Properties

Label 1.53
Level $1$
Weight $0$
Character 1.1
Symmetry even
\(R\) 35.84167
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 35.84167643258283919350012393229143\ldots \pm 2 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= -1.49723926 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.53340249 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +1.24172540 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.82860211 \pm 1 \cdot 10^{-8} \) \(a_{6}= -2.29587041 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +1.23872045 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.36192076 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.35132320 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +1.24061561 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.32453388 \pm 1 \cdot 10^{-8} \) \(a_{12}= +1.90406482 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.42010672 \pm 1 \cdot 10^{-8} \) \(a_{14}= -1.85466088 \pm 1 \cdot 10^{-8} \) \(a_{15}= -1.27058054 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.69984343 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.43374515 \pm 1 \cdot 10^{-8} \) \(a_{18}= -2.02325415 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.24157433 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.02889629 \pm 1 \cdot 10^{-8} \) \(a_{21}= +1.89945702 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.48590486 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.83256940 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.55497019 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.31341854 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.62900028 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.53871987 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +1.53815064 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.01735927 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.90236307 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.09682680 \pm 1 \cdot 10^{-8} \) \(a_{32}= +1.40975382 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.49764105 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.64942027 \pm 1 \cdot 10^{-8} \) \(a_{35}= -1.02640638 \pm 1 \cdot 10^{-8} \) \(a_{36}= +1.67797234 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.77785720 \pm 1 \cdot 10^{-8} \) \(a_{38}= -1.85893383 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.64419270 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.29988830 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.64593889 \pm 1 \cdot 10^{-8} \) \(a_{42}= -2.84394162 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.37756430 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.40298196 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.11970926 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.24655558 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.15540883 \pm 1 \cdot 10^{-8} \) \(a_{48}= -1.07314167 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.53442834 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.46926254 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.66510590 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.52165719 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.39468543 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.80659254 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.26890946 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.44831864 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.90383317 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.02599098 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.91195519 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.57771213 \pm 1 \cdot 10^{-8} \)

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