Properties

Label 73.41
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.811576
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: \(2.81157666429928415128043703228 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.21073581 \pm 2.5 \) \(a_{3}= +1.70141359 \pm 2.4 \)
\(a_{4}= +0.46588118 \pm 2.6 \) \(a_{5}= +0.18342632 \pm 2.3 \) \(a_{6}= +2.05996233 \pm 2.8 \)
\(a_{7}= +1.06572900 \pm 2.2 \) \(a_{8}= -0.64667679 \pm 2.5 \) \(a_{9}= +1.89480816 \pm 2.3 \)
\(a_{10}= +0.22208082 \pm 2.8 \) \(a_{11}= -1.25449217 \pm 2.1 \) \(a_{12}= +0.79265656 \pm 2.9 \)
\(a_{13}= +0.50415874 \pm 2.1 \) \(a_{14}= +1.29031624 \pm 2.7 \) \(a_{15}= +0.31208404 \pm 2.6 \)
\(a_{16}= -1.24883591 \pm 2.5 \) \(a_{17}= -0.43048469 \pm 2.0 \) \(a_{18}= +2.29411208 \pm 2.9 \)
\(a_{19}= +1.27562366 \pm 2.1 \) \(a_{20}= +0.08545487 \pm 3.0 \) \(a_{21}= +1.81324577 \pm 2.4 \)
\(a_{22}= -1.51885857 \pm 2.6 \) \(a_{23}= -1.13297062 \pm 1.9 \) \(a_{24}= -1.10026466 \pm 2.6 \)
\(a_{25}= -0.96635479 \pm 2.1 \) \(a_{26}= +0.61040303 \pm 2.5 \) \(a_{27}= +1.52243875 \pm 2.4 \)
\(a_{28}= +0.49650307 \pm 2.9 \) \(a_{29}= -0.55002999 \pm 2.1 \) \(a_{30}= +0.37785132 \pm 3.0 \)
\(a_{31}= -0.97109596 \pm 2.0 \) \(a_{32}= -0.86533356 \pm 2.5 \) \(a_{33}= -2.13441000 \pm 2.2 \)
\(a_{34}= -0.52120323 \pm 2.5 \) \(a_{35}= +0.19548275 \pm 2.4 \) \(a_{36}= +0.88275545 \pm 2.9 \)
\(a_{37}= +1.30498592 \pm 2.1 \) \(a_{38}= +1.54444322 \pm 2.6 \) \(a_{39}= +0.85778252 \pm 2.4 \)
\(a_{40}= -0.11861754 \pm 2.5 \) \(a_{41}= -1.55676211 \pm 2.0 \) \(a_{42}= +2.19536157 \pm 2.9 \)
\(a_{43}= +0.45971242 \pm 2.1 \) \(a_{44}= -0.58444428 \pm 2.7 \) \(a_{45}= +0.34755770 \pm 2.6 \)
\(a_{46}= -1.37172809 \pm 2.1 \) \(a_{47}= +1.02113020 \pm 1.9 \) \(a_{48}= -2.12478638 \pm 2.4 \)
\(a_{49}= +0.13577827 \pm 2.1 \) \(a_{50}= -1.17000034 \pm 2.5 \) \(a_{51}= -0.73243250 \pm 2.1 \)
\(a_{52}= +0.23487806 \pm 2.6 \) \(a_{53}= +1.02658050 \pm 2.1 \) \(a_{54}= +1.84327109 \pm 3.0 \)
\(a_{55}= -0.23010688 \pm 2.2 \) \(a_{56}= -0.68918220 \pm 2.7 \) \(a_{57}= +2.17036340 \pm 2.3 \)
\(a_{58}= -0.66594100 \pm 2.3 \) \(a_{59}= +0.73127516 \pm 2.0 \) \(a_{60}= +0.14539408 \pm 3.1 \)

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