Properties

Label 29.46
Level $29$
Weight $0$
Character 29.1
Symmetry even
\(R\) 4.924644
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: \(4.92464456348645956190829352358 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.75646359 \pm 2.3 \cdot 10^{-8} \) \(a_{3}= -1.54462148 \pm 2.0 \cdot 10^{-8} \)
\(a_{4}= +2.08516433 \pm 2.4 \cdot 10^{-8} \) \(a_{5}= -1.71867425 \pm 2.0 \cdot 10^{-8} \) \(a_{6}= +2.71307138 \pm 2.3 \cdot 10^{-8} \)
\(a_{7}= +1.10824917 \pm 1.9 \cdot 10^{-8} \) \(a_{8}= -1.90605164 \pm 2.8 \cdot 10^{-8} \) \(a_{9}= +1.38585551 \pm 2.0 \cdot 10^{-8} \)
\(a_{10}= +3.01878875 \pm 2.2 \cdot 10^{-8} \) \(a_{11}= -0.77823194 \pm 1.8 \cdot 10^{-8} \) \(a_{12}= -3.22078962 \pm 2.0 \cdot 10^{-8} \)
\(a_{13}= +0.89661519 \pm 2.0 \cdot 10^{-8} \) \(a_{14}= -1.94659930 \pm 1.7 \cdot 10^{-8} \) \(a_{15}= +2.65470117 \pm 1.8 \cdot 10^{-8} \)
\(a_{16}= +1.26274597 \pm 3.0 \cdot 10^{-8} \) \(a_{17}= -0.03564343 \pm 1.8 \cdot 10^{-8} \) \(a_{18}= -2.43420475 \pm 2.6 \cdot 10^{-8} \)
\(a_{19}= +0.16738351 \pm 1.6 \cdot 10^{-8} \) \(a_{20}= -3.58371826 \pm 2.2 \cdot 10^{-8} \) \(a_{21}= -1.71182546 \pm 2.0 \cdot 10^{-8} \)
\(a_{22}= +1.36693607 \pm 2.0 \cdot 10^{-8} \) \(a_{23}= +0.63056769 \pm 1.9 \cdot 10^{-8} \) \(a_{24}= +2.94412830 \pm 2.4 \cdot 10^{-8} \)
\(a_{25}= +1.95384119 \pm 2.0 \cdot 10^{-8} \) \(a_{26}= -1.57487194 \pm 2.4 \cdot 10^{-8} \) \(a_{27}= -0.59600072 \pm 2.1 \cdot 10^{-8} \)
\(a_{28}= +2.31088163 \pm 1.6 \cdot 10^{-8} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -4.66288594 \pm 2.2 \cdot 10^{-8} \)
\(a_{31}= -0.63757959 \pm 1.9 \cdot 10^{-8} \) \(a_{32}= -0.31191567 \pm 3.2 \cdot 10^{-8} \) \(a_{33}= +1.20207378 \pm 1.8 \cdot 10^{-8} \)
\(a_{34}= +0.06260639 \pm 2.4 \cdot 10^{-8} \) \(a_{35}= -1.90471931 \pm 2.1 \cdot 10^{-8} \) \(a_{36}= +2.88973649 \pm 2.5 \cdot 10^{-8} \)
\(a_{37}= -1.00194492 \pm 2.0 \cdot 10^{-8} \) \(a_{38}= -0.29400304 \pm 1.7 \cdot 10^{-8} \) \(a_{39}= -1.38493108 \pm 1.9 \cdot 10^{-8} \)
\(a_{40}= +3.27588188 \pm 2.6 \cdot 10^{-8} \) \(a_{41}= +1.18105179 \pm 1.8 \cdot 10^{-8} \) \(a_{42}= +3.00675910 \pm 1.8 \cdot 10^{-8} \)
\(a_{43}= -0.98350563 \pm 1.9 \cdot 10^{-8} \) \(a_{44}= -1.62274150 \pm 2.1 \cdot 10^{-8} \) \(a_{45}= -2.38183419 \pm 1.7 \cdot 10^{-8} \)
\(a_{46}= -1.10756918 \pm 1.9 \cdot 10^{-8} \) \(a_{47}= +1.25191329 \pm 1.7 \cdot 10^{-8} \) \(a_{48}= -1.95046454 \pm 2.5 \cdot 10^{-8} \)
\(a_{49}= +0.22821621 \pm 1.6 \cdot 10^{-8} \) \(a_{50}= -3.43185091 \pm 2.1 \cdot 10^{-8} \) \(a_{51}= +0.05505561 \pm 1.9 \cdot 10^{-8} \)
\(a_{52}= +1.86959002 \pm 2.7 \cdot 10^{-8} \) \(a_{53}= +1.10888756 \pm 2.0 \cdot 10^{-8} \) \(a_{54}= +1.04685355 \pm 2.7 \cdot 10^{-8} \)
\(a_{55}= +1.33752721 \pm 1.8 \cdot 10^{-8} \) \(a_{56}= -2.11238014 \pm 2.0 \cdot 10^{-8} \) \(a_{57}= -0.25854417 \pm 1.6 \cdot 10^{-8} \)
\(a_{58}= -0.32616710 \pm 3.4 \cdot 10^{-8} \) \(a_{59}= -1.62550489 \pm 1.8 \cdot 10^{-8} \) \(a_{60}= +5.53548820 \pm 2.1 \cdot 10^{-8} \)

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