Properties

Label 2.32
Level $2$
Weight $0$
Character 2.1
Symmetry even
\(R\) 22.08904
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: not computed rigorously
Spectral parameter: \(22.0890454668192578773032661018 \pm 3 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= \pm0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.16040571 \pm 1.2 \cdot 10^{-4} \)
\(a_{4}= \pm0.5 \) \(a_{5}= +1.62780155 \pm 9.9 \cdot 10^{-5} \) \(a_{6}= \pm0.82053075 \pm 8.6 \cdot 10^{-5} \)
\(a_{7}= -1.26807218 \pm 9.1 \cdot 10^{-5} \) \(a_{8}= \pm0.35355339 \pm 1.0 \cdot 10^{-8} \) \(a_{9}= +0.34654142 \pm 2.6 \cdot 10^{-5} \)
\(a_{10}= \pm1.15102951 \pm 7.0 \cdot 10^{-5} \) \(a_{11}= -0.74934386 \pm 6.2 \cdot 10^{-5} \) \(a_{12}= \pm0.58020286 \pm 6.1 \cdot 10^{-5} \)
\(a_{13}= +0.32035835 \pm 9.2 \cdot 10^{-5} \) \(a_{14}= \pm0.89666244 \pm 6.4 \cdot 10^{-5} \) \(a_{15}= -1.88891021 \pm 1.1 \cdot 10^{-4} \)
\(a_{16}= \pm0.25 \) \(a_{17}= -0.57721923 \pm 3.8 \cdot 10^{-5} \) \(a_{18}= \pm0.24504179 \pm 1.9 \cdot 10^{-5} \)
\(a_{19}= -0.00850153 \pm 8.1 \cdot 10^{-5} \) \(a_{20}= \pm0.81390077 \pm 4.9 \cdot 10^{-5} \) \(a_{21}= +1.47147820 \pm 1.0 \cdot 10^{-4} \)
\(a_{22}= \pm0.52986612 \pm 4.4 \cdot 10^{-5} \) \(a_{23}= +0.33903249 \pm 1.0 \cdot 10^{-5} \) \(a_{24}= \pm0.41026537 \pm 4.3 \cdot 10^{-5} \)
\(a_{25}= +1.64973787 \pm 2.0 \cdot 10^{-5} \) \(a_{26}= \pm0.22652756 \pm 6.5 \cdot 10^{-5} \) \(a_{27}= +0.75827707 \pm 9.4 \cdot 10^{-5} \)
\(a_{28}= \pm0.63403609 \pm 4.5 \cdot 10^{-5} \) \(a_{29}= +0.01999078 \pm 1.9 \cdot 10^{-4} \) \(a_{30}= \pm1.33566122 \pm 7.8 \cdot 10^{-5} \)
\(a_{31}= -0.72455230 \pm 1.7 \cdot 10^{-4} \) \(a_{32}= \pm0.17677670 \pm 1.0 \cdot 10^{-8} \) \(a_{33}= +0.86954289 \pm 6.8 \cdot 10^{-5} \)
\(a_{34}= \pm0.40815563 \pm 2.6 \cdot 10^{-5} \) \(a_{35}= -2.06416986 \pm 8.2 \cdot 10^{-5} \) \(a_{36}= \pm0.17327071 \pm 1.3 \cdot 10^{-5} \)
\(a_{37}= +1.78875846 \pm 8.4 \cdot 10^{-5} \) \(a_{38}= \pm0.00601149 \pm 5.7 \cdot 10^{-5} \) \(a_{39}= -0.37174566 \pm 1.0 \cdot 10^{-4} \)
\(a_{40}= \pm0.57551476 \pm 3.5 \cdot 10^{-5} \) \(a_{41}= -0.00732486 \pm 8.2 \cdot 10^{-5} \) \(a_{42}= \pm1.04049222 \pm 7.1 \cdot 10^{-5} \)
\(a_{43}= +1.68710967 \pm 8.8 \cdot 10^{-5} \) \(a_{44}= \pm0.37467193 \pm 3.1 \cdot 10^{-5} \) \(a_{45}= +0.56410065 \pm 2.4 \cdot 10^{-5} \)
\(a_{46}= \pm0.23973217 \pm 7.7 \cdot 10^{-6} \) \(a_{47}= -0.47062990 \pm 1.1 \cdot 10^{-4} \) \(a_{48}= \pm0.29010143 \pm 3.0 \cdot 10^{-5} \)
\(a_{49}= +0.60800706 \pm 3.6 \cdot 10^{-5} \) \(a_{50}= \pm1.16654084 \pm 1.4 \cdot 10^{-5} \) \(a_{51}= +0.66980849 \pm 4.4 \cdot 10^{-5} \)
\(a_{52}= \pm0.16017918 \pm 4.6 \cdot 10^{-5} \) \(a_{53}= +1.29190537 \pm 1.2 \cdot 10^{-4} \) \(a_{54}= \pm0.53618286 \pm 6.7 \cdot 10^{-5} \)
\(a_{55}= -1.21978309 \pm 5.6 \cdot 10^{-5} \) \(a_{56}= \pm0.44833122 \pm 3.2 \cdot 10^{-5} \) \(a_{57}= +0.00986522 \pm 8.9 \cdot 10^{-5} \)
\(a_{58}= \pm0.01413562 \pm 1.3 \cdot 10^{-4} \) \(a_{59}= +0.09414930 \pm 1.7 \cdot 10^{-5} \) \(a_{60}= \pm0.94445511 \pm 5.5 \cdot 10^{-5} \)

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