Properties

Label 14.21
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 6.591939
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(6.59193983827603760685421536511 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.86994212 \pm 3.8 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.63980237 \pm 2.9 \cdot 10^{-8} \) \(a_{6}= -1.32224875 \pm 4.9 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.49668353 \pm 3.0 \cdot 10^{-8} \)
\(a_{10}= -0.45240859 \pm 4.0 \cdot 10^{-8} \) \(a_{11}= +0.40385661 \pm 3.0 \cdot 10^{-8} \) \(a_{12}= -0.93497106 \pm 4.9 \cdot 10^{-8} \)
\(a_{13}= +1.50840800 \pm 2.8 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +1.19639340 \pm 3.7 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.46575662 \pm 1.9 \cdot 10^{-8} \) \(a_{18}= +1.76542186 \pm 4.1 \cdot 10^{-8} \)
\(a_{19}= -0.73058617 \pm 2.9 \cdot 10^{-8} \) \(a_{20}= -0.31990118 \pm 4.0 \cdot 10^{-8} \) \(a_{21}= +0.70677169 \pm 4.9 \cdot 10^{-8} \)
\(a_{22}= +0.28556975 \pm 4.1 \cdot 10^{-8} \) \(a_{23}= +0.76982978 \pm 2.7 \cdot 10^{-8} \) \(a_{24}= -0.66112438 \pm 4.9 \cdot 10^{-8} \)
\(a_{25}= -0.59065293 \pm 2.3 \cdot 10^{-8} \) \(a_{26}= +1.06660552 \pm 3.9 \cdot 10^{-8} \) \(a_{27}= -2.79871158 \pm 2.8 \cdot 10^{-8} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +1.44818905 \pm 3.3 \cdot 10^{-8} \) \(a_{30}= +0.84597788 \pm 7.9 \cdot 10^{-8} \)
\(a_{31}= +0.50607476 \pm 3.2 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.75518848 \pm 3.6 \cdot 10^{-8} \)
\(a_{34}= -0.32933967 \pm 3.0 \cdot 10^{-8} \) \(a_{35}= +0.24182256 \pm 4.0 \cdot 10^{-8} \) \(a_{36}= +1.24834177 \pm 4.1 \cdot 10^{-8} \)
\(a_{37}= +1.31433900 \pm 2.3 \cdot 10^{-8} \) \(a_{38}= -0.51660244 \pm 4.0 \cdot 10^{-8} \) \(a_{39}= -2.82063565 \pm 3.3 \cdot 10^{-8} \)
\(a_{40}= -0.22620430 \pm 4.0 \cdot 10^{-8} \) \(a_{41}= +0.57912690 \pm 1.9 \cdot 10^{-8} \) \(a_{42}= +0.49976305 \pm 4.9 \cdot 10^{-8} \)
\(a_{43}= +0.37696802 \pm 3.0 \cdot 10^{-8} \) \(a_{44}= +0.20192830 \pm 4.1 \cdot 10^{-8} \) \(a_{45}= -1.59738404 \pm 2.6 \cdot 10^{-8} \)
\(a_{46}= +0.54435186 \pm 3.7 \cdot 10^{-8} \) \(a_{47}= +0.45080554 \pm 2.1 \cdot 10^{-8} \) \(a_{48}= -0.46748553 \pm 4.9 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.41765469 \pm 3.3 \cdot 10^{-8} \) \(a_{51}= +0.87093793 \pm 2.3 \cdot 10^{-8} \)
\(a_{52}= +0.75420400 \pm 3.9 \cdot 10^{-8} \) \(a_{53}= -0.21726435 \pm 2.9 \cdot 10^{-8} \) \(a_{54}= -1.97898793 \pm 3.9 \cdot 10^{-8} \)
\(a_{55}= -0.25838841 \pm 2.8 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +1.36615386 \pm 4.2 \cdot 10^{-8} \)
\(a_{58}= +1.02402430 \pm 4.3 \cdot 10^{-8} \) \(a_{59}= +0.09200219 \pm 3.1 \cdot 10^{-8} \) \(a_{60}= +0.59819670 \pm 7.9 \cdot 10^{-8} \)

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