Properties

Label 1.48
Level $1$
Weight $0$
Character 1.1
Symmetry even
\(R\) 34.45627
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 34.45627153303102836553281621651428\ldots \pm 2 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= -1.23572393 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.55399001 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.52701363 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.90085324 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.68457872 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.61467142 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.58448058 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.69309506 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -1.11320591 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.47766115 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.29196029 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -1.48091215 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.75956419 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.49906370 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.24927026 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.66952119 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.85647416 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.10543233 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.47476193 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.34052183 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -1.82598124 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.57098256 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.32379640 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.18846344 \pm 1 \cdot 10^{-8} \) \(a_{26}= +1.82999858 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.93795776 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.32394022 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.45279883 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.61670496 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.33744383 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.95927258 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.81860952 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.82734335 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.55372875 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.36527054 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.27276815 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.13028526 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.82041054 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.52653122 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.64285433 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.42079097 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.33225128 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.77874756 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.62437694 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.70557682 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.33471913 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.69208325 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.62217904 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.23288878 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.37090805 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.78046088 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.54836339 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.15905685 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +1.33115583 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.35926351 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.05840846 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.79525828 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.87798714 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.26301337 \pm 1 \cdot 10^{-8} \)

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