Properties

Label 3.55
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 20.40943
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(20.4094388902703688987155695619 \pm 10 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.76955543 \pm 9.7 \cdot 10^{-2} \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.40778443 \pm 1.7 \cdot 10^{-1} \) \(a_{5}= -0.24977912 \pm 1.3 \cdot 10^{-1} \) \(a_{6}= \pm0.44430304 \pm 5.6 \cdot 10^{-2} \)
\(a_{7}= -0.54180923 \pm 1.1 \cdot 10^{-1} \) \(a_{8}= +1.08336816 \pm 1.1 \cdot 10^{-1} \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= +0.19221888 \pm 7.7 \cdot 10^{-2} \) \(a_{11}= -0.60561611 \pm 1.2 \cdot 10^{-1} \) \(a_{12}= \pm0.23543445 \pm 1.0 \cdot 10^{-1} \)
\(a_{13}= +1.62354307 \pm 1.1 \cdot 10^{-1} \) \(a_{14}= +0.41695224 \pm 7.5 \cdot 10^{-2} \) \(a_{15}= \pm0.14421004 \pm 7.7 \cdot 10^{-2} \)
\(a_{16}= -0.42592742 \pm 1.4 \cdot 10^{-1} \) \(a_{17}= +0.42782663 \pm 9.0 \cdot 10^{-2} \) \(a_{18}= \pm0.25651848 \pm 3.2 \cdot 10^{-2} \)
\(a_{19}= +1.14527548 \pm 7.3 \cdot 10^{-2} \) \(a_{20}= +0.10185604 \pm 1.2 \cdot 10^{-1} \) \(a_{21}= \pm0.31281371 \pm 6.3 \cdot 10^{-2} \)
\(a_{22}= +0.46605517 \pm 6.2 \cdot 10^{-2} \) \(a_{23}= +0.74811490 \pm 2.6 \cdot 10^{-1} \) \(a_{24}= \pm0.62548290 \pm 6.9 \cdot 10^{-2} \)
\(a_{25}= -0.93761039 \pm 1.1 \cdot 10^{-1} \) \(a_{26}= -1.24940640 \pm 4.2 \cdot 10^{-2} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= +0.22094137 \pm 7.3 \cdot 10^{-2} \) \(a_{29}= -1.26224600 \pm 2.5 \cdot 10^{-1} \) \(a_{30}= \pm0.11097762 \pm 4.4 \cdot 10^{-2} \)
\(a_{31}= -1.56533086 \pm 1.1 \cdot 10^{-1} \) \(a_{32}= -0.75559340 \pm 1.5 \cdot 10^{-1} \) \(a_{33}= \pm0.34965263 \pm 7.0 \cdot 10^{-2} \)
\(a_{34}= -0.32923630 \pm 1.0 \cdot 10^{-1} \) \(a_{35}= +0.13533263 \pm 4.8 \cdot 10^{-2} \) \(a_{36}= \pm0.13592814 \pm 5.9 \cdot 10^{-2} \)
\(a_{37}= +0.24810186 \pm 1.3 \cdot 10^{-1} \) \(a_{38}= -0.88135297 \pm 3.3 \cdot 10^{-2} \) \(a_{39}= \pm0.93735303 \pm 6.9 \cdot 10^{-2} \)
\(a_{40}= -0.27060274 \pm 7.4 \cdot 10^{-2} \) \(a_{41}= +1.62610287 \pm 2.5 \cdot 10^{-1} \) \(a_{42}= \pm0.24072749 \pm 4.3 \cdot 10^{-2} \)
\(a_{43}= -0.29849590 \pm 1.7 \cdot 10^{-1} \) \(a_{44}= +0.24696082 \pm 1.0 \cdot 10^{-1} \) \(a_{45}= \pm0.08325971 \pm 4.4 \cdot 10^{-2} \)
\(a_{46}= -0.57571588 \pm 7.8 \cdot 10^{-2} \) \(a_{47}= +0.12131644 \pm 2.1 \cdot 10^{-1} \) \(a_{48}= \pm0.24590931 \pm 8.3 \cdot 10^{-2} \)
\(a_{49}= -0.70644275 \pm 1.8 \cdot 10^{-1} \) \(a_{50}= +0.72154317 \pm 5.4 \cdot 10^{-2} \) \(a_{51}= \pm0.24700582 \pm 5.2 \cdot 10^{-2} \)
\(a_{52}= -0.66205559 \pm 1.0 \cdot 10^{-1} \) \(a_{53}= +1.27836064 \pm 1.0 \cdot 10^{-1} \) \(a_{54}= \pm0.14810101 \pm 1.8 \cdot 10^{-2} \)
\(a_{55}= +0.15127026 \pm 8.6 \cdot 10^{-2} \) \(a_{56}= -0.58697887 \pm 1.0 \cdot 10^{-1} \) \(a_{57}= \pm0.66122510 \pm 4.2 \cdot 10^{-2} \)
\(a_{58}= +0.97136827 \pm 1.0 \cdot 10^{-1} \) \(a_{59}= -1.64265548 \pm 1.7 \cdot 10^{-1} \) \(a_{60}= \pm0.05880661 \pm 7.2 \cdot 10^{-2} \)

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