Properties

Level $72$
Weight $0$
Character 72.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( 0 \)
Character: 72.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.40189452021 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.000000000\) \(a_{4}=+0.000000000\) \(a_{5}=-1.563221586\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.803938690\) \(a_{8}=+0.000000000\) \(a_{9}=+0.000000000\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.407536829\) \(a_{12}=+0.000000000\) \(a_{13}=+0.533271889\) \(a_{14}=+0.000000000\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.624186934\) \(a_{18}=+0.000000000\) \(a_{19}=-0.317115988\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.000000000\) \(a_{23}=+1.149494196\) \(a_{24}=+0.000000000\) \(a_{25}=+1.443661748\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.000000000\) \(a_{28}=+0.000000000\) \(a_{29}=+1.854939173\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.838551635\) \(a_{32}=+0.000000000\) \(a_{33}=+0.000000000\) \(a_{34}=+0.000000000\) \(a_{35}=-1.256734304\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.310804704\) \(a_{38}=+0.000000000\) \(a_{39}=+0.000000000\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.514402880\) \(a_{42}=+0.000000000\) \(a_{43}=+0.597541798\) \(a_{44}=+0.000000000\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.162482250\) \(a_{48}=+0.000000000\) \(a_{49}=-0.353682667\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.000000000\) \(a_{53}=-0.675442688\) \(a_{54}=+0.000000000\) \(a_{55}=-2.200291854\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.000000000\) \(a_{58}=+0.000000000\) \(a_{59}=+0.681574010\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.342080870\) \(a_{62}=+0.000000000\) \(a_{63}=+0.000000000\) \(a_{64}=+0.000000000\) \(a_{65}=-0.833622166\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.565479137\) \(a_{68}=+0.000000000\) \(a_{69}=+0.000000000\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.208092255\) \(a_{72}=+0.000000000\) \(a_{73}=+0.672237135\) \(a_{74}=+0.000000000\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.131573403\) \(a_{78}=+0.000000000\) \(a_{79}=+0.850985801\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.000000000\) \(a_{83}=-0.892596729\) \(a_{84}=+0.000000000\) \(a_{85}=+0.975742478\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.000000000\) \(a_{88}=+0.000000000\) \(a_{89}=-0.311397743\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.428717898\) \(a_{92}=+0.000000000\) \(a_{93}=+0.000000000\) \(a_{94}=+0.000000000\) \(a_{95}=+0.495722571\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.662382355\) \(a_{98}=+0.000000000\) \(a_{99}=+0.000000000\) \(a_{100}=+0.000000000\)

Showing 100 of 382 available coefficients

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