LMFDB - Embedded newform 2592.2.s.g.1727.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.s (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:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 864)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1727.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2592.1727
Dual form			2592.2.s.g.863.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.34607 + 1.93185i) q^{5} +(3.23205 + 1.86603i) q^{7} +O(q^{10})$	$q+(-3.34607 + 1.93185i) q^{5} +(3.23205 + 1.86603i) q^{7} +(0.517638 - 0.896575i) q^{11} +(-2.23205 - 3.86603i) q^{13} +1.79315i q^{17} +1.73205i q^{19} +(4.38134 + 7.58871i) q^{23} +(4.96410 - 8.59808i) q^{25} +(6.69213 + 3.86370i) q^{29} +(6.46410 - 3.73205i) q^{31} -14.4195 q^{35} +0.464102 q^{37} +(-6.69213 + 3.86370i) q^{41} +(-0.464102 - 0.267949i) q^{43} +(-2.31079 + 4.00240i) q^{47} +(3.46410 + 6.00000i) q^{49} +3.58630i q^{53} +4.00000i q^{55} +(-6.17449 - 10.6945i) q^{59} +(-5.69615 + 9.86603i) q^{61} +(14.9372 + 8.62398i) q^{65} +(-5.42820 + 3.13397i) q^{67} -11.3137 q^{71} -3.92820 q^{73} +(3.34607 - 1.93185i) q^{77} +(4.16025 + 2.40192i) q^{79} +(1.03528 - 1.79315i) q^{83} +(-3.46410 - 6.00000i) q^{85} +1.79315i q^{89} -16.6603i q^{91} +(-3.34607 - 5.79555i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{7}+O(q^{10}) $ 8 * q + 12 * q^7	$ 8 q + 12 q^{7} - 4 q^{13} + 12 q^{25} + 24 q^{31} - 24 q^{37} + 24 q^{43} - 4 q^{61} + 12 q^{67} + 24 q^{73} - 36 q^{79} - 28 q^{97}+O(q^{100}) $ 8 * q + 12 * q^7 - 4 * q^13 + 12 * q^25 + 24 * q^31 - 24 * q^37 + 24 * q^43 - 4 * q^61 + 12 * q^67 + 24 * q^73 - 36 * q^79 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$3$		0			0
$4$		0			0
$5$	−3.34607	+	1.93185i	−1.49641	+	0.863950i	−0.999991	−	0.00413535i	$-0.998684\pi$
$5$	−3.34607	+	1.93185i	−1.49641	+	0.863950i	−0.496414	+	0.868086i	$0.665350\pi$
$6$		0			0
$7$	3.23205	+	1.86603i	1.22160	+	0.705291i	0.965259	−	0.261295i	$-0.0841495\pi$
$7$	3.23205	+	1.86603i	1.22160	+	0.705291i	0.256341	+	0.966586i	$0.417483\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.517638	−	0.896575i	0.156074	−	0.270328i	−0.777376	−	0.629037i	$-0.783450\pi$
$11$	0.517638	−	0.896575i	0.156074	−	0.270328i	0.933449	+	0.358709i	$0.116783\pi$
$12$		0			0
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	−0.989658	−	0.143449i	$-0.954181\pi$
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	0.370598	−	0.928793i	$-0.379153\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.79315i			0.434903i	0.976071	+	0.217451i	$0.0697744\pi$
$17$			1.79315i			0.434903i	−0.976071	+	0.217451i	$0.930226\pi$
$18$		0			0
$19$			1.73205i			0.397360i	0.980064	+	0.198680i	$0.0636654\pi$
$19$			1.73205i			0.397360i	−0.980064	+	0.198680i	$0.936335\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.38134	+	7.58871i	0.913573	+	1.58235i	0.808977	+	0.587840i	$0.200021\pi$
$23$	4.38134	+	7.58871i	0.913573	+	1.58235i	0.104595	+	0.994515i	$0.466645\pi$
$24$		0			0
$25$	4.96410	−	8.59808i	0.992820	−	1.71962i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.69213	+	3.86370i	1.24270	+	0.717472i	0.969643	−	0.244527i	$-0.0786326\pi$
$29$	6.69213	+	3.86370i	1.24270	+	0.717472i	0.273055	+	0.961998i	$0.411966\pi$
$30$		0			0
$31$	6.46410	−	3.73205i	1.16099	−	0.670296i	0.209447	−	0.977820i	$-0.432834\pi$
$31$	6.46410	−	3.73205i	1.16099	−	0.670296i	0.951540	+	0.307524i	$0.0995004\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−14.4195			−2.43735
$36$		0			0
$37$	0.464102			0.0762978			0.0381489	−	0.999272i	$-0.487854\pi$
$37$	0.464102			0.0762978			0.0381489	+	0.999272i	$0.487854\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.69213	+	3.86370i	−1.04514	+	0.603409i	−0.921283	−	0.388892i	$-0.872858\pi$
$41$	−6.69213	+	3.86370i	−1.04514	+	0.603409i	−0.123852	+	0.992301i	$0.539525\pi$
$42$		0			0
$43$	−0.464102	−	0.267949i	−0.0707748	−	0.0408619i	0.464195	−	0.885733i	$-0.346344\pi$
$43$	−0.464102	−	0.267949i	−0.0707748	−	0.0408619i	−0.534970	+	0.844871i	$0.679677\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.31079	+	4.00240i	−0.337063	+	0.583811i	−0.983879	−	0.178836i	$-0.942767\pi$
$47$	−2.31079	+	4.00240i	−0.337063	+	0.583811i	0.646816	+	0.762646i	$0.276100\pi$
$48$		0			0
$49$	3.46410	+	6.00000i	0.494872	+	0.857143i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			3.58630i			0.492616i	0.969192	+	0.246308i	$0.0792175\pi$
$53$			3.58630i			0.492616i	−0.969192	+	0.246308i	$0.920782\pi$
$54$		0			0
$55$			4.00000i			0.539360i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.17449	−	10.6945i	−0.803850	−	1.39231i	−0.917064	−	0.398739i	$-0.869448\pi$
$59$	−6.17449	−	10.6945i	−0.803850	−	1.39231i	0.113214	−	0.993571i	$-0.463885\pi$
$60$		0			0
$61$	−5.69615	+	9.86603i	−0.729318	+	1.26322i	0.227854	+	0.973695i	$0.426829\pi$
$61$	−5.69615	+	9.86603i	−0.729318	+	1.26322i	−0.957172	+	0.289520i	$0.906504\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	14.9372	+	8.62398i	1.85273	+	1.06967i
$66$		0			0
$67$	−5.42820	+	3.13397i	−0.663161	+	0.382876i	−0.793480	−	0.608596i	$-0.791733\pi$
$67$	−5.42820	+	3.13397i	−0.663161	+	0.382876i	0.130320	+	0.991472i	$0.458400\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−11.3137			−1.34269			−0.671345	−	0.741145i	$-0.734283\pi$
$71$	−11.3137			−1.34269			−0.671345	+	0.741145i	$0.734283\pi$
$72$		0			0
$73$	−3.92820			−0.459761			−0.229881	−	0.973219i	$-0.573834\pi$
$73$	−3.92820			−0.459761			−0.229881	+	0.973219i	$0.573834\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.34607	−	1.93185i	0.381320	−	0.220155i
$78$		0			0
$79$	4.16025	+	2.40192i	0.468065	+	0.270238i	0.715429	−	0.698685i	$-0.246231\pi$
