Properties

Label 101.7
Level $101$
Weight $0$
Character 101.1
Symmetry odd
\(R\) 1.113562
Fricke sign not computed rigorously

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 101 \)
Weight: \( 0 \)
Character: 101.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(1.11356288230187048505356429167 \pm 5 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.99375829 \pm 1.0 \) \(a_{3}= -1.56850133 \pm 9.5 \cdot 10^{-1} \)
\(a_{4}= -0.01244858 \pm 1.0 \) \(a_{5}= -1.75856336 \pm 9.3 \cdot 10^{-1} \) \(a_{6}= -1.55870795 \pm 1.1 \)
\(a_{7}= +1.25532080 \pm 8.9 \cdot 10^{-1} \) \(a_{8}= -1.00612909 \pm 1.0 \) \(a_{9}= +1.46018936 \pm 9.6 \cdot 10^{-1} \)
\(a_{10}= -1.74758329 \pm 1.0 \) \(a_{11}= +0.34461812 \pm 8.5 \cdot 10^{-1} \) \(a_{12}= +0.01952559 \pm 1.1 \)
\(a_{13}= -0.12162129 \pm 8.4 \cdot 10^{-1} \) \(a_{14}= +1.24748287 \pm 1.0 \) \(a_{15}= +2.75830335 \pm 1.0 \)
\(a_{16}= -0.98739849 \pm 1.0 \) \(a_{17}= -1.18243716 \pm 8.2 \cdot 10^{-1} \) \(a_{18}= +1.45107228 \pm 1.1 \)
\(a_{19}= -1.00618153 \pm 8.9 \cdot 10^{-1} \) \(a_{20}= +0.02189157 \pm 1.1 \) \(a_{21}= -1.96896837 \pm 1.0 \)
\(a_{22}= +0.34246639 \pm 1.0 \) \(a_{23}= -0.42077890 \pm 8.3 \cdot 10^{-1} \) \(a_{24}= +1.57811162 \pm 1.1 \)
\(a_{25}= +2.09253683 \pm 9.3 \cdot 10^{-1} \) \(a_{26}= -0.12086191 \pm 9.5 \cdot 10^{-1} \) \(a_{27}= -0.72180301 \pm 9.1 \cdot 10^{-1} \)
\(a_{28}= -0.01562693 \pm 1.0 \) \(a_{29}= -1.37125589 \pm 8.5 \cdot 10^{-1} \) \(a_{30}= +2.74108115 \pm 1.2 \)
\(a_{31}= +0.03257429 \pm 8.3 \cdot 10^{-1} \) \(a_{32}= +0.02489570 \pm 9.7 \cdot 10^{-1} \) \(a_{33}= -0.54053286 \pm 9.2 \cdot 10^{-1} \)
\(a_{34}= -1.17505429 \pm 9.7 \cdot 10^{-1} \) \(a_{35}= -2.20755671 \pm 9.5 \cdot 10^{-1} \) \(a_{36}= -0.01817724 \pm 1.0 \)
\(a_{37}= +0.61798923 \pm 8.0 \cdot 10^{-1} \) \(a_{38}= -0.99989917 \pm 1.0 \) \(a_{39}= +0.19076279 \pm 9.1 \cdot 10^{-1} \)
\(a_{40}= +1.76933819 \pm 1.1 \) \(a_{41}= +0.51955784 \pm 8.5 \cdot 10^{-1} \) \(a_{42}= -1.95667457 \pm 1.3 \)
\(a_{43}= +1.07915412 \pm 8.6 \cdot 10^{-1} \) \(a_{44}= -0.00429000 \pm 1.1 \) \(a_{45}= -2.56783033 \pm 9.8 \cdot 10^{-1} \)
\(a_{46}= -0.41815166 \pm 1.0 \) \(a_{47}= +0.13080785 \pm 8.2 \cdot 10^{-1} \) \(a_{48}= +1.54873267 \pm 1.2 \)
\(a_{49}= +0.57582511 \pm 8.4 \cdot 10^{-1} \) \(a_{50}= +2.07947148 \pm 1.0 \) \(a_{51}= +1.85465048 \pm 8.6 \cdot 10^{-1} \)
\(a_{52}= +0.00151401 \pm 9.8 \cdot 10^{-1} \) \(a_{53}= -0.85821434 \pm 8.7 \cdot 10^{-1} \) \(a_{54}= -0.71729623 \pm 1.1 \)
\(a_{55}= -0.60603154 \pm 9.5 \cdot 10^{-1} \) \(a_{56}= -1.26301222 \pm 1.0 \) \(a_{57}= +1.57819387 \pm 9.9 \cdot 10^{-1} \)
\(a_{58}= -1.36269409 \pm 1.0 \) \(a_{59}= +0.30819767 \pm 8.2 \cdot 10^{-1} \) \(a_{60}= -0.03433689 \pm 1.3 \)

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