Properties

Label 73.32
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.476074
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: \(2.47607415362270008237616245889 \pm 7 \cdot 10^{-5}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.03575867 \pm 12. \) \(a_{3}= +1.81958021 \pm 12. \)
\(a_{4}= +0.07279601 \pm 13. \) \(a_{5}= +1.16649105 \pm 11. \) \(a_{6}= -1.88464597 \pm 14. \)
\(a_{7}= -1.35181659 \pm 11. \) \(a_{8}= +0.96035956 \pm 12. \) \(a_{9}= +2.31087215 \pm 11. \)
\(a_{10}= -1.20820321 \pm 14. \) \(a_{11}= +0.33677942 \pm 10. \) \(a_{12}= +0.13245818 \pm 14. \)
\(a_{13}= +1.76974158 \pm 10. \) \(a_{14}= +1.40015574 \pm 13. \) \(a_{15}= +2.12252404 \pm 13. \)
\(a_{16}= -1.06749675 \pm 12. \) \(a_{17}= +0.90801997 \pm 10. \) \(a_{18}= -2.39350585 \pm 14. \)
\(a_{19}= +0.00690057 \pm 10. \) \(a_{20}= +0.08491590 \pm 15. \) \(a_{21}= -2.45973872 \pm 12. \)
\(a_{22}= -0.34882220 \pm 13. \) \(a_{23}= -0.60839132 \pm 9.6 \) \(a_{24}= +1.74745126 \pm 13. \)
\(a_{25}= +0.36070138 \pm 10. \) \(a_{26}= -1.83302517 \pm 12. \) \(a_{27}= +2.38523704 \pm 12. \)
\(a_{28}= -0.09840685 \pm 14. \) \(a_{29}= +0.20594552 \pm 10. \) \(a_{30}= -2.19842266 \pm 15. \)
\(a_{31}= -0.40073053 \pm 10. \) \(a_{32}= +0.14530945 \pm 12. \) \(a_{33}= +0.61279718 \pm 11. \)
\(a_{34}= -0.94048955 \pm 12. \) \(a_{35}= -1.57688196 \pm 12. \) \(a_{36}= +0.16822227 \pm 14. \)
\(a_{37}= -0.50753294 \pm 10. \) \(a_{38}= -0.00714732 \pm 13. \) \(a_{39}= +3.22018677 \pm 12. \)
\(a_{40}= +1.12025084 \pm 12. \) \(a_{41}= +1.01150794 \pm 10. \) \(a_{42}= +2.54769569 \pm 14. \)
\(a_{43}= -1.80225406 \pm 10. \) \(a_{44}= +0.02451619 \pm 13. \) \(a_{45}= +2.69561170 \pm 13. \)
\(a_{46}= +0.63014658 \pm 10. \) \(a_{47}= -0.40363212 \pm 9.7 \) \(a_{48}= -1.94239596 \pm 12. \)
\(a_{49}= +0.82740811 \pm 10. \) \(a_{50}= -0.37359958 \pm 12. \) \(a_{51}= +1.65221517 \pm 10. \)
\(a_{52}= +0.12883012 \pm 13. \) \(a_{53}= -1.57948630 \pm 10. \) \(a_{54}= -2.47052993 \pm 15. \)
\(a_{55}= +0.39285019 \pm 11. \) \(a_{56}= -1.29822999 \pm 13. \) \(a_{57}= +0.01255614 \pm 11. \)
\(a_{58}= -0.21330986 \pm 11. \) \(a_{59}= -1.08579813 \pm 10. \) \(a_{60}= +0.15451128 \pm 15. \)

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