Properties

Label 14.99
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 14.08975
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: \(14.0897505881232104433761565336 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.68725087 \pm 1.5 \cdot 10^{-4} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.83278044 \pm 1.2 \cdot 10^{-4} \) \(a_{6}= -0.48595975 \pm 1.5 \cdot 10^{-4} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.52768624 \pm 1.2 \cdot 10^{-4} \)
\(a_{10}= +0.58886470 \pm 1.2 \cdot 10^{-4} \) \(a_{11}= -0.70747999 \pm 1.2 \cdot 10^{-4} \) \(a_{12}= +0.34362544 \pm 1.5 \cdot 10^{-4} \)
\(a_{13}= -1.62946420 \pm 1.1 \cdot 10^{-4} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.57232909 \pm 1.5 \cdot 10^{-4} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.73678067 \pm 8.0 \cdot 10^{-5} \) \(a_{18}= +0.37313052 \pm 1.2 \cdot 10^{-4} \)
\(a_{19}= +0.05597363 \pm 1.2 \cdot 10^{-4} \) \(a_{20}= -0.41639022 \pm 1.2 \cdot 10^{-4} \) \(a_{21}= +0.25975641 \pm 1.5 \cdot 10^{-4} \)
\(a_{22}= +0.50026390 \pm 1.2 \cdot 10^{-4} \) \(a_{23}= +0.65105044 \pm 1.1 \cdot 10^{-4} \) \(a_{24}= -0.24297988 \pm 1.5 \cdot 10^{-4} \)
\(a_{25}= -0.30647673 \pm 9.4 \cdot 10^{-5} \) \(a_{26}= +1.15220518 \pm 1.1 \cdot 10^{-4} \) \(a_{27}= -1.04990370 \pm 1.1 \cdot 10^{-4} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.95908650 \pm 1.3 \cdot 10^{-4} \) \(a_{30}= +0.40469778 \pm 2.7 \cdot 10^{-4} \)
\(a_{31}= +1.30782099 \pm 1.3 \cdot 10^{-4} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.48621624 \pm 1.4 \cdot 10^{-4} \)
\(a_{34}= -1.22808939 \pm 8.0 \cdot 10^{-5} \) \(a_{35}= -0.31476142 \pm 1.2 \cdot 10^{-4} \) \(a_{36}= -0.26384312 \pm 1.2 \cdot 10^{-4} \)
\(a_{37}= +0.56864891 \pm 9.5 \cdot 10^{-5} \) \(a_{38}= -0.03957933 \pm 1.2 \cdot 10^{-4} \) \(a_{39}= -1.11985069 \pm 1.3 \cdot 10^{-4} \)
\(a_{40}= +0.29443235 \pm 1.2 \cdot 10^{-4} \) \(a_{41}= -1.63927394 \pm 7.8 \cdot 10^{-5} \) \(a_{42}= -0.18367552 \pm 1.5 \cdot 10^{-4} \)
\(a_{43}= +0.33301611 \pm 1.2 \cdot 10^{-4} \) \(a_{44}= -0.35373999 \pm 1.2 \cdot 10^{-4} \) \(a_{45}= +0.43944678 \pm 1.0 \cdot 10^{-4} \)
\(a_{46}= -0.46036218 \pm 1.1 \cdot 10^{-4} \) \(a_{47}= -1.03784259 \pm 8.8 \cdot 10^{-5} \) \(a_{48}= +0.17181272 \pm 1.5 \cdot 10^{-4} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.21671178 \pm 9.4 \cdot 10^{-5} \) \(a_{51}= +1.19360403 \pm 9.5 \cdot 10^{-5} \)
\(a_{52}= -0.81473210 \pm 1.1 \cdot 10^{-4} \) \(a_{53}= +1.70689132 \pm 1.1 \cdot 10^{-4} \) \(a_{54}= +0.74239403 \pm 1.1 \cdot 10^{-4} \)
\(a_{55}= +0.58917550 \pm 1.1 \cdot 10^{-4} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.03846793 \pm 1.7 \cdot 10^{-4} \)
\(a_{58}= +0.67817657 \pm 1.3 \cdot 10^{-4} \) \(a_{59}= +0.92903825 \pm 1.2 \cdot 10^{-4} \) \(a_{60}= -0.28616454 \pm 2.7 \cdot 10^{-4} \)

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