Properties

Level $55$
Weight $0$
Character 55.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 55 = 5 \cdot 11 \)
Weight: \( 0 \)
Character: 55.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.661575152344 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.300346647\) \(a_{3}=-1.056442566\) \(a_{4}=-0.909791891\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.317298983\) \(a_{7}=+1.203506489\) \(a_{8}=+0.573599592\) \(a_{9}=+0.116070895\) \(a_{10}=+0.134319104\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.961142880\) \(a_{13}=-0.393113241\) \(a_{14}=-0.361469139\) \(a_{15}=+0.472455478\)
\(a_{16}=+0.737513177\) \(a_{17}=-0.457679135\) \(a_{18}=-0.034861504\) \(a_{19}=+0.733103867\) \(a_{20}=+0.406871303\)
\(a_{21}=-1.271435483\) \(a_{22}=+0.090557922\) \(a_{23}=-0.820648785\) \(a_{24}=-0.605975025\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.118070244\) \(a_{27}=+0.933820332\) \(a_{28}=-1.094940444\) \(a_{29}=-0.877397825\) \(a_{30}=-0.141900419\)
\(a_{31}=+1.115302992\) \(a_{32}=-0.795109202\) \(a_{33}=+0.318529419\) \(a_{34}=+0.137462394\) \(a_{35}=-0.538224464\)
\(a_{36}=-0.105600359\) \(a_{37}=-0.666209403\) \(a_{38}=-0.220185289\) \(a_{39}=+0.415301561\) \(a_{40}=-0.256521536\)
\(a_{41}=-0.324184208\) \(a_{42}=+0.381871385\) \(a_{43}=+1.554749330\) \(a_{44}=+0.274312576\) \(a_{45}=-0.051908482\)
\(a_{46}=+0.246479111\) \(a_{47}=-0.081843084\) \(a_{48}=-0.779140313\) \(a_{49}=+0.448427868\) \(a_{50}=-0.060069329\)
\(a_{51}=+0.483511719\) \(a_{52}=+0.357651239\) \(a_{53}=+1.355247166\) \(a_{54}=-0.280469806\) \(a_{55}=+0.134839972\)
\(a_{56}=+0.690330831\) \(a_{57}=-0.774482130\) \(a_{58}=+0.263523495\) \(a_{59}=+0.779317926\) \(a_{60}=-0.429836163\)
\(a_{61}=-0.190063484\) \(a_{62}=-0.334977515\) \(a_{63}=+0.139692075\) \(a_{64}=-0.498704794\) \(a_{65}=+0.175805586\)
\(a_{66}=-0.095669243\) \(a_{67}=-1.616033921\) \(a_{68}=+0.416392765\) \(a_{69}=+0.866968308\) \(a_{70}=+0.161653913\)
\(a_{71}=-0.190731066\) \(a_{72}=+0.066578218\) \(a_{73}=+0.043151035\) \(a_{74}=+0.200093761\) \(a_{75}=-0.211288513\)
\(a_{76}=-0.666971954\) \(a_{77}=-0.362870860\) \(a_{78}=-0.124734432\) \(a_{79}=-1.030819888\) \(a_{80}=-0.329825920\)
\(a_{81}=-1.102598442\) \(a_{82}=+0.097367640\) \(a_{83}=-0.820645545\) \(a_{84}=+1.156741693\) \(a_{85}=+0.204680331\)
\(a_{86}=-0.466963749\) \(a_{87}=+0.926920410\) \(a_{88}=-0.172946784\) \(a_{89}=+1.264873806\) \(a_{90}=+0.015590539\)
\(a_{91}=-0.473114337\) \(a_{92}=+0.746619610\) \(a_{93}=-1.178253555\) \(a_{94}=+0.024581296\) \(a_{95}=-0.327854016\)
\(a_{96}=+0.839987206\) \(a_{97}=-0.813736221\) \(a_{98}=-0.134683807\) \(a_{99}=-0.034996692\) \(a_{100}=-0.181958378\)

Showing 100 of 556 available coefficients

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