Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 26.7760271783 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.334892347\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.236804649\) \(a_{7}=+1.017133205\) \(a_{8}=-0.353553391\) \(a_{9}=-0.887847116\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.314089431\) \(a_{12}=+0.167446173\) \(a_{13}=+0.451924767\) \(a_{14}=-0.719221786\) \(a_{15}=+0.149768410\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.706749339\) \(a_{18}=+0.627802717\) \(a_{19}=+0.062837386\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.340630126\) \(a_{22}=+0.929201548\) \(a_{23}=-1.401645572\) \(a_{24}=-0.118402325\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.319559067\) \(a_{27}=-0.632225551\) \(a_{28}=+0.508566602\) \(a_{29}=+0.490113637\) \(a_{30}=-0.105902259\)
\(a_{31}=+0.137761105\) \(a_{32}=-0.176776695\) \(a_{33}=-0.440078493\) \(a_{34}=-1.206854031\) \(a_{35}=+0.454875798\)
\(a_{36}=-0.443923558\) \(a_{37}=+0.835132146\) \(a_{38}=-0.044432742\) \(a_{39}=+0.151346146\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.371555800\) \(a_{42}=-0.240861872\) \(a_{43}=-1.339934434\) \(a_{44}=-0.657044716\) \(a_{45}=-0.397057301\)
\(a_{46}=+0.991113088\) \(a_{47}=+0.303594668\) \(a_{48}=+0.083723087\) \(a_{49}=+0.034559956\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.571577291\) \(a_{52}=+0.225962383\) \(a_{53}=-1.627055048\) \(a_{54}=+0.447050974\) \(a_{55}=-0.587678659\)
\(a_{56}=-0.359610893\) \(a_{57}=+0.021043760\) \(a_{58}=-0.346562676\) \(a_{59}=+1.010234070\) \(a_{60}=+0.074884205\)
\(a_{61}=-1.226527876\) \(a_{62}=-0.097411811\) \(a_{63}=-0.903058783\) \(a_{64}=+0.125000000\) \(a_{65}=+0.202106900\)
\(a_{66}=+0.311182487\) \(a_{67}=-1.013188746\) \(a_{68}=+0.853374669\) \(a_{69}=-0.469400375\) \(a_{70}=-0.321645761\)
\(a_{71}=+1.851024254\) \(a_{72}=+0.313901358\) \(a_{73}=-1.066237728\) \(a_{74}=-0.590527603\) \(a_{75}=+0.066978469\)
\(a_{76}=+0.031418693\) \(a_{77}=-1.336603994\) \(a_{78}=-0.107017886\) \(a_{79}=+1.233758359\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.676119618\) \(a_{82}=+0.262729626\) \(a_{83}=+0.512048633\) \(a_{84}=+0.170315063\) \(a_{85}=+0.763281508\)
\(a_{86}=+0.947476725\) \(a_{87}=+0.164135306\) \(a_{88}=+0.464600774\) \(a_{89}=+0.829254449\) \(a_{90}=+0.280761910\)
\(a_{91}=+0.459667686\) \(a_{92}=-0.700822786\) \(a_{93}=+0.046135140\) \(a_{94}=-0.214673848\) \(a_{95}=+0.028101733\)
\(a_{96}=-0.059201162\) \(a_{97}=+0.784337665\) \(a_{98}=-0.024437579\) \(a_{99}=+1.166710512\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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