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: \( 3.89978494774 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.824046688\) \(a_{4}=+0.000000000\) \(a_{5}=+1.041087261\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.580548901\) \(a_{8}=+0.000000000\) \(a_{9}=+2.327146321\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.889068495\) \(a_{12}=+0.000000000\) \(a_{13}=+0.806437816\) \(a_{14}=+0.000000000\) \(a_{15}=-1.898991771\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+1.109526338\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.058948301\) \(a_{22}=+0.000000000\) \(a_{23}=-1.069018066\) \(a_{24}=+0.000000000\) \(a_{25}=+0.083862685\)
\(a_{26}=+0.000000000\) \(a_{27}=-2.420776853\) \(a_{28}=+0.000000000\) \(a_{29}=-1.742723986\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.512702728\) \(a_{32}=+0.000000000\) \(a_{33}=+3.445749133\) \(a_{34}=+0.000000000\) \(a_{35}=+0.604402066\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.584565056\) \(a_{38}=+0.000000000\) \(a_{39}=-1.470980227\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.537074007\) \(a_{42}=+0.000000000\) \(a_{43}=-1.124136199\) \(a_{44}=+0.000000000\) \(a_{45}=+2.422762390\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.227461902\) \(a_{48}=+0.000000000\) \(a_{49}=-0.662962973\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.442396304\) \(a_{52}=+0.000000000\) \(a_{53}=-0.162601981\) \(a_{54}=+0.000000000\) \(a_{55}=-1.966685145\)
\(a_{56}=+0.000000000\) \(a_{57}=-2.023827843\) \(a_{58}=+0.000000000\) \(a_{59}=-0.913022156\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.314875204\) \(a_{62}=+0.000000000\) \(a_{63}=+1.351022240\) \(a_{64}=+0.000000000\) \(a_{65}=+0.839572137\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.668122429\) \(a_{68}=+0.000000000\) \(a_{69}=+1.949938863\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.318383961\) \(a_{72}=+0.000000000\) \(a_{73}=+0.369745344\) \(a_{74}=+0.000000000\) \(a_{75}=-0.152969453\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.096696640\) \(a_{78}=+0.000000000\) \(a_{79}=-0.767797088\) \(a_{80}=+0.000000000\)
\(a_{81}=+2.088463680\) \(a_{82}=+0.000000000\) \(a_{83}=+0.431577805\) \(a_{84}=+0.000000000\) \(a_{85}=+0.252500750\)
\(a_{86}=+0.000000000\) \(a_{87}=+3.178809916\) \(a_{88}=+0.000000000\) \(a_{89}=-1.680472406\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.468176588\) \(a_{92}=+0.000000000\) \(a_{93}=-0.935193713\) \(a_{94}=+0.000000000\) \(a_{95}=+1.155113736\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.573724448\) \(a_{98}=+0.000000000\) \(a_{99}=-4.396138800\) \(a_{100}=+0.000000000\)

Showing 100 of 750 available coefficients

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