Properties

Label 73.25
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.280823
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: \(2.28082369836835176953973214147 \pm 9 \cdot 10^{-5}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.00656605 \pm 7.5 \) \(a_{3}= +1.25777913 \pm 7.0 \)
\(a_{4}= -0.99995689 \pm 7.8 \) \(a_{5}= -1.69180506 \pm 6.7 \) \(a_{6}= -0.00825863 \pm 8.3 \)
\(a_{7}= -0.09625356 \pm 6.5 \) \(a_{8}= +0.01313181 \pm 7.5 \) \(a_{9}= +0.58200836 \pm 6.9 \)
\(a_{10}= +0.01110847 \pm 8.3 \) \(a_{11}= -0.18988738 \pm 6.1 \) \(a_{12}= -1.25772491 \pm 8.4 \)
\(a_{13}= -0.18053669 \pm 6.2 \) \(a_{14}= +0.00063200 \pm 8.1 \) \(a_{15}= -2.12791711 \pm 7.7 \)
\(a_{16}= +0.99987066 \pm 7.2 \) \(a_{17}= -0.78925004 \pm 5.9 \) \(a_{18}= -0.00382149 \pm 8.5 \)
\(a_{19}= -0.71519337 \pm 6.1 \) \(a_{20}= +1.69173212 \pm 8.7 \) \(a_{21}= -0.12106573 \pm 7.1 \)
\(a_{22}= +0.00124681 \pm 7.6 \) \(a_{23}= +0.64600486 \pm 5.6 \) \(a_{24}= +0.01651691 \pm 7.7 \)
\(a_{25}= +1.86220436 \pm 6.3 \) \(a_{26}= +0.00118541 \pm 7.5 \) \(a_{27}= -0.52574116 \pm 7.0 \)
\(a_{28}= +0.09624941 \pm 8.4 \) \(a_{29}= +1.65229507 \pm 6.1 \) \(a_{30}= +0.01397200 \pm 8.8 \)
\(a_{31}= -0.92294417 \pm 5.9 \) \(a_{32}= -0.01969701 \pm 7.2 \) \(a_{33}= -0.23883640 \pm 6.6 \)
\(a_{34}= +0.00518225 \pm 7.5 \) \(a_{35}= +0.16284227 \pm 7.2 \) \(a_{36}= -0.58198327 \pm 8.6 \)
\(a_{37}= -1.89994841 \pm 6.2 \) \(a_{38}= +0.00469599 \pm 7.7 \) \(a_{39}= -0.22707528 \pm 7.1 \)
\(a_{40}= -0.02221646 \pm 7.5 \) \(a_{41}= -1.01075255 \pm 5.9 \) \(a_{42}= +0.00079492 \pm 8.4 \)
\(a_{43}= -0.22708286 \pm 6.3 \) \(a_{44}= +0.18987920 \pm 7.8 \) \(a_{45}= -0.98464469 \pm 7.7 \)
\(a_{46}= -0.00424169 \pm 6.1 \) \(a_{47}= +1.37248178 \pm 5.6 \) \(a_{48}= +1.25761646 \pm 7.1 \)
\(a_{49}= -0.99073525 \pm 6.2 \) \(a_{50}= -0.01222732 \pm 7.4 \) \(a_{51}= -0.99270223 \pm 6.3 \)
\(a_{52}= +0.18052890 \pm 7.6 \) \(a_{53}= +1.28065865 \pm 6.2 \) \(a_{54}= +0.00345204 \pm 8.8 \)
\(a_{55}= +0.32125245 \pm 6.4 \) \(a_{56}= -0.00126398 \pm 7.9 \) \(a_{57}= -0.89955531 \pm 6.7 \)
\(a_{58}= -0.01084905 \pm 6.9 \) \(a_{59}= -1.53146155 \pm 5.9 \) \(a_{60}= +2.12782537 \pm 9.2 \)

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