Properties

Label 3.49
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 19.02677
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(19.0267767277159515990093036122 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.08613898 \pm 2.7 \cdot 10^{-2} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.99258008 \pm 4.9 \cdot 10^{-2} \) \(a_{5}= +0.10078856 \pm 3.7 \cdot 10^{-2} \) \(a_{6}= +0.04973236 \pm 2.7 \cdot 10^{-2} \)
\(a_{7}= +1.22782462 \pm 3.0 \cdot 10^{-2} \) \(a_{8}= +0.17163881 \pm 3.3 \cdot 10^{-2} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.00868182 \pm 2.1 \cdot 10^{-2} \) \(a_{11}= +0.68050424 \pm 3.4 \cdot 10^{-2} \) \(a_{12}= +0.57306637 \pm 4.9 \cdot 10^{-2} \)
\(a_{13}= -1.18003931 \pm 3.3 \cdot 10^{-2} \) \(a_{14}= -0.10576356 \pm 2.1 \cdot 10^{-2} \) \(a_{15}= -0.05819030 \pm 3.7 \cdot 10^{-2} \)
\(a_{16}= +0.97779528 \pm 4.0 \cdot 10^{-2} \) \(a_{17}= +0.15753027 \pm 2.5 \cdot 10^{-2} \) \(a_{18}= -0.02871299 \pm 2.7 \cdot 10^{-2} \)
\(a_{19}= +0.92577735 \pm 2.0 \cdot 10^{-2} \) \(a_{20}= -0.10004072 \pm 3.5 \cdot 10^{-2} \) \(a_{21}= -0.70888488 \pm 3.0 \cdot 10^{-2} \)
\(a_{22}= -0.05861794 \pm 1.7 \cdot 10^{-2} \) \(a_{23}= -1.85747795 \pm 7.5 \cdot 10^{-2} \) \(a_{24}= -0.09909572 \pm 3.3 \cdot 10^{-2} \)
\(a_{25}= -0.98984167 \pm 3.1 \cdot 10^{-2} \) \(a_{26}= +0.10164738 \pm 1.1 \cdot 10^{-2} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -1.21871426 \pm 2.0 \cdot 10^{-2} \) \(a_{29}= -1.13235323 \pm 7.1 \cdot 10^{-2} \) \(a_{30}= +0.00501245 \pm 6.4 \cdot 10^{-2} \)
\(a_{31}= +0.73662808 \pm 3.1 \cdot 10^{-2} \) \(a_{32}= -0.25586510 \pm 4.4 \cdot 10^{-2} \) \(a_{33}= -0.39288931 \pm 3.4 \cdot 10^{-2} \)
\(a_{34}= -0.01356950 \pm 3.0 \cdot 10^{-2} \) \(a_{35}= +0.12375067 \pm 1.3 \cdot 10^{-2} \) \(a_{36}= -0.33086003 \pm 4.9 \cdot 10^{-2} \)
\(a_{37}= -0.69030342 \pm 3.8 \cdot 10^{-2} \) \(a_{38}= -0.07974552 \pm 9.2 \cdot 10^{-3} \) \(a_{39}= +0.68129601 \pm 3.3 \cdot 10^{-2} \)
\(a_{40}= +0.01729923 \pm 2.0 \cdot 10^{-2} \) \(a_{41}= +0.73078552 \pm 7.2 \cdot 10^{-2} \) \(a_{42}= +0.06106262 \pm 5.8 \cdot 10^{-2} \)
\(a_{43}= -0.83201477 \pm 4.8 \cdot 10^{-2} \) \(a_{44}= -0.67545495 \pm 3.0 \cdot 10^{-2} \) \(a_{45}= +0.03359619 \pm 3.7 \cdot 10^{-2} \)
\(a_{46}= +0.16000125 \pm 2.1 \cdot 10^{-2} \) \(a_{47}= +0.70211362 \pm 5.9 \cdot 10^{-2} \) \(a_{48}= -0.56453037 \pm 4.0 \cdot 10^{-2} \)
\(a_{49}= +0.50755330 \pm 5.2 \cdot 10^{-2} \) \(a_{50}= +0.08526395 \pm 1.5 \cdot 10^{-2} \) \(a_{51}= -0.09095014 \pm 2.5 \cdot 10^{-2} \)
\(a_{52}= +1.17128351 \pm 3.0 \cdot 10^{-2} \) \(a_{53}= -1.84333098 \pm 3.0 \cdot 10^{-2} \) \(a_{54}= +0.01657745 \pm 2.7 \cdot 10^{-2} \)
\(a_{55}= +0.06858704 \pm 2.4 \cdot 10^{-2} \) \(a_{56}= +0.21074236 \pm 2.9 \cdot 10^{-2} \) \(a_{57}= -0.53449780 \pm 2.0 \cdot 10^{-2} \)
\(a_{58}= +0.09753975 \pm 2.9 \cdot 10^{-2} \) \(a_{59}= +1.07935213 \pm 4.8 \cdot 10^{-2} \) \(a_{60}= +0.05775853 \pm 8.7 \cdot 10^{-2} \)

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