$79$	4.16025	+	2.40192i	0.468065	+	0.270238i	−0.247364	+	0.968923i	$0.579564\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.03528	−	1.79315i	0.113636	−	0.196824i	−0.803597	−	0.595173i	$-0.797083\pi$
$83$	1.03528	−	1.79315i	0.113636	−	0.196824i	0.917234	+	0.398349i	$0.130417\pi$
$84$		0			0
$85$	−3.46410	−	6.00000i	−0.375735	−	0.650791i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			1.79315i			0.190074i	0.995474	+	0.0950368i	$0.0302969\pi$
$89$			1.79315i			0.190074i	−0.995474	+	0.0950368i	$0.969703\pi$
$90$		0			0
$91$		−	16.6603i		−	1.74647i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.34607	−	5.79555i	−0.343299	−	0.594611i
$96$		0			0
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.58630	−	2.07055i	−0.356850	−	0.206028i	0.310848	−	0.950460i	$-0.399387\pi$
$101$	−3.58630	−	2.07055i	−0.356850	−	0.206028i	−0.667698	+	0.744432i	$0.732720\pi$
$102$		0			0
$103$	−11.7679	+	6.79423i	−1.15953	+	0.669455i	−0.951191	−	0.308601i	$-0.900139\pi$
$103$	−11.7679	+	6.79423i	−1.15953	+	0.669455i	−0.208339	+	0.978057i	$0.566806\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.2784			−0.993654			−0.496827	−	0.867850i	$-0.665502\pi$
$107$	−10.2784			−0.993654			−0.496827	+	0.867850i	$0.665502\pi$
$108$		0			0
$109$	12.9282			1.23830			0.619149	−	0.785274i	$-0.287478\pi$
$109$	12.9282			1.23830			0.619149	+	0.785274i	$0.287478\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.13922	−	2.96713i	0.483457	−	0.279124i	−0.238399	−	0.971167i	$-0.576623\pi$
$113$	5.13922	−	2.96713i	0.483457	−	0.279124i	0.721856	+	0.692043i	$0.243289\pi$
$114$		0			0
$115$	−29.3205	−	16.9282i	−2.73415	−	1.57856i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.34607	+	5.79555i	−0.306733	+	0.531278i
$120$		0			0
$121$	4.96410	+	8.59808i	0.451282	+	0.781643i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			19.0411i			1.70309i
$126$		0			0
$127$			3.46410i			0.307389i	0.988118	+	0.153695i	$0.0491172\pi$
$127$			3.46410i			0.307389i	−0.988118	+	0.153695i	$0.950883\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.03528	−	1.79315i	−0.0904525	−	0.156668i	0.817249	−	0.576285i	$-0.195498\pi$
$131$	−1.03528	−	1.79315i	−0.0904525	−	0.156668i	−0.907702	+	0.419616i	$0.862165\pi$
$132$		0			0
$133$	−3.23205	+	5.59808i	−0.280254	+	0.485415i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.8313	−	6.83083i	−1.01082	−	0.583597i	−0.0993885	−	0.995049i	$-0.531689\pi$
$137$	−11.8313	−	6.83083i	−1.01082	−	0.583597i	−0.911432	+	0.411451i	$0.865022\pi$
$138$		0			0
$139$	−7.96410	+	4.59808i	−0.675506	+	0.390004i	−0.798160	−	0.602446i	$-0.794193\pi$
$139$	−7.96410	+	4.59808i	−0.675506	+	0.390004i	0.122653	+	0.992450i	$0.460860\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.62158			−0.386476
$144$		0			0
$145$	−29.8564			−2.47944
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.79796	+	5.65685i	−0.802680	+	0.463428i	−0.844407	−	0.535701i	$-0.820047\pi$
$149$	−9.79796	+	5.65685i	−0.802680	+	0.463428i	0.0417274	+	0.999129i	$0.486714\pi$
$150$		0			0
$151$	10.1603	+	5.86603i	0.826830	+	0.477370i	0.852766	−	0.522293i	$-0.174923\pi$
$151$	10.1603	+	5.86603i	0.826830	+	0.477370i	−0.0259362	+	0.999664i	$0.508257\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.4195	+	24.9754i	−1.15821	+	2.00607i
$156$		0			0
$157$	8.46410	+	14.6603i	0.675509	+	1.17002i	0.976320	+	0.216332i	$0.0694093\pi$
$157$	8.46410	+	14.6603i	0.675509	+	1.17002i	−0.300811	+	0.953684i	$0.597257\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			32.7028i			2.57734i
$162$		0			0
$163$			15.5885i			1.22098i	0.792023	+	0.610491i	$0.209028\pi$
$163$			15.5885i			1.22098i	−0.792023	+	0.610491i	$0.790972\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.0735	−	19.1798i	−0.856891	−	1.48418i	−0.874880	−	0.484341i	$-0.839060\pi$
$167$	−11.0735	−	19.1798i	−0.856891	−	1.48418i	0.0179886	−	0.999838i	$-0.494274\pi$
$168$		0			0
$169$	−3.46410	+	6.00000i	−0.266469	+	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	16.4901	+	9.52056i	1.25372	+	0.723835i	0.971846	−	0.235617i	$-0.0757112\pi$
$173$	16.4901	+	9.52056i	1.25372	+	0.723835i	0.281872	+	0.959452i	$0.409045\pi$
$174$		0			0
$175$	32.0885	−	18.5263i	2.42566	−	1.40046i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	19.5959			1.46467			0.732334	−	0.680946i	$-0.238431\pi$
$179$	19.5959			1.46467			0.732334	+	0.680946i	$0.238431\pi$
$180$		0			0
$181$	0.464102			0.0344964			0.0172482	−	0.999851i	$-0.494509\pi$
$181$	0.464102			0.0344964			0.0172482	+	0.999851i	$0.494509\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.55291	+	0.896575i	−0.114173	+	0.0659175i
$186$		0			0
$187$	1.60770	+	0.928203i	0.117566	+	0.0678769i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.41662	+	9.38186i	−0.391933	+	0.678847i	−0.992704	−	0.120573i	$-0.961527\pi$
$191$	−5.41662	+	9.38186i	−0.391933	+	0.678847i	0.600772	+	0.799421i	$0.294860\pi$
$192$		0			0
$193$	−6.96410	−	12.0622i	−0.501287	−	0.868255i	−0.999999	−	0.00148674i	$-0.999527\pi$
$193$	−6.96410	−	12.0622i	−0.501287	−	0.868255i	0.498712	−	0.866768i	$-0.333807\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			0.277401i			0.0197640i	0.999951	+	0.00988202i	$0.00314559\pi$
$197$			0.277401i			0.0197640i	−0.999951	+	0.00988202i	$0.996854\pi$
$198$		0			0
$199$		−	5.58846i		−	0.396155i	−0.980186	−	0.198078i	$-0.936530\pi$
$199$		−	5.58846i		−	0.396155i	0.980186	−	0.198078i	$-0.0634698\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	14.4195	+	24.9754i	1.01205	+	1.75293i
$204$		0			0
$205$	14.9282	−	25.8564i	1.04263	−	1.80589i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.55291	+	0.896575i	0.107417	+	0.0620174i
$210$		0			0
$211$	−15.8205	+	9.13397i	−1.08913	+	0.628809i	−0.933344	−	0.358982i	$-0.883124\pi$
$211$	−15.8205	+	9.13397i	−1.08913	+	0.628809i	−0.155784	+	0.987791i	$0.549790\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.07055			0.141210
