Properties

Label 2.19
Level $2$
Weight $0$
Character 2.1
Symmetry odd
\(R\) 17.49311
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(17.4931127226685992093991119089 \pm 5 \cdot 10^{-6}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.68121955 \pm 6.5 \cdot 10^{-4} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.81602816 \pm 4.7 \cdot 10^{-4} \) \(a_{6}= +1.18880175 \pm 6.5 \cdot 10^{-4} \)
\(a_{7}= +0.33076893 \pm 5.4 \cdot 10^{-4} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +1.82649919 \pm 1.1 \cdot 10^{-3} \)
\(a_{10}= -0.57701904 \pm 4.7 \cdot 10^{-4} \) \(a_{11}= +0.79862660 \pm 1.5 \cdot 10^{-3} \) \(a_{12}= -0.84060978 \pm 6.5 \cdot 10^{-4} \)
\(a_{13}= -1.41850327 \pm 1.2 \cdot 10^{-3} \) \(a_{14}= -0.23388895 \pm 5.4 \cdot 10^{-4} \) \(a_{15}= -1.37192250 \pm 3.5 \cdot 10^{-4} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.48398811 \pm 9.0 \cdot 10^{-4} \) \(a_{18}= -1.29152996 \pm 1.1 \cdot 10^{-3} \)
\(a_{19}= +0.79258632 \pm 6.4 \cdot 10^{-4} \) \(a_{20}= +0.40801408 \pm 4.7 \cdot 10^{-4} \) \(a_{21}= -0.55609520 \pm 2.7 \cdot 10^{-4} \)
\(a_{22}= -0.56471428 \pm 1.5 \cdot 10^{-3} \) \(a_{23}= +0.07303840 \pm 6.5 \cdot 10^{-4} \) \(a_{24}= +0.59440087 \pm 6.5 \cdot 10^{-4} \)
\(a_{25}= -0.33409804 \pm 1.2 \cdot 10^{-3} \) \(a_{26}= +1.00303328 \pm 1.2 \cdot 10^{-3} \) \(a_{27}= -1.38952659 \pm 1.0 \cdot 10^{-3} \)
\(a_{28}= +0.16538447 \pm 5.4 \cdot 10^{-4} \) \(a_{29}= -0.41502370 \pm 1.1 \cdot 10^{-3} \) \(a_{30}= +0.97009570 \pm 1.1 \cdot 10^{-3} \)
\(a_{31}= +0.49763209 \pm 1.2 \cdot 10^{-3} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.34266665 \pm 6.2 \cdot 10^{-4} \)
\(a_{34}= +0.34223128 \pm 9.0 \cdot 10^{-4} \) \(a_{35}= +0.26991676 \pm 1.3 \cdot 10^{-4} \) \(a_{36}= +0.91324959 \pm 1.1 \cdot 10^{-3} \)
\(a_{37}= -1.21954370 \pm 1.6 \cdot 10^{-3} \) \(a_{38}= -0.56044316 \pm 6.4 \cdot 10^{-4} \) \(a_{39}= +2.38481544 \pm 4.9 \cdot 10^{-4} \)
\(a_{40}= -0.28850952 \pm 4.7 \cdot 10^{-4} \) \(a_{41}= -1.86645137 \pm 1.6 \cdot 10^{-3} \) \(a_{42}= +0.39321868 \pm 1.1 \cdot 10^{-3} \)
\(a_{43}= -0.58566433 \pm 3.7 \cdot 10^{-4} \) \(a_{44}= +0.39931330 \pm 1.5 \cdot 10^{-3} \) \(a_{45}= +1.49047477 \pm 2.8 \cdot 10^{-4} \)
\(a_{46}= -0.05164594 \pm 6.5 \cdot 10^{-4} \) \(a_{47}= -0.34943216 \pm 1.1 \cdot 10^{-3} \) \(a_{48}= -0.42030489 \pm 6.5 \cdot 10^{-4} \)
\(a_{49}= -0.89059191 \pm 1.1 \cdot 10^{-3} \) \(a_{50}= +0.23624299 \pm 1.2 \cdot 10^{-3} \) \(a_{51}= +0.81369028 \pm 6.7 \cdot 10^{-4} \)
\(a_{52}= -0.70925164 \pm 1.2 \cdot 10^{-3} \) \(a_{53}= -0.13143755 \pm 1.3 \cdot 10^{-3} \) \(a_{54}= +0.98254368 \pm 1.0 \cdot 10^{-3} \)
\(a_{55}= +0.65170179 \pm 3.9 \cdot 10^{-4} \) \(a_{56}= -0.11694448 \pm 5.4 \cdot 10^{-4} \) \(a_{57}= -1.33251162 \pm 5.5 \cdot 10^{-4} \)
\(a_{58}= +0.29346607 \pm 1.1 \cdot 10^{-3} \) \(a_{59}= -0.38820915 \pm 1.1 \cdot 10^{-3} \) \(a_{60}= -0.68596125 \pm 1.1 \cdot 10^{-3} \)

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