Properties

Label 5.25
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 10.24630
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(10.2463013805270121750530441218 \pm 6 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.01624402 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.63907484 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.99973613 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.02662517 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.32493634 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.03248376 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.68656634 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.00726455 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.09961259 \pm 1 \cdot 10^{-8} \) \(a_{12}= +1.63864234 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.19482900 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.02152230 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.73301655 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.99920846 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.70098840 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.02739662 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -1.22846819 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.44709559 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +2.17166983 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.00161811 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.41718153 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.05324332 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.00316481 \pm 1 \cdot 10^{-8} \) \(a_{27}= -1.12533362 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +1.32458673 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.39668619 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.01190714 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.44121375 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.04871493 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.16327248 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.01138687 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.59252955 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -1.68612131 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.04512503 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.01995527 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.31933932 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.01452718 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +1.44099787 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.03527666 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.53679678 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.09958630 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.75425540 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.02302073 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.02569594 \pm 1 \cdot 10^{-8} \) \(a_{48}= -1.63777746 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.75545631 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.00324880 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +1.14897244 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.19477759 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.22055137 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.01827995 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.04454810 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +0.04303892 \pm 1 \cdot 10^{-8} \) \(a_{57}= +2.01355130 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.00644378 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.53721441 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.73282313 \pm 1.0 \cdot 10^{-8} \)

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