	+	1.31778i
$836$		0			0
$837$	−18.3646	+	10.6028i	−0.634772	+	0.366486i
$838$		0			0
$839$		−	4.72104i		−	0.162988i	−0.996674	−	0.0814942i	$-0.974031\pi$
$839$		−	4.72104i		−	0.162988i	0.996674	−	0.0814942i	$-0.0259692\pi$
$840$		0			0
$841$	−2.97220			−0.102490
$842$		0			0
$843$	4.52894	−	2.61479i	0.155985	−	0.0900580i
$844$		0			0
$845$	−31.5561	+	18.1028i	−1.08556	+	0.622755i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−19.2489	+	33.3401i	−0.660620	+	1.14423i
$850$		0			0
$851$	20.5965	−	11.8914i	0.706040	−	0.407633i
$852$		0			0
$853$			48.8428i			1.67234i	0.548467	+	0.836172i	$0.315212\pi$
$853$			48.8428i			1.67234i	−0.548467	+	0.836172i	$0.684788\pi$
$854$		0			0
$855$	9.42069			0.322181
$856$		0			0
$857$	−7.49820	−	12.9873i	−0.256134	−	0.443636i	0.709069	−	0.705139i	$-0.249115\pi$
$857$	−7.49820	−	12.9873i	−0.256134	−	0.443636i	−0.965203	+	0.261502i	$0.915782\pi$
$858$		0			0
$859$	16.5232	−	28.6190i	0.563764	−	0.976468i	−0.433399	−	0.901202i	$-0.642686\pi$
$859$	16.5232	−	28.6190i	0.563764	−	0.976468i	0.997163	−	0.0752662i	$-0.0239807\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40.8004	−	23.5561i	−1.38886	−	0.801859i	−0.395674	−	0.918391i	$-0.629489\pi$
$863$	−40.8004	−	23.5561i	−1.38886	−	0.801859i	−0.993187	+	0.116532i	$0.962822\pi$
$864$		0			0
$865$	1.00718	−	0.581498i	0.0342453	−	0.0197715i
$866$		0			0
$867$	−40.6080			−1.37912
$868$		0			0
$869$			7.57367i			0.256919i
$870$		0			0
$871$	−42.9970	−	24.9037i	−1.45690	−	0.843828i
$872$		0			0
$873$	−9.88384	−	5.70644i	−0.334517	−	0.193134i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.84222	+	3.37301i	0.197278	+	0.113898i	0.595385	−	0.803441i	$-0.297000\pi$
$877$	5.84222	+	3.37301i	0.197278	+	0.113898i	−0.398107	+	0.917339i	$0.630333\pi$
$878$		0			0
$879$	−33.3955	+	19.2809i	−1.12640	+	0.650329i
$880$		0			0
$881$	22.5679			0.760333			0.380166	−	0.924918i	$-0.375867\pi$
$881$	22.5679			0.760333			0.380166	+	0.924918i	$0.375867\pi$
$882$		0			0
$883$	−19.2628			−0.648245			−0.324122	−	0.946015i	$-0.605069\pi$
$883$	−19.2628			−0.648245			−0.324122	+	0.946015i	$0.605069\pi$
$884$		0			0
$885$	21.5824	+	37.3818i	0.725484	+	1.25657i
$886$		0			0
$887$	0.426329	−	0.738424i	0.0143147	−	0.0247938i	−0.858779	−	0.512346i	$-0.828777\pi$
$887$	0.426329	−	0.738424i	0.0143147	−	0.0247938i	0.873094	+	0.487552i	$0.162110\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.91679	+	1.68401i	0.0977160	+	0.0564164i
$892$		0			0
$893$	9.12417	+	15.8035i	0.305329	+	0.528845i
$894$		0			0
$895$		−	10.9361i		−	0.365555i
$896$		0			0
$897$	−8.91378	−	15.4885i	−0.297623	−	0.517147i
$898$		0			0
$899$	16.7398	−	9.66473i	0.558304	−	0.322337i
$900$		0			0
$901$	4.09833	−	7.09852i	0.136535	−	0.236486i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.6124	+	6.70441i	0.386009	+	0.222862i
$906$		0			0
$907$	−23.3797	−	40.4948i	−0.776310	−	1.34461i	−0.934055	−	0.357129i	$-0.883756\pi$
$907$	−23.3797	−	40.4948i	−0.776310	−	1.34461i	0.157745	−	0.987480i	$-0.449578\pi$
$908$		0			0
$909$	−11.1019			−0.368226
$910$		0			0
$911$	−33.7415			−1.11791			−0.558954	−	0.829199i	$-0.688797\pi$
$911$	−33.7415			−1.11791			−0.558954	+	0.829199i	$0.688797\pi$
$912$		0			0
$913$	−8.58655	−	14.8723i	−0.284173	−	0.492203i
$914$		0			0
