Properties

Label 5.23
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 9.833412
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(9.83341273669329222090473071373 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.79691448 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.98776139 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.22890167 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +1.77492274 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.33439417 \pm 1 \cdot 10^{-8} \) \(a_{8}= +2.20823120 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.02432744 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.80360459 \pm 1.9 \cdot 10^{-8} \) \(a_{11}= -0.05515508 \pm 1 \cdot 10^{-8} \) \(a_{12}= +2.20162300 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.73784552 \pm 1 \cdot 10^{-8} \) \(a_{14}= -2.39779220 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.44174032 \pm 2.0 \cdot 10^{-8} \)
\(a_{16}= +1.73910097 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.26816639 \pm 1.0 \cdot 10^{-8} \) \(a_{18}= -0.04371434 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.75485922 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.99679513 \pm 1.8 \cdot 10^{-8} \) \(a_{21}= -1.31806303 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.09910897 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.94909817 \pm 1 \cdot 10^{-8} \) \(a_{24}= +2.18120551 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +1.32584530 \pm 1 \cdot 10^{-8} \) \(a_{27}= -1.01179110 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -2.97423338 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.29892865 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.79376958 \pm 2.9 \cdot 10^{-8} \)
\(a_{31}= -0.91803988 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.91678452 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.05448006 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.48187207 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.59675921 \pm 1.4 \cdot 10^{-8} \) \(a_{36}= -0.05422348 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.69534423 \pm 1.2 \cdot 10^{-8} \) \(a_{38}= -1.35641746 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.72881531 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.98755102 \pm 1.8 \cdot 10^{-8} \) \(a_{41}= +0.08171084 \pm 1.0 \cdot 10^{-8} \) \(a_{42}= -2.36844655 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.51173697 \pm 1.0 \cdot 10^{-8} \) \(a_{44}= -0.12293526 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.01087956 \pm 1.5 \cdot 10^{-8} \)
\(a_{46}= -1.70544824 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.26294078 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.71781678 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.78060779 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.35938290 \pm 1.9 \cdot 10^{-8} \) \(a_{51}= +0.26488440 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +1.64458511 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.04064245 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.81810208 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.02466610 \pm 1.5 \cdot 10^{-8} \) \(a_{56}= -2.94665083 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.74562078 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +2.33406371 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.10390142 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.98459574 \pm 2.8 \cdot 10^{-8} \)

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