Properties

Label 73.18
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 1.964156
Fricke sign $+1$

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(1.96415694760994221117702822027 \pm 2 \cdot 10^{-5}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.84057092 \pm 5.7 \cdot 10^{-2} \) \(a_{3}= -0.28907129 \pm 5.3 \cdot 10^{-2} \)
\(a_{4}= +2.38770130 \pm 5.9 \cdot 10^{-2} \) \(a_{5}= +1.36015855 \pm 5.1 \cdot 10^{-2} \) \(a_{6}= +0.53205622 \pm 6.3 \cdot 10^{-2} \)
\(a_{7}= -0.97777461 \pm 4.9 \cdot 10^{-2} \) \(a_{8}= -2.55416264 \pm 5.7 \cdot 10^{-2} \) \(a_{9}= -0.91643779 \pm 5.2 \cdot 10^{-2} \)
\(a_{10}= -2.50346827 \pm 6.3 \cdot 10^{-2} \) \(a_{11}= +0.96441944 \pm 4.6 \cdot 10^{-2} \) \(a_{12}= -0.69021590 \pm 6.4 \cdot 10^{-2} \)
\(a_{13}= -0.47077974 \pm 4.7 \cdot 10^{-2} \) \(a_{14}= +1.79966350 \pm 6.1 \cdot 10^{-2} \) \(a_{15}= -0.39318279 \pm 5.9 \cdot 10^{-2} \)
\(a_{16}= +2.31341618 \pm 5.5 \cdot 10^{-2} \) \(a_{17}= -1.76815764 \pm 4.5 \cdot 10^{-2} \) \(a_{18}= +1.68676874 \pm 6.5 \cdot 10^{-2} \)
\(a_{19}= -1.31224089 \pm 4.7 \cdot 10^{-2} \) \(a_{20}= +3.24765233 \pm 6.6 \cdot 10^{-2} \) \(a_{21}= +0.28264657 \pm 5.4 \cdot 10^{-2} \)
\(a_{22}= -1.77508238 \pm 5.8 \cdot 10^{-2} \) \(a_{23}= -0.21992318 \pm 4.2 \cdot 10^{-2} \) \(a_{24}= +0.73833510 \pm 5.9 \cdot 10^{-2} \)
\(a_{25}= +0.85003128 \pm 4.8 \cdot 10^{-2} \) \(a_{26}= +0.86650350 \pm 5.7 \cdot 10^{-2} \) \(a_{27}= +0.55398715 \pm 5.3 \cdot 10^{-2} \)
\(a_{28}= -2.33463369 \pm 6.4 \cdot 10^{-2} \) \(a_{29}= -0.37524839 \pm 4.6 \cdot 10^{-2} \) \(a_{30}= +0.72368081 \pm 6.6 \cdot 10^{-2} \)
\(a_{31}= +0.10848487 \pm 4.5 \cdot 10^{-2} \) \(a_{32}= -1.70384389 \pm 5.5 \cdot 10^{-2} \) \(a_{33}= -0.27878598 \pm 5.0 \cdot 10^{-2} \)
\(a_{34}= +3.25441954 \pm 5.7 \cdot 10^{-2} \) \(a_{35}= -1.32992849 \pm 5.4 \cdot 10^{-2} \) \(a_{36}= -2.18817969 \pm 6.5 \cdot 10^{-2} \)
\(a_{37}= -1.87319592 \pm 4.7 \cdot 10^{-2} \) \(a_{38}= +2.41527241 \pm 5.8 \cdot 10^{-2} \) \(a_{39}= +0.13608891 \pm 5.4 \cdot 10^{-2} \)
\(a_{40}= -3.47406616 \pm 5.7 \cdot 10^{-2} \) \(a_{41}= +0.95537476 \pm 4.5 \cdot 10^{-2} \) \(a_{42}= -0.52023106 \pm 6.4 \cdot 10^{-2} \)
\(a_{43}= +0.63809146 \pm 4.8 \cdot 10^{-2} \) \(a_{44}= +2.30274555 \pm 6.0 \cdot 10^{-2} \) \(a_{45}= -1.24650069 \pm 5.9 \cdot 10^{-2} \)
\(a_{46}= +0.40478422 \pm 4.7 \cdot 10^{-2} \) \(a_{47}= +0.57067635 \pm 4.3 \cdot 10^{-2} \) \(a_{48}= -0.66874221 \pm 5.4 \cdot 10^{-2} \)
\(a_{49}= -0.04395682 \pm 4.7 \cdot 10^{-2} \) \(a_{50}= -1.56454286 \pm 5.6 \cdot 10^{-2} \) \(a_{51}= +0.51112362 \pm 4.8 \cdot 10^{-2} \)
\(a_{52}= -1.12408140 \pm 5.8 \cdot 10^{-2} \) \(a_{53}= -1.12331270 \pm 4.7 \cdot 10^{-2} \) \(a_{54}= -1.01965264 \pm 6.7 \cdot 10^{-2} \)
\(a_{55}= +1.31176335 \pm 4.8 \cdot 10^{-2} \) \(a_{56}= +2.49739537 \pm 6.0 \cdot 10^{-2} \) \(a_{57}= +0.37933117 \pm 5.1 \cdot 10^{-2} \)
\(a_{58}= +0.69067127 \pm 5.2 \cdot 10^{-2} \) \(a_{59}= +0.82567449 \pm 4.5 \cdot 10^{-2} \) \(a_{60}= -0.93880306 \pm 7.0 \cdot 10^{-2} \)

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