$915$	−43.4121	−	25.0640i	−1.43516	−	0.828589i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	11.7170	−	20.2945i	0.386509	−	0.669453i	−0.605468	−	0.795869i	$-0.707014\pi$
$919$	11.7170	−	20.2945i	0.386509	−	0.669453i	0.991977	+	0.126416i	$0.0403475\pi$
$920$		0			0
$921$	20.8298	−	12.0261i	0.686364	−	0.396272i
$922$		0			0
$923$	11.8885	−	6.84191i	0.391314	−	0.225204i
$924$		0			0
$925$			17.5754i			0.577876i
$926$		0			0
$927$	0.345855	+	0.599038i	0.0113594	+	0.0196750i
$928$		0			0
$929$	−9.51123	−	5.49131i	−0.312053	−	0.180164i	0.335792	−	0.941936i	$-0.390996\pi$
$929$	−9.51123	−	5.49131i	−0.312053	−	0.180164i	−0.647845	+	0.761772i	$0.724330\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	10.2920	−	17.8264i	0.336947	−	0.583609i
$934$		0			0
$935$	10.0538	+	17.4137i	0.328795	+	0.569489i
$936$		0			0
$937$	47.5028			1.55185			0.775924	−	0.630826i	$-0.217284\pi$
$937$	47.5028			1.55185			0.775924	+	0.630826i	$0.217284\pi$
$938$		0			0
$939$	2.32302			0.0758090
$940$		0			0
$941$	−7.00541	+	4.04458i	−0.228370	+	0.131849i	−0.609820	−	0.792540i	$-0.708758\pi$
$941$	−7.00541	+	4.04458i	−0.228370	+	0.131849i	0.381450	+	0.924390i	$0.375425\pi$
$942$		0			0
$943$	3.28600	+	1.89717i	0.107007	+	0.0617804i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.2176	−	9.36323i	−0.527001	−	0.304264i	0.212793	−	0.977097i	$-0.431744\pi$
$947$	−16.2176	−	9.36323i	−0.527001	−	0.304264i	−0.739794	+	0.672833i	$0.765077\pi$
$948$		0			0
$949$	−9.95530	−	5.76606i	−0.323163	−	0.187174i
$950$		0			0
$951$		−	20.7382i		−	0.672482i
$952$		0			0
$953$	47.2451			1.53042			0.765209	−	0.643781i	$-0.222635\pi$
$953$	47.2451			1.53042			0.765209	+	0.643781i	$0.222635\pi$
$954$		0			0
$955$	20.9128	−	12.0740i	0.676723	−	0.390706i
$956$		0			0
$957$	−5.90362	−	3.40846i	−0.190837	−	0.110180i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−8.32252	+	14.4150i	−0.268468	+	0.465001i
$962$		0			0
$963$	6.25806	+	10.8393i	0.201663	+	0.349291i
$964$		0			0
$965$	−68.4320			−2.20290
$966$		0			0
$967$			39.7889i			1.27952i	0.768573	+	0.639762i	$0.220967\pi$
$967$			39.7889i			1.27952i	−0.768573	+	0.639762i	$0.779033\pi$
$968$		0			0
$969$	−19.7773	+	11.4184i	−0.635339	+	0.366813i
$970$		0			0
$971$	−5.00663	+	8.67174i	−0.160670	+	0.278289i	−0.935109	−	0.354359i	$-0.884699\pi$
$971$	−5.00663	+	8.67174i	−0.160670	+	0.278289i	0.774439	+	0.632649i	$0.218032\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	13.2061	+	0.0182573i	0.422935	+	0.000584703i
$976$		0			0
$977$	−51.0164	+	29.4543i	−1.63216	+	0.942328i	−0.648734	+	0.761015i	$0.724701\pi$
$977$	−51.0164	+	29.4543i	−1.63216	+	0.942328i	−0.983425	+	0.181313i	$0.941965\pi$
$978$		0			0
$979$	12.2879			0.392722
$980$		0			0
$981$			18.1549i			0.579640i
$982$		0			0
$983$	−4.46527	+	2.57802i	−0.142420	+	0.0822262i	−0.569517	−	0.821980i	$-0.692870\pi$
$983$	−4.46527	+	2.57802i	−0.142420	+	0.0822262i	0.427097	+	0.904206i	$0.359536\pi$
$984$		0			0
$985$	−9.99229	+	17.3071i	−0.318381	+	0.551452i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.07466	−	1.86136i	0.0341721	−	0.0591878i
$990$		0			0
$991$	31.3453	+	54.2916i	0.995715	+	1.72463i	0.577941	+	0.816078i	$0.303856\pi$
$991$	31.3453	+	54.2916i	0.995715	+	1.72463i	0.417774	+	0.908551i	$0.362810\pi$
$992$		0			0
$993$			8.81982i			0.279889i
$994$		0			0
$995$			2.80640i			0.0889687i
$996$		0			0
