Properties

Label 1.47
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 34.18596
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 34.18596993308634633793490589946673\ldots \pm 5 \cdot 10^{-92} \) (toggle for full precision) Copy content Toggle raw display

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.50706305 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.11602338 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +1.27123905 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.36364574 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.17485455 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.79831992 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.40877435 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.98653858 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.54803706 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.79829943 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.14749345 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.92727221 \pm 1 \cdot 10^{-8} \) \(a_{14}= -2.71018151 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.04219141 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.65519033 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.74155074 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.48677584 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.38163767 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.46228067 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.20864716 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +1.20308758 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.13076939 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.04742738 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.86776178 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.39745769 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.23048492 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -2.28609450 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.57719955 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.06358511 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.22648205 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.39618749 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.09262140 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +1.11756373 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.65395138 \pm 1 \cdot 10^{-8} \) \(a_{36}= -1.25412636 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.40380813 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.57515203 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.10758526 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.14864905 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.45015166 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.31444442 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.57732599 \pm 1 \cdot 10^{-8} \) \(a_{44}= +1.01482941 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.35875055 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.19707771 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.21830879 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.07601740 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +2.23395453 \pm 1 \cdot 10^{-8} \) \(a_{50}= -1.30777171 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.08603722 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -1.17878464 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.12750672 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.34735531 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.29029819 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.73510706 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.04427889 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.86987611 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.34526154 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.05363537 \pm 1 \cdot 10^{-8} \)

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