Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.59070811042 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.747550612\) \(a_{3}=-1.385881709\) \(a_{4}=-0.441168083\) \(a_{5}=-0.127750181\)
\(a_{6}=+1.036016719\) \(a_{7}=-1.752389587\) \(a_{8}=+1.077346082\) \(a_{9}=+0.920668112\) \(a_{10}=+0.095499726\)
\(a_{11}=+0.624106186\) \(a_{12}=+0.611406777\) \(a_{13}=-0.779900271\) \(a_{14}=+1.309999907\) \(a_{15}=+0.177046639\)
\(a_{16}=-0.364202639\) \(a_{17}=-1.060992084\) \(a_{18}=-0.688246010\) \(a_{19}=-0.229415734\) \(a_{20}=+0.056359302\)
\(a_{21}=+2.428604675\) \(a_{22}=-0.466550961\) \(a_{23}=+1.060158286\) \(a_{24}=-1.493074229\) \(a_{25}=-0.983679891\)
\(a_{26}=+0.583014925\) \(a_{27}=+0.109944613\) \(a_{28}=+0.773098355\) \(a_{29}=-0.179004344\) \(a_{30}=-0.132351323\)
\(a_{31}=+1.551624519\) \(a_{32}=-0.805086176\) \(a_{33}=-0.864937347\) \(a_{34}=+0.793145281\) \(a_{35}=+0.223868087\)
\(a_{36}=-0.406169386\) \(a_{37}=-1.250244157\) \(a_{38}=+0.171499872\) \(a_{39}=+1.080849521\) \(a_{40}=-0.137631157\)
\(a_{41}=-0.184254254\) \(a_{42}=-1.815504909\) \(a_{43}=-0.300636938\) \(a_{44}=-0.275335728\) \(a_{45}=-0.117615518\)
\(a_{46}=-0.792521976\) \(a_{47}=+0.956343603\) \(a_{48}=+0.504741764\) \(a_{49}=+2.070869272\) \(a_{50}=+0.735350506\)
\(a_{51}=+1.470409512\) \(a_{52}=+0.344067132\) \(a_{53}=-0.220388636\) \(a_{54}=-0.082189131\) \(a_{55}=-0.079729665\)
\(a_{56}=-1.887930106\) \(a_{57}=+0.317943172\) \(a_{58}=+0.133814807\) \(a_{59}=-1.365629261\) \(a_{60}=-0.078107327\)
\(a_{61}=+0.741004896\) \(a_{62}=-1.159917858\) \(a_{63}=-1.613369211\) \(a_{64}=+0.966045302\) \(a_{65}=+0.099632400\)
\(a_{66}=+0.646584443\) \(a_{67}=+0.277723094\) \(a_{68}=+0.468075846\) \(a_{69}=-1.469253979\) \(a_{70}=-0.167352727\)
\(a_{71}=-1.394710214\) \(a_{72}=+0.991878185\) \(a_{73}=+0.777632653\) \(a_{74}=+0.934620782\) \(a_{75}=+1.363263964\)
\(a_{76}=+0.101210895\) \(a_{77}=-1.093677180\) \(a_{78}=-0.807989708\) \(a_{79}=+1.002988998\) \(a_{80}=+0.046526943\)
\(a_{81}=-1.073038363\) \(a_{82}=+0.137739387\) \(a_{83}=+0.873807943\) \(a_{84}=-1.071422853\) \(a_{85}=+0.135541946\)
\(a_{86}=+0.224741170\) \(a_{87}=+0.248078877\) \(a_{88}=+0.672378383\) \(a_{89}=+1.413533689\) \(a_{90}=+0.087923571\)
\(a_{91}=+1.366689117\) \(a_{92}=-0.467707999\) \(a_{93}=-2.150368044\) \(a_{94}=-0.714915246\) \(a_{95}=+0.029307906\)
\(a_{96}=+1.115754210\) \(a_{97}=-0.513105832\) \(a_{98}=-1.548079585\) \(a_{99}=+0.574594660\) \(a_{100}=+0.433968169\)

Showing 100 of 1500 available coefficients

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