Properties

Label 22.11
Level $22$
Weight $0$
Character 22.1
Symmetry odd
\(R\) 3.711363
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.71136347889612880409892633242 \pm 10 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.58623992 \pm 1.0 \cdot 10^{-7} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.98738911 \pm 8.3 \cdot 10^{-8} \) \(a_{6}= +0.41453422 \pm 1.2 \cdot 10^{-7} \)
\(a_{7}= +1.05540735 \pm 8.3 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.65632276 \pm 9.2 \cdot 10^{-8} \)
\(a_{10}= +0.69818954 \pm 9.3 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.29311996 \pm 1.2 \cdot 10^{-7} \)
\(a_{13}= -1.53918875 \pm 8.0 \cdot 10^{-8} \) \(a_{14}= +0.74628569 \pm 9.4 \cdot 10^{-8} \) \(a_{15}= +0.57884691 \pm 9.9 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.88397777 \pm 7.5 \cdot 10^{-8} \) \(a_{18}= -0.46409027 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= -0.18377385 \pm 9.4 \cdot 10^{-8} \) \(a_{20}= +0.49369456 \pm 9.3 \cdot 10^{-8} \) \(a_{21}= +0.61872192 \pm 1.0 \cdot 10^{-7} \)
\(a_{22}= -0.21320072 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.06863902 \pm 7.5 \cdot 10^{-8} \) \(a_{24}= +0.20726711 \pm 1.2 \cdot 10^{-7} \)
\(a_{25}= -0.02506274 \pm 7.7 \cdot 10^{-8} \) \(a_{26}= -1.08837080 \pm 9.1 \cdot 10^{-8} \) \(a_{27}= -0.97100252 \pm 9.2 \cdot 10^{-8} \)
\(a_{28}= +0.52770367 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -1.38430419 \pm 9.6 \cdot 10^{-8} \) \(a_{30}= +0.40930658 \pm 2.0 \cdot 10^{-7} \)
\(a_{31}= -0.21602443 \pm 6.9 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.17675799 \pm 1.2 \cdot 10^{-7} \)
\(a_{34}= +0.62506668 \pm 8.6 \cdot 10^{-8} \) \(a_{35}= +1.04209773 \pm 6.0 \cdot 10^{-8} \) \(a_{36}= -0.32816138 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +1.00442886 \pm 8.9 \cdot 10^{-8} \) \(a_{38}= -0.12994774 \pm 1.0 \cdot 10^{-7} \) \(a_{39}= -0.90233389 \pm 8.4 \cdot 10^{-8} \)
\(a_{40}= +0.34909477 \pm 9.3 \cdot 10^{-8} \) \(a_{41}= +1.83476154 \pm 9.8 \cdot 10^{-8} \) \(a_{42}= +0.43750246 \pm 2.0 \cdot 10^{-7} \)
\(a_{43}= -0.58402499 \pm 9.0 \cdot 10^{-8} \) \(a_{44}= -0.15075567 \pm 1.4 \cdot 10^{-7} \) \(a_{45}= -0.64804595 \pm 8.6 \cdot 10^{-8} \)
\(a_{46}= +0.04853512 \pm 8.6 \cdot 10^{-8} \) \(a_{47}= -1.18472106 \pm 9.6 \cdot 10^{-8} \) \(a_{48}= +0.14655998 \pm 1.2 \cdot 10^{-7} \)
\(a_{49}= +0.11388467 \pm 6.2 \cdot 10^{-8} \) \(a_{50}= -0.01772203 \pm 8.7 \cdot 10^{-8} \) \(a_{51}= +0.51822306 \pm 9.0 \cdot 10^{-8} \)
\(a_{52}= -0.76959438 \pm 9.1 \cdot 10^{-8} \) \(a_{53}= -0.43341932 \pm 6.8 \cdot 10^{-8} \) \(a_{54}= -0.68660247 \pm 1.0 \cdot 10^{-7} \)
\(a_{55}= -0.29770902 \pm 9.3 \cdot 10^{-8} \) \(a_{56}= +0.37314285 \pm 9.4 \cdot 10^{-8} \) \(a_{57}= -0.10773557 \pm 9.8 \cdot 10^{-8} \)
\(a_{58}= -0.97885088 \pm 1.0 \cdot 10^{-7} \) \(a_{59}= +1.63431212 \pm 8.6 \cdot 10^{-8} \) \(a_{60}= +0.28942346 \pm 2.0 \cdot 10^{-7} \)

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