Properties

Label 14.35
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 8.499465
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: \(8.4994650504545723858091007147 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.00276266 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.18662402 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.00195350 \pm 1.3 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.99999237 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.13196311 \pm 1.4 \cdot 10^{-8} \) \(a_{11}= +0.03723391 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.00138133 \pm 1.3 \cdot 10^{-8} \)
\(a_{13}= +0.41200522 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.00051558 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.94281528 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.70710138 \pm 1.3 \cdot 10^{-8} \)
\(a_{19}= -1.52953030 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.09331201 \pm 1.4 \cdot 10^{-8} \) \(a_{21}= +0.00104419 \pm 1.3 \cdot 10^{-8} \)
\(a_{22}= +0.02632835 \pm 1.4 \cdot 10^{-8} \) \(a_{23}= -0.71152550 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.00097675 \pm 1.3 \cdot 10^{-8} \)
\(a_{25}= -0.96517148 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.29133168 \pm 1.3 \cdot 10^{-8} \) \(a_{27}= +0.00552530 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.65083998 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.00036457 \pm 1.6 \cdot 10^{-8} \)
\(a_{31}= -0.48659216 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.00010286 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.66667108 \pm 1.4 \cdot 10^{-8} \) \(a_{35}= +0.07053725 \pm 1.4 \cdot 10^{-8} \) \(a_{36}= -0.49999618 \pm 1.3 \cdot 10^{-8} \)
\(a_{37}= +0.57971965 \pm 1 \cdot 10^{-8} \) \(a_{38}= -1.08154124 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= -0.00113823 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.06598155 \pm 1.4 \cdot 10^{-8} \) \(a_{41}= +1.38489418 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.00073835 \pm 1.3 \cdot 10^{-8} \)
\(a_{43}= +0.51784787 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.01861696 \pm 1.4 \cdot 10^{-8} \) \(a_{45}= +0.18662259 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.50312450 \pm 1.2 \cdot 10^{-8} \) \(a_{47}= -0.08277888 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.00069067 \pm 1.3 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.68247930 \pm 1.4 \cdot 10^{-8} \) \(a_{51}= +0.00260468 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.20600261 \pm 1.3 \cdot 10^{-8} \) \(a_{53}= -1.33256876 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.00390698 \pm 1.3 \cdot 10^{-8} \)
\(a_{55}= -0.00694874 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.00422557 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.46021337 \pm 1.3 \cdot 10^{-8} \) \(a_{59}= +0.96433100 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.00025779 \pm 1.6 \cdot 10^{-8} \)

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