Properties

Label 73.23
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.229394
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: \(2.22939448140919127354874241994 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.79479449 \pm 7.4 \cdot 10^{-1} \) \(a_{3}= -0.52281832 \pm 6.9 \cdot 10^{-1} \)
\(a_{4}= -0.36830173 \pm 7.7 \cdot 10^{-1} \) \(a_{5}= -0.12159921 \pm 6.7 \cdot 10^{-1} \) \(a_{6}= -0.41553311 \pm 8.3 \cdot 10^{-1} \)
\(a_{7}= -0.35897587 \pm 6.5 \cdot 10^{-1} \) \(a_{8}= -1.08751867 \pm 7.5 \cdot 10^{-1} \) \(a_{9}= -0.72666101 \pm 6.9 \cdot 10^{-1} \)
\(a_{10}= -0.09664638 \pm 8.2 \cdot 10^{-1} \) \(a_{11}= -0.61459345 \pm 6.0 \cdot 10^{-1} \) \(a_{12}= +0.19255489 \pm 8.4 \cdot 10^{-1} \)
\(a_{13}= +1.07521950 \pm 6.2 \cdot 10^{-1} \) \(a_{14}= -0.28531204 \pm 8.0 \cdot 10^{-1} \) \(a_{15}= +0.06357429 \pm 7.7 \cdot 10^{-1} \)
\(a_{16}= -0.49605211 \pm 7.2 \cdot 10^{-1} \) \(a_{17}= +0.51648607 \pm 5.9 \cdot 10^{-1} \) \(a_{18}= -0.57754616 \pm 8.5 \cdot 10^{-1} \)
\(a_{19}= -0.04609143 \pm 6.1 \cdot 10^{-1} \) \(a_{20}= +0.04478520 \pm 8.7 \cdot 10^{-1} \) \(a_{21}= +0.18767916 \pm 7.1 \cdot 10^{-1} \)
\(a_{22}= -0.48847548 \pm 7.6 \cdot 10^{-1} \) \(a_{23}= +0.05516816 \pm 5.5 \cdot 10^{-1} \) \(a_{24}= +0.56857468 \pm 7.7 \cdot 10^{-1} \)
\(a_{25}= -0.98521363 \pm 6.3 \cdot 10^{-1} \) \(a_{26}= +0.85457853 \pm 7.5 \cdot 10^{-1} \) \(a_{27}= +0.90273000 \pm 6.9 \cdot 10^{-1} \)
\(a_{28}= +0.13221143 \pm 8.4 \cdot 10^{-1} \) \(a_{29}= -1.70060990 \pm 6.1 \cdot 10^{-1} \) \(a_{30}= +0.05052850 \pm 8.7 \cdot 10^{-1} \)
\(a_{31}= +0.11682545 \pm 5.9 \cdot 10^{-1} \) \(a_{32}= +0.69325918 \pm 7.2 \cdot 10^{-1} \) \(a_{33}= +0.32132071 \pm 6.5 \cdot 10^{-1} \)
\(a_{34}= +0.41050028 \pm 7.5 \cdot 10^{-1} \) \(a_{35}= +0.04365118 \pm 7.1 \cdot 10^{-1} \) \(a_{36}= +0.26763050 \pm 8.5 \cdot 10^{-1} \)
\(a_{37}= -0.40723150 \pm 6.1 \cdot 10^{-1} \) \(a_{38}= -0.03663321 \pm 7.7 \cdot 10^{-1} \) \(a_{39}= -0.56214445 \pm 7.1 \cdot 10^{-1} \)
\(a_{40}= +0.13224141 \pm 7.4 \cdot 10^{-1} \) \(a_{41}= +0.22026252 \pm 5.8 \cdot 10^{-1} \) \(a_{42}= +0.14916636 \pm 8.4 \cdot 10^{-1} \)
\(a_{43}= -1.18674970 \pm 6.3 \cdot 10^{-1} \) \(a_{44}= +0.22635583 \pm 7.8 \cdot 10^{-1} \) \(a_{45}= +0.08836141 \pm 7.7 \cdot 10^{-1} \)
\(a_{46}= +0.04384735 \pm 6.1 \cdot 10^{-1} \) \(a_{47}= +0.19340473 \pm 5.6 \cdot 10^{-1} \) \(a_{48}= +0.25934513 \pm 7.0 \cdot 10^{-1} \)
\(a_{49}= -0.87113633 \pm 6.2 \cdot 10^{-1} \) \(a_{50}= -0.78304236 \pm 7.4 \cdot 10^{-1} \) \(a_{51}= -0.27002838 \pm 6.2 \cdot 10^{-1} \)
\(a_{52}= -0.39600520 \pm 7.5 \cdot 10^{-1} \) \(a_{53}= -0.46150403 \pm 6.2 \cdot 10^{-1} \) \(a_{54}= +0.71748483 \pm 8.7 \cdot 10^{-1} \)
\(a_{55}= +0.07473408 \pm 6.3 \cdot 10^{-1} \) \(a_{56}= +0.39039296 \pm 7.8 \cdot 10^{-1} \) \(a_{57}= +0.02409744 \pm 6.6 \cdot 10^{-1} \)
\(a_{58}= -1.35163537 \pm 6.8 \cdot 10^{-1} \) \(a_{59}= -0.24113790 \pm 5.9 \cdot 10^{-1} \) \(a_{60}= -0.02341452 \pm 9.1 \cdot 10^{-1} \)

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