LMFDB - Embedded newform 2548.2.y.f.961.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(753,2548)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			961.5
Root			$-1.12031 - 0.646813i$ of defining polynomial
Character	$\chi$	$=$	2548.961
Dual form			2548.2.y.f.753.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.646813 + 1.12031i) q^{3} +(-2.42353 - 1.39923i) q^{5} +(0.663266 - 1.14881i) q^{9} +(-0.894522 + 0.516453i) q^{11} +(-1.79846 + 3.12499i) q^{13} -3.62016i q^{15} +(3.47818 + 6.02438i) q^{17} +(-2.19774 - 1.26887i) q^{19} +(1.91568 - 3.31806i) q^{23} +(1.41568 + 2.45203i) q^{25} +5.59691 q^{27} -5.10175 q^{29} +(3.28119 - 1.89440i) q^{31} +(-1.15718 - 0.668097i) q^{33} +(-5.37577 - 3.10370i) q^{37} +(-4.66423 + 0.00644825i) q^{39} -0.990338i q^{41} +0.560979 q^{43} +(-3.21489 + 1.85612i) q^{45} +(-6.22741 - 3.59540i) q^{47} +(-4.49946 + 7.79329i) q^{51} +(-0.589150 - 1.02044i) q^{53} +2.89054 q^{55} -3.28288i q^{57} +(-10.3260 + 5.96172i) q^{59} +(-6.92345 + 11.9918i) q^{61} +(8.73120 - 5.05707i) q^{65} +(-11.9348 + 6.89054i) q^{67} +4.95635 q^{69} -3.80432i q^{71} +(-2.76331 + 1.59540i) q^{73} +(-1.83136 + 3.17201i) q^{75} +(-3.66620 + 6.35004i) q^{79} +(1.63036 + 2.82387i) q^{81} +16.6260i q^{83} -19.4670i q^{85} +(-3.29988 - 5.71555i) q^{87} +(-10.3026 - 5.94820i) q^{89} +(4.24464 + 2.45064i) q^{93} +(3.55087 + 6.15029i) q^{95} +8.60355i q^{97} +1.37018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.151909	−	0.988395i	$-0.548542\pi$
$5$	−2.42353	−	1.39923i	−1.08384	−	0.625754i	−0.931929	+	0.362641i	$0.881875\pi$
$6$		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	−0.628755	−	0.777603i	$-0.716435\pi$
$11$	−0.894522	+	0.516453i	−0.269709	+	0.155716i	0.359047	+	0.933320i	$0.383102\pi$
$12$		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	0.226248	−	0.974070i	$-0.427354\pi$
$19$	−2.19774	−	1.26887i	−0.504197	−	0.291098i	−0.730445	+	0.682971i	$0.760687\pi$
$20$		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	−0.175509	−	0.984478i	$-0.556157\pi$
$31$	3.28119	−	1.89440i	0.589320	−	0.340244i	0.764828	+	0.644234i	$0.222824\pi$
$32$		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	−0.0118717	−	0.999930i	$-0.503779\pi$
$37$	−5.37577	−	3.10370i	−0.883772	−	0.510246i	−0.871900	+	0.489684i	$0.837112\pi$
$38$		0			0
$39$	−4.66423	+	0.00644825i	−0.746875	+	0.00103255i
$40$		0			0
$41$		−	0.990338i		−	0.154665i	−0.997005	−	0.0773324i	$-0.975360\pi$
$41$		−	0.990338i		−	0.154665i	0.997005	−	0.0773324i	$-0.0246403\pi$
$42$		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	−0.0284580	−	0.999595i	$-0.509060\pi$
$47$	−6.22741	−	3.59540i	−0.908362	−	0.524443i	−0.879904	+	0.475152i	$0.842393\pi$
$48$		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	−0.987440	−	0.157996i	$-0.949497\pi$
$59$	−10.3260	+	5.96172i	−1.34433	+	0.776150i	−0.356892	+	0.934146i	$0.616163\pi$
$60$		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
$65$	8.73120	−	5.05707i	1.08297	−	0.627252i
$66$		0			0
