Properties

Label 6.24
Level $6$
Weight $0$
Character 6.1
Symmetry odd
\(R\) 12.11622
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(12.1162222939339244410266171732 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.49666880 \pm 9.1 \cdot 10^{-8} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +1.41990760 \pm 9.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -1.05830466 \pm 1.0 \cdot 10^{-7} \) \(a_{11}= -0.58299700 \pm 7.1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -0.96665175 \pm 1.1 \cdot 10^{-7} \) \(a_{14}= -1.00402629 \pm 1.0 \cdot 10^{-7} \) \(a_{15}= +0.86410214 \pm 1.0 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.57590387 \pm 7.2 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +0.41263974 \pm 1.5 \cdot 10^{-7} \) \(a_{20}= +0.74833440 \pm 1.0 \cdot 10^{-7} \) \(a_{21}= +0.81978404 \pm 1.0 \cdot 10^{-7} \)
\(a_{22}= +0.41224113 \pm 8.2 \cdot 10^{-8} \) \(a_{23}= -0.46178627 \pm 1.1 \cdot 10^{-7} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= +1.24001751 \pm 8.7 \cdot 10^{-8} \) \(a_{26}= +0.68352600 \pm 1.2 \cdot 10^{-7} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.70995380 \pm 1.0 \cdot 10^{-7} \) \(a_{29}= -1.21125758 \pm 8.5 \cdot 10^{-8} \) \(a_{30}= -0.61101248 \pm 1.0 \cdot 10^{-7} \)
\(a_{31}= +0.90724731 \pm 1.4 \cdot 10^{-7} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.33659347 \pm 8.2 \cdot 10^{-8} \)
\(a_{34}= -1.11433231 \pm 8.3 \cdot 10^{-8} \) \(a_{35}= +2.12513141 \pm 7.2 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +0.77366380 \pm 1.2 \cdot 10^{-7} \) \(a_{38}= -0.29178036 \pm 1.7 \cdot 10^{-7} \) \(a_{39}= -0.55809665 \pm 1.2 \cdot 10^{-7} \)
\(a_{40}= -0.52915233 \pm 1.0 \cdot 10^{-7} \) \(a_{41}= -0.39182704 \pm 6.9 \cdot 10^{-8} \) \(a_{42}= -0.57967485 \pm 1.0 \cdot 10^{-7} \)
\(a_{43}= +0.54555449 \pm 6.8 \cdot 10^{-8} \) \(a_{44}= -0.29149850 \pm 8.2 \cdot 10^{-8} \) \(a_{45}= +0.49888960 \pm 1.0 \cdot 10^{-7} \)
\(a_{46}= +0.32653220 \pm 1.2 \cdot 10^{-7} \) \(a_{47}= -0.18924609 \pm 1.0 \cdot 10^{-7} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +1.01613759 \pm 9.9 \cdot 10^{-8} \) \(a_{50}= -0.87682479 \pm 9.8 \cdot 10^{-8} \) \(a_{51}= +0.90984852 \pm 8.3 \cdot 10^{-8} \)
\(a_{52}= -0.48332587 \pm 1.2 \cdot 10^{-7} \) \(a_{53}= -0.08160840 \pm 1.5 \cdot 10^{-7} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -0.87255342 \pm 7.6 \cdot 10^{-8} \) \(a_{56}= -0.50201315 \pm 1.0 \cdot 10^{-7} \) \(a_{57}= +0.23823767 \pm 1.7 \cdot 10^{-7} \)
\(a_{58}= +0.85648845 \pm 9.6 \cdot 10^{-8} \) \(a_{59}= -1.21904501 \pm 1.2 \cdot 10^{-7} \) \(a_{60}= +0.43205107 \pm 1.0 \cdot 10^{-7} \)

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