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: \( 29.2867591963 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.941148686\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.665492618\) \(a_{7}=+1.385586559\) \(a_{8}=+0.353553391\) \(a_{9}=-0.114239152\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.091940944\) \(a_{12}=-0.470574343\) \(a_{13}=+1.397785265\) \(a_{14}=+0.979757652\) \(a_{15}=-0.420894488\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.665694746\) \(a_{18}=-0.080779279\) \(a_{19}=+1.356875560\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.304042969\) \(a_{22}=+0.772118846\) \(a_{23}=-0.109655468\) \(a_{24}=-0.332746309\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.988383439\) \(a_{27}=+1.048664713\) \(a_{28}=+0.692793280\) \(a_{29}=+0.812676636\) \(a_{30}=-0.297617346\)
\(a_{31}=-0.706899098\) \(a_{32}=+0.176776695\) \(a_{33}=-1.027678784\) \(a_{34}=+1.177824050\) \(a_{35}=+0.619653147\)
\(a_{36}=-0.057119576\) \(a_{37}=-0.228881977\) \(a_{38}=+0.959455910\) \(a_{39}=-1.315523764\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.084974605\) \(a_{42}=-0.922097626\) \(a_{43}=+0.385881661\) \(a_{44}=+0.545970472\) \(a_{45}=-0.051089302\)
\(a_{46}=-0.077538125\) \(a_{47}=+1.499114762\) \(a_{48}=-0.235287171\) \(a_{49}=+0.919850114\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.567666421\) \(a_{52}=+0.698892632\) \(a_{53}=+1.090658381\) \(a_{54}=+0.741517930\) \(a_{55}=+0.488330836\)
\(a_{56}=+0.489878826\) \(a_{57}=-1.277021650\) \(a_{58}=+0.574649160\) \(a_{59}=+0.289128190\) \(a_{60}=-0.210447244\)
\(a_{61}=-1.428006347\) \(a_{62}=-0.499853146\) \(a_{63}=-0.158288233\) \(a_{64}=+0.125000000\) \(a_{65}=+0.625108574\)
\(a_{66}=-0.726678637\) \(a_{67}=-0.613260373\) \(a_{68}=+0.832847373\) \(a_{69}=+0.103202100\) \(a_{70}=+0.438160942\)
\(a_{71}=-1.747817715\) \(a_{72}=-0.040389639\) \(a_{73}=-1.637560811\) \(a_{74}=-0.161843998\) \(a_{75}=-0.188229737\)
\(a_{76}=+0.678437780\) \(a_{77}=+1.512978696\) \(a_{78}=-0.930215775\) \(a_{79}=-0.867019901\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.872710265\) \(a_{82}=-0.060086120\) \(a_{83}=-1.713868181\) \(a_{84}=-0.652021485\) \(a_{85}=+0.744921336\)
\(a_{86}=+0.272859539\) \(a_{87}=-0.764849547\) \(a_{88}=+0.386059423\) \(a_{89}=-0.454485975\) \(a_{90}=-0.036125592\)
\(a_{91}=+1.936752476\) \(a_{92}=-0.054827734\) \(a_{93}=+0.665297157\) \(a_{94}=+1.060034214\) \(a_{95}=+0.606813198\)
\(a_{96}=-0.166373154\) \(a_{97}=+0.769166587\) \(a_{98}=+0.650432253\) \(a_{99}=-0.124742407\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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