Properties

Label 29.48
Level $29$
Weight $0$
Character 29.1
Symmetry odd
\(R\) 4.972579
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(4.97257972342255902425338092781 \pm 8 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.71292486 \pm 3.4 \cdot 10^{-6} \) \(a_{3}= -1.31100812 \pm 3.2 \cdot 10^{-6} \)
\(a_{4}= -0.49173814 \pm 3.4 \cdot 10^{-6} \) \(a_{5}= -0.55940195 \pm 3.0 \cdot 10^{-6} \) \(a_{6}= -0.93465028 \pm 3.9 \cdot 10^{-6} \)
\(a_{7}= +0.94471222 \pm 2.8 \cdot 10^{-6} \) \(a_{8}= -1.06349721 \pm 2.8 \cdot 10^{-6} \) \(a_{9}= +0.71874229 \pm 3.0 \cdot 10^{-6} \)
\(a_{10}= -0.39881156 \pm 3.7 \cdot 10^{-6} \) \(a_{11}= +0.29455363 \pm 2.8 \cdot 10^{-6} \) \(a_{12}= +0.64467270 \pm 4.0 \cdot 10^{-6} \)
\(a_{13}= +1.73246649 \pm 2.6 \cdot 10^{-6} \) \(a_{14}= +0.67350882 \pm 3.7 \cdot 10^{-6} \) \(a_{15}= +0.73338050 \pm 3.4 \cdot 10^{-6} \)
\(a_{16}= -0.26645545 \pm 2.9 \cdot 10^{-6} \) \(a_{17}= +0.50592909 \pm 3.0 \cdot 10^{-6} \) \(a_{18}= +0.51240924 \pm 3.9 \cdot 10^{-6} \)
\(a_{19}= -1.67939020 \pm 2.4 \cdot 10^{-6} \) \(a_{20}= +0.27507928 \pm 3.6 \cdot 10^{-6} \) \(a_{21}= -1.23852538 \pm 3.0 \cdot 10^{-6} \)
\(a_{22}= +0.20999461 \pm 3.5 \cdot 10^{-6} \) \(a_{23}= +0.67195812 \pm 2.9 \cdot 10^{-6} \) \(a_{24}= +1.39425347 \pm 3.1 \cdot 10^{-6} \)
\(a_{25}= -0.68706946 \pm 2.8 \cdot 10^{-6} \) \(a_{26}= +1.23511843 \pm 2.8 \cdot 10^{-6} \) \(a_{27}= +0.36873114 \pm 2.8 \cdot 10^{-6} \)
\(a_{28}= -0.46455103 \pm 3.7 \cdot 10^{-6} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +0.52284519 \pm 3.7 \cdot 10^{-6} \)
\(a_{31}= +0.35487615 \pm 2.7 \cdot 10^{-6} \) \(a_{32}= +0.87353449 \pm 3.0 \cdot 10^{-6} \) \(a_{33}= -0.38616220 \pm 3.2 \cdot 10^{-6} \)
\(a_{34}= +0.36068943 \pm 2.9 \cdot 10^{-6} \) \(a_{35}= -0.52847385 \pm 3.0 \cdot 10^{-6} \) \(a_{36}= -0.35343300 \pm 3.9 \cdot 10^{-6} \)
\(a_{37}= +1.00884185 \pm 2.6 \cdot 10^{-6} \) \(a_{38}= -1.19727902 \pm 2.6 \cdot 10^{-6} \) \(a_{39}= -2.27127764 \pm 2.9 \cdot 10^{-6} \)
\(a_{40}= +0.59492241 \pm 3.1 \cdot 10^{-6} \) \(a_{41}= -0.01190022 \pm 2.7 \cdot 10^{-6} \) \(a_{42}= -0.88297554 \pm 4.0 \cdot 10^{-6} \)
\(a_{43}= +1.34783997 \pm 2.5 \cdot 10^{-6} \) \(a_{44}= -0.14484326 \pm 3.2 \cdot 10^{-6} \) \(a_{45}= -0.40206584 \pm 3.1 \cdot 10^{-6} \)
\(a_{46}= +0.47905565 \pm 3.8 \cdot 10^{-6} \) \(a_{47}= +1.25977340 \pm 2.4 \cdot 10^{-6} \) \(a_{48}= +0.34932526 \pm 3.1 \cdot 10^{-6} \)
\(a_{49}= -0.10751883 \pm 2.6 \cdot 10^{-6} \) \(a_{50}= -0.48982890 \pm 3.2 \cdot 10^{-6} \) \(a_{51}= -0.66327715 \pm 3.0 \cdot 10^{-6} \)
\(a_{52}= -0.85191986 \pm 3.3 \cdot 10^{-6} \) \(a_{53}= +0.03221596 \pm 2.7 \cdot 10^{-6} \) \(a_{54}= +0.26287760 \pm 3.5 \cdot 10^{-6} \)
\(a_{55}= -0.16477388 \pm 2.9 \cdot 10^{-6} \) \(a_{56}= -1.00469880 \pm 3.3 \cdot 10^{-6} \) \(a_{57}= +2.20169418 \pm 2.7 \cdot 10^{-6} \)
\(a_{58}= +0.13238682 \pm 3.4 \cdot 10^{-6} \) \(a_{59}= +1.20317293 \pm 2.6 \cdot 10^{-6} \) \(a_{60}= -0.36063116 \pm 3.8 \cdot 10^{-6} \)

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