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: \( 9.44243727649 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.950600520\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.672176074\) \(a_{7}=+1.651226410\) \(a_{8}=+0.353553391\) \(a_{9}=-0.096358652\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.725122105\) \(a_{12}=+0.475300260\) \(a_{13}=-0.977539160\) \(a_{14}=+1.167593392\) \(a_{15}=-0.425121476\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.925369999\) \(a_{18}=-0.068135856\) \(a_{19}=+0.001200818\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.569656683\) \(a_{22}=+0.512738758\) \(a_{23}=+0.777016468\) \(a_{24}=+0.336088037\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.691224569\) \(a_{27}=-1.042199104\) \(a_{28}=+0.825613205\) \(a_{29}=+0.301591395\) \(a_{30}=-0.300606279\)
\(a_{31}=+0.483969645\) \(a_{32}=+0.176776695\) \(a_{33}=+0.689301450\) \(a_{34}=+1.361442183\) \(a_{35}=-0.738450900\)
\(a_{36}=-0.048179326\) \(a_{37}=-0.575121022\) \(a_{38}=+0.000849106\) \(a_{39}=-0.929249233\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.091684447\) \(a_{42}=+1.109914885\) \(a_{43}=-0.926878974\) \(a_{44}=+0.362561053\) \(a_{45}=+0.043092899\)
\(a_{46}=+0.549433613\) \(a_{47}=-1.482400170\) \(a_{48}=+0.237650130\) \(a_{49}=+1.726548657\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.830257722\) \(a_{52}=-0.488769580\) \(a_{53}=-1.578952742\) \(a_{54}=-0.736946054\) \(a_{55}=-0.324284464\)
\(a_{56}=+0.583796696\) \(a_{57}=+0.001141498\) \(a_{58}=+0.213257321\) \(a_{59}=-1.375605357\) \(a_{60}=-0.212560738\)
\(a_{61}=+0.143321016\) \(a_{62}=+0.342218218\) \(a_{63}=-0.159109951\) \(a_{64}=+0.125000000\) \(a_{65}=+0.437168802\)
\(a_{66}=+0.487409730\) \(a_{67}=-0.040813069\) \(a_{68}=+0.962685000\) \(a_{69}=+0.738632258\) \(a_{70}=-0.522163639\)
\(a_{71}=-0.651437539\) \(a_{72}=-0.034067928\) \(a_{73}=-0.618907820\) \(a_{74}=-0.406671975\) \(a_{75}=+0.190120104\)
\(a_{76}=+0.000600409\) \(a_{77}=+1.197340771\) \(a_{78}=-0.657078434\) \(a_{79}=+0.731247117\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.894356358\) \(a_{82}=-0.064830694\) \(a_{83}=-0.698656897\) \(a_{84}=+0.784828342\) \(a_{85}=-0.861051640\)
\(a_{86}=-0.655402408\) \(a_{87}=+0.286692937\) \(a_{88}=+0.256369379\) \(a_{89}=+1.542260090\) \(a_{90}=+0.030471281\)
\(a_{91}=-1.614138477\) \(a_{92}=+0.388508234\) \(a_{93}=+0.460061796\) \(a_{94}=-1.048215212\) \(a_{95}=-0.000537022\)
\(a_{96}=+0.168044018\) \(a_{97}=+1.525308600\) \(a_{98}=+1.220854263\) \(a_{99}=-0.069871789\) \(a_{100}=+0.099975586\)

Showing 100 of 148 available coefficients

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