Properties

Label 14.84
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 12.97071
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: \(12.9707194030509437521312479484 \pm 3 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.82138308 \pm 1.7 \cdot 10^{-7} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.80718382 \pm 2.6 \cdot 10^{-7} \) \(a_{6}= +0.58080554 \pm 1.8 \cdot 10^{-7} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.32532984 \pm 2.4 \cdot 10^{-7} \)
\(a_{10}= -1.27787194 \pm 2.7 \cdot 10^{-7} \) \(a_{11}= -0.76289104 \pm 3.1 \cdot 10^{-7} \) \(a_{12}= +0.41069154 \pm 1.8 \cdot 10^{-7} \)
\(a_{13}= +0.78738989 \pm 2.2 \cdot 10^{-7} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -1.48439021 \pm 1.8 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.00193573 \pm 2.9 \cdot 10^{-7} \) \(a_{18}= -0.23004294 \pm 2.5 \cdot 10^{-7} \)
\(a_{19}= +1.05939729 \pm 1.9 \cdot 10^{-7} \) \(a_{20}= -0.90359191 \pm 2.7 \cdot 10^{-7} \) \(a_{21}= +0.31045362 \pm 1.8 \cdot 10^{-7} \)
\(a_{22}= -0.53944543 \pm 3.2 \cdot 10^{-7} \) \(a_{23}= +1.69178660 \pm 1.5 \cdot 10^{-7} \) \(a_{24}= +0.29040277 \pm 1.8 \cdot 10^{-7} \)
\(a_{25}= +2.26591337 \pm 3.1 \cdot 10^{-7} \) \(a_{26}= +0.55676873 \pm 2.3 \cdot 10^{-7} \) \(a_{27}= -1.08860350 \pm 1.9 \cdot 10^{-7} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +0.95218856 \pm 2.4 \cdot 10^{-7} \) \(a_{30}= -1.04962238 \pm 4.5 \cdot 10^{-7} \)
\(a_{31}= -0.78276390 \pm 2.8 \cdot 10^{-7} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.62662579 \pm 1.6 \cdot 10^{-7} \)
\(a_{34}= +0.70847555 \pm 3.0 \cdot 10^{-7} \) \(a_{35}= -0.68305128 \pm 2.7 \cdot 10^{-7} \) \(a_{36}= -0.16266492 \pm 2.5 \cdot 10^{-7} \)
\(a_{37}= +0.36741876 \pm 1.2 \cdot 10^{-7} \) \(a_{38}= +0.74910701 \pm 2.0 \cdot 10^{-7} \) \(a_{39}= +0.64674873 \pm 2.5 \cdot 10^{-7} \)
\(a_{40}= -0.63893597 \pm 2.7 \cdot 10^{-7} \) \(a_{41}= +0.82264413 \pm 2.5 \cdot 10^{-7} \) \(a_{42}= +0.21952386 \pm 1.8 \cdot 10^{-7} \)
\(a_{43}= -0.97907934 \pm 1.7 \cdot 10^{-7} \) \(a_{44}= -0.38144552 \pm 3.2 \cdot 10^{-7} \) \(a_{45}= +0.58793083 \pm 2.6 \cdot 10^{-7} \)
\(a_{46}= +1.19627377 \pm 1.6 \cdot 10^{-7} \) \(a_{47}= -0.47825688 \pm 2.1 \cdot 10^{-7} \) \(a_{48}= +0.20534577 \pm 1.8 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +1.60224271 \pm 3.2 \cdot 10^{-7} \) \(a_{51}= +0.82297305 \pm 1.4 \cdot 10^{-7} \)
\(a_{52}= +0.39369495 \pm 2.3 \cdot 10^{-7} \) \(a_{53}= +0.27318282 \pm 2.8 \cdot 10^{-7} \) \(a_{54}= -0.76975892 \pm 2.0 \cdot 10^{-7} \)
\(a_{55}= +1.37868435 \pm 2.8 \cdot 10^{-7} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.87017101 \pm 1.6 \cdot 10^{-7} \)
\(a_{58}= +0.67329899 \pm 2.5 \cdot 10^{-7} \) \(a_{59}= +0.00319503 \pm 2.2 \cdot 10^{-7} \) \(a_{60}= -0.74219510 \pm 4.5 \cdot 10^{-7} \)

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