Properties

Level $20$
Weight $0$
Character 20.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 20 = 2^{2} \cdot 5 \)
Weight: \( 0 \)
Character: 20.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.00967417707 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.300073428\) \(a_{4}=+0.000000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.195552407\) \(a_{8}=+0.000000000\) \(a_{9}=+0.690190919\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.542440583\) \(a_{12}=+0.000000000\) \(a_{13}=-0.198430653\) \(a_{14}=+0.000000000\) \(a_{15}=-0.581410512\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.174962101\) \(a_{18}=+0.000000000\) \(a_{19}=+0.524946225\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.554305917\) \(a_{22}=+0.000000000\) \(a_{23}=+0.337648057\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.402774554\) \(a_{28}=+0.000000000\) \(a_{29}=-0.132828069\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.734221829\) \(a_{32}=+0.000000000\) \(a_{33}=+2.005286017\) \(a_{34}=+0.000000000\) \(a_{35}=+0.534667291\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.144786633\) \(a_{38}=+0.000000000\) \(a_{39}=-0.257974420\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.560901000\) \(a_{42}=+0.000000000\) \(a_{43}=-1.757077856\) \(a_{44}=+0.000000000\) \(a_{45}=-0.308662762\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.928496780\) \(a_{48}=+0.000000000\) \(a_{49}=+0.429345560\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.227463576\) \(a_{52}=+0.000000000\) \(a_{53}=+0.373225603\) \(a_{54}=+0.000000000\) \(a_{55}=-0.689800407\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.682468644\) \(a_{58}=+0.000000000\) \(a_{59}=+0.130117137\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.151112541\) \(a_{62}=+0.000000000\) \(a_{63}=-0.825159281\) \(a_{64}=+0.000000000\) \(a_{65}=+0.088740804\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.546364726\) \(a_{68}=+0.000000000\) \(a_{69}=+0.438967801\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.373688997\) \(a_{72}=+0.000000000\) \(a_{73}=-1.376839267\) \(a_{74}=+0.000000000\) \(a_{75}=+0.260015118\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.844072924\) \(a_{78}=+0.000000000\) \(a_{79}=-1.073769116\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.213778533\) \(a_{82}=+0.000000000\) \(a_{83}=+1.196823443\) \(a_{84}=+0.000000000\) \(a_{85}=+0.078283929\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.172950035\) \(a_{88}=+0.000000000\) \(a_{89}=-0.146969899\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.233521720\) \(a_{92}=+0.000000000\) \(a_{93}=+0.954544323\) \(a_{94}=+0.000000000\) \(a_{95}=-0.234760615\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.883327622\) \(a_{98}=+0.000000000\) \(a_{99}=+1.064585902\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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