Properties

Label 3.51
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 19.56691
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(19.5669106110084192363326335694 \pm 3 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.56540759 \pm 1.6 \cdot 10^{-2} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.45050094 \pm 2.9 \cdot 10^{-2} \) \(a_{5}= +0.62263423 \pm 2.2 \cdot 10^{-2} \) \(a_{6}= -0.90378850 \pm 1.6 \cdot 10^{-2} \)
\(a_{7}= -1.93480398 \pm 1.8 \cdot 10^{-2} \) \(a_{8}= +0.70521759 \pm 2.0 \cdot 10^{-2} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.97467635 \pm 1.2 \cdot 10^{-2} \) \(a_{11}= -0.55777999 \pm 2.0 \cdot 10^{-2} \) \(a_{12}= -0.83744711 \pm 2.9 \cdot 10^{-2} \)
\(a_{13}= +0.10703289 \pm 2.0 \cdot 10^{-2} \) \(a_{14}= -3.02875685 \pm 1.2 \cdot 10^{-2} \) \(a_{15}= -0.35947804 \pm 2.2 \cdot 10^{-2} \)
\(a_{16}= -0.34654797 \pm 2.4 \cdot 10^{-2} \) \(a_{17}= +0.36348609 \pm 1.5 \cdot 10^{-2} \) \(a_{18}= +0.52180253 \pm 1.6 \cdot 10^{-2} \)
\(a_{19}= -0.79914212 \pm 1.2 \cdot 10^{-2} \) \(a_{20}= +0.90313153 \pm 2.1 \cdot 10^{-2} \) \(a_{21}= +1.11705960 \pm 1.8 \cdot 10^{-2} \)
\(a_{22}= -0.87315303 \pm 1.0 \cdot 10^{-2} \) \(a_{23}= -1.65986030 \pm 4.5 \cdot 10^{-2} \) \(a_{24}= -0.40715756 \pm 2.0 \cdot 10^{-2} \)
\(a_{25}= -0.61232662 \pm 1.8 \cdot 10^{-2} \) \(a_{26}= +0.16755010 \pm 7.0 \cdot 10^{-3} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -2.80643499 \pm 1.2 \cdot 10^{-2} \) \(a_{29}= +0.75651318 \pm 4.2 \cdot 10^{-2} \) \(a_{30}= -0.56272965 \pm 3.8 \cdot 10^{-2} \)
\(a_{31}= +0.19858530 \pm 1.9 \cdot 10^{-2} \) \(a_{32}= -1.24770641 \pm 2.6 \cdot 10^{-2} \) \(a_{33}= +0.32203443 \pm 2.0 \cdot 10^{-2} \)
\(a_{34}= +0.56900389 \pm 1.8 \cdot 10^{-2} \) \(a_{35}= -1.20467519 \pm 8.2 \cdot 10^{-3} \) \(a_{36}= +0.48350031 \pm 2.9 \cdot 10^{-2} \)
\(a_{37}= +0.52272516 \pm 2.2 \cdot 10^{-2} \) \(a_{38}= -1.25098314 \pm 5.5 \cdot 10^{-3} \) \(a_{39}= -0.06179547 \pm 2.0 \cdot 10^{-2} \)
\(a_{40}= +0.43909261 \pm 1.2 \cdot 10^{-2} \) \(a_{41}= -1.19949848 \pm 4.3 \cdot 10^{-2} \) \(a_{42}= +1.74865358 \pm 3.4 \cdot 10^{-2} \)
\(a_{43}= +0.93640580 \pm 2.8 \cdot 10^{-2} \) \(a_{44}= -0.80906039 \pm 1.8 \cdot 10^{-2} \) \(a_{45}= +0.20754474 \pm 2.2 \cdot 10^{-2} \)
\(a_{46}= -2.59835791 \pm 1.3 \cdot 10^{-2} \) \(a_{47}= +0.22929349 \pm 3.6 \cdot 10^{-2} \) \(a_{48}= +0.20007956 \pm 2.4 \cdot 10^{-2} \)
\(a_{49}= +2.74346646 \pm 3.1 \cdot 10^{-2} \) \(a_{50}= -0.95854074 \pm 9.1 \cdot 10^{-3} \) \(a_{51}= -0.20985879 \pm 1.5 \cdot 10^{-2} \)
\(a_{52}= +0.15525131 \pm 1.8 \cdot 10^{-2} \) \(a_{53}= +0.06021017 \pm 1.8 \cdot 10^{-2} \) \(a_{54}= -0.30126283 \pm 1.6 \cdot 10^{-2} \)
\(a_{55}= -0.34729291 \pm 1.4 \cdot 10^{-2} \) \(a_{56}= -1.36445780 \pm 1.7 \cdot 10^{-2} \) \(a_{57}= +0.46138492 \pm 1.2 \cdot 10^{-2} \)
\(a_{58}= +1.18425147 \pm 1.7 \cdot 10^{-2} \) \(a_{59}= +0.09877301 \pm 2.8 \cdot 10^{-2} \) \(a_{60}= -0.52142323 \pm 5.2 \cdot 10^{-2} \)

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