Properties

Label 6.10
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 7.386274
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: \(7.38627450581586415779132114734 \pm 2 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.09856581 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -1.48570553 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.06969655 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.99923097 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -1.34679465 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.05055246 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.05690700 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.73419593 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= -1.13410256 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.04928290 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.85777249 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.70656300 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +1.36320691 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.99028478 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.95232763 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.74285277 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.14358963 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.04023932 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.36973412 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.57690627 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.51915492 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.14643977 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +1.25626416 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.80193161 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.77757225 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.03484828 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -0.15258651 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.60653674 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.89399174 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.49961549 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.03285527 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.96393285 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -0.27761026 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +1.20732093 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.70023708 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +0.42388822 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.67339732 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +0.58777932 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= +0.09849001 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.52527623 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.65477442 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.10153320 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= -1.64298114 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.02845350 \pm 1.0 \cdot 10^{-8} \)

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