Properties

Label 31.78
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 6.010134
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(6.01013486749678917468081959838 \pm 8 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.76551895 \pm 2.1 \cdot 10^{-7} \) \(a_{3}= -1.51339664 \pm 1.9 \cdot 10^{-7} \)
\(a_{4}= +2.11705716 \pm 2.1 \cdot 10^{-7} \) \(a_{5}= +0.65173273 \pm 1.8 \cdot 10^{-7} \) \(a_{6}= +2.67193044 \pm 2.1 \cdot 10^{-7} \)
\(a_{7}= -1.55306900 \pm 1.8 \cdot 10^{-7} \) \(a_{8}= -1.97218558 \pm 2.0 \cdot 10^{-7} \) \(a_{9}= +1.29036938 \pm 1.8 \cdot 10^{-7} \)
\(a_{10}= -1.15064649 \pm 1.7 \cdot 10^{-7} \) \(a_{11}= +0.28596728 \pm 1.8 \cdot 10^{-7} \) \(a_{12}= -3.20394718 \pm 2.0 \cdot 10^{-7} \)
\(a_{13}= -1.54917250 \pm 1.4 \cdot 10^{-7} \) \(a_{14}= +2.74197274 \pm 2.5 \cdot 10^{-7} \) \(a_{15}= -0.98633012 \pm 1.9 \cdot 10^{-7} \)
\(a_{16}= +1.36487385 \pm 2.2 \cdot 10^{-7} \) \(a_{17}= -1.47852406 \pm 1.7 \cdot 10^{-7} \) \(a_{18}= -2.27817158 \pm 1.6 \cdot 10^{-7} \)
\(a_{19}= -0.52722110 \pm 1.6 \cdot 10^{-7} \) \(a_{20}= +1.37975545 \pm 1.8 \cdot 10^{-7} \) \(a_{21}= +2.35040939 \pm 1.8 \cdot 10^{-7} \)
\(a_{22}= -0.50488066 \pm 2.1 \cdot 10^{-7} \) \(a_{23}= -0.55509874 \pm 1.4 \cdot 10^{-7} \) \(a_{24}= +2.98469902 \pm 2.2 \cdot 10^{-7} \)
\(a_{25}= -0.57524445 \pm 1.9 \cdot 10^{-7} \) \(a_{26}= +2.73509341 \pm 1.6 \cdot 10^{-7} \) \(a_{27}= -0.43944404 \pm 1.8 \cdot 10^{-7} \)
\(a_{28}= -3.28793583 \pm 2.6 \cdot 10^{-7} \) \(a_{29}= -1.58135448 \pm 1.7 \cdot 10^{-7} \) \(a_{30}= +1.74138452 \pm 1.9 \cdot 10^{-7} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.43752507 \pm 2.1 \cdot 10^{-7} \) \(a_{33}= -0.43278193 \pm 2.0 \cdot 10^{-7} \)
\(a_{34}= +2.61036224 \pm 1.8 \cdot 10^{-7} \) \(a_{35}= -1.01218590 \pm 1.9 \cdot 10^{-7} \) \(a_{36}= +2.73178572 \pm 1.6 \cdot 10^{-7} \)
\(a_{37}= -0.10506213 \pm 1.8 \cdot 10^{-7} \) \(a_{38}= +0.93081885 \pm 2.1 \cdot 10^{-7} \) \(a_{39}= +2.34451245 \pm 1.8 \cdot 10^{-7} \)
\(a_{40}= -1.28533790 \pm 1.7 \cdot 10^{-7} \) \(a_{41}= -1.25189377 \pm 1.4 \cdot 10^{-7} \) \(a_{42}= -4.14969232 \pm 2.4 \cdot 10^{-7} \)
\(a_{43}= -0.33379233 \pm 1.8 \cdot 10^{-7} \) \(a_{44}= +0.60540909 \pm 2.2 \cdot 10^{-7} \) \(a_{45}= +0.84097596 \pm 1.8 \cdot 10^{-7} \)
\(a_{46}= +0.98003734 \pm 1.8 \cdot 10^{-7} \) \(a_{47}= -0.76796764 \pm 1.6 \cdot 10^{-7} \) \(a_{48}= -2.06559550 \pm 2.0 \cdot 10^{-7} \)
\(a_{49}= +1.41202331 \pm 1.6 \cdot 10^{-7} \) \(a_{50}= +1.01560497 \pm 1.8 \cdot 10^{-7} \) \(a_{51}= +2.23759333 \pm 1.6 \cdot 10^{-7} \)
\(a_{52}= -3.27968674 \pm 1.6 \cdot 10^{-7} \) \(a_{53}= -0.93279258 \pm 1.8 \cdot 10^{-7} \) \(a_{54}= +0.77584677 \pm 2.0 \cdot 10^{-7} \)
\(a_{55}= +0.18637424 \pm 1.9 \cdot 10^{-7} \) \(a_{56}= +3.06294028 \pm 2.7 \cdot 10^{-7} \) \(a_{57}= +0.79789464 \pm 1.5 \cdot 10^{-7} \)
\(a_{58}= +2.79191131 \pm 2.1 \cdot 10^{-7} \) \(a_{59}= +0.73710523 \pm 1.4 \cdot 10^{-7} \) \(a_{60}= -2.08811725 \pm 1.8 \cdot 10^{-7} \)

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