Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 15.7048957513 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.368517376\) \(a_{3}=+0.577350269\) \(a_{4}=+0.872839808\) \(a_{5}=-1.413387963\)
\(a_{6}=-0.790113875\) \(a_{7}=+1.088784410\) \(a_{8}=+0.174020932\) \(a_{9}=+0.333333333\) \(a_{10}=+1.934245986\)
\(a_{11}=-0.296611514\) \(a_{12}=+0.503934298\) \(a_{13}=+1.225643224\) \(a_{14}=-1.490020383\) \(a_{15}=-0.816019921\)
\(a_{16}=-1.110990478\) \(a_{17}=+0.245563899\) \(a_{18}=-0.456172459\) \(a_{19}=-1.066072686\) \(a_{20}=-1.233661278\)
\(a_{21}=+0.628609972\) \(a_{22}=+0.405918010\) \(a_{23}=-1.033468070\) \(a_{24}=+0.100471032\) \(a_{25}=+0.997665533\)
\(a_{26}=-1.677314048\) \(a_{27}=+0.192450090\) \(a_{28}=+0.950334375\) \(a_{29}=-1.127627257\) \(a_{30}=+1.116737441\)
\(a_{31}=-1.069778663\) \(a_{32}=+1.346388841\) \(a_{33}=-0.171248737\) \(a_{34}=-0.336058462\) \(a_{35}=-1.538874779\)
\(a_{36}=+0.290946603\) \(a_{37}=+0.249233809\) \(a_{38}=+1.458938994\) \(a_{39}=+0.707625445\) \(a_{40}=-0.245959091\)
\(a_{41}=-1.514938145\) \(a_{42}=-0.860263669\) \(a_{43}=+0.855731906\) \(a_{44}=-0.258894337\) \(a_{45}=-0.471129321\)
\(a_{46}=+1.414319011\) \(a_{47}=+0.799673751\) \(a_{48}=-0.641430651\) \(a_{49}=+0.185451491\) \(a_{50}=-1.365322617\)
\(a_{51}=+0.141776383\) \(a_{52}=+1.069790196\) \(a_{53}=-0.923468881\) \(a_{54}=-0.263371292\) \(a_{55}=+0.419227143\)
\(a_{56}=+0.189471278\) \(a_{57}=-0.615497352\) \(a_{58}=+1.543177494\) \(a_{59}=-0.535815721\) \(a_{60}=-0.712254671\)
\(a_{61}=-0.180638294\) \(a_{62}=+1.464010689\) \(a_{63}=+0.362928137\) \(a_{64}=-0.731566046\) \(a_{65}=-1.732309379\)
\(a_{66}=+0.234356872\) \(a_{67}=+0.043080332\) \(a_{68}=+0.214337946\) \(a_{69}=-0.596673068\) \(a_{70}=+2.105976874\)
\(a_{71}=-0.125438606\) \(a_{72}=+0.058006977\) \(a_{73}=+0.121700439\) \(a_{74}=-0.341080798\) \(a_{75}=+0.576002464\)
\(a_{76}=-0.930510678\) \(a_{77}=-0.322945992\) \(a_{78}=-0.968397717\) \(a_{79}=-1.732757631\) \(a_{80}=+1.570260568\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.073219175\) \(a_{83}=+0.276991090\) \(a_{84}=+0.548675807\) \(a_{85}=-0.347077059\)
\(a_{86}=-1.171083982\) \(a_{87}=-0.651035900\) \(a_{88}=-0.051616612\) \(a_{89}=-0.466268792\) \(a_{90}=+0.644748662\)
\(a_{91}=+1.334461234\) \(a_{92}=-0.902052072\) \(a_{93}=-0.617636999\) \(a_{94}=-1.094367423\) \(a_{95}=+1.506774302\)
\(a_{96}=+0.777337960\) \(a_{97}=-1.106959494\) \(a_{98}=-0.253793587\) \(a_{99}=-0.098870505\) \(a_{100}=+0.870802192\)

Showing 100 of 1228 available coefficients

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