Properties

Label 87.48
Level $87$
Weight $0$
Character 87.1
Symmetry even
\(R\) 3.235693
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(3.23569304687226033477135573994 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.50231385 \pm 2.6 \cdot 10^{-5} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.74768079 \pm 2.8 \cdot 10^{-5} \) \(a_{5}= -0.90225733 \pm 2.3 \cdot 10^{-5} \) \(a_{6}= -0.29001104 \pm 2.6 \cdot 10^{-5} \)
\(a_{7}= -1.17711366 \pm 2.2 \cdot 10^{-5} \) \(a_{8}= +0.87788427 \pm 2.7 \cdot 10^{-5} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.45321636 \pm 2.9 \cdot 10^{-5} \) \(a_{11}= +0.83786416 \pm 2.2 \cdot 10^{-5} \) \(a_{12}= -0.43167371 \pm 2.8 \cdot 10^{-5} \)
\(a_{13}= +0.81709224 \pm 2.0 \cdot 10^{-5} \) \(a_{14}= +0.59128050 \pm 2.8 \cdot 10^{-5} \) \(a_{15}= -0.52091851 \pm 2.3 \cdot 10^{-5} \)
\(a_{16}= +0.30670736 \pm 2.4 \cdot 10^{-5} \) \(a_{17}= -0.41156697 \pm 2.2 \cdot 10^{-5} \) \(a_{18}= -0.16743795 \pm 2.6 \cdot 10^{-5} \)
\(a_{19}= -0.69512051 \pm 2.2 \cdot 10^{-5} \) \(a_{20}= +0.67460047 \pm 2.9 \cdot 10^{-5} \) \(a_{21}= -0.67960689 \pm 2.2 \cdot 10^{-5} \)
\(a_{22}= -0.42087077 \pm 2.7 \cdot 10^{-5} \) \(a_{23}= +0.72979359 \pm 2.1 \cdot 10^{-5} \) \(a_{24}= +0.50684672 \pm 2.7 \cdot 10^{-5} \)
\(a_{25}= -0.18593171 \pm 2.4 \cdot 10^{-5} \) \(a_{26}= -0.41043675 \pm 2.6 \cdot 10^{-5} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.88010527 \pm 3.0 \cdot 10^{-5} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +0.26166459 \pm 5.0 \cdot 10^{-5} \)
\(a_{31}= +0.90134863 \pm 2.2 \cdot 10^{-5} \) \(a_{32}= -1.03194763 \pm 2.6 \cdot 10^{-5} \) \(a_{33}= +0.48374110 \pm 2.2 \cdot 10^{-5} \)
\(a_{34}= +0.20673579 \pm 2.8 \cdot 10^{-5} \) \(a_{35}= +1.06205942 \pm 2.3 \cdot 10^{-5} \) \(a_{36}= -0.24922693 \pm 2.8 \cdot 10^{-5} \)
\(a_{37}= +1.72533048 \pm 2.3 \cdot 10^{-5} \) \(a_{38}= +0.34916866 \pm 2.5 \cdot 10^{-5} \) \(a_{39}= +0.47174842 \pm 2.0 \cdot 10^{-5} \)
\(a_{40}= -0.79207752 \pm 2.7 \cdot 10^{-5} \) \(a_{41}= -0.46359139 \pm 2.1 \cdot 10^{-5} \) \(a_{42}= +0.34137595 \pm 4.8 \cdot 10^{-5} \)
\(a_{43}= +1.93012984 \pm 2.1 \cdot 10^{-5} \) \(a_{44}= -0.62645494 \pm 3.0 \cdot 10^{-5} \) \(a_{45}= -0.30075244 \pm 2.3 \cdot 10^{-5} \)
\(a_{46}= -0.36658543 \pm 2.6 \cdot 10^{-5} \) \(a_{47}= -1.45986171 \pm 2.1 \cdot 10^{-5} \) \(a_{48}= +0.17707758 \pm 2.4 \cdot 10^{-5} \)
\(a_{49}= +0.38559656 \pm 2.3 \cdot 10^{-5} \) \(a_{50}= +0.09339607 \pm 3.0 \cdot 10^{-5} \) \(a_{51}= -0.23761830 \pm 2.2 \cdot 10^{-5} \)
\(a_{52}= -0.61092417 \pm 2.7 \cdot 10^{-5} \) \(a_{53}= -0.35619944 \pm 2.1 \cdot 10^{-5} \) \(a_{54}= -0.09667035 \pm 2.6 \cdot 10^{-5} \)
\(a_{55}= -0.75596908 \pm 2.5 \cdot 10^{-5} \) \(a_{56}= -1.03336957 \pm 2.9 \cdot 10^{-5} \) \(a_{57}= -0.40132801 \pm 2.2 \cdot 10^{-5} \)
\(a_{58}= -0.09327734 \pm 2.6 \cdot 10^{-5} \) \(a_{59}= +1.39302235 \pm 2.1 \cdot 10^{-5} \) \(a_{60}= +0.38948077 \pm 5.1 \cdot 10^{-5} \)

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