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: \( 6.4845713681 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.595578529\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=-1.128244397\) \(a_{7}=+1.429328252\) \(a_{8}=+0.353553391\) \(a_{9}=+1.545870841\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.165764734\) \(a_{12}=-0.797789264\) \(a_{13}=+0.577731306\) \(a_{14}=+1.010687700\) \(a_{15}=-0.713564411\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.964544706\) \(a_{18}=+1.093095754\) \(a_{19}=+1.762468763\) \(a_{20}=+0.223606798\)
\(a_{21}=-2.280605470\) \(a_{22}=+0.117213368\) \(a_{23}=+0.272053286\) \(a_{24}=-0.564122199\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.408517724\) \(a_{27}=-0.870979793\) \(a_{28}=+0.714664126\) \(a_{29}=+0.611671210\) \(a_{30}=-0.504566234\)
\(a_{31}=+0.589121985\) \(a_{32}=+0.176776695\) \(a_{33}=-0.264490651\) \(a_{34}=-0.682036103\) \(a_{35}=+0.639215027\)
\(a_{36}=+0.772935420\) \(a_{37}=-1.405112331\) \(a_{38}=+1.246253614\) \(a_{39}=-0.921815668\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.288727059\) \(a_{42}=-1.612631593\) \(a_{43}=-0.780251746\) \(a_{44}=+0.082882367\) \(a_{45}=+0.691334457\)
\(a_{46}=+0.192370724\) \(a_{47}=+1.046107630\) \(a_{48}=-0.398894632\) \(a_{49}=+1.042979253\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.539006823\) \(a_{52}=+0.288865653\) \(a_{53}=-1.311551785\) \(a_{54}=-0.615875718\) \(a_{55}=+0.074132243\)
\(a_{56}=+0.505343850\) \(a_{57}=-2.812157315\) \(a_{58}=+0.432516861\) \(a_{59}=-0.925550214\) \(a_{60}=-0.356782205\)
\(a_{61}=+0.122720205\) \(a_{62}=+0.416572151\) \(a_{63}=+2.209556867\) \(a_{64}=+0.125000000\) \(a_{65}=+0.258369295\)
\(a_{66}=-0.187023133\) \(a_{67}=-0.343113807\) \(a_{68}=-0.482272353\) \(a_{69}=-0.434082382\) \(a_{70}=+0.451993280\)
\(a_{71}=+0.444035480\) \(a_{72}=+0.546547877\) \(a_{73}=+0.085529360\) \(a_{74}=-0.993564457\) \(a_{75}=-0.319115706\)
\(a_{76}=+0.881234381\) \(a_{77}=+0.236932218\) \(a_{78}=-0.651822110\) \(a_{79}=+1.295369600\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.156154184\) \(a_{82}=+0.204160861\) \(a_{83}=-0.924409800\) \(a_{84}=-1.140302735\) \(a_{85}=-0.431357506\)
\(a_{86}=-0.551721301\) \(a_{87}=-0.975969449\) \(a_{88}=+0.058606684\) \(a_{89}=+1.050752997\) \(a_{90}=+0.488847283\)
\(a_{91}=+0.825767678\) \(a_{92}=+0.136026643\) \(a_{93}=-0.939990390\) \(a_{94}=+0.739709799\) \(a_{95}=+0.788199992\)
\(a_{96}=-0.282061099\) \(a_{97}=-0.900330000\) \(a_{98}=+0.737497702\) \(a_{99}=+0.256250869\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

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