Properties

Level $32$
Weight $0$
Character 32.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 32 = 2^{5} \)
Weight: \( 0 \)
Character: 32.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.58298402715 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.900576756\) \(a_{4}=+0.000000000\) \(a_{5}=+0.720612825\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.029869170\) \(a_{8}=+0.000000000\) \(a_{9}=-0.188961502\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.429121764\) \(a_{12}=+0.000000000\) \(a_{13}=-0.330489886\) \(a_{14}=+0.000000000\) \(a_{15}=+0.648967161\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.142201723\) \(a_{18}=+0.000000000\) \(a_{19}=+1.455800948\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.927476234\) \(a_{22}=+0.000000000\) \(a_{23}=-0.277484480\) \(a_{24}=+0.000000000\) \(a_{25}=-0.480717150\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.070751091\) \(a_{28}=+0.000000000\) \(a_{29}=+1.125608494\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.334167079\) \(a_{32}=+0.000000000\) \(a_{33}=-0.386457069\) \(a_{34}=+0.000000000\) \(a_{35}=-0.742136935\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.360482017\) \(a_{38}=+0.000000000\) \(a_{39}=-0.297631522\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.716632892\) \(a_{42}=+0.000000000\) \(a_{43}=+0.963942877\) \(a_{44}=+0.000000000\) \(a_{45}=-0.136168078\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.032634368\) \(a_{48}=+0.000000000\) \(a_{49}=+0.060630506\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.028640334\) \(a_{52}=+0.000000000\) \(a_{53}=+0.527674057\) \(a_{54}=+0.000000000\) \(a_{55}=-0.309230667\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.311060463\) \(a_{58}=+0.000000000\) \(a_{59}=-0.512284089\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.808314830\) \(a_{62}=+0.000000000\) \(a_{63}=+0.194605549\) \(a_{64}=+0.000000000\) \(a_{65}=-0.238155191\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.302201228\) \(a_{68}=+0.000000000\) \(a_{69}=-0.249896072\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.255527231\) \(a_{72}=+0.000000000\) \(a_{73}=+0.956737519\) \(a_{74}=+0.000000000\) \(a_{75}=-0.432922664\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.441939230\) \(a_{78}=+0.000000000\) \(a_{79}=-1.587144675\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.775332054\) \(a_{82}=+0.000000000\) \(a_{83}=+1.325666323\) \(a_{84}=+0.000000000\) \(a_{85}=+0.823085307\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.013696890\) \(a_{88}=+0.000000000\) \(a_{89}=-0.295146803\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.340361339\) \(a_{92}=+0.000000000\) \(a_{93}=-0.300943110\) \(a_{94}=+0.000000000\) \(a_{95}=+1.049068812\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.721395947\) \(a_{98}=+0.000000000\) \(a_{99}=+0.081087583\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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