Properties

Label 73.28
Level $73$
Weight $0$
Character 73.1
Symmetry even
\(R\) 2.342675
Fricke sign $+1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(2.34267515761647982879028679445 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.95740597 \pm 5.0 \cdot 10^{-5} \) \(a_{3}= -0.64378098 \pm 4.7 \cdot 10^{-5} \)
\(a_{4}= +2.83143815 \pm 5.3 \cdot 10^{-5} \) \(a_{5}= -0.37889577 \pm 4.4 \cdot 10^{-5} \) \(a_{6}= +1.26014074 \pm 5.8 \cdot 10^{-5} \)
\(a_{7}= +1.63959717 \pm 4.3 \cdot 10^{-5} \) \(a_{8}= -3.58486797 \pm 5.5 \cdot 10^{-5} \) \(a_{9}= -0.58554605 \pm 5.0 \cdot 10^{-5} \)
\(a_{10}= +0.74165284 \pm 5.1 \cdot 10^{-5} \) \(a_{11}= +0.28539295 \pm 4.3 \cdot 10^{-5} \) \(a_{12}= -1.82282603 \pm 6.1 \cdot 10^{-5} \)
\(a_{13}= +0.19885251 \pm 4.2 \cdot 10^{-5} \) \(a_{14}= -3.20935730 \pm 5.1 \cdot 10^{-5} \) \(a_{15}= +0.24392589 \pm 4.6 \cdot 10^{-5} \)
\(a_{16}= +4.18560384 \pm 5.7 \cdot 10^{-5} \) \(a_{17}= +0.69927931 \pm 4.3 \cdot 10^{-5} \) \(a_{18}= +1.14615133 \pm 6.0 \cdot 10^{-5} \)
\(a_{19}= +0.18633436 \pm 4.0 \cdot 10^{-5} \) \(a_{20}= -1.07281993 \pm 5.4 \cdot 10^{-5} \) \(a_{21}= -1.05554148 \pm 4.7 \cdot 10^{-5} \)
\(a_{22}= -0.55862986 \pm 5.0 \cdot 10^{-5} \) \(a_{23}= +1.71036513 \pm 3.9 \cdot 10^{-5} \) \(a_{24}= +2.30786982 \pm 6.1 \cdot 10^{-5} \)
\(a_{25}= -0.85643800 \pm 4.7 \cdot 10^{-5} \) \(a_{26}= -0.38923509 \pm 5.0 \cdot 10^{-5} \) \(a_{27}= +1.02074439 \pm 5.1 \cdot 10^{-5} \)
\(a_{28}= +4.64241798 \pm 5.5 \cdot 10^{-5} \) \(a_{29}= -1.08593706 \pm 3.9 \cdot 10^{-5} \) \(a_{30}= -0.47746199 \pm 6.2 \cdot 10^{-5} \)
\(a_{31}= +0.09797828 \pm 4.1 \cdot 10^{-5} \) \(a_{32}= -4.60805799 \pm 5.5 \cdot 10^{-5} \) \(a_{33}= -0.18373055 \pm 4.8 \cdot 10^{-5} \)
\(a_{34}= -1.36877350 \pm 4.9 \cdot 10^{-5} \) \(a_{35}= -0.62123643 \pm 4.3 \cdot 10^{-5} \) \(a_{36}= -1.65793742 \pm 6.6 \cdot 10^{-5} \)
\(a_{37}= +0.84573712 \pm 4.3 \cdot 10^{-5} \) \(a_{38}= -0.36473199 \pm 4.8 \cdot 10^{-5} \) \(a_{39}= -0.12801746 \pm 5.1 \cdot 10^{-5} \)
\(a_{40}= +1.35829131 \pm 5.7 \cdot 10^{-5} \) \(a_{41}= +0.41907330 \pm 4.1 \cdot 10^{-5} \) \(a_{42}= +2.06612319 \pm 6.2 \cdot 10^{-5} \)
\(a_{43}= +0.80682847 \pm 3.7 \cdot 10^{-5} \) \(a_{44}= +0.80807247 \pm 4.8 \cdot 10^{-5} \) \(a_{45}= +0.22186092 \pm 4.9 \cdot 10^{-5} \)
\(a_{46}= -3.34787893 \pm 4.9 \cdot 10^{-5} \) \(a_{47}= +0.80364750 \pm 4.1 \cdot 10^{-5} \) \(a_{48}= -2.69461215 \pm 6.1 \cdot 10^{-5} \)
\(a_{49}= +1.68827888 \pm 4.2 \cdot 10^{-5} \) \(a_{50}= +1.67639685 \pm 5.7 \cdot 10^{-5} \) \(a_{51}= -0.45018272 \pm 4.8 \cdot 10^{-5} \)
\(a_{52}= +0.56303859 \pm 5.2 \cdot 10^{-5} \) \(a_{53}= +1.19737729 \pm 4.0 \cdot 10^{-5} \) \(a_{54}= -1.99801117 \pm 6.2 \cdot 10^{-5} \)
\(a_{55}= -0.10813418 \pm 4.6 \cdot 10^{-5} \) \(a_{56}= -5.87773939 \pm 6.2 \cdot 10^{-5} \) \(a_{57}= -0.11995852 \pm 4.3 \cdot 10^{-5} \)
\(a_{58}= +2.12561968 \pm 4.3 \cdot 10^{-5} \) \(a_{59}= -1.46460802 \pm 4.0 \cdot 10^{-5} \) \(a_{60}= +0.69066107 \pm 6.7 \cdot 10^{-5} \)

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