Properties

Label 73.16
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 1.819977
Fricke sign $-1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(1.81997776737794750528347217762 \pm 2 \cdot 10^{-5}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.49690091 \pm 2.8 \cdot 10^{-2} \) \(a_{3}= -1.47377171 \pm 2.6 \cdot 10^{-2} \)
\(a_{4}= +1.24071234 \pm 3.0 \cdot 10^{-2} \) \(a_{5}= -1.59733383 \pm 2.6 \cdot 10^{-2} \) \(a_{6}= +2.20609021 \pm 3.2 \cdot 10^{-2} \)
\(a_{7}= +0.37231348 \pm 2.5 \cdot 10^{-2} \) \(a_{8}= -0.36032251 \pm 2.8 \cdot 10^{-2} \) \(a_{9}= +1.17200305 \pm 2.6 \cdot 10^{-2} \)
\(a_{10}= +2.39105047 \pm 3.1 \cdot 10^{-2} \) \(a_{11}= -1.40051433 \pm 2.3 \cdot 10^{-2} \) \(a_{12}= -1.82852674 \pm 3.2 \cdot 10^{-2} \)
\(a_{13}= +1.43498612 \pm 2.3 \cdot 10^{-2} \) \(a_{14}= -0.55731638 \pm 3.1 \cdot 10^{-2} \) \(a_{15}= +2.35410542 \pm 2.9 \cdot 10^{-2} \)
\(a_{16}= -0.70134524 \pm 2.7 \cdot 10^{-2} \) \(a_{17}= -0.48621274 \pm 2.2 \cdot 10^{-2} \) \(a_{18}= -1.75437244 \pm 3.2 \cdot 10^{-2} \)
\(a_{19}= -1.27883205 \pm 2.3 \cdot 10^{-2} \) \(a_{20}= -1.98183179 \pm 3.3 \cdot 10^{-2} \) \(a_{21}= -0.54870507 \pm 2.7 \cdot 10^{-2} \)
\(a_{22}= +2.09643117 \pm 2.9 \cdot 10^{-2} \) \(a_{23}= +0.09324545 \pm 2.1 \cdot 10^{-2} \) \(a_{24}= +0.53103313 \pm 2.9 \cdot 10^{-2} \)
\(a_{25}= +1.55147538 \pm 2.4 \cdot 10^{-2} \) \(a_{26}= -2.14803203 \pm 2.8 \cdot 10^{-2} \) \(a_{27}= -0.25349323 \pm 2.6 \cdot 10^{-2} \)
\(a_{28}= +0.46193392 \pm 3.2 \cdot 10^{-2} \) \(a_{29}= +0.77467378 \pm 2.3 \cdot 10^{-2} \) \(a_{30}= -3.52386254 \pm 3.3 \cdot 10^{-2} \)
\(a_{31}= +0.25550558 \pm 2.3 \cdot 10^{-2} \) \(a_{32}= +1.41016684 \pm 2.7 \cdot 10^{-2} \) \(a_{33}= +2.06403839 \pm 2.5 \cdot 10^{-2} \)
\(a_{34}= +0.72781229 \pm 2.8 \cdot 10^{-2} \) \(a_{35}= -0.59470891 \pm 2.7 \cdot 10^{-2} \) \(a_{36}= +1.45411864 \pm 3.3 \cdot 10^{-2} \)
\(a_{37}= +0.88156126 \pm 2.3 \cdot 10^{-2} \) \(a_{38}= +1.91428486 \pm 2.9 \cdot 10^{-2} \) \(a_{39}= -2.11484195 \pm 2.7 \cdot 10^{-2} \)
\(a_{40}= +0.57555534 \pm 2.8 \cdot 10^{-2} \) \(a_{41}= +0.73818938 \pm 2.2 \cdot 10^{-2} \) \(a_{42}= +0.82135712 \pm 3.2 \cdot 10^{-2} \)
\(a_{43}= -1.64116386 \pm 2.4 \cdot 10^{-2} \) \(a_{44}= -1.73763540 \pm 3.0 \cdot 10^{-2} \) \(a_{45}= -1.87208013 \pm 2.9 \cdot 10^{-2} \)
\(a_{46}= -0.13957919 \pm 2.3 \cdot 10^{-2} \) \(a_{47}= +1.18210286 \pm 2.1 \cdot 10^{-2} \) \(a_{48}= +1.03362277 \pm 2.7 \cdot 10^{-2} \)
\(a_{49}= -0.86138267 \pm 2.4 \cdot 10^{-2} \) \(a_{50}= -2.32240490 \pm 2.8 \cdot 10^{-2} \) \(a_{51}= +0.71656658 \pm 2.4 \cdot 10^{-2} \)
\(a_{52}= +1.78040498 \pm 2.9 \cdot 10^{-2} \) \(a_{53}= -0.28117795 \pm 2.4 \cdot 10^{-2} \) \(a_{54}= +0.37945425 \pm 3.3 \cdot 10^{-2} \)
\(a_{55}= +2.23708892 \pm 2.4 \cdot 10^{-2} \) \(a_{56}= -0.13415293 \pm 3.0 \cdot 10^{-2} \) \(a_{57}= +1.88470649 \pm 2.5 \cdot 10^{-2} \)
\(a_{58}= -1.15960988 \pm 2.6 \cdot 10^{-2} \) \(a_{59}= -0.42457002 \pm 2.2 \cdot 10^{-2} \) \(a_{60}= +2.92076763 \pm 3.5 \cdot 10^{-2} \)

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