Properties

Label 10.27
Level $10$
Weight $0$
Character 10.1
Symmetry odd
\(R\) 9.029774
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: \(9.02977428596339036525552573285 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.93908612 \pm 3.9 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +1.37114095 \pm 5.0 \cdot 10^{-8} \)
\(a_{7}= +0.57013214 \pm 4.9 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.76005500 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.58878924 \pm 3.8 \cdot 10^{-8} \) \(a_{12}= -0.96954306 \pm 5.0 \cdot 10^{-8} \)
\(a_{13}= -0.36720627 \pm 4.3 \cdot 10^{-8} \) \(a_{14}= -0.40314430 \pm 5.9 \cdot 10^{-8} \) \(a_{15}= +0.86718568 \pm 5.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.69678430 \pm 2.6 \cdot 10^{-8} \) \(a_{18}= -1.95165361 \pm 5.3 \cdot 10^{-8} \)
\(a_{19}= -0.49018532 \pm 3.4 \cdot 10^{-8} \) \(a_{20}= -0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= -1.10553531 \pm 4.1 \cdot 10^{-8} \)
\(a_{22}= -0.41633687 \pm 4.8 \cdot 10^{-8} \) \(a_{23}= +1.24628156 \pm 6.0 \cdot 10^{-8} \) \(a_{24}= +0.68557047 \pm 5.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.25965405 \pm 5.4 \cdot 10^{-8} \) \(a_{27}= -3.41289823 \pm 4.7 \cdot 10^{-8} \)
\(a_{28}= +0.28506607 \pm 5.9 \cdot 10^{-8} \) \(a_{29}= +1.68672868 \pm 6.2 \cdot 10^{-8} \) \(a_{30}= -0.61319287 \pm 5.0 \cdot 10^{-8} \)
\(a_{31}= +0.22355247 \pm 3.6 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.14171305 \pm 3.1 \cdot 10^{-8} \)
\(a_{34}= +0.49270090 \pm 3.6 \cdot 10^{-8} \) \(a_{35}= -0.25497084 \pm 5.9 \cdot 10^{-8} \) \(a_{36}= +1.38002750 \pm 5.3 \cdot 10^{-8} \)
\(a_{37}= -1.46695694 \pm 4.7 \cdot 10^{-8} \) \(a_{38}= +0.34661336 \pm 4.4 \cdot 10^{-8} \) \(a_{39}= +0.71204459 \pm 3.5 \cdot 10^{-8} \)
\(a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -0.53855574 \pm 3.0 \cdot 10^{-8} \) \(a_{42}= +0.78173152 \pm 9.9 \cdot 10^{-8} \)
\(a_{43}= +0.54812701 \pm 4.2 \cdot 10^{-8} \) \(a_{44}= +0.29439462 \pm 4.8 \cdot 10^{-8} \) \(a_{45}= -1.23433412 \pm 5.3 \cdot 10^{-8} \)
\(a_{46}= -0.88125414 \pm 7.0 \cdot 10^{-8} \) \(a_{47}= +0.24082429 \pm 3.1 \cdot 10^{-8} \) \(a_{48}= -0.48477153 \pm 5.0 \cdot 10^{-8} \)
\(a_{49}= -0.67494935 \pm 4.9 \cdot 10^{-8} \) \(a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= +1.35112477 \pm 3.1 \cdot 10^{-8} \)
\(a_{52}= -0.18360314 \pm 5.4 \cdot 10^{-8} \) \(a_{53}= -1.07094713 \pm 4.4 \cdot 10^{-8} \) \(a_{54}= +2.41328348 \pm 5.8 \cdot 10^{-8} \)
\(a_{55}= -0.26331455 \pm 4.8 \cdot 10^{-8} \) \(a_{56}= -0.20157215 \pm 5.9 \cdot 10^{-8} \) \(a_{57}= +0.95051155 \pm 3.0 \cdot 10^{-8} \)
\(a_{58}= -1.19269729 \pm 7.2 \cdot 10^{-8} \) \(a_{59}= -0.40346256 \pm 3.2 \cdot 10^{-8} \) \(a_{60}= +0.43359284 \pm 5.0 \cdot 10^{-8} \)

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