Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 26.3524008204 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.411244700\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.290793916\) \(a_{7}=-0.703642669\) \(a_{8}=+0.353553391\) \(a_{9}=-0.830877797\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.203409645\) \(a_{12}=-0.205622350\) \(a_{13}=+0.339570871\) \(a_{14}=-0.497550503\) \(a_{15}=-0.183914221\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.776667700\) \(a_{18}=-0.587519324\) \(a_{19}=-0.421631161\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.289369319\) \(a_{22}=+0.143832339\) \(a_{23}=+0.771187765\) \(a_{24}=-0.145396958\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.240112866\) \(a_{27}=+0.752938790\) \(a_{28}=-0.351821335\) \(a_{29}=-0.146712838\) \(a_{30}=-0.130046993\)
\(a_{31}=+0.316899118\) \(a_{32}=+0.176776695\) \(a_{33}=-0.083651138\) \(a_{34}=+0.549186997\) \(a_{35}=-0.314678568\)
\(a_{36}=-0.415438898\) \(a_{37}=-0.880440502\) \(a_{38}=-0.298138253\) \(a_{39}=-0.139646721\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.552590284\) \(a_{42}=+0.204615007\) \(a_{43}=-0.881361138\) \(a_{44}=+0.101704822\) \(a_{45}=-0.371579847\)
\(a_{46}=+0.545312099\) \(a_{47}=+0.680364069\) \(a_{48}=-0.102811175\) \(a_{49}=-0.504886994\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.319400475\) \(a_{52}=+0.169785436\) \(a_{53}=-0.970105073\) \(a_{54}=+0.532408125\) \(a_{55}=+0.090967559\)
\(a_{56}=-0.248775252\) \(a_{57}=+0.173393580\) \(a_{58}=-0.103741643\) \(a_{59}=+1.325231502\) \(a_{60}=-0.091957110\)
\(a_{61}=+1.244749642\) \(a_{62}=+0.224081516\) \(a_{63}=+0.584641071\) \(a_{64}=+0.125000000\) \(a_{65}=+0.151860710\)
\(a_{66}=-0.059150287\) \(a_{67}=-0.091849745\) \(a_{68}=+0.388333850\) \(a_{69}=-0.317146881\) \(a_{70}=-0.222511349\)
\(a_{71}=-1.518815403\) \(a_{72}=-0.293759662\) \(a_{73}=-0.169881045\) \(a_{74}=-0.622565449\) \(a_{75}=-0.082248940\)
\(a_{76}=-0.210815581\) \(a_{77}=-0.143127705\) \(a_{78}=-0.098745143\) \(a_{79}=+0.543020944\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.521235709\) \(a_{82}=-0.390740337\) \(a_{83}=-1.517548765\) \(a_{84}=+0.144684659\) \(a_{85}=+0.347336355\)
\(a_{86}=-0.623216438\) \(a_{87}=+0.060334877\) \(a_{88}=+0.071916170\) \(a_{89}=+0.212078769\) \(a_{90}=-0.262746629\)
\(a_{91}=-0.238936554\) \(a_{92}=+0.385593883\) \(a_{93}=-0.130323083\) \(a_{94}=+0.481090047\) \(a_{95}=-0.188559188\)
\(a_{96}=-0.072698479\) \(a_{97}=-1.295959530\) \(a_{98}=-0.357009017\) \(a_{99}=-0.169008557\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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