Properties

Label 5.122
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 20.69460
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(20.694603450454793256678635786 \pm 2 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.48527584 \pm 3.1 \) \(a_{3}= -1.15858351 \pm 3.4 \)
\(a_{4}= +1.20604432 \pm 2.7 \) \(a_{5}= \pm0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +1.72081610 \pm 3.2 \)
\(a_{7}= -1.02213154 \pm 1.3 \) \(a_{8}= -0.30603265 \pm 2.9 \) \(a_{9}= +0.34231575 \pm 1.6 \)
\(a_{10}= \pm0.66423555 \pm 1.4 \) \(a_{11}= -1.45783486 \pm 1.7 \) \(a_{12}= -1.39730306 \pm 2.8 \)
\(a_{13}= -0.87106161 \pm 2.2 \) \(a_{14}= +1.51814728 \pm 1.3 \) \(a_{15}= \pm0.51813430 \pm 1.5 \)
\(a_{16}= -0.75150141 \pm 1.4 \) \(a_{17}= +1.22199460 \pm 3.5 \) \(a_{18}= -0.50843331 \pm 1.4 \)
\(a_{19}= -0.70196536 \pm 3.2 \) \(a_{20}= \pm0.53935942 \pm 1.2 \) \(a_{21}= +1.18422474 \pm 1.4 \)
\(a_{22}= +2.16528690 \pm 1.8 \) \(a_{23}= +0.95288806 \pm 1.3 \) \(a_{24}= +0.35456439 \pm 3.0 \)
\(a_{25}= \pm0.2 \) \(a_{26}= +1.29376677 \pm 2.6 \) \(a_{27}= +0.76198213 \pm 2.6 \)
\(a_{28}= -1.23273594 \pm 1.0 \) \(a_{29}= +0.83930508 \pm 1.5 \) \(a_{30}= \pm0.76957235 \pm 1.4 \)
\(a_{31}= +0.40955389 \pm 3.3 \) \(a_{32}= +1.42221955 \pm 3.4 \) \(a_{33}= +1.68902343 \pm 1.2 \)
\(a_{34}= -1.81499906 \pm 3.3 \) \(a_{35}= \pm0.45711112 \pm 5.8 \cdot 10^{-1} \) \(a_{36}= +0.41284797 \pm 7.8 \cdot 10^{-1} \)
\(a_{37}= +0.24954787 \pm 4.2 \) \(a_{38}= +1.04261218 \pm 2.2 \) \(a_{39}= +1.00919762 \pm 1.7 \)
\(a_{40}= \pm0.13686196 \pm 1.3 \) \(a_{41}= -1.35168901 \pm 3.5 \) \(a_{42}= -1.75890040 \pm 1.3 \)
\(a_{43}= +1.66979038 \pm 3.5 \) \(a_{44}= -1.75821346 \pm 1.3 \) \(a_{45}= \pm0.15308826 \pm 7.5 \cdot 10^{-1} \)
\(a_{46}= -1.41530162 \pm 1.6 \) \(a_{47}= -0.23487679 \pm 2.1 \) \(a_{48}= +0.87067715 \pm 1.4 \)
\(a_{49}= +0.04475288 \pm 2.8 \) \(a_{50}= \pm0.29705517 \pm 6.3 \cdot 10^{-1} \) \(a_{51}= -1.41578279 \pm 3.4 \)
\(a_{52}= -1.05053891 \pm 2.1 \) \(a_{53}= -1.28007225 \pm 3.3 \) \(a_{54}= -1.13175365 \pm 2.7 \)
\(a_{55}= \pm0.65196357 \pm 7.8 \cdot 10^{-1} \) \(a_{56}= +0.31280563 \pm 1.1 \) \(a_{57}= +0.81328549 \pm 3.7 \)
\(a_{58}= -1.24659956 \pm 1.2 \) \(a_{59}= -0.67847923 \pm 2.6 \) \(a_{60}= \pm0.62489293 \pm 1.2 \)

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