Properties

Label 5.18
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 8.817897
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(8.81789729862314026895815340765 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.05112499 \pm 3.6 \cdot 10^{-7} \) \(a_{3}= -0.46269436 \pm 3.9 \cdot 10^{-7} \)
\(a_{4}= +0.10486373 \pm 3.2 \cdot 10^{-7} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.48634960 \pm 3.7 \cdot 10^{-7} \)
\(a_{7}= -0.42678947 \pm 1.5 \cdot 10^{-7} \) \(a_{8}= -0.94090009 \pm 3.4 \cdot 10^{-7} \) \(a_{9}= -0.78591393 \pm 1.9 \cdot 10^{-7} \)
\(a_{10}= -0.47007738 \pm 3.7 \cdot 10^{-7} \) \(a_{11}= -0.41453593 \pm 2.0 \cdot 10^{-7} \) \(a_{12}= -0.04851986 \pm 3.3 \cdot 10^{-7} \)
\(a_{13}= +0.35374619 \pm 2.6 \cdot 10^{-7} \) \(a_{14}= -0.44860907 \pm 1.5 \cdot 10^{-7} \) \(a_{15}= +0.20692321 \pm 4.0 \cdot 10^{-7} \)
\(a_{16}= -1.09386733 \pm 1.6 \cdot 10^{-7} \) \(a_{17}= +0.43298064 \pm 4.0 \cdot 10^{-7} \) \(a_{18}= -0.82609377 \pm 1.7 \cdot 10^{-7} \)
\(a_{19}= +1.83440938 \pm 3.8 \cdot 10^{-7} \) \(a_{20}= -0.04689649 \pm 3.3 \cdot 10^{-7} \) \(a_{21}= +0.19747308 \pm 1.6 \cdot 10^{-7} \)
\(a_{22}= -0.43572907 \pm 2.1 \cdot 10^{-7} \) \(a_{23}= -1.79416231 \pm 1.5 \cdot 10^{-7} \) \(a_{24}= +0.43534916 \pm 3.5 \cdot 10^{-7} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.37183146 \pm 3.1 \cdot 10^{-7} \) \(a_{27}= +0.82633230 \pm 3.0 \cdot 10^{-7} \)
\(a_{28}= -0.04475474 \pm 1.2 \cdot 10^{-7} \) \(a_{29}= +0.30209585 \pm 1.8 \cdot 10^{-7} \) \(a_{30}= +0.21750215 \pm 7.7 \cdot 10^{-7} \)
\(a_{31}= -1.49217646 \pm 3.9 \cdot 10^{-7} \) \(a_{32}= -0.20889119 \pm 4.0 \cdot 10^{-7} \) \(a_{33}= +0.19180343 \pm 1.4 \cdot 10^{-7} \)
\(a_{34}= +0.45511677 \pm 3.8 \cdot 10^{-7} \) \(a_{35}= +0.19086605 \pm 1.6 \cdot 10^{-7} \) \(a_{36}= -0.08241387 \pm 9.0 \cdot 10^{-8} \)
\(a_{37}= -1.66799917 \pm 4.8 \cdot 10^{-7} \) \(a_{38}= +1.92819353 \pm 2.6 \cdot 10^{-7} \) \(a_{39}= -0.16367637 \pm 2.0 \cdot 10^{-7} \)
\(a_{40}= +0.42078331 \pm 3.5 \cdot 10^{-7} \) \(a_{41}= -0.51503384 \pm 4.1 \cdot 10^{-7} \) \(a_{42}= +0.20756889 \pm 1.5 \cdot 10^{-7} \)
\(a_{43}= +0.31015562 \pm 4.1 \cdot 10^{-7} \) \(a_{44}= -0.04346979 \pm 1.5 \cdot 10^{-7} \) \(a_{45}= +0.35147140 \pm 2.0 \cdot 10^{-7} \)
\(a_{46}= -1.88588884 \pm 1.9 \cdot 10^{-7} \) \(a_{47}= +0.38986023 \pm 2.4 \cdot 10^{-7} \) \(a_{48}= +0.50612624 \pm 1.6 \cdot 10^{-7} \)
\(a_{49}= -0.81785075 \pm 3.3 \cdot 10^{-7} \) \(a_{50}= +0.21022500 \pm 3.7 \cdot 10^{-7} \) \(a_{51}= -0.20033770 \pm 3.9 \cdot 10^{-7} \)
\(a_{52}= +0.03709515 \pm 2.4 \cdot 10^{-7} \) \(a_{53}= +0.96114429 \pm 3.8 \cdot 10^{-7} \) \(a_{54}= +0.86857853 \pm 3.1 \cdot 10^{-7} \)
\(a_{55}= +0.18538610 \pm 2.1 \cdot 10^{-7} \) \(a_{56}= +0.40156625 \pm 1.3 \cdot 10^{-7} \) \(a_{57}= -0.84877087 \pm 4.3 \cdot 10^{-7} \)
\(a_{58}= +0.31754050 \pm 1.4 \cdot 10^{-7} \) \(a_{59}= -0.90327268 \pm 3.1 \cdot 10^{-7} \) \(a_{60}= +0.02169874 \pm 7.3 \cdot 10^{-7} \)

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