$67$	−11.9348	+	6.89054i	−1.45806	+	0.841813i	−0.998916	−	0.0465465i	$-0.985178\pi$
$67$	−11.9348	+	6.89054i	−1.45806	+	0.841813i	−0.459148	+	0.888360i	$0.651845\pi$
$68$		0			0
$69$	4.95635			0.596674
$70$		0			0
$71$		−	3.80432i		−	0.451490i	−0.974186	−	0.225745i	$-0.927518\pi$
$71$		−	3.80432i		−	0.451490i	0.974186	−	0.225745i	$-0.0724816\pi$
$72$		0			0
$73$	−2.76331	+	1.59540i	−0.323421	+	0.186727i	−0.652917	−	0.757430i	$-0.726455\pi$
$73$	−2.76331	+	1.59540i	−0.323421	+	0.186727i	0.329495	+	0.944157i	$0.393121\pi$
$74$		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	$0.365829\pi$
$83$			16.6260i			1.82494i	−0.409140	+	0.912472i	$0.634171\pi$
$84$		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	−0.157945	−	0.987448i	$-0.550487\pi$
$89$	−10.3026	−	5.94820i	−1.09207	−	0.630508i	−0.934127	+	0.356940i	$0.883820\pi$
$90$		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	$0.143881\pi$
$97$			8.60355i			0.873558i	−0.899569	+	0.436779i	$0.856119\pi$
$98$		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	0.190003	−	0.981784i	$-0.439150\pi$
$109$	11.8524	−	6.84298i	1.13525	−	0.655439i	0.945251	+	0.326345i	$0.105817\pi$
$110$		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
$117$	2.39716	+	4.13878i	0.221618	+	0.382631i
$118$		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	0.0565956	−	0.998397i	$-0.481975\pi$
$137$	11.1140	−	6.41665i	0.949531	−	0.548212i	0.892935	+	0.450185i	$0.148642\pi$
$138$		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
$143$	−0.00514865	−	3.72419i	−0.000430552	−	0.311432i
$144$		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	0.102429	−	0.994740i	$-0.467338\pi$
$149$	−8.64012	−	4.98838i	−0.707827	−	0.408664i	−0.810256	+	0.586076i	$0.800672\pi$
$150$		0			0
$151$	−12.1714	+	7.02715i	−0.990493	+	0.571861i	−0.905422	−	0.424513i	$-0.860445\pi$
$151$	−12.1714	+	7.02715i	−0.990493	+	0.571861i	−0.0850714	+	0.996375i	$0.527112\pi$
$152$		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	0.729338	−	0.684153i	$-0.239828\pi$
$163$	6.40289	+	3.69671i	0.501513	+	0.289549i	−0.227825	+	0.973702i	$0.573161\pi$
$164$		0			0
$165$	1.86964	+	3.23831i	0.145551	+	0.252102i
$166$		0			0
$167$		−	15.7122i		−	1.21585i	−0.793995	−	0.607925i	$-0.792002\pi$
$167$		−	15.7122i		−	1.21585i	0.793995	−	0.607925i	$-0.207998\pi$
$168$		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	$-0.324142\pi$
$193$	21.1773	−	12.2267i	1.52438	−	0.880100i	0.999583	−	0.0288702i	$-0.00919095\pi$
$194$		0			0
$195$	11.3129	+	6.51070i	0.810137	+	0.466241i
$196$		0			0
$197$		−	7.14128i		−	0.508795i	−0.967100	−	0.254398i	$-0.918123\pi$
$197$		−	7.14128i		−	0.508795i	0.967100	−	0.254398i	$-0.0818772\pi$
$198$		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
$221$	−25.0815	+	0.0346748i	−1.68716	+	0.00233248i
$222$		0			0
$223$			17.7540i			1.18890i	0.804133	+	0.594449i	$0.202630\pi$
$223$			17.7540i			1.18890i	−0.804133	+	0.594449i	$0.797370\pi$
$224$		0			0
$225$	3.75589			0.250393
$226$		0			0
