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: \( 29.6238435169 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.728464029\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.222208636\) \(a_{7}=-1.591276423\) \(a_{8}=-0.353553391\) \(a_{9}=+1.987587900\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.374229501\) \(a_{12}=-0.864232015\) \(a_{13}=+0.767009833\) \(a_{14}=+1.125202350\) \(a_{15}=+0.772992613\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.735607965\) \(a_{18}=-1.405436883\) \(a_{19}=-1.337389649\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.750464058\) \(a_{22}=+0.264620218\) \(a_{23}=+1.453240906\) \(a_{24}=+0.611104318\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.542357854\) \(a_{27}=-1.707010162\) \(a_{28}=-0.795638212\) \(a_{29}=+1.487343956\) \(a_{30}=-0.546588319\)
\(a_{31}=-0.927615335\) \(a_{32}=-0.176776695\) \(a_{33}=+0.646842230\) \(a_{34}=-0.520153380\) \(a_{35}=+0.711640451\)
\(a_{36}=+0.993793950\) \(a_{37}=+0.080176777\) \(a_{38}=+0.945677290\) \(a_{39}=-1.325748906\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.030118863\) \(a_{42}=-1.944871787\) \(a_{43}=+1.640377125\) \(a_{44}=-0.187114750\) \(a_{45}=-0.888876331\)
\(a_{46}=-1.027596499\) \(a_{47}=+1.115743896\) \(a_{48}=-0.432116007\) \(a_{49}=+1.532160655\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.271471907\) \(a_{52}=+0.383504916\) \(a_{53}=+1.220969775\) \(a_{54}=+1.207038461\) \(a_{55}=+0.167360520\)
\(a_{56}=+0.562601175\) \(a_{57}=+2.311629901\) \(a_{58}=-1.051710997\) \(a_{59}=+0.093045925\) \(a_{60}=+0.386496307\)
\(a_{61}=-1.355674256\) \(a_{62}=+0.655923094\) \(a_{63}=-3.162801765\) \(a_{64}=+0.125000000\) \(a_{65}=-0.343017225\)
\(a_{66}=-0.457386527\) \(a_{67}=-1.001415649\) \(a_{68}=+0.367803983\) \(a_{69}=-2.511874631\) \(a_{70}=-0.503205788\)
\(a_{71}=-0.100177569\) \(a_{72}=-0.702718441\) \(a_{73}=+0.504927676\) \(a_{74}=-0.056693542\) \(a_{75}=-0.345692806\)
\(a_{76}=-0.668694824\) \(a_{77}=+0.595502581\) \(a_{78}=+0.937446041\) \(a_{79}=-1.304073388\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.962917762\) \(a_{82}=-0.021297252\) \(a_{83}=-1.068544459\) \(a_{84}=+1.375232029\) \(a_{85}=-0.328973883\)
\(a_{86}=-1.159921789\) \(a_{87}=-2.570820527\) \(a_{88}=+0.132310109\) \(a_{89}=+0.446206724\) \(a_{90}=+0.628530482\)
\(a_{91}=-1.220524663\) \(a_{92}=+0.726620453\) \(a_{93}=+1.603349739\) \(a_{94}=-0.788950075\) \(a_{95}=+0.598098833\)
\(a_{96}=+0.305552159\) \(a_{97}=-1.709251367\) \(a_{98}=-1.083401189\) \(a_{99}=-0.743814027\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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