Properties

Level $68$
Weight $0$
Character 68.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.08705117502 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.226017506\) \(a_{4}=+0.000000000\) \(a_{5}=+1.190441492\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.300599296\) \(a_{8}=+0.000000000\) \(a_{9}=+0.503118924\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.479679530\) \(a_{12}=+0.000000000\) \(a_{13}=+0.788944841\) \(a_{14}=+0.000000000\) \(a_{15}=-1.459502109\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-1.154530166\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.368540000\) \(a_{22}=+0.000000000\) \(a_{23}=-0.900506799\) \(a_{24}=+0.000000000\) \(a_{25}=+0.417150947\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.609184897\) \(a_{28}=+0.000000000\) \(a_{29}=+0.625925200\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.977477768\) \(a_{32}=+0.000000000\) \(a_{33}=-0.588095501\) \(a_{34}=+0.000000000\) \(a_{35}=-0.357845875\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.221158325\) \(a_{38}=+0.000000000\) \(a_{39}=-0.967260186\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.268782822\) \(a_{42}=+0.000000000\) \(a_{43}=+0.401088698\) \(a_{44}=+0.000000000\) \(a_{45}=+0.598933643\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.334910100\) \(a_{48}=+0.000000000\) \(a_{49}=-0.909640063\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.297352922\) \(a_{52}=+0.000000000\) \(a_{53}=+0.361623865\) \(a_{54}=+0.000000000\) \(a_{55}=+0.571030416\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.415474195\) \(a_{58}=+0.000000000\) \(a_{59}=+0.365816312\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.137109836\) \(a_{62}=+0.000000000\) \(a_{63}=-0.151237195\) \(a_{64}=+0.000000000\) \(a_{65}=+0.939192674\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.696805675\) \(a_{68}=+0.000000000\) \(a_{69}=+1.104037099\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.154131717\) \(a_{72}=+0.000000000\) \(a_{73}=+0.486717220\) \(a_{74}=+0.000000000\) \(a_{75}=-0.511434363\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.144191329\) \(a_{78}=+0.000000000\) \(a_{79}=-0.202598249\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.249990272\) \(a_{82}=+0.000000000\) \(a_{83}=-1.511649001\) \(a_{84}=+0.000000000\) \(a_{85}=-0.288724471\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.767395253\) \(a_{88}=+0.000000000\) \(a_{89}=+1.028396005\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.237156264\) \(a_{92}=+0.000000000\) \(a_{93}=+2.424422360\) \(a_{94}=+0.000000000\) \(a_{95}=-1.374400614\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.779207839\) \(a_{98}=+0.000000000\) \(a_{99}=+0.241335849\) \(a_{100}=+0.000000000\)

Showing 100 of 642 available coefficients

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