Properties

Label 14.40
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 9.012234
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: \(9.01223427143471551134852797462 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.32605651 \pm 3.0 \cdot 10^{-7} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.06778317 \pm 2.3 \cdot 10^{-7} \) \(a_{6}= -0.23055677 \pm 3.1 \cdot 10^{-7} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.89368715 \pm 2.3 \cdot 10^{-7} \)
\(a_{10}= -0.04792994 \pm 2.4 \cdot 10^{-7} \) \(a_{11}= +0.91213181 \pm 2.3 \cdot 10^{-7} \) \(a_{12}= +0.16302826 \pm 3.1 \cdot 10^{-7} \)
\(a_{13}= +1.66764889 \pm 2.2 \cdot 10^{-7} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.02210114 \pm 2.8 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.53705740 \pm 1.5 \cdot 10^{-7} \) \(a_{18}= +0.63193225 \pm 2.4 \cdot 10^{-7} \)
\(a_{19}= +0.04254184 \pm 2.3 \cdot 10^{-7} \) \(a_{20}= +0.03389158 \pm 2.4 \cdot 10^{-7} \) \(a_{21}= -0.12323778 \pm 3.1 \cdot 10^{-7} \)
\(a_{22}= -0.64497459 \pm 2.5 \cdot 10^{-7} \) \(a_{23}= +0.10518264 \pm 2.1 \cdot 10^{-7} \) \(a_{24}= -0.11527838 \pm 3.1 \cdot 10^{-7} \)
\(a_{25}= -0.99540544 \pm 1.8 \cdot 10^{-7} \) \(a_{26}= -1.17920584 \pm 2.3 \cdot 10^{-7} \) \(a_{27}= -0.61744902 \pm 2.2 \cdot 10^{-7} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.15169290 \pm 2.5 \cdot 10^{-7} \) \(a_{30}= -0.01562787 \pm 5.4 \cdot 10^{-7} \)
\(a_{31}= -0.95062884 \pm 2.5 \cdot 10^{-7} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.29740651 \pm 2.8 \cdot 10^{-7} \)
\(a_{34}= +1.08686371 \pm 1.6 \cdot 10^{-7} \) \(a_{35}= -0.02561963 \pm 2.4 \cdot 10^{-7} \) \(a_{36}= -0.44684358 \pm 2.4 \cdot 10^{-7} \)
\(a_{37}= -0.06347719 \pm 1.8 \cdot 10^{-7} \) \(a_{38}= -0.03008162 \pm 2.4 \cdot 10^{-7} \) \(a_{39}= +0.54374778 \pm 2.6 \cdot 10^{-7} \)
\(a_{40}= -0.02396497 \pm 2.4 \cdot 10^{-7} \) \(a_{41}= -1.45557654 \pm 1.5 \cdot 10^{-7} \) \(a_{42}= +0.08714227 \pm 3.1 \cdot 10^{-7} \)
\(a_{43}= -1.56575486 \pm 2.3 \cdot 10^{-7} \) \(a_{44}= +0.45606590 \pm 2.5 \cdot 10^{-7} \) \(a_{45}= -0.06057695 \pm 2.0 \cdot 10^{-7} \)
\(a_{46}= -0.07437536 \pm 2.2 \cdot 10^{-7} \) \(a_{47}= +0.62511989 \pm 1.6 \cdot 10^{-7} \) \(a_{48}= +0.08151413 \pm 3.1 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.70385794 \pm 1.9 \cdot 10^{-7} \) \(a_{51}= -0.50116757 \pm 1.8 \cdot 10^{-7} \)
\(a_{52}= +0.83382445 \pm 2.3 \cdot 10^{-7} \) \(a_{53}= -0.91106271 \pm 2.2 \cdot 10^{-7} \) \(a_{54}= +0.43660239 \pm 2.3 \cdot 10^{-7} \)
\(a_{55}= +0.06182718 \pm 2.2 \cdot 10^{-7} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.01387104 \pm 3.2 \cdot 10^{-7} \)
\(a_{58}= +0.10726307 \pm 2.6 \cdot 10^{-7} \) \(a_{59}= -0.88868345 \pm 2.4 \cdot 10^{-7} \) \(a_{60}= +0.01105057 \pm 5.4 \cdot 10^{-7} \)

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