Properties

Label 14.39
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 8.962464
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: \(8.96246431384067503947859676439 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.82356591 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.35541637 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.28945582 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.32539263 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.95842411 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= +1.26202172 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.91178296 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +0.24183677 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -2.47169109 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.96456120 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.64430090 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= +0.83672995 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.67770819 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= +0.68924313 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.89238412 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= -1.17867796 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.64472791 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.83715354 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.17100442 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +2.41694083 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.18256218 \pm 1 \cdot 10^{-8} \) \(a_{30}= -1.74774953 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= -0.95866357 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +2.30137979 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.68204777 \pm 1.1 \cdot 10^{-8} \) \(a_{35}= -0.51229923 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= +1.16269632 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -0.42418212 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.59165742 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.44100529 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.47921205 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= -0.48278922 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.48736849 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.20323361 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.63101086 \pm 1.1 \cdot 10^{-8} \) \(a_{45}= -3.15187525 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.83345118 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +1.27766073 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.45589148 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.59195694 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= +1.75894092 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.12091838 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= -1.43645387 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.70903525 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -1.71056490 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +1.52583222 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.12909096 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= +0.32723311 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.23584555 \pm 1.1 \cdot 10^{-8} \)

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