Properties

Label 1.33
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 30.27904
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 30.27904849914749971973434423081743\ldots \pm 2 \cdot 10^{-91} \) (toggle for full precision) Copy content Toggle raw display

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.78178313 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.00544179 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.17475112 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.79409937 \pm 1 \cdot 10^{-8} \) \(a_{6}= -1.79147922 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.10779559 \pm 1 \cdot 10^{-8} \) \(a_{8}= -2.09315172 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.01091320 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +1.41491286 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.40193101 \pm 1 \cdot 10^{-8} \) \(a_{12}= +2.18658566 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.56119605 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.19206836 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.79842070 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +1.55479130 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.37520603 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.01944496 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.04449612 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.72696849 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.10838219 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -2.49793703 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.24883817 \pm 1 \cdot 10^{-8} \) \(a_{24}= -2.10454222 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.36940619 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.99992965 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.99446921 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.23442858 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.28183588 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.42261253 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.13482047 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.67714919 \pm 1 \cdot 10^{-8} \) \(a_{33}= +1.40956003 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.66853578 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.08560041 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.02373350 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.14260710 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.07928243 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.56424996 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.66217046 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.22729738 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.19311356 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -1.81736657 \pm 1 \cdot 10^{-8} \) \(a_{44}= +3.04885104 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.00866617 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -2.22515877 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.05741026 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.56325216 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.98838011 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.65820172 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.37724783 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -1.22046173 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.40359418 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.77192845 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -1.11327254 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.22563252 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.04473826 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.50217041 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.31958995 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.73636630 \pm 1 \cdot 10^{-8} \)

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