Properties

Label 33.46
Level $33$
Weight $0$
Character 33.1
Symmetry even
\(R\) 5.234758
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(5.23475835661477416029529629589 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.63079417 \pm 1.9 \cdot 10^{-7} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.65948963 \pm 2.2 \cdot 10^{-7} \) \(a_{5}= +1.14312244 \pm 1.6 \cdot 10^{-7} \) \(a_{6}= +0.94153945 \pm 2.0 \cdot 10^{-7} \)
\(a_{7}= -0.57400937 \pm 1.6 \cdot 10^{-7} \) \(a_{8}= +1.07549185 \pm 2.4 \cdot 10^{-7} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +1.86419741 \pm 1.7 \cdot 10^{-7} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.95810679 \pm 2.3 \cdot 10^{-7} \)
\(a_{13}= +1.33287039 \pm 1.6 \cdot 10^{-7} \) \(a_{14}= -0.93609113 \pm 2.1 \cdot 10^{-7} \) \(a_{15}= +0.65998205 \pm 1.8 \cdot 10^{-7} \)
\(a_{16}= +0.09441621 \pm 2.6 \cdot 10^{-7} \) \(a_{17}= +0.02157439 \pm 1.7 \cdot 10^{-7} \) \(a_{18}= +0.54359806 \pm 2.0 \cdot 10^{-7} \)
\(a_{19}= -1.07556753 \pm 1.6 \cdot 10^{-7} \) \(a_{20}= +1.89699984 \pm 1.9 \cdot 10^{-7} \) \(a_{21}= -0.33140446 \pm 1.7 \cdot 10^{-7} \)
\(a_{22}= +0.49170294 \pm 2.0 \cdot 10^{-7} \) \(a_{23}= +1.13450087 \pm 1.5 \cdot 10^{-7} \) \(a_{24}= +0.62093551 \pm 2.5 \cdot 10^{-7} \)
\(a_{25}= +0.30672891 \pm 1.6 \cdot 10^{-7} \) \(a_{26}= +2.17363727 \pm 1.8 \cdot 10^{-7} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.95256260 \pm 2.1 \cdot 10^{-7} \) \(a_{29}= -0.37528308 \pm 1.4 \cdot 10^{-7} \) \(a_{30}= +1.07629488 \pm 3.7 \cdot 10^{-7} \)
\(a_{31}= -1.24030640 \pm 1.2 \cdot 10^{-7} \) \(a_{32}= -0.92151845 \pm 2.6 \cdot 10^{-7} \) \(a_{33}= +0.17407766 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.03518339 \pm 2.0 \cdot 10^{-7} \) \(a_{35}= -0.65616299 \pm 1.4 \cdot 10^{-7} \) \(a_{36}= +0.55316321 \pm 2.3 \cdot 10^{-7} \)
\(a_{37}= -0.92579276 \pm 1.5 \cdot 10^{-7} \) \(a_{38}= -1.75402927 \pm 1.8 \cdot 10^{-7} \) \(a_{39}= +0.76953308 \pm 1.7 \cdot 10^{-7} \)
\(a_{40}= +1.22941887 \pm 1.8 \cdot 10^{-7} \) \(a_{41}= +1.78378083 \pm 1.4 \cdot 10^{-7} \) \(a_{42}= -0.54045247 \pm 3.7 \cdot 10^{-7} \)
\(a_{43}= -1.44944338 \pm 1.8 \cdot 10^{-7} \) \(a_{44}= +0.50035495 \pm 2.3 \cdot 10^{-7} \) \(a_{45}= +0.38104081 \pm 1.8 \cdot 10^{-7} \)
\(a_{46}= +1.85013742 \pm 1.7 \cdot 10^{-7} \) \(a_{47}= -0.96741051 \pm 1.4 \cdot 10^{-7} \) \(a_{48}= +0.05451122 \pm 2.7 \cdot 10^{-7} \)
\(a_{49}= -0.67051324 \pm 1.6 \cdot 10^{-7} \) \(a_{50}= +0.50021172 \pm 1.8 \cdot 10^{-7} \) \(a_{51}= +0.01245598 \pm 1.8 \cdot 10^{-7} \)
\(a_{52}= +2.21188460 \pm 2.1 \cdot 10^{-7} \) \(a_{53}= +0.82270107 \pm 1.2 \cdot 10^{-7} \) \(a_{54}= +0.31384648 \pm 2.0 \cdot 10^{-7} \)
\(a_{55}= +0.34466438 \pm 1.8 \cdot 10^{-7} \) \(a_{56}= -0.61734240 \pm 2.2 \cdot 10^{-7} \) \(a_{57}= -0.62097921 \pm 1.8 \cdot 10^{-7} \)
\(a_{58}= -0.61200947 \pm 2.0 \cdot 10^{-7} \) \(a_{59}= -1.94366312 \pm 1.4 \cdot 10^{-7} \) \(a_{60}= +1.09523337 \pm 4.0 \cdot 10^{-7} \)

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