Properties

Label 29.37
Level $29$
Weight $0$
Character 29.1
Symmetry even
\(R\) 4.396760
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: \(4.3967606392743823364994195848 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.44551521 \pm 2.6 \cdot 10^{-8} \) \(a_{3}= -0.24673958 \pm 2.3 \cdot 10^{-8} \)
\(a_{4}= +1.08951423 \pm 2.7 \cdot 10^{-8} \) \(a_{5}= -1.70042823 \pm 2.2 \cdot 10^{-8} \) \(a_{6}= -0.35666582 \pm 2.6 \cdot 10^{-8} \)
\(a_{7}= -0.50572547 \pm 2.1 \cdot 10^{-8} \) \(a_{8}= +0.12939418 \pm 3.2 \cdot 10^{-8} \) \(a_{9}= -0.93911958 \pm 2.2 \cdot 10^{-8} \)
\(a_{10}= -2.45799488 \pm 2.5 \cdot 10^{-8} \) \(a_{11}= +0.75424580 \pm 2.1 \cdot 10^{-8} \) \(a_{12}= -0.26882629 \pm 2.3 \cdot 10^{-8} \)
\(a_{13}= +1.39329904 \pm 2.2 \cdot 10^{-8} \) \(a_{14}= -0.73103386 \pm 1.9 \cdot 10^{-8} \) \(a_{15}= +0.41956295 \pm 2.1 \cdot 10^{-8} \)
\(a_{16}= -0.90247297 \pm 3.4 \cdot 10^{-8} \) \(a_{17}= -1.01255510 \pm 2.1 \cdot 10^{-8} \) \(a_{18}= -1.35751164 \pm 2.9 \cdot 10^{-8} \)
\(a_{19}= +0.43750129 \pm 1.9 \cdot 10^{-8} \) \(a_{20}= -1.85264076 \pm 2.5 \cdot 10^{-8} \) \(a_{21}= +0.12478249 \pm 2.2 \cdot 10^{-8} \)
\(a_{22}= +1.09027378 \pm 2.3 \cdot 10^{-8} \) \(a_{23}= -1.40391256 \pm 2.2 \cdot 10^{-8} \) \(a_{24}= -0.03192667 \pm 2.7 \cdot 10^{-8} \)
\(a_{25}= +1.89145618 \pm 2.2 \cdot 10^{-8} \) \(a_{26}= +2.01403496 \pm 2.7 \cdot 10^{-8} \) \(a_{27}= +0.47845756 \pm 2.3 \cdot 10^{-8} \)
\(a_{28}= -0.55099510 \pm 1.8 \cdot 10^{-8} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +0.60648463 \pm 2.5 \cdot 10^{-8} \)
\(a_{31}= -0.60564025 \pm 2.1 \cdot 10^{-8} \) \(a_{32}= -1.43393259 \pm 3.6 \cdot 10^{-8} \) \(a_{33}= -0.18610230 \pm 2.0 \cdot 10^{-8} \)
\(a_{34}= -1.46366381 \pm 2.7 \cdot 10^{-8} \) \(a_{35}= +0.85994987 \pm 2.4 \cdot 10^{-8} \) \(a_{36}= -1.02318414 \pm 2.8 \cdot 10^{-8} \)
\(a_{37}= +1.15600546 \pm 2.2 \cdot 10^{-8} \) \(a_{38}= +0.63241477 \pm 1.9 \cdot 10^{-8} \) \(a_{39}= -0.34378203 \pm 2.2 \cdot 10^{-8} \)
\(a_{40}= -0.22002552 \pm 2.9 \cdot 10^{-8} \) \(a_{41}= -1.42676996 \pm 2.1 \cdot 10^{-8} \) \(a_{42}= +0.18037499 \pm 2.1 \cdot 10^{-8} \)
\(a_{43}= -1.14035250 \pm 2.1 \cdot 10^{-8} \) \(a_{44}= +0.82176153 \pm 2.3 \cdot 10^{-8} \) \(a_{45}= +1.59690545 \pm 1.9 \cdot 10^{-8} \)
\(a_{46}= -2.02937697 \pm 2.1 \cdot 10^{-8} \) \(a_{47}= -0.53143172 \pm 2.0 \cdot 10^{-8} \) \(a_{48}= +0.22267581 \pm 2.8 \cdot 10^{-8} \)
\(a_{49}= -0.74424175 \pm 1.8 \cdot 10^{-8} \) \(a_{50}= +2.73412868 \pm 2.4 \cdot 10^{-8} \) \(a_{51}= +0.24983742 \pm 2.2 \cdot 10^{-8} \)
\(a_{52}= +1.51801914 \pm 3.0 \cdot 10^{-8} \) \(a_{53}= +0.12833951 \pm 2.3 \cdot 10^{-8} \) \(a_{54}= +0.69161768 \pm 3.0 \cdot 10^{-8} \)
\(a_{55}= -1.28254086 \pm 2.0 \cdot 10^{-8} \) \(a_{56}= -0.06543793 \pm 2.3 \cdot 10^{-8} \) \(a_{57}= -0.10794889 \pm 1.9 \cdot 10^{-8} \)
\(a_{58}= +0.26842544 \pm 3.7 \cdot 10^{-8} \) \(a_{59}= +0.84387344 \pm 2.0 \cdot 10^{-8} \) \(a_{60}= +0.45711981 \pm 2.4 \cdot 10^{-8} \)

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