Properties

Label 10.1
Level $10$
Weight $0$
Character 10.1
Symmetry odd
\(R\) 1.446399
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: \(1.44639913340300919227740092604 \pm 6 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.50834095 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.35945134 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.08483578 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.74158947 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.24526381 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.25417048 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +1.03793609 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.05998795 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.22733699 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.05663155 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.52438295 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -0.31364879 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= -0.04312550 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.17342771 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -1.67038673 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.17972567 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.73393165 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.88532126 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.04241789 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +1.26525111 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.16075152 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.55693258 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.12467764 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.04004456 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.03793971 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.37079474 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.24632041 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.22178318 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.52762542 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -0.40958558 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.03049433 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.65627723 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.12263191 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.33164889 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +1.18114179 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +0.82107241 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.12708524 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.99280289 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= +0.02878814 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.51896805 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +1.12260378 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.62601666 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.10968531 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.02999398 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.15944052 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.89466764 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= -0.24333197 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.11366849 \pm 1.0 \cdot 10^{-8} \)

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