Properties

Label 29.1
Level $29$
Weight $0$
Character 29.1
Symmetry even
\(R\) 1.017266
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(1.01726655080297786279547388594 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.06020148 \pm 3.6 \cdot 10^{-8} \) \(a_{3}= -1.20080741 \pm 3.2 \cdot 10^{-8} \)
\(a_{4}= +0.12402719 \pm 3.8 \cdot 10^{-8} \) \(a_{5}= +1.42469458 \pm 3.1 \cdot 10^{-8} \) \(a_{6}= +1.27309780 \pm 3.6 \cdot 10^{-8} \)
\(a_{7}= -0.90972597 \pm 2.9 \cdot 10^{-8} \) \(a_{8}= +0.92870768 \pm 4.4 \cdot 10^{-8} \) \(a_{9}= +0.44193845 \pm 3.1 \cdot 10^{-8} \)
\(a_{10}= -1.51046331 \pm 3.5 \cdot 10^{-8} \) \(a_{11}= +0.10592285 \pm 2.9 \cdot 10^{-8} \) \(a_{12}= -0.14893277 \pm 3.2 \cdot 10^{-8} \)
\(a_{13}= +0.38892195 \pm 3.1 \cdot 10^{-8} \) \(a_{14}= +0.96449282 \pm 2.7 \cdot 10^{-8} \) \(a_{15}= -1.71078382 \pm 2.9 \cdot 10^{-8} \)
\(a_{16}= -1.10864445 \pm 4.7 \cdot 10^{-8} \) \(a_{17}= -0.36979700 \pm 2.9 \cdot 10^{-8} \) \(a_{18}= -0.46854380 \pm 4.0 \cdot 10^{-8} \)
\(a_{19}= +0.73686146 \pm 2.6 \cdot 10^{-8} \) \(a_{20}= +0.17670086 \pm 3.5 \cdot 10^{-8} \) \(a_{21}= +1.09240569 \pm 3.1 \cdot 10^{-8} \)
\(a_{22}= -0.11229957 \pm 3.2 \cdot 10^{-8} \) \(a_{23}= +0.74134540 \pm 3.0 \cdot 10^{-8} \) \(a_{24}= -1.11519906 \pm 3.7 \cdot 10^{-8} \)
\(a_{25}= +1.02975465 \pm 3.1 \cdot 10^{-8} \) \(a_{26}= -0.41233563 \pm 3.7 \cdot 10^{-8} \) \(a_{27}= +0.67012445 \pm 3.2 \cdot 10^{-8} \)
\(a_{28}= -0.11283075 \pm 2.6 \cdot 10^{-8} \) \(a_{29}= -0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +1.81377554 \pm 3.5 \cdot 10^{-8} \)
\(a_{31}= -0.60778684 \pm 2.9 \cdot 10^{-8} \) \(a_{32}= +0.24667881 \pm 5.0 \cdot 10^{-8} \) \(a_{33}= -0.12719295 \pm 2.8 \cdot 10^{-8} \)
\(a_{34}= +0.39205933 \pm 3.8 \cdot 10^{-8} \) \(a_{35}= -1.29608166 \pm 3.3 \cdot 10^{-8} \) \(a_{36}= +0.05481238 \pm 3.9 \cdot 10^{-8} \)
\(a_{37}= -1.60816151 \pm 3.1 \cdot 10^{-8} \) \(a_{38}= -0.78122162 \pm 2.7 \cdot 10^{-8} \) \(a_{39}= -0.46702037 \pm 3.0 \cdot 10^{-8} \)
\(a_{40}= +1.32312479 \pm 4.1 \cdot 10^{-8} \) \(a_{41}= +1.33230545 \pm 2.9 \cdot 10^{-8} \) \(a_{42}= -1.15817013 \pm 2.9 \cdot 10^{-8} \)
\(a_{43}= +0.58681987 \pm 2.9 \cdot 10^{-8} \) \(a_{44}= +0.01313731 \pm 3.2 \cdot 10^{-8} \) \(a_{45}= +0.62962731 \pm 2.7 \cdot 10^{-8} \)
\(a_{46}= -0.78597549 \pm 3.0 \cdot 10^{-8} \) \(a_{47}= -1.22966560 \pm 2.7 \cdot 10^{-8} \) \(a_{48}= +1.33126847 \pm 3.9 \cdot 10^{-8} \)
\(a_{49}= -0.17239867 \pm 2.5 \cdot 10^{-8} \) \(a_{50}= -1.09174741 \pm 3.3 \cdot 10^{-8} \) \(a_{51}= +0.44405498 \pm 3.0 \cdot 10^{-8} \)
\(a_{52}= +0.04823690 \pm 4.2 \cdot 10^{-8} \) \(a_{53}= +1.70894944 \pm 3.2 \cdot 10^{-8} \) \(a_{54}= -0.71046694 \pm 4.2 \cdot 10^{-8} \)
\(a_{55}= +0.15090772 \pm 2.9 \cdot 10^{-8} \) \(a_{56}= -0.84486949 \pm 3.1 \cdot 10^{-8} \) \(a_{57}= -0.88482871 \pm 2.6 \cdot 10^{-8} \)
\(a_{58}= +0.19687447 \pm 4.7 \cdot 10^{-8} \) \(a_{59}= -0.06036045 \pm 2.8 \cdot 10^{-8} \) \(a_{60}= -0.21218371 \pm 3.3 \cdot 10^{-8} \)

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