Properties

Label 14.20
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 6.492565
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: \(6.4925656074380383424260045973 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.22382707 \pm 5.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.28248102 \pm 3.8 \cdot 10^{-8} \) \(a_{6}= -0.86537642 \pm 6.1 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.49775271 \pm 3.9 \cdot 10^{-8} \)
\(a_{10}= +0.19974425 \pm 4.9 \cdot 10^{-8} \) \(a_{11}= +0.89794832 \pm 3.9 \cdot 10^{-8} \) \(a_{12}= +0.61191354 \pm 6.1 \cdot 10^{-8} \)
\(a_{13}= +0.29003037 \pm 3.7 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.34570792 \pm 4.8 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.32917667 \pm 2.5 \cdot 10^{-8} \) \(a_{18}= -0.35196431 \pm 5.0 \cdot 10^{-8} \)
\(a_{19}= +1.34350421 \pm 3.8 \cdot 10^{-8} \) \(a_{20}= -0.14124051 \pm 4.9 \cdot 10^{-8} \) \(a_{21}= +0.46256315 \pm 6.1 \cdot 10^{-8} \)
\(a_{22}= -0.63494535 \pm 5.0 \cdot 10^{-8} \) \(a_{23}= +0.60489660 \pm 3.5 \cdot 10^{-8} \) \(a_{24}= -0.43268821 \pm 6.1 \cdot 10^{-8} \)
\(a_{25}= -0.92020447 \pm 3.0 \cdot 10^{-8} \) \(a_{26}= -0.20508244 \pm 4.7 \cdot 10^{-8} \) \(a_{27}= -0.61466384 \pm 3.7 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +1.51900790 \pm 4.3 \cdot 10^{-8} \) \(a_{30}= +0.24445242 \pm 9.9 \cdot 10^{-8} \)
\(a_{31}= -0.56825713 \pm 4.2 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +1.09893346 \pm 4.7 \cdot 10^{-8} \)
\(a_{34}= -0.93986984 \pm 3.6 \cdot 10^{-8} \) \(a_{35}= -0.10676779 \pm 4.9 \cdot 10^{-8} \) \(a_{36}= +0.24887635 \pm 5.0 \cdot 10^{-8} \)
\(a_{37}= +1.92710911 \pm 3.0 \cdot 10^{-8} \) \(a_{38}= -0.95000094 \pm 4.9 \cdot 10^{-8} \) \(a_{39}= +0.35494702 \pm 4.3 \cdot 10^{-8} \)
\(a_{40}= +0.09987212 \pm 4.9 \cdot 10^{-8} \) \(a_{41}= -0.59659368 \pm 2.5 \cdot 10^{-8} \) \(a_{42}= -0.32708154 \pm 6.1 \cdot 10^{-8} \)
\(a_{43}= -1.77495323 \pm 3.9 \cdot 10^{-8} \) \(a_{44}= +0.44897416 \pm 5.0 \cdot 10^{-8} \) \(a_{45}= -0.14060569 \pm 3.4 \cdot 10^{-8} \)
\(a_{46}= -0.42772649 \pm 4.5 \cdot 10^{-8} \) \(a_{47}= -0.55854787 \pm 2.8 \cdot 10^{-8} \) \(a_{48}= +0.30595677 \pm 6.1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.65068282 \pm 4.0 \cdot 10^{-8} \) \(a_{51}= +1.62668240 \pm 3.0 \cdot 10^{-8} \)
\(a_{52}= +0.14501519 \pm 4.7 \cdot 10^{-8} \) \(a_{53}= -0.19240874 \pm 3.7 \cdot 10^{-8} \) \(a_{54}= +0.43463297 \pm 4.7 \cdot 10^{-8} \)
\(a_{55}= -0.25365336 \pm 3.6 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +1.64421682 \pm 5.4 \cdot 10^{-8} \)
\(a_{58}= -1.07410078 \pm 5.3 \cdot 10^{-8} \) \(a_{59}= -0.47432916 \pm 4.0 \cdot 10^{-8} \) \(a_{60}= -0.17285396 \pm 9.9 \cdot 10^{-8} \)

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