Properties

Label 14.30
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 7.873827
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: \(7.87382712891465986769670563022 \pm 6 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.36999772 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.17054788 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.96873468 \pm 1.3 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.87689376 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.82770235 \pm 1.4 \cdot 10^{-8} \) \(a_{11}= -1.50412794 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.68499886 \pm 1.3 \cdot 10^{-8} \)
\(a_{13}= +1.59984689 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -1.60364794 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.15792340 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.62005753 \pm 1.4 \cdot 10^{-8} \)
\(a_{19}= -0.93893155 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.58527394 \pm 1.4 \cdot 10^{-8} \) \(a_{21}= +0.51781047 \pm 1.3 \cdot 10^{-8} \)
\(a_{22}= +1.06357907 \pm 1.5 \cdot 10^{-8} \) \(a_{23}= -0.65106737 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.48436734 \pm 1.3 \cdot 10^{-8} \)
\(a_{25}= +0.37018235 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.13126259 \pm 1.3 \cdot 10^{-8} \) \(a_{27}= -0.16865527 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -1.11816317 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.13395033 \pm 1.6 \cdot 10^{-8} \)
\(a_{31}= +0.02659883 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -2.06065186 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.81877549 \pm 1.4 \cdot 10^{-8} \) \(a_{35}= -0.44242551 \pm 1.4 \cdot 10^{-8} \) \(a_{36}= +0.43844688 \pm 1.4 \cdot 10^{-8} \)
\(a_{37}= -0.82537214 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.66392487 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= +2.19178660 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.41385117 \pm 1.4 \cdot 10^{-8} \) \(a_{41}= +0.28666375 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.36614729 \pm 1.3 \cdot 10^{-8} \)
\(a_{43}= -0.45106685 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.75206397 \pm 1.5 \cdot 10^{-8} \) \(a_{45}= -1.02644614 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.46037415 \pm 1.2 \cdot 10^{-8} \) \(a_{47}= -0.86609084 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.34249943 \pm 1.3 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.26175845 \pm 1.5 \cdot 10^{-8} \) \(a_{51}= -1.58635243 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.79992345 \pm 1.3 \cdot 10^{-8} \) \(a_{53}= +0.42878621 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.11925728 \pm 1.3 \cdot 10^{-8} \)
\(a_{55}= +1.76065378 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= -1.28633409 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.79066076 \pm 1.3 \cdot 10^{-8} \) \(a_{59}= +1.11555433 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.80182397 \pm 1.6 \cdot 10^{-8} \)

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