$216$		0			0
$217$	27.8564			1.89102
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.93237	−	4.00240i	0.466321	−	0.269231i
$222$		0			0
$223$	14.3205	+	8.26795i	0.958972	+	0.553663i	0.895857	−	0.444343i	$-0.146563\pi$
$223$	14.3205	+	8.26795i	0.958972	+	0.553663i	0.0631156	+	0.998006i	$0.479896\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.72741	+	13.3843i	−0.512886	+	0.888345i	0.487002	+	0.873401i	$0.338090\pi$
$227$	−7.72741	+	13.3843i	−0.512886	+	0.888345i	−0.999888	+	0.0149439i	$0.995243\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			11.3137i			0.741186i	0.928795	+	0.370593i	$0.120845\pi$
$233$			11.3137i			0.741186i	−0.928795	+	0.370593i	$0.879155\pi$
$234$		0			0
$235$		−	17.8564i		−	1.16482i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.07055	−	3.58630i	−0.133933	−	0.231979i	0.791256	−	0.611484i	$-0.209427\pi$
$239$	−2.07055	−	3.58630i	−0.133933	−	0.231979i	−0.925189	+	0.379506i	$0.876094\pi$
$240$		0			0
$241$	3.96410	−	6.86603i	0.255350	−	0.442280i	−0.709640	−	0.704564i	$-0.751143\pi$
$241$	3.96410	−	6.86603i	0.255350	−	0.442280i	0.964991	+	0.262285i	$0.0844759\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−23.1822	−	13.3843i	−1.48106	−	0.855089i
$246$		0			0
$247$	6.69615	−	3.86603i	0.426066	−	0.245989i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.3843			0.844807			0.422404	−	0.906408i	$-0.361187\pi$
$251$	13.3843			0.844807			0.422404	+	0.906408i	$0.361187\pi$
$252$		0			0
$253$	9.07180			0.570339
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.69213	−	3.86370i	0.417444	−	0.241011i	−0.276539	−	0.961003i	$-0.589188\pi$
$257$	6.69213	−	3.86370i	0.417444	−	0.241011i	0.693983	+	0.719991i	$0.255854\pi$
$258$		0			0
$259$	1.50000	+	0.866025i	0.0932055	+	0.0538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.07055	−	3.58630i	0.127676	−	0.221141i	−0.795100	−	0.606478i	$-0.792582\pi$
$263$	2.07055	−	3.58630i	0.127676	−	0.221141i	0.922776	+	0.385338i	$0.125915\pi$
$264$		0			0
$265$	−6.92820	−	12.0000i	−0.425596	−	0.737154i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			11.5911i			0.706722i	0.935487	+	0.353361i	$0.114961\pi$
$269$			11.5911i			0.706722i	−0.935487	+	0.353361i	$0.885039\pi$
$270$		0			0
$271$			25.0526i			1.52183i	0.648849	+	0.760917i	$0.275251\pi$
$271$			25.0526i			1.52183i	−0.648849	+	0.760917i	$0.724749\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.13922	−	8.90138i	−0.309906	−	0.536774i
$276$		0			0
$277$	−3.53590	+	6.12436i	−0.212452	+	0.367977i	−0.952481	−	0.304597i	$-0.901478\pi$
$277$	−3.53590	+	6.12436i	−0.212452	+	0.367977i	0.740030	+	0.672574i	$0.234811\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.2784	−	5.93426i	−0.613160	−	0.354008i	0.161041	−	0.986948i	$-0.448515\pi$
$281$	−10.2784	−	5.93426i	−0.613160	−	0.354008i	−0.774201	+	0.632940i	$0.781848\pi$
$282$		0			0
$283$	−6.46410	+	3.73205i	−0.384251	+	0.221847i	−0.679666	−	0.733522i	$-0.737875\pi$
$283$	−6.46410	+	3.73205i	−0.384251	+	0.221847i	0.295415	+	0.955369i	$0.404542\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−28.8391			−1.70232
$288$		0			0
$289$	13.7846			0.810859
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.86559	−	1.65445i	0.167410	−	0.0966540i	−0.413954	−	0.910298i	$-0.635853\pi$
$293$	2.86559	−	1.65445i	0.167410	−	0.0966540i	0.581364	+	0.813644i	$0.302519\pi$
$294$		0			0
$295$	41.3205	+	23.8564i	2.40577	+	1.38897i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.5588	−	33.8768i	1.13111	−	1.95914i
$300$		0			0
$301$	−1.00000	−	1.73205i	−0.0576390	−	0.0998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	44.0165i		−	2.52038i
$306$		0			0
$307$		−	1.60770i		−	0.0917560i	−0.998947	−	0.0458780i	$-0.985391\pi$
$307$		−	1.60770i		−	0.0917560i	0.998947	−	0.0458780i	$-0.0146086\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.1087	−	20.9730i	−0.686624	−	1.18927i	−0.972923	−	0.231128i	$-0.925759\pi$
$311$	−12.1087	−	20.9730i	−0.686624	−	1.18927i	0.286299	−	0.958140i	$-0.407575\pi$
$312$		0			0
$313$	3.03590	−	5.25833i	0.171599	−	0.297218i	−0.767380	−	0.641193i	$-0.778440\pi$
$313$	3.03590	−	5.25833i	0.171599	−	0.297218i	0.938979	+	0.343974i	$0.111773\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.69213	+	3.86370i	0.375867	+	0.217007i	0.676019	−	0.736884i	$-0.263704\pi$
$317$	6.69213	+	3.86370i	0.375867	+	0.217007i	−0.300151	+	0.953892i	$0.597037\pi$
$318$		0			0
$319$	6.92820	−	4.00000i	0.387905	−	0.223957i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.10583			−0.172813
$324$		0			0
$325$	−44.3205			−2.45846
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.9372	+	8.62398i	−0.823513	+	0.475456i
$330$		0			0
$331$	−12.8205	−	7.40192i	−0.704679	−	0.406847i	0.104409	−	0.994534i	$-0.466705\pi$
$331$	−12.8205	−	7.40192i	−0.704679	−	0.406847i	−0.809088	+	0.587688i	$0.800038\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	12.1087	−	20.9730i	0.661572	−	1.14588i
$336$		0			0
$337$	−6.42820	−	11.1340i	−0.350167	−	0.606506i	0.636112	−	0.771597i	$-0.280542\pi$
$337$	−6.42820	−	11.1340i	−0.350167	−	0.606506i	−0.986278	+	0.165091i	$0.947208\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	7.72741i		−	0.418463i
$342$		0			0
$343$		−	0.267949i		−	0.0144679i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.07055	−	3.58630i	−0.111153	−	0.192523i	0.805082	−	0.593163i	$-0.202121\pi$
$347$	−2.07055	−	3.58630i	−0.111153	−	0.192523i	−0.916235	+	0.400640i	$0.868788\pi$
$348$		0			0
$349$	12.1603	−	21.0622i	0.650923	−	1.12743i	−0.331976	−	0.943288i	$-0.607715\pi$
$349$	12.1603	−	21.0622i	0.650923	−	1.12743i	0.982899	−	0.184145i	$-0.0589515\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.5569	+	11.8685i	1.09413	+	0.631697i	0.934673	−	0.355508i	$-0.115692\pi$
