Properties

Label 14.22
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 6.716314
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: \(6.71631419389318421520419728568 \pm 4 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.12058904 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.50760027 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.08526933 \pm 1.1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.98545828 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +1.06603438 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= +0.66822078 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.06029452 \pm 1.1 \cdot 10^{-8} \)
\(a_{13}= +0.85901338 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.18180007 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.49000872 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.69682423 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= -1.31652653 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.75380014 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= +0.04557837 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= -0.47250344 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= +1.29291644 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.04263466 \pm 1.1 \cdot 10^{-8} \)
\(a_{25}= +1.27285858 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.60741419 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +0.23942451 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +0.93027161 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.12855206 \pm 1.2 \cdot 10^{-8} \)
\(a_{31}= -0.36294163 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.08058010 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.05359527 \pm 1.1 \cdot 10^{-8} \) \(a_{35}= +0.56981934 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -0.49272914 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -1.46605557 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.93092484 \pm 1.1 \cdot 10^{-8} \) \(a_{39}= -0.10358760 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.53301719 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +0.67822954 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.03222878 \pm 1.1 \cdot 10^{-8} \)
\(a_{43}= +0.64919903 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.33411039 \pm 1.1 \cdot 10^{-8} \) \(a_{45}= +1.48567718 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.91422998 \pm 1.1 \cdot 10^{-8} \) \(a_{47}= -0.79855654 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.03014726 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.90004694 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= -0.17967872 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.42950669 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= +0.40713606 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.16929869 \pm 1.1 \cdot 10^{-8} \)
\(a_{55}= -1.00740982 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.15875867 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.65780137 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= -0.61689880 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.09090004 \pm 1.2 \cdot 10^{-8} \)

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