Properties

Level $8$
Weight $0$
Character 8.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.62812092942 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.290863620\) \(a_{4}=+0.000000000\) \(a_{5}=+1.302421768\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.311629495\) \(a_{8}=+0.000000000\) \(a_{9}=-0.915398355\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.876435296\) \(a_{12}=+0.000000000\) \(a_{13}=+0.262972540\) \(a_{14}=+0.000000000\) \(a_{15}=+0.378827110\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.414076945\) \(a_{18}=+0.000000000\) \(a_{19}=+0.348294403\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.381505303\) \(a_{22}=+0.000000000\) \(a_{23}=+0.265155498\) \(a_{24}=+0.000000000\) \(a_{25}=+0.696302461\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.557119699\) \(a_{28}=+0.000000000\) \(a_{29}=-0.830889824\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.586278151\) \(a_{32}=+0.000000000\) \(a_{33}=+0.254923143\) \(a_{34}=+0.000000000\) \(a_{35}=+1.708294806\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.822700936\) \(a_{38}=+0.000000000\) \(a_{39}=+0.076489145\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.449642499\) \(a_{42}=+0.000000000\) \(a_{43}=-1.487324559\) \(a_{44}=+0.000000000\) \(a_{45}=-1.192234743\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.137241165\) \(a_{48}=+0.000000000\) \(a_{49}=+0.720371933\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.411303539\) \(a_{52}=+0.000000000\) \(a_{53}=+0.227389551\) \(a_{54}=+0.000000000\) \(a_{55}=+1.141488407\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.101306171\) \(a_{58}=+0.000000000\) \(a_{59}=+0.946798859\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.441274831\) \(a_{62}=+0.000000000\) \(a_{63}=-1.200663482\) \(a_{64}=+0.000000000\) \(a_{65}=+0.342501161\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.226935011\) \(a_{68}=+0.000000000\) \(a_{69}=+0.077124083\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.074997734\) \(a_{72}=+0.000000000\) \(a_{73}=+0.293574956\) \(a_{74}=+0.000000000\) \(a_{75}=+0.202529054\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.149558385\) \(a_{78}=+0.000000000\) \(a_{79}=-0.315599195\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.753352502\) \(a_{82}=+0.000000000\) \(a_{83}=+0.371688622\) \(a_{84}=+0.000000000\) \(a_{85}=-1.841724595\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.241675623\) \(a_{88}=+0.000000000\) \(a_{89}=-0.734545589\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.344922540\) \(a_{92}=+0.000000000\) \(a_{93}=-0.170526984\) \(a_{94}=+0.000000000\) \(a_{95}=+0.453626209\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.214979007\) \(a_{98}=+0.000000000\) \(a_{99}=-0.802287428\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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