Properties

Label 3.17
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 11.88997
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(11.8899755746457276696737304641 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.48875054 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.21637817 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.05751345 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.85953053 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +1.38681493 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.32213312 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +1.57437372 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.86133456 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.70227626 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -0.35392162 \pm 1 \cdot 10^{-8} \) \(a_{14}= +2.06462147 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.61055567 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.73680232 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.46036502 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.49625018 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -1.26693887 \pm 1 \cdot 10^{-8} \) \(a_{20}= +1.28633627 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.80067797 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +1.28231229 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.95212914 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.18598364 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.11833469 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.52690101 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +1.68689140 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.26788428 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.90896509 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.24009795 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.41904797 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.49729174 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.68536868 \pm 1 \cdot 10^{-8} \) \(a_{35}= +1.46657544 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.40545939 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= +0.22069137 \pm 1 \cdot 10^{-8} \) \(a_{38}= -1.88615592 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.20433675 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.34066010 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.02289290 \pm 1 \cdot 10^{-8} \) \(a_{42}= -1.19200976 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.77379092 \pm 1 \cdot 10^{-8} \) \(a_{44}= +1.04770855 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.35250448 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -1.41748278 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.16073558 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.42539302 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= +0.92325564 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.17617084 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.26579187 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.43050254 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.60254607 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.28651018 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.91087288 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.44673902 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.73146750 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.39881287 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.79376959 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.74266659 \pm 1.0 \cdot 10^{-8} \)

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