$227$	15.4391	−	8.91378i	1.02473	−	0.591629i	0.109260	−	0.994013i	$-0.465152\pi$
$227$	15.4391	−	8.91378i	1.02473	−	0.591629i	0.915471	+	0.402385i	$0.131819\pi$
$228$		0			0
$229$	3.64963	+	2.10712i	0.241175	+	0.139242i	0.615716	−	0.787968i	$-0.288867\pi$
$229$	3.64963	+	2.10712i	0.241175	+	0.139242i	−0.374542	+	0.927210i	$0.622200\pi$
$230$		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	$0.0934108\pi$
$239$			8.94385i			0.578530i	−0.957249	+	0.289265i	$0.906589\pi$
$240$		0			0
$241$	−14.7241	+	8.50097i	−0.948464	+	0.547596i	−0.892603	−	0.450843i	$-0.851124\pi$
$241$	−14.7241	+	8.50097i	−0.948464	+	0.547596i	−0.0558604	+	0.998439i	$0.517790\pi$
$242$		0			0
$243$	6.28629	−	10.8882i	0.403266	−	0.698477i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.91775	−	4.58592i	0.503794	−	0.291795i
$248$		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	0.735707	−	0.677300i	$-0.236850\pi$
$271$	8.51092	+	4.91378i	0.517002	+	0.298491i	−0.218705	+	0.975791i	$0.570183\pi$
$272$		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	$0.0384753\pi$
$281$			4.04257i			0.241159i	−0.992704	+	0.120580i	$0.961525\pi$
$282$		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	$-0.663645\pi$
$293$		−	29.8091i		−	1.74147i	0.491755	−	0.870733i	$-0.336355\pi$
$294$		0			0
$295$	33.3673			1.94272
$296$		0			0
$297$	−5.00656	+	2.89054i	−0.290510	+	0.167726i
$298$		0			0
$299$	6.92362	+	11.9539i	0.400403	+	0.691310i
$300$		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	$0.178023\pi$
$307$			18.5928i			1.06115i	−0.847639	+	0.530574i	$0.821977\pi$
$308$		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	0.836347	−	0.548201i	$-0.184687\pi$
$317$	13.8833	+	8.01553i	0.779764	+	0.450197i	−0.0565827	+	0.998398i	$0.518020\pi$
$318$		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
$325$	−10.2086	+	0.0141133i	−0.566272	+	0.000782865i
$326$		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	0.328875	−	0.944374i	$-0.393331\pi$
$331$	−5.90448	−	3.40895i	−0.324540	−	0.187373i	−0.653414	+	0.757001i	$0.726664\pi$
$332$		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	$-0.928936\pi$
$349$		−	8.27233i		−	0.442808i	0.975182	−	0.221404i	$-0.0710639\pi$
$350$		0			0
$351$	−10.0658	+	17.4903i	−0.537273	+	0.933563i
$352$		0			0
$353$	14.1949	−	8.19541i	0.755516	−	0.436197i	−0.0721674	−	0.997393i	$-0.522992\pi$
$353$	14.1949	−	8.19541i	0.755516	−	0.436197i	0.827684	+	0.561195i	$0.189658\pi$
$354$		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	0.999416	−	0.0341658i	$-0.0108774\pi$
$359$	27.8437	+	16.0756i	1.46954	+	0.848437i	0.470120	+	0.882603i	$0.344211\pi$
$360$		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	$0.284176\pi$
$379$			30.3236i			1.55762i	−0.627261	+	0.778809i	$0.715824\pi$
$380$		0			0
$381$	−7.07168	−	12.2485i	−0.362293	−	0.627510i
$382$		0			0
$383$	−12.1411	−	7.00966i	−0.620381	−	0.358177i	0.156636	−	0.987656i	$-0.449935\pi$
$383$	−12.1411	−	7.00966i	−0.620381	−	0.358177i	−0.777017	+	0.629479i	$0.783268\pi$