$353$	20.5569	+	11.8685i	1.09413	+	0.631697i	0.159458	+	0.987205i	$0.449025\pi$
$354$		0			0
$355$	37.8564	−	21.8564i	2.00921	−	1.16002i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	27.2490			1.43815			0.719073	−	0.694934i	$-0.244566\pi$
$359$	27.2490			1.43815			0.719073	+	0.694934i	$0.244566\pi$
$360$		0			0
$361$	16.0000			0.842105
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.1440	−	7.58871i	0.687990	−	0.397211i
$366$		0			0
$367$	−18.2321	−	10.5263i	−0.951705	−	0.549467i	−0.0580950	−	0.998311i	$-0.518503\pi$
$367$	−18.2321	−	10.5263i	−0.951705	−	0.549467i	−0.893610	+	0.448844i	$0.851836\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.69213	+	11.5911i	−0.347438	+	0.601780i
$372$		0			0
$373$	17.6244	+	30.5263i	0.912555	+	1.58059i	0.810443	+	0.585818i	$0.199227\pi$
$373$	17.6244	+	30.5263i	0.912555	+	1.58059i	0.102112	+	0.994773i	$0.467440\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	34.4959i		−	1.77663i
$378$		0			0
$379$		−	1.19615i		−	0.0614422i	−0.999528	−	0.0307211i	$-0.990220\pi$
$379$		−	1.19615i		−	0.0614422i	0.999528	−	0.0307211i	$-0.00978037\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.8685	+	20.5569i	0.606453	+	1.05041i	0.991820	+	0.127644i	$0.0407413\pi$
$383$	11.8685	+	20.5569i	0.606453	+	1.05041i	−0.385368	+	0.922763i	$0.625925\pi$
$384$		0			0
$385$	−7.46410	+	12.9282i	−0.380406	+	0.658882i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.240237	+	0.138701i	0.0121805	+	0.00703241i	0.506078	−	0.862488i	$-0.331095\pi$
$389$	0.240237	+	0.138701i	0.0121805	+	0.00703241i	−0.493897	+	0.869520i	$0.664428\pi$
$390$		0			0
$391$	−13.6077	+	7.85641i	−0.688171	+	0.397316i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−18.5606			−0.933887
$396$		0			0
$397$	−14.7846			−0.742018			−0.371009	−	0.928629i	$-0.620988\pi$
$397$	−14.7846			−0.742018			−0.371009	+	0.928629i	$0.620988\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.5959	−	11.3137i	0.978573	−	0.564980i	0.0767343	−	0.997052i	$-0.475551\pi$
$401$	19.5959	−	11.3137i	0.978573	−	0.564980i	0.901839	+	0.432072i	$0.142217\pi$
$402$		0			0
$403$	−28.8564	−	16.6603i	−1.43744	−	0.829906i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.240237	−	0.416102i	0.0119081	−	0.0206254i
$408$		0			0
$409$	6.50000	+	11.2583i	0.321404	+	0.556689i	0.980778	−	0.195127i	$-0.0625118\pi$
$409$	6.50000	+	11.2583i	0.321404	+	0.556689i	−0.659374	+	0.751815i	$0.729178\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	46.0870i		−	2.26779i
$414$		0			0
$415$			8.00000i			0.392705i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.28032	+	16.0740i	0.453373	+	0.785266i	0.998593	−	0.0530275i	$-0.0168871\pi$
$419$	9.28032	+	16.0740i	0.453373	+	0.785266i	−0.545220	+	0.838293i	$0.683554\pi$
$420$		0			0
$421$	−8.23205	+	14.2583i	−0.401206	+	0.694908i	−0.993872	−	0.110540i	$-0.964742\pi$
$421$	−8.23205	+	14.2583i	−0.401206	+	0.694908i	0.592666	+	0.805448i	$0.298075\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	15.4176	+	8.90138i	0.747866	+	0.431781i
$426$		0			0
$427$	−36.8205	+	21.2583i	−1.78187	+	1.02876i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.0764			0.967046			0.483523	−	0.875332i	$-0.339357\pi$
$431$	20.0764			0.967046			0.483523	+	0.875332i	$0.339357\pi$
$432$		0			0
$433$	14.7846			0.710503			0.355251	−	0.934771i	$-0.384395\pi$
$433$	14.7846			0.710503			0.355251	+	0.934771i	$0.384395\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.1440	+	7.58871i	−0.628764	+	0.363017i
$438$		0			0
$439$	−11.5359	−	6.66025i	−0.550578	−	0.317877i	0.198777	−	0.980045i	$-0.436303\pi$
$439$	−11.5359	−	6.66025i	−0.550578	−	0.317877i	−0.749355	+	0.662168i	$0.769636\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.8332	−	18.7637i	0.514703	−	0.891491i	−0.485152	−	0.874430i	$-0.661236\pi$
$443$	10.8332	−	18.7637i	0.514703	−	0.891491i	0.999854	−	0.0170611i	$-0.00543097\pi$
$444$		0			0
$445$	−3.46410	−	6.00000i	−0.164214	−	0.284427i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			21.3891i			1.00941i	0.863291	+	0.504706i	$0.168399\pi$
$449$			21.3891i			1.00941i	−0.863291	+	0.504706i	$0.831601\pi$
$450$		0			0
$451$			8.00000i			0.376705i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	32.1851	+	55.7463i	1.50886	+	2.61343i
$456$		0			0
$457$	−3.39230	+	5.87564i	−0.158685	+	0.274851i	−0.934395	−	0.356239i	$-0.884059\pi$
$457$	−3.39230	+	5.87564i	−0.158685	+	0.274851i	0.775710	+	0.631090i	$0.217392\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.55772	−	5.51815i	−0.445148	−	0.257006i	0.260631	−	0.965438i	$-0.416069\pi$
$461$	−9.55772	−	5.51815i	−0.445148	−	0.257006i	−0.705779	+	0.708432i	$0.749403\pi$
$462$		0			0
$463$	−18.0167	+	10.4019i	−0.837305	+	0.483418i	−0.856347	−	0.516400i	$-0.827272\pi$
$463$	−18.0167	+	10.4019i	−0.837305	+	0.483418i	0.0190421	+	0.999819i	$0.493938\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.06678			0.188188			0.0940940	−	0.995563i	$-0.470005\pi$
$467$	4.06678			0.188188			0.0940940	+	0.995563i	$0.470005\pi$
$468$		0			0
$469$	−23.3923			−1.08016
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.480473	+	0.277401i	−0.0220922	+	0.0127549i
$474$		0			0
$475$	14.8923	+	8.59808i	0.683306	+	0.394507i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.3490	−	21.3891i	0.564240	−	0.977292i	−0.432880	−	0.901451i	$-0.642503\pi$
$479$	12.3490	−	21.3891i	0.564240	−	0.977292i	0.997120	−	0.0758402i	$-0.0241639\pi$
$480$		0			0
$481$	−1.03590	−	1.79423i	−0.0472329	−	0.0818098i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	27.0459i		−	1.22809i
$486$		0			0
$487$		−	35.4449i		−	1.60616i	−0.595871	−	0.803080i	$-0.703193\pi$
