Properties

Level $269$
Weight $0$
Character 269.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 269 \)
Weight: \( 0 \)
Character: 269.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.90501261621 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.299610242\) \(a_{3}=-1.812855196\) \(a_{4}=-0.910233703\) \(a_{5}=+0.314083735\)
\(a_{6}=-0.543149978\) \(a_{7}=-0.208288382\) \(a_{8}=-0.572325576\) \(a_{9}=+2.286443939\) \(a_{10}=+0.094102705\)
\(a_{11}=-0.552581120\) \(a_{12}=+1.650121901\) \(a_{13}=+0.455030171\) \(a_{14}=-0.062405325\) \(a_{15}=-0.569388326\)
\(a_{16}=+0.738759097\) \(a_{17}=+0.767885382\) \(a_{18}=+0.685042016\) \(a_{19}=+1.536133310\) \(a_{20}=-0.285889598\)
\(a_{21}=+0.377596670\) \(a_{22}=-0.165558953\) \(a_{23}=+0.733223325\) \(a_{24}=+1.037543390\) \(a_{25}=-0.901351404\)
\(a_{26}=+0.136331700\) \(a_{27}=-2.332136561\) \(a_{28}=+0.189591110\) \(a_{29}=+1.153363610\) \(a_{30}=-0.170594581\)
\(a_{31}=-1.372363253\) \(a_{32}=+0.793665366\) \(a_{33}=+1.001749531\) \(a_{34}=+0.230066331\) \(a_{35}=-0.065419992\)
\(a_{36}=-2.081198320\) \(a_{37}=-0.524549515\) \(a_{38}=+0.460241284\) \(a_{39}=-0.824903815\) \(a_{40}=-0.179758165\)
\(a_{41}=+1.189914775\) \(a_{42}=+0.113131814\) \(a_{43}=-0.646717121\) \(a_{44}=+0.502977952\) \(a_{45}=+0.718134874\)
\(a_{46}=+0.219681227\) \(a_{47}=+0.678094684\) \(a_{48}=-1.339263272\) \(a_{49}=-0.956615943\) \(a_{50}=-0.270054131\)
\(a_{51}=-1.392065010\) \(a_{52}=-0.414183799\) \(a_{53}=-0.855365526\) \(a_{54}=-0.698732007\) \(a_{55}=-0.173556725\)
\(a_{56}=+0.119208747\) \(a_{57}=-2.784787254\) \(a_{58}=+0.345559546\) \(a_{59}=+1.192242042\) \(a_{60}=+0.518276445\)
\(a_{61}=+1.903668986\) \(a_{62}=-0.411174080\) \(a_{63}=-0.476239691\) \(a_{64}=-0.500968813\) \(a_{65}=+0.142917568\)
\(a_{66}=+0.300134415\) \(a_{67}=+1.768546154\) \(a_{68}=-0.698955170\) \(a_{69}=-1.329227722\) \(a_{70}=-0.019600518\)
\(a_{71}=+0.453269354\) \(a_{72}=-1.308590352\) \(a_{73}=+0.417444582\) \(a_{74}=-0.157160397\) \(a_{75}=+1.634019548\)
\(a_{76}=-1.398240318\) \(a_{77}=+0.115096221\) \(a_{78}=-0.247149604\) \(a_{79}=+0.823869692\) \(a_{80}=+0.232032231\)
\(a_{81}=+1.941381925\) \(a_{82}=+0.356510654\) \(a_{83}=+1.239517717\) \(a_{84}=-0.343701206\) \(a_{85}=+0.241180308\)
\(a_{86}=-0.193763034\) \(a_{87}=-2.090881231\) \(a_{88}=+0.316256322\) \(a_{89}=+1.176354754\) \(a_{90}=+0.215160560\)
\(a_{91}=-0.094777529\) \(a_{92}=-0.667404579\) \(a_{93}=+2.487895834\) \(a_{94}=+0.203164147\) \(a_{95}=+0.482474503\)
\(a_{96}=-1.438800388\) \(a_{97}=+0.908443844\) \(a_{98}=-0.286611956\) \(a_{99}=-1.263445720\) \(a_{100}=+0.820440400\)

Showing 100 of 882 available coefficients

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