Properties

Label 1.11
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 20.10669
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 20.10669468255231285599308915504965\ldots \pm 7 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= +0.85884762 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.18727861 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.26238077 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.39554793 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.16084379 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.77669505 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.08419272 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.96492672 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -1.19856302 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.38735587 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.04913831 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.68824412 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.66706270 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.26135628 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.66877557 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.23459525 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.82872502 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.09475974 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.36616494 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.14545837 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.33267967 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.03382156 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.20304611 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.94755403 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.59109682 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.36798875 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.20378984 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.23735080 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.22446522 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.13458881 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.50981641 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.07254347 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +1.06032919 \pm 1 \cdot 10^{-8} \) \(a_{35}= -1.08391518 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.25317821 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.16067977 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.08138417 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.12889340 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.51304290 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.31082431 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.12492658 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.61580311 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.10163473 \pm 1 \cdot 10^{-8} \) \(a_{45}= +1.34660149 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.02904757 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.96753780 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.12524736 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.39674479 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.81380452 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.23121329 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.18058202 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.46364243 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.31604626 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.54057369 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.84208712 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.01774647 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +1.06269579 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.04871674 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.06857486 \pm 1 \cdot 10^{-8} \)

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