$487$		−	35.4449i		−	1.60616i	0.595871	−	0.803080i	$-0.296807\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.28032	−	16.0740i	−0.418815	−	0.725409i	0.577006	−	0.816740i	$-0.304221\pi$
$491$	−9.28032	−	16.0740i	−0.418815	−	0.725409i	−0.995821	+	0.0913313i	$0.970888\pi$
$492$		0			0
$493$	−6.92820	+	12.0000i	−0.312031	+	0.540453i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−36.5665	−	21.1117i	−1.64023	−	0.946988i
$498$		0			0
$499$	−16.8564	+	9.73205i	−0.754596	+	0.435666i	−0.827352	−	0.561683i	$-0.810154\pi$
$499$	−16.8564	+	9.73205i	−0.754596	+	0.435666i	0.0727559	+	0.997350i	$0.476821\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.9743			−0.667673			−0.333836	−	0.942631i	$-0.608343\pi$
$503$	−14.9743			−0.667673			−0.333836	+	0.942631i	$0.608343\pi$
$504$		0			0
$505$	16.0000			0.711991
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.6245	+	7.86611i	−0.603895	+	0.348659i	−0.770572	−	0.637352i	$-0.780030\pi$
$509$	−13.6245	+	7.86611i	−0.603895	+	0.348659i	0.166677	+	0.986012i	$0.446696\pi$
$510$		0			0
$511$	−12.6962	−	7.33013i	−0.561645	−	0.324266i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	26.2509	−	45.4679i	1.15675	−	2.00355i
$516$		0			0
$517$	2.39230	+	4.14359i	0.105213	+	0.182235i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			6.48906i			0.284291i	0.989846	+	0.142145i	$0.0454001\pi$
$521$			6.48906i			0.284291i	−0.989846	+	0.142145i	$0.954600\pi$
$522$		0			0
$523$		−	21.1962i		−	0.926843i	−0.886138	−	0.463422i	$-0.846622\pi$
$523$		−	21.1962i		−	0.926843i	0.886138	−	0.463422i	$-0.153378\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.69213	+	11.5911i	0.291514	+	0.504917i
$528$		0			0
$529$	−26.8923	+	46.5788i	−1.16923	+	2.02517i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	29.8744	+	17.2480i	1.29400	+	0.747092i
$534$		0			0
$535$	34.3923	−	19.8564i	1.48691	−	0.858467i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.17260			0.308946
$540$		0			0
$541$	35.3923			1.52163			0.760817	−	0.648966i	$-0.224798\pi$
$541$	35.3923			1.52163			0.760817	+	0.648966i	$0.224798\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−43.2586	+	24.9754i	−1.85300	+	1.06983i
$546$		0			0
$547$	1.96410	+	1.13397i	0.0839789	+	0.0484853i	0.541401	−	0.840764i	$-0.317894\pi$
$547$	1.96410	+	1.13397i	0.0839789	+	0.0484853i	−0.457422	+	0.889249i	$0.651227\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.69213	+	11.5911i	−0.285094	+	0.493798i
$552$		0			0
$553$	8.96410	+	15.5263i	0.381192	+	0.660245i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	15.1774i		−	0.643088i	−0.946895	−	0.321544i	$-0.895798\pi$
$557$		−	15.1774i		−	0.643088i	0.946895	−	0.321544i	$-0.104202\pi$
$558$		0			0
$559$			2.39230i			0.101184i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.62158	+	8.00481i	0.194776	+	0.337362i	0.946827	−	0.321743i	$-0.104269\pi$
$563$	4.62158	+	8.00481i	0.194776	+	0.337362i	−0.752051	+	0.659105i	$0.770935\pi$
$564$		0			0
$565$	−11.4641	+	19.8564i	−0.482298	+	0.835365i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−37.6389	−	21.7308i	−1.57791	−	0.911004i	−0.995151	−	0.0983559i	$-0.968642\pi$
$569$	−37.6389	−	21.7308i	−1.57791	−	0.911004i	−0.582754	−	0.812648i	$-0.698025\pi$
$570$		0			0
$571$	−13.0359	+	7.52628i	−0.545535	+	0.314965i	−0.747319	−	0.664465i	$-0.768659\pi$
$571$	−13.0359	+	7.52628i	−0.545535	+	0.314965i	0.201784	+	0.979430i	$0.435326\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	86.9977			3.62805
$576$		0			0
$577$	−39.9282			−1.66223			−0.831116	−	0.556098i	$-0.812298\pi$
$577$	−39.9282			−1.66223			−0.831116	+	0.556098i	$0.812298\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.69213	−	3.86370i	0.277636	−	0.160293i
$582$		0			0
$583$	3.21539	+	1.85641i	0.133168	+	0.0768845i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.20977	+	12.4877i	−0.297579	+	0.515422i	−0.975582	−	0.219638i	$-0.929512\pi$
$587$	−7.20977	+	12.4877i	−0.297579	+	0.515422i	0.678003	+	0.735060i	$0.262846\pi$
$588$		0			0
$589$	6.46410	+	11.1962i	0.266349	+	0.461329i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	42.7781i		−	1.75669i	−0.478029	−	0.878344i	$-0.658649\pi$
$593$		−	42.7781i		−	1.75669i	0.478029	−	0.878344i	$-0.341351\pi$
$594$		0			0
$595$		−	25.8564i		−	1.06001i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.76268	+	15.1774i	0.358034	+	0.620132i	0.987632	−	0.156788i	$-0.0501140\pi$
$599$	8.76268	+	15.1774i	0.358034	+	0.620132i	−0.629599	+	0.776920i	$0.716781\pi$
$600$		0			0
$601$	17.3923	−	30.1244i	0.709447	−	1.22880i	−0.255616	−	0.966778i	$-0.582278\pi$
$601$	17.3923	−	30.1244i	0.709447	−	1.22880i	0.965063	−	0.262020i	$-0.0843885\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−33.2204	−	19.1798i	−1.35060	−	0.779770i
$606$		0			0
$607$	−5.76795	+	3.33013i	−0.234114	+	0.135166i	−0.612468	−	0.790495i	$-0.709823\pi$
$607$	−5.76795	+	3.33013i	−0.234114	+	0.135166i	0.378355	+	0.925661i	$0.376490\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	20.6312			0.834649
$612$		0			0
$613$	−16.6077			−0.670778			−0.335389	−	0.942080i	$-0.608868\pi$
$613$	−16.6077			−0.670778			−0.335389	+	0.942080i	$0.608868\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	38.1194	−	22.0082i	1.53463	−	0.886018i	0.535490	−	0.844542i	$-0.320127\pi$
$617$	38.1194	−	22.0082i	1.53463	−	0.886018i	0.999139	−	0.0414767i	$-0.0132062\pi$
$618$		0			0
$619$	−14.4282	−	8.33013i	−0.579918	−	0.334816i	0.181183	−	0.983449i	$-0.442008\pi$
$619$	−14.4282	−	8.33013i	−0.579918	−	0.334816i	−0.761101	+	0.648633i	$0.775341\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.34607	+	5.79555i	−0.134057	+	0.232194i
$624$		0			0
$625$	−11.9641	−	20.7224i	−0.478564	−	0.828897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			0.832204i			0.0331822i
$630$		0			0
