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: \( 5.3302064817 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.882715629\) \(a_{4}=+0.000000000\) \(a_{5}=-0.366856679\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.181820838\) \(a_{8}=+0.000000000\) \(a_{9}=-0.220813119\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.852807875\) \(a_{12}=+0.000000000\) \(a_{13}=+1.607763955\) \(a_{14}=+0.000000000\) \(a_{15}=+0.323830124\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+1.480186175\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.160496095\) \(a_{22}=+0.000000000\) \(a_{23}=-1.533104243\) \(a_{24}=+0.000000000\) \(a_{25}=-0.865416177\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.077630820\) \(a_{28}=+0.000000000\) \(a_{29}=-0.366320301\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.076808480\) \(a_{32}=+0.000000000\) \(a_{33}=-0.752786840\) \(a_{34}=+0.000000000\) \(a_{35}=+0.066702189\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.121337521\) \(a_{38}=+0.000000000\) \(a_{39}=-1.419198370\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.100959684\) \(a_{42}=+0.000000000\) \(a_{43}=-1.740846456\) \(a_{44}=+0.000000000\) \(a_{45}=+0.081006767\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.777095443\) \(a_{48}=+0.000000000\) \(a_{49}=-0.966941183\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.214089987\) \(a_{52}=+0.000000000\) \(a_{53}=-0.742509441\) \(a_{54}=+0.000000000\) \(a_{55}=-0.312858265\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.306583470\) \(a_{58}=+0.000000000\) \(a_{59}=+1.039381253\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.679664756\) \(a_{62}=+0.000000000\) \(a_{63}=+0.040148426\) \(a_{64}=+0.000000000\) \(a_{65}=-0.589818945\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.512532111\) \(a_{68}=+0.000000000\) \(a_{69}=+1.353295076\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.400931661\) \(a_{72}=+0.000000000\) \(a_{73}=-0.376618873\) \(a_{74}=+0.000000000\) \(a_{75}=+0.763916385\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.155058243\) \(a_{78}=+0.000000000\) \(a_{79}=-0.655417584\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.730428448\) \(a_{82}=+0.000000000\) \(a_{83}=+0.279126336\) \(a_{84}=+0.000000000\) \(a_{85}=+0.088975814\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.323356655\) \(a_{88}=+0.000000000\) \(a_{89}=-0.644559585\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.292324990\) \(a_{92}=+0.000000000\) \(a_{93}=-0.067800046\) \(a_{94}=+0.000000000\) \(a_{95}=-0.543016184\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.604385886\) \(a_{98}=+0.000000000\) \(a_{99}=-0.188311167\) \(a_{100}=+0.000000000\)

Showing 100 of 718 available coefficients

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