Properties

Label 87.28
Level $87$
Weight $0$
Character 87.1
Symmetry even
\(R\) 2.457327
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: \(2.45732755703849183832514558607 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.23458093 \pm 2.2 \cdot 10^{-5} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.94497179 \pm 2.3 \cdot 10^{-5} \) \(a_{5}= -0.58696924 \pm 2.0 \cdot 10^{-5} \) \(a_{6}= +0.13543536 \pm 2.2 \cdot 10^{-5} \)
\(a_{7}= +0.02850440 \pm 1.8 \cdot 10^{-5} \) \(a_{8}= -0.45625328 \pm 2.2 \cdot 10^{-5} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.13769179 \pm 2.4 \cdot 10^{-5} \) \(a_{11}= -0.93461320 \pm 1.8 \cdot 10^{-5} \) \(a_{12}= -0.54557972 \pm 2.3 \cdot 10^{-5} \)
\(a_{13}= -0.25560976 \pm 1.7 \cdot 10^{-5} \) \(a_{14}= +0.00668659 \pm 2.4 \cdot 10^{-5} \) \(a_{15}= -0.33888685 \pm 2.0 \cdot 10^{-5} \)
\(a_{16}= +0.83794347 \pm 2.0 \cdot 10^{-5} \) \(a_{17}= +0.02874228 \pm 1.8 \cdot 10^{-5} \) \(a_{18}= +0.07819364 \pm 2.2 \cdot 10^{-5} \)
\(a_{19}= -0.40594108 \pm 1.9 \cdot 10^{-5} \) \(a_{20}= +0.55466938 \pm 2.4 \cdot 10^{-5} \) \(a_{21}= +0.01645703 \pm 1.8 \cdot 10^{-5} \)
\(a_{22}= -0.21924243 \pm 2.2 \cdot 10^{-5} \) \(a_{23}= +0.04484607 \pm 1.8 \cdot 10^{-5} \) \(a_{24}= -0.26341796 \pm 2.2 \cdot 10^{-5} \)
\(a_{25}= -0.65546711 \pm 2.0 \cdot 10^{-5} \) \(a_{26}= -0.05996118 \pm 2.2 \cdot 10^{-5} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.02693586 \pm 2.5 \cdot 10^{-5} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.07949639 \pm 4.2 \cdot 10^{-5} \)
\(a_{31}= -1.91650282 \pm 1.8 \cdot 10^{-5} \) \(a_{32}= +0.65281884 \pm 2.2 \cdot 10^{-5} \) \(a_{33}= -0.53959918 \pm 1.8 \cdot 10^{-5} \)
\(a_{34}= +0.00674239 \pm 2.4 \cdot 10^{-5} \) \(a_{35}= -0.01673121 \pm 1.9 \cdot 10^{-5} \) \(a_{36}= -0.31499060 \pm 2.3 \cdot 10^{-5} \)
\(a_{37}= -0.92407947 \pm 1.9 \cdot 10^{-5} \) \(a_{38}= -0.09522603 \pm 2.1 \cdot 10^{-5} \) \(a_{39}= -0.14757637 \pm 1.7 \cdot 10^{-5} \)
\(a_{40}= +0.26780664 \pm 2.3 \cdot 10^{-5} \) \(a_{41}= -0.17908623 \pm 1.7 \cdot 10^{-5} \) \(a_{42}= +0.00386050 \pm 4.1 \cdot 10^{-5} \)
\(a_{43}= +0.93407614 \pm 1.8 \cdot 10^{-5} \) \(a_{44}= +0.88318311 \pm 2.5 \cdot 10^{-5} \) \(a_{45}= -0.19565641 \pm 2.0 \cdot 10^{-5} \)
\(a_{46}= +0.01052003 \pm 2.2 \cdot 10^{-5} \) \(a_{47}= +1.54914423 \pm 1.8 \cdot 10^{-5} \) \(a_{48}= +0.48378689 \pm 2.0 \cdot 10^{-5} \)
\(a_{49}= -0.99918750 \pm 1.9 \cdot 10^{-5} \) \(a_{50}= -0.15376008 \pm 2.5 \cdot 10^{-5} \) \(a_{51}= +0.01659436 \pm 1.8 \cdot 10^{-5} \)
\(a_{52}= +0.24154402 \pm 2.3 \cdot 10^{-5} \) \(a_{53}= +0.60641336 \pm 1.7 \cdot 10^{-5} \) \(a_{54}= +0.04514512 \pm 2.2 \cdot 10^{-5} \)
\(a_{55}= +0.54858920 \pm 2.1 \cdot 10^{-5} \) \(a_{56}= -0.01300523 \pm 2.5 \cdot 10^{-5} \) \(a_{57}= -0.23437019 \pm 1.9 \cdot 10^{-5} \)
\(a_{58}= -0.04356058 \pm 2.2 \cdot 10^{-5} \) \(a_{59}= -0.20760756 \pm 1.8 \cdot 10^{-5} \) \(a_{60}= +0.32023851 \pm 4.3 \cdot 10^{-5} \)

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