Properties

Label 14.46
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 9.615741
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: \(9.6157410480843738310823441407 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.71232722 \pm 9.7 \cdot 10^{-7} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.15974547 \pm 7.4 \cdot 10^{-7} \) \(a_{6}= +1.21079819 \pm 9.8 \cdot 10^{-7} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +1.93206450 \pm 7.6 \cdot 10^{-7} \)
\(a_{10}= +0.82006389 \pm 7.6 \cdot 10^{-7} \) \(a_{11}= +1.49733547 \pm 7.6 \cdot 10^{-7} \) \(a_{12}= +0.85616361 \pm 9.8 \cdot 10^{-7} \)
\(a_{13}= -1.23443747 \pm 7.2 \cdot 10^{-7} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +1.98586373 \pm 9.2 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.57020896 \pm 4.9 \cdot 10^{-7} \) \(a_{18}= +1.36617591 \pm 7.7 \cdot 10^{-7} \)
\(a_{19}= -0.80781892 \pm 7.4 \cdot 10^{-7} \) \(a_{20}= +0.57987273 \pm 7.6 \cdot 10^{-7} \) \(a_{21}= -0.64719885 \pm 9.8 \cdot 10^{-7} \)
\(a_{22}= +1.05877607 \pm 7.8 \cdot 10^{-7} \) \(a_{23}= +0.78026450 \pm 6.8 \cdot 10^{-7} \) \(a_{24}= +0.60539909 \pm 9.8 \cdot 10^{-7} \)
\(a_{25}= +0.34500955 \pm 5.8 \cdot 10^{-7} \) \(a_{26}= -0.87287911 \pm 7.3 \cdot 10^{-7} \) \(a_{27}= +1.59599941 \pm 7.1 \cdot 10^{-7} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.34000398 \pm 8.3 \cdot 10^{-7} \) \(a_{30}= +1.40421771 \pm 1.7 \cdot 10^{-6} \)
\(a_{31}= +0.32143315 \pm 8.2 \cdot 10^{-7} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +2.56392829 \pm 9.1 \cdot 10^{-7} \)
\(a_{34}= -1.11030540 \pm 5.0 \cdot 10^{-7} \) \(a_{35}= -0.43834259 \pm 7.6 \cdot 10^{-7} \) \(a_{36}= +0.96603225 \pm 7.7 \cdot 10^{-7} \)
\(a_{37}= +0.70479254 \pm 5.9 \cdot 10^{-7} \) \(a_{38}= -0.57121424 \pm 7.5 \cdot 10^{-7} \) \(a_{39}= -2.11376088 \pm 8.3 \cdot 10^{-7} \)
\(a_{40}= +0.41003194 \pm 7.6 \cdot 10^{-7} \) \(a_{41}= -0.46993306 \pm 4.8 \cdot 10^{-7} \) \(a_{42}= -0.45763870 \pm 9.8 \cdot 10^{-7} \)
\(a_{43}= +0.94981999 \pm 7.5 \cdot 10^{-7} \) \(a_{44}= +0.74866774 \pm 7.8 \cdot 10^{-7} \) \(a_{45}= +2.24070305 \pm 6.6 \cdot 10^{-7} \)
\(a_{46}= +0.55173032 \pm 6.9 \cdot 10^{-7} \) \(a_{47}= -0.44431620 \pm 5.4 \cdot 10^{-7} \) \(a_{48}= +0.42808180 \pm 9.8 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.24395860 \pm 5.9 \cdot 10^{-7} \) \(a_{51}= -2.68871153 \pm 5.8 \cdot 10^{-7} \)
\(a_{52}= -0.61721873 \pm 7.3 \cdot 10^{-7} \) \(a_{53}= -0.32805540 \pm 7.2 \cdot 10^{-7} \) \(a_{54}= +1.12854200 \pm 7.2 \cdot 10^{-7} \)
\(a_{55}= +1.73652803 \pm 7.1 \cdot 10^{-7} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= -1.38325033 \pm 1.0 \cdot 10^{-6} \)
\(a_{58}= -0.24041912 \pm 8.4 \cdot 10^{-7} \) \(a_{59}= -0.16073985 \pm 7.8 \cdot 10^{-7} \) \(a_{60}= +0.99293187 \pm 1.7 \cdot 10^{-6} \)

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