$997$	7.06884	+	12.2436i	0.223872	+	0.387758i	0.955981	−	0.293430i	$-0.0947968\pi$
$997$	7.06884	+	12.2436i	0.223872	+	0.387758i	−0.732108	+	0.681188i	$0.761463\pi$
$998$		0			0
$999$	30.0877	+	17.3712i	0.951934	+	0.549600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.y.f.961.6		16
7.2	even	3		364.2.g.a.337.3	✓	8
7.3	odd	6		2548.2.y.e.753.4		16
7.4	even	3	inner	2548.2.y.f.753.5		16
7.5	odd	6		2548.2.g.g.2157.6		8
7.6	odd	2		2548.2.y.e.961.3		16
13.12	even	2	inner	2548.2.y.f.961.5		16
21.2	odd	6		3276.2.e.f.2521.8		8
28.23	odd	6		1456.2.k.d.337.5		8
91.12	odd	6		2548.2.g.g.2157.5		8
91.25	even	6	inner	2548.2.y.f.753.6		16
91.38	odd	6		2548.2.y.e.753.3		16
91.44	odd	12		4732.2.a.o.1.2		4
91.51	even	6		364.2.g.a.337.4	yes	8
91.86	odd	12		4732.2.a.p.1.2		4
91.90	odd	2		2548.2.y.e.961.4		16
273.233	odd	6		3276.2.e.f.2521.1		8
364.51	odd	6		1456.2.k.d.337.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.g.a.337.3	✓	8	7.2	even	3
364.2.g.a.337.4	yes	8	91.51	even	6
1456.2.k.d.337.5		8	28.23	odd	6
1456.2.k.d.337.6		8	364.51	odd	6
2548.2.g.g.2157.5		8	91.12	odd	6
2548.2.g.g.2157.6		8	7.5	odd	6
2548.2.y.e.753.3		16	91.38	odd	6
2548.2.y.e.753.4		16	7.3	odd	6
2548.2.y.e.961.3		16	7.6	odd	2
2548.2.y.e.961.4		16	91.90	odd	2
2548.2.y.f.753.5		16	7.4	even	3	inner
2548.2.y.f.753.6		16	91.25	even	6	inner
2548.2.y.f.961.5		16	13.12	even	2	inner
2548.2.y.f.961.6		16	1.1	even	1	trivial
3276.2.e.f.2521.1		8	273.233	odd	6
3276.2.e.f.2521.8		8	21.2	odd	6
4732.2.a.o.1.2		4	91.44	odd	12
4732.2.a.p.1.2		4	91.86	odd	12

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.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.646813 + 1.12031i) q^{3} +(2.42353 + 1.39923i) q^{5} +(0.663266 - 1.14881i) q^{9} +(0.894522 - 0.516453i) q^{11} +(-1.79846 - 3.12499i) q^{13} +3.62016i q^{15} +(3.47818 + 6.02438i) q^{17} +(2.19774 + 1.26887i) q^{19} +(1.91568 - 3.31806i) q^{23} +(1.41568 + 2.45203i) q^{25} +5.59691 q^{27} -5.10175 q^{29} +(-3.28119 + 1.89440i) q^{31} +(1.15718 + 0.668097i) q^{33} +(5.37577 + 3.10370i) q^{37} +(2.33770 - 4.03612i) q^{39} +0.990338i q^{41} +0.560979 q^{43} +(3.21489 - 1.85612i) q^{45} +(6.22741 + 3.59540i) q^{47} +(-4.49946 + 7.79329i) q^{51} +(-0.589150 - 1.02044i) q^{53} +2.89054 q^{55} +3.28288i q^{57} +(10.3260 - 5.96172i) q^{59} +(-6.92345 + 11.9918i) q^{61} +(0.0139493 - 10.0900i) q^{65} +(11.9348 - 6.89054i) q^{67} +4.95635 q^{69} +3.80432i q^{71} +(2.76331 - 1.59540i) q^{73} +(-1.83136 + 3.17201i) q^{75} +(-3.66620 + 6.35004i) q^{79} +(1.63036 + 2.82387i) q^{81} -16.6260i q^{83} +19.4670i q^{85} +(-3.29988 - 5.71555i) q^{87} +(10.3026 + 5.94820i) q^{89} +(-4.24464 - 2.45064i) q^{93} +(3.55087 + 6.15029i) q^{95} -8.60355i q^{97} -1.37018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} + 4 q^{13} - 4 q^{17} + 6 q^{23} - 2 q^{25} + 24 q^{27} - 4 q^{29} - 12 q^{43} + 8 q^{51} - 22 q^{53} - 40 q^{55} - 8 q^{61} + 6 q^{65} - 40 q^{69} + 20 q^{75} + 26 q^{79} + 24 q^{81} + 32 q^{87}+ \cdots + 18 q^{95}+O(q^{100}) \) 16 * q - 8 * q^9 + 4 * q^13 - 4 * q^17 + 6 * q^23 - 2 * q^25 + 24 * q^27 - 4 * q^29 - 12 * q^43 + 8 * q^51 - 22 * q^53 - 40 * q^55 - 8 * q^61 + 6 * q^65 - 40 * q^69 + 20 * q^75 + 26 * q^79 + 24 * q^81 + 32 * q^87 + 18 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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