Properties

Level $8$
Weight $0$
Character 8.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.48301811751 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.095023767\) \(a_{4}=+0.000000000\) \(a_{5}=-0.584536233\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.459673881\) \(a_{8}=+0.000000000\) \(a_{9}=+0.199077049\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.679210517\) \(a_{12}=+0.000000000\) \(a_{13}=+0.800076279\) \(a_{14}=+0.000000000\) \(a_{15}=-0.640081068\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.763908687\) \(a_{18}=+0.000000000\) \(a_{19}=-1.114237067\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.598377591\) \(a_{22}=+0.000000000\) \(a_{23}=+0.234827097\) \(a_{24}=+0.000000000\) \(a_{25}=-0.658317392\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.877029666\) \(a_{28}=+0.000000000\) \(a_{29}=+0.002063745\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.185223850\) \(a_{32}=+0.000000000\) \(a_{33}=+1.838775427\) \(a_{34}=+0.000000000\) \(a_{35}=-0.853232276\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.674824809\) \(a_{38}=+0.000000000\) \(a_{39}=+0.876102540\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.931533222\) \(a_{42}=+0.000000000\) \(a_{43}=-0.342762129\) \(a_{44}=+0.000000000\) \(a_{45}=-0.116367749\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.110299215\) \(a_{48}=+0.000000000\) \(a_{49}=+1.130647838\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.836498168\) \(a_{52}=+0.000000000\) \(a_{53}=+0.483552046\) \(a_{54}=+0.000000000\) \(a_{55}=-0.981559390\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.220116070\) \(a_{58}=+0.000000000\) \(a_{59}=-0.591663814\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.692912644\) \(a_{62}=+0.000000000\) \(a_{63}=+0.290587569\) \(a_{64}=+0.000000000\) \(a_{65}=-0.467673574\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.427567149\) \(a_{68}=+0.000000000\) \(a_{69}=+0.257141254\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.724351784\) \(a_{72}=+0.000000000\) \(a_{73}=-1.470707660\) \(a_{74}=+0.000000000\) \(a_{75}=-0.720873184\)
\(a_{76}=+0.000000000\) \(a_{77}=+2.451099749\) \(a_{78}=+0.000000000\) \(a_{79}=-1.354814675\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.159445378\) \(a_{82}=+0.000000000\) \(a_{83}=-0.709528292\) \(a_{84}=+0.000000000\) \(a_{85}=-0.446532306\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.002259850\) \(a_{88}=+0.000000000\) \(a_{89}=+1.273476965\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.167850447\) \(a_{92}=+0.000000000\) \(a_{93}=+0.202824519\) \(a_{94}=+0.000000000\) \(a_{95}=+0.651311938\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.428643691\) \(a_{98}=+0.000000000\) \(a_{99}=+0.334292275\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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