Properties

Label 29.29
Level $29$
Weight $0$
Character 29.1
Symmetry odd
\(R\) 3.920214
Fricke sign $+1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(3.92021463299001056757884602947 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.16471155 \pm 7.9 \cdot 10^{-7} \) \(a_{3}= +0.89855403 \pm 7.5 \cdot 10^{-7} \)
\(a_{4}= +0.35655299 \pm 7.9 \cdot 10^{-7} \) \(a_{5}= +1.16749461 \pm 7.1 \cdot 10^{-7} \) \(a_{6}= -1.04655625 \pm 9.1 \cdot 10^{-7} \)
\(a_{7}= -1.79463362 \pm 6.6 \cdot 10^{-7} \) \(a_{8}= +0.74943017 \pm 6.6 \cdot 10^{-7} \) \(a_{9}= -0.19260065 \pm 7.0 \cdot 10^{-7} \)
\(a_{10}= -1.35979446 \pm 8.7 \cdot 10^{-7} \) \(a_{11}= -0.23873791 \pm 6.5 \cdot 10^{-7} \) \(a_{12}= +0.32038212 \pm 9.2 \cdot 10^{-7} \)
\(a_{13}= -0.42302497 \pm 6.1 \cdot 10^{-7} \) \(a_{14}= +2.09023050 \pm 8.7 \cdot 10^{-7} \) \(a_{15}= +1.04905699 \pm 7.9 \cdot 10^{-7} \)
\(a_{16}= -1.22942295 \pm 6.9 \cdot 10^{-7} \) \(a_{17}= -1.18105996 \pm 7.0 \cdot 10^{-7} \) \(a_{18}= +0.22432421 \pm 9.1 \cdot 10^{-7} \)
\(a_{19}= -1.47482995 \pm 5.7 \cdot 10^{-7} \) \(a_{20}= +0.41627369 \pm 8.4 \cdot 10^{-7} \) \(a_{21}= -1.61257527 \pm 7.1 \cdot 10^{-7} \)
\(a_{22}= +0.27806080 \pm 8.1 \cdot 10^{-7} \) \(a_{23}= +1.09171771 \pm 6.8 \cdot 10^{-7} \) \(a_{24}= +0.67340350 \pm 7.2 \cdot 10^{-7} \)
\(a_{25}= +0.36304367 \pm 6.5 \cdot 10^{-7} \) \(a_{26}= +0.49270206 \pm 6.6 \cdot 10^{-7} \) \(a_{27}= -1.07161612 \pm 6.6 \cdot 10^{-7} \)
\(a_{28}= -0.63988198 \pm 8.7 \cdot 10^{-7} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -1.22184879 \pm 8.6 \cdot 10^{-7} \)
\(a_{31}= +1.39730023 \pm 6.2 \cdot 10^{-7} \) \(a_{32}= +0.68249294 \pm 6.9 \cdot 10^{-7} \) \(a_{33}= -0.21451891 \pm 7.5 \cdot 10^{-7} \)
\(a_{34}= +1.37559417 \pm 6.9 \cdot 10^{-7} \) \(a_{35}= -2.09522508 \pm 7.0 \cdot 10^{-7} \) \(a_{36}= -0.06867234 \pm 9.1 \cdot 10^{-7} \)
\(a_{37}= -0.76189270 \pm 6.2 \cdot 10^{-7} \) \(a_{38}= +1.71775147 \pm 6.0 \cdot 10^{-7} \) \(a_{39}= -0.38011079 \pm 6.9 \cdot 10^{-7} \)
\(a_{40}= +0.87495568 \pm 7.3 \cdot 10^{-7} \) \(a_{41}= -1.05187351 \pm 6.4 \cdot 10^{-7} \) \(a_{42}= +1.87818504 \pm 9.3 \cdot 10^{-7} \)
\(a_{43}= +0.28469827 \pm 5.7 \cdot 10^{-7} \) \(a_{44}= -0.08512271 \pm 7.4 \cdot 10^{-7} \) \(a_{45}= -0.22486023 \pm 7.3 \cdot 10^{-7} \)
\(a_{46}= -1.27153622 \pm 8.9 \cdot 10^{-7} \) \(a_{47}= +0.41535887 \pm 5.7 \cdot 10^{-7} \) \(a_{48}= -1.10470295 \pm 7.3 \cdot 10^{-7} \)
\(a_{49}= +2.22070983 \pm 6.1 \cdot 10^{-7} \) \(a_{50}= -0.42284115 \pm 7.4 \cdot 10^{-7} \) \(a_{51}= -1.06124619 \pm 7.0 \cdot 10^{-7} \)
\(a_{52}= -0.15083082 \pm 7.7 \cdot 10^{-7} \) \(a_{53}= -0.49589302 \pm 6.2 \cdot 10^{-7} \) \(a_{54}= +1.24812367 \pm 8.2 \cdot 10^{-7} \)
\(a_{55}= -0.27872522 \pm 6.7 \cdot 10^{-7} \) \(a_{56}= -1.34495257 \pm 7.7 \cdot 10^{-7} \) \(a_{57}= -1.32521439 \pm 6.3 \cdot 10^{-7} \)
\(a_{58}= +0.21628150 \pm 8.1 \cdot 10^{-7} \) \(a_{59}= +0.64036426 \pm 6.0 \cdot 10^{-7} \) \(a_{60}= +0.37404440 \pm 8.8 \cdot 10^{-7} \)

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