$631$			31.9808i			1.27313i	0.771221	+	0.636567i	$0.219646\pi$
$631$			31.9808i			1.27313i	−0.771221	+	0.636567i	$0.780354\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.69213	−	11.5911i	−0.265569	−	0.459979i
$636$		0			0
$637$	15.4641	−	26.7846i	0.612710	−	1.06124i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.62536	+	1.51575i	0.103695	+	0.0598685i	0.550951	−	0.834538i	$-0.314265\pi$
$641$	2.62536	+	1.51575i	0.103695	+	0.0598685i	−0.447255	+	0.894406i	$0.647599\pi$
$642$		0			0
$643$	33.2487	−	19.1962i	1.31120	−	0.757022i	0.328906	−	0.944363i	$-0.393320\pi$
$643$	33.2487	−	19.1962i	1.31120	−	0.757022i	0.982295	+	0.187340i	$0.0599867\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.21166			0.244205			0.122103	−	0.992517i	$-0.461036\pi$
$647$	6.21166			0.244205			0.122103	+	0.992517i	$0.461036\pi$
$648$		0			0
$649$	−12.7846			−0.501840
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−33.4607	+	19.3185i	−1.30942	+	0.755992i	−0.981999	−	0.188888i	$-0.939512\pi$
$653$	−33.4607	+	19.3185i	−1.30942	+	0.755992i	−0.327418	+	0.944880i	$0.606178\pi$
$654$		0			0
$655$	6.92820	+	4.00000i	0.270707	+	0.156293i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.55103	−	4.41851i	0.0993739	−	0.172121i	−0.812052	−	0.583585i	$-0.801649\pi$
$659$	2.55103	−	4.41851i	0.0993739	−	0.172121i	0.911426	+	0.411465i	$0.134983\pi$
$660$		0			0
$661$	−2.62436	−	4.54552i	−0.102076	−	0.176800i	0.810464	−	0.585788i	$-0.199215\pi$
$661$	−2.62436	−	4.54552i	−0.102076	−	0.176800i	−0.912540	+	0.408988i	$0.865882\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	24.9754i		−	0.968503i
$666$		0			0
$667$			67.7128i			2.62185i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.89709	+	10.2141i	0.227655	+	0.394309i
$672$		0			0
$673$	3.42820	−	5.93782i	0.132148	−	0.228886i	−0.792357	−	0.610058i	$-0.791146\pi$
$673$	3.42820	−	5.93782i	0.132148	−	0.228886i	0.924504	+	0.381172i	$0.124479\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.9420	−	13.2456i	−0.881732	−	0.509068i	−0.0105029	−	0.999945i	$-0.503343\pi$
$677$	−22.9420	−	13.2456i	−0.881732	−	0.509068i	−0.871229	+	0.490877i	$0.836677\pi$
$678$		0			0
$679$	−22.6244	+	13.0622i	−0.868243	+	0.501280i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.9411			1.29872			0.649361	−	0.760481i	$-0.275037\pi$
$683$	33.9411			1.29872			0.649361	+	0.760481i	$0.275037\pi$
$684$		0			0
$685$	52.7846			2.01680
$686$		0			0
$687$		0			0
$688$		0			0
$689$	13.8647	−	8.00481i	0.528204	−	0.304959i
$690$		0			0
$691$	8.32051	+	4.80385i	0.316527	+	0.182747i	0.649844	−	0.760068i	$-0.274834\pi$
$691$	8.32051	+	4.80385i	0.316527	+	0.182747i	−0.333316	+	0.942815i	$0.608168\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17.7656	−	30.7709i	0.673888	−	1.16721i
$696$		0			0
$697$	−6.92820	−	12.0000i	−0.262424	−	0.454532i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			24.0144i			0.907012i	0.891253	+	0.453506i	$0.149827\pi$
$701$			24.0144i			0.907012i	−0.891253	+	0.453506i	$0.850173\pi$
$702$		0			0
$703$			0.803848i			0.0303177i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.72741	−	13.3843i	−0.290619	−	0.503367i
$708$		0			0
$709$	25.0885	−	43.4545i	0.942217	−	1.63197i	0.180987	−	0.983486i	$-0.442071\pi$
$709$	25.0885	−	43.4545i	0.942217	−	1.63197i	0.761230	−	0.648482i	$-0.224596\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	56.6429	+	32.7028i	2.12129	+	1.22473i
$714$		0			0
$715$	15.4641	−	8.92820i	0.578325	−	0.333896i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.3843			−0.499149			−0.249574	−	0.968356i	$-0.580291\pi$
$719$	−13.3843			−0.499149			−0.249574	+	0.968356i	$0.580291\pi$
$720$		0			0
$721$	−50.7128			−1.88864
$722$		0			0
$723$		0			0
$724$		0			0
$725$	66.4408	−	38.3596i	2.46755	−	1.42464i
$726$		0			0
$727$	−11.5359	−	6.66025i	−0.427843	−	0.247015i	0.270584	−	0.962696i	$-0.412783\pi$
$727$	−11.5359	−	6.66025i	−0.427843	−	0.247015i	−0.698427	+	0.715681i	$0.746116\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.480473	−	0.832204i	0.0177709	−	0.0307802i
$732$		0			0
$733$	9.53590	+	16.5167i	0.352216	+	0.610057i	0.986637	−	0.162931i	$-0.0520948\pi$
$733$	9.53590	+	16.5167i	0.352216	+	0.610057i	−0.634421	+	0.772988i	$0.718761\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			6.48906i			0.239028i
$738$		0			0
$739$			6.39230i			0.235145i	0.993064	+	0.117572i	$0.0375112\pi$
$739$			6.39230i			0.235145i	−0.993064	+	0.117572i	$0.962489\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.1793	−	24.5593i	−0.520188	−	0.900992i	−0.999725	−	0.0234702i	$-0.992529\pi$
$743$	−14.1793	−	24.5593i	−0.520188	−	0.900992i	0.479536	−	0.877522i	$-0.340805\pi$
$744$		0			0
$745$	21.8564	−	37.8564i	0.800757	−	1.38695i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−33.2204	−	19.1798i	−1.21385	−	0.700815i
$750$		0			0
$751$	6.23205	−	3.59808i	0.227411	−	0.131296i	−0.381966	−	0.924176i	$-0.624753\pi$
$751$	6.23205	−	3.59808i	0.227411	−	0.131296i	0.609377	+	0.792881i	$0.291420\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−45.3292			−1.64970
$756$		0			0
$757$	15.3923			0.559443			0.279721	−	0.960081i	$-0.409758\pi$
$757$	15.3923			0.559443			0.279721	+	0.960081i	$0.409758\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.6961	−	14.8356i	0.931482	−	0.537791i	0.0442022	−	0.999023i	$-0.485925\pi$
$761$	25.6961	−	14.8356i	0.931482	−	0.537791i	0.887280	+	0.461231i	$0.152592\pi$
$762$		0			0
$763$	41.7846	+	24.1244i	1.51270	+	0.873360i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.5636	+	47.7415i	−0.995263	+	1.72385i
$768$		0			0
$769$	7.42820	+	12.8660i	0.267868	+	0.463961i	0.968311	−	0.249747i	$-0.0803476\pi$
$769$	7.42820	+	12.8660i	0.267868	+	0.463961i	−0.700443	+	0.713708i	$0.747014\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			30.3548i			1.09179i	0.837855	+	0.545894i	$0.183810\pi$
