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: \( 3.52454363828 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.350255583\) \(a_{3}=+1.208366825\) \(a_{4}=-0.877321027\) \(a_{5}=-1.070170023\)
\(a_{6}=-0.423237227\) \(a_{7}=-1.523690101\) \(a_{8}=+0.657542170\) \(a_{9}=+0.460150384\) \(a_{10}=+0.374833025\)
\(a_{11}=+1.132758657\) \(a_{12}=-1.060125624\) \(a_{13}=-1.088602641\) \(a_{14}=+0.533680964\) \(a_{15}=-1.293157953\)
\(a_{16}=+0.647013211\) \(a_{17}=-0.476080184\) \(a_{18}=-0.161170241\) \(a_{19}=+0.992956763\) \(a_{20}=+0.938882663\)
\(a_{21}=-1.841176570\) \(a_{22}=-0.396755043\) \(a_{23}=-0.208514414\) \(a_{24}=+0.794552145\) \(a_{25}=+0.145263877\)
\(a_{26}=+0.381289152\) \(a_{27}=-0.652336367\) \(a_{28}=+1.336765364\) \(a_{29}=-0.949179963\) \(a_{30}=+0.452935792\)
\(a_{31}=+0.348266448\) \(a_{32}=-0.884162160\) \(a_{33}=+1.368787982\) \(a_{34}=+0.166749742\) \(a_{35}=+1.630607470\)
\(a_{36}=-0.403699607\) \(a_{37}=-1.538012139\) \(a_{38}=-0.347788650\) \(a_{39}=-1.315431317\) \(a_{40}=-0.703681919\)
\(a_{41}=-1.076028311\) \(a_{42}=+0.644882373\) \(a_{43}=+1.653116990\) \(a_{44}=-0.993792988\) \(a_{45}=-0.492439147\)
\(a_{46}=+0.073033338\) \(a_{47}=-0.108762748\) \(a_{48}=+0.781829299\) \(a_{49}=+1.321631525\) \(a_{50}=-0.050879484\)
\(a_{51}=-0.575279500\) \(a_{52}=+0.955053986\) \(a_{53}=-0.321522977\) \(a_{54}=+0.228484454\) \(a_{55}=-1.212244357\)
\(a_{56}=-1.001890496\) \(a_{57}=+1.199856012\) \(a_{58}=+0.332455581\) \(a_{59}=+0.340017493\) \(a_{60}=+1.134514663\)
\(a_{61}=+0.421065394\) \(a_{62}=-0.121982268\) \(a_{63}=-0.701126585\) \(a_{64}=-0.337330478\) \(a_{65}=+1.164989913\)
\(a_{66}=-0.479425632\) \(a_{67}=-0.560252083\) \(a_{68}=+0.417675156\) \(a_{69}=-0.251961901\) \(a_{70}=-0.571129370\)
\(a_{71}=-0.172868454\) \(a_{72}=+0.302568282\) \(a_{73}=-0.876983813\) \(a_{74}=+0.538697338\) \(a_{75}=+0.175532050\)
\(a_{76}=-0.871141847\) \(a_{77}=-1.725973152\) \(a_{78}=+0.460737162\) \(a_{79}=+1.013972016\) \(a_{80}=-0.692414142\)
\(a_{81}=-1.248412008\) \(a_{82}=+0.376884923\) \(a_{83}=-0.573862684\) \(a_{84}=+1.615302919\) \(a_{85}=+0.509486741\)
\(a_{86}=-0.579013455\) \(a_{87}=-1.146957578\) \(a_{88}=+0.744836586\) \(a_{89}=+1.032879601\) \(a_{90}=+0.172479560\)
\(a_{91}=+1.658693068\) \(a_{92}=+0.182934080\) \(a_{93}=+0.420833623\) \(a_{94}=+0.038094760\) \(a_{95}=-1.062632562\)
\(a_{96}=-1.068392222\) \(a_{97}=+0.708387021\) \(a_{98}=-0.462908820\) \(a_{99}=+0.521239331\) \(a_{100}=-0.127443054\)

Showing 100 of 546 available coefficients

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