Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.29700635907 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.075989199\) \(a_{3}=-0.826094806\) \(a_{4}=+0.157752757\) \(a_{5}=+0.381748858\)
\(a_{6}=+0.888869089\) \(a_{7}=-0.854128279\) \(a_{8}=+0.906248937\) \(a_{9}=-0.317567371\) \(a_{10}=-0.410757648\)
\(a_{11}=-1.156351589\) \(a_{12}=-0.130318733\) \(a_{13}=-0.100430770\) \(a_{14}=+0.919032803\) \(a_{15}=-0.315360749\)
\(a_{16}=-1.132866825\) \(a_{17}=+1.713487786\) \(a_{18}=+0.341699061\) \(a_{19}=-0.229415734\) \(a_{20}=+0.060221935\)
\(a_{21}=+0.705590935\) \(a_{22}=+1.244221820\) \(a_{23}=-1.577562990\) \(a_{24}=-0.748647540\) \(a_{25}=-0.854267809\)
\(a_{26}=+0.108062423\) \(a_{27}=+1.088435562\) \(a_{28}=-0.134741091\) \(a_{29}=+0.192864726\) \(a_{30}=+0.339324760\)
\(a_{31}=-0.983391772\) \(a_{32}=+0.312703531\) \(a_{33}=+0.955256042\) \(a_{34}=-1.843694350\) \(a_{35}=-0.326062495\)
\(a_{36}=-0.050097128\) \(a_{37}=+0.190900113\) \(a_{38}=+0.246848852\) \(a_{39}=+0.082965337\) \(a_{40}=+0.345959497\)
\(a_{41}=+0.093636825\) \(a_{42}=-0.759208225\) \(a_{43}=+0.166795993\) \(a_{44}=-0.182417651\) \(a_{45}=-0.121230981\)
\(a_{46}=+1.697440739\) \(a_{47}=+1.463704479\) \(a_{48}=+0.935855400\) \(a_{49}=-0.270464883\) \(a_{50}=+0.919182936\)
\(a_{51}=-1.415503360\) \(a_{52}=-0.015843231\) \(a_{53}=-0.431496124\) \(a_{54}=-1.171144909\) \(a_{55}=-0.441435899\)
\(a_{56}=-0.774052845\) \(a_{57}=+0.189519146\) \(a_{58}=-0.207520362\) \(a_{59}=-0.996020230\) \(a_{60}=-0.049749028\)
\(a_{61}=-1.226789204\) \(a_{62}=+1.058118926\) \(a_{63}=+0.271243272\) \(a_{64}=+0.796401203\) \(a_{65}=-0.038339332\)
\(a_{66}=-1.027845183\) \(a_{67}=-0.371116479\) \(a_{68}=+0.270307422\) \(a_{69}=+1.303216593\) \(a_{70}=+0.350839723\)
\(a_{71}=+1.310719702\) \(a_{72}=-0.287795092\) \(a_{73}=-0.094659582\) \(a_{74}=-0.205406460\) \(a_{75}=+0.705706200\)
\(a_{76}=-0.036190965\) \(a_{77}=+0.987672593\) \(a_{78}=-0.089269807\) \(a_{79}=+0.519310801\) \(a_{80}=-0.432470617\)
\(a_{81}=-0.581583593\) \(a_{82}=-0.100752213\) \(a_{83}=-1.365636113\) \(a_{84}=+0.111308915\) \(a_{85}=+0.654122006\)
\(a_{86}=-0.179470687\) \(a_{87}=-0.159324548\) \(a_{88}=-1.047942398\) \(a_{89}=+0.652525046\) \(a_{90}=+0.130443227\)
\(a_{91}=+0.085780760\) \(a_{92}=-0.248864911\) \(a_{93}=+0.812374835\) \(a_{94}=-1.574930210\) \(a_{95}=-0.087579195\)
\(a_{96}=-0.258322763\) \(a_{97}=+0.416883890\) \(a_{98}=+0.291017293\) \(a_{99}=+0.367219534\) \(a_{100}=-0.134763102\)

Showing 100 of 546 available coefficients

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