Properties

Label 3.61
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 21.10869
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: \(21.1086958873217964417746407169 \pm 2 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.00192450 \pm 2.3 \cdot 10^{-1} \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.00385271 \pm 4.3 \cdot 10^{-1} \) \(a_{5}= +0.52988547 \pm 3.2 \cdot 10^{-1} \) \(a_{6}= \pm0.57846138 \pm 1.3 \cdot 10^{-1} \)
\(a_{7}= +0.46727889 \pm 2.6 \cdot 10^{-1} \) \(a_{8}= -0.99806438 \pm 2.9 \cdot 10^{-1} \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= +0.53090524 \pm 1.8 \cdot 10^{-1} \) \(a_{11}= +1.08438107 \pm 2.9 \cdot 10^{-1} \) \(a_{12}= \pm0.00222436 \pm 2.4 \cdot 10^{-1} \)
\(a_{13}= -0.76823709 \pm 2.9 \cdot 10^{-1} \) \(a_{14}= +0.46817817 \pm 1.8 \cdot 10^{-1} \) \(a_{15}= \pm0.30592952 \pm 1.8 \cdot 10^{-1} \)
\(a_{16}= -1.00383787 \pm 3.4 \cdot 10^{-1} \) \(a_{17}= -1.72161513 \pm 2.1 \cdot 10^{-1} \) \(a_{18}= \pm0.33397483 \pm 7.9 \cdot 10^{-2} \)
\(a_{19}= -0.41615581 \pm 1.7 \cdot 10^{-1} \) \(a_{20}= +0.00204150 \pm 3.0 \cdot 10^{-1} \) \(a_{21}= \pm0.26978360 \pm 1.5 \cdot 10^{-1} \)
\(a_{22}= +1.08646797 \pm 1.5 \cdot 10^{-1} \) \(a_{23}= +0.60292757 \pm 6.5 \cdot 10^{-1} \) \(a_{24}= \pm0.57623274 \pm 1.6 \cdot 10^{-1} \)
\(a_{25}= -0.71922139 \pm 2.7 \cdot 10^{-1} \) \(a_{26}= -0.76971556 \pm 1.0 \cdot 10^{-1} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= +0.00180029 \pm 1.7 \cdot 10^{-1} \) \(a_{29}= -1.43049394 \pm 6.1 \cdot 10^{-1} \) \(a_{30}= \pm0.30651828 \pm 1.0 \cdot 10^{-1} \)
\(a_{31}= -0.99019983 \pm 2.7 \cdot 10^{-1} \) \(a_{32}= -0.00770538 \pm 3.8 \cdot 10^{-1} \) \(a_{33}= \pm0.62606770 \pm 1.7 \cdot 10^{-1} \)
\(a_{34}= -1.72492838 \pm 2.6 \cdot 10^{-1} \) \(a_{35}= +0.24760430 \pm 1.1 \cdot 10^{-1} \) \(a_{36}= \pm0.00128424 \pm 1.4 \cdot 10^{-1} \)
\(a_{37}= +0.14775703 \pm 3.3 \cdot 10^{-1} \) \(a_{38}= -0.41695671 \pm 8.0 \cdot 10^{-2} \) \(a_{39}= \pm0.44354189 \pm 1.6 \cdot 10^{-1} \)
\(a_{40}= -0.52885981 \pm 1.7 \cdot 10^{-1} \) \(a_{41}= -1.61442358 \pm 6.3 \cdot 10^{-1} \) \(a_{42}= \pm0.27030279 \pm 1.0 \cdot 10^{-1} \)
\(a_{43}= +1.53834739 \pm 4.1 \cdot 10^{-1} \) \(a_{44}= +0.00417781 \pm 2.6 \cdot 10^{-1} \) \(a_{45}= \pm0.17662849 \pm 1.0 \cdot 10^{-1} \)
\(a_{46}= +0.60408791 \pm 1.9 \cdot 10^{-1} \) \(a_{47}= -1.44990599 \pm 5.2 \cdot 10^{-1} \) \(a_{48}= \pm0.57956606 \pm 2.0 \cdot 10^{-1} \)
\(a_{49}= -0.78165044 \pm 4.5 \cdot 10^{-1} \) \(a_{50}= -0.72060553 \pm 1.3 \cdot 10^{-1} \) \(a_{51}= \pm0.99397496 \pm 1.2 \cdot 10^{-1} \)
\(a_{52}= -0.00295980 \pm 2.6 \cdot 10^{-1} \) \(a_{53}= +0.61794411 \pm 2.6 \cdot 10^{-1} \) \(a_{54}= \pm0.19282046 \pm 4.5 \cdot 10^{-2} \)
\(a_{55}= +0.57459778 \pm 2.0 \cdot 10^{-1} \) \(a_{56}= -0.46637442 \pm 2.5 \cdot 10^{-1} \) \(a_{57}= \pm0.24026767 \pm 1.0 \cdot 10^{-1} \)
\(a_{58}= -1.43324693 \pm 2.5 \cdot 10^{-1} \) \(a_{59}= +0.16682293 \pm 4.1 \cdot 10^{-1} \) \(a_{60}= \pm0.00117866 \pm 1.7 \cdot 10^{-1} \)

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