Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 32.5081177599 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.812750172\) \(a_{3}=+1.171151066\) \(a_{4}=+2.286063186\) \(a_{5}=-0.414880715\)
\(a_{6}=+2.123004297\) \(a_{7}=+0.323447256\) \(a_{8}=+2.331311261\) \(a_{9}=+0.371594820\) \(a_{10}=-0.752075088\)
\(a_{11}=+0.301845171\) \(a_{12}=+2.677325337\) \(a_{13}=+1.438641250\) \(a_{14}=+0.586329069\) \(a_{15}=-0.485887992\)
\(a_{16}=+1.940021703\) \(a_{17}=-0.615681312\) \(a_{18}=+0.673608574\) \(a_{19}=-1.213317365\) \(a_{20}=-0.948443530\)
\(a_{21}=+0.378805599\) \(a_{22}=+0.547169885\) \(a_{23}=-0.069583073\) \(a_{24}=+2.730317669\) \(a_{25}=-0.827873992\)
\(a_{26}=+2.607897172\) \(a_{27}=-0.735957397\) \(a_{28}=+0.739420865\) \(a_{29}=+1.434271993\) \(a_{30}=-0.880793541\)
\(a_{31}=-0.324684595\) \(a_{32}=+1.185463415\) \(a_{33}=+0.353506293\) \(a_{34}=-1.116076406\) \(a_{35}=-0.134192029\)
\(a_{36}=+0.849489238\) \(a_{37}=+0.835668325\) \(a_{38}=-2.199441262\) \(a_{39}=+1.684866233\) \(a_{40}=-0.967216084\)
\(a_{41}=+0.423951971\) \(a_{42}=+0.686679914\) \(a_{43}=-1.211474649\) \(a_{44}=+0.690037132\) \(a_{45}=-0.154167525\)
\(a_{46}=-0.126136728\) \(a_{47}=-0.733521162\) \(a_{48}=+2.272058486\) \(a_{49}=-0.895381873\) \(a_{50}=-1.500728721\)
\(a_{51}=-0.721055826\) \(a_{52}=+3.288824798\) \(a_{53}=-0.685496248\) \(a_{54}=-1.334106897\) \(a_{55}=-0.125229740\)
\(a_{56}=+0.754056230\) \(a_{57}=-1.420977926\) \(a_{58}=+2.599976803\) \(a_{59}=-1.004595245\) \(a_{60}=-1.110770650\)
\(a_{61}=+1.090808427\) \(a_{62}=-0.588572056\) \(a_{63}=+0.120191323\) \(a_{64}=+0.208927304\) \(a_{65}=-0.596864483\)
\(a_{66}=+0.640818594\) \(a_{67}=+1.048400894\) \(a_{68}=-1.407486383\) \(a_{69}=-0.081492291\) \(a_{70}=-0.243256624\)
\(a_{71}=-0.069823800\) \(a_{72}=+0.866303188\) \(a_{73}=-0.072957178\) \(a_{74}=+1.514857899\) \(a_{75}=-0.969565508\)
\(a_{76}=-2.773720160\) \(a_{77}=+0.097630992\) \(a_{78}=+3.054241554\) \(a_{79}=+0.219025925\) \(a_{80}=-0.804877592\)
\(a_{81}=-1.233512110\) \(a_{82}=+0.768519008\) \(a_{83}=-0.557595584\) \(a_{84}=+0.865973534\) \(a_{85}=+0.255434303\)
\(a_{86}=-2.196100878\) \(a_{87}=+1.679749174\) \(a_{88}=+0.703695045\) \(a_{89}=-0.587619203\) \(a_{90}=-0.279467207\)
\(a_{91}=+0.465324565\) \(a_{92}=-0.159071303\) \(a_{93}=-0.380254709\) \(a_{94}=-1.329690613\) \(a_{95}=+0.503381976\)
\(a_{96}=+1.388356742\) \(a_{97}=+1.603656363\) \(a_{98}=-1.623103643\) \(a_{99}=+0.112164102\) \(a_{100}=-1.892572255\)

Showing 100 of 5000 available coefficients

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