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: \( 4.88226240518 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.654008438\) \(a_{3}=+0.963224174\) \(a_{4}=-0.572272963\) \(a_{5}=+0.617924504\)
\(a_{6}=-0.629956738\) \(a_{7}=-0.383987531\) \(a_{8}=+1.028279785\) \(a_{9}=-0.072199190\) \(a_{10}=-0.404127840\)
\(a_{11}=-0.645539078\) \(a_{12}=-0.551227152\) \(a_{13}=-1.923636832\) \(a_{14}=+0.251131086\) \(a_{15}=+0.595199820\)
\(a_{16}=-0.100230693\) \(a_{17}=+0.458279749\) \(a_{18}=+0.047218880\) \(a_{19}=-1.418727349\) \(a_{20}=-0.353621487\)
\(a_{21}=-0.369866073\) \(a_{22}=+0.422188004\) \(a_{23}=+0.208514414\) \(a_{24}=+0.990463947\) \(a_{25}=-0.618169307\)
\(a_{26}=+1.258074720\) \(a_{27}=-1.032768180\) \(a_{28}=+0.219745682\) \(a_{29}=+0.726531908\) \(a_{30}=-0.389265705\)
\(a_{31}=-0.156631243\) \(a_{32}=-0.962728065\) \(a_{33}=-0.621798845\) \(a_{34}=-0.299718823\) \(a_{35}=-0.237275305\)
\(a_{36}=+0.041317644\) \(a_{37}=+0.450414315\) \(a_{38}=+0.927859658\) \(a_{39}=-1.852893499\) \(a_{40}=+0.635399276\)
\(a_{41}=+0.133034482\) \(a_{42}=+0.241895533\) \(a_{43}=+0.481487010\) \(a_{44}=+0.369424561\) \(a_{45}=-0.044613650\)
\(a_{46}=-0.136370187\) \(a_{47}=+0.676638999\) \(a_{48}=-0.096544627\) \(a_{49}=-0.852553577\) \(a_{50}=+0.404287944\)
\(a_{51}=+0.441426134\) \(a_{52}=+1.100845347\) \(a_{53}=-0.064149613\) \(a_{54}=+0.675439112\) \(a_{55}=-0.398894415\)
\(a_{56}=-0.394846623\) \(a_{57}=-1.366552482\) \(a_{58}=-0.475157994\) \(a_{59}=+0.544572699\) \(a_{60}=-0.340616772\)
\(a_{61}=-0.866914460\) \(a_{62}=+0.102438129\) \(a_{63}=+0.027723555\) \(a_{64}=+0.729863037\) \(a_{65}=-1.188662295\)
\(a_{66}=+0.406661668\) \(a_{67}=+0.177903520\) \(a_{68}=-0.262261046\) \(a_{69}=+0.200846114\) \(a_{70}=+0.155180050\)
\(a_{71}=-1.857810202\) \(a_{72}=-0.074240971\) \(a_{73}=+1.482750979\) \(a_{74}=-0.294574768\) \(a_{75}=-0.595435602\)
\(a_{76}=+0.811899280\) \(a_{77}=+0.247878933\) \(a_{78}=+1.211808038\) \(a_{79}=+0.998523550\) \(a_{80}=-0.061935032\)
\(a_{81}=-0.922588104\) \(a_{82}=-0.087005651\) \(a_{83}=+1.844873635\) \(a_{84}=+0.211664288\) \(a_{85}=+0.283182383\)
\(a_{86}=-0.314896527\) \(a_{87}=+0.699813098\) \(a_{88}=-0.663794751\) \(a_{89}=-1.680444086\) \(a_{90}=+0.029177650\)
\(a_{91}=+0.738652651\) \(a_{92}=-0.119327215\) \(a_{93}=-0.150871025\) \(a_{94}=-0.442527581\) \(a_{95}=-0.876666393\)
\(a_{96}=-0.927322878\) \(a_{97}=-0.032678536\) \(a_{98}=+0.557577223\) \(a_{99}=+0.046607440\) \(a_{100}=+0.353761553\)

Showing 100 of 1500 available coefficients

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