$384$		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	0.144688	−	0.989477i	$-0.453782\pi$
$397$	−12.7495	−	7.36095i	−0.639881	−	0.369436i	−0.784569	+	0.620042i	$0.787116\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	17.0098	+	9.82062i	0.849429	+	0.490418i	0.860458	−	0.509521i	$-0.170177\pi$
$401$	17.0098	+	9.82062i	0.849429	+	0.490418i	−0.0110289	+	0.999939i	$0.503511\pi$
$402$		0			0
$403$	0.0188858	+	13.6607i	0.000940766	+	0.680487i
$404$		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	−0.917722	−	0.397223i	$-0.869974\pi$
$409$	−20.8826	+	12.0566i	−1.03258	+	0.596160i	−0.114856	+	0.993382i	$0.536641\pi$
$410$		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	$0.154311\pi$
$421$			19.1237i			0.932033i	−0.884776	+	0.466016i	$0.845689\pi$
$422$		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
$429$	4.16893	−	2.41462i	0.201278	−	0.116579i
$430$		0			0
$431$	−7.68673	+	4.43794i	−0.370257	+	0.213768i	−0.673571	−	0.739123i	$-0.735240\pi$
$431$	−7.68673	+	4.43794i	−0.370257	+	0.213768i	0.303314	+	0.952891i	$0.401907\pi$
$432$		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	$0.250826\pi$
$449$			30.0443i			1.41788i	−0.705269	+	0.708940i	$0.749174\pi$
$450$		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	0.951449	−	0.307807i	$-0.0995952\pi$
$457$	24.8109	+	14.3246i	1.16060	+	0.670075i	0.209156	+	0.977882i	$0.432929\pi$
$458$		0			0
$459$	19.4670	+	33.7179i	0.908644	+	1.57382i
$460$		0			0
$461$		−	0.922363i		−	0.0429587i	−0.999769	−	0.0214794i	$-0.993162\pi$
$461$		−	0.922363i		−	0.0429587i	0.999769	−	0.0214794i	$-0.00683762\pi$
$462$		0			0
$463$			26.0929i			1.21264i	0.795220	+	0.606321i	$0.207355\pi$
$463$			26.0929i			1.21264i	−0.795220	+	0.606321i	$0.792645\pi$
$464$		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	−0.780356	−	0.625336i	$-0.784962\pi$
$479$	−13.7658	+	7.94771i	−0.628977	+	0.363140i	0.151379	+	0.988476i	$0.451629\pi$
$480$		0			0
$481$	19.3671	−	11.2174i	0.883066	−	0.511467i
$482$		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	−0.498329	−	0.866988i	$-0.666053\pi$
$487$	0.0737279	−	0.0425668i	0.00334093	−	0.00192889i	0.501670	+	0.865059i	$0.332719\pi$
$488$		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	−0.172973	−	0.984927i	$-0.555337\pi$
$499$	−24.8498	−	14.3470i	−1.11243	−	0.642262i	−0.939458	+	0.342664i	$0.888671\pi$
$500$		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
$507$	8.36827	−	14.5873i	0.371648	−	0.647843i
$508$		0			0
$509$	−22.5979	−	13.0469i	−1.00164	−	0.578295i	−0.0929037	−	0.995675i	$-0.529615\pi$
$509$	−22.5979	−	13.0469i	−1.00164	−	0.578295i	−0.908732	+	0.417381i	$0.862948\pi$
$510$		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	0.650245	−	0.759724i	$-0.274666\pi$
$541$	7.38318	+	4.26268i	0.317428	+	0.183267i	−0.332818	+	0.942991i	$0.607999\pi$
$542$		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	$-0.304784\pi$
$557$	37.0897	−	21.4137i	1.57154	−	0.907329i	0.995981	−	0.0895693i	$-0.0285491\pi$
