Properties

Label 33.35
Level $33$
Weight $0$
Character 33.1
Symmetry even
\(R\) 4.594615
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: \(4.5946155688954181178518455835 \pm 7 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.66900710 \pm 1.8 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.78558472 \pm 2.0 \cdot 10^{-8} \) \(a_{5}= -1.34844046 \pm 1.5 \cdot 10^{-8} \) \(a_{6}= +0.96360170 \pm 2.8 \cdot 10^{-8} \)
\(a_{7}= +1.41289632 \pm 1.4 \cdot 10^{-8} \) \(a_{8}= -1.31114647 \pm 2.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +2.25055671 \pm 1.5 \cdot 10^{-8} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -1.03090782 \pm 3.1 \cdot 10^{-8} \)
\(a_{13}= -0.50616290 \pm 1.4 \cdot 10^{-8} \) \(a_{14}= -2.35813399 \pm 1.9 \cdot 10^{-8} \) \(a_{15}= +0.77852246 \pm 2.5 \cdot 10^{-8} \)
\(a_{16}= +0.40272806 \pm 2.3 \cdot 10^{-8} \) \(a_{17}= +0.82109859 \pm 1.6 \cdot 10^{-8} \) \(a_{18}= -0.55633570 \pm 2.8 \cdot 10^{-8} \)
\(a_{19}= +1.01627049 \pm 1.5 \cdot 10^{-8} \) \(a_{20}= -2.40775468 \pm 1.7 \cdot 10^{-8} \) \(a_{21}= -0.81573607 \pm 2.5 \cdot 10^{-8} \)
\(a_{22}= -0.50322458 \pm 2.8 \cdot 10^{-8} \) \(a_{23}= -1.52439300 \pm 1.3 \cdot 10^{-8} \) \(a_{24}= +0.75699077 \pm 3.2 \cdot 10^{-8} \)
\(a_{25}= +0.81829168 \pm 1.4 \cdot 10^{-8} \) \(a_{26}= +0.84478947 \pm 1.7 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +2.52284607 \pm 1.9 \cdot 10^{-8} \) \(a_{29}= +0.61574383 \pm 1.3 \cdot 10^{-8} \) \(a_{30}= -1.29935952 \pm 4.4 \cdot 10^{-8} \)
\(a_{31}= -0.98853169 \pm 1.1 \cdot 10^{-8} \) \(a_{32}= +0.63899047 \pm 2.4 \cdot 10^{-8} \) \(a_{33}= -0.17407766 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -1.37041938 \pm 1.8 \cdot 10^{-8} \) \(a_{35}= -1.90520656 \pm 1.3 \cdot 10^{-8} \) \(a_{36}= +0.59519491 \pm 3.1 \cdot 10^{-8} \)
\(a_{37}= +1.54089868 \pm 1.3 \cdot 10^{-8} \) \(a_{38}= -1.69616267 \pm 1.6 \cdot 10^{-8} \) \(a_{39}= +0.29223328 \pm 2.5 \cdot 10^{-8} \)
\(a_{40}= +1.76800296 \pm 1.7 \cdot 10^{-8} \) \(a_{41}= -1.19330951 \pm 1.3 \cdot 10^{-8} \) \(a_{42}= +1.36146929 \pm 4.3 \cdot 10^{-8} \)
\(a_{43}= -1.35773541 \pm 1.7 \cdot 10^{-8} \) \(a_{44}= +0.53837405 \pm 3.1 \cdot 10^{-8} \) \(a_{45}= -0.44948015 \pm 2.5 \cdot 10^{-8} \)
\(a_{46}= +2.54422274 \pm 1.6 \cdot 10^{-8} \) \(a_{47}= -0.08326439 \pm 1.3 \cdot 10^{-8} \) \(a_{48}= -0.23251516 \pm 3.4 \cdot 10^{-8} \)
\(a_{49}= +0.99627600 \pm 1.4 \cdot 10^{-8} \) \(a_{50}= -1.36573463 \pm 1.7 \cdot 10^{-8} \) \(a_{51}= -0.47406149 \pm 2.6 \cdot 10^{-8} \)
\(a_{52}= -0.90379673 \pm 1.9 \cdot 10^{-8} \) \(a_{53}= -1.16568025 \pm 1.1 \cdot 10^{-8} \) \(a_{54}= +0.32120057 \pm 2.8 \cdot 10^{-8} \)
\(a_{55}= -0.40657010 \pm 2.5 \cdot 10^{-8} \) \(a_{56}= -1.85251402 \pm 2.0 \cdot 10^{-8} \) \(a_{57}= -0.58674404 \pm 2.5 \cdot 10^{-8} \)
\(a_{58}= -1.02768082 \pm 1.8 \cdot 10^{-8} \) \(a_{59}= +1.40339032 \pm 1.3 \cdot 10^{-8} \) \(a_{60}= +1.39011781 \pm 4.6 \cdot 10^{-8} \)

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