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: \( 3.23574197248 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.803316879\) \(a_{3}=+0.849299965\) \(a_{4}=+2.251951766\) \(a_{5}=-1.542194100\)
\(a_{6}=+1.531556962\) \(a_{7}=-0.543382935\) \(a_{8}=+2.257665751\) \(a_{9}=-0.278689570\) \(a_{10}=-2.781064652\)
\(a_{11}=+1.154823192\) \(a_{12}=+1.912582556\) \(a_{13}=+1.134429191\) \(a_{14}=-0.979891619\) \(a_{15}=-1.309785395\)
\(a_{16}=+1.819334990\) \(a_{17}=+0.027984837\) \(a_{18}=-0.502565605\) \(a_{19}=-1.034053700\) \(a_{20}=-3.472946728\)
\(a_{21}=-0.461495108\) \(a_{22}=+2.082512155\) \(a_{23}=-0.208514414\) \(a_{24}=+1.917435443\) \(a_{25}=+1.378362643\)
\(a_{26}=+2.045735307\) \(a_{27}=-1.085991007\) \(a_{28}=-1.223672161\) \(a_{29}=+0.999465197\) \(a_{30}=-2.361958111\)
\(a_{31}=-0.066817124\) \(a_{32}=+1.023171746\) \(a_{33}=+0.980791297\) \(a_{34}=+0.050465529\) \(a_{35}=+0.838001957\)
\(a_{36}=-0.627595468\) \(a_{37}=+0.505137483\) \(a_{38}=-1.864726492\) \(a_{39}=+0.963470673\) \(a_{40}=-3.481758802\)
\(a_{41}=-1.372197376\) \(a_{42}=-0.832221918\) \(a_{43}=-0.190891268\) \(a_{44}=+2.600606133\) \(a_{45}=+0.429793408\)
\(a_{46}=-0.376017566\) \(a_{47}=+0.398855585\) \(a_{48}=+1.545161138\) \(a_{49}=-0.704734969\) \(a_{50}=+2.485624618\)
\(a_{51}=+0.023767519\) \(a_{52}=+2.554679813\) \(a_{53}=+0.496792500\) \(a_{54}=-1.958385910\) \(a_{55}=-1.780961508\)
\(a_{56}=-1.226777044\) \(a_{57}=-0.878221775\) \(a_{58}=+1.802352461\) \(a_{59}=+0.598768670\) \(a_{60}=-2.949573525\)
\(a_{61}=+1.311516268\) \(a_{62}=-0.120492440\) \(a_{63}=+0.151435150\) \(a_{64}=+0.025767826\) \(a_{65}=-1.749510093\)
\(a_{66}=+1.768677499\) \(a_{67}=-0.901521255\) \(a_{68}=+0.063020508\) \(a_{69}=-0.177091295\) \(a_{70}=+1.511183066\)
\(a_{71}=+1.239619996\) \(a_{72}=-0.629187875\) \(a_{73}=-0.013846965\) \(a_{74}=+0.910922947\) \(a_{75}=+1.170643321\)
\(a_{76}=-2.328639067\) \(a_{77}=-0.627511167\) \(a_{78}=+1.737442892\) \(a_{79}=+1.082632489\) \(a_{80}=-2.805767752\)
\(a_{81}=-0.643642580\) \(a_{82}=-2.474506638\) \(a_{83}=+0.665334322\) \(a_{84}=-1.039264741\) \(a_{85}=-0.043158017\)
\(a_{86}=-0.344237498\) \(a_{87}=+0.848845803\) \(a_{88}=+2.607204764\) \(a_{89}=-0.485254101\) \(a_{90}=+0.775053725\)
\(a_{91}=-0.616429534\) \(a_{92}=-0.469564347\) \(a_{93}=-0.056747747\) \(a_{94}=+0.719262949\) \(a_{95}=+1.594711496\)
\(a_{96}=+0.868979777\) \(a_{97}=-1.515741678\) \(a_{98}=-1.270860456\) \(a_{99}=-0.321837175\) \(a_{100}=+3.104006188\)

Showing 100 of 1500 available coefficients

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