Properties

Label 14.7
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 3.716548
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: \(3.71654847808296773906123655693 \pm 5 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.75081033 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.59303407 \pm 1 \cdot 10^{-8} \) \(a_{6}= -1.23800986 \pm 1.4 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.06533683 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.41933841 \pm 1.3 \cdot 10^{-8} \) \(a_{11}= -0.67434613 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.87540517 \pm 1.4 \cdot 10^{-8} \)
\(a_{13}= -0.89956731 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +1.03829018 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.66977162 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.46041367 \pm 1.3 \cdot 10^{-8} \)
\(a_{19}= -1.73829756 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.29651704 \pm 1.3 \cdot 10^{-8} \) \(a_{21}= +0.66174411 \pm 1.4 \cdot 10^{-8} \)
\(a_{22}= +0.47683472 \pm 1.3 \cdot 10^{-8} \) \(a_{23}= +0.83161743 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.61900493 \pm 1.4 \cdot 10^{-8} \)
\(a_{25}= -0.64831059 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.63609014 \pm 1.3 \cdot 10^{-8} \) \(a_{27}= +1.86520272 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.34267426 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.73418203 \pm 1.7 \cdot 10^{-8} \)
\(a_{31}= -0.36151347 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.18065218 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.47360005 \pm 1.2 \cdot 10^{-8} \) \(a_{35}= +0.22414581 \pm 1.3 \cdot 10^{-8} \) \(a_{36}= +1.03266841 \pm 1.3 \cdot 10^{-8} \)
\(a_{37}= -0.22887846 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.22916199 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= -1.57497174 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.20966921 \pm 1.3 \cdot 10^{-8} \) \(a_{41}= -0.04153373 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.46792374 \pm 1.4 \cdot 10^{-8} \)
\(a_{43}= +0.62800368 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.33717307 \pm 1.3 \cdot 10^{-8} \) \(a_{45}= +1.22481511 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.58804233 \pm 1.3 \cdot 10^{-8} \) \(a_{47}= +1.17366232 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.43770258 \pm 1.4 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.45842481 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= +1.17264307 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.44978365 \pm 1.3 \cdot 10^{-8} \) \(a_{53}= -0.14101023 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.31889749 \pm 1.3 \cdot 10^{-8} \)
\(a_{55}= -0.39991023 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= -3.04342933 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.24230730 \pm 1.3 \cdot 10^{-8} \) \(a_{59}= -0.03739206 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.51914509 \pm 1.7 \cdot 10^{-8} \)

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