Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.84003520889 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.144509007\) \(a_{3}=+1.265814965\) \(a_{4}=+0.309900866\) \(a_{5}=-0.098842678\)
\(a_{6}=-1.448736628\) \(a_{7}=+0.888824270\) \(a_{8}=+0.789824674\) \(a_{9}=+0.602287524\) \(a_{10}=+0.113126335\)
\(a_{11}=+0.911874681\) \(a_{12}=+0.392277154\) \(a_{13}=+0.550404536\) \(a_{14}=-1.017267382\) \(a_{15}=-0.125116541\)
\(a_{16}=-1.213862319\) \(a_{17}=+0.443840018\) \(a_{18}=-0.689323496\) \(a_{19}=+1.361392586\) \(a_{20}=-0.030631432\)
\(a_{21}=+1.125087062\) \(a_{22}=-1.043648785\) \(a_{23}=-0.208514414\) \(a_{24}=+0.999771892\) \(a_{25}=-0.990230125\)
\(a_{26}=-0.629942949\) \(a_{27}=-0.503430403\) \(a_{28}=+0.275447411\) \(a_{29}=+1.637944725\) \(a_{30}=+0.143197008\)
\(a_{31}=-0.888576529\) \(a_{32}=+0.599451683\) \(a_{33}=+1.154264617\) \(a_{34}=-0.507978898\) \(a_{35}=-0.087853771\)
\(a_{36}=+0.186649425\) \(a_{37}=+0.207937287\) \(a_{38}=-1.558126076\) \(a_{39}=+0.696710299\) \(a_{40}=-0.078068386\)
\(a_{41}=+1.408720191\) \(a_{42}=-1.287672276\) \(a_{43}=-1.593015813\) \(a_{44}=+0.282590754\) \(a_{45}=-0.059531712\)
\(a_{46}=+0.238646624\) \(a_{47}=-0.449440333\) \(a_{48}=-1.536525088\) \(a_{49}=-0.209991416\) \(a_{50}=+1.133327297\)
\(a_{51}=+0.561819335\) \(a_{52}=+0.170570842\) \(a_{53}=+0.632420137\) \(a_{54}=+0.576180632\) \(a_{55}=-0.090132136\)
\(a_{56}=+0.702015333\) \(a_{57}=+1.723271110\) \(a_{58}=-1.874642482\) \(a_{59}=-0.235936969\) \(a_{60}=-0.038773724\)
\(a_{61}=-0.980097720\) \(a_{62}=+1.016983840\) \(a_{63}=+0.535327770\) \(a_{64}=+0.527784471\) \(a_{65}=-0.054403458\)
\(a_{66}=-1.321066251\) \(a_{67}=+1.724864017\) \(a_{68}=+0.137546406\) \(a_{69}=-0.263940666\) \(a_{70}=+0.100549435\)
\(a_{71}=-0.114589138\) \(a_{72}=+0.475701542\) \(a_{73}=-1.744414938\) \(a_{74}=-0.237986093\) \(a_{75}=-1.253448094\)
\(a_{76}=+0.421896768\) \(a_{77}=+0.810496328\) \(a_{78}=-0.797391221\) \(a_{79}=-1.360274077\) \(a_{80}=+0.119981393\)
\(a_{81}=-1.239537261\) \(a_{82}=-1.612292949\) \(a_{83}=+0.569630386\) \(a_{84}=+0.348665452\) \(a_{85}=-0.043870337\)
\(a_{86}=+1.823220947\) \(a_{87}=+2.073334937\) \(a_{88}=+0.720221126\) \(a_{89}=-0.538591187\) \(a_{90}=+0.068134588\)
\(a_{91}=+0.489212905\) \(a_{92}=-0.064618807\) \(a_{93}=-1.124773496\) \(a_{94}=+0.514388501\) \(a_{95}=-0.134563756\)
\(a_{96}=+0.758794935\) \(a_{97}=+1.453741786\) \(a_{98}=+0.240337128\) \(a_{99}=+0.549210493\) \(a_{100}=-0.306873129\)

Showing 100 of 1500 available coefficients

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