Properties

Label 15.28
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 6.540894
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(6.54089429078622357205063720462 \pm 5 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.21680370 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.48061125 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.70252194 \pm 1.3 \cdot 10^{-8} \)
\(a_{7}= -0.72609643 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.63199416 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.54417116 \pm 1.3 \cdot 10^{-8} \) \(a_{11}= -1.38613571 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.27748103 \pm 1.3 \cdot 10^{-8} \)
\(a_{13}= -1.37182490 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.88351683 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -1.24962408 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.19374160 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.40560123 \pm 1.3 \cdot 10^{-8} \)
\(a_{19}= -0.61687356 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.21493588 \pm 1.3 \cdot 10^{-8} \) \(a_{21}= +0.41921197 \pm 1.2 \cdot 10^{-8} \)
\(a_{22}= -1.68665506 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.52021647 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.36488200 \pm 1.3 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.66924161 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.34897011 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.30604442 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.31417736 \pm 1.3 \cdot 10^{-8} \)
\(a_{31}= -0.07362738 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.88855304 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.80028583 \pm 1.2 \cdot 10^{-8} \)
\(a_{34}= +1.45254919 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.32472020 \pm 1.2 \cdot 10^{-8} \) \(a_{36}= +0.16020375 \pm 1.3 \cdot 10^{-8} \)
\(a_{37}= -0.81929561 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.75061404 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.79202347 \pm 1.2 \cdot 10^{-8} \)
\(a_{40}= -0.28263638 \pm 1.3 \cdot 10^{-8} \) \(a_{41}= -0.04785263 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.51009868 \pm 1.5 \cdot 10^{-8} \)
\(a_{43}= +0.55212937 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.66619241 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.63300133 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.66488996 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.72147080 \pm 1.2 \cdot 10^{-8} \)
\(a_{49}= -0.47278397 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.24336074 \pm 1.3 \cdot 10^{-8} \) \(a_{51}= -0.68920703 \pm 1.2 \cdot 10^{-8} \)
\(a_{52}= -0.65931447 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.74079949 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.23417398 \pm 1.3 \cdot 10^{-8} \)
\(a_{55}= -0.61989874 \pm 1.2 \cdot 10^{-8} \) \(a_{56}= +0.45888870 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.35615212 \pm 1.2 \cdot 10^{-8} \)
\(a_{58}= +1.58919969 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.94941216 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.12409329 \pm 1.3 \cdot 10^{-8} \)

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