Properties

Label 73.45
Level $73$
Weight $0$
Character 73.1
Symmetry even
\(R\) 2.917711
Fricke sign $+1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(2.91771124139345125512572079106 \pm 10 \cdot 10^{-8}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -0.92389631 \pm 3.1 \cdot 10^{-5} \) \(a_{3}= +1.54839851 \pm 3.0 \cdot 10^{-5} \)
\(a_{4}= -0.14641560 \pm 3.3 \cdot 10^{-5} \) \(a_{5}= -0.73970918 \pm 2.8 \cdot 10^{-5} \) \(a_{6}= -1.43055968 \pm 3.6 \cdot 10^{-5} \)
\(a_{7}= +1.79824010 \pm 2.7 \cdot 10^{-5} \) \(a_{8}= +1.05916915 \pm 3.4 \cdot 10^{-5} \) \(a_{9}= +1.39753796 \pm 3.1 \cdot 10^{-5} \)
\(a_{10}= +0.68341458 \pm 3.2 \cdot 10^{-5} \) \(a_{11}= -0.99544745 \pm 2.7 \cdot 10^{-5} \) \(a_{12}= -0.22670970 \pm 3.8 \cdot 10^{-5} \)
\(a_{13}= +1.75936569 \pm 2.6 \cdot 10^{-5} \) \(a_{14}= -1.66138740 \pm 3.2 \cdot 10^{-5} \) \(a_{15}= -1.14536459 \pm 2.9 \cdot 10^{-5} \)
\(a_{16}= -0.83214687 \pm 3.6 \cdot 10^{-5} \) \(a_{17}= +0.07834152 \pm 2.7 \cdot 10^{-5} \) \(a_{18}= -1.29118017 \pm 3.7 \cdot 10^{-5} \)
\(a_{19}= -0.31267867 \pm 2.5 \cdot 10^{-5} \) \(a_{20}= +0.10830496 \pm 3.4 \cdot 10^{-5} \) \(a_{21}= +2.78439230 \pm 2.9 \cdot 10^{-5} \)
\(a_{22}= +0.91969023 \pm 3.1 \cdot 10^{-5} \) \(a_{23}= +1.12769487 \pm 2.4 \cdot 10^{-5} \) \(a_{24}= +1.64001594 \pm 3.8 \cdot 10^{-5} \)
\(a_{25}= -0.45283033 \pm 2.9 \cdot 10^{-5} \) \(a_{26}= -1.62547147 \pm 3.2 \cdot 10^{-5} \) \(a_{27}= +0.61554718 \pm 3.2 \cdot 10^{-5} \)
\(a_{28}= -0.26329041 \pm 3.5 \cdot 10^{-5} \) \(a_{29}= +1.04057752 \pm 2.4 \cdot 10^{-5} \) \(a_{30}= +1.05819812 \pm 3.9 \cdot 10^{-5} \)
\(a_{31}= +1.44559028 \pm 2.6 \cdot 10^{-5} \) \(a_{32}= -0.29035172 \pm 3.5 \cdot 10^{-5} \) \(a_{33}= -1.54134935 \pm 3.0 \cdot 10^{-5} \)
\(a_{34}= -0.07237944 \pm 3.1 \cdot 10^{-5} \) \(a_{35}= -1.33017471 \pm 2.7 \cdot 10^{-5} \) \(a_{36}= -0.20462136 \pm 4.2 \cdot 10^{-5} \)
\(a_{37}= +0.78386225 \pm 2.7 \cdot 10^{-5} \) \(a_{38}= +0.28888267 \pm 3.0 \cdot 10^{-5} \) \(a_{39}= +2.72419922 \pm 3.2 \cdot 10^{-5} \)
\(a_{40}= -0.78347714 \pm 3.6 \cdot 10^{-5} \) \(a_{41}= -0.94779933 \pm 2.6 \cdot 10^{-5} \) \(a_{42}= -2.57248978 \pm 3.9 \cdot 10^{-5} \)
\(a_{43}= -0.14914800 \pm 2.3 \cdot 10^{-5} \) \(a_{44}= +0.14574904 \pm 3.0 \cdot 10^{-5} \) \(a_{45}= -1.03377165 \pm 3.1 \cdot 10^{-5} \)
\(a_{46}= -1.04187314 \pm 3.1 \cdot 10^{-5} \) \(a_{47}= +0.28992090 \pm 2.6 \cdot 10^{-5} \) \(a_{48}= -1.28849498 \pm 3.8 \cdot 10^{-5} \)
\(a_{49}= +2.23366746 \pm 2.6 \cdot 10^{-5} \) \(a_{50}= +0.41836827 \pm 3.6 \cdot 10^{-5} \) \(a_{51}= +0.12130389 \pm 3.0 \cdot 10^{-5} \)
\(a_{52}= -0.25759859 \pm 3.2 \cdot 10^{-5} \) \(a_{53}= -0.96274095 \pm 2.5 \cdot 10^{-5} \) \(a_{54}= -0.56870177 \pm 3.9 \cdot 10^{-5} \)
\(a_{55}= +0.73634161 \pm 2.9 \cdot 10^{-5} \) \(a_{56}= +1.90464043 \pm 3.9 \cdot 10^{-5} \) \(a_{57}= -0.48415119 \pm 2.7 \cdot 10^{-5} \)
\(a_{58}= -0.96138574 \pm 2.7 \cdot 10^{-5} \) \(a_{59}= +0.56394560 \pm 2.5 \cdot 10^{-5} \) \(a_{60}= +0.16769925 \pm 4.2 \cdot 10^{-5} \)

Displaying $a_n$ with $n$ up to: 60 180 1000