Properties

Label 73.2
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 0.581705
Fricke sign $-1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(0.581705353025076015237186426026 \pm 8 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.31481404 \pm 2.9 \cdot 10^{-3} \) \(a_{3}= -0.89365736 \pm 2.7 \cdot 10^{-3} \)
\(a_{4}= +0.72873596 \pm 3.0 \cdot 10^{-3} \) \(a_{5}= +1.12823690 \pm 2.6 \cdot 10^{-3} \) \(a_{6}= +1.17499325 \pm 3.2 \cdot 10^{-3} \)
\(a_{7}= +1.31764578 \pm 2.5 \cdot 10^{-3} \) \(a_{8}= +0.35666177 \pm 2.9 \cdot 10^{-3} \) \(a_{9}= -0.20137652 \pm 2.6 \cdot 10^{-3} \)
\(a_{10}= -1.48342171 \pm 3.2 \cdot 10^{-3} \) \(a_{11}= +0.35266386 \pm 2.3 \cdot 10^{-3} \) \(a_{12}= -0.65124025 \pm 3.2 \cdot 10^{-3} \)
\(a_{13}= +0.56369412 \pm 2.4 \cdot 10^{-3} \) \(a_{14}= -1.73245918 \pm 3.1 \cdot 10^{-3} \) \(a_{15}= -1.00825721 \pm 3.0 \cdot 10^{-3} \)
\(a_{16}= -1.19767986 \pm 2.8 \cdot 10^{-3} \) \(a_{17}= +1.26083477 \pm 2.3 \cdot 10^{-3} \) \(a_{18}= +0.26477268 \pm 3.3 \cdot 10^{-3} \)
\(a_{19}= -0.54630671 \pm 2.3 \cdot 10^{-3} \) \(a_{20}= +0.82218680 \pm 3.3 \cdot 10^{-3} \) \(a_{21}= -1.17752386 \pm 2.7 \cdot 10^{-3} \)
\(a_{22}= -0.46368740 \pm 2.9 \cdot 10^{-3} \) \(a_{23}= -0.02752669 \pm 2.1 \cdot 10^{-3} \) \(a_{24}= -0.31873342 \pm 3.0 \cdot 10^{-3} \)
\(a_{25}= +0.27291850 \pm 2.4 \cdot 10^{-3} \) \(a_{26}= -0.74115294 \pm 2.9 \cdot 10^{-3} \) \(a_{27}= +1.07361897 \pm 2.7 \cdot 10^{-3} \)
\(a_{28}= +0.96021587 \pm 3.2 \cdot 10^{-3} \) \(a_{29}= -0.38155300 \pm 2.3 \cdot 10^{-3} \) \(a_{30}= +1.32567073 \pm 3.4 \cdot 10^{-3} \)
\(a_{31}= +0.90102118 \pm 2.3 \cdot 10^{-3} \) \(a_{32}= +1.21806453 \pm 2.8 \cdot 10^{-3} \) \(a_{33}= -0.31516066 \pm 2.5 \cdot 10^{-3} \)
\(a_{34}= -1.65776326 \pm 2.9 \cdot 10^{-3} \) \(a_{35}= +1.48661659 \pm 2.7 \cdot 10^{-3} \) \(a_{36}= -0.14675031 \pm 3.3 \cdot 10^{-3} \)
\(a_{37}= -1.44045004 \pm 2.4 \cdot 10^{-3} \) \(a_{38}= +0.71829173 \pm 2.9 \cdot 10^{-3} \) \(a_{39}= -0.50374940 \pm 2.7 \cdot 10^{-3} \)
\(a_{40}= +0.40239897 \pm 2.9 \cdot 10^{-3} \) \(a_{41}= -0.26320984 \pm 2.2 \cdot 10^{-3} \) \(a_{42}= +1.54822490 \pm 3.2 \cdot 10^{-3} \)
\(a_{43}= +0.80871416 \pm 2.4 \cdot 10^{-3} \) \(a_{44}= +0.25699884 \pm 3.0 \cdot 10^{-3} \) \(a_{45}= -0.22720042 \pm 3.0 \cdot 10^{-3} \)
\(a_{46}= +0.03619247 \pm 2.3 \cdot 10^{-3} \) \(a_{47}= -1.27925309 \pm 2.2 \cdot 10^{-3} \) \(a_{48}= +1.07031542 \pm 2.7 \cdot 10^{-3} \)
\(a_{49}= +0.73619041 \pm 2.4 \cdot 10^{-3} \) \(a_{50}= -0.35883707 \pm 2.8 \cdot 10^{-3} \) \(a_{51}= -1.12675428 \pm 2.4 \cdot 10^{-3} \)
\(a_{52}= +0.41078418 \pm 2.9 \cdot 10^{-3} \) \(a_{53}= -0.91296801 \pm 2.4 \cdot 10^{-3} \) \(a_{54}= -1.41160930 \pm 3.4 \cdot 10^{-3} \)
\(a_{55}= +0.39788838 \pm 2.4 \cdot 10^{-3} \) \(a_{56}= +0.46995388 \pm 3.0 \cdot 10^{-3} \) \(a_{57}= +0.48821101 \pm 2.5 \cdot 10^{-3} \)
\(a_{58}= +0.50167124 \pm 2.6 \cdot 10^{-3} \) \(a_{59}= -0.33352770 \pm 2.3 \cdot 10^{-3} \) \(a_{60}= -0.73475328 \pm 3.5 \cdot 10^{-3} \)

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