Properties

Label 3.39
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 17.28832
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(17.2883277696958706487727893028 \pm 6 \cdot 10^{-6}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.15268036 \pm 5.8 \cdot 10^{-4} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.97668871 \pm 1.0 \cdot 10^{-3} \) \(a_{5}= -1.63487950 \pm 8.0 \cdot 10^{-4} \) \(a_{6}= +0.08815005 \pm 5.8 \cdot 10^{-4} \)
\(a_{7}= +0.43448281 \pm 6.6 \cdot 10^{-4} \) \(a_{8}= -0.30180154 \pm 7.1 \cdot 10^{-4} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.24961399 \pm 4.6 \cdot 10^{-4} \) \(a_{11}= +1.63699990 \pm 7.3 \cdot 10^{-4} \) \(a_{12}= -0.56389149 \pm 1.0 \cdot 10^{-3} \)
\(a_{13}= -0.82216821 \pm 7.1 \cdot 10^{-4} \) \(a_{14}= +0.06633699 \pm 4.5 \cdot 10^{-4} \) \(a_{15}= -0.94389812 \pm 8.0 \cdot 10^{-4} \)
\(a_{16}= +0.93060954 \pm 8.6 \cdot 10^{-4} \) \(a_{17}= -0.04830386 \pm 5.3 \cdot 10^{-4} \) \(a_{18}= +0.05089345 \pm 5.8 \cdot 10^{-4} \)
\(a_{19}= +1.12670635 \pm 4.3 \cdot 10^{-4} \) \(a_{20}= +1.59676834 \pm 7.5 \cdot 10^{-4} \) \(a_{21}= +0.25084877 \pm 6.6 \cdot 10^{-4} \)
\(a_{22}= +0.24993773 \pm 3.7 \cdot 10^{-4} \) \(a_{23}= +0.32871172 \pm 1.6 \cdot 10^{-3} \) \(a_{24}= -0.17424520 \pm 7.1 \cdot 10^{-4} \)
\(a_{25}= +1.67283097 \pm 6.6 \cdot 10^{-4} \) \(a_{26}= -0.12552894 \pm 2.5 \cdot 10^{-4} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.42435445 \pm 4.3 \cdot 10^{-4} \) \(a_{29}= +0.27864256 \pm 1.5 \cdot 10^{-3} \) \(a_{30}= -0.14411470 \pm 1.3 \cdot 10^{-3} \)
\(a_{31}= -0.35895031 \pm 6.8 \cdot 10^{-4} \) \(a_{32}= +0.44388734 \pm 9.5 \cdot 10^{-4} \) \(a_{33}= +0.94512233 \pm 7.3 \cdot 10^{-4} \)
\(a_{34}= -0.00737505 \pm 6.5 \cdot 10^{-4} \) \(a_{35}= -0.71032703 \pm 2.9 \cdot 10^{-4} \) \(a_{36}= -0.32556290 \pm 1.0 \cdot 10^{-3} \)
\(a_{37}= +0.05009193 \pm 8.1 \cdot 10^{-4} \) \(a_{38}= +0.17202593 \pm 1.9 \cdot 10^{-4} \) \(a_{39}= -0.47467904 \pm 7.1 \cdot 10^{-4} \)
\(a_{40}= +0.49340915 \pm 4.4 \cdot 10^{-4} \) \(a_{41}= +0.36101357 \pm 1.5 \cdot 10^{-3} \) \(a_{42}= +0.03829968 \pm 1.2 \cdot 10^{-3} \)
\(a_{43}= +1.16288445 \pm 1.0 \cdot 10^{-3} \) \(a_{44}= -1.59883931 \pm 6.4 \cdot 10^{-4} \) \(a_{45}= -0.54495983 \pm 8.0 \cdot 10^{-4} \)
\(a_{46}= +0.05018782 \pm 4.6 \cdot 10^{-4} \) \(a_{47}= +0.42383768 \pm 1.2 \cdot 10^{-3} \) \(a_{48}= +0.53728767 \pm 8.6 \cdot 10^{-4} \)
\(a_{49}= -0.81122469 \pm 1.1 \cdot 10^{-3} \) \(a_{50}= +0.25540843 \pm 3.2 \cdot 10^{-4} \) \(a_{51}= -0.02788825 \pm 5.3 \cdot 10^{-4} \)
\(a_{52}= +0.80300240 \pm 6.5 \cdot 10^{-4} \) \(a_{53}= +0.96210845 \pm 6.4 \cdot 10^{-4} \) \(a_{54}= +0.02938335 \pm 5.8 \cdot 10^{-4} \)
\(a_{55}= -2.67629757 \pm 5.1 \cdot 10^{-4} \) \(a_{56}= -0.13112758 \pm 6.3 \cdot 10^{-4} \) \(a_{57}= +0.65050421 \pm 4.3 \cdot 10^{-4} \)
\(a_{58}= +0.04254325 \pm 6.3 \cdot 10^{-4} \) \(a_{59}= +0.27465322 \pm 1.0 \cdot 10^{-3} \) \(a_{60}= +0.92189463 \pm 1.8 \cdot 10^{-3} \)

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