Properties

Label 14.23
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 6.755298
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: \(6.75529844582064249219773781201 \pm 4 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.82627355 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.64804579 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.58426363 \pm 1.2 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.31727203 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.45823758 \pm 1.3 \cdot 10^{-8} \) \(a_{11}= -1.05702564 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.41313677 \pm 1.2 \cdot 10^{-8} \)
\(a_{13}= -1.66353822 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.53546310 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.00373705 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.22434520 \pm 1.2 \cdot 10^{-8} \)
\(a_{19}= -0.54407171 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.32402290 \pm 1.3 \cdot 10^{-8} \) \(a_{21}= +0.31230205 \pm 1.2 \cdot 10^{-8} \)
\(a_{22}= -0.74743000 \pm 1.3 \cdot 10^{-8} \) \(a_{23}= +0.53665100 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.29213181 \pm 1.2 \cdot 10^{-8} \)
\(a_{25}= -0.58003665 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.17629915 \pm 1.2 \cdot 10^{-8} \) \(a_{27}= +1.08842703 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.93854623 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.37862959 \pm 1.4 \cdot 10^{-8} \)
\(a_{31}= +1.34296159 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.87339233 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.00264249 \pm 1.3 \cdot 10^{-8} \) \(a_{35}= -0.24493829 \pm 1.3 \cdot 10^{-8} \) \(a_{36}= -0.15863601 \pm 1.2 \cdot 10^{-8} \)
\(a_{37}= -0.94842185 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.38471680 \pm 1.2 \cdot 10^{-8} \) \(a_{39}= +1.37453762 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.22911879 \pm 1.3 \cdot 10^{-8} \) \(a_{41}= +0.01677296 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.22083089 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= -1.03326708 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.52851282 \pm 1.3 \cdot 10^{-8} \) \(a_{45}= -0.20560680 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.37946956 \pm 1.1 \cdot 10^{-8} \) \(a_{47}= -0.11274862 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.20656839 \pm 1.2 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.41014785 \pm 1.3 \cdot 10^{-8} \) \(a_{51}= +0.00308782 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.83176911 \pm 1.2 \cdot 10^{-8} \) \(a_{53}= +1.56919839 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.76963413 \pm 1.2 \cdot 10^{-8} \)
\(a_{55}= -0.68500102 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.44955206 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.66365241 \pm 1.2 \cdot 10^{-8} \) \(a_{59}= +1.81293420 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.26773155 \pm 1.4 \cdot 10^{-8} \)

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