Properties

Label 87.41
Level $87$
Weight $0$
Character 87.1
Symmetry even
\(R\) 2.943555
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: \(2.94355524597704441845971145246 \pm 9 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.88721129 \pm 5.3 \cdot 10^{-6} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.56156646 \pm 5.6 \cdot 10^{-6} \) \(a_{5}= +0.84106253 \pm 4.8 \cdot 10^{-6} \) \(a_{6}= -1.08958195 \pm 5.3 \cdot 10^{-6} \)
\(a_{7}= -0.98097906 \pm 4.4 \cdot 10^{-6} \) \(a_{8}= -2.94700585 \pm 5.4 \cdot 10^{-6} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -1.58726270 \pm 5.9 \cdot 10^{-6} \) \(a_{11}= +1.52970918 \pm 4.4 \cdot 10^{-6} \) \(a_{12}= +1.47892108 \pm 5.6 \cdot 10^{-6} \)
\(a_{13}= -1.74138360 \pm 4.0 \cdot 10^{-6} \) \(a_{14}= +1.85131476 \pm 5.8 \cdot 10^{-6} \) \(a_{15}= +0.48558768 \pm 4.8 \cdot 10^{-6} \)
\(a_{16}= +3.00005626 \pm 5.0 \cdot 10^{-6} \) \(a_{17}= -1.48635621 \pm 4.4 \cdot 10^{-6} \) \(a_{18}= -0.62907043 \pm 5.3 \cdot 10^{-6} \)
\(a_{19}= -0.09971701 \pm 4.5 \cdot 10^{-6} \) \(a_{20}= +2.15443757 \pm 5.9 \cdot 10^{-6} \) \(a_{21}= -0.56636852 \pm 4.5 \cdot 10^{-6} \)
\(a_{22}= -2.88688444 \pm 5.4 \cdot 10^{-6} \) \(a_{23}= +0.20960887 \pm 4.3 \cdot 10^{-6} \) \(a_{24}= -1.70145462 \pm 5.5 \cdot 10^{-6} \)
\(a_{25}= -0.29261382 \pm 4.8 \cdot 10^{-6} \) \(a_{26}= +3.28635880 \pm 5.3 \cdot 10^{-6} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -2.51284306 \pm 6.0 \cdot 10^{-6} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.91640655 \pm 1.0 \cdot 10^{-5} \)
\(a_{31}= -1.15224858 \pm 4.5 \cdot 10^{-6} \) \(a_{32}= -2.71473420 \pm 5.3 \cdot 10^{-6} \) \(a_{33}= +0.88317801 \pm 4.4 \cdot 10^{-6} \)
\(a_{34}= +2.80506822 \pm 5.7 \cdot 10^{-6} \) \(a_{35}= -0.82506473 \pm 4.7 \cdot 10^{-6} \) \(a_{36}= +0.85385549 \pm 5.6 \cdot 10^{-6} \)
\(a_{37}= -0.70694646 \pm 4.6 \cdot 10^{-6} \) \(a_{38}= +0.18818706 \pm 5.1 \cdot 10^{-6} \) \(a_{39}= -1.00538829 \pm 4.0 \cdot 10^{-6} \)
\(a_{40}= -2.47861620 \pm 5.5 \cdot 10^{-6} \) \(a_{41}= -0.21528798 \pm 4.2 \cdot 10^{-6} \) \(a_{42}= +1.06885708 \pm 9.8 \cdot 10^{-6} \)
\(a_{43}= +0.52411176 \pm 4.3 \cdot 10^{-6} \) \(a_{44}= +3.91845173 \pm 6.2 \cdot 10^{-6} \) \(a_{45}= +0.28035418 \pm 4.8 \cdot 10^{-6} \)
\(a_{46}= -0.39557622 \pm 5.3 \cdot 10^{-6} \) \(a_{47}= -1.34799635 \pm 4.3 \cdot 10^{-6} \) \(a_{48}= +1.73208329 \pm 5.0 \cdot 10^{-6} \)
\(a_{49}= -0.03768008 \pm 4.7 \cdot 10^{-6} \) \(a_{50}= +0.55222411 \pm 6.0 \cdot 10^{-6} \) \(a_{51}= -0.85814816 \pm 4.4 \cdot 10^{-6} \)
\(a_{52}= -4.46066983 \pm 5.5 \cdot 10^{-6} \) \(a_{53}= +0.60485304 \pm 4.2 \cdot 10^{-6} \) \(a_{54}= -0.36319398 \pm 5.3 \cdot 10^{-6} \)
\(a_{55}= +1.28658107 \pm 5.0 \cdot 10^{-6} \) \(a_{56}= +2.89095103 \pm 6.0 \cdot 10^{-6} \) \(a_{57}= -0.05757164 \pm 4.5 \cdot 10^{-6} \)
\(a_{58}= +0.35044634 \pm 5.3 \cdot 10^{-6} \) \(a_{59}= -0.16700206 \pm 4.3 \cdot 10^{-6} \) \(a_{60}= +1.24386511 \pm 1.0 \cdot 10^{-5} \)

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