Properties

Label 3.26
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 14.62623
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(14.6262358403662403553443790824 \pm 5 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.55536200 \pm 3.0 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.69157305 \pm 1.8 \cdot 10^{-8} \) \(a_{5}= -0.95281834 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.32063840 \pm 4.0 \cdot 10^{-8} \)
\(a_{7}= +1.83744158 \pm 1.7 \cdot 10^{-8} \) \(a_{8}= -0.93943539 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.52915910 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.01575162 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.39927988 \pm 2.9 \cdot 10^{-8} \)
\(a_{13}= +1.03096988 \pm 1.2 \cdot 10^{-8} \) \(a_{14}= +1.02044524 \pm 2.2 \cdot 10^{-8} \) \(a_{15}= +0.55010992 \pm 1.3 \cdot 10^{-8} \)
\(a_{16}= +0.16984632 \pm 2.6 \cdot 10^{-8} \) \(a_{17}= +0.64782636 \pm 2.1 \cdot 10^{-8} \) \(a_{18}= +0.18512067 \pm 4.0 \cdot 10^{-8} \)
\(a_{19}= +0.63339593 \pm 3.4 \cdot 10^{-8} \) \(a_{20}= +0.65894348 \pm 1 \cdot 10^{-8} \) \(a_{21}= -1.06084739 \pm 2.7 \cdot 10^{-8} \)
\(a_{22}= -0.00874785 \pm 1.2 \cdot 10^{-8} \) \(a_{23}= +0.20959728 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.54238328 \pm 1.7 \cdot 10^{-8} \)
\(a_{25}= -0.09213721 \pm 2.2 \cdot 10^{-8} \) \(a_{26}= +0.57256150 \pm 1.7 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -1.27072507 \pm 1.4 \cdot 10^{-8} \) \(a_{29}= +0.31961885 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.30551015 \pm 4.3 \cdot 10^{-8} \)
\(a_{31}= -0.20102882 \pm 2.5 \cdot 10^{-8} \) \(a_{32}= +1.03376159 \pm 2.8 \cdot 10^{-8} \) \(a_{33}= +0.00909420 \pm 1.9 \cdot 10^{-8} \)
\(a_{34}= +0.35977815 \pm 2.9 \cdot 10^{-8} \) \(a_{35}= -1.75074803 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.23052435 \pm 2.9 \cdot 10^{-8} \)
\(a_{37}= +0.79454377 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.35176403 \pm 4.6 \cdot 10^{-8} \) \(a_{39}= -0.59523074 \pm 2.3 \cdot 10^{-8} \)
\(a_{40}= +0.89511127 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.17596149 \pm 2.4 \cdot 10^{-8} \) \(a_{42}= -0.58915433 \pm 5.8 \cdot 10^{-8} \)
\(a_{43}= +0.77907495 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.01089339 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.31760611 \pm 1.3 \cdot 10^{-8} \)
\(a_{46}= +0.11640236 \pm 1.1 \cdot 10^{-8} \) \(a_{47}= -1.83642604 \pm 2.2 \cdot 10^{-8} \) \(a_{48}= -0.09806082 \pm 3.6 \cdot 10^{-8} \)
\(a_{49}= +2.37619156 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.05116951 \pm 3.0 \cdot 10^{-8} \) \(a_{51}= -0.37402273 \pm 3.2 \cdot 10^{-8} \)
\(a_{52}= -0.71299098 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= +1.34409416 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.10687947 \pm 4.0 \cdot 10^{-8} \)
\(a_{55}= +0.01500843 \pm 1 \cdot 10^{-8} \) \(a_{56}= -1.72615766 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.36569131 \pm 4.5 \cdot 10^{-8} \)
\(a_{58}= +0.17750416 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.01496206 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.38044120 \pm 3.1 \cdot 10^{-8} \)

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