Properties

Label 67.1
Level $67$
Weight $0$
Character 67.1
Symmetry odd
\(R\) 0.677590
Fricke sign $-1$

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Maass form invariants

Level: \( 67 \)
Weight: \( 0 \)
Character: 67.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(0.677590209166743664641479951164 \pm 10 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.21682371 \pm 1.1 \cdot 10^{-3} \) \(a_{3}= +1.74959096 \pm 1.0 \cdot 10^{-3} \)
\(a_{4}= +0.48065993 \pm 1.1 \cdot 10^{-3} \) \(a_{5}= -0.12151259 \pm 1.0 \cdot 10^{-3} \) \(a_{6}= -2.12894376 \pm 1.3 \cdot 10^{-3} \)
\(a_{7}= +0.26775085 \pm 1.0 \cdot 10^{-3} \) \(a_{8}= +0.63194530 \pm 1.1 \cdot 10^{-3} \) \(a_{9}= +2.06106853 \pm 1.1 \cdot 10^{-3} \)
\(a_{10}= +0.14785939 \pm 1.2 \cdot 10^{-3} \) \(a_{11}= +0.26290126 \pm 9.6 \cdot 10^{-4} \) \(a_{12}= +0.84095828 \pm 1.2 \cdot 10^{-3} \)
\(a_{13}= -1.11682620 \pm 9.6 \cdot 10^{-4} \) \(a_{14}= -0.32580559 \pm 1.2 \cdot 10^{-3} \) \(a_{15}= -0.21259732 \pm 1.0 \cdot 10^{-3} \)
\(a_{16}= -1.24962596 \pm 1.1 \cdot 10^{-3} \) \(a_{17}= -1.25433319 \pm 9.6 \cdot 10^{-4} \) \(a_{18}= -2.50795705 \pm 1.3 \cdot 10^{-3} \)
\(a_{19}= +0.18022578 \pm 1.0 \cdot 10^{-3} \) \(a_{20}= -0.05840623 \pm 1.2 \cdot 10^{-3} \) \(a_{21}= +0.46845447 \pm 1.1 \cdot 10^{-3} \)
\(a_{22}= -0.31990449 \pm 1.2 \cdot 10^{-3} \) \(a_{23}= +0.38657671 \pm 9.5 \cdot 10^{-4} \) \(a_{24}= +1.10564579 \pm 1.3 \cdot 10^{-3} \)
\(a_{25}= -0.98523469 \pm 9.9 \cdot 10^{-4} \) \(a_{26}= +1.35898059 \pm 1.0 \cdot 10^{-3} \) \(a_{27}= +1.85643592 \pm 1.0 \cdot 10^{-3} \)
\(a_{28}= +0.12869711 \pm 1.2 \cdot 10^{-3} \) \(a_{29}= -1.29093859 \pm 9.8 \cdot 10^{-4} \) \(a_{30}= +0.25869346 \pm 1.3 \cdot 10^{-3} \)
\(a_{31}= -0.24674552 \pm 8.8 \cdot 10^{-4} \) \(a_{32}= +0.88862919 \pm 1.1 \cdot 10^{-3} \) \(a_{33}= +0.45996967 \pm 9.7 \cdot 10^{-4} \)
\(a_{34}= +1.52630236 \pm 1.0 \cdot 10^{-3} \) \(a_{35}= -0.03253510 \pm 1.0 \cdot 10^{-3} \) \(a_{36}= +0.99067307 \pm 1.2 \cdot 10^{-3} \)
\(a_{37}= +0.92678224 \pm 9.1 \cdot 10^{-4} \) \(a_{38}= -0.21930300 \pm 1.1 \cdot 10^{-3} \) \(a_{39}= -1.95398902 \pm 1.1 \cdot 10^{-3} \)
\(a_{40}= -0.07678931 \pm 1.1 \cdot 10^{-3} \) \(a_{41}= +1.19240548 \pm 9.1 \cdot 10^{-4} \) \(a_{42}= -0.57002651 \pm 1.3 \cdot 10^{-3} \)
\(a_{43}= +1.35667593 \pm 8.9 \cdot 10^{-4} \) \(a_{44}= +0.12636610 \pm 1.3 \cdot 10^{-3} \) \(a_{45}= -0.25044577 \pm 1.0 \cdot 10^{-3} \)
\(a_{46}= -0.47039571 \pm 1.1 \cdot 10^{-3} \) \(a_{47}= +0.33749192 \pm 9.7 \cdot 10^{-4} \) \(a_{48}= -2.18633429 \pm 1.3 \cdot 10^{-3} \)
\(a_{49}= -0.92830948 \pm 1.0 \cdot 10^{-3} \) \(a_{50}= +1.19885693 \pm 1.2 \cdot 10^{-3} \) \(a_{51}= -2.19457000 \pm 1.0 \cdot 10^{-3} \)
\(a_{52}= -0.53681361 \pm 1.0 \cdot 10^{-3} \) \(a_{53}= +0.52807629 \pm 9.4 \cdot 10^{-4} \) \(a_{54}= -2.25895523 \pm 1.2 \cdot 10^{-3} \)
\(a_{55}= -0.03194581 \pm 1.0 \cdot 10^{-3} \) \(a_{56}= +0.16920389 \pm 1.0 \cdot 10^{-3} \) \(a_{57}= +0.31532140 \pm 1.1 \cdot 10^{-3} \)
\(a_{58}= +1.57084468 \pm 1.2 \cdot 10^{-3} \) \(a_{59}= -1.60644843 \pm 9.8 \cdot 10^{-4} \) \(a_{60}= -0.10218701 \pm 1.3 \cdot 10^{-3} \)

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