Properties

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

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.28315858769 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.218296925\) \(a_{3}=+0.076006205\) \(a_{4}=+0.484247395\) \(a_{5}=-1.439783038\)
\(a_{6}=-0.092598126\) \(a_{7}=+1.485030356\) \(a_{8}=+0.628339811\) \(a_{9}=-0.994223057\) \(a_{10}=+1.754083246\)
\(a_{11}=-0.263802309\) \(a_{12}=+0.036805806\) \(a_{13}=+1.697409544\) \(a_{14}=-1.809207915\) \(a_{15}=-0.109432445\)
\(a_{16}=-1.249751856\) \(a_{17}=+0.959070378\) \(a_{18}=+1.211258893\) \(a_{19}=-0.229415734\) \(a_{20}=-0.697211187\)
\(a_{21}=+0.112871522\) \(a_{22}=+0.321389541\) \(a_{23}=+0.038668378\) \(a_{24}=+0.047757724\) \(a_{25}=+1.072975194\)
\(a_{26}=-2.067948827\) \(a_{27}=-0.151573326\) \(a_{28}=+0.719122083\) \(a_{29}=+0.806003513\) \(a_{30}=+0.133321210\)
\(a_{31}=+0.917904746\) \(a_{32}=+0.894229031\) \(a_{33}=-0.020050612\) \(a_{34}=-1.168432491\) \(a_{35}=-2.138121516\)
\(a_{36}=-0.481449926\) \(a_{37}=+1.008922036\) \(a_{38}=+0.279496483\) \(a_{39}=+0.129013658\) \(a_{40}=-0.904673002\)
\(a_{41}=-0.953416069\) \(a_{42}=-0.137511027\) \(a_{43}=+0.553844578\) \(a_{44}=-0.127745581\) \(a_{45}=+1.431465493\)
\(a_{46}=-0.047109568\) \(a_{47}=+0.302083683\) \(a_{48}=-0.094988897\) \(a_{49}=+1.205315161\) \(a_{50}=-1.307202378\)
\(a_{51}=+0.072895293\) \(a_{52}=+0.821966158\) \(a_{53}=+0.640795367\) \(a_{54}=+0.184661323\) \(a_{55}=+0.379818079\)
\(a_{56}=+0.933103673\) \(a_{57}=-0.017437019\) \(a_{58}=-0.981951603\) \(a_{59}=-1.214869397\) \(a_{60}=-0.052992376\)
\(a_{61}=+0.688283641\) \(a_{62}=-1.118280528\) \(a_{63}=-1.476451420\) \(a_{64}=+0.160315380\) \(a_{65}=-2.443901469\)
\(a_{66}=+0.024427596\) \(a_{67}=+0.422555144\) \(a_{68}=+0.464427335\) \(a_{69}=+0.002939040\) \(a_{70}=+2.604866863\)
\(a_{71}=+0.937094224\) \(a_{72}=-0.624709925\) \(a_{73}=+0.433437108\) \(a_{74}=-1.229166607\) \(a_{75}=+0.081552757\)
\(a_{76}=-0.111093981\) \(a_{77}=-0.391754438\) \(a_{78}=-0.157176927\) \(a_{79}=-0.465521128\) \(a_{80}=+1.799371474\)
\(a_{81}=+0.982702520\) \(a_{82}=+1.161543844\) \(a_{83}=+0.947894371\) \(a_{84}=+0.054657740\) \(a_{85}=-1.380853258\)
\(a_{86}=-0.674747143\) \(a_{87}=+0.061261266\) \(a_{88}=-0.165757502\) \(a_{89}=-1.610612172\) \(a_{90}=-1.743950004\)
\(a_{91}=+2.520704709\) \(a_{92}=+0.018725064\) \(a_{93}=+0.069766434\) \(a_{94}=-0.368027613\) \(a_{95}=+0.330308873\)
\(a_{96}=+0.067966966\) \(a_{97}=-0.810158717\) \(a_{98}=-1.468431752\) \(a_{99}=+0.262278387\) \(a_{100}=+0.519585377\)

Showing 100 of 1500 available coefficients

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