Properties

Label 6.16
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 9.660466
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(9.66046617806916288172996862068 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.02032171 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.67912023 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.72147640 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= +0.90161109 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= +0.98054509 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.48021052 \pm 1.1 \cdot 10^{-8} \) \(a_{15}= +0.58908302 \pm 1.1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.66778128 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= -1.85536574 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.51016086 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= -0.39209025 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= +0.63753531 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= +0.06994107 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= +0.04105640 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.69335008 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.33956011 \pm 1.1 \cdot 10^{-8} \) \(a_{29}= -1.48109664 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.41654460 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= -0.57792906 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.52054540 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +1.17929945 \pm 1.1 \cdot 10^{-8} \) \(a_{35}= -0.69292111 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +0.80865412 \pm 1 \cdot 10^{-8} \) \(a_{38}= -1.31194170 \pm 1.1 \cdot 10^{-8} \) \(a_{39}= +0.56611797 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= +0.36073820 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= -1.17678338 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.27724967 \pm 1.1 \cdot 10^{-8} \)
\(a_{43}= -0.14867385 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.45080554 \pm 1.1 \cdot 10^{-8} \) \(a_{45}= +0.34010724 \pm 1.1 \cdot 10^{-8} \)
\(a_{46}= +0.04945581 \pm 1.1 \cdot 10^{-8} \) \(a_{47}= -0.03748592 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= -0.53879572 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.02903126 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= +0.96289397 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +0.49027255 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= -0.75647717 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= +0.91993337 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.24010526 \pm 1.1 \cdot 10^{-8} \) \(a_{57}= -1.07119591 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= -1.04729348 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= -0.49223916 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.29454151 \pm 1.1 \cdot 10^{-8} \)

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