Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 14.0972037339 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.523137556\) \(a_{4}=+0.500000000\) \(a_{5}=+0.538489032\)
\(a_{6}=-1.077020895\) \(a_{7}=+1.105047713\) \(a_{8}=+0.353553391\) \(a_{9}=+1.319948015\) \(a_{10}=+0.380769246\)
\(a_{11}=+1.065335905\) \(a_{12}=-0.761568774\) \(a_{13}=+0.530695332\) \(a_{14}=+0.781386732\) \(a_{15}=-0.820192869\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.519277670\) \(a_{18}=+0.933344192\) \(a_{19}=-0.126023658\) \(a_{20}=+0.269244516\)
\(a_{21}=-1.683139673\) \(a_{22}=+0.753306243\) \(a_{23}=+1.302569051\) \(a_{24}=-0.538510447\) \(a_{25}=-0.710029562\)
\(a_{26}=+0.375258268\) \(a_{27}=-0.487324837\) \(a_{28}=+0.552523857\) \(a_{29}=-0.034359096\) \(a_{30}=-0.579963939\)
\(a_{31}=+1.312997564\) \(a_{32}=+0.176776695\) \(a_{33}=-1.622653128\) \(a_{34}=-0.367184761\) \(a_{35}=+0.595056074\)
\(a_{36}=+0.659974007\) \(a_{37}=+0.469382758\) \(a_{38}=-0.089112183\) \(a_{39}=-0.808321990\) \(a_{40}=+0.190384623\)
\(a_{41}=+0.127537921\) \(a_{42}=-1.190159477\) \(a_{43}=+0.469168181\) \(a_{44}=+0.532667953\) \(a_{45}=+0.710777529\)
\(a_{46}=+0.921055409\) \(a_{47}=-1.688531541\) \(a_{48}=-0.380784389\) \(a_{49}=+0.221130449\) \(a_{50}=-0.502066718\)
\(a_{51}=+0.790931320\) \(a_{52}=+0.265347667\) \(a_{53}=-0.327582907\) \(a_{54}=-0.344590698\) \(a_{55}=+0.573671703\)
\(a_{56}=+0.390693365\) \(a_{57}=+0.191951368\) \(a_{58}=-0.024295541\) \(a_{59}=-1.153618510\) \(a_{60}=-0.410096434\)
\(a_{61}=-0.848470591\) \(a_{62}=+0.928429481\) \(a_{63}=+1.458605535\) \(a_{64}=+0.125000000\) \(a_{65}=+0.285773616\)
\(a_{66}=-1.147389030\) \(a_{67}=+0.776944543\) \(a_{68}=-0.259638835\) \(a_{69}=-1.983991841\) \(a_{70}=+0.420768185\)
\(a_{71}=+1.160580104\) \(a_{72}=+0.466672096\) \(a_{73}=-1.480530849\) \(a_{74}=+0.331903731\) \(a_{75}=+1.081472692\)
\(a_{76}=-0.063011829\) \(a_{77}=+1.177247006\) \(a_{78}=-0.571569961\) \(a_{79}=-1.603243253\) \(a_{80}=+0.134622258\)
\(a_{81}=-0.577685253\) \(a_{82}=+0.090182929\) \(a_{83}=+1.602496719\) \(a_{84}=-0.841569837\) \(a_{85}=-0.279625330\)
\(a_{86}=+0.331752002\) \(a_{87}=+0.052333629\) \(a_{88}=+0.376653121\) \(a_{89}=-0.256230392\) \(a_{90}=+0.502595611\)
\(a_{91}=+0.586443663\) \(a_{92}=+0.651284525\) \(a_{93}=-1.999875901\) \(a_{94}=-1.193972101\) \(a_{95}=-0.067862359\)
\(a_{96}=-0.269255224\) \(a_{97}=+1.196334812\) \(a_{98}=+0.156362834\) \(a_{99}=+1.406188016\) \(a_{100}=-0.355014779\)

Showing 100 of 5000 available coefficients

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