Properties

Label 2.14
Level $2$
Weight $0$
Character 2.1
Symmetry even
\(R\) 15.31419
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(15.3141965841790996306418247371 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.05270933 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.41821650 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.03727112 \pm 1.3 \cdot 10^{-8} \)
\(a_{7}= +0.26666023 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.99722173 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -1.00283050 \pm 1.3 \cdot 10^{-8} \) \(a_{11}= -0.86652814 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.02635466 \pm 1.3 \cdot 10^{-8} \)
\(a_{13}= -1.35196476 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.18855726 \pm 1.3 \cdot 10^{-8} \) \(a_{15}= +0.07475324 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.74279692 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.70514225 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= +1.76178013 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.70910825 \pm 1.3 \cdot 10^{-8} \) \(a_{21}= -0.01405548 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.61272793 \pm 1.2 \cdot 10^{-8} \) \(a_{23}= +0.30024567 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.01863556 \pm 1.3 \cdot 10^{-8} \)
\(a_{25}= +1.01133804 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.95598345 \pm 1.3 \cdot 10^{-8} \) \(a_{27}= +0.10527222 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.13333012 \pm 1.3 \cdot 10^{-8} \) \(a_{29}= -0.57033584 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.05285852 \pm 1.6 \cdot 10^{-8} \)
\(a_{31}= +0.71005260 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.04567412 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.52523674 \pm 1.1 \cdot 10^{-8} \) \(a_{35}= -0.37818194 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.49861086 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= +0.38842085 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.24576667 \pm 1.2 \cdot 10^{-8} \) \(a_{39}= +0.07126115 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.50141525 \pm 1.3 \cdot 10^{-8} \) \(a_{41}= -0.42764681 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.00993873 \pm 1.6 \cdot 10^{-8} \)
\(a_{43}= -0.49029491 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.43326407 \pm 1.2 \cdot 10^{-8} \) \(a_{45}= +1.41427631 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.21230575 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -0.13804474 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.01317733 \pm 1.3 \cdot 10^{-8} \)
\(a_{49}= -0.92889232 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.71512398 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= +0.03915233 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.67598238 \pm 1.3 \cdot 10^{-8} \) \(a_{53}= -0.38061124 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.07443870 \pm 1.3 \cdot 10^{-8} \)
\(a_{55}= +1.22892451 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.09427863 \pm 1.3 \cdot 10^{-8} \) \(a_{57}= -0.09286225 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.40328834 \pm 1.5 \cdot 10^{-8} \) \(a_{59}= +0.49612585 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.03737662 \pm 1.6 \cdot 10^{-8} \)

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