Properties

Label 14.96
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 13.72298
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(13.7229827041542024618797899614 \pm 5 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.97406954 \pm 5.7 \cdot 10^{-7} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.99642243 \pm 8.6 \cdot 10^{-7} \) \(a_{6}= +1.39587796 \pm 5.8 \cdot 10^{-7} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.89695054 \pm 7.9 \cdot 10^{-7} \)
\(a_{10}= +0.70457706 \pm 8.7 \cdot 10^{-7} \) \(a_{11}= -0.81746955 \pm 1.0 \cdot 10^{-6} \) \(a_{12}= +0.98703477 \pm 5.8 \cdot 10^{-7} \)
\(a_{13}= +0.08680522 \pm 7.3 \cdot 10^{-7} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +1.96700717 \pm 5.8 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.26373710 \pm 9.4 \cdot 10^{-7} \) \(a_{18}= +2.04845337 \pm 8.0 \cdot 10^{-7} \)
\(a_{19}= +1.14289288 \pm 6.2 \cdot 10^{-7} \) \(a_{20}= +0.49821122 \pm 8.7 \cdot 10^{-7} \) \(a_{21}= +0.74612815 \pm 5.8 \cdot 10^{-7} \)
\(a_{22}= -0.57803826 \pm 1.0 \cdot 10^{-6} \) \(a_{23}= +0.08959890 \pm 5.1 \cdot 10^{-7} \) \(a_{24}= +0.69793898 \pm 5.8 \cdot 10^{-7} \)
\(a_{25}= -0.00714234 \pm 1.0 \cdot 10^{-6} \) \(a_{26}= +0.06138056 \pm 7.4 \cdot 10^{-7} \) \(a_{27}= +3.74471228 \pm 6.2 \cdot 10^{-7} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.32649023 \pm 7.8 \cdot 10^{-7} \) \(a_{30}= +1.39088411 \pm 1.4 \cdot 10^{-6} \)
\(a_{31}= +0.07066552 \pm 9.1 \cdot 10^{-7} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.61374173 \pm 5.3 \cdot 10^{-7} \)
\(a_{34}= -0.89359707 \pm 9.5 \cdot 10^{-7} \) \(a_{35}= +0.37661228 \pm 8.7 \cdot 10^{-7} \) \(a_{36}= +1.44847527 \pm 8.0 \cdot 10^{-7} \)
\(a_{37}= -1.16605999 \pm 3.9 \cdot 10^{-7} \) \(a_{38}= +0.80814731 \pm 6.3 \cdot 10^{-7} \) \(a_{39}= +0.17135954 \pm 8.1 \cdot 10^{-7} \)
\(a_{40}= +0.35228853 \pm 8.7 \cdot 10^{-7} \) \(a_{41}= -1.71470670 \pm 8.2 \cdot 10^{-7} \) \(a_{42}= +0.52759228 \pm 5.8 \cdot 10^{-7} \)
\(a_{43}= -1.60534037 \pm 5.8 \cdot 10^{-7} \) \(a_{44}= -0.40873477 \pm 1.0 \cdot 10^{-6} \) \(a_{45}= +2.88658651 \pm 8.7 \cdot 10^{-7} \)
\(a_{46}= +0.06335599 \pm 5.2 \cdot 10^{-7} \) \(a_{47}= +0.26777542 \pm 6.9 \cdot 10^{-7} \) \(a_{48}= +0.49351738 \pm 5.8 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.00505039 \pm 1.0 \cdot 10^{-6} \) \(a_{51}= -2.49470491 \pm 4.7 \cdot 10^{-7} \)
\(a_{52}= +0.04340261 \pm 7.4 \cdot 10^{-7} \) \(a_{53}= +0.91881566 \pm 9.2 \cdot 10^{-7} \) \(a_{54}= +2.64791145 \pm 6.3 \cdot 10^{-7} \)
\(a_{55}= -0.81454499 \pm 9.1 \cdot 10^{-7} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +2.25615002 \pm 5.3 \cdot 10^{-7} \)
\(a_{58}= -0.23086346 \pm 7.9 \cdot 10^{-7} \) \(a_{59}= +0.95545462 \pm 7.3 \cdot 10^{-7} \) \(a_{60}= +0.98350359 \pm 1.4 \cdot 10^{-6} \)

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