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: \( 3.91221753176 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.009423936\) \(a_{3}=+1.502802021\) \(a_{4}=+0.018936682\) \(a_{5}=+1.708393294\)
\(a_{6}=+1.516964331\) \(a_{7}=-1.168093872\) \(a_{8}=-0.990308796\) \(a_{9}=+1.258413915\) \(a_{10}=+1.724493083\)
\(a_{11}=+0.585529368\) \(a_{12}=+0.028458084\) \(a_{13}=-0.467070508\) \(a_{14}=-1.179101914\) \(a_{15}=+2.567376896\)
\(a_{16}=-1.018578084\) \(a_{17}=-0.739305836\) \(a_{18}=+1.270273127\) \(a_{19}=-0.282212174\) \(a_{20}=+0.032351301\)
\(a_{21}=-1.755413832\) \(a_{22}=+0.591047359\) \(a_{23}=-0.208514414\) \(a_{24}=-1.488238060\) \(a_{25}=+1.918607647\)
\(a_{26}=-0.471472150\) \(a_{27}=+0.388344954\) \(a_{28}=-0.022119822\) \(a_{29}=-1.205390214\) \(a_{30}=+2.591571691\)
\(a_{31}=+1.598922976\) \(a_{32}=-0.037868303\) \(a_{33}=+0.879934718\) \(a_{34}=-0.746273006\) \(a_{35}=-1.995563738\)
\(a_{36}=+0.023830184\) \(a_{37}=+0.860177080\) \(a_{38}=-0.284871723\) \(a_{39}=-0.701914503\) \(a_{40}=-1.691836906\)
\(a_{41}=+0.388462533\) \(a_{42}=-1.771956739\) \(a_{43}=-0.428237075\) \(a_{44}=+0.011087983\) \(a_{45}=+2.149865894\)
\(a_{46}=-0.210479440\) \(a_{47}=+1.623116393\) \(a_{48}=-1.530721204\) \(a_{49}=+0.364443293\) \(a_{50}=+1.936688482\)
\(a_{51}=-1.111030303\) \(a_{52}=-0.008844765\) \(a_{53}=-0.568688416\) \(a_{54}=+0.392004691\) \(a_{55}=+1.000314446\)
\(a_{56}=+1.156773639\) \(a_{57}=-0.424109026\) \(a_{58}=-1.216749738\) \(a_{59}=-0.253338446\) \(a_{60}=+0.048617604\)
\(a_{61}=-0.677207983\) \(a_{62}=+1.613991118\) \(a_{63}=-1.469945595\) \(a_{64}=+0.980352909\) \(a_{65}=-0.797940128\)
\(a_{66}=+0.888227168\) \(a_{67}=-0.299707750\) \(a_{68}=-0.013999992\) \(a_{69}=-0.313355887\) \(a_{70}=-2.014369816\)
\(a_{71}=+1.088282041\) \(a_{72}=-1.246218361\) \(a_{73}=+1.667749166\) \(a_{74}=+0.868283346\) \(a_{75}=+2.883287429\)
\(a_{76}=-0.005344212\) \(a_{77}=-0.683953284\) \(a_{78}=-0.708529245\) \(a_{79}=-0.927377756\) \(a_{80}=-1.740131964\)
\(a_{81}=-0.674808336\) \(a_{82}=+0.392123377\) \(a_{83}=+0.427354922\) \(a_{84}=-0.033241712\) \(a_{85}=-1.263025130\)
\(a_{86}=-0.432272754\) \(a_{87}=-1.811462859\) \(a_{88}=-0.579854886\) \(a_{89}=-0.637137301\) \(a_{90}=+2.170126114\)
\(a_{91}=+0.545582199\) \(a_{92}=-0.003948584\) \(a_{93}=+2.402864679\) \(a_{94}=+1.638412538\) \(a_{95}=-0.482129391\)
\(a_{96}=-0.056908536\) \(a_{97}=+0.924095591\) \(a_{98}=+0.367877715\) \(a_{99}=+0.736838307\) \(a_{100}=+0.036332296\)

Showing 100 of 1500 available coefficients

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