Properties

Level $23$
Weight $0$
Character 23.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.8189248762 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.927405917\) \(a_{3}=-0.316312472\) \(a_{4}=+2.714893569\) \(a_{5}=+1.249430280\)
\(a_{6}=-0.609662529\) \(a_{7}=-1.033259423\) \(a_{8}=+3.305296013\) \(a_{9}=-0.899946420\) \(a_{10}=+2.408159315\)
\(a_{11}=-0.092907070\) \(a_{12}=-0.858754695\) \(a_{13}=-1.019639392\) \(a_{14}=-1.991510326\) \(a_{15}=-0.395210380\)
\(a_{16}=+3.655753524\) \(a_{17}=-0.409440420\) \(a_{18}=-1.734562056\) \(a_{19}=+0.378654444\) \(a_{20}=+3.392070233\)
\(a_{21}=+0.326832842\) \(a_{22}=-0.179069636\) \(a_{23}=+0.208514414\) \(a_{24}=-1.045506351\) \(a_{25}=+0.561076025\)
\(a_{26}=-1.965258997\) \(a_{27}=+0.600976748\) \(a_{28}=-2.805189364\) \(a_{29}=-0.406184167\) \(a_{30}=-0.761730825\)
\(a_{31}=+1.030029591\) \(a_{32}=+3.740824961\) \(a_{33}=+0.029387665\) \(a_{34}=-0.789157888\) \(a_{35}=-1.290985611\)
\(a_{36}=-2.443258749\) \(a_{37}=+0.840549014\) \(a_{38}=+0.729820816\) \(a_{39}=+0.322524656\) \(a_{40}=+4.129736924\)
\(a_{41}=-1.408408912\) \(a_{42}=+0.629939553\) \(a_{43}=+0.650093360\) \(a_{44}=-0.252232807\) \(a_{45}=-1.124420308\)
\(a_{46}=+0.401891915\) \(a_{47}=-0.701233178\) \(a_{48}=-1.156360433\) \(a_{49}=+0.067625036\) \(a_{50}=+1.081421251\)
\(a_{51}=+0.129511111\) \(a_{52}=-2.768212427\) \(a_{53}=+1.381995233\) \(a_{54}=+1.158326140\) \(a_{55}=-0.116080906\)
\(a_{56}=-3.415228252\) \(a_{57}=-0.119773123\) \(a_{58}=-0.782881767\) \(a_{59}=+1.377305201\) \(a_{60}=-1.072954119\)
\(a_{61}=+0.431800240\) \(a_{62}=+1.985285128\) \(a_{63}=+0.929878119\) \(a_{64}=+3.554334640\) \(a_{65}=-1.273968331\)
\(a_{66}=+0.056641959\) \(a_{67}=+1.531696018\) \(a_{68}=-1.111587163\) \(a_{69}=-0.065955710\) \(a_{70}=-2.488253305\)
\(a_{71}=-0.915161067\) \(a_{72}=-2.974589315\) \(a_{73}=-1.165322731\) \(a_{74}=+1.620079143\) \(a_{75}=-0.177475344\)
\(a_{76}=+1.028006515\) \(a_{77}=+0.095997105\) \(a_{78}=+0.621635930\) \(a_{79}=-0.025310888\) \(a_{80}=+4.567609150\)
\(a_{81}=+0.709849980\) \(a_{82}=-2.714575671\) \(a_{83}=-0.040239868\) \(a_{84}=+0.887316381\) \(a_{85}=-0.511567259\)
\(a_{86}=+1.252993789\) \(a_{87}=+0.128481118\) \(a_{88}=-0.307085368\) \(a_{89}=-0.339481877\) \(a_{90}=-2.167214355\)
\(a_{91}=+1.053552010\) \(a_{92}=+0.566094442\) \(a_{93}=-0.325811206\) \(a_{94}=-1.351560977\) \(a_{95}=+0.473102328\)
\(a_{96}=-1.183269589\) \(a_{97}=+0.543775644\) \(a_{98}=+0.130340894\) \(a_{99}=+0.083611385\) \(a_{100}=+1.523261693\)

Showing 100 of 546 available coefficients

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