Properties

Level $29$
Weight $0$
Character 29.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.39676063927 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.445515212\) \(a_{3}=-0.246739583\) \(a_{4}=+1.089514230\) \(a_{5}=-1.700428233\)
\(a_{6}=-0.356665822\) \(a_{7}=-0.505725472\) \(a_{8}=+0.129394181\) \(a_{9}=-0.939119578\) \(a_{10}=-2.457994880\)
\(a_{11}=+0.754245801\) \(a_{12}=-0.268826287\) \(a_{13}=+1.393299044\) \(a_{14}=-0.731033863\) \(a_{15}=+0.419562954\)
\(a_{16}=-0.902472973\) \(a_{17}=-1.012555103\) \(a_{18}=-1.357511636\) \(a_{19}=+0.437501291\) \(a_{20}=-1.852640757\)
\(a_{21}=+0.124782492\) \(a_{22}=+1.090273780\) \(a_{23}=-1.403912562\) \(a_{24}=-0.031926666\) \(a_{25}=+1.891456178\)
\(a_{26}=+2.014034964\) \(a_{27}=+0.478457557\) \(a_{28}=-0.550995098\) \(a_{29}=+0.185695338\) \(a_{30}=+0.606484633\)
\(a_{31}=-0.605640253\) \(a_{32}=-1.433932592\) \(a_{33}=-0.186102295\) \(a_{34}=-1.463663805\) \(a_{35}=+0.859949871\)
\(a_{36}=-1.023184144\) \(a_{37}=+1.156005458\) \(a_{38}=+0.632414772\) \(a_{39}=-0.343782025\) \(a_{40}=-0.220025519\)
\(a_{41}=-1.426769960\) \(a_{42}=+0.180374990\) \(a_{43}=-1.140352498\) \(a_{44}=+0.821761536\) \(a_{45}=+1.596905445\)
\(a_{46}=-2.029376967\) \(a_{47}=-0.531431724\) \(a_{48}=+0.222675807\) \(a_{49}=-0.744241744\) \(a_{50}=+2.734128676\)
\(a_{51}=+0.249837420\) \(a_{52}=+1.518019142\) \(a_{53}=+0.128339515\) \(a_{54}=+0.691617677\) \(a_{55}=-1.282540867\)
\(a_{56}=-0.065437940\) \(a_{57}=-0.107948872\) \(a_{58}=+0.268425445\) \(a_{59}=+0.843873440\) \(a_{60}=+0.457119786\)
\(a_{61}=+0.347653556\) \(a_{62}=-0.875462157\) \(a_{63}=+0.474936717\) \(a_{64}=-1.170298430\) \(a_{65}=-2.369205076\)
\(a_{66}=-0.269013688\) \(a_{67}=+0.137679983\) \(a_{68}=-1.103193154\) \(a_{69}=+0.346400718\) \(a_{70}=+1.243070558\)
\(a_{71}=-0.566254796\) \(a_{72}=-0.121516567\) \(a_{73}=+0.668744897\) \(a_{74}=+1.671023399\) \(a_{75}=-0.466697157\)
\(a_{76}=+0.476663951\) \(a_{77}=-0.381441217\) \(a_{78}=-0.496942120\) \(a_{79}=-1.134965524\) \(a_{80}=+1.534590506\)
\(a_{81}=+0.821065200\) \(a_{82}=-2.062417694\) \(a_{83}=-0.584704463\) \(a_{84}=+0.135952243\) \(a_{85}=+1.721777263\)
\(a_{86}=-1.648396739\) \(a_{87}=-0.045818319\) \(a_{88}=+0.097594987\) \(a_{89}=+0.683403473\) \(a_{90}=+2.308351148\)
\(a_{91}=-0.704626738\) \(a_{92}=-1.529582673\) \(a_{93}=+0.149435343\) \(a_{94}=-0.768192765\) \(a_{95}=-0.743939577\)
\(a_{96}=+0.353807967\) \(a_{97}=+0.196118777\) \(a_{98}=-1.075812726\) \(a_{99}=-0.708327076\) \(a_{100}=+2.060768390\)

Showing 100 of 1500 available coefficients

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