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: \( 20.6936600416 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.339850216\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.947417173\) \(a_{7}=+0.758059368\) \(a_{8}=+0.353553391\) \(a_{9}=+0.795198601\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.718011073\) \(a_{12}=-0.669925108\) \(a_{13}=+1.578773940\) \(a_{14}=+0.536028920\) \(a_{15}=-0.599199232\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.033399283\) \(a_{18}=+0.562290323\) \(a_{19}=-0.363469586\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.015686008\) \(a_{22}=+1.214817280\) \(a_{23}=+1.122444300\) \(a_{24}=-0.473708587\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.116361759\) \(a_{27}=+0.274403199\) \(a_{28}=+0.379029684\) \(a_{29}=+0.031628922\) \(a_{30}=-0.423697841\)
\(a_{31}=-1.807098426\) \(a_{32}=+0.176776695\) \(a_{33}=-2.301877508\) \(a_{34}=-0.730723641\) \(a_{35}=+0.339014456\)
\(a_{36}=+0.397599301\) \(a_{37}=+0.875977124\) \(a_{38}=-0.257011809\) \(a_{39}=-2.115320604\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.699021965\) \(a_{42}=-0.718198464\) \(a_{43}=-1.017312019\) \(a_{44}=+0.859005537\) \(a_{45}=+0.355623626\)
\(a_{46}=+0.793687976\) \(a_{47}=-0.148493920\) \(a_{48}=-0.334962554\) \(a_{49}=-0.425345994\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.384600253\) \(a_{52}=+0.789386970\) \(a_{53}=-0.664374796\) \(a_{54}=+0.194032362\) \(a_{55}=+0.768317909\)
\(a_{56}=+0.268014460\) \(a_{57}=+0.486994803\) \(a_{58}=+0.022365025\) \(a_{59}=+1.077380030\) \(a_{60}=-0.299599616\)
\(a_{61}=+1.358705432\) \(a_{62}=-1.277811551\) \(a_{63}=+0.602807749\) \(a_{64}=+0.125000000\) \(a_{65}=+0.706049170\)
\(a_{66}=-1.627673195\) \(a_{67}=-0.373081907\) \(a_{68}=-0.516699642\) \(a_{69}=-1.503907238\) \(a_{70}=+0.239719421\)
\(a_{71}=-1.061083836\) \(a_{72}=+0.281145162\) \(a_{73}=+0.621044585\) \(a_{74}=+0.619409365\) \(a_{75}=-0.267970043\)
\(a_{76}=-0.181734793\) \(a_{77}=+1.302354389\) \(a_{78}=-1.495757544\) \(a_{79}=+0.392714544\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.162857786\) \(a_{82}=+0.494283171\) \(a_{83}=+1.382984188\) \(a_{84}=-0.507843004\) \(a_{85}=-0.462150209\)
\(a_{86}=-0.719348227\) \(a_{87}=-0.042378018\) \(a_{88}=+0.607408640\) \(a_{89}=+1.162666628\) \(a_{90}=+0.251463877\)
\(a_{91}=+1.196804375\) \(a_{92}=+0.561222150\) \(a_{93}=+2.421241216\) \(a_{94}=-0.105001058\) \(a_{95}=-0.162548540\)
\(a_{96}=-0.236854293\) \(a_{97}=-0.874630993\) \(a_{98}=-0.300765037\) \(a_{99}=+1.366160002\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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