Properties

Label 15.41
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 7.763330
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(7.76333046177552089358528249615 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.12760350 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.98371735 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.07367192 \pm 1.2 \cdot 10^{-8} \)
\(a_{7}= -1.05886184 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.25312929 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.05706602 \pm 1.2 \cdot 10^{-8} \) \(a_{11}= -1.26499776 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.56794947 \pm 1.2 \cdot 10^{-8} \)
\(a_{13}= -0.14321873 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.13511448 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.95141716 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.96939605 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.04253450 \pm 1.2 \cdot 10^{-8} \)
\(a_{19}= +0.71773154 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.43993177 \pm 1.2 \cdot 10^{-8} \) \(a_{21}= +0.61133417 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= -0.16141815 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.14193257 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.14614426 \pm 1.2 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.01827521 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +1.04162076 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.32427348 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.03294708 \pm 1.2 \cdot 10^{-8} \)
\(a_{31}= +1.54651753 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.37453345 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.73034680 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.12369833 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.47353741 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -0.32790578 \pm 1.2 \cdot 10^{-8} \)
\(a_{37}= -1.57439501 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.09158506 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.08268737 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= +0.11320286 \pm 1.2 \cdot 10^{-8} \) \(a_{41}= -0.78000760 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.07800838 \pm 1.3 \cdot 10^{-8} \)
\(a_{43}= -0.50701566 \pm 1 \cdot 10^{-8} \) \(a_{44}= +1.24440024 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.01811109 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.55577976 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.54930095 \pm 1.2 \cdot 10^{-8} \)
\(a_{49}= +0.12118839 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.02552070 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= -0.55968107 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +0.14088675 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.85134830 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.02455731 \pm 1.2 \cdot 10^{-8} \)
\(a_{55}= +0.56572420 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= +0.26802894 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.41438250 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= -0.16898194 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.90190961 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.25399473 \pm 1.2 \cdot 10^{-8} \)

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