$773$			30.3548i			1.09179i	−0.837855	+	0.545894i	$0.816190\pi$
$774$		0			0
$775$		−	74.1051i		−	2.66193i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.69213	−	11.5911i	−0.239770	−	0.415295i
$780$		0			0
$781$	−5.85641	+	10.1436i	−0.209559	+	0.362966i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−56.6429	−	32.7028i	−2.02167	−	1.16721i
$786$		0			0
$787$	29.2128	−	16.8660i	1.04132	−	0.601209i	0.121116	−	0.992638i	$-0.461353\pi$
$787$	29.2128	−	16.8660i	1.04132	−	0.601209i	0.920208	+	0.391429i	$0.128019\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	22.1469			0.787455
$792$		0			0
$793$	50.8564			1.80596
$794$		0			0
$795$		0			0
$796$		0			0
$797$	36.5665	−	21.1117i	1.29525	−	0.747814i	0.315671	−	0.948869i	$-0.397770\pi$
$797$	36.5665	−	21.1117i	1.29525	−	0.747814i	0.979580	+	0.201055i	$0.0644370\pi$
$798$		0			0
$799$	−7.17691	−	4.14359i	−0.253901	−	0.146590i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.03339	+	3.52193i	−0.0717567	+	0.124286i
$804$		0			0
$805$	−63.1769	−	109.426i	−2.22669	−	3.85675i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			19.5959i			0.688956i	0.938794	+	0.344478i	$0.111944\pi$
$809$			19.5959i			0.688956i	−0.938794	+	0.344478i	$0.888056\pi$
$810$		0			0
$811$			8.53590i			0.299736i	0.988706	+	0.149868i	$0.0478849\pi$
$811$			8.53590i			0.299736i	−0.988706	+	0.149868i	$0.952115\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−30.1146	−	52.1600i	−1.05487	−	1.82708i
$816$		0			0
$817$	0.464102	−	0.803848i	0.0162369	−	0.0281231i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.9420	+	13.2456i	0.800681	+	0.462273i	0.843709	−	0.536801i	$-0.180367\pi$
$821$	22.9420	+	13.2456i	0.800681	+	0.462273i	−0.0430284	+	0.999074i	$0.513701\pi$
$822$		0			0
$823$	10.3756	−	5.99038i	0.361672	−	0.208812i	−0.308142	−	0.951340i	$-0.599707\pi$
$823$	10.3756	−	5.99038i	0.361672	−	0.208812i	0.669814	+	0.742529i	$0.266374\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.9134			1.00542			0.502709	−	0.864456i	$-0.332337\pi$
$827$	28.9134			1.00542			0.502709	+	0.864456i	$0.332337\pi$
$828$		0			0
$829$	50.3205			1.74770			0.873852	−	0.486192i	$-0.161615\pi$
$829$	50.3205			1.74770			0.873852	+	0.486192i	$0.161615\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.7589	+	6.21166i	−0.372774	+	0.215221i
$834$		0			0
$835$	74.1051	+	42.7846i	2.56451	+	1.48062i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.5921	−	37.3987i	0.745443	−	1.29115i	−0.204544	−	0.978857i	$-0.565571\pi$
$839$	21.5921	−	37.3987i	0.745443	−	1.29115i	0.949987	−	0.312289i	$-0.101096\pi$
$840$		0			0
$841$	15.3564	+	26.5981i	0.529531	+	0.917175i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	26.7685i		−	0.920865i
$846$		0			0
$847$			37.0526i			1.27314i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.03339	+	3.52193i	0.0697036	+	0.120730i
$852$		0			0
$853$	−23.6962	+	41.0429i	−0.811341	+	1.40528i	0.100585	+	0.994928i	$0.467929\pi$
$853$	−23.6962	+	41.0429i	−0.811341	+	1.40528i	−0.911926	+	0.410355i	$0.865405\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.0096	+	9.24316i	0.546878	+	0.315740i	0.747862	−	0.663854i	$-0.231081\pi$
$857$	16.0096	+	9.24316i	0.546878	+	0.315740i	−0.200984	+	0.979595i	$0.564414\pi$
$858$		0			0
$859$	22.9641	−	13.2583i	0.783525	−	0.452368i	−0.0541531	−	0.998533i	$-0.517246\pi$
$859$	22.9641	−	13.2583i	0.783525	−	0.452368i	0.837678	+	0.546164i	$0.183913\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−53.0566			−1.80607			−0.903033	−	0.429570i	$-0.858665\pi$
$863$	−53.0566			−1.80607			−0.903033	+	0.429570i	$0.858665\pi$
$864$		0			0
$865$	−73.5692			−2.50143
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.30701	−	2.48665i	0.146105	−	0.0843540i
$870$		0			0
$871$	24.2321	+	13.9904i	0.821072	+	0.474046i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−35.5312	+	61.5419i	−1.20117	+	2.08049i
$876$		0			0
$877$	11.6244	+	20.1340i	0.392527	+	0.679876i	0.992782	−	0.119932i	$-0.0382678\pi$
$877$	11.6244	+	20.1340i	0.392527	+	0.679876i	−0.600255	+	0.799808i	$0.704934\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	21.3891i		−	0.720616i	−0.932833	−	0.360308i	$-0.882672\pi$
$881$		−	21.3891i		−	0.720616i	0.932833	−	0.360308i	$-0.117328\pi$
$882$		0			0
$883$		−	0.124356i		−	0.00418490i	−0.999998	−	0.00209245i	$-0.999334\pi$
$883$		−	0.124356i		−	0.00418490i	0.999998	−	0.00209245i	$-0.000666048\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.76268	−	15.1774i	−0.294222	−	0.509608i	0.680582	−	0.732672i	$-0.261727\pi$
$887$	−8.76268	−	15.1774i	−0.294222	−	0.509608i	−0.974804	+	0.223065i	$0.928394\pi$
$888$		0			0
$889$	−6.46410	+	11.1962i	−0.216799	+	0.375507i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.93237	−	4.00240i	−0.231983	−	0.133935i
$894$		0			0
$895$	−65.5692	+	37.8564i	−2.19174	+	1.26540i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	57.6781			1.92367
$900$		0			0
$901$	−6.43078			−0.214240
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.55291	+	0.896575i	−0.0516206	+	0.0298032i
$906$		0			0
$907$	8.21281	+	4.74167i	0.272702	+	0.157445i	0.630115	−	0.776502i	$-0.283008\pi$
$907$	8.21281	+	4.74167i	0.272702	+	0.157445i	−0.357413	+	0.933946i	$0.616341\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.4195	+	24.9754i	−0.477741	+	0.827471i	−0.999674	−	0.0255150i	$-0.991877\pi$
$911$	−14.4195	+	24.9754i	−0.477741	+	0.827471i	0.521934	+	0.852986i	$0.325211\pi$
$912$		0			0
$913$	−1.07180	−	1.85641i	−0.0354713	−	0.0614381i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	7.72741i		−	0.255181i
$918$		0			0
$919$			33.0333i			1.08967i	0.838544	+	0.544834i	$0.183407\pi$
