Properties

Label 1.54
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 35.85867
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 35.85867349169739180638774080779311\ldots \pm 2 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= +1.32123900 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.16708289 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.74567251 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.74864618 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.54199543 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.01093070 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.33602740 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.36208246 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -2.31037953 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.52256790 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.87026162 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.62794346 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.01444206 \pm 1 \cdot 10^{-8} \) \(a_{15}= -2.04081503 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.18964502 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.68870818 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.47839747 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.24088904 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.30391738 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.01275703 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.69043709 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.38728801 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.39217183 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +2.05776345 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.82966339 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.74450264 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.00815072 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.77385097 \pm 1 \cdot 10^{-8} \) \(a_{30}= -2.69640441 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.73483983 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.23577800 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.60988005 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.90994811 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.01911392 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.26999494 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.80085214 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.31827199 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.73286206 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.58759303 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.09930285 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.01685508 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.01034323 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.38966451 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.63315411 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.83293904 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.12383042 \pm 1 \cdot 10^{-8} \) \(a_{48}= -1.38841434 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.99988052 \pm 1 \cdot 10^{-8} \) \(a_{50}= +2.71879733 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.80377953 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.46824017 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.30780844 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.98366593 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.91378635 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.00367301 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.28113747 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.02244209 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.65442252 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.52177966 \pm 1 \cdot 10^{-8} \)

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