Properties

Label 10.13
Level $10$
Weight $0$
Character 10.1
Symmetry even
\(R\) 6.378797
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(6.37879720848661938376584920503 \pm 5 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.22388403 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.15830992 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.49872783 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.94987594 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.64606333 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.11194202 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -0.08714684 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.35265383 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.10012398 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.62344882 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.67166372 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -1.08554119 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= -0.11165720 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.45683576 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +1.03672930 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.07915496 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.06162212 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= -0.43654609 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.24936392 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.34721129 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.07079835 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.64010219 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.14464326 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +1.14795167 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -0.22303787 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.47493797 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= +1.58273717 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.76759354 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.01951079 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -0.96611102 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.07895356 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.29710288 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.32303167 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.42479743 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.73307832 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +1.36302574 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.05597101 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.75127055 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= -0.36346427 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.04357342 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +0.24889608 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.30868470 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.28892831 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +0.17632692 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.24303534 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.24551546 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +1.95682568 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.05006199 \pm 1.0 \cdot 10^{-8} \)

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