Properties

Label 73.6
Level $73$
Weight $0$
Character 73.1
Symmetry even
\(R\) 1.184465
Fricke sign $+1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(1.18446512992280084837106579491 \pm 5 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.06675422 \pm 9.6 \cdot 10^{-6} \) \(a_{3}= -0.08170148 \pm 9.1 \cdot 10^{-6} \)
\(a_{4}= -0.99554387 \pm 1.0 \cdot 10^{-5} \) \(a_{5}= +1.54288464 \pm 8.5 \cdot 10^{-6} \) \(a_{6}= -0.00545392 \pm 1.1 \cdot 10^{-5} \)
\(a_{7}= -1.29769652 \pm 8.2 \cdot 10^{-6} \) \(a_{8}= -0.13321098 \pm 1.0 \cdot 10^{-5} \) \(a_{9}= -0.99332487 \pm 9.6 \cdot 10^{-6} \)
\(a_{10}= +0.10299406 \pm 9.8 \cdot 10^{-6} \) \(a_{11}= +1.55394798 \pm 8.3 \cdot 10^{-6} \) \(a_{12}= +0.08133740 \pm 1.1 \cdot 10^{-5} \)
\(a_{13}= +0.85149077 \pm 8.1 \cdot 10^{-6} \) \(a_{14}= -0.08662672 \pm 9.7 \cdot 10^{-6} \) \(a_{15}= -0.12605595 \pm 8.8 \cdot 10^{-6} \)
\(a_{16}= +0.98665148 \pm 1.0 \cdot 10^{-5} \) \(a_{17}= +1.23116849 \pm 8.3 \cdot 10^{-6} \) \(a_{18}= -0.06630863 \pm 1.1 \cdot 10^{-5} \)
\(a_{19}= -0.92631112 \pm 7.8 \cdot 10^{-6} \) \(a_{20}= -1.53600935 \pm 1.0 \cdot 10^{-5} \) \(a_{21}= +0.10602372 \pm 9.0 \cdot 10^{-6} \)
\(a_{22}= +0.10373259 \pm 9.5 \cdot 10^{-6} \) \(a_{23}= -0.53531330 \pm 7.5 \cdot 10^{-6} \) \(a_{24}= +0.01088353 \pm 1.1 \cdot 10^{-5} \)
\(a_{25}= +1.38049302 \pm 9.0 \cdot 10^{-6} \) \(a_{26}= +0.05684060 \pm 9.7 \cdot 10^{-6} \) \(a_{27}= +0.16285759 \pm 9.9 \cdot 10^{-6} \)
\(a_{28}= +1.29191382 \pm 1.0 \cdot 10^{-5} \) \(a_{29}= -0.05728360 \pm 7.5 \cdot 10^{-6} \) \(a_{30}= -0.00841477 \pm 1.2 \cdot 10^{-5} \)
\(a_{31}= -0.80375917 \pm 7.9 \cdot 10^{-6} \) \(a_{32}= +0.19907413 \pm 1.0 \cdot 10^{-5} \) \(a_{33}= -0.12695984 \pm 9.3 \cdot 10^{-6} \)
\(a_{34}= +0.08218569 \pm 9.5 \cdot 10^{-6} \) \(a_{35}= -2.00219604 \pm 8.4 \cdot 10^{-6} \) \(a_{36}= +0.98889849 \pm 1.2 \cdot 10^{-5} \)
\(a_{37}= +0.09336283 \pm 8.3 \cdot 10^{-6} \) \(a_{38}= -0.06183518 \pm 9.2 \cdot 10^{-6} \) \(a_{39}= -0.06956805 \pm 9.8 \cdot 10^{-6} \)
\(a_{40}= -0.20552917 \pm 1.0 \cdot 10^{-5} \) \(a_{41}= -1.08551850 \pm 7.9 \cdot 10^{-6} \) \(a_{42}= +0.00707753 \pm 1.1 \cdot 10^{-5} \)
\(a_{43}= +0.22147930 \pm 7.1 \cdot 10^{-6} \) \(a_{44}= -1.54702339 \pm 9.2 \cdot 10^{-6} \) \(a_{45}= -1.53258569 \pm 9.4 \cdot 10^{-6} \)
\(a_{46}= -0.03573442 \pm 9.5 \cdot 10^{-6} \) \(a_{47}= +0.27327851 \pm 8.0 \cdot 10^{-6} \) \(a_{48}= -0.08061088 \pm 1.1 \cdot 10^{-5} \)
\(a_{49}= +0.68401627 \pm 8.0 \cdot 10^{-6} \) \(a_{50}= +0.09215374 \pm 1.0 \cdot 10^{-5} \) \(a_{51}= -0.10058828 \pm 9.3 \cdot 10^{-6} \)
\(a_{52}= -0.84769642 \pm 1.0 \cdot 10^{-5} \) \(a_{53}= +1.89130444 \pm 7.8 \cdot 10^{-6} \) \(a_{54}= +0.01087143 \pm 1.1 \cdot 10^{-5} \)
\(a_{55}= +2.39756247 \pm 8.8 \cdot 10^{-6} \) \(a_{56}= +0.17286742 \pm 1.1 \cdot 10^{-5} \) \(a_{57}= +0.07568099 \pm 8.3 \cdot 10^{-6} \)
\(a_{58}= -0.00382392 \pm 8.2 \cdot 10^{-6} \) \(a_{59}= -0.68462299 \pm 7.6 \cdot 10^{-6} \) \(a_{60}= +0.12549423 \pm 1.2 \cdot 10^{-5} \)

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