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: \( 25.7889209812 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.435001809\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.014699510\) \(a_{7}=-0.835511720\) \(a_{8}=+0.353553391\) \(a_{9}=+1.059230193\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.560085518\) \(a_{12}=-0.717500905\) \(a_{13}=+1.538986234\) \(a_{14}=-0.590796003\) \(a_{15}=+0.641752319\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.344575699\) \(a_{18}=+0.748988852\) \(a_{19}=-1.757439325\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.198960830\) \(a_{22}=-0.396040268\) \(a_{23}=+1.166174342\) \(a_{24}=-0.507349755\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.088227602\) \(a_{27}=-0.084995434\) \(a_{28}=-0.417755860\) \(a_{29}=+1.412334494\) \(a_{30}=+0.453787416\)
\(a_{31}=+1.099286370\) \(a_{32}=+0.176776695\) \(a_{33}=+0.803723732\) \(a_{34}=-0.950758595\) \(a_{35}=+0.373652200\)
\(a_{36}=+0.529615096\) \(a_{37}=-0.530462835\) \(a_{38}=-1.242697264\) \(a_{39}=-2.208448030\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.875711628\) \(a_{42}=+0.847793333\) \(a_{43}=+0.570923767\) \(a_{44}=-0.280042759\) \(a_{45}=-0.473702143\)
\(a_{46}=+0.824609786\) \(a_{47}=-0.398822448\) \(a_{48}=-0.358750452\) \(a_{49}=-0.301920166\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.929468561\) \(a_{52}=+0.769493117\) \(a_{53}=+0.304778129\) \(a_{54}=-0.060100848\) \(a_{55}=+0.250477858\)
\(a_{56}=-0.295398001\) \(a_{57}=+2.521928612\) \(a_{58}=+0.998671298\) \(a_{59}=-0.759768273\) \(a_{60}=+0.320876159\)
\(a_{61}=+1.431714139\) \(a_{62}=+0.777312847\) \(a_{63}=-0.884999240\) \(a_{64}=+0.125000000\) \(a_{65}=-0.688255567\)
\(a_{66}=+0.568318501\) \(a_{67}=+0.286284214\) \(a_{68}=-0.672287850\) \(a_{69}=-1.673462291\) \(a_{70}=+0.264212005\)
\(a_{71}=-0.535103323\) \(a_{72}=+0.374494426\) \(a_{73}=+0.361399338\) \(a_{74}=-0.375093868\) \(a_{75}=-0.287000362\)
\(a_{76}=-0.878719663\) \(a_{77}=+0.467958015\) \(a_{78}=-1.561608578\) \(a_{79}=+1.712780141\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.937261591\) \(a_{82}=+0.619221630\) \(a_{83}=+0.401675291\) \(a_{84}=+0.599480415\) \(a_{85}=+0.601312533\)
\(a_{86}=+0.403704067\) \(a_{87}=-2.026702555\) \(a_{88}=-0.198020134\) \(a_{89}=-0.599004671\) \(a_{90}=-0.334957998\)
\(a_{91}=-1.285841035\) \(a_{92}=+0.583087171\) \(a_{93}=-1.577477930\) \(a_{94}=-0.282010058\) \(a_{95}=+0.785950760\)
\(a_{96}=-0.253674878\) \(a_{97}=-0.040360821\) \(a_{98}=-0.213489797\) \(a_{99}=-0.593259492\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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