Properties

Label 73.24
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.278242
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: \(2.27824263875231932456767312242 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.77079916 \pm 10. \) \(a_{3}= -0.34320247 \pm 10. \)
\(a_{4}= -0.40586866 \pm 11. \) \(a_{5}= -0.09803222 \pm 9.8 \) \(a_{6}= +0.26454017 \pm 12. \)
\(a_{7}= +0.82373659 \pm 9.5 \) \(a_{8}= +1.08364238 \pm 10. \) \(a_{9}= -0.88221207 \pm 10. \)
\(a_{10}= +0.07556316 \pm 12. \) \(a_{11}= +1.60272246 \pm 8.8 \) \(a_{12}= +0.13929513 \pm 12. \)
\(a_{13}= +0.59613983 \pm 9.0 \) \(a_{14}= -0.63493547 \pm 11. \) \(a_{15}= +0.03364491 \pm 11. \)
\(a_{16}= -0.42940197 \pm 10. \) \(a_{17}= -0.39834511 \pm 8.6 \) \(a_{18}= +0.68000832 \pm 12. \)
\(a_{19}= +1.49208340 \pm 8.9 \) \(a_{20}= +0.03978820 \pm 12. \) \(a_{21}= -0.28270843 \pm 10. \)
\(a_{22}= -1.23537712 \pm 11. \) \(a_{23}= -1.33091550 \pm 8.1 \) \(a_{24}= -0.37190874 \pm 11. \)
\(a_{25}= -0.99038969 \pm 9.1 \) \(a_{26}= -0.45950408 \pm 10. \) \(a_{27}= +0.64597983 \pm 10. \)
\(a_{28}= -0.33432887 \pm 12. \) \(a_{29}= +1.14749616 \pm 8.9 \) \(a_{30}= -0.02593346 \pm 12. \)
\(a_{31}= +1.30894936 \pm 8.7 \) \(a_{32}= -0.75265971 \pm 10. \) \(a_{33}= -0.55005830 \pm 9.5 \)
\(a_{34}= +0.30704408 \pm 10. \) \(a_{35}= -0.08075273 \pm 10. \) \(a_{36}= +0.35806223 \pm 12. \)
\(a_{37}= +1.77847672 \pm 9.0 \) \(a_{38}= -1.15009663 \pm 11. \) \(a_{39}= -0.20459666 \pm 10. \)
\(a_{40}= -0.10623188 \pm 10. \) \(a_{41}= -0.07936648 \pm 8.5 \) \(a_{42}= +0.21791142 \pm 12. \)
\(a_{43}= +1.36146408 \pm 9.2 \) \(a_{44}= -0.65049482 \pm 11. \) \(a_{45}= +0.08648522 \pm 11. \)
\(a_{46}= +1.02586854 \pm 8.9 \) \(a_{47}= +0.06445925 \pm 8.2 \) \(a_{48}= +0.14737181 \pm 10. \)
\(a_{49}= -0.32145803 \pm 9.1 \) \(a_{50}= +0.76339153 \pm 10. \) \(a_{51}= +0.13671303 \pm 9.1 \)
\(a_{52}= -0.24195448 \pm 11. \) \(a_{53}= +1.28207637 \pm 9.1 \) \(a_{54}= -0.49792071 \pm 12. \)
\(a_{55}= -0.15711845 \pm 9.3 \) \(a_{56}= +0.89263588 \pm 11. \) \(a_{57}= -0.51208670 \pm 9.7 \)
\(a_{58}= -0.88448908 \pm 10. \) \(a_{59}= -1.42957166 \pm 8.6 \) \(a_{60}= -0.01365542 \pm 13. \)

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