Properties

Label 3.24
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 13.99317
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(13.9931761915667650038932006134 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.64166864 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.58826136 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.23230069 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.37046756 \pm 1.9 \cdot 10^{-8} \)
\(a_{7}= +0.49911333 \pm 1 \cdot 10^{-8} \) \(a_{8}= +1.01913750 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.14906007 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.34627569 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.33963285 \pm 1.6 \cdot 10^{-8} \)
\(a_{13}= -1.95599330 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.32026537 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.13411886 \pm 1.1 \cdot 10^{-8} \)
\(a_{16}= -0.06568722 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.39631315 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.21388955 \pm 1.9 \cdot 10^{-8} \)
\(a_{19}= +0.47163237 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= -0.13665352 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.28816322 \pm 1.5 \cdot 10^{-8} \)
\(a_{22}= +0.22219425 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.19833433 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.58839931 \pm 1.2 \cdot 10^{-8} \)
\(a_{25}= -0.94603639 \pm 1 \cdot 10^{-8} \) \(a_{26}= +1.25509956 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.29360908 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.27586335 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.08605987 \pm 2.0 \cdot 10^{-8} \)
\(a_{31}= +0.52058242 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.97698808 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.19992236 \pm 1.3 \cdot 10^{-8} \)
\(a_{34}= +0.89597036 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.11594437 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.19608712 \pm 1.6 \cdot 10^{-8} \)
\(a_{37}= +0.93320094 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.30263170 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= -1.12929326 \pm 1.4 \cdot 10^{-8} \)
\(a_{40}= +0.23674634 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.78294135 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.18490530 \pm 2.4 \cdot 10^{-8} \)
\(a_{43}= +1.51636211 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.20370061 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.07743356 \pm 1.1 \cdot 10^{-8} \)
\(a_{46}= +0.76893356 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.40858951 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.03792453 \pm 1.8 \cdot 10^{-8} \)
\(a_{49}= -0.75088588 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.60704188 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.80616177 \pm 1.6 \cdot 10^{-8} \)
\(a_{52}= +1.15063527 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.02788536 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.12348919 \pm 1.9 \cdot 10^{-8} \)
\(a_{55}= -0.08044008 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.50866511 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.27229707 \pm 2.0 \cdot 10^{-8} \)
\(a_{58}= +0.17701286 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.78692022 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.07889694 \pm 1.6 \cdot 10^{-8} \)

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