Properties

Label 22.30
Level $22$
Weight $0$
Character 22.1
Symmetry even
\(R\) 5.997981
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: \(5.99798116734820455263178366569 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.54823635 \pm 1.8 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.51580651 \pm 2.2 \cdot 10^{-8} \) \(a_{6}= +0.38766164 \pm 2.9 \cdot 10^{-8} \)
\(a_{7}= -1.29976547 \pm 2.5 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.69943690 \pm 1.8 \cdot 10^{-8} \)
\(a_{10}= +1.07183706 \pm 3.2 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.27411818 \pm 2.9 \cdot 10^{-8} \)
\(a_{13}= -1.08176577 \pm 1.5 \cdot 10^{-8} \) \(a_{14}= +0.91907298 \pm 3.5 \cdot 10^{-8} \) \(a_{15}= +0.83102023 \pm 2.2 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.50410971 \pm 1.6 \cdot 10^{-8} \) \(a_{18}= +0.49457658 \pm 2.8 \cdot 10^{-8} \)
\(a_{19}= +0.14069615 \pm 2.1 \cdot 10^{-8} \) \(a_{20}= -0.75790326 \pm 3.2 \cdot 10^{-8} \) \(a_{21}= +0.71257868 \pm 2.2 \cdot 10^{-8} \)
\(a_{22}= +0.21320072 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -1.13686951 \pm 1.9 \cdot 10^{-8} \) \(a_{24}= +0.19383082 \pm 2.9 \cdot 10^{-8} \)
\(a_{25}= +1.29766938 \pm 2.6 \cdot 10^{-8} \) \(a_{26}= +0.76492391 \pm 2.5 \cdot 10^{-8} \) \(a_{27}= +0.93169309 \pm 1.6 \cdot 10^{-8} \)
\(a_{28}= -0.64988273 \pm 3.5 \cdot 10^{-8} \) \(a_{29}= -1.22269600 \pm 1.9 \cdot 10^{-8} \) \(a_{30}= -0.58762004 \pm 5.1 \cdot 10^{-8} \)
\(a_{31}= -0.08310782 \pm 2.2 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.16529948 \pm 2.9 \cdot 10^{-8} \)
\(a_{34}= -1.06356618 \pm 2.6 \cdot 10^{-8} \) \(a_{35}= +1.97019296 \pm 2.4 \cdot 10^{-8} \) \(a_{36}= -0.34971845 \pm 2.8 \cdot 10^{-8} \)
\(a_{37}= +1.86200770 \pm 1.7 \cdot 10^{-8} \) \(a_{38}= -0.09948720 \pm 3.1 \cdot 10^{-8} \) \(a_{39}= +0.59306332 \pm 1.4 \cdot 10^{-8} \)
\(a_{40}= +0.53591853 \pm 3.2 \cdot 10^{-8} \) \(a_{41}= -1.23706210 \pm 1.9 \cdot 10^{-8} \) \(a_{42}= -0.50386922 \pm 5.4 \cdot 10^{-8} \)
\(a_{43}= -0.34385836 \pm 1.6 \cdot 10^{-8} \) \(a_{44}= -0.15075567 \pm 1.4 \cdot 10^{-7} \) \(a_{45}= +1.06021101 \pm 1.4 \cdot 10^{-8} \)
\(a_{46}= +0.80388814 \pm 3.0 \cdot 10^{-8} \) \(a_{47}= -1.07715861 \pm 2.2 \cdot 10^{-8} \) \(a_{48}= -0.13705909 \pm 2.9 \cdot 10^{-8} \)
\(a_{49}= +0.68939027 \pm 2.2 \cdot 10^{-8} \) \(a_{50}= -0.91759082 \pm 3.7 \cdot 10^{-8} \) \(a_{51}= -0.82460762 \pm 1.6 \cdot 10^{-8} \)
\(a_{52}= -0.54088288 \pm 2.5 \cdot 10^{-8} \) \(a_{53}= -0.80546460 \pm 2.3 \cdot 10^{-8} \) \(a_{54}= -0.65880650 \pm 2.7 \cdot 10^{-8} \)
\(a_{55}= +0.45703286 \pm 3.2 \cdot 10^{-8} \) \(a_{56}= +0.45953649 \pm 3.5 \cdot 10^{-8} \) \(a_{57}= -0.07713474 \pm 1.7 \cdot 10^{-8} \)
\(a_{58}= +0.86457663 \pm 3.0 \cdot 10^{-8} \) \(a_{59}= +0.50393347 \pm 1.3 \cdot 10^{-8} \) \(a_{60}= +0.41551012 \pm 5.1 \cdot 10^{-8} \)

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