$919$			33.0333i			1.08967i	−0.838544	+	0.544834i	$0.816593\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	25.2528	+	43.7391i	0.831205	+	1.43969i
$924$		0			0
$925$	2.30385	−	3.99038i	0.0757500	−	0.131203i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.5959	−	11.3137i	−0.642921	−	0.371191i	0.142818	−	0.989749i	$-0.454384\pi$
$929$	−19.5959	−	11.3137i	−0.642921	−	0.371191i	−0.785739	+	0.618558i	$0.787717\pi$
$930$		0			0
$931$	−10.3923	+	6.00000i	−0.340594	+	0.196642i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.17260			−0.234569
$936$		0			0
$937$	47.7846			1.56106			0.780528	−	0.625121i	$-0.214951\pi$
$937$	47.7846			1.56106			0.780528	+	0.625121i	$0.214951\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.5187	−	6.07296i	0.342899	−	0.197973i	−0.318654	−	0.947871i	$-0.603231\pi$
$941$	10.5187	−	6.07296i	0.342899	−	0.197973i	0.661553	+	0.749898i	$0.269898\pi$
$942$		0			0
$943$	−58.6410	−	33.8564i	−1.90961	−	1.10252i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.20977	−	12.4877i	0.234286	−	0.405795i	−0.724779	−	0.688981i	$-0.758058\pi$
$947$	7.20977	−	12.4877i	0.234286	−	0.405795i	0.959065	+	0.283186i	$0.0913915\pi$
$948$		0			0
$949$	8.76795	+	15.1865i	0.284620	+	0.492976i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			21.3891i			0.692860i	0.938076	+	0.346430i	$0.112606\pi$
$953$			21.3891i			0.692860i	−0.938076	+	0.346430i	$0.887394\pi$
$954$		0			0
$955$		−	41.8564i		−	1.35444i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−25.4930	−	44.1552i	−0.823212	−	1.42585i
$960$		0			0
$961$	12.3564	−	21.4019i	0.398594	−	0.690385i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	46.6047	+	26.9072i	1.50026	+	0.866174i
$966$		0			0
$967$	7.16025	−	4.13397i	0.230258	−	0.132940i	−0.380433	−	0.924809i	$-0.624225\pi$
$967$	7.16025	−	4.13397i	0.230258	−	0.132940i	0.610691	+	0.791869i	$0.290892\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	26.8429			0.861428			0.430714	−	0.902488i	$-0.358262\pi$
$971$	26.8429			0.861428			0.430714	+	0.902488i	$0.358262\pi$
$972$		0			0
$973$	−34.3205			−1.10026
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.4901	+	9.52056i	−0.527565	+	0.304590i	−0.740024	−	0.672580i	$-0.765186\pi$
$977$	−16.4901	+	9.52056i	−0.527565	+	0.304590i	0.212459	+	0.977170i	$0.431853\pi$
$978$		0			0
$979$	1.60770	+	0.928203i	0.0513822	+	0.0296655i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.86181	+	8.42091i	−0.155068	+	0.268585i	−0.933084	−	0.359659i	$-0.882893\pi$
$983$	−4.86181	+	8.42091i	−0.155068	+	0.268585i	0.778016	+	0.628245i	$0.216226\pi$
$984$		0			0
$985$	−0.535898	−	0.928203i	−0.0170751	−	0.0295750i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	4.69591i		−	0.149321i
$990$		0			0
$991$		−	52.5167i		−	1.66825i	−0.551578	−	0.834123i	$-0.685974\pi$
$991$		−	52.5167i		−	1.66825i	0.551578	−	0.834123i	$-0.314026\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	10.7961	+	18.6993i	0.342258	+	0.592809i
$996$		0			0
$997$	−17.3923	+	30.1244i	−0.550820	+	0.954048i	0.447396	+	0.894336i	$0.352352\pi$
$997$	−17.3923	+	30.1244i	−0.550820	+	0.954048i	−0.998216	+	0.0597119i	$0.980982\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.g.1727.1		8
3.2	odd	2	inner	2592.2.s.g.1727.4		8
4.3	odd	2		2592.2.s.c.1727.1		8
9.2	odd	6		864.2.c.b.863.7	yes	8
9.4	even	3		2592.2.s.c.863.4		8
9.5	odd	6		2592.2.s.c.863.1		8
9.7	even	3		864.2.c.b.863.1	✓	8
12.11	even	2		2592.2.s.c.1727.4		8
36.7	odd	6		864.2.c.b.863.2	yes	8
36.11	even	6		864.2.c.b.863.8	yes	8
36.23	even	6	inner	2592.2.s.g.863.1		8
36.31	odd	6	inner	2592.2.s.g.863.4		8
72.11	even	6		1728.2.c.f.1727.2		8
72.29	odd	6		1728.2.c.f.1727.1		8
72.43	odd	6		1728.2.c.f.1727.8		8
72.61	even	6		1728.2.c.f.1727.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.c.b.863.1	✓	8	9.7	even	3
864.2.c.b.863.2	yes	8	36.7	odd	6
864.2.c.b.863.7	yes	8	9.2	odd	6
864.2.c.b.863.8	yes	8	36.11	even	6
1728.2.c.f.1727.1		8	72.29	odd	6
1728.2.c.f.1727.2		8	72.11	even	6
1728.2.c.f.1727.7		8	72.61	even	6
1728.2.c.f.1727.8		8	72.43	odd	6
2592.2.s.c.863.1		8	9.5	odd	6
2592.2.s.c.863.4		8	9.4	even	3
2592.2.s.c.1727.1		8	4.3	odd	2
2592.2.s.c.1727.4		8	12.11	even	2
2592.2.s.g.863.1		8	36.23	even	6	inner
2592.2.s.g.863.4		8	36.31	odd	6	inner
2592.2.s.g.1727.1		8	1.1	even	1	trivial
2592.2.s.g.1727.4		8	3.2	odd	2	inner

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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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.34607 + 1.93185i) q^{5} +(3.23205 + 1.86603i) q^{7} +O(q^{10})\)	\(q+(-3.34607 + 1.93185i) q^{5} +(3.23205 + 1.86603i) q^{7} +(0.517638 - 0.896575i) q^{11} +(-2.23205 - 3.86603i) q^{13} +1.79315i q^{17} +1.73205i q^{19} +(4.38134 + 7.58871i) q^{23} +(4.96410 - 8.59808i) q^{25} +(6.69213 + 3.86370i) q^{29} +(6.46410 - 3.73205i) q^{31} -14.4195 q^{35} +0.464102 q^{37} +(-6.69213 + 3.86370i) q^{41} +(-0.464102 - 0.267949i) q^{43} +(-2.31079 + 4.00240i) q^{47} +(3.46410 + 6.00000i) q^{49} +3.58630i q^{53} +4.00000i q^{55} +(-6.17449 - 10.6945i) q^{59} +(-5.69615 + 9.86603i) q^{61} +(14.9372 + 8.62398i) q^{65} +(-5.42820 + 3.13397i) q^{67} -11.3137 q^{71} -3.92820 q^{73} +(3.34607 - 1.93185i) q^{77} +(4.16025 + 2.40192i) q^{79} +(1.03528 - 1.79315i) q^{83} +(-3.46410 - 6.00000i) q^{85} +1.79315i q^{89} -16.6603i q^{91} +(-3.34607 - 5.79555i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{7}+O(q^{10}) \) 8 * q + 12 * q^7	\( 8 q + 12 q^{7} - 4 q^{13} + 12 q^{25} + 24 q^{31} - 24 q^{37} + 24 q^{43} - 4 q^{61} + 12 q^{67} + 24 q^{73} - 36 q^{79} - 28 q^{97}+O(q^{100}) \) 8 * q + 12 * q^7 - 4 * q^13 + 12 * q^25 + 24 * q^31 - 24 * q^37 + 24 * q^43 - 4 * q^61 + 12 * q^67 + 24 * q^73 - 36 * q^79 - 28 * q^97

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