Properties

Label 87.46
Level $87$
Weight $0$
Character 87.1
Symmetry even
\(R\) 3.132620
Fricke sign $+1$

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(3.13262040402003940216182029457 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.65782177 \pm 2.2 \cdot 10^{-5} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.74837303 \pm 2.3 \cdot 10^{-5} \) \(a_{5}= +1.98462071 \pm 2.0 \cdot 10^{-5} \) \(a_{6}= -0.95714385 \pm 2.2 \cdot 10^{-5} \)
\(a_{7}= +0.07002136 \pm 1.9 \cdot 10^{-5} \) \(a_{8}= +1.24066910 \pm 2.3 \cdot 10^{-5} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +3.29014742 \pm 2.5 \cdot 10^{-5} \) \(a_{11}= +1.01037217 \pm 1.8 \cdot 10^{-5} \) \(a_{12}= -1.00942364 \pm 2.3 \cdot 10^{-5} \)
\(a_{13}= -0.76409146 \pm 1.7 \cdot 10^{-5} \) \(a_{14}= +0.11608293 \pm 2.4 \cdot 10^{-5} \) \(a_{15}= -1.14582130 \pm 2.0 \cdot 10^{-5} \)
\(a_{16}= +0.30843522 \pm 2.1 \cdot 10^{-5} \) \(a_{17}= -0.26469402 \pm 1.8 \cdot 10^{-5} \) \(a_{18}= +0.55260726 \pm 2.2 \cdot 10^{-5} \)
\(a_{19}= +0.65115611 \pm 1.9 \cdot 10^{-5} \) \(a_{20}= +3.46985732 \pm 2.5 \cdot 10^{-5} \) \(a_{21}= -0.04042685 \pm 1.9 \cdot 10^{-5} \)
\(a_{22}= +1.67501698 \pm 2.3 \cdot 10^{-5} \) \(a_{23}= -1.33948901 \pm 1.8 \cdot 10^{-5} \) \(a_{24}= -0.71630064 \pm 2.3 \cdot 10^{-5} \)
\(a_{25}= +2.93871936 \pm 2.0 \cdot 10^{-5} \) \(a_{26}= -1.26672746 \pm 2.2 \cdot 10^{-5} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.12242345 \pm 2.5 \cdot 10^{-5} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -1.89956750 \pm 4.3 \cdot 10^{-5} \)
\(a_{31}= +0.71406412 \pm 1.9 \cdot 10^{-5} \) \(a_{32}= -0.72933848 \pm 2.2 \cdot 10^{-5} \) \(a_{33}= -0.58333864 \pm 1.8 \cdot 10^{-5} \)
\(a_{34}= -0.43881551 \pm 2.4 \cdot 10^{-5} \) \(a_{35}= +0.13896583 \pm 2.0 \cdot 10^{-5} \) \(a_{36}= +0.58279101 \pm 2.3 \cdot 10^{-5} \)
\(a_{37}= -1.16713045 \pm 1.9 \cdot 10^{-5} \) \(a_{38}= +1.07950078 \pm 2.1 \cdot 10^{-5} \) \(a_{39}= +0.44114841 \pm 1.7 \cdot 10^{-5} \)
\(a_{40}= +2.46225759 \pm 2.3 \cdot 10^{-5} \) \(a_{41}= -1.57033434 \pm 1.7 \cdot 10^{-5} \) \(a_{42}= -0.06702051 \pm 4.1 \cdot 10^{-5} \)
\(a_{43}= +0.65909033 \pm 1.8 \cdot 10^{-5} \) \(a_{44}= +1.76650745 \pm 2.6 \cdot 10^{-5} \) \(a_{45}= +0.66154024 \pm 2.0 \cdot 10^{-5} \)
\(a_{46}= -2.22063405 \pm 2.2 \cdot 10^{-5} \) \(a_{47}= +0.44814276 \pm 1.8 \cdot 10^{-5} \) \(a_{48}= -0.17807516 \pm 2.1 \cdot 10^{-5} \)
\(a_{49}= -0.99509701 \pm 2.0 \cdot 10^{-5} \) \(a_{50}= +4.87187293 \pm 2.5 \cdot 10^{-5} \) \(a_{51}= +0.15282116 \pm 1.8 \cdot 10^{-5} \)
\(a_{52}= -1.33591690 \pm 2.3 \cdot 10^{-5} \) \(a_{53}= +0.83772156 \pm 1.7 \cdot 10^{-5} \) \(a_{54}= -0.31904795 \pm 2.2 \cdot 10^{-5} \)
\(a_{55}= +2.00520553 \pm 2.1 \cdot 10^{-5} \) \(a_{56}= +0.08687333 \pm 2.5 \cdot 10^{-5} \) \(a_{57}= -0.37594516 \pm 1.9 \cdot 10^{-5} \)
\(a_{58}= -0.30784977 \pm 2.2 \cdot 10^{-5} \) \(a_{59}= -1.46629650 \pm 1.8 \cdot 10^{-5} \) \(a_{60}= -2.00332306 \pm 4.4 \cdot 10^{-5} \)

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