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: \( 28.017178146 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.956122763\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.676080889\) \(a_{7}=-0.404454099\) \(a_{8}=+0.353553391\) \(a_{9}=-0.085829262\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.271361523\) \(a_{12}=-0.478061382\) \(a_{13}=+0.822806279\) \(a_{14}=-0.285992236\) \(a_{15}=-0.427591099\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.010767096\) \(a_{18}=-0.060690453\) \(a_{19}=-0.643049218\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.386707771\) \(a_{22}=+0.191881573\) \(a_{23}=-1.626134828\) \(a_{24}=-0.338040445\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.581811899\) \(a_{27}=+1.038186074\) \(a_{28}=-0.202227050\) \(a_{29}=+0.479805768\) \(a_{30}=-0.302352565\)
\(a_{31}=+0.553892674\) \(a_{32}=+0.176776695\) \(a_{33}=-0.259454930\) \(a_{34}=+0.007613486\) \(a_{35}=-0.180877372\)
\(a_{36}=-0.042914631\) \(a_{37}=+1.767876601\) \(a_{38}=-0.454704462\) \(a_{39}=-0.786703813\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.060515264\) \(a_{42}=+0.273443687\) \(a_{43}=-1.232862843\) \(a_{44}=+0.135680762\) \(a_{45}=-0.038384013\)
\(a_{46}=-1.149850964\) \(a_{47}=-0.078773809\) \(a_{48}=-0.239030691\) \(a_{49}=-0.836416882\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.010294665\) \(a_{52}=+0.411403139\) \(a_{53}=-0.646994811\) \(a_{54}=+0.734108413\) \(a_{55}=+0.121356563\)
\(a_{56}=-0.142996118\) \(a_{57}=+0.614833995\) \(a_{58}=+0.339273912\) \(a_{59}=+0.229391599\) \(a_{60}=-0.213795549\)
\(a_{61}=+0.360086543\) \(a_{62}=+0.391661266\) \(a_{63}=+0.034713997\) \(a_{64}=+0.125000000\) \(a_{65}=+0.367970154\)
\(a_{66}=-0.183462340\) \(a_{67}=-0.483749132\) \(a_{68}=+0.005383548\) \(a_{69}=+1.554784525\) \(a_{70}=-0.127899616\)
\(a_{71}=+1.125481844\) \(a_{72}=-0.030345227\) \(a_{73}=+1.851654511\) \(a_{74}=+1.250077533\) \(a_{75}=-0.191224553\)
\(a_{76}=-0.321524609\) \(a_{77}=-0.109753281\) \(a_{78}=-0.556283601\) \(a_{79}=-1.117908447\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.906804076\) \(a_{82}=-0.042790754\) \(a_{83}=+0.181911723\) \(a_{84}=+0.193353885\) \(a_{85}=+0.004815192\)
\(a_{86}=-0.871765676\) \(a_{87}=-0.458753217\) \(a_{88}=+0.095940787\) \(a_{89}=-0.154824547\) \(a_{90}=-0.027141596\)
\(a_{91}=-0.332787372\) \(a_{92}=-0.813067414\) \(a_{93}=-0.529589394\) \(a_{94}=-0.055701495\) \(a_{95}=-0.287580353\)
\(a_{96}=-0.169020222\) \(a_{97}=+0.581859617\) \(a_{98}=-0.591436049\) \(a_{99}=-0.023290759\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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