Properties

Label 3.10
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 9.743749
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(9.7437493991582837378928949276 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.29550564 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.91267642 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.45139206 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.17061026 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.93959439 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.56520666 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.42889453 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.03585245 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.52693398 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +0.26517500 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.27765544 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.83796160 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.74565466 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.20243030 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.09850188 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +1.54229255 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.32465131 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.54247507 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.01059460 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.53674600 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.32632222 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +1.10653891 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.07836071 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.85754564 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.47260595 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.24762237 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +1.24074471 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.78555182 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.02069942 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.05981929 \pm 1 \cdot 10^{-8} \) \(a_{35}= +1.36371983 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.30422547 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.30157452 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.45575614 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.15309886 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.82033646 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.00314483 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.16030444 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.36921516 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.03272168 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.48379735 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.15861147 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.62740327 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.43050392 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.11716239 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.32698849 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.11687319 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.24201897 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.51432031 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.05687009 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.05203596 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.53106501 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.89044302 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.13965772 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.45945852 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.76478779 \pm 1.0 \cdot 10^{-8} \)

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