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: \( 5.58136438337 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.075218245\) \(a_{4}=+0.000000000\) \(a_{5}=-1.547329796\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.021460885\) \(a_{8}=+0.000000000\) \(a_{9}=-0.994342216\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.264781206\) \(a_{12}=+0.000000000\) \(a_{13}=-1.171093923\) \(a_{14}=+0.000000000\) \(a_{15}=+0.116387432\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.898431433\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.076832495\) \(a_{22}=+0.000000000\) \(a_{23}=-1.456844184\) \(a_{24}=+0.000000000\) \(a_{25}=+1.394229497\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.150010921\) \(a_{28}=+0.000000000\) \(a_{29}=+1.595594574\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.130303104\) \(a_{32}=+0.000000000\) \(a_{33}=+0.019916378\) \(a_{34}=+0.000000000\) \(a_{35}=-1.580536862\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.222686168\) \(a_{38}=+0.000000000\) \(a_{39}=+0.088087630\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.292990463\) \(a_{42}=+0.000000000\) \(a_{43}=+1.289476201\) \(a_{44}=+0.000000000\) \(a_{45}=+1.538575337\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.004487387\) \(a_{48}=+0.000000000\) \(a_{49}=+0.043382339\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.018243104\) \(a_{52}=+0.000000000\) \(a_{53}=+1.530207859\) \(a_{54}=+0.000000000\) \(a_{55}=+0.409703849\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.067578436\) \(a_{58}=+0.000000000\) \(a_{59}=+1.023340430\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.960524172\) \(a_{62}=+0.000000000\) \(a_{63}=-1.015681679\) \(a_{64}=+0.000000000\) \(a_{65}=+1.812068520\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.362634439\) \(a_{68}=+0.000000000\) \(a_{69}=+0.109581263\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.892678893\) \(a_{72}=+0.000000000\) \(a_{73}=+0.625460351\) \(a_{74}=+0.000000000\) \(a_{75}=-0.104871496\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.270463645\) \(a_{78}=+0.000000000\) \(a_{79}=-1.069670200\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.983058657\) \(a_{82}=+0.000000000\) \(a_{83}=+0.985784304\) \(a_{84}=+0.000000000\) \(a_{85}=-0.375282599\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.120017823\) \(a_{88}=+0.000000000\) \(a_{89}=-0.497661612\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.196226634\) \(a_{92}=+0.000000000\) \(a_{93}=-0.009801171\) \(a_{94}=+0.000000000\) \(a_{95}=+1.390169726\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.953739000\) \(a_{98}=+0.000000000\) \(a_{99}=+0.263283131\) \(a_{100}=+0.000000000\)

Showing 100 of 690 available coefficients

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