Properties

Label 73.43
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.837206
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: \(2.83720694270450026134529624661 \pm 5 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.26329223 \pm 10. \) \(a_{3}= +0.36567198 \pm 10. \)
\(a_{4}= -0.93067720 \pm 11. \) \(a_{5}= +1.26994147 \pm 9.8 \) \(a_{6}= +0.09627860 \pm 12. \)
\(a_{7}= -0.99351295 \pm 9.5 \) \(a_{8}= -0.50833230 \pm 10. \) \(a_{9}= -0.86628399 \pm 10. \)
\(a_{10}= +0.33436573 \pm 12. \) \(a_{11}= -0.56414063 \pm 8.8 \) \(a_{12}= -0.34032257 \pm 12. \)
\(a_{13}= -1.28952233 \pm 9.0 \) \(a_{14}= -0.26158423 \pm 11. \) \(a_{15}= +0.46438203 \pm 11. \)
\(a_{16}= +0.79683725 \pm 10. \) \(a_{17}= -0.73347698 \pm 8.6 \) \(a_{18}= -0.22808584 \pm 12. \)
\(a_{19}= +0.71919626 \pm 9.0 \) \(a_{20}= -1.18190558 \pm 12. \) \(a_{21}= -0.36329982 \pm 10. \)
\(a_{22}= -0.14853385 \pm 11. \) \(a_{23}= -0.87351732 \pm 8.1 \) \(a_{24}= -0.18588289 \pm 11. \)
\(a_{25}= +0.61275136 \pm 9.2 \) \(a_{26}= -0.33952120 \pm 10. \) \(a_{27}= -0.68244776 \pm 10. \)
\(a_{28}= +0.92463985 \pm 12. \) \(a_{29}= +1.86255863 \pm 8.9 \) \(a_{30}= +0.12226817 \pm 12. \)
\(a_{31}= +0.77698782 \pm 8.7 \) \(a_{32}= +0.71813335 \pm 10. \) \(a_{33}= -0.20629044 \pm 9.6 \)
\(a_{34}= -0.19311879 \pm 10. \) \(a_{35}= -1.26170327 \pm 10. \) \(a_{36}= +0.80623077 \pm 12. \)
\(a_{37}= +0.07543838 \pm 9.0 \) \(a_{38}= +0.18935881 \pm 11. \) \(a_{39}= -0.47154218 \pm 10. \)
\(a_{40}= -0.64555229 \pm 10. \) \(a_{41}= -0.65867899 \pm 8.6 \) \(a_{42}= -0.09565403 \pm 12. \)
\(a_{43}= -0.04927619 \pm 9.2 \) \(a_{44}= +0.52503282 \pm 11. \) \(a_{45}= -1.10012999 \pm 11. \)
\(a_{46}= -0.22999032 \pm 9.0 \) \(a_{47}= -1.20724396 \pm 8.2 \) \(a_{48}= +0.29138106 \pm 10. \)
\(a_{49}= -0.01293203 \pm 9.1 \) \(a_{50}= +0.16133267 \pm 10. \) \(a_{51}= -0.26821199 \pm 9.2 \)
\(a_{52}= +1.20012903 \pm 11. \) \(a_{53}= -1.53198006 \pm 9.1 \) \(a_{54}= -0.17968320 \pm 12. \)
\(a_{55}= -0.71642560 \pm 9.3 \) \(a_{56}= +0.50503470 \pm 11. \) \(a_{57}= +0.26298995 \pm 9.7 \)
\(a_{58}= +0.49039723 \pm 10. \) \(a_{59}= +1.51736598 \pm 8.6 \) \(a_{60}= -0.43218976 \pm 13. \)

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