Properties

Label 1.58
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 36.98881
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 36.98881539054350323266075303033361\ldots \pm 4 \cdot 10^{-92} \) (toggle for full precision) Copy content Toggle raw display

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.53152851 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.87689256 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.71747744 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.65368139 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.46609340 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +1.23189215 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.91288822 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.23105943 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.87897880 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.83428578 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.62915064 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.22639108 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.65478580 \pm 1 \cdot 10^{-8} \) \(a_{15}= +1.45010092 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.23225133 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.00609085 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.12281467 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.46454801 \pm 1 \cdot 10^{-8} \) \(a_{20}= +1.18647910 \pm 1 \cdot 10^{-8} \) \(a_{21}= -1.08023707 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.44344668 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.05397608 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.80050490 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +1.73466215 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.12033331 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.07950686 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.88385483 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.18759114 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.77076998 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.44597324 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.03633643 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.73157900 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.00323746 \pm 1 \cdot 10^{-8} \) \(a_{35}= -2.03715713 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16577993 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.17298583 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.24692051 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.19852066 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -1.50962627 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.81778867 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.57417680 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.49730258 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.59858123 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.38209868 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.02868983 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.23919406 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.20365946 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.51755827 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.92202239 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.00534102 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.16243049 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.24524546 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.57378867 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -1.37964288 \pm 1 \cdot 10^{-8} \) \(a_{56}= +1.12457984 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.40735869 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.09971004 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.55167249 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.04041470 \pm 1 \cdot 10^{-8} \)

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