Properties

Label 61.4
Level $61$
Weight $0$
Character 61.1
Symmetry odd
\(R\) 0.988037
Fricke sign $-1$

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Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(0.98803782409461983060629487577 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.72871372 \pm 1.8 \cdot 10^{-5} \) \(a_{3}= -1.59607866 \pm 1.7 \cdot 10^{-5} \)
\(a_{4}= +1.98845111 \pm 1.9 \cdot 10^{-5} \) \(a_{5}= +0.87895274 \pm 1.6 \cdot 10^{-5} \) \(a_{6}= +2.75916307 \pm 2.1 \cdot 10^{-5} \)
\(a_{7}= +0.44738222 \pm 1.5 \cdot 10^{-5} \) \(a_{8}= -1.70874899 \pm 1.9 \cdot 10^{-5} \) \(a_{9}= +1.54746708 \pm 1.7 \cdot 10^{-5} \)
\(a_{10}= -1.51945765 \pm 2.1 \cdot 10^{-5} \) \(a_{11}= +0.62757698 \pm 1.4 \cdot 10^{-5} \) \(a_{12}= -3.17372438 \pm 2.2 \cdot 10^{-5} \)
\(a_{13}= +0.04571295 \pm 1.4 \cdot 10^{-5} \) \(a_{14}= -0.77339578 \pm 1.9 \cdot 10^{-5} \) \(a_{15}= -1.40287770 \pm 1.7 \cdot 10^{-5} \)
\(a_{16}= +0.96548671 \pm 1.7 \cdot 10^{-5} \) \(a_{17}= +1.41084210 \pm 1.4 \cdot 10^{-5} \) \(a_{18}= -2.67512757 \pm 2.1 \cdot 10^{-5} \)
\(a_{19}= +1.64368378 \pm 1.4 \cdot 10^{-5} \) \(a_{20}= +1.74775454 \pm 2.2 \cdot 10^{-5} \) \(a_{21}= -0.71405721 \pm 1.7 \cdot 10^{-5} \)
\(a_{22}= -1.08490093 \pm 1.5 \cdot 10^{-5} \) \(a_{23}= -1.06724161 \pm 1.4 \cdot 10^{-5} \) \(a_{24}= +2.72729780 \pm 2.3 \cdot 10^{-5} \)
\(a_{25}= -0.22744209 \pm 1.7 \cdot 10^{-5} \) \(a_{26}= -0.07902461 \pm 1.7 \cdot 10^{-5} \) \(a_{27}= -0.87380053 \pm 1.6 \cdot 10^{-5} \)
\(a_{28}= +0.88959767 \pm 1.9 \cdot 10^{-5} \) \(a_{29}= +0.27699472 \pm 1.4 \cdot 10^{-5} \) \(a_{30}= +2.42517393 \pm 2.4 \cdot 10^{-5} \)
\(a_{31}= +0.98432277 \pm 1.5 \cdot 10^{-5} \) \(a_{32}= +0.03969888 \pm 1.7 \cdot 10^{-5} \) \(a_{33}= -1.00166222 \pm 1.6 \cdot 10^{-5} \)
\(a_{34}= -2.43894209 \pm 1.8 \cdot 10^{-5} \) \(a_{35}= +0.39322782 \pm 1.7 \cdot 10^{-5} \) \(a_{36}= +3.07706264 \pm 2.1 \cdot 10^{-5} \)
\(a_{37}= +0.52547237 \pm 1.5 \cdot 10^{-5} \) \(a_{38}= -2.84145870 \pm 1.8 \cdot 10^{-5} \) \(a_{39}= -0.07296147 \pm 1.5 \cdot 10^{-5} \)
\(a_{40}= -1.50190960 \pm 2.2 \cdot 10^{-5} \) \(a_{41}= -0.90376440 \pm 1.4 \cdot 10^{-5} \) \(a_{42}= +1.23440049 \pm 2.1 \cdot 10^{-5} \)
\(a_{43}= -0.39311067 \pm 1.5 \cdot 10^{-5} \) \(a_{44}= +1.24790614 \pm 1.6 \cdot 10^{-5} \) \(a_{45}= +1.36015043 \pm 1.7 \cdot 10^{-5} \)
\(a_{46}= +1.84495522 \pm 1.6 \cdot 10^{-5} \) \(a_{47}= +0.04359248 \pm 1.4 \cdot 10^{-5} \) \(a_{48}= -1.54099273 \pm 2.1 \cdot 10^{-5} \)
\(a_{49}= -0.79984915 \pm 1.5 \cdot 10^{-5} \) \(a_{50}= +0.39318226 \pm 2.1 \cdot 10^{-5} \) \(a_{51}= -2.25181497 \pm 1.6 \cdot 10^{-5} \)
\(a_{52}= +0.09089797 \pm 1.7 \cdot 10^{-5} \) \(a_{53}= +0.96201345 \pm 1.3 \cdot 10^{-5} \) \(a_{54}= +1.51055096 \pm 1.9 \cdot 10^{-5} \)
\(a_{55}= +0.55161050 \pm 1.3 \cdot 10^{-5} \) \(a_{56}= -0.76446391 \pm 1.9 \cdot 10^{-5} \) \(a_{57}= -2.62344860 \pm 1.8 \cdot 10^{-5} \)
\(a_{58}= -0.47884457 \pm 1.7 \cdot 10^{-5} \) \(a_{59}= -0.75599241 \pm 1.5 \cdot 10^{-5} \) \(a_{60}= -2.78955373 \pm 2.7 \cdot 10^{-5} \)

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