Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.23123939014 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.813576096\) \(a_{3}=-1.258457446\) \(a_{4}=-0.338093936\) \(a_{5}=+1.458631098\)
\(a_{6}=-1.023850896\) \(a_{7}=-1.619178827\) \(a_{8}=-1.088641241\) \(a_{9}=+0.583715144\) \(a_{10}=+1.186707394\)
\(a_{11}=-0.717657946\) \(a_{12}=+0.425476832\) \(a_{13}=+0.559381878\) \(a_{14}=-1.317325188\) \(a_{15}=-1.835625167\)
\(a_{16}=-0.547598554\) \(a_{17}=+0.720122985\) \(a_{18}=+0.474896688\) \(a_{19}=-0.262358870\) \(a_{20}=-0.493154329\)
\(a_{21}=+2.037667651\) \(a_{22}=-0.583869350\) \(a_{23}=-1.461805585\) \(a_{24}=+1.370008676\) \(a_{25}=+1.127604680\)
\(a_{26}=+0.455099724\) \(a_{27}=+0.523876777\) \(a_{28}=+0.547434543\) \(a_{29}=-1.383630883\) \(a_{30}=-1.493420757\)
\(a_{31}=+0.179605302\) \(a_{32}=+0.643128147\) \(a_{33}=+0.903141987\) \(a_{34}=+0.585874847\) \(a_{35}=-2.361784590\)
\(a_{36}=-0.197350551\) \(a_{37}=-0.859296043\) \(a_{38}=-0.213448905\) \(a_{39}=-0.703958289\) \(a_{40}=-1.587925968\)
\(a_{41}=+0.160826127\) \(a_{42}=+1.657797692\) \(a_{43}=+0.612099218\) \(a_{44}=+0.242635800\) \(a_{45}=+0.851425062\)
\(a_{46}=-1.189290081\) \(a_{47}=+0.873074769\) \(a_{48}=+0.689129478\) \(a_{49}=+1.621740072\) \(a_{50}=+0.917392214\)
\(a_{51}=-0.906244133\) \(a_{52}=-0.189123621\) \(a_{53}=-1.608158346\) \(a_{54}=+0.426213623\) \(a_{55}=-1.046798198\)
\(a_{56}=+1.762704846\) \(a_{57}=+0.330167474\) \(a_{58}=-1.125689012\) \(a_{59}=+0.690086194\) \(a_{60}=+0.620613738\)
\(a_{61}=-1.877347220\) \(a_{62}=+0.146122580\) \(a_{63}=-0.945139202\) \(a_{64}=+1.070832241\) \(a_{65}=+0.815931802\)
\(a_{66}=+0.734774731\) \(a_{67}=-0.070345852\) \(a_{68}=-0.243469214\) \(a_{69}=+1.839620124\) \(a_{70}=-1.921491486\)
\(a_{71}=-0.330203895\) \(a_{72}=-0.635456379\) \(a_{73}=+0.020757386\) \(a_{74}=-0.699102720\) \(a_{75}=-1.419042507\)
\(a_{76}=+0.088701943\) \(a_{77}=+1.162016552\) \(a_{78}=-0.572723637\) \(a_{79}=-0.256091888\) \(a_{80}=-0.798744280\)
\(a_{81}=-1.242991775\) \(a_{82}=+0.130844293\) \(a_{83}=+0.936482052\) \(a_{84}=-0.688923077\) \(a_{85}=+1.050393780\)
\(a_{86}=+0.497989292\) \(a_{87}=+1.741240588\) \(a_{88}=+0.781272037\) \(a_{89}=-0.790316666\) \(a_{90}=+0.692699078\)
\(a_{91}=-0.905739292\) \(a_{92}=+0.494227604\) \(a_{93}=-0.226025630\) \(a_{94}=+0.710312762\) \(a_{95}=-0.382684807\)
\(a_{96}=-0.809349405\) \(a_{97}=+0.779220941\) \(a_{98}=+1.319408957\) \(a_{99}=-0.418907812\) \(a_{100}=-0.381236305\)

Showing 100 of 546 available coefficients

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