Properties

Label 87.40
Level $87$
Weight $0$
Character 87.1
Symmetry odd
\(R\) 2.903639
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: \(2.90363905872431059028448229527 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.85163745 \pm 5.3 \cdot 10^{-3} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.27471365 \pm 5.9 \cdot 10^{-3} \) \(a_{5}= +0.89520935 \pm 4.6 \cdot 10^{-3} \) \(a_{6}= -0.49169311 \pm 5.3 \cdot 10^{-3} \)
\(a_{7}= +0.86526230 \pm 4.7 \cdot 10^{-3} \) \(a_{8}= -1.08559388 \pm 6.5 \cdot 10^{-3} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.76239381 \pm 5.4 \cdot 10^{-3} \) \(a_{11}= +1.38016533 \pm 4.8 \cdot 10^{-3} \) \(a_{12}= +0.15860600 \pm 5.9 \cdot 10^{-3} \)
\(a_{13}= +1.56492653 \pm 4.7 \cdot 10^{-3} \) \(a_{14}= +0.73688978 \pm 5.3 \cdot 10^{-3} \) \(a_{15}= -0.51684936 \pm 4.6 \cdot 10^{-3} \)
\(a_{16}= -0.64981876 \pm 6.7 \cdot 10^{-3} \) \(a_{17}= -0.07311750 \pm 4.2 \cdot 10^{-3} \) \(a_{18}= +0.28387915 \pm 5.3 \cdot 10^{-3} \)
\(a_{19}= +0.34766272 \pm 4.4 \cdot 10^{-3} \) \(a_{20}= -0.24592622 \pm 6.4 \cdot 10^{-3} \) \(a_{21}= -0.49955942 \pm 4.7 \cdot 10^{-3} \)
\(a_{22}= +1.17540048 \pm 5.8 \cdot 10^{-3} \) \(a_{23}= -0.19354694 \pm 4.2 \cdot 10^{-3} \) \(a_{24}= +0.62676792 \pm 6.5 \cdot 10^{-3} \)
\(a_{25}= -0.19860023 \pm 4.4 \cdot 10^{-3} \) \(a_{26}= +1.33275004 \pm 5.1 \cdot 10^{-3} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.23769936 \pm 6.1 \cdot 10^{-3} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.44016827 \pm 1.0 \cdot 10^{-2} \)
\(a_{31}= +0.13344521 \pm 4.4 \cdot 10^{-3} \) \(a_{32}= +0.53218389 \pm 6.2 \cdot 10^{-3} \) \(a_{33}= -0.79683882 \pm 4.8 \cdot 10^{-3} \)
\(a_{34}= -0.06226960 \pm 4.9 \cdot 10^{-3} \) \(a_{35}= +0.77459090 \pm 4.7 \cdot 10^{-3} \) \(a_{36}= -0.09157122 \pm 5.9 \cdot 10^{-3} \)
\(a_{37}= +0.33894325 \pm 4.2 \cdot 10^{-3} \) \(a_{38}= +0.29608259 \pm 5.9 \cdot 10^{-3} \) \(a_{39}= -0.90351075 \pm 4.7 \cdot 10^{-3} \)
\(a_{40}= -0.97183379 \pm 7.0 \cdot 10^{-3} \) \(a_{41}= -0.08167557 \pm 4.5 \cdot 10^{-3} \) \(a_{42}= -0.42544351 \pm 1.0 \cdot 10^{-2} \)
\(a_{43}= +0.51759599 \pm 4.5 \cdot 10^{-3} \) \(a_{44}= -0.37915025 \pm 6.2 \cdot 10^{-3} \) \(a_{45}= +0.29840312 \pm 4.6 \cdot 10^{-3} \)
\(a_{46}= -0.16483182 \pm 5.5 \cdot 10^{-3} \) \(a_{47}= -0.45442605 \pm 4.7 \cdot 10^{-3} \) \(a_{48}= +0.37517304 \pm 6.7 \cdot 10^{-3} \)
\(a_{49}= -0.25132115 \pm 4.4 \cdot 10^{-3} \) \(a_{50}= -0.16913539 \pm 4.9 \cdot 10^{-3} \) \(a_{51}= +0.04221441 \pm 4.2 \cdot 10^{-3} \)
\(a_{52}= -0.42990667 \pm 5.2 \cdot 10^{-3} \) \(a_{53}= +1.03352466 \pm 4.0 \cdot 10^{-3} \) \(a_{54}= -0.16389770 \pm 5.3 \cdot 10^{-3} \)
\(a_{55}= +1.23553690 \pm 4.9 \cdot 10^{-3} \) \(a_{56}= -0.93932346 \pm 6.2 \cdot 10^{-3} \) \(a_{57}= -0.20072316 \pm 4.4 \cdot 10^{-3} \)
\(a_{58}= +0.15814510 \pm 5.3 \cdot 10^{-3} \) \(a_{59}= -1.05680158 \pm 4.8 \cdot 10^{-3} \) \(a_{60}= +0.14198557 \pm 1.0 \cdot 10^{-2} \)

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