Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 14.3585095183 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.230915191\) \(a_{3}=+0.695594986\) \(a_{4}=-0.946678174\) \(a_{5}=-1.298284599\)
\(a_{6}=-0.160623449\) \(a_{7}=-0.483281982\) \(a_{8}=+0.449517563\) \(a_{9}=-0.516147615\) \(a_{10}=+0.299793637\)
\(a_{11}=+0.177498073\) \(a_{12}=-0.658504592\) \(a_{13}=+0.625443542\) \(a_{14}=+0.111597151\) \(a_{15}=-0.903080258\)
\(a_{16}=+0.842877740\) \(a_{17}=-0.151559499\) \(a_{18}=+0.119186325\) \(a_{19}=-0.980264797\) \(a_{20}=+1.229057694\)
\(a_{21}=-0.336168523\) \(a_{22}=-0.040987001\) \(a_{23}=-0.568015294\) \(a_{24}=+0.312682163\) \(a_{25}=+0.685542900\)
\(a_{26}=-0.144424415\) \(a_{27}=-1.054624679\) \(a_{28}=+0.457512504\) \(a_{29}=+0.381344552\) \(a_{30}=+0.208534950\)
\(a_{31}=-0.129584231\) \(a_{32}=-0.644150837\) \(a_{33}=+0.123466770\) \(a_{34}=+0.034997391\) \(a_{35}=+0.627437554\)
\(a_{36}=+0.488625682\) \(a_{37}=-1.486023675\) \(a_{38}=+0.226358033\) \(a_{39}=+0.435055392\) \(a_{40}=-0.583601729\)
\(a_{41}=+1.293637359\) \(a_{42}=+0.077626419\) \(a_{43}=-1.388869973\) \(a_{44}=-0.168033552\) \(a_{45}=+0.670106499\)
\(a_{46}=+0.131163360\) \(a_{47}=+0.053102429\) \(a_{48}=+0.586301530\) \(a_{49}=-0.766438526\) \(a_{50}=-0.158302270\)
\(a_{51}=-0.105424027\) \(a_{52}=-0.592093751\) \(a_{53}=+1.307122839\) \(a_{54}=+0.243528858\) \(a_{55}=-0.230443015\)
\(a_{56}=-0.217243737\) \(a_{57}=-0.681867270\) \(a_{58}=-0.088058250\) \(a_{59}=+0.040557104\) \(a_{60}=+0.854926370\)
\(a_{61}=+0.025628294\) \(a_{62}=+0.029922968\) \(a_{63}=+0.249444842\) \(a_{64}=-0.694133527\) \(a_{65}=-0.812003718\)
\(a_{66}=-0.028510353\) \(a_{67}=+1.238556435\) \(a_{68}=+0.143478070\) \(a_{69}=-0.395108590\) \(a_{70}=-0.144884863\)
\(a_{71}=+0.903164021\) \(a_{72}=-0.232017418\) \(a_{73}=-1.826184887\) \(a_{74}=+0.343145441\) \(a_{75}=+0.476860204\)
\(a_{76}=+0.927995288\) \(a_{77}=-0.085781620\) \(a_{78}=-0.100460899\) \(a_{79}=+0.528391701\) \(a_{80}=-1.094295189\)
\(a_{81}=-0.217444024\) \(a_{82}=-0.298720518\) \(a_{83}=+0.326121778\) \(a_{84}=+0.318243404\) \(a_{85}=+0.196767363\)
\(a_{86}=+0.320711175\) \(a_{87}=+0.265261359\) \(a_{88}=+0.079788501\) \(a_{89}=-1.068845312\) \(a_{90}=-0.154737770\)
\(a_{91}=-0.302265595\) \(a_{92}=+0.537727681\) \(a_{93}=-0.090138142\) \(a_{94}=-0.012262157\) \(a_{95}=+1.272662688\)
\(a_{96}=-0.448068094\) \(a_{97}=-0.293812737\) \(a_{98}=+0.176982300\) \(a_{99}=-0.091615204\) \(a_{100}=-0.648988510\)

Showing 100 of 5000 available coefficients

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