Properties

Label 29.17
Level $29$
Weight $0$
Character 29.1
Symmetry odd
\(R\) 3.160570
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.16057099990595423363267668125 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.38820748 \pm 4.4 \cdot 10^{-7} \) \(a_{3}= +1.65977492 \pm 4.2 \cdot 10^{-7} \)
\(a_{4}= -0.84929495 \pm 4.4 \cdot 10^{-7} \) \(a_{5}= +1.31517686 \pm 3.9 \cdot 10^{-7} \) \(a_{6}= +0.64433704 \pm 5.1 \cdot 10^{-7} \)
\(a_{7}= +1.00965746 \pm 3.7 \cdot 10^{-7} \) \(a_{8}= -0.71791014 \pm 3.6 \cdot 10^{-7} \) \(a_{9}= +1.75485280 \pm 3.9 \cdot 10^{-7} \)
\(a_{10}= +0.51056150 \pm 4.8 \cdot 10^{-7} \) \(a_{11}= -0.97489630 \pm 3.6 \cdot 10^{-7} \) \(a_{12}= -1.40963846 \pm 5.1 \cdot 10^{-7} \)
\(a_{13}= -1.60171360 \pm 3.4 \cdot 10^{-7} \) \(a_{14}= +0.39195658 \pm 4.8 \cdot 10^{-7} \) \(a_{15}= +2.18289758 \pm 4.4 \cdot 10^{-7} \)
\(a_{16}= +0.57059687 \pm 3.8 \cdot 10^{-7} \) \(a_{17}= -0.74368983 \pm 3.8 \cdot 10^{-7} \) \(a_{18}= +0.68124699 \pm 5.0 \cdot 10^{-7} \)
\(a_{19}= +0.53150505 \pm 3.2 \cdot 10^{-7} \) \(a_{20}= -1.11697307 \pm 4.6 \cdot 10^{-7} \) \(a_{21}= +1.67580414 \pm 3.9 \cdot 10^{-7} \)
\(a_{22}= -0.37846204 \pm 4.5 \cdot 10^{-7} \) \(a_{23}= -0.30235114 \pm 3.8 \cdot 10^{-7} \) \(a_{24}= -1.19156924 \pm 4.0 \cdot 10^{-7} \)
\(a_{25}= +0.72969018 \pm 3.6 \cdot 10^{-7} \) \(a_{26}= -0.62179720 \pm 3.7 \cdot 10^{-7} \) \(a_{27}= +1.25288575 \pm 3.7 \cdot 10^{-7} \)
\(a_{28}= -0.85749698 \pm 4.8 \cdot 10^{-7} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +0.84741717 \pm 4.7 \cdot 10^{-7} \)
\(a_{31}= +0.24394694 \pm 3.4 \cdot 10^{-7} \) \(a_{32}= +0.93942011 \pm 3.8 \cdot 10^{-7} \) \(a_{33}= -1.61810843 \pm 4.1 \cdot 10^{-7} \)
\(a_{34}= -0.28870596 \pm 3.8 \cdot 10^{-7} \) \(a_{35}= +1.32787813 \pm 3.9 \cdot 10^{-7} \) \(a_{36}= -1.49038762 \pm 5.0 \cdot 10^{-7} \)
\(a_{37}= -1.03433007 \pm 3.4 \cdot 10^{-7} \) \(a_{38}= +0.20633424 \pm 3.3 \cdot 10^{-7} \) \(a_{39}= -2.65848407 \pm 3.8 \cdot 10^{-7} \)
\(a_{40}= -0.94417880 \pm 4.0 \cdot 10^{-7} \) \(a_{41}= +0.19983054 \pm 3.5 \cdot 10^{-7} \) \(a_{42}= +0.65055970 \pm 5.1 \cdot 10^{-7} \)
\(a_{43}= +1.73371168 \pm 3.2 \cdot 10^{-7} \) \(a_{44}= +0.82797450 \pm 4.1 \cdot 10^{-7} \) \(a_{45}= +2.30794180 \pm 4.1 \cdot 10^{-7} \)
\(a_{46}= -0.11737497 \pm 4.9 \cdot 10^{-7} \) \(a_{47}= -0.73880461 \pm 3.2 \cdot 10^{-7} \) \(a_{48}= +0.94706237 \pm 4.0 \cdot 10^{-7} \)
\(a_{49}= +0.01940819 \pm 3.4 \cdot 10^{-7} \) \(a_{50}= +0.28327119 \pm 4.1 \cdot 10^{-7} \) \(a_{51}= -1.23435773 \pm 3.9 \cdot 10^{-7} \)
\(a_{52}= +1.36032728 \pm 4.3 \cdot 10^{-7} \) \(a_{53}= +0.23970374 \pm 3.4 \cdot 10^{-7} \) \(a_{54}= +0.48637962 \pm 4.6 \cdot 10^{-7} \)
\(a_{55}= -1.28216106 \pm 3.7 \cdot 10^{-7} \) \(a_{56}= -0.72484333 \pm 4.2 \cdot 10^{-7} \) \(a_{57}= +0.88217875 \pm 3.5 \cdot 10^{-7} \)
\(a_{58}= +0.07208832 \pm 4.5 \cdot 10^{-7} \) \(a_{59}= +0.12465193 \pm 3.3 \cdot 10^{-7} \) \(a_{60}= -1.85392389 \pm 4.9 \cdot 10^{-7} \)

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