Properties

Label 10.17
Level $10$
Weight $0$
Character 10.1
Symmetry even
\(R\) 6.993272
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: \(6.99327291741167387176629117244 \pm 5 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.51834558 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +1.07363245 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.62431974 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +1.30537329 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +1.59649681 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.75917279 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -1.28941523 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.44146072 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.67902478 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.88840627 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.92303831 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -0.93799323 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= -0.94793312 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +1.12889372 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -0.57696170 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.53681623 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.91175425 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.46366218 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.31215987 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.69361410 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.48014303 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.05264175 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +2.42403387 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.62819810 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -0.27920428 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.65268665 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.07336304 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.66326138 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -1.95777792 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= +1.64092416 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.67028994 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.97646508 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.79824841 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.58378068 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.40797353 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +0.24364435 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.37958639 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.61022486 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= +1.34890773 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.64470762 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +0.46790259 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.32785867 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.71397508 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.22073036 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -1.42419788 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.49045924 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= -0.27862661 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.33951239 \pm 1.0 \cdot 10^{-8} \)

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