Properties

Label 10.23
Level $10$
Weight $0$
Character 10.1
Symmetry odd
\(R\) 8.423388
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(8.42338862094813782250280224667 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.14911412 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.10543961 \pm 1.4 \cdot 10^{-8} \)
\(a_{7}= -1.32642196 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.97776498 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +1.67605934 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.07455706 \pm 1.4 \cdot 10^{-8} \)
\(a_{13}= -0.57506067 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.93792196 \pm 1.5 \cdot 10^{-8} \) \(a_{15}= -0.06668586 \pm 1.4 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.37759571 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.69138425 \pm 1.4 \cdot 10^{-8} \)
\(a_{19}= +0.52860462 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= +0.19778825 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -1.18515292 \pm 1.4 \cdot 10^{-8} \) \(a_{23}= +0.04410534 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.05271980 \pm 1.4 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.40662930 \pm 1.5 \cdot 10^{-8} \) \(a_{27}= +0.29491269 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.66321098 \pm 1.5 \cdot 10^{-8} \) \(a_{29}= +1.30709968 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.04715403 \pm 1.4 \cdot 10^{-8} \)
\(a_{31}= +0.61019073 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.24992412 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.97410727 \pm 1.3 \cdot 10^{-8} \) \(a_{35}= -0.59319393 \pm 1.5 \cdot 10^{-8} \) \(a_{36}= -0.48888249 \pm 1.4 \cdot 10^{-8} \)
\(a_{37}= +1.43214181 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.37377991 \pm 1.4 \cdot 10^{-8} \) \(a_{39}= +0.08574967 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= +0.23082620 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.13985741 \pm 1.9 \cdot 10^{-8} \)
\(a_{43}= -0.18740678 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.83802967 \pm 1.4 \cdot 10^{-8} \) \(a_{45}= -0.43726979 \pm 1.4 \cdot 10^{-8} \)
\(a_{46}= -0.03118719 \pm 1.6 \cdot 10^{-8} \) \(a_{47}= +0.51320320 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.03727853 \pm 1.4 \cdot 10^{-8} \)
\(a_{49}= +0.75939522 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= -0.20541898 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.28753033 \pm 1.5 \cdot 10^{-8} \) \(a_{53}= -1.14453758 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.20853476 \pm 1.5 \cdot 10^{-8} \)
\(a_{55}= +0.74955652 \pm 1.4 \cdot 10^{-8} \) \(a_{56}= +0.46896098 \pm 1.5 \cdot 10^{-8} \) \(a_{57}= -0.07882241 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.92425905 \pm 1.7 \cdot 10^{-8} \) \(a_{59}= -1.25066459 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.03334293 \pm 1.4 \cdot 10^{-8} \)

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