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: \( 2.73410555925 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.379492818\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.975448726\) \(a_{7}=+0.453621611\) \(a_{8}=-0.353553391\) \(a_{9}=+0.903000435\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.249643910\) \(a_{12}=+0.689746409\) \(a_{13}=+0.985232523\) \(a_{14}=-0.320758917\) \(a_{15}=-0.616927943\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.615662962\) \(a_{18}=-0.638517731\) \(a_{19}=-0.083047251\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.625767753\) \(a_{22}=+0.883631686\) \(a_{23}=+0.933594379\) \(a_{24}=-0.487724375\) \(a_{25}=+0.200000007\)
\(a_{26}=-0.696664566\) \(a_{27}=-0.133810256\) \(a_{28}=+0.226810756\) \(a_{29}=+0.368494334\) \(a_{30}=+0.436233891\)
\(a_{31}=-1.045601366\) \(a_{32}=-0.176776695\) \(a_{33}=-1.723874798\) \(a_{34}=+0.435339455\) \(a_{35}=-0.202865752\)
\(a_{36}=+0.451500217\) \(a_{37}=+0.270237230\) \(a_{38}=+0.058723275\) \(a_{39}=+1.359121189\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.280300176\) \(a_{42}=-0.442484623\) \(a_{43}=+0.171218128\) \(a_{44}=-0.624821955\) \(a_{45}=-0.403834071\)
\(a_{46}=-0.660150914\) \(a_{47}=-0.281637792\) \(a_{48}=+0.344873204\) \(a_{49}=-0.794227435\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.849302624\) \(a_{52}=+0.492616266\) \(a_{53}=+1.183504189\) \(a_{54}=+0.094618127\) \(a_{55}=+0.558857613\)
\(a_{56}=-0.160379358\) \(a_{57}=-0.114563198\) \(a_{58}=-0.260564765\) \(a_{59}=-1.846303163\) \(a_{60}=-0.308465072\)
\(a_{61}=+1.162882376\) \(a_{62}=+0.739350976\) \(a_{63}=+0.409622004\) \(a_{64}=+0.124999534\) \(a_{65}=-0.440614163\)
\(a_{66}=+1.218961840\) \(a_{67}=+0.144066114\) \(a_{68}=-0.307815704\) \(a_{69}=+1.287932364\) \(a_{70}=+0.143454765\)
\(a_{71}=-1.196364025\) \(a_{72}=-0.319028887\) \(a_{73}=-1.235235552\) \(a_{74}=-0.191086576\) \(a_{75}=+0.275898549\)
\(a_{76}=-0.041523652\) \(a_{77}=-0.566865479\) \(a_{78}=-0.961043793\) \(a_{79}=+1.019953681\) \(a_{80}=-0.111803370\)
\(a_{81}=-1.087590556\) \(a_{82}=-0.905308902\) \(a_{83}=+1.830933183\) \(a_{84}=+0.312884014\) \(a_{85}=+0.275333981\)
\(a_{86}=-0.121069308\) \(a_{87}=+0.508334922\) \(a_{88}=+0.441816257\) \(a_{89}=+0.596813303\) \(a_{90}=+0.285553622\)
\(a_{91}=+0.446922988\) \(a_{92}=+0.466797991\) \(a_{93}=-1.442398561\) \(a_{94}=+0.199149715\) \(a_{95}=+0.037146210\)
\(a_{96}=-0.243843153\) \(a_{97}=-0.261856066\) \(a_{98}=+0.561585836\) \(a_{99}=-1.128422245\) \(a_{100}=+0.099959689\)

Showing 100 of 2000 available coefficients

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