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: \( 5.099118331 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.942600180\) \(a_{4}=+0.000000000\) \(a_{5}=+0.967329837\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.686837819\) \(a_{8}=+0.000000000\) \(a_{9}=-0.111504901\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.502711912\) \(a_{12}=+0.000000000\) \(a_{13}=-0.088860486\) \(a_{14}=+0.000000000\) \(a_{15}=-0.911805278\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.521493804\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.647413451\) \(a_{22}=+0.000000000\) \(a_{23}=+0.307603033\) \(a_{24}=+0.000000000\) \(a_{25}=-0.064272988\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.047704720\) \(a_{28}=+0.000000000\) \(a_{29}=+0.775533331\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.928303758\) \(a_{32}=+0.000000000\) \(a_{33}=+0.473856339\) \(a_{34}=+0.000000000\) \(a_{35}=+0.664398715\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.002756519\) \(a_{38}=+0.000000000\) \(a_{39}=+0.083759910\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.025526903\) \(a_{42}=+0.000000000\) \(a_{43}=+0.083183579\) \(a_{44}=+0.000000000\) \(a_{45}=-0.107862018\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.275468750\) \(a_{48}=+0.000000000\) \(a_{49}=-0.528253811\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.228614124\) \(a_{52}=+0.000000000\) \(a_{53}=+1.060126849\) \(a_{54}=+0.000000000\) \(a_{55}=-0.486288232\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.491560153\) \(a_{58}=+0.000000000\) \(a_{59}=+1.084987144\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.119429676\) \(a_{62}=+0.000000000\) \(a_{63}=-0.076585783\) \(a_{64}=+0.000000000\) \(a_{65}=-0.085957399\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.922266449\) \(a_{68}=+0.000000000\) \(a_{69}=-0.289946674\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.271777357\) \(a_{72}=+0.000000000\) \(a_{73}=+0.782775032\) \(a_{74}=+0.000000000\) \(a_{75}=+0.060583729\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.345281553\) \(a_{78}=+0.000000000\) \(a_{79}=+1.556331616\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.876061756\) \(a_{82}=+0.000000000\) \(a_{83}=-0.433042393\) \(a_{84}=+0.000000000\) \(a_{85}=-0.234611947\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.731017858\) \(a_{88}=+0.000000000\) \(a_{89}=+0.060269959\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.061032742\) \(a_{92}=+0.000000000\) \(a_{93}=-1.817619469\) \(a_{94}=+0.000000000\) \(a_{95}=-0.504456516\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.488860680\) \(a_{98}=+0.000000000\) \(a_{99}=+0.056054842\) \(a_{100}=+0.000000000\)

Showing 100 of 640 available coefficients

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