Properties

Label 29.30
Level $29$
Weight $0$
Character 29.1
Symmetry odd
\(R\) 4.003611
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(4.00361102662478373194051468741 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.23038571 \pm 7.3 \cdot 10^{-7} \) \(a_{3}= -1.72773637 \pm 6.9 \cdot 10^{-7} \)
\(a_{4}= -0.94692242 \pm 7.3 \cdot 10^{-7} \) \(a_{5}= +1.91334301 \pm 6.5 \cdot 10^{-7} \) \(a_{6}= -0.39804577 \pm 8.4 \cdot 10^{-7} \)
\(a_{7}= -0.64961391 \pm 6.1 \cdot 10^{-7} \) \(a_{8}= -0.44854311 \pm 6.1 \cdot 10^{-7} \) \(a_{9}= +1.98507297 \pm 6.4 \cdot 10^{-7} \)
\(a_{10}= +0.44080689 \pm 8.0 \cdot 10^{-7} \) \(a_{11}= +0.29686329 \pm 6.0 \cdot 10^{-7} \) \(a_{12}= +1.63603231 \pm 8.5 \cdot 10^{-7} \)
\(a_{13}= +0.00961264 \pm 5.7 \cdot 10^{-7} \) \(a_{14}= -0.14966176 \pm 8.0 \cdot 10^{-7} \) \(a_{15}= -3.30575231 \pm 7.3 \cdot 10^{-7} \)
\(a_{16}= +0.84358450 \pm 6.3 \cdot 10^{-7} \) \(a_{17}= +0.86347394 \pm 6.4 \cdot 10^{-7} \) \(a_{18}= +0.45733245 \pm 8.4 \cdot 10^{-7} \)
\(a_{19}= +0.87837493 \pm 5.3 \cdot 10^{-7} \) \(a_{20}= -1.81178740 \pm 7.7 \cdot 10^{-7} \) \(a_{21}= +1.12236158 \pm 6.6 \cdot 10^{-7} \)
\(a_{22}= +0.06839306 \pm 7.5 \cdot 10^{-7} \) \(a_{23}= -0.92786699 \pm 6.3 \cdot 10^{-7} \) \(a_{24}= +0.77496424 \pm 6.6 \cdot 10^{-7} \)
\(a_{25}= +2.66088148 \pm 6.0 \cdot 10^{-7} \) \(a_{26}= +0.00221461 \pm 6.1 \cdot 10^{-7} \) \(a_{27}= -1.70194640 \pm 6.1 \cdot 10^{-7} \)
\(a_{28}= +0.61513398 \pm 8.1 \cdot 10^{-7} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.76159810 \pm 7.9 \cdot 10^{-7} \)
\(a_{31}= +0.80275448 \pm 5.7 \cdot 10^{-7} \) \(a_{32}= +0.64289292 \pm 6.4 \cdot 10^{-7} \) \(a_{33}= -0.51290151 \pm 6.9 \cdot 10^{-7} \)
\(a_{34}= +0.19893206 \pm 6.4 \cdot 10^{-7} \) \(a_{35}= -1.24293423 \pm 6.5 \cdot 10^{-7} \) \(a_{36}= -1.87971011 \pm 8.4 \cdot 10^{-7} \)
\(a_{37}= +0.12699191 \pm 5.7 \cdot 10^{-7} \) \(a_{38}= +0.20236503 \pm 5.5 \cdot 10^{-7} \) \(a_{39}= -0.01660811 \pm 6.3 \cdot 10^{-7} \)
\(a_{40}= -0.85821682 \pm 6.7 \cdot 10^{-7} \) \(a_{41}= +0.32359359 \pm 5.9 \cdot 10^{-7} \) \(a_{42}= +0.25857607 \pm 8.6 \cdot 10^{-7} \)
\(a_{43}= -0.35714316 \pm 5.3 \cdot 10^{-7} \) \(a_{44}= -0.28110651 \pm 6.8 \cdot 10^{-7} \) \(a_{45}= +3.79812550 \pm 6.8 \cdot 10^{-7} \)
\(a_{46}= -0.21376730 \pm 8.2 \cdot 10^{-7} \) \(a_{47}= +1.33206087 \pm 5.3 \cdot 10^{-7} \) \(a_{48}= -1.45749163 \pm 6.7 \cdot 10^{-7} \)
\(a_{49}= -0.57800177 \pm 5.7 \cdot 10^{-7} \) \(a_{50}= +0.61302907 \pm 6.9 \cdot 10^{-7} \) \(a_{51}= -1.49185533 \pm 6.5 \cdot 10^{-7} \)
\(a_{52}= -0.00910242 \pm 7.1 \cdot 10^{-7} \) \(a_{53}= -0.46856434 \pm 5.8 \cdot 10^{-7} \) \(a_{54}= -0.39210413 \pm 7.6 \cdot 10^{-7} \)
\(a_{55}= +0.56800131 \pm 6.2 \cdot 10^{-7} \) \(a_{56}= +0.29137984 \pm 7.1 \cdot 10^{-7} \) \(a_{57}= -1.51760031 \pm 5.8 \cdot 10^{-7} \)
\(a_{58}= +0.04278155 \pm 7.4 \cdot 10^{-7} \) \(a_{59}= +0.73743606 \pm 5.6 \cdot 10^{-7} \) \(a_{60}= +3.13029099 \pm 8.1 \cdot 10^{-7} \)

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