Properties

Label 10.50
Level $10$
Weight $0$
Character 10.1
Symmetry even
\(R\) 12.15352
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: \(12.1535251870315474893970296811 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.07979012 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.76352691 \pm 1.6 \cdot 10^{-8} \)
\(a_{7}= +0.51359108 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.16594670 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -1.12474881 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.53989506 \pm 1.6 \cdot 10^{-8} \)
\(a_{13}= -0.11719747 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.36316374 \pm 1.4 \cdot 10^{-8} \) \(a_{15}= +0.48289682 \pm 1.6 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.61533963 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.11734204 \pm 1.5 \cdot 10^{-8} \)
\(a_{19}= -1.36584736 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= -0.55457058 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.79531751 \pm 1.6 \cdot 10^{-8} \) \(a_{23}= -1.23097942 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.38176346 \pm 1.6 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.08287113 \pm 1.4 \cdot 10^{-8} \) \(a_{27}= +0.90060251 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.25679554 \pm 1.4 \cdot 10^{-8} \) \(a_{29}= +0.33202312 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.34145962 \pm 1.6 \cdot 10^{-8} \)
\(a_{31}= +0.67912520 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +1.21449265 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +1.14221760 \pm 1.6 \cdot 10^{-8} \) \(a_{35}= -0.22968491 \pm 1.4 \cdot 10^{-8} \) \(a_{36}= +0.08297335 \pm 1.5 \cdot 10^{-8} \)
\(a_{37}= +0.93659270 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.96579993 \pm 1.4 \cdot 10^{-8} \) \(a_{39}= +0.12654867 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -0.74138695 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.39214061 \pm 2.0 \cdot 10^{-8} \)
\(a_{43}= -0.19745191 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.56237440 \pm 1.6 \cdot 10^{-8} \) \(a_{45}= -0.07421362 \pm 1.5 \cdot 10^{-8} \)
\(a_{46}= +0.87043389 \pm 1.4 \cdot 10^{-8} \) \(a_{47}= +1.06428372 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.26994753 \pm 1.6 \cdot 10^{-8} \)
\(a_{49}= -0.73622420 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= +1.74422777 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.05859874 \pm 1.4 \cdot 10^{-8} \) \(a_{53}= -0.25522389 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.63682214 \pm 1.3 \cdot 10^{-8} \)
\(a_{55}= +0.50300296 \pm 1.6 \cdot 10^{-8} \) \(a_{56}= -0.18158187 \pm 1.4 \cdot 10^{-8} \) \(a_{57}= +1.47482848 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.23477580 \pm 1.3 \cdot 10^{-8} \) \(a_{59}= -1.32471403 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.24144841 \pm 1.6 \cdot 10^{-8} \)

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