Properties

Label 87.702
Level $87$
Weight $0$
Character 87.1
Symmetry odd
\(R\) 12.24592
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: \(12.2459291792487909757365486492 \pm 4 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.19604762 \pm 4.1 \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.96156533 \pm 4.6 \) \(a_{5}= +0.94455912 \pm 3.5 \) \(a_{6}= \pm0.11318815 \pm 2.3 \)
\(a_{7}= +0.50277097 \pm 3.6 \) \(a_{8}= +0.38456021 \pm 5.0 \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= -0.18517857 \pm 4.2 \) \(a_{11}= +1.43146058 \pm 3.7 \) \(a_{12}= \pm0.55516000 \pm 2.6 \)
\(a_{13}= +0.17342511 \pm 3.6 \) \(a_{14}= -0.09856705 \pm 4.0 \) \(a_{15}= \pm0.54534146 \pm 2.0 \)
\(a_{16}= +0.88617322 \pm 5.2 \) \(a_{17}= +0.33265398 \pm 3.2 \) \(a_{18}= \pm0.06534921 \pm 1.3 \)
\(a_{19}= +1.16656509 \pm 3.4 \) \(a_{20}= -0.90825530 \pm 4.9 \) \(a_{21}= \pm0.29027495 \pm 2.1 \)
\(a_{22}= -0.28063444 \pm 4.5 \) \(a_{23}= -1.32404106 \pm 3.2 \) \(a_{24}= \pm0.22202594 \pm 2.9 \)
\(a_{25}= -0.10780807 \pm 3.4 \) \(a_{26}= -0.03399958 \pm 3.9 \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -0.48344713 \pm 4.7 \) \(a_{29}= \pm0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= \pm0.10691290 \pm 2.4 \)
\(a_{31}= +0.49740460 \pm 3.4 \) \(a_{32}= -0.55829236 \pm 4.8 \) \(a_{33}= \pm0.82645415 \pm 2.1 \)
\(a_{34}= -0.06521602 \pm 3.7 \) \(a_{35}= +0.47489690 \pm 3.6 \) \(a_{36}= \pm0.32052178 \pm 1.5 \)
\(a_{37}= +0.00300896 \pm 3.2 \) \(a_{38}= -0.22870231 \pm 4.5 \) \(a_{39}= \pm0.10012703 \pm 2.1 \)
\(a_{40}= +0.36323986 \pm 5.4 \) \(a_{41}= -0.94530114 \pm 3.4 \) \(a_{42}= \pm0.05690771 \pm 2.3 \)
\(a_{43}= +0.03274824 \pm 3.5 \) \(a_{44}= -1.37644286 \pm 4.8 \) \(a_{45}= \pm0.31485304 \pm 1.1 \)
\(a_{46}= +0.25957510 \pm 4.2 \) \(a_{47}= -1.10481686 \pm 3.6 \) \(a_{48}= \pm0.51163234 \pm 3.0 \)
\(a_{49}= -0.74722135 \pm 3.4 \) \(a_{50}= +0.02113552 \pm 3.8 \) \(a_{51}= \pm0.19205787 \pm 1.8 \)
\(a_{52}= -0.16675957 \pm 4.0 \) \(a_{53}= -0.56686777 \pm 3.1 \) \(a_{54}= \pm0.03772938 \pm 7.9 \cdot 10^{-1} \)
\(a_{55}= +1.35209914 \pm 3.8 \) \(a_{56}= +0.19334571 \pm 4.8 \) \(a_{57}= \pm0.67351667 \pm 1.9 \)
\(a_{58}= \pm0.03640513 \pm 7.7 \cdot 10^{-1} \) \(a_{59}= -1.36848590 \pm 3.7 \) \(a_{60}= \pm0.52438144 \pm 2.8 \)

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