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: \( 13.9895535537 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.091059412\) \(a_{4}=+0.000000000\) \(a_{5}=-0.595658905\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.472341926\) \(a_{8}=+0.000000000\) \(a_{9}=+0.190410641\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.486391969\) \(a_{12}=+0.000000000\) \(a_{13}=-1.369652853\) \(a_{14}=+0.000000000\) \(a_{15}=+0.649899255\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.153007816\) \(a_{18}=+0.000000000\) \(a_{19}=-0.276110710\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.515353104\) \(a_{22}=+0.000000000\) \(a_{23}=-1.952397119\) \(a_{24}=+0.000000000\) \(a_{25}=-0.645190469\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.883310090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.535478593\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.283825064\) \(a_{32}=+0.000000000\) \(a_{33}=+1.621741948\) \(a_{34}=+0.000000000\) \(a_{35}=+0.281354674\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.786002391\) \(a_{38}=+0.000000000\) \(a_{39}=+1.494372640\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.209023686\) \(a_{42}=+0.000000000\) \(a_{43}=+1.215381155\) \(a_{44}=+0.000000000\) \(a_{45}=-0.113419794\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.135110465\) \(a_{48}=+0.000000000\) \(a_{49}=-0.776893105\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.166940617\) \(a_{52}=+0.000000000\) \(a_{53}=+1.280567888\) \(a_{54}=+0.000000000\) \(a_{55}=+0.885382613\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.301253189\) \(a_{58}=+0.000000000\) \(a_{59}=-1.247252970\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.531219006\) \(a_{62}=+0.000000000\) \(a_{63}=-0.089938929\) \(a_{64}=+0.000000000\) \(a_{65}=+0.815845920\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.373668831\) \(a_{68}=+0.000000000\) \(a_{69}=+2.130181254\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.295184093\) \(a_{72}=+0.000000000\) \(a_{73}=+0.323691022\) \(a_{74}=+0.000000000\) \(a_{75}=+0.703941142\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.702085232\) \(a_{78}=+0.000000000\) \(a_{79}=-0.558983802\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.154154405\) \(a_{82}=+0.000000000\) \(a_{83}=-0.122293101\) \(a_{84}=+0.000000000\) \(a_{85}=+0.091140468\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.675298371\) \(a_{88}=+0.000000000\) \(a_{89}=+1.770885820\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.646944466\) \(a_{92}=+0.000000000\) \(a_{93}=+0.309670007\) \(a_{94}=+0.000000000\) \(a_{95}=+0.164467803\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.651571834\) \(a_{98}=+0.000000000\) \(a_{99}=-0.283024848\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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