Properties

Label 3.72
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 22.67111
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: \(22.6711177685244672920555186727 \pm 6 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.06470954 \pm 8.4 \cdot 10^{-1} \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.99581268 \pm 1.5 \) \(a_{5}= +1.71719791 \pm 1.1 \) \(a_{6}= \pm0.03736007 \pm 4.8 \cdot 10^{-1} \)
\(a_{7}= -1.39368354 \pm 9.5 \cdot 10^{-1} \) \(a_{8}= -0.12914812 \pm 1.0 \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= +0.11111909 \pm 6.6 \cdot 10^{-1} \) \(a_{11}= +0.59609143 \pm 1.0 \) \(a_{12}= \pm0.57493272 \pm 8.8 \cdot 10^{-1} \)
\(a_{13}= +0.67598258 \pm 1.0 \) \(a_{14}= -0.09018462 \pm 6.5 \cdot 10^{-1} \) \(a_{15}= \pm0.99142468 \pm 6.6 \cdot 10^{-1} \)
\(a_{16}= +0.98745556 \pm 1.2 \) \(a_{17}= +0.34828965 \pm 7.7 \cdot 10^{-1} \) \(a_{18}= \pm0.02156985 \pm 2.8 \cdot 10^{-1} \)
\(a_{19}= +0.27396279 \pm 6.2 \cdot 10^{-1} \) \(a_{20}= -1.71000745 \pm 1.0 \) \(a_{21}= \pm0.80464357 \pm 5.5 \cdot 10^{-1} \)
\(a_{22}= +0.03857280 \pm 5.3 \cdot 10^{-1} \) \(a_{23}= -1.19018916 \pm 2.3 \) \(a_{24}= \pm0.07456370 \pm 5.9 \cdot 10^{-1} \)
\(a_{25}= +1.94876867 \pm 9.5 \cdot 10^{-1} \) \(a_{26}= +0.04374252 \pm 3.6 \cdot 10^{-1} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= +1.38784774 \pm 6.3 \cdot 10^{-1} \) \(a_{29}= -0.94503907 \pm 2.1 \) \(a_{30}= \pm0.06415463 \pm 3.8 \cdot 10^{-1} \)
\(a_{31}= -1.11058425 \pm 9.7 \cdot 10^{-1} \) \(a_{32}= +0.19304591 \pm 1.3 \) \(a_{33}= \pm0.34415355 \pm 6.1 \cdot 10^{-1} \)
\(a_{34}= +0.02253766 \pm 9.3 \cdot 10^{-1} \) \(a_{35}= -2.39323047 \pm 4.2 \cdot 10^{-1} \) \(a_{36}= \pm0.33193756 \pm 5.0 \cdot 10^{-1} \)
\(a_{37}= -0.83646081 \pm 1.1 \) \(a_{38}= +0.01772801 \pm 2.8 \cdot 10^{-1} \) \(a_{39}= \pm0.39027873 \pm 5.9 \cdot 10^{-1} \)
\(a_{40}= -0.22177288 \pm 6.3 \cdot 10^{-1} \) \(a_{41}= -0.21089030 \pm 2.2 \) \(a_{42}= \pm0.05206811 \pm 3.7 \cdot 10^{-1} \)
\(a_{43}= -1.29372433 \pm 1.4 \) \(a_{44}= -0.59359541 \pm 9.3 \cdot 10^{-1} \) \(a_{45}= \pm0.57239930 \pm 3.8 \cdot 10^{-1} \)
\(a_{46}= -0.07701659 \pm 6.7 \cdot 10^{-1} \) \(a_{47}= +0.03521353 \pm 1.8 \) \(a_{48}= \pm0.57010773 \pm 7.1 \cdot 10^{-1} \)
\(a_{49}= +0.94235382 \pm 1.6 \) \(a_{50}= +0.12610392 \pm 4.7 \cdot 10^{-1} \) \(a_{51}= \pm0.20108512 \pm 4.4 \cdot 10^{-1} \)
\(a_{52}= -0.67315202 \pm 9.4 \cdot 10^{-1} \) \(a_{53}= -0.90582113 \pm 9.2 \cdot 10^{-1} \) \(a_{54}= \pm0.01245336 \pm 1.6 \cdot 10^{-1} \)
\(a_{55}= +1.02360697 \pm 7.4 \cdot 10^{-1} \) \(a_{56}= +0.17999161 \pm 9.1 \cdot 10^{-1} \) \(a_{57}= \pm0.15817249 \pm 3.6 \cdot 10^{-1} \)
\(a_{58}= -0.06115304 \pm 9.1 \cdot 10^{-1} \) \(a_{59}= +0.11306681 \pm 1.4 \) \(a_{60}= \pm0.98727326 \pm 6.2 \cdot 10^{-1} \)

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