Properties

Label 87.704
Level $87$
Weight $0$
Character 87.1
Symmetry odd
\(R\) 12.28702
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(12.2870223565179944621893813132 \pm 3 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.80095748 \pm 1.0 \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.35846711 \pm 1.1 \) \(a_{5}= +1.24762319 \pm 8.6 \cdot 10^{-1} \) \(a_{6}= \pm0.46243302 \pm 5.7 \cdot 10^{-1} \)
\(a_{7}= -1.54760260 \pm 8.8 \cdot 10^{-1} \) \(a_{8}= +1.08807440 \pm 1.2 \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= -0.99929313 \pm 1.0 \) \(a_{11}= -1.07901853 \pm 8.9 \cdot 10^{-1} \) \(a_{12}= \pm0.20696108 \pm 6.4 \cdot 10^{-1} \)
\(a_{13}= -0.09141281 \pm 8.8 \cdot 10^{-1} \) \(a_{14}= +1.23956388 \pm 9.8 \cdot 10^{-1} \) \(a_{15}= \pm0.72031559 \pm 4.9 \cdot 10^{-1} \)
\(a_{16}= -0.51303422 \pm 1.2 \) \(a_{17}= -1.50458650 \pm 7.8 \cdot 10^{-1} \) \(a_{18}= \pm0.26698583 \pm 3.3 \cdot 10^{-1} \)
\(a_{19}= +1.37911424 \pm 8.3 \cdot 10^{-1} \) \(a_{20}= -0.44723188 \pm 1.2 \) \(a_{21}= \pm0.89350878 \pm 5.1 \cdot 10^{-1} \)
\(a_{22}= +0.86424797 \pm 1.0 \) \(a_{23}= -1.33655127 \pm 7.9 \cdot 10^{-1} \) \(a_{24}= \pm0.62820005 \pm 7.0 \cdot 10^{-1} \)
\(a_{25}= +0.55656363 \pm 8.2 \cdot 10^{-1} \) \(a_{26}= +0.07321778 \pm 9.5 \cdot 10^{-1} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= +0.55476464 \pm 1.1 \) \(a_{29}= \pm0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= \pm0.57694216 \pm 5.8 \cdot 10^{-1} \)
\(a_{31}= -0.56544006 \pm 8.3 \cdot 10^{-1} \) \(a_{32}= -0.67715580 \pm 1.1 \) \(a_{33}= \pm0.62297164 \pm 5.1 \cdot 10^{-1} \)
\(a_{34}= +1.20510982 \pm 9.1 \cdot 10^{-1} \) \(a_{35}= -1.93082490 \pm 8.8 \cdot 10^{-1} \) \(a_{36}= \pm0.11948904 \pm 3.7 \cdot 10^{-1} \)
\(a_{37}= +0.68322764 \pm 7.9 \cdot 10^{-1} \) \(a_{38}= -1.10461187 \pm 1.0 \) \(a_{39}= \pm0.05277721 \pm 5.1 \cdot 10^{-1} \)
\(a_{40}= +1.35750685 \pm 1.3 \) \(a_{41}= -1.81332736 \pm 8.3 \cdot 10^{-1} \) \(a_{42}= \pm0.71566254 \pm 5.6 \cdot 10^{-1} \)
\(a_{43}= -1.36123961 \pm 8.5 \cdot 10^{-1} \) \(a_{44}= +0.38679266 \pm 1.1 \) \(a_{45}= \pm0.41587440 \pm 2.8 \cdot 10^{-1} \)
\(a_{46}= +1.07052074 \pm 1.0 \) \(a_{47}= +0.44335549 \pm 8.7 \cdot 10^{-1} \) \(a_{48}= \pm0.29620044 \pm 7.2 \cdot 10^{-1} \)
\(a_{49}= +1.39507381 \pm 8.3 \cdot 10^{-1} \) \(a_{50}= -0.44578381 \pm 9.2 \cdot 10^{-1} \) \(a_{51}= \pm0.86867342 \pm 4.5 \cdot 10^{-1} \)
\(a_{52}= +0.03276849 \pm 9.7 \cdot 10^{-1} \) \(a_{53}= +0.35038439 \pm 7.4 \cdot 10^{-1} \) \(a_{54}= \pm0.15414434 \pm 1.9 \cdot 10^{-1} \)
\(a_{55}= -1.34620855 \pm 9.1 \cdot 10^{-1} \) \(a_{56}= -1.68390677 \pm 1.1 \) \(a_{57}= \pm0.79623198 \pm 4.8 \cdot 10^{-1} \)
\(a_{58}= \pm0.14873407 \pm 1.8 \cdot 10^{-1} \) \(a_{59}= -0.50416117 \pm 9.0 \cdot 10^{-1} \) \(a_{60}= \pm0.25820945 \pm 6.9 \cdot 10^{-1} \)

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