Properties

Level $33$
Weight $0$
Character 33.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.82341375434 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.781642116\) \(a_{3}=+0.577350269\) \(a_{4}=+2.174248629\) \(a_{5}=+1.260927423\)
\(a_{6}=-1.028631555\) \(a_{7}=+0.629997017\) \(a_{8}=-2.092090811\) \(a_{9}=+0.333333333\) \(a_{10}=-2.246521401\)
\(a_{11}=-0.301511345\) \(a_{12}=+1.255303031\) \(a_{13}=+1.244755047\) \(a_{14}=-1.122429219\) \(a_{15}=+0.727996787\)
\(a_{16}=+1.553108470\) \(a_{17}=+0.041391039\) \(a_{18}=-0.593880705\) \(a_{19}=-1.288175234\) \(a_{20}=+2.741569719\)
\(a_{21}=+0.363728947\) \(a_{22}=+0.537185310\) \(a_{23}=-0.712198186\) \(a_{24}=-1.207869193\) \(a_{25}=+0.589937965\)
\(a_{26}=-2.217708015\) \(a_{27}=+0.192450090\) \(a_{28}=+1.369770151\) \(a_{29}=+0.127557827\) \(a_{30}=-1.297029736\)
\(a_{31}=-1.217883361\) \(a_{32}=-0.674992649\) \(a_{33}=-0.174077656\) \(a_{34}=-0.073744019\) \(a_{35}=+0.794380516\)
\(a_{36}=+0.724749543\) \(a_{37}=+1.160183354\) \(a_{38}=+2.295067248\) \(a_{39}=+0.718659663\) \(a_{40}=-2.637974671\)
\(a_{41}=-0.237434523\) \(a_{42}=-0.648034813\) \(a_{43}=-0.345200010\) \(a_{44}=-0.655560629\) \(a_{45}=+0.420309139\)
\(a_{46}=+1.268882291\) \(a_{47}=-0.616185601\) \(a_{48}=+0.896687607\) \(a_{49}=-0.603103770\) \(a_{50}=-1.051058320\)
\(a_{51}=+0.023897134\) \(a_{52}=+2.706406936\) \(a_{53}=-0.559791007\) \(a_{54}=-0.342877208\) \(a_{55}=-0.380183901\)
\(a_{56}=-1.318010992\) \(a_{57}=-0.743728311\) \(a_{58}=-0.227262386\) \(a_{59}=+0.388743272\) \(a_{60}=+1.582846068\)
\(a_{61}=-0.877411495\) \(a_{62}=+2.169832329\) \(a_{63}=+0.209999015\) \(a_{64}=-0.350513187\) \(a_{65}=+1.569545867\)
\(a_{66}=+0.310144082\) \(a_{67}=+1.580556600\) \(a_{68}=+0.089994412\) \(a_{69}=-0.411187818\) \(a_{70}=-1.415301814\)
\(a_{71}=+0.022062878\) \(a_{72}=-0.697363630\) \(a_{73}=-0.985782206\) \(a_{74}=-2.067031398\) \(a_{75}=+0.340600825\)
\(a_{76}=-2.800813311\) \(a_{77}=-0.189951183\) \(a_{78}=-1.280394399\) \(a_{79}=-0.450245343\) \(a_{80}=+1.958357347\)
\(a_{81}=+0.111111100\) \(a_{82}=+0.423023279\) \(a_{83}=+0.237723673\) \(a_{84}=+0.790837116\) \(a_{85}=+0.052191261\)
\(a_{86}=+0.615022879\) \(a_{87}=+0.073645547\) \(a_{88}=+0.630789111\) \(a_{89}=+0.649375804\) \(a_{90}=-0.748840473\)
\(a_{91}=+0.784191975\) \(a_{92}=-1.548495944\) \(a_{93}=-0.703145290\) \(a_{94}=+1.097822183\) \(a_{95}=-1.624295481\)
\(a_{96}=-0.389707204\) \(a_{97}=+1.573377281\) \(a_{98}=+1.074514954\) \(a_{99}=-0.100503756\) \(a_{100}=+1.282671813\)

Showing 100 of 2000 available coefficients

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