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: \( 29.868898766 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.676533093\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.478381137\) \(a_{7}=-1.328416192\) \(a_{8}=-0.353553391\) \(a_{9}=-0.542302975\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.219594563\) \(a_{12}=-0.338266546\) \(a_{13}=-1.549725223\) \(a_{14}=+0.939332097\) \(a_{15}=+0.302554797\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.299431691\) \(a_{18}=+0.383466111\) \(a_{19}=-0.724687436\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.898717515\) \(a_{22}=-0.862383586\) \(a_{23}=-1.312003664\) \(a_{24}=+0.239190569\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.095821214\) \(a_{27}=+1.043419001\) \(a_{28}=-0.664208096\) \(a_{29}=+1.371287322\) \(a_{30}=-0.213938549\)
\(a_{31}=+1.470714165\) \(a_{32}=-0.176776695\) \(a_{33}=-0.825096081\) \(a_{34}=+0.211730179\) \(a_{35}=+0.594085781\)
\(a_{36}=-0.271151487\) \(a_{37}=-1.276863490\) \(a_{38}=+0.512431400\) \(a_{39}=+1.048440398\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.636859228\) \(a_{42}=-0.635489249\) \(a_{43}=-0.132931119\) \(a_{44}=+0.609797281\) \(a_{45}=+0.242525263\)
\(a_{46}=+0.927726688\) \(a_{47}=-1.449656700\) \(a_{48}=-0.169133273\) \(a_{49}=+0.764689579\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.202575448\) \(a_{52}=-0.774862611\) \(a_{53}=+0.173082041\) \(a_{54}=-0.737808651\) \(a_{55}=-0.545419270\)
\(a_{56}=+0.469666049\) \(a_{57}=+0.490275032\) \(a_{58}=-0.969646564\) \(a_{59}=-1.730291426\) \(a_{60}=+0.151277398\)
\(a_{61}=+0.539399143\) \(a_{62}=-1.039951960\) \(a_{63}=+0.720404052\) \(a_{64}=+0.125000000\) \(a_{65}=+0.693058189\)
\(a_{66}=+0.583431034\) \(a_{67}=+1.871316762\) \(a_{68}=-0.149715846\) \(a_{69}=+0.887613897\) \(a_{70}=-0.420082085\)
\(a_{71}=+0.101693570\) \(a_{72}=+0.191733055\) \(a_{73}=-0.008275055\) \(a_{74}=+0.902878832\) \(a_{75}=-0.135306619\)
\(a_{76}=-0.362343718\) \(a_{77}=-1.620129165\) \(a_{78}=-0.741359315\) \(a_{79}=+1.030820136\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.163604509\) \(a_{82}=-0.450327479\) \(a_{83}=+1.305190742\) \(a_{84}=+0.449358757\) \(a_{85}=+0.133909923\)
\(a_{86}=+0.093996496\) \(a_{87}=-0.927721253\) \(a_{88}=-0.431191793\) \(a_{89}=+0.601075378\) \(a_{90}=-0.171491258\)
\(a_{91}=+2.058680079\) \(a_{92}=-0.656001832\) \(a_{93}=-0.994986803\) \(a_{94}=+1.025062083\) \(a_{95}=+0.324090074\)
\(a_{96}=+0.119595284\) \(a_{97}=-0.015956350\) \(a_{98}=-0.540717187\) \(a_{99}=-0.661389759\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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