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: \( 30.2223231519 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.532180173\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.376308209\) \(a_{7}=-1.376558912\) \(a_{8}=+0.353553391\) \(a_{9}=-0.716784264\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.484182386\) \(a_{12}=+0.266090086\) \(a_{13}=+0.890670567\) \(a_{14}=-0.973374142\) \(a_{15}=+0.237998209\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.733400254\) \(a_{18}=-0.506843014\) \(a_{19}=+0.338092230\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.732577360\) \(a_{22}=-0.342368648\) \(a_{23}=+0.424407198\) \(a_{24}=+0.188154104\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.629799198\) \(a_{27}=-0.913638546\) \(a_{28}=-0.688279456\) \(a_{29}=-0.294361814\) \(a_{30}=+0.168290147\)
\(a_{31}=-1.549600262\) \(a_{32}=+0.176776695\) \(a_{33}=-0.257672266\) \(a_{34}=+0.518592293\) \(a_{35}=-0.615615861\)
\(a_{36}=-0.358392132\) \(a_{37}=+0.048805347\) \(a_{38}=+0.239067308\) \(a_{39}=+0.473997216\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.662318294\) \(a_{42}=-0.518010419\) \(a_{43}=-0.543739692\) \(a_{44}=-0.242091193\) \(a_{45}=-0.320555668\)
\(a_{46}=+0.300101207\) \(a_{47}=+1.281581798\) \(a_{48}=+0.133045043\) \(a_{49}=+0.894914439\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.390301074\) \(a_{52}=+0.445335284\) \(a_{53}=-0.289481786\) \(a_{54}=-0.646040011\) \(a_{55}=-0.216532946\)
\(a_{56}=-0.486687071\) \(a_{57}=+0.179925981\) \(a_{58}=-0.208145235\) \(a_{59}=+1.687168490\) \(a_{60}=+0.118999104\)
\(a_{61}=-0.456928467\) \(a_{62}=-1.095732853\) \(a_{63}=+0.986695766\) \(a_{64}=+0.125000000\) \(a_{65}=+0.398319987\)
\(a_{66}=-0.182201806\) \(a_{67}=+0.548550481\) \(a_{68}=+0.366700127\) \(a_{69}=+0.225861096\) \(a_{70}=-0.435306150\)
\(a_{71}=+1.221208248\) \(a_{72}=-0.253421507\) \(a_{73}=+0.557209255\) \(a_{74}=+0.034510592\) \(a_{75}=+0.106436035\)
\(a_{76}=+0.169046115\) \(a_{77}=+0.666505578\) \(a_{78}=+0.335166646\) \(a_{79}=-1.702077541\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.230563944\) \(a_{82}=+0.468329757\) \(a_{83}=+0.916120118\) \(a_{84}=-0.366288680\) \(a_{85}=+0.327986564\)
\(a_{86}=-0.384482023\) \(a_{87}=-0.156653521\) \(a_{88}=-0.171184324\) \(a_{89}=-0.951344905\) \(a_{90}=-0.226667086\)
\(a_{91}=-1.226060507\) \(a_{92}=+0.212203599\) \(a_{93}=-0.824666535\) \(a_{94}=+0.906215180\) \(a_{95}=+0.151199442\)
\(a_{96}=+0.094077052\) \(a_{97}=+1.069860047\) \(a_{98}=+0.632800068\) \(a_{99}=+0.347054315\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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