Properties

Label 17.34
Level $17$
Weight $0$
Character 17.1
Symmetry even
\(R\) 5.791487
Fricke sign $+1$

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Maass form invariants

Level: \( 17 \)
Weight: \( 0 \)
Character: 17.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(5.79148751943769257594911409788 \pm 5 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.42960017 \pm 1.3 \cdot 10^{-8} \) \(a_{3}= -0.92710092 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.81544369 \pm 1.2 \cdot 10^{-8} \) \(a_{5}= -0.55014656 \pm 1.2 \cdot 10^{-8} \) \(a_{6}= -0.39828272 \pm 1.3 \cdot 10^{-8} \)
\(a_{7}= +1.77993587 \pm 1.1 \cdot 10^{-8} \) \(a_{8}= -0.77991493 \pm 1.3 \cdot 10^{-8} \) \(a_{9}= -0.14048388 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.23634306 \pm 1.6 \cdot 10^{-8} \) \(a_{11}= +1.50743325 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.75599860 \pm 1.4 \cdot 10^{-8} \)
\(a_{13}= +0.21511302 \pm 1.1 \cdot 10^{-8} \) \(a_{14}= +0.76466076 \pm 1.1 \cdot 10^{-8} \) \(a_{15}= +0.51004138 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.48039210 \pm 1.3 \cdot 10^{-8} \) \(a_{17}= -0.24253563 \pm 1.0 \cdot 10^{-8} \) \(a_{18}= -0.06035190 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= -0.58700084 \pm 1.1 \cdot 10^{-8} \) \(a_{20}= +0.44861354 \pm 1.3 \cdot 10^{-8} \) \(a_{21}= -1.65018018 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.64759359 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= +1.31420367 \pm 1.0 \cdot 10^{-8} \) \(a_{24}= +0.72305985 \pm 1.3 \cdot 10^{-8} \)
\(a_{25}= -0.69733876 \pm 1.0 \cdot 10^{-8} \) \(a_{26}= +0.09241259 \pm 1.2 \cdot 10^{-8} \) \(a_{27}= +1.05734366 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -1.45143747 \pm 1.2 \cdot 10^{-8} \) \(a_{29}= -0.22963332 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +0.21911387 \pm 1.4 \cdot 10^{-8} \)
\(a_{31}= +1.74447020 \pm 1.1 \cdot 10^{-8} \) \(a_{32}= +0.98629146 \pm 1.1 \cdot 10^{-8} \) \(a_{33}= -1.39754275 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.10419335 \pm 2.4 \cdot 10^{-8} \) \(a_{35}= -0.97922560 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.11455670 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -0.30740343 \pm 1.0 \cdot 10^{-8} \) \(a_{38}= -0.25217566 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= -0.19943148 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.42906752 \pm 1.2 \cdot 10^{-8} \) \(a_{41}= +0.31667830 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.70891770 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= +0.46861569 \pm 1.2 \cdot 10^{-8} \) \(a_{44}= -1.22922693 \pm 1.1 \cdot 10^{-8} \) \(a_{45}= +0.07728672 \pm 1.1 \cdot 10^{-8} \)
\(a_{46}= +0.56458213 \pm 1.2 \cdot 10^{-8} \) \(a_{47}= +1.04135544 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.44537196 \pm 1.2 \cdot 10^{-8} \)
\(a_{49}= +2.16817170 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.29957685 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= +0.22485500 \pm 2.1 \cdot 10^{-8} \)
\(a_{52}= -0.17541256 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= -0.64588244 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.45423502 \pm 1.2 \cdot 10^{-8} \)
\(a_{55}= -0.82930922 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= -1.38819855 \pm 1.3 \cdot 10^{-8} \) \(a_{57}= +0.54420902 \pm 1.2 \cdot 10^{-8} \)
\(a_{58}= -0.09865051 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= -0.03695301 \pm 1.1 \cdot 10^{-8} \) \(a_{60}= -0.41591003 \pm 1.5 \cdot 10^{-8} \)

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