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: \( 12.93885778 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.871671046\) \(a_{4}=+0.000000000\) \(a_{5}=+0.063037997\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.960385161\) \(a_{8}=+0.000000000\) \(a_{9}=+2.503152506\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.299134275\) \(a_{12}=+0.000000000\) \(a_{13}=+0.064796236\) \(a_{14}=+0.000000000\) \(a_{15}=-0.117986394\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.357234048\) \(a_{18}=+0.000000000\) \(a_{19}=-0.652875569\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.797525098\) \(a_{22}=+0.000000000\) \(a_{23}=-0.542996247\) \(a_{24}=+0.000000000\) \(a_{25}=-0.996026211\)
\(a_{26}=+0.000000000\) \(a_{27}=-2.813407024\) \(a_{28}=+0.000000000\) \(a_{29}=+1.121227451\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.271020712\) \(a_{32}=+0.000000000\) \(a_{33}=-2.431552007\) \(a_{34}=+0.000000000\) \(a_{35}=-0.060540757\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.824389013\) \(a_{38}=+0.000000000\) \(a_{39}=-0.121277238\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.015776953\) \(a_{42}=+0.000000000\) \(a_{43}=-0.512537452\) \(a_{44}=+0.000000000\) \(a_{45}=+0.157793779\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.037640364\) \(a_{48}=+0.000000000\) \(a_{49}=-0.077660343\) \(a_{50}=+0.000000000\)
\(a_{51}=-2.540295671\) \(a_{52}=+0.000000000\) \(a_{53}=+0.321298034\) \(a_{54}=+0.000000000\) \(a_{55}=+0.081894822\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.221968299\) \(a_{58}=+0.000000000\) \(a_{59}=+0.592244021\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.150874092\) \(a_{62}=+0.000000000\) \(a_{63}=-2.403990521\) \(a_{64}=+0.000000000\) \(a_{65}=+0.004084625\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.535853027\) \(a_{68}=+0.000000000\) \(a_{69}=+1.016310354\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.588785590\) \(a_{72}=+0.000000000\) \(a_{73}=-0.354311259\) \(a_{74}=+0.000000000\) \(a_{75}=+1.864233421\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.247669280\) \(a_{78}=+0.000000000\) \(a_{79}=-1.417800269\) \(a_{80}=+0.000000000\)
\(a_{81}=+2.762619966\) \(a_{82}=+0.000000000\) \(a_{83}=+0.605372228\) \(a_{84}=+0.000000000\) \(a_{85}=+0.085557329\)
\(a_{86}=+0.000000000\) \(a_{87}=-2.098568950\) \(a_{88}=+0.000000000\) \(a_{89}=-1.037486282\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.062229344\) \(a_{92}=+0.000000000\) \(a_{93}=+0.507261619\) \(a_{94}=+0.000000000\) \(a_{95}=-0.041155968\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.859218054\) \(a_{98}=+0.000000000\) \(a_{99}=+3.251931215\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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