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: \( 4.85889850005 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.316017181\) \(a_{3}=-0.348480216\) \(a_{4}=+0.731901219\) \(a_{5}=-0.648230179\)
\(a_{6}=-0.458605951\) \(a_{7}=-1.231827737\) \(a_{8}=-0.352822602\) \(a_{9}=-0.878561539\) \(a_{10}=-0.853082051\)
\(a_{11}=+1.875095034\) \(a_{12}=-0.255053094\) \(a_{13}=-1.073147841\) \(a_{14}=-1.621106465\) \(a_{15}=+0.225895392\)
\(a_{16}=-1.196221825\) \(a_{17}=-0.119808220\) \(a_{18}=-1.156202080\) \(a_{19}=+0.759731534\) \(a_{20}=-0.474440458\)
\(a_{21}=+0.429267595\) \(a_{22}=+2.467657279\) \(a_{23}=+0.208514414\) \(a_{24}=+0.122951696\) \(a_{25}=-0.579797635\)
\(a_{26}=-1.412280997\) \(a_{27}=+0.654641531\) \(a_{28}=-0.901576222\) \(a_{29}=+0.478779292\) \(a_{30}=+0.297282217\)
\(a_{31}=+0.033738493\) \(a_{32}=-1.221425870\) \(a_{33}=-0.653433521\) \(a_{34}=-0.157669676\) \(a_{35}=+0.798507913\)
\(a_{36}=-0.643020262\) \(a_{37}=-1.388497928\) \(a_{38}=+0.999819750\) \(a_{39}=+0.373970791\) \(a_{40}=+0.228710259\)
\(a_{41}=+1.257978191\) \(a_{42}=+0.564923533\) \(a_{43}=-1.685342905\) \(a_{44}=+1.372384341\) \(a_{45}=+0.569510096\)
\(a_{46}=+0.274408549\) \(a_{47}=-0.607403521\) \(a_{48}=+0.416859637\) \(a_{49}=+0.517399567\) \(a_{50}=-0.763023647\)
\(a_{51}=+0.041750799\) \(a_{52}=-0.785438227\) \(a_{53}=-0.730878106\) \(a_{54}=+0.861519550\) \(a_{55}=-1.215493203\)
\(a_{56}=+0.434616626\) \(a_{57}=-0.264751416\) \(a_{58}=+0.630081812\) \(a_{59}=-0.069042969\) \(a_{60}=+0.165333122\)
\(a_{61}=-0.971376265\) \(a_{62}=+0.044400377\) \(a_{63}=+1.082236498\) \(a_{64}=-0.411195637\) \(a_{65}=+0.695646862\)
\(a_{66}=-0.859929754\) \(a_{67}=-0.632485402\) \(a_{68}=-0.087687704\) \(a_{69}=-0.072663180\) \(a_{70}=+1.050850106\)
\(a_{71}=+0.987743343\) \(a_{72}=+0.309976369\) \(a_{73}=-0.800850905\) \(a_{74}=-1.827287183\) \(a_{75}=+0.202048100\)
\(a_{76}=+0.556048387\) \(a_{77}=-2.309794097\) \(a_{78}=+0.492151943\) \(a_{79}=+0.895220511\) \(a_{80}=+0.775427143\)
\(a_{81}=+0.650431893\) \(a_{82}=+1.655520824\) \(a_{83}=+0.379169525\) \(a_{84}=+0.314181424\) \(a_{85}=+0.077662984\)
\(a_{86}=-2.217940269\) \(a_{87}=-0.166845178\) \(a_{88}=-0.661575706\) \(a_{89}=+0.470710260\) \(a_{90}=+0.749484963\)
\(a_{91}=+1.321933348\) \(a_{92}=+0.152611927\) \(a_{93}=-0.011757074\) \(a_{94}=-0.799353498\) \(a_{95}=-0.492480997\)
\(a_{96}=+0.425642864\) \(a_{97}=+1.188034661\) \(a_{98}=+0.680906772\) \(a_{99}=-1.647386579\) \(a_{100}=-0.424354543\)

Showing 100 of 1500 available coefficients

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