Properties

Label 7.78
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 13.64642
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(13.6464251756107760805689320314 \pm 10 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.10186869 \pm 2.0 \cdot 10^{-5} \) \(a_{3}= +1.69538000 \pm 1.3 \cdot 10^{-5} \)
\(a_{4}= +0.21411460 \pm 1.2 \cdot 10^{-5} \) \(a_{5}= +0.60513581 \pm 1.4 \cdot 10^{-5} \) \(a_{6}= -1.86808613 \pm 1.6 \cdot 10^{-5} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.86594251 \pm 1.3 \cdot 10^{-5} \) \(a_{9}= +1.87431334 \pm 1.2 \cdot 10^{-5} \)
\(a_{10}= -0.66678020 \pm 1.4 \cdot 10^{-5} \) \(a_{11}= +1.89052988 \pm 1.2 \cdot 10^{-5} \) \(a_{12}= +0.36300561 \pm 1.0 \cdot 10^{-5} \)
\(a_{13}= -1.10103763 \pm 1.4 \cdot 10^{-5} \) \(a_{14}= -0.41646722 \pm 2.0 \cdot 10^{-5} \) \(a_{15}= +1.02593515 \pm 1.1 \cdot 10^{-5} \)
\(a_{16}= -1.16826954 \pm 1.7 \cdot 10^{-5} \) \(a_{17}= -0.14475559 \pm 1.1 \cdot 10^{-5} \) \(a_{18}= -2.06524718 \pm 1.2 \cdot 10^{-5} \)
\(a_{19}= +0.01073463 \pm 1.4 \cdot 10^{-5} \) \(a_{20}= +0.12956841 \pm 9.4 \cdot 10^{-6} \) \(a_{21}= +0.64079341 \pm 1.3 \cdot 10^{-5} \)
\(a_{22}= -2.08311567 \pm 1.2 \cdot 10^{-5} \) \(a_{23}= +0.51808125 \pm 1.8 \cdot 10^{-5} \) \(a_{24}= +1.46810161 \pm 8.9 \cdot 10^{-6} \)
\(a_{25}= -0.63381065 \pm 1.3 \cdot 10^{-5} \) \(a_{26}= +1.21319889 \pm 1.8 \cdot 10^{-5} \) \(a_{27}= +1.48229335 \pm 1.4 \cdot 10^{-5} \)
\(a_{28}= +0.08092771 \pm 1.2 \cdot 10^{-5} \) \(a_{29}= +0.84404815 \pm 1.3 \cdot 10^{-5} \) \(a_{30}= -1.13044581 \pm 1.3 \cdot 10^{-5} \)
\(a_{31}= -0.83050119 \pm 1.1 \cdot 10^{-5} \) \(a_{32}= +0.42133711 \pm 1.7 \cdot 10^{-5} \) \(a_{33}= +3.20516654 \pm 1.0 \cdot 10^{-5} \)
\(a_{34}= +0.15950165 \pm 1.3 \cdot 10^{-5} \) \(a_{35}= +0.22871984 \pm 1.4 \cdot 10^{-5} \) \(a_{36}= +0.40131785 \pm 7.2 \cdot 10^{-6} \)
\(a_{37}= +0.27337155 \pm 1.3 \cdot 10^{-5} \) \(a_{38}= -0.01182815 \pm 1.4 \cdot 10^{-5} \) \(a_{39}= -1.86667718 \pm 1.1 \cdot 10^{-5} \)
\(a_{40}= +0.52401282 \pm 1.3 \cdot 10^{-5} \) \(a_{41}= +0.49049139 \pm 1.7 \cdot 10^{-5} \) \(a_{42}= -0.70607019 \pm 3.4 \cdot 10^{-5} \)
\(a_{43}= +0.59393313 \pm 1.0 \cdot 10^{-5} \) \(a_{44}= +0.40479005 \pm 9.1 \cdot 10^{-6} \) \(a_{45}= +1.13421412 \pm 1.1 \cdot 10^{-5} \)
\(a_{46}= -0.57085750 \pm 2.1 \cdot 10^{-5} \) \(a_{47}= +1.63308929 \pm 1.6 \cdot 10^{-5} \) \(a_{48}= -1.98066081 \pm 1.3 \cdot 10^{-5} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.69837611 \pm 1.6 \cdot 10^{-5} \) \(a_{51}= -0.24541573 \pm 8.2 \cdot 10^{-6} \)
\(a_{52}= -0.23574823 \pm 9.7 \cdot 10^{-6} \) \(a_{53}= +0.16040889 \pm 1.1 \cdot 10^{-5} \) \(a_{54}= -1.63329262 \pm 1.8 \cdot 10^{-5} \)
\(a_{55}= +1.14402733 \pm 1.2 \cdot 10^{-5} \) \(a_{56}= +0.32729550 \pm 1.3 \cdot 10^{-5} \) \(a_{57}= +0.01819927 \pm 7.1 \cdot 10^{-6} \)
\(a_{58}= -0.93003022 \pm 1.3 \cdot 10^{-5} \) \(a_{59}= -0.49808499 \pm 2.2 \cdot 10^{-5} \) \(a_{60}= +0.21966770 \pm 9.2 \cdot 10^{-6} \)

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