Properties

Label 87.1
Level $87$
Weight $0$
Character 87.1
Symmetry odd
\(R\) 0.421867
Fricke sign $+1$

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(0.421867190508416479585620615512 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.39105230 \pm 1.5 \cdot 10^{-4} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.84707810 \pm 1.7 \cdot 10^{-4} \) \(a_{5}= -0.68672744 \pm 1.3 \cdot 10^{-4} \) \(a_{6}= +0.22577415 \pm 1.5 \cdot 10^{-4} \)
\(a_{7}= -1.29410936 \pm 1.3 \cdot 10^{-4} \) \(a_{8}= +0.72230414 \pm 1.8 \cdot 10^{-4} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.26854635 \pm 1.5 \cdot 10^{-4} \) \(a_{11}= +0.00889570 \pm 1.3 \cdot 10^{-4} \) \(a_{12}= +0.48906077 \pm 1.7 \cdot 10^{-4} \)
\(a_{13}= -0.82544447 \pm 1.3 \cdot 10^{-4} \) \(a_{14}= +0.50606445 \pm 1.5 \cdot 10^{-4} \) \(a_{15}= +0.39648227 \pm 1.3 \cdot 10^{-4} \)
\(a_{16}= +0.56461940 \pm 1.9 \cdot 10^{-4} \) \(a_{17}= -0.13678551 \pm 1.2 \cdot 10^{-4} \) \(a_{18}= -0.13035077 \pm 1.5 \cdot 10^{-4} \)
\(a_{19}= +0.44503496 \pm 1.2 \cdot 10^{-4} \) \(a_{20}= +0.58171177 \pm 1.8 \cdot 10^{-4} \) \(a_{21}= +0.74715439 \pm 1.3 \cdot 10^{-4} \)
\(a_{22}= -0.00347869 \pm 1.7 \cdot 10^{-4} \) \(a_{23}= +0.10231489 \pm 1.2 \cdot 10^{-4} \) \(a_{24}= -0.41702249 \pm 1.8 \cdot 10^{-4} \)
\(a_{25}= -0.52840542 \pm 1.2 \cdot 10^{-4} \) \(a_{26}= +0.32279196 \pm 1.4 \cdot 10^{-4} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +1.09621169 \pm 1.7 \cdot 10^{-4} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.15504531 \pm 2.9 \cdot 10^{-4} \)
\(a_{31}= -0.57625682 \pm 1.2 \cdot 10^{-4} \) \(a_{32}= -0.94309986 \pm 1.8 \cdot 10^{-4} \) \(a_{33}= -0.00513594 \pm 1.3 \cdot 10^{-4} \)
\(a_{34}= +0.05349029 \pm 1.4 \cdot 10^{-4} \) \(a_{35}= +0.88870041 \pm 1.3 \cdot 10^{-4} \) \(a_{36}= -0.28235937 \pm 1.7 \cdot 10^{-4} \)
\(a_{37}= +0.85492373 \pm 1.2 \cdot 10^{-4} \) \(a_{38}= -0.17403194 \pm 1.7 \cdot 10^{-4} \) \(a_{39}= +0.47657058 \pm 1.3 \cdot 10^{-4} \)
\(a_{40}= -0.49602607 \pm 2.0 \cdot 10^{-4} \) \(a_{41}= -1.45011825 \pm 1.3 \cdot 10^{-4} \) \(a_{42}= -0.29217644 \pm 2.9 \cdot 10^{-4} \)
\(a_{43}= -1.06431446 \pm 1.3 \cdot 10^{-4} \) \(a_{44}= -0.00753536 \pm 1.8 \cdot 10^{-4} \) \(a_{45}= -0.22890915 \pm 1.3 \cdot 10^{-4} \)
\(a_{46}= -0.04001047 \pm 1.5 \cdot 10^{-4} \) \(a_{47}= -0.87647130 \pm 1.3 \cdot 10^{-4} \) \(a_{48}= -0.32598316 \pm 1.9 \cdot 10^{-4} \)
\(a_{49}= +0.67471904 \pm 1.2 \cdot 10^{-4} \) \(a_{50}= +0.20663416 \pm 1.4 \cdot 10^{-4} \) \(a_{51}= +0.07897315 \pm 1.2 \cdot 10^{-4} \)
\(a_{52}= +0.69921593 \pm 1.5 \cdot 10^{-4} \) \(a_{53}= -1.11291622 \pm 1.1 \cdot 10^{-4} \) \(a_{54}= +0.07525805 \pm 1.5 \cdot 10^{-4} \)
\(a_{55}= -0.00610892 \pm 1.4 \cdot 10^{-4} \) \(a_{56}= -0.93474055 \pm 1.8 \cdot 10^{-4} \) \(a_{57}= -0.25694105 \pm 1.2 \cdot 10^{-4} \)
\(a_{58}= +0.07261659 \pm 1.5 \cdot 10^{-4} \) \(a_{59}= +0.87749846 \pm 1.4 \cdot 10^{-4} \) \(a_{60}= -0.33585145 \pm 3.0 \cdot 10^{-4} \)

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