$558$		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	−0.878803	−	0.477185i	$-0.841657\pi$
$577$	−21.7376	+	12.5502i	−0.904950	+	0.522473i	−0.0261471	+	0.999658i	$0.508324\pi$
$578$		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
$585$	−0.0185042	−	13.3847i	−0.000765053	−	0.553388i
$586$		0			0
$587$			28.2963i			1.16791i	0.811784	+	0.583957i	$0.198497\pi$
$587$			28.2963i			1.16791i	−0.811784	+	0.583957i	$0.801503\pi$
$588$		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	0.710991	−	0.703201i	$-0.248247\pi$
$593$	11.1408	+	6.43213i	0.457497	+	0.264136i	−0.253494	+	0.967337i	$0.581580\pi$
$594$		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
$611$	22.4353	−	12.9944i	0.907636	−	0.525698i
$612$		0			0
$613$	3.66910	−	2.11836i	0.148194	−	0.0855596i	−0.424070	−	0.905630i	$-0.639399\pi$
$613$	3.66910	−	2.11836i	0.148194	−	0.0855596i	0.572263	+	0.820070i	$0.306066\pi$
$614$		0			0
$615$	−3.58518			−0.144568
$616$		0			0
$617$			14.0193i			0.564397i	0.959356	+	0.282198i	$0.0910636\pi$
$617$			14.0193i			0.564397i	−0.959356	+	0.282198i	$0.908936\pi$
$618$		0			0
$619$	20.6520	−	11.9234i	0.830074	−	0.479244i	−0.0238037	−	0.999717i	$-0.507578\pi$
$619$	20.6520	−	11.9234i	0.830074	−	0.479244i	0.853878	+	0.520473i	$0.174244\pi$
$620$		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	$0.0456877\pi$
$631$			7.18624i			0.286080i	−0.989717	+	0.143040i	$0.954312\pi$
$632$		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	$-0.810691\pi$
$643$		−	28.4148i		−	1.12057i	0.828300	−	0.560286i	$-0.189309\pi$
$644$		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	0.369403	−	0.929269i	$-0.379562\pi$
$661$	34.9366	−	20.1706i	1.35888	−	0.784547i	0.989472	+	0.144722i	$0.0462288\pi$
$662$		0			0
$663$	−16.2619	−	28.0767i	−0.631558	−	1.09041i
$664$		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	−0.592933	−	0.805252i	$-0.702030\pi$
$683$	−5.01860	+	2.89749i	−0.192031	+	0.110869i	0.400902	+	0.916121i	$0.368697\pi$
$684$		0			0
$685$	−35.9135			−1.37218
$686$		0			0
$687$			5.45164i			0.207993i
$688$		0			0
$689$	4.24842	−	0.00587339i	0.161852	−	0.000223758i
$690$		0			0
$691$	23.4877	+	13.5606i	0.893515	+	0.515871i	0.875091	−	0.483959i	$-0.160802\pi$
$691$	23.4877	+	13.5606i	0.893515	+	0.515871i	0.0184246	+	0.999830i	$0.494135\pi$
$692$		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	$-0.949455\pi$
$709$	−43.0844	−	24.8748i	−1.61807	−	0.934193i	−0.630651	−	0.776067i	$-0.717212\pi$
$710$		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	0.169294	−	0.985566i	$-0.445851\pi$
$733$	−16.2331	−	9.37219i	−0.599584	−	0.346170i	−0.768878	+	0.639396i	$0.779185\pi$
$734$		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	−0.667451	−	0.744654i	$-0.732615\pi$
$739$	−9.68550	+	5.59192i	−0.356287	+	0.205702i	0.311164	+	0.950356i	$0.399281\pi$
$740$		0			0
$741$	10.2590	+	5.90412i	0.376873	+	0.216893i
$742$		0			0
$743$			32.7986i			1.20326i	0.798774	+	0.601632i	$0.205482\pi$
$743$			32.7986i			1.20326i	−0.798774	+	0.601632i	$0.794518\pi$
