Properties

Level $32$
Weight $0$
Character 32.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 32 = 2^{5} \)
Weight: \( 0 \)
Character: 32.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.58298402762 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.900576756\) \(a_{4}=+0.000000000\) \(a_{5}=+0.720612822\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.029869169\) \(a_{8}=+0.000000000\) \(a_{9}=-0.188961495\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.429121765\) \(a_{12}=+0.000000000\) \(a_{13}=-0.330489882\) \(a_{14}=+0.000000000\) \(a_{15}=-0.648967163\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.142201704\) \(a_{18}=+0.000000000\) \(a_{19}=-1.455800942\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.927476232\) \(a_{22}=+0.000000000\) \(a_{23}=+0.277484489\) \(a_{24}=+0.000000000\) \(a_{25}=-0.480717128\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.070751073\) \(a_{28}=+0.000000000\) \(a_{29}=+1.125608468\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.334167060\) \(a_{32}=+0.000000000\) \(a_{33}=-0.386457082\) \(a_{34}=+0.000000000\) \(a_{35}=+0.742137002\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.360482126\) \(a_{38}=+0.000000000\) \(a_{39}=+0.297631500\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.716632959\) \(a_{42}=+0.000000000\) \(a_{43}=-0.963943096\) \(a_{44}=+0.000000000\) \(a_{45}=-0.136168336\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.032634337\) \(a_{48}=+0.000000000\) \(a_{49}=+0.060630517\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.028640314\) \(a_{52}=+0.000000000\) \(a_{53}=+0.527674077\) \(a_{54}=+0.000000000\) \(a_{55}=+0.309230675\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.311060467\) \(a_{58}=+0.000000000\) \(a_{59}=+0.512284087\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.808314852\) \(a_{62}=+0.000000000\) \(a_{63}=-0.194605641\) \(a_{64}=+0.000000000\) \(a_{65}=-0.238155174\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.302201248\) \(a_{68}=+0.000000000\) \(a_{69}=-0.249896098\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.255527207\) \(a_{72}=+0.000000000\) \(a_{73}=+0.956737543\) \(a_{74}=+0.000000000\) \(a_{75}=+0.432922629\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.441939293\) \(a_{78}=+0.000000000\) \(a_{79}=+1.587144701\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.775332144\) \(a_{82}=+0.000000000\) \(a_{83}=-1.325666307\) \(a_{84}=+0.000000000\) \(a_{85}=+0.823085246\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.013696834\) \(a_{88}=+0.000000000\) \(a_{89}=-0.295146788\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.340361377\) \(a_{92}=+0.000000000\) \(a_{93}=-0.300943108\) \(a_{94}=+0.000000000\) \(a_{95}=-1.049068872\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.721395952\) \(a_{98}=+0.000000000\) \(a_{99}=-0.081087478\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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