Properties

Label 17.37
Level $17$
Weight $0$
Character 17.1
Symmetry even
\(R\) 5.829670
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 17 \)
Weight: \( 0 \)
Character: 17.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(5.82967064319846954112515431043 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.82301108 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.82280751 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.32336940 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.78777845 \pm 1 \cdot 10^{-8} \) \(a_{6}= +3.32299828 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.30275593 \pm 1 \cdot 10^{-8} \) \(a_{8}= -2.41251707 \pm 1 \cdot 10^{-8} \) \(a_{9}= +2.32262721 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +1.43612885 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.27822510 \pm 1 \cdot 10^{-8} \) \(a_{12}= -4.23505518 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.00816382 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.55192741 \pm 1 \cdot 10^{-8} \) \(a_{15}= +1.43596848 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +2.07467596 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.24253563 \pm 1.0 \cdot 10^{-8} \) \(a_{18}= -4.23417514 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.80230929 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.83030035 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.55186578 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.50720744 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.61006919 \pm 1 \cdot 10^{-8} \) \(a_{24}= +4.39755424 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.37940511 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.01488273 \pm 1 \cdot 10^{-8} \) \(a_{27}= -2.41089481 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.70341386 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.34579182 \pm 1 \cdot 10^{-8} \) \(a_{30}= -2.61778644 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.21292663 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.36964019 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.50715080 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.44214513 \pm 1.2 \cdot 10^{-8} \) \(a_{35}= -0.23850460 \pm 1 \cdot 10^{-8} \) \(a_{36}= +5.39632098 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.22201324 \pm 1 \cdot 10^{-8} \) \(a_{38}= -3.28562980 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.01488107 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.90052897 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.15990648 \pm 1 \cdot 10^{-8} \) \(a_{42}= +1.00605743 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.53616323 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.64641968 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.82971567 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.11216289 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.12866980 \pm 1 \cdot 10^{-8} \) \(a_{48}= -3.78173492 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.90833885 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.69165972 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.44209576 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +0.01896756 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.53616428 \pm 1 \cdot 10^{-8} \) \(a_{54}= +4.39508795 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.21917974 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.73040384 \pm 1 \cdot 10^{-8} \) \(a_{57}= -3.28526290 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.63038232 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.94189174 \pm 1 \cdot 10^{-8} \) \(a_{60}= +3.33628521 \pm 1 \cdot 10^{-8} \)

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