Properties

Label 87.22
Level $87$
Weight $0$
Character 87.1
Symmetry odd
\(R\) 2.189242
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: \(2.18924247558655620836021167806 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.83778837 \pm 1.2 \cdot 10^{-3} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.29811064 \pm 1.4 \cdot 10^{-3} \) \(a_{5}= +0.57982127 \pm 1.0 \cdot 10^{-3} \) \(a_{6}= -0.48369734 \pm 1.2 \cdot 10^{-3} \)
\(a_{7}= -1.30430126 \pm 1.1 \cdot 10^{-3} \) \(a_{8}= -1.08754200 \pm 1.5 \cdot 10^{-3} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.48576752 \pm 1.2 \cdot 10^{-3} \) \(a_{11}= -0.89216513 \pm 1.1 \cdot 10^{-3} \) \(a_{12}= +0.17211426 \pm 1.4 \cdot 10^{-3} \)
\(a_{13}= -1.07203018 \pm 1.1 \cdot 10^{-3} \) \(a_{14}= -1.09272843 \pm 1.2 \cdot 10^{-3} \) \(a_{15}= -0.33475997 \pm 1.0 \cdot 10^{-3} \)
\(a_{16}= -0.61301941 \pm 1.5 \cdot 10^{-3} \) \(a_{17}= +1.63591343 \pm 9.8 \cdot 10^{-4} \) \(a_{18}= +0.27926279 \pm 1.2 \cdot 10^{-3} \)
\(a_{19}= +1.89461042 \pm 1.0 \cdot 10^{-3} \) \(a_{20}= -0.17285089 \pm 1.5 \cdot 10^{-3} \) \(a_{21}= +0.75303868 \pm 1.1 \cdot 10^{-3} \)
\(a_{22}= -0.74744557 \pm 1.3 \cdot 10^{-3} \) \(a_{23}= -1.32659639 \pm 9.9 \cdot 10^{-4} \) \(a_{24}= +0.62789267 \pm 1.5 \cdot 10^{-3} \)
\(a_{25}= -0.66380730 \pm 1.0 \cdot 10^{-3} \) \(a_{26}= -0.89813442 \pm 1.2 \cdot 10^{-3} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.38882608 \pm 1.4 \cdot 10^{-3} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.28045801 \pm 2.3 \cdot 10^{-3} \)
\(a_{31}= -0.38047553 \pm 1.0 \cdot 10^{-3} \) \(a_{32}= +0.57396147 \pm 1.4 \cdot 10^{-3} \) \(a_{33}= +0.51509178 \pm 1.1 \cdot 10^{-3} \)
\(a_{34}= +1.37054925 \pm 1.1 \cdot 10^{-3} \) \(a_{35}= -0.75626161 \pm 1.1 \cdot 10^{-3} \) \(a_{36}= -0.09937021 \pm 1.4 \cdot 10^{-3} \)
\(a_{37}= -1.32374608 \pm 9.9 \cdot 10^{-4} \) \(a_{38}= +1.58728258 \pm 1.3 \cdot 10^{-3} \) \(a_{39}= +0.61893691 \pm 1.1 \cdot 10^{-3} \)
\(a_{40}= -0.63057998 \pm 1.6 \cdot 10^{-3} \) \(a_{41}= +1.00788670 \pm 1.0 \cdot 10^{-3} \) \(a_{42}= +0.63088706 \pm 2.3 \cdot 10^{-3} \)
\(a_{43}= -0.03613569 \pm 1.0 \cdot 10^{-3} \) \(a_{44}= +0.26596392 \pm 1.4 \cdot 10^{-3} \) \(a_{45}= +0.19327376 \pm 1.0 \cdot 10^{-3} \)
\(a_{46}= -1.11140703 \pm 1.2 \cdot 10^{-3} \) \(a_{47}= -1.57129568 \pm 1.1 \cdot 10^{-3} \) \(a_{48}= +0.35392692 \pm 1.5 \cdot 10^{-3} \)
\(a_{49}= +0.70120178 \pm 1.0 \cdot 10^{-3} \) \(a_{50}= -0.55613003 \pm 1.1 \cdot 10^{-3} \) \(a_{51}= -0.94449506 \pm 9.8 \cdot 10^{-4} \)
\(a_{52}= +0.31958360 \pm 1.2 \cdot 10^{-3} \) \(a_{53}= -0.12471294 \pm 9.4 \cdot 10^{-4} \) \(a_{54}= -0.16123245 \pm 1.2 \cdot 10^{-3} \)
\(a_{55}= -0.51729632 \pm 1.1 \cdot 10^{-3} \) \(a_{56}= +1.41848241 \pm 1.4 \cdot 10^{-3} \) \(a_{57}= -1.09385384 \pm 1.0 \cdot 10^{-3} \)
\(a_{58}= -0.15557340 \pm 1.2 \cdot 10^{-3} \) \(a_{59}= -0.79587847 \pm 1.1 \cdot 10^{-3} \) \(a_{60}= +0.09979551 \pm 2.4 \cdot 10^{-3} \)

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