Properties

Label 2.34
Level $2$
Weight $0$
Character 2.1
Symmetry even
\(R\) 22.75821
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: not computed rigorously
Spectral parameter: \(22.7582184886991529054041038537 \pm 6 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= \pm0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.69564349 \pm 1.4 \cdot 10^{-4} \)
\(a_{4}= \pm0.5 \) \(a_{5}= -0.25510796 \pm 1.1 \cdot 10^{-4} \) \(a_{6}= \pm0.49189423 \pm 1.0 \cdot 10^{-4} \)
\(a_{7}= -1.48407981 \pm 1.0 \cdot 10^{-4} \) \(a_{8}= \pm0.35355339 \pm 1.0 \cdot 10^{-8} \) \(a_{9}= -0.51608013 \pm 3.2 \cdot 10^{-5} \)
\(a_{10}= \pm0.18038857 \pm 8.4 \cdot 10^{-5} \) \(a_{11}= -0.77208940 \pm 7.4 \cdot 10^{-5} \) \(a_{12}= \pm0.34782175 \pm 7.3 \cdot 10^{-5} \)
\(a_{13}= -0.90792109 \pm 1.1 \cdot 10^{-4} \) \(a_{14}= \pm1.04940289 \pm 7.7 \cdot 10^{-5} \) \(a_{15}= -0.17746419 \pm 1.3 \cdot 10^{-4} \)
\(a_{16}= \pm0.25 \) \(a_{17}= +1.01066209 \pm 4.5 \cdot 10^{-5} \) \(a_{18}= \pm0.36492376 \pm 2.2 \cdot 10^{-5} \)
\(a_{19}= +0.94531266 \pm 9.6 \cdot 10^{-5} \) \(a_{20}= \pm0.12755398 \pm 5.9 \cdot 10^{-5} \) \(a_{21}= -1.03239046 \pm 1.2 \cdot 10^{-4} \)
\(a_{22}= \pm0.54594965 \pm 5.2 \cdot 10^{-5} \) \(a_{23}= -1.54522778 \pm 1.3 \cdot 10^{-5} \) \(a_{24}= \pm0.24594712 \pm 5.1 \cdot 10^{-5} \)
\(a_{25}= -0.93491993 \pm 2.4 \cdot 10^{-5} \) \(a_{26}= \pm0.64199716 \pm 7.8 \cdot 10^{-5} \) \(a_{27}= -1.05465128 \pm 1.1 \cdot 10^{-4} \)
\(a_{28}= \pm0.74203990 \pm 5.4 \cdot 10^{-5} \) \(a_{29}= +1.26706849 \pm 2.2 \cdot 10^{-4} \) \(a_{30}= \pm0.12548614 \pm 9.3 \cdot 10^{-5} \)
\(a_{31}= -1.34507150 \pm 2.0 \cdot 10^{-4} \) \(a_{32}= \pm0.17677670 \pm 1.0 \cdot 10^{-8} \) \(a_{33}= -0.53709897 \pm 8.2 \cdot 10^{-5} \)
\(a_{34}= \pm0.71464602 \pm 3.2 \cdot 10^{-5} \) \(a_{35}= +0.37860058 \pm 9.8 \cdot 10^{-5} \) \(a_{36}= \pm0.25804007 \pm 1.6 \cdot 10^{-5} \)
\(a_{37}= -0.68704600 \pm 1.0 \cdot 10^{-4} \) \(a_{38}= \pm0.66843699 \pm 6.8 \cdot 10^{-5} \) \(a_{39}= -0.63158940 \pm 1.2 \cdot 10^{-4} \)
\(a_{40}= \pm0.09019429 \pm 4.2 \cdot 10^{-5} \) \(a_{41}= +0.70790335 \pm 9.8 \cdot 10^{-5} \) \(a_{42}= \pm0.73001030 \pm 8.5 \cdot 10^{-5} \)
\(a_{43}= +1.12779579 \pm 1.0 \cdot 10^{-4} \) \(a_{44}= \pm0.38604470 \pm 3.7 \cdot 10^{-5} \) \(a_{45}= +0.13165615 \pm 2.8 \cdot 10^{-5} \)
\(a_{46}= \pm1.09264104 \pm 9.2 \cdot 10^{-6} \) \(a_{47}= -0.04620758 \pm 1.3 \cdot 10^{-4} \) \(a_{48}= \pm0.17391087 \pm 3.6 \cdot 10^{-5} \)
\(a_{49}= +1.20249287 \pm 4.3 \cdot 10^{-5} \) \(a_{50}= \pm0.66108822 \pm 1.7 \cdot 10^{-5} \) \(a_{51}= +0.70306051 \pm 5.3 \cdot 10^{-5} \)
\(a_{52}= \pm0.45396055 \pm 5.5 \cdot 10^{-5} \) \(a_{53}= -0.10428699 \pm 1.5 \cdot 10^{-4} \) \(a_{54}= \pm0.74575107 \pm 8.0 \cdot 10^{-5} \)
\(a_{55}= +0.19696615 \pm 6.7 \cdot 10^{-5} \) \(a_{56}= \pm0.52470145 \pm 3.8 \cdot 10^{-5} \) \(a_{57}= +0.65760060 \pm 1.0 \cdot 10^{-4} \)
\(a_{58}= \pm0.89595272 \pm 1.6 \cdot 10^{-4} \) \(a_{59}= +0.38767502 \pm 2.1 \cdot 10^{-5} \) \(a_{60}= \pm0.08873210 \pm 6.6 \cdot 10^{-5} \)

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