Properties

Label 22.10
Level $22$
Weight $0$
Character 22.1
Symmetry even
\(R\) 3.606537
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(3.60653766124394379661380047071 \pm 9 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.15150895 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.74666331 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.81423979 \pm 1.1 \cdot 10^{-8} \)
\(a_{7}= -0.57117182 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.32597286 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.52797069 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.57575447 \pm 1.1 \cdot 10^{-8} \)
\(a_{13}= -1.14708381 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.40387947 \pm 1.1 \cdot 10^{-8} \) \(a_{15}= +0.85978949 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.54689930 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.23049762 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= +1.54844301 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.37333166 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= +0.65770946 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.21320072 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -1.76728098 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.40711989 \pm 1.1 \cdot 10^{-8} \)
\(a_{25}= -0.44249390 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.81111074 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +0.77614828 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.28558591 \pm 1.1 \cdot 10^{-8} \) \(a_{29}= -0.21884949 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.60796298 \pm 1.2 \cdot 10^{-8} \)
\(a_{31}= -0.48194126 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.34719301 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.38671621 \pm 1.1 \cdot 10^{-8} \) \(a_{35}= +0.42647304 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16298643 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -1.69402704 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.09491455 \pm 1.1 \cdot 10^{-8} \) \(a_{39}= +1.32087727 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.26398535 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= -0.73149486 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.46507082 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= +1.00576429 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.15075567 \pm 1.4 \cdot 10^{-7} \) \(a_{45}= -0.24339198 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -1.24965637 \pm 1.1 \cdot 10^{-8} \) \(a_{47}= +1.58963570 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.28787724 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= -0.67376275 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.31289044 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= -0.62975944 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.57354190 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= +0.00936086 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.54881971 \pm 1.1 \cdot 10^{-8} \)
\(a_{55}= +0.22512746 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= -0.20193973 \pm 1.1 \cdot 10^{-8} \) \(a_{57}= -1.78304598 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.15474996 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= +1.23194655 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.42989474 \pm 1.2 \cdot 10^{-8} \)

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