Properties

Label 73.8
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 1.330476
Fricke sign $+1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(1.33047658331129989857973580075 \pm 2 \cdot 10^{-5}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.39496302 \pm 2.9 \cdot 10^{-2} \) \(a_{3}= -1.12208389 \pm 2.7 \cdot 10^{-2} \)
\(a_{4}= -0.84400421 \pm 3.0 \cdot 10^{-2} \) \(a_{5}= -0.71405949 \pm 2.6 \cdot 10^{-2} \) \(a_{6}= -0.44318165 \pm 3.2 \cdot 10^{-2} \)
\(a_{7}= +0.38306159 \pm 2.5 \cdot 10^{-2} \) \(a_{8}= -0.72831348 \pm 2.9 \cdot 10^{-2} \) \(a_{9}= +0.25907227 \pm 2.7 \cdot 10^{-2} \)
\(a_{10}= -0.28202710 \pm 3.2 \cdot 10^{-2} \) \(a_{11}= +1.07083020 \pm 2.4 \cdot 10^{-2} \) \(a_{12}= +0.94704353 \pm 3.3 \cdot 10^{-2} \)
\(a_{13}= -1.13709378 \pm 2.4 \cdot 10^{-2} \) \(a_{14}= +0.15129516 \pm 3.2 \cdot 10^{-2} \) \(a_{15}= +0.80123466 \pm 3.0 \cdot 10^{-2} \)
\(a_{16}= +0.55634732 \pm 2.8 \cdot 10^{-2} \) \(a_{17}= -0.30358155 \pm 2.3 \cdot 10^{-2} \) \(a_{18}= +0.10232397 \pm 3.3 \cdot 10^{-2} \)
\(a_{19}= -0.92887547 \pm 2.4 \cdot 10^{-2} \) \(a_{20}= +0.60266922 \pm 3.4 \cdot 10^{-2} \) \(a_{21}= -0.42982724 \pm 2.8 \cdot 10^{-2} \)
\(a_{22}= +0.42293833 \pm 3.0 \cdot 10^{-2} \) \(a_{23}= -0.42946840 \pm 2.2 \cdot 10^{-2} \) \(a_{24}= +0.81722882 \pm 3.0 \cdot 10^{-2} \)
\(a_{25}= -0.49011904 \pm 2.4 \cdot 10^{-2} \) \(a_{26}= -0.44911000 \pm 2.9 \cdot 10^{-2} \) \(a_{27}= +0.83138308 \pm 2.7 \cdot 10^{-2} \)
\(a_{28}= -0.32330559 \pm 3.3 \cdot 10^{-2} \) \(a_{29}= +1.11746406 \pm 2.4 \cdot 10^{-2} \) \(a_{30}= +0.31645806 \pm 3.4 \cdot 10^{-2} \)
\(a_{31}= -1.72723961 \pm 2.3 \cdot 10^{-2} \) \(a_{32}= +0.94805010 \pm 2.8 \cdot 10^{-2} \) \(a_{33}= -1.20156132 \pm 2.6 \cdot 10^{-2} \)
\(a_{34}= -0.11990349 \pm 2.9 \cdot 10^{-2} \) \(a_{35}= -0.27352876 \pm 2.8 \cdot 10^{-2} \) \(a_{36}= -0.21865808 \pm 3.3 \cdot 10^{-2} \)
\(a_{37}= -0.00941714 \pm 2.4 \cdot 10^{-2} \) \(a_{38}= -0.36687146 \pm 3.0 \cdot 10^{-2} \) \(a_{39}= +1.27591462 \pm 2.8 \cdot 10^{-2} \)
\(a_{40}= +0.52005915 \pm 2.9 \cdot 10^{-2} \) \(a_{41}= -0.43275362 \pm 2.3 \cdot 10^{-2} \) \(a_{42}= -0.16976587 \pm 3.3 \cdot 10^{-2} \)
\(a_{43}= +1.19228958 \pm 2.5 \cdot 10^{-2} \) \(a_{44}= -0.90378520 \pm 3.1 \cdot 10^{-2} \) \(a_{45}= -0.18499301 \pm 3.0 \cdot 10^{-2} \)
\(a_{46}= -0.16962414 \pm 2.4 \cdot 10^{-2} \) \(a_{47}= -1.09103331 \pm 2.2 \cdot 10^{-2} \) \(a_{48}= -0.62426836 \pm 2.8 \cdot 10^{-2} \)
\(a_{49}= -0.85326382 \pm 2.4 \cdot 10^{-2} \) \(a_{50}= -0.19357890 \pm 2.9 \cdot 10^{-2} \) \(a_{51}= +0.34064397 \pm 2.4 \cdot 10^{-2} \)
\(a_{52}= +0.95971194 \pm 3.0 \cdot 10^{-2} \) \(a_{53}= -1.19979743 \pm 2.4 \cdot 10^{-2} \) \(a_{54}= +0.32836557 \pm 3.4 \cdot 10^{-2} \)
\(a_{55}= -0.76463647 \pm 2.5 \cdot 10^{-2} \) \(a_{56}= -0.27898892 \pm 3.1 \cdot 10^{-2} \) \(a_{57}= +1.04227620 \pm 2.6 \cdot 10^{-2} \)
\(a_{58}= +0.44135698 \pm 2.7 \cdot 10^{-2} \) \(a_{59}= +0.26012504 \pm 2.3 \cdot 10^{-2} \) \(a_{60}= -0.67624542 \pm 3.6 \cdot 10^{-2} \)

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