Properties

Label 87.5
Level $87$
Weight $0$
Character 87.1
Symmetry odd
\(R\) 1.056538
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: \(1.0565380782581096520420260247 \pm 10 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.30655770 \pm 1.2 \cdot 10^{-4} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.70709301 \pm 1.3 \cdot 10^{-4} \) \(a_{5}= +0.27023368 \pm 1.0 \cdot 10^{-4} \) \(a_{6}= -0.75434144 \pm 1.2 \cdot 10^{-4} \)
\(a_{7}= +0.40750848 \pm 1.0 \cdot 10^{-4} \) \(a_{8}= +0.38269988 \pm 1.4 \cdot 10^{-4} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.35307590 \pm 1.2 \cdot 10^{-4} \) \(a_{11}= +1.49268745 \pm 1.1 \cdot 10^{-4} \) \(a_{12}= +0.40824034 \pm 1.3 \cdot 10^{-4} \)
\(a_{13}= +1.33455504 \pm 1.0 \cdot 10^{-4} \) \(a_{14}= -0.53243334 \pm 1.2 \cdot 10^{-4} \) \(a_{15}= +0.15601949 \pm 1.0 \cdot 10^{-4} \)
\(a_{16}= -1.20711248 \pm 1.5 \cdot 10^{-4} \) \(a_{17}= -1.37918670 \pm 9.6 \cdot 10^{-5} \) \(a_{18}= -0.43551923 \pm 1.2 \cdot 10^{-4} \)
\(a_{19}= +0.64099459 \pm 1.0 \cdot 10^{-4} \) \(a_{20}= +0.19108035 \pm 1.4 \cdot 10^{-4} \) \(a_{21}= +0.23527513 \pm 1.0 \cdot 10^{-4} \)
\(a_{22}= -1.95028227 \pm 1.3 \cdot 10^{-4} \) \(a_{23}= -0.30161244 \pm 9.7 \cdot 10^{-5} \) \(a_{24}= +0.22095188 \pm 1.4 \cdot 10^{-4} \)
\(a_{25}= -0.92697376 \pm 1.0 \cdot 10^{-4} \) \(a_{26}= -1.74367316 \pm 1.1 \cdot 10^{-4} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.28814640 \pm 1.4 \cdot 10^{-4} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.20384846 \pm 2.2 \cdot 10^{-4} \)
\(a_{31}= -0.68787755 \pm 1.0 \cdot 10^{-4} \) \(a_{32}= +1.19446223 \pm 1.4 \cdot 10^{-4} \) \(a_{33}= +0.86180350 \pm 1.1 \cdot 10^{-4} \)
\(a_{34}= +1.80198699 \pm 1.1 \cdot 10^{-4} \) \(a_{35}= +0.11012252 \pm 1.0 \cdot 10^{-4} \) \(a_{36}= +0.23569767 \pm 1.3 \cdot 10^{-4} \)
\(a_{37}= +0.76946874 \pm 9.7 \cdot 10^{-5} \) \(a_{38}= -0.83749641 \pm 1.3 \cdot 10^{-4} \) \(a_{39}= +0.77050571 \pm 1.0 \cdot 10^{-4} \)
\(a_{40}= +0.10341840 \pm 1.6 \cdot 10^{-4} \) \(a_{41}= -1.27216342 \pm 1.0 \cdot 10^{-4} \) \(a_{42}= -0.30740053 \pm 2.3 \cdot 10^{-4} \)
\(a_{43}= +1.26904424 \pm 1.0 \cdot 10^{-4} \) \(a_{44}= +1.05546886 \pm 1.4 \cdot 10^{-4} \) \(a_{45}= +0.09007789 \pm 1.0 \cdot 10^{-4} \)
\(a_{46}= +0.39407405 \pm 1.2 \cdot 10^{-4} \) \(a_{47}= +1.15939018 \pm 1.0 \cdot 10^{-4} \) \(a_{48}= -0.69692672 \pm 1.5 \cdot 10^{-4} \)
\(a_{49}= -0.83393684 \pm 1.0 \cdot 10^{-4} \) \(a_{50}= +1.21114470 \pm 1.1 \cdot 10^{-4} \) \(a_{51}= -0.79627381 \pm 9.6 \cdot 10^{-5} \)
\(a_{52}= +0.94365455 \pm 1.2 \cdot 10^{-4} \) \(a_{53}= -0.04963810 \pm 9.1 \cdot 10^{-5} \) \(a_{54}= -0.25144715 \pm 1.2 \cdot 10^{-4} \)
\(a_{55}= +0.40337442 \pm 1.1 \cdot 10^{-4} \) \(a_{56}= +0.15595344 \pm 1.4 \cdot 10^{-4} \) \(a_{57}= +0.37007840 \pm 1.0 \cdot 10^{-4} \)
\(a_{58}= +0.24262167 \pm 1.2 \cdot 10^{-4} \) \(a_{59}= -1.97863784 \pm 1.1 \cdot 10^{-4} \) \(a_{60}= +0.11032029 \pm 2.4 \cdot 10^{-4} \)

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