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: \( 4.73923930491 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.289888489\) \(a_{3}=-0.052025257\) \(a_{4}=+0.663812313\) \(a_{5}=+1.335551081\)
\(a_{6}=+0.067106780\) \(a_{7}=-0.772659169\) \(a_{8}=+0.433644627\) \(a_{9}=-0.997293373\) \(a_{10}=-1.722711966\)
\(a_{11}=+1.559283273\) \(a_{12}=-0.034535006\) \(a_{13}=-0.632408277\) \(a_{14}=+0.996644167\) \(a_{15}=-0.069482388\)
\(a_{16}=-1.223165526\) \(a_{17}=-1.809921251\) \(a_{18}=+1.286397241\) \(a_{19}=-0.044831433\) \(a_{20}=+0.886555252\)
\(a_{21}=+0.040197792\) \(a_{22}=-2.011301545\) \(a_{23}=-0.208514414\) \(a_{24}=-0.022560473\) \(a_{25}=+0.783696690\)
\(a_{26}=+0.815736156\) \(a_{27}=+0.103909701\) \(a_{28}=-0.512900670\) \(a_{29}=-0.577296471\) \(a_{30}=+0.089624533\)
\(a_{31}=-1.573331879\) \(a_{32}=+1.144102504\) \(a_{33}=-0.081122113\) \(a_{34}=+2.334596587\) \(a_{35}=-1.031925788\)
\(a_{36}=-0.662015621\) \(a_{37}=+0.489402460\) \(a_{38}=+0.057827550\) \(a_{39}=+0.032901203\) \(a_{40}=+0.579154551\)
\(a_{41}=+0.360507836\) \(a_{42}=-0.051850669\) \(a_{43}=-0.543975587\) \(a_{44}=+1.035071437\) \(a_{45}=-1.331936242\)
\(a_{46}=+0.268960342\) \(a_{47}=-1.428765920\) \(a_{48}=+0.063635501\) \(a_{49}=-0.402997809\) \(a_{50}=-1.010881339\)
\(a_{51}=+0.094161618\) \(a_{52}=-0.419800401\) \(a_{53}=-0.420813139\) \(a_{54}=-0.134031927\) \(a_{55}=+2.082502462\)
\(a_{56}=-0.335059497\) \(a_{57}=+0.002332367\) \(a_{58}=+0.744648072\) \(a_{59}=-0.062106946\) \(a_{60}=-0.046123265\)
\(a_{61}=+0.679371847\) \(a_{62}=+2.029422679\) \(a_{63}=+0.770567868\) \(a_{64}=-0.252599124\) \(a_{65}=-0.844613557\)
\(a_{66}=+0.104638480\) \(a_{67}=-0.672835055\) \(a_{68}=-1.201448012\) \(a_{69}=+0.010848016\) \(a_{70}=+1.331069195\)
\(a_{71}=-0.662193393\) \(a_{72}=-0.432470913\) \(a_{73}=+1.673598135\) \(a_{74}=-0.631274599\) \(a_{75}=-0.040772022\)
\(a_{76}=-0.029759658\) \(a_{77}=-1.204794518\) \(a_{78}=-0.042438883\) \(a_{79}=-0.402692604\) \(a_{80}=-1.633600041\)
\(a_{81}=+0.991887444\) \(a_{82}=-0.465014907\) \(a_{83}=-0.795590542\) \(a_{84}=+0.026683789\) \(a_{85}=-2.417242284\)
\(a_{86}=+0.701667847\) \(a_{87}=+0.030033997\) \(a_{88}=+0.676174814\) \(a_{89}=+1.256290296\) \(a_{90}=+1.718049226\)
\(a_{91}=+0.488636053\) \(a_{92}=-0.138414436\) \(a_{93}=+0.081852995\) \(a_{94}=+1.842948713\) \(a_{95}=-0.059874669\)
\(a_{96}=-0.059522227\) \(a_{97}=-1.235668815\) \(a_{98}=+0.519822235\) \(a_{99}=-1.555062875\) \(a_{100}=+0.520227513\)

Showing 100 of 546 available coefficients

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