Properties

Label 6.18
Level $6$
Weight $0$
Character 6.1
Symmetry odd
\(R\) 10.19612
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: \(10.1961201777286022110710364105 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.16609433 \pm 3.4 \cdot 10^{-7} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -1.22121809 \pm 3.3 \cdot 10^{-7} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.82455321 \pm 3.5 \cdot 10^{-7} \) \(a_{11}= +0.66633898 \pm 2.6 \cdot 10^{-7} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= +1.10843532 \pm 4.4 \cdot 10^{-7} \) \(a_{14}= +0.86353159 \pm 3.4 \cdot 10^{-7} \) \(a_{15}= +0.67324488 \pm 3.5 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.81084087 \pm 2.7 \cdot 10^{-7} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +1.81939405 \pm 5.9 \cdot 10^{-7} \) \(a_{20}= +0.58304717 \pm 3.5 \cdot 10^{-7} \) \(a_{21}= -0.70507059 \pm 3.4 \cdot 10^{-7} \)
\(a_{22}= -0.47117281 \pm 2.7 \cdot 10^{-7} \) \(a_{23}= +0.90816965 \pm 4.2 \cdot 10^{-7} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= +0.35977600 \pm 3.2 \cdot 10^{-7} \) \(a_{26}= -0.78378213 \pm 4.5 \cdot 10^{-7} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.61060905 \pm 3.4 \cdot 10^{-7} \) \(a_{29}= +0.55744999 \pm 3.2 \cdot 10^{-7} \) \(a_{30}= -0.47605602 \pm 3.5 \cdot 10^{-7} \)
\(a_{31}= +1.22404245 \pm 5.5 \cdot 10^{-7} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.38471099 \pm 2.7 \cdot 10^{-7} \)
\(a_{34}= +0.57335108 \pm 2.8 \cdot 10^{-7} \) \(a_{35}= -1.42405550 \pm 2.6 \cdot 10^{-7} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +0.05711803 \pm 4.7 \cdot 10^{-7} \) \(a_{38}= -1.28650587 \pm 6.0 \cdot 10^{-7} \) \(a_{39}= +0.63995543 \pm 4.5 \cdot 10^{-7} \)
\(a_{40}= -0.41227661 \pm 3.5 \cdot 10^{-7} \) \(a_{41}= -0.00975442 \pm 2.5 \cdot 10^{-7} \) \(a_{42}= +0.49856020 \pm 3.4 \cdot 10^{-7} \)
\(a_{43}= +1.35478126 \pm 2.5 \cdot 10^{-7} \) \(a_{44}= +0.33316949 \pm 2.7 \cdot 10^{-7} \) \(a_{45}= +0.38869811 \pm 3.5 \cdot 10^{-7} \)
\(a_{46}= -0.64217292 \pm 4.3 \cdot 10^{-7} \) \(a_{47}= -1.36877108 \pm 3.8 \cdot 10^{-7} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +0.49137363 \pm 3.7 \cdot 10^{-7} \) \(a_{50}= -0.25440005 \pm 3.3 \cdot 10^{-7} \) \(a_{51}= -0.46813920 \pm 2.8 \cdot 10^{-7} \)
\(a_{52}= +0.55421766 \pm 4.5 \cdot 10^{-7} \) \(a_{53}= -1.37827780 \pm 5.9 \cdot 10^{-7} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= +0.77701411 \pm 2.8 \cdot 10^{-7} \) \(a_{56}= +0.43176580 \pm 3.4 \cdot 10^{-7} \) \(a_{57}= +1.05042765 \pm 6.0 \cdot 10^{-7} \)
\(a_{58}= -0.39417667 \pm 3.3 \cdot 10^{-7} \) \(a_{59}= +0.28180059 \pm 4.7 \cdot 10^{-7} \) \(a_{60}= +0.33662244 \pm 3.5 \cdot 10^{-7} \)

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