Properties

Label 73.13
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 1.629972
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(1.62997279819218100583473505118 \pm 2 \cdot 10^{-5}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.06840533 \pm 6.8 \cdot 10^{-1} \) \(a_{3}= +1.06488896 \pm 6.3 \cdot 10^{-1} \)
\(a_{4}= -0.99532071 \pm 7.0 \cdot 10^{-1} \) \(a_{5}= +1.43283026 \pm 6.1 \cdot 10^{-1} \) \(a_{6}= +0.07284408 \pm 7.5 \cdot 10^{-1} \)
\(a_{7}= +1.45690410 \pm 5.9 \cdot 10^{-1} \) \(a_{8}= -0.13649058 \pm 6.8 \cdot 10^{-1} \) \(a_{9}= +0.13398850 \pm 6.2 \cdot 10^{-1} \)
\(a_{10}= +0.09801323 \pm 7.5 \cdot 10^{-1} \) \(a_{11}= -0.61807093 \pm 5.5 \cdot 10^{-1} \) \(a_{12}= -1.05990604 \pm 7.6 \cdot 10^{-1} \)
\(a_{13}= +0.39615053 \pm 5.6 \cdot 10^{-1} \) \(a_{14}= +0.09966001 \pm 7.3 \cdot 10^{-1} \) \(a_{15}= +1.52580513 \pm 7.0 \cdot 10^{-1} \)
\(a_{16}= +0.98598403 \pm 6.5 \cdot 10^{-1} \) \(a_{17}= -1.00173320 \pm 5.3 \cdot 10^{-1} \) \(a_{18}= +0.00916553 \pm 7.7 \cdot 10^{-1} \)
\(a_{19}= -1.39922019 \pm 5.5 \cdot 10^{-1} \) \(a_{20}= -1.42612563 \pm 7.9 \cdot 10^{-1} \) \(a_{21}= +1.55144110 \pm 6.4 \cdot 10^{-1} \)
\(a_{22}= -0.04227935 \pm 6.9 \cdot 10^{-1} \) \(a_{23}= -0.53910244 \pm 5.0 \cdot 10^{-1} \) \(a_{24}= -0.14534731 \pm 7.0 \cdot 10^{-1} \)
\(a_{25}= +1.05300256 \pm 5.7 \cdot 10^{-1} \) \(a_{26}= +0.02709881 \pm 6.8 \cdot 10^{-1} \) \(a_{27}= -0.92220608 \pm 6.3 \cdot 10^{-1} \)
\(a_{28}= -1.45008683 \pm 7.6 \cdot 10^{-1} \) \(a_{29}= -1.06094124 \pm 5.5 \cdot 10^{-1} \) \(a_{30}= +0.10437321 \pm 7.9 \cdot 10^{-1} \)
\(a_{31}= +1.08917078 \pm 5.4 \cdot 10^{-1} \) \(a_{32}= +0.20393714 \pm 6.5 \cdot 10^{-1} \) \(a_{33}= -0.65817691 \pm 5.9 \cdot 10^{-1} \)
\(a_{34}= -0.06852389 \pm 6.8 \cdot 10^{-1} \) \(a_{35}= +2.08749629 \pm 6.5 \cdot 10^{-1} \) \(a_{36}= -0.13336153 \pm 7.7 \cdot 10^{-1} \)
\(a_{37}= +1.06135004 \pm 5.6 \cdot 10^{-1} \) \(a_{38}= -0.09571412 \pm 7.0 \cdot 10^{-1} \) \(a_{39}= +0.42185633 \pm 6.5 \cdot 10^{-1} \)
\(a_{40}= -0.19556783 \pm 6.7 \cdot 10^{-1} \) \(a_{41}= +1.73960194 \pm 5.3 \cdot 10^{-1} \) \(a_{42}= +0.10612685 \pm 7.6 \cdot 10^{-1} \)
\(a_{43}= -0.97842764 \pm 5.7 \cdot 10^{-1} \) \(a_{44}= +0.61517880 \pm 7.1 \cdot 10^{-1} \) \(a_{45}= +0.19198278 \pm 7.0 \cdot 10^{-1} \)
\(a_{46}= -0.03687748 \pm 5.6 \cdot 10^{-1} \) \(a_{47}= -1.01115224 \pm 5.1 \cdot 10^{-1} \) \(a_{48}= +1.04996351 \pm 6.4 \cdot 10^{-1} \)
\(a_{49}= +1.12256957 \pm 5.6 \cdot 10^{-1} \) \(a_{50}= +0.07203099 \pm 6.7 \cdot 10^{-1} \) \(a_{51}= -1.06673462 \pm 5.7 \cdot 10^{-1} \)
\(a_{52}= -0.39429683 \pm 6.9 \cdot 10^{-1} \) \(a_{53}= +0.87661188 \pm 5.6 \cdot 10^{-1} \) \(a_{54}= -0.06308381 \pm 7.9 \cdot 10^{-1} \)
\(a_{55}= -0.88559073 \pm 5.8 \cdot 10^{-1} \) \(a_{56}= -0.19885368 \pm 7.1 \cdot 10^{-1} \) \(a_{57}= -1.49001413 \pm 6.0 \cdot 10^{-1} \)
\(a_{58}= -0.07257404 \pm 6.2 \cdot 10^{-1} \) \(a_{59}= -0.31550985 \pm 5.3 \cdot 10^{-1} \) \(a_{60}= -1.51866545 \pm 8.3 \cdot 10^{-1} \)

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