$744$		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	−0.0440211	−	0.999031i	$-0.514017\pi$
$761$	−25.6888	−	14.8314i	−0.931218	−	0.537639i	−0.887196	+	0.461392i	$0.847350\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−22.3639	−	12.9118i	−0.808570	−	0.466828i
$766$		0			0
$767$	−0.0594340	−	42.9906i	−0.00214604	−	1.55230i
$768$		0			0
$769$		−	40.8488i		−	1.47305i	−0.676412	−	0.736523i	$-0.736466\pi$
$769$		−	40.8488i		−	1.47305i	0.676412	−	0.736523i	$-0.263534\pi$
$770$		0			0
$771$	18.9718			0.683251
$772$		0			0
$773$	16.8048	−	9.70226i	0.604427	−	0.348966i	−0.166354	−	0.986066i	$-0.553200\pi$
$773$	16.8048	−	9.70226i	0.604427	−	0.348966i	0.770781	+	0.637100i	$0.219866\pi$
$774$		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	−0.647608	−	0.761974i	$-0.724231\pi$
$787$	−8.73934	+	5.04566i	−0.311524	+	0.179858i	0.336084	+	0.941832i	$0.390897\pi$
$788$		0			0
$789$	−3.89787	+	6.75131i	−0.138768	+	0.240353i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−25.0226	−	43.2024i	−0.888578	−	1.53416i
$794$		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	$0.217472\pi$
$811$			35.9555i			1.26257i	−0.775552	+	0.631284i	$0.782528\pi$
$812$		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	0.710758	−	0.703437i	$-0.248352\pi$
$821$	13.0928	+	7.55913i	0.456942	+	0.263816i	−0.253816	+	0.967253i	$0.581686\pi$
$822$		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	$-0.659421\pi$
$827$		−	50.4513i		−	1.75436i	0.480158	−	0.877182i	$-0.340579\pi$
$828$		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	$0.0259692\pi$
$839$			4.72104i			0.162988i	−0.996674	+	0.0814942i	$0.974031\pi$
$840$		0			0
$841$	−2.97220			−0.102490
$842$		0			0
$843$	−4.52894	+	2.61479i	−0.155985	+	0.0900580i
$844$		0			0
$845$	0.100590	+	36.3798i	0.00346039	+	1.25150i
$846$		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	$-0.684788\pi$
$853$		−	48.8428i		−	1.67234i	0.548467	−	0.836172i	$-0.315212\pi$
$854$		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	0.993187	−	0.116532i	$-0.0371778\pi$
$863$	40.8004	+	23.5561i	1.38886	+	0.801859i	0.395674	+	0.918391i	$0.370511\pi$
$864$		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
$871$	−0.0686936	−	49.6883i	−0.00232759	−	1.68363i
$872$		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	0.398107	−	0.917339i	$-0.369667\pi$
$877$	−5.84222	−	3.37301i	−0.197278	−	0.113898i	−0.595385	+	0.803441i	$0.703000\pi$
$878$		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	0.647845	−	0.761772i	$-0.275670\pi$
$929$	9.51123	+	5.49131i	0.312053	+	0.180164i	−0.335792	+	0.941936i	$0.609004\pi$
$930$		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	−0.381450	−	0.924390i	$-0.624575\pi$
$941$	7.00541	−	4.04458i	0.228370	−	0.131849i	0.609820	+	0.792540i	$0.291242\pi$
$942$		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	0.739794	−	0.672833i	$-0.234923\pi$
$947$	16.2176	+	9.36323i	0.527001	+	0.304264i	−0.212793	+	0.977097i	$0.568256\pi$
$948$		0			0
