Properties

Label 14.11
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 4.589405
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: \(4.58940589266960591223447404034 \pm 10 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.98353672 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.54739212 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.69546548 \pm 1.6 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.03265553 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.38706468 \pm 1.5 \cdot 10^{-8} \) \(a_{11}= +1.49404316 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.49176836 \pm 1.6 \cdot 10^{-8} \)
\(a_{13}= +1.24705038 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.53838024 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.55348948 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.02309094 \pm 1.5 \cdot 10^{-8} \)
\(a_{19}= +0.38706721 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.27369606 \pm 1.5 \cdot 10^{-8} \) \(a_{21}= -0.37174194 \pm 1.6 \cdot 10^{-8} \)
\(a_{22}= -1.05644805 \pm 1.5 \cdot 10^{-8} \) \(a_{23}= +0.73198177 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.34773274 \pm 1.6 \cdot 10^{-8} \)
\(a_{25}= -0.70036187 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.88179778 \pm 1.5 \cdot 10^{-8} \) \(a_{27}= +1.01565463 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +1.56246294 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.38069232 \pm 2.1 \cdot 10^{-8} \)
\(a_{31}= +0.22664571 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.46944630 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.39137616 \pm 1.3 \cdot 10^{-8} \) \(a_{35}= +0.20689477 \pm 1.5 \cdot 10^{-8} \) \(a_{36}= -0.01632776 \pm 1.5 \cdot 10^{-8} \)
\(a_{37}= -1.64103625 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.27369785 \pm 1.5 \cdot 10^{-8} \) \(a_{39}= -1.22651984 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.19353234 \pm 1.5 \cdot 10^{-8} \) \(a_{41}= +1.50447766 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.26286124 \pm 1.6 \cdot 10^{-8} \)
\(a_{43}= +0.29583513 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.74702158 \pm 1.5 \cdot 10^{-8} \) \(a_{45}= -0.01787538 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.51758927 \pm 1.4 \cdot 10^{-8} \) \(a_{47}= +1.01760252 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.24588418 \pm 1.6 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.49523063 \pm 1.4 \cdot 10^{-8} \) \(a_{51}= +0.54437722 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.62352519 \pm 1.5 \cdot 10^{-8} \) \(a_{53}= -1.66998253 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.71817627 \pm 1.5 \cdot 10^{-8} \)
\(a_{55}= +0.81782745 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= -0.38069481 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.10482814 \pm 1.5 \cdot 10^{-8} \) \(a_{59}= +1.16513110 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.26919012 \pm 2.1 \cdot 10^{-8} \)

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