Properties

Label 3.36
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 16.96539
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: \(16.9653979482295206395782966382 \pm 4 \cdot 10^{-6}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.27140621 \pm 3.9 \cdot 10^{-3} \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.92633867 \pm 7.0 \cdot 10^{-3} \) \(a_{5}= +0.88701142 \pm 5.3 \cdot 10^{-3} \) \(a_{6}= \pm0.15669645 \pm 2.2 \cdot 10^{-3} \)
\(a_{7}= +0.44233409 \pm 4.4 \cdot 10^{-3} \) \(a_{8}= +0.52282028 \pm 4.7 \cdot 10^{-3} \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= -0.24074041 \pm 3.0 \cdot 10^{-3} \) \(a_{11}= -0.48209419 \pm 4.9 \cdot 10^{-3} \) \(a_{12}= \pm0.53482188 \pm 4.0 \cdot 10^{-3} \)
\(a_{13}= +1.36615398 \pm 4.7 \cdot 10^{-3} \) \(a_{14}= -0.12005222 \pm 3.0 \cdot 10^{-3} \) \(a_{15}= \pm0.51211628 \pm 3.1 \cdot 10^{-3} \)
\(a_{16}= +0.78444199 \pm 5.7 \cdot 10^{-3} \) \(a_{17}= -1.20406801 \pm 3.5 \cdot 10^{-3} \) \(a_{18}= \pm0.09046874 \pm 1.3 \cdot 10^{-3} \)
\(a_{19}= -1.58490148 \pm 2.9 \cdot 10^{-3} \) \(a_{20}= -0.82167298 \pm 5.0 \cdot 10^{-3} \) \(a_{21}= \pm0.25538170 \pm 2.5 \cdot 10^{-3} \)
\(a_{22}= +0.13084336 \pm 2.4 \cdot 10^{-3} \) \(a_{23}= -0.88938742 \pm 1.0 \cdot 10^{-2} \) \(a_{24}= \pm0.30185043 \pm 2.7 \cdot 10^{-3} \)
\(a_{25}= -0.21321074 \pm 4.4 \cdot 10^{-3} \) \(a_{26}= -0.37078268 \pm 1.6 \cdot 10^{-3} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -0.40975117 \pm 2.9 \cdot 10^{-3} \) \(a_{29}= +1.36067712 \pm 1.0 \cdot 10^{-2} \) \(a_{30}= \pm0.13899154 \pm 1.7 \cdot 10^{-3} \)
\(a_{31}= -1.05564852 \pm 4.5 \cdot 10^{-3} \) \(a_{32}= -0.73572271 \pm 6.3 \cdot 10^{-3} \) \(a_{33}= \pm0.27833721 \pm 2.8 \cdot 10^{-3} \)
\(a_{34}= +0.32679154 \pm 4.3 \cdot 10^{-3} \) \(a_{35}= +0.39235539 \pm 1.9 \cdot 10^{-3} \) \(a_{36}= \pm0.30877956 \pm 2.3 \cdot 10^{-3} \)
\(a_{37}= +0.35776429 \pm 5.4 \cdot 10^{-3} \) \(a_{38}= +0.43015211 \pm 1.3 \cdot 10^{-3} \) \(a_{39}= \pm0.78874937 \pm 2.7 \cdot 10^{-3} \)
\(a_{40}= +0.46374756 \pm 2.9 \cdot 10^{-3} \) \(a_{41}= -1.34131023 \pm 1.0 \cdot 10^{-2} \) \(a_{42}= \pm0.06931218 \pm 1.7 \cdot 10^{-3} \)
\(a_{43}= +0.57469831 \pm 6.8 \cdot 10^{-3} \) \(a_{44}= +0.44658249 \pm 4.3 \cdot 10^{-3} \) \(a_{45}= \pm0.29567047 \pm 1.7 \cdot 10^{-3} \)
\(a_{46}= +0.24138527 \pm 3.1 \cdot 10^{-3} \) \(a_{47}= -0.04214236 \pm 8.5 \cdot 10^{-3} \) \(a_{48}= \pm0.45289780 \pm 3.3 \cdot 10^{-3} \)
\(a_{49}= -0.80434055 \pm 7.4 \cdot 10^{-3} \) \(a_{50}= +0.05786672 \pm 2.1 \cdot 10^{-3} \) \(a_{51}= \pm0.69516899 \pm 2.0 \cdot 10^{-3} \)
\(a_{52}= -1.26552126 \pm 4.3 \cdot 10^{-3} \) \(a_{53}= +1.30030034 \pm 4.2 \cdot 10^{-3} \) \(a_{54}= \pm0.05223215 \pm 7.5 \cdot 10^{-4} \)
\(a_{55}= -0.42762305 \pm 3.4 \cdot 10^{-3} \) \(a_{56}= +0.23126123 \pm 4.2 \cdot 10^{-3} \) \(a_{57}= \pm0.91504330 \pm 1.6 \cdot 10^{-3} \)
\(a_{58}= -0.36929623 \pm 4.2 \cdot 10^{-3} \) \(a_{59}= -0.53475422 \pm 6.8 \cdot 10^{-3} \) \(a_{60}= \pm0.47439311 \pm 2.8 \cdot 10^{-3} \)

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