Properties

Label 87.703
Level $87$
Weight $0$
Character 87.1
Symmetry even
\(R\) 12.28540
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: even
Fricke sign: not computed rigorously
Spectral parameter: \(12.2854018983053064108688518402 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.66212665 \pm 1.3 \cdot 10^{-1} \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.76266499 \pm 1.4 \cdot 10^{-1} \) \(a_{5}= -1.11766954 \pm 1.2 \cdot 10^{-1} \) \(a_{6}= \pm0.95962927 \pm 7.9 \cdot 10^{-2} \)
\(a_{7}= -0.89727870 \pm 1.1 \cdot 10^{-1} \) \(a_{8}= +1.26764579 \pm 1.4 \cdot 10^{-1} \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= -1.85770832 \pm 1.5 \cdot 10^{-1} \) \(a_{11}= -1.16607076 \pm 1.1 \cdot 10^{-1} \) \(a_{12}= \pm1.01767510 \pm 8.4 \cdot 10^{-2} \)
\(a_{13}= -0.86629166 \pm 1.0 \cdot 10^{-1} \) \(a_{14}= -1.49139084 \pm 1.5 \cdot 10^{-1} \) \(a_{15}= \pm0.64528681 \pm 7.1 \cdot 10^{-2} \)
\(a_{16}= +0.34432286 \pm 1.2 \cdot 10^{-1} \) \(a_{17}= +0.41611929 \pm 1.1 \cdot 10^{-1} \) \(a_{18}= \pm0.55404222 \pm 4.5 \cdot 10^{-2} \)
\(a_{19}= -0.05952101 \pm 1.1 \cdot 10^{-1} \) \(a_{20}= -1.97007696 \pm 1.5 \cdot 10^{-1} \) \(a_{21}= \pm0.51804410 \pm 6.6 \cdot 10^{-2} \)
\(a_{22}= -1.93815729 \pm 1.4 \cdot 10^{-1} \) \(a_{23}= -1.46377847 \pm 1.1 \cdot 10^{-1} \) \(a_{24}= \pm0.73187564 \pm 8.1 \cdot 10^{-2} \)
\(a_{25}= +0.24918520 \pm 1.2 \cdot 10^{-1} \) \(a_{26}= -1.43988645 \pm 1.3 \cdot 10^{-1} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -1.58160175 \pm 1.5 \cdot 10^{-1} \) \(a_{29}= \pm0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= \pm1.07254840 \pm 8.7 \cdot 10^{-2} \)
\(a_{31}= -0.82189777 \pm 1.1 \cdot 10^{-1} \) \(a_{32}= -0.69533759 \pm 1.3 \cdot 10^{-1} \) \(a_{33}= \pm0.67323127 \pm 6.6 \cdot 10^{-2} \)
\(a_{34}= +0.69164296 \pm 1.4 \cdot 10^{-1} \) \(a_{35}= +1.00286107 \pm 1.2 \cdot 10^{-1} \) \(a_{36}= \pm0.58755500 \pm 4.8 \cdot 10^{-2} \)
\(a_{37}= +0.67965918 \pm 1.1 \cdot 10^{-1} \) \(a_{38}= -0.09893145 \pm 1.3 \cdot 10^{-1} \) \(a_{39}= \pm0.50015372 \pm 6.0 \cdot 10^{-2} \)
\(a_{40}= -1.41680909 \pm 1.4 \cdot 10^{-1} \) \(a_{41}= -1.17534618 \pm 1.0 \cdot 10^{-1} \) \(a_{42}= \pm0.86105490 \pm 8.6 \cdot 10^{-2} \)
\(a_{43}= -1.23853826 \pm 1.1 \cdot 10^{-1} \) \(a_{44}= -2.05539210 \pm 1.6 \cdot 10^{-1} \) \(a_{45}= \pm0.37255651 \pm 4.1 \cdot 10^{-2} \)
\(a_{46}= -2.43298520 \pm 1.3 \cdot 10^{-1} \) \(a_{47}= -0.72440775 \pm 1.1 \cdot 10^{-1} \) \(a_{48}= \pm0.19879490 \pm 7.4 \cdot 10^{-2} \)
\(a_{49}= -0.19489093 \pm 1.2 \cdot 10^{-1} \) \(a_{50}= +0.41417735 \pm 1.5 \cdot 10^{-1} \) \(a_{51}= \pm0.24024659 \pm 6.6 \cdot 10^{-2} \)
\(a_{52}= -1.52698198 \pm 1.4 \cdot 10^{-1} \) \(a_{53}= +1.02764607 \pm 1.0 \cdot 10^{-1} \) \(a_{54}= \pm0.31987642 \pm 2.6 \cdot 10^{-2} \)
\(a_{55}= +1.30328177 \pm 1.3 \cdot 10^{-1} \) \(a_{56}= -1.13743157 \pm 1.5 \cdot 10^{-1} \) \(a_{57}= \pm0.03436447 \pm 6.7 \cdot 10^{-2} \)
\(a_{58}= \pm0.30864917 \pm 2.5 \cdot 10^{-2} \) \(a_{59}= +1.24573320 \pm 1.1 \cdot 10^{-1} \) \(a_{60}= \pm1.13742446 \pm 8.8 \cdot 10^{-2} \)

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