Properties

Label 13.191
Level $13$
Weight $0$
Character 13.1
Symmetry odd
\(R\) 14.52910
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(14.5291035368307225057606860365 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.35980387 \pm 9.6 \cdot 10^{-3} \) \(a_{3}= +1.89545750 \pm 9.3 \cdot 10^{-3} \)
\(a_{4}= +0.84906658 \pm 8.7 \cdot 10^{-3} \) \(a_{5}= +0.24196165 \pm 8.2 \cdot 10^{-3} \) \(a_{6}= -2.57745045 \pm 1.0 \cdot 10^{-2} \)
\(a_{7}= -1.56763269 \pm 8.5 \cdot 10^{-3} \) \(a_{8}= +0.20523986 \pm 7.3 \cdot 10^{-3} \) \(a_{9}= +2.59275914 \pm 9.0 \cdot 10^{-3} \)
\(a_{10}= -0.32902039 \pm 9.4 \cdot 10^{-3} \) \(a_{11}= +0.24728223 \pm 7.8 \cdot 10^{-3} \) \(a_{12}= +1.60936961 \pm 9.4 \cdot 10^{-3} \)
\(a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +2.13167300 \pm 9.2 \cdot 10^{-3} \) \(a_{15}= +0.45862802 \pm 1.0 \cdot 10^{-2} \)
\(a_{16}= -1.12815253 \pm 7.5 \cdot 10^{-3} \) \(a_{17}= -0.92142361 \pm 8.5 \cdot 10^{-3} \) \(a_{18}= -3.52564393 \pm 1.0 \cdot 10^{-2} \)
\(a_{19}= +1.37675535 \pm 6.9 \cdot 10^{-3} \) \(a_{20}= +0.20544155 \pm 8.5 \cdot 10^{-3} \) \(a_{21}= -2.97138114 \pm 7.2 \cdot 10^{-3} \)
\(a_{22}= -0.33625534 \pm 8.6 \cdot 10^{-3} \) \(a_{23}= -0.97728476 \pm 7.1 \cdot 10^{-3} \) \(a_{24}= +0.38902342 \pm 7.1 \cdot 10^{-3} \)
\(a_{25}= -0.94145456 \pm 6.4 \cdot 10^{-3} \) \(a_{26}= +0.37714174 \pm 9.6 \cdot 10^{-3} \) \(a_{27}= +3.01900727 \pm 7.5 \cdot 10^{-3} \)
\(a_{28}= -1.33102452 \pm 7.9 \cdot 10^{-3} \) \(a_{29}= -0.73056686 \pm 6.3 \cdot 10^{-3} \) \(a_{30}= -0.62364416 \pm 1.2 \cdot 10^{-2} \)
\(a_{31}= -0.28247439 \pm 9.0 \cdot 10^{-3} \) \(a_{32}= +1.32882632 \pm 9.8 \cdot 10^{-3} \) \(a_{33}= +0.46871296 \pm 6.8 \cdot 10^{-3} \)
\(a_{34}= +1.25295539 \pm 9.2 \cdot 10^{-3} \) \(a_{35}= -0.37930699 \pm 6.8 \cdot 10^{-3} \) \(a_{36}= +2.20142513 \pm 8.5 \cdot 10^{-3} \)
\(a_{37}= +0.89230613 \pm 1.0 \cdot 10^{-2} \) \(a_{38}= -1.87211726 \pm 6.6 \cdot 10^{-3} \) \(a_{39}= -0.52570532 \pm 9.3 \cdot 10^{-3} \)
\(a_{40}= +0.04966017 \pm 7.2 \cdot 10^{-3} \) \(a_{41}= +0.15103577 \pm 7.6 \cdot 10^{-3} \) \(a_{42}= +4.04049559 \pm 6.0 \cdot 10^{-3} \)
\(a_{43}= -1.20762525 \pm 8.5 \cdot 10^{-3} \) \(a_{44}= +0.20995908 \pm 8.1 \cdot 10^{-3} \) \(a_{45}= +0.62734828 \pm 9.1 \cdot 10^{-3} \)
\(a_{46}= +1.32891560 \pm 9.1 \cdot 10^{-3} \) \(a_{47}= -0.90814642 \pm 8.8 \cdot 10^{-3} \) \(a_{48}= -2.13836517 \pm 8.6 \cdot 10^{-3} \)
\(a_{49}= +1.45747225 \pm 7.7 \cdot 10^{-3} \) \(a_{50}= +1.28019356 \pm 7.6 \cdot 10^{-3} \) \(a_{51}= -1.74651929 \pm 9.9 \cdot 10^{-3} \)
\(a_{52}= -0.23548870 \pm 8.7 \cdot 10^{-3} \) \(a_{53}= -0.76158617 \pm 6.4 \cdot 10^{-3} \) \(a_{54}= -4.10525778 \pm 8.7 \cdot 10^{-3} \)
\(a_{55}= +0.05983282 \pm 5.6 \cdot 10^{-3} \) \(a_{56}= -0.32174071 \pm 6.4 \cdot 10^{-3} \) \(a_{57}= +2.60958126 \pm 6.7 \cdot 10^{-3} \)
\(a_{58}= +0.99342765 \pm 6.1 \cdot 10^{-3} \) \(a_{59}= +0.43979777 \pm 7.8 \cdot 10^{-3} \) \(a_{60}= +0.38940573 \pm 1.0 \cdot 10^{-2} \)

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