$949$	−0.0159050	−	11.5046i	−0.000516297	−	0.373454i
$950$		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	$-0.779033\pi$
$967$		−	39.7889i		−	1.27952i	0.768573	−	0.639762i	$-0.220967\pi$
$968$		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
$975$	−6.61888	−	11.4277i	−0.211974	−	0.365980i
$976$		0			0
$977$	51.0164	−	29.4543i	1.63216	−	0.942328i	0.648734	−	0.761015i	$-0.275299\pi$
$977$	51.0164	−	29.4543i	1.63216	−	0.942328i	0.983425	−	0.181313i	$-0.0580347\pi$
$978$		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	−0.427097	−	0.904206i	$-0.640464\pi$
$983$	4.46527	−	2.57802i	0.142420	−	0.0822262i	0.569517	+	0.821980i	$0.307130\pi$
$984$		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.961.5		16
7.2	even	3		364.2.g.a.337.4	yes	8
7.3	odd	6		2548.2.y.e.753.3		16
7.4	even	3	inner	2548.2.y.f.753.6		16
7.5	odd	6		2548.2.g.g.2157.5		8
7.6	odd	2		2548.2.y.e.961.4		16
13.12	even	2	inner	2548.2.y.f.961.6		16
21.2	odd	6		3276.2.e.f.2521.1		8
28.23	odd	6		1456.2.k.d.337.6		8
91.12	odd	6		2548.2.g.g.2157.6		8
91.25	even	6	inner	2548.2.y.f.753.5		16
91.38	odd	6		2548.2.y.e.753.4		16
91.44	odd	12		4732.2.a.p.1.2		4
91.51	even	6		364.2.g.a.337.3	✓	8
91.86	odd	12		4732.2.a.o.1.2		4
91.90	odd	2		2548.2.y.e.961.3		16
273.233	odd	6		3276.2.e.f.2521.8		8
364.51	odd	6		1456.2.k.d.337.5		8

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

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)

\(f(q)\)	\(=\)	\(q+(0.646813 + 1.12031i) q^{3} +(-2.42353 - 1.39923i) q^{5} +(0.663266 - 1.14881i) q^{9} +(-0.894522 + 0.516453i) q^{11} +(-1.79846 + 3.12499i) q^{13} -3.62016i q^{15} +(3.47818 + 6.02438i) q^{17} +(-2.19774 - 1.26887i) q^{19} +(1.91568 - 3.31806i) q^{23} +(1.41568 + 2.45203i) q^{25} +5.59691 q^{27} -5.10175 q^{29} +(3.28119 - 1.89440i) q^{31} +(-1.15718 - 0.668097i) q^{33} +(-5.37577 - 3.10370i) q^{37} +(-4.66423 + 0.00644825i) q^{39} -0.990338i q^{41} +0.560979 q^{43} +(-3.21489 + 1.85612i) q^{45} +(-6.22741 - 3.59540i) q^{47} +(-4.49946 + 7.79329i) q^{51} +(-0.589150 - 1.02044i) q^{53} +2.89054 q^{55} -3.28288i q^{57} +(-10.3260 + 5.96172i) q^{59} +(-6.92345 + 11.9918i) q^{61} +(8.73120 - 5.05707i) q^{65} +(-11.9348 + 6.89054i) q^{67} +4.95635 q^{69} -3.80432i q^{71} +(-2.76331 + 1.59540i) q^{73} +(-1.83136 + 3.17201i) q^{75} +(-3.66620 + 6.35004i) q^{79} +(1.63036 + 2.82387i) q^{81} +16.6260i q^{83} -19.4670i q^{85} +(-3.29988 - 5.71555i) q^{87} +(-10.3026 - 5.94820i) q^{89} +(4.24464 + 2.45064i) q^{93} +(3.55087 + 6.15029i) q^{95} +8.60355i q^{97} +1.37018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} + 4 q^{13} - 4 q^{17} + 6 q^{23} - 2 q^{25} + 24 q^{27} - 4 q^{29} - 12 q^{43} + 8 q^{51} - 22 q^{53} - 40 q^{55} - 8 q^{61} + 6 q^{65} - 40 q^{69} + 20 q^{75} + 26 q^{79} + 24 q^{81} + 32 q^{87}+ \cdots + 18 q^{95}+O(q^{100}) \) 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

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Database

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