Properties

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

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.306309004 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.549124188\) \(a_{4}=+0.000000000\) \(a_{5}=+1.785069798\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.698555369\) \(a_{8}=+0.000000000\) \(a_{9}=+1.399785750\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.734107254\) \(a_{12}=+0.000000000\) \(a_{13}=-1.238126731\) \(a_{14}=+0.000000000\) \(a_{15}=+2.765294800\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.519752480\) \(a_{20}=+0.000000000\)
\(a_{21}=+2.631273206\) \(a_{22}=+0.000000000\) \(a_{23}=+0.431441760\) \(a_{24}=+0.000000000\) \(a_{25}=+2.186474182\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.619317774\) \(a_{28}=+0.000000000\) \(a_{29}=-0.477944798\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.668351031\) \(a_{32}=+0.000000000\) \(a_{33}=-1.137223304\) \(a_{34}=+0.000000000\) \(a_{35}=+3.032039889\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.136693560\) \(a_{38}=+0.000000000\) \(a_{39}=-1.918012066\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.189042614\) \(a_{42}=+0.000000000\) \(a_{43}=+0.451189057\) \(a_{44}=+0.000000000\) \(a_{45}=+2.498715264\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.842081963\) \(a_{48}=+0.000000000\) \(a_{49}=+1.885090341\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.375717803\) \(a_{52}=+0.000000000\) \(a_{53}=+0.592746962\) \(a_{54}=+0.000000000\) \(a_{55}=-1.310432688\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.805161138\) \(a_{58}=+0.000000000\) \(a_{59}=-0.251633796\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.073906267\) \(a_{62}=+0.000000000\) \(a_{63}=+2.377613600\) \(a_{64}=+0.000000000\) \(a_{65}=-2.210142633\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.774790550\) \(a_{68}=+0.000000000\) \(a_{69}=+0.668356867\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.284795524\) \(a_{72}=+0.000000000\) \(a_{73}=+1.312185010\) \(a_{74}=+0.000000000\) \(a_{75}=+3.387120042\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.246921818\) \(a_{78}=+0.000000000\) \(a_{79}=+1.481826849\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.440385605\) \(a_{82}=+0.000000000\) \(a_{83}=-0.355301244\) \(a_{84}=+0.000000000\) \(a_{85}=-0.432943019\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.740395847\) \(a_{88}=+0.000000000\) \(a_{89}=-0.198364014\) \(a_{90}=+0.000000000\)
\(a_{91}=-2.103026807\) \(a_{92}=+0.000000000\) \(a_{93}=-2.584482936\) \(a_{94}=+0.000000000\) \(a_{95}=-0.927794453\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.924938783\) \(a_{98}=+0.000000000\) \(a_{99}=-1.027592873\) \(a_{100}=+0.000000000\)

Showing 100 of 612 available coefficients

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