Properties

Label 73.40
Level $73$
Weight $0$
Character 73.1
Symmetry even
\(R\) 2.811108
Fricke sign $-1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(2.81110814874877299643762512071 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.84956970 \pm 2.1 \cdot 10^{-4} \) \(a_{3}= +1.72942382 \pm 2.0 \cdot 10^{-4} \)
\(a_{4}= +2.42090806 \pm 2.3 \cdot 10^{-4} \) \(a_{5}= +0.04235488 \pm 1.9 \cdot 10^{-4} \) \(a_{6}= -3.19868988 \pm 2.5 \cdot 10^{-4} \)
\(a_{7}= -1.32249430 \pm 1.8 \cdot 10^{-4} \) \(a_{8}= -2.62806850 \pm 2.3 \cdot 10^{-4} \) \(a_{9}= +1.99090674 \pm 2.1 \cdot 10^{-4} \)
\(a_{10}= -0.07833830 \pm 2.2 \cdot 10^{-4} \) \(a_{11}= -0.93852004 \pm 1.8 \cdot 10^{-4} \) \(a_{12}= +4.18677606 \pm 2.6 \cdot 10^{-4} \)
\(a_{13}= -1.84497023 \pm 1.8 \cdot 10^{-4} \) \(a_{14}= +2.44604539 \pm 2.2 \cdot 10^{-4} \) \(a_{15}= +0.07324954 \pm 1.9 \cdot 10^{-4} \)
\(a_{16}= +2.43988779 \pm 2.4 \cdot 10^{-4} \) \(a_{17}= -0.41400604 \pm 1.8 \cdot 10^{-4} \) \(a_{18}= -3.68232077 \pm 2.5 \cdot 10^{-4} \)
\(a_{19}= -0.42963565 \pm 1.7 \cdot 10^{-4} \) \(a_{20}= +0.10253727 \pm 2.3 \cdot 10^{-4} \) \(a_{21}= -2.28715314 \pm 2.0 \cdot 10^{-4} \)
\(a_{22}= +1.73585823 \pm 2.1 \cdot 10^{-4} \) \(a_{23}= +0.34049461 \pm 1.7 \cdot 10^{-4} \) \(a_{24}= -4.54504425 \pm 2.6 \cdot 10^{-4} \)
\(a_{25}= -0.99820606 \pm 2.0 \cdot 10^{-4} \) \(a_{26}= +3.41240103 \pm 2.2 \cdot 10^{-4} \) \(a_{27}= +1.71369771 \pm 2.2 \cdot 10^{-4} \)
\(a_{28}= -3.20163712 \pm 2.4 \cdot 10^{-4} \) \(a_{29}= +0.90027622 \pm 1.6 \cdot 10^{-4} \) \(a_{30}= -0.13548012 \pm 2.7 \cdot 10^{-4} \)
\(a_{31}= +0.04088743 \pm 1.7 \cdot 10^{-4} \) \(a_{32}= -1.88467403 \pm 2.3 \cdot 10^{-4} \) \(a_{33}= -1.62309892 \pm 2.0 \cdot 10^{-4} \)
\(a_{34}= +0.76573303 \pm 2.1 \cdot 10^{-4} \) \(a_{35}= -0.05601409 \pm 1.8 \cdot 10^{-4} \) \(a_{36}= +4.81980217 \pm 2.8 \cdot 10^{-4} \)
\(a_{37}= +0.00838787 \pm 1.8 \cdot 10^{-4} \) \(a_{38}= +0.79464108 \pm 2.0 \cdot 10^{-4} \) \(a_{39}= -3.19073546 \pm 2.2 \cdot 10^{-4} \)
\(a_{40}= -0.11131152 \pm 2.4 \cdot 10^{-4} \) \(a_{41}= -0.41437854 \pm 1.7 \cdot 10^{-4} \) \(a_{42}= +4.23024915 \pm 2.6 \cdot 10^{-4} \)
\(a_{43}= -0.91900581 \pm 1.6 \cdot 10^{-4} \) \(a_{44}= -2.27207074 \pm 2.0 \cdot 10^{-4} \) \(a_{45}= +0.08432461 \pm 2.1 \cdot 10^{-4} \)
\(a_{46}= -0.62976851 \pm 2.1 \cdot 10^{-4} \) \(a_{47}= +1.29921536 \pm 1.8 \cdot 10^{-4} \) \(a_{48}= +4.21960006 \pm 2.6 \cdot 10^{-4} \)
\(a_{49}= +0.74899118 \pm 1.8 \cdot 10^{-4} \) \(a_{50}= +1.84625169 \pm 2.4 \cdot 10^{-4} \) \(a_{51}= -0.71599191 \pm 2.1 \cdot 10^{-4} \)
\(a_{52}= -4.46650331 \pm 2.2 \cdot 10^{-4} \) \(a_{53}= +0.72851625 \pm 1.7 \cdot 10^{-4} \) \(a_{54}= -3.16960335 \pm 2.6 \cdot 10^{-4} \)
\(a_{55}= -0.03975090 \pm 1.9 \cdot 10^{-4} \) \(a_{56}= +3.47560562 \pm 2.6 \cdot 10^{-4} \) \(a_{57}= -0.74302213 \pm 1.8 \cdot 10^{-4} \)
\(a_{58}= -1.66512361 \pm 1.8 \cdot 10^{-4} \) \(a_{59}= +0.19229991 \pm 1.7 \cdot 10^{-4} \) \(a_{60}= +0.17733040 \pm 2.8 \cdot 10^{-4} \)

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