Properties

Label 14.10
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 4.522084
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: \(4.52208412028612686745489020782 \pm 10 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.32467011 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.13167540 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.93668322 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.75475091 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.09310857 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.10577529 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.66233506 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -1.84479213 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.17442647 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.97938942 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.53368949 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +1.65887722 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.06583770 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +0.50067824 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.07479443 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -0.93516861 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.46834161 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= -0.98266159 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.30446502 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= -0.32487414 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +0.35132938 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.12333814 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +1.24279344 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.14011737 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.69253290 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.04976862 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.37737545 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -0.23292103 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.17300333 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -2.44374100 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.04655428 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +1.75198818 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.35403298 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.19939104 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.05288765 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.09938213 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.66126407 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +0.01862931 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.33116753 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.69484667 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -1.29736789 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.92239606 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +0.08272793 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.22972071 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.01392800 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +2.19746508 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.24842739 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +0.52927526 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.08721323 \pm 1.0 \cdot 10^{-8} \)

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