Properties

Label 73.35
Level $73$
Weight $0$
Character 73.1
Symmetry even
\(R\) 2.589579
Fricke sign $-1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(2.5895791747070862738626863877 \pm 3 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.06732048 \pm 1.1 \cdot 10^{-4} \) \(a_{3}= +0.91537316 \pm 1.0 \cdot 10^{-4} \)
\(a_{4}= -0.99546795 \pm 1.1 \cdot 10^{-4} \) \(a_{5}= +0.00979546 \pm 9.7 \cdot 10^{-5} \) \(a_{6}= -0.06162336 \pm 1.2 \cdot 10^{-4} \)
\(a_{7}= -1.30713767 \pm 9.4 \cdot 10^{-5} \) \(a_{8}= +0.13433586 \pm 1.2 \cdot 10^{-4} \) \(a_{9}= -0.16209197 \pm 1.1 \cdot 10^{-4} \)
\(a_{10}= -0.00065943 \pm 1.1 \cdot 10^{-4} \) \(a_{11}= -0.20046870 \pm 9.5 \cdot 10^{-5} \) \(a_{12}= -0.91122465 \pm 1.3 \cdot 10^{-4} \)
\(a_{13}= +0.81947891 \pm 9.3 \cdot 10^{-5} \) \(a_{14}= +0.08799714 \pm 1.1 \cdot 10^{-4} \) \(a_{15}= +0.00896650 \pm 1.0 \cdot 10^{-4} \)
\(a_{16}= +0.98642440 \pm 1.2 \cdot 10^{-4} \) \(a_{17}= -1.41386089 \pm 9.5 \cdot 10^{-5} \) \(a_{18}= +0.01091211 \pm 1.3 \cdot 10^{-4} \)
\(a_{19}= +0.67086170 \pm 8.9 \cdot 10^{-5} \) \(a_{20}= -0.00975106 \pm 1.1 \cdot 10^{-4} \) \(a_{21}= -1.19651874 \pm 1.0 \cdot 10^{-4} \)
\(a_{22}= +0.01349565 \pm 1.0 \cdot 10^{-4} \) \(a_{23}= +0.29332238 \pm 8.6 \cdot 10^{-5} \) \(a_{24}= +0.12296744 \pm 1.3 \cdot 10^{-4} \)
\(a_{25}= -0.99990405 \pm 1.0 \cdot 10^{-4} \) \(a_{26}= -0.05516771 \pm 1.1 \cdot 10^{-4} \) \(a_{27}= -1.06374780 \pm 1.1 \cdot 10^{-4} \)
\(a_{28}= +1.30121366 \pm 1.2 \cdot 10^{-4} \) \(a_{29}= -1.04989655 \pm 8.5 \cdot 10^{-5} \) \(a_{30}= -0.00060363 \pm 1.3 \cdot 10^{-4} \)
\(a_{31}= -1.91012676 \pm 9.1 \cdot 10^{-5} \) \(a_{32}= -0.20074243 \pm 1.2 \cdot 10^{-4} \) \(a_{33}= -0.18350366 \pm 1.0 \cdot 10^{-4} \)
\(a_{34}= +0.09518179 \pm 1.0 \cdot 10^{-4} \) \(a_{35}= -0.01280401 \pm 9.6 \cdot 10^{-5} \) \(a_{36}= +0.16135736 \pm 1.4 \cdot 10^{-4} \)
\(a_{37}= +1.17374024 \pm 9.5 \cdot 10^{-5} \) \(a_{38}= -0.04516273 \pm 1.0 \cdot 10^{-4} \) \(a_{39}= +0.75012900 \pm 1.1 \cdot 10^{-4} \)
\(a_{40}= +0.00131588 \pm 1.2 \cdot 10^{-4} \) \(a_{41}= +1.32381016 \pm 9.0 \cdot 10^{-5} \) \(a_{42}= +0.08055022 \pm 1.3 \cdot 10^{-4} \)
\(a_{43}= +0.98946696 \pm 8.1 \cdot 10^{-5} \) \(a_{44}= +0.19956016 \pm 1.0 \cdot 10^{-4} \) \(a_{45}= -0.00158777 \pm 1.0 \cdot 10^{-4} \)
\(a_{46}= -0.01974660 \pm 1.0 \cdot 10^{-4} \) \(a_{47}= -0.74519930 \pm 9.1 \cdot 10^{-5} \) \(a_{48}= +0.90294642 \pm 1.3 \cdot 10^{-4} \)
\(a_{49}= +0.70860889 \pm 9.2 \cdot 10^{-5} \) \(a_{50}= +0.06731402 \pm 1.2 \cdot 10^{-4} \) \(a_{51}= -1.29421032 \pm 1.0 \cdot 10^{-4} \)
\(a_{52}= -0.81576499 \pm 1.1 \cdot 10^{-4} \) \(a_{53}= +0.07297901 \pm 8.9 \cdot 10^{-5} \) \(a_{54}= +0.07161201 \pm 1.3 \cdot 10^{-4} \)
\(a_{55}= -0.00196368 \pm 1.0 \cdot 10^{-4} \) \(a_{56}= -0.17559547 \pm 1.3 \cdot 10^{-4} \) \(a_{57}= +0.61408880 \pm 9.5 \cdot 10^{-5} \)
\(a_{58}= +0.07067954 \pm 9.4 \cdot 10^{-5} \) \(a_{59}= -0.33771366 \pm 8.8 \cdot 10^{-5} \) \(a_{60}= -0.00892586 \pm 1.4 \